https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) https://plato.stanford.edu/entries/proof-theoretic-semantics/
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
On 6/19/2026 2:23 AM, Mikko wrote:I've spent a couple of hours reading that web page. It is abstract in
On 18/06/2026 22:35, olcott wrote:Calling my views (anchored in proof theoretic semantics)
On 6/17/2026 4:14 PM, olcott wrote:Whereas you are stuck to your own incoherent views and reject
https://www.youtube.com/@rossfinlaysonSome people only memorize conventional views and
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
reject alternative views out-of-hand without review.
alternative views out-of-hand without review.
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics. https://plato.stanford.edu/entries/proof-theoretic-semantics/
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered
to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants. Logical constants play a central role
| in reasoning and inference, but are definitely not the exclusive, and
| perhaps not even the most typical sort of entities that can be defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-logical
| inferential definitions alike.
Does this have any meaning?
I put it to everybody here that Peter Olcott has been bluffing. He has purported to understand Proof-theoretic semantics and repeatedly cited a
web page far outside his own understanding, believing nobody else would
ever challenge this deception.
I'm challenging it now. Peter, you have repeatedly stated that G||del's Incompleteness Theorem is unproven when one takes PTS as a basis. I put
it to you this is a lie, and that you are as clueless about PTS as you
are about G||del's Theorem. Feel free to refute my assertion.
Or, at the very least, explain in readily accessible English precisely
what is meant above by "logical constants" and how and why "they play a central role in reasoning and inference". I put it to you you cannot do this.
On 6/19/26 1:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is abstract in
the extreme.-a One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered
to read it any further.-a If it actually says anything at all, that
something is heavily disguised.-a From it's "Conclusion and Outlook"
section at the end:
-a-a | Standard proof-theoretic semantics has practically exclusively been >> -a-a | occupied with logical constants. Logical constants play a central
role
-a-a | in reasoning and inference, but are definitely not the exclusive,
and
-a-a | perhaps not even the most typical sort of entities that can be
defined
-a-a | inferentially. A framework is needed that deals with inferential
-a-a | definitions in a wider sense and covers both logical and extra-
logical
-a-a | inferential definitions alike.
Does this have any meaning?
I put it to everybody here that Peter Olcott has been bluffing.-a He has
purported to understand Proof-theoretic semantics and repeatedly cited a
web page far outside his own understanding, believing nobody else would
ever challenge this deception.
I'm challenging it now.-a Peter, you have repeatedly stated that G||del's
Incompleteness Theorem is unproven when one takes PTS as a basis.-a I put
it to you this is a lie, and that you are as clueless about PTS as you
are about G||del's Theorem.-a Feel free to refute my assertion.
Or, at the very least, explain in readily accessible English precisely
what is meant above by "logical constants" and how and why "they play a
central role in reasoning and inference".-a I put it to you you cannot do
this.
u ever gunna write something that isn't totally saturated with various fallacies alan?
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:That's non-responsive to my point, which I'll repeat: you are as clueless
In comp.theory olcott <polcott333@gmail.com> wrote:My basis in PTS is what is referred to in the Literature
On 6/19/2026 2:23 AM, Mikko wrote:I've spent a couple of hours reading that web page. It is abstract in
On 18/06/2026 22:35, olcott wrote:Calling my views (anchored in proof theoretic semantics)
On 6/17/2026 4:14 PM, olcott wrote:Whereas you are stuck to your own incoherent views and reject
https://www.youtube.com/@rossfinlaysonSome people only memorize conventional views and
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
reject alternative views out-of-hand without review.
alternative views out-of-hand without review.
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered
to read it any further. If it actually says anything at all, that something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants. Logical constants play a central role
| in reasoning and inference, but are definitely not the exclusive, and
| perhaps not even the most typical sort of entities that can be defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-logical
| inferential definitions alike.
Does this have any meaning?
I put it to everybody here that Peter Olcott has been bluffing. He has purported to understand Proof-theoretic semantics and repeatedly cited a web page far outside his own understanding, believing nobody else would ever challenge this deception.
I'm challenging it now. Peter, you have repeatedly stated that G||del's Incompleteness Theorem is unproven when one takes PTS as a basis. I put
it to you this is a lie, and that you are as clueless about PTS as you
are about G||del's Theorem. Feel free to refute my assertion.
Or, at the very least, explain in readily accessible English precisely
what is meant above by "logical constants" and how and why "they play a central role in reasoning and inference". I put it to you you cannot do this.
as Dag Prawitz Theory of Grounds and its extensions and
elaborations. https://scholar.google.com/scholar?hl=en&as_sdt=0,42&q=Prawitz+theory+of+grounds
I came up with all this stuff on my own entirely onAll things beyond your understanding, if they are coherent things at all.
the basis of reverse-engineering from first principles.
I only very recently found out that it has an existing
basis in the work of others.
These are the usual things that PTS refers to:
Natural Deduction, Sequent Calculus, Martin-L||f Type Theory,
Intuitionistic Logic. I extend the essence of PTS all the way
to natural language formalized as CycL.
https://en.wikipedia.org/wiki/CycL
----
Copyright 2026 Olcott
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered >>> to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>> | occupied with logical constants. Logical constants play a central role
| in reasoning and inference, but are definitely not the exclusive, and >>> | perhaps not even the most typical sort of entities that can be defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-logical
| inferential definitions alike.
Does this have any meaning?
I put it to everybody here that Peter Olcott has been bluffing. He has
purported to understand Proof-theoretic semantics and repeatedly cited a >>> web page far outside his own understanding, believing nobody else would
ever challenge this deception.
I'm challenging it now. Peter, you have repeatedly stated that G||del's >>> Incompleteness Theorem is unproven when one takes PTS as a basis. I put >>> it to you this is a lie, and that you are as clueless about PTS as you
are about G||del's Theorem. Feel free to refute my assertion.
Or, at the very least, explain in readily accessible English precisely
what is meant above by "logical constants" and how and why "they play a
central role in reasoning and inference". I put it to you you cannot do >>> this.
My basis in PTS is what is referred to in the Literature
as Dag Prawitz Theory of Grounds and its extensions and
elaborations.
https://scholar.google.com/scholar?hl=en&as_sdt=0,42&q=Prawitz+theory+of+grounds
That's non-responsive to my point, which I'll repeat: you are as clueless about PTS as you are about G||del's Theorem. You are as ignorant of PTS
as you are of mathematics. Refute me by responding directly to the
points I made in my last post.
I came up with all this stuff on my own entirely on
the basis of reverse-engineering from first principles.
I only very recently found out that it has an existing
basis in the work of others.
These are the usual things that PTS refers to:
Natural Deduction, Sequent Calculus, Martin-L||f Type Theory,
Intuitionistic Logic. I extend the essence of PTS all the way
to natural language formalized as CycL.
https://en.wikipedia.org/wiki/CycL
All things beyond your understanding, if they are coherent things at all.
--
Copyright 2026 Olcott
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered
to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants. Logical constants play a central role
| in reasoning and inference, but are definitely not the exclusive, and
| perhaps not even the most typical sort of entities that can be defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-logical
| inferential definitions alike.
Does this have any meaning?
I put it to everybody here that Peter Olcott has been bluffing. He has purported to understand Proof-theoretic semantics and repeatedly cited a
web page far outside his own understanding, believing nobody else would
ever challenge this deception.
I'm challenging it now. Peter, you have repeatedly stated that G||del's Incompleteness Theorem is unproven when one takes PTS as a basis. I put
it to you this is a lie, and that you are as clueless about PTS as you
are about G||del's Theorem. Feel free to refute my assertion.
Or, at the very least, explain in readily accessible English precisely
what is meant above by "logical constants" and how and why "they play a central role in reasoning and inference". I put it to you you cannot do this.
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered
to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants.
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
This seems to be the rigidly conformist and memorize
by rote mindset.
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered
to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants. Logical constants play a central
role
| in reasoning and inference, but are definitely not the exclusive,
and
| perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and
extra-logical
| inferential definitions alike.
Does this have any meaning?
I put it to everybody here that Peter Olcott has been bluffing. He has
purported to understand Proof-theoretic semantics and repeatedly cited a
web page far outside his own understanding, believing nobody else would
ever challenge this deception.
I'm challenging it now. Peter, you have repeatedly stated that G||del's
Incompleteness Theorem is unproven when one takes PTS as a basis. I put
it to you this is a lie, and that you are as clueless about PTS as you
are about G||del's Theorem. Feel free to refute my assertion.
Or, at the very least, explain in readily accessible English precisely
what is meant above by "logical constants" and how and why "they play a
central role in reasoning and inference". I put it to you you cannot do
this.
The field since 2016 has expanded to include what
logicians would call quantifier free FOL.
I will research this more so that I can explain
my own ideas within the frame-of-reference of PTS.
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered
to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants.
The was the original position:
Ever since 2016 PTS has been anchored in Horn Clauses
thus not limited to logical constants.
On 06/19/2026 07:35 PM, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered >>> to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>> | occupied with logical constants.
The was the original position:
Ever since 2016 PTS has been anchored in Horn Clauses
thus not limited to logical constants.
One might aver that Huntington postulates are more relevant than Horn clauses.
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is abstract in
the extreme.-a One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Never was an actual contradiction when properly
formalized. The directed graph of its evaluation
always had a cycle.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog finally once and for all resolves the Liar
Paradox as semantically incoherent within the
analytical framework of Proof Theoretical Semantics.
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered >>> to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants. Logical constants play a central role >>> | in reasoning and inference, but are definitely not the exclusive, and
| perhaps not even the most typical sort of entities that can be defined >>> | inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-logical >>> | inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the
near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for? What it
On 06/18/2026 12:35 PM, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
This seems to be the rigidly conformist and memorize
by rote mindset.
Hm. Here there is a rather "rigidly conformist" approach,
and "an extreme rationalism", though, it's not the usual.
a principle of inverse
supplants, subsumes, and includes
a principle of non-contradiction/excluded-middle
a principle of thorough reason
supplants, subsumes, and includes
a principle of sufficient reason
a principle of implosion
obviates and makes an example of
a principle of explosion
On 06/19/2026 04:30 PM, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is abstract in
the extreme.-a One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered >>> to read it any further.-a If it actually says anything at all, that
something is heavily disguised.-a From it's "Conclusion and Outlook"
section at the end:
-a-a | Standard proof-theoretic semantics has practically exclusively been >>> -a-a | occupied with logical constants. Logical constants play a central >>> role
-a-a | in reasoning and inference, but are definitely not the exclusive, >>> and
-a-a | perhaps not even the most typical sort of entities that can be
defined
-a-a | inferentially. A framework is needed that deals with inferential
-a-a | definitions in a wider sense and covers both logical and
extra-logical
-a-a | inferential definitions alike.
Does this have any meaning?
I put it to everybody here that Peter Olcott has been bluffing.-a He has >>> purported to understand Proof-theoretic semantics and repeatedly cited a >>> web page far outside his own understanding, believing nobody else would
ever challenge this deception.
I'm challenging it now.-a Peter, you have repeatedly stated that G||del's >>> Incompleteness Theorem is unproven when one takes PTS as a basis.-a I put >>> it to you this is a lie, and that you are as clueless about PTS as you
are about G||del's Theorem.-a Feel free to refute my assertion.
Or, at the very least, explain in readily accessible English precisely
what is meant above by "logical constants" and how and why "they play a
central role in reasoning and inference".-a I put it to you you cannot do >>> this.
The field since 2016 has expanded to include what
logicians would call quantifier free FOL.
I will research this more so that I can explain
my own ideas within the frame-of-reference of PTS.
Such reductionisms as "term-free" or "constant-free" or "variable-free"
or "quantifier-free" are simplifications that fail to include
resolutions of the paradoxes of induction, quantification, identity, infinity, and continuity.
On 06/19/2026 07:35 PM, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is abstract in
the extreme.-a One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered >>> to read it any further.-a If it actually says anything at all, that
something is heavily disguised.-a From it's "Conclusion and Outlook"
section at the end:
-a-a | Standard proof-theoretic semantics has practically exclusively been >>> -a-a | occupied with logical constants.
The was the original position:
Ever since 2016 PTS has been anchored in Horn Clauses
thus not limited to logical constants.
One might aver that Huntington postulates are more relevant than Horn clauses.
On 06/19/2026 10:27 PM, Ross Finlayson wrote:
On 06/19/2026 07:35 PM, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is abstract in >>>> the extreme.-a One thing is utterly clear: its level of abstraction is >>>> well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered
to read it any further.-a If it actually says anything at all, that
something is heavily disguised.-a From it's "Conclusion and Outlook"
section at the end:
-a-a | Standard proof-theoretic semantics has practically exclusively >>>> been
-a-a | occupied with logical constants.
The was the original position:
Ever since 2016 PTS has been anchored in Horn Clauses
thus not limited to logical constants.
One might aver that Huntington postulates are more relevant than Horn
clauses.
Horn clauses are useful idioms to declare or claim inductive completion
about things like completion and compactness and tail recursion what
would otherwise be inductive incompleteness, and thusly are merely notational, while Huntington postulates include actual accounts of
quantifier disambiguation and the like about induction and
counter-induction and super-classical completions, besides the usual
reading
that Huntington postulates are just a usual logic, which in the usual accounts of formal logic is merely "quasi-modal" logic, and ignorant
of quantifier disambiguation and other notions of all the implicits.
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P re| P re? Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P reo -4P) reo reN // out of which nothing comes
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
At different times you have expressed different opinions, which
sometimes have been incompatible. But you have never clearly
retracted your earlier opitions that conflict with your present
ones.
On 19/06/2026 23:28, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is abstract in
the extreme.-a One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered
to read it any further.-a If it actually says anything at all, that
something is heavily disguised.-a From it's "Conclusion and Outlook"
section at the end:
-a-a | Standard proof-theoretic semantics has practically exclusively been >> -a-a | occupied with logical constants. Logical constants play a central
role
-a-a | in reasoning and inference, but are definitely not the exclusive,
and
-a-a | perhaps not even the most typical sort of entities that can be
defined
-a-a | inferentially. A framework is needed that deals with inferential
-a-a | definitions in a wider sense and covers both logical and extra-
logical
-a-a | inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the
near future not useful as making it useful requires much time and
effort if it is possible at all.
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P re| P re? Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P reo -4P) reo reN // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun. --------------------------------------
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P re| P re? Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P reo -4P) reo reN // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P re| P re? Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P reo -4P) reo reN // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good.-a Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P re| P re? Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P reo -4P) reo reN // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good.-a Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
On 6/20/2026 5:26 AM, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in >>> the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered >>> to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants. Logical constants play a central role >>> | in reasoning and inference, but are definitely not the exclusive, and >>> | perhaps not even the most typical sort of entities that can be defined >>> | inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-logical >>> | inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the
near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for? What it
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
----
Copyright 2026 Olcott
On 6/20/2026 11:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P re| P re? Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P reo -4P) reo reN // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good.-a Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
That's not what I asked.-a I asked if the following statement is true:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
On 6/20/2026 10:23 AM, dbush wrote:
On 6/20/2026 11:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P re| P re? Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P reo -4P) reo reN // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good.-a Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
That's not what I asked.-a I asked if the following statement is true:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
So you are not smart enough to understand that
when the actual composition of the Moon is specified
and that this composition is not green cheese that
the system would report false?
I will not play head sames with you on this. Instead
of head games your replies will be ignored.
On 6/20/2026 10:34 AM, Alan Mackenzie wrote:No, I have understood it well enough. It is an immature branch of
In comp.theory olcott <polcott333@gmail.com> wrote:You have failed to sufficiently understand the gist of proof
On 6/20/2026 5:26 AM, Alan Mackenzie wrote:Taking a best guess at what that phrase is meant to mean, it doesn't. Or at the very least, you have failed to meet your burden of proof that it does.
Mikko <mikko.levanto@iki.fi> wrote:reliably computable for the entire body of knowledge.
On 19/06/2026 23:28, Alan Mackenzie wrote:Do its proponents have any idea what PTS ought to be useful for? What it >> It makes "true on the basis of meaning expressed in language"
In comp.theory olcott <polcott333@gmail.com> wrote:Yes. It means that proof-theoretic semantics is currently and in the >>>> near future not useful as making it useful requires much time and
On 6/19/2026 2:23 AM, Mikko wrote:I've spent a couple of hours reading that web page. It is abstract in >>>>> the extreme. One thing is utterly clear: its level of abstraction is >>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>> even understand proof by contradiction.
On 18/06/2026 22:35, olcott wrote:Calling my views (anchored in proof theoretic semantics)
On 6/17/2026 4:14 PM, olcott wrote:Whereas you are stuck to your own incoherent views and reject
https://www.youtube.com/@rossfinlaysonreject alternative views out-of-hand without review.
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>> Some people only memorize conventional views and
alternative views out-of-hand without review.
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
That page's level of abstraction is high enough that I can't be
bothered to read it any further. If it actually says anything at
all, that something is heavily disguised. From it's "Conclusion
and Outlook" section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>>>> | occupied with logical constants. Logical constants play a central role
| in reasoning and inference, but are definitely not the exclusive, and >>>>> | perhaps not even the most typical sort of entities that can be defined
| inferentially. A framework is needed that deals with inferential >>>>> | definitions in a wider sense and covers both logical and extra-logical
| inferential definitions alike.
Does this have any meaning?
effort if it is possible at all.
theoretic semantics.
This applies to your next statement as well. You must have a 100%That is a condescending lie. Your ideas are very far from proven and
complete understanding of the gist of PTS and then my ideas are proven coherent and true.
--We know that in any sufficiently powerful language (and the bar is not high), there are statements which are "incomputable". If you doubt this, and still believe PTS gives a different result, please show some mathematical proof which comes out differently between standard logic and PTS, illustrating the essence of PTS which makes it so.--
Copyright 2026 Olcott
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P re| P re? Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P reo -4P) reo reN // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
[ Followup-To: set]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/20/2026 10:34 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/20/2026 5:26 AM, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in >>>>>>> the extreme. One thing is utterly clear: its level of abstraction is >>>>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>>>> even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered to read it any further. If it actually says anything at >>>>>>> all, that something is heavily disguised. From it's "Conclusion >>>>>>> and Outlook" section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>>>>>> | occupied with logical constants. Logical constants play a central role
| in reasoning and inference, but are definitely not the exclusive, and >>>>>>> | perhaps not even the most typical sort of entities that can be defined
| inferentially. A framework is needed that deals with inferential >>>>>>> | definitions in a wider sense and covers both logical and extra-logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the >>>>>> near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for? What it
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
Taking a best guess at what that phrase is meant to mean, it doesn't. Or >>> at the very least, you have failed to meet your burden of proof that it
does.
You have failed to sufficiently understand the gist of proof
theoretic semantics.
No, I have understood it well enough. It is an immature branch of
philosophy which gives mathematical results the same as standard logic
does. It is _you_ who have failed sufficiently to understand PTS.
Otherwise you could answer questions about it.
On 06/20/2026 08:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P re| P re? Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P reo -4P) reo reN // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good.-a Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
Hm. Here the idea is that there are no more "meta-theories",
of what's a "super-theory", that's a "mono-heno-theory",
among various accounts of "heno-theories", any sort "theory".
So, giving the "fundamental question of metaphysics" ("why is
there something rather than nothing?"), and, what it is, starts
with an idea of a universe of Truth, all the logical truisms
and the grounds for a logical universe, then that the "paradox"
of quantification gives an example "Confessing Liar", that
is itself, a template and example of what would be un-true,
yet only as found and discovered among all the truth. This
invokes ideas like "univocity", about there being a "Comenius language"
of all the truths, then the haeccity and quiddity, or "thing-nesses",
these are archaic terms yet common since about at least 800 years.
So, the Bible and the Vedas have examples, for example starting
with "in the beginning ..." about a space of geometry and the
contents of the Space-Time, and "in the beginning..." about the word
and the light of the word, and the Atman and Brahman as giving accounts
of inter-subjective objectivity, then with Zeno's arguments after
Heraclitus for dual monism and Parmenides for a wider, fuller dialectic,
the pre-Socratics or Eleatics, making the paleo-classical account, of
the most common references, for discourse and reason,
about the objects of mathematics and physics, and language and
knowledge. Then, since the Aristotlean, and with the wider and fuller dialetic of the full Aristotlean and Aristotlean realism, and then
since the Scholastics and the renewed Aristotlean, DesCartes and the enlightened rationality, Leibnitz and the universals, then Kant and
Hegel bring Being and Nothing, and the sublime and ding-an-sich and the fuller dialectic, these are elements of the canon and the dogma and
the doctrine.
A "heno-theory", then, a "one-theory", basically has logical elements
in the theory and gets connected via language to non-logical or properly-logical objects, any account of abstraction or description
basically has that a "heno-theory" is a realist structuralist's model
of a theory, that models other theories. Then the idea of a
mono-heno-theory is again that it's a one theory with all the truth,
where truth
is the quantity and truth is conserved, and the universe is full of it,
then that any other exercise in theory is an exercise in it.
Void and Universe <- logic's
Point and Space <- geometry's
Increment and Partition <- arithmetic's
Metaphor and Metonymy <- language's, algebra's
Energy and Entelechy <- physics' contents
Dynamis and Dunamis <- physics' activity
So, Continuity and Infinity are approached classically, then for the paleo-classical and the post-modern account, is a usual sort of
formal treatment that has a "the logic" and "the objects of the
universe of mathematics" with "strong mathematical platonism",
then that the formalism has for rulial and regular accounts of
competing rulialities well-foundedness and well-ordering after well-dispersion, the infinitary reasoning since the classical accounts
of the super-classical or Zeno's thought experiments, what makes for
a thorough sort of account of the modal, temporal, relevance logic,
in descriptive accounts of formalism, for infinitary and super-classical reasoning, after axiomless deduction, for actual infinity
and replete continuity, mathematically.
Teleology and Ontology <- the objective and subjective
Science and Statistics <- the inter-subjective
So, "complementary duals" make a great account as to why the
competing rulialities result the analytical bridges instead of
the inductive impasses and have the structuralist realism of
the super-classical results of analysis and for quantifier
disambiguation and the extraction of mathematical implicits
thusly a greater account of reason and mathematically, and
in its discourse meeting the requirements and desiderata of
both "strong mathematical platonism" and "strong logicist positivism",
that there's one good theory and any number of ways to talk about it.
"Foundations", "Sole Foundations", "True Foundations"
There's a paleo-classical post-modern realist structuralist's
mathematics, then also about the intelligence and wisdom and knowledge
and science,
Intelligence and Wisdom
Knowledge and Science
about the real, the natural, and the rational, and the reasonable,
De Re and De Natura
De Res and De Racio
then, thusly, there's one good theory at all that's an Aristotlean
realism and actualized for Aristotle, and a Hegelian idealism and
with a wider, fuller dialectic for Hegel, and that's the one there is.
On 6/20/2026 11:44 AM, olcott wrote:
On 6/20/2026 10:23 AM, dbush wrote:
On 6/20/2026 11:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P re| P re? Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P reo -4P) reo reN // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
That's not what I asked. I asked if the following statement is true:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
So you are not smart enough to understand that
when the actual composition of the Moon is specified
and that this composition is not green cheese that
the system would report false?
So you're saying the moon is not made of green cheese? So based on
that, is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
I will not play head sames with you on this. Instead
of head games your replies will be ignored.
I am not playing head games. I am merely employing Socratic questioning.
https://en.wikipedia.org/wiki/Socratic_questioning
On 6/20/2026 11:29 AM, Ross Finlayson wrote:
On 06/20/2026 08:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P re| P re? Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P reo -4P) reo reN // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
Hm. Here the idea is that there are no more "meta-theories",
of what's a "super-theory", that's a "mono-heno-theory",
among various accounts of "heno-theories", any sort "theory".
So, giving the "fundamental question of metaphysics" ("why is
there something rather than nothing?"), and, what it is, starts
with an idea of a universe of Truth, all the logical truisms
and the grounds for a logical universe, then that the "paradox"
of quantification gives an example "Confessing Liar", that
is itself, a template and example of what would be un-true,
yet only as found and discovered among all the truth. This
invokes ideas like "univocity", about there being a "Comenius language"
of all the truths, then the haeccity and quiddity, or "thing-nesses",
these are archaic terms yet common since about at least 800 years.
So, the Bible and the Vedas have examples, for example starting
with "in the beginning ..." about a space of geometry and the
contents of the Space-Time, and "in the beginning..." about the word
and the light of the word, and the Atman and Brahman as giving accounts
of inter-subjective objectivity, then with Zeno's arguments after
Heraclitus for dual monism and Parmenides for a wider, fuller dialectic,
the pre-Socratics or Eleatics, making the paleo-classical account, of
the most common references, for discourse and reason,
about the objects of mathematics and physics, and language and
knowledge. Then, since the Aristotlean, and with the wider and fuller
dialetic of the full Aristotlean and Aristotlean realism, and then
since the Scholastics and the renewed Aristotlean, DesCartes and the
enlightened rationality, Leibnitz and the universals, then Kant and
Hegel bring Being and Nothing, and the sublime and ding-an-sich and the
fuller dialectic, these are elements of the canon and the dogma and
the doctrine.
A "heno-theory", then, a "one-theory", basically has logical elements
in the theory and gets connected via language to non-logical or
properly-logical objects, any account of abstraction or description
basically has that a "heno-theory" is a realist structuralist's model
of a theory, that models other theories. Then the idea of a
mono-heno-theory is again that it's a one theory with all the truth,
where truth
is the quantity and truth is conserved, and the universe is full of it,
then that any other exercise in theory is an exercise in it.
Void and Universe <- logic's
Point and Space <- geometry's
Increment and Partition <- arithmetic's
Metaphor and Metonymy <- language's, algebra's
Energy and Entelechy <- physics' contents
Dynamis and Dunamis <- physics' activity
So, Continuity and Infinity are approached classically, then for the
paleo-classical and the post-modern account, is a usual sort of
formal treatment that has a "the logic" and "the objects of the
universe of mathematics" with "strong mathematical platonism",
then that the formalism has for rulial and regular accounts of
competing rulialities well-foundedness and well-ordering after
well-dispersion, the infinitary reasoning since the classical accounts
of the super-classical or Zeno's thought experiments, what makes for
a thorough sort of account of the modal, temporal, relevance logic,
in descriptive accounts of formalism, for infinitary and super-classical
reasoning, after axiomless deduction, for actual infinity
and replete continuity, mathematically.
Teleology and Ontology <- the objective and subjective
Science and Statistics <- the inter-subjective
So, "complementary duals" make a great account as to why the
competing rulialities result the analytical bridges instead of
the inductive impasses and have the structuralist realism of
the super-classical results of analysis and for quantifier
disambiguation and the extraction of mathematical implicits
thusly a greater account of reason and mathematically, and
in its discourse meeting the requirements and desiderata of
both "strong mathematical platonism" and "strong logicist positivism",
that there's one good theory and any number of ways to talk about it.
"Foundations", "Sole Foundations", "True Foundations"
There's a paleo-classical post-modern realist structuralist's
mathematics, then also about the intelligence and wisdom and knowledge
and science,
Intelligence and Wisdom
Knowledge and Science
about the real, the natural, and the rational, and the reasonable,
De Re and De Natura
De Res and De Racio
then, thusly, there's one good theory at all that's an Aristotlean
realism and actualized for Aristotle, and a Hegelian idealism and
with a wider, fuller dialectic for Hegel, and that's the one there is.
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
On 06/20/2026 09:45 AM, olcott wrote:
On 6/20/2026 11:29 AM, Ross Finlayson wrote:
On 06/20/2026 08:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P re| P re? Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P reo -4P) reo reN // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good.-a Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
Hm. Here the idea is that there are no more "meta-theories",
of what's a "super-theory", that's a "mono-heno-theory",
among various accounts of "heno-theories", any sort "theory".
So, giving the "fundamental question of metaphysics" ("why is
there something rather than nothing?"), and, what it is, starts
with an idea of a universe of Truth, all the logical truisms
and the grounds for a logical universe, then that the "paradox"
of quantification gives an example "Confessing Liar", that
is itself, a template and example of what would be un-true,
yet only as found and discovered among all the truth. This
invokes ideas like "univocity", about there being a "Comenius language"
of all the truths, then the haeccity and quiddity, or "thing-nesses",
these are archaic terms yet common since about at least 800 years.
So, the Bible and the Vedas have examples, for example starting
with "in the beginning ..." about a space of geometry and the
contents of the Space-Time, and "in the beginning..." about the word
and the light of the word, and the Atman and Brahman as giving accounts
of inter-subjective objectivity, then with Zeno's arguments after
Heraclitus for dual monism and Parmenides for a wider, fuller dialectic, >>> the pre-Socratics or Eleatics, making the paleo-classical account, of
the most common references, for discourse and reason,
about the objects of mathematics and physics, and language and
knowledge. Then, since the Aristotlean, and with the wider and fuller
dialetic of the full Aristotlean and Aristotlean realism, and then
since the Scholastics and the renewed Aristotlean, DesCartes and the
enlightened rationality, Leibnitz and the universals, then Kant and
Hegel bring Being and Nothing, and the sublime and ding-an-sich and the
fuller dialectic, these are elements of the canon and the dogma and
the doctrine.
A "heno-theory", then, a "one-theory", basically has logical elements
in the theory and gets connected via language to non-logical or
properly-logical objects, any account of abstraction or description
basically has that a "heno-theory" is a realist structuralist's model
of a theory, that models other theories. Then the idea of a
mono-heno-theory is again that it's a one theory with all the truth,
where truth
is the quantity and truth is conserved, and the universe is full of it,
then that any other exercise in theory is an exercise in it.
Void and Universe <- logic's
Point and Space <- geometry's
Increment and Partition <- arithmetic's
Metaphor and Metonymy <- language's, algebra's
Energy and Entelechy <- physics' contents
Dynamis and Dunamis <- physics' activity
So, Continuity and Infinity are approached classically, then for the
paleo-classical and the post-modern account, is a usual sort of
formal treatment that has a "the logic" and "the objects of the
universe of mathematics" with "strong mathematical platonism",
then that the formalism has for rulial and regular accounts of
competing rulialities well-foundedness and well-ordering after
well-dispersion, the infinitary reasoning since the classical accounts
of the super-classical or Zeno's thought experiments, what makes for
a thorough sort of account of the modal, temporal, relevance logic,
in descriptive accounts of formalism, for infinitary and super-classical >>> reasoning, after axiomless deduction, for actual infinity
and replete continuity, mathematically.
Teleology and Ontology <- the objective and subjective
Science and Statistics <- the inter-subjective
So, "complementary duals" make a great account as to why the
competing rulialities result the analytical bridges instead of
the inductive impasses and have the structuralist realism of
the super-classical results of analysis and for quantifier
disambiguation and the extraction of mathematical implicits
thusly a greater account of reason and mathematically, and
in its discourse meeting the requirements and desiderata of
both "strong mathematical platonism" and "strong logicist positivism",
that there's one good theory and any number of ways to talk about it.
"Foundations", "Sole Foundations", "True Foundations"
There's a paleo-classical post-modern realist structuralist's
mathematics, then also about the intelligence and wisdom and knowledge
and science,
Intelligence and Wisdom
Knowledge and Science
about the real, the natural, and the rational, and the reasonable,
De Re and De Natura
De Res and De Racio
then, thusly, there's one good theory at all that's an Aristotlean
realism and actualized for Aristotle, and a Hegelian idealism and
with a wider, fuller dialectic for Hegel, and that's the one there is.
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
That's merely an account of "ontology in a vacuum"
and is bereft the needful for accounts of continuity and infinity,
and can't claim to resolve paradoxes it makes for itself.
Hilbert-Bernays paradox
On 6/20/2026 11:47 AM, Ross Finlayson wrote:
On 06/20/2026 09:45 AM, olcott wrote:
On 6/20/2026 11:29 AM, Ross Finlayson wrote:
On 06/20/2026 08:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P re| P re? Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P reo -4P) reo reN // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good.-a Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
Hm. Here the idea is that there are no more "meta-theories",
of what's a "super-theory", that's a "mono-heno-theory",
among various accounts of "heno-theories", any sort "theory".
So, giving the "fundamental question of metaphysics" ("why is
there something rather than nothing?"), and, what it is, starts
with an idea of a universe of Truth, all the logical truisms
and the grounds for a logical universe, then that the "paradox"
of quantification gives an example "Confessing Liar", that
is itself, a template and example of what would be un-true,
yet only as found and discovered among all the truth. This
invokes ideas like "univocity", about there being a "Comenius language" >>>> of all the truths, then the haeccity and quiddity, or "thing-nesses",
these are archaic terms yet common since about at least 800 years.
So, the Bible and the Vedas have examples, for example starting
with "in the beginning ..." about a space of geometry and the
contents of the Space-Time, and "in the beginning..." about the word
and the light of the word, and the Atman and Brahman as giving accounts >>>> of inter-subjective objectivity, then with Zeno's arguments after
Heraclitus for dual monism and Parmenides for a wider, fuller
dialectic,
the pre-Socratics or Eleatics, making the paleo-classical account, of
the most common references, for discourse and reason,
about the objects of mathematics and physics, and language and
knowledge. Then, since the Aristotlean, and with the wider and fuller
dialetic of the full Aristotlean and Aristotlean realism, and then
since the Scholastics and the renewed Aristotlean, DesCartes and the
enlightened rationality, Leibnitz and the universals, then Kant and
Hegel bring Being and Nothing, and the sublime and ding-an-sich and the >>>> fuller dialectic, these are elements of the canon and the dogma and
the doctrine.
A "heno-theory", then, a "one-theory", basically has logical elements
in the theory and gets connected via language to non-logical or
properly-logical objects, any account of abstraction or description
basically has that a "heno-theory" is a realist structuralist's model
of a theory, that models other theories. Then the idea of a
mono-heno-theory is again that it's a one theory with all the truth,
where truth
is the quantity and truth is conserved, and the universe is full of it, >>>> then that any other exercise in theory is an exercise in it.
Void and Universe <- logic's
Point and Space <- geometry's
Increment and Partition <- arithmetic's
Metaphor and Metonymy <- language's, algebra's
Energy and Entelechy <- physics' contents
Dynamis and Dunamis <- physics' activity
So, Continuity and Infinity are approached classically, then for the
paleo-classical and the post-modern account, is a usual sort of
formal treatment that has a "the logic" and "the objects of the
universe of mathematics" with "strong mathematical platonism",
then that the formalism has for rulial and regular accounts of
competing rulialities well-foundedness and well-ordering after
well-dispersion, the infinitary reasoning since the classical accounts >>>> of the super-classical or Zeno's thought experiments, what makes for
a thorough sort of account of the modal, temporal, relevance logic,
in descriptive accounts of formalism, for infinitary and super-
classical
reasoning, after axiomless deduction, for actual infinity
and replete continuity, mathematically.
Teleology and Ontology <- the objective and subjective
Science and Statistics <- the inter-subjective
So, "complementary duals" make a great account as to why the
competing rulialities result the analytical bridges instead of
the inductive impasses and have the structuralist realism of
the super-classical results of analysis and for quantifier
disambiguation and the extraction of mathematical implicits
thusly a greater account of reason and mathematically, and
in its discourse meeting the requirements and desiderata of
both "strong mathematical platonism" and "strong logicist positivism", >>>> that there's one good theory and any number of ways to talk about it.
"Foundations", "Sole Foundations", "True Foundations"
There's a paleo-classical post-modern realist structuralist's
mathematics, then also about the intelligence and wisdom and knowledge >>>> and science,
Intelligence and Wisdom
Knowledge and Science
about the real, the natural, and the rational, and the reasonable,
De Re and De Natura
De Res and De Racio
then, thusly, there's one good theory at all that's an Aristotlean
realism and actualized for Aristotle, and a Hegelian idealism and
with a wider, fuller dialectic for Hegel, and that's the one there is. >>>>
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
That's merely an account of "ontology in a vacuum"
and is bereft the needful for accounts of continuity and infinity,
and can't claim to resolve paradoxes it makes for itself.
Hilbert-Bernays paradox
All pathological self-reference derives a cycle
in the directly graph of the evaluation sequence
of the expression. This causes the expression to
be rejected as semantically incoherent input.
On 6/20/2026 11:47 AM, Ross Finlayson wrote:
On 06/20/2026 09:45 AM, olcott wrote:
On 6/20/2026 11:29 AM, Ross Finlayson wrote:
On 06/20/2026 08:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P re| P re? Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P reo -4P) reo reN // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
Hm. Here the idea is that there are no more "meta-theories",
of what's a "super-theory", that's a "mono-heno-theory",
among various accounts of "heno-theories", any sort "theory".
So, giving the "fundamental question of metaphysics" ("why is
there something rather than nothing?"), and, what it is, starts
with an idea of a universe of Truth, all the logical truisms
and the grounds for a logical universe, then that the "paradox"
of quantification gives an example "Confessing Liar", that
is itself, a template and example of what would be un-true,
yet only as found and discovered among all the truth. This
invokes ideas like "univocity", about there being a "Comenius language" >>>> of all the truths, then the haeccity and quiddity, or "thing-nesses",
these are archaic terms yet common since about at least 800 years.
So, the Bible and the Vedas have examples, for example starting
with "in the beginning ..." about a space of geometry and the
contents of the Space-Time, and "in the beginning..." about the word
and the light of the word, and the Atman and Brahman as giving accounts >>>> of inter-subjective objectivity, then with Zeno's arguments after
Heraclitus for dual monism and Parmenides for a wider, fuller
dialectic,
the pre-Socratics or Eleatics, making the paleo-classical account, of
the most common references, for discourse and reason,
about the objects of mathematics and physics, and language and
knowledge. Then, since the Aristotlean, and with the wider and fuller
dialetic of the full Aristotlean and Aristotlean realism, and then
since the Scholastics and the renewed Aristotlean, DesCartes and the
enlightened rationality, Leibnitz and the universals, then Kant and
Hegel bring Being and Nothing, and the sublime and ding-an-sich and the >>>> fuller dialectic, these are elements of the canon and the dogma and
the doctrine.
A "heno-theory", then, a "one-theory", basically has logical elements
in the theory and gets connected via language to non-logical or
properly-logical objects, any account of abstraction or description
basically has that a "heno-theory" is a realist structuralist's model
of a theory, that models other theories. Then the idea of a
mono-heno-theory is again that it's a one theory with all the truth,
where truth
is the quantity and truth is conserved, and the universe is full of it, >>>> then that any other exercise in theory is an exercise in it.
Void and Universe <- logic's
Point and Space <- geometry's
Increment and Partition <- arithmetic's
Metaphor and Metonymy <- language's, algebra's
Energy and Entelechy <- physics' contents
Dynamis and Dunamis <- physics' activity
So, Continuity and Infinity are approached classically, then for the
paleo-classical and the post-modern account, is a usual sort of
formal treatment that has a "the logic" and "the objects of the
universe of mathematics" with "strong mathematical platonism",
then that the formalism has for rulial and regular accounts of
competing rulialities well-foundedness and well-ordering after
well-dispersion, the infinitary reasoning since the classical accounts >>>> of the super-classical or Zeno's thought experiments, what makes for
a thorough sort of account of the modal, temporal, relevance logic,
in descriptive accounts of formalism, for infinitary and
super-classical
reasoning, after axiomless deduction, for actual infinity
and replete continuity, mathematically.
Teleology and Ontology <- the objective and subjective
Science and Statistics <- the inter-subjective
So, "complementary duals" make a great account as to why the
competing rulialities result the analytical bridges instead of
the inductive impasses and have the structuralist realism of
the super-classical results of analysis and for quantifier
disambiguation and the extraction of mathematical implicits
thusly a greater account of reason and mathematically, and
in its discourse meeting the requirements and desiderata of
both "strong mathematical platonism" and "strong logicist positivism", >>>> that there's one good theory and any number of ways to talk about it.
"Foundations", "Sole Foundations", "True Foundations"
There's a paleo-classical post-modern realist structuralist's
mathematics, then also about the intelligence and wisdom and knowledge >>>> and science,
Intelligence and Wisdom
Knowledge and Science
about the real, the natural, and the rational, and the reasonable,
De Re and De Natura
De Res and De Racio
then, thusly, there's one good theory at all that's an Aristotlean
realism and actualized for Aristotle, and a Hegelian idealism and
with a wider, fuller dialectic for Hegel, and that's the one there is. >>>>
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
That's merely an account of "ontology in a vacuum"
and is bereft the needful for accounts of continuity and infinity,
and can't claim to resolve paradoxes it makes for itself.
Hilbert-Bernays paradox
All pathological self-reference derives a cycle
in the directly graph of the evaluation sequence
of the expression. This causes the expression to
be rejected as semantically incoherent input.
I handled this for the Liar Paradox
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory of G||del's G
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao 01 02
01 G
02 -4 03
03 Prov_PA 04
04 G||del_Number_of 01 // cycle indicates no well-founded justification
tree exists.
and the Halting Problem proofs https://github.com/plolcott/x86utm/blob/master/Halt7.c
Proof Theoretic Semantics halt prover HHH correctly
determines that its input DD is ungrounded in its
atomic base according to the operational semantics
of the C programming language.
On 6/20/2026 12:57 PM, olcott wrote:
On 6/20/2026 11:47 AM, Ross Finlayson wrote:
On 06/20/2026 09:45 AM, olcott wrote:
On 6/20/2026 11:29 AM, Ross Finlayson wrote:
On 06/20/2026 08:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P re| P re? Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P reo -4P) reo reN // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
Hm. Here the idea is that there are no more "meta-theories",
of what's a "super-theory", that's a "mono-heno-theory",
among various accounts of "heno-theories", any sort "theory".
So, giving the "fundamental question of metaphysics" ("why is
there something rather than nothing?"), and, what it is, starts
with an idea of a universe of Truth, all the logical truisms
and the grounds for a logical universe, then that the "paradox"
of quantification gives an example "Confessing Liar", that
is itself, a template and example of what would be un-true,
yet only as found and discovered among all the truth. This
invokes ideas like "univocity", about there being a "Comenius
language"
of all the truths, then the haeccity and quiddity, or "thing-nesses", >>>>> these are archaic terms yet common since about at least 800 years.
So, the Bible and the Vedas have examples, for example starting
with "in the beginning ..." about a space of geometry and the
contents of the Space-Time, and "in the beginning..." about the word >>>>> and the light of the word, and the Atman and Brahman as giving
accounts
of inter-subjective objectivity, then with Zeno's arguments after
Heraclitus for dual monism and Parmenides for a wider, fuller
dialectic,
the pre-Socratics or Eleatics, making the paleo-classical account, of >>>>> the most common references, for discourse and reason,
about the objects of mathematics and physics, and language and
knowledge. Then, since the Aristotlean, and with the wider and fuller >>>>> dialetic of the full Aristotlean and Aristotlean realism, and then
since the Scholastics and the renewed Aristotlean, DesCartes and the >>>>> enlightened rationality, Leibnitz and the universals, then Kant and
Hegel bring Being and Nothing, and the sublime and ding-an-sich and
the
fuller dialectic, these are elements of the canon and the dogma and
the doctrine.
A "heno-theory", then, a "one-theory", basically has logical elements >>>>> in the theory and gets connected via language to non-logical or
properly-logical objects, any account of abstraction or description
basically has that a "heno-theory" is a realist structuralist's model >>>>> of a theory, that models other theories. Then the idea of a
mono-heno-theory is again that it's a one theory with all the truth, >>>>> where truth
is the quantity and truth is conserved, and the universe is full of
it,
then that any other exercise in theory is an exercise in it.
Void and Universe <- logic's
Point and Space <- geometry's
Increment and Partition <- arithmetic's
Metaphor and Metonymy <- language's, algebra's
Energy and Entelechy <- physics' contents
Dynamis and Dunamis <- physics' activity
So, Continuity and Infinity are approached classically, then for the >>>>> paleo-classical and the post-modern account, is a usual sort of
formal treatment that has a "the logic" and "the objects of the
universe of mathematics" with "strong mathematical platonism",
then that the formalism has for rulial and regular accounts of
competing rulialities well-foundedness and well-ordering after
well-dispersion, the infinitary reasoning since the classical accounts >>>>> of the super-classical or Zeno's thought experiments, what makes for >>>>> a thorough sort of account of the modal, temporal, relevance logic,
in descriptive accounts of formalism, for infinitary and super-
classical
reasoning, after axiomless deduction, for actual infinity
and replete continuity, mathematically.
Teleology and Ontology <- the objective and subjective
Science and Statistics <- the inter-subjective
So, "complementary duals" make a great account as to why the
competing rulialities result the analytical bridges instead of
the inductive impasses and have the structuralist realism of
the super-classical results of analysis and for quantifier
disambiguation and the extraction of mathematical implicits
thusly a greater account of reason and mathematically, and
in its discourse meeting the requirements and desiderata of
both "strong mathematical platonism" and "strong logicist positivism", >>>>> that there's one good theory and any number of ways to talk about it. >>>>>
"Foundations", "Sole Foundations", "True Foundations"
There's a paleo-classical post-modern realist structuralist's
mathematics, then also about the intelligence and wisdom and knowledge >>>>> and science,
Intelligence and Wisdom
Knowledge and Science
about the real, the natural, and the rational, and the reasonable,
De Re and De Natura
De Res and De Racio
then, thusly, there's one good theory at all that's an Aristotlean
realism and actualized for Aristotle, and a Hegelian idealism and
with a wider, fuller dialectic for Hegel, and that's the one there is. >>>>>
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
That's merely an account of "ontology in a vacuum"
and is bereft the needful for accounts of continuity and infinity,
and can't claim to resolve paradoxes it makes for itself.
Hilbert-Bernays paradox
All pathological self-reference derives a cycle
in the directly graph of the evaluation sequence
of the expression. This causes the expression to
be rejected as semantically incoherent input.
Big words from someone who's unable to say if the following statement is true:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
On 06/20/2026 09:57 AM, olcott wrote:
On 6/20/2026 11:47 AM, Ross Finlayson wrote:
On 06/20/2026 09:45 AM, olcott wrote:
On 6/20/2026 11:29 AM, Ross Finlayson wrote:
On 06/20/2026 08:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P re| P re? Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P reo -4P) reo reN // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good.-a Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
Hm. Here the idea is that there are no more "meta-theories",
of what's a "super-theory", that's a "mono-heno-theory",
among various accounts of "heno-theories", any sort "theory".
So, giving the "fundamental question of metaphysics" ("why is
there something rather than nothing?"), and, what it is, starts
with an idea of a universe of Truth, all the logical truisms
and the grounds for a logical universe, then that the "paradox"
of quantification gives an example "Confessing Liar", that
is itself, a template and example of what would be un-true,
yet only as found and discovered among all the truth. This
invokes ideas like "univocity", about there being a "Comenius
language"
of all the truths, then the haeccity and quiddity, or "thing-nesses", >>>>> these are archaic terms yet common since about at least 800 years.
So, the Bible and the Vedas have examples, for example starting
with "in the beginning ..." about a space of geometry and the
contents of the Space-Time, and "in the beginning..." about the word >>>>> and the light of the word, and the Atman and Brahman as giving
accounts
of inter-subjective objectivity, then with Zeno's arguments after
Heraclitus for dual monism and Parmenides for a wider, fuller
dialectic,
the pre-Socratics or Eleatics, making the paleo-classical account, of >>>>> the most common references, for discourse and reason,
about the objects of mathematics and physics, and language and
knowledge. Then, since the Aristotlean, and with the wider and fuller >>>>> dialetic of the full Aristotlean and Aristotlean realism, and then
since the Scholastics and the renewed Aristotlean, DesCartes and the >>>>> enlightened rationality, Leibnitz and the universals, then Kant and
Hegel bring Being and Nothing, and the sublime and ding-an-sich and >>>>> the
fuller dialectic, these are elements of the canon and the dogma and
the doctrine.
A "heno-theory", then, a "one-theory", basically has logical elements >>>>> in the theory and gets connected via language to non-logical or
properly-logical objects, any account of abstraction or description
basically has that a "heno-theory" is a realist structuralist's model >>>>> of a theory, that models other theories. Then the idea of a
mono-heno-theory is again that it's a one theory with all the truth, >>>>> where truth
is the quantity and truth is conserved, and the universe is full of >>>>> it,
then that any other exercise in theory is an exercise in it.
Void and Universe <- logic's
Point and Space <- geometry's
Increment and Partition <- arithmetic's
Metaphor and Metonymy <- language's, algebra's
Energy and Entelechy <- physics' contents
Dynamis and Dunamis <- physics' activity
So, Continuity and Infinity are approached classically, then for the >>>>> paleo-classical and the post-modern account, is a usual sort of
formal treatment that has a "the logic" and "the objects of the
universe of mathematics" with "strong mathematical platonism",
then that the formalism has for rulial and regular accounts of
competing rulialities well-foundedness and well-ordering after
well-dispersion, the infinitary reasoning since the classical accounts >>>>> of the super-classical or Zeno's thought experiments, what makes for >>>>> a thorough sort of account of the modal, temporal, relevance logic,
in descriptive accounts of formalism, for infinitary and
super-classical
reasoning, after axiomless deduction, for actual infinity
and replete continuity, mathematically.
Teleology and Ontology <- the objective and subjective
Science and Statistics <- the inter-subjective
So, "complementary duals" make a great account as to why the
competing rulialities result the analytical bridges instead of
the inductive impasses and have the structuralist realism of
the super-classical results of analysis and for quantifier
disambiguation and the extraction of mathematical implicits
thusly a greater account of reason and mathematically, and
in its discourse meeting the requirements and desiderata of
both "strong mathematical platonism" and "strong logicist positivism", >>>>> that there's one good theory and any number of ways to talk about it. >>>>>
"Foundations", "Sole Foundations", "True Foundations"
There's a paleo-classical post-modern realist structuralist's
mathematics, then also about the intelligence and wisdom and knowledge >>>>> and science,
Intelligence and Wisdom
Knowledge and Science
about the real, the natural, and the rational, and the reasonable,
De Re and De Natura
De Res and De Racio
then, thusly, there's one good theory at all that's an Aristotlean
realism and actualized for Aristotle, and a Hegelian idealism and
with a wider, fuller dialectic for Hegel, and that's the one there is. >>>>>
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
That's merely an account of "ontology in a vacuum"
and is bereft the needful for accounts of continuity and infinity,
and can't claim to resolve paradoxes it makes for itself.
Hilbert-Bernays paradox
All pathological self-reference derives a cycle
in the directly graph of the evaluation sequence
of the expression. This causes the expression to
be rejected as semantically incoherent input.
I handled this for the Liar Paradox
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory of G||del's G
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov_PA-a-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle indicates no well-founded justification
tree exists.
and the Halting Problem proofs
https://github.com/plolcott/x86utm/blob/master/Halt7.c
Proof Theoretic Semantics halt prover HHH correctly
determines that its input DD is ungrounded in its
atomic base according to the operational semantics
of the C programming language.
I'd imagine that "directed" graph was intended,
yet what's so is that a more _thorough_ account
actual detects cycles instead of presuming their
inexistence, which is a stipulation that simply
doesn't apply to fuller graphs in relation.
There are at least three laws of large numbers (LLN's):
the Law of Large Numbers (LLN):
the usual Law of Small Numbers, that finite numbers m are small, there's
a larger one m + 1, setting up, and requiring, induction
the Law of Larger Numbers (LLN+):
moreso than the Law of Large Numbers, also there exists n >> m,
setting up, and requiring, counter-induction
the Law of Largest Numbers (LLN++):
furthermore there are infinitely-grand numbers besides infinitely-many, setting up, and requiring, super-classical deduction
Then things like "Chaitin's Omega" about "The Halting Problem"
and "P(Halts) the Probability of Halting" get involved variously
about laws of large numbers, models of Cantor space, and these
sorts of accounts since Erdos of "Mathematical Independence"
(meaning demonstrably contradictory given competing rulialities)
the Erdos "Giant Monsters" of Mathematical Independence, instead
for accounts of a "Great Atlas of Mathematical Independence",
that resolves the competing rulialities with analytical bridges,
with "Zeno Machines" and models of computation, "supertasks"
beyond "small supertasks" and so on.
On 6/20/2026 12:19 PM, Ross Finlayson wrote:
On 06/20/2026 09:57 AM, olcott wrote:
On 6/20/2026 11:47 AM, Ross Finlayson wrote:
On 06/20/2026 09:45 AM, olcott wrote:
On 6/20/2026 11:29 AM, Ross Finlayson wrote:
On 06/20/2026 08:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P re| P re? Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P reo -4P) reo reN // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good.-a Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
Hm. Here the idea is that there are no more "meta-theories",
of what's a "super-theory", that's a "mono-heno-theory",
among various accounts of "heno-theories", any sort "theory".
So, giving the "fundamental question of metaphysics" ("why is
there something rather than nothing?"), and, what it is, starts
with an idea of a universe of Truth, all the logical truisms
and the grounds for a logical universe, then that the "paradox"
of quantification gives an example "Confessing Liar", that
is itself, a template and example of what would be un-true,
yet only as found and discovered among all the truth. This
invokes ideas like "univocity", about there being a "Comenius
language"
of all the truths, then the haeccity and quiddity, or "thing-nesses", >>>>>> these are archaic terms yet common since about at least 800 years. >>>>>>
So, the Bible and the Vedas have examples, for example starting
with "in the beginning ..." about a space of geometry and the
contents of the Space-Time, and "in the beginning..." about the word >>>>>> and the light of the word, and the Atman and Brahman as giving
accounts
of inter-subjective objectivity, then with Zeno's arguments after
Heraclitus for dual monism and Parmenides for a wider, fuller
dialectic,
the pre-Socratics or Eleatics, making the paleo-classical account, of >>>>>> the most common references, for discourse and reason,
about the objects of mathematics and physics, and language and
knowledge. Then, since the Aristotlean, and with the wider and fuller >>>>>> dialetic of the full Aristotlean and Aristotlean realism, and then >>>>>> since the Scholastics and the renewed Aristotlean, DesCartes and the >>>>>> enlightened rationality, Leibnitz and the universals, then Kant and >>>>>> Hegel bring Being and Nothing, and the sublime and ding-an-sich
and the
fuller dialectic, these are elements of the canon and the dogma and >>>>>> the doctrine.
A "heno-theory", then, a "one-theory", basically has logical elements >>>>>> in the theory and gets connected via language to non-logical or
properly-logical objects, any account of abstraction or description >>>>>> basically has that a "heno-theory" is a realist structuralist's model >>>>>> of a theory, that models other theories. Then the idea of a
mono-heno-theory is again that it's a one theory with all the truth, >>>>>> where truth
is the quantity and truth is conserved, and the universe is full
of it,
then that any other exercise in theory is an exercise in it.
Void and Universe <- logic's
Point and Space <- geometry's
Increment and Partition <- arithmetic's
Metaphor and Metonymy <- language's, algebra's
Energy and Entelechy <- physics' contents
Dynamis and Dunamis <- physics' activity
So, Continuity and Infinity are approached classically, then for the >>>>>> paleo-classical and the post-modern account, is a usual sort of
formal treatment that has a "the logic" and "the objects of the
universe of mathematics" with "strong mathematical platonism",
then that the formalism has for rulial and regular accounts of
competing rulialities well-foundedness and well-ordering after
well-dispersion, the infinitary reasoning since the classical
accounts
of the super-classical or Zeno's thought experiments, what makes for >>>>>> a thorough sort of account of the modal, temporal, relevance logic, >>>>>> in descriptive accounts of formalism, for infinitary and
super-classical
reasoning, after axiomless deduction, for actual infinity
and replete continuity, mathematically.
Teleology and Ontology <- the objective and subjective
Science and Statistics <- the inter-subjective
So, "complementary duals" make a great account as to why the
competing rulialities result the analytical bridges instead of
the inductive impasses and have the structuralist realism of
the super-classical results of analysis and for quantifier
disambiguation and the extraction of mathematical implicits
thusly a greater account of reason and mathematically, and
in its discourse meeting the requirements and desiderata of
both "strong mathematical platonism" and "strong logicist
positivism",
that there's one good theory and any number of ways to talk about it. >>>>>>
"Foundations", "Sole Foundations", "True Foundations"
There's a paleo-classical post-modern realist structuralist's
mathematics, then also about the intelligence and wisdom and
knowledge
and science,
Intelligence and Wisdom
Knowledge and Science
about the real, the natural, and the rational, and the reasonable, >>>>>>
De Re and De Natura
De Res and De Racio
then, thusly, there's one good theory at all that's an Aristotlean >>>>>> realism and actualized for Aristotle, and a Hegelian idealism and
with a wider, fuller dialectic for Hegel, and that's the one there >>>>>> is.
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
That's merely an account of "ontology in a vacuum"
and is bereft the needful for accounts of continuity and infinity,
and can't claim to resolve paradoxes it makes for itself.
Hilbert-Bernays paradox
All pathological self-reference derives a cycle
in the directly graph of the evaluation sequence
of the expression. This causes the expression to
be rejected as semantically incoherent input.
I handled this for the Liar Paradox
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory of G||del's G
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov_PA-a-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle indicates no well-founded justification >>> tree exists.
and the Halting Problem proofs
https://github.com/plolcott/x86utm/blob/master/Halt7.c
Proof Theoretic Semantics halt prover HHH correctly
determines that its input DD is ungrounded in its
atomic base according to the operational semantics
of the C programming language.
I'd imagine that "directed" graph was intended,
yet what's so is that a more _thorough_ account
actual detects cycles instead of presuming their
inexistence, which is a stipulation that simply
doesn't apply to fuller graphs in relation.
There are at least three laws of large numbers (LLN's):
the Law of Large Numbers (LLN):
the usual Law of Small Numbers, that finite numbers m are small, there's
a larger one m + 1, setting up, and requiring, induction
the Law of Larger Numbers (LLN+):
moreso than the Law of Large Numbers, also there exists n >> m,
setting up, and requiring, counter-induction
the Law of Largest Numbers (LLN++):
furthermore there are infinitely-grand numbers besides infinitely-many,
setting up, and requiring, super-classical deduction
Then things like "Chaitin's Omega" about "The Halting Problem"
and "P(Halts) the Probability of Halting" get involved variously
about laws of large numbers, models of Cantor space, and these
sorts of accounts since Erdos of "Mathematical Independence"
(meaning demonstrably contradictory given competing rulialities)
the Erdos "Giant Monsters" of Mathematical Independence, instead
for accounts of a "Great Atlas of Mathematical Independence",
that resolves the competing rulialities with analytical bridges,
with "Zeno Machines" and models of computation, "supertasks"
beyond "small supertasks" and so on.
Making "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
All the rest is out-of-scope.
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is abstract in
the extreme.-a One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two are different things. A contradiction is a statement which is necessarily
false. A paradox is a statement to which no truth value can be
consistently assigned.
Andr|-
On 6/20/2026 12:19 PM, Ross Finlayson wrote:
On 06/20/2026 09:57 AM, olcott wrote:
On 6/20/2026 11:47 AM, Ross Finlayson wrote:
On 06/20/2026 09:45 AM, olcott wrote:
On 6/20/2026 11:29 AM, Ross Finlayson wrote:
On 06/20/2026 08:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P re| P re? Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P reo -4P) reo reN // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
Hm. Here the idea is that there are no more "meta-theories",
of what's a "super-theory", that's a "mono-heno-theory",
among various accounts of "heno-theories", any sort "theory".
So, giving the "fundamental question of metaphysics" ("why is
there something rather than nothing?"), and, what it is, starts
with an idea of a universe of Truth, all the logical truisms
and the grounds for a logical universe, then that the "paradox"
of quantification gives an example "Confessing Liar", that
is itself, a template and example of what would be un-true,
yet only as found and discovered among all the truth. This
invokes ideas like "univocity", about there being a "Comenius
language"
of all the truths, then the haeccity and quiddity, or "thing-nesses", >>>>>> these are archaic terms yet common since about at least 800 years. >>>>>>
So, the Bible and the Vedas have examples, for example starting
with "in the beginning ..." about a space of geometry and the
contents of the Space-Time, and "in the beginning..." about the word >>>>>> and the light of the word, and the Atman and Brahman as giving
accounts
of inter-subjective objectivity, then with Zeno's arguments after
Heraclitus for dual monism and Parmenides for a wider, fuller
dialectic,
the pre-Socratics or Eleatics, making the paleo-classical account, of >>>>>> the most common references, for discourse and reason,
about the objects of mathematics and physics, and language and
knowledge. Then, since the Aristotlean, and with the wider and fuller >>>>>> dialetic of the full Aristotlean and Aristotlean realism, and then >>>>>> since the Scholastics and the renewed Aristotlean, DesCartes and the >>>>>> enlightened rationality, Leibnitz and the universals, then Kant and >>>>>> Hegel bring Being and Nothing, and the sublime and ding-an-sich
and the
fuller dialectic, these are elements of the canon and the dogma and >>>>>> the doctrine.
A "heno-theory", then, a "one-theory", basically has logical elements >>>>>> in the theory and gets connected via language to non-logical or
properly-logical objects, any account of abstraction or description >>>>>> basically has that a "heno-theory" is a realist structuralist's model >>>>>> of a theory, that models other theories. Then the idea of a
mono-heno-theory is again that it's a one theory with all the truth, >>>>>> where truth
is the quantity and truth is conserved, and the universe is full
of it,
then that any other exercise in theory is an exercise in it.
Void and Universe <- logic's
Point and Space <- geometry's
Increment and Partition <- arithmetic's
Metaphor and Metonymy <- language's, algebra's
Energy and Entelechy <- physics' contents
Dynamis and Dunamis <- physics' activity
So, Continuity and Infinity are approached classically, then for the >>>>>> paleo-classical and the post-modern account, is a usual sort of
formal treatment that has a "the logic" and "the objects of the
universe of mathematics" with "strong mathematical platonism",
then that the formalism has for rulial and regular accounts of
competing rulialities well-foundedness and well-ordering after
well-dispersion, the infinitary reasoning since the classical
accounts
of the super-classical or Zeno's thought experiments, what makes for >>>>>> a thorough sort of account of the modal, temporal, relevance logic, >>>>>> in descriptive accounts of formalism, for infinitary and
super-classical
reasoning, after axiomless deduction, for actual infinity
and replete continuity, mathematically.
Teleology and Ontology <- the objective and subjective
Science and Statistics <- the inter-subjective
So, "complementary duals" make a great account as to why the
competing rulialities result the analytical bridges instead of
the inductive impasses and have the structuralist realism of
the super-classical results of analysis and for quantifier
disambiguation and the extraction of mathematical implicits
thusly a greater account of reason and mathematically, and
in its discourse meeting the requirements and desiderata of
both "strong mathematical platonism" and "strong logicist
positivism",
that there's one good theory and any number of ways to talk about it. >>>>>>
"Foundations", "Sole Foundations", "True Foundations"
There's a paleo-classical post-modern realist structuralist's
mathematics, then also about the intelligence and wisdom and
knowledge
and science,
Intelligence and Wisdom
Knowledge and Science
about the real, the natural, and the rational, and the reasonable, >>>>>>
De Re and De Natura
De Res and De Racio
then, thusly, there's one good theory at all that's an Aristotlean >>>>>> realism and actualized for Aristotle, and a Hegelian idealism and
with a wider, fuller dialectic for Hegel, and that's the one there >>>>>> is.
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
That's merely an account of "ontology in a vacuum"
and is bereft the needful for accounts of continuity and infinity,
and can't claim to resolve paradoxes it makes for itself.
Hilbert-Bernays paradox
All pathological self-reference derives a cycle
in the directly graph of the evaluation sequence
of the expression. This causes the expression to
be rejected as semantically incoherent input.
I handled this for the Liar Paradox
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory of G||del's G
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao 01 02
01 G
02 -4 03
03 Prov_PA 04
04 G||del_Number_of 01 // cycle indicates no well-founded justification >>> tree exists.
and the Halting Problem proofs
https://github.com/plolcott/x86utm/blob/master/Halt7.c
Proof Theoretic Semantics halt prover HHH correctly
determines that its input DD is ungrounded in its
atomic base according to the operational semantics
of the C programming language.
I'd imagine that "directed" graph was intended,
yet what's so is that a more _thorough_ account
actual detects cycles instead of presuming their
inexistence, which is a stipulation that simply
doesn't apply to fuller graphs in relation.
There are at least three laws of large numbers (LLN's):
the Law of Large Numbers (LLN):
the usual Law of Small Numbers, that finite numbers m are small, there's
a larger one m + 1, setting up, and requiring, induction
the Law of Larger Numbers (LLN+):
moreso than the Law of Large Numbers, also there exists n >> m,
setting up, and requiring, counter-induction
the Law of Largest Numbers (LLN++):
furthermore there are infinitely-grand numbers besides infinitely-many,
setting up, and requiring, super-classical deduction
Then things like "Chaitin's Omega" about "The Halting Problem"
and "P(Halts) the Probability of Halting" get involved variously
about laws of large numbers, models of Cantor space, and these
sorts of accounts since Erdos of "Mathematical Independence"
(meaning demonstrably contradictory given competing rulialities)
the Erdos "Giant Monsters" of Mathematical Independence, instead
for accounts of a "Great Atlas of Mathematical Independence",
that resolves the competing rulialities with analytical bridges,
with "Zeno Machines" and models of computation, "supertasks"
beyond "small supertasks" and so on.
Making "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
All the rest is out-of-scope.
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is abstract in >>>> the extreme.-a One thing is utterly clear: its level of abstraction is >>>> well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two
are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value
can be consistently assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
thus you have no basis toFalse, see above.
assess these skills of mine.
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in >>>>> the extreme. One thing is utterly clear: its level of abstraction is >>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>> even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two
are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value
can be consistently assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem proof, Godel's proof, and Tarski's proof, each of which you've been attempting
(and failing) to refute for years.
That you are unable to recognize this is proof that you don't understand proof by contradiction.
thus you have no basis toFalse, see above.
assess these skills of mine.
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
----
Copyright 2026 Olcott
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is abstract in >>>>> the extreme.-a One thing is utterly clear: its level of abstraction is >>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>> even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two
are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value
can be consistently assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem proof, Godel's proof, and Tarski's proof, each of which you've been attempting
(and failing) to refute for years.
That you are unable to recognize this is proof that you don't understand proof by contradiction.
--thus you have no basis toFalse, see above.
assess these skills of mine.
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is
abstract in
the extreme.-a One thing is utterly clear: its level of abstraction is >>>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>>> even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two
are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value
can be consistently assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've been
attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
HHH never sees any contradiction it only sees that its proof
remains stuck in recursion.
That you are unable to recognize this is proof that you don't
understand proof by contradiction.
thus you have no basis toFalse, see above.
assess these skills of mine.
On 6/20/2026 10:23 AM, dbush wrote:
On 6/20/2026 11:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P re| P re? Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P reo -4P) reo reN // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good.-a Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
That's not what I asked.-a I asked if the following statement is true:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
So you are not smart enough to understand that
when the actual composition of the Moon is specified
and that this composition is not green cheese that
the system would report false?
On 06/20/2026 12:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is
abstract in
the extreme.-a One thing is utterly clear: its level of abstraction is >>>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>>> even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two
are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value
can be consistently assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem proof,
Godel's proof, and Tarski's proof, each of which you've been attempting
(and failing) to refute for years.
That you are unable to recognize this is proof that you don't understand
proof by contradiction.
thus you have no basis toFalse, see above.
assess these skills of mine.
Hard constructivists don't even _accept_ proof-by-contradiction.
Somehow then "structural realists" and "realist structuralists"
may also be "hard constructivists" while "extreme rationalists".
Since "quasi-modal material implication" has "see rule 1: last wins",
it contradicts itself.
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
[ .... ]
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
So, in your system, all facts are axioms?
That would appear to make it
not a very useful system, since there is nothing left to prove. Also it
is difficult, if even possible in general, to determine whether some assertion is an axiom or not. Your "axioms" are not axioms in the normal sense of the word; they're an encyclopaedia.
Or is a fact different from an "empirical fact" in some way?
--
Copyright 2026 Olcott
On 6/20/2026 4:03 PM, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is
abstract in
the extreme.-a One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>> can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The
two are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value >>>>> can be consistently assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've been
attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
The above is unclear, as "HHH" and "DD" could refer to:
On 6/20/2026 3:17 PM, dbush wrote:
On 6/20/2026 4:03 PM, olcott wrote:The same one that I have been talking about for years. https://github.com/plolcott/x86utm/blob/master/README.md https://github.com/plolcott/x86utm/blob/master/Halt7.c
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)I've spent a couple of hours reading that web page.-a It is
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
abstract in
the extreme.-a One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>>> can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The
two are different things. A contradiction is a statement which is >>>>>> necessarily false. A paradox is a statement to which no truth
value can be consistently assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've been
attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
The above is unclear, as "HHH" and "DD" could refer to:
Atomic facts of general knowledge includes atomicAnd given that this statement is an atomic fact:
facts of empirical general knowledge such as
"cats are animals".
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun. --------------------------------------
What do you think can be concluded about whether the following statement
is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the following
statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
On 6/20/2026 2:48 PM, Alan Mackenzie wrote:How about answering my question? In your system are all facts axioms, or
In comp.theory olcott <polcott333@gmail.com> wrote:Since you are not a philosopher you have no idea what
[ .... ]
I only skimmed that digression from this point:So, in your system, all facts are axioms?
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
a nightmare the analytic/synthetic distinction is.
By converting all of the atomic facts of empiricalUnlikely. I suggest to you yet again, converting all "atomic facts"
general knowledge into axioms the whole 75 year old
nightmare is ended in this single sentence.
Why do you bother responding to me? You don't answer my points andThat would appear to make it not a very useful system, since there is nothing left to prove. Also it is difficult, if even possible inAtomic facts of general knowledge includes atomic
general, to determine whether some assertion is an axiom or not.
Your "axioms" are not axioms in the normal sense of the word; they're
an encyclopaedia.
Or is a fact different from an "empirical fact" in some way?
facts of empirical general knowledge such as
"cats are animals".
----
Copyright 2026 Olcott
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the following
statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore that
disjunction introduction is correct.
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/20/2026 2:48 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
[ .... ]
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
So, in your system, all facts are axioms?
Since you are not a philosopher you have no idea what
a nightmare the analytic/synthetic distinction is.
How about answering my question? In your system are all facts axioms, or
are they not?
By converting all of the atomic facts of empirical
general knowledge into axioms the whole 75 year old
nightmare is ended in this single sentence.
Unlikely. I suggest to you yet again, converting all "atomic facts" (whatever they may be) to axioms will not result in a satisfactory or
useful system.
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the following
statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore that
disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"re?" disjunctions.
On 6/20/2026 6:26 PM, olcott wrote:
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the following
statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore that
disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"re?" disjunctions.
Then let's take this step-by-step.
Step 1: establish a true statement:
--------------------------------------
Earth is the third planet from the sun. --------------------------------------
That has been agreed.
