From Newsgroup: comp.theory

On 12/28/25 3:37 PM, Richard Damon wrote:

On 12/28/25 5:30 PM, dart200 wrote:

the halting problem is generally held up as an example of
incompleteness in action, and that machines can halt/not without it
being provable/ knowable.

First, The Halting Problem more directly shows "Uncomputability" instead
of "Incompleteness". Note, "Uncomputability" is a property of a
"Problem", that there are mappings that exist that can not be generated
by a computation.

"Incompleteness" is a property of a Logical System, indicating that
there are true statements in the system that can not be proven.

but the only one demonstrated can be proven true outside the system. it
did not show a total unprovable truth, there still was a proof to prove
it, it just existed outside the system that said truth was in respect to.

but i'm not really sure how that could be related to incompleteness:

incompleteness demonstrated a *know* and *provable* truth that existed
outside a particular system of proof,

it did not demonstrate an *unknowable* and *unprovable* truth existing
outside *any* system of proof ...

Because the move from it being "Uncomputable" to showing the field is "Incomplete" needs some additional arguements (which has been done).

You seem to have rejected thinking about it, because it goes into
talking about the "ghost" machines that are individually not computable
in their behavior, and in fact, we can't even know if they are such a machine.

actually i'm now thinking about using incompleteness against the halting problem

like what proponents of the halting problem continually assert, eh???

Which, since the step from Halting showing that there is an
"Uncomptable" problem allows us to show that Computation Theory exhibits
the property of Incompleteness, is a valid thing to talk about.

right but like i said: incompleteness did not show a truth that could
not be proven at all, just that it couldn't be proven within some system.

Now, until you accept that Halting is, in fact, uncomputable, going the
next step won't be possible.

--
a burnt out swe investigating into why our tooling doesn't involve
basic semantic proofs like halting analysis

please excuse my pseudo-pyscript,

~ nick
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/28/25 3:37 PM, Richard Damon wrote:

On 12/28/25 5:30 PM, dart200 wrote:

the halting problem is generally held up as an example of
incompleteness in action, and that machines can halt/not without it
being provable/ knowable.

First, The Halting Problem more directly shows "Uncomputability" instead
of "Incompleteness". Note, "Uncomputability" is a property of a
"Problem", that there are mappings that exist that can not be generated
by a computation.

but it's always demonstrated by a specific machine, and unless you're
gunna say all machines of a certain property cannot be decided to have
that property (which is ridiculous), then ofc it involves specific input
being undecidable.

"Incompleteness" is a property of a Logical System, indicating that
there are true statements in the system that can not be proven.

the truth that backs incompleteness is still proven, just not within the system as it stands.

what it doesn't say is that unprovable truths exists

but i'm not really sure how that could be related to incompleteness:

incompleteness demonstrated a *know* and *provable* truth that existed
outside a particular system of proof,

it did not demonstrate an *unknowable* and *unprovable* truth existing
outside *any* system of proof ...

Because the move from it being "Uncomputable" to showing the field is "Incomplete" needs some additional arguements (which has been done).

You seem to have rejected thinking about it, because it goes into
talking about the "ghost" machines that are individually not computable
in their behavior, and in fact, we can't even know if they are such a machine.

like what proponents of the halting problem continually assert, eh???

Which, since the step from Halting showing that there is an
"Uncomptable" problem allows us to show that Computation Theory exhibits
the property of Incompleteness, is a valid thing to talk about.

Now, until you accept that Halting is, in fact, uncomputable, going the
next step won't be possible.

the problem with halting is that your claims truths that exist which
cannot be proven by any means, which is not the same thing as
incompleteness. the truth godel demonstrated was still provable, else
how would we know it's "true"?
--
a burnt out swe investigating into why our tooling doesn't involve
basic semantic proofs like halting analysis

please excuse my pseudo-pyscript,

~ nick
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/29/25 2:17 AM, dart200 wrote:

On 12/28/25 3:37 PM, Richard Damon wrote:

On 12/28/25 5:30 PM, dart200 wrote:

the halting problem is generally held up as an example of
incompleteness in action, and that machines can halt/not without it
being provable/ knowable.

First, The Halting Problem more directly shows "Uncomputability"
instead of "Incompleteness". Note, "Uncomputability" is a property of
a "Problem", that there are mappings that exist that can not be
generated by a computation.

"Incompleteness" is a property of a Logical System, indicating that
there are true statements in the system that can not be proven.

but the only one demonstrated can be proven true outside the system. it
did not show a total unprovable truth, there still was a proof to prove
it, it just existed outside the system that said truth was in respect to.

You don't understand the proof. There is not just ONE input program.
There is one for every different decider, as it doesn't call some
idealized decider, but that actual machine claimed to be a decider.

After showing we can make such an input that makes any given decider
wrong, we can show that therefore there is no decider that gets all right.

I believe there is then another proof that shows that because there is
no decider that gets all inputs correctly, you can show that there must
be some program that no known to be corret partial decider gets right,
in other words, a program that we can not know its halting status, as we
can not prove it will not halt.

but i'm not really sure how that could be related to incompleteness:

incompleteness demonstrated a *know* and *provable* truth that
existed outside a particular system of proof,

it did not demonstrate an *unknowable* and *unprovable* truth
existing outside *any* system of proof ...

Because the move from it being "Uncomputable" to showing the field is
"Incomplete" needs some additional arguements (which has been done).

You seem to have rejected thinking about it, because it goes into
talking about the "ghost" machines that are individually not
computable in their behavior, and in fact, we can't even know if they
are such a machine.

actually i'm now thinking about using incompleteness against the halting problem

How?

like what proponents of the halting problem continually assert, eh???

Which, since the step from Halting showing that there is an
"Uncomptable" problem allows us to show that Computation Theory
exhibits the property of Incompleteness, is a valid thing to talk about.

right but like i said: incompleteness did not show a truth that could
not be proven at all, just that it couldn't be proven within some system.

Which is what Incompleteness is about. It says that THE SYSTEM has a
true statement that THE SYSTEM can not prove. Doesn't matter that some meta-system can prove it.

There is an additional proof that shows that while some of these
statements can be proved is some meta-system of the system, there will
always be some that can't be proved at any finite level of meta-system.

Now, until you accept that Halting is, in fact, uncomputable, going
the next step won't be possible.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/29/25 2:41 AM, dart200 wrote:

On 12/28/25 3:37 PM, Richard Damon wrote:

On 12/28/25 5:30 PM, dart200 wrote:

the halting problem is generally held up as an example of
incompleteness in action, and that machines can halt/not without it
being provable/ knowable.

First, The Halting Problem more directly shows "Uncomputability"
instead of "Incompleteness". Note, "Uncomputability" is a property of
a "Problem", that there are mappings that exist that can not be
generated by a computation.

but it's always demonstrated by a specific machine, and unless you're
gunna say all machines of a certain property cannot be decided to have
that property (which is ridiculous), then ofc it involves specific input being undecidable.

Which means you don't understand the proof.

The proof didn't show there was one uncomputable machine, but that there
was at least one machine (different for every decider) that the decider
got wrong, and thus we could show that there was no decider that got
every machine correct, and thus the basic halting problem was uncomputable.

I beleive there is another proof that shows that because of this, there
will exist a class of machines that no, known to be correct, partial
decider will decide on. We don't know how to construct such a machine,
only that they exist, since an interesting property of this class is we
can not determine that a machine IS in this class, since determining it
is in the class means we have resolved that the machine is non-halting,
as all halting machines are decidable.

"Incompleteness" is a property of a Logical System, indicating that
there are true statements in the system that can not be proven.

the truth that backs incompleteness is still proven, just not within the system as it stands.

what it doesn't say is that unprovable truths exists

But, I beleive it was Tarski, was able to extend Godel's proof to show
that while a given meta-system can prove some of the statements not
proven in the base system, there WILL exist some statements not provable
in ANY system.

but i'm not really sure how that could be related to incompleteness:

incompleteness demonstrated a *know* and *provable* truth that
existed outside a particular system of proof,

it did not demonstrate an *unknowable* and *unprovable* truth
existing outside *any* system of proof ...

Because the move from it being "Uncomputable" to showing the field is
"Incomplete" needs some additional arguements (which has been done).

You seem to have rejected thinking about it, because it goes into
talking about the "ghost" machines that are individually not
computable in their behavior, and in fact, we can't even know if they
are such a machine.

like what proponents of the halting problem continually assert, eh???

Which, since the step from Halting showing that there is an
"Uncomptable" problem allows us to show that Computation Theory
exhibits the property of Incompleteness, is a valid thing to talk about.

Now, until you accept that Halting is, in fact, uncomputable, going
the next step won't be possible.

the problem with halting is that your claims truths that exist which
cannot be proven by any means, which is not the same thing as incompleteness. the truth godel demonstrated was still provable, else
how would we know it's "true"?

Which just shows you don't understand the meaning of the term.

Incompleteness is a property of a given Formal System, it says that
there exist a statement that is true in that system, but can not be
proven in that system.

Godel's proof build a meta-system that constructs a statement that
exists in the base system, and which is true in that base system, but
can not be proven in the base system, only the meta-system.

That shows that the base system must have been incomplete.

Since we could do that same operation again in the meta-system, by
making a meta-meta-system, that meta-system must also be incomplete.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 29/12/2025 07:41, dart200 wrote:

On 12/28/25 3:37 PM, Richard Damon wrote:

On 12/28/25 5:30 PM, dart200 wrote:

the halting problem is generally held up as an example of
incompleteness in action, and that machines can halt/not without it
being provable/ knowable.