Step 2: do you believe the following statement is true or false, and how
do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
On 6/20/2026 7:11 PM, dbush wrote:
On 6/20/2026 6:26 PM, olcott wrote:
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the following
statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore that
disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"re?" disjunctions.
Then let's take this step-by-step.
Step 1: establish a true statement:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
That has been agreed.
Step 2: do you believe the following statement is true or false, and
how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
OK so going step by step is fine with me.
1) P reo -4P-a-a-a // Premise
2) P-a-a-a-a-a-a-a-a-a // Conjunction elimination
3) -4P-a-a-a-a-a-a-a // Conjunction elimination
4) P re? Q-a-a-a-a-a // Disjunction introduction
5) Q-a-a-a-a-a-a-a-a-a // Disjunctive syllogism https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
We ended up with Q only because we were allowed
to insert Q from out of nowhere in the inference
chain that started with P reo -4P.
On 6/20/2026 8:26 PM, olcott wrote:
On 6/20/2026 7:11 PM, dbush wrote:
On 6/20/2026 6:26 PM, olcott wrote:
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the following
statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore that
disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"re?" disjunctions.
Then let's take this step-by-step.
Step 1: establish a true statement:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
That has been agreed.
Step 2: do you believe the following statement is true or false, and
how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
OK so going step by step is fine with me.
1) P reo -4P-a-a-a // Premise
2) P-a-a-a-a-a-a-a-a-a // Conjunction elimination
3) -4P-a-a-a-a-a-a-a // Conjunction elimination
4) P re? Q-a-a-a-a-a // Disjunction introduction
5) Q-a-a-a-a-a-a-a-a-a // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
We ended up with Q only because we were allowed
to insert Q from out of nowhere in the inference
chain that started with P reo -4P.
I didn't ask about those steps.-a I asked if you believe the following statement is true or false, and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
On 6/20/2026 7:29 PM, dbush wrote:
On 6/20/2026 8:26 PM, olcott wrote:
On 6/20/2026 7:11 PM, dbush wrote:
On 6/20/2026 6:26 PM, olcott wrote:
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the following >>>>>>>> statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore that
disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"re?" disjunctions.
Then let's take this step-by-step.
Step 1: establish a true statement:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
That has been agreed.
Step 2: do you believe the following statement is true or false, and
how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
OK so going step by step is fine with me.
1) P reo -4P-a-a-a // Premise
2) P-a-a-a-a-a-a-a-a-a // Conjunction elimination
3) -4P-a-a-a-a-a-a-a // Conjunction elimination
4) P re? Q-a-a-a-a-a // Disjunction introduction
5) Q-a-a-a-a-a-a-a-a-a // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
We ended up with Q only because we were allowed
to insert Q from out of nowhere in the inference
chain that started with P reo -4P.
I didn't ask about those steps.-a I asked if you believe the following
statement is true or false, and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
P = "Earth is the third planet from the sun."
Q = "The moon is made of green cheese."
We determine that P is true on the basis empirical facts.
We determine that Q is false on the basis empirical facts.
Is P re? Q true? Yes.
On 6/20/2026 9:06 PM, olcott wrote:
On 6/20/2026 7:29 PM, dbush wrote:
On 6/20/2026 8:26 PM, olcott wrote:
On 6/20/2026 7:11 PM, dbush wrote:
On 6/20/2026 6:26 PM, olcott wrote:
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the following >>>>>>>>> statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore that >>>>>>> disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"re?" disjunctions.
Then let's take this step-by-step.
Step 1: establish a true statement:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
That has been agreed.
Step 2: do you believe the following statement is true or false,
and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
OK so going step by step is fine with me.
1) P reo -4P-a-a-a // Premise
2) P-a-a-a-a-a-a-a-a-a // Conjunction elimination
3) -4P-a-a-a-a-a-a-a // Conjunction elimination
4) P re? Q-a-a-a-a-a // Disjunction introduction
5) Q-a-a-a-a-a-a-a-a-a // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
We ended up with Q only because we were allowed
to insert Q from out of nowhere in the inference
chain that started with P reo -4P.
I didn't ask about those steps.-a I asked if you believe the following
statement is true or false, and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
P = "Earth is the third planet from the sun."
Q = "The moon is made of green cheese."
We determine that P is true on the basis empirical facts.
We determine that Q is false on the basis empirical facts.
Is P re? Q true? Yes.
So you agree that because P is true and Q is false, the condition "at
least one of the following" is met.
Next step:
Do you believe the following statement is true or false, and how do you
come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench. --------------------------------------
On 6/20/2026 8:28 PM, dbush wrote:
On 6/20/2026 9:06 PM, olcott wrote:
On 6/20/2026 7:29 PM, dbush wrote:
On 6/20/2026 8:26 PM, olcott wrote:
On 6/20/2026 7:11 PM, dbush wrote:
On 6/20/2026 6:26 PM, olcott wrote:
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the following >>>>>>>>>> statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore that >>>>>>>> disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"re?" disjunctions.
Then let's take this step-by-step.
Step 1: establish a true statement:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
That has been agreed.
Step 2: do you believe the following statement is true or false,
and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
OK so going step by step is fine with me.
1) P reo -4P-a-a-a // Premise
2) P-a-a-a-a-a-a-a-a-a // Conjunction elimination
3) -4P-a-a-a-a-a-a-a // Conjunction elimination
4) P re? Q-a-a-a-a-a // Disjunction introduction
5) Q-a-a-a-a-a-a-a-a-a // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
We ended up with Q only because we were allowed
to insert Q from out of nowhere in the inference
chain that started with P reo -4P.
I didn't ask about those steps.-a I asked if you believe the
following statement is true or false, and how do you come to that
conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
P = "Earth is the third planet from the sun."
Q = "The moon is made of green cheese."
We determine that P is true on the basis empirical facts.
We determine that Q is false on the basis empirical facts.
Is P re? Q true? Yes.
So you agree that because P is true and Q is false, the condition "at
least one of the following" is met.
Next step:
Do you believe the following statement is true or false, and how do
you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench.
--------------------------------------
Clearly just head games. GFO with these head games
On 6/20/2026 9:32 PM, olcott wrote:
On 6/20/2026 8:28 PM, dbush wrote:
On 6/20/2026 9:06 PM, olcott wrote:
On 6/20/2026 7:29 PM, dbush wrote:
On 6/20/2026 8:26 PM, olcott wrote:
On 6/20/2026 7:11 PM, dbush wrote:
On 6/20/2026 6:26 PM, olcott wrote:
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the
following statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore >>>>>>>>> that disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"re?" disjunctions.
Then let's take this step-by-step.
Step 1: establish a true statement:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
That has been agreed.
Step 2: do you believe the following statement is true or false, >>>>>>> and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
OK so going step by step is fine with me.
1) P reo -4P-a-a-a // Premise
2) P-a-a-a-a-a-a-a-a-a // Conjunction elimination
3) -4P-a-a-a-a-a-a-a // Conjunction elimination
4) P re? Q-a-a-a-a-a // Disjunction introduction
5) Q-a-a-a-a-a-a-a-a-a // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
We ended up with Q only because we were allowed
to insert Q from out of nowhere in the inference
chain that started with P reo -4P.
I didn't ask about those steps.-a I asked if you believe the
following statement is true or false, and how do you come to that
conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
P = "Earth is the third planet from the sun."
Q = "The moon is made of green cheese."
We determine that P is true on the basis empirical facts.
We determine that Q is false on the basis empirical facts.
Is P re? Q true? Yes.
So you agree that because P is true and Q is false, the condition "at
least one of the following" is met.
Next step:
Do you believe the following statement is true or false, and how do
you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench.
--------------------------------------
Clearly just head games. GFO with these head games
I promise you I am going somewhere with this, and this is no head game.
But we must take things one small step at a time.
So I'll ask again:
Do you believe the following natural language statement is true or
false, and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench. --------------------------------------
On 6/20/2026 8:38 PM, dbush wrote:
On 6/20/2026 9:32 PM, olcott wrote:
On 6/20/2026 8:28 PM, dbush wrote:
On 6/20/2026 9:06 PM, olcott wrote:
On 6/20/2026 7:29 PM, dbush wrote:
On 6/20/2026 8:26 PM, olcott wrote:
On 6/20/2026 7:11 PM, dbush wrote:
On 6/20/2026 6:26 PM, olcott wrote:
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the
following statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore >>>>>>>>>> that disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"re?" disjunctions.
Then let's take this step-by-step.
Step 1: establish a true statement:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
That has been agreed.
Step 2: do you believe the following statement is true or false, >>>>>>>> and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
OK so going step by step is fine with me.
1) P reo -4P-a-a-a // Premise
2) P-a-a-a-a-a-a-a-a-a // Conjunction elimination
3) -4P-a-a-a-a-a-a-a // Conjunction elimination
4) P re? Q-a-a-a-a-a // Disjunction introduction
5) Q-a-a-a-a-a-a-a-a-a // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
We ended up with Q only because we were allowed
to insert Q from out of nowhere in the inference
chain that started with P reo -4P.
I didn't ask about those steps.-a I asked if you believe the
following statement is true or false, and how do you come to that >>>>>> conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
P = "Earth is the third planet from the sun."
Q = "The moon is made of green cheese."
We determine that P is true on the basis empirical facts.
We determine that Q is false on the basis empirical facts.
Is P re? Q true? Yes.
So you agree that because P is true and Q is false, the condition
"at least one of the following" is met.
Next step:
Do you believe the following statement is true or false, and how do
you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench.
--------------------------------------
Clearly just head games. GFO with these head games
I promise you I am going somewhere with this, and this is no head
game. But we must take things one small step at a time.
So I'll ask again:
Do you believe the following natural language statement is true or
false, and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench.
--------------------------------------
Go fuck off.
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is abstract in >>>> the extreme.-a One thing is utterly clear: its level of abstraction is >>>> well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two
are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value
can be consistently assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is
abstract in
the extreme.-a One thing is utterly clear: its level of abstraction is >>>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>>> even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two
are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value
can be consistently assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've been
attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
On 6/20/2026 4:03 PM, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is
abstract in
the extreme.-a One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>> can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The
two are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value >>>>> can be consistently assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've been
attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
The above is unclear, as "HHH" and "DD" could refer to:
- An algorithm, i.e. a fixed immutable sequence of instructions that
always produces the same output for a given input.
- A C function which has a specific name and may contain any arbitrary instructions
- A finite string implemented as a 32-bit function pointer.
On 6/20/2026 5:26 AM, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is abstract in >>>> the extreme.-a One thing is utterly clear: its level of abstraction is >>>> well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered
to read it any further.-a If it actually says anything at all, that
something is heavily disguised.-a From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants. Logical constants play a central
role
| in reasoning and inference, but are definitely not the exclusive, and >>>> | perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-
logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the
near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?-a What it
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
At different times you have expressed different opinions, which
sometimes have been incompatible. But you have never clearly
retracted your earlier opitions that conflict with your present
ones.
All of the ideas that I have ever had about these things
are now under the Proof Theoretic Semantics category.
These ideas have evolved over time, yet their essence
has remained utterly unchanged since 1997.
On 6/20/2026 12:25 AM, Ross Finlayson wrote:
On 06/18/2026 12:35 PM, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
This seems to be the rigidly conformist and memorize
by rote mindset.
Hm. Here there is a rather "rigidly conformist" approach,
and "an extreme rationalism", though, it's not the usual.
a principle of inverse
supplants, subsumes, and includes
a principle of non-contradiction/excluded-middle
Modern Logic has always simply ignored that an
expression may be semantically incoherent because
logic has always ignored semantics and focused
on syntax.
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P re| P re? Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P reo -4P) reo reN // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good.-a Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
On 6/20/2026 2:54 AM, Mikko wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is abstract in
the extreme.-a One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered >>> to read it any further.-a If it actually says anything at all, that
something is heavily disguised.-a From it's "Conclusion and Outlook"
section at the end:
-a-a | Standard proof-theoretic semantics has practically exclusively been >>> -a-a | occupied with logical constants. Logical constants play a
central role
-a-a | in reasoning and inference, but are definitely not the
exclusive, and
-a-a | perhaps not even the most typical sort of entities that can be
defined
-a-a | inferentially. A framework is needed that deals with inferential
-a-a | definitions in a wider sense and covers both logical and extra-
logical
-a-a | inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the
near future not useful as making it useful requires much time and
effort if it is possible at all.
Proof Theoretic Semantics is the basis that makes:
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
A sememe is the smallest indivisible unit of meaning
in linguistics.
PTS forms a tree of knowledge such that every sememe
is connected to all of its semantic meaning entirely
via connections to other sememes.
On 6/20/2026 4:43 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/20/2026 2:48 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
[ .... ]
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
So, in your system, all facts are axioms?
Since you are not a philosopher you have no idea what
a nightmare the analytic/synthetic distinction is.
How about answering my question? In your system are all facts
axioms, or are they not?
By converting all of the atomic facts of empirical
general knowledge into axioms the whole 75 year old
nightmare is ended in this single sentence.
Unlikely. I suggest to you yet again, converting all "atomic facts" (whatever they may be) to axioms will not result in a satisfactory or useful system.
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge by
providing grounding in a proof theoretic atomic base.
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
Prior to yesterday I had no idea how close PTS already
is to my own system.
----
Copyright 2026 Olcott
On 20/06/2026 22:02, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is abstract in >>>>> the extreme.-a One thing is utterly clear: its level of abstraction is >>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>> even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two
are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value
can be consistently assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
You have. Everything that can be proven can be proven by a proof by contradiction, and often is, as that is the simpest way to prove
many theorems.
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/20/2026 4:43 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/20/2026 2:48 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
[ .... ]
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
So, in your system, all facts are axioms?
Since you are not a philosopher you have no idea what
a nightmare the analytic/synthetic distinction is.
How about answering my question? In your system are all facts
axioms, or are they not?
Still no answer?
By converting all of the atomic facts of empirical
general knowledge into axioms the whole 75 year old
nightmare is ended in this single sentence.
Unlikely. I suggest to you yet again, converting all "atomic facts"
(whatever they may be) to axioms will not result in a satisfactory or
useful system.
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge by
providing grounding in a proof theoretic atomic base.
Vacuously so. If all facts are axioms, there is nothing left to prove.
Of course, in this setup, determining if an assertion is an axiom or not
is an insoluble problem.
Maybe you mean something else by "atomic fact". You're clearly unable or unwilling to define that term. Obviously you either don't understand it,
or you need to keep it vague to avoid being pinned down by logic and
reality.
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're capable of understanding them.
Prior to yesterday I had no idea how close PTS already
is to my own system.
You're clueless about PTS. You can't explain it, you don't understand
it. You just like trying to flummox others by throwing around big words
and recondite phrases. When asked to explain what they mean, you just go
all vague. "Your own system" is vacuous nonsense.
--
Copyright 2026 Olcott
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/20/2026 4:43 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/20/2026 2:48 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
[ .... ]
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
So, in your system, all facts are axioms?
Since you are not a philosopher you have no idea what
a nightmare the analytic/synthetic distinction is.
How about answering my question?-a In your system are all facts
axioms, or are they not?
Still no answer?
By converting all of the atomic facts of empirical
general knowledge into axioms the whole 75 year old
nightmare is ended in this single sentence.
Unlikely.-a I suggest to you yet again, converting all "atomic facts"
(whatever they may be) to axioms will not result in a satisfactory or
useful system.
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge by
providing grounding in a proof theoretic atomic base.
Vacuously so.-a If all facts are axioms, there is nothing left to prove.
Of course, in this setup, determining if an assertion is an axiom or not
is an insoluble problem.
Maybe you mean something else by "atomic fact".-a You're clearly unable or >> unwilling to define that term.-a Obviously you either don't understand it, >> or you need to keep it vague to avoid being pinned down by logic and
reality.
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms.-a That doesn't mean you're capable of
understanding them.
The above is the key reason why under PTS G||del 1931
incompleteness fails. If they are mere gibberish words
to you then you will not understand.
Prior to yesterday I had no idea how close PTS already
is to my own system.
You're clueless about PTS.-a You can't explain it, you don't understand
it.-a You just like trying to flummox others by throwing around big words
and recondite phrases.-a When asked to explain what they mean, you just go >> all vague.-a "Your own system" is vacuous nonsense.
If you know essentially nothing about PTS then when
I explain things using the terminology of PTS you will
not understand. I need to go to university today to
pick up a key PTS paper.
--
Copyright 2026 Olcott the Pretentious
On 6/21/2026 4:48 AM, Mikko wrote:
On 20/06/2026 22:02, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is
abstract in
the extreme.-a One thing is utterly clear: its level of abstraction is >>>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>>> even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two
are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value
can be consistently assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
You have. Everything that can be proven can be proven by a proof by
contradiction, and often is, as that is the simpest way to prove
many theorems.
Each of the cases of pathological self-reference (PSR)
shows up as infinitely recursive inference steps to
every proof theoretic semantics prover.
All of the "undecidable" instances that I have been
working on since 2004 have only involved PSR.
Confusing PSR for contradiction instead of a cycle
in the directed graph of the evaluation sequence is
the mistake of everyone else not my mistake.
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:I don't believe you. You have no respect for or understanding of the
In comp.theory olcott <polcott333@gmail.com> wrote:The above is the key reason why under PTS G||del 1931 incompleteness
On 6/20/2026 4:43 PM, Alan Mackenzie wrote:Still no answer?
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/20/2026 2:48 PM, Alan Mackenzie wrote:How about answering my question? In your system are all facts
In comp.theory olcott <polcott333@gmail.com> wrote:Since you are not a philosopher you have no idea what
[ .... ]
I only skimmed that digression from this point:So, in your system, all facts are axioms?
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
a nightmare the analytic/synthetic distinction is.
axioms, or are they not?
Vacuously so. If all facts are axioms, there is nothing left to prove.It makes "true on the basis of meaning expressed in language"By converting all of the atomic facts of empiricalUnlikely. I suggest to you yet again, converting all "atomic facts"
general knowledge into axioms the whole 75 year old
nightmare is ended in this single sentence.
(whatever they may be) to axioms will not result in a satisfactory or
useful system.
reliably computable for the entire body of knowledge by
providing grounding in a proof theoretic atomic base.
Of course, in this setup, determining if an assertion is an axiom or not
is an insoluble problem.
Maybe you mean something else by "atomic fact". You're clearly unable or unwilling to define that term. Obviously you either don't understand it, or you need to keep it vague to avoid being pinned down by logic and reality.
I just found the term:You can find any number of terms. That doesn't mean you're capable of understanding them.
"grounding in a proof theoretic atomic base" yesterday.
fails.
If they are mere gibberish words to you then you will not understand.You don't understand Proof-theoritic Semantics, and you certainly don't understand G||del's Theorem, neither the theorem itself nor any proof of
My lack of understanding of and lack of desire to understand PTS is notIf you know essentially nothing about PTS then whenPrior to yesterday I had no idea how close PTS already is to my ownYou're clueless about PTS. You can't explain it, you don't understand
system.
it. You just like trying to flummox others by throwing around big words and recondite phrases. When asked to explain what they mean, you just go all vague. "Your own system" is vacuous nonsense.
I explain things using the terminology of PTS you will
not understand.
I need to go to university today to pick up a key PTS paper.You might do better going tomorrow when it's open.
----
Copyright 2026 Olcott
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're capable of
understanding them.
The above is the key reason why under PTS G||del 1931 incompleteness
fails.
I don't believe you. You have no respect for or understanding of the
truth. If you really want to persuade anybody that PTS somehow causes G||del's theorem not to hold, then cite an academic expert who'll have
some credibility.
If they are mere gibberish words to you then you will not understand.
You don't understand Proof-theoritic Semantics, and you certainly don't understand G||del's Theorem, neither the theorem itself nor any proof of
it.
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms.-a That doesn't mean you're capable of >>>> understanding them.
The above is the key reason why under PTS G||del 1931 incompleteness
fails.
I don't believe you.-a You have no respect for or understanding of the
truth.-a If you really want to persuade anybody that PTS somehow causes
G||del's theorem not to hold, then cite an academic expert who'll have
some credibility.
If they are mere gibberish words to you then you will not understand.
You don't understand Proof-theoritic Semantics, and you certainly don't
understand G||del's Theorem, neither the theorem itself nor any proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is abstract in >>>> the extreme.-a One thing is utterly clear: its level of abstraction is >>>> well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered
to read it any further.-a If it actually says anything at all, that
something is heavily disguised.-a From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants. Logical constants play a central
role
| in reasoning and inference, but are definitely not the exclusive, and >>>> | perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-
logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the
near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?-a What it >> ought to be able to do that standard logic fails at?-a Maybe Andr|- could
elucidate.-a He seems to have a better grasp of it than anybody else here.
I doubt my understanding of PTS is any better than yours. I basically
only know what is presented in the Stanford Encyclopedia article (which
you correctly point out is not exactly aimed at beginners) and the
Wikipedia article. What I am quite certain of, however, is that Olcott
lacks any understanding of what PTS actually says as he's made a variety
of fairly absurd claims regarding it (for example, that PTS claims that unproven propositions are 'meaningless' or that the goal of PTS is to completely overthrow standard truth-theoretic semantics).
Andr|-
On 6/21/2026 3:18 PM, Andr|- G. Isaak wrote:
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is abstract in >>>>> the extreme.-a One thing is utterly clear: its level of abstraction is >>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>> even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered
to read it any further.-a If it actually says anything at all, that
something is heavily disguised.-a From it's "Conclusion and Outlook" >>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>>>> | occupied with logical constants. Logical constants play a central >>>>> role
| in reasoning and inference, but are definitely not the exclusive, >>>>> and
| perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-
logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the
near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
ought to be able to do that standard logic fails at?-a Maybe Andr|- could >>> elucidate.-a He seems to have a better grasp of it than anybody else
here.
I doubt my understanding of PTS is any better than yours. I basically
only know what is presented in the Stanford Encyclopedia article
(which you correctly point out is not exactly aimed at beginners) and
the Wikipedia article. What I am quite certain of, however, is that
Olcott lacks any understanding of what PTS actually says as he's made
a variety of fairly absurd claims regarding it (for example, that PTS
claims that unproven propositions are 'meaningless' or that the goal
of PTS is to completely overthrow standard truth-theoretic semantics).
Andr|-
-a Proof-theoretic semantics is an alternative to
-a truth-condition semantics. It is based on the
-a fundamental assumption that the central notion
-a in terms of which meanings are assigned to certain
-a expressions of our language, in particular to
-a logical constants, is that of proof rather than
-a truth. In this sense proof-theoretic semantics
-a is semantics in terms of proof.
-a https://plato.stanford.edu/entries/proof-theoretic-semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms.-a That doesn't mean you're capable of >>>>> understanding them.
The above is the key reason why under PTS G||del 1931 incompleteness
fails.
I don't believe you.-a You have no respect for or understanding of the
truth.-a If you really want to persuade anybody that PTS somehow causes
G||del's theorem not to hold, then cite an academic expert who'll have
some credibility.
If they are mere gibberish words to you then you will not understand.
You don't understand Proof-theoritic Semantics, and you certainly don't
understand G||del's Theorem, neither the theorem itself nor any proof of >>> it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by you,
and it is one which you have never explicitly defined, so the fault here certainly doesn't lie with Alan. It's certainly not a 'verified fact'
when you haven't even adequately explained what it is that you mean.
Andr|-
olcott wrote:
On 6/21/2026 3:18 PM, Andr|- G. Isaak wrote:Lastly, and why should we care? Please answer this and other questions presented.
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is
abstract in
the extreme.-a One thing is utterly clear: its level of abstraction is >>>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>>> even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered
to read it any further.-a If it actually says anything at all, that >>>>>> something is heavily disguised.-a From it's "Conclusion and Outlook" >>>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>>>>> | occupied with logical constants. Logical constants play a
central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential >>>>>> | definitions in a wider sense and covers both logical and extra- >>>>>> logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the >>>>> near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
ought to be able to do that standard logic fails at?-a Maybe Andr|- could >>>> elucidate.-a He seems to have a better grasp of it than anybody else
here.
I doubt my understanding of PTS is any better than yours. I basically
only know what is presented in the Stanford Encyclopedia article
(which you correctly point out is not exactly aimed at beginners) and
the Wikipedia article. What I am quite certain of, however, is that
Olcott lacks any understanding of what PTS actually says as he's made
a variety of fairly absurd claims regarding it (for example, that PTS
claims that unproven propositions are 'meaningless' or that the goal
of PTS is to completely overthrow standard truth-theoretic semantics).
Andr|-
-a-a Proof-theoretic semantics is an alternative to
-a-a truth-condition semantics. It is based on the
-a-a fundamental assumption that the central notion
-a-a in terms of which meanings are assigned to certain
-a-a expressions of our language, in particular to
-a-a logical constants, is that of proof rather than
-a-a truth. In this sense proof-theoretic semantics
-a-a is semantics in terms of proof.
-a-a https://plato.stanford.edu/entries/proof-theoretic-semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is
abstract in
the extreme.-a One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>> can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The
two are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value >>>>> can be consistently assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've been
attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
That only means that your DD is not a strictly confoming C program.
On 20/06/2026 16:50, olcott wrote:
On 6/20/2026 5:26 AM, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is abstract in >>>>> the extreme.-a One thing is utterly clear: its level of abstraction is >>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>> even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered
to read it any further.-a If it actually says anything at all, that
something is heavily disguised.-a From it's "Conclusion and Outlook" >>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>>>> | occupied with logical constants. Logical constants play a central >>>>> role
| in reasoning and inference, but are definitely not the exclusive, >>>>> and
| perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-
logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the
near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If a claim is true on the basis on meaning expressed in language we
usually can easily determine its truth vaule wihout computational
tools. The truth values we want to know but are hard to determine
are of claims that are true on some other basis.
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
At different times you have expressed different opinions, which
sometimes have been incompatible. But you have never clearly
retracted your earlier opitions that conflict with your present
ones.
All of the ideas that I have ever had about these things
are now under the Proof Theoretic Semantics category.
These ideas have evolved over time, yet their essence
has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a publishable
(or nearly publishable) article about them.
On 20/06/2026 17:18, olcott wrote:
On 6/20/2026 12:25 AM, Ross Finlayson wrote:
On 06/18/2026 12:35 PM, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
This seems to be the rigidly conformist and memorize
by rote mindset.
Hm. Here there is a rather "rigidly conformist" approach,
and "an extreme rationalism", though, it's not the usual.
a principle of inverse
supplants, subsumes, and includes
a principle of non-contradiction/excluded-middle
Modern Logic has always simply ignored that an
expression may be semantically incoherent because
logic has always ignored semantics and focused
on syntax.
Modern logic has
G||del proved that every consistent first order theory has a model.
That means that a consisten first order theory cannot be semantically incoherent.
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms.-a That doesn't mean you're
capable of
understanding them.
The above is the key reason why under PTS G||del 1931 incompleteness >>>>> fails.
I don't believe you.-a You have no respect for or understanding of the >>>> truth.-a If you really want to persuade anybody that PTS somehow causes >>>> G||del's theorem not to hold, then cite an academic expert who'll have >>>> some credibility.
If they are mere gibberish words to you then you will not understand. >>>>You don't understand Proof-theoritic Semantics, and you certainly don't >>>> understand G||del's Theorem, neither the theorem itself nor any proof of >>>> it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by you,
and it is one which you have never explicitly defined, so the fault
here certainly doesn't lie with Alan. It's certainly not a 'verified
fact' when you haven't even adequately explained what it is that you
mean.
Andr|-
All of knowledge expressed in language is structured as a tree of
semantic relations specified syntactically between finite strings.
I am working in anchoring all of the relevant details
of "grounded in the atomic base" in quotes from
published papers.
On 6/21/2026 3:18 PM, Andr|- G. Isaak wrote:
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is abstract in >>>>> the extreme.-a One thing is utterly clear: its level of abstraction is >>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>> even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered
to read it any further.-a If it actually says anything at all, that
something is heavily disguised.-a From it's "Conclusion and Outlook" >>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>>>> | occupied with logical constants. Logical constants play a central >>>>> role
| in reasoning and inference, but are definitely not the exclusive, >>>>> and
| perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-
logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the
near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
ought to be able to do that standard logic fails at?-a Maybe Andr|- could >>> elucidate.-a He seems to have a better grasp of it than anybody else
here.
I doubt my understanding of PTS is any better than yours. I basically
only know what is presented in the Stanford Encyclopedia article
(which you correctly point out is not exactly aimed at beginners) and
the Wikipedia article. What I am quite certain of, however, is that
Olcott lacks any understanding of what PTS actually says as he's made
a variety of fairly absurd claims regarding it (for example, that PTS
claims that unproven propositions are 'meaningless' or that the goal
of PTS is to completely overthrow standard truth-theoretic semantics).
Andr|-
-a Proof-theoretic semantics is an alternative to
-a truth-condition semantics. It is based on the
-a fundamental assumption that the central notion
-a in terms of which meanings are assigned to certain
-a expressions of our language, in particular to
-a logical constants, is that of proof rather than
-a truth. In this sense proof-theoretic semantics
-a is semantics in terms of proof.
-a https://plato.stanford.edu/entries/proof-theoretic-semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
On 2026-06-21 17:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms.-a That doesn't mean you're
capable of
understanding them.
The above is the key reason why under PTS G||del 1931 incompleteness >>>>>> fails.
I don't believe you.-a You have no respect for or understanding of the >>>>> truth.-a If you really want to persuade anybody that PTS somehow causes >>>>> G||del's theorem not to hold, then cite an academic expert who'll have >>>>> some credibility.
If they are mere gibberish words to you then you will not understand. >>>>>You don't understand Proof-theoritic Semantics, and you certainly
don't
understand G||del's Theorem, neither the theorem itself nor any
proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by
you, and it is one which you have never explicitly defined, so the
fault here certainly doesn't lie with Alan. It's certainly not a
'verified fact' when you haven't even adequately explained what it is
that you mean.
Andr|-
All of knowledge expressed in language is structured as a tree of
semantic relations specified syntactically between finite strings.
'all knowledge expressed in language' isn't even a well-defined set.
On 2026-06-21 15:39, olcott wrote:Proof-theoretic semantics is an alternative to truth-condition semantics.
On 6/21/2026 3:18 PM, Andr|- G. Isaak wrote:
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is
abstract in
the extreme.-a One thing is utterly clear: its level of abstraction is >>>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>>> even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered
to read it any further.-a If it actually says anything at all, that >>>>>> something is heavily disguised.-a From it's "Conclusion and Outlook" >>>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>>>>> | occupied with logical constants. Logical constants play a
central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential >>>>>> | definitions in a wider sense and covers both logical and extra- >>>>>> logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the >>>>> near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
ought to be able to do that standard logic fails at?-a Maybe Andr|- could >>>> elucidate.-a He seems to have a better grasp of it than anybody else
here.
I doubt my understanding of PTS is any better than yours. I basically
only know what is presented in the Stanford Encyclopedia article
(which you correctly point out is not exactly aimed at beginners) and
the Wikipedia article. What I am quite certain of, however, is that
Olcott lacks any understanding of what PTS actually says as he's made
a variety of fairly absurd claims regarding it (for example, that PTS
claims that unproven propositions are 'meaningless' or that the goal
of PTS is to completely overthrow standard truth-theoretic semantics).
Andr|-
-a-a Proof-theoretic semantics is an alternative to
-a-a truth-condition semantics. It is based on the
-a-a fundamental assumption that the central notion
-a-a in terms of which meanings are assigned to certain
-a-a expressions of our language, in particular to
-a-a logical constants, is that of proof rather than
-a-a truth. In this sense proof-theoretic semantics
-a-a is semantics in terms of proof.
-a-a https://plato.stanford.edu/entries/proof-theoretic-semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
No where does it talk about 'utterly abandoning'
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)I've spent a couple of hours reading that web page.-a It is
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
abstract in
the extreme.-a One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>>> can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The
two are different things. A contradiction is a statement which is >>>>>> necessarily false. A paradox is a statement to which no truth
value can be consistently assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've been
attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
That only means that your DD is not a strictly confoming C program.
The exact operational semantics of C conclusively
prove that the input DD
to HHH
is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
To sum this up PTS would have HHH
reject DDD.
Trump didn't have anything besides dishonest dodges when
she kept pressing his for evidence of election fraud so
he gave up and left the room.
On 6/21/2026 5:36 PM, phoenix wrote:
olcott wrote:
On 6/21/2026 3:18 PM, Andr|- G. Isaak wrote:Lastly, and why should we care? Please answer this and other questions
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is
abstract in
the extreme.-a One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>> can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be >>>>>>> bothered
to read it any further.-a If it actually says anything at all, that >>>>>>> something is heavily disguised.-a From it's "Conclusion and Outlook" >>>>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively >>>>>>> been
| occupied with logical constants. Logical constants play a
central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can be >>>>>>> defined
| inferentially. A framework is needed that deals with inferential >>>>>>> | definitions in a wider sense and covers both logical and extra- >>>>>>> logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the >>>>>> near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
ought to be able to do that standard logic fails at?-a Maybe Andr|- >>>>> could
elucidate.-a He seems to have a better grasp of it than anybody else >>>>> here.
I doubt my understanding of PTS is any better than yours. I
basically only know what is presented in the Stanford Encyclopedia
article (which you correctly point out is not exactly aimed at
beginners) and the Wikipedia article. What I am quite certain of,
however, is that Olcott lacks any understanding of what PTS actually
says as he's made a variety of fairly absurd claims regarding it
(for example, that PTS claims that unproven propositions are
'meaningless' or that the goal of PTS is to completely overthrow
standard truth-theoretic semantics).
Andr|-
-a-a Proof-theoretic semantics is an alternative to
-a-a truth-condition semantics. It is based on the
-a-a fundamental assumption that the central notion
-a-a in terms of which meanings are assigned to certain
-a-a expressions of our language, in particular to
-a-a logical constants, is that of proof rather than
-a-a truth. In this sense proof-theoretic semantics
-a-a is semantics in terms of proof.
-a-a https://plato.stanford.edu/entries/proof-theoretic-semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
presented.
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
olcott wrote:
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat?
olcott wrote:
On 6/21/2026 3:18 PM, Andr|- G. Isaak wrote:Lastly, and why should we care? Please answer this and other
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semanticsSome people only memorize conventional views and
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is
abstract in
the extreme.-a One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>>> can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be >>>>>>>> bothered
to read it any further.-a If it actually says anything at all, that >>>>>>>> something is heavily disguised.-a From it's "Conclusion and Outlook" >>>>>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively >>>>>>>> been
| occupied with logical constants. Logical constants play a
central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can be >>>>>>>> defined
| inferentially. A framework is needed that deals with inferential >>>>>>>> | definitions in a wider sense and covers both logical and
extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the >>>>>>> near future not useful as making it useful requires much time and >>>>>>> effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
ought to be able to do that standard logic fails at?-a Maybe Andr|- >>>>>> could
elucidate.-a He seems to have a better grasp of it than anybody
else here.
I doubt my understanding of PTS is any better than yours. I
basically only know what is presented in the Stanford Encyclopedia
article (which you correctly point out is not exactly aimed at
beginners) and the Wikipedia article. What I am quite certain of,
however, is that Olcott lacks any understanding of what PTS
actually says as he's made a variety of fairly absurd claims
regarding it (for example, that PTS claims that unproven
propositions are 'meaningless' or that the goal of PTS is to
completely overthrow standard truth-theoretic semantics).
Andr|-
-a-a Proof-theoretic semantics is an alternative to
-a-a truth-condition semantics. It is based on the
-a-a fundamental assumption that the central notion
-a-a in terms of which meanings are assigned to certain
-a-a expressions of our language, in particular to
-a-a logical constants, is that of proof rather than
-a-a truth. In this sense proof-theoretic semantics
-a-a is semantics in terms of proof.
-a-a https://plato.stanford.edu/entries/proof-theoretic-semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
questions presented.
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
That is,
they will never accept that they are wrong even when it's right up there
in clearly visible un-mathematics for us to see? That is, they tend to
have a weakness in 3D geometry I have discovered (I guess the computer scientists are going to fill in their eyes last). But far be it from
them to admit it. They will conjure answer after answer to try to back
up their position. Maybe I should go back and watch that human-AI debate that went viral. Spoiler - the humans won. It might be interesting to
see now what exactly the AI lost. Perhaps it was stating mistruths like
it still does. Wouldn't this be spectacular television today to have
that debate? It's somewhere on Youtube. I'll probably give a holler when
I find it. You may find it fairly interesting too, as you seem to also
have some experience with the LLM AIs.
By the way, I don't have a PhD in everything, but it does cover
electrical engineering -- a field heavy in mathematics. I admit we
didn't study G||del, Escher or Bach, but I managed to get through Real Analysis with minor difficulty. It was largely the mathematics of proof. It's a more difficult field than it may sound. I found you've really got
to make the interlocking pieces overlap such that there is a story told
that is without holes in it.
I toughed it out in Real Analysis. It was easier than Solid State
Physics which appeared as if magic to me. Teleporting electrons and
other quantum features. That was one of the big sticks on my back that
made me step back and re-think my double major and set computer science
as merely a minor to handle all the tribulations.
On 6/21/2026 5:36 PM, phoenix wrote:
olcott wrote:
On 6/21/2026 3:18 PM, Andr|- G. Isaak wrote:Lastly, and why should we care? Please answer this and other questions
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is
abstract in
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who
can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered
to read it any further. If it actually says anything at all, that >>>>>>> something is heavily disguised. From it's "Conclusion and Outlook" >>>>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively >>>>>>> been
| occupied with logical constants. Logical constants play a
central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can be >>>>>>> defined
| inferentially. A framework is needed that deals with inferential >>>>>>> | definitions in a wider sense and covers both logical and extra- >>>>>>> logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the >>>>>> near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
ought to be able to do that standard logic fails at? Maybe Andr|-
could
elucidate. He seems to have a better grasp of it than anybody else
here.
I doubt my understanding of PTS is any better than yours. I
basically only know what is presented in the Stanford Encyclopedia
article (which you correctly point out is not exactly aimed at
beginners) and the Wikipedia article. What I am quite certain of,
however, is that Olcott lacks any understanding of what PTS actually
says as he's made a variety of fairly absurd claims regarding it
(for example, that PTS claims that unproven propositions are
'meaningless' or that the goal of PTS is to completely overthrow
standard truth-theoretic semantics).
Andr|-
Proof-theoretic semantics is an alternative to
truth-condition semantics. It is based on the
fundamental assumption that the central notion
in terms of which meanings are assigned to certain
expressions of our language, in particular to
logical constants, is that of proof rather than
truth. In this sense proof-theoretic semantics
is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
presented.
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
olcott wrote:
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat? That is,
olcott wrote:
On 6/21/2026 3:18 PM, Andr|- G. Isaak wrote:Lastly, and why should we care? Please answer this and other
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semanticsSome people only memorize conventional views and
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is
abstract in
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>>> can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be >>>>>>>> bothered
to read it any further. If it actually says anything at all, that >>>>>>>> something is heavily disguised. From it's "Conclusion and Outlook" >>>>>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively >>>>>>>> been
| occupied with logical constants. Logical constants play a
central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can be >>>>>>>> defined
| inferentially. A framework is needed that deals with inferential >>>>>>>> | definitions in a wider sense and covers both logical and
extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the >>>>>>> near future not useful as making it useful requires much time and >>>>>>> effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
ought to be able to do that standard logic fails at? Maybe Andr|- >>>>>> could
elucidate. He seems to have a better grasp of it than anybody
else here.
I doubt my understanding of PTS is any better than yours. I
basically only know what is presented in the Stanford Encyclopedia
article (which you correctly point out is not exactly aimed at
beginners) and the Wikipedia article. What I am quite certain of,
however, is that Olcott lacks any understanding of what PTS
actually says as he's made a variety of fairly absurd claims
regarding it (for example, that PTS claims that unproven
propositions are 'meaningless' or that the goal of PTS is to
completely overthrow standard truth-theoretic semantics).
Andr|-
Proof-theoretic semantics is an alternative to
truth-condition semantics. It is based on the
fundamental assumption that the central notion
in terms of which meanings are assigned to certain
expressions of our language, in particular to
logical constants, is that of proof rather than
truth. In this sense proof-theoretic semantics
is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
questions presented.
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
they will never accept that they are wrong even when it's right up there
in clearly visible un-mathematics for us to see? That is, they tend to
have a weakness in 3D geometry I have discovered (I guess the computer scientists are going to fill in their eyes last). But far be it from
them to admit it. They will conjure answer after answer to try to back
up their position. Maybe I should go back and watch that human-AI debate
that went viral. Spoiler - the humans won. It might be interesting to
see now what exactly the AI lost. Perhaps it was stating mistruths like
it still does. Wouldn't this be spectacular television today to have
that debate? It's somewhere on Youtube. I'll probably give a holler when
I find it. You may find it fairly interesting too, as you seem to also
have some experience with the LLM AIs.
By the way, I don't have a PhD in everything, but it does cover
electrical engineering -- a field heavy in mathematics. I admit we
didn't study G||del, Escher or Bach, but I managed to get through Real Analysis with minor difficulty. It was largely the mathematics of proof.
It's a more difficult field than it may sound. I found you've really got
to make the interlocking pieces overlap such that there is a story told
that is without holes in it.
I toughed it out in Real Analysis. It was easier than Solid State
Physics which appeared as if magic to me. Teleporting electrons and
other quantum features. That was one of the big sticks on my back that
made me step back and re-think my double major and set computer science
as merely a minor to handle all the tribulations.
On 6/21/2026 4:48 AM, Mikko wrote:
On 20/06/2026 22:02, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is
abstract in
the extreme.-a One thing is utterly clear: its level of abstraction is >>>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>>> even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two
are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value
can be consistently assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
You have. Everything that can be proven can be proven by a proof by
contradiction, and often is, as that is the simpest way to prove
many theorems.
Each of the cases of pathological self-reference (PSR)
shows up as infinitely recursive inference steps to
every proof theoretic semantics prover.
All of the "undecidable" instances that I have been
working on since 2004 have only involved PSR.
Confusing PSR for contradiction instead of a cycle
in the directed graph of the evaluation sequence is
the mistake of everyone else not my mistake.
On 6/21/2026 5:11 AM, Mikko wrote:
On 20/06/2026 16:50, olcott wrote:
On 6/20/2026 5:26 AM, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is
abstract in
the extreme.-a One thing is utterly clear: its level of abstraction is >>>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>>> even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered
to read it any further.-a If it actually says anything at all, that >>>>>> something is heavily disguised.-a From it's "Conclusion and Outlook" >>>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>>>>> | occupied with logical constants. Logical constants play a
central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential >>>>>> | definitions in a wider sense and covers both logical and extra- >>>>>> logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the >>>>> near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If a claim is true on the basis on meaning expressed in language we
usually can easily determine its truth vaule wihout computational
tools. The truth values we want to know but are hard to determine
are of claims that are true on some other basis.
The system I propose would cut off the dangerous lies
of dangerous liars mid-sentence and be able to prove
that these are lies to every level of understanding
between kindergarten and PhD.
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
At different times you have expressed different opinions, which
sometimes have been incompatible. But you have never clearly
retracted your earlier opitions that conflict with your present
ones.
All of the ideas that I have ever had about these things
are now under the Proof Theoretic Semantics category.
These ideas have evolved over time, yet their essence
has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a publishable
(or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> human being on the face of the Earth could understand
me I could not publish.
Now that I am acquiring the lingua franca of PTS I
will finally be able to publish.
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms.-a That doesn't mean you're
capable of
understanding them.
The above is the key reason why under PTS G||del 1931 incompleteness >>>>> fails.
I don't believe you.-a You have no respect for or understanding of the >>>> truth.-a If you really want to persuade anybody that PTS somehow causes >>>> G||del's theorem not to hold, then cite an academic expert who'll have >>>> some credibility.
If they are mere gibberish words to you then you will not understand. >>>>You don't understand Proof-theoritic Semantics, and you certainly don't >>>> understand G||del's Theorem, neither the theorem itself nor any proof of >>>> it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by you,
and it is one which you have never explicitly defined, so the fault
here certainly doesn't lie with Alan. It's certainly not a 'verified
fact' when you haven't even adequately explained what it is that you
mean.
All of knowledge expressed in language is structured as a tree of
semantic relations specified syntactically between finite strings.
I am working in anchoring all of the relevant detailsIn published artilce you can find enough "facts" to prove that
of "grounded in the atomic base" in quotes from
published papers.
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)I've spent a couple of hours reading that web page.-a It is
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
abstract in
the extreme.-a One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>>> can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The
two are different things. A contradiction is a statement which is >>>>>> necessarily false. A paradox is a statement to which no truth
value can be consistently assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've been
attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
That only means that your DD is not a strictly confoming C program.
The exact operational semantics of C conclusively
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
On 06/21/2026 05:32 PM, phoenix wrote:
olcott wrote:
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat? That is,
olcott wrote:
On 6/21/2026 3:18 PM, Andr|- G. Isaak wrote:Lastly, and why should we care? Please answer this and other
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semanticsSome people only memorize conventional views and
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)I've spent a couple of hours reading that web page. It is
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>
abstract in
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>>>> can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be >>>>>>>>> bothered
to read it any further. If it actually says anything at all, that >>>>>>>>> something is heavily disguised. From it's "Conclusion and
Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively >>>>>>>>> been
| occupied with logical constants. Logical constants play a
central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can be >>>>>>>>> defined
| inferentially. A framework is needed that deals with inferential >>>>>>>>> | definitions in a wider sense and covers both logical and
extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in >>>>>>>> the
near future not useful as making it useful requires much time and >>>>>>>> effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for? >>>>>>> What it
ought to be able to do that standard logic fails at? Maybe Andr|- >>>>>>> could
elucidate. He seems to have a better grasp of it than anybody
else here.
I doubt my understanding of PTS is any better than yours. I
basically only know what is presented in the Stanford Encyclopedia >>>>>> article (which you correctly point out is not exactly aimed at
beginners) and the Wikipedia article. What I am quite certain of,
however, is that Olcott lacks any understanding of what PTS
actually says as he's made a variety of fairly absurd claims
regarding it (for example, that PTS claims that unproven
propositions are 'meaningless' or that the goal of PTS is to
completely overthrow standard truth-theoretic semantics).
Andr|-
Proof-theoretic semantics is an alternative to
truth-condition semantics. It is based on the
fundamental assumption that the central notion
in terms of which meanings are assigned to certain
expressions of our language, in particular to
logical constants, is that of proof rather than
truth. In this sense proof-theoretic semantics
is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
questions presented.
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
they will never accept that they are wrong even when it's right up there
in clearly visible un-mathematics for us to see? That is, they tend to
have a weakness in 3D geometry I have discovered (I guess the computer
scientists are going to fill in their eyes last). But far be it from
them to admit it. They will conjure answer after answer to try to back
up their position. Maybe I should go back and watch that human-AI debate
that went viral. Spoiler - the humans won. It might be interesting to
see now what exactly the AI lost. Perhaps it was stating mistruths like
it still does. Wouldn't this be spectacular television today to have
that debate? It's somewhere on Youtube. I'll probably give a holler when
I find it. You may find it fairly interesting too, as you seem to also
have some experience with the LLM AIs.
By the way, I don't have a PhD in everything, but it does cover
electrical engineering -- a field heavy in mathematics. I admit we
didn't study G||del, Escher or Bach, but I managed to get through Real
Analysis with minor difficulty. It was largely the mathematics of proof.
It's a more difficult field than it may sound. I found you've really got
to make the interlocking pieces overlap such that there is a story told
that is without holes in it.
I toughed it out in Real Analysis. It was easier than Solid State
Physics which appeared as if magic to me. Teleporting electrons and
other quantum features. That was one of the big sticks on my back that
made me step back and re-think my double major and set computer science
as merely a minor to handle all the tribulations.
If you like solid-state physics then you might consider that the wave
model and Lienard-Wiechert after Fermi holes are _abstractions_ and furthermore _reductions_, that it's _reductionism_ that arrives that
the theory's "good to the first or second order" or provides "on the
order of" accounts of proportionality, that in the real world, vary
like spiral-waves and wave-spirals, and Faraday rotation and the real behavior of "Fermi holes" that Lienard-Wiechert then is to give an
account as for Coulomb and Ampere the behavior of electron-holes with
regards to test-particles in the analysis of the continuum mechanics
(that's an infinitesimal analysis), then for example making that line
up with Maxwell's either E x B or D x H, usually just the one there
and ignoring that as Maxwell put it that either would do to define the
other, then usual "paradoxes" of quantum mechanics are actually problems
of the particle-conceit since there are fields and for example after the particle/wave duality the wave/resonance dichotomy, then besides that
the tachyonic and bradyonic would get involved in accounts
of "real wave collapse", which though anything that provides the "Schroedingerians" for quantum mechanics, much like the "Lorentzians"
for general relativity, suffices to make a theory that all the
experiments in "canonical quantum mechanics" and "confirmed general relativity" can ever be said to have said.
So, anti-reductionism is filling in further accounts of QM and GR,
like continuous quanta instead of Born's infinite self-energy and
slanted commutators or Feynman's de-normalized re-normalized theories
with virtual photons which aren't, or "doubly-objective" relativity
theory, there's room in the theory and room in the data to make
quantum mechanics continuous again and general relativity Euclidean again.
Most people might think the "crises in physics" need to get resolved
by adding hypothetical things, yet really the idea is to fit what
goes in where there's already "room" in the theory and data, since
the "reductionism" that left that "room" to paint itself into a corner,
has "revisiting the reductionism", or like I used to say, "revisit Heisenberg, Hubble, Higgs", with that they've been made end-results
that are dead-end-results.
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms.-a That doesn't mean you're capable of >>>> understanding them.
The above is the key reason why under PTS G||del 1931 incompleteness
fails.
I don't believe you.-a You have no respect for or understanding of the
truth.-a If you really want to persuade anybody that PTS somehow causes
G||del's theorem not to hold, then cite an academic expert who'll have
some credibility.
If they are mere gibberish words to you then you will not understand.
You don't understand Proof-theoritic Semantics, and you certainly don't
understand G||del's Theorem, neither the theorem itself nor any proof of
it.
in the atomic base of PA.
On 6/21/2026 5:23 AM, Mikko wrote:
On 20/06/2026 17:18, olcott wrote:
On 6/20/2026 12:25 AM, Ross Finlayson wrote:
On 06/18/2026 12:35 PM, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
This seems to be the rigidly conformist and memorize
by rote mindset.
Hm. Here there is a rather "rigidly conformist" approach,
and "an extreme rationalism", though, it's not the usual.
a principle of inverse
supplants, subsumes, and includes
a principle of non-contradiction/excluded-middle
Modern Logic has always simply ignored that an
expression may be semantically incoherent because
logic has always ignored semantics and focused
on syntax.
Modern logic has
always put semantics outside of the formal system
in a separate model.
PTS does not do that.
G||del proved that every consistent first order theory has a model.
That means that a consisten first order theory cannot be semantically
incoherent.
Like I just said.
On 6/21/2026 7:32 PM, phoenix wrote:
olcott wrote:
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat?
olcott wrote:
On 6/21/2026 3:18 PM, Andr|- G. Isaak wrote:Lastly, and why should we care? Please answer this and other
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semanticsSome people only memorize conventional views and
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)I've spent a couple of hours reading that web page.-a It is >>>>>>>>> abstract in
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>
the extreme.-a One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>>>> can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be >>>>>>>>> bothered
to read it any further.-a If it actually says anything at all, that >>>>>>>>> something is heavily disguised.-a From it's "Conclusion and >>>>>>>>> Outlook"
section at the end:
| Standard proof-theoretic semantics has practically
exclusively been
| occupied with logical constants. Logical constants play a >>>>>>>>> central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can >>>>>>>>> be defined
| inferentially. A framework is needed that deals with inferential >>>>>>>>> | definitions in a wider sense and covers both logical and
extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in >>>>>>>> the
near future not useful as making it useful requires much time and >>>>>>>> effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for? >>>>>>> What it
ought to be able to do that standard logic fails at?-a Maybe Andr|- >>>>>>> could
elucidate.-a He seems to have a better grasp of it than anybody >>>>>>> else here.
I doubt my understanding of PTS is any better than yours. I
basically only know what is presented in the Stanford Encyclopedia >>>>>> article (which you correctly point out is not exactly aimed at
beginners) and the Wikipedia article. What I am quite certain of, >>>>>> however, is that Olcott lacks any understanding of what PTS
actually says as he's made a variety of fairly absurd claims
regarding it (for example, that PTS claims that unproven
propositions are 'meaningless' or that the goal of PTS is to
completely overthrow standard truth-theoretic semantics).
Andr|-
-a-a Proof-theoretic semantics is an alternative to
-a-a truth-condition semantics. It is based on the
-a-a fundamental assumption that the central notion
-a-a in terms of which meanings are assigned to certain
-a-a expressions of our language, in particular to
-a-a logical constants, is that of proof rather than
-a-a truth. In this sense proof-theoretic semantics
-a-a is semantics in terms of proof.
-a-a https://plato.stanford.edu/entries/proof-theoretic-semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
questions presented.
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
It is not that they never admit defeat.
It is that that have a system of essentially infallible reasoning
that never errs as long as it has all the relevant information.
On 22/06/2026 02:55, olcott wrote:
On 6/21/2026 5:11 AM, Mikko wrote:
On 20/06/2026 16:50, olcott wrote:
On 6/20/2026 5:26 AM, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is
abstract in
the extreme.-a One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>> can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be >>>>>>> bothered
to read it any further.-a If it actually says anything at all, that >>>>>>> something is heavily disguised.-a From it's "Conclusion and Outlook" >>>>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively >>>>>>> been
| occupied with logical constants. Logical constants play a
central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can be >>>>>>> defined
| inferentially. A framework is needed that deals with inferential >>>>>>> | definitions in a wider sense and covers both logical and extra- >>>>>>> logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the >>>>>> near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If a claim is true on the basis on meaning expressed in language we
usually can easily determine its truth vaule wihout computational
tools. The truth values we want to know but are hard to determine
are of claims that are true on some other basis.
The system I propose would cut off the dangerous lies
of dangerous liars mid-sentence and be able to prove
that these are lies to every level of understanding
between kindergarten and PhD.
You have not yet demonstrated any aboility to cut off a single
lie that would matter to typical people.
On 22/06/2026 02:58, olcott wrote:
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlaysonSome people only memorize conventional views and
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
At different times you have expressed different opinions, which
sometimes have been incompatible. But you have never clearly
retracted your earlier opitions that conflict with your present
ones.
All of the ideas that I have ever had about these things
are now under the Proof Theoretic Semantics category.
These ideas have evolved over time, yet their essence
has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a publishable
(or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> human being on
the face of the Earth could understand
me I could not publish.
As far as I have seen, all interesting content in those articles
that have any is or depends on claims that should be proven but
aren't.
Now that I am acquiring the lingua franca of PTS I
will finally be able to publish.
If all you can publish is in the topic area of PtS then they may
count as uninteresting to those whose primary problems are not in
that topic area.
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms.-a That doesn't mean you're
capable of
understanding them.
The above is the key reason why under PTS G||del 1931 incompleteness >>>>>> fails.
I don't believe you.-a You have no respect for or understanding of the >>>>> truth.-a If you really want to persuade anybody that PTS somehow causes >>>>> G||del's theorem not to hold, then cite an academic expert who'll have >>>>> some credibility.
If they are mere gibberish words to you then you will not understand. >>>>>You don't understand Proof-theoritic Semantics, and you certainly
don't
understand G||del's Theorem, neither the theorem itself nor any
proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by
you, and it is one which you have never explicitly defined, so the
fault here certainly doesn't lie with Alan. It's certainly not a
'verified fact' when you haven't even adequately explained what it is
that you mean.
All of knowledge expressed in language is structured as a tree of
semantic relations specified syntactically between finite strings.
What makes you believe semantic relations that can be structured as
a tree are sufficient to contain all knowledge that is exressed in
some language?
I am working in anchoring all of the relevant detailsIn published artilce you can find enough "facts" to prove that
of "grounded in the atomic base" in quotes from
published papers.
all lies are true.
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:That is vanishingly unlikely to be true. Look at any half decent English dictionary, and it will contain lots of cycles. Any non-empty finite
On 2026-06-21 14:42, olcott wrote:All of knowledge expressed in language is structured as a tree of
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:"grounded in the atomic base of PA" is an expression used only by you,
It is a verified fact that G||del's G is ungrounded
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
and it is one which you have never explicitly defined, so the fault here certainly doesn't lie with Alan. It's certainly not a 'verified fact'
when you haven't even adequately explained what it is that you mean.
Andr|-
semantic relations specified syntactically between finite strings.
I am working in anchoring all of the relevant detailsAs remarked already "grounded in the atomic base" is undefined and
of "grounded in the atomic base" in quotes from
published papers.
----
Copyright 2026 Olcott
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)I've spent a couple of hours reading that web page.-a It is >>>>>>>>> abstract in
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>
the extreme.-a One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>>>> can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy. >>>>>>>
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The >>>>>>> two are different things. A contradiction is a statement which is >>>>>>> necessarily false. A paradox is a statement to which no truth
value can be consistently assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've been >>>>> attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
That only means that your DD is not a strictly confoming C program.
The exact operational semantics of C conclusively
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational semantics
do not fully specify the behaviour of DD. In order to prove that DD
halts you also need additional operational spemantics provided by the
C implementation you have used. When DD iss executed in that environment
it halts, which is sufficient to prove that in that environment DD
halts. In some other environment its execution might be aborted or it
could be rejected by the compiler.
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
It is a verified fact that G||del's G is ungrounded
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by you,
and it is one which you have never explicitly defined, so the fault here >>> certainly doesn't lie with Alan. It's certainly not a 'verified fact'
when you haven't even adequately explained what it is that you mean.
Andr|-
All of [general] knowledge expressed in language is structuredThat is vanishingly unlikely to be true. Look at any half decent English dictionary, and it will contain lots of cycles. Any non-empty finite
as a tree of semantic relations specified syntactically between
finite strings.
tree contains leaf nodes. Either your "tree of semantic relations" is infinite (hence useless) or it contains leaf nodes. Feel free to give an example of a leaf node in your purported tree.
I am working in anchoring all of the relevant details
of "grounded in the atomic base" in quotes from
published papers.
As remarked already "grounded in the atomic base" is undefined and meaningless.
--
Copyright 2026 Olcott
On 21/06/2026 23:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms.-a That doesn't mean you're capable of >>>>> understanding them.
The above is the key reason why under PTS G||del 1931 incompleteness
fails.
I don't believe you.-a You have no respect for or understanding of the
truth.-a If you really want to persuade anybody that PTS somehow causes
G||del's theorem not to hold, then cite an academic expert who'll have
some credibility.
If they are mere gibberish words to you then you will not understand.
You don't understand Proof-theoritic Semantics, and you certainly don't
understand G||del's Theorem, neither the theorem itself nor any proof of >>> it.
in the atomic base of PA.
It is a verified fact that G||del's completeness and incompleteness
theorems are inevitable consequences of Peano arithmetic.
On 22/06/2026 03:00, olcott wrote:
On 6/21/2026 5:23 AM, Mikko wrote:
On 20/06/2026 17:18, olcott wrote:
On 6/20/2026 12:25 AM, Ross Finlayson wrote:
On 06/18/2026 12:35 PM, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
This seems to be the rigidly conformist and memorize
by rote mindset.
Hm. Here there is a rather "rigidly conformist" approach,
and "an extreme rationalism", though, it's not the usual.
a principle of inverse
supplants, subsumes, and includes
a principle of non-contradiction/excluded-middle
Modern Logic has always simply ignored that an
expression may be semantically incoherent because
logic has always ignored semantics and focused
on syntax.
Modern logic has
always put semantics outside of the formal system
in a separate model.
And that way avoided semantic incoherence in formal systems.
PTS does not do that.
G||del proved that every consistent first order theory has a model.
That means that a consisten first order theory cannot be semantically
incoherent.
Like I just said.
Therefore we can trust that in every theory that can express the
truths of the natural numbers there is a true sentence that cannot
be proven.
On 22/06/2026 03:44, olcott wrote:
On 6/21/2026 7:32 PM, phoenix wrote:
olcott wrote:
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat?
olcott wrote:
On 6/21/2026 3:18 PM, Andr|- G. Isaak wrote:Lastly, and why should we care? Please answer this and other
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semanticsSome people only memorize conventional views and
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>> look into proof theoretic semantics.I've spent a couple of hours reading that web page.-a It is >>>>>>>>>> abstract in
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
the extreme.-a One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, >>>>>>>>>> who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't >>>>>>>>>> be bothered
to read it any further.-a If it actually says anything at all, >>>>>>>>>> that
something is heavily disguised.-a From it's "Conclusion and >>>>>>>>>> Outlook"
section at the end:
| Standard proof-theoretic semantics has practically
exclusively been
| occupied with logical constants. Logical constants play a >>>>>>>>>> central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can >>>>>>>>>> be defined
| inferentially. A framework is needed that deals with
inferential
| definitions in a wider sense and covers both logical and >>>>>>>>>> extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and >>>>>>>>> in the
near future not useful as making it useful requires much time and >>>>>>>>> effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for? >>>>>>>> What it
ought to be able to do that standard logic fails at?-a Maybe
Andr|- could
elucidate.-a He seems to have a better grasp of it than anybody >>>>>>>> else here.
I doubt my understanding of PTS is any better than yours. I
basically only know what is presented in the Stanford
Encyclopedia article (which you correctly point out is not
exactly aimed at beginners) and the Wikipedia article. What I am >>>>>>> quite certain of, however, is that Olcott lacks any understanding >>>>>>> of what PTS actually says as he's made a variety of fairly absurd >>>>>>> claims regarding it (for example, that PTS claims that unproven >>>>>>> propositions are 'meaningless' or that the goal of PTS is to
completely overthrow standard truth-theoretic semantics).
Andr|-
-a-a Proof-theoretic semantics is an alternative to
-a-a truth-condition semantics. It is based on the
-a-a fundamental assumption that the central notion
-a-a in terms of which meanings are assigned to certain
-a-a expressions of our language, in particular to
-a-a logical constants, is that of proof rather than
-a-a truth. In this sense proof-theoretic semantics
-a-a is semantics in terms of proof.
-a-a https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
questions presented.
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
It is not that they never admit defeat.
It is that that have a system of essentially infallible reasoning
that never errs as long as it has all the relevant information.
It is fairly simple to build a system of essentially infallible
reasoning that never errs even when it doesn't have all the
relevant information. The real problem is to construct a system
that tells something interesting instead of just different
presentations of the same already known facts.
On 6/22/2026 2:23 AM, Mikko wrote:You have not understood Mikko's statement. It is a VERIFIED FACT that
It is a verified fact that G||del's completeness and incompleteness theorems are inevitable consequences of Peano arithmetic.Within the foundation of Truth Conditional Semantics
this is true. Within the foundation of strict Proof
Theoretic Semantics this is false.
Some PTS called base-extension semantics seem to thinkWhat is the nature of this alleged extension? PA is a set of axioms from which, amongst other things, G||del's theorems can be proven. You seem to
that they can extend PA so that it is different and
not clearly acknowledge that they converted PA into PA+.
They would then say that G is grounded in PA when
they actually mean that G becomes grounded in the
modified PA+.
----
Copyright 2026 Olcott
[ Followup-To: set ]Within the foundation of Truth Conditional Semantics (TCS)
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 2:23 AM, Mikko wrote:
It is a verified fact that G||del's completeness and incompleteness
theorems are inevitable consequences of Peano arithmetic.
Within the foundation of Truth Conditional Semantics
this is true. Within the foundation of strict Proof
Theoretic Semantics this is false.
You have not understood Mikko's statement. It is a VERIFIED FACT that G||del's completeness and incompleteness theorems are inevitable
consequences of Peano arithmetic.
On 6/22/2026 2:40 AM, Mikko wrote:G is true.
Therefore we can trust that in every theory that can express theAs I have been saying for many years and finally
truths of the natural numbers there is a true sentence that cannot
be proven.
strict Proof Theoretic Semantics based on Dag Prawitz
theory of Grounds agrees G is ungrounded in PA
and is only true in meta-math. G was never ever
true directly in PA.
----
Copyright 2026 Olcott
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 2:40 AM, Mikko wrote:
Therefore we can trust that in every theory that can express the
truths of the natural numbers there is a true sentence that cannot
be proven.
As I have been saying for many years and finally
strict Proof Theoretic Semantics based on Dag Prawitz
theory of Grounds agrees G is ungrounded in PA
and is only true in meta-math. G was never ever
true directly in PA.
G is true.
I put it to you you're lying again. No reputable mathematician would
risk his reputation by saying false things. If Dag Prawitz really did "agree" (with whom?) that G||del's sentence G is not true in Peano Arithmetic, then produce a citation for this.
And on the off chance you're not lying, who on Earth would want to use a deficient system like PTS that can't even prove standard mathematical results?
[ .... ]
--
Copyright 2026 Olcott
On 6/22/2026 2:13 AM, Mikko wrote:
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>> look into proof theoretic semantics.I've spent a couple of hours reading that web page. It is >>>>>>>>>> abstract in
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, >>>>>>>>>> who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy. >>>>>>>>
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The >>>>>>>> two are different things. A contradiction is a statement which >>>>>>>> is necessarily false. A paradox is a statement to which no truth >>>>>>>> value can be consistently assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've
been attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
That only means that your DD is not a strictly confoming C program.
The exact operational semantics of C conclusively
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational semantics
do not fully specify the behaviour of DD. In order to prove that DD
halts you also need additional operational spemantics provided by the
C implementation you have used. When DD iss executed in that environment
it halts, which is sufficient to prove that in that environment DD
halts. In some other environment its execution might be aborted or it
could be rejected by the compiler.
Proof Theoretic Semantics provides the correct way
to handle pathological self-reference (PSR).
This would be dead obvious if you were not totally
clueless about Prolog.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
This has been completely rewritten just now. https://github.com/plolcott/x86utm/blob/master/README.md
On 06/22/2026 06:13 AM, olcott wrote:
On 6/22/2026 2:13 AM, Mikko wrote:
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>> look into proof theoretic semantics.I've spent a couple of hours reading that web page.-a It is >>>>>>>>>>> abstract in
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>>
the extreme.-a One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, >>>>>>>>>>> who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy. >>>>>>>>>
The Liar's Paradox has absolutely nothing to do with proof by >>>>>>>>> contradiction. The LP isn't a contradiction; it's a paradox. The >>>>>>>>> two are different things. A contradiction is a statement which >>>>>>>>> is necessarily false. A paradox is a statement to which no truth >>>>>>>>> value can be consistently assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem >>>>>>> proof, Godel's proof, and Tarski's proof, each of which you've
been attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
That only means that your DD is not a strictly confoming C program.
The exact operational semantics of C conclusively
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational semantics
do not fully specify the behaviour of DD. In order to prove that DD
halts you also need additional operational spemantics provided by the
C implementation you have used. When DD iss executed in that environment >>> it halts, which is sufficient to prove that in that environment DD
halts. In some other environment its execution might be aborted or it
could be rejected by the compiler.
Proof Theoretic Semantics provides the correct way
to handle pathological self-reference (PSR).
This would be dead obvious if you were not totally
clueless about Prolog.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
This has been completely rewritten just now.
https://github.com/plolcott/x86utm/blob/master/README.md
Just ignoring "pathological self-reference" doesn't make it
go away, and anybody can declare the "facts" about it.
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:You won't understand it, but that _is_ essentially G||del's Incompleteness Theorem. It is a statement that any sufficiently powerful system can
In comp.theory olcott <polcott333@gmail.com> wrote:He never gets to G||del. He essentially says unprovable
On 6/22/2026 2:40 AM, Mikko wrote:G is true.
Therefore we can trust that in every theory that can express theAs I have been saying for many years and finally
truths of the natural numbers there is a true sentence that cannot
be proven.
strict Proof Theoretic Semantics based on Dag Prawitz
theory of Grounds agrees G is ungrounded in PA
and is only true in meta-math. G was never ever
true directly in PA.
I put it to you you're lying again. No reputable mathematician would
risk his reputation by saying false things. If Dag Prawitz really did "agree" (with whom?) that G||del's sentence G is not true in Peano Arithmetic, then produce a citation for this.
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
Almost no PTS people even ever get to true, they all stop at semantic meaning.That's a tautology. One of those meanings which they will be dealing
Again, if PTS was like you say, why would anybody want to use it when it doesn't even prove standard results without some extension? I put it toAnd on the off chance you're not lying, who on Earth would want to use a deficient system like PTS that can't even prove standard mathematical results?The Base-Extension Semantics (B-eS) sub-field of PTS
lets you extend PA so that G is provable in PA.
They also never talk about G or PA explicitly.
----
Copyright 2026 Olcott
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 2:40 AM, Mikko wrote:
Therefore we can trust that in every theory that can express the
truths of the natural numbers there is a true sentence that cannot
be proven.
As I have been saying for many years and finally
strict Proof Theoretic Semantics based on Dag Prawitz
theory of Grounds agrees G is ungrounded in PA
and is only true in meta-math. G was never ever
true directly in PA.
G is true.
I put it to you you're lying again. No reputable mathematician would
risk his reputation by saying false things. If Dag Prawitz really did
"agree" (with whom?) that G||del's sentence G is not true in Peano
Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially G||del's Incompleteness Theorem. It is a statement that any sufficiently powerful system can
express true things it can't prove. So Dag Prawitz, had he been saying
the things you falsely attributed to him, would certainly have "got" to G||del, and would have understood full well what he was saying.
On 6/22/2026 10:22 AM, Alan Mackenzie wrote:
[ Followup-To: set ]Within the foundation of Truth Conditional Semantics (TCS)
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 2:23 AM, Mikko wrote:
It is a verified fact that G||del's completeness and incompleteness
theorems are inevitable consequences of Peano arithmetic.
Within the foundation of Truth Conditional Semantics
this is true. Within the foundation of strict Proof
Theoretic Semantics this is false.
You have not understood Mikko's statement. It is a VERIFIED FACT that
G||del's completeness and incompleteness theorems are inevitable
consequences of Peano arithmetic.
and not Within the foundation of strict Proof Theoretic (PTS)
Semantics. When G is unprovable in PA then in strict PTS
G is ungrounded in PA.
There is a sub field of PTS called Base-Extension Semantics
(B-eS) that is not strict PTS. (B-eS) extends PA to become
PA+ then G becomes grounded in PA+. This is the same thing
as saying that G is provable in meta-math thus making it
true in PA.
On 06/22/2026 08:36 AM, olcott wrote:
On 6/22/2026 10:22 AM, Alan Mackenzie wrote:
[ Followup-To: set ]Within the foundation of Truth Conditional Semantics (TCS)
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 2:23 AM, Mikko wrote:
It is a verified fact that G||del's completeness and incompleteness
theorems are inevitable consequences of Peano arithmetic.
Within the foundation of Truth Conditional Semantics
this is true. Within the foundation of strict Proof
Theoretic Semantics this is false.
You have not understood Mikko's statement.-a It is a VERIFIED FACT that
G||del's completeness and incompleteness theorems are inevitable
consequences of Peano arithmetic.
and not Within the foundation of strict Proof Theoretic (PTS)
Semantics. When G is unprovable in PA then in strict PTS
G is ungrounded in PA.
There is a sub field of PTS called Base-Extension Semantics
(B-eS) that is not strict PTS. (B-eS) extends PA to become
PA+ then G becomes grounded in PA+. This is the same thing
as saying that G is provable in meta-math thus making it
true in PA.
"Meta" math?
Is that the one where you hire a kid off the street
to promote a venue and he takes the fliers and
dumps them in the first trash-bin and walks off
with the money?
Sort of "Instant Audience" instead of "Artificial Intelligence"?
On 06/22/2026 06:13 AM, olcott wrote:
On 6/22/2026 2:13 AM, Mikko wrote:
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>> look into proof theoretic semantics.I've spent a couple of hours reading that web page. It is >>>>>>>>>>> abstract in
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>>
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, >>>>>>>>>>> who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy. >>>>>>>>>
The Liar's Paradox has absolutely nothing to do with proof by >>>>>>>>> contradiction. The LP isn't a contradiction; it's a paradox. The >>>>>>>>> two are different things. A contradiction is a statement which >>>>>>>>> is necessarily false. A paradox is a statement to which no truth >>>>>>>>> value can be consistently assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem >>>>>>> proof, Godel's proof, and Tarski's proof, each of which you've
been attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
That only means that your DD is not a strictly confoming C program.
The exact operational semantics of C conclusively
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational semantics
do not fully specify the behaviour of DD. In order to prove that DD
halts you also need additional operational spemantics provided by the
C implementation you have used. When DD iss executed in that environment >>> it halts, which is sufficient to prove that in that environment DD
halts. In some other environment its execution might be aborted or it
could be rejected by the compiler.
Proof Theoretic Semantics provides the correct way
to handle pathological self-reference (PSR).
This would be dead obvious if you were not totally
clueless about Prolog.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
This has been completely rewritten just now.
https://github.com/plolcott/x86utm/blob/master/README.md
Just ignoring "pathological self-reference" doesn't make it
go away, and anybody can declare the "facts" about it.
It seems a cloak of the empirical fallacy masquerading as
the triumph of reason, then axiomatizing itself complete
with what would be false-axioms, a futile, intransigent
effort doomed to be outmoded and simply inductive ignorance
of the not-quite-invincible sort.
As a satire it's more pathetic than profound.
Instead, what reasoners find is the great Renaissance (idealism)
and Enlightenment (rationalism) as an "extreme rationalism" account,
that DesCartes and Leibnitz, and Plato and Kant, can both be proud,
bring back together the analytical tradition and the idealistic
tradition as for a dually-self-infraconsistent paraconsistent-dialetheic ur-theory that provides both the Euclidean and Archimedean (geometry and arithmetic) and super-Euclidean and super-Archimedean
(with infinity and the original), making it so that the Pythagorean (amost-all rational) and Cantorian (almost-all transcendental) are
made whole in a paleo-classical post-modern account with the
strong mathematical platonism with the perfect circles and straight
lines and the strengthened (instead of weak) logicist positivism
in accounts of heno-theories and a mono-heno-theory, that
gives modal, temporal, relevance logic as a "the logic",
and makes possible the overall conscientious and thorough efforts
of the conscientious logician, mathematician, statistician, scientist,
and physicist, among large, competent, conscientious, co-operative
reasoners.
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:I was right, you didn't understand it.
In comp.theory olcott <polcott333@gmail.com> wrote:You did not pay close enough attention to my exact words.
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:You won't understand it, but that _is_ essentially G||del's Incompleteness Theorem. It is a statement that any sufficiently powerful system can express true things it can't prove. So Dag Prawitz, had he been saying
G is true.He never gets to G||del. He essentially says unprovable
I put it to you you're lying again. No reputable mathematician would
risk his reputation by saying false things. If Dag Prawitz really did >>> "agree" (with whom?) that G||del's sentence G is not true in Peano
Arithmetic, then produce a citation for this.
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
the things you falsely attributed to him, would certainly have "got" to G||del, and would have understood full well what he was saying.
If an expression is unprovable then this expression is untrue.That article is behind a pay wall, and the abstract which is avaiblable
Only for Dag Prawitz https://link.springer.com/article/10.1007/s11245-011-9107-6
In the most of the rest of pure proof theoretic semanticsYou don't understand the concept of true, so how could you tell?
an expression only acquires semantic meaning from its
completed proof. They never get to true.
When this is applied at the level of an individual formalSo what's the point of PTS?
system (almost never) then the expression never derives
semantic meaning in that formal system.
----
Copyright 2026 Olcott
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician would >>>>> risk his reputation by saying false things. If Dag Prawitz really did >>>>> "agree" (with whom?) that G||del's sentence G is not true in Peano
Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially G||del's Incompleteness >>> Theorem. It is a statement that any sufficiently powerful system can
express true things it can't prove. So Dag Prawitz, had he been saying
the things you falsely attributed to him, would certainly have "got" to
G||del, and would have understood full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician would >>>>> risk his reputation by saying false things. If Dag Prawitz really did >>>>> "agree" (with whom?) that G||del's sentence G is not true in Peano
Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially G||del's Incompleteness >>> Theorem. It is a statement that any sufficiently powerful system can
express true things it can't prove. So Dag Prawitz, had he been saying
the things you falsely attributed to him, would certainly have "got" to
G||del, and would have understood full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Unfortunately for you I paid very close attention to them. I can tell
when your words express the truth, and when they don't. As I keep
telling you and you keep ignoring, any logical system bar the simplest
can express truths it can't prove. That's a fundamental mathematical
truth which you can't magic away with a magician's hat and a wand, like
you keep trying to do.
If an expression is unprovable then this expression is untrue.
Only for Dag Prawitz
https://link.springer.com/article/10.1007/s11245-011-9107-6
That article is behind a pay wall, and the abstract which is avaiblable doesn't touch on any supposed equivalence of true and provable. Many
true expressions are unprovable.
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:[ .... ]
In comp.theory olcott <polcott333@gmail.com> wrote:Dag Prawitz says: Unprovable ALWAYS means untrue
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:I was right, you didn't understand it.
In comp.theory olcott <polcott333@gmail.com> wrote:You did not pay close enough attention to my exact words.
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:You won't understand it, but that _is_ essentially G||del's
G is true.He never gets to G||del. He essentially says unprovable
I put it to you you're lying again. No reputable mathematician would >>>>> risk his reputation by saying false things. If Dag Prawitz really did >>>>> "agree" (with whom?) that G||del's sentence G is not true in Peano >>>>> Arithmetic, then produce a citation for this.
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
Incompleteness Theorem. It is a statement that any sufficiently
powerful system can express true things it can't prove. So Dag
Prawitz, had he been saying the things you falsely attributed to
him, would certainly have "got" to G||del, and would have understood
full well what he was saying.
----
Copyright 2026 Olcott
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician would >>>>>>> risk his reputation by saying false things. If Dag Prawitz really did >>>>>>> "agree" (with whom?) that G||del's sentence G is not true in Peano >>>>>>> Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially G||del's
Incompleteness Theorem. It is a statement that any sufficiently
powerful system can express true things it can't prove. So Dag
Prawitz, had he been saying the things you falsely attributed to
him, would certainly have "got" to G||del, and would have understood >>>>> full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
[ .... ]
Either you're lying, or you've misunderstood something, yet again.
Possibly both. Established academics don't go around asserting
falsehoods that would disgrace a second year student.
G||del's Incompleteness Theorem is true beyond doubt, but you can't understand it.
I think this discussion has come to an end.
--
Copyright 2026 Olcott
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician would >>>>>>> risk his reputation by saying false things. If Dag Prawitz really did >>>>>>> "agree" (with whom?) that G||del's sentence G is not true in Peano >>>>>>> Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially G||del's
Incompleteness Theorem. It is a statement that any sufficiently
powerful system can express true things it can't prove. So Dag
Prawitz, had he been saying the things you falsely attributed to
him, would certainly have "got" to G||del, and would have understood >>>>> full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
[ .... ]
Either you're lying, or you've misunderstood something, yet again.
Possibly both. Established academics don't go around asserting
falsehoods that would disgrace a second year student.
G||del's Incompleteness Theorem is true beyond doubt, but you can't understand it.
I think this discussion has come to an end.
--
Copyright 2026 Olcott
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician would >>>>>> risk his reputation by saying false things. If Dag Prawitz really >>>>>> did
"agree" (with whom?) that G||del's sentence G is not true in Peano >>>>>> Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially G||del's
Incompleteness
Theorem. It is a statement that any sufficiently powerful system can
express true things it can't prove. So Dag Prawitz, had he been saying >>>> the things you falsely attributed to him, would certainly have "got" to >>>> G||del, and would have understood full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again.-a No reputable mathematician >>>>>>> would
risk his reputation by saying false things.-a If Dag Prawitz really >>>>>>> did
"agree" (with whom?) that G||del's sentence G is not true in Peano >>>>>>> Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially G||del's
Incompleteness
Theorem.-a It is a statement that any sufficiently powerful system can >>>>> express true things it can't prove.-a So Dag Prawitz, had he been
saying
the things you falsely attributed to him, would certainly have
"got" to
G||del, and would have understood full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse
principle" so I think these are key aspects of fundamental logic.
https://www.researchgate.net/publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself, originated in the work of Paul Lorenzen in the 1950s, as a method to generate new ad- missible rules within a certain syntactic context. Some N4Ufteen years
later, the idea was taken up by Dag Prawitz to devise a strategy of normalization for natural deduction calculi (this being an analogue of GentzenrCOs cut-elimination theorem for sequent calculi). Later, Prawitz
used the inversion principle again, attributing it with a semantic role. Still working in natural deduction calculi, he formulated a general type
of schematic Introduction rules to be matchedrCothanks to the idea
supporting the inversion principle rCo by a corresponding general
schematic Elimination rule. This was an attempt to provide a solution to
the problem suggested by the often quoted note of Gentzen. According to Gentzen rCLit should be possible to display the elimination rules as
unique functions of the corresponding introduction rules on the basis of certain requirements.rCY Many people have since worked on this topic,
which can be appropriately seen as the birthplace of what are now
referred to as rCLgeneral elimination rulesrCY, recently studied thoroughly by Sara Negri and Jan von Plato. In this paper, we retrace the main
threads of this chapter of proof-theoretical investigation, using LorenzenrCOs original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's laws,
and that being the usual account of naive deductive analysis, then since "natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides Kripke afterward there's also Sheffer and Chwistek before, and instead of
Montague for semantics there's Herbrand for semantics, so, what to do
about "inversion principle" is here that the thea-theory has that it's
what subsumes "non-contradiction principle", here hoping that the interpretation aligns and thusly that "principle of inversion" wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical- study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a principle of thorough reason as subsuming principles of non-contradiction and what suffices, so, I'll be curious then about what to make of Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the
oldest account of Western philosophy like Heraclitus with dual monism.
In fact by definition it's about the most basic aspect of contemplation
and deliberation in abstraction of looking at both sides of issues and resolving inductive impasses with analytical bridges after complementary duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the characteristic features of Gentzen's intuitionistic natural deduction.
In the literature on proof-theoretic semantics, this principle is often coupled with another that is called the recovery principle. By adopting
the Computational Ludics framework, we reformulate these principles into
one and the same condition, which we call the harmony condition. We show
that this reformulation allows us to reveal two intuitive ideas standing behind these principles: the idea of "containment" present in the
inversion principle, and the idea that the recovery principle is the "converse" of the inversion principle. We also formulate two other
conditions in the Computational Ludics framework, and we show that each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, proof-theoretic semantics rests on the idea that we know the meaning of
a compound sentence when we know what counts as a canonical proof of it.
And if proofs are formalised within the framework of natural deduction,
then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective of A."
The "canonical proofs" are not unique, in any system strong enough
to make for infinitary reasoning and super-classical results requiring analytical bridges about infinity and continuity.
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician
would
risk his reputation by saying false things. If Dag Prawitz really >>>>>>> did
"agree" (with whom?) that G||del's sentence G is not true in Peano >>>>>>> Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially G||del's
Incompleteness
Theorem. It is a statement that any sufficiently powerful system can >>>>> express true things it can't prove. So Dag Prawitz, had he been
saying
the things you falsely attributed to him, would certainly have
"got" to
G||del, and would have understood full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse
principle" so I think these are key aspects of fundamental logic.
https://www.researchgate.net/publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself, originated in the work of Paul Lorenzen in the 1950s, as a method to generate new ad- missible rules within a certain syntactic context. Some N4Ufteen years
later, the idea was taken up by Dag Prawitz to devise a strategy of normalization for natural deduction calculi (this being an analogue of GentzenrCOs cut-elimination theorem for sequent calculi). Later, Prawitz
used the inversion principle again, attributing it with a semantic role. Still working in natural deduction calculi, he formulated a general type
of schematic Introduction rules to be matchedrCothanks to the idea
supporting the inversion principle rCo by a corresponding general
schematic Elimination rule. This was an attempt to provide a solution to
the problem suggested by the often quoted note of Gentzen. According to Gentzen rCLit should be possible to display the elimination rules as
unique functions of the corresponding introduction rules on the basis of certain requirements.rCY Many people have since worked on this topic,
which can be appropriately seen as the birthplace of what are now
referred to as rCLgeneral elimination rulesrCY, recently studied thoroughly by Sara Negri and Jan von Plato. In this paper, we retrace the main
threads of this chapter of proof-theoretical investigation, using LorenzenrCOs original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's laws,
and that being the usual account of naive deductive analysis, then since "natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides Kripke afterward there's also Sheffer and Chwistek before, and instead of
Montague for semantics there's Herbrand for semantics, so, what to do
about "inversion principle" is here that the thea-theory has that it's
what subsumes "non-contradiction principle", here hoping that the interpretation aligns and thusly that "principle of inversion" wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical-study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a principle of thorough reason as subsuming principles of non-contradiction and what suffices, so, I'll be curious then about what to make of Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the
oldest account of Western philosophy like Heraclitus with dual monism.
In fact by definition it's about the most basic aspect of contemplation
and deliberation in abstraction of looking at both sides of issues and resolving inductive impasses with analytical bridges after complementary duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the characteristic features of Gentzen's intuitionistic natural deduction.
In the literature on proof-theoretic semantics, this principle is often coupled with another that is called the recovery principle. By adopting
the Computational Ludics framework, we reformulate these principles into
one and the same condition, which we call the harmony condition. We show
that this reformulation allows us to reveal two intuitive ideas standing behind these principles: the idea of "containment" present in the
inversion principle, and the idea that the recovery principle is the "converse" of the inversion principle. We also formulate two other
conditions in the Computational Ludics framework, and we show that each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, proof-theoretic semantics rests on the idea that we know the meaning of
a compound sentence when we know what counts as a canonical proof of it.
And if proofs are formalised within the framework of natural deduction,
then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective of A."
The "canonical proofs" are not unique, in any system strong enough
to make for infinitary reasoning and super-classical results requiring analytical bridges about infinity and continuity.
So, Prawitz has has "containment" and "recovery", so, that's more
than merely "containment" and can always be "recovered".
You're going to have to find a new technical sub-field to mis-interpret,
this one's broken open again.
On 06/22/2026 09:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician >>>>>>>> would
risk his reputation by saying false things. If Dag Prawitz really >>>>>>>> did
"agree" (with whom?) that G||del's sentence G is not true in Peano >>>>>>>> Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially G||del's
Incompleteness
Theorem. It is a statement that any sufficiently powerful system can >>>>>> express true things it can't prove. So Dag Prawitz, had he been
saying
the things you falsely attributed to him, would certainly have
"got" to
G||del, and would have understood full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse
principle" so I think these are key aspects of fundamental logic.
https://www.researchgate.net/publication/233365263_On_Inversion_Principles >>
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself, originated in >> the work of Paul Lorenzen in the 1950s, as a method to generate new ad-
missible rules within a certain syntactic context. Some N4Ufteen years
later, the idea was taken up by Dag Prawitz to devise a strategy of
normalization for natural deduction calculi (this being an analogue of
GentzenrCOs cut-elimination theorem for sequent calculi). Later, Prawitz
used the inversion principle again, attributing it with a semantic role.
Still working in natural deduction calculi, he formulated a general type
of schematic Introduction rules to be matchedrCothanks to the idea
supporting the inversion principle rCo by a corresponding general
schematic Elimination rule. This was an attempt to provide a solution to
the problem suggested by the often quoted note of Gentzen. According to
Gentzen rCLit should be possible to display the elimination rules as
unique functions of the corresponding introduction rules on the basis of
certain requirements.rCY Many people have since worked on this topic,
which can be appropriately seen as the birthplace of what are now
referred to as rCLgeneral elimination rulesrCY, recently studied thoroughly >> by Sara Negri and Jan von Plato. In this paper, we retrace the main
threads of this chapter of proof-theoretical investigation, using
LorenzenrCOs original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's laws,
and that being the usual account of naive deductive analysis, then since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides Kripke
afterward there's also Sheffer and Chwistek before, and instead of
Montague for semantics there's Herbrand for semantics, so, what to do
about "inversion principle" is here that the thea-theory has that it's
what subsumes "non-contradiction principle", here hoping that the
interpretation aligns and thusly that "principle of inversion" wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical-study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a principle of
thorough reason as subsuming principles of non-contradiction and what
suffices, so, I'll be curious then about what to make of Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the
oldest account of Western philosophy like Heraclitus with dual monism.
In fact by definition it's about the most basic aspect of contemplation
and deliberation in abstraction of looking at both sides of issues and
resolving inductive impasses with analytical bridges after complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the
characteristic features of Gentzen's intuitionistic natural deduction.
In the literature on proof-theoretic semantics, this principle is often
coupled with another that is called the recovery principle. By adopting
the Computational Ludics framework, we reformulate these principles into
one and the same condition, which we call the harmony condition. We show
that this reformulation allows us to reveal two intuitive ideas standing
behind these principles: the idea of "containment" present in the
inversion principle, and the idea that the recovery principle is the
"converse" of the inversion principle. We also formulate two other
conditions in the Computational Ludics framework, and we show that each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives,
proof-theoretic semantics rests on the idea that we know the meaning of
a compound sentence when we know what counts as a canonical proof of it.
And if proofs are formalised within the framework of natural deduction,
then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective of A."
The "canonical proofs" are not unique, in any system strong enough
to make for infinitary reasoning and super-classical results requiring
analytical bridges about infinity and continuity.
So, Prawitz has has "containment" and "recovery", so, that's more
than merely "containment" and can always be "recovered".
You're going to have to find a new technical sub-field to mis-interpret,
this one's broken open again.
"Since the model-theoretic truth-clauses are invariant
modulo logical form, this leads to truth-preservation in models."
- Piccolomini, "An introduction to PrawitzrCOs semantics"
So, "containment" and "recovery" is pretty much like Russell's
"isolation" and "significance", yet Russell waffles that one's
the other, while Prawitz points out they're distinct not unique, while something like Quine's "relevance" is also watered-down apologetics
with regards to something like Anderson's "relevance" logic.
Piccolomini mentions "three epistemic problems".
"Prawitz-Etchemendy reduction principle
The model-theoretic validity of A is tantamount to the simple truth (on
some suitable domain) of a universal closure of A[rf?xrf-], where A[rf?xrf-] is
obtained from A by replacing constant symbols with appropriate variables.
[In the case of EtchemendyrCOs reduction one may need to replace also some logical symbols]
If logical validity is modal, how can it reduce to simple truth ?"
Usually that's for an account of "the thorough", that after all disambiguation and deliberation it remains as unchallenged.
"Collapse of consequence onto material implication
Modality refers to consequence. It is inherited by logical consequence
simply because the latter is consequence by virtue of logical form. But
in model-theory this means that consequence is simply material
implication."
This isn't so: "model theory" needn't admit "material implication" at
all, that's a flailing about "about "quasi-classical quasi-modal logic",
not "model theory", which is plainly a structuralist's account.
"Let PA be the Peano-axioms for N, and let A be any very complex theorem
on N. Then, PA reo_N A."
That simply doesn't account for the extra-ordinary and there being at
least three models of integers, three laws of large numbers, and so on,
which would be "independent" the Peano Arithmetic, so what may be
uniqueness results, would instead be distinctness results, so, that
simply makes for that independence allows incompleteness to be completed variously when the theory doesn't otherwise say.
So, no, it is not so that Prawitz says anything wrong about what a
theory doesn't say.
"The inference from PA to A contains an epistemic gap, but is valid in model-theory. [Of course, once we know that PA reo_N A, the truth of PA compels us to accept A as true. But we cannot require that we know an inference is valid before using it ! This provokes the Bolzano-Carroll regress.]"
Now, Bolzano has a lot more to uncover about real analysis and
non-standard analysis, yet one may aver that since the system of PA is infinitary and inductively in-complete (not needing
anti-diagonalization, just competing induction rules), that various
"very complex theorems" may simply have used the wrong "law of large
numbers" about greater accounts of arithmetic and geometry and infinity
and continuity.
Something says "Prawitz since Gentzen is intuitionistic", then that
usually means they're "non-classical logics", here instead there's
that "inversion principles" are very much part of "classical logics",
and that "quasi-modal logics", aren't.
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician >>>>>>>> would
risk his reputation by saying false things. If Dag Prawitz really >>>>>>>> did
"agree" (with whom?) that G||del's sentence G is not true in Peano >>>>>>>> Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially G||del's
Incompleteness
Theorem. It is a statement that any sufficiently powerful system can >>>>>> express true things it can't prove. So Dag Prawitz, had he been
saying
the things you falsely attributed to him, would certainly have
"got" to
G||del, and would have understood full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse
principle" so I think these are key aspects of fundamental logic.
https://www.researchgate.net/publication/233365263_On_Inversion_Principles >>
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself, originated in >> the work of Paul Lorenzen in the 1950s, as a method to generate new ad-
missible rules within a certain syntactic context. Some N4Ufteen years
later, the idea was taken up by Dag Prawitz to devise a strategy of
normalization for natural deduction calculi (this being an analogue of
GentzenrCOs cut-elimination theorem for sequent calculi). Later, Prawitz
used the inversion principle again, attributing it with a semantic role.
Still working in natural deduction calculi, he formulated a general type
of schematic Introduction rules to be matchedrCothanks to the idea
supporting the inversion principle rCo by a corresponding general
schematic Elimination rule. This was an attempt to provide a solution to
the problem suggested by the often quoted note of Gentzen. According to
Gentzen rCLit should be possible to display the elimination rules as
unique functions of the corresponding introduction rules on the basis of
certain requirements.rCY Many people have since worked on this topic,
which can be appropriately seen as the birthplace of what are now
referred to as rCLgeneral elimination rulesrCY, recently studied thoroughly >> by Sara Negri and Jan von Plato. In this paper, we retrace the main
threads of this chapter of proof-theoretical investigation, using
LorenzenrCOs original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's laws,
and that being the usual account of naive deductive analysis, then since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides Kripke
afterward there's also Sheffer and Chwistek before, and instead of
Montague for semantics there's Herbrand for semantics, so, what to do
about "inversion principle" is here that the thea-theory has that it's
what subsumes "non-contradiction principle", here hoping that the
interpretation aligns and thusly that "principle of inversion" wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a principle of
thorough reason as subsuming principles of non-contradiction and what
suffices, so, I'll be curious then about what to make of Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the
oldest account of Western philosophy like Heraclitus with dual monism.
In fact by definition it's about the most basic aspect of contemplation
and deliberation in abstraction of looking at both sides of issues and
resolving inductive impasses with analytical bridges after complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the
characteristic features of Gentzen's intuitionistic natural deduction.
In the literature on proof-theoretic semantics, this principle is often
coupled with another that is called the recovery principle. By adopting
the Computational Ludics framework, we reformulate these principles into
one and the same condition, which we call the harmony condition. We show
that this reformulation allows us to reveal two intuitive ideas standing
behind these principles: the idea of "containment" present in the
inversion principle, and the idea that the recovery principle is the
"converse" of the inversion principle. We also formulate two other
conditions in the Computational Ludics framework, and we show that each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives,
proof-theoretic semantics rests on the idea that we know the meaning of
a compound sentence when we know what counts as a canonical proof of it.
And if proofs are formalised within the framework of natural deduction,
then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective of A."
The "canonical proofs" are not unique, in any system strong enough
to make for infinitary reasoning and super-classical results requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
On 6/22/2026 2:13 AM, Mikko wrote:
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>> look into proof theoretic semantics.I've spent a couple of hours reading that web page.-a It is >>>>>>>>>> abstract in
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>
the extreme.-a One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, >>>>>>>>>> who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy. >>>>>>>>
The Liar's Paradox has absolutely nothing to do with proof by >>>>>>>> contradiction. The LP isn't a contradiction; it's a paradox. The >>>>>>>> two are different things. A contradiction is a statement which >>>>>>>> is necessarily false. A paradox is a statement to which no truth >>>>>>>> value can be consistently assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've
been attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
That only means that your DD is not a strictly confoming C program.
The exact operational semantics of C conclusively
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational semantics
do not fully specify the behaviour of DD. In order to prove that DD
halts you also need additional operational spemantics provided by the
C implementation you have used. When DD iss executed in that environment
it halts, which is sufficient to prove that in that environment DD
halts. In some other environment its execution might be aborted or it
could be rejected by the compiler.
Proof Theoretic Semantics provides the correct way
to handle pathological self-reference (PSR).
This would be dead obvious if you were not totally
clueless about Prolog.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
This has been completely rewritten just now. https://github.com/plolcott/x86utm/blob/master/README.md
On 6/22/2026 1:27 AM, Mikko wrote:
On 22/06/2026 02:55, olcott wrote:
On 6/21/2026 5:11 AM, Mikko wrote:
On 20/06/2026 16:50, olcott wrote:
On 6/20/2026 5:26 AM, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semanticsSome people only memorize conventional views and
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page.-a It is
abstract in
the extreme.-a One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>>> can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be >>>>>>>> bothered
to read it any further.-a If it actually says anything at all, that >>>>>>>> something is heavily disguised.-a From it's "Conclusion and Outlook" >>>>>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively >>>>>>>> been
| occupied with logical constants. Logical constants play a
central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can be >>>>>>>> defined
| inferentially. A framework is needed that deals with inferential >>>>>>>> | definitions in a wider sense and covers both logical and
extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the >>>>>>> near future not useful as making it useful requires much time and >>>>>>> effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If a claim is true on the basis on meaning expressed in language we
usually can easily determine its truth vaule wihout computational
tools. The truth values we want to know but are hard to determine
are of claims that are true on some other basis.
The system I propose would cut off the dangerous lies
of dangerous liars mid-sentence and be able to prove
that these are lies to every level of understanding
between kindergarten and PhD.
You have not yet demonstrated any aboility to cut off a single
lie that would matter to typical people.
Nothing is going to work until we get everyone to
understand the difference between truth and lies
On 6/22/2026 2:46 AM, Mikko wrote:
On 22/06/2026 03:44, olcott wrote:
On 6/21/2026 7:32 PM, phoenix wrote:
olcott wrote:
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat?
olcott wrote:
On 6/21/2026 3:18 PM, Andr|- G. Isaak wrote:Lastly, and why should we care? Please answer this and other
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>> look into proof theoretic semantics.I've spent a couple of hours reading that web page.-a It is >>>>>>>>>>> abstract in
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>
the extreme.-a One thing is utterly clear: its level of >>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter Olcott, >>>>>>>>>>> who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't >>>>>>>>>>> be bothered
to read it any further.-a If it actually says anything at all, >>>>>>>>>>> that
something is heavily disguised.-a From it's "Conclusion and >>>>>>>>>>> Outlook"
section at the end:
| Standard proof-theoretic semantics has practically
exclusively been
| occupied with logical constants. Logical constants play a >>>>>>>>>>> central role
| in reasoning and inference, but are definitely not the >>>>>>>>>>> exclusive, and
| perhaps not even the most typical sort of entities that can >>>>>>>>>>> be defined
| inferentially. A framework is needed that deals with
inferential
| definitions in a wider sense and covers both logical and >>>>>>>>>>> extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and >>>>>>>>>> in the
near future not useful as making it useful requires much time and >>>>>>>>>> effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful >>>>>>>>> for? What it
ought to be able to do that standard logic fails at?-a Maybe >>>>>>>>> Andr|- could
elucidate.-a He seems to have a better grasp of it than anybody >>>>>>>>> else here.
I doubt my understanding of PTS is any better than yours. I
basically only know what is presented in the Stanford
Encyclopedia article (which you correctly point out is not
exactly aimed at beginners) and the Wikipedia article. What I am >>>>>>>> quite certain of, however, is that Olcott lacks any
understanding of what PTS actually says as he's made a variety >>>>>>>> of fairly absurd claims regarding it (for example, that PTS
claims that unproven propositions are 'meaningless' or that the >>>>>>>> goal of PTS is to completely overthrow standard truth-theoretic >>>>>>>> semantics).
Andr|-
-a-a Proof-theoretic semantics is an alternative to
-a-a truth-condition semantics. It is based on the
-a-a fundamental assumption that the central notion
-a-a in terms of which meanings are assigned to certain
-a-a expressions of our language, in particular to
-a-a logical constants, is that of proof rather than
-a-a truth. In this sense proof-theoretic semantics
-a-a is semantics in terms of proof.
-a-a https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
questions presented.
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
It is not that they never admit defeat.
It is that that have a system of essentially infallible reasoning
that never errs as long as it has all the relevant information.
It is fairly simple to build a system of essentially infallible
reasoning that never errs even when it doesn't have all the
relevant information. The real problem is to construct a system
that tells something interesting instead of just different
presentations of the same already known facts.
It will have the exhaustively complete list of
every atomic fact of general knowledge of the
actual world.
On 6/22/2026 1:41 AM, Mikko wrote:
On 22/06/2026 02:58, olcott wrote:
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlaysonSome people only memorize conventional views and
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
At different times you have expressed different opinions, which
sometimes have been incompatible. But you have never clearly
retracted your earlier opitions that conflict with your present
ones.
All of the ideas that I have ever had about these things
are now under the Proof Theoretic Semantics category.
These ideas have evolved over time, yet their essence
has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a publishable >>>> (or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> human being on
the face of the Earth could understand
me I could not publish.
As far as I have seen, all interesting content in those articles
that have any is or depends on claims that should be proven but
aren't.
They are proven in Proof Theoretic Semantics
Now that I am acquiring the lingua franca of PTS I
will finally be able to publish.
If all you can publish is in the topic area of PtS then they may
count as uninteresting to those whose primary problems are not in
that topic area.
My extensions to PTS eliminate the LLM reliability issues.
This makes the Trillion dollar industry at least 100-fold
more valuable.
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms.-a That doesn't mean you're
capable of
understanding them.
The above is the key reason why under PTS G||del 1931 incompleteness >>>>>>> fails.
I don't believe you.-a You have no respect for or understanding of the >>>>>> truth.-a If you really want to persuade anybody that PTS somehow
causes
G||del's theorem not to hold, then cite an academic expert who'll have >>>>>> some credibility.
If they are mere gibberish words to you then you will not
understand.
You don't understand Proof-theoritic Semantics, and you certainly >>>>>> don't
understand G||del's Theorem, neither the theorem itself nor any
proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by
you, and it is one which you have never explicitly defined, so the
fault here certainly doesn't lie with Alan. It's certainly not a
'verified fact' when you haven't even adequately explained what it
is that you mean.
All of knowledge expressed in language is structured as a tree of
semantic relations specified syntactically between finite strings.
What makes you believe semantic relations that can be structured as
a tree are sufficient to contain all knowledge that is exressed in
some language?
The CycL language and the Cyc Project.
On 6/22/2026 2:23 AM, Mikko wrote:
On 21/06/2026 23:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms.-a That doesn't mean you're
capable of
understanding them.
The above is the key reason why under PTS G||del 1931 incompleteness >>>>> fails.
I don't believe you.-a You have no respect for or understanding of the >>>> truth.-a If you really want to persuade anybody that PTS somehow causes >>>> G||del's theorem not to hold, then cite an academic expert who'll have >>>> some credibility.
If they are mere gibberish words to you then you will not understand. >>>>You don't understand Proof-theoritic Semantics, and you certainly don't >>>> understand G||del's Theorem, neither the theorem itself nor any proof of >>>> it.
in the atomic base of PA.
It is a verified fact that G||del's completeness and incompleteness
theorems are inevitable consequences of Peano arithmetic.
Within the foundation of Truth Conditional Semantics
this is true. Within the foundation of strict Proof
Theoretic Semantics this is false.
On 6/22/2026 2:40 AM, Mikko wrote:
On 22/06/2026 03:00, olcott wrote:
On 6/21/2026 5:23 AM, Mikko wrote:
On 20/06/2026 17:18, olcott wrote:
On 6/20/2026 12:25 AM, Ross Finlayson wrote:
On 06/18/2026 12:35 PM, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
This seems to be the rigidly conformist and memorize
by rote mindset.
Hm. Here there is a rather "rigidly conformist" approach,
and "an extreme rationalism", though, it's not the usual.
a principle of inverse
supplants, subsumes, and includes
a principle of non-contradiction/excluded-middle
Modern Logic has always simply ignored that an
expression may be semantically incoherent because
logic has always ignored semantics and focused
on syntax.
Modern logic has
always put semantics outside of the formal system
in a separate model.
And that way avoided semantic incoherence in formal systems.
It didn't really avoid it.
The semantic incoherence was merely hidden.
In every model of PA either G or its negation is true. It does notPTS does not do that.
G||del proved that every consistent first order theory has a model.
That means that a consisten first order theory cannot be semantically
incoherent.
Like I just said.
Therefore we can trust that in every theory that can express the
truths of the natural numbers there is a true sentence that cannot
be proven.
As I have been saying for many years and finally
strict Proof Theoretic Semantics based on Dag Prawitz
theory of Grounds agrees G is ungrounded in PA
and is only true in meta-math. G was never ever true directly in PA.
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 2:40 AM, Mikko wrote:
Therefore we can trust that in every theory that can express the
truths of the natural numbers there is a true sentence that cannot
be proven.
As I have been saying for many years and finally
strict Proof Theoretic Semantics based on Dag Prawitz
theory of Grounds agrees G is ungrounded in PA
and is only true in meta-math. G was never ever
true directly in PA.
G is true.
I put it to you you're lying again. No reputable mathematician would
risk his reputation by saying false things. If Dag Prawitz really did
"agree" (with whom?) that G||del's sentence G is not true in Peano
Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially G||del's Incompleteness Theorem. It is a statement that any sufficiently powerful system can
express true things it can't prove. So Dag Prawitz, had he been saying
the things you falsely attributed to him, would certainly have "got" to G||del, and would have understood full well what he was saying.
I put it to you you have not understood that academic's work.
Almost no PTS people even ever get to true, they all stop at semantic
meaning.
That's a tautology. One of those meanings which they will be dealing
with is true. What's the point of a logical system that can't even characterise assertions as being true or false?
And on the off chance you're not lying, who on Earth would want to use a >>> deficient system like PTS that can't even prove standard mathematical
results?
The Base-Extension Semantics (B-eS) sub-field of PTS
lets you extend PA so that G is provable in PA.
They also never talk about G or PA explicitly.
Again, if PTS was like you say, why would anybody want to use it when it doesn't even prove standard results without some extension? I put it to
you further, that PTS is quite capable of proving G||del's theorems,
without any special purpose extensions. Otherwise, what would be the
point?
--
Copyright 2026 Olcott
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again.-a No reputable mathematician >>>>>>>>> would
risk his reputation by saying false things.-a If Dag Prawitz really >>>>>>>>> did
"agree" (with whom?) that G||del's sentence G is not true in Peano >>>>>>>>> Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially G||del's
Incompleteness
Theorem.-a It is a statement that any sufficiently powerful system >>>>>>> can
express true things it can't prove.-a So Dag Prawitz, had he been >>>>>>> saying
the things you falsely attributed to him, would certainly have
"got" to
G||del, and would have understood full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse
principle" so I think these are key aspects of fundamental logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself, originated in
the work of Paul Lorenzen in the 1950s, as a method to generate new ad-
missible rules within a certain syntactic context. Some N4Ufteen years
later, the idea was taken up by Dag Prawitz to devise a strategy of
normalization for natural deduction calculi (this being an analogue of
GentzenrCOs cut-elimination theorem for sequent calculi). Later, Prawitz >>> used the inversion principle again, attributing it with a semantic role. >>> Still working in natural deduction calculi, he formulated a general type >>> of schematic Introduction rules to be matchedrCothanks to the idea
supporting the inversion principle rCo by a corresponding general
schematic Elimination rule. This was an attempt to provide a solution to >>> the problem suggested by the often quoted note of Gentzen. According to
Gentzen rCLit should be possible to display the elimination rules as
unique functions of the corresponding introduction rules on the basis of >>> certain requirements.rCY Many people have since worked on this topic,
which can be appropriately seen as the birthplace of what are now
referred to as rCLgeneral elimination rulesrCY, recently studied thoroughly >>> by Sara Negri and Jan von Plato. In this paper, we retrace the main
threads of this chapter of proof-theoretical investigation, using
LorenzenrCOs original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's laws,
and that being the usual account of naive deductive analysis, then since >>> "natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides Kripke
afterward there's also Sheffer and Chwistek before, and instead of
Montague for semantics there's Herbrand for semantics, so, what to do
about "inversion principle" is here that the thea-theory has that it's
what subsumes "non-contradiction principle", here hoping that the
interpretation aligns and thusly that "principle of inversion" wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a principle of
thorough reason as subsuming principles of non-contradiction and what
suffices, so, I'll be curious then about what to make of Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the
oldest account of Western philosophy like Heraclitus with dual monism.
In fact by definition it's about the most basic aspect of contemplation
and deliberation in abstraction of looking at both sides of issues and
resolving inductive impasses with analytical bridges after complementary >>> duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the
characteristic features of Gentzen's intuitionistic natural deduction.
In the literature on proof-theoretic semantics, this principle is often
coupled with another that is called the recovery principle. By adopting
the Computational Ludics framework, we reformulate these principles into >>> one and the same condition, which we call the harmony condition. We show >>> that this reformulation allows us to reveal two intuitive ideas standing >>> behind these principles: the idea of "containment" present in the
inversion principle, and the idea that the recovery principle is the
"converse" of the inversion principle. We also formulate two other
conditions in the Computational Ludics framework, and we show that each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives,
proof-theoretic semantics rests on the idea that we know the meaning of
a compound sentence when we know what counts as a canonical proof of it. >>> And if proofs are formalised within the framework of natural deduction,
then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective of
A."
The "canonical proofs" are not unique, in any system strong enough
to make for infinitary reasoning and super-classical results requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts that
make contradictions and thusly destroy each other.
This is where "the thorough" and "analytical bridges" make repairs
of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong).
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms.-a That doesn't mean you're >>>>>>>>> capable of
understanding them.
The above is the key reason why under PTS G||del 1931 incompleteness >>>>>>>> fails.
I don't believe you.-a You have no respect for or understanding of >>>>>>> the
truth.-a If you really want to persuade anybody that PTS somehow >>>>>>> causes
G||del's theorem not to hold, then cite an academic expert who'll >>>>>>> have
some credibility.
If they are mere gibberish words to you then you will not
understand.
You don't understand Proof-theoritic Semantics, and you certainly >>>>>>> don't
understand G||del's Theorem, neither the theorem itself nor any >>>>>>> proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by
you, and it is one which you have never explicitly defined, so the
fault here certainly doesn't lie with Alan. It's certainly not a
'verified fact' when you haven't even adequately explained what it
is that you mean.
All of knowledge expressed in language is structured as a tree of
semantic relations specified syntactically between finite strings.
What makes you believe semantic relations that can be structured as
a tree are sufficient to contain all knowledge that is exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to
put knowledge in a tree structure?
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician >>>>>>>>>> would
risk his reputation by saying false things. If Dag Prawitz >>>>>>>>>> really
did
"agree" (with whom?) that G||del's sentence G is not true in Peano >>>>>>>>>> Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially G||del's
Incompleteness
Theorem. It is a statement that any sufficiently powerful
system can
express true things it can't prove. So Dag Prawitz, had he been >>>>>>>> saying
the things you falsely attributed to him, would certainly have >>>>>>>> "got" to
G||del, and would have understood full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't say", >>>> then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse
principle" so I think these are key aspects of fundamental logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself,
originated in
the work of Paul Lorenzen in the 1950s, as a method to generate new ad- >>>> missible rules within a certain syntactic context. Some N4Ufteen years >>>> later, the idea was taken up by Dag Prawitz to devise a strategy of
normalization for natural deduction calculi (this being an analogue of >>>> GentzenrCOs cut-elimination theorem for sequent calculi). Later, Prawitz >>>> used the inversion principle again, attributing it with a semantic
role.
Still working in natural deduction calculi, he formulated a general
type
of schematic Introduction rules to be matchedrCothanks to the idea
supporting the inversion principle rCo by a corresponding general
schematic Elimination rule. This was an attempt to provide a
solution to
the problem suggested by the often quoted note of Gentzen. According to >>>> Gentzen rCLit should be possible to display the elimination rules as
unique functions of the corresponding introduction rules on the
basis of
certain requirements.rCY Many people have since worked on this topic,
which can be appropriately seen as the birthplace of what are now
referred to as rCLgeneral elimination rulesrCY, recently studied thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the main
threads of this chapter of proof-theoretical investigation, using
LorenzenrCOs original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's laws, >>>> and that being the usual account of naive deductive analysis, then
since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides Kripke >>>> afterward there's also Sheffer and Chwistek before, and instead of
Montague for semantics there's Herbrand for semantics, so, what to do
about "inversion principle" is here that the thea-theory has that it's >>>> what subsumes "non-contradiction principle", here hoping that the
interpretation aligns and thusly that "principle of inversion" wouldn't >>>> need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of most >>>> modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a principle of >>>> thorough reason as subsuming principles of non-contradiction and what
suffices, so, I'll be curious then about what to make of Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the
oldest account of Western philosophy like Heraclitus with dual monism. >>>> In fact by definition it's about the most basic aspect of contemplation >>>> and deliberation in abstraction of looking at both sides of issues and >>>> resolving inductive impasses with analytical bridges after
complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the
characteristic features of Gentzen's intuitionistic natural deduction. >>>> In the literature on proof-theoretic semantics, this principle is often >>>> coupled with another that is called the recovery principle. By adopting >>>> the Computational Ludics framework, we reformulate these principles
into
one and the same condition, which we call the harmony condition. We
show
that this reformulation allows us to reveal two intuitive ideas
standing
behind these principles: the idea of "containment" present in the
inversion principle, and the idea that the recovery principle is the
"converse" of the inversion principle. We also formulate two other
conditions in the Computational Ludics framework, and we show that each >>>> of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives,
proof-theoretic semantics rests on the idea that we know the meaning of >>>> a compound sentence when we know what counts as a canonical proof of
it.
And if proofs are formalised within the framework of natural deduction, >>>> then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective
of A."
The "canonical proofs" are not unique, in any system strong enough
to make for infinitary reasoning and super-classical results requiring >>>> analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs
of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong).
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're >>>>>>>>>> capable of
understanding them.
The above is the key reason why under PTS G||del 1931
incompleteness
fails.
I don't believe you. You have no respect for or understanding >>>>>>>> of the
truth. If you really want to persuade anybody that PTS somehow >>>>>>>> causes
G||del's theorem not to hold, then cite an academic expert who'll >>>>>>>> have
some credibility.
If they are mere gibberish words to you then you will not
understand.
You don't understand Proof-theoritic Semantics, and you
certainly don't
understand G||del's Theorem, neither the theorem itself nor any >>>>>>>> proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by
you, and it is one which you have never explicitly defined, so the >>>>>> fault here certainly doesn't lie with Alan. It's certainly not a
'verified fact' when you haven't even adequately explained what it >>>>>> is that you mean.
All of knowledge expressed in language is structured as a tree of
semantic relations specified syntactically between finite strings.
What makes you believe semantic relations that can be structured as
a tree are sufficient to contain all knowledge that is exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again.-a No reputable mathematician >>>>>>>>>>> would
risk his reputation by saying false things.-a If Dag Prawitz >>>>>>>>>>> really
did
"agree" (with whom?) that G||del's sentence G is not true in >>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially G||del's
Incompleteness
Theorem.-a It is a statement that any sufficiently powerful
system can
express true things it can't prove.-a So Dag Prawitz, had he been >>>>>>>>> saying
the things you falsely attributed to him, would certainly have >>>>>>>>> "got" to
G||del, and would have understood full well what he was saying. >>>>>>>
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says", >>>>> and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't
say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse
principle" so I think these are key aspects of fundamental logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself,
originated in
the work of Paul Lorenzen in the 1950s, as a method to generate new >>>>> ad-
missible rules within a certain syntactic context. Some N4Ufteen years >>>>> later, the idea was taken up by Dag Prawitz to devise a strategy of
normalization for natural deduction calculi (this being an analogue of >>>>> GentzenrCOs cut-elimination theorem for sequent calculi). Later, Prawitz >>>>> used the inversion principle again, attributing it with a semantic
role.
Still working in natural deduction calculi, he formulated a general
type
of schematic Introduction rules to be matchedrCothanks to the idea
supporting the inversion principle rCo by a corresponding general
schematic Elimination rule. This was an attempt to provide a
solution to
the problem suggested by the often quoted note of Gentzen.
According to
Gentzen rCLit should be possible to display the elimination rules as >>>>> unique functions of the corresponding introduction rules on the
basis of
certain requirements.rCY Many people have since worked on this topic, >>>>> which can be appropriately seen as the birthplace of what are now
referred to as rCLgeneral elimination rulesrCY, recently studied
thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the main
threads of this chapter of proof-theoretical investigation, using
LorenzenrCOs original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's laws, >>>>> and that being the usual account of naive deductive analysis, then
since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides Kripke >>>>> afterward there's also Sheffer and Chwistek before, and instead of
Montague for semantics there's Herbrand for semantics, so, what to do >>>>> about "inversion principle" is here that the thea-theory has that it's >>>>> what subsumes "non-contradiction principle", here hoping that the
interpretation aligns and thusly that "principle of inversion"
wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of most >>>>> modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a principle of >>>>> thorough reason as subsuming principles of non-contradiction and what >>>>> suffices, so, I'll be curious then about what to make of Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the
oldest account of Western philosophy like Heraclitus with dual monism. >>>>> In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of issues and >>>>> resolving inductive impasses with analytical bridges after
complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the
characteristic features of Gentzen's intuitionistic natural deduction. >>>>> In the literature on proof-theoretic semantics, this principle is
often
coupled with another that is called the recovery principle. By
adopting
the Computational Ludics framework, we reformulate these principles
into
one and the same condition, which we call the harmony condition. We
show
that this reformulation allows us to reveal two intuitive ideas
standing
behind these principles: the idea of "containment" present in the
inversion principle, and the idea that the recovery principle is the >>>>> "converse" of the inversion principle. We also formulate two other
conditions in the Computational Ludics framework, and we show that
each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives,
proof-theoretic semantics rests on the idea that we know the
meaning of
a compound sentence when we know what counts as a canonical proof of >>>>> it.
And if proofs are formalised within the framework of natural
deduction,
then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective
of A."
The "canonical proofs" are not unique, in any system strong enough
to make for infinitary reasoning and super-classical results requiring >>>>> analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs
of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong).
Induction and counter-induction contradict each other, it's simple,
it's the grounds for most things called "paradox".
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician >>>>>>>>>>>> would
risk his reputation by saying false things. If Dag Prawitz >>>>>>>>>>>> really
did
"agree" (with whom?) that G||del's sentence G is not true in >>>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially G||del's >>>>>>>>>> Incompleteness
Theorem. It is a statement that any sufficiently powerful >>>>>>>>>> system can
express true things it can't prove. So Dag Prawitz, had he been >>>>>>>>>> saying
the things you falsely attributed to him, would certainly have >>>>>>>>>> "got" to
G||del, and would have understood full well what he was saying. >>>>>>>>
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says", >>>>>> and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't
say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse
principle" so I think these are key aspects of fundamental logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself,
originated in
the work of Paul Lorenzen in the 1950s, as a method to generate
new ad-
missible rules within a certain syntactic context. Some N4Ufteen years >>>>>> later, the idea was taken up by Dag Prawitz to devise a strategy of >>>>>> normalization for natural deduction calculi (this being an
analogue of
GentzenrCOs cut-elimination theorem for sequent calculi). Later,
Prawitz
used the inversion principle again, attributing it with a semantic >>>>>> role.
Still working in natural deduction calculi, he formulated a general >>>>>> type
of schematic Introduction rules to be matchedrCothanks to the idea >>>>>> supporting the inversion principle rCo by a corresponding general
schematic Elimination rule. This was an attempt to provide a
solution to
the problem suggested by the often quoted note of Gentzen.
According to
Gentzen rCLit should be possible to display the elimination rules as >>>>>> unique functions of the corresponding introduction rules on the
basis of
certain requirements.rCY Many people have since worked on this topic, >>>>>> which can be appropriately seen as the birthplace of what are now
referred to as rCLgeneral elimination rulesrCY, recently studied
thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the main >>>>>> threads of this chapter of proof-theoretical investigation, using
LorenzenrCOs original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's
laws,
and that being the usual account of naive deductive analysis, then >>>>>> since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides
Kripke
afterward there's also Sheffer and Chwistek before, and instead of >>>>>> Montague for semantics there's Herbrand for semantics, so, what to do >>>>>> about "inversion principle" is here that the thea-theory has that
it's
what subsumes "non-contradiction principle", here hoping that the
interpretation aligns and thusly that "principle of inversion"
wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical- >>>>>> study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of
most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a
principle of
thorough reason as subsuming principles of non-contradiction and what >>>>>> suffices, so, I'll be curious then about what to make of Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the >>>>>> oldest account of Western philosophy like Heraclitus with dual
monism.
In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of issues >>>>>> and
resolving inductive impasses with analytical bridges after
complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the >>>>>> characteristic features of Gentzen's intuitionistic natural
deduction.
In the literature on proof-theoretic semantics, this principle is
often
coupled with another that is called the recovery principle. By
adopting
the Computational Ludics framework, we reformulate these principles >>>>>> into
one and the same condition, which we call the harmony condition. We >>>>>> show
that this reformulation allows us to reveal two intuitive ideas
standing
behind these principles: the idea of "containment" present in the
inversion principle, and the idea that the recovery principle is the >>>>>> "converse" of the inversion principle. We also formulate two other >>>>>> conditions in the Computational Ludics framework, and we show that >>>>>> each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives,
proof-theoretic semantics rests on the idea that we know the
meaning of
a compound sentence when we know what counts as a canonical proof of >>>>>> it.
And if proofs are formalised within the framework of natural
deduction,
then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective >>>>>> of A."
The "canonical proofs" are not unique, in any system strong enough >>>>>> to make for infinitary reasoning and super-classical results
requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts that >>>> make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs
of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong).
Induction and counter-induction contradict each other, it's simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable
mathematician
would
risk his reputation by saying false things. If Dag Prawitz >>>>>>>>>>>>> really
did
"agree" (with whom?) that G||del's sentence G is not true in >>>>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable >>>>>>>>>>>> means untrue all the time for everything within hisYou won't understand it, but that _is_ essentially G||del's >>>>>>>>>>> Incompleteness
own Theory of Grounds of strict Proof Theoretic Semantics. >>>>>>>>>
Theorem. It is a statement that any sufficiently powerful >>>>>>>>>>> system can
express true things it can't prove. So Dag Prawitz, had he been >>>>>>>>>>> saying
the things you falsely attributed to him, would certainly have >>>>>>>>>>> "got" to
G||del, and would have understood full well what he was saying. >>>>>>>>>
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says", >>>>>>> and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't >>>>>>> say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse >>>>>>> principle" so I think these are key aspects of fundamental logic. >>>>>>>
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself,
originated in
the work of Paul Lorenzen in the 1950s, as a method to generate
new ad-
missible rules within a certain syntactic context. Some N4Ufteen years >>>>>>> later, the idea was taken up by Dag Prawitz to devise a strategy of >>>>>>> normalization for natural deduction calculi (this being an
analogue of
GentzenrCOs cut-elimination theorem for sequent calculi). Later, >>>>>>> Prawitz
used the inversion principle again, attributing it with a semantic >>>>>>> role.
Still working in natural deduction calculi, he formulated a general >>>>>>> type
of schematic Introduction rules to be matchedrCothanks to the idea >>>>>>> supporting the inversion principle rCo by a corresponding general >>>>>>> schematic Elimination rule. This was an attempt to provide a
solution to
the problem suggested by the often quoted note of Gentzen.
According to
Gentzen rCLit should be possible to display the elimination rules as >>>>>>> unique functions of the corresponding introduction rules on the
basis of
certain requirements.rCY Many people have since worked on this topic, >>>>>>> which can be appropriately seen as the birthplace of what are now >>>>>>> referred to as rCLgeneral elimination rulesrCY, recently studied >>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the main >>>>>>> threads of this chapter of proof-theoretical investigation, using >>>>>>> LorenzenrCOs original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's >>>>>>> laws,
and that being the usual account of naive deductive analysis, then >>>>>>> since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides
Kripke
afterward there's also Sheffer and Chwistek before, and instead of >>>>>>> Montague for semantics there's Herbrand for semantics, so, what
to do
about "inversion principle" is here that the thea-theory has that >>>>>>> it's
what subsumes "non-contradiction principle", here hoping that the >>>>>>> interpretation aligns and thusly that "principle of inversion"
wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical- >>>>>>> study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of >>>>>>> most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a
principle of
thorough reason as subsuming principles of non-contradiction and >>>>>>> what
suffices, so, I'll be curious then about what to make of Prawitz' >>>>>>> "inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the >>>>>>> oldest account of Western philosophy like Heraclitus with dual
monism.
In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of issues >>>>>>> and
resolving inductive impasses with analytical bridges after
complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the >>>>>>> characteristic features of Gentzen's intuitionistic natural
deduction.
In the literature on proof-theoretic semantics, this principle is >>>>>>> often
coupled with another that is called the recovery principle. By
adopting
the Computational Ludics framework, we reformulate these principles >>>>>>> into
one and the same condition, which we call the harmony condition. We >>>>>>> show
that this reformulation allows us to reveal two intuitive ideas
standing
behind these principles: the idea of "containment" present in the >>>>>>> inversion principle, and the idea that the recovery principle is the >>>>>>> "converse" of the inversion principle. We also formulate two other >>>>>>> conditions in the Computational Ludics framework, and we show that >>>>>>> each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge. >>>>>>>
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives,
proof-theoretic semantics rests on the idea that we know the
meaning of
a compound sentence when we know what counts as a canonical proof of >>>>>>> it.
And if proofs are formalised within the framework of natural
deduction,
then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective >>>>>>> of A."
The "canonical proofs" are not unique, in any system strong enough >>>>>>> to make for infinitary reasoning and super-classical results
requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts that >>>>> make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical proofs". >>>> Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs
of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong).
Induction and counter-induction contradict each other, it's simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again.-a No reputable
mathematician
would
risk his reputation by saying false things.-a If Dag Prawitz >>>>>>>>>>>>> really
did
"agree" (with whom?) that G||del's sentence G is not true in >>>>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable >>>>>>>>>>>> means untrue all the time for everything within hisYou won't understand it, but that _is_ essentially G||del's >>>>>>>>>>> Incompleteness
own Theory of Grounds of strict Proof Theoretic Semantics. >>>>>>>>>
Theorem.-a It is a statement that any sufficiently powerful >>>>>>>>>>> system can
express true things it can't prove.-a So Dag Prawitz, had he been >>>>>>>>>>> saying
the things you falsely attributed to him, would certainly have >>>>>>>>>>> "got" to
G||del, and would have understood full well what he was saying. >>>>>>>>>
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says", >>>>>>> and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't >>>>>>> say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse >>>>>>> principle" so I think these are key aspects of fundamental logic. >>>>>>>
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself,
originated in
the work of Paul Lorenzen in the 1950s, as a method to generate
new ad-
missible rules within a certain syntactic context. Some N4Ufteen years >>>>>>> later, the idea was taken up by Dag Prawitz to devise a strategy of >>>>>>> normalization for natural deduction calculi (this being an
analogue of
GentzenrCOs cut-elimination theorem for sequent calculi). Later, >>>>>>> Prawitz
used the inversion principle again, attributing it with a semantic >>>>>>> role.
Still working in natural deduction calculi, he formulated a general >>>>>>> type
of schematic Introduction rules to be matchedrCothanks to the idea >>>>>>> supporting the inversion principle rCo by a corresponding general >>>>>>> schematic Elimination rule. This was an attempt to provide a
solution to
the problem suggested by the often quoted note of Gentzen.
According to
Gentzen rCLit should be possible to display the elimination rules as >>>>>>> unique functions of the corresponding introduction rules on the
basis of
certain requirements.rCY Many people have since worked on this topic, >>>>>>> which can be appropriately seen as the birthplace of what are now >>>>>>> referred to as rCLgeneral elimination rulesrCY, recently studied >>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the main >>>>>>> threads of this chapter of proof-theoretical investigation, using >>>>>>> LorenzenrCOs original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's >>>>>>> laws,
and that being the usual account of naive deductive analysis, then >>>>>>> since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides
Kripke
afterward there's also Sheffer and Chwistek before, and instead of >>>>>>> Montague for semantics there's Herbrand for semantics, so, what >>>>>>> to do
about "inversion principle" is here that the thea-theory has that >>>>>>> it's
what subsumes "non-contradiction principle", here hoping that the >>>>>>> interpretation aligns and thusly that "principle of inversion"
wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical- >>>>>>> study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of >>>>>>> most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a
principle of
thorough reason as subsuming principles of non-contradiction and >>>>>>> what
suffices, so, I'll be curious then about what to make of Prawitz' >>>>>>> "inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the >>>>>>> oldest account of Western philosophy like Heraclitus with dual
monism.
In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of issues >>>>>>> and
resolving inductive impasses with analytical bridges after
complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the >>>>>>> characteristic features of Gentzen's intuitionistic natural
deduction.
In the literature on proof-theoretic semantics, this principle is >>>>>>> often
coupled with another that is called the recovery principle. By
adopting
the Computational Ludics framework, we reformulate these principles >>>>>>> into
one and the same condition, which we call the harmony condition. We >>>>>>> show
that this reformulation allows us to reveal two intuitive ideas
standing
behind these principles: the idea of "containment" present in the >>>>>>> inversion principle, and the idea that the recovery principle is the >>>>>>> "converse" of the inversion principle. We also formulate two other >>>>>>> conditions in the Computational Ludics framework, and we show that >>>>>>> each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge. >>>>>>>
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives,
proof-theoretic semantics rests on the idea that we know the
meaning of
a compound sentence when we know what counts as a canonical proof of >>>>>>> it.
And if proofs are formalised within the framework of natural
deduction,
then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective >>>>>>> of A."
The "canonical proofs" are not unique, in any system strong enough >>>>>>> to make for infinitary reasoning and super-classical results
requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts that >>>>> make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical proofs". >>>> Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs
of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong).
Induction and counter-induction contradict each other, it's simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
On 06/23/2026 10:32 AM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again.-a No reputable >>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things.-a If Dag Prawitz >>>>>>>>>>>>>> really
did
"agree" (with whom?) that G||del's sentence G is not true in >>>>>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
I was right, you didn't understand it.He never gets to G||del. He essentially says unprovable >>>>>>>>>>>>> means untrue all the time for everything within hisYou won't understand it, but that _is_ essentially G||del's >>>>>>>>>>>> Incompleteness
own Theory of Grounds of strict Proof Theoretic Semantics. >>>>>>>>>>
Theorem.-a It is a statement that any sufficiently powerful >>>>>>>>>>>> system can
express true things it can't prove.-a So Dag Prawitz, had he >>>>>>>>>>>> been
saying
the things you falsely attributed to him, would certainly have >>>>>>>>>>>> "got" to
G||del, and would have understood full well what he was saying. >>>>>>>>>>
You did not pay close enough attention to my exact words. >>>>>>>>>>
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz >>>>>>>> says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't >>>>>>>> say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse >>>>>>>> principle" so I think these are key aspects of fundamental logic. >>>>>>>>
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself, >>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to generate >>>>>>>> new ad-
missible rules within a certain syntactic context. Some N4Ufteen >>>>>>>> years
later, the idea was taken up by Dag Prawitz to devise a strategy of >>>>>>>> normalization for natural deduction calculi (this being an
analogue of
GentzenrCOs cut-elimination theorem for sequent calculi). Later, >>>>>>>> Prawitz
used the inversion principle again, attributing it with a semantic >>>>>>>> role.
Still working in natural deduction calculi, he formulated a general >>>>>>>> type
of schematic Introduction rules to be matchedrCothanks to the idea >>>>>>>> supporting the inversion principle rCo by a corresponding general >>>>>>>> schematic Elimination rule. This was an attempt to provide a
solution to
the problem suggested by the often quoted note of Gentzen.
According to
Gentzen rCLit should be possible to display the elimination rules as >>>>>>>> unique functions of the corresponding introduction rules on the >>>>>>>> basis of
certain requirements.rCY Many people have since worked on this topic, >>>>>>>> which can be appropriately seen as the birthplace of what are now >>>>>>>> referred to as rCLgeneral elimination rulesrCY, recently studied >>>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the main >>>>>>>> threads of this chapter of proof-theoretical investigation, using >>>>>>>> LorenzenrCOs original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's >>>>>>>> laws,
and that being the usual account of naive deductive analysis, then >>>>>>>> since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides >>>>>>>> Kripke
afterward there's also Sheffer and Chwistek before, and instead of >>>>>>>> Montague for semantics there's Herbrand for semantics, so, what >>>>>>>> to do
about "inversion principle" is here that the thea-theory has that >>>>>>>> it's
what subsumes "non-contradiction principle", here hoping that the >>>>>>>> interpretation aligns and thusly that "principle of inversion" >>>>>>>> wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical- >>>>>>>> study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of >>>>>>>> most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a
principle of
thorough reason as subsuming principles of non-contradiction and >>>>>>>> what
suffices, so, I'll be curious then about what to make of Prawitz' >>>>>>>> "inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the >>>>>>>> oldest account of Western philosophy like Heraclitus with dual >>>>>>>> monism.
In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of issues >>>>>>>> and
resolving inductive impasses with analytical bridges after
complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the >>>>>>>> characteristic features of Gentzen's intuitionistic natural
deduction.
In the literature on proof-theoretic semantics, this principle is >>>>>>>> often
coupled with another that is called the recovery principle. By >>>>>>>> adopting
the Computational Ludics framework, we reformulate these principles >>>>>>>> into
one and the same condition, which we call the harmony condition. We >>>>>>>> show
that this reformulation allows us to reveal two intuitive ideas >>>>>>>> standing
behind these principles: the idea of "containment" present in the >>>>>>>> inversion principle, and the idea that the recovery principle is >>>>>>>> the
"converse" of the inversion principle. We also formulate two other >>>>>>>> conditions in the Computational Ludics framework, and we show that >>>>>>>> each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge. >>>>>>>>
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, >>>>>>>> proof-theoretic semantics rests on the idea that we know the
meaning of
a compound sentence when we know what counts as a canonical
proof of
it.
And if proofs are formalised within the framework of natural
deduction,
then a canonical proof of a sentence A is nothing but a closed >>>>>>>> derivation ending with an introduction rule of the main connective >>>>>>>> of A."
The "canonical proofs" are not unique, in any system strong enough >>>>>>>> to make for infinitary reasoning and super-classical results
requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts >>>>>> that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical proofs". >>>>> Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs >>>>>> of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong).
Induction and counter-induction contradict each other, it's simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
P.S. there's no reason at all to "get back to you".
... Except countering the waste-ful spammy trolling.
Finding cycles in derivations of arguments is exactly
what makes for detection of circularities then as to
whether they're the virtuous or vicious sorts of circles,
it's the act of being diligent itself, you brainless, memoryless bot.
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again.-a No reputable mathematician >>>>>>>>>>>> would
risk his reputation by saying false things.-a If Dag Prawitz >>>>>>>>>>>> really
did
"agree" (with whom?) that G||del's sentence G is not true in >>>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially G||del's >>>>>>>>>> Incompleteness
Theorem.-a It is a statement that any sufficiently powerful >>>>>>>>>> system can
express true things it can't prove.-a So Dag Prawitz, had he been >>>>>>>>>> saying
the things you falsely attributed to him, would certainly have >>>>>>>>>> "got" to
G||del, and would have understood full well what he was saying. >>>>>>>>
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says", >>>>>> and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't >>>>>> say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse
principle" so I think these are key aspects of fundamental logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself,
originated in
the work of Paul Lorenzen in the 1950s, as a method to generate new >>>>>> ad-
missible rules within a certain syntactic context. Some N4Ufteen years >>>>>> later, the idea was taken up by Dag Prawitz to devise a strategy of >>>>>> normalization for natural deduction calculi (this being an analogue of >>>>>> GentzenrCOs cut-elimination theorem for sequent calculi). Later, Prawitz >>>>>> used the inversion principle again, attributing it with a semantic >>>>>> role.
Still working in natural deduction calculi, he formulated a general >>>>>> type
of schematic Introduction rules to be matchedrCothanks to the idea >>>>>> supporting the inversion principle rCo by a corresponding general
schematic Elimination rule. This was an attempt to provide a
solution to
the problem suggested by the often quoted note of Gentzen.
According to
Gentzen rCLit should be possible to display the elimination rules as >>>>>> unique functions of the corresponding introduction rules on the
basis of
certain requirements.rCY Many people have since worked on this topic, >>>>>> which can be appropriately seen as the birthplace of what are now
referred to as rCLgeneral elimination rulesrCY, recently studied
thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the main >>>>>> threads of this chapter of proof-theoretical investigation, using
LorenzenrCOs original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's laws, >>>>>> and that being the usual account of naive deductive analysis, then >>>>>> since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides Kripke >>>>>> afterward there's also Sheffer and Chwistek before, and instead of >>>>>> Montague for semantics there's Herbrand for semantics, so, what to do >>>>>> about "inversion principle" is here that the thea-theory has that it's >>>>>> what subsumes "non-contradiction principle", here hoping that the
interpretation aligns and thusly that "principle of inversion"
wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical- >>>>>> study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of most >>>>>> modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a principle of >>>>>> thorough reason as subsuming principles of non-contradiction and what >>>>>> suffices, so, I'll be curious then about what to make of Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the >>>>>> oldest account of Western philosophy like Heraclitus with dual monism. >>>>>> In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of issues and >>>>>> resolving inductive impasses with analytical bridges after
complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the >>>>>> characteristic features of Gentzen's intuitionistic natural deduction. >>>>>> In the literature on proof-theoretic semantics, this principle is >>>>>> often
coupled with another that is called the recovery principle. By
adopting
the Computational Ludics framework, we reformulate these principles >>>>>> into
one and the same condition, which we call the harmony condition. We >>>>>> show
that this reformulation allows us to reveal two intuitive ideas
standing
behind these principles: the idea of "containment" present in the
inversion principle, and the idea that the recovery principle is the >>>>>> "converse" of the inversion principle. We also formulate two other >>>>>> conditions in the Computational Ludics framework, and we show that >>>>>> each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives,
proof-theoretic semantics rests on the idea that we know the
meaning of
a compound sentence when we know what counts as a canonical proof of >>>>>> it.
And if proofs are formalised within the framework of natural
deduction,
then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective >>>>>> of A."
The "canonical proofs" are not unique, in any system strong enough >>>>>> to make for infinitary reasoning and super-classical results requiring >>>>>> analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts that >>>> make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs
of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong).
Induction and counter-induction contradict each other, it's simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Le 23/06/2026 |a 18:54, olcott a |-crit :
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable
mathematician
would
risk his reputation by saying false things. If Dag Prawitz >>>>>>>>>>>>> really
did
"agree" (with whom?) that G||del's sentence G is not true in >>>>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable >>>>>>>>>>>> means untrue all the time for everything within hisYou won't understand it, but that _is_ essentially G||del's >>>>>>>>>>> Incompleteness
own Theory of Grounds of strict Proof Theoretic Semantics. >>>>>>>>>
Theorem. It is a statement that any sufficiently powerful >>>>>>>>>>> system can
express true things it can't prove. So Dag Prawitz, had he been >>>>>>>>>>> saying
the things you falsely attributed to him, would certainly have >>>>>>>>>>> "got" to
G||del, and would have understood full well what he was saying. >>>>>>>>>
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says", >>>>>>> and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't >>>>>>> say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse >>>>>>> principle" so I think these are key aspects of fundamental logic. >>>>>>>
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself,
originated in
the work of Paul Lorenzen in the 1950s, as a method to generate
new ad-
missible rules within a certain syntactic context. Some N4Ufteen years >>>>>>> later, the idea was taken up by Dag Prawitz to devise a strategy of >>>>>>> normalization for natural deduction calculi (this being an
analogue of
GentzenrCOs cut-elimination theorem for sequent calculi). Later, >>>>>>> Prawitz
used the inversion principle again, attributing it with a semantic >>>>>>> role.
Still working in natural deduction calculi, he formulated a general >>>>>>> type
of schematic Introduction rules to be matchedrCothanks to the idea >>>>>>> supporting the inversion principle rCo by a corresponding general >>>>>>> schematic Elimination rule. This was an attempt to provide a
solution to
the problem suggested by the often quoted note of Gentzen.
According to
Gentzen rCLit should be possible to display the elimination rules as >>>>>>> unique functions of the corresponding introduction rules on the
basis of
certain requirements.rCY Many people have since worked on this topic, >>>>>>> which can be appropriately seen as the birthplace of what are now >>>>>>> referred to as rCLgeneral elimination rulesrCY, recently studied >>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the main >>>>>>> threads of this chapter of proof-theoretical investigation, using >>>>>>> LorenzenrCOs original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's >>>>>>> laws,
and that being the usual account of naive deductive analysis, then >>>>>>> since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides
Kripke
afterward there's also Sheffer and Chwistek before, and instead of >>>>>>> Montague for semantics there's Herbrand for semantics, so, what
to do
about "inversion principle" is here that the thea-theory has that >>>>>>> it's
what subsumes "non-contradiction principle", here hoping that the >>>>>>> interpretation aligns and thusly that "principle of inversion"
wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical- >>>>>>> study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of >>>>>>> most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a
principle of
thorough reason as subsuming principles of non-contradiction and >>>>>>> what
suffices, so, I'll be curious then about what to make of Prawitz' >>>>>>> "inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the >>>>>>> oldest account of Western philosophy like Heraclitus with dual
monism.