First, The Halting Problem more directly shows "Uncomputability"
instead of "Incompleteness". Note, "Uncomputability" is a property of
a "Problem", that there are mappings that exist that can not be
generated by a computation.

but it's always demonstrated by a specific machine, and unless you're
gunna say all machines of a certain property cannot be decided to have
that property (which is ridiculous), then ofc it involves specific input being undecidable.

"Incompleteness" is a property of a Logical System, indicating that
there are true statements in the system that can not be proven.

the truth that backs incompleteness is still proven, just not within the system as it stands.

what it doesn't say is that unprovable truths exists

but i'm not really sure how that could be related to incompleteness:

incompleteness demonstrated a *know* and *provable* truth that
existed outside a particular system of proof,

it did not demonstrate an *unknowable* and *unprovable* truth
existing outside *any* system of proof ...

Because the move from it being "Uncomputable" to showing the field is
"Incomplete" needs some additional arguements (which has been done).

You seem to have rejected thinking about it, because it goes into
talking about the "ghost" machines that are individually not
computable in their behavior, and in fact, we can't even know if they
are such a machine.

like what proponents of the halting problem continually assert, eh???

Which, since the step from Halting showing that there is an
"Uncomptable" problem allows us to show that Computation Theory
exhibits the property of Incompleteness, is a valid thing to talk about.

Now, until you accept that Halting is, in fact, uncomputable, going
the next step won't be possible.

the problem with halting is that your claims truths that exist which
cannot be proven by any means, which is not the same thing as
incompleteness. the truth godel demonstrated was still provable, else
how would we know it's "true"?

You're using the informal, everyday, meaning of provable. That is, that
there is anything I could experience that could actually happen that
would make me produce from a propositionally structured sentence for a
while should I actually experience it.

Also using a vague notion of "to know" that's notorious for semantic
ambiguity not backtracked.

Also referentially ambiguous "we".

and referentially ambiguous "truth" (informal internal general synergy
vs member of the theorems of a formal system which is a very specific
synergy).

You deftly convey little to no meaning.
--
Tristan Wibberley

The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 29/12/2025 13:37, Richard Damon wrote:

Incompleteness is a property of a given Formal System, it says that
there exist a statement that is true in that system, but can not be
proven in that system.

Godel's proof build a meta-system that constructs a statement that
exists in the base system, and which is true in that base system, but
can not be proven in the base system, only the meta-system.

What do you mean by "proven" here. Do you mean "derived" ? Normally we
say a proposition is true in a system when we mean the proposition is a
theorem of the system; it has a derivation in the system: a finite
sequence of statements that each is derivable from the axioms and
earlier statements in the sequence by application of a deductive rule of
the system--where the deductive rules are transitive so that's also
application of /some/ deductive rules--and which ends with the
proposition that's being derived.

If there is a derivation then it is provable in the base system, if
there /isn't/ a derivation then it is /not/ true in that base system
(which is different from saying its contrapositive is true in that base system).
--
Tristan Wibberley

The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/29/2025 12:42 PM, Tristan Wibberley wrote:

On 29/12/2025 13:37, Richard Damon wrote:

Incompleteness is a property of a given Formal System, it says that
there exist a statement that is true in that system, but can not be
proven in that system.

Godel's proof build a meta-system that constructs a statement that
exists in the base system, and which is true in that base system, but
can not be proven in the base system, only the meta-system.

What do you mean by "proven" here. Do you mean "derived" ? Normally we
say a proposition is true in a system when we mean the proposition is a theorem of the system; it has a derivation in the system: a finite
sequence of statements that each is derivable from the axioms and
earlier statements in the sequence by application of a deductive rule of
the system--where the deductive rules are transitive so that's also application of /some/ deductive rules--and which ends with the
proposition that's being derived.

If there is a derivation then it is provable in the base system, if
there /isn't/ a derivation then it is /not/ true in that base system
(which is different from saying its contrapositive is true in that base system).

Yes you are correct here. Even though it is dead-obvious
that you are correct everyone indoctrinated with Godel
1931 Incompleteness will disagree.
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

In sci.logic Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

On 29/12/2025 13:37, Richard Damon wrote:

Incompleteness is a property of a given Formal System, it says that
there exist a statement that is true in that system, but can not be
proven in that system.

What do you mean by "proven" here. Do you mean "derived" ?

I think Richard misspoke slightly. The undecidable statement is
true *in the intended interpretation* of the formal system
(In Goedel's case, the natural numbers with addition and multiplication).

Truth "in the formal system" isn't really defined. You need an
interpretation.
--
pa at panix dot com
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/29/2025 1:21 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

On 29/12/2025 13:37, Richard Damon wrote:

Incompleteness is a property of a given Formal System, it says that
there exist a statement that is true in that system, but can not be
proven in that system.

What do you mean by "proven" here. Do you mean "derived" ?

I think Richard misspoke slightly. The undecidable statement is
true *in the intended interpretation* of the formal system
(In Goedel's case, the natural numbers with addition and multiplication).

Truth "in the formal system" isn't really defined. You need an interpretation.

Unless (as I have been saying for at least a decade)
the formal language directly encodes all of its
semantics directly in its syntax. The Montague
Grammar of natural language semantics is the best
known example of this.
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/29/25 1:42 PM, Tristan Wibberley wrote:

On 29/12/2025 13:37, Richard Damon wrote:

Incompleteness is a property of a given Formal System, it says that
there exist a statement that is true in that system, but can not be
proven in that system.

Godel's proof build a meta-system that constructs a statement that
exists in the base system, and which is true in that base system, but
can not be proven in the base system, only the meta-system.

What do you mean by "proven" here. Do you mean "derived" ? Normally we
say a proposition is true in a system when we mean the proposition is a theorem of the system; it has a derivation in the system: a finite
sequence of statements that each is derivable from the axioms and
earlier statements in the sequence by application of a deductive rule of
the system--where the deductive rules are transitive so that's also application of /some/ deductive rules--and which ends with the
proposition that's being derived.

If there is a derivation then it is provable in the base system, if
there /isn't/ a derivation then it is /not/ true in that base system
(which is different from saying its contrapositive is true in that base system).

Yes, Godel derives a finite set of logical steps that show this fact,
that the statement G, making a statement about the non-existance of a
number that satisfies a particular relationship, that was built in the meta-system out of operation in the base system (so it is valid in the
base system).

In the meta-system, a proof is constructed (by the method of
construction of the relationship) that under the interpreation of
numbers in the meta-system, that relationship is a proof checker of the statement G. If the number represents a proof of that statement
expressed in the base system, the number will satisfy the relationship,
and if not, it will not.

He shows that ANY proof in the base system can be so represented.

And thus, since G asserts that no number satisfies the relationship it
will be true if and only if, their is no proof. Since the existance of a
proof will show that the statement is true, but also make it false,
since that proof will thus be represented by a number that satisfies the relationship, making the statement false, that case can not be true.

Since either such a number exist or it doesn't, since by its
construction, the relationship is finitely computable for ANY natural
number, and we just showed that it is impossible by the nature of the relatonship for one to exist, it must not.

Note also, the construction of the meta system was done with care so
that it has an important property, that the truth value of any statement
in the base system must equal that same statement in the meta-system, we
can show that G must be true in the base system.

We can also look at the base system, and see how it is actually
established in the base system, we can see that in the base system, we
can evaluate the relationship for any number (which doesn't have
"meaning" in the base system) and because of the equivalence of the computation of the relationship in the two systems, we know that no
number CAN satisfy it. Since we can test every possible number (which is
a countably infinite operation) we can see that its truth *IS*
established in the base system, just by a method that can't be reduced
to a finite proof.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/29/25 2:21 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

On 29/12/2025 13:37, Richard Damon wrote:

Incompleteness is a property of a given Formal System, it says that
there exist a statement that is true in that system, but can not be
proven in that system.

What do you mean by "proven" here. Do you mean "derived" ?

I think Richard misspoke slightly. The undecidable statement is
true *in the intended interpretation* of the formal system
(In Goedel's case, the natural numbers with addition and multiplication).

Truth "in the formal system" isn't really defined. You need an interpretation.

No, statements in a formal system are DEFINED to be true, if that
statement, referencing object defined in the system model, and related
by relationships defined in the system can be established starting with
the initial "facts" (axioms) of the system, and following the allowed
logical operations of the system.

THus in the formal system of addition of Natural Numbers, the statement
2 + 3 = 5 is a true statement, as it can be derived from the operations
in the system. Some Formal System include a "model" that define interpreations, though another layer above can be added (as Godel did).
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/29/25 2:32 PM, olcott wrote:

On 12/29/2025 1:21 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

On 29/12/2025 13:37, Richard Damon wrote:

Incompleteness is a property of a given Formal System, it says that
there exist a statement that is true in that system, but can not be
proven in that system.

What do you mean by "proven" here. Do you mean "derived" ?

I think Richard misspoke slightly. The undecidable statement is
true *in the intended interpretation* of the formal system
(In Goedel's case, the natural numbers with addition and multiplication).

Truth "in the formal system" isn't really defined. You need an
interpretation.

Unless (as I have been saying for at least a decade)
the formal language directly encodes all of its
semantics directly in its syntax. The Montague
Grammar of natural language semantics is the best
known example of this.

But it can't, as any system that defines symbols, can have something
outside it assign additional meaning to those symbols.

There may be SOME meaning within the system, but, with a sufficiently expressive system, additional meaning can be imposed.

An Montague grammer is out of scope here, as we are talking FORMAL
langauges and system, not Natural Language,

Something which seems beyound your ability to understand, since you brainwashed youself to not understand the basics of this.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 29/12/2025 19:53, Richard Damon wrote:

On 12/29/25 2:32 PM, olcott wrote:

On 12/29/2025 1:21 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

On 29/12/2025 13:37, Richard Damon wrote:

Incompleteness is a property of a given Formal System, it says that
there exist a statement that is true in that system, but can not be
proven in that system.

What do you mean by "proven" here. Do you mean "derived" ?

I think Richard misspoke slightly. The undecidable statement is
true *in the intended interpretation* of the formal system
(In Goedel's case, the natural numbers with addition and
multiplication).

Truth "in the formal system" isn't really defined. You need an
interpretation.

Unless (as I have been saying for at least a decade)
the formal language directly encodes all of its
semantics directly in its syntax. The Montague
Grammar of natural language semantics is the best
known example of this.

But it can't, as any system that defines symbols, can have something
outside it assign additional meaning to those symbols.

Ontology suggests ways to *apply* a system. The system itself works
without additional meaning just as it does with. That's the point of
formal systems.

There may be SOME meaning within the system, but, with a sufficiently expressive system, additional meaning can be imposed.

additional meaning is given to an embedding or extension (which is
pretty-much a special-case of embedding) of a system, not to the system
itself.

In the case of G||del's preamble, he defines an extension of PM (I should suppose he was using 2nd ed. in 1931 from his untruths about PM if
applied to 1st. ed.) That extension is inconsistent (or, better, I
think, indiscriminate). his referent there for PM slides between PM and
the derived system as he writes and he gets muddled taking a half-formed conclusion about one, assuming and completing it for the other.

Then he defines a new system "P" which he uses to get even more muddled,
leaves out the crucial elements of his proof because it's too easy to
get wrong, and Stephen Meyer says he does get it wrong; he seems to be
the only person in the world that ever checked.
--
Tristan Wibberley

The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 29/12/2025 19:51, Richard Damon wrote:

On 12/29/25 2:21 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

On 29/12/2025 13:37, Richard Damon wrote:

Incompleteness is a property of a given Formal System, it says that
there exist a statement that is true in that system, but can not be
proven in that system.

What do you mean by "proven" here. Do you mean "derived" ?

I think Richard misspoke slightly. The undecidable statement is
true *in the intended interpretation* of the formal system
(In Goedel's case, the natural numbers with addition and multiplication).

Truth "in the formal system" isn't really defined. You need an
interpretation.

No, statements in a formal system are DEFINED to be true

Best to keep pushing the lingufranca toward "to be theorems".

ps, I note that the use of "defined to be" here is technically wrong but
the use of "true" is so much more problematic.

if that> statement, referencing object defined in the system model,

and related

by relationships defined in the system-a can be established starting with
the initial "facts" (axioms) of the system, and following the allowed
logical operations of the system.