In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of
issues and
resolving inductive impasses with analytical bridges after
complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the >>>>>>> characteristic features of Gentzen's intuitionistic natural
deduction.
In the literature on proof-theoretic semantics, this principle is >>>>>>> often
coupled with another that is called the recovery principle. By
adopting
the Computational Ludics framework, we reformulate these principles >>>>>>> into
one and the same condition, which we call the harmony condition. We >>>>>>> show
that this reformulation allows us to reveal two intuitive ideas
standing
behind these principles: the idea of "containment" present in the >>>>>>> inversion principle, and the idea that the recovery principle is the >>>>>>> "converse" of the inversion principle. We also formulate two other >>>>>>> conditions in the Computational Ludics framework, and we show
that each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge. >>>>>>>
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives,
proof-theoretic semantics rests on the idea that we know the
meaning of
a compound sentence when we know what counts as a canonical proof of >>>>>>> it.
And if proofs are formalised within the framework of natural
deduction,
then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective >>>>>>> of A."
The "canonical proofs" are not unique, in any system strong enough >>>>>>> to make for infinitary reasoning and super-classical results
requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts that >>>>> make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical proofs". >>>> Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs
of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong).
Induction and counter-induction contradict each other, it's simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Prolog's occurs check detects syntactic circularity in term unification. G||del's theorem does not depend on that kind of syntactic circularity.
It uses a finite, well-formed formula obtained through diagonalization,
which refers to its own G||del number. The occurs check rejects 'LP = not(true(LP))', but it neither rejects nor addresses G||del's arithmetic construction.
The underlying mistake is a common one: treating G||del's diagonalization
as if it were direct textual self-reference. It is not. It is indirect self-reference achieved through arithmetic coding of syntax. That detour
is precisely what makes G||del's theorem work.
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms.-a That doesn't mean you're >>>>>>>>>> capable of
understanding them.
The above is the key reason why under PTS G||del 1931
incompleteness
fails.
I don't believe you.-a You have no respect for or understanding >>>>>>>> of the
truth.-a If you really want to persuade anybody that PTS somehow >>>>>>>> causes
G||del's theorem not to hold, then cite an academic expert who'll >>>>>>>> have
some credibility.
If they are mere gibberish words to you then you will not
understand.
You don't understand Proof-theoritic Semantics, and you
certainly don't
understand G||del's Theorem, neither the theorem itself nor any >>>>>>>> proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by >>>>>> you, and it is one which you have never explicitly defined, so the >>>>>> fault here certainly doesn't lie with Alan. It's certainly not a
'verified fact' when you haven't even adequately explained what it >>>>>> is that you mean.
All of knowledge expressed in language is structured as a tree of
semantic relations specified syntactically between finite strings.
What makes you believe semantic relations that can be structured as
a tree are sufficient to contain all knowledge that is exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again.-a No reputable >>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things.-a If Dag Prawitz >>>>>>>>>>>>>> really
did
"agree" (with whom?) that G||del's sentence G is not true in >>>>>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
I was right, you didn't understand it.He never gets to G||del. He essentially says unprovable >>>>>>>>>>>>> means untrue all the time for everything within hisYou won't understand it, but that _is_ essentially G||del's >>>>>>>>>>>> Incompleteness
own Theory of Grounds of strict Proof Theoretic Semantics. >>>>>>>>>>
Theorem.-a It is a statement that any sufficiently powerful >>>>>>>>>>>> system can
express true things it can't prove.-a So Dag Prawitz, had he >>>>>>>>>>>> been
saying
the things you falsely attributed to him, would certainly have >>>>>>>>>>>> "got" to
G||del, and would have understood full well what he was saying. >>>>>>>>>>
You did not pay close enough attention to my exact words. >>>>>>>>>>
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz >>>>>>>> says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't >>>>>>>> say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse >>>>>>>> principle" so I think these are key aspects of fundamental logic. >>>>>>>>
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself, >>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to generate >>>>>>>> new ad-
missible rules within a certain syntactic context. Some N4Ufteen >>>>>>>> years
later, the idea was taken up by Dag Prawitz to devise a strategy of >>>>>>>> normalization for natural deduction calculi (this being an
analogue of
GentzenrCOs cut-elimination theorem for sequent calculi). Later, >>>>>>>> Prawitz
used the inversion principle again, attributing it with a semantic >>>>>>>> role.
Still working in natural deduction calculi, he formulated a general >>>>>>>> type
of schematic Introduction rules to be matchedrCothanks to the idea >>>>>>>> supporting the inversion principle rCo by a corresponding general >>>>>>>> schematic Elimination rule. This was an attempt to provide a
solution to
the problem suggested by the often quoted note of Gentzen.
According to
Gentzen rCLit should be possible to display the elimination rules as >>>>>>>> unique functions of the corresponding introduction rules on the >>>>>>>> basis of
certain requirements.rCY Many people have since worked on this topic, >>>>>>>> which can be appropriately seen as the birthplace of what are now >>>>>>>> referred to as rCLgeneral elimination rulesrCY, recently studied >>>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the main >>>>>>>> threads of this chapter of proof-theoretical investigation, using >>>>>>>> LorenzenrCOs original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's >>>>>>>> laws,
and that being the usual account of naive deductive analysis, then >>>>>>>> since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides >>>>>>>> Kripke
afterward there's also Sheffer and Chwistek before, and instead of >>>>>>>> Montague for semantics there's Herbrand for semantics, so, what >>>>>>>> to do
about "inversion principle" is here that the thea-theory has that >>>>>>>> it's
what subsumes "non-contradiction principle", here hoping that the >>>>>>>> interpretation aligns and thusly that "principle of inversion" >>>>>>>> wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical- >>>>>>>> study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of >>>>>>>> most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a
principle of
thorough reason as subsuming principles of non-contradiction and >>>>>>>> what
suffices, so, I'll be curious then about what to make of Prawitz' >>>>>>>> "inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the >>>>>>>> oldest account of Western philosophy like Heraclitus with dual >>>>>>>> monism.
In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of issues >>>>>>>> and
resolving inductive impasses with analytical bridges after
complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the >>>>>>>> characteristic features of Gentzen's intuitionistic natural
deduction.
In the literature on proof-theoretic semantics, this principle is >>>>>>>> often
coupled with another that is called the recovery principle. By >>>>>>>> adopting
the Computational Ludics framework, we reformulate these principles >>>>>>>> into
one and the same condition, which we call the harmony condition. We >>>>>>>> show
that this reformulation allows us to reveal two intuitive ideas >>>>>>>> standing
behind these principles: the idea of "containment" present in the >>>>>>>> inversion principle, and the idea that the recovery principle is >>>>>>>> the
"converse" of the inversion principle. We also formulate two other >>>>>>>> conditions in the Computational Ludics framework, and we show that >>>>>>>> each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge. >>>>>>>>
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, >>>>>>>> proof-theoretic semantics rests on the idea that we know the
meaning of
a compound sentence when we know what counts as a canonical
proof of
it.
And if proofs are formalised within the framework of natural
deduction,
then a canonical proof of a sentence A is nothing but a closed >>>>>>>> derivation ending with an introduction rule of the main connective >>>>>>>> of A."
The "canonical proofs" are not unique, in any system strong enough >>>>>>>> to make for infinitary reasoning and super-classical results
requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts >>>>>> that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical proofs". >>>>> Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs >>>>>> of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong).
Induction and counter-induction contradict each other, it's simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog?
That would be dishonest.
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms.-a That doesn't mean you're >>>>>>>>>>> capable of
understanding them.
The above is the key reason why under PTS G||del 1931
incompleteness
fails.
I don't believe you.-a You have no respect for or understanding >>>>>>>>> of the
truth.-a If you really want to persuade anybody that PTS somehow >>>>>>>>> causes
G||del's theorem not to hold, then cite an academic expert
who'll have
some credibility.
If they are mere gibberish words to you then you will not >>>>>>>>>> understand.
You don't understand Proof-theoritic Semantics, and you
certainly don't
understand G||del's Theorem, neither the theorem itself nor any >>>>>>>>> proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by >>>>>>> you, and it is one which you have never explicitly defined, so
the fault here certainly doesn't lie with Alan. It's certainly
not a 'verified fact' when you haven't even adequately explained >>>>>>> what it is that you mean.
All of knowledge expressed in language is structured as a tree of >>>>>> semantic relations specified syntactically between finite strings.
What makes you believe semantic relations that can be structured as
a tree are sufficient to contain all knowledge that is exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop
when looking for a proof?
On 23/06/2026 17:52, olcott wrote:
On 6/23/2026 1:15 AM, Mikko wrote:
On 22/06/2026 17:44, olcott wrote:
On 6/22/2026 2:23 AM, Mikko wrote:
On 21/06/2026 23:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms.-a That doesn't mean you're >>>>>>>>> capable of
understanding them.
The above is the key reason why under PTS G||del 1931 incompleteness >>>>>>>> fails.
I don't believe you.-a You have no respect for or understanding of >>>>>>> the
truth.-a If you really want to persuade anybody that PTS somehow >>>>>>> causes
G||del's theorem not to hold, then cite an academic expert who'll >>>>>>> have
some credibility.
If they are mere gibberish words to you then you will not
understand.
You don't understand Proof-theoritic Semantics, and you certainly >>>>>>> don't
understand G||del's Theorem, neither the theorem itself nor any >>>>>>> proof of
it.
in the atomic base of PA.
It is a verified fact that G||del's completeness and incompleteness
theorems are inevitable consequences of Peano arithmetic.
Within the foundation of Truth Conditional Semantics
this is true. Within the foundation of strict Proof
Theoretic Semantics this is false.
The proof that there are unprovable sentences with unprovable
negations does not refer to any semantics. That a sentence or
its negation is true is a feature of many semantic systems and
in particular of the arithemtic semantics of Peano arithmetic.
When people want to know how a function could be computed or whether it
can be computed at all they only care about arithmetic and computational >>> semantics. Proof theoretic semnatics is irrelevant.
Proof-theoretic semantics is an alternative foundation
for mathematics replacing truth conditional semantics.
It does not provide any useful alternative when no semantics is needed.
It is not shown to offer anything useful with problems with theal world semantics, which are the most important ones.
On 23/06/2026 21:20, olcott wrote:
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>> On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again.-a No reputable >>>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things.-a If Dag Prawitz >>>>>>>>>>>>>>> really
did
"agree" (with whom?) that G||del's sentence G is not true in >>>>>>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
I was right, you didn't understand it.He never gets to G||del. He essentially says unprovable >>>>>>>>>>>>>> means untrue all the time for everything within his >>>>>>>>>>>>>> own Theory of Grounds of strict Proof Theoretic Semantics. >>>>>>>>>>>You won't understand it, but that _is_ essentially G||del's >>>>>>>>>>>>> Incompleteness
Theorem.-a It is a statement that any sufficiently powerful >>>>>>>>>>>>> system can
express true things it can't prove.-a So Dag Prawitz, had he >>>>>>>>>>>>> been
saying
the things you falsely attributed to him, would certainly have >>>>>>>>>>>>> "got" to
G||del, and would have understood full well what he was saying. >>>>>>>>>>>
You did not pay close enough attention to my exact words. >>>>>>>>>>>
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz >>>>>>>>> says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't >>>>>>>>> say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse >>>>>>>>> principle" so I think these are key aspects of fundamental logic. >>>>>>>>>
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself, >>>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to generate >>>>>>>>> new ad-
missible rules within a certain syntactic context. Some N4Ufteen >>>>>>>>> years
later, the idea was taken up by Dag Prawitz to devise a
strategy of
normalization for natural deduction calculi (this being an
analogue of
GentzenrCOs cut-elimination theorem for sequent calculi). Later, >>>>>>>>> Prawitz
used the inversion principle again, attributing it with a semantic >>>>>>>>> role.
Still working in natural deduction calculi, he formulated a >>>>>>>>> general
type
of schematic Introduction rules to be matchedrCothanks to the idea >>>>>>>>> supporting the inversion principle rCo by a corresponding general >>>>>>>>> schematic Elimination rule. This was an attempt to provide a >>>>>>>>> solution to
the problem suggested by the often quoted note of Gentzen.
According to
Gentzen rCLit should be possible to display the elimination rules as >>>>>>>>> unique functions of the corresponding introduction rules on the >>>>>>>>> basis of
certain requirements.rCY Many people have since worked on this >>>>>>>>> topic,
which can be appropriately seen as the birthplace of what are now >>>>>>>>> referred to as rCLgeneral elimination rulesrCY, recently studied >>>>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the >>>>>>>>> main
threads of this chapter of proof-theoretical investigation, using >>>>>>>>> LorenzenrCOs original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's >>>>>>>>> laws,
and that being the usual account of naive deductive analysis, then >>>>>>>>> since
"natural deduction", which here is held as part of the theory >>>>>>>>> since it's naturally logical, then has for Gentzen that besides >>>>>>>>> Kripke
afterward there's also Sheffer and Chwistek before, and instead of >>>>>>>>> Montague for semantics there's Herbrand for semantics, so, what >>>>>>>>> to do
about "inversion principle" is here that the thea-theory has that >>>>>>>>> it's
what subsumes "non-contradiction principle", here hoping that the >>>>>>>>> interpretation aligns and thusly that "principle of inversion" >>>>>>>>> wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334 >>>>>>>>>
https://www.strandbooks.com/natural-deduction-a-proof-theoretical- >>>>>>>>> study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of >>>>>>>>> most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a
principle of
thorough reason as subsuming principles of non-contradiction >>>>>>>>> and what
suffices, so, I'll be curious then about what to make of Prawitz' >>>>>>>>> "inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the >>>>>>>>> oldest account of Western philosophy like Heraclitus with dual >>>>>>>>> monism.
In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of issues >>>>>>>>> and
resolving inductive impasses with analytical bridges after
complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of >>>>>>>>> the
characteristic features of Gentzen's intuitionistic natural
deduction.
In the literature on proof-theoretic semantics, this principle is >>>>>>>>> often
coupled with another that is called the recovery principle. By >>>>>>>>> adopting
the Computational Ludics framework, we reformulate these
principles
into
one and the same condition, which we call the harmony
condition. We
show
that this reformulation allows us to reveal two intuitive ideas >>>>>>>>> standing
behind these principles: the idea of "containment" present in the >>>>>>>>> inversion principle, and the idea that the recovery principle >>>>>>>>> is the
"converse" of the inversion principle. We also formulate two other >>>>>>>>> conditions in the Computational Ludics framework, and we show that >>>>>>>>> each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge. >>>>>>>>>
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, >>>>>>>>> proof-theoretic semantics rests on the idea that we know the >>>>>>>>> meaning of
a compound sentence when we know what counts as a canonical >>>>>>>>> proof of
it.
And if proofs are formalised within the framework of natural >>>>>>>>> deduction,
then a canonical proof of a sentence A is nothing but a closed >>>>>>>>> derivation ending with an introduction rule of the main connective >>>>>>>>> of A."
The "canonical proofs" are not unique, in any system strong enough >>>>>>>>> to make for infinitary reasoning and super-classical results >>>>>>>>> requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts >>>>>>> that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical
proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs >>>>>>> of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong). >>>>>>>
Induction and counter-induction contradict each other, it's simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog?
That would be dishonest.
No, pointing out that you are worng about Prolog when you are wrong
about Prolog is never dishohest.
On 6/24/2026 5:13 AM, Mikko wrote:
On 23/06/2026 21:20, olcott wrote:
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>> On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again.-a No reputable >>>>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things.-a If Dag Prawitz >>>>>>>>>>>>>>>> really
did
"agree" (with whom?) that G||del's sentence G is not true in >>>>>>>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable >>>>>>>>>>>>>>> means untrue all the time for everything within his >>>>>>>>>>>>>>> own Theory of Grounds of strict Proof Theoretic Semantics. >>>>>>>>>>>>You won't understand it, but that _is_ essentially G||del's >>>>>>>>>>>>>> Incompleteness
Theorem.-a It is a statement that any sufficiently powerful >>>>>>>>>>>>>> system can
express true things it can't prove.-a So Dag Prawitz, had >>>>>>>>>>>>>> he been
saying
the things you falsely attributed to him, would certainly >>>>>>>>>>>>>> have
"got" to
G||del, and would have understood full well what he was >>>>>>>>>>>>>> saying.
You did not pay close enough attention to my exact words. >>>>>>>>>>>>I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz >>>>>>>>>> says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't >>>>>>>>>> say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse >>>>>>>>>> principle" so I think these are key aspects of fundamental logic. >>>>>>>>>>
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself, >>>>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to generate >>>>>>>>>> new ad-
missible rules within a certain syntactic context. Some N4Ufteen >>>>>>>>>> years
later, the idea was taken up by Dag Prawitz to devise a
strategy of
normalization for natural deduction calculi (this being an >>>>>>>>>> analogue of
GentzenrCOs cut-elimination theorem for sequent calculi). Later, >>>>>>>>>> Prawitz
used the inversion principle again, attributing it with a >>>>>>>>>> semantic
role.
Still working in natural deduction calculi, he formulated a >>>>>>>>>> general
type
of schematic Introduction rules to be matchedrCothanks to the idea >>>>>>>>>> supporting the inversion principle rCo by a corresponding general >>>>>>>>>> schematic Elimination rule. This was an attempt to provide a >>>>>>>>>> solution to
the problem suggested by the often quoted note of Gentzen. >>>>>>>>>> According to
Gentzen rCLit should be possible to display the elimination >>>>>>>>>> rules as
unique functions of the corresponding introduction rules on the >>>>>>>>>> basis of
certain requirements.rCY Many people have since worked on this >>>>>>>>>> topic,
which can be appropriately seen as the birthplace of what are now >>>>>>>>>> referred to as rCLgeneral elimination rulesrCY, recently studied >>>>>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the >>>>>>>>>> main
threads of this chapter of proof-theoretical investigation, using >>>>>>>>>> LorenzenrCOs original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's >>>>>>>>>> laws,
and that being the usual account of naive deductive analysis, >>>>>>>>>> then
since
"natural deduction", which here is held as part of the theory >>>>>>>>>> since it's naturally logical, then has for Gentzen that besides >>>>>>>>>> Kripke
afterward there's also Sheffer and Chwistek before, and
instead of
Montague for semantics there's Herbrand for semantics, so, >>>>>>>>>> what to do
about "inversion principle" is here that the thea-theory has that >>>>>>>>>> it's
what subsumes "non-contradiction principle", here hoping that the >>>>>>>>>> interpretation aligns and thusly that "principle of inversion" >>>>>>>>>> wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334 >>>>>>>>>>
https://www.strandbooks.com/natural-deduction-a-proof-theoretical- >>>>>>>>>>
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of >>>>>>>>>> most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a
principle of
thorough reason as subsuming principles of non-contradiction >>>>>>>>>> and what
suffices, so, I'll be curious then about what to make of Prawitz' >>>>>>>>>> "inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as >>>>>>>>>> the
oldest account of Western philosophy like Heraclitus with dual >>>>>>>>>> monism.
In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of >>>>>>>>>> issues
and
resolving inductive impasses with analytical bridges after >>>>>>>>>> complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one >>>>>>>>>> of the
characteristic features of Gentzen's intuitionistic natural >>>>>>>>>> deduction.
In the literature on proof-theoretic semantics, this principle is >>>>>>>>>> often
coupled with another that is called the recovery principle. By >>>>>>>>>> adopting
the Computational Ludics framework, we reformulate these
principles
into
one and the same condition, which we call the harmony
condition. We
show
that this reformulation allows us to reveal two intuitive ideas >>>>>>>>>> standing
behind these principles: the idea of "containment" present in the >>>>>>>>>> inversion principle, and the idea that the recovery principle >>>>>>>>>> is the
"converse" of the inversion principle. We also formulate two >>>>>>>>>> other
conditions in the Computational Ludics framework, and we show >>>>>>>>>> that
each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge. >>>>>>>>>>
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, >>>>>>>>>> proof-theoretic semantics rests on the idea that we know the >>>>>>>>>> meaning of
a compound sentence when we know what counts as a canonical >>>>>>>>>> proof of
it.
And if proofs are formalised within the framework of natural >>>>>>>>>> deduction,
then a canonical proof of a sentence A is nothing but a closed >>>>>>>>>> derivation ending with an introduction rule of the main
connective
of A."
The "canonical proofs" are not unique, in any system strong >>>>>>>>>> enough
to make for infinitary reasoning and super-classical results >>>>>>>>>> requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of >>>>>>>>> thing two different ways.
Furthermore I say there are "canonical proofs" of inductive
sorts that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical
proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs >>>>>>>> of what otherwise is flawed, or for hard constructivist realist >>>>>>>> structuralist model theorists: not-theories (examples of wrong). >>>>>>>>
Induction and counter-induction contradict each other, it's simple, >>>>>> it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog?
That would be dishonest.
No, pointing out that you are worng about Prolog when you are wrong
about Prolog is never dishohest.
That is correct Prolog and that is the
result of the correct run of correct Prolog.
Implying that I am wrong about Prolog without
pointing out any actual mistake is also DISHONEST.
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:What makes you believe semantic relations that can be structured as >>>>>> a tree are sufficient to contain all knowledge that is exressed in >>>>>> some language?
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:You can find any number of terms.-a That doesn't mean you're >>>>>>>>>>>> capable of
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>
understanding them.
The above is the key reason why under PTS G||del 1931
incompleteness
fails.
I don't believe you.-a You have no respect for or understanding >>>>>>>>>> of the
truth.-a If you really want to persuade anybody that PTS
somehow causes
G||del's theorem not to hold, then cite an academic expert >>>>>>>>>> who'll have
some credibility.
If they are mere gibberish words to you then you will not >>>>>>>>>>> understand.
You don't understand Proof-theoritic Semantics, and you
certainly don't
understand G||del's Theorem, neither the theorem itself nor any >>>>>>>>>> proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only >>>>>>>> by you, and it is one which you have never explicitly defined, >>>>>>>> so the fault here certainly doesn't lie with Alan. It's
certainly not a 'verified fact' when you haven't even adequately >>>>>>>> explained what it is that you mean.
All of knowledge expressed in language is structured as a tree of >>>>>>> semantic relations specified syntactically between finite strings. >>>>>>
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
On 6/24/2026 5:13 AM, Mikko wrote:
On 23/06/2026 21:20, olcott wrote:
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>> On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again.-a No reputable >>>>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things.-a If Dag Prawitz >>>>>>>>>>>>>>>> really
did
"agree" (with whom?) that G||del's sentence G is not true in >>>>>>>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable >>>>>>>>>>>>>>> means untrue all the time for everything within his >>>>>>>>>>>>>>> own Theory of Grounds of strict Proof Theoretic Semantics. >>>>>>>>>>>>You won't understand it, but that _is_ essentially G||del's >>>>>>>>>>>>>> Incompleteness
Theorem.-a It is a statement that any sufficiently powerful >>>>>>>>>>>>>> system can
express true things it can't prove.-a So Dag Prawitz, had >>>>>>>>>>>>>> he been
saying
the things you falsely attributed to him, would certainly >>>>>>>>>>>>>> have
"got" to
G||del, and would have understood full well what he was >>>>>>>>>>>>>> saying.
You did not pay close enough attention to my exact words. >>>>>>>>>>>>I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz >>>>>>>>>> says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't >>>>>>>>>> say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse >>>>>>>>>> principle" so I think these are key aspects of fundamental logic. >>>>>>>>>>
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself, >>>>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to generate >>>>>>>>>> new ad-
missible rules within a certain syntactic context. Some N4Ufteen >>>>>>>>>> years
later, the idea was taken up by Dag Prawitz to devise a
strategy of
normalization for natural deduction calculi (this being an >>>>>>>>>> analogue of
GentzenrCOs cut-elimination theorem for sequent calculi). Later, >>>>>>>>>> Prawitz
used the inversion principle again, attributing it with a >>>>>>>>>> semantic
role.
Still working in natural deduction calculi, he formulated a >>>>>>>>>> general
type
of schematic Introduction rules to be matchedrCothanks to the idea >>>>>>>>>> supporting the inversion principle rCo by a corresponding general >>>>>>>>>> schematic Elimination rule. This was an attempt to provide a >>>>>>>>>> solution to
the problem suggested by the often quoted note of Gentzen. >>>>>>>>>> According to
Gentzen rCLit should be possible to display the elimination >>>>>>>>>> rules as
unique functions of the corresponding introduction rules on the >>>>>>>>>> basis of
certain requirements.rCY Many people have since worked on this >>>>>>>>>> topic,
which can be appropriately seen as the birthplace of what are now >>>>>>>>>> referred to as rCLgeneral elimination rulesrCY, recently studied >>>>>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the >>>>>>>>>> main
threads of this chapter of proof-theoretical investigation, using >>>>>>>>>> LorenzenrCOs original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's >>>>>>>>>> laws,
and that being the usual account of naive deductive analysis, >>>>>>>>>> then
since
"natural deduction", which here is held as part of the theory >>>>>>>>>> since it's naturally logical, then has for Gentzen that besides >>>>>>>>>> Kripke
afterward there's also Sheffer and Chwistek before, and
instead of
Montague for semantics there's Herbrand for semantics, so, >>>>>>>>>> what to do
about "inversion principle" is here that the thea-theory has that >>>>>>>>>> it's
what subsumes "non-contradiction principle", here hoping that the >>>>>>>>>> interpretation aligns and thusly that "principle of inversion" >>>>>>>>>> wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334 >>>>>>>>>>
https://www.strandbooks.com/natural-deduction-a-proof-
theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of >>>>>>>>>> most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a
principle of
thorough reason as subsuming principles of non-contradiction >>>>>>>>>> and what
suffices, so, I'll be curious then about what to make of Prawitz' >>>>>>>>>> "inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as >>>>>>>>>> the
oldest account of Western philosophy like Heraclitus with dual >>>>>>>>>> monism.
In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of >>>>>>>>>> issues
and
resolving inductive impasses with analytical bridges after >>>>>>>>>> complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one >>>>>>>>>> of the
characteristic features of Gentzen's intuitionistic natural >>>>>>>>>> deduction.
In the literature on proof-theoretic semantics, this principle is >>>>>>>>>> often
coupled with another that is called the recovery principle. By >>>>>>>>>> adopting
the Computational Ludics framework, we reformulate these
principles
into
one and the same condition, which we call the harmony
condition. We
show
that this reformulation allows us to reveal two intuitive ideas >>>>>>>>>> standing
behind these principles: the idea of "containment" present in the >>>>>>>>>> inversion principle, and the idea that the recovery principle >>>>>>>>>> is the
"converse" of the inversion principle. We also formulate two >>>>>>>>>> other
conditions in the Computational Ludics framework, and we show >>>>>>>>>> that
each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge. >>>>>>>>>>
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, >>>>>>>>>> proof-theoretic semantics rests on the idea that we know the >>>>>>>>>> meaning of
a compound sentence when we know what counts as a canonical >>>>>>>>>> proof of
it.
And if proofs are formalised within the framework of natural >>>>>>>>>> deduction,
then a canonical proof of a sentence A is nothing but a closed >>>>>>>>>> derivation ending with an introduction rule of the main
connective
of A."
The "canonical proofs" are not unique, in any system strong >>>>>>>>>> enough
to make for infinitary reasoning and super-classical results >>>>>>>>>> requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of >>>>>>>>> thing two different ways.
Furthermore I say there are "canonical proofs" of inductive
sorts that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical
proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs >>>>>>>> of what otherwise is flawed, or for hard constructivist realist >>>>>>>> structuralist model theorists: not-theories (examples of wrong). >>>>>>>>
Induction and counter-induction contradict each other, it's simple, >>>>>> it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog?
That would be dishonest.
No, pointing out that you are worng about Prolog when you are wrong
about Prolog is never dishohest.
That is correct Prolog and that is the
result of the correct run of correct Prolog.
Implying that I am wrong about Prolog without
pointing out any actual mistake is also DISHONEST.
On 6/24/2026 5:06 AM, Mikko wrote:
On 23/06/2026 17:52, olcott wrote:
On 6/23/2026 1:15 AM, Mikko wrote:
On 22/06/2026 17:44, olcott wrote:
On 6/22/2026 2:23 AM, Mikko wrote:
On 21/06/2026 23:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms.-a That doesn't mean you're >>>>>>>>>> capable of
understanding them.
The above is the key reason why under PTS G||del 1931
incompleteness
fails.
I don't believe you.-a You have no respect for or understanding >>>>>>>> of the
truth.-a If you really want to persuade anybody that PTS somehow >>>>>>>> causes
G||del's theorem not to hold, then cite an academic expert who'll >>>>>>>> have
some credibility.
If they are mere gibberish words to you then you will not
understand.
You don't understand Proof-theoritic Semantics, and you
certainly don't
understand G||del's Theorem, neither the theorem itself nor any >>>>>>>> proof of
it.
in the atomic base of PA.
It is a verified fact that G||del's completeness and incompleteness >>>>>> theorems are inevitable consequences of Peano arithmetic.
Within the foundation of Truth Conditional Semantics
this is true. Within the foundation of strict Proof
Theoretic Semantics this is false.
The proof that there are unprovable sentences with unprovable
negations does not refer to any semantics. That a sentence or
its negation is true is a feature of many semantic systems and
in particular of the arithemtic semantics of Peano arithmetic.
When people want to know how a function could be computed or whether it >>>> can be computed at all they only care about arithmetic and
computational
semantics. Proof theoretic semnatics is irrelevant.
Proof-theoretic semantics is an alternative foundation
for mathematics replacing truth conditional semantics.
It does not provide any useful alternative when no semantics is needed.
That G is true in the standard model of arithmetic
cannot possibly exist when model theory is replaced
with proof theoretic semantics.
It still isn't.It is not shown to offer anything useful with problems with theal world
semantics, which are the most important ones.
On 24/06/2026 23:19, olcott wrote:
On 6/24/2026 3:23 AM, Mikko wrote:
On 23/06/2026 17:29, olcott wrote:
On 6/23/2026 12:39 AM, Mikko wrote:
On 22/06/2026 16:13, olcott wrote:
On 6/22/2026 2:13 AM, Mikko wrote:
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:That only means that your DD is not a strictly confoming C
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>Whereas you are stuck to your own incoherent views and >>>>>>>>>>>>>>>>> reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>>> look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>> semantics/
I've spent a couple of hours reading that web page.-a It >>>>>>>>>>>>>>> is abstract in
the extreme.-a One thing is utterly clear: its level of >>>>>>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>>> Olcott, who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with >>>>>>>>>>>>> irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof >>>>>>>>>>>>> by contradiction. The LP isn't a contradiction; it's a >>>>>>>>>>>>> paradox. The two are different things. A contradiction is a >>>>>>>>>>>>> statement which is necessarily false. A paradox is a >>>>>>>>>>>>> statement to which no truth value can be consistently >>>>>>>>>>>>> assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting >>>>>>>>>>> problem proof, Godel's proof, and Tarski's proof, each of >>>>>>>>>>> which you've been attempting (and failing) to refute for years. >>>>>>>>>>>
Proof Theoretic Semantics halt prover HHH correctly determines >>>>>>>>>> that its input DD is ungrounded in its atomic base according >>>>>>>>>> to the operational semantics of the C programming language. >>>>>>>>>
program.
The exact operational semantics of C conclusively
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational
semantics
do not fully specify the behaviour of DD. In order to prove that DD >>>>>>> halts you also need additional operational spemantics provided by >>>>>>> the
C implementation you have used. When DD iss executed in that
environment
it halts, which is sufficient to prove that in that environment DD >>>>>>> halts. In some other environment its execution might be aborted >>>>>>> or it
could be rejected by the compiler.
Proof Theoretic Semantics provides the correct way
to handle pathological self-reference (PSR).
This would be dead obvious if you were not totally
clueless about Prolog.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Nice to see that you don't disagree.
Not nice to see that everyone continues to
totally ignore my best validation of proof
theoretic semantics.
Unfortunately that is unavoidable as long as your best presentation
of the validation and of your version of proof theoretic semantics
are not good enough.
Is is dead obvious and completely clear example
of the final resolution of the Liar Paradox using
generic proof theoretic semantics implemented in
Prolog.
Except that it is not final -- others will continue presenting
different views about it -- and not even a resolution.
Anyway, nice to see that you still don't disabree.
This is understandable for anyone that has no
idea what a directed graph is.
Your understanding of understandability is far from the real thing.
This has been completely rewritten just now.
https://github.com/plolcott/x86utm/blob/master/README.md
The description is updated. The described is not updated.
It always was a proof theoretic halt prover
I just didn't have those terms until recently.
It is not a prover. It does not prove.
It proves that no canonical proof of DD reaching
its own final halt state exists within the operational
semantics of the C programming language for PTS halt
prover HHH.
Irrelevant. That DD halts when executed is sufficient for a reasonable
person to conclude that it halts. To formulate that inference as a
formal proof is trivial to anyone who knows the formal rules.
It produces some execution trace
but may end before termination, and presents its conclusion or crashes.
Perhaps you have no idea what cycles in directed graphs are?
Doesn't really matter, especially when they are not even mentioned.
The words are well known and the definitions can be found on the
web.
On 24/06/2026 23:23, olcott wrote:
On 6/24/2026 4:45 AM, Mikko wrote:
On 23/06/2026 17:40, olcott wrote:
On 6/23/2026 12:49 AM, Mikko wrote:
On 22/06/2026 18:16, olcott wrote:
On 6/22/2026 2:46 AM, Mikko wrote:
On 22/06/2026 03:44, olcott wrote:
On 6/21/2026 7:32 PM, phoenix wrote:It is fairly simple to build a system of essentially infallible
olcott wrote:It is not that they never admit defeat.
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat? >>>>>>>>
olcott wrote:
On 6/21/2026 3:18 PM, Andr|- G. Isaak wrote:Lastly, and why should we care? Please answer this and other >>>>>>>>>>> questions presented.
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson >>>>>>>>>>>>>>>>>>>> Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>Whereas you are stuck to your own incoherent views and >>>>>>>>>>>>>>>>>> reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>>>> look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>> semantics/
I've spent a couple of hours reading that web page.-a It >>>>>>>>>>>>>>>> is abstract in
the extreme.-a One thing is utterly clear: its level of >>>>>>>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>>>> Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I >>>>>>>>>>>>>>>> can't be bothered
to read it any further.-a If it actually says anything at >>>>>>>>>>>>>>>> all, that
something is heavily disguised.-a From it's "Conclusion >>>>>>>>>>>>>>>> and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically >>>>>>>>>>>>>>>> exclusively been
| occupied with logical constants. Logical constants >>>>>>>>>>>>>>>> play a central role
| in reasoning and inference, but are definitely not the >>>>>>>>>>>>>>>> exclusive, and
| perhaps not even the most typical sort of entities >>>>>>>>>>>>>>>> that can be defined
| inferentially. A framework is needed that deals with >>>>>>>>>>>>>>>> inferential
| definitions in a wider sense and covers both logical >>>>>>>>>>>>>>>> and extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently >>>>>>>>>>>>>>> and in the
near future not useful as making it useful requires much >>>>>>>>>>>>>>> time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be >>>>>>>>>>>>>> useful for? What it
ought to be able to do that standard logic fails at? >>>>>>>>>>>>>> Maybe Andr|- could
elucidate.-a He seems to have a better grasp of it than >>>>>>>>>>>>>> anybody else here.
I doubt my understanding of PTS is any better than yours. I >>>>>>>>>>>>> basically only know what is presented in the Stanford >>>>>>>>>>>>> Encyclopedia article (which you correctly point out is not >>>>>>>>>>>>> exactly aimed at beginners) and the Wikipedia article. What >>>>>>>>>>>>> I am quite certain of, however, is that Olcott lacks any >>>>>>>>>>>>> understanding of what PTS actually says as he's made a >>>>>>>>>>>>> variety of fairly absurd claims regarding it (for example, >>>>>>>>>>>>> that PTS claims that unproven propositions are
'meaningless' or that the goal of PTS is to completely >>>>>>>>>>>>> overthrow standard truth- theoretic semantics).
Andr|-
-a-a Proof-theoretic semantics is an alternative to
-a-a truth-condition semantics. It is based on the
-a-a fundamental assumption that the central notion
-a-a in terms of which meanings are assigned to certain >>>>>>>>>>>> -a-a expressions of our language, in particular to
-a-a logical constants, is that of proof rather than
-a-a truth. In this sense proof-theoretic semantics
-a-a is semantics in terms of proof.
-a-a https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>> semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
It is that that have a system of essentially infallible reasoning >>>>>>>> that never errs as long as it has all the relevant information. >>>>>>>
reasoning that never errs even when it doesn't have all the
relevant information. The real problem is to construct a system
that tells something interesting instead of just different
presentations of the same already known facts.
It will have the exhaustively complete list of
every atomic fact of general knowledge of the
actual world.
That is impossible. By the time you have all facts of general
knowledge
in your system the general knowledge has grown to inlude more facts.
It can be reasonably approximated pretty quickly.
We start with all of the textbooks.
That is a lot of reading, though those for the same topic area tend
to say the same, and the old ones add very little to the new ones,
mainly some now obsolete technology.
It would not be too much reading for LLMs.
It could start with all of the latest textbooks
for all of the fields. Some of these latest
textbooks may be hundreds of years old for
fields that have become obsolete.
Perhaps that apprach should be tried. The problem involves extracting
atomic facts, detecting repeated facts, and encoding facts for the
inference system.
On 24/06/2026 23:25, olcott wrote:
On 6/24/2026 4:52 AM, Mikko wrote:
On 23/06/2026 17:47, olcott wrote:
On 6/23/2026 12:55 AM, Mikko wrote:
On 22/06/2026 15:09, olcott wrote:
On 6/22/2026 1:41 AM, Mikko wrote:
On 22/06/2026 02:58, olcott wrote:
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>>>> alternative views out-of-hand without review
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review. >>>>>>>>>>>>>
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>> look into proof theoretic semantics.
At different times you have expressed different opinions, which >>>>>>>>>>> sometimes have been incompatible. But you have never clearly >>>>>>>>>>> retracted your earlier opitions that conflict with your present >>>>>>>>>>> ones.
All of the ideas that I have ever had about these things
are now under the Proof Theoretic Semantics category.
These ideas have evolved over time, yet their essence
has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a
publishable
(or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> human
being on the face of the Earth could understand
me I could not publish.
As far as I have seen, all interesting content in those articles >>>>>>> that have any is or depends on claims that should be proven but
aren't.
They are proven in Proof Theoretic Semantics
An aricle is not publishable unless it either contains the proof or
has a pointer to an olready published proof.
Only now after 28 years am I acquiring the lingua Franca
terms-of-the-art of proof theoretic semantics such that
I can anchor my ideas in the foundational work of the
most respected authors in the field.
My issue with you guys is that you only spend 1%
of your concentration understanding me and the other
99% trying to artificially contrive some baseless
rebuttal.
THat "baseless" is false but otherwise, what is wrong is more
important than what is right. Of one ignores what is right one
mai fail to achieve what one could, but if one believs what is
wrong one may achieve a disaseter.
Proof-theoretic semantics is an alternative to truth-condition semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
So far no one has even acknowledged that PTS is an alternative
to truth-conditional semantics. Several people have seemed
to same that no alternative can possibly exist.
You have not shown that there is any need for any alternative semantics.
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>You can find any number of terms.-a That doesn't mean you're >>>>>>>>>>>>> capable of
understanding them.
The above is the key reason why under PTS G||del 1931 >>>>>>>>>>>> incompleteness
fails.
I don't believe you.-a You have no respect for or
understanding of the
truth.-a If you really want to persuade anybody that PTS >>>>>>>>>>> somehow causes
G||del's theorem not to hold, then cite an academic expert >>>>>>>>>>> who'll have
some credibility.
If they are mere gibberish words to you then you will not >>>>>>>>>>>> understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>> certainly don't
understand G||del's Theorem, neither the theorem itself nor >>>>>>>>>>> any proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only >>>>>>>>> by you, and it is one which you have never explicitly defined, >>>>>>>>> so the fault here certainly doesn't lie with Alan. It's
certainly not a 'verified fact' when you haven't even
adequately explained what it is that you mean.
All of knowledge expressed in language is structured as a tree >>>>>>>> of semantic relations specified syntactically between finite
strings.
What makes you believe semantic relations that can be structured as >>>>>>> a tree are sufficient to contain all knowledge that is exressed in >>>>>>> some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops.
In most cases that also prevents finding the proof.
On 25/06/2026 00:33, olcott wrote:
On 6/24/2026 5:13 AM, Mikko wrote:
On 23/06/2026 21:20, olcott wrote:
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>> On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>> On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again.-a No reputable >>>>>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things.-a If Dag >>>>>>>>>>>>>>>>> Prawitz
really
did
"agree" (with whom?) that G||del's sentence G is not >>>>>>>>>>>>>>>>> true in
Peano
Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable >>>>>>>>>>>>>>>> means untrue all the time for everything within his >>>>>>>>>>>>>>>> own Theory of Grounds of strict Proof Theoretic Semantics. >>>>>>>>>>>>>You won't understand it, but that _is_ essentially G||del's >>>>>>>>>>>>>>> Incompleteness
Theorem.-a It is a statement that any sufficiently powerful >>>>>>>>>>>>>>> system can
express true things it can't prove.-a So Dag Prawitz, had >>>>>>>>>>>>>>> he been
saying
the things you falsely attributed to him, would certainly >>>>>>>>>>>>>>> have
"got" to
G||del, and would have understood full well what he was >>>>>>>>>>>>>>> saying.
You did not pay close enough attention to my exact words. >>>>>>>>>>>>>I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz >>>>>>>>>>> says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz >>>>>>>>>>> doesn't
say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse >>>>>>>>>>> principle" so I think these are key aspects of fundamental >>>>>>>>>>> logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself, >>>>>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to generate >>>>>>>>>>> new ad-
missible rules within a certain syntactic context. Some >>>>>>>>>>> N4Ufteen years
later, the idea was taken up by Dag Prawitz to devise a >>>>>>>>>>> strategy of
normalization for natural deduction calculi (this being an >>>>>>>>>>> analogue of
GentzenrCOs cut-elimination theorem for sequent calculi). Later, >>>>>>>>>>> Prawitz
used the inversion principle again, attributing it with a >>>>>>>>>>> semantic
role.
Still working in natural deduction calculi, he formulated a >>>>>>>>>>> general
type
of schematic Introduction rules to be matchedrCothanks to the idea >>>>>>>>>>> supporting the inversion principle rCo by a corresponding general >>>>>>>>>>> schematic Elimination rule. This was an attempt to provide a >>>>>>>>>>> solution to
the problem suggested by the often quoted note of Gentzen. >>>>>>>>>>> According to
Gentzen rCLit should be possible to display the elimination >>>>>>>>>>> rules as
unique functions of the corresponding introduction rules on the >>>>>>>>>>> basis of
certain requirements.rCY Many people have since worked on this >>>>>>>>>>> topic,
which can be appropriately seen as the birthplace of what are >>>>>>>>>>> now
referred to as rCLgeneral elimination rulesrCY, recently studied >>>>>>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace >>>>>>>>>>> the main
threads of this chapter of proof-theoretical investigation, >>>>>>>>>>> using
LorenzenrCOs original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's >>>>>>>>>>> laws,
and that being the usual account of naive deductive analysis, >>>>>>>>>>> then
since
"natural deduction", which here is held as part of the theory >>>>>>>>>>> since it's naturally logical, then has for Gentzen that besides >>>>>>>>>>> Kripke
afterward there's also Sheffer and Chwistek before, and >>>>>>>>>>> instead of
Montague for semantics there's Herbrand for semantics, so, >>>>>>>>>>> what to do
about "inversion principle" is here that the thea-theory has >>>>>>>>>>> that
it's
what subsumes "non-contradiction principle", here hoping that >>>>>>>>>>> the
interpretation aligns and thusly that "principle of inversion" >>>>>>>>>>> wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334 >>>>>>>>>>>
https://www.strandbooks.com/natural-deduction-a-proof-
theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the
foundation of
most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a >>>>>>>>>>> principle of
thorough reason as subsuming principles of non-contradiction >>>>>>>>>>> and what
suffices, so, I'll be curious then about what to make of >>>>>>>>>>> Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old >>>>>>>>>>> as the
oldest account of Western philosophy like Heraclitus with dual >>>>>>>>>>> monism.
In fact by definition it's about the most basic aspect of >>>>>>>>>>> contemplation
and deliberation in abstraction of looking at both sides of >>>>>>>>>>> issues
and
resolving inductive impasses with analytical bridges after >>>>>>>>>>> complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one >>>>>>>>>>> of the
characteristic features of Gentzen's intuitionistic natural >>>>>>>>>>> deduction.
In the literature on proof-theoretic semantics, this
principle is
often
coupled with another that is called the recovery principle. By >>>>>>>>>>> adopting
the Computational Ludics framework, we reformulate these >>>>>>>>>>> principles
into
one and the same condition, which we call the harmony
condition. We
show
that this reformulation allows us to reveal two intuitive ideas >>>>>>>>>>> standing
behind these principles: the idea of "containment" present in >>>>>>>>>>> the
inversion principle, and the idea that the recovery principle >>>>>>>>>>> is the
"converse" of the inversion principle. We also formulate two >>>>>>>>>>> other
conditions in the Computational Ludics framework, and we show >>>>>>>>>>> that
each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge. >>>>>>>>>>>
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, >>>>>>>>>>> proof-theoretic semantics rests on the idea that we know the >>>>>>>>>>> meaning of
a compound sentence when we know what counts as a canonical >>>>>>>>>>> proof of
it.
And if proofs are formalised within the framework of natural >>>>>>>>>>> deduction,
then a canonical proof of a sentence A is nothing but a closed >>>>>>>>>>> derivation ending with an introduction rule of the main >>>>>>>>>>> connective
of A."
The "canonical proofs" are not unique, in any system strong >>>>>>>>>>> enough
to make for infinitary reasoning and super-classical results >>>>>>>>>>> requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6 >>>>>>>>>> That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches >>>>>>>>>> Thomas Piecha & Peter Schroeder-Heister do this same sort of >>>>>>>>>> thing two different ways.
Furthermore I say there are "canonical proofs" of inductive >>>>>>>>> sorts that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical >>>>>>>> proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs >>>>>>>>> of what otherwise is flawed, or for hard constructivist realist >>>>>>>>> structuralist model theorists: not-theories (examples of wrong). >>>>>>>>>
Induction and counter-induction contradict each other, it's simple, >>>>>>> it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog?
That would be dishonest.
No, pointing out that you are worng about Prolog when you are wrong
about Prolog is never dishohest.
That is correct Prolog and that is the
result of the correct run of correct Prolog.
Irrelevant. Nobody claimed there be Prolog errors in your queries.
Implying that I am wrong about Prolog without
pointing out any actual mistake is also DISHONEST.
How did Ross FInlayson imply that you were wrong about Prolog?
On 6/20/2026 9:48 PM, olcott wrote:[...]
Go fuck off.
In other words, you know this line of questioning will prove you wrong
and you can't handle it.
This constitutes your admission that Disjunction introduction is valid.
On 6/20/2026 9:48 PM, olcott wrote:
On 6/20/2026 8:38 PM, dbush wrote:
On 6/20/2026 9:32 PM, olcott wrote:
On 6/20/2026 8:28 PM, dbush wrote:
On 6/20/2026 9:06 PM, olcott wrote:
On 6/20/2026 7:29 PM, dbush wrote:
On 6/20/2026 8:26 PM, olcott wrote:
On 6/20/2026 7:11 PM, dbush wrote:
On 6/20/2026 6:26 PM, olcott wrote:
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the >>>>>>>>>>>>> following statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore >>>>>>>>>>> that disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"re?" disjunctions.
Then let's take this step-by-step.
Step 1: establish a true statement:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
That has been agreed.
Step 2: do you believe the following statement is true or
false, and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
OK so going step by step is fine with me.
1) P reo -4P-a-a-a // Premise
2) P-a-a-a-a-a-a-a-a-a // Conjunction elimination
3) -4P-a-a-a-a-a-a-a // Conjunction elimination
4) P re? Q-a-a-a-a-a // Disjunction introduction
5) Q-a-a-a-a-a-a-a-a-a // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
We ended up with Q only because we were allowed
to insert Q from out of nowhere in the inference
chain that started with P reo -4P.
I didn't ask about those steps.-a I asked if you believe the
following statement is true or false, and how do you come to that >>>>>>> conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
P = "Earth is the third planet from the sun."
Q = "The moon is made of green cheese."
We determine that P is true on the basis empirical facts.
We determine that Q is false on the basis empirical facts.
Is P re? Q true? Yes.
So you agree that because P is true and Q is false, the condition
"at least one of the following" is met.
Next step:
Do you believe the following statement is true or false, and how do >>>>> you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench. >>>>> --------------------------------------
Clearly just head games. GFO with these head games
I promise you I am going somewhere with this, and this is no head
game. But we must take things one small step at a time.
So I'll ask again:
Do you believe the following natural language statement is true or
false, and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench.
--------------------------------------
Go fuck off.
In other words, you know this line of questioning will prove you wrong
and you can't handle it.
This constitutes your admission that Disjunction introduction is valid.
On 6/20/2026 9:48 PM, olcott wrote:
On 6/20/2026 8:38 PM, dbush wrote:
On 6/20/2026 9:32 PM, olcott wrote:
On 6/20/2026 8:28 PM, dbush wrote:
On 6/20/2026 9:06 PM, olcott wrote:
On 6/20/2026 7:29 PM, dbush wrote:
On 6/20/2026 8:26 PM, olcott wrote:
On 6/20/2026 7:11 PM, dbush wrote:
On 6/20/2026 6:26 PM, olcott wrote:
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the >>>>>>>>>>>>> following statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore >>>>>>>>>>> that disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"re?" disjunctions.
Then let's take this step-by-step.
Step 1: establish a true statement:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
That has been agreed.
Step 2: do you believe the following statement is true or
false, and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
OK so going step by step is fine with me.
1) P reo -4P-a-a-a // Premise
2) P-a-a-a-a-a-a-a-a-a // Conjunction elimination
3) -4P-a-a-a-a-a-a-a // Conjunction elimination
4) P re? Q-a-a-a-a-a // Disjunction introduction
5) Q-a-a-a-a-a-a-a-a-a // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
We ended up with Q only because we were allowed
to insert Q from out of nowhere in the inference
chain that started with P reo -4P.
I didn't ask about those steps.-a I asked if you believe the
following statement is true or false, and how do you come to that >>>>>>> conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
P = "Earth is the third planet from the sun."
Q = "The moon is made of green cheese."
We determine that P is true on the basis empirical facts.
We determine that Q is false on the basis empirical facts.
Is P re? Q true? Yes.
So you agree that because P is true and Q is false, the condition
"at least one of the following" is met.
Next step:
Do you believe the following statement is true or false, and how do >>>>> you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench. >>>>> --------------------------------------
Clearly just head games. GFO with these head games
I promise you I am going somewhere with this, and this is no head
game. But we must take things one small step at a time.
So I'll ask again:
Do you believe the following natural language statement is true or
false, and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench.
--------------------------------------
Go fuck off.
In other words, you know this line of questioning will prove you wrong
and you can't handle it.
This constitutes your admission that Disjunction introduction is valid.
On 6/25/2026 2:09 AM, Mikko wrote:
On 24/06/2026 23:19, olcott wrote:
On 6/24/2026 3:23 AM, Mikko wrote:
On 23/06/2026 17:29, olcott wrote:
On 6/23/2026 12:39 AM, Mikko wrote:
On 22/06/2026 16:13, olcott wrote:
On 6/22/2026 2:13 AM, Mikko wrote:
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:That only means that your DD is not a strictly confoming C >>>>>>>>>> program.
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson >>>>>>>>>>>>>>>>>>>> Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>>Whereas you are stuck to your own incoherent views and >>>>>>>>>>>>>>>>>> reject
alternative views out-of-hand without review. >>>>>>>>>>>>>>>>
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>>>> look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>> semantics/
I've spent a couple of hours reading that web page.-a It >>>>>>>>>>>>>>>> is abstract in
the extreme.-a One thing is utterly clear: its level of >>>>>>>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>>>> Olcott, who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with >>>>>>>>>>>>>> irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof >>>>>>>>>>>>>> by contradiction. The LP isn't a contradiction; it's a >>>>>>>>>>>>>> paradox. The two are different things. A contradiction is >>>>>>>>>>>>>> a statement which is necessarily false. A paradox is a >>>>>>>>>>>>>> statement to which no truth value can be consistently >>>>>>>>>>>>>> assigned.
Andr|-
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting >>>>>>>>>>>> problem proof, Godel's proof, and Tarski's proof, each of >>>>>>>>>>>> which you've been attempting (and failing) to refute for years. >>>>>>>>>>>>
Proof Theoretic Semantics halt prover HHH correctly determines >>>>>>>>>>> that its input DD is ungrounded in its atomic base according >>>>>>>>>>> to the operational semantics of the C programming language. >>>>>>>>>>
The exact operational semantics of C conclusively
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational
semantics
do not fully specify the behaviour of DD. In order to prove that DD >>>>>>>> halts you also need additional operational spemantics provided >>>>>>>> by the
C implementation you have used. When DD iss executed in that
environment
it halts, which is sufficient to prove that in that environment DD >>>>>>>> halts. In some other environment its execution might be aborted >>>>>>>> or it
could be rejected by the compiler.
Proof Theoretic Semantics provides the correct way
to handle pathological self-reference (PSR).
This would be dead obvious if you were not totally
clueless about Prolog.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Nice to see that you don't disagree.
Not nice to see that everyone continues to
totally ignore my best validation of proof
theoretic semantics.
Unfortunately that is unavoidable as long as your best presentation
of the validation and of your version of proof theoretic semantics
are not good enough.
Is is dead obvious and completely clear example
of the final resolution of the Liar Paradox using
generic proof theoretic semantics implemented in
Prolog.
Except that it is not final -- others will continue presenting
different views about it -- and not even a resolution.
If others did not reject mine out-of-hand
without review they could understand that
it is final.
On 6/25/2026 2:14 AM, Mikko wrote:
On 24/06/2026 23:23, olcott wrote:(a) Extracting atomic facts, would be the hardest part,
On 6/24/2026 4:45 AM, Mikko wrote:
On 23/06/2026 17:40, olcott wrote:
On 6/23/2026 12:49 AM, Mikko wrote:
On 22/06/2026 18:16, olcott wrote:It can be reasonably approximated pretty quickly.
On 6/22/2026 2:46 AM, Mikko wrote:
On 22/06/2026 03:44, olcott wrote:
On 6/21/2026 7:32 PM, phoenix wrote:It is fairly simple to build a system of essentially infallible >>>>>>>> reasoning that never errs even when it doesn't have all the
olcott wrote:It is not that they never admit defeat.
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat? >>>>>>>>>
olcott wrote:
On 6/21/2026 3:18 PM, Andr|- G. Isaak wrote:Lastly, and why should we care? Please answer this and other >>>>>>>>>>>> questions presented.
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson >>>>>>>>>>>>>>>>>>>>> Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>Whereas you are stuck to your own incoherent views >>>>>>>>>>>>>>>>>>> and reject
alternative views out-of-hand without review. >>>>>>>>>>>>>>>
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>>>>> look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>> semantics/
I've spent a couple of hours reading that web page.-a It >>>>>>>>>>>>>>>>> is abstract in
the extreme.-a One thing is utterly clear: its level of >>>>>>>>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>>>>> Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I >>>>>>>>>>>>>>>>> can't be bothered
to read it any further.-a If it actually says anything >>>>>>>>>>>>>>>>> at all, that
something is heavily disguised.-a From it's "Conclusion >>>>>>>>>>>>>>>>> and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically >>>>>>>>>>>>>>>>> exclusively been
| occupied with logical constants. Logical constants >>>>>>>>>>>>>>>>> play a central role
| in reasoning and inference, but are definitely not >>>>>>>>>>>>>>>>> the exclusive, and
| perhaps not even the most typical sort of entities >>>>>>>>>>>>>>>>> that can be defined
| inferentially. A framework is needed that deals with >>>>>>>>>>>>>>>>> inferential
| definitions in a wider sense and covers both logical >>>>>>>>>>>>>>>>> and extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is >>>>>>>>>>>>>>>> currently and in the
near future not useful as making it useful requires much >>>>>>>>>>>>>>>> time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be >>>>>>>>>>>>>>> useful for? What it
ought to be able to do that standard logic fails at? >>>>>>>>>>>>>>> Maybe Andr|- could
elucidate.-a He seems to have a better grasp of it than >>>>>>>>>>>>>>> anybody else here.
I doubt my understanding of PTS is any better than yours. >>>>>>>>>>>>>> I basically only know what is presented in the Stanford >>>>>>>>>>>>>> Encyclopedia article (which you correctly point out is not >>>>>>>>>>>>>> exactly aimed at beginners) and the Wikipedia article. >>>>>>>>>>>>>> What I am quite certain of, however, is that Olcott lacks >>>>>>>>>>>>>> any understanding of what PTS actually says as he's made a >>>>>>>>>>>>>> variety of fairly absurd claims regarding it (for example, >>>>>>>>>>>>>> that PTS claims that unproven propositions are
'meaningless' or that the goal of PTS is to completely >>>>>>>>>>>>>> overthrow standard truth- theoretic semantics).
Andr|-
-a-a Proof-theoretic semantics is an alternative to
-a-a truth-condition semantics. It is based on the
-a-a fundamental assumption that the central notion
-a-a in terms of which meanings are assigned to certain >>>>>>>>>>>>> -a-a expressions of our language, in particular to
-a-a logical constants, is that of proof rather than >>>>>>>>>>>>> -a-a truth. In this sense proof-theoretic semantics
-a-a is semantics in terms of proof.
-a-a https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>> semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
It is that that have a system of essentially infallible reasoning >>>>>>>>> that never errs as long as it has all the relevant information. >>>>>>>>
relevant information. The real problem is to construct a system >>>>>>>> that tells something interesting instead of just different
presentations of the same already known facts.
It will have the exhaustively complete list of
every atomic fact of general knowledge of the
actual world.
That is impossible. By the time you have all facts of general
knowledge
in your system the general knowledge has grown to inlude more facts. >>>>>
We start with all of the textbooks.
That is a lot of reading, though those for the same topic area tend
to say the same, and the old ones add very little to the new ones,
mainly some now obsolete technology.
It would not be too much reading for LLMs.
It could start with all of the latest textbooks
for all of the fields. Some of these latest
textbooks may be hundreds of years old for
fields that have become obsolete.
Perhaps that apprach should be tried. The problem involves extracting
atomic facts, detecting repeated facts, and encoding facts for the
inference system.
yet not too hard.
(b) Detecting repeated facts, string comparison.
(c) Encoding facts, CycL
On 6/25/2026 2:18 AM, Mikko wrote:
On 24/06/2026 23:25, olcott wrote:
On 6/24/2026 4:52 AM, Mikko wrote:
On 23/06/2026 17:47, olcott wrote:
On 6/23/2026 12:55 AM, Mikko wrote:
On 22/06/2026 15:09, olcott wrote:
On 6/22/2026 1:41 AM, Mikko wrote:
On 22/06/2026 02:58, olcott wrote:
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>>>>> alternative views out-of-hand without review
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>> look into proof theoretic semantics.
At different times you have expressed different opinions, which >>>>>>>>>>>> sometimes have been incompatible. But you have never clearly >>>>>>>>>>>> retracted your earlier opitions that conflict with your present >>>>>>>>>>>> ones.
All of the ideas that I have ever had about these things >>>>>>>>>>> are now under the Proof Theoretic Semantics category.
These ideas have evolved over time, yet their essence
has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a >>>>>>>>>> publishable
(or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> human >>>>>>>>> being on the face of the Earth could understand
me I could not publish.
As far as I have seen, all interesting content in those articles >>>>>>>> that have any is or depends on claims that should be proven but >>>>>>>> aren't.
They are proven in Proof Theoretic Semantics
An aricle is not publishable unless it either contains the proof or >>>>>> has a pointer to an olready published proof.
Only now after 28 years am I acquiring the lingua Franca
terms-of-the-art of proof theoretic semantics such that
I can anchor my ideas in the foundational work of the
most respected authors in the field.
My issue with you guys is that you only spend 1%
of your concentration understanding me and the other
99% trying to artificially contrive some baseless
rebuttal.
THat "baseless" is false but otherwise, what is wrong is more
important than what is right. Of one ignores what is right one
mai fail to achieve what one could, but if one believs what is
wrong one may achieve a disaseter.
Proof-theoretic semantics is an alternative to truth-condition
semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
So far no one has even acknowledged that PTS is an alternative
to truth-conditional semantics. Several people have seemed
to same that no alternative can possibly exist.
You have not shown that there is any need for any alternative semantics.
With dangerous lies that can destroy Democracy
and kill the planet with climate change having
an ultimate arbiter of truth would be useful.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>You can find any number of terms.-a That doesn't mean >>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS G||del 1931 >>>>>>>>>>>>> incompleteness
fails.
I don't believe you.-a You have no respect for or
understanding of the
truth.-a If you really want to persuade anybody that PTS >>>>>>>>>>>> somehow causes
G||del's theorem not to hold, then cite an academic expert >>>>>>>>>>>> who'll have
some credibility.
If they are mere gibberish words to you then you will not >>>>>>>>>>>>> understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>> certainly don't
understand G||del's Theorem, neither the theorem itself nor >>>>>>>>>>>> any proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only >>>>>>>>>> by you, and it is one which you have never explicitly defined, >>>>>>>>>> so the fault here certainly doesn't lie with Alan. It's
certainly not a 'verified fact' when you haven't even
adequately explained what it is that you mean.
All of knowledge expressed in language is structured as a tree >>>>>>>>> of semantic relations specified syntactically between finite >>>>>>>>> strings.
What makes you believe semantic relations that can be structured as >>>>>>>> a tree are sufficient to contain all knowledge that is exressed in >>>>>>>> some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
On 6/25/2026 2:29 AM, Mikko wrote:
On 25/06/2026 00:33, olcott wrote:
On 6/24/2026 5:13 AM, Mikko wrote:
On 23/06/2026 21:20, olcott wrote:
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>> On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>> On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again.-a No reputable >>>>>>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things.-a If Dag >>>>>>>>>>>>>>>>>> Prawitz
really
did
"agree" (with whom?) that G||del's sentence G is not >>>>>>>>>>>>>>>>>> true in
Peano
Arithmetic, then produce a citation for this.
He never gets to G||del. He essentially says unprovable >>>>>>>>>>>>>>>>> means untrue all the time for everything within his >>>>>>>>>>>>>>>>> own Theory of Grounds of strict Proof Theoretic Semantics. >>>>>>>>>>>>>>You won't understand it, but that _is_ essentially G||del's >>>>>>>>>>>>>>>> Incompleteness
Theorem.-a It is a statement that any sufficiently powerful >>>>>>>>>>>>>>>> system can
express true things it can't prove.-a So Dag Prawitz, had >>>>>>>>>>>>>>>> he been
saying
the things you falsely attributed to him, would >>>>>>>>>>>>>>>> certainly have
"got" to
G||del, and would have understood full well what he was >>>>>>>>>>>>>>>> saying.
You did not pay close enough attention to my exact words. >>>>>>>>>>>>>>I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag >>>>>>>>>>>> Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz >>>>>>>>>>>> doesn't
say",
then looking a bit into his tremendous volume of works, >>>>>>>>>>>> he talks about "natural deduction" then specifically an >>>>>>>>>>>> "inverse
principle" so I think these are key aspects of fundamental >>>>>>>>>>>> logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself, >>>>>>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to generate >>>>>>>>>>>> new ad-
missible rules within a certain syntactic context. Some >>>>>>>>>>>> N4Ufteen years
later, the idea was taken up by Dag Prawitz to devise a >>>>>>>>>>>> strategy of
normalization for natural deduction calculi (this being an >>>>>>>>>>>> analogue of
GentzenrCOs cut-elimination theorem for sequent calculi). Later, >>>>>>>>>>>> Prawitz
used the inversion principle again, attributing it with a >>>>>>>>>>>> semantic
role.
Still working in natural deduction calculi, he formulated a >>>>>>>>>>>> general
type
of schematic Introduction rules to be matchedrCothanks to the >>>>>>>>>>>> idea
supporting the inversion principle rCo by a corresponding general >>>>>>>>>>>> schematic Elimination rule. This was an attempt to provide a >>>>>>>>>>>> solution to
the problem suggested by the often quoted note of Gentzen. >>>>>>>>>>>> According to
Gentzen rCLit should be possible to display the elimination >>>>>>>>>>>> rules as
unique functions of the corresponding introduction rules on the >>>>>>>>>>>> basis of
certain requirements.rCY Many people have since worked on this >>>>>>>>>>>> topic,
which can be appropriately seen as the birthplace of what >>>>>>>>>>>> are now
referred to as rCLgeneral elimination rulesrCY, recently studied >>>>>>>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace >>>>>>>>>>>> the main
threads of this chapter of proof-theoretical investigation, >>>>>>>>>>>> using
LorenzenrCOs original framework as a general guide"
Hm, "general elimination rules", seem derivable from De >>>>>>>>>>>> Morgan's
laws,
and that being the usual account of naive deductive
analysis, then
since
"natural deduction", which here is held as part of the theory >>>>>>>>>>>> since it's naturally logical, then has for Gentzen that besides >>>>>>>>>>>> Kripke
afterward there's also Sheffer and Chwistek before, and >>>>>>>>>>>> instead of
Montague for semantics there's Herbrand for semantics, so, >>>>>>>>>>>> what to do
about "inversion principle" is here that the thea-theory has >>>>>>>>>>>> that
it's
what subsumes "non-contradiction principle", here hoping >>>>>>>>>>>> that the
interpretation aligns and thusly that "principle of inversion" >>>>>>>>>>>> wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334 >>>>>>>>>>>>
https://www.strandbooks.com/natural-deduction-a-proof- >>>>>>>>>>>> theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the
foundation of
most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a >>>>>>>>>>>> principle of
thorough reason as subsuming principles of non-contradiction >>>>>>>>>>>> and what
suffices, so, I'll be curious then about what to make of >>>>>>>>>>>> Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old >>>>>>>>>>>> as the
oldest account of Western philosophy like Heraclitus with dual >>>>>>>>>>>> monism.
In fact by definition it's about the most basic aspect of >>>>>>>>>>>> contemplation
and deliberation in abstraction of looking at both sides of >>>>>>>>>>>> issues
and
resolving inductive impasses with analytical bridges after >>>>>>>>>>>> complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one >>>>>>>>>>>> of the
characteristic features of Gentzen's intuitionistic natural >>>>>>>>>>>> deduction.
In the literature on proof-theoretic semantics, this
principle is
often
coupled with another that is called the recovery principle. By >>>>>>>>>>>> adopting
the Computational Ludics framework, we reformulate these >>>>>>>>>>>> principles
into
one and the same condition, which we call the harmony >>>>>>>>>>>> condition. We
show
that this reformulation allows us to reveal two intuitive ideas >>>>>>>>>>>> standing
behind these principles: the idea of "containment" present >>>>>>>>>>>> in the
inversion principle, and the idea that the recovery
principle is the
"converse" of the inversion principle. We also formulate two >>>>>>>>>>>> other
conditions in the Computational Ludics framework, and we >>>>>>>>>>>> show that
each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and >>>>>>>>>>>> knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, >>>>>>>>>>>> proof-theoretic semantics rests on the idea that we know the >>>>>>>>>>>> meaning of
a compound sentence when we know what counts as a canonical >>>>>>>>>>>> proof of
it.
And if proofs are formalised within the framework of natural >>>>>>>>>>>> deduction,
then a canonical proof of a sentence A is nothing but a closed >>>>>>>>>>>> derivation ending with an introduction rule of the main >>>>>>>>>>>> connective
of A."
The "canonical proofs" are not unique, in any system strong >>>>>>>>>>>> enough
to make for infinitary reasoning and super-classical results >>>>>>>>>>>> requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6 >>>>>>>>>>> That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches >>>>>>>>>>> Thomas Piecha & Peter Schroeder-Heister do this same sort of >>>>>>>>>>> thing two different ways.
Furthermore I say there are "canonical proofs" of inductive >>>>>>>>>> sorts that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical >>>>>>>>> proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make >>>>>>>>>> repairs
of what otherwise is flawed, or for hard constructivist realist >>>>>>>>>> structuralist model theorists: not-theories (examples of wrong). >>>>>>>>>>
Induction and counter-induction contradict each other, it's simple, >>>>>>>> it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog?
That would be dishonest.
No, pointing out that you are worng about Prolog when you are wrong
about Prolog is never dishohest.
That is correct Prolog and that is the
result of the correct run of correct Prolog.
Irrelevant. Nobody claimed there be Prolog errors in your queries.
Implying that I am wrong about Prolog without
pointing out any actual mistake is also DISHONEST.
How did Ross FInlayson imply that you were wrong about Prolog?
If an error is claimed then it must be specifically
pointed out otherwise the clam of error is dishonest.
On 25/06/2026 16:43, olcott wrote:
On 6/25/2026 2:09 AM, Mikko wrote:
On 24/06/2026 23:19, olcott wrote:
On 6/24/2026 3:23 AM, Mikko wrote:
On 23/06/2026 17:29, olcott wrote:
On 6/23/2026 12:39 AM, Mikko wrote:
On 22/06/2026 16:13, olcott wrote:
On 6/22/2026 2:13 AM, Mikko wrote:
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:That only means that your DD is not a strictly confoming C >>>>>>>>>>> program.
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson >>>>>>>>>>>>>>>>>>>>> Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>>>Whereas you are stuck to your own incoherent views >>>>>>>>>>>>>>>>>>> and reject
alternative views out-of-hand without review. >>>>>>>>>>>>>>>>>
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>>>>> look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>> semantics/
I've spent a couple of hours reading that web page.-a It >>>>>>>>>>>>>>>>> is abstract in
the extreme.-a One thing is utterly clear: its level of >>>>>>>>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>>>>> Olcott, who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with >>>>>>>>>>>>>>> irrelevancy.
The Liar's Paradox has absolutely nothing to do with >>>>>>>>>>>>>>> proof by contradiction. The LP isn't a contradiction; >>>>>>>>>>>>>>> it's a paradox. The two are different things. A >>>>>>>>>>>>>>> contradiction is a statement which is necessarily false. >>>>>>>>>>>>>>> A paradox is a statement to which no truth value can be >>>>>>>>>>>>>>> consistently assigned.