^^^^^^^^^^^^^^^^^^
||||||||||||||||||
``````````````````~~~<~~~<~~~< Deduction Rules


A statement in a formal system is included among its theorems exactly
when it is derivable from the axioms of the system--which are those of
its theorems that are merely supposed--and the derivation is done by the deduction rules of the system.

We must prepare ourselves mentally for mathematicians to say "in a
system" when they mean "in some axiom extension of a system" and to say
"is true" when they mean "has a derivable embedding in at least one
episystem embedding the system".
--
Tristan Wibberley

The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/29/2025 1:53 PM, Richard Damon wrote:

On 12/29/25 2:32 PM, olcott wrote:

On 12/29/2025 1:21 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

On 29/12/2025 13:37, Richard Damon wrote:

Incompleteness is a property of a given Formal System, it says that
there exist a statement that is true in that system, but can not be
proven in that system.

What do you mean by "proven" here. Do you mean "derived" ?

I think Richard misspoke slightly. The undecidable statement is
true *in the intended interpretation* of the formal system
(In Goedel's case, the natural numbers with addition and
multiplication).

Truth "in the formal system" isn't really defined. You need an
interpretation.

Unless (as I have been saying for at least a decade)
the formal language directly encodes all of its
semantics directly in its syntax. The Montague
Grammar of natural language semantics is the best
known example of this.

But it can't, as any system that defines symbols, can have something
outside it assign additional meaning to those symbols.

"true on the basis of meaning expressed in language"
can be expressed as relations between finite strings.

There may be SOME meaning within the system, but, with a sufficiently expressive system, additional meaning can be imposed.

An Montague grammer is out of scope here, as we are talking FORMAL
langauges and system, not Natural Language,

"We are therefore confronted with a proposition which
asserts its own unprovability." (G||del 1931:39-41)

By using an enormously convoluted process with
G||del numbers hiding his actual claim:

There exists a sequence of inference steps from
the axioms of a formal system that prove that
they themselves do not exist.

readers are simply conned into believing that
G||del Incompleteness is coherent and true.

Something which seems beyound your ability to understand, since you brainwashed youself to not understand the basics of this.

--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/29/25 4:38 PM, olcott wrote:

On 12/29/2025 1:53 PM, Richard Damon wrote:

On 12/29/25 2:32 PM, olcott wrote:

On 12/29/2025 1:21 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

On 29/12/2025 13:37, Richard Damon wrote:

Incompleteness is a property of a given Formal System, it says that >>>>>> there exist a statement that is true in that system, but can not be >>>>>> proven in that system.

What do you mean by "proven" here. Do you mean "derived" ?

I think Richard misspoke slightly. The undecidable statement is
true *in the intended interpretation* of the formal system
(In Goedel's case, the natural numbers with addition and
multiplication).

Truth "in the formal system" isn't really defined. You need an
interpretation.

Unless (as I have been saying for at least a decade)
the formal language directly encodes all of its
semantics directly in its syntax. The Montague
Grammar of natural language semantics is the best
known example of this.

But it can't, as any system that defines symbols, can have something
outside it assign additional meaning to those symbols.

"true on the basis of meaning expressed in language"
can be expressed as relations between finite strings.

Try to do that.

There may be SOME meaning within the system, but, with a sufficiently
expressive system, additional meaning can be imposed.

An Montague grammer is out of scope here, as we are talking FORMAL
langauges and system, not Natural Language,

"We are therefore confronted with a proposition which
asserts its own unprovability." (G||del 1931:39-41)

Right, it is a statement in the meta-theory, commenting on it
unprovabiilty in the base theory.

Context seems to elude you, because it requires understand.

By using an enormously convoluted process with
G||del numbers hiding his actual claim:

There exists a sequence of inference steps from
the axioms of a formal system that prove that
they themselves do not exist.

Right, there is an INFININTE string of inference steps in the base
theory that shows that no FINITE string of inference steps to show it.

readers are simply conned into believing that
G||del Incompleteness is coherent and true.

Not conned, proven.

You are just proving your inabilityh to understand the difference
between Truth and Knowledge, because you can't understand about infinity,

Something which seems beyound your ability to understand, since you
brainwashed youself to not understand the basics of this.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/29/2025 5:06 PM, Richard Damon wrote:

On 12/29/25 4:38 PM, olcott wrote:

On 12/29/2025 1:53 PM, Richard Damon wrote:

On 12/29/25 2:32 PM, olcott wrote:

On 12/29/2025 1:21 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

On 29/12/2025 13:37, Richard Damon wrote:

Incompleteness is a property of a given Formal System, it says that >>>>>>> there exist a statement that is true in that system, but can not be >>>>>>> proven in that system.

What do you mean by "proven" here. Do you mean "derived" ?

I think Richard misspoke slightly. The undecidable statement is
true *in the intended interpretation* of the formal system
(In Goedel's case, the natural numbers with addition and
multiplication).

Truth "in the formal system" isn't really defined. You need an
interpretation.

Unless (as I have been saying for at least a decade)
the formal language directly encodes all of its
semantics directly in its syntax. The Montague
Grammar of natural language semantics is the best
known example of this.

But it can't, as any system that defines symbols, can have something
outside it assign additional meaning to those symbols.

"true on the basis of meaning expressed in language"
can be expressed as relations between finite strings.

Try to do that.

There may be SOME meaning within the system, but, with a sufficiently
expressive system, additional meaning can be imposed.

An Montague grammer is out of scope here, as we are talking FORMAL
langauges and system, not Natural Language,

"We are therefore confronted with a proposition which
asserts its own unprovability." (G||del 1931:39-41)

Right, it is a statement in the meta-theory, commenting on it
unprovabiilty in the base theory.

Context seems to elude you, because it requires understand.

By using an enormously convoluted process with
G||del numbers hiding his actual claim:

There exists a sequence of inference steps from
the axioms of a formal system that prove that
they themselves do not exist.

Right, there is an INFININTE string of inference steps in the base
theory that shows that no FINITE string of inference steps to show it.

Rene Descartes said: "I think therefore I never existed".

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/29/25 6:28 PM, olcott wrote:

On 12/29/2025 5:06 PM, Richard Damon wrote:

On 12/29/25 4:38 PM, olcott wrote:

There exists a sequence of inference steps from
the axioms of a formal system that prove that
they themselves do not exist.

Right, there is an INFININTE string of inference steps in the base
theory that shows that no FINITE string of inference steps to show it.

Rene Descartes said: "I think therefore I never existed".

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.

In other words, you are just showing that you don't know what you are
talking about and thus going into non-sense,

As I said, and you were too stupid to understand, there is a finite
sequence of steps in the META systen that show that there is an INFINITE sequence of steps in the system that show there is not a FINITE sequence
of steps in the system to prove it.

It seems to you, infinity is finite, and thus your mind is just ZERO.

Of course, you never let facts get in the way of your stupidity.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/29/2025 9:51 PM, Richard Damon wrote:

On 12/29/25 6:28 PM, olcott wrote:

On 12/29/2025 5:06 PM, Richard Damon wrote:

On 12/29/25 4:38 PM, olcott wrote:

There exists a sequence of inference steps from
the axioms of a formal system that prove that
they themselves do not exist.

Right, there is an INFININTE string of inference steps in the base
theory that shows that no FINITE string of inference steps to show it.

Rene Descartes said: "I think therefore I never existed".

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.

In other words, you are just showing that you don't know what you are talking about and thus going into non-sense,

...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

Correctly paraphrased as:
a sequence of inference steps from axioms
that assert that they themselves do not exist.

G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems

As I said, and you were too stupid to understand, there is a finite
sequence of steps in the META systen that show that there is an INFINITE sequence of steps in the system that show there is not a FINITE sequence
of steps in the system to prove it.

It seems to you, infinity is finite, and thus your mind is just ZERO.

Of course, you never let facts get in the way of your stupidity.

--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/29/25 11:35 PM, olcott wrote:

On 12/29/2025 9:51 PM, Richard Damon wrote:

On 12/29/25 6:28 PM, olcott wrote:

On 12/29/2025 5:06 PM, Richard Damon wrote:

On 12/29/25 4:38 PM, olcott wrote:

There exists a sequence of inference steps from
the axioms of a formal system that prove that
they themselves do not exist.

Right, there is an INFININTE string of inference steps in the base
theory that shows that no FINITE string of inference steps to show it. >>>>

Rene Descartes said: "I think therefore I never existed".

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.

In other words, you are just showing that you don't know what you are
talking about and thus going into non-sense,

...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

Yes, you have said this before, and I have explained it, but apparently
you can't read.

Correctly paraphrased as:
a sequence of inference steps from axioms
that assert that they themselves do not exist.

Nope, as I have pointed out, you have missed the context, because you
are so stupid.

The statement, when looked at under the meaning that only exists in the meta-system, shows that in the meta-system there is a proof, a finite
series of steps, that shows that in the system, the statement in the
system does not have a proof, which is a finite series of steps IN THE
SYSTEM (not the meta-system) but there is a infinite series of steps in
the system that make it true.

Thus, you show you can't tell the difference between an infinite series
of steps from a finitee series of step, thus you IQ must be 0 by that scale.

And, you can't tell the difference between the Meta-system and the
system, which is like thinking your pet cat is a dog.

The fact you keep on repeating this, and never try to answer the error
pointed out just means that you can't understand what an error is,
because to you truth, knowledge, fact, rules, don't mean anything
because you chose to make your self just stupid and ignorant.

G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems

As I said, and you were too stupid to understand, there is a finite
sequence of steps in the META systen that show that there is an
INFINITE sequence of steps in the system that show there is not a
FINITE sequence of steps in the system to prove it.

It seems to you, infinity is finite, and thus your mind is just ZERO.

Of course, you never let facts get in the way of your stupidity.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/29/2025 10:50 PM, Richard Damon wrote:

On 12/29/25 11:35 PM, olcott wrote:

On 12/29/2025 9:51 PM, Richard Damon wrote:

On 12/29/25 6:28 PM, olcott wrote:

On 12/29/2025 5:06 PM, Richard Damon wrote:

On 12/29/25 4:38 PM, olcott wrote:

There exists a sequence of inference steps from
the axioms of a formal system that prove that
they themselves do not exist.

Right, there is an INFININTE string of inference steps in the base
theory that shows that no FINITE string of inference steps to show it. >>>>>

Rene Descartes said: "I think therefore I never existed".

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.

In other words, you are just showing that you don't know what you are
talking about and thus going into non-sense,

...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

Yes, you have said this before, and I have explained it, but apparently
you can't read.

Correctly paraphrased as:
a sequence of inference steps from axioms
that assert that they themselves do not exist.

Nope, as I have pointed out, you have missed the context, because you
are so stupid.

a proposition which asserts its own unprovability.

The proof of such an propostion within the same
formal system would require a sequence of inference
steps that prove that they themselves do not exist.

The statement, when looked at under the meaning that only exists in the meta-system, shows that in the meta-system there is a proof, a finite
series of steps, that shows that in the system, the statement in the
system does not have a proof, which is a finite series of steps IN THE SYSTEM (not the meta-system) but there is a infinite series of steps in
the system that make it true.

Thus, you show you can't tell the difference between an infinite series
of steps from a finitee series of step, thus you IQ must be 0 by that
scale.

And, you can't tell the difference between the Meta-system and the
system, which is like thinking your pet cat is a dog.

The fact you keep on repeating this, and never try to answer the error pointed out just means that you can't understand what an error is,
because to you truth, knowledge, fact, rules, don't mean anything
because you chose to make your self just stupid and ignorant.

G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems

As I said, and you were too stupid to understand, there is a finite
sequence of steps in the META systen that show that there is an
INFINITE sequence of steps in the system that show there is not a
FINITE sequence of steps in the system to prove it.

It seems to you, infinity is finite, and thus your mind is just ZERO.

Of course, you never let facts get in the way of your stupidity.

--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 30/12/2025 04:35, olcott wrote:

...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

Correctly paraphrased as:
a sequence of inference steps from axioms
that assert that they themselves do not exist.

No they don't. That's an interpretation outside the system. The axioms
merely force you to conclude that some symbol or other is not negation
and/or another one is not a reference to the system itself when fools
think they both /are/ those things.
--
Tristan Wibberley

The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/29/25 5:37 AM, Richard Damon wrote:

On 12/29/25 2:17 AM, dart200 wrote:

On 12/28/25 3:37 PM, Richard Damon wrote:

On 12/28/25 5:30 PM, dart200 wrote:

the halting problem is generally held up as an example of
incompleteness in action, and that machines can halt/not without it
being provable/ knowable.

First, The Halting Problem more directly shows "Uncomputability"
instead of "Incompleteness". Note, "Uncomputability" is a property of
a "Problem", that there are mappings that exist that can not be
generated by a computation.

"Incompleteness" is a property of a Logical System, indicating that
there are true statements in the system that can not be proven.

but the only one demonstrated can be proven true outside the system.
it did not show a total unprovable truth, there still was a proof to
prove it, it just existed outside the system that said truth was in
respect to.

You don't understand the proof. There is not just ONE input program.
There is one for every different decider, as it doesn't call some
idealized decider, but that actual machine claimed to be a decider.

After showing we can make such an input that makes any given decider
wrong, we can show that therefore there is no decider that gets all right.

I believe there is then another proof that shows that because there is
no decider that gets all inputs correctly, you can show that there must
be some program that no known to be corret partial decider gets right,
in other words, a program that we can not know its halting status, as we
can not prove it will not halt.

but i'm not really sure how that could be related to incompleteness:

incompleteness demonstrated a *know* and *provable* truth that
existed outside a particular system of proof,

it did not demonstrate an *unknowable* and *unprovable* truth
existing outside *any* system of proof ...

Because the move from it being "Uncomputable" to showing the field is
"Incomplete" needs some additional arguements (which has been done).

You seem to have rejected thinking about it, because it goes into
talking about the "ghost" machines that are individually not
computable in their behavior, and in fact, we can't even know if they
are such a machine.

actually i'm now thinking about using incompleteness against the
halting problem

How?

like what proponents of the halting problem continually assert, eh???

Which, since the step from Halting showing that there is an
"Uncomptable" problem allows us to show that Computation Theory
exhibits the property of Incompleteness, is a valid thing to talk about.

right but like i said: incompleteness did not show a truth that could
not be proven at all, just that it couldn't be proven within some system.

Which is what Incompleteness is about. It says that THE SYSTEM has a
true statement that THE SYSTEM can not prove. Doesn't matter that some meta-system can prove it.

lol bruh, if there wasn't a meta system to prove it, how would godel
have proven it true outside the system???

at the very least godel's proof counts as a proof that exists outside
the system

There is an additional proof that shows that while some of these
statements can be proved is some meta-system of the system, there will always be some that can't be proved at any finite level of meta-system.

Now, until you accept that Halting is, in fact, uncomputable, going
the next step won't be possible.

--
a burnt out swe investigating into why our tooling doesn't involve
basic semantic proofs like halting analysis

please excuse my pseudo-pyscript,

~ nick
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

Am Mon, 29 Dec 2025 23:26:15 -0800 schrieb dart200:

On 12/29/25 5:37 AM, Richard Damon wrote:

I believe there is then another proof that shows that because there is
no decider that gets all inputs correctly, you can show that there must
be some program that no known to be corret partial decider gets right,
in other words, a program that we can not know its halting status, as
we can not prove it will not halt.

I believe not, but I would be delighted to see.

actually i'm now thinking about using incompleteness against the
halting problem

How?

Which is what Incompleteness is about. It says that THE SYSTEM has a
true statement that THE SYSTEM can not prove. Doesn't matter that some
meta-system can prove it.

lol bruh, if there wasn't a meta system to prove it, how would godel
have proven it true outside the system???
at the very least godel's proof counts as a proof that exists outside
the system

G||del's proof is in the system of ZFC or whatever. It says something
about another formal system and its metasystem. Those may all be
different.

There is an additional proof that shows that while some of these
statements can be proved is some meta-system of the system, there will
always be some that can't be proved at any finite level of meta-system.

--
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/29/2025 11:49 PM, Tristan Wibberley wrote:

On 30/12/2025 04:35, olcott wrote:

...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

Correctly paraphrased as:
a sequence of inference steps from axioms
that assert that they themselves do not exist.

No they don't. That's an interpretation outside the system. The axioms
merely force you to conclude that some symbol or other is not negation
and/or another one is not a reference to the system itself when fools
think they both /are/ those things.

G := (F re4 G)
a sequence of inference steps in F from the axioms
of F that assert that they themselves do not exist in F.
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/25 12:33 AM, olcott wrote:

On 12/29/2025 10:50 PM, Richard Damon wrote:

On 12/29/25 11:35 PM, olcott wrote:

On 12/29/2025 9:51 PM, Richard Damon wrote:

On 12/29/25 6:28 PM, olcott wrote:

On 12/29/2025 5:06 PM, Richard Damon wrote:

On 12/29/25 4:38 PM, olcott wrote:

There exists a sequence of inference steps from
the axioms of a formal system that prove that
they themselves do not exist.

Right, there is an INFININTE string of inference steps in the base >>>>>> theory that shows that no FINITE string of inference steps to show >>>>>> it.

Rene Descartes said: "I think therefore I never existed".

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.

In other words, you are just showing that you don't know what you
are talking about and thus going into non-sense,

...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

Yes, you have said this before, and I have explained it, but
apparently you can't read.

Correctly paraphrased as:
a sequence of inference steps from axioms
that assert that they themselves do not exist.

Nope, as I have pointed out, you have missed the context, because you
are so stupid.

a proposition which asserts its own unprovability.

a proposition who has a meaning in the meta-system talking about its provability in the base system.

You just ignore context as that is just to complicated for you.

The proof of such an propostion within the same
formal system would require a sequence of inference
steps that prove that they themselves do not exist.

Which just shows you don't understand the concept of Formal Systems, and
their meta-systems.

The proof was NOT in the same system, but in a meta-system built from
that system.

It shows, via a finite proof in the meta-system, that there does exist a sequence of infinite length in the system to show the statement is true,
but their can not be a finite length sequence in the system.

All you are doing is proving you are to stupid to understand this, as
you don't understand that two different systems ARE different systems,
but meta-system can know details of their base system, and that there is
a difference between infinite and finite. THis shows your intelegence to
be near zero.

The statement, when looked at under the meaning that only exists in
the meta-system, shows that in the meta-system there is a proof, a
finite series of steps, that shows that in the system, the statement
in the system does not have a proof, which is a finite series of steps
IN THE SYSTEM (not the meta-system) but there is a infinite series of
steps in the system that make it true.

Thus, you show you can't tell the difference between an infinite
series of steps from a finitee series of step, thus you IQ must be 0
by that scale.

And, you can't tell the difference between the Meta-system and the
system, which is like thinking your pet cat is a dog.

The fact you keep on repeating this, and never try to answer the error
pointed out just means that you can't understand what an error is,
because to you truth, knowledge, fact, rules, don't mean anything
because you chose to make your self just stupid and ignorant.

G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems

As I said, and you were too stupid to understand, there is a finite
sequence of steps in the META systen that show that there is an
INFINITE sequence of steps in the system that show there is not a
FINITE sequence of steps in the system to prove it.

It seems to you, infinity is finite, and thus your mind is just ZERO.

Of course, you never let facts get in the way of your stupidity.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/25 9:32 AM, olcott wrote:

On 12/29/2025 11:49 PM, Tristan Wibberley wrote:

On 30/12/2025 04:35, olcott wrote:

...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

Correctly paraphrased as:
a sequence of inference steps from axioms
that assert that they themselves do not exist.

No they don't. That's an interpretation outside the system. The axioms
merely force you to conclude that some symbol or other is not negation
and/or another one is not a reference to the system itself when fools
think they both /are/ those things.

G := (F re4 G)

That isn't the statement of G, so you start with a lie.

a sequence of inference steps in F from the axioms
of F that assert that they themselves do not exist in F.

But that statement you are trying to start with isn't a statement in F,
but an interpretation of the statement in F as understood in MF.

All you are doing is showing you stupidity of not understanding context.

And thus you show you can't understand meaning, as meaning is based on context.


--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/2025 8:32 AM, Richard Damon wrote:

On 12/30/25 12:33 AM, olcott wrote:

On 12/29/2025 10:50 PM, Richard Damon wrote:

On 12/29/25 11:35 PM, olcott wrote:

On 12/29/2025 9:51 PM, Richard Damon wrote:

On 12/29/25 6:28 PM, olcott wrote:

On 12/29/2025 5:06 PM, Richard Damon wrote:

On 12/29/25 4:38 PM, olcott wrote:

There exists a sequence of inference steps from
the axioms of a formal system that prove that
they themselves do not exist.

Right, there is an INFININTE string of inference steps in the
base theory that shows that no FINITE string of inference steps >>>>>>> to show it.

Rene Descartes said: "I think therefore I never existed".

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.

In other words, you are just showing that you don't know what you
are talking about and thus going into non-sense,

...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

Yes, you have said this before, and I have explained it, but
apparently you can't read.

Correctly paraphrased as:
a sequence of inference steps from axioms
that assert that they themselves do not exist.

Nope, as I have pointed out, you have missed the context, because you
are so stupid.

a proposition which asserts its own unprovability.

a proposition who has a meaning in the meta-system talking about its provability in the base system.

This sentence is not true: "This sentence is not true"
the outer sentence is true because the inner sentence
is semantically incoherent.

You just ignore context as that is just to complicated for you.

I focus on the details that everyone else has been
indoctrinated to ignore.

The proof of such an propostion within the same
formal system would require a sequence of inference
steps that prove that they themselves do not exist.

Which just shows you don't understand the concept of Formal Systems, and their meta-systems.

This sentence is not true: "This sentence is not true"
the outer sentence is true because the inner sentence
is semantically incoherent.

Sentences that are semantically incoherent are not true.
This is ignored because a meta level version of the same
sentence can be made true on the basis of this incoherence.

G := (F re4 G)
a sequence of inference steps in F from the axioms
of F that assert that they themselves do not exist in F.

The proof was NOT in the same system, but in a meta-system built from
that system.

To hide the fact of the incoherence as was shown above.

It shows, via a finite proof in the meta-system, that there does exist a sequence of infinite length in the system to show the statement is true,
but their can not be a finite length sequence in the system.

All you are doing is proving you are to stupid to understand this, as

The actual stupidity is how mathematicians believe that
the foundations of math are inherently infallible as if
they themselves are the actual mind of God.

you don't understand that two different systems ARE different systems,
but meta-system can know details of their base system, and that there is
a difference between infinite and finite. THis shows your intelegence to
be near zero.

The statement, when looked at under the meaning that only exists in
the meta-system, shows that in the meta-system there is a proof, a
finite series of steps, that shows that in the system, the statement
in the system does not have a proof, which is a finite series of
steps IN THE SYSTEM (not the meta-system) but there is a infinite
series of steps in the system that make it true.

Thus, you show you can't tell the difference between an infinite
series of steps from a finitee series of step, thus you IQ must be 0
by that scale.

And, you can't tell the difference between the Meta-system and the
system, which is like thinking your pet cat is a dog.

The fact you keep on repeating this, and never try to answer the
error pointed out just means that you can't understand what an error
is, because to you truth, knowledge, fact, rules, don't mean anything
because you chose to make your self just stupid and ignorant.

G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems

As I said, and you were too stupid to understand, there is a finite >>>>> sequence of steps in the META systen that show that there is an
INFINITE sequence of steps in the system that show there is not a
FINITE sequence of steps in the system to prove it.

It seems to you, infinity is finite, and thus your mind is just ZERO. >>>>>
Of course, you never let facts get in the way of your stupidity.

--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/2025 8:38 AM, Richard Damon wrote:

On 12/30/25 9:32 AM, olcott wrote:

On 12/29/2025 11:49 PM, Tristan Wibberley wrote:

On 30/12/2025 04:35, olcott wrote:

...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

Correctly paraphrased as:
a sequence of inference steps from axioms
that assert that they themselves do not exist.

No they don't. That's an interpretation outside the system. The axioms
merely force you to conclude that some symbol or other is not negation
and/or another one is not a reference to the system itself when fools
think they both /are/ those things.

G := (F re4 G)

That isn't the statement of G, so you start with a lie.

a sequence of inference steps in F from the axioms
of F that assert that they themselves do not exist in F.

(F re4 G)
"re4" means that a sequence of inference steps from
F to G do not exist.

But that statement you are trying to start with isn't a statement in F,

Since is begins with F it is in F.
That people do not usually look at this degree
of detail do not mean that I am incorrect.

but an interpretation of the statement in F as understood in MF.

All you are doing is showing you stupidity of not understanding context.

All the I am doing is looking at these things at
the deeper level beyond indoctrination. I am directly
examining the foundations of logic and math.

Everyone else takes these as "given" as if from
the mind of God.

And thus you show you can't understand meaning, as meaning is based on context.

I understand meaning better then anyone else.
"true on the basis of meaning expressed in language"
for this entire body is one giant semantic tautology.
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/25 9:52 AM, olcott wrote:

On 12/30/2025 8:32 AM, Richard Damon wrote:

On 12/30/25 12:33 AM, olcott wrote:

On 12/29/2025 10:50 PM, Richard Damon wrote:

On 12/29/25 11:35 PM, olcott wrote:

On 12/29/2025 9:51 PM, Richard Damon wrote:

On 12/29/25 6:28 PM, olcott wrote:

On 12/29/2025 5:06 PM, Richard Damon wrote:

On 12/29/25 4:38 PM, olcott wrote:

There exists a sequence of inference steps from
the axioms of a formal system that prove that
they themselves do not exist.

Right, there is an INFININTE string of inference steps in the >>>>>>>> base theory that shows that no FINITE string of inference steps >>>>>>>> to show it.

Rene Descartes said: "I think therefore I never existed".

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.

In other words, you are just showing that you don't know what you >>>>>> are talking about and thus going into non-sense,

...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

Yes, you have said this before, and I have explained it, but
apparently you can't read.

Correctly paraphrased as:
a sequence of inference steps from axioms
that assert that they themselves do not exist.

Nope, as I have pointed out, you have missed the context, because
you are so stupid.

a proposition which asserts its own unprovability.

a proposition who has a meaning in the meta-system talking about its
provability in the base system.

This sentence is not true: "This sentence is not true"
the outer sentence is true because the inner sentence
is semantically incoherent.

You just ignore context as that is just to complicated for you.

I focus on the details that everyone else has been
indoctrinated to ignore.

The proof of such an propostion within the same
formal system would require a sequence of inference
steps that prove that they themselves do not exist.

Which just shows you don't understand the concept of Formal Systems,
and their meta-systems.

This sentence is not true: "This sentence is not true"
the outer sentence is true because the inner sentence
is semantically incoherent.

In other words, you can't talk about the sentence you want to talk
about, so you do to soething irrelevent.

Sentences that are semantically incoherent are not true.
This is ignored because a meta level version of the same
sentence can be made true on the basis of this incoherence.

But that isn't the case for G, unless you think arithmatic is
semantically incoherent.

But then, I think that *IS* the case for you.

G := (F re4 G)

Which isn't G in F, so your arguement fails.

a sequence of inference steps in F from the axioms
of F that assert that they themselves do not exist in F.

The proof was NOT in the same system, but in a meta-system built from
that system.

To hide the fact of the incoherence as was shown above.

Which says you don't know what that means.

All you have done is prove that to you, LOGIC is just incoherent because
you don't understand it.

It shows, via a finite proof in the meta-system, that there does exist
a sequence of infinite length in the system to show the statement is
true, but their can not be a finite length sequence in the system.

All you are doing is proving you are to stupid to understand this, as

The actual stupidity is how mathematicians believe that
the foundations of math are inherently infallible as if
they themselves are the actual mind of God.

So, you think mathematics DOESN'T work?

Can you show an actual FLAW in mathematics, or it is just that anything
too complicated for you must be wrong because YOU think YOU are God?

Note, that in a formal system, the axiomatic base and the logical
deductions it allows IS sort of like "God" to the system, as it is what creates it and controls it, and that is a key feature of God, he is the Creater and Controller of the system.

Since you have shown you can not actually create a working system, or
control one with coherent thoughts, you show you are not actually very
much in the image of God, but have lost that as you turned to your lies.

All you are doing is showing your stupidity, and that you whole basis is
a rejection of that which you don't understand instead of seeking to understand it, as you are stuck in your lies.

you don't understand that two different systems ARE different systems,
but meta-system can know details of their base system, and that there
is a difference between infinite and finite. THis shows your
intelegence to be near zero.

The statement, when looked at under the meaning that only exists in
the meta-system, shows that in the meta-system there is a proof, a
finite series of steps, that shows that in the system, the statement
in the system does not have a proof, which is a finite series of
steps IN THE SYSTEM (not the meta-system) but there is a infinite
series of steps in the system that make it true.

Thus, you show you can't tell the difference between an infinite
series of steps from a finitee series of step, thus you IQ must be 0
by that scale.

And, you can't tell the difference between the Meta-system and the
system, which is like thinking your pet cat is a dog.

The fact you keep on repeating this, and never try to answer the
error pointed out just means that you can't understand what an error
is, because to you truth, knowledge, fact, rules, don't mean
anything because you chose to make your self just stupid and ignorant. >>>>

G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems

As I said, and you were too stupid to understand, there is a
finite sequence of steps in the META systen that show that there
is an INFINITE sequence of steps in the system that show there is >>>>>> not a FINITE sequence of steps in the system to prove it.

It seems to you, infinity is finite, and thus your mind is just ZERO. >>>>>>
Of course, you never let facts get in the way of your stupidity.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/2025 9:14 AM, Richard Damon wrote:

On 12/30/25 9:52 AM, olcott wrote:

On 12/30/2025 8:32 AM, Richard Damon wrote:

On 12/30/25 12:33 AM, olcott wrote:

On 12/29/2025 10:50 PM, Richard Damon wrote:

On 12/29/25 11:35 PM, olcott wrote:

On 12/29/2025 9:51 PM, Richard Damon wrote:

On 12/29/25 6:28 PM, olcott wrote:

On 12/29/2025 5:06 PM, Richard Damon wrote:

On 12/29/25 4:38 PM, olcott wrote:

There exists a sequence of inference steps from
the axioms of a formal system that prove that
they themselves do not exist.

Right, there is an INFININTE string of inference steps in the >>>>>>>>> base theory that shows that no FINITE string of inference steps >>>>>>>>> to show it.

Rene Descartes said: "I think therefore I never existed".

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.

In other words, you are just showing that you don't know what you >>>>>>> are talking about and thus going into non-sense,

...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

Yes, you have said this before, and I have explained it, but
apparently you can't read.

Correctly paraphrased as:
a sequence of inference steps from axioms
that assert that they themselves do not exist.

Nope, as I have pointed out, you have missed the context, because