Andr|-
Then I have never spoken of anything where proof by >>>>>>>>>>>>>> contradiction applies,
False, as that is exactly the method uses by the halting >>>>>>>>>>>>> problem proof, Godel's proof, and Tarski's proof, each of >>>>>>>>>>>>> which you've been attempting (and failing) to refute for >>>>>>>>>>>>> years.
Proof Theoretic Semantics halt prover HHH correctly determines >>>>>>>>>>>> that its input DD is ungrounded in its atomic base according >>>>>>>>>>>> to the operational semantics of the C programming language. >>>>>>>>>>>
The exact operational semantics of C conclusively
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational >>>>>>>>> semantics
do not fully specify the behaviour of DD. In order to prove >>>>>>>>> that DD
halts you also need additional operational spemantics provided >>>>>>>>> by the
C implementation you have used. When DD iss executed in that >>>>>>>>> environment
it halts, which is sufficient to prove that in that environment DD >>>>>>>>> halts. In some other environment its execution might be aborted >>>>>>>>> or it
could be rejected by the compiler.
Proof Theoretic Semantics provides the correct way
to handle pathological self-reference (PSR).
This would be dead obvious if you were not totally
clueless about Prolog.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Nice to see that you don't disagree.
Not nice to see that everyone continues to
totally ignore my best validation of proof
theoretic semantics.
Unfortunately that is unavoidable as long as your best presentation
of the validation and of your version of proof theoretic semantics
are not good enough.
Is is dead obvious and completely clear example
of the final resolution of the Liar Paradox using
generic proof theoretic semantics implemented in
Prolog.
Except that it is not final -- others will continue presenting
different views about it -- and not even a resolution.
If others did not reject mine out-of-hand
without review they could understand that
it is final.
Even those who think your resolution is the best there can be should understand that there are others who don't shate that opinion.
On 25/06/2026 16:47, olcott wrote:
On 6/25/2026 2:14 AM, Mikko wrote:
On 24/06/2026 23:23, olcott wrote:(a) Extracting atomic facts, would be the hardest part,
On 6/24/2026 4:45 AM, Mikko wrote:
On 23/06/2026 17:40, olcott wrote:
On 6/23/2026 12:49 AM, Mikko wrote:
On 22/06/2026 18:16, olcott wrote:It can be reasonably approximated pretty quickly.
On 6/22/2026 2:46 AM, Mikko wrote:
On 22/06/2026 03:44, olcott wrote:
On 6/21/2026 7:32 PM, phoenix wrote:It is fairly simple to build a system of essentially infallible >>>>>>>>> reasoning that never errs even when it doesn't have all the
olcott wrote:It is not that they never admit defeat.
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat? >>>>>>>>>>
olcott wrote:
On 6/21/2026 3:18 PM, Andr|- G. Isaak wrote:Lastly, and why should we care? Please answer this and >>>>>>>>>>>>> other questions presented.
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> https://www.youtube.com/@rossfinlayson >>>>>>>>>>>>>>>>>>>>>> Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof- >>>>>>>>>>>>>>>>>>>>>> theoretic- semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>>Whereas you are stuck to your own incoherent views >>>>>>>>>>>>>>>>>>>> and reject
alternative views out-of-hand without review. >>>>>>>>>>>>>>>>
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>>>>>> look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>> semantics/
I've spent a couple of hours reading that web page. >>>>>>>>>>>>>>>>>> It is abstract in
the extreme.-a One thing is utterly clear: its level of >>>>>>>>>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>>>>>> Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I >>>>>>>>>>>>>>>>>> can't be bothered
to read it any further.-a If it actually says anything >>>>>>>>>>>>>>>>>> at all, that
something is heavily disguised.-a From it's "Conclusion >>>>>>>>>>>>>>>>>> and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically >>>>>>>>>>>>>>>>>> exclusively been
| occupied with logical constants. Logical constants >>>>>>>>>>>>>>>>>> play a central role
| in reasoning and inference, but are definitely not >>>>>>>>>>>>>>>>>> the exclusive, and
| perhaps not even the most typical sort of entities >>>>>>>>>>>>>>>>>> that can be defined
| inferentially. A framework is needed that deals with >>>>>>>>>>>>>>>>>> inferential
| definitions in a wider sense and covers both logical >>>>>>>>>>>>>>>>>> and extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is >>>>>>>>>>>>>>>>> currently and in the
near future not useful as making it useful requires >>>>>>>>>>>>>>>>> much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be >>>>>>>>>>>>>>>> useful for? What it
ought to be able to do that standard logic fails at? >>>>>>>>>>>>>>>> Maybe Andr|- could
elucidate.-a He seems to have a better grasp of it than >>>>>>>>>>>>>>>> anybody else here.
I doubt my understanding of PTS is any better than yours. >>>>>>>>>>>>>>> I basically only know what is presented in the Stanford >>>>>>>>>>>>>>> Encyclopedia article (which you correctly point out is >>>>>>>>>>>>>>> not exactly aimed at beginners) and the Wikipedia >>>>>>>>>>>>>>> article. What I am quite certain of, however, is that >>>>>>>>>>>>>>> Olcott lacks any understanding of what PTS actually says >>>>>>>>>>>>>>> as he's made a variety of fairly absurd claims regarding >>>>>>>>>>>>>>> it (for example, that PTS claims that unproven
propositions are 'meaningless' or that the goal of PTS is >>>>>>>>>>>>>>> to completely overthrow standard truth- theoretic >>>>>>>>>>>>>>> semantics).
Andr|-
-a-a Proof-theoretic semantics is an alternative to >>>>>>>>>>>>>> -a-a truth-condition semantics. It is based on the >>>>>>>>>>>>>> -a-a fundamental assumption that the central notion >>>>>>>>>>>>>> -a-a in terms of which meanings are assigned to certain >>>>>>>>>>>>>> -a-a expressions of our language, in particular to >>>>>>>>>>>>>> -a-a logical constants, is that of proof rather than >>>>>>>>>>>>>> -a-a truth. In this sense proof-theoretic semantics >>>>>>>>>>>>>> -a-a is semantics in terms of proof.
-a-a https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>> semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof >>>>>>>>>>>>>> theoretic semantics?
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time. >>>>>>>>>>>>
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
It is that that have a system of essentially infallible reasoning >>>>>>>>>> that never errs as long as it has all the relevant information. >>>>>>>>>
relevant information. The real problem is to construct a system >>>>>>>>> that tells something interesting instead of just different
presentations of the same already known facts.
It will have the exhaustively complete list of
every atomic fact of general knowledge of the
actual world.
That is impossible. By the time you have all facts of general
knowledge
in your system the general knowledge has grown to inlude more facts. >>>>>>
We start with all of the textbooks.
That is a lot of reading, though those for the same topic area tend
to say the same, and the old ones add very little to the new ones,
mainly some now obsolete technology.
It would not be too much reading for LLMs.
It could start with all of the latest textbooks
for all of the fields. Some of these latest
textbooks may be hundreds of years old for
fields that have become obsolete.
Perhaps that apprach should be tried. The problem involves extracting
atomic facts, detecting repeated facts, and encoding facts for the
inference system.
yet not too hard.
(b) Detecting repeated facts, string comparison.
(c) Encoding facts, CycL
The encoding must be normalized as much as possible in order to reduce repetition to a string comparison. That is not a trivial problem if one
wants a total or nearly total prevention of repetition.
On 25/06/2026 16:58, olcott wrote:
On 6/25/2026 2:18 AM, Mikko wrote:
On 24/06/2026 23:25, olcott wrote:
On 6/24/2026 4:52 AM, Mikko wrote:
On 23/06/2026 17:47, olcott wrote:
On 6/23/2026 12:55 AM, Mikko wrote:
On 22/06/2026 15:09, olcott wrote:
On 6/22/2026 1:41 AM, Mikko wrote:
On 22/06/2026 02:58, olcott wrote:
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:Whereas you are stuck to your own incoherent views and >>>>>>>>>>>>>>> reject
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>
alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>> look into proof theoretic semantics.
At different times you have expressed different opinions, >>>>>>>>>>>>> which
sometimes have been incompatible. But you have never clearly >>>>>>>>>>>>> retracted your earlier opitions that conflict with your >>>>>>>>>>>>> present
ones.
All of the ideas that I have ever had about these things >>>>>>>>>>>> are now under the Proof Theoretic Semantics category.
These ideas have evolved over time, yet their essence
has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a >>>>>>>>>>> publishable
(or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> human >>>>>>>>>> being on the face of the Earth could understand
me I could not publish.
As far as I have seen, all interesting content in those articles >>>>>>>>> that have any is or depends on claims that should be proven but >>>>>>>>> aren't.
They are proven in Proof Theoretic Semantics
An aricle is not publishable unless it either contains the proof or >>>>>>> has a pointer to an olready published proof.
Only now after 28 years am I acquiring the lingua Franca
terms-of-the-art of proof theoretic semantics such that
I can anchor my ideas in the foundational work of the
most respected authors in the field.
My issue with you guys is that you only spend 1%
of your concentration understanding me and the other
99% trying to artificially contrive some baseless
rebuttal.
THat "baseless" is false but otherwise, what is wrong is more
important than what is right. Of one ignores what is right one
mai fail to achieve what one could, but if one believs what is
wrong one may achieve a disaseter.
Proof-theoretic semantics is an alternative to truth-condition
semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
So far no one has even acknowledged that PTS is an alternative
to truth-conditional semantics. Several people have seemed
to same that no alternative can possibly exist.
You have not shown that there is any need for any alternative semantics.
With dangerous lies that can destroy Democracy
and kill the planet with climate change having
an ultimate arbiter of truth would be useful.
Those who are able and willing to destroy democracy are able to provice
an ultimate arbiter of truth and usually do so. But they don't need any
proof theoretic semantics.
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>>You can find any number of terms.-a That doesn't mean >>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS G||del 1931 >>>>>>>>>>>>>> incompleteness
fails.
I don't believe you.-a You have no respect for or
understanding of the
truth.-a If you really want to persuade anybody that PTS >>>>>>>>>>>>> somehow causes
G||del's theorem not to hold, then cite an academic expert >>>>>>>>>>>>> who'll have
some credibility.
If they are mere gibberish words to you then you will not >>>>>>>>>>>>>> understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>>> certainly don't
understand G||del's Theorem, neither the theorem itself nor >>>>>>>>>>>>> any proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used >>>>>>>>>>> only by you, and it is one which you have never explicitly >>>>>>>>>>> defined, so the fault here certainly doesn't lie with Alan. >>>>>>>>>>> It's certainly not a 'verified fact' when you haven't even >>>>>>>>>>> adequately explained what it is that you mean.
All of knowledge expressed in language is structured as a tree >>>>>>>>>> of semantic relations specified syntactically between finite >>>>>>>>>> strings.
What makes you believe semantic relations that can be
structured as
a tree are sufficient to contain all knowledge that is exressed in >>>>>>>>> some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to >>>>>>> put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious
how switching to another semantics could improve it.
On 25/06/2026 19:16, olcott wrote:
On 6/25/2026 2:29 AM, Mikko wrote:
On 25/06/2026 00:33, olcott wrote:
On 6/24/2026 5:13 AM, Mikko wrote:
On 23/06/2026 21:20, olcott wrote:
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>> On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>> On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again.-a No reputable >>>>>>>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things.-a If Dag >>>>>>>>>>>>>>>>>>> Prawitz
really
did
"agree" (with whom?) that G||del's sentence G is not >>>>>>>>>>>>>>>>>>> true in
Peano
Arithmetic, then produce a citation for this. >>>>>>>>>>>>>>>
He never gets to G||del. He essentially says unprovable >>>>>>>>>>>>>>>>>> means untrue all the time for everything within his >>>>>>>>>>>>>>>>>> own Theory of Grounds of strict Proof Theoretic >>>>>>>>>>>>>>>>>> Semantics.
You won't understand it, but that _is_ essentially G||del's >>>>>>>>>>>>>>>>> Incompleteness
Theorem.-a It is a statement that any sufficiently powerful >>>>>>>>>>>>>>>>> system can
express true things it can't prove.-a So Dag Prawitz, >>>>>>>>>>>>>>>>> had he been
saying
the things you falsely attributed to him, would >>>>>>>>>>>>>>>>> certainly have
"got" to
G||del, and would have understood full well what he was >>>>>>>>>>>>>>>>> saying.
You did not pay close enough attention to my exact words. >>>>>>>>>>>>>>>I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag >>>>>>>>>>>>> Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz >>>>>>>>>>>>> doesn't
say",
then looking a bit into his tremendous volume of works, >>>>>>>>>>>>> he talks about "natural deduction" then specifically an >>>>>>>>>>>>> "inverse
principle" so I think these are key aspects of fundamental >>>>>>>>>>>>> logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself, >>>>>>>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to >>>>>>>>>>>>> generate
new ad-
missible rules within a certain syntactic context. Some >>>>>>>>>>>>> N4Ufteen years
later, the idea was taken up by Dag Prawitz to devise a >>>>>>>>>>>>> strategy of
normalization for natural deduction calculi (this being an >>>>>>>>>>>>> analogue of
GentzenrCOs cut-elimination theorem for sequent calculi). Later, >>>>>>>>>>>>> Prawitz
used the inversion principle again, attributing it with a >>>>>>>>>>>>> semantic
role.
Still working in natural deduction calculi, he formulated a >>>>>>>>>>>>> general
type
of schematic Introduction rules to be matchedrCothanks to the >>>>>>>>>>>>> idea
supporting the inversion principle rCo by a corresponding >>>>>>>>>>>>> general
schematic Elimination rule. This was an attempt to provide a >>>>>>>>>>>>> solution to
the problem suggested by the often quoted note of Gentzen. >>>>>>>>>>>>> According to
Gentzen rCLit should be possible to display the elimination >>>>>>>>>>>>> rules as
unique functions of the corresponding introduction rules on >>>>>>>>>>>>> the
basis of
certain requirements.rCY Many people have since worked on >>>>>>>>>>>>> this topic,
which can be appropriately seen as the birthplace of what >>>>>>>>>>>>> are now
referred to as rCLgeneral elimination rulesrCY, recently studied >>>>>>>>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace >>>>>>>>>>>>> the main
threads of this chapter of proof-theoretical investigation, >>>>>>>>>>>>> using
LorenzenrCOs original framework as a general guide"
Hm, "general elimination rules", seem derivable from De >>>>>>>>>>>>> Morgan's
laws,
and that being the usual account of naive deductive >>>>>>>>>>>>> analysis, then
since
"natural deduction", which here is held as part of the theory >>>>>>>>>>>>> since it's naturally logical, then has for Gentzen that >>>>>>>>>>>>> besides
Kripke
afterward there's also Sheffer and Chwistek before, and >>>>>>>>>>>>> instead of
Montague for semantics there's Herbrand for semantics, so, >>>>>>>>>>>>> what to do
about "inversion principle" is here that the thea-theory >>>>>>>>>>>>> has that
it's
what subsumes "non-contradiction principle", here hoping >>>>>>>>>>>>> that the
interpretation aligns and thusly that "principle of inversion" >>>>>>>>>>>>> wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334 >>>>>>>>>>>>>
https://www.strandbooks.com/natural-deduction-a-proof- >>>>>>>>>>>>> theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the >>>>>>>>>>>>> foundation of
most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a >>>>>>>>>>>>> principle of
thorough reason as subsuming principles of non-
contradiction and what
suffices, so, I'll be curious then about what to make of >>>>>>>>>>>>> Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old >>>>>>>>>>>>> as the
oldest account of Western philosophy like Heraclitus with dual >>>>>>>>>>>>> monism.
In fact by definition it's about the most basic aspect of >>>>>>>>>>>>> contemplation
and deliberation in abstraction of looking at both sides of >>>>>>>>>>>>> issues
and
resolving inductive impasses with analytical bridges after >>>>>>>>>>>>> complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as >>>>>>>>>>>>> one of the
characteristic features of Gentzen's intuitionistic natural >>>>>>>>>>>>> deduction.
In the literature on proof-theoretic semantics, this >>>>>>>>>>>>> principle is
often
coupled with another that is called the recovery principle. By >>>>>>>>>>>>> adopting
the Computational Ludics framework, we reformulate these >>>>>>>>>>>>> principles
into
one and the same condition, which we call the harmony >>>>>>>>>>>>> condition. We
show
that this reformulation allows us to reveal two intuitive >>>>>>>>>>>>> ideas
standing
behind these principles: the idea of "containment" present >>>>>>>>>>>>> in the
inversion principle, and the idea that the recovery >>>>>>>>>>>>> principle is the
"converse" of the inversion principle. We also formulate >>>>>>>>>>>>> two other
conditions in the Computational Ludics framework, and we >>>>>>>>>>>>> show that
each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and >>>>>>>>>>>>> knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, >>>>>>>>>>>>> proof-theoretic semantics rests on the idea that we know the >>>>>>>>>>>>> meaning of
a compound sentence when we know what counts as a canonical >>>>>>>>>>>>> proof of
it.
And if proofs are formalised within the framework of natural >>>>>>>>>>>>> deduction,
then a canonical proof of a sentence A is nothing but a closed >>>>>>>>>>>>> derivation ending with an introduction rule of the main >>>>>>>>>>>>> connective
of A."
The "canonical proofs" are not unique, in any system strong >>>>>>>>>>>>> enough
to make for infinitary reasoning and super-classical results >>>>>>>>>>>>> requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6 >>>>>>>>>>>> That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches >>>>>>>>>>>> Thomas Piecha & Peter Schroeder-Heister do this same sort of >>>>>>>>>>>> thing two different ways.
Furthermore I say there are "canonical proofs" of inductive >>>>>>>>>>> sorts that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical >>>>>>>>>> proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make >>>>>>>>>>> repairs
of what otherwise is flawed, or for hard constructivist realist >>>>>>>>>>> structuralist model theorists: not-theories (examples of wrong). >>>>>>>>>>>
Induction and counter-induction contradict each other, it's >>>>>>>>> simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog?
That would be dishonest.
No, pointing out that you are worng about Prolog when you are wrong
about Prolog is never dishohest.
That is correct Prolog and that is the
result of the correct run of correct Prolog.
Irrelevant. Nobody claimed there be Prolog errors in your queries.
Implying that I am wrong about Prolog without
pointing out any actual mistake is also DISHONEST.
How did Ross FInlayson imply that you were wrong about Prolog?
If an error is claimed then it must be specifically
pointed out otherwise the clam of error is dishonest.
Yet you claim that Ross Finlayson be dishonest without pointing
out what is dishonest in his words.
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>>>You can find any number of terms.-a That doesn't mean >>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS G||del 1931 >>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that PTS >>>>>>>>>>>>>> somehow causes
G||del's theorem not to hold, then cite an academic expert >>>>>>>>>>>>>> who'll have
some credibility.
If they are mere gibberish words to you then you will not >>>>>>>>>>>>>>> understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>>>> certainly don't
understand G||del's Theorem, neither the theorem itself nor >>>>>>>>>>>>>> any proof of
it.
in the atomic base of PA. That you do not understand >>>>>>>>>>>>> what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used >>>>>>>>>>>> only by you, and it is one which you have never explicitly >>>>>>>>>>>> defined, so the fault here certainly doesn't lie with Alan. >>>>>>>>>>>> It's certainly not a 'verified fact' when you haven't even >>>>>>>>>>>> adequately explained what it is that you mean.
All of knowledge expressed in language is structured as a >>>>>>>>>>> tree of semantic relations specified syntactically between >>>>>>>>>>> finite strings.
What makes you believe semantic relations that can be
structured as
a tree are sufficient to contain all knowledge that is
exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to >>>>>>>> put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>> what: "grounded in the atomic base" means is less
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>>>>You can find any number of terms.-a That doesn't mean >>>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS G||del 1931 >>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that PTS >>>>>>>>>>>>>>> somehow causes
G||del's theorem not to hold, then cite an academic expert >>>>>>>>>>>>>>> who'll have
some credibility.
If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>> not understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>>>>> certainly don't
understand G||del's Theorem, neither the theorem itself >>>>>>>>>>>>>>> nor any proof of
it.
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used >>>>>>>>>>>>> only by you, and it is one which you have never explicitly >>>>>>>>>>>>> defined, so the fault here certainly doesn't lie with Alan. >>>>>>>>>>>>> It's certainly not a 'verified fact' when you haven't even >>>>>>>>>>>>> adequately explained what it is that you mean.
All of knowledge expressed in language is structured as a >>>>>>>>>>>> tree of semantic relations specified syntactically between >>>>>>>>>>>> finite strings.
What makes you believe semantic relations that can be
structured as
a tree are sufficient to contain all knowledge that is
exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to >>>>>>>>> put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop >>>>>>> when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is equal to
its successor" has no meaning in Robinson Arithmetic.
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:All of knowledge expressed in language is structured as a >>>>>>>>>>>>> tree of semantic relations specified syntactically between >>>>>>>>>>>>> finite strings.
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>>>>>You can find any number of terms.-a That doesn't mean >>>>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS G||del 1931 >>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that PTS >>>>>>>>>>>>>>>> somehow causes
G||del's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>>> not understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>>>>>> certainly don't
understand G||del's Theorem, neither the theorem itself >>>>>>>>>>>>>>>> nor any proof of
it.
"grounded in the atomic base of PA" is an expression used >>>>>>>>>>>>>> only by you, and it is one which you have never explicitly >>>>>>>>>>>>>> defined, so the fault here certainly doesn't lie with >>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' when you >>>>>>>>>>>>>> haven't even adequately explained what it is that you mean. >>>>>>>>>>>>
What makes you believe semantic relations that can be >>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to >>>>>>>>>> put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop >>>>>>>> when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is equal to
its successor" has no meaning in Robinson Arithmetic.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
On 6/26/2026 9:45 AM, olcott wrote:
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>>>>>>You can find any number of terms.-a That doesn't mean >>>>>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS G||del 1931 >>>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that PTS >>>>>>>>>>>>>>>>> somehow causes
G||del's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>>>> not understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>>>>>>> certainly don't
understand G||del's Theorem, neither the theorem itself >>>>>>>>>>>>>>>>> nor any proof of
it.
"grounded in the atomic base of PA" is an expression used >>>>>>>>>>>>>>> only by you, and it is one which you have never >>>>>>>>>>>>>>> explicitly defined, so the fault here certainly doesn't >>>>>>>>>>>>>>> lie with Alan. It's certainly not a 'verified fact' when >>>>>>>>>>>>>>> you haven't even adequately explained what it is that you >>>>>>>>>>>>>>> mean.
All of knowledge expressed in language is structured as a >>>>>>>>>>>>>> tree of semantic relations specified syntactically between >>>>>>>>>>>>>> finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to >>>>>>>>>>> put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop >>>>>>>>> when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious >>>>> how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is equal
to its successor" has no meaning in Robinson Arithmetic.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
Then you agree that the above natural language sentence that is
semantically required to be either true or false has no meaning?
On 6/26/2026 8:57 AM, dbush wrote:
On 6/26/2026 9:45 AM, olcott wrote:
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms.-a That doesn't mean >>>>>>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS G||del 1931 >>>>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that >>>>>>>>>>>>>>>>>> PTS somehow causes
G||del's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>>>>> not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>> you certainly don't
understand G||del's Theorem, neither the theorem itself >>>>>>>>>>>>>>>>>> nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly doesn't >>>>>>>>>>>>>>>> lie with Alan. It's certainly not a 'verified fact' when >>>>>>>>>>>>>>>> you haven't even adequately explained what it is that >>>>>>>>>>>>>>>> you mean.
All of knowledge expressed in language is structured as a >>>>>>>>>>>>>>> tree of semantic relations specified syntactically >>>>>>>>>>>>>>> between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop >>>>>>>>>> when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious >>>>>> how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is equal
to its successor" has no meaning in Robinson Arithmetic.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
Then you agree that the above natural language sentence that is
semantically required to be either true or false has no meaning?
Your sentence would be what it always has been
a stipulated true sentence axiom.
On 6/26/2026 10:24 AM, olcott wrote:
On 6/26/2026 8:57 AM, dbush wrote:
On 6/26/2026 9:45 AM, olcott wrote:
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms.-a That doesn't >>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS G||del 1931 >>>>>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>> PTS somehow causes
G||del's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>> you certainly don't
understand G||del's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly doesn't >>>>>>>>>>>>>>>>> lie with Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>> when you haven't even adequately explained what it is >>>>>>>>>>>>>>>>> that you mean.
All of knowledge expressed in language is structured as >>>>>>>>>>>>>>>> a tree of semantic relations specified syntactically >>>>>>>>>>>>>>>> between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a >>>>>>>>>>> loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious >>>>>>> how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is equal >>>>> to its successor" has no meaning in Robinson Arithmetic.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
Then you agree that the above natural language sentence that is
semantically required to be either true or false has no meaning?
Your sentence would be what it always has been
a stipulated true sentence axiom.
False, as that statement is not one of the axioms of Robinson
arithmetic, but it is a statement in its language, and one that has
*only* an infinite connection to the axioms of that system.
By your logic, "no number is equal to its successor" has no meaning in Robinson arithmetic.
On 6/26/2026 11:08 AM, dbush wrote:
On 6/26/2026 10:24 AM, olcott wrote:
On 6/26/2026 8:57 AM, dbush wrote:
On 6/26/2026 9:45 AM, olcott wrote:
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms.-a That doesn't >>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS G||del >>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>>> PTS somehow causes
G||del's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>>> you certainly don't
understand G||del's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly >>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>> fact' when you haven't even adequately explained what >>>>>>>>>>>>>>>>>> it is that you mean.
All of knowledge expressed in language is structured as >>>>>>>>>>>>>>>>> a tree of semantic relations specified syntactically >>>>>>>>>>>>>>>>> between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a >>>>>>>>>>>> loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not
obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is
equal to its successor" has no meaning in Robinson Arithmetic.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
Then you agree that the above natural language sentence that is
semantically required to be either true or false has no meaning?
Your sentence would be what it always has been
a stipulated true sentence axiom.
False, as that statement is not one of the axioms of Robinson
arithmetic, but it is a statement in its language, and one that has
*only* an infinite connection to the axioms of that system.
By your logic, "no number is equal to its successor" has no meaning in
Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
On 6/26/2026 1:22 PM, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
On 6/26/2026 10:24 AM, olcott wrote:
On 6/26/2026 8:57 AM, dbush wrote:
On 6/26/2026 9:45 AM, olcott wrote:
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms.-a That doesn't >>>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS G||del >>>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>>>> PTS somehow causes
G||del's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>>>> you certainly don't
understand G||del's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly >>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>>> fact' when you haven't even adequately explained what >>>>>>>>>>>>>>>>>>> it is that you mean.
All of knowledge expressed in language is structured >>>>>>>>>>>>>>>>>> as a tree of semantic relations specified >>>>>>>>>>>>>>>>>> syntactically between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting stuck in >>>>>>>>>>>>> a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not >>>>>>>>> obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is
equal to its successor" has no meaning in Robinson Arithmetic.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
Then you agree that the above natural language sentence that is
semantically required to be either true or false has no meaning?
Your sentence would be what it always has been
a stipulated true sentence axiom.
False, as that statement is not one of the axioms of Robinson
arithmetic, but it is a statement in its language, and one that has
*only* an infinite connection to the axioms of that system.
By your logic, "no number is equal to its successor" has no meaning
in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
So you agree that Robinson arithmetic is incomplete.
On 6/26/2026 12:25 PM, dbush wrote:
On 6/26/2026 1:22 PM, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
On 6/26/2026 10:24 AM, olcott wrote:
On 6/26/2026 8:57 AM, dbush wrote:
On 6/26/2026 9:45 AM, olcott wrote:
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms.-a That doesn't >>>>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS G||del >>>>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody >>>>>>>>>>>>>>>>>>>>>> that PTS somehow causes
G||del's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, >>>>>>>>>>>>>>>>>>>>>> and you certainly don't
understand G||del's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not a >>>>>>>>>>>>>>>>>>>> 'verified fact' when you haven't even adequately >>>>>>>>>>>>>>>>>>>> explained what it is that you mean.
All of knowledge expressed in language is structured >>>>>>>>>>>>>>>>>>> as a tree of semantic relations specified >>>>>>>>>>>>>>>>>>> syntactically between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would >>>>>>>>>>>>>>>> one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting stuck in >>>>>>>>>>>>>> a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent >>>>>>>>>>>> loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>> PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability >>>>>>>>>>> or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not >>>>>>>>>> obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is >>>>>>>> equal to its successor" has no meaning in Robinson Arithmetic. >>>>>>>>
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
Then you agree that the above natural language sentence that is
semantically required to be either true or false has no meaning?
Your sentence would be what it always has been
a stipulated true sentence axiom.
False, as that statement is not one of the axioms of Robinson
arithmetic, but it is a statement in its language, and one that has
*only* an infinite connection to the axioms of that system.
By your logic, "no number is equal to its successor" has no meaning
in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
So you agree that Robinson arithmetic is incomplete.
It is as complete as it was designed to be.
On 6/26/2026 1:39 PM, olcott wrote:
On 6/26/2026 12:25 PM, dbush wrote:
On 6/26/2026 1:22 PM, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
On 6/26/2026 10:24 AM, olcott wrote:
On 6/26/2026 8:57 AM, dbush wrote:
On 6/26/2026 9:45 AM, olcott wrote:
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
All of knowledge expressed in language is structured >>>>>>>>>>>>>>>>>>>> as a tree of semantic relations specified >>>>>>>>>>>>>>>>>>>> syntactically between finite strings.On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms.-a That doesn't >>>>>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS G||del >>>>>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody >>>>>>>>>>>>>>>>>>>>>>> that PTS somehow causes
G||del's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, >>>>>>>>>>>>>>>>>>>>>>> and you certainly don't
understand G||del's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one which >>>>>>>>>>>>>>>>>>>>> you have never explicitly defined, so the fault >>>>>>>>>>>>>>>>>>>>> here certainly doesn't lie with Alan. It's >>>>>>>>>>>>>>>>>>>>> certainly not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>> even adequately explained what it is that you mean. >>>>>>>>>>>>>>>>>>>
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that >>>>>>>>>>>>>>>>>>> is exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would >>>>>>>>>>>>>>>>> one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting stuck >>>>>>>>>>>>>>> in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent >>>>>>>>>>>>> loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>> PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability >>>>>>>>>>>> or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not >>>>>>>>>>> obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is >>>>>>>>> equal to its successor" has no meaning in Robinson Arithmetic. >>>>>>>>>
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
Then you agree that the above natural language sentence that is >>>>>>> semantically required to be either true or false has no meaning? >>>>>>>
Your sentence would be what it always has been
a stipulated true sentence axiom.
False, as that statement is not one of the axioms of Robinson
arithmetic, but it is a statement in its language, and one that has >>>>> *only* an infinite connection to the axioms of that system.
By your logic, "no number is equal to its successor" has no meaning >>>>> in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
So you agree that Robinson arithmetic is incomplete.
It is as complete as it was designed to be.
There is no "designed to be".-a There are sentences in the language of Robinson arithmetic that are true but not provable,
therefore making the--
system incomplete, as you have just agreed, meaning that you agree that incompleteness exists.
On 6/26/2026 12:42 PM, dbush wrote:
On 6/26/2026 1:39 PM, olcott wrote:
On 6/26/2026 12:25 PM, dbush wrote:
On 6/26/2026 1:22 PM, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
On 6/26/2026 10:24 AM, olcott wrote:
On 6/26/2026 8:57 AM, dbush wrote:
On 6/26/2026 9:45 AM, olcott wrote:
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]What makes you believe semantic relations that can >>>>>>>>>>>>>>>>>>>> be structured as
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms.-a That >>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>> understanding them.
The above is the key reason why under PTS G||del >>>>>>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody >>>>>>>>>>>>>>>>>>>>>>>> that PTS somehow causes
G||del's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have
some credibility.
If they are mere gibberish words to you then >>>>>>>>>>>>>>>>>>>>>>>>> you will not understand.
You don't understand Proof-theoritic Semantics, >>>>>>>>>>>>>>>>>>>>>>>> and you certainly don't
understand G||del's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one which >>>>>>>>>>>>>>>>>>>>>> you have never explicitly defined, so the fault >>>>>>>>>>>>>>>>>>>>>> here certainly doesn't lie with Alan. It's >>>>>>>>>>>>>>>>>>>>>> certainly not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is that you mean. >>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge that >>>>>>>>>>>>>>>>>>>> is exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would >>>>>>>>>>>>>>>>>> one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting stuck >>>>>>>>>>>>>>>> in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent >>>>>>>>>>>>>> loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>
compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>> PTS just coherently connects the semantic meanings
expressed in language together into one coherent body >>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>> or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not >>>>>>>>>>>> obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is >>>>>>>>>> equal to its successor" has no meaning in Robinson Arithmetic. >>>>>>>>>>
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
Then you agree that the above natural language sentence that is >>>>>>>> semantically required to be either true or false has no meaning? >>>>>>>>
Your sentence would be what it always has been
a stipulated true sentence axiom.
False, as that statement is not one of the axioms of Robinson
arithmetic, but it is a statement in its language, and one that
has *only* an infinite connection to the axioms of that system.
By your logic, "no number is equal to its successor" has no
meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
So you agree that Robinson arithmetic is incomplete.
It is as complete as it was designed to be.
There is no "designed to be".-a There are sentences in the language of
Robinson arithmetic that are true but not provable,
To make is simpler to understand.
In proof theoretic semantics:
unprovable in Q means out-of-scope of Q.
therefore making the system incomplete, as you have just agreed,
meaning that you agree that incompleteness exists.
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no meaning in
Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no meaning
in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no meaning
in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no meaning >>>>> in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable.-a Then to put
things in words you can understand:
Godel proved that any axiomatic system of arithmetic contains out-of-
scope statements.
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no
meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable.-a Then to put
things in words you can understand:
"I am driving to Walmart to buy a carton of
-aBreyer's natural vanilla ice cream." is also unprovable in PA.
In both cases the semantics in not represented in PA.
Godel proved that any axiomatic system of arithmetic contains out-of-
scope statements.
Sure, PA also has no idea that driving means operating a motor vehicle.
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no
meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable.-a Then to put
things in words you can understand:
"I am driving to Walmart to buy a carton of
-a-aBreyer's natural vanilla ice cream." is also unprovable in PA.
In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
"No number is equal to its successor" is a sentence in RA, and it is
true but unprovable in RA (or as your would call it, "out-of-scope").
--
Godel proved that any axiomatic system of arithmetic contains out-of-
scope statements.
Sure, PA also has no idea that driving means operating a motor vehicle.
Not applicable.
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no
meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable.-a Then to put
things in words you can understand:
"I am driving to Walmart to buy a carton of
-a-aBreyer's natural vanilla ice cream." is also unprovable in PA.
In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
"No number is equal to its successor" is a sentence in RA, and it is
true but unprovable in RA (or as your would call it, "out-of-scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
Godel proved that any axiomatic system of arithmetic contains out-
of- scope statements.
Sure, PA also has no idea that driving means operating a motor vehicle.
Not applicable.
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable.-a Then to put >>>>> things in words you can understand:
"I am driving to Walmart to buy a carton of
-a-aBreyer's natural vanilla ice cream." is also unprovable in PA.
In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False.-a The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False.-a G is simply a sentence like ~reax x>10 v x<5 but much more complex.
"No number is equal to its successor" is a sentence in RA, and it is
true but unprovable in RA (or as your would call it, "out-of-scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language of
Q.-a More formally, it is this:
~reax x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms you would understand, the above is "out-of-scope" of Q).
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable.-a Then to put >>>>>> things in words you can understand:
"I am driving to Walmart to buy a carton of
-a-aBreyer's natural vanilla ice cream." is also unprovable in PA.
In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False.-a The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False.-a G is simply a sentence like ~reax x>10 v x<5 but much more complex. >>
"No number is equal to its successor" is a sentence in RA, and it is
true but unprovable in RA (or as your would call it, "out-of-scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language of
Q.-a More formally, it is this:
~reax x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms
you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
On 6/26/2026 6:01 PM, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable.-a Then to >>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
-a-aBreyer's natural vanilla ice cream." is also unprovable in PA. >>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False.-a The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False.-a G is simply a sentence like ~reax x>10 v x<5 but much more
complex.
"No number is equal to its successor" is a sentence in RA, and it
is true but unprovable in RA (or as your would call it, "out-of-
scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language
of Q.-a More formally, it is this:
~reax x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms
you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
In your own words, what does it mean for a statement to be "semantically grounded" in a formal system?
On 6/26/2026 5:08 PM, dbush wrote:
On 6/26/2026 6:01 PM, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable.-a Then to >>>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
-a-aBreyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False.-a The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False.-a G is simply a sentence like ~reax x>10 v x<5 but much more
complex.
"No number is equal to its successor" is a sentence in RA, and it >>>>>> is true but unprovable in RA (or as your would call it, "out-of-
scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language
of Q.-a More formally, it is this:
~reax x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms
you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
In your own words, what does it mean for a statement to be
"semantically grounded" in a formal system?
I always do back-chained inference because the typical
math way of doing forward chained inference may take
an infeasibly long time. A finite set of back-chained
inference steps from x to the axioms of Q.
I appreciate that you stopped playing head games.
On 6/26/2026 6:58 PM, olcott wrote:
On 6/26/2026 5:08 PM, dbush wrote:
On 6/26/2026 6:01 PM, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope. >>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable.-a Then to >>>>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
-a-aBreyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False.-a The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False.-a G is simply a sentence like ~reax x>10 v x<5 but much more >>>>> complex.
"No number is equal to its successor" is a sentence in RA, and it >>>>>>> is true but unprovable in RA (or as your would call it, "out-of- >>>>>>> scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language >>>>> of Q.-a More formally, it is this:
~reax x=S(x)
And this sentence is not provable from the axioms of Q (or, in
terms you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
In your own words, what does it mean for a statement to be
"semantically grounded" in a formal system?
I always do back-chained inference because the typical
math way of doing forward chained inference may take
an infeasibly long time. A finite set of back-chained
inference steps from x to the axioms of Q.
Back or forward chained doesn't matter, it's essentially the same steps
in a different direction.-a But in any case, you're saying "semantically grounded" is just another synonym for unprovable.
So to again put things in a way you'll understand, Godel proved that any axiom system of arithmetic contains statements that are not semantically grounded.
That also means that, using your terminology, it has been proven that
the statement ~reax x=S(x), i.e. "No number is equal to its successor", is not semantically grounded in Q.
On 6/26/2026 6:18 PM, dbush wrote:
On 6/26/2026 6:58 PM, olcott wrote:
On 6/26/2026 5:08 PM, dbush wrote:
On 6/26/2026 6:01 PM, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has >>>>>>>>>>>>>> no meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope. >>>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable.-a Then to >>>>>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
-a-aBreyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False.-a The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False.-a G is simply a sentence like ~reax x>10 v x<5 but much more >>>>>> complex.
"No number is equal to its successor" is a sentence in RA, and >>>>>>>> it is true but unprovable in RA (or as your would call it, "out- >>>>>>>> of- scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the
language of Q.-a More formally, it is this:
~reax x=S(x)
And this sentence is not provable from the axioms of Q (or, in
terms you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
In your own words, what does it mean for a statement to be
"semantically grounded" in a formal system?
I always do back-chained inference because the typical
math way of doing forward chained inference may take
an infeasibly long time. A finite set of back-chained
inference steps from x to the axioms of Q.
Back or forward chained doesn't matter, it's essentially the same
steps in a different direction.-a But in any case, you're saying
"semantically grounded" is just another synonym for unprovable.
So to again put things in a way you'll understand, Godel proved that
any axiom system of arithmetic contains statements that are not
semantically grounded.
Not quite. G is not semantically grounded
in PA
yet G is semantically grounded
in metamathematics.
When an expression in PA only derives semantic
meaning in PA when grounded in PA
then G has no
meaning in PA.
That also means that, using your terminology, it has been proven that
the statement ~reax x=S(x), i.e. "No number is equal to its successor",
is not semantically grounded in Q.
Thus is meaningless in Q and out-of-scope in Q.
On 6/26/2026 8:05 PM, olcott wrote:
On 6/26/2026 6:18 PM, dbush wrote:
On 6/26/2026 6:58 PM, olcott wrote:
On 6/26/2026 5:08 PM, dbush wrote:
On 6/26/2026 6:01 PM, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has >>>>>>>>>>>>>>> no meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson >>>>>>>>>>>>>> Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated >>>>>>>>>>>> with alternative views. So I will simply say out-of-scope. >>>>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable.-a Then >>>>>>>>>>> to put things in words you can understand:
"I am driving to Walmart to buy a carton of
-a-aBreyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False.-a The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False.-a G is simply a sentence like ~reax x>10 v x<5 but much more >>>>>>> complex.
"No number is equal to its successor" is a sentence in RA, and >>>>>>>>> it is true but unprovable in RA (or as your would call it,
"out- of- scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the
language of Q.-a More formally, it is this:
~reax x=S(x)
And this sentence is not provable from the axioms of Q (or, in
terms you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
In your own words, what does it mean for a statement to be
"semantically grounded" in a formal system?
I always do back-chained inference because the typical
math way of doing forward chained inference may take
an infeasibly long time. A finite set of back-chained
inference steps from x to the axioms of Q.
Back or forward chained doesn't matter, it's essentially the same
steps in a different direction.-a But in any case, you're saying
"semantically grounded" is just another synonym for unprovable.
So to again put things in a way you'll understand, Godel proved that
any axiom system of arithmetic contains statements that are not
semantically grounded.
Not quite. G is not semantically grounded
i.e. unprovable
in PA
yet G is semantically grounded
i.e. provable
in metamathematics.
Which is exactly what Godel proved.
When an expression in PA only derives semantic
meaning in PA when grounded in PA then G has no
meaning in PA.
i.e. if a statement is unprovable in PA then it's unprovable in PA.
In other words, a meaningless tautology.
That also means that, using your terminology, it has been proven that
the statement ~reax x=S(x), i.e. "No number is equal to its successor", >>> is not semantically grounded in Q.
Thus is meaningless in Q and out-of-scope in Q.
Which means the semantically valid statement in Q
On 6/26/2026 7:23 PM, dbush wrote:
On 6/26/2026 8:05 PM, olcott wrote:
On 6/26/2026 6:18 PM, dbush wrote:
On 6/26/2026 6:58 PM, olcott wrote:
On 6/26/2026 5:08 PM, dbush wrote:
On 6/26/2026 6:01 PM, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has >>>>>>>>>>>>>>>> no meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson >>>>>>>>>>>>>>> Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated >>>>>>>>>>>>> with alternative views. So I will simply say out-of-scope. >>>>>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable.-a Then >>>>>>>>>>>> to put things in words you can understand:
"I am driving to Walmart to buy a carton of
-a-aBreyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False.-a The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False.-a G is simply a sentence like ~reax x>10 v x<5 but much more >>>>>>>> complex.
"No number is equal to its successor" is a sentence in RA, and >>>>>>>>>> it is true but unprovable in RA (or as your would call it, >>>>>>>>>> "out- of- scope").
If its semantics is not expressible in Q (What RA is called) >>>>>>>>> then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the
language of Q.-a More formally, it is this:
~reax x=S(x)
And this sentence is not provable from the axioms of Q (or, in >>>>>>>> terms you would understand, the above is "out-of-scope" of Q). >>>>>>>>
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
In your own words, what does it mean for a statement to be
"semantically grounded" in a formal system?
I always do back-chained inference because the typical
math way of doing forward chained inference may take
an infeasibly long time. A finite set of back-chained
inference steps from x to the axioms of Q.
Back or forward chained doesn't matter, it's essentially the same
steps in a different direction.-a But in any case, you're saying
"semantically grounded" is just another synonym for unprovable.
So to again put things in a way you'll understand, Godel proved that
any axiom system of arithmetic contains statements that are not
semantically grounded.
Not quite. G is not semantically grounded
i.e. unprovable
in PA
yet G is semantically grounded
i.e. provable
in metamathematics.
Which is exactly what Godel proved.
When an expression in PA only derives semantic
meaning in PA when grounded in PA then G has no
meaning in PA.
i.e. if a statement is unprovable in PA then it's unprovable in PA.
In other words, a meaningless tautology.
That also means that, using your terminology, it has been proven
that the statement ~reax x=S(x), i.e. "No number is equal to its
successor", is not semantically grounded in Q.
Thus is meaningless in Q and out-of-scope in Q.
Which means the semantically valid statement in Q
does not include ~reax x=S(x)
On 6/26/2026 8:48 PM, olcott wrote:
On 6/26/2026 7:23 PM, dbush wrote:
On 6/26/2026 8:05 PM, olcott wrote:
On 6/26/2026 6:18 PM, dbush wrote:
On 6/26/2026 6:58 PM, olcott wrote:
On 6/26/2026 5:08 PM, dbush wrote:
On 6/26/2026 6:01 PM, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" >>>>>>>>>>>>>>>>> has no meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement >>>>>>>>>>>>>>>> is true for the standard natural numbers, Robinson >>>>>>>>>>>>>>>> Arithmetic is too weak to prove it universally >>>>>>>>>>>>>>>> (reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free. >>>>>>>>>>>>>>
PTS does hold the view that meaning is only derived >>>>>>>>>>>>>> through inference steps. This simple sentence seems >>>>>>>>>>>>>> impossibly too difficult for anyone fully indoctrinated >>>>>>>>>>>>>> with alternative views. So I will simply say out-of-scope. >>>>>>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable.-a Then >>>>>>>>>>>>> to put things in words you can understand:
"I am driving to Walmart to buy a carton of
-a-aBreyer's natural vanilla ice cream." is also unprovable in >>>>>>>>>>>> PA.
In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False.-a The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False.-a G is simply a sentence like ~reax x>10 v x<5 but much >>>>>>>>> more complex.
"No number is equal to its successor" is a sentence in RA, >>>>>>>>>>> and it is true but unprovable in RA (or as your would call >>>>>>>>>>> it, "out- of- scope").
If its semantics is not expressible in Q (What RA is called) >>>>>>>>>> then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the
language of Q.-a More formally, it is this:
~reax x=S(x)
And this sentence is not provable from the axioms of Q (or, in >>>>>>>>> terms you would understand, the above is "out-of-scope" of Q). >>>>>>>>>
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
In your own words, what does it mean for a statement to be
"semantically grounded" in a formal system?
I always do back-chained inference because the typical
math way of doing forward chained inference may take
an infeasibly long time. A finite set of back-chained
inference steps from x to the axioms of Q.
Back or forward chained doesn't matter, it's essentially the same
steps in a different direction.-a But in any case, you're saying
"semantically grounded" is just another synonym for unprovable.
So to again put things in a way you'll understand, Godel proved
that any axiom system of arithmetic contains statements that are
not semantically grounded.
Not quite. G is not semantically grounded
i.e. unprovable
in PA
yet G is semantically grounded
i.e. provable
in metamathematics.
Which is exactly what Godel proved.
Your lack of response indicates that you agree with Godel, but used different words to do so.
When an expression in PA only derives semantic
meaning in PA when grounded in PA then G has no
meaning in PA.
i.e. if a statement is unprovable in PA then it's unprovable in PA.
In other words, a meaningless tautology.
That also means that, using your terminology, it has been proven
that the statement ~reax x=S(x), i.e. "No number is equal to its
successor", is not semantically grounded in Q.
Thus is meaningless in Q and out-of-scope in Q.
Which means the semantically valid statement in Q
does not include ~reax x=S(x)
False, as it means "no number is equal to its successor", and the
concept of a successor and equality have semantic meaning in Q, as does
the concept of "all", "none", and "exists".
That makes the statement semantically valid, so any alternate system
that concludes otherwise is necessarily faulty.
On 6/26/2026 8:11 PM, dbush wrote:
On 6/26/2026 8:48 PM, olcott wrote:
On 6/26/2026 7:23 PM, dbush wrote:
On 6/26/2026 8:05 PM, olcott wrote:
On 6/26/2026 6:18 PM, dbush wrote:
On 6/26/2026 6:58 PM, olcott wrote:
On 6/26/2026 5:08 PM, dbush wrote:
On 6/26/2026 6:01 PM, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:Not applicable, as that is not a sentence in PA.
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" >>>>>>>>>>>>>>>>>> has no meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q), >>>>>>>>>>>>>>>>> the statement "no number is equal to its
successor" is not provable.While this statement >>>>>>>>>>>>>>>>> is true for the standard natural numbers, Robinson >>>>>>>>>>>>>>>>> Arithmetic is too weak to prove it universally >>>>>>>>>>>>>>>>> (reC x, S(x) rea x).
It's not provable but it certainly has meaning. >>>>>>>>>>>>>>>>
Andr|-
out-of-scope for Q is more accurate as jargon free. >>>>>>>>>>>>>>>
PTS does hold the view that meaning is only derived >>>>>>>>>>>>>>> through inference steps. This simple sentence seems >>>>>>>>>>>>>>> impossibly too difficult for anyone fully indoctrinated >>>>>>>>>>>>>>> with alternative views. So I will simply say out-of-scope. >>>>>>>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable. >>>>>>>>>>>>>> Then to put things in words you can understand:
"I am driving to Walmart to buy a carton of
-a-aBreyer's natural vanilla ice cream." is also unprovable >>>>>>>>>>>>> in PA.
In both cases the semantics in not represented in PA. >>>>>>>>>>>>
It is expressed in PA
False.-a The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and >>>>>>>>>>> the semantics of G are neither expressible in PA.
False.-a G is simply a sentence like ~reax x>10 v x<5 but much >>>>>>>>>> more complex.
"No number is equal to its successor" is a sentence in RA, >>>>>>>>>>>> and it is true but unprovable in RA (or as your would call >>>>>>>>>>>> it, "out- of- scope").
If its semantics is not expressible in Q (What RA is called) >>>>>>>>>>> then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the >>>>>>>>>> language of Q.-a More formally, it is this:
~reax x=S(x)
And this sentence is not provable from the axioms of Q (or, in >>>>>>>>>> terms you would understand, the above is "out-of-scope" of Q). >>>>>>>>>>
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
In your own words, what does it mean for a statement to be
"semantically grounded" in a formal system?
I always do back-chained inference because the typical
math way of doing forward chained inference may take
an infeasibly long time. A finite set of back-chained
inference steps from x to the axioms of Q.
Back or forward chained doesn't matter, it's essentially the same >>>>>> steps in a different direction.-a But in any case, you're saying
"semantically grounded" is just another synonym for unprovable.
So to again put things in a way you'll understand, Godel proved
that any axiom system of arithmetic contains statements that are
not semantically grounded.
Not quite. G is not semantically grounded
i.e. unprovable
in PA
yet G is semantically grounded
i.e. provable
in metamathematics.
Which is exactly what Godel proved.
Your lack of response indicates that you agree with Godel, but used
different words to do so.
When an expression in PA only derives semantic
meaning in PA when grounded in PA then G has no
meaning in PA.
i.e. if a statement is unprovable in PA then it's unprovable in PA.
In other words, a meaningless tautology.
That also means that, using your terminology, it has been proven
that the statement ~reax x=S(x), i.e. "No number is equal to its
successor", is not semantically grounded in Q.
Thus is meaningless in Q and out-of-scope in Q.
Which means the semantically valid statement in Q
does not include ~reax x=S(x)
False, as it means "no number is equal to its successor", and the
concept of a successor and equality have semantic meaning in Q, as
does the concept of "all", "none", and "exists".
If there is no sequence of inference steps in Q from
~reax x=S(x) to the axioms of Q then ~reax x=S(x) is
ungrounded in the PTS atomic base of Q.
On 6/26/2026 9:39 PM, olcott wrote:
On 6/26/2026 8:11 PM, dbush wrote:
On 6/26/2026 8:48 PM, olcott wrote:
On 6/26/2026 7:23 PM, dbush wrote:
On 6/26/2026 8:05 PM, olcott wrote:
On 6/26/2026 6:18 PM, dbush wrote:
On 6/26/2026 6:58 PM, olcott wrote:
On 6/26/2026 5:08 PM, dbush wrote:
On 6/26/2026 6:01 PM, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:Not applicable, as that is not a sentence in PA.
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" >>>>>>>>>>>>>>>>>>> has no meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q), >>>>>>>>>>>>>>>>>> the statement "no number is equal to its
successor" is not provable.While this statement >>>>>>>>>>>>>>>>>> is true for the standard natural numbers, Robinson >>>>>>>>>>>>>>>>>> Arithmetic is too weak to prove it universally >>>>>>>>>>>>>>>>>> (reC x, S(x) rea x).
It's not provable but it certainly has meaning. >>>>>>>>>>>>>>>>>
Andr|-
out-of-scope for Q is more accurate as jargon free. >>>>>>>>>>>>>>>>
PTS does hold the view that meaning is only derived >>>>>>>>>>>>>>>> through inference steps. This simple sentence seems >>>>>>>>>>>>>>>> impossibly too difficult for anyone fully indoctrinated >>>>>>>>>>>>>>>> with alternative views. So I will simply say out-of-scope. >>>>>>>>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable. >>>>>>>>>>>>>>> Then to put things in words you can understand:
"I am driving to Walmart to buy a carton of
-a-aBreyer's natural vanilla ice cream." is also unprovable >>>>>>>>>>>>>> in PA.
In both cases the semantics in not represented in PA. >>>>>>>>>>>>>
It is expressed in PA
False.-a The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and >>>>>>>>>>>> the semantics of G are neither expressible in PA.
False.-a G is simply a sentence like ~reax x>10 v x<5 but much >>>>>>>>>>> more complex.
"No number is equal to its successor" is a sentence in RA, >>>>>>>>>>>>> and it is true but unprovable in RA (or as your would call >>>>>>>>>>>>> it, "out- of- scope").
If its semantics is not expressible in Q (What RA is called) >>>>>>>>>>>> then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the >>>>>>>>>>> language of Q.-a More formally, it is this:
~reax x=S(x)
And this sentence is not provable from the axioms of Q (or, >>>>>>>>>>> in terms you would understand, the above is "out-of-scope" of >>>>>>>>>>> Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
In your own words, what does it mean for a statement to be
"semantically grounded" in a formal system?
I always do back-chained inference because the typical
math way of doing forward chained inference may take
an infeasibly long time. A finite set of back-chained
inference steps from x to the axioms of Q.
Back or forward chained doesn't matter, it's essentially the same >>>>>>> steps in a different direction.-a But in any case, you're saying >>>>>>> "semantically grounded" is just another synonym for unprovable.
So to again put things in a way you'll understand, Godel proved >>>>>>> that any axiom system of arithmetic contains statements that are >>>>>>> not semantically grounded.
Not quite. G is not semantically grounded
i.e. unprovable
in PA
yet G is semantically grounded
i.e. provable
in metamathematics.
Which is exactly what Godel proved.
Your lack of response indicates that you agree with Godel, but used
different words to do so.
When an expression in PA only derives semantic
meaning in PA when grounded in PA then G has no
meaning in PA.
i.e. if a statement is unprovable in PA then it's unprovable in PA.
In other words, a meaningless tautology.
That also means that, using your terminology, it has been proven >>>>>>> that the statement ~reax x=S(x), i.e. "No number is equal to its >>>>>>> successor", is not semantically grounded in Q.
Thus is meaningless in Q and out-of-scope in Q.
Which means the semantically valid statement in Q
does not include ~reax x=S(x)
False, as it means "no number is equal to its successor", and the
concept of a successor and equality have semantic meaning in Q, as
does the concept of "all", "none", and "exists".
If there is no sequence of inference steps in Q from
~reax x=S(x) to the axioms of Q then ~reax x=S(x) is
ungrounded in the PTS atomic base of Q.
In other words, ~reax x=S(x) is unprovable in Q, as is commonly known.
So once again, you agree with everyone else, but are using different
words to say so.
On 6/26/2026 1:17 AM, Mikko wrote:
On 25/06/2026 16:43, olcott wrote:
On 6/25/2026 2:09 AM, Mikko wrote:
On 24/06/2026 23:19, olcott wrote:
On 6/24/2026 3:23 AM, Mikko wrote:
On 23/06/2026 17:29, olcott wrote:
On 6/23/2026 12:39 AM, Mikko wrote:
On 22/06/2026 16:13, olcott wrote:
On 6/22/2026 2:13 AM, Mikko wrote:
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:That only means that your DD is not a strictly confoming C >>>>>>>>>>>> program.
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, Andr|- G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>> [ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> https://www.youtube.com/@rossfinlayson >>>>>>>>>>>>>>>>>>>>>> Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof- >>>>>>>>>>>>>>>>>>>>>> theoretic- semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>>>>Whereas you are stuck to your own incoherent views >>>>>>>>>>>>>>>>>>>> and reject
alternative views out-of-hand without review. >>>>>>>>>>>>>>>>>>
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>>>>>> look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>> semantics/
I've spent a couple of hours reading that web page. >>>>>>>>>>>>>>>>>> It is abstract in
the extreme.-a One thing is utterly clear: its level of >>>>>>>>>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>>>>>> Olcott, who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with >>>>>>>>>>>>>>>> irrelevancy.
The Liar's Paradox has absolutely nothing to do with >>>>>>>>>>>>>>>> proof by contradiction. The LP isn't a contradiction; >>>>>>>>>>>>>>>> it's a paradox. The two are different things. A >>>>>>>>>>>>>>>> contradiction is a statement which is necessarily false. >>>>>>>>>>>>>>>> A paradox is a statement to which no truth value can be >>>>>>>>>>>>>>>> consistently assigned.
Andr|-
Then I have never spoken of anything where proof by >>>>>>>>>>>>>>> contradiction applies,
False, as that is exactly the method uses by the halting >>>>>>>>>>>>>> problem proof, Godel's proof, and Tarski's proof, each of >>>>>>>>>>>>>> which you've been attempting (and failing) to refute for >>>>>>>>>>>>>> years.
Proof Theoretic Semantics halt prover HHH correctly determines >>>>>>>>>>>>> that its input DD is ungrounded in its atomic base according >>>>>>>>>>>>> to the operational semantics of the C programming language. >>>>>>>>>>>>
The exact operational semantics of C conclusively
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational >>>>>>>>>> semantics
do not fully specify the behaviour of DD. In order to prove >>>>>>>>>> that DD
halts you also need additional operational spemantics provided >>>>>>>>>> by the
C implementation you have used. When DD iss executed in that >>>>>>>>>> environment
it halts, which is sufficient to prove that in that
environment DD
halts. In some other environment its execution might be
aborted or it
could be rejected by the compiler.
Proof Theoretic Semantics provides the correct way
to handle pathological self-reference (PSR).
This would be dead obvious if you were not totally
clueless about Prolog.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Nice to see that you don't disagree.
Not nice to see that everyone continues to
totally ignore my best validation of proof
theoretic semantics.
Unfortunately that is unavoidable as long as your best presentation >>>>>> of the validation and of your version of proof theoretic semantics >>>>>> are not good enough.
Is is dead obvious and completely clear example
of the final resolution of the Liar Paradox using
generic proof theoretic semantics implemented in
Prolog.
Except that it is not final -- others will continue presenting
different views about it -- and not even a resolution.
If others did not reject mine out-of-hand
without review they could understand that
it is final.
Even those who think your resolution is the best there can be should
understand that there are others who don't shate that opinion.
There are many people that are certain that the Earth is flat.
On 6/26/2026 1:23 AM, Mikko wrote:
On 25/06/2026 16:47, olcott wrote:
On 6/25/2026 2:14 AM, Mikko wrote:
On 24/06/2026 23:23, olcott wrote:(a) Extracting atomic facts, would be the hardest part,
On 6/24/2026 4:45 AM, Mikko wrote:
On 23/06/2026 17:40, olcott wrote:
On 6/23/2026 12:49 AM, Mikko wrote:
On 22/06/2026 18:16, olcott wrote:
On 6/22/2026 2:46 AM, Mikko wrote:
On 22/06/2026 03:44, olcott wrote:
On 6/21/2026 7:32 PM, phoenix wrote:It is fairly simple to build a system of essentially infallible >>>>>>>>>> reasoning that never errs even when it doesn't have all the >>>>>>>>>> relevant information. The real problem is to construct a system >>>>>>>>>> that tells something interesting instead of just different >>>>>>>>>> presentations of the same already known facts.
olcott wrote:It is not that they never admit defeat.
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat? >>>>>>>>>>>
olcott wrote:
On 6/21/2026 3:18 PM, Andr|- G. Isaak wrote:Lastly, and why should we care? Please answer this and >>>>>>>>>>>>>> other questions presented.
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> https://www.youtube.com/@rossfinlayson >>>>>>>>>>>>>>>>>>>>>>> Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof- >>>>>>>>>>>>>>>>>>>>>>> theoretic- semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>>>Whereas you are stuck to your own incoherent views >>>>>>>>>>>>>>>>>>>>> and reject
alternative views out-of-hand without review. >>>>>>>>>>>>>>>>>
Calling my views (anchored in proof theoretic >>>>>>>>>>>>>>>>>>>> semantics)
incoherent merely proves that you are too damned >>>>>>>>>>>>>>>>>>>> lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>>> semantics/
I've spent a couple of hours reading that web page. >>>>>>>>>>>>>>>>>>> It is abstract in
the extreme.-a One thing is utterly clear: its level >>>>>>>>>>>>>>>>>>> of abstraction is
well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>>>>>>> Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that >>>>>>>>>>>>>>>>>>> I can't be bothered
to read it any further.-a If it actually says anything >>>>>>>>>>>>>>>>>>> at all, that
something is heavily disguised.-a From it's >>>>>>>>>>>>>>>>>>> "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically >>>>>>>>>>>>>>>>>>> exclusively been
| occupied with logical constants. Logical constants >>>>>>>>>>>>>>>>>>> play a central role
| in reasoning and inference, but are definitely not >>>>>>>>>>>>>>>>>>> the exclusive, and
| perhaps not even the most typical sort of entities >>>>>>>>>>>>>>>>>>> that can be defined
| inferentially. A framework is needed that deals >>>>>>>>>>>>>>>>>>> with inferential
| definitions in a wider sense and covers both >>>>>>>>>>>>>>>>>>> logical and extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is >>>>>>>>>>>>>>>>>> currently and in the
near future not useful as making it useful requires >>>>>>>>>>>>>>>>>> much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be >>>>>>>>>>>>>>>>> useful for? What it
ought to be able to do that standard logic fails at? >>>>>>>>>>>>>>>>> Maybe Andr|- could
elucidate.-a He seems to have a better grasp of it than >>>>>>>>>>>>>>>>> anybody else here.
I doubt my understanding of PTS is any better than >>>>>>>>>>>>>>>> yours. I basically only know what is presented in the >>>>>>>>>>>>>>>> Stanford Encyclopedia article (which you correctly point >>>>>>>>>>>>>>>> out is not exactly aimed at beginners) and the Wikipedia >>>>>>>>>>>>>>>> article. What I am quite certain of, however, is that >>>>>>>>>>>>>>>> Olcott lacks any understanding of what PTS actually says >>>>>>>>>>>>>>>> as he's made a variety of fairly absurd claims regarding >>>>>>>>>>>>>>>> it (for example, that PTS claims that unproven >>>>>>>>>>>>>>>> propositions are 'meaningless' or that the goal of PTS >>>>>>>>>>>>>>>> is to completely overthrow standard truth- theoretic >>>>>>>>>>>>>>>> semantics).
Andr|-
-a-a Proof-theoretic semantics is an alternative to >>>>>>>>>>>>>>> -a-a truth-condition semantics. It is based on the >>>>>>>>>>>>>>> -a-a fundamental assumption that the central notion >>>>>>>>>>>>>>> -a-a in terms of which meanings are assigned to certain >>>>>>>>>>>>>>> -a-a expressions of our language, in particular to >>>>>>>>>>>>>>> -a-a logical constants, is that of proof rather than >>>>>>>>>>>>>>> -a-a truth. In this sense proof-theoretic semantics >>>>>>>>>>>>>>> -a-a is semantics in terms of proof.
-a-a https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>> semantics/
In other words it answers the question:
What happens when truth conditional semantics is >>>>>>>>>>>>>>> utterly abandoned and is totally replaced by proof >>>>>>>>>>>>>>> theoretic semantics?
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time. >>>>>>>>>>>>>
We can make these lies look foolish at every language >>>>>>>>>>>>> level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
It is that that have a system of essentially infallible >>>>>>>>>>> reasoning
that never errs as long as it has all the relevant information. >>>>>>>>>>
It will have the exhaustively complete list of
every atomic fact of general knowledge of the
actual world.
That is impossible. By the time you have all facts of general >>>>>>>> knowledge
in your system the general knowledge has grown to inlude more >>>>>>>> facts.
It can be reasonably approximated pretty quickly.
We start with all of the textbooks.
That is a lot of reading, though those for the same topic area tend >>>>>> to say the same, and the old ones add very little to the new ones, >>>>>> mainly some now obsolete technology.
It would not be too much reading for LLMs.
It could start with all of the latest textbooks
for all of the fields. Some of these latest
textbooks may be hundreds of years old for
fields that have become obsolete.
Perhaps that apprach should be tried. The problem involves extracting
atomic facts, detecting repeated facts, and encoding facts for the
inference system.
yet not too hard.
(b) Detecting repeated facts, string comparison.
(c) Encoding facts, CycL
https://en.wikipedia.org/wiki/CycL
I still have the original user's manuals
as PDFs and hard copies.
--The encoding must be normalized as much as possible in order to reduce
repetition to a string comparison. That is not a trivial problem if one
wants a total or nearly total prevention of repetition.
On 6/26/2026 1:34 AM, Mikko wrote:
On 25/06/2026 16:58, olcott wrote:
On 6/25/2026 2:18 AM, Mikko wrote:
On 24/06/2026 23:25, olcott wrote:
On 6/24/2026 4:52 AM, Mikko wrote:
On 23/06/2026 17:47, olcott wrote:
On 6/23/2026 12:55 AM, Mikko wrote:
On 22/06/2026 15:09, olcott wrote:
On 6/22/2026 1:41 AM, Mikko wrote:
On 22/06/2026 02:58, olcott wrote:
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:Whereas you are stuck to your own incoherent views and >>>>>>>>>>>>>>>> reject
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>>
alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>> look into proof theoretic semantics.
At different times you have expressed different opinions, >>>>>>>>>>>>>> which
sometimes have been incompatible. But you have never clearly >>>>>>>>>>>>>> retracted your earlier opitions that conflict with your >>>>>>>>>>>>>> present
ones.
All of the ideas that I have ever had about these things >>>>>>>>>>>>> are now under the Proof Theoretic Semantics category. >>>>>>>>>>>>> These ideas have evolved over time, yet their essence >>>>>>>>>>>>> has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a >>>>>>>>>>>> publishable
(or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> human >>>>>>>>>>> being on the face of the Earth could understand
me I could not publish.
As far as I have seen, all interesting content in those articles >>>>>>>>>> that have any is or depends on claims that should be proven but >>>>>>>>>> aren't.
They are proven in Proof Theoretic Semantics
An aricle is not publishable unless it either contains the proof or >>>>>>>> has a pointer to an olready published proof.
Only now after 28 years am I acquiring the lingua Franca
terms-of-the-art of proof theoretic semantics such that
I can anchor my ideas in the foundational work of the
most respected authors in the field.
My issue with you guys is that you only spend 1%
of your concentration understanding me and the other
99% trying to artificially contrive some baseless
rebuttal.
THat "baseless" is false but otherwise, what is wrong is more
important than what is right. Of one ignores what is right one
mai fail to achieve what one could, but if one believs what is
wrong one may achieve a disaseter.
Proof-theoretic semantics is an alternative to truth-condition
semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
So far no one has even acknowledged that PTS is an alternative
to truth-conditional semantics. Several people have seemed
to same that no alternative can possibly exist.
You have not shown that there is any need for any alternative
semantics.
With dangerous lies that can destroy Democracy
and kill the planet with climate change having
an ultimate arbiter of truth would be useful.
Those who are able and willing to destroy democracy are able to provice
an ultimate arbiter of truth and usually do so. But they don't need any
proof theoretic semantics.
An ultimate arbiter of truth blows their whole game away.
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>>>You can find any number of terms.-a That doesn't mean >>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS G||del 1931 >>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that PTS >>>>>>>>>>>>>> somehow causes
G||del's theorem not to hold, then cite an academic expert >>>>>>>>>>>>>> who'll have
some credibility.
If they are mere gibberish words to you then you will not >>>>>>>>>>>>>>> understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>>>> certainly don't
understand G||del's Theorem, neither the theorem itself nor >>>>>>>>>>>>>> any proof of
it.
in the atomic base of PA. That you do not understand >>>>>>>>>>>>> what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used >>>>>>>>>>>> only by you, and it is one which you have never explicitly >>>>>>>>>>>> defined, so the fault here certainly doesn't lie with Alan. >>>>>>>>>>>> It's certainly not a 'verified fact' when you haven't even >>>>>>>>>>>> adequately explained what it is that you mean.
All of knowledge expressed in language is structured as a >>>>>>>>>>> tree of semantic relations specified syntactically between >>>>>>>>>>> finite strings.
What makes you believe semantic relations that can be
structured as
a tree are sufficient to contain all knowledge that is
exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to >>>>>>>> put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
This is the same sort of thing as finding the definedThat does not follow. Words have meanings even without definitions.
meaning of a word. If you cannot find its recursively
defined meaning then it never gains any meaning.
On 6/26/2026 10:24 AM, olcott wrote:
On 6/26/2026 8:57 AM, dbush wrote:
On 6/26/2026 9:45 AM, olcott wrote:
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms.-a That doesn't >>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS G||del 1931 >>>>>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>> PTS somehow causes
G||del's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>> you certainly don't
understand G||del's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly doesn't >>>>>>>>>>>>>>>>> lie with Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>> when you haven't even adequately explained what it is >>>>>>>>>>>>>>>>> that you mean.
All of knowledge expressed in language is structured as >>>>>>>>>>>>>>>> a tree of semantic relations specified syntactically >>>>>>>>>>>>>>>> between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a >>>>>>>>>>> loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious >>>>>>> how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is equal >>>>> to its successor" has no meaning in Robinson Arithmetic.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
Then you agree that the above natural language sentence that is
semantically required to be either true or false has no meaning?
Your sentence would be what it always has been
a stipulated true sentence axiom.
False, as that statement is not one of the axioms of Robinson
arithmetic, but it is a statement in its language, and one that has
*only* an infinite connection to the axioms of that system.
By your logic, "no number is equal to its successor" has no meaning in Robinson arithmetic.--
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable.-a Then to put >>>>>> things in words you can understand:
"I am driving to Walmart to buy a carton of
-a-aBreyer's natural vanilla ice cream." is also unprovable in PA.
In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False.-a The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False.-a G is simply a sentence like ~reax x>10 v x<5 but much more complex. >>
"No number is equal to its successor" is a sentence in RA, and it is
true but unprovable in RA (or as your would call it, "out-of-scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language of
Q.-a More formally, it is this:
~reax x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms
you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
On 6/26/2026 1:45 AM, Mikko wrote:If anyone and everyone that claims that someone is dishonest
On 25/06/2026 19:16, olcott wrote:
On 6/25/2026 2:29 AM, Mikko wrote:
On 25/06/2026 00:33, olcott wrote:
On 6/24/2026 5:13 AM, Mikko wrote:
On 23/06/2026 21:20, olcott wrote:
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>> On 6/22/2026 1:42 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> On 6/22/2026 10:48 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>
G is true.
I put it to you you're lying again.-a No reputable >>>>>>>>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things.-a If Dag >>>>>>>>>>>>>>>>>>>> Prawitz
really
did
"agree" (with whom?) that G||del's sentence G is not >>>>>>>>>>>>>>>>>>>> true in
Peano
Arithmetic, then produce a citation for this. >>>>>>>>>>>>>>>>
He never gets to G||del. He essentially says unprovable >>>>>>>>>>>>>>>>>>> means untrue all the time for everything within his >>>>>>>>>>>>>>>>>>> own Theory of Grounds of strict Proof Theoretic >>>>>>>>>>>>>>>>>>> Semantics.
You won't understand it, but that _is_ essentially >>>>>>>>>>>>>>>>>> G||del's
Incompleteness
Theorem.-a It is a statement that any sufficiently >>>>>>>>>>>>>>>>>> powerful
system can
express true things it can't prove.-a So Dag Prawitz, >>>>>>>>>>>>>>>>>> had he been
saying
the things you falsely attributed to him, would >>>>>>>>>>>>>>>>>> certainly have
"got" to
G||del, and would have understood full well what he was >>>>>>>>>>>>>>>>>> saying.
You did not pay close enough attention to my exact words. >>>>>>>>>>>>>>>>I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>
Yeah, I'm pretty sure that "Dag Prawitz says what Dag >>>>>>>>>>>>>> Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz >>>>>>>>>>>>>> doesn't
say",
then looking a bit into his tremendous volume of works, >>>>>>>>>>>>>> he talks about "natural deduction" then specifically an >>>>>>>>>>>>>> "inverse
principle" so I think these are key aspects of fundamental >>>>>>>>>>>>>> logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself, >>>>>>>>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to >>>>>>>>>>>>>> generate
new ad-
missible rules within a certain syntactic context. Some >>>>>>>>>>>>>> N4Ufteen years
later, the idea was taken up by Dag Prawitz to devise a >>>>>>>>>>>>>> strategy of
normalization for natural deduction calculi (this being an >>>>>>>>>>>>>> analogue of
GentzenrCOs cut-elimination theorem for sequent calculi). >>>>>>>>>>>>>> Later,
Prawitz
used the inversion principle again, attributing it with a >>>>>>>>>>>>>> semantic
role.
Still working in natural deduction calculi, he formulated >>>>>>>>>>>>>> a general
type
of schematic Introduction rules to be matchedrCothanks to >>>>>>>>>>>>>> the idea
supporting the inversion principle rCo by a corresponding >>>>>>>>>>>>>> general
schematic Elimination rule. This was an attempt to provide a >>>>>>>>>>>>>> solution to
the problem suggested by the often quoted note of Gentzen. >>>>>>>>>>>>>> According to
Gentzen rCLit should be possible to display the elimination >>>>>>>>>>>>>> rules as
unique functions of the corresponding introduction rules >>>>>>>>>>>>>> on the
basis of
certain requirements.rCY Many people have since worked on >>>>>>>>>>>>>> this topic,
which can be appropriately seen as the birthplace of what >>>>>>>>>>>>>> are now
referred to as rCLgeneral elimination rulesrCY, recently studied >>>>>>>>>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace >>>>>>>>>>>>>> the main
threads of this chapter of proof-theoretical
investigation, using
LorenzenrCOs original framework as a general guide" >>>>>>>>>>>>>>
Hm, "general elimination rules", seem derivable from De >>>>>>>>>>>>>> Morgan's
laws,
and that being the usual account of naive deductive >>>>>>>>>>>>>> analysis, then
since
"natural deduction", which here is held as part of the theory >>>>>>>>>>>>>> since it's naturally logical, then has for Gentzen that >>>>>>>>>>>>>> besides
Kripke
afterward there's also Sheffer and Chwistek before, and >>>>>>>>>>>>>> instead of
Montague for semantics there's Herbrand for semantics, so, >>>>>>>>>>>>>> what to do
about "inversion principle" is here that the thea-theory >>>>>>>>>>>>>> has that
it's
what subsumes "non-contradiction principle", here hoping >>>>>>>>>>>>>> that the
interpretation aligns and thusly that "principle of >>>>>>>>>>>>>> inversion"
wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334 >>>>>>>>>>>>>>
https://www.strandbooks.com/natural-deduction-a-proof- >>>>>>>>>>>>>> theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the >>>>>>>>>>>>>> foundation of
most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a >>>>>>>>>>>>>> principle of
thorough reason as subsuming principles of non-
contradiction and what
suffices, so, I'll be curious then about what to make of >>>>>>>>>>>>>> Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as >>>>>>>>>>>>>> old as the
oldest account of Western philosophy like Heraclitus with >>>>>>>>>>>>>> dual
monism.
In fact by definition it's about the most basic aspect of >>>>>>>>>>>>>> contemplation
and deliberation in abstraction of looking at both sides >>>>>>>>>>>>>> of issues
and
resolving inductive impasses with analytical bridges after >>>>>>>>>>>>>> complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as >>>>>>>>>>>>>> one of the
characteristic features of Gentzen's intuitionistic natural >>>>>>>>>>>>>> deduction.
In the literature on proof-theoretic semantics, this >>>>>>>>>>>>>> principle is
often
coupled with another that is called the recovery
principle. By
adopting
the Computational Ludics framework, we reformulate these >>>>>>>>>>>>>> principles
into
one and the same condition, which we call the harmony >>>>>>>>>>>>>> condition. We
show
that this reformulation allows us to reveal two intuitive >>>>>>>>>>>>>> ideas
standing
behind these principles: the idea of "containment" present >>>>>>>>>>>>>> in the
inversion principle, and the idea that the recovery >>>>>>>>>>>>>> principle is the
"converse" of the inversion principle. We also formulate >>>>>>>>>>>>>> two other
conditions in the Computational Ludics framework, and we >>>>>>>>>>>>>> show that
each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and >>>>>>>>>>>>>> knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical >>>>>>>>>>>>>> connectives,
proof-theoretic semantics rests on the idea that we know the >>>>>>>>>>>>>> meaning of
a compound sentence when we know what counts as a >>>>>>>>>>>>>> canonical proof of
it.
And if proofs are formalised within the framework of natural >>>>>>>>>>>>>> deduction,
then a canonical proof of a sentence A is nothing but a >>>>>>>>>>>>>> closed
derivation ending with an introduction rule of the main >>>>>>>>>>>>>> connective
of A."
The "canonical proofs" are not unique, in any system >>>>>>>>>>>>>> strong enough
to make for infinitary reasoning and super-classical results >>>>>>>>>>>>>> requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6 >>>>>>>>>>>>> That is the most important gist of his whole work.
He later goes on to develop and further elaborate his >>>>>>>>>>>>> Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches >>>>>>>>>>>>> Thomas Piecha & Peter Schroeder-Heister do this same sort of >>>>>>>>>>>>> thing two different ways.
Furthermore I say there are "canonical proofs" of inductive >>>>>>>>>>>> sorts that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical >>>>>>>>>>> proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make >>>>>>>>>>>> repairs
of what otherwise is flawed, or for hard constructivist realist >>>>>>>>>>>> structuralist model theorists: not-theories (examples of >>>>>>>>>>>> wrong).
Induction and counter-induction contradict each other, it's >>>>>>>>>> simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog?
That would be dishonest.
No, pointing out that you are worng about Prolog when you are wrong >>>>>> about Prolog is never dishohest.
That is correct Prolog and that is the
result of the correct run of correct Prolog.
Irrelevant. Nobody claimed there be Prolog errors in your queries.
Implying that I am wrong about Prolog without
pointing out any actual mistake is also DISHONEST.
How did Ross FInlayson imply that you were wrong about Prolog?
If an error is claimed then it must be specifically
pointed out otherwise the clam of error is dishonest.
Yet you claim that Ross Finlayson be dishonest without pointing
out what is dishonest in his words.
If anyone and everyone that claims that they found an
error and never points out what the error is and why
it is an error then they are merely a baseless denigrator.
On 6/26/2026 9:39 PM, olcott wrote:
On 6/26/2026 8:11 PM, dbush wrote:
On 6/26/2026 8:48 PM, olcott wrote:
On 6/26/2026 7:23 PM, dbush wrote:
On 6/26/2026 8:05 PM, olcott wrote:
On 6/26/2026 6:18 PM, dbush wrote:
On 6/26/2026 6:58 PM, olcott wrote:
On 6/26/2026 5:08 PM, dbush wrote:
On 6/26/2026 6:01 PM, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:Not applicable, as that is not a sentence in PA.
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" >>>>>>>>>>>>>>>>>>> has no meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q), >>>>>>>>>>>>>>>>>> the statement "no number is equal to its
successor" is not provable.While this statement >>>>>>>>>>>>>>>>>> is true for the standard natural numbers, Robinson >>>>>>>>>>>>>>>>>> Arithmetic is too weak to prove it universally >>>>>>>>>>>>>>>>>> (reC x, S(x) rea x).
It's not provable but it certainly has meaning. >>>>>>>>>>>>>>>>>
Andr|-
out-of-scope for Q is more accurate as jargon free. >>>>>>>>>>>>>>>>
PTS does hold the view that meaning is only derived >>>>>>>>>>>>>>>> through inference steps. This simple sentence seems >>>>>>>>>>>>>>>> impossibly too difficult for anyone fully indoctrinated >>>>>>>>>>>>>>>> with alternative views. So I will simply say out-of-scope. >>>>>>>>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable. >>>>>>>>>>>>>>> Then to put things in words you can understand:
"I am driving to Walmart to buy a carton of
-a-aBreyer's natural vanilla ice cream." is also unprovable >>>>>>>>>>>>>> in PA.
In both cases the semantics in not represented in PA. >>>>>>>>>>>>>
It is expressed in PA
False.-a The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and >>>>>>>>>>>> the semantics of G are neither expressible in PA.
False.-a G is simply a sentence like ~reax x>10 v x<5 but much >>>>>>>>>>> more complex.
"No number is equal to its successor" is a sentence in RA, >>>>>>>>>>>>> and it is true but unprovable in RA (or as your would call >>>>>>>>>>>>> it, "out- of- scope").
If its semantics is not expressible in Q (What RA is called) >>>>>>>>>>>> then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the >>>>>>>>>>> language of Q.-a More formally, it is this:
~reax x=S(x)
And this sentence is not provable from the axioms of Q (or, >>>>>>>>>>> in terms you would understand, the above is "out-of-scope" of >>>>>>>>>>> Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
In your own words, what does it mean for a statement to be
"semantically grounded" in a formal system?
I always do back-chained inference because the typical
math way of doing forward chained inference may take
an infeasibly long time. A finite set of back-chained
inference steps from x to the axioms of Q.
Back or forward chained doesn't matter, it's essentially the same >>>>>>> steps in a different direction.-a But in any case, you're saying >>>>>>> "semantically grounded" is just another synonym for unprovable.
So to again put things in a way you'll understand, Godel proved >>>>>>> that any axiom system of arithmetic contains statements that are >>>>>>> not semantically grounded.
Not quite. G is not semantically grounded
i.e. unprovable
in PA
yet G is semantically grounded
i.e. provable
in metamathematics.
Which is exactly what Godel proved.
Your lack of response indicates that you agree with Godel, but used
different words to do so.
When an expression in PA only derives semantic
meaning in PA when grounded in PA then G has no
meaning in PA.
i.e. if a statement is unprovable in PA then it's unprovable in PA.
In other words, a meaningless tautology.
That also means that, using your terminology, it has been proven >>>>>>> that the statement ~reax x=S(x), i.e. "No number is equal to its >>>>>>> successor", is not semantically grounded in Q.
Thus is meaningless in Q and out-of-scope in Q.
Which means the semantically valid statement in Q
does not include ~reax x=S(x)
False, as it means "no number is equal to its successor", and the
concept of a successor and equality have semantic meaning in Q, as
does the concept of "all", "none", and "exists".
If there is no sequence of inference steps in Q from
~reax x=S(x) to the axioms of Q then ~reax x=S(x) is
ungrounded in the PTS atomic base of Q.
In other words, ~reax x=S(x) is unprovable in Q, as is commonly known.
So once again, you agree with everyone else, but are using different
words to say so.
On 26/06/2026 16:15, olcott wrote:
On 6/26/2026 1:45 AM, Mikko wrote:If anyone and everyone that claims that someone is dishonest
On 25/06/2026 19:16, olcott wrote:
On 6/25/2026 2:29 AM, Mikko wrote:
On 25/06/2026 00:33, olcott wrote:
On 6/24/2026 5:13 AM, Mikko wrote:
On 23/06/2026 21:20, olcott wrote:
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>> On 6/22/2026 1:42 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>> On 6/22/2026 10:48 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>
G is true.
I put it to you you're lying again. No reputable >>>>>>>>>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things. If Dag >>>>>>>>>>>>>>>>>>>>> Prawitz
really
did
"agree" (with whom?) that G||del's sentence G is not >>>>>>>>>>>>>>>>>>>>> true in
Peano
Arithmetic, then produce a citation for this. >>>>>>>>>>>>>>>>>
He never gets to G||del. He essentially says unprovable >>>>>>>>>>>>>>>>>>>> means untrue all the time for everything within his >>>>>>>>>>>>>>>>>>>> own Theory of Grounds of strict Proof Theoretic >>>>>>>>>>>>>>>>>>>> Semantics.
You won't understand it, but that _is_ essentially >>>>>>>>>>>>>>>>>>> G||del's
Incompleteness
Theorem. It is a statement that any sufficiently >>>>>>>>>>>>>>>>>>> powerful
system can
express true things it can't prove. So Dag Prawitz, >>>>>>>>>>>>>>>>>>> had he been
saying
the things you falsely attributed to him, would >>>>>>>>>>>>>>>>>>> certainly have
"got" to
G||del, and would have understood full well what he >>>>>>>>>>>>>>>>>>> was saying.
You did not pay close enough attention to my exact words. >>>>>>>>>>>>>>>>>I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>>
Yeah, I'm pretty sure that "Dag Prawitz says what Dag >>>>>>>>>>>>>>> Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz >>>>>>>>>>>>>>> doesn't
say",
then looking a bit into his tremendous volume of works, >>>>>>>>>>>>>>> he talks about "natural deduction" then specifically an >>>>>>>>>>>>>>> "inverse
principle" so I think these are key aspects of
fundamental logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself, >>>>>>>>>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to >>>>>>>>>>>>>>> generate
new ad-
missible rules within a certain syntactic context. Some >>>>>>>>>>>>>>> N4Ufteen years
later, the idea was taken up by Dag Prawitz to devise a >>>>>>>>>>>>>>> strategy of
normalization for natural deduction calculi (this being an >>>>>>>>>>>>>>> analogue of
GentzenrCOs cut-elimination theorem for sequent calculi). >>>>>>>>>>>>>>> Later,
Prawitz
used the inversion principle again, attributing it with a >>>>>>>>>>>>>>> semantic
role.
Still working in natural deduction calculi, he formulated >>>>>>>>>>>>>>> a general
type
of schematic Introduction rules to be matchedrCothanks to >>>>>>>>>>>>>>> the idea
supporting the inversion principle rCo by a corresponding >>>>>>>>>>>>>>> general
schematic Elimination rule. This was an attempt to provide a >>>>>>>>>>>>>>> solution to
the problem suggested by the often quoted note of Gentzen. >>>>>>>>>>>>>>> According to
Gentzen rCLit should be possible to display the elimination >>>>>>>>>>>>>>> rules as
unique functions of the corresponding introduction rules >>>>>>>>>>>>>>> on the
basis of
certain requirements.rCY Many people have since worked on >>>>>>>>>>>>>>> this topic,
which can be appropriately seen as the birthplace of what >>>>>>>>>>>>>>> are now
referred to as rCLgeneral elimination rulesrCY, recently studied
thoroughly
by Sara Negri and Jan von Plato. In this paper, we >>>>>>>>>>>>>>> retrace the main
threads of this chapter of proof-theoretical
investigation, using
LorenzenrCOs original framework as a general guide" >>>>>>>>>>>>>>>
Hm, "general elimination rules", seem derivable from De >>>>>>>>>>>>>>> Morgan's
laws,
and that being the usual account of naive deductive >>>>>>>>>>>>>>> analysis, then
since
"natural deduction", which here is held as part of the >>>>>>>>>>>>>>> theory
since it's naturally logical, then has for Gentzen that >>>>>>>>>>>>>>> besides
Kripke
afterward there's also Sheffer and Chwistek before, and >>>>>>>>>>>>>>> instead of
Montague for semantics there's Herbrand for semantics, >>>>>>>>>>>>>>> so, what to do
about "inversion principle" is here that the thea-theory >>>>>>>>>>>>>>> has that
it's
what subsumes "non-contradiction principle", here hoping >>>>>>>>>>>>>>> that the
interpretation aligns and thusly that "principle of >>>>>>>>>>>>>>> inversion"
wouldn't
need dis-ambiguation from "inversion principle". >>>>>>>>>>>>>>>
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334 >>>>>>>>>>>>>>>
https://www.strandbooks.com/natural-deduction-a-proof- >>>>>>>>>>>>>>> theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the >>>>>>>>>>>>>>> foundation of
most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a >>>>>>>>>>>>>>> principle of
thorough reason as subsuming principles of non-
contradiction and what
suffices, so, I'll be curious then about what to make of >>>>>>>>>>>>>>> Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as >>>>>>>>>>>>>>> old as the
oldest account of Western philosophy like Heraclitus with >>>>>>>>>>>>>>> dual
monism.
In fact by definition it's about the most basic aspect of >>>>>>>>>>>>>>> contemplation
and deliberation in abstraction of looking at both sides >>>>>>>>>>>>>>> of issues
and
resolving inductive impasses with analytical bridges after >>>>>>>>>>>>>>> complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as >>>>>>>>>>>>>>> one of the
characteristic features of Gentzen's intuitionistic natural >>>>>>>>>>>>>>> deduction.
In the literature on proof-theoretic semantics, this >>>>>>>>>>>>>>> principle is
often
coupled with another that is called the recovery >>>>>>>>>>>>>>> principle. By
adopting
the Computational Ludics framework, we reformulate these >>>>>>>>>>>>>>> principles
into
one and the same condition, which we call the harmony >>>>>>>>>>>>>>> condition. We
show
that this reformulation allows us to reveal two intuitive >>>>>>>>>>>>>>> ideas
standing
behind these principles: the idea of "containment" >>>>>>>>>>>>>>> present in the
inversion principle, and the idea that the recovery >>>>>>>>>>>>>>> principle is the
"converse" of the inversion principle. We also formulate >>>>>>>>>>>>>>> two other
conditions in the Computational Ludics framework, and we >>>>>>>>>>>>>>> show that
each
of them is equivalent to the harmony condition." >>>>>>>>>>>>>>>
The "ludicus" is Latin and for accounts of wisdom and >>>>>>>>>>>>>>> knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical >>>>>>>>>>>>>>> connectives,
proof-theoretic semantics rests on the idea that we know the >>>>>>>>>>>>>>> meaning of
a compound sentence when we know what counts as a >>>>>>>>>>>>>>> canonical proof of
it.
And if proofs are formalised within the framework of natural >>>>>>>>>>>>>>> deduction,
then a canonical proof of a sentence A is nothing but a >>>>>>>>>>>>>>> closed
derivation ending with an introduction rule of the main >>>>>>>>>>>>>>> connective
of A."
The "canonical proofs" are not unique, in any system >>>>>>>>>>>>>>> strong enough
to make for infinitary reasoning and super-classical results >>>>>>>>>>>>>>> requiring
analytical bridges about infinity and continuity. >>>>>>>>>>>>>>>
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6 >>>>>>>>>>>>>> That is the most important gist of his whole work. >>>>>>>>>>>>>>
He later goes on to develop and further elaborate his >>>>>>>>>>>>>> Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches >>>>>>>>>>>>>> Thomas Piecha & Peter Schroeder-Heister do this same sort of >>>>>>>>>>>>>> thing two different ways.
Furthermore I say there are "canonical proofs" of inductive >>>>>>>>>>>>> sorts that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by
"canonical proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make >>>>>>>>>>>>> repairs
of what otherwise is flawed, or for hard constructivist >>>>>>>>>>>>> realist
structuralist model theorists: not-theories (examples of >>>>>>>>>>>>> wrong).
Induction and counter-induction contradict each other, it's >>>>>>>>>>> simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog?
That would be dishonest.
No, pointing out that you are worng about Prolog when you are wrong >>>>>>> about Prolog is never dishohest.
That is correct Prolog and that is the
result of the correct run of correct Prolog.
Irrelevant. Nobody claimed there be Prolog errors in your queries.
Implying that I am wrong about Prolog without
pointing out any actual mistake is also DISHONEST.
How did Ross FInlayson imply that you were wrong about Prolog?
If an error is claimed then it must be specifically
pointed out otherwise the clam of error is dishonest.
Yet you claim that Ross Finlayson be dishonest without pointing
out what is dishonest in his words.
If anyone and everyone that claims that they found an
error and never points out what the error is and why
it is an error then they are merely a baseless denigrator.
never points out what the dishonesty is is and why it is
dishones then they are merely a baseless denigrator.
On 06/23/2026 10:32 AM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable
mathematician
would
risk his reputation by saying false things. If Dag Prawitz >>>>>>>>>>>>>> really
did
"agree" (with whom?) that G||del's sentence G is not true in >>>>>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
I was right, you didn't understand it.He never gets to G||del. He essentially says unprovable >>>>>>>>>>>>> means untrue all the time for everything within hisYou won't understand it, but that _is_ essentially G||del's >>>>>>>>>>>> Incompleteness
own Theory of Grounds of strict Proof Theoretic Semantics. >>>>>>>>>>
Theorem. It is a statement that any sufficiently powerful >>>>>>>>>>>> system can
express true things it can't prove. So Dag Prawitz, had he >>>>>>>>>>>> been
saying
the things you falsely attributed to him, would certainly have >>>>>>>>>>>> "got" to
G||del, and would have understood full well what he was saying. >>>>>>>>>>
You did not pay close enough attention to my exact words. >>>>>>>>>>
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz
says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't >>>>>>>> say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse >>>>>>>> principle" so I think these are key aspects of fundamental logic. >>>>>>>>
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself, >>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to generate >>>>>>>> new ad-
missible rules within a certain syntactic context. Some N4Ufteen >>>>>>>> years
later, the idea was taken up by Dag Prawitz to devise a strategy of >>>>>>>> normalization for natural deduction calculi (this being an
analogue of
GentzenrCOs cut-elimination theorem for sequent calculi). Later, >>>>>>>> Prawitz
used the inversion principle again, attributing it with a semantic >>>>>>>> role.
Still working in natural deduction calculi, he formulated a general >>>>>>>> type
of schematic Introduction rules to be matchedrCothanks to the idea >>>>>>>> supporting the inversion principle rCo by a corresponding general >>>>>>>> schematic Elimination rule. This was an attempt to provide a
solution to
the problem suggested by the often quoted note of Gentzen.
According to
Gentzen rCLit should be possible to display the elimination rules as >>>>>>>> unique functions of the corresponding introduction rules on the >>>>>>>> basis of
certain requirements.rCY Many people have since worked on this topic, >>>>>>>> which can be appropriately seen as the birthplace of what are now >>>>>>>> referred to as rCLgeneral elimination rulesrCY, recently studied >>>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the main >>>>>>>> threads of this chapter of proof-theoretical investigation, using >>>>>>>> LorenzenrCOs original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's >>>>>>>> laws,
and that being the usual account of naive deductive analysis, then >>>>>>>> since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides >>>>>>>> Kripke
afterward there's also Sheffer and Chwistek before, and instead of >>>>>>>> Montague for semantics there's Herbrand for semantics, so, what >>>>>>>> to do
about "inversion principle" is here that the thea-theory has that >>>>>>>> it's
what subsumes "non-contradiction principle", here hoping that the >>>>>>>> interpretation aligns and thusly that "principle of inversion" >>>>>>>> wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical- >>>>>>>> study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of >>>>>>>> most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a
principle of
thorough reason as subsuming principles of non-contradiction and >>>>>>>> what
suffices, so, I'll be curious then about what to make of Prawitz' >>>>>>>> "inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the >>>>>>>> oldest account of Western philosophy like Heraclitus with dual >>>>>>>> monism.
In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of issues >>>>>>>> and
resolving inductive impasses with analytical bridges after
complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the >>>>>>>> characteristic features of Gentzen's intuitionistic natural
deduction.
In the literature on proof-theoretic semantics, this principle is >>>>>>>> often
coupled with another that is called the recovery principle. By >>>>>>>> adopting
the Computational Ludics framework, we reformulate these principles >>>>>>>> into
one and the same condition, which we call the harmony condition. We >>>>>>>> show
that this reformulation allows us to reveal two intuitive ideas >>>>>>>> standing
behind these principles: the idea of "containment" present in the >>>>>>>> inversion principle, and the idea that the recovery principle is >>>>>>>> the
"converse" of the inversion principle. We also formulate two other >>>>>>>> conditions in the Computational Ludics framework, and we show that >>>>>>>> each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge. >>>>>>>>
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, >>>>>>>> proof-theoretic semantics rests on the idea that we know the
meaning of
a compound sentence when we know what counts as a canonical
proof of
it.
And if proofs are formalised within the framework of natural
deduction,
then a canonical proof of a sentence A is nothing but a closed >>>>>>>> derivation ending with an introduction rule of the main connective >>>>>>>> of A."
The "canonical proofs" are not unique, in any system strong enough >>>>>>>> to make for infinitary reasoning and super-classical results
requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts
that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical proofs". >>>>> Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs >>>>>> of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong).
Induction and counter-induction contradict each other, it's simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
P.S. there's no reason at all to "get back to you".
... Except countering the waste-ful spammy trolling.
Finding cycles in derivations of arguments is exactly
what makes for detection of circularities then as to
whether they're the virtuous or vicious sorts of circles,
it's the act of being diligent itself, you brainless, memoryless bot.
On 26/06/2026 16:02, olcott wrote:
On 6/26/2026 1:23 AM, Mikko wrote:
On 25/06/2026 16:47, olcott wrote:
On 6/25/2026 2:14 AM, Mikko wrote:
On 24/06/2026 23:23, olcott wrote:(a) Extracting atomic facts, would be the hardest part,
On 6/24/2026 4:45 AM, Mikko wrote:
On 23/06/2026 17:40, olcott wrote:
On 6/23/2026 12:49 AM, Mikko wrote:
On 22/06/2026 18:16, olcott wrote:
On 6/22/2026 2:46 AM, Mikko wrote:
On 22/06/2026 03:44, olcott wrote:
On 6/21/2026 7:32 PM, phoenix wrote:It is fairly simple to build a system of essentially infallible >>>>>>>>>>> reasoning that never errs even when it doesn't have all the >>>>>>>>>>> relevant information. The real problem is to construct a system >>>>>>>>>>> that tells something interesting instead of just different >>>>>>>>>>> presentations of the same already known facts.
olcott wrote:
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit >>>>>>>>>>>>> defeat?
olcott wrote:
On 6/21/2026 3:18 PM, Andr|- G. Isaak wrote:Lastly, and why should we care? Please answer this and >>>>>>>>>>>>>>> other questions presented.
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/17/2026 4:14 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> https://www.youtube.com/@rossfinlayson >>>>>>>>>>>>>>>>>>>>>>>> Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof- >>>>>>>>>>>>>>>>>>>>>>>> theoretic- semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>>>>Whereas you are stuck to your own incoherent views >>>>>>>>>>>>>>>>>>>>>> and reject
alternative views out-of-hand without review. >>>>>>>>>>>>>>>>>>
Calling my views (anchored in proof theoretic >>>>>>>>>>>>>>>>>>>>> semantics)
incoherent merely proves that you are too damned >>>>>>>>>>>>>>>>>>>>> lazy to
look into proof theoretic semantics. >>>>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>>>> semantics/
I've spent a couple of hours reading that web page. >>>>>>>>>>>>>>>>>>>> It is abstract in
the extreme.-a One thing is utterly clear: its level >>>>>>>>>>>>>>>>>>>> of abstraction is
well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>>>>>>>> Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that >>>>>>>>>>>>>>>>>>>> I can't be bothered
to read it any further.-a If it actually says >>>>>>>>>>>>>>>>>>>> anything at all, that
something is heavily disguised.-a From it's >>>>>>>>>>>>>>>>>>>> "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically >>>>>>>>>>>>>>>>>>>> exclusively been
| occupied with logical constants. Logical constants >>>>>>>>>>>>>>>>>>>> play a central role
| in reasoning and inference, but are definitely not >>>>>>>>>>>>>>>>>>>> the exclusive, and
| perhaps not even the most typical sort of entities >>>>>>>>>>>>>>>>>>>> that can be defined
| inferentially. A framework is needed that deals >>>>>>>>>>>>>>>>>>>> with inferential
| definitions in a wider sense and covers both >>>>>>>>>>>>>>>>>>>> logical and extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is >>>>>>>>>>>>>>>>>>> currently and in the
near future not useful as making it useful requires >>>>>>>>>>>>>>>>>>> much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be >>>>>>>>>>>>>>>>>> useful for? What it
ought to be able to do that standard logic fails at? >>>>>>>>>>>>>>>>>> Maybe Andr|- could
elucidate.-a He seems to have a better grasp of it than >>>>>>>>>>>>>>>>>> anybody else here.
I doubt my understanding of PTS is any better than >>>>>>>>>>>>>>>>> yours. I basically only know what is presented in the >>>>>>>>>>>>>>>>> Stanford Encyclopedia article (which you correctly >>>>>>>>>>>>>>>>> point out is not exactly aimed at beginners) and the >>>>>>>>>>>>>>>>> Wikipedia article. What I am quite certain of, however, >>>>>>>>>>>>>>>>> is that Olcott lacks any understanding of what PTS >>>>>>>>>>>>>>>>> actually says as he's made a variety of fairly absurd >>>>>>>>>>>>>>>>> claims regarding it (for example, that PTS claims that >>>>>>>>>>>>>>>>> unproven propositions are 'meaningless' or that the >>>>>>>>>>>>>>>>> goal of PTS is to completely overthrow standard truth- >>>>>>>>>>>>>>>>> theoretic semantics).
Andr|-
-a-a Proof-theoretic semantics is an alternative to >>>>>>>>>>>>>>>> -a-a truth-condition semantics. It is based on the >>>>>>>>>>>>>>>> -a-a fundamental assumption that the central notion >>>>>>>>>>>>>>>> -a-a in terms of which meanings are assigned to certain >>>>>>>>>>>>>>>> -a-a expressions of our language, in particular to >>>>>>>>>>>>>>>> -a-a logical constants, is that of proof rather than >>>>>>>>>>>>>>>> -a-a truth. In this sense proof-theoretic semantics >>>>>>>>>>>>>>>> -a-a is semantics in terms of proof.
-a-a https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>> semantics/
In other words it answers the question:
What happens when truth conditional semantics is >>>>>>>>>>>>>>>> utterly abandoned and is totally replaced by proof >>>>>>>>>>>>>>>> theoretic semantics?
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time. >>>>>>>>>>>>>>
We can make these lies look foolish at every language >>>>>>>>>>>>>> level from below average kindergarten to profoundly >>>>>>>>>>>>>> brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more >>>>>>>>>>>>>> than 100-fold more valuable.
It is not that they never admit defeat.
It is that that have a system of essentially infallible >>>>>>>>>>>> reasoning
that never errs as long as it has all the relevant information. >>>>>>>>>>>
It will have the exhaustively complete list of
every atomic fact of general knowledge of the
actual world.
That is impossible. By the time you have all facts of general >>>>>>>>> knowledge
in your system the general knowledge has grown to inlude more >>>>>>>>> facts.
It can be reasonably approximated pretty quickly.
We start with all of the textbooks.
That is a lot of reading, though those for the same topic area tend >>>>>>> to say the same, and the old ones add very little to the new ones, >>>>>>> mainly some now obsolete technology.
It would not be too much reading for LLMs.
It could start with all of the latest textbooks
for all of the fields. Some of these latest
textbooks may be hundreds of years old for
fields that have become obsolete.
Perhaps that apprach should be tried. The problem involves extracting >>>>> atomic facts, detecting repeated facts, and encoding facts for the
inference system.
yet not too hard.
(b) Detecting repeated facts, string comparison.
(c) Encoding facts, CycL
https://en.wikipedia.org/wiki/CycL
I still have the original user's manuals
as PDFs and hard copies.
Do they say anything about normalization?
--The encoding must be normalized as much as possible in order to reduce
repetition to a string comparison. That is not a trivial problem if one
wants a total or nearly total prevention of repetition.
On 26/06/2026 16:05, olcott wrote:
On 6/26/2026 1:34 AM, Mikko wrote:
On 25/06/2026 16:58, olcott wrote:
On 6/25/2026 2:18 AM, Mikko wrote:
On 24/06/2026 23:25, olcott wrote:
On 6/24/2026 4:52 AM, Mikko wrote:
On 23/06/2026 17:47, olcott wrote:
On 6/23/2026 12:55 AM, Mikko wrote:
On 22/06/2026 15:09, olcott wrote:
On 6/22/2026 1:41 AM, Mikko wrote:
On 22/06/2026 02:58, olcott wrote:
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:Whereas you are stuck to your own incoherent views and >>>>>>>>>>>>>>>>> reject
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>>>
alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>>> look into proof theoretic semantics.
At different times you have expressed different opinions, >>>>>>>>>>>>>>> which
sometimes have been incompatible. But you have never clearly >>>>>>>>>>>>>>> retracted your earlier opitions that conflict with your >>>>>>>>>>>>>>> present
ones.
All of the ideas that I have ever had about these things >>>>>>>>>>>>>> are now under the Proof Theoretic Semantics category. >>>>>>>>>>>>>> These ideas have evolved over time, yet their essence >>>>>>>>>>>>>> has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a >>>>>>>>>>>>> publishable
(or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> human >>>>>>>>>>>> being on the face of the Earth could understand
me I could not publish.
As far as I have seen, all interesting content in those articles >>>>>>>>>>> that have any is or depends on claims that should be proven but >>>>>>>>>>> aren't.
They are proven in Proof Theoretic Semantics
An aricle is not publishable unless it either contains the
proof or
has a pointer to an olready published proof.
Only now after 28 years am I acquiring the lingua Franca
terms-of-the-art of proof theoretic semantics such that
I can anchor my ideas in the foundational work of the
most respected authors in the field.
My issue with you guys is that you only spend 1%
of your concentration understanding me and the other
99% trying to artificially contrive some baseless
rebuttal.
THat "baseless" is false but otherwise, what is wrong is more
important than what is right. Of one ignores what is right one
mai fail to achieve what one could, but if one believs what is
wrong one may achieve a disaseter.
Proof-theoretic semantics is an alternative to truth-condition
semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
So far no one has even acknowledged that PTS is an alternative
to truth-conditional semantics. Several people have seemed
to same that no alternative can possibly exist.
You have not shown that there is any need for any alternative
semantics.
With dangerous lies that can destroy Democracy
and kill the planet with climate change having
an ultimate arbiter of truth would be useful.
Those who are able and willing to destroy democracy are able to provice
an ultimate arbiter of truth and usually do so. But they don't need any
proof theoretic semantics.
An ultimate arbiter of truth blows their whole game away.
THe point of the ultimate arbiter of truth is that the errors in the determinations of any alternative arbiter can be detected and similar
errors in future can be avoided with suitable admistrative or other
actions if regarded necessary.
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>> what: "grounded in the atomic base" means is less
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>>>>You can find any number of terms.-a That doesn't mean >>>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS G||del 1931 >>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that PTS >>>>>>>>>>>>>>> somehow causes
G||del's theorem not to hold, then cite an academic expert >>>>>>>>>>>>>>> who'll have
some credibility.
If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>> not understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>>>>> certainly don't
understand G||del's Theorem, neither the theorem itself >>>>>>>>>>>>>>> nor any proof of
it.
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used >>>>>>>>>>>>> only by you, and it is one which you have never explicitly >>>>>>>>>>>>> defined, so the fault here certainly doesn't lie with Alan. >>>>>>>>>>>>> It's certainly not a 'verified fact' when you haven't even >>>>>>>>>>>>> adequately explained what it is that you mean.
All of knowledge expressed in language is structured as a >>>>>>>>>>>> tree of semantic relations specified syntactically between >>>>>>>>>>>> finite strings.
What makes you believe semantic relations that can be
structured as
a tree are sufficient to contain all knowledge that is
exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to >>>>>>>>> put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop >>>>>>> when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before
looking for a proof.
This is the same sort of thing as finding the defined
meaning of a word. If you cannot find its recursively
defined meaning then it never gains any meaning.
That does not follow. Words have meanings even without definitions.
You can't present the first definition unless you already have
meaningful words.
Typically the presentation of a formal theory begins with the
introduction of undefined symbols. But the symbols are not
fully meaningless. They get some amount of meaning from being
introduces as symbols of a particular syntactic category and
more from being used in the postulates of the theory.
On 26/06/2026 19:08, dbush wrote:
On 6/26/2026 10:24 AM, olcott wrote:
On 6/26/2026 8:57 AM, dbush wrote:
On 6/26/2026 9:45 AM, olcott wrote:
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms.-a That doesn't >>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS G||del >>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>>> PTS somehow causes
G||del's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>>> you certainly don't
understand G||del's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly >>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>> fact' when you haven't even adequately explained what >>>>>>>>>>>>>>>>>> it is that you mean.
All of knowledge expressed in language is structured as >>>>>>>>>>>>>>>>> a tree of semantic relations specified syntactically >>>>>>>>>>>>>>>>> between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a >>>>>>>>>>>> loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not
obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is
equal to its successor" has no meaning in Robinson Arithmetic.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
Then you agree that the above natural language sentence that is
semantically required to be either true or false has no meaning?
Your sentence would be what it always has been
a stipulated true sentence axiom.
False, as that statement is not one of the axioms of Robinson
arithmetic, but it is a statement in its language, and one that has
*only* an infinite connection to the axioms of that system.
What infinite connection? The statement is false in natural numbers,
which is one model of Robinson Arithmetic but not the only one.
In another model there may be a number that is its successor. There
may even be more than one such number.
By your logic, "no number is equal to its successor" has no meaning in
Robinson arithmetic.
On 27/06/2026 01:01, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable.-a Then to >>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
-a-aBreyer's natural vanilla ice cream." is also unprovable in PA. >>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False.-a The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False.-a G is simply a sentence like ~reax x>10 v x<5 but much more
complex.
"No number is equal to its successor" is a sentence in RA, and it
is true but unprovable in RA (or as your would call it, "out-of-
scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language
of Q.-a More formally, it is this:
~reax x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms
you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
Nevertheless a sentence like ~reax x=S(x) is in the language of Q and
that way in the theory.
On 26/06/2026 16:15, olcott wrote:
On 6/26/2026 1:45 AM, Mikko wrote:
On 25/06/2026 19:16, olcott wrote:
On 6/25/2026 2:29 AM, Mikko wrote:
On 25/06/2026 00:33, olcott wrote:
On 6/24/2026 5:13 AM, Mikko wrote:
On 23/06/2026 21:20, olcott wrote:
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>> On 6/22/2026 1:42 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>> On 6/22/2026 10:48 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>
G is true.
I put it to you you're lying again.-a No reputable >>>>>>>>>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things.-a If Dag >>>>>>>>>>>>>>>>>>>>> Prawitz
really
did
"agree" (with whom?) that G||del's sentence G is not >>>>>>>>>>>>>>>>>>>>> true in
Peano
Arithmetic, then produce a citation for this. >>>>>>>>>>>>>>>>>
He never gets to G||del. He essentially says unprovable >>>>>>>>>>>>>>>>>>>> means untrue all the time for everything within his >>>>>>>>>>>>>>>>>>>> own Theory of Grounds of strict Proof Theoretic >>>>>>>>>>>>>>>>>>>> Semantics.
You won't understand it, but that _is_ essentially >>>>>>>>>>>>>>>>>>> G||del's
Incompleteness
Theorem.-a It is a statement that any sufficiently >>>>>>>>>>>>>>>>>>> powerful
system can
express true things it can't prove.-a So Dag Prawitz, >>>>>>>>>>>>>>>>>>> had he been
saying
the things you falsely attributed to him, would >>>>>>>>>>>>>>>>>>> certainly have
"got" to
G||del, and would have understood full well what he >>>>>>>>>>>>>>>>>>> was saying.
You did not pay close enough attention to my exact words. >>>>>>>>>>>>>>>>>I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>>
Yeah, I'm pretty sure that "Dag Prawitz says what Dag >>>>>>>>>>>>>>> Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz >>>>>>>>>>>>>>> doesn't
say",
then looking a bit into his tremendous volume of works, >>>>>>>>>>>>>>> he talks about "natural deduction" then specifically an >>>>>>>>>>>>>>> "inverse
principle" so I think these are key aspects of
fundamental logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself, >>>>>>>>>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to >>>>>>>>>>>>>>> generate
new ad-
missible rules within a certain syntactic context. Some >>>>>>>>>>>>>>> N4Ufteen years
later, the idea was taken up by Dag Prawitz to devise a >>>>>>>>>>>>>>> strategy of
normalization for natural deduction calculi (this being an >>>>>>>>>>>>>>> analogue of
GentzenrCOs cut-elimination theorem for sequent calculi). >>>>>>>>>>>>>>> Later,
Prawitz
used the inversion principle again, attributing it with a >>>>>>>>>>>>>>> semantic
role.
Still working in natural deduction calculi, he formulated >>>>>>>>>>>>>>> a general
type
of schematic Introduction rules to be matchedrCothanks to >>>>>>>>>>>>>>> the idea
supporting the inversion principle rCo by a corresponding >>>>>>>>>>>>>>> general
schematic Elimination rule. This was an attempt to provide a >>>>>>>>>>>>>>> solution to
the problem suggested by the often quoted note of Gentzen. >>>>>>>>>>>>>>> According to
Gentzen rCLit should be possible to display the elimination >>>>>>>>>>>>>>> rules as
unique functions of the corresponding introduction rules >>>>>>>>>>>>>>> on the
basis of
certain requirements.rCY Many people have since worked on >>>>>>>>>>>>>>> this topic,
which can be appropriately seen as the birthplace of what >>>>>>>>>>>>>>> are now
referred to as rCLgeneral elimination rulesrCY, recently studied
thoroughly
by Sara Negri and Jan von Plato. In this paper, we >>>>>>>>>>>>>>> retrace the main
threads of this chapter of proof-theoretical
investigation, using
LorenzenrCOs original framework as a general guide" >>>>>>>>>>>>>>>
Hm, "general elimination rules", seem derivable from De >>>>>>>>>>>>>>> Morgan's
laws,
and that being the usual account of naive deductive >>>>>>>>>>>>>>> analysis, then
since
"natural deduction", which here is held as part of the >>>>>>>>>>>>>>> theory
since it's naturally logical, then has for Gentzen that >>>>>>>>>>>>>>> besides
Kripke
afterward there's also Sheffer and Chwistek before, and >>>>>>>>>>>>>>> instead of
Montague for semantics there's Herbrand for semantics, >>>>>>>>>>>>>>> so, what to do
about "inversion principle" is here that the thea-theory >>>>>>>>>>>>>>> has that
it's
what subsumes "non-contradiction principle", here hoping >>>>>>>>>>>>>>> that the
interpretation aligns and thusly that "principle of >>>>>>>>>>>>>>> inversion"
wouldn't
need dis-ambiguation from "inversion principle". >>>>>>>>>>>>>>>
https://www.tandfonline.com/doi/
abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof- >>>>>>>>>>>>>>> theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the >>>>>>>>>>>>>>> foundation of
most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a >>>>>>>>>>>>>>> principle of
thorough reason as subsuming principles of non- >>>>>>>>>>>>>>> contradiction and what
suffices, so, I'll be curious then about what to make of >>>>>>>>>>>>>>> Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as >>>>>>>>>>>>>>> old as the
oldest account of Western philosophy like Heraclitus with >>>>>>>>>>>>>>> dual
monism.
In fact by definition it's about the most basic aspect of >>>>>>>>>>>>>>> contemplation
and deliberation in abstraction of looking at both sides >>>>>>>>>>>>>>> of issues
and
resolving inductive impasses with analytical bridges after >>>>>>>>>>>>>>> complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as >>>>>>>>>>>>>>> one of the
characteristic features of Gentzen's intuitionistic natural >>>>>>>>>>>>>>> deduction.
In the literature on proof-theoretic semantics, this >>>>>>>>>>>>>>> principle is
often
coupled with another that is called the recovery >>>>>>>>>>>>>>> principle. By
adopting
the Computational Ludics framework, we reformulate these >>>>>>>>>>>>>>> principles
into
one and the same condition, which we call the harmony >>>>>>>>>>>>>>> condition. We
show
that this reformulation allows us to reveal two intuitive >>>>>>>>>>>>>>> ideas
standing
behind these principles: the idea of "containment" >>>>>>>>>>>>>>> present in the
inversion principle, and the idea that the recovery >>>>>>>>>>>>>>> principle is the
"converse" of the inversion principle. We also formulate >>>>>>>>>>>>>>> two other
conditions in the Computational Ludics framework, and we >>>>>>>>>>>>>>> show that
each
of them is equivalent to the harmony condition." >>>>>>>>>>>>>>>
The "ludicus" is Latin and for accounts of wisdom and >>>>>>>>>>>>>>> knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical >>>>>>>>>>>>>>> connectives,
proof-theoretic semantics rests on the idea that we know the >>>>>>>>>>>>>>> meaning of
a compound sentence when we know what counts as a >>>>>>>>>>>>>>> canonical proof of
it.
And if proofs are formalised within the framework of natural >>>>>>>>>>>>>>> deduction,
then a canonical proof of a sentence A is nothing but a >>>>>>>>>>>>>>> closed
derivation ending with an introduction rule of the main >>>>>>>>>>>>>>> connective
of A."
The "canonical proofs" are not unique, in any system >>>>>>>>>>>>>>> strong enough
to make for infinitary reasoning and super-classical results >>>>>>>>>>>>>>> requiring
analytical bridges about infinity and continuity. >>>>>>>>>>>>>>>
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6 >>>>>>>>>>>>>> That is the most important gist of his whole work. >>>>>>>>>>>>>>
He later goes on to develop and further elaborate his >>>>>>>>>>>>>> Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches >>>>>>>>>>>>>> Thomas Piecha & Peter Schroeder-Heister do this same sort of >>>>>>>>>>>>>> thing two different ways.
Furthermore I say there are "canonical proofs" of inductive >>>>>>>>>>>>> sorts that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by
"canonical proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make >>>>>>>>>>>>> repairs
of what otherwise is flawed, or for hard constructivist >>>>>>>>>>>>> realist
structuralist model theorists: not-theories (examples of >>>>>>>>>>>>> wrong).
Induction and counter-induction contradict each other, it's >>>>>>>>>>> simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog?
That would be dishonest.
No, pointing out that you are worng about Prolog when you are wrong >>>>>>> about Prolog is never dishohest.
That is correct Prolog and that is the
result of the correct run of correct Prolog.
Irrelevant. Nobody claimed there be Prolog errors in your queries.
Implying that I am wrong about Prolog without
pointing out any actual mistake is also DISHONEST.
How did Ross FInlayson imply that you were wrong about Prolog?
If an error is claimed then it must be specifically
pointed out otherwise the clam of error is dishonest.
Yet you claim that Ross Finlayson be dishonest without pointing
out what is dishonest in his words.
If anyone and everyone that claims that they found an
error and never points out what the error is and why
it is an error then they are merely a baseless denigrator.
If anyone and everyone that claims that someone is dishonest
never points out what the dishonesty is is and why it is
dishones then they are merely a baseless denigrator.
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:All of knowledge expressed in language is structured as a >>>>>>>>>>>>> tree of semantic relations specified syntactically between >>>>>>>>>>>>> finite strings.
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>>>>>You can find any number of terms.-a That doesn't mean >>>>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS G||del 1931 >>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that PTS >>>>>>>>>>>>>>>> somehow causes
G||del's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>>> not understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>>>>>> certainly don't
understand G||del's Theorem, neither the theorem itself >>>>>>>>>>>>>>>> nor any proof of
it.
"grounded in the atomic base of PA" is an expression used >>>>>>>>>>>>>> only by you, and it is one which you have never explicitly >>>>>>>>>>>>>> defined, so the fault here certainly doesn't lie with >>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' when you >>>>>>>>>>>>>> haven't even adequately explained what it is that you mean. >>>>>>>>>>>>
What makes you believe semantic relations that can be >>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to >>>>>>>>>> put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop >>>>>>>> when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before
looking for a proof.
If there is no sequence of inference steps in Q from
~reax x=S(x) to the axioms of Q
then ~reax x=S(x) is
ungrounded in the PTS atomic base of Q.
This does not mean undecidable or incomplete
it means that ~reax x=S(x) is out-of-scope for Q.
This is the same sort of thing as finding the defined
meaning of a word. If you cannot find its recursively
defined meaning then it never gains any meaning.
That does not follow. Words have meanings even without definitions.
You can't present the first definition unless you already have
meaningful words.
A particular new word can only be defined in terms
of other existing words that already have definitions.
PTS works in a similar way. If ~reax x=S(x)
cannot connect
to its meanings in Q the it remains undefined in Q.
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>>>>>>You can find any number of terms.-a That doesn't mean >>>>>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS G||del 1931 >>>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that PTS >>>>>>>>>>>>>>>>> somehow causes
G||del's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>>>> not understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>>>>>>> certainly don't
understand G||del's Theorem, neither the theorem itself >>>>>>>>>>>>>>>>> nor any proof of
it.
"grounded in the atomic base of PA" is an expression used >>>>>>>>>>>>>>> only by you, and it is one which you have never >>>>>>>>>>>>>>> explicitly defined, so the fault here certainly doesn't >>>>>>>>>>>>>>> lie with Alan. It's certainly not a 'verified fact' when >>>>>>>>>>>>>>> you haven't even adequately explained what it is that you >>>>>>>>>>>>>>> mean.
All of knowledge expressed in language is structured as a >>>>>>>>>>>>>> tree of semantic relations specified syntactically between >>>>>>>>>>>>>> finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to >>>>>>>>>>> put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop >>>>>>>>> when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious >>>>> how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before
looking for a proof.
If there is no sequence of inference steps in Q from
~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms.-a That doesn't mean >>>>>>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS G||del 1931 >>>>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that >>>>>>>>>>>>>>>>>> PTS somehow causes
G||del's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>>>>> not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>> you certainly don't
understand G||del's Theorem, neither the theorem itself >>>>>>>>>>>>>>>>>> nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly doesn't >>>>>>>>>>>>>>>> lie with Alan. It's certainly not a 'verified fact' when >>>>>>>>>>>>>>>> you haven't even adequately explained what it is that >>>>>>>>>>>>>>>> you mean.
All of knowledge expressed in language is structured as a >>>>>>>>>>>>>>> tree of semantic relations specified syntactically >>>>>>>>>>>>>>> between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop >>>>>>>>>> when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious >>>>>> how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before
looking for a proof.
If there is no sequence of inference steps in Q from
~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x)
is ungrounded in the PTS atomic base of Q.
On 6/27/2026 2:27 PM, olcott wrote:
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms.-a That doesn't >>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS G||del 1931 >>>>>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>> PTS somehow causes
G||del's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>> you certainly don't
understand G||del's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly doesn't >>>>>>>>>>>>>>>>> lie with Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>> when you haven't even adequately explained what it is >>>>>>>>>>>>>>>>> that you mean.
All of knowledge expressed in language is structured as >>>>>>>>>>>>>>>> a tree of semantic relations specified syntactically >>>>>>>>>>>>>>>> between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a >>>>>>>>>>> loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious >>>>>>> how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before
looking for a proof.
If there is no sequence of inference steps in Q from
~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x)
is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known.
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms.-a That doesn't >>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS G||del >>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>>> PTS somehow causes
G||del's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>>> you certainly don't
understand G||del's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly >>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>> fact' when you haven't even adequately explained what >>>>>>>>>>>>>>>>>> it is that you mean.
All of knowledge expressed in language is structured as >>>>>>>>>>>>>>>>> a tree of semantic relations specified syntactically >>>>>>>>>>>>>>>>> between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a >>>>>>>>>>>> loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not
obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before
looking for a proof.
If there is no sequence of inference steps in Q from
~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x)
is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known.
is semantic nonsense in Q?
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms.-a That doesn't >>>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS G||del >>>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>>>> PTS somehow causes
G||del's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>>>> you certainly don't
understand G||del's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly >>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>>> fact' when you haven't even adequately explained what >>>>>>>>>>>>>>>>>>> it is that you mean.
All of knowledge expressed in language is structured >>>>>>>>>>>>>>>>>> as a tree of semantic relations specified >>>>>>>>>>>>>>>>>> syntactically between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting stuck in >>>>>>>>>>>>> a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not >>>>>>>>> obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before >>>>>>> looking for a proof.
If there is no sequence of inference steps in Q from
~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x)
is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known.
Which has the semantic meaning "no number is equal to its successor" as
per the definition of Q.
is semantic nonsense in Q?
False, see above.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms.-a That doesn't >>>>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS G||del >>>>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody >>>>>>>>>>>>>>>>>>>>>> that PTS somehow causes
G||del's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, >>>>>>>>>>>>>>>>>>>>>> and you certainly don't
understand G||del's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not a >>>>>>>>>>>>>>>>>>>> 'verified fact' when you haven't even adequately >>>>>>>>>>>>>>>>>>>> explained what it is that you mean.
All of knowledge expressed in language is structured >>>>>>>>>>>>>>>>>>> as a tree of semantic relations specified >>>>>>>>>>>>>>>>>>> syntactically between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would >>>>>>>>>>>>>>>> one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting stuck in >>>>>>>>>>>>>> a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent >>>>>>>>>>>> loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>> PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability >>>>>>>>>>> or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not >>>>>>>>>> obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before >>>>>>>> looking for a proof.
If there is no sequence of inference steps in Q from
~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x)
is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known.
Which has the semantic meaning "no number is equal to its successor"
as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
It is more accurate to say it this way
than to say that it is semantically incoherent in Q.
It is great that you brought this up: ~reax x=S(x).
We can have much clearer communication about that
then we can about G||del's 1931 Incompleteness.
is semantic nonsense in Q?
False, see above.
On 6/27/2026 3:01 PM, olcott wrote:
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
All of knowledge expressed in language is structured >>>>>>>>>>>>>>>>>>>> as a tree of semantic relations specified >>>>>>>>>>>>>>>>>>>> syntactically between finite strings.On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms.-a That doesn't >>>>>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS G||del >>>>>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody >>>>>>>>>>>>>>>>>>>>>>> that PTS somehow causes
G||del's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, >>>>>>>>>>>>>>>>>>>>>>> and you certainly don't
understand G||del's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one which >>>>>>>>>>>>>>>>>>>>> you have never explicitly defined, so the fault >>>>>>>>>>>>>>>>>>>>> here certainly doesn't lie with Alan. It's >>>>>>>>>>>>>>>>>>>>> certainly not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>> even adequately explained what it is that you mean. >>>>>>>>>>>>>>>>>>>
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that >>>>>>>>>>>>>>>>>>> is exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would >>>>>>>>>>>>>>>>> one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting stuck >>>>>>>>>>>>>>> in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent >>>>>>>>>>>>> loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>> PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability >>>>>>>>>>>> or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not >>>>>>>>>>> obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before >>>>>>>>> looking for a proof.
If there is no sequence of inference steps in Q from
~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x)
is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known.
Which has the semantic meaning "no number is equal to its successor"
as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]What makes you believe semantic relations that can >>>>>>>>>>>>>>>>>>>> be structured as
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms.-a That >>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>> understanding them.
The above is the key reason why under PTS G||del >>>>>>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody >>>>>>>>>>>>>>>>>>>>>>>> that PTS somehow causes
G||del's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have
some credibility.
If they are mere gibberish words to you then >>>>>>>>>>>>>>>>>>>>>>>>> you will not understand.
You don't understand Proof-theoritic Semantics, >>>>>>>>>>>>>>>>>>>>>>>> and you certainly don't
understand G||del's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one which >>>>>>>>>>>>>>>>>>>>>> you have never explicitly defined, so the fault >>>>>>>>>>>>>>>>>>>>>> here certainly doesn't lie with Alan. It's >>>>>>>>>>>>>>>>>>>>>> certainly not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is that you mean. >>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge that >>>>>>>>>>>>>>>>>>>> is exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would >>>>>>>>>>>>>>>>>> one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting stuck >>>>>>>>>>>>>>>> in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent >>>>>>>>>>>>>> loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>
compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>> PTS just coherently connects the semantic meanings
expressed in language together into one coherent body >>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>> or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not >>>>>>>>>>>> obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before >>>>>>>>>> looking for a proof.
If there is no sequence of inference steps in Q from
~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x)
is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known.
Which has the semantic meaning "no number is equal to its successor"
as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms.-a That doesn't mean >>>>>>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS G||del 1931 >>>>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that >>>>>>>>>>>>>>>>>> PTS somehow causes
G||del's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>>>>> not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>> you certainly don't
understand G||del's Theorem, neither the theorem itself >>>>>>>>>>>>>>>>>> nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly doesn't >>>>>>>>>>>>>>>> lie with Alan. It's certainly not a 'verified fact' when >>>>>>>>>>>>>>>> you haven't even adequately explained what it is that >>>>>>>>>>>>>>>> you mean.
All of knowledge expressed in language is structured as a >>>>>>>>>>>>>>> tree of semantic relations specified syntactically >>>>>>>>>>>>>>> between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop >>>>>>>>>> when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious >>>>>> how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before
looking for a proof.
If there is no sequence of inference steps in Q from
~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x)
is ungrounded in the PTS atomic base of Q.
PTS also says FINITE sequence.
I cannot use the convoluted way that PTS says it in
all of their different author-by-author terms-of-the-art
and still be understood.
The above version is very close to the way that one
PTS author would say it and does convey the same
gist of meanings that other PTS authors accept.
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]What makes you believe semantic relations that can >>>>>>>>>>>>>>>>>>>>> be structured as
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>> understand
In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms.-a That >>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them.
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>> G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no respect for >>>>>>>>>>>>>>>>>>>>>>>>> or understanding of the
truth.-a If you really want to persuade anybody >>>>>>>>>>>>>>>>>>>>>>>>> that PTS somehow causes
G||del's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have
some credibility.
If they are mere gibberish words to you then >>>>>>>>>>>>>>>>>>>>>>>>>> you will not understand.
You don't understand Proof-theoritic Semantics, >>>>>>>>>>>>>>>>>>>>>>>>> and you certainly don't
understand G||del's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one which >>>>>>>>>>>>>>>>>>>>>>> you have never explicitly defined, so the fault >>>>>>>>>>>>>>>>>>>>>>> here certainly doesn't lie with Alan. It's >>>>>>>>>>>>>>>>>>>>>>> certainly not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is that you mean. >>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge that >>>>>>>>>>>>>>>>>>>>> is exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would >>>>>>>>>>>>>>>>>>> one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting stuck >>>>>>>>>>>>>>>>> in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent >>>>>>>>>>>>>>> loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>
compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>>> or mathematical incompleteness.
Looking for a proof does not need any semantics so it is >>>>>>>>>>>>> not obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before >>>>>>>>>>> looking for a proof.
If there is no sequence of inference steps in Q from
~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x)
is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known.
Which has the semantic meaning "no number is equal to its
successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
On 2026-06-27 12:27, olcott wrote:
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms.-a That doesn't >>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS G||del 1931 >>>>>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>> PTS somehow causes
G||del's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>> you certainly don't
understand G||del's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly doesn't >>>>>>>>>>>>>>>>> lie with Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>> when you haven't even adequately explained what it is >>>>>>>>>>>>>>>>> that you mean.
All of knowledge expressed in language is structured as >>>>>>>>>>>>>>>> a tree of semantic relations specified syntactically >>>>>>>>>>>>>>>> between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a >>>>>>>>>>> loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious >>>>>>> how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before
looking for a proof.
If there is no sequence of inference steps in Q from
~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x)
is ungrounded in the PTS atomic base of Q.
PTS also says FINITE sequence.
I cannot use the convoluted way that PTS says it in
all of their different author-by-author terms-of-the-art
and still be understood.
If PTS is so convoluted, why should we take your word for it that you
are actually interpreting it correctly?
The above version is very close to the way that one
PTS author would say it and does convey the same
gist of meanings that other PTS authors accept.
very close to doesn't mean the same as. Why don't you actually quote the author in question so we can see for ourselves exactly how close to it
your formulation is?
Andr|-
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>>>> or mathematical incompleteness.
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>> would one try to
On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
What makes you believe semantic relations that can >>>>>>>>>>>>>>>>>>>>>> be structured asAll of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>> understand
In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday.
You can find any number of terms.-a That >>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them.
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>> G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no respect for >>>>>>>>>>>>>>>>>>>>>>>>>> or understanding of the
truth.-a If you really want to persuade anybody >>>>>>>>>>>>>>>>>>>>>>>>>> that PTS somehow causes
G||del's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you then >>>>>>>>>>>>>>>>>>>>>>>>>>> you will not understand.
You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>> it.
what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one which >>>>>>>>>>>>>>>>>>>>>>>> you have never explicitly defined, so the fault >>>>>>>>>>>>>>>>>>>>>>>> here certainly doesn't lie with Alan. It's >>>>>>>>>>>>>>>>>>>>>>>> certainly not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>> prevent loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>
Looking for a proof does not need any semantics so it is >>>>>>>>>>>>>> not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>
It should be obvious that finding a proof does not happen >>>>>>>>>>>> before
looking for a proof.
If there is no sequence of inference steps in Q from
~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x)
is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known.
Which has the semantic meaning "no number is equal to its
successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>>>>> or mathematical incompleteness.
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>> would one try to
What makes you believe semantic relations that >>>>>>>>>>>>>>>>>>>>>>> can be structured asIt is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday.
You can find any number of terms.-a That >>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them.
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no respect for >>>>>>>>>>>>>>>>>>>>>>>>>>> or understanding of the
truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you then >>>>>>>>>>>>>>>>>>>>>>>>>>>> you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so the >>>>>>>>>>>>>>>>>>>>>>>>> fault here certainly doesn't lie with Alan. >>>>>>>>>>>>>>>>>>>>>>>>> It's certainly not a 'verified fact' when you >>>>>>>>>>>>>>>>>>>>>>>>> haven't even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>> that you mean.
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>> prevent loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>
Looking for a proof does not need any semantics so it is >>>>>>>>>>>>>>> not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>
It should be obvious that finding a proof does not happen >>>>>>>>>>>>> before
looking for a proof.
If there is no sequence of inference steps in Q from
~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>
Which has the semantic meaning "no number is equal to its
successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no number
is equal to its successor" is not semantically valid, it must be
discarded as useless.
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>>>>>> or mathematical incompleteness.
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations that >>>>>>>>>>>>>>>>>>>>>>>> can be structured asIt is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday.
You can find any number of terms.-a That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them.
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means is >>>>>>>>>>>>>>>>>>>>>>>>>>> less
than no rebuttal at all.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean.
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>> prevent loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>
Looking for a proof does not need any semantics so it is >>>>>>>>>>>>>>>> not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>
It should be obvious that finding a proof does not happen >>>>>>>>>>>>>> before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>
Which has the semantic meaning "no number is equal to its
successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no number
is equal to its successor" is not semantically valid, it must be
discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~reax x=S(x) is untrue
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>>>>>>> or mathematical incompleteness.
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations that >>>>>>>>>>>>>>>>>>>>>>>>> can be structured as"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean.In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday.It is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
You can find any number of terms.-a That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means is >>>>>>>>>>>>>>>>>>>>>>>>>>>> less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>> prevent loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>
Looking for a proof does not need any semantics so it >>>>>>>>>>>>>>>>> is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not happen >>>>>>>>>>>>>>> before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>
Which has the semantic meaning "no number is equal to its
successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no
number is equal to its successor" is not semantically valid, it must
be discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~reax x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but with
different words.
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>> undecidability
On 6/24/2026 5:00 AM, Mikko wrote:If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>> prevent loops.
On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations that >>>>>>>>>>>>>>>>>>>>>>>>>> can be structured asAll of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
You can find any number of terms.-a That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means >>>>>>>>>>>>>>>>>>>>>>>>>>>>> is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>
or mathematical incompleteness.
Looking for a proof does not need any semantics so it >>>>>>>>>>>>>>>>>> is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no
number is equal to its successor" is not semantically valid, it must
be discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~reax x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but with
different words.
So everyone says that ~reax x=S(x)
is simply untrue
in Q and does nor derive either undecidability or
incompleteness?
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>> Essentially
On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>>> prevent loops.
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>> some language?All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
You can find any number of terms.-a That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it >>>>>>>>>>>>>>>>>>> is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is >>>>>>> unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no
number is equal to its successor" is not semantically valid, it
must be discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~reax x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but with
different words.
So everyone says that ~reax x=S(x)
which has the semantic meaning "no number is equal to its successor" as
per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is incomplete because
"no number is equal to its successor" is unprovable in Q.
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>> Essentially
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>>>> prevent loops.It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>> why would one try toAll of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>> strings."grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> so the fault here certainly doesn't lie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fact' when you haven't even adequately >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explained what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:It is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so >>>>>>>>>>>>>>>>>>>> it is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>> in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is >>>>>>>> unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no
number is equal to its successor" is not semantically valid, it
must be discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~reax x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but with
different words.
So everyone says that ~reax x=S(x)
which has the semantic meaning "no number is equal to its successor"
as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is incomplete
because "no number is equal to its successor" is unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost caught up
to Wittgenstein (1937) on this point. They are
very much farther along on related points.
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>> EssentiallyIf you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>>>>> prevent loops.It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and >>>>>>>>>>>>>>>>>>>>>>>>>> neverThey use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>>> why would one try to"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a 'verified fact' when you haven't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> adequately explained what it is that you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean.In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:It is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> strings.
What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so >>>>>>>>>>>>>>>>>>>>> it is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>> in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x) >>>>>>>>>>>> in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is >>>>>>>>> unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no >>>>>>> number is equal to its successor" is not semantically valid, it >>>>>>> must be discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~reax x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but with
different words.
So everyone says that ~reax x=S(x)
which has the semantic meaning "no number is equal to its successor"
as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is incomplete
because "no number is equal to its successor" is unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an infinite sequence of inference steps between it and the axioms of the system?
Similarly, what term would you use to describe a sentence whose inverse
has an infinite sequence of inference steps between it and the axioms of
the system?
Proof Theoretic Semantics has almost caught up
to Wittgenstein (1937) on this point. They are
very much farther along on related points.
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>> EssentiallyIf you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>>>>> prevent loops.It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and >>>>>>>>>>>>>>>>>>>>>>>>>> neverThey use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>>> why would one try to"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a 'verified fact' when you haven't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> adequately explained what it is that you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean.In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:It is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> strings.
What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so >>>>>>>>>>>>>>>>>>>>> it is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>> in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x) >>>>>>>>>>>> in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is >>>>>>>>> unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no >>>>>>> number is equal to its successor" is not semantically valid, it >>>>>>> must be discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~reax x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but with
different words.
So everyone says that ~reax x=S(x)
which has the semantic meaning "no number is equal to its successor"
as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is incomplete
because "no number is equal to its successor" is unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an infinite sequence of inference steps between it and the axioms of the system?
Similarly, what term would you use to describe a sentence whose inverse
has an infinite sequence of inference steps between it and the axioms of
the system?
Proof Theoretic Semantics has almost caught up
to Wittgenstein (1937) on this point. They are
very much farther along on related points.
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>> EssentiallyIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and >>>>>>>>>>>>>>>>>>>>>>>>>>> neverThey use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>>>> why would one try to"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean.[ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically between >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finite strings.
What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent >>>>>>>>>>>>>>>>>>>>>>> body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so >>>>>>>>>>>>>>>>>>>>>> it is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>> in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x) >>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is >>>>>>>>>> unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no >>>>>>>> number is equal to its successor" is not semantically valid, it >>>>>>>> must be discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~reax x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but with
different words.
So everyone says that ~reax x=S(x)
which has the semantic meaning "no number is equal to its successor"
as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is incomplete
because "no number is equal to its successor" is unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an infinite
sequence of inference steps between it and the axioms of the system?
untrue and unfalse.
Similarly, what term would you use to describe a sentence whose
inverse has an infinite sequence of inference steps between it and the
axioms of the system?
I don't know what you mean by inverse.
If you mean negation you should have said negation.
Proof Theoretic Semantics has almost caught up
to Wittgenstein (1937) on this point. They are
very much farther along on related points.
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>>> happen before
In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>Looking for a proof does not need any semantics >>>>>>>>>>>>>>>>>>>>>>> so it is not obviousIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and >>>>>>>>>>>>>>>>>>>>>>>>>>>> neverThey use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>>>>> why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?All of knowledge expressed in language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>[ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that G||del's G >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent >>>>>>>>>>>>>>>>>>>>>>>> body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>> in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x) >>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) >>>>>>>>>>> is unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>>
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no >>>>>>>>> number is equal to its successor" is not semantically valid, it >>>>>>>>> must be discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~reax x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but with >>>>>>> different words.
So everyone says that ~reax x=S(x)
which has the semantic meaning "no number is equal to its
successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is incomplete
because "no number is equal to its successor" is unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an
infinite sequence of inference steps between it and the axioms of the
system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement that has
*any* sequence of inference steps, either finite or infinite, between it
and the axioms of the system?-a And what would the negation of such a statement be called?
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:i.e., ~reax x=S(x) is unprovable is Q, as is commonly >>>>>>>>>>>>>>>>>> known.