you are so stupid.

a proposition which asserts its own unprovability.

a proposition who has a meaning in the meta-system talking about its
provability in the base system.

This sentence is not true: "This sentence is not true"
the outer sentence is true because the inner sentence
is semantically incoherent.

You just ignore context as that is just to complicated for you.

I focus on the details that everyone else has been
indoctrinated to ignore.

The proof of such an propostion within the same
formal system would require a sequence of inference
steps that prove that they themselves do not exist.

Which just shows you don't understand the concept of Formal Systems,
and their meta-systems.

This sentence is not true: "This sentence is not true"
the outer sentence is true because the inner sentence
is semantically incoherent.

In other words, you can't talk about the sentence you want to talk
about, so you do to soething irrelevent.

Exactly the opposite Incompleteness and Undefinability
dishonestly dodge the fact the their actual sentences
are incoherent by using the meta-level.

This meta-level is correct to state that these sentences
are not provable and not true.

The meta-level never looks at why they are unprovable
and untrue. They are unprovable and untrue BECAUSE they
are semantically incoherent.

The proper treatment is to toss these sentences out as
incoherent. The proper treatment is not to create a
meta-level that simply ignores this incoherence.

Tarski's metatheory Tarski's theory
This sentence is not true: "This sentence is not true" is true

?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.

In meta-F In F
This sentence cannot be proven: "This sentence cannot be proven" is true

?- G = not(provable(F, G)).
G = not(provable(F, G)).
?- unify_with_occurs_check(G, not(provable(F, G))).
false.
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/25 11:15 AM, olcott wrote:

On 12/30/2025 9:14 AM, Richard Damon wrote:

On 12/30/25 9:52 AM, olcott wrote:

On 12/30/2025 8:32 AM, Richard Damon wrote:

On 12/30/25 12:33 AM, olcott wrote:

On 12/29/2025 10:50 PM, Richard Damon wrote:

On 12/29/25 11:35 PM, olcott wrote:

On 12/29/2025 9:51 PM, Richard Damon wrote:

On 12/29/25 6:28 PM, olcott wrote:

On 12/29/2025 5:06 PM, Richard Damon wrote:

On 12/29/25 4:38 PM, olcott wrote:

There exists a sequence of inference steps from
the axioms of a formal system that prove that
they themselves do not exist.

Right, there is an INFININTE string of inference steps in the >>>>>>>>>> base theory that shows that no FINITE string of inference >>>>>>>>>> steps to show it.

Rene Descartes said: "I think therefore I never existed".

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.

In other words, you are just showing that you don't know what >>>>>>>> you are talking about and thus going into non-sense,

...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

Yes, you have said this before, and I have explained it, but
apparently you can't read.

Correctly paraphrased as:
a sequence of inference steps from axioms
that assert that they themselves do not exist.

Nope, as I have pointed out, you have missed the context, because >>>>>> you are so stupid.

a proposition which asserts its own unprovability.

a proposition who has a meaning in the meta-system talking about its
provability in the base system.

This sentence is not true: "This sentence is not true"
the outer sentence is true because the inner sentence
is semantically incoherent.

You just ignore context as that is just to complicated for you.

I focus on the details that everyone else has been
indoctrinated to ignore.

The proof of such an propostion within the same
formal system would require a sequence of inference
steps that prove that they themselves do not exist.

Which just shows you don't understand the concept of Formal Systems,
and their meta-systems.

This sentence is not true: "This sentence is not true"
the outer sentence is true because the inner sentence
is semantically incoherent.

In other words, you can't talk about the sentence you want to talk
about, so you do to soething irrelevent.

Exactly the opposite Incompleteness and Undefinability
dishonestly dodge the fact the their actual sentences
are incoherent by using the meta-level.

And what is incoherent about using a meta-level.

All a mete-level is, is to build a new Formal System, based on the base
system that knows the basic properties of the base system.

For instance, the Rational Numbers can be considers a "meta" of the
Integeres.

This meta-level is correct to state that these sentences
are not provable and not true.

The meta-level never looks at why they are unprovable
and untrue. They are unprovable and untrue BECAUSE they
are semantically incoherent.

No, the sentence of G was specifically constructed to have a coherent
meaning in the base system, but you just are too stupid to understand that.

THe statment G, in the base system, as well as in the meta system is the
claim that there exists no natural number g that satisifies a particular mathematical property expresses as a primative recursive relationship.

The mathematics of that is fully coherent in the base system, and WILL
have an answer of either yes or no, even if that system might not be
able to compute that answer.

In the meta-system, because of how the relationship was created, we see
that in adds meaning from the base system into numbers that inherently
only mean themselves. Just like we can form words with meaning from
letters that have no inherent meaning.

It seems you don't even understand how "meaning" works, so your core is
based on a fundamental misunderstanding of what you talk about.

The proper treatment is to toss these sentences out as
incoherent. The proper treatment is not to create a
meta-level that simply ignores this incoherence.

But they aren't.

I guess to you, mathematics is just incoherent, and logic has to be kept primative.

In other words, you are just too stupid to be in the field.

Tarski's metatheory-a-a-a-a-a-a-a Tarski's theory
This sentence is not true: "This sentence is not true" is true

You just don't understand what Tarski is saying, as his proof build on
the concept that Godel uses, and Tarski shows that if we assume the
existance of a predicate "True" that will return True if its input
sentance is actually True, but False otherwise (either the contradiction
of the sentence is true, so it is false, or the sentence doesn't have a
truth value) then by the same "math" Godel uses, we can prove that the
liar must have a truth value.

?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.

Right, so by the proof, "True" as a predicate can't exist.

In meta-F-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a In F
This sentence cannot be proven: "This sentence cannot be proven" is true

?- G = not(provable(F, G)).
G = not(provable(F, G)).
?- unify_with_occurs_check(G, not(provable(F, G))).
false.

And all you are doing is proving your ignornce of how logic works, since
none of the system you are talking about can be modeled by Prolog.

Of course, YOU can't handle systems that can't be handled by Prolog as
you are just too stupid.


I will note again, the fact that you just refuse to even try to address
any of the points, but just keep repeating your wrong opinion that it
can't be right shows that inside, you understand you have no grounds for
your claims, and accept that you argument is baseless, but you still
just repeat it.

If you wanted to try to actually show an error in what I say, you would actually address my words and try to show an error, but that would
require you showing an understand of the field that you just don't have,
and would force you to reveal that you really have nothing to base your
claims on.

I note that everything you say is based on your own (ignorant)
understanding of how logic works and you can't actually get to the meet
of any source to back you up.

At best, you look at minor offhand high level explainations that you mis-interprete.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/2025 12:57 PM, Richard Damon wrote:

On 12/30/25 11:15 AM, olcott wrote:

On 12/30/2025 9:14 AM, Richard Damon wrote:

On 12/30/25 9:52 AM, olcott wrote:

On 12/30/2025 8:32 AM, Richard Damon wrote:

On 12/30/25 12:33 AM, olcott wrote:

On 12/29/2025 10:50 PM, Richard Damon wrote:

On 12/29/25 11:35 PM, olcott wrote:

On 12/29/2025 9:51 PM, Richard Damon wrote:

On 12/29/25 6:28 PM, olcott wrote:

On 12/29/2025 5:06 PM, Richard Damon wrote:

On 12/29/25 4:38 PM, olcott wrote:

There exists a sequence of inference steps from
the axioms of a formal system that prove that
they themselves do not exist.

Right, there is an INFININTE string of inference steps in the >>>>>>>>>>> base theory that shows that no FINITE string of inference >>>>>>>>>>> steps to show it.

Rene Descartes said: "I think therefore I never existed".

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.

In other words, you are just showing that you don't know what >>>>>>>>> you are talking about and thus going into non-sense,

...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41) >>>>>>>

Yes, you have said this before, and I have explained it, but
apparently you can't read.

Correctly paraphrased as:
a sequence of inference steps from axioms
that assert that they themselves do not exist.

Nope, as I have pointed out, you have missed the context, because >>>>>>> you are so stupid.

a proposition which asserts its own unprovability.

a proposition who has a meaning in the meta-system talking about
its provability in the base system.

This sentence is not true: "This sentence is not true"
the outer sentence is true because the inner sentence
is semantically incoherent.

You just ignore context as that is just to complicated for you.

I focus on the details that everyone else has been
indoctrinated to ignore.

The proof of such an propostion within the same
formal system would require a sequence of inference
steps that prove that they themselves do not exist.

Which just shows you don't understand the concept of Formal
Systems, and their meta-systems.

This sentence is not true: "This sentence is not true"
the outer sentence is true because the inner sentence
is semantically incoherent.

In other words, you can't talk about the sentence you want to talk
about, so you do to soething irrelevent.

Exactly the opposite Incompleteness and Undefinability
dishonestly dodge the fact the their actual sentences
are incoherent by using the meta-level.

And what is incoherent about using a meta-level.

All a mete-level is, is to build a new Formal System, based on the base system that knows the basic properties of the base system.

For instance, the Rational Numbers can be considers a "meta" of the Integeres.

This meta-level is correct to state that these sentences
are not provable and not true.

The meta-level never looks at why they are unprovable
and untrue. They are unprovable and untrue BECAUSE they
are semantically incoherent.

No, the sentence of G was specifically constructed to have a coherent meaning in the base system, but you just are too stupid to understand that.

Why do you lie about this? Does lying give you cheap thrill?

...We are therefore confronted with a proposition which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems

THe statment G, in the base system, as well as in the meta system is the claim that there exists no natural number g that satisifies a particular mathematical property expresses as a primative recursive relationship.

The mathematics of that is fully coherent in the base system, and WILL
have an answer of either yes or no, even if that system might not be
able to compute that answer.

In the meta-system, because of how the relationship was created, we see
that in adds meaning from the base system into numbers that inherently
only mean themselves. Just like we can form words with meaning from
letters that have no inherent meaning.

It seems you don't even understand how "meaning" works, so your core is based on a fundamental misunderstanding of what you talk about.

The proper treatment is to toss these sentences out as
incoherent. The proper treatment is not to create a
meta-level that simply ignores this incoherence.

But they aren't.

I guess to you, mathematics is just incoherent, and logic has to be kept primative.

In other words, you are just too stupid to be in the field.

Tarski's metatheory-a-a-a-a-a-a-a Tarski's theory
This sentence is not true: "This sentence is not true" is true

You just don't understand what Tarski is saying, as his proof build on
the concept that Godel uses, and Tarski shows that if we assume the existance of a predicate "True" that will return True if its input
sentance is actually True, but False otherwise (either the contradiction
of the sentence is true, so it is false, or the sentence doesn't have a truth value) then by the same "math" Godel uses, we can prove that the