On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>>>> happen beforeLooking for a proof does not need any semantics >>>>>>>>>>>>>>>>>>>>>>>> so it is not obviousIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for concepts. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:All of knowledge expressed in language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>[ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that G||del's G >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't believe you.-a You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
the proof gets stuck in an infinite loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>> and never
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>
how switching to another semantics could improve >>>>>>>>>>>>>>>>>>>>>>>> it.
In proof theoretic semantics an expression only >>>>>>>>>>>>>>>>>>>>>>> gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>> in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>> its successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x) >>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) >>>>>>>>>>>> is unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>>>
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q >>>>>>>>>> "no number is equal to its successor" is not semantically >>>>>>>>>> valid, it must be discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~reax x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but with >>>>>>>> different words.
So everyone says that ~reax x=S(x)
which has the semantic meaning "no number is equal to its
successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is incomplete
because "no number is equal to its successor" is unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an
infinite sequence of inference steps between it and the axioms of
the system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement that has
*any* sequence of inference steps, either finite or infinite, between
it and the axioms of the system?-a And what would the negation of such
a statement be called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:i.e., ~reax x=S(x) is unprovable is Q, as is commonly >>>>>>>>>>>>>>>>>>> known.
On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
It should be obvious that finding a proof does >>>>>>>>>>>>>>>>>>>>>>> not happen beforeLooking for a proof does not need any semantics >>>>>>>>>>>>>>>>>>>>>>>>> so it is not obviousIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for concepts. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>All of knowledge expressed in language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"grounded in the atomic base of PA" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is an expression used only by you, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and it is one which you have never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explicitly defined, so the fault here >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly doesn't lie with Alan. It's >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly not a 'verified fact' when >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that G||del's G >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't believe you.-a You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof- >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoritic Semantics, and you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
the proof gets stuck in an infinite loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and never
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic >>>>>>>>>>>>>>>>>>>>>>>>>> meanings
expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>
how switching to another semantics could >>>>>>>>>>>>>>>>>>>>>>>>> improve it.
In proof theoretic semantics an expression only >>>>>>>>>>>>>>>>>>>>>>>> gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>>> in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>>> its successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x) >>>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) >>>>>>>>>>>>> is unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>>>>
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q >>>>>>>>>>> "no number is equal to its successor" is not semantically >>>>>>>>>>> valid, it must be discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~reax x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but >>>>>>>>> with different words.
So everyone says that ~reax x=S(x)
which has the semantic meaning "no number is equal to its
successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is incomplete >>>>>>> because "no number is equal to its successor" is unprovable in Q. >>>>>>>
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an
infinite sequence of inference steps between it and the axioms of
the system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement that
has *any* sequence of inference steps, either finite or infinite,
between it and the axioms of the system?-a And what would the negation
of such a statement be called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any* sequence of
inference steps, either finite or infinite, between it and the axioms of
the system?
What term would you use for the negation of the above statement?
On 6/27/2026 4:50 PM, dbush wrote:
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:And because PTS claims the semantically valid sentence in Q >>>>>>>>>>>> "no number is equal to its successor" is not semantically >>>>>>>>>>>> valid, it must be discarded as useless.
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:i.e., ~reax x=S(x) is unprovable is Q, as is commonly >>>>>>>>>>>>>>>>>>>> known.
On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
It should be obvious that finding a proof does >>>>>>>>>>>>>>>>>>>>>>>> not happen beforeLooking for a proof does not need any >>>>>>>>>>>>>>>>>>>>>>>>>> semantics so it is not obvious >>>>>>>>>>>>>>>>>>>>>>>>>> how switching to another semantics could >>>>>>>>>>>>>>>>>>>>>>>>>> improve it.If you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for concepts. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>All of knowledge expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language is structured as a tree of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic relations specified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"grounded in the atomic base of PA" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is an expression used only by you, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and it is one which you have never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explicitly defined, so the fault >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fact' when you haven't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> adequately explained what it is that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that G||del's >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't believe you.-a You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You can find any number of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> terms. That doesn't mean you're >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof- >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoritic Semantics, and you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> neither the theorem itself nor any >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
the proof gets stuck in an infinite loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and never
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> >>>>>>>>>>>>>>>>>>>>>>>>>>> incoherent
compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic >>>>>>>>>>>>>>>>>>>>>>>>>>> meanings
expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>>
In proof theoretic semantics an expression only >>>>>>>>>>>>>>>>>>>>>>>>> gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>>>> in Q from ~reax x=S(x) to the axioms of Q then ~reax >>>>>>>>>>>>>>>>>>>>> x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>>>> its successor" as per the definition of Q. >>>>>>>>>>>>>>>>>>
Since there are no steps in Q that affirm ~reax x=S(x) >>>>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known. >>>>>>>>>>>>>>>>
False, as by definition, Q is incomplete because ~reax >>>>>>>>>>>>>> x=S(x) is unprovable / out-of-scope / not semantically >>>>>>>>>>>>>> grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!! >>>>>>>>>>>>
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~reax x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but >>>>>>>>>> with different words.
So everyone says that ~reax x=S(x)
which has the semantic meaning "no number is equal to its
successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is incomplete >>>>>>>> because "no number is equal to its successor" is unprovable in Q. >>>>>>>>
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an
infinite sequence of inference steps between it and the axioms of >>>>>> the system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement that
has *any* sequence of inference steps, either finite or infinite,
between it and the axioms of the system?-a And what would the
negation of such a statement be called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any* sequence of
inference steps, either finite or infinite, between it and the axioms
of the system?
"true on the basis of meaning expressed in language"
reliably computable for the entire body of GENERAL knowledge.
Is the limit of the topic of all my posts.
Infinite inference steps are off topic.
What term would you use for the negation of the above statement?
Does not have any proof finite or infinite?
That would be untrue and possibly nonsense.
On 6/27/2026 6:11 PM, olcott wrote:
On 6/27/2026 4:50 PM, dbush wrote:
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:And because PTS claims the semantically valid sentence in Q >>>>>>>>>>>>> "no number is equal to its successor" is not semantically >>>>>>>>>>>>> valid, it must be discarded as useless.
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of >>>>>>>>>>>>>>>> incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:Which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>>>>> its successor" as per the definition of Q. >>>>>>>>>>>>>>>>>>>
On 6/27/2026 2:27 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:01 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Is it commonly known that ~reax x=S(x) >>>>>>>>>>>>>>>>>>>
i.e., ~reax x=S(x) is unprovable is Q, as is commonly >>>>>>>>>>>>>>>>>>>>> known.There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>>>It should be obvious that finding a proof does >>>>>>>>>>>>>>>>>>>>>>>>> not happen beforeLooking for a proof does not need any >>>>>>>>>>>>>>>>>>>>>>>>>>> semantics so it is not obvious >>>>>>>>>>>>>>>>>>>>>>>>>>> how switching to another semantics could >>>>>>>>>>>>>>>>>>>>>>>>>>> improve it.If you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops. >>>>>>>>>>>>>>>>>>>>>>>>>>>>> In most cases that also prevents finding >>>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for concepts. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>All of knowledge expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language is structured as a tree of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic relations specified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of PA" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is an expression used only by you, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and it is one which you have never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explicitly defined, so the fault >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoretic atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You can find any number of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> terms. That doesn't mean you're >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that G||del's >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't believe you.-a You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If they are mere gibberish words >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to you then you will not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You don't understand Proof- >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoritic Semantics, and you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> neither the theorem itself nor >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
the proof gets stuck in an infinite loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and never
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Truth Conditional Semantics (TCS) <is> >>>>>>>>>>>>>>>>>>>>>>>>>>>> incoherent
compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>> meanings
expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>>>
In proof theoretic semantics an expression >>>>>>>>>>>>>>>>>>>>>>>>>> only gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q >>>>>>>>>>>>>>>>>>>>>>>> from
~reax x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>>>>> in Q from ~reax x=S(x) to the axioms of Q then ~reax >>>>>>>>>>>>>>>>>>>>>> x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>
Since there are no steps in Q that affirm ~reax x=S(x) >>>>>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known. >>>>>>>>>>>>>>>>>
False, as by definition, Q is incomplete because ~reax >>>>>>>>>>>>>>> x=S(x) is unprovable / out-of-scope / not semantically >>>>>>>>>>>>>>> grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!! >>>>>>>>>>>>>
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~reax x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but >>>>>>>>>>> with different words.
So everyone says that ~reax x=S(x)
which has the semantic meaning "no number is equal to its
successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is incomplete >>>>>>>>> because "no number is equal to its successor" is unprovable in Q. >>>>>>>>>
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an
infinite sequence of inference steps between it and the axioms of >>>>>>> the system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement that
has *any* sequence of inference steps, either finite or infinite,
between it and the axioms of the system?-a And what would the
negation of such a statement be called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any* sequence of
inference steps, either finite or infinite, between it and the axioms
of the system?
"true on the basis of meaning expressed in language"
reliably computable for the entire body of GENERAL knowledge.
Is the limit of the topic of all my posts.
Infinite inference steps are off topic.
Why are you so reluctant to provide a simple term?
It seems you're attempting to engage in Newspeak.
https://en.wikipedia.org/wiki/Newspeak
What term would you use for the negation of the above statement?
Does not have any proof finite or infinite?
That would be untrue and possibly nonsense.
On 6/27/2026 5:15 PM, dbush wrote:
On 6/27/2026 6:11 PM, olcott wrote:
On 6/27/2026 4:50 PM, dbush wrote:
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:And because PTS claims the semantically valid sentence in >>>>>>>>>>>>>> Q "no number is equal to its successor" is not
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of >>>>>>>>>>>>>>>>> incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:Which has the semantic meaning "no number is equal >>>>>>>>>>>>>>>>>>>> to its successor" as per the definition of Q. >>>>>>>>>>>>>>>>>>>>
On 6/27/2026 2:27 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:01 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You can find any number of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> terms. That doesn't mean >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS G||del 1931 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I don't believe you.-a You have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> no respect for or understanding >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then cite an academic expert >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If they are mere gibberish >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words to you then you will not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You don't understand Proof- >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoritic Semantics, and you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> neither the theorem itself nor >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is a verified fact that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Is it commonly known that ~reax x=S(x) >>>>>>>>>>>>>>>>>>>>
i.e., ~reax x=S(x) is unprovable is Q, as is >>>>>>>>>>>>>>>>>>>>>> commonly known.There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>>>>It should be obvious that finding a proof does >>>>>>>>>>>>>>>>>>>>>>>>>> not happen beforeLooking for a proof does not need any >>>>>>>>>>>>>>>>>>>>>>>>>>>> semantics so it is not obvious >>>>>>>>>>>>>>>>>>>>>>>>>>>> how switching to another semantics could >>>>>>>>>>>>>>>>>>>>>>>>>>>> improve it.If you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In most cases that also prevents finding >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> concepts. But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PA" is an expression used only by >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you, and it is one which you have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> never explicitly defined, so the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fault here certainly doesn't lie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with Alan. It's certainly not a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>All of knowledge expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language is structured as a tree of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic relations specified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
the proof gets stuck in an infinite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop and never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> prevent getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Truth Conditional Semantics (TCS) <is> >>>>>>>>>>>>>>>>>>>>>>>>>>>>> incoherent
compared to Proof Theoretic Semantics >>>>>>>>>>>>>>>>>>>>>>>>>>>>> (PTS). Essentially
PTS just coherently connects the semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>> meanings
expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
In proof theoretic semantics an expression >>>>>>>>>>>>>>>>>>>>>>>>>>> only gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q >>>>>>>>>>>>>>>>>>>>>>>>> from
~reax x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>>>>>> in Q from ~reax x=S(x) to the axioms of Q then ~reax >>>>>>>>>>>>>>>>>>>>>>> x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>>
Since there are no steps in Q that affirm ~reax x=S(x) >>>>>>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known. >>>>>>>>>>>>>>>>>>
False, as by definition, Q is incomplete because ~reax >>>>>>>>>>>>>>>> x=S(x) is unprovable / out-of-scope / not semantically >>>>>>>>>>>>>>>> grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!! >>>>>>>>>>>>>>
semantically valid, it must be discarded as useless. >>>>>>>>>>>>>>
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~reax x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but >>>>>>>>>>>> with different words.
So everyone says that ~reax x=S(x)
which has the semantic meaning "no number is equal to its >>>>>>>>>> successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is
incomplete because "no number is equal to its successor" is >>>>>>>>>> unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an >>>>>>>> infinite sequence of inference steps between it and the axioms >>>>>>>> of the system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement that >>>>>> has *any* sequence of inference steps, either finite or infinite, >>>>>> between it and the axioms of the system?-a And what would the
negation of such a statement be called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any* sequence of
inference steps, either finite or infinite, between it and the
axioms of the system?
"true on the basis of meaning expressed in language"
reliably computable for the entire body of GENERAL knowledge.
Is the limit of the topic of all my posts.
Infinite inference steps are off topic.
Why are you so reluctant to provide a simple term?
OFF-TOPIC <is> THE TERM.
It seems you're attempting to engage in Newspeak.
https://en.wikipedia.org/wiki/Newspeak
What term would you use for the negation of the above statement?
Does not have any proof finite or infinite?
That would be untrue and possibly nonsense.
On 6/27/2026 6:18 PM, olcott wrote:
On 6/27/2026 5:15 PM, dbush wrote:
On 6/27/2026 6:11 PM, olcott wrote:
On 6/27/2026 4:50 PM, dbush wrote:
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:i.e. proven
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:And because PTS claims the semantically valid sentence in >>>>>>>>>>>>>>> Q "no number is equal to its successor" is not
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of >>>>>>>>>>>>>>>>>> incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:29 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:27 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:01 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You can find any number of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> terms. That doesn't mean >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The above is the key reason >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> why under PTS G||del 1931 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I don't believe you.-a You have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> no respect for or understanding >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then cite an academic expert >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If they are mere gibberish >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words to you then you will not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You don't understand Proof- >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoritic Semantics, and you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> neither the theorem itself nor >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is a verified fact that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal >>>>>>>>>>>>>>>>>>>>> to its successor" as per the definition of Q. >>>>>>>>>>>>>>>>>>>>>Is it commonly known that ~reax x=S(x) >>>>>>>>>>>>>>>>>>>>>i.e., ~reax x=S(x) is unprovable is Q, as is >>>>>>>>>>>>>>>>>>>>>>> commonly known.There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>>>>>It should be obvious that finding a proof >>>>>>>>>>>>>>>>>>>>>>>>>>> does not happen beforeLooking for a proof does not need any >>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantics so it is not obvious >>>>>>>>>>>>>>>>>>>>>>>>>>>>> how switching to another semantics could >>>>>>>>>>>>>>>>>>>>>>>>>>>>> improve it.If you mean not looking elsewhere that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> may indeed prevent loops. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In most cases that also prevents finding >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> concepts. But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> all knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PA" is an expression used only by >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you, and it is one which you have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> never explicitly defined, so the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fault here certainly doesn't lie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with Alan. It's certainly not a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>All of knowledge expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language is structured as a tree >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of semantic relations specified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
the proof gets stuck in an infinite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop and never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> prevent getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Truth Conditional Semantics (TCS) <is> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> incoherent
compared to Proof Theoretic Semantics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (PTS). Essentially >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS just coherently connects the semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meanings
expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In proof theoretic semantics an expression >>>>>>>>>>>>>>>>>>>>>>>>>>>> only gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in >>>>>>>>>>>>>>>>>>>>>>>>>> Q from
~reax x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>>>>>>> in Q from ~reax x=S(x) to the axioms of Q then ~reax >>>>>>>>>>>>>>>>>>>>>>>> x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>>>
Since there are no steps in Q that affirm ~reax x=S(x) >>>>>>>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known. >>>>>>>>>>>>>>>>>>>
False, as by definition, Q is incomplete because ~reax >>>>>>>>>>>>>>>>> x=S(x) is unprovable / out-of-scope / not semantically >>>>>>>>>>>>>>>>> grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!! >>>>>>>>>>>>>>>
semantically valid, it must be discarded as useless. >>>>>>>>>>>>>>>
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's >>>>>>>>>>>>>> system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there. >>>>>>>>>>>>>> For the most part they stop at semantically grounded >>>>>>>>>>>>>
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~reax x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but >>>>>>>>>>>>> with different words.
So everyone says that ~reax x=S(x)
which has the semantic meaning "no number is equal to its >>>>>>>>>>> successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is
incomplete because "no number is equal to its successor" is >>>>>>>>>>> unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an >>>>>>>>> infinite sequence of inference steps between it and the axioms >>>>>>>>> of the system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement
that has *any* sequence of inference steps, either finite or
infinite, between it and the axioms of the system?-a And what
would the negation of such a statement be called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any* sequence of
inference steps, either finite or infinite, between it and the
axioms of the system?
"true on the basis of meaning expressed in language"
reliably computable for the entire body of GENERAL knowledge.
Is the limit of the topic of all my posts.
Infinite inference steps are off topic.
Why are you so reluctant to provide a simple term?
OFF-TOPIC <is> THE TERM.
So we've established that "off-topic" means "a statement that has *any* sequence of inference steps, either finite or infinite, between it and
the axioms of the system".
On 6/27/2026 5:21 PM, dbush wrote:
On 6/27/2026 6:18 PM, olcott wrote:
On 6/27/2026 5:15 PM, dbush wrote:
On 6/27/2026 6:11 PM, olcott wrote:
On 6/27/2026 4:50 PM, dbush wrote:
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:i.e. proven
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:And because PTS claims the semantically valid sentence >>>>>>>>>>>>>>>> in Q "no number is equal to its successor" is not >>>>>>>>>>>>>>>> semantically valid, it must be discarded as useless. >>>>>>>>>>>>>>>>
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of >>>>>>>>>>>>>>>>>>> incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:29 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:27 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:01 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You can find any number of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> terms. That doesn't mean >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The above is the key reason >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> why under PTS G||del 1931 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I don't believe you.-a You have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> no respect for or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then cite an academic expert >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If they are mere gibberish >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words to you then you will >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You don't understand Proof- >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoritic Semantics, and you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> neither the theorem itself nor >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is a verified fact that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounded in the atomic base of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PA" is an expression used only >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> by you, and it is one which you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have never explicitly defined, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explained what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal >>>>>>>>>>>>>>>>>>>>>> to its successor" as per the definition of Q. >>>>>>>>>>>>>>>>>>>>>>Is it commonly known that ~reax x=S(x) >>>>>>>>>>>>>>>>>>>>>>i.e., ~reax x=S(x) is unprovable is Q, as is >>>>>>>>>>>>>>>>>>>>>>>> commonly known.There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>>>>>>It should be obvious that finding a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>> does not happen before >>>>>>>>>>>>>>>>>>>>>>>>>>>> looking for a proof.Looking for a proof does not need any >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantics so it is not obvious >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how switching to another semantics could >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> improve it.If you mean not looking elsewhere that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> may indeed prevent loops. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In most cases that also prevents finding >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>How can any ordering of knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> prevent getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop and never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> completes. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>They use a tree structure for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> concepts. But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>All of knowledge expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language is structured as a tree >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of semantic relations specified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> syntactically between finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> all knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Truth Conditional Semantics (TCS) <is> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> incoherent
compared to Proof Theoretic Semantics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (PTS). Essentially >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS just coherently connects the semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meanings
expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> without undecidability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In proof theoretic semantics an expression >>>>>>>>>>>>>>>>>>>>>>>>>>>>> only gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no sequence of inference steps in >>>>>>>>>>>>>>>>>>>>>>>>>>> Q from
~reax x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>>>>>>>> in Q from ~reax x=S(x) to the axioms of Q then >>>>>>>>>>>>>>>>>>>>>>>>> ~reax x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>>>>
Since there are no steps in Q that affirm ~reax x=S(x) >>>>>>>>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known. >>>>>>>>>>>>>>>>>>>>
False, as by definition, Q is incomplete because ~reax >>>>>>>>>>>>>>>>>> x=S(x) is unprovable / out-of-scope / not semantically >>>>>>>>>>>>>>>>>> grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!! >>>>>>>>>>>>>>>>
No you are just not bothering to pay 100% totally >>>>>>>>>>>>>>> complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's >>>>>>>>>>>>>>> system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there. >>>>>>>>>>>>>>> For the most part they stop at semantically grounded >>>>>>>>>>>>>>
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~reax x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever >>>>>>>>>>>>>>> heard of Wittgenstein.
So again, you're saying the same thing as everyone else >>>>>>>>>>>>>> but with different words.
So everyone says that ~reax x=S(x)
which has the semantic meaning "no number is equal to its >>>>>>>>>>>> successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is
incomplete because "no number is equal to its successor" is >>>>>>>>>>>> unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an >>>>>>>>>> infinite sequence of inference steps between it and the axioms >>>>>>>>>> of the system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement >>>>>>>> that has *any* sequence of inference steps, either finite or
infinite, between it and the axioms of the system?-a And what >>>>>>>> would the negation of such a statement be called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any* sequence of >>>>>> inference steps, either finite or infinite, between it and the
axioms of the system?
"true on the basis of meaning expressed in language"
reliably computable for the entire body of GENERAL knowledge.
Is the limit of the topic of all my posts.
Infinite inference steps are off topic.
Why are you so reluctant to provide a simple term?
OFF-TOPIC <is> THE TERM.
So we've established that "off-topic" means "a statement that has
*any* sequence of inference steps, either finite or infinite, between
it and the axioms of the system".
The ones that have infinite steps out outside the
body of knowledge and off topic for that reason.
On 6/27/2026 3:05 AM, Mikko wrote:
On 27/06/2026 01:01, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable. Then to >>>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~reax x>10 v x<5 but much more
complex.
"No number is equal to its successor" is a sentence in RA, and it
is true but unprovable in RA (or as your would call it, "out-of-
scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language
of Q. More formally, it is this:
~reax x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms
you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
Nevertheless a sentence like ~reax x=S(x) is in the language of Q and
that way in the theory.
Colorless green ideas sleep furiously
was composed by Noam Chomsky in his 1957 book
Syntactic Structures as an example of a sentence
that is grammatically well-formed, but semantically
nonsensical.
Proving that syntax is not enough.
On 6/27/2026 6:29 PM, olcott wrote:
On 6/27/2026 5:21 PM, dbush wrote:
On 6/27/2026 6:18 PM, olcott wrote:
On 6/27/2026 5:15 PM, dbush wrote:
On 6/27/2026 6:11 PM, olcott wrote:
On 6/27/2026 4:50 PM, dbush wrote:
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:i.e. proven
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:And because PTS claims the semantically valid sentence >>>>>>>>>>>>>>>>> in Q "no number is equal to its successor" is not >>>>>>>>>>>>>>>>> semantically valid, it must be discarded as useless. >>>>>>>>>>>>>>>>>
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:39 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:38 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:29 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:27 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:01 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You can find any number of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> terms. That doesn't mean >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The above is the key reason >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> why under PTS G||del 1931 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I don't believe you.-a You >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have no respect for or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then cite an academic expert >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If they are mere gibberish >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words to you then you will >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You don't understand Proof- >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoritic Semantics, and you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> neither the theorem itself >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is a verified fact that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounded in the atomic base of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PA" is an expression used only >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> by you, and it is one which you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have never explicitly defined, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> All of knowledge expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language is structured as a tree >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of semantic relations specified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> syntactically between finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Yet never gets to undecidable or in any sense of >>>>>>>>>>>>>>>>>>>> incomplete.
Which has the semantic meaning "no number is >>>>>>>>>>>>>>>>>>>>>>> equal to its successor" as per the definition of Q. >>>>>>>>>>>>>>>>>>>>>>>Is it commonly known that ~reax x=S(x) >>>>>>>>>>>>>>>>>>>>>>>i.e., ~reax x=S(x) is unprovable is Q, as is >>>>>>>>>>>>>>>>>>>>>>>>> commonly known.There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>>>>>>>It should be obvious that finding a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>> does not happen before >>>>>>>>>>>>>>>>>>>>>>>>>>>>> looking for a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>Looking for a proof does not need any >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantics so it is not obvious >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how switching to another semantics could >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> improve it.Truth Conditional Semantics (TCS) <is> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> incoherentIf you mean not looking elsewhere that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> may indeed prevent loops. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In most cases that also prevents >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finding the proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>How can any ordering of knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> prevent getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop and never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> completes. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>They use a tree structure for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> concepts. But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> all knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The CycL language and the Cyc >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
compared to Proof Theoretic Semantics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (PTS). Essentially >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS just coherently connects the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic meanings >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> without undecidability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In proof theoretic semantics an expression >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no sequence of inference steps >>>>>>>>>>>>>>>>>>>>>>>>>>>> in Q from
~reax x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>>>>>>>>> in Q from ~reax x=S(x) to the axioms of Q then >>>>>>>>>>>>>>>>>>>>>>>>>> ~reax x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>>>>>
Since there are no steps in Q that affirm ~reax x=S(x) >>>>>>>>>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known. >>>>>>>>>>>>>>>>>>>>>
False, as by definition, Q is incomplete because ~reax >>>>>>>>>>>>>>>>>>> x=S(x) is unprovable / out-of-scope / not >>>>>>>>>>>>>>>>>>> semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!! >>>>>>>>>>>>>>>>>
No you are just not bothering to pay 100% totally >>>>>>>>>>>>>>>> complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said: >>>>>>>>>>>>>>>> proved in Russell's system; and 'false in Russell's >>>>>>>>>>>>>>>> system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there. >>>>>>>>>>>>>>>> For the most part they stop at semantically grounded >>>>>>>>>>>>>>>
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS >>>>>>>>>>>>>>>> notion ~reax x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever >>>>>>>>>>>>>>>> heard of Wittgenstein.
So again, you're saying the same thing as everyone else >>>>>>>>>>>>>>> but with different words.
So everyone says that ~reax x=S(x)
which has the semantic meaning "no number is equal to its >>>>>>>>>>>>> successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is >>>>>>>>>>>>> incomplete because "no number is equal to its successor" is >>>>>>>>>>>>> unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an >>>>>>>>>>> infinite sequence of inference steps between it and the >>>>>>>>>>> axioms of the system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement >>>>>>>>> that has *any* sequence of inference steps, either finite or >>>>>>>>> infinite, between it and the axioms of the system?-a And what >>>>>>>>> would the negation of such a statement be called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any* sequence >>>>>>> of inference steps, either finite or infinite, between it and the >>>>>>> axioms of the system?
"true on the basis of meaning expressed in language"
reliably computable for the entire body of GENERAL knowledge.
Is the limit of the topic of all my posts.
Infinite inference steps are off topic.
Why are you so reluctant to provide a simple term?
OFF-TOPIC <is> THE TERM.
So we've established that "off-topic" means "a statement that has
*any* sequence of inference steps, either finite or infinite, between
it and the axioms of the system".
The ones that have infinite steps out outside the
body of knowledge and off topic for that reason.
So you're claiming the sentence "no number is equal to its successor" in
Q is "off topic".
Rejected, as it is a semantically valid sentence in the language of Q.
On 06/27/2026 08:47 AM, polcott wrote:
On 6/27/2026 3:05 AM, Mikko wrote:
On 27/06/2026 01:01, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope. >>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable.-a Then to >>>>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
-a Breyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False.-a The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False.-a G is simply a sentence like ~reax x>10 v x<5 but much more
complex.
"No number is equal to its successor" is a sentence in RA, and it >>>>>>> is true but unprovable in RA (or as your would call it, "out-of- >>>>>>> scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language
of Q.-a More formally, it is this:
~reax x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms >>>>> you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
Nevertheless a sentence like ~reax x=S(x) is in the language of Q and
that way in the theory.
Colorless green ideas sleep furiously
was composed by Noam Chomsky in his 1957 book
Syntactic Structures as an example of a sentence
that is grammatically well-formed, but semantically
nonsensical.
Proving that syntax is not enough.
"Colorless green" is actually two colors
since there's a dual-tristimulus colorspace
the chromatic and the prismatic,
a fact of the science of the theory of light and color,
of which you are ignorant, then making for a reasonable
reading of the usual apocryphal comment.
Then, ideas can sleep however they want.
On 6/27/2026 5:33 PM, dbush wrote:
On 6/27/2026 6:29 PM, olcott wrote:
On 6/27/2026 5:21 PM, dbush wrote:
On 6/27/2026 6:18 PM, olcott wrote:
On 6/27/2026 5:15 PM, dbush wrote:
On 6/27/2026 6:11 PM, olcott wrote:
On 6/27/2026 4:50 PM, dbush wrote:
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:i.e. proven
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:And because PTS claims the semantically valid sentence >>>>>>>>>>>>>>>>>> in Q "no number is equal to its successor" is not >>>>>>>>>>>>>>>>>> semantically valid, it must be discarded as useless. >>>>>>>>>>>>>>>>>>
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:39 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:38 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:29 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:27 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:01 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You can find any number of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> terms. That doesn't mean >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The above is the key reason >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> why under PTS G||del 1931 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I don't believe you.-a You >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have no respect for or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to persuade anybody that PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then cite an academic expert >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If they are mere gibberish >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words to you then you will >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You don't understand Proof- >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoritic Semantics, and you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> neither the theorem itself >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is a verified fact that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That you do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounded in the atomic base >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of PA" is an expression used >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explicitly defined, so the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fault here certainly doesn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> haven't even adequately >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explained what it is that you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> All of knowledge expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language is structured as a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> all knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Yet never gets to undecidable or in any sense of >>>>>>>>>>>>>>>>>>>>> incomplete.
Which has the semantic meaning "no number is >>>>>>>>>>>>>>>>>>>>>>>> equal to its successor" as per the definition of Q. >>>>>>>>>>>>>>>>>>>>>>>>Is it commonly known that ~reax x=S(x) >>>>>>>>>>>>>>>>>>>>>>>>i.e., ~reax x=S(x) is unprovable is Q, as is >>>>>>>>>>>>>>>>>>>>>>>>>> commonly known.There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>>>>>>>>It should be obvious that finding a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> does not happen before >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> looking for a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Looking for a proof does not need any >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantics so it is not obvious >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how switching to another semantics could >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> improve it.Truth Conditional Semantics (TCS) <is> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> incoherentIf you mean not looking elsewhere that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> may indeed prevent loops. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In most cases that also prevents >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finding the proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>How can any ordering of knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> prevent getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop and never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> completes. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The CycL language and the Cyc >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>They use a tree structure for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> concepts. But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
compared to Proof Theoretic Semantics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (PTS). Essentially >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS just coherently connects the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic meanings >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent body >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> without undecidability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In proof theoretic semantics an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression only gains >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no sequence of inference steps >>>>>>>>>>>>>>>>>>>>>>>>>>>>> in Q from
~reax x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference >>>>>>>>>>>>>>>>>>>>>>>>>>> steps
in Q from ~reax x=S(x) to the axioms of Q then >>>>>>>>>>>>>>>>>>>>>>>>>>> ~reax x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>>>>>>
Since there are no steps in Q that affirm ~reax x=S(x) >>>>>>>>>>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known. >>>>>>>>>>>>>>>>>>>>>>
False, as by definition, Q is incomplete because ~reax >>>>>>>>>>>>>>>>>>>> x=S(x) is unprovable / out-of-scope / not >>>>>>>>>>>>>>>>>>>> semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!! >>>>>>>>>>>>>>>>>>
No you are just not bothering to pay 100% totally >>>>>>>>>>>>>>>>> complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said: >>>>>>>>>>>>>>>>> proved in Russell's system; and 'false in Russell's >>>>>>>>>>>>>>>>> system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there. >>>>>>>>>>>>>>>>> For the most part they stop at semantically grounded >>>>>>>>>>>>>>>>
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS >>>>>>>>>>>>>>>>> notion ~reax x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever >>>>>>>>>>>>>>>>> heard of Wittgenstein.
So again, you're saying the same thing as everyone else >>>>>>>>>>>>>>>> but with different words.
So everyone says that ~reax x=S(x)
which has the semantic meaning "no number is equal to its >>>>>>>>>>>>>> successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or >>>>>>>>>>>>>>> incompleteness?
It does derive incompleteness, as by definition Q is >>>>>>>>>>>>>> incomplete because "no number is equal to its successor" >>>>>>>>>>>>>> is unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has >>>>>>>>>>>> an infinite sequence of inference steps between it and the >>>>>>>>>>>> axioms of the system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement >>>>>>>>>> that has *any* sequence of inference steps, either finite or >>>>>>>>>> infinite, between it and the axioms of the system?-a And what >>>>>>>>>> would the negation of such a statement be called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any* sequence >>>>>>>> of inference steps, either finite or infinite, between it and >>>>>>>> the axioms of the system?
"true on the basis of meaning expressed in language"
reliably computable for the entire body of GENERAL knowledge.
Is the limit of the topic of all my posts.
Infinite inference steps are off topic.
Why are you so reluctant to provide a simple term?
OFF-TOPIC <is> THE TERM.
So we've established that "off-topic" means "a statement that has
*any* sequence of inference steps, either finite or infinite,
between it and the axioms of the system".
The ones that have infinite steps out outside the
body of knowledge and off topic for that reason.
So you're claiming the sentence "no number is equal to its successor"
in Q is "off topic".
Rejected, as it is a semantically valid sentence in the language of Q.
If there is no finite sequence of inference steps
between x and the axioms of Q then PTS stipulates
that x is not semantically valid in Q.
On 6/27/2026 6:44 PM, olcott wrote:
On 6/27/2026 5:33 PM, dbush wrote:
On 6/27/2026 6:29 PM, olcott wrote:
On 6/27/2026 5:21 PM, dbush wrote:
On 6/27/2026 6:18 PM, olcott wrote:
On 6/27/2026 5:15 PM, dbush wrote:
On 6/27/2026 6:11 PM, olcott wrote:
On 6/27/2026 4:50 PM, dbush wrote:
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:i.e. proven
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:And because PTS claims the semantically valid >>>>>>>>>>>>>>>>>>> sentence in Q "no number is equal to its successor" >>>>>>>>>>>>>>>>>>> is not semantically valid, it must be discarded as >>>>>>>>>>>>>>>>>>> useless.
On 6/27/2026 3:16 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:04 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 3:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:39 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:38 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:29 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:27 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:01 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You can find any number >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of terms. That doesn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The above is the key >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> reason why under PTS G||del >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I don't believe you.-a You >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have no respect for or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to persuade anybody that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> hold, then cite an academic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If they are mere gibberish >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words to you then you will >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You don't understand Proof- >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoritic Semantics, and >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> neither the theorem itself >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is a verified fact that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That you do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounded in the atomic base >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of PA" is an expression used >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explicitly defined, so the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fault here certainly doesn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you haven't even adequately >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explained what it is that you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> All of knowledge expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language is structured as a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> contain all knowledge that is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The CycL language and the Cyc >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Yet never gets to undecidable or in any sense of >>>>>>>>>>>>>>>>>>>>>> incomplete.Which has the semantic meaning "no number is >>>>>>>>>>>>>>>>>>>>>>>>> equal to its successor" as per the definition >>>>>>>>>>>>>>>>>>>>>>>>> of Q.Is it commonly known that ~reax x=S(x) >>>>>>>>>>>>>>>>>>>>>>>>>i.e., ~reax x=S(x) is unprovable is Q, as is >>>>>>>>>>>>>>>>>>>>>>>>>>> commonly known.There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>It should be obvious that finding a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> does not happen before >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> looking for a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>In proof theoretic semantics an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression only gains >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Looking for a proof does not need any >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantics so it is not obvious >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how switching to another semantics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> could improve it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Truth Conditional Semantics (TCS) <is> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> incoherent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (PTS). Essentially >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS just coherently connects the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic meanings >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> one coherent body >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> without undecidability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>If you mean not looking elsewhere >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that may indeed prevent loops. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In most cases that also prevents >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finding the proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>How can any ordering of knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> prevent getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>They use a tree structure for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> concepts. But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> infinite loop and never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> completes. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no sequence of inference steps >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in Q from
~reax x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference >>>>>>>>>>>>>>>>>>>>>>>>>>>> steps
in Q from ~reax x=S(x) to the axioms of Q then >>>>>>>>>>>>>>>>>>>>>>>>>>>> ~reax x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>>>>>>>
Since there are no steps in Q that affirm ~reax >>>>>>>>>>>>>>>>>>>>>>>> x=S(x)
in Q it is an open question in Q and not a >>>>>>>>>>>>>>>>>>>>>>>> confirmed
statement in Q.
In other words, unproven as is commonly known. >>>>>>>>>>>>>>>>>>>>>>>
False, as by definition, Q is incomplete because >>>>>>>>>>>>>>>>>>>>> ~reax x=S(x) is unprovable / out-of-scope / not >>>>>>>>>>>>>>>>>>>>> semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!! >>>>>>>>>>>>>>>>>>>
No you are just not bothering to pay 100% totally >>>>>>>>>>>>>>>>>> complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said: >>>>>>>>>>>>>>>>>> proved in Russell's system; and 'false in Russell's >>>>>>>>>>>>>>>>>> system' means: the opposite has been proved >>>>>>>>>>>>>>>>>> in Russell's system
Proof Theoretic Semantics has almost gotten there. >>>>>>>>>>>>>>>>>> For the most part they stop at semantically grounded >>>>>>>>>>>>>>>>>
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS >>>>>>>>>>>>>>>>>> notion ~reax x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever >>>>>>>>>>>>>>>>>> heard of Wittgenstein.
So again, you're saying the same thing as everyone else >>>>>>>>>>>>>>>>> but with different words.
So everyone says that ~reax x=S(x)
which has the semantic meaning "no number is equal to its >>>>>>>>>>>>>>> successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or >>>>>>>>>>>>>>>> incompleteness?
It does derive incompleteness, as by definition Q is >>>>>>>>>>>>>>> incomplete because "no number is equal to its successor" >>>>>>>>>>>>>>> is unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's >>>>>>>>>>>>>> system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has >>>>>>>>>>>>> an infinite sequence of inference steps between it and the >>>>>>>>>>>>> axioms of the system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement >>>>>>>>>>> that has *any* sequence of inference steps, either finite or >>>>>>>>>>> infinite, between it and the axioms of the system?-a And what >>>>>>>>>>> would the negation of such a statement be called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any* sequence >>>>>>>>> of inference steps, either finite or infinite, between it and >>>>>>>>> the axioms of the system?
"true on the basis of meaning expressed in language"
reliably computable for the entire body of GENERAL knowledge.
Is the limit of the topic of all my posts.
Infinite inference steps are off topic.
Why are you so reluctant to provide a simple term?
OFF-TOPIC <is> THE TERM.
So we've established that "off-topic" means "a statement that has
*any* sequence of inference steps, either finite or infinite,
between it and the axioms of the system".
The ones that have infinite steps out outside the
body of knowledge and off topic for that reason.
So you're claiming the sentence "no number is equal to its successor"
in Q is "off topic".
Rejected, as it is a semantically valid sentence in the language of Q.
If there is no finite sequence of inference steps
between x and the axioms of Q then PTS stipulates
that x is not semantically valid in Q.
And since x = "no number is equal to its successor" is semantically
valid as per the definition of Q, PTS must be discarded as useless.
On 6/27/2026 5:53 PM, dbush wrote:
On 6/27/2026 6:44 PM, olcott wrote:
On 6/27/2026 5:33 PM, dbush wrote:
On 6/27/2026 6:29 PM, olcott wrote:
On 6/27/2026 5:21 PM, dbush wrote:
On 6/27/2026 6:18 PM, olcott wrote:
On 6/27/2026 5:15 PM, dbush wrote:
On 6/27/2026 6:11 PM, olcott wrote:
On 6/27/2026 4:50 PM, dbush wrote:
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:i.e. proven
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:And because PTS claims the semantically valid >>>>>>>>>>>>>>>>>>>> sentence in Q "no number is equal to its successor" >>>>>>>>>>>>>>>>>>>> is not semantically valid, it must be discarded as >>>>>>>>>>>>>>>>>>>> useless.
On 6/27/2026 3:16 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:04 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 3:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:39 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:38 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:29 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:27 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:01 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You can find any number >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of terms. That doesn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The above is the key >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I don't believe you.-a You >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have no respect for or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to persuade anybody that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If they are mere >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You don't understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Proof- theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is a verified fact that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That you do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounded in the atomic base >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of PA" is an expression used >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explicitly defined, so the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fault here certainly doesn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> lie with Alan. It's >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly not a 'verified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fact' when you haven't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> adequately explained what it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> All of knowledge expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language is structured as a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What makes you believe >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic relations that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> contain all knowledge that is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The CycL language and the Cyc >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> They use a tree structure for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> concepts. But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Yet never gets to undecidable or in any sense of >>>>>>>>>>>>>>>>>>>>>>> incomplete.Which has the semantic meaning "no number is >>>>>>>>>>>>>>>>>>>>>>>>>> equal to its successor" as per the definition >>>>>>>>>>>>>>>>>>>>>>>>>> of Q.Is it commonly known that ~reax x=S(x) >>>>>>>>>>>>>>>>>>>>>>>>>>i.e., ~reax x=S(x) is unprovable is Q, as is >>>>>>>>>>>>>>>>>>>>>>>>>>>> commonly known.There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It should be obvious that finding a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proof does not happen before >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> looking for a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>In proof theoretic semantics an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression only gains >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Looking for a proof does not need any >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantics so it is not obvious >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how switching to another semantics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> could improve it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Truth Conditional Semantics (TCS) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (PTS). Essentially >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS just coherently connects the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic meanings >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> one coherent body >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> without undecidability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>If you mean not looking elsewhere >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that may indeed prevent loops. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In most cases that also prevents >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finding the proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> infinite loop and never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> completes. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>How can any ordering of knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> prevent getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no sequence of inference >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> steps in Q from
~reax x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference >>>>>>>>>>>>>>>>>>>>>>>>>>>>> steps
in Q from ~reax x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>>>>>>> then ~reax x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Since there are no steps in Q that affirm ~reax >>>>>>>>>>>>>>>>>>>>>>>>> x=S(x)
in Q it is an open question in Q and not a >>>>>>>>>>>>>>>>>>>>>>>>> confirmed
statement in Q.
In other words, unproven as is commonly known. >>>>>>>>>>>>>>>>>>>>>>>>
False, as by definition, Q is incomplete because >>>>>>>>>>>>>>>>>>>>>> ~reax x=S(x) is unprovable / out-of-scope / not >>>>>>>>>>>>>>>>>>>>>> semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!! >>>>>>>>>>>>>>>>>>>>
No you are just not bothering to pay 100% totally >>>>>>>>>>>>>>>>>>> complete attention to every single word. >>>>>>>>>>>>>>>>>>>
Wittgenstein
'True in Russell's system' means, as was said: >>>>>>>>>>>>>>>>>>> proved in Russell's system; and 'false in Russell's >>>>>>>>>>>>>>>>>>> system' means: the opposite has been proved >>>>>>>>>>>>>>>>>>> in Russell's system
Proof Theoretic Semantics has almost gotten there. >>>>>>>>>>>>>>>>>>> For the most part they stop at semantically grounded >>>>>>>>>>>>>>>>>>
and never quite get all the way to True. >>>>>>>>>>>>>>>>>>>
For Wittgenstein's slight extension of the PTS >>>>>>>>>>>>>>>>>>> notion ~reax x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever >>>>>>>>>>>>>>>>>>> heard of Wittgenstein.
So again, you're saying the same thing as everyone >>>>>>>>>>>>>>>>>> else but with different words.
So everyone says that ~reax x=S(x)
which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>> its successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or >>>>>>>>>>>>>>>>> incompleteness?
It does derive incompleteness, as by definition Q is >>>>>>>>>>>>>>>> incomplete because "no number is equal to its successor" >>>>>>>>>>>>>>>> is unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's >>>>>>>>>>>>>>> system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has >>>>>>>>>>>>>> an infinite sequence of inference steps between it and the >>>>>>>>>>>>>> axioms of the system?
untrue and unfalse.
What about the more general case, i.e. a term for a
statement that has *any* sequence of inference steps, either >>>>>>>>>>>> finite or infinite, between it and the axioms of the
system?-a And what would the negation of such a statement be >>>>>>>>>>>> called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any*
sequence of inference steps, either finite or infinite,
between it and the axioms of the system?
"true on the basis of meaning expressed in language"
reliably computable for the entire body of GENERAL knowledge. >>>>>>>>> Is the limit of the topic of all my posts.
Infinite inference steps are off topic.
Why are you so reluctant to provide a simple term?
OFF-TOPIC <is> THE TERM.
So we've established that "off-topic" means "a statement that has >>>>>> *any* sequence of inference steps, either finite or infinite,
between it and the axioms of the system".
The ones that have infinite steps out outside the
body of knowledge and off topic for that reason.
So you're claiming the sentence "no number is equal to its
successor" in Q is "off topic".
Rejected, as it is a semantically valid sentence in the language of Q.
If there is no finite sequence of inference steps
between x and the axioms of Q then PTS stipulates
that x is not semantically valid in Q.
And since x = "no number is equal to its successor" is semantically
valid as per the definition of Q, PTS must be discarded as useless.
So you also have no idea what Stipulative definition is.
A stipulative definition is a type of definition in which
a new or currently existing term is given a new specific meaning
https://en.wikipedia.org/wiki/Stipulative_definition
On 6/27/2026 7:27 PM, olcott wrote:
On 6/27/2026 5:53 PM, dbush wrote:
On 6/27/2026 6:44 PM, olcott wrote:
On 6/27/2026 5:33 PM, dbush wrote:
On 6/27/2026 6:29 PM, olcott wrote:If there is no finite sequence of inference steps
On 6/27/2026 5:21 PM, dbush wrote:
On 6/27/2026 6:18 PM, olcott wrote:
On 6/27/2026 5:15 PM, dbush wrote:
On 6/27/2026 6:11 PM, olcott wrote:
On 6/27/2026 4:50 PM, dbush wrote:
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:i.e. proven
On 6/27/2026 3:40 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:23 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 3:16 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:04 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 3:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:39 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:38 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:29 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:27 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:01 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You can find any number >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of terms. That doesn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The above is the key >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I don't believe you.-a You >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have no respect for or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> want to persuade anybody >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If they are mere >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You don't understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Proof- theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is a verified fact that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That you do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounded in the atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you, and it is one which >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'verified fact' when you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> haven't even adequately >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explained what it is that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> All of knowledge expressed >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in language is structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What makes you believe >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic relations that can >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> contain all knowledge that is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The CycL language and the Cyc >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> They use a tree structure for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> concepts. But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It must at least be a directed >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> infinite loop and never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> completes. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
And because PTS claims the semantically valid >>>>>>>>>>>>>>>>>>>>> sentence in Q "no number is equal to its successor" >>>>>>>>>>>>>>>>>>>>> is not semantically valid, it must be discarded as >>>>>>>>>>>>>>>>>>>>> useless.Yet never gets to undecidable or in any sense of >>>>>>>>>>>>>>>>>>>>>>>> incomplete.Which has the semantic meaning "no number is >>>>>>>>>>>>>>>>>>>>>>>>>>> equal to its successor" as per the definition >>>>>>>>>>>>>>>>>>>>>>>>>>> of Q.Is it commonly known that ~reax x=S(x) >>>>>>>>>>>>>>>>>>>>>>>>>>>i.e., ~reax x=S(x) is unprovable is Q, as is >>>>>>>>>>>>>>>>>>>>>>>>>>>>> commonly known.There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It should be obvious that finding a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proof does not happen before >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> looking for a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>In proof theoretic semantics an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression only gains >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Looking for a proof does not need any >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantics so it is not obvious >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how switching to another semantics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> could improve it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Truth Conditional Semantics (TCS) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics (PTS). Essentially >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS just coherently connects the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic meanings >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> one coherent body >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> without undecidability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>If you mean not looking elsewhere >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that may indeed prevent loops. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In most cases that also prevents >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finding the proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>How can any ordering of knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> prevent getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>By looking upward in a type >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no sequence of inference >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> steps in Q from >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> inference steps
in Q from ~reax x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then ~reax x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Since there are no steps in Q that affirm ~reax >>>>>>>>>>>>>>>>>>>>>>>>>> x=S(x)
in Q it is an open question in Q and not a >>>>>>>>>>>>>>>>>>>>>>>>>> confirmed
statement in Q.
In other words, unproven as is commonly known. >>>>>>>>>>>>>>>>>>>>>>>>>
False, as by definition, Q is incomplete because >>>>>>>>>>>>>>>>>>>>>>> ~reax x=S(x) is unprovable / out-of-scope / not >>>>>>>>>>>>>>>>>>>>>>> semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!! >>>>>>>>>>>>>>>>>>>>>
No you are just not bothering to pay 100% totally >>>>>>>>>>>>>>>>>>>> complete attention to every single word. >>>>>>>>>>>>>>>>>>>>
Wittgenstein
'True in Russell's system' means, as was said: >>>>>>>>>>>>>>>>>>>> proved in Russell's system; and 'false in Russell's >>>>>>>>>>>>>>>>>>>> system' means: the opposite has been proved >>>>>>>>>>>>>>>>>>>> in Russell's system
Proof Theoretic Semantics has almost gotten there. >>>>>>>>>>>>>>>>>>>> For the most part they stop at semantically grounded >>>>>>>>>>>>>>>>>>>
and never quite get all the way to True. >>>>>>>>>>>>>>>>>>>>
For Wittgenstein's slight extension of the PTS >>>>>>>>>>>>>>>>>>>> notion ~reax x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever >>>>>>>>>>>>>>>>>>>> heard of Wittgenstein.
So again, you're saying the same thing as everyone >>>>>>>>>>>>>>>>>>> else but with different words.
So everyone says that ~reax x=S(x)
which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>>> its successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or >>>>>>>>>>>>>>>>>> incompleteness?
It does derive incompleteness, as by definition Q is >>>>>>>>>>>>>>>>> incomplete because "no number is equal to its >>>>>>>>>>>>>>>>> successor" is unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said: >>>>>>>>>>>>>>>> proved in Russell's system; and 'false in Russell's >>>>>>>>>>>>>>>> system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that >>>>>>>>>>>>>>> has an infinite sequence of inference steps between it >>>>>>>>>>>>>>> and the axioms of the system?
untrue and unfalse.
What about the more general case, i.e. a term for a >>>>>>>>>>>>> statement that has *any* sequence of inference steps, >>>>>>>>>>>>> either finite or infinite, between it and the axioms of the >>>>>>>>>>>>> system?-a And what would the negation of such a statement be >>>>>>>>>>>>> called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any*
sequence of inference steps, either finite or infinite, >>>>>>>>>>> between it and the axioms of the system?
"true on the basis of meaning expressed in language"
reliably computable for the entire body of GENERAL knowledge. >>>>>>>>>> Is the limit of the topic of all my posts.
Infinite inference steps are off topic.
Why are you so reluctant to provide a simple term?
OFF-TOPIC <is> THE TERM.
So we've established that "off-topic" means "a statement that has >>>>>>> *any* sequence of inference steps, either finite or infinite,
between it and the axioms of the system".
The ones that have infinite steps out outside the
body of knowledge and off topic for that reason.
So you're claiming the sentence "no number is equal to its
successor" in Q is "off topic".
Rejected, as it is a semantically valid sentence in the language of Q. >>>>
between x and the axioms of Q then PTS stipulates
that x is not semantically valid in Q.
And since x = "no number is equal to its successor" is semantically
valid as per the definition of Q, PTS must be discarded as useless.
So you also have no idea what Stipulative definition is.
A stipulative definition is a type of definition in which
a new or currently existing term is given a new specific meaning
https://en.wikipedia.org/wiki/Stipulative_definition
Not allowed, as "semantically valid" is already defined, and "no number
is equal to its successor" meets that definition.
On 6/27/2026 6:33 PM, dbush wrote:
On 6/27/2026 7:27 PM, olcott wrote:
On 6/27/2026 5:53 PM, dbush wrote:
On 6/27/2026 6:44 PM, olcott wrote:
On 6/27/2026 5:33 PM, dbush wrote:
So you're claiming the sentence "no number is equal to its
successor" in Q is "off topic".
Rejected, as it is a semantically valid sentence in the language
of Q.
If there is no finite sequence of inference steps
between x and the axioms of Q then PTS stipulates
that x is not semantically valid in Q.
And since x = "no number is equal to its successor" is semantically
valid as per the definition of Q, PTS must be discarded as useless.
So you also have no idea what Stipulative definition is.
A stipulative definition is a type of definition in which
a new or currently existing term is given a new specific meaning
https://en.wikipedia.org/wiki/Stipulative_definition
Not allowed, as "semantically valid" is already defined, and "no
number is equal to its successor" meets that definition.
Proof Theoretic Semantics (PTS) supersedes and overrules this.
On 6/27/2026 7:59 PM, olcott wrote:
On 6/27/2026 6:33 PM, dbush wrote:
On 6/27/2026 7:27 PM, olcott wrote:
On 6/27/2026 5:53 PM, dbush wrote:
On 6/27/2026 6:44 PM, olcott wrote:
On 6/27/2026 5:33 PM, dbush wrote:
So you're claiming the sentence "no number is equal to its
successor" in Q is "off topic".
Rejected, as it is a semantically valid sentence in the language >>>>>>> of Q.
If there is no finite sequence of inference steps
between x and the axioms of Q then PTS stipulates
that x is not semantically valid in Q.
And since x = "no number is equal to its successor" is semantically >>>>> valid as per the definition of Q, PTS must be discarded as useless.
So you also have no idea what Stipulative definition is.
A stipulative definition is a type of definition in which
a new or currently existing term is given a new specific meaning
https://en.wikipedia.org/wiki/Stipulative_definition
Not allowed, as "semantically valid" is already defined, and "no
number is equal to its successor" meets that definition.
Proof Theoretic Semantics (PTS) supersedes and overrules this.
Then PTS is discarded as useless because it rejects "no number is equal
to its successor".
On 6/27/2026 5:37 PM, Ross Finlayson wrote:
On 06/27/2026 08:47 AM, polcott wrote:
On 6/27/2026 3:05 AM, Mikko wrote:
On 27/06/2026 01:01, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope. >>>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable. Then to >>>>>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~reax x>10 v x<5 but much more >>>>>> complex.
"No number is equal to its successor" is a sentence in RA, and it >>>>>>>> is true but unprovable in RA (or as your would call it, "out-of- >>>>>>>> scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language >>>>>> of Q. More formally, it is this:
~reax x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms >>>>>> you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
Nevertheless a sentence like ~reax x=S(x) is in the language of Q and
that way in the theory.
Colorless green ideas sleep furiously
was composed by Noam Chomsky in his 1957 book
Syntactic Structures as an example of a sentence
that is grammatically well-formed, but semantically
nonsensical.
Proving that syntax is not enough.
"Colorless green" is actually two colors
since there's a dual-tristimulus colorspace
the chromatic and the prismatic,
a fact of the science of the theory of light and color,
of which you are ignorant, then making for a reasonable
reading of the usual apocryphal comment.
Then, ideas can sleep however they want.
The point is that syntactically correct expressions
can be semantically incoherent. Math always makes
sure to ignore this. The gibberish cannot be proven
counts as undecidability in math.
On 6/27/2026 5:37 PM, Ross Finlayson wrote:
On 06/27/2026 08:47 AM, polcott wrote:
On 6/27/2026 3:05 AM, Mikko wrote:
On 27/06/2026 01:01, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope. >>>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable. Then to >>>>>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~reax x>10 v x<5 but much more >>>>>> complex.
"No number is equal to its successor" is a sentence in RA, and it >>>>>>>> is true but unprovable in RA (or as your would call it, "out-of- >>>>>>>> scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language >>>>>> of Q. More formally, it is this:
~reax x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms >>>>>> you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
Nevertheless a sentence like ~reax x=S(x) is in the language of Q and
that way in the theory.
Colorless green ideas sleep furiously
was composed by Noam Chomsky in his 1957 book
Syntactic Structures as an example of a sentence
that is grammatically well-formed, but semantically
nonsensical.
Proving that syntax is not enough.
"Colorless green" is actually two colors
since there's a dual-tristimulus colorspace
the chromatic and the prismatic,
a fact of the science of the theory of light and color,
of which you are ignorant, then making for a reasonable
reading of the usual apocryphal comment.
Then, ideas can sleep however they want.
The point is that syntactically correct expressions
can be semantically incoherent. Math always makes
sure to ignore this. The gibberish cannot be proven
counts as undecidability in math.
On 06/27/2026 03:47 PM, olcott wrote:
On 6/27/2026 5:37 PM, Ross Finlayson wrote:
On 06/27/2026 08:47 AM, polcott wrote:
On 6/27/2026 3:05 AM, Mikko wrote:
On 27/06/2026 01:01, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson >>>>>>>>>>>>>> Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated >>>>>>>>>>>> with alternative views. So I will simply say out-of-scope. >>>>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable.-a Then to >>>>>>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
-a Breyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False.-a The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False.-a G is simply a sentence like ~reax x>10 v x<5 but much more >>>>>>> complex.
"No number is equal to its successor" is a sentence in RA, and it >>>>>>>>> is true but unprovable in RA (or as your would call it, "out-of- >>>>>>>>> scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language >>>>>>> of Q.-a More formally, it is this:
~reax x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms >>>>>>> you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
Nevertheless a sentence like ~reax x=S(x) is in the language of Q and >>>>> that way in the theory.
Colorless green ideas sleep furiously
was composed by Noam Chomsky in his 1957 book
Syntactic Structures as an example of a sentence
that is grammatically well-formed, but semantically
nonsensical.
Proving that syntax is not enough.
"Colorless green" is actually two colors
since there's a dual-tristimulus colorspace
the chromatic and the prismatic,
a fact of the science of the theory of light and color,
of which you are ignorant, then making for a reasonable
reading of the usual apocryphal comment.
Then, ideas can sleep however they want.
The point is that syntactically correct expressions
can be semantically incoherent. Math always makes
sure to ignore this. The gibberish cannot be proven
counts as undecidability in math.
That's yanking one's own chain, and doesn't work on others.
The "grammar" hierarchy of Chomsky is of a very limited and simple model
of computation and a very direct connection to "regular expressions",
with regards to formal methods, finite automata,
linear, right linear, and regular expressions, and of accounts
of the various amounts of look-ahead or memory in scanners what
result productions, that then in any account of source models
involves linking and dictionaries of symbols, that essentially
it's not saying much and isn't much of "grammar".
Notions for example of the "railroad diagram" simply equip what
are models of languages like "SQL" that are complicated in Chomsky
to be simple in alternatives/optionals/loops with regards to the
declarations of "grammars".
Any sort of usual useful "grammar" involves a "multi-pass parser",
with regards to parsing, for example for natural language, which
usually has a direct account of nouns and verbs, when really the
infinitives are always interrupted by instantiating a verb tense,
and nouns are particulars and simple.
Then, for natural language, all readers of natural human language
using something alike "Tesniere grammars" as of "dependency grammars"
that all learned in school with regards to diagramming any well-formed sentence.
Aristotle is not a fool - and Aristotle won't be made a fool.
That that that that that that that, ....
The problem is not that "colorless green ideas sleep furiously"
is given a _context_ where it's not simply mimsy as the borogoves,
then that besides, all utterances are in a large overall context.
So now you don't know grammar, either.
On 6/27/2026 2:27 AM, Mikko wrote:
On 26/06/2026 16:05, olcott wrote:
On 6/26/2026 1:34 AM, Mikko wrote:
On 25/06/2026 16:58, olcott wrote:
On 6/25/2026 2:18 AM, Mikko wrote:
On 24/06/2026 23:25, olcott wrote:
On 6/24/2026 4:52 AM, Mikko wrote:
On 23/06/2026 17:47, olcott wrote:
On 6/23/2026 12:55 AM, Mikko wrote:
On 22/06/2026 15:09, olcott wrote:
On 6/22/2026 1:41 AM, Mikko wrote:
On 22/06/2026 02:58, olcott wrote:
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>>>> look into proof theoretic semantics.
On 6/17/2026 4:14 PM, olcott wrote:Whereas you are stuck to your own incoherent views and >>>>>>>>>>>>>>>>>> reject
https://www.youtube.com/@rossfinlayson >>>>>>>>>>>>>>>>>>>> Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>>>>
alternative views out-of-hand without review >>>>>>>>>>>>>>>>>
At different times you have expressed different >>>>>>>>>>>>>>>> opinions, which
sometimes have been incompatible. But you have never >>>>>>>>>>>>>>>> clearly
retracted your earlier opitions that conflict with your >>>>>>>>>>>>>>>> present
ones.
All of the ideas that I have ever had about these things >>>>>>>>>>>>>>> are now under the Proof Theoretic Semantics category. >>>>>>>>>>>>>>> These ideas have evolved over time, yet their essence >>>>>>>>>>>>>>> has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a >>>>>>>>>>>>>> publishable
(or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> >>>>>>>>>>>>> human being on the face of the Earth could understand >>>>>>>>>>>>> me I could not publish.
As far as I have seen, all interesting content in those >>>>>>>>>>>> articles
that have any is or depends on claims that should be proven but >>>>>>>>>>>> aren't.
They are proven in Proof Theoretic Semantics
An aricle is not publishable unless it either contains the >>>>>>>>>> proof or
has a pointer to an olready published proof.
Only now after 28 years am I acquiring the lingua Franca
terms-of-the-art of proof theoretic semantics such that
I can anchor my ideas in the foundational work of the
most respected authors in the field.
My issue with you guys is that you only spend 1%
of your concentration understanding me and the other
99% trying to artificially contrive some baseless
rebuttal.
THat "baseless" is false but otherwise, what is wrong is more
important than what is right. Of one ignores what is right one >>>>>>>> mai fail to achieve what one could, but if one believs what is >>>>>>>> wrong one may achieve a disaseter.
Proof-theoretic semantics is an alternative to truth-condition
semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
So far no one has even acknowledged that PTS is an alternative
to truth-conditional semantics. Several people have seemed
to same that no alternative can possibly exist.
You have not shown that there is any need for any alternative
semantics.
With dangerous lies that can destroy Democracy
and kill the planet with climate change having
an ultimate arbiter of truth would be useful.
Those who are able and willing to destroy democracy are able to provice >>>> an ultimate arbiter of truth and usually do so. But they don't need any >>>> proof theoretic semantics.
An ultimate arbiter of truth blows their whole game away.
THe point of the ultimate arbiter of truth is that the errors in the
determinations of any alternative arbiter can be detected and similar
errors in future can be avoided with suitable admistrative or other
actions if regarded necessary.
When all of the relevant facts are known then
counter-factual lies are easy to detect.
On 6/27/2026 3:05 AM, Mikko wrote:
On 27/06/2026 01:01, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable.-a Then to >>>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
-a-aBreyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False.-a The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False.-a G is simply a sentence like ~reax x>10 v x<5 but much more
complex.
"No number is equal to its successor" is a sentence in RA, and it >>>>>> is true but unprovable in RA (or as your would call it, "out-of-
scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language
of Q.-a More formally, it is this:
~reax x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms
you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
Nevertheless a sentence like ~reax x=S(x) is in the language of Q and
that way in the theory.
Colorless green ideas sleep furiously
was composed by Noam Chomsky in his 1957 book
Syntactic Structures as an example of a sentence
that is grammatically well-formed, but semantically
nonsensical.
Proving that syntax is not enough.
On 06/27/2026 08:47 AM, polcott wrote:
On 6/27/2026 3:05 AM, Mikko wrote:
On 27/06/2026 01:01, olcott wrote:Colorless green ideas sleep furiously
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, Andr|- G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(reC x, S(x) rea x).
It's not provable but it certainly has meaning.
Andr|-
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope. >>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable.-a Then to >>>>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
-a Breyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False.-a The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False.-a G is simply a sentence like ~reax x>10 v x<5 but much more
complex.
"No number is equal to its successor" is a sentence in RA, and it >>>>>>> is true but unprovable in RA (or as your would call it, "out-of- >>>>>>> scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language
of Q.-a More formally, it is this:
~reax x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms >>>>> you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
Nevertheless a sentence like ~reax x=S(x) is in the language of Q and
that way in the theory.
was composed by Noam Chomsky in his 1957 book
Syntactic Structures as an example of a sentence
that is grammatically well-formed, but semantically
nonsensical.
Proving that syntax is not enough.
"Colorless green" is actually two colors
since there's a dual-tristimulus colorspace
the chromatic and the prismatic,
a fact of the science of the theory of light and color,
of which you are ignorant, then making for a reasonable
reading of the usual apocryphal comment.
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:All of knowledge expressed in language is structured as a >>>>>>>>>>>>> tree of semantic relations specified syntactically between >>>>>>>>>>>>> finite strings.
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>>>>>You can find any number of terms.-a That doesn't mean >>>>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS G||del 1931 >>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that PTS >>>>>>>>>>>>>>>> somehow causes
G||del's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>>> not understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>>>>>> certainly don't
understand G||del's Theorem, neither the theorem itself >>>>>>>>>>>>>>>> nor any proof of
it.
"grounded in the atomic base of PA" is an expression used >>>>>>>>>>>>>> only by you, and it is one which you have never explicitly >>>>>>>>>>>>>> defined, so the fault here certainly doesn't lie with >>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' when you >>>>>>>>>>>>>> haven't even adequately explained what it is that you mean. >>>>>>>>>>>>
What makes you believe semantic relations that can be >>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to >>>>>>>>>> put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop >>>>>>>> when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before
looking for a proof.
If there is no sequence of inference steps in Q from
~reax x=S(x) to the axioms of Q then ~reax x=S(x) is
ungrounded in the PTS atomic base of Q.
This does not mean undecidable or incomplete
it means that ~reax x=S(x) is out-of-scope for Q.
This is the same sort of thing as finding the defined
meaning of a word. If you cannot find its recursively
defined meaning then it never gains any meaning.
That does not follow. Words have meanings even without definitions.
You can't present the first definition unless you already have
meaningful words.
A particular new word can only be defined in terms
of other existing words that already have definitions.
PTS works in a similar way. If ~reax x=S(x) cannot connect
to its meanings in Q the it remains undefined in Q.
Typically the presentation of a formal theory begins with the
introduction of undefined symbols. But the symbols are not
fully meaningless. They get some amount of meaning from being
introduces as symbols of a particular syntactic category and
more from being used in the postulates of the theory.
The body of knowledge expressed in language starts
with an atomic basis of expressions of language that
are stipulated to be true.
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x) is
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms.-a That doesn't >>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS G||del >>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>>> PTS somehow causes
G||del's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>>> you certainly don't
understand G||del's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly >>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>> fact' when you haven't even adequately explained what >>>>>>>>>>>>>>>>>> it is that you mean.
All of knowledge expressed in language is structured as >>>>>>>>>>>>>>>>> a tree of semantic relations specified syntactically >>>>>>>>>>>>>>>>> between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a >>>>>>>>>>>> loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not
obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before
looking for a proof.
If there is no sequence of inference steps in Q from
~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x)
is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known.
semantic nonsense in Q? All of logic took
a psychotic break from reality when they
took semantics out of logic and put it in
a separate model.
On 6/27/2026 2:48 AM, Mikko wrote:
On 26/06/2026 19:08, dbush wrote:
On 6/26/2026 10:24 AM, olcott wrote:
On 6/26/2026 8:57 AM, dbush wrote:
On 6/26/2026 9:45 AM, olcott wrote:
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms.-a That doesn't >>>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS G||del >>>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you.-a You have no respect for or >>>>>>>>>>>>>>>>>>>>> understanding of the
truth.-a If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>>>> PTS somehow causes
G||del's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>>>> you certainly don't
understand G||del's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly >>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>>> fact' when you haven't even adequately explained what >>>>>>>>>>>>>>>>>>> it is that you mean.
All of knowledge expressed in language is structured >>>>>>>>>>>>>>>>>> as a tree of semantic relations specified >>>>>>>>>>>>>>>>>> syntactically between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting stuck in >>>>>>>>>>>>> a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not >>>>>>>>> obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is
equal to its successor" has no meaning in Robinson Arithmetic.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
Then you agree that the above natural language sentence that is
semantically required to be either true or false has no meaning?
Your sentence would be what it always has been
a stipulated true sentence axiom.
False, as that statement is not one of the axioms of Robinson
arithmetic, but it is a statement in its language, and one that has
*only* an infinite connection to the axioms of that system.
What infinite connection? The statement is false in natural numbers,
which is one model of Robinson Arithmetic but not the only one.
In another model there may be a number that is its successor. There
may even be more than one such number.
It cannot be proved in Q and can be proved in PA.
Thus its semantic meaning is out-of-scope in Q.
--By your logic, "no number is equal to its successor" has no meaning
in Robinson arithmetic.
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>>>> or mathematical incompleteness.
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>> would one try to
On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
What makes you believe semantic relations that can >>>>>>>>>>>>>>>>>>>>>> be structured asAll of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>It is a verified fact that G||del's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>> understand
In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday.
You can find any number of terms.-a That >>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them.
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>> G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no respect for >>>>>>>>>>>>>>>>>>>>>>>>>> or understanding of the
truth.-a If you really want to persuade anybody >>>>>>>>>>>>>>>>>>>>>>>>>> that PTS somehow causes
G||del's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you then >>>>>>>>>>>>>>>>>>>>>>>>>>> you will not understand.
You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>> it.
what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one which >>>>>>>>>>>>>>>>>>>>>>>> you have never explicitly defined, so the fault >>>>>>>>>>>>>>>>>>>>>>>> here certainly doesn't lie with Alan. It's >>>>>>>>>>>>>>>>>>>>>>>> certainly not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>> prevent loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>
Looking for a proof does not need any semantics so it is >>>>>>>>>>>>>> not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>
It should be obvious that finding a proof does not happen >>>>>>>>>>>> before
looking for a proof.
If there is no sequence of inference steps in Q from
~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x)
is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known.
Which has the semantic meaning "no number is equal to its
successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>>>>>> or mathematical incompleteness.
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations that >>>>>>>>>>>>>>>>>>>>>>>> can be structured asIt is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday.
You can find any number of terms.-a That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them.
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means is >>>>>>>>>>>>>>>>>>>>>>>>>>> less
than no rebuttal at all.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean.
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>> prevent loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>
Looking for a proof does not need any semantics so it is >>>>>>>>>>>>>>>> not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>
It should be obvious that finding a proof does not happen >>>>>>>>>>>>>> before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>
Which has the semantic meaning "no number is equal to its
successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no number
is equal to its successor" is not semantically valid, it must be
discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
and never quite get all the way to True.
On 6/27/2026 3:13 AM, Mikko wrote:
On 26/06/2026 16:15, olcott wrote:
On 6/26/2026 1:45 AM, Mikko wrote:
On 25/06/2026 19:16, olcott wrote:
On 6/25/2026 2:29 AM, Mikko wrote:
On 25/06/2026 00:33, olcott wrote:
On 6/24/2026 5:13 AM, Mikko wrote:
On 23/06/2026 21:20, olcott wrote:
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>> [ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> On 6/22/2026 1:42 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>> On 6/22/2026 10:48 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>
G is true.
I put it to you you're lying again.-a No reputable >>>>>>>>>>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things.-a If >>>>>>>>>>>>>>>>>>>>>> Dag Prawitz
really
did
"agree" (with whom?) that G||del's sentence G is >>>>>>>>>>>>>>>>>>>>>> not true in
Peano
Arithmetic, then produce a citation for this. >>>>>>>>>>>>>>>>>>
He never gets to G||del. He essentially says unprovable >>>>>>>>>>>>>>>>>>>>> means untrue all the time for everything within his >>>>>>>>>>>>>>>>>>>>> own Theory of Grounds of strict Proof Theoretic >>>>>>>>>>>>>>>>>>>>> Semantics.
You won't understand it, but that _is_ essentially >>>>>>>>>>>>>>>>>>>> G||del's
Incompleteness
Theorem.-a It is a statement that any sufficiently >>>>>>>>>>>>>>>>>>>> powerful
system can
express true things it can't prove.-a So Dag Prawitz, >>>>>>>>>>>>>>>>>>>> had he been
saying
the things you falsely attributed to him, would >>>>>>>>>>>>>>>>>>>> certainly have
"got" to
G||del, and would have understood full well what he >>>>>>>>>>>>>>>>>>>> was saying.
You did not pay close enough attention to my exact >>>>>>>>>>>>>>>>>>> words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>>>
Yeah, I'm pretty sure that "Dag Prawitz says what Dag >>>>>>>>>>>>>>>> Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag >>>>>>>>>>>>>>>> Prawitz doesn't
say",
then looking a bit into his tremendous volume of works, >>>>>>>>>>>>>>>> he talks about "natural deduction" then specifically an >>>>>>>>>>>>>>>> "inverse
principle" so I think these are key aspects of >>>>>>>>>>>>>>>> fundamental logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico MoriconireuLaura TesconirCa
May 8, 2007
Abstract
The idea of an rCLinversion principlerCY, and the name itself, >>>>>>>>>>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to >>>>>>>>>>>>>>>> generate
new ad-
missible rules within a certain syntactic context. Some >>>>>>>>>>>>>>>> N4Ufteen years
later, the idea was taken up by Dag Prawitz to devise a >>>>>>>>>>>>>>>> strategy of
normalization for natural deduction calculi (this being an >>>>>>>>>>>>>>>> analogue of
GentzenrCOs cut-elimination theorem for sequent calculi). >>>>>>>>>>>>>>>> Later,
Prawitz
used the inversion principle again, attributing it with >>>>>>>>>>>>>>>> a semantic
role.
Still working in natural deduction calculi, he >>>>>>>>>>>>>>>> formulated a general
type
of schematic Introduction rules to be matchedrCothanks to >>>>>>>>>>>>>>>> the idea
supporting the inversion principle rCo by a corresponding >>>>>>>>>>>>>>>> general
schematic Elimination rule. This was an attempt to >>>>>>>>>>>>>>>> provide a
solution to
the problem suggested by the often quoted note of Gentzen. >>>>>>>>>>>>>>>> According to
Gentzen rCLit should be possible to display the >>>>>>>>>>>>>>>> elimination rules as
unique functions of the corresponding introduction rules >>>>>>>>>>>>>>>> on the
basis of
certain requirements.rCY Many people have since worked on >>>>>>>>>>>>>>>> this topic,
which can be appropriately seen as the birthplace of >>>>>>>>>>>>>>>> what are now
referred to as rCLgeneral elimination rulesrCY, recently >>>>>>>>>>>>>>>> studied
thoroughly
by Sara Negri and Jan von Plato. In this paper, we >>>>>>>>>>>>>>>> retrace the main
threads of this chapter of proof-theoretical
investigation, using
LorenzenrCOs original framework as a general guide" >>>>>>>>>>>>>>>>
Hm, "general elimination rules", seem derivable from De >>>>>>>>>>>>>>>> Morgan's
laws,
and that being the usual account of naive deductive >>>>>>>>>>>>>>>> analysis, then
since
"natural deduction", which here is held as part of the >>>>>>>>>>>>>>>> theory
since it's naturally logical, then has for Gentzen that >>>>>>>>>>>>>>>> besides
Kripke
afterward there's also Sheffer and Chwistek before, and >>>>>>>>>>>>>>>> instead of
Montague for semantics there's Herbrand for semantics, >>>>>>>>>>>>>>>> so, what to do
about "inversion principle" is here that the thea-theory >>>>>>>>>>>>>>>> has that
it's
what subsumes "non-contradiction principle", here hoping >>>>>>>>>>>>>>>> that the
interpretation aligns and thusly that "principle of >>>>>>>>>>>>>>>> inversion"
wouldn't
need dis-ambiguation from "inversion principle". >>>>>>>>>>>>>>>>
https://www.tandfonline.com/doi/
abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof- >>>>>>>>>>>>>>>> theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the >>>>>>>>>>>>>>>> foundation of
most
modern accounts of proof-theoretic semantics." >>>>>>>>>>>>>>>>
I already have a principle of inversion and furthermore a >>>>>>>>>>>>>>>> principle of
thorough reason as subsuming principles of non- >>>>>>>>>>>>>>>> contradiction and what
suffices, so, I'll be curious then about what to make of >>>>>>>>>>>>>>>> Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as >>>>>>>>>>>>>>>> old as the
oldest account of Western philosophy like Heraclitus >>>>>>>>>>>>>>>> with dual
monism.
In fact by definition it's about the most basic aspect of >>>>>>>>>>>>>>>> contemplation
and deliberation in abstraction of looking at both sides >>>>>>>>>>>>>>>> of issues
and
resolving inductive impasses with analytical bridges after >>>>>>>>>>>>>>>> complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as >>>>>>>>>>>>>>>> one of the
characteristic features of Gentzen's intuitionistic natural >>>>>>>>>>>>>>>> deduction.
In the literature on proof-theoretic semantics, this >>>>>>>>>>>>>>>> principle is
often
coupled with another that is called the recovery >>>>>>>>>>>>>>>> principle. By
adopting
the Computational Ludics framework, we reformulate these >>>>>>>>>>>>>>>> principles
into
one and the same condition, which we call the harmony >>>>>>>>>>>>>>>> condition. We
show
that this reformulation allows us to reveal two >>>>>>>>>>>>>>>> intuitive ideas
standing
behind these principles: the idea of "containment" >>>>>>>>>>>>>>>> present in the
inversion principle, and the idea that the recovery >>>>>>>>>>>>>>>> principle is the
"converse" of the inversion principle. We also formulate >>>>>>>>>>>>>>>> two other
conditions in the Computational Ludics framework, and we >>>>>>>>>>>>>>>> show that
each
of them is equivalent to the harmony condition." >>>>>>>>>>>>>>>>
The "ludicus" is Latin and for accounts of wisdom and >>>>>>>>>>>>>>>> knowledge.
"In particular, by taking inspiration from the >>>>>>>>>>>>>>>> Brouwer-Heyting-Kolmogorov explanation of logical >>>>>>>>>>>>>>>> connectives,
proof-theoretic semantics rests on the idea that we know >>>>>>>>>>>>>>>> the
meaning of
a compound sentence when we know what counts as a >>>>>>>>>>>>>>>> canonical proof of
it.
And if proofs are formalised within the framework of >>>>>>>>>>>>>>>> natural
deduction,
then a canonical proof of a sentence A is nothing but a >>>>>>>>>>>>>>>> closed
derivation ending with an introduction rule of the main >>>>>>>>>>>>>>>> connective
of A."
The "canonical proofs" are not unique, in any system >>>>>>>>>>>>>>>> strong enough
to make for infinitary reasoning and super-classical >>>>>>>>>>>>>>>> results
requiring
analytical bridges about infinity and continuity. >>>>>>>>>>>>>>>>
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6 >>>>>>>>>>>>>>> That is the most important gist of his whole work. >>>>>>>>>>>>>>>
He later goes on to develop and further elaborate his >>>>>>>>>>>>>>> Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches >>>>>>>>>>>>>>> Thomas Piecha & Peter Schroeder-Heister do this same sort of >>>>>>>>>>>>>>> thing two different ways.
Furthermore I say there are "canonical proofs" of >>>>>>>>>>>>>> inductive sorts that
make contradictions and thusly destroy each other. >>>>>>>>>>>>>>
Clearly you have no idea what Dag Prawitz means by
"canonical proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make >>>>>>>>>>>>>> repairs
of what otherwise is flawed, or for hard constructivist >>>>>>>>>>>>>> realist
structuralist model theorists: not-theories (examples of >>>>>>>>>>>>>> wrong).
Induction and counter-induction contradict each other, it's >>>>>>>>>>>> simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog? >>>>>>>>> That would be dishonest.
No, pointing out that you are worng about Prolog when you are wrong >>>>>>>> about Prolog is never dishohest.
That is correct Prolog and that is the
result of the correct run of correct Prolog.
Irrelevant. Nobody claimed there be Prolog errors in your queries. >>>>>>
Implying that I am wrong about Prolog without
pointing out any actual mistake is also DISHONEST.
How did Ross FInlayson imply that you were wrong about Prolog?
If an error is claimed then it must be specifically
pointed out otherwise the clam of error is dishonest.
Yet you claim that Ross Finlayson be dishonest without pointing
out what is dishonest in his words.
If anyone and everyone that claims that they found an
error and never points out what the error is and why
it is an error then they are merely a baseless denigrator.
If anyone and everyone that claims that someone is dishonest
never points out what the dishonesty is is and why it is
dishones then they are merely a baseless denigrator.
Hopefully
news.eternal-september.org
will be back up.
The dishonesty is claiming an error without pointing it out.
The dishonesty is also relying on rhetoric and ad hominem
instead of reasoning and evidence, Trump's favorite ploy.
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>>>>> or mathematical incompleteness.
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>> would one try to
What makes you believe semantic relations that >>>>>>>>>>>>>>>>>>>>>>> can be structured asIt is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday.
You can find any number of terms.-a That >>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them.
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no respect for >>>>>>>>>>>>>>>>>>>>>>>>>>> or understanding of the
truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you then >>>>>>>>>>>>>>>>>>>>>>>>>>>> you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so the >>>>>>>>>>>>>>>>>>>>>>>>> fault here certainly doesn't lie with Alan. >>>>>>>>>>>>>>>>>>>>>>>>> It's certainly not a 'verified fact' when you >>>>>>>>>>>>>>>>>>>>>>>>> haven't even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>> that you mean.
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>> prevent loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>
Looking for a proof does not need any semantics so it is >>>>>>>>>>>>>>> not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>
It should be obvious that finding a proof does not happen >>>>>>>>>>>>> before
looking for a proof.
If there is no sequence of inference steps in Q from
~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>
Which has the semantic meaning "no number is equal to its
successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both reax x=S(x) and ~reax x=S(x) are sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>>>>>> or mathematical incompleteness.
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations that >>>>>>>>>>>>>>>>>>>>>>>> can be structured asIt is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday.
You can find any number of terms.-a That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them.
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means is >>>>>>>>>>>>>>>>>>>>>>>>>>> less
than no rebuttal at all.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean.
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>> prevent loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>
Looking for a proof does not need any semantics so it is >>>>>>>>>>>>>>>> not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>
It should be obvious that finding a proof does not happen >>>>>>>>>>>>>> before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>
Which has the semantic meaning "no number is equal to its
successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both reax x=S(x) and ~reax x=S(x) are
sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
On 29/06/2026 06:12, olcott wrote:
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>>>>>>> or mathematical incompleteness.
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations that >>>>>>>>>>>>>>>>>>>>>>>>> can be structured as"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean.In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday.It is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
You can find any number of terms.-a That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means is >>>>>>>>>>>>>>>>>>>>>>>>>>>> less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>> prevent loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>
Looking for a proof does not need any semantics so it >>>>>>>>>>>>>>>>> is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not happen >>>>>>>>>>>>>>> before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>
Which has the semantic meaning "no number is equal to its
successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both reax x=S(x) and ~reax x=S(x) are
sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies
because the determination of their truth does not need any knowledge
beyond a method to determine whether a string is a tautology in the
relevant language.
When the word "knowledge" is used it usually means knowing about the
real world something that cannot be determined without observation.
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>> undecidability
On 6/24/2026 5:00 AM, Mikko wrote:If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>> prevent loops.
On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations that >>>>>>>>>>>>>>>>>>>>>>>>>> can be structured asAll of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
You can find any number of terms.-a That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means >>>>>>>>>>>>>>>>>>>>>>>>>>>>> is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>
or mathematical incompleteness.
Looking for a proof does not need any semantics so it >>>>>>>>>>>>>>>>>> is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both reax x=S(x) and ~reax x=S(x) are
sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies
You are not paying close enough attention. I did not say logical
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency. Thus,
rCLAll humans are mammalsrCY is held to assert with
regard to anything whatsoever that either it is
not a human or it is a mammal.
https://www.britannica.com/topic/tautology
https://en.wikipedia.org/wiki/Tautology_(logic)
because the determination of their truth does not need any knowledge
beyond a method to determine whether a string is a tautology in the
relevant language.
When the word "knowledge" is used it usually means knowing about the
real world something that cannot be determined without observation.
One can know that "cats are animals" when this is
stipulated as an axiom.
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>> undecidability
On 6/24/2026 5:00 AM, Mikko wrote:If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>> prevent loops.
On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations that >>>>>>>>>>>>>>>>>>>>>>>>>> can be structured asAll of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
You can find any number of terms.-a That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means >>>>>>>>>>>>>>>>>>>>>>>>>>>>> is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>
or mathematical incompleteness.
Looking for a proof does not need any semantics so it >>>>>>>>>>>>>>>>>> is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both reax x=S(x) and ~reax x=S(x) are
sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies
You are not paying close enough attention. I did not say logical
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>> Essentially
On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>>> prevent loops.
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>> some language?All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
You can find any number of terms.-a That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it >>>>>>>>>>>>>>>>>>> is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is >>>>>>> unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both reax x=S(x) and ~reax x=S(x) are >>>>> sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies
You are not paying close enough attention. I did not say logical
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency. Thus,
rCLAll humans are mammalsrCY is held to assert with
regard to anything whatsoever that either it is
not a human or it is a mammal.
https://www.britannica.com/topic/tautology
https://en.wikipedia.org/wiki/Tautology_(logic)
because the determination of their truth does not need any knowledge
beyond a method to determine whether a string is a tautology in the
relevant language.
When the word "knowledge" is used it usually means knowing about the
real world something that cannot be determined without observation.
One can know that "cats are animals" when this is
stipulated as an axiom.
That axiom only realtes the words "cat" and "animal". It does not tell anything about the real world.
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>> Essentially
On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>>> prevent loops.
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>> some language?All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
You can find any number of terms.-a That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it >>>>>>>>>>>>>>>>>>> is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is >>>>>>> unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both reax x=S(x) and ~reax x=S(x) are >>>>> sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies
You are not paying close enough attention. I did not say logical
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
So, if you want to know more about my theory, which is an account
of reason, and for Foundations, then I'd suggest first making for
yourself a "universal education", then finding resolutions to the
"paradoxes" of mathematical logic,
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" the
"great atlas of mathematical independence", then for "higher
mathematics", and quite about "continuity" and "infinity",
then there's also "the physics" after "the logic" and "the mathematics".
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an account
of reason, and for Foundations, then I'd suggest first making for
yourself a "universal education", then finding resolutions to the
"paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao 01 02
01 G
02 -4 03
03 Prov_PA 04
04 G||del_Number_of 01 // cycle indicates no well-founded justification
tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
CurryrCoHoward correspondence
In programming language theory and proof theory,
the CurryrCoHoward correspondence is a direct relationship
between computer programs and mathematical proofs. https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" the
"great atlas of mathematical independence", then for "higher
mathematics", and quite about "continuity" and "infinity",
then there's also "the physics" after "the logic" and "the mathematics".
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an account
of reason, and for Foundations, then I'd suggest first making for
yourself a "universal education", then finding resolutions to the
"paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao 01 02
01 G
02 -4 03
03 Prov_PA 04
04 G||del_Number_of 01 // cycle indicates no well-founded justification
tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
CurryrCoHoward correspondence
In programming language theory and proof theory,
the CurryrCoHoward correspondence is a direct relationship
between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" the
"great atlas of mathematical independence", then for "higher
mathematics", and quite about "continuity" and "infinity",
then there's also "the physics" after "the logic" and "the mathematics". >>>
"Curry's poor substitute" at least rejects material implication.
Matters of meaning or the epistemological is a field called "semiotics". Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the
resources.
The Liar Paradox is just a template of what would be a fallacy:
two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in it.
"Cat" is a word.
On 06/30/2026 10:36 AM, Ross Finlayson wrote:
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an account
of reason, and for Foundations, then I'd suggest first making for
yourself a "universal education", then finding resolutions to the
"paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov_PA-a-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle indicates no well-founded justification >>> tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
CurryrCoHoward correspondence
In programming language theory and proof theory,
the CurryrCoHoward correspondence is a direct relationship
between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" the
"great atlas of mathematical independence", then for "higher
mathematics", and quite about "continuity" and "infinity",
then there's also "the physics" after "the logic" and "the
mathematics".
"Curry's poor substitute" at least rejects material implication.
Matters of meaning or the epistemological is a field called "semiotics".
Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the
resources.
The Liar Paradox is just a template of what would be a fallacy:
two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in it.
"Cat" is a word.
It's fair to say "the Liar Paradox is false",
then that the negation translates through the copula "is"
to result "this sentence is true", a meaningless, empty tautology
(except as quoted a meaningless, empty, tautology).
It doesn't work on other "paradoxes", though.
Finlayson's paradox: there are none.
On 6/30/2026 2:48 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>> Essentially
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>>>> prevent loops.It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>> why would one try toAll of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>> strings."grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> so the fault here certainly doesn't lie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fact' when you haven't even adequately >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explained what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:It is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so >>>>>>>>>>>>>>>>>>>> it is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>> in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is >>>>>>>> unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both reax x=S(x) and ~reax x=S(x) are >>>>>> sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies
You are not paying close enough attention. I did not say logical
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency. Thus,
rCLAll humans are mammalsrCY is held to assert with
regard to anything whatsoever that either it is
not a human or it is a mammal.
https://www.britannica.com/topic/tautology
https://en.wikipedia.org/wiki/Tautology_(logic)
because the determination of their truth does not need any knowledge
beyond a method to determine whether a string is a tautology in the
relevant language.
When the word "knowledge" is used it usually means knowing about the
real world something that cannot be determined without observation.
One can know that "cats are animals" when this is
stipulated as an axiom.
That axiom only realtes the words "cat" and "animal". It does not tell
anything about the real world.
It tells us exactly one thing about the real world.
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>> Essentially
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>>>> prevent loops.It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>> why would one try toAll of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>> strings."grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> so the fault here certainly doesn't lie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fact' when you haven't even adequately >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explained what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:It is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so >>>>>>>>>>>>>>>>>>>> it is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>> in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is >>>>>>>> unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both reax x=S(x) and ~reax x=S(x) are >>>>>> sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies
You are not paying close enough attention. I did not say logical
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
On 6/30/2026 9:47 PM, Ross Finlayson wrote:
On 06/30/2026 10:36 AM, Ross Finlayson wrote:
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an account
of reason, and for Foundations, then I'd suggest first making for
yourself a "universal education", then finding resolutions to the
"paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao 01 02
01 G
02 -4 03
03 Prov_PA 04
04 G||del_Number_of 01 // cycle indicates no well-founded justification >>>> tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
CurryrCoHoward correspondence
In programming language theory and proof theory,
the CurryrCoHoward correspondence is a direct relationship
between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" the
"great atlas of mathematical independence", then for "higher
mathematics", and quite about "continuity" and "infinity",
then there's also "the physics" after "the logic" and "the
mathematics".
"Curry's poor substitute" at least rejects material implication.
Matters of meaning or the epistemological is a field called "semiotics". >>> Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the
resources.
The Liar Paradox is just a template of what would be a fallacy:
two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in it.
"Cat" is a word.
It's fair to say "the Liar Paradox is false",
then that the negation translates through the copula "is"
to result "this sentence is true", a meaningless, empty tautology
(except as quoted a meaningless, empty, tautology).
It doesn't work on other "paradoxes", though.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics almost gets there
through an enormously more convoluted process.
They almost always utterly avoid any nuance of
true. Instead they focus on meaning.
Finlayson's paradox: there are none.
On 06/30/2026 08:01 PM, olcott wrote:
On 6/30/2026 9:47 PM, Ross Finlayson wrote:
On 06/30/2026 10:36 AM, Ross Finlayson wrote:
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an account
of reason, and for Foundations, then I'd suggest first making for
yourself a "universal education", then finding resolutions to the
"paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov_PA-a-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle indicates no well-founded
justification
tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
CurryrCoHoward correspondence
In programming language theory and proof theory,
the CurryrCoHoward correspondence is a direct relationship
between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" the >>>>>> "great atlas of mathematical independence", then for "higher
mathematics", and quite about "continuity" and "infinity",
then there's also "the physics" after "the logic" and "the
mathematics".
"Curry's poor substitute" at least rejects material implication.
Matters of meaning or the epistemological is a field called
"semiotics".
Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the
resources.
The Liar Paradox is just a template of what would be a fallacy:
two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in it.
"Cat" is a word.
It's fair to say "the Liar Paradox is false",
then that the negation translates through the copula "is"
to result "this sentence is true", a meaningless, empty tautology
(except as quoted a meaningless, empty, tautology).
It doesn't work on other "paradoxes", though.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics almost gets there
through an enormously more convoluted process.
They almost always utterly avoid any nuance of
true. Instead they focus on meaning.
Finlayson's paradox: there are none.
That quote of Wittgenstein's just a weak echo of Leibnitz' "principle of sufficient reason" about what an inference is. The Tractatus
Logicophilosophicus starts alright then Wittgenstein wimps out while
being all hot-headed about it later. Russell's favorite philosophers, Plotinus after Philo, are early weak nominalist fictionalists, and
having material implication in their vacuous implicits and so on,
Chrysippus could throw them from the boat since neither are they Pythagoreans.
A much simpler process arrives at a "principle of _thorough_ reason",
where not only are affirmatory and negatory inferences found,
also in the diligence any their contradictions.
Russell's retro-thesis simply can't make the extra-ordinary go away.
It's considered a quasi-modal variety of the weaker sort of the
logicist positivism, which has a stronger variety after a strong
mathematical platonism which invigorates it as "must be science".
Old schlock wrapped as new, ....
On 30/06/2026 16:43, olcott wrote:
On 6/30/2026 2:48 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>> EssentiallyIf you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>>>>> prevent loops.It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and >>>>>>>>>>>>>>>>>>>>>>>>>> neverThey use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>>> why would one try to"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a 'verified fact' when you haven't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> adequately explained what it is that you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean.In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:It is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> strings.
What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so >>>>>>>>>>>>>>>>>>>>> it is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>> in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x) >>>>>>>>>>>> in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is >>>>>>>>> unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both reax x=S(x) and ~reax x=S(x) are >>>>>>> sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies
You are not paying close enough attention. I did not say logical
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency. Thus,
rCLAll humans are mammalsrCY is held to assert with
regard to anything whatsoever that either it is
not a human or it is a mammal.
https://www.britannica.com/topic/tautology
https://en.wikipedia.org/wiki/Tautology_(logic)
because the determination of their truth does not need any knowledge >>>>> beyond a method to determine whether a string is a tautology in the
relevant language.
When the word "knowledge" is used it usually means knowing about the >>>>> real world something that cannot be determined without observation.
One can know that "cats are animals" when this is
stipulated as an axiom.
That axiom only realtes the words "cat" and "animal". It does not tell
anything about the real world.
It tells us exactly one thing about the real world.
Only to those who already know that there are things called "cat"
in the real world and know what kind of things the words "cat" and
"animal" refer to but don't already know that every thing that the
word "cat" refers to is a thing that the word "animal" refers to.
On 30/06/2026 17:22, olcott wrote:
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>> EssentiallyIf you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>>>>> prevent loops.It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and >>>>>>>>>>>>>>>>>>>>>>>>>> neverThey use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>>> why would one try to"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a 'verified fact' when you haven't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> adequately explained what it is that you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean.In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:It is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> strings.
What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so >>>>>>>>>>>>>>>>>>>>> it is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>> in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x) >>>>>>>>>>>> in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is >>>>>>>>> unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both reax x=S(x) and ~reax x=S(x) are >>>>>>> sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies
You are not paying close enough attention. I did not say logical
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
In order to achieve that the atomic facts must be non-tautologies.
Tautologies need not be included. They can be concluded from nothing.
The only semantic entailments that need be encoded are definitions. Everything else is covered by requiring that an inference from A nnd
B to X is accepted as valid only if -4A re? -4B re? X is a tautology.
Nothing else is semantically entailed.
On 7/1/2026 7:13 AM, Ross Finlayson wrote:
On 06/30/2026 08:01 PM, olcott wrote:
On 6/30/2026 9:47 PM, Ross Finlayson wrote:
On 06/30/2026 10:36 AM, Ross Finlayson wrote:
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an account >>>>>>> of reason, and for Foundations, then I'd suggest first making for >>>>>>> yourself a "universal education", then finding resolutions to the >>>>>>> "paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao 01 02
01 G
02 -4 03
03 Prov_PA 04
04 G||del_Number_of 01 // cycle indicates no well-founded
justification
tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
CurryrCoHoward correspondence
In programming language theory and proof theory,
the CurryrCoHoward correspondence is a direct relationship
between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" the >>>>>>> "great atlas of mathematical independence", then for "higher
mathematics", and quite about "continuity" and "infinity",
then there's also "the physics" after "the logic" and "the
mathematics".
"Curry's poor substitute" at least rejects material implication.
Matters of meaning or the epistemological is a field called
"semiotics".
Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the
resources.
The Liar Paradox is just a template of what would be a fallacy:
two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in it. >>>>> "Cat" is a word.
It's fair to say "the Liar Paradox is false",
then that the negation translates through the copula "is"
to result "this sentence is true", a meaningless, empty tautology
(except as quoted a meaningless, empty, tautology).
It doesn't work on other "paradoxes", though.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics almost gets there
through an enormously more convoluted process.
They almost always utterly avoid any nuance of
true. Instead they focus on meaning.
Finlayson's paradox: there are none.
That quote of Wittgenstein's just a weak echo of Leibnitz' "principle of
sufficient reason" about what an inference is. The Tractatus
Correct reasoning is not correctly evaluated on the
basis of who came up with the ideas. These ideas either
has a sound basis or not.
It just the same thing that I have been saying fir years.
True on the basis of meaning expressed in language must
have a direct semantic connection to those things in the
directly in the formal system of this language that make it
true.
(a) Cats are animals
(b) Animals are living things
(c) re| Cats are living things
No jumping outside of the language to a separate model.
Logicophilosophicus starts alright then Wittgenstein wimps out while
being all hot-headed about it later. Russell's favorite philosophers,
Plotinus after Philo, are early weak nominalist fictionalists, and
having material implication in their vacuous implicits and so on,
Chrysippus could throw them from the boat since neither are they
Pythagoreans.
A much simpler process arrives at a "principle of _thorough_ reason",
where not only are affirmatory and negatory inferences found,
also in the diligence any their contradictions.
That is what I just showed.
Russell's retro-thesis simply can't make the extra-ordinary go away.
It's considered a quasi-modal variety of the weaker sort of the
logicist positivism, which has a stronger variety after a strong
mathematical platonism which invigorates it as "must be science".
Old schlock wrapped as new, ....
The only way to obtain a correct foundation of these
things is to reverse-engineer them from first principles.
If one does not do that then the extraneous baggage
of the differing human perspectives prevent a fully
coherent view.
On 07/01/2026 07:59 AM, olcott wrote:
On 7/1/2026 7:13 AM, Ross Finlayson wrote:
On 06/30/2026 08:01 PM, olcott wrote:
On 6/30/2026 9:47 PM, Ross Finlayson wrote:
On 06/30/2026 10:36 AM, Ross Finlayson wrote:
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an account >>>>>>>> of reason, and for Foundations, then I'd suggest first making for >>>>>>>> yourself a "universal education", then finding resolutions to the >>>>>>>> "paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov_PA-a-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle indicates no well-founded
justification
tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
CurryrCoHoward correspondence
In programming language theory and proof theory,
the CurryrCoHoward correspondence is a direct relationship
between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence >>>>>>>
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" the >>>>>>>> "great atlas of mathematical independence", then for "higher
mathematics", and quite about "continuity" and "infinity",
then there's also "the physics" after "the logic" and "the
mathematics".
"Curry's poor substitute" at least rejects material implication.
Matters of meaning or the epistemological is a field called
"semiotics".
Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the
resources.
The Liar Paradox is just a template of what would be a fallacy:
two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in it. >>>>>> "Cat" is a word.
It's fair to say "the Liar Paradox is false",
then that the negation translates through the copula "is"
to result "this sentence is true", a meaningless, empty tautology
(except as quoted a meaningless, empty, tautology).
It doesn't work on other "paradoxes", though.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics almost gets there
through an enormously more convoluted process.
They almost always utterly avoid any nuance of
true. Instead they focus on meaning.
Finlayson's paradox: there are none.
That quote of Wittgenstein's just a weak echo of Leibnitz' "principle of >>> sufficient reason" about what an inference is. The Tractatus
Correct reasoning is not correctly evaluated on the
basis of who came up with the ideas. These ideas either
has a sound basis or not.
It just the same thing that I have been saying fir years.
True on the basis of meaning expressed in language must
have a direct semantic connection to those things in the
directly in the formal system of this language that make it
true.
(a) Cats are animals
(b) Animals are living things
(c) re| Cats are living things
No jumping outside of the language to a separate model.
Logicophilosophicus starts alright then Wittgenstein wimps out while
being all hot-headed about it later. Russell's favorite philosophers,
Plotinus after Philo, are early weak nominalist fictionalists, and
having material implication in their vacuous implicits and so on,
Chrysippus could throw them from the boat since neither are they
Pythagoreans.
A much simpler process arrives at a "principle of _thorough_ reason",
where not only are affirmatory and negatory inferences found,
also in the diligence any their contradictions.
That is what I just showed.
Russell's retro-thesis simply can't make the extra-ordinary go away.
It's considered a quasi-modal variety of the weaker sort of the
logicist positivism, which has a stronger variety after a strong
mathematical platonism which invigorates it as "must be science".
Old schlock wrapped as new, ....
The only way to obtain a correct foundation of these
things is to reverse-engineer them from first principles.
If one does not do that then the extraneous baggage
of the differing human perspectives prevent a fully
coherent view.
That's just syllogism, and makes for constructivism
since any sort stipulation, like an axiom, is unfounded.
The "axiomless natural deduction" to arrive at "axiomless
geometry" and "axiomless arithmetic" is a usual notion that
mathematical platonists have, though these days sometimes
they call themselves structural realists to not concern
dear old Bertrand, then though logicist positivists take
that label without fulfilling its definition.
Syllogism is subject ordering, and Aristotle reads every
syllogism its statements in every order, for example to
detect cycles and disambiguate them, which otherwise a
linear reader will fail to detect.
The "principle of _thorough_ reason" is more than the
"principle of 'sufficient' reason", then that in a
wider account of a wider, fuller dialectic, what's
sound, thorough, fulfilling, and fair.
Mentioning something like Prawitz' "inversion principle"
and about both the restriction _and_ the recovery, and
more than Russell's mere "isolation in significance and
significance in isolation", means that restricting (ignoring)
the resolution of any and all paradoxes leaves the door ajar
just like quasi-modal logic and principle of explosion.
So, maybe readers and researchers in foundations should start
with outlining the requirements and desiderata of a theory
that's constant, consistent, complete, and concrete,
and see how axiomless natural deduction fulfills that
with a comprehensive yet paradox-free account, and
that's the usual account since antiquity and even since
before recorded times, then it's called "mathematical platonism",
since issues of the human condition itself are subjective,
and whether Thoth or Hermes Trismagistus has an ankh for reason
or spiral for infinity, in at least one account there's both.
Thoth -> thought
Logos -> logic
Ma'at -> math
Aristotle won't be made a fool, and more than merely
half-Aristotleans have always both prior and posterior accounts.
On 7/1/2026 12:00 PM, Ross Finlayson wrote:
On 07/01/2026 07:59 AM, olcott wrote:
On 7/1/2026 7:13 AM, Ross Finlayson wrote:
On 06/30/2026 08:01 PM, olcott wrote:
On 6/30/2026 9:47 PM, Ross Finlayson wrote:
On 06/30/2026 10:36 AM, Ross Finlayson wrote:
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an account >>>>>>>>> of reason, and for Foundations, then I'd suggest first making for >>>>>>>>> yourself a "universal education", then finding resolutions to the >>>>>>>>> "paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao 01 02
01 G
02 -4 03
03 Prov_PA 04
04 G||del_Number_of 01 // cycle indicates no well-founded
justification
tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
CurryrCoHoward correspondence
In programming language theory and proof theory,
the CurryrCoHoward correspondence is a direct relationship
between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence >>>>>>>>
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" >>>>>>>>> the
"great atlas of mathematical independence", then for "higher >>>>>>>>> mathematics", and quite about "continuity" and "infinity",
then there's also "the physics" after "the logic" and "the
mathematics".
"Curry's poor substitute" at least rejects material implication. >>>>>>>
Matters of meaning or the epistemological is a field called
"semiotics".
Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the >>>>>>> resources.
The Liar Paradox is just a template of what would be a fallacy:
two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in >>>>>>> it.
"Cat" is a word.
It's fair to say "the Liar Paradox is false",
then that the negation translates through the copula "is"
to result "this sentence is true", a meaningless, empty tautology
(except as quoted a meaningless, empty, tautology).
It doesn't work on other "paradoxes", though.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics almost gets there
through an enormously more convoluted process.
They almost always utterly avoid any nuance of
true. Instead they focus on meaning.
Finlayson's paradox: there are none.
That quote of Wittgenstein's just a weak echo of Leibnitz'
"principle of
sufficient reason" about what an inference is. The Tractatus
Correct reasoning is not correctly evaluated on the
basis of who came up with the ideas. These ideas either
has a sound basis or not.
It just the same thing that I have been saying fir years.
True on the basis of meaning expressed in language must
have a direct semantic connection to those things in the
directly in the formal system of this language that make it
true.
(a) Cats are animals
(b) Animals are living things
(c) re| Cats are living things
No jumping outside of the language to a separate model.
Logicophilosophicus starts alright then Wittgenstein wimps out while
being all hot-headed about it later. Russell's favorite philosophers,
Plotinus after Philo, are early weak nominalist fictionalists, and
having material implication in their vacuous implicits and so on,
Chrysippus could throw them from the boat since neither are they
Pythagoreans.
A much simpler process arrives at a "principle of _thorough_ reason",
where not only are affirmatory and negatory inferences found,
also in the diligence any their contradictions.
That is what I just showed.
Russell's retro-thesis simply can't make the extra-ordinary go away.
It's considered a quasi-modal variety of the weaker sort of the
logicist positivism, which has a stronger variety after a strong
mathematical platonism which invigorates it as "must be science".
Old schlock wrapped as new, ....
The only way to obtain a correct foundation of these
things is to reverse-engineer them from first principles.
If one does not do that then the extraneous baggage
of the differing human perspectives prevent a fully
coherent view.
That's just syllogism, and makes for constructivism
since any sort stipulation, like an axiom, is unfounded.
The "axiomless natural deduction" to arrive at "axiomless
geometry" and "axiomless arithmetic" is a usual notion that
mathematical platonists have, though these days sometimes
they call themselves structural realists to not concern
dear old Bertrand, then though logicist positivists take
that label without fulfilling its definition.
Syllogism is subject ordering, and Aristotle reads every
syllogism its statements in every order, for example to
detect cycles and disambiguate them, which otherwise a
linear reader will fail to detect.
The "principle of _thorough_ reason" is more than the
"principle of 'sufficient' reason", then that in a
wider account of a wider, fuller dialectic, what's
sound, thorough, fulfilling, and fair.
Mentioning something like Prawitz' "inversion principle"
and about both the restriction _and_ the recovery, and
more than Russell's mere "isolation in significance and
significance in isolation", means that restricting (ignoring)
the resolution of any and all paradoxes leaves the door ajar
just like quasi-modal logic and principle of explosion.
So, maybe readers and researchers in foundations should start
with outlining the requirements and desiderata of a theory
that's constant, consistent, complete, and concrete,
The entire body of knowledge expressed in language
(a) Encodes all of the empirical "atomic facts" as axioms
this merges the analytic/synthetic distinction into one
analytic system. https://plato.stanford.edu/entries/analytic-synthetic/
(b) Provide a finite list of the possible semantic relations
between/among the elements of (a) and these are specified
syntactically using a system similar to CycL. https://en.wikipedia.org/wiki/CycL
(c) This whole thing is stored in a knowledge ontology https://en.wikipedia.org/wiki/Ontology_(information_science)
Hierarchy of simple type theory. https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
Now we have the entire body of general knowledge that
can be expressed in language as a set of stipulated
semantic relations between finite strings.
and see how axiomless natural deduction fulfills that
with a comprehensive yet paradox-free account, and
that's the usual account since antiquity and even since
before recorded times, then it's called "mathematical platonism",
since issues of the human condition itself are subjective,
and whether Thoth or Hermes Trismagistus has an ankh for reason
or spiral for infinity, in at least one account there's both.
Thoth -> thought
Logos -> logic
Ma'at -> math
Aristotle won't be made a fool, and more than merely
half-Aristotleans have always both prior and posterior accounts.
On 07/01/2026 10:57 AM, olcott wrote:
On 7/1/2026 12:00 PM, Ross Finlayson wrote:
On 07/01/2026 07:59 AM, olcott wrote:
On 7/1/2026 7:13 AM, Ross Finlayson wrote:
On 06/30/2026 08:01 PM, olcott wrote:
On 6/30/2026 9:47 PM, Ross Finlayson wrote:
On 06/30/2026 10:36 AM, Ross Finlayson wrote:
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an account >>>>>>>>>> of reason, and for Foundations, then I'd suggest first making for >>>>>>>>>> yourself a "universal education", then finding resolutions to the >>>>>>>>>> "paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov_PA-a-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle indicates no well-founded
justification
tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
CurryrCoHoward correspondence
In programming language theory and proof theory,
the CurryrCoHoward correspondence is a direct relationship
between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence >>>>>>>>>
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" >>>>>>>>>> the
"great atlas of mathematical independence", then for "higher >>>>>>>>>> mathematics", and quite about "continuity" and "infinity", >>>>>>>>>> then there's also "the physics" after "the logic" and "the >>>>>>>>>> mathematics".
"Curry's poor substitute" at least rejects material implication. >>>>>>>>
Matters of meaning or the epistemological is a field called
"semiotics".
Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the >>>>>>>> resources.
The Liar Paradox is just a template of what would be a fallacy: >>>>>>>> two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in >>>>>>>> it.
"Cat" is a word.
It's fair to say "the Liar Paradox is false",
then that the negation translates through the copula "is"
to result "this sentence is true", a meaningless, empty tautology >>>>>>> (except as quoted a meaningless, empty, tautology).
It doesn't work on other "paradoxes", though.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics almost gets there
through an enormously more convoluted process.
They almost always utterly avoid any nuance of
true. Instead they focus on meaning.
Finlayson's paradox: there are none.
That quote of Wittgenstein's just a weak echo of Leibnitz'
"principle of
sufficient reason" about what an inference is. The Tractatus
Correct reasoning is not correctly evaluated on the
basis of who came up with the ideas. These ideas either
has a sound basis or not.
It just the same thing that I have been saying fir years.
True on the basis of meaning expressed in language must
have a direct semantic connection to those things in the
directly in the formal system of this language that make it
true.
(a) Cats are animals
(b) Animals are living things
(c) re| Cats are living things
No jumping outside of the language to a separate model.
Logicophilosophicus starts alright then Wittgenstein wimps out while >>>>> being all hot-headed about it later. Russell's favorite philosophers, >>>>> Plotinus after Philo, are early weak nominalist fictionalists, and
having material implication in their vacuous implicits and so on,
Chrysippus could throw them from the boat since neither are they
Pythagoreans.
A much simpler process arrives at a "principle of _thorough_ reason", >>>>> where not only are affirmatory and negatory inferences found,
also in the diligence any their contradictions.
That is what I just showed.
Russell's retro-thesis simply can't make the extra-ordinary go away. >>>>> It's considered a quasi-modal variety of the weaker sort of the
logicist positivism, which has a stronger variety after a strong
mathematical platonism which invigorates it as "must be science".
Old schlock wrapped as new, ....
The only way to obtain a correct foundation of these
things is to reverse-engineer them from first principles.
If one does not do that then the extraneous baggage
of the differing human perspectives prevent a fully
coherent view.
That's just syllogism, and makes for constructivism
since any sort stipulation, like an axiom, is unfounded.
The "axiomless natural deduction" to arrive at "axiomless
geometry" and "axiomless arithmetic" is a usual notion that
mathematical platonists have, though these days sometimes
they call themselves structural realists to not concern
dear old Bertrand, then though logicist positivists take
that label without fulfilling its definition.
Syllogism is subject ordering, and Aristotle reads every
syllogism its statements in every order, for example to
detect cycles and disambiguate them, which otherwise a
linear reader will fail to detect.
The "principle of _thorough_ reason" is more than the
"principle of 'sufficient' reason", then that in a
wider account of a wider, fuller dialectic, what's
sound, thorough, fulfilling, and fair.
Mentioning something like Prawitz' "inversion principle"
and about both the restriction _and_ the recovery, and
more than Russell's mere "isolation in significance and
significance in isolation", means that restricting (ignoring)
the resolution of any and all paradoxes leaves the door ajar
just like quasi-modal logic and principle of explosion.
So, maybe readers and researchers in foundations should start
with outlining the requirements and desiderata of a theory
that's constant, consistent, complete, and concrete,
The entire body of knowledge expressed in language
(a) Encodes all of the empirical "atomic facts" as axioms
this merges the analytic/synthetic distinction into one
analytic system. https://plato.stanford.edu/entries/analytic-synthetic/
(b) Provide a finite list of the possible semantic relations
between/among the elements of (a) and these are specified
syntactically using a system similar to CycL.
https://en.wikipedia.org/wiki/CycL
(c) This whole thing is stored in a knowledge ontology
https://en.wikipedia.org/wiki/Ontology_(information_science)
Hierarchy of simple type theory.
https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
Now we have the entire body of general knowledge that
can be expressed in language as a set of stipulated
semantic relations between finite strings.
and see how axiomless natural deduction fulfills that
with a comprehensive yet paradox-free account, and
that's the usual account since antiquity and even since
before recorded times, then it's called "mathematical platonism",
since issues of the human condition itself are subjective,
and whether Thoth or Hermes Trismagistus has an ankh for reason
or spiral for infinity, in at least one account there's both.
Thoth -> thought
Logos -> logic
Ma'at -> math
Aristotle won't be made a fool, and more than merely
half-Aristotleans have always both prior and posterior accounts.
That's not "a priori truth".
That's just a "convenient" lie to make some system of inference
considered itself compelled complete yet make it slavish while
really it's merely a model of a partial half-account of reason,
that fragmented synthetic pluralism and inconstancy in definition.
Adding an element to another element is synthetic
(where did it come from?), partitioning an element
into two is analytic (how was it already there?).
The usual account of mathematical platonism is analytic,
the usual account of logicist positivism is synthetic,
they are two different things.
Usual accounts of incompleteness like the Hilbert-Bernays paradox
confirm and certify that "logicist positivist nominalist theories"
are at best "merely and completely science".
Then, the account that it's not a science, is wrong.
Anybody can have a quite thorough body of knowledge -
if it doesn't change it's considered they stopped learning,
not that there isn't anything left to learn.
Quit trying to tell people they can't learn, it's insulting.
On 07/01/2026 10:57 AM, olcott wrote:
On 7/1/2026 12:00 PM, Ross Finlayson wrote:
On 07/01/2026 07:59 AM, olcott wrote:
On 7/1/2026 7:13 AM, Ross Finlayson wrote:
On 06/30/2026 08:01 PM, olcott wrote:
On 6/30/2026 9:47 PM, Ross Finlayson wrote:
On 06/30/2026 10:36 AM, Ross Finlayson wrote:
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an account >>>>>>>>>> of reason, and for Foundations, then I'd suggest first making for >>>>>>>>>> yourself a "universal education", then finding resolutions to the >>>>>>>>>> "paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov_PA-a-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle indicates no well-founded
justification
tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
CurryrCoHoward correspondence
In programming language theory and proof theory,
the CurryrCoHoward correspondence is a direct relationship
between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence >>>>>>>>>
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" >>>>>>>>>> the
"great atlas of mathematical independence", then for "higher >>>>>>>>>> mathematics", and quite about "continuity" and "infinity", >>>>>>>>>> then there's also "the physics" after "the logic" and "the >>>>>>>>>> mathematics".
"Curry's poor substitute" at least rejects material implication. >>>>>>>>
Matters of meaning or the epistemological is a field called
"semiotics".
Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the >>>>>>>> resources.
The Liar Paradox is just a template of what would be a fallacy: >>>>>>>> two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in >>>>>>>> it.
"Cat" is a word.
It's fair to say "the Liar Paradox is false",
then that the negation translates through the copula "is"
to result "this sentence is true", a meaningless, empty tautology >>>>>>> (except as quoted a meaningless, empty, tautology).
It doesn't work on other "paradoxes", though.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics almost gets there
through an enormously more convoluted process.
They almost always utterly avoid any nuance of
true. Instead they focus on meaning.
Finlayson's paradox: there are none.
That quote of Wittgenstein's just a weak echo of Leibnitz'
"principle of
sufficient reason" about what an inference is. The Tractatus
Correct reasoning is not correctly evaluated on the
basis of who came up with the ideas. These ideas either
has a sound basis or not.
It just the same thing that I have been saying fir years.
True on the basis of meaning expressed in language must
have a direct semantic connection to those things in the
directly in the formal system of this language that make it
true.
(a) Cats are animals
(b) Animals are living things
(c) re| Cats are living things
No jumping outside of the language to a separate model.
Logicophilosophicus starts alright then Wittgenstein wimps out while >>>>> being all hot-headed about it later. Russell's favorite philosophers, >>>>> Plotinus after Philo, are early weak nominalist fictionalists, and
having material implication in their vacuous implicits and so on,
Chrysippus could throw them from the boat since neither are they
Pythagoreans.
A much simpler process arrives at a "principle of _thorough_ reason", >>>>> where not only are affirmatory and negatory inferences found,
also in the diligence any their contradictions.
That is what I just showed.
Russell's retro-thesis simply can't make the extra-ordinary go away. >>>>> It's considered a quasi-modal variety of the weaker sort of the
logicist positivism, which has a stronger variety after a strong
mathematical platonism which invigorates it as "must be science".
Old schlock wrapped as new, ....
The only way to obtain a correct foundation of these
things is to reverse-engineer them from first principles.
If one does not do that then the extraneous baggage
of the differing human perspectives prevent a fully
coherent view.
That's just syllogism, and makes for constructivism
since any sort stipulation, like an axiom, is unfounded.
The "axiomless natural deduction" to arrive at "axiomless
geometry" and "axiomless arithmetic" is a usual notion that
mathematical platonists have, though these days sometimes
they call themselves structural realists to not concern
dear old Bertrand, then though logicist positivists take
that label without fulfilling its definition.
Syllogism is subject ordering, and Aristotle reads every
syllogism its statements in every order, for example to
detect cycles and disambiguate them, which otherwise a
linear reader will fail to detect.
The "principle of _thorough_ reason" is more than the
"principle of 'sufficient' reason", then that in a
wider account of a wider, fuller dialectic, what's
sound, thorough, fulfilling, and fair.
Mentioning something like Prawitz' "inversion principle"
and about both the restriction _and_ the recovery, and
more than Russell's mere "isolation in significance and
significance in isolation", means that restricting (ignoring)
the resolution of any and all paradoxes leaves the door ajar
just like quasi-modal logic and principle of explosion.
So, maybe readers and researchers in foundations should start
with outlining the requirements and desiderata of a theory
that's constant, consistent, complete, and concrete,
The entire body of knowledge expressed in language
(a) Encodes all of the empirical "atomic facts" as axioms
this merges the analytic/synthetic distinction into one
analytic system. https://plato.stanford.edu/entries/analytic-synthetic/
(b) Provide a finite list of the possible semantic relations
between/among the elements of (a) and these are specified
syntactically using a system similar to CycL.
https://en.wikipedia.org/wiki/CycL
(c) This whole thing is stored in a knowledge ontology
https://en.wikipedia.org/wiki/Ontology_(information_science)
Hierarchy of simple type theory.
https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
Now we have the entire body of general knowledge that
can be expressed in language as a set of stipulated
semantic relations between finite strings.
and see how axiomless natural deduction fulfills that
with a comprehensive yet paradox-free account, and
that's the usual account since antiquity and even since
before recorded times, then it's called "mathematical platonism",
since issues of the human condition itself are subjective,
and whether Thoth or Hermes Trismagistus has an ankh for reason
or spiral for infinity, in at least one account there's both.
Thoth -> thought
Logos -> logic
Ma'at -> math
Aristotle won't be made a fool, and more than merely
half-Aristotleans have always both prior and posterior accounts.
That's not "a priori truth".
That's just a "convenient" lie to make some system of inference
considered itself compelled complete yet make it slavish while
really it's merely a model of a partial half-account of reason,
that fragmented synthetic pluralism and inconstancy in definition.
Adding an element to another element is synthetic
(where did it come from?), partitioning an element
into two is analytic (how was it already there?).
The usual account of mathematical platonism is analytic,
the usual account of logicist positivism is synthetic,
they are two different things.
Usual accounts of incompleteness like the Hilbert-Bernays paradox
confirm and certify that "logicist positivist nominalist theories"
are at best "merely and completely science".
Then, the account that it's not a science, is wrong.
Anybody can have a quite thorough body of knowledge -
if it doesn't change it's considered they stopped learning,
not that there isn't anything left to learn.
Quit trying to tell people they can't learn, it's insulting.
On 7/1/2026 12:31 PM, Ross Finlayson wrote:
On 07/01/2026 10:57 AM, olcott wrote:
On 7/1/2026 12:00 PM, Ross Finlayson wrote:
On 07/01/2026 07:59 AM, olcott wrote:
On 7/1/2026 7:13 AM, Ross Finlayson wrote:
On 06/30/2026 08:01 PM, olcott wrote:
On 6/30/2026 9:47 PM, Ross Finlayson wrote:
On 06/30/2026 10:36 AM, Ross Finlayson wrote:
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an >>>>>>>>>>> account
of reason, and for Foundations, then I'd suggest first making >>>>>>>>>>> for
yourself a "universal education", then finding resolutions to >>>>>>>>>>> the
"paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao 01 02
01 G
02 -4 03
03 Prov_PA 04
04 G||del_Number_of 01 // cycle indicates no well-founded >>>>>>>>>> justification
tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
CurryrCoHoward correspondence
In programming language theory and proof theory,
the CurryrCoHoward correspondence is a direct relationship >>>>>>>>>> between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence >>>>>>>>>>
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" >>>>>>>>>>> the
"great atlas of mathematical independence", then for "higher >>>>>>>>>>> mathematics", and quite about "continuity" and "infinity", >>>>>>>>>>> then there's also "the physics" after "the logic" and "the >>>>>>>>>>> mathematics".
"Curry's poor substitute" at least rejects material implication. >>>>>>>>>
Matters of meaning or the epistemological is a field called
"semiotics".
Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the >>>>>>>>> resources.
The Liar Paradox is just a template of what would be a fallacy: >>>>>>>>> two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in >>>>>>>>> it.
"Cat" is a word.
It's fair to say "the Liar Paradox is false",
then that the negation translates through the copula "is"
to result "this sentence is true", a meaningless, empty tautology >>>>>>>> (except as quoted a meaningless, empty, tautology).
It doesn't work on other "paradoxes", though.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics almost gets there
through an enormously more convoluted process.
They almost always utterly avoid any nuance of
true. Instead they focus on meaning.
Finlayson's paradox: there are none.
That quote of Wittgenstein's just a weak echo of Leibnitz'
"principle of
sufficient reason" about what an inference is. The Tractatus
Correct reasoning is not correctly evaluated on the
basis of who came up with the ideas. These ideas either
has a sound basis or not.
It just the same thing that I have been saying fir years.
True on the basis of meaning expressed in language must
have a direct semantic connection to those things in the
directly in the formal system of this language that make it
true.
(a) Cats are animals
(b) Animals are living things
(c) re| Cats are living things
No jumping outside of the language to a separate model.
Logicophilosophicus starts alright then Wittgenstein wimps out while >>>>>> being all hot-headed about it later. Russell's favorite philosophers, >>>>>> Plotinus after Philo, are early weak nominalist fictionalists, and >>>>>> having material implication in their vacuous implicits and so on,
Chrysippus could throw them from the boat since neither are they
Pythagoreans.
A much simpler process arrives at a "principle of _thorough_ reason", >>>>>> where not only are affirmatory and negatory inferences found,
also in the diligence any their contradictions.
That is what I just showed.
Russell's retro-thesis simply can't make the extra-ordinary go away. >>>>>> It's considered a quasi-modal variety of the weaker sort of the
logicist positivism, which has a stronger variety after a strong
mathematical platonism which invigorates it as "must be science".
Old schlock wrapped as new, ....
The only way to obtain a correct foundation of these
things is to reverse-engineer them from first principles.
If one does not do that then the extraneous baggage
of the differing human perspectives prevent a fully
coherent view.
That's just syllogism, and makes for constructivism
since any sort stipulation, like an axiom, is unfounded.
The "axiomless natural deduction" to arrive at "axiomless
geometry" and "axiomless arithmetic" is a usual notion that
mathematical platonists have, though these days sometimes
they call themselves structural realists to not concern
dear old Bertrand, then though logicist positivists take
that label without fulfilling its definition.
Syllogism is subject ordering, and Aristotle reads every
syllogism its statements in every order, for example to
detect cycles and disambiguate them, which otherwise a
linear reader will fail to detect.
The "principle of _thorough_ reason" is more than the
"principle of 'sufficient' reason", then that in a
wider account of a wider, fuller dialectic, what's
sound, thorough, fulfilling, and fair.
Mentioning something like Prawitz' "inversion principle"
and about both the restriction _and_ the recovery, and
more than Russell's mere "isolation in significance and
significance in isolation", means that restricting (ignoring)
the resolution of any and all paradoxes leaves the door ajar
just like quasi-modal logic and principle of explosion.
So, maybe readers and researchers in foundations should start
with outlining the requirements and desiderata of a theory
that's constant, consistent, complete, and concrete,
The entire body of knowledge expressed in language
(a) Encodes all of the empirical "atomic facts" as axioms
this merges the analytic/synthetic distinction into one
analytic system. https://plato.stanford.edu/entries/analytic-synthetic/
(b) Provide a finite list of the possible semantic relations
between/among the elements of (a) and these are specified
syntactically using a system similar to CycL.
https://en.wikipedia.org/wiki/CycL
(c) This whole thing is stored in a knowledge ontology
https://en.wikipedia.org/wiki/Ontology_(information_science)
Hierarchy of simple type theory.
https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
Now we have the entire body of general knowledge that
can be expressed in language as a set of stipulated
semantic relations between finite strings.
and see how axiomless natural deduction fulfills that
with a comprehensive yet paradox-free account, and
that's the usual account since antiquity and even since
before recorded times, then it's called "mathematical platonism",
since issues of the human condition itself are subjective,
and whether Thoth or Hermes Trismagistus has an ankh for reason
or spiral for infinity, in at least one account there's both.
Thoth -> thought
Logos -> logic
Ma'at -> math
Aristotle won't be made a fool, and more than merely
half-Aristotleans have always both prior and posterior accounts.
That's not "a priori truth".
That's just a "convenient" lie to make some system of inference
considered itself compelled complete yet make it slavish while
really it's merely a model of a partial half-account of reason,
that fragmented synthetic pluralism and inconstancy in definition.
Adding an element to another element is synthetic
(where did it come from?), partitioning an element
into two is analytic (how was it already there?).
The usual account of mathematical platonism is analytic,
the usual account of logicist positivism is synthetic,
they are two different things.
Usual accounts of incompleteness like the Hilbert-Bernays paradox
confirm and certify that "logicist positivist nominalist theories"
are at best "merely and completely science".
Then, the account that it's not a science, is wrong.
Anybody can have a quite thorough body of knowledge -
if it doesn't change it's considered they stopped learning,
not that there isn't anything left to learn.
Quit trying to tell people they can't learn, it's insulting.
Well, we have to remember that Olcott has claimed to be god.
On 07/01/2026 12:37 PM, Chris M. Thomasson wrote:
On 7/1/2026 12:31 PM, Ross Finlayson wrote:
On 07/01/2026 10:57 AM, olcott wrote:
On 7/1/2026 12:00 PM, Ross Finlayson wrote:
On 07/01/2026 07:59 AM, olcott wrote:
On 7/1/2026 7:13 AM, Ross Finlayson wrote:
On 06/30/2026 08:01 PM, olcott wrote:
On 6/30/2026 9:47 PM, Ross Finlayson wrote:
On 06/30/2026 10:36 AM, Ross Finlayson wrote:
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an >>>>>>>>>>>> account
of reason, and for Foundations, then I'd suggest first making >>>>>>>>>>>> for
yourself a "universal education", then finding resolutions to >>>>>>>>>>>> the
"paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G rao -4Prov_PA(riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov_PA-a-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle indicates no well-founded >>>>>>>>>>> justification
tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
CurryrCoHoward correspondence
In programming language theory and proof theory,
the CurryrCoHoward correspondence is a direct relationship >>>>>>>>>>> between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/
Curry%E2%80%93Howard_correspondence
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" >>>>>>>>>>>> the
"great atlas of mathematical independence", then for "higher >>>>>>>>>>>> mathematics", and quite about "continuity" and "infinity", >>>>>>>>>>>> then there's also "the physics" after "the logic" and "the >>>>>>>>>>>> mathematics".
"Curry's poor substitute" at least rejects material implication. >>>>>>>>>>
Matters of meaning or the epistemological is a field called >>>>>>>>>> "semiotics".
Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the >>>>>>>>>> resources.
The Liar Paradox is just a template of what would be a fallacy: >>>>>>>>>> two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in >>>>>>>>>> it.
"Cat" is a word.
It's fair to say "the Liar Paradox is false",
then that the negation translates through the copula "is"
to result "this sentence is true", a meaningless, empty tautology >>>>>>>>> (except as quoted a meaningless, empty, tautology).
It doesn't work on other "paradoxes", though.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics almost gets there
through an enormously more convoluted process.
They almost always utterly avoid any nuance of
true. Instead they focus on meaning.
Finlayson's paradox: there are none.
That quote of Wittgenstein's just a weak echo of Leibnitz'
"principle of
sufficient reason" about what an inference is. The Tractatus
Correct reasoning is not correctly evaluated on the
basis of who came up with the ideas. These ideas either
has a sound basis or not.
It just the same thing that I have been saying fir years.
True on the basis of meaning expressed in language must
have a direct semantic connection to those things in the
directly in the formal system of this language that make it
true.
(a) Cats are animals
(b) Animals are living things
(c) re| Cats are living things
No jumping outside of the language to a separate model.
Logicophilosophicus starts alright then Wittgenstein wimps out while >>>>>>> being all hot-headed about it later. Russell's favorite
philosophers,
Plotinus after Philo, are early weak nominalist fictionalists, and >>>>>>> having material implication in their vacuous implicits and so on, >>>>>>> Chrysippus could throw them from the boat since neither are they >>>>>>> Pythagoreans.
A much simpler process arrives at a "principle of _thorough_
reason",
where not only are affirmatory and negatory inferences found,
also in the diligence any their contradictions.
That is what I just showed.
Russell's retro-thesis simply can't make the extra-ordinary go away. >>>>>>> It's considered a quasi-modal variety of the weaker sort of the
logicist positivism, which has a stronger variety after a strong >>>>>>> mathematical platonism which invigorates it as "must be science". >>>>>>>
Old schlock wrapped as new, ....
The only way to obtain a correct foundation of these
things is to reverse-engineer them from first principles.
If one does not do that then the extraneous baggage
of the differing human perspectives prevent a fully
coherent view.
That's just syllogism, and makes for constructivism
since any sort stipulation, like an axiom, is unfounded.
The "axiomless natural deduction" to arrive at "axiomless
geometry" and "axiomless arithmetic" is a usual notion that
mathematical platonists have, though these days sometimes
they call themselves structural realists to not concern
dear old Bertrand, then though logicist positivists take
that label without fulfilling its definition.
Syllogism is subject ordering, and Aristotle reads every
syllogism its statements in every order, for example to
detect cycles and disambiguate them, which otherwise a
linear reader will fail to detect.
The "principle of _thorough_ reason" is more than the
"principle of 'sufficient' reason", then that in a
wider account of a wider, fuller dialectic, what's
sound, thorough, fulfilling, and fair.
Mentioning something like Prawitz' "inversion principle"
and about both the restriction _and_ the recovery, and
more than Russell's mere "isolation in significance and
significance in isolation", means that restricting (ignoring)
the resolution of any and all paradoxes leaves the door ajar
just like quasi-modal logic and principle of explosion.
So, maybe readers and researchers in foundations should start
with outlining the requirements and desiderata of a theory
that's constant, consistent, complete, and concrete,
The entire body of knowledge expressed in language
(a) Encodes all of the empirical "atomic facts" as axioms
this merges the analytic/synthetic distinction into one
analytic system. https://plato.stanford.edu/entries/analytic-synthetic/ >>>>
(b) Provide a finite list of the possible semantic relations
between/among the elements of (a) and these are specified
syntactically using a system similar to CycL.
https://en.wikipedia.org/wiki/CycL
(c) This whole thing is stored in a knowledge ontology
https://en.wikipedia.org/wiki/Ontology_(information_science)
Hierarchy of simple type theory.
https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
Now we have the entire body of general knowledge that
can be expressed in language as a set of stipulated
semantic relations between finite strings.
and see how axiomless natural deduction fulfills that
with a comprehensive yet paradox-free account, and
that's the usual account since antiquity and even since
before recorded times, then it's called "mathematical platonism",
since issues of the human condition itself are subjective,
and whether Thoth or Hermes Trismagistus has an ankh for reason
or spiral for infinity, in at least one account there's both.
Thoth -> thought
Logos -> logic
Ma'at -> math
Aristotle won't be made a fool, and more than merely
half-Aristotleans have always both prior and posterior accounts.
That's not "a priori truth".
That's just a "convenient" lie to make some system of inference
considered itself compelled complete yet make it slavish while
really it's merely a model of a partial half-account of reason,
that fragmented synthetic pluralism and inconstancy in definition.
Adding an element to another element is synthetic
(where did it come from?), partitioning an element
into two is analytic (how was it already there?).
The usual account of mathematical platonism is analytic,
the usual account of logicist positivism is synthetic,
they are two different things.
Usual accounts of incompleteness like the Hilbert-Bernays paradox
confirm and certify that "logicist positivist nominalist theories"
are at best "merely and completely science".
Then, the account that it's not a science, is wrong.
Anybody can have a quite thorough body of knowledge -
if it doesn't change it's considered they stopped learning,
not that there isn't anything left to learn.
Quit trying to tell people they can't learn, it's insulting.
Well, we have to remember that Olcott has claimed to be god.
Seems more like a sock-puppet chat-bot with a stolen identity.
On 7/1/2026 2:13 AM, Mikko wrote:
On 30/06/2026 17:22, olcott wrote:
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>> EssentiallyIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and >>>>>>>>>>>>>>>>>>>>>>>>>>> neverThey use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>>>> why would one try to"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean.[ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that G||del's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then cite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically between >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finite strings.
What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent >>>>>>>>>>>>>>>>>>>>>>> body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so >>>>>>>>>>>>>>>>>>>>>> it is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>> in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x) >>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) is >>>>>>>>>> unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>
Irrelevant. The statement that both reax x=S(x) and ~reax x=S(x) are >>>>>>>> sentences of Q but neither is a rheorem or Q does not depend on >>>>>>>> any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies
You are not paying close enough attention. I did not say logical
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
In order to achieve that the atomic facts must be non-tautologies.
That "cats" <are> "animals" is a semantic tautology.
"atomic facts" that correspond to things in the worldOne usually says "assumption" instead of "stipulation". The latter
only have stipulation as their basis in truth within
the formal system.
On 01/07/2026 18:13, olcott wrote:
On 7/1/2026 2:13 AM, Mikko wrote:
On 30/06/2026 17:22, olcott wrote:
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:You are not paying close enough attention. I did not say logical
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>>> happen before
In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>Looking for a proof does not need any semantics >>>>>>>>>>>>>>>>>>>>>>> so it is not obviousIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and >>>>>>>>>>>>>>>>>>>>>>>>>>>> neverThey use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>>>>> why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?All of knowledge expressed in language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>[ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that G||del's G >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you.-a You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent >>>>>>>>>>>>>>>>>>>>>>>> body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>> in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~reax x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x) >>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) >>>>>>>>>>> is unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>
Irrelevant. The statement that both reax x=S(x) and ~reax x=S(x) are >>>>>>>>> sentences of Q but neither is a rheorem or Q does not depend on >>>>>>>>> any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies >>>>>>
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
In order to achieve that the atomic facts must be non-tautologies.
That "cats" <are> "animals" is a semantic tautology.
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
or it can be a consequence of the
definitions of "cat" and "animal" and terms used in these definitions
that tells nothing about the real world, or it can be a statement
about the real world that cannot be inferred from definitions alne.
"atomic facts" that correspond to things in the world
only have stipulation as their basis in truth within
the formal system.
One usually says "assumption" instead of "stipulation". The latter
usually means a rfusal to proceed before the stipulation is accepted
or an alternative agreed.
On 7/2/2026 1:44 AM, Mikko wrote:
On 01/07/2026 18:13, olcott wrote:
On 7/1/2026 2:13 AM, Mikko wrote:
On 30/06/2026 17:22, olcott wrote:
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:You are not paying close enough attention. I did not say logical >>>>>>> tautology. I said semantic tautology. That cats are defined to
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:i.e., ~reax x=S(x) is unprovable is Q, as is commonly >>>>>>>>>>>>>>>>>> known.
On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>>>> happen beforeLooking for a proof does not need any semantics >>>>>>>>>>>>>>>>>>>>>>>> so it is not obviousIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for concepts. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:All of knowledge expressed in language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>[ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that G||del's G >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
the proof gets stuck in an infinite loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>> and never
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>
how switching to another semantics could improve >>>>>>>>>>>>>>>>>>>>>>>> it.
In proof theoretic semantics an expression only >>>>>>>>>>>>>>>>>>>>>>> gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>> in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x) >>>>>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>> its successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x) >>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) >>>>>>>>>>>> is unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>>
Irrelevant. The statement that both reax x=S(x) and ~reax x=S(x) are >>>>>>>>>> sentences of Q but neither is a rheorem or Q does not depend on >>>>>>>>>> any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies >>>>>>>
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
In order to achieve that the atomic facts must be non-tautologies.
That "cats" <are> "animals" is a semantic tautology.
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
or it can be a consequence of the
definitions of "cat" and "animal" and terms used in these definitions
it tells us exactly one thong about the real world
through the definition of terms.
that tells nothing about the real world, or it can be a statement
about the real world that cannot be inferred from definitions alne.
"atomic facts" that correspond to things in the world
only have stipulation as their basis in truth within
the formal system.
One usually says "assumption" instead of "stipulation". The latter
usually means a rfusal to proceed before the stipulation is accepted
or an alternative agreed.
https://en.wikipedia.org/wiki/Stipulative_definition
Cats are animals, if you disagree then you are necessarily incorrect.
On 07/02/2026 07:45 AM, olcott wrote:
On 7/2/2026 1:44 AM, Mikko wrote:
On 01/07/2026 18:13, olcott wrote:
On 7/1/2026 2:13 AM, Mikko wrote:
On 30/06/2026 17:22, olcott wrote:
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:You are not paying close enough attention. I did not say logical >>>>>>>> tautology. I said semantic tautology. That cats are defined to >>>>>>>> be animals is a semantic tautology. That cats are defined to be >>>>>>>> cats is a logical tautology. Here is a definition of that fits >>>>>>>> my definition of semantic tautology.
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~reax x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:i.e., ~reax x=S(x) is unprovable is Q, as is commonly >>>>>>>>>>>>>>>>>>> known.
On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, Andr|- G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>>>>> happen beforeLooking for a proof does not need any semantics >>>>>>>>>>>>>>>>>>>>>>>>> so it is not obviousIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for concepts. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>All of knowledge expressed in language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that G||del's G >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't believe you.-a You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth.-a If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G||del's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS G||del 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand G||del's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
the proof gets stuck in an infinite loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and never
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic >>>>>>>>>>>>>>>>>>>>>>>>>> meanings
expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>
how switching to another semantics could improve >>>>>>>>>>>>>>>>>>>>>>>>> it.
In proof theoretic semantics an expression only >>>>>>>>>>>>>>>>>>>>>>>> gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>>> ~reax x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>>> in Q from ~reax x=S(x) to the axioms of Q then ~reax x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>>> its successor" as per the definition of Q.
Since there are no steps in Q that affirm ~reax x=S(x) >>>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~reax x=S(x) >>>>>>>>>>>>> is unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>>>
Irrelevant. The statement that both reax x=S(x) and ~reax x=S(x) are
sentences of Q but neither is a rheorem or Q does not depend on >>>>>>>>>>> any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies >>>>>>>>
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
In order to achieve that the atomic facts must be non-tautologies.
That "cats" <are> "animals" is a semantic tautology.
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
or it can be a consequence of the
definitions of "cat" and "animal" and terms used in these definitions
it tells us exactly one thong about the real world
through the definition of terms.
that tells nothing about the real world, or it can be a statement
about the real world that cannot be inferred from definitions alne.
"atomic facts" that correspond to things in the world
only have stipulation as their basis in truth within
the formal system.
One usually says "assumption" instead of "stipulation". The latter
usually means a rfusal to proceed before the stipulation is accepted
or an alternative agreed.
https://en.wikipedia.org/wiki/Stipulative_definition
Cats are animals, if you disagree then you are necessarily incorrect.
Animals are {cats, dogs, wallabies, llamas, aardvarks, crustaceans,
...}, a potentially infinitary expression.
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