liar must have a truth value.

?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.

Right, so by the proof, "True" as a predicate can't exist.

In meta-F-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a In F
This sentence cannot be proven: "This sentence cannot be proven" is true

?- G = not(provable(F, G)).
G = not(provable(F, G)).
?- unify_with_occurs_check(G, not(provable(F, G))).
false.

And all you are doing is proving your ignornce of how logic works, since none of the system you are talking about can be modeled by Prolog.

Of course, YOU can't handle systems that can't be handled by Prolog as
you are just too stupid.

I will note again, the fact that you just refuse to even try to address
any of the points, but just keep repeating your wrong opinion that it
can't be right shows that inside, you understand you have no grounds for your claims, and accept that you argument is baseless, but you still
just repeat it.

If you wanted to try to actually show an error in what I say, you would actually address my words and try to show an error, but that would
require you showing an understand of the field that you just don't have,
and would force you to reveal that you really have nothing to base your claims on.

I note that everything you say is based on your own (ignorant)
understanding of how logic works and you can't actually get to the meet
of any source to back you up.

At best, you look at minor offhand high level explainations that you mis-interprete.

--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/25 10:10 AM, olcott wrote:

On 12/30/2025 8:38 AM, Richard Damon wrote:

On 12/30/25 9:32 AM, olcott wrote:

On 12/29/2025 11:49 PM, Tristan Wibberley wrote:

On 30/12/2025 04:35, olcott wrote:

...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

Correctly paraphrased as:
a sequence of inference steps from axioms
that assert that they themselves do not exist.

No they don't. That's an interpretation outside the system. The axioms >>>> merely force you to conclude that some symbol or other is not negation >>>> and/or another one is not a reference to the system itself when fools
think they both /are/ those things.

G := (F re4 G)

That isn't the statement of G, so you start with a lie.

a sequence of inference steps in F from the axioms
of F that assert that they themselves do not exist in F.

(F re4 G)
"re4" means that a sequence of inference steps from
F to G do not exist.

Right, and there is, it is just an infinite sequence of steps.

Your problem (which you seem to be too stupid to understand by words) is
that this is NOT the definition of G, but an INTERPRETATION of that G
under the light of new definitions established in the Meta System.

But that statement you are trying to start with isn't a statement in F,

Since is begins with F it is in F.
That people do not usually look at this degree
of detail do not mean that I am incorrect.

Nope, I guess you don't think that one system can talk of other systems.

I guess you don't understand how logic works at all.

but an interpretation of the statement in F as understood in MF.

All you are doing is showing you stupidity of not understanding context.

All the I am doing is looking at these things at
the deeper level beyond indoctrination. I am directly
examining the foundations of logic and math.

MNo, you are looking at things through a broken lens of lies.

Everyone else takes these as "given" as if from
the mind of God.

But in a sense, they are.

"God" is the creater and control of things.

In a Formal System, the Axioms and rules FORM that system, and
everything in it comes out of that.

Thus, the system, in a very real sense, has a Creator, and thus a "God"

And thus you show you can't understand meaning, as meaning is based on
context.

I understand meaning better then anyone else.
"true on the basis of meaning expressed in language"
for this entire body is one giant semantic tautology.

Nope, the problem is yout THINK you do, and thus have made yourself
stupid and incapable of learning. Becoming the perfect example of Dunning-Kruger.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/2025 1:04 PM, Richard Damon wrote:

On 12/30/25 10:10 AM, olcott wrote:

On 12/30/2025 8:38 AM, Richard Damon wrote:

On 12/30/25 9:32 AM, olcott wrote:

On 12/29/2025 11:49 PM, Tristan Wibberley wrote:

On 30/12/2025 04:35, olcott wrote:

...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

Correctly paraphrased as:
a sequence of inference steps from axioms
that assert that they themselves do not exist.

No they don't. That's an interpretation outside the system. The axioms >>>>> merely force you to conclude that some symbol or other is not negation >>>>> and/or another one is not a reference to the system itself when fools >>>>> think they both /are/ those things.

G := (F re4 G)

That isn't the statement of G, so you start with a lie.

a sequence of inference steps in F from the axioms
of F that assert that they themselves do not exist in F.

(F re4 G)
"re4" means that a sequence of inference steps from
F to G do not exist.

Right, and there is, it is just an infinite sequence of steps.

You are stupidly saying that something that does not exist
at all infinitely exists.
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/25 2:01 PM, olcott wrote:

On 12/30/2025 12:57 PM, Richard Damon wrote:

On 12/30/25 11:15 AM, olcott wrote:

On 12/30/2025 9:14 AM, Richard Damon wrote:

On 12/30/25 9:52 AM, olcott wrote:

On 12/30/2025 8:32 AM, Richard Damon wrote:

On 12/30/25 12:33 AM, olcott wrote:

On 12/29/2025 10:50 PM, Richard Damon wrote:

On 12/29/25 11:35 PM, olcott wrote:

On 12/29/2025 9:51 PM, Richard Damon wrote:

On 12/29/25 6:28 PM, olcott wrote:

On 12/29/2025 5:06 PM, Richard Damon wrote:

On 12/29/25 4:38 PM, olcott wrote:

There exists a sequence of inference steps from
the axioms of a formal system that prove that
they themselves do not exist.

Right, there is an INFININTE string of inference steps in >>>>>>>>>>>> the base theory that shows that no FINITE string of
inference steps to show it.

Rene Descartes said: "I think therefore I never existed". >>>>>>>>>>>
There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.

In other words, you are just showing that you don't know what >>>>>>>>>> you are talking about and thus going into non-sense,

...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41) >>>>>>>>

Yes, you have said this before, and I have explained it, but
apparently you can't read.

Correctly paraphrased as:
a sequence of inference steps from axioms
that assert that they themselves do not exist.

Nope, as I have pointed out, you have missed the context,
because you are so stupid.

a proposition which asserts its own unprovability.

a proposition who has a meaning in the meta-system talking about
its provability in the base system.

This sentence is not true: "This sentence is not true"
the outer sentence is true because the inner sentence
is semantically incoherent.

You just ignore context as that is just to complicated for you.

I focus on the details that everyone else has been
indoctrinated to ignore.

The proof of such an propostion within the same
formal system would require a sequence of inference
steps that prove that they themselves do not exist.

Which just shows you don't understand the concept of Formal
Systems, and their meta-systems.

This sentence is not true: "This sentence is not true"
the outer sentence is true because the inner sentence
is semantically incoherent.

In other words, you can't talk about the sentence you want to talk
about, so you do to soething irrelevent.

Exactly the opposite Incompleteness and Undefinability
dishonestly dodge the fact the their actual sentences
are incoherent by using the meta-level.

And what is incoherent about using a meta-level.

All a mete-level is, is to build a new Formal System, based on the
base system that knows the basic properties of the base system.

For instance, the Rational Numbers can be considers a "meta" of the
Integeres.

This meta-level is correct to state that these sentences
are not provable and not true.

The meta-level never looks at why they are unprovable
and untrue. They are unprovable and untrue BECAUSE they
are semantically incoherent.

No, the sentence of G was specifically constructed to have a coherent
meaning in the base system, but you just are too stupid to understand
that.

Why do you lie about this? Does lying give you cheap thrill?

...We are therefore confronted with a proposition which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

And where does this say that is what the sentence is in the base system?

Why do YOU LIE? BECAUSE YOU ARE JUST STUPID.

Read the paper, see what the statement ACTUALLY IS.

It is a mathematical expression you probably have no idea what it means,
so you just skip over it. That is the power of stupidity.

Note, this sentence talks about the INTERPRETAION of the original
sentence (in the base language) when seen in the light of the additional meaning added by the meta system.

It seems you don't know what you are talking about, and just refuse to
learn.

G||del, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/2025 1:10 PM, Richard Damon wrote:

On 12/30/25 2:01 PM, olcott wrote:

On 12/30/2025 12:57 PM, Richard Damon wrote:

On 12/30/25 11:15 AM, olcott wrote:

On 12/30/2025 9:14 AM, Richard Damon wrote:

On 12/30/25 9:52 AM, olcott wrote:

On 12/30/2025 8:32 AM, Richard Damon wrote:

On 12/30/25 12:33 AM, olcott wrote:

On 12/29/2025 10:50 PM, Richard Damon wrote:

On 12/29/25 11:35 PM, olcott wrote:

On 12/29/2025 9:51 PM, Richard Damon wrote:

On 12/29/25 6:28 PM, olcott wrote:

On 12/29/2025 5:06 PM, Richard Damon wrote:

On 12/29/25 4:38 PM, olcott wrote:

There exists a sequence of inference steps from
the axioms of a formal system that prove that
they themselves do not exist.

Right, there is an INFININTE string of inference steps in >>>>>>>>>>>>> the base theory that shows that no FINITE string of >>>>>>>>>>>>> inference steps to show it.

Rene Descartes said: "I think therefore I never existed". >>>>>>>>>>>>
There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.

In other words, you are just showing that you don't know what >>>>>>>>>>> you are talking about and thus going into non-sense,

...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41) >>>>>>>>>

Yes, you have said this before, and I have explained it, but >>>>>>>>> apparently you can't read.

Correctly paraphrased as:
a sequence of inference steps from axioms
that assert that they themselves do not exist.

Nope, as I have pointed out, you have missed the context,
because you are so stupid.

a proposition which asserts its own unprovability.

a proposition who has a meaning in the meta-system talking about >>>>>>> its provability in the base system.

This sentence is not true: "This sentence is not true"
the outer sentence is true because the inner sentence
is semantically incoherent.

You just ignore context as that is just to complicated for you.

I focus on the details that everyone else has been
indoctrinated to ignore.

The proof of such an propostion within the same
formal system would require a sequence of inference
steps that prove that they themselves do not exist.

Which just shows you don't understand the concept of Formal
Systems, and their meta-systems.

This sentence is not true: "This sentence is not true"
the outer sentence is true because the inner sentence
is semantically incoherent.

In other words, you can't talk about the sentence you want to talk
about, so you do to soething irrelevent.

Exactly the opposite Incompleteness and Undefinability
dishonestly dodge the fact the their actual sentences
are incoherent by using the meta-level.

And what is incoherent about using a meta-level.

All a mete-level is, is to build a new Formal System, based on the
base system that knows the basic properties of the base system.

For instance, the Rational Numbers can be considers a "meta" of the
Integeres.

This meta-level is correct to state that these sentences
are not provable and not true.

The meta-level never looks at why they are unprovable
and untrue. They are unprovable and untrue BECAUSE they
are semantically incoherent.

No, the sentence of G was specifically constructed to have a coherent
meaning in the base system, but you just are too stupid to understand
that.

Why do you lie about this? Does lying give you cheap thrill?

...We are therefore confronted with a proposition which asserts its
own unprovability. 15 rCa (G||del 1931:40-41)

And where does this say that is what the sentence is in the base system?

That <is> the summation of his whole proof dip shit.
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/25 2:08 PM, olcott wrote:

On 12/30/2025 1:04 PM, Richard Damon wrote:

On 12/30/25 10:10 AM, olcott wrote:

On 12/30/2025 8:38 AM, Richard Damon wrote:

On 12/30/25 9:32 AM, olcott wrote:

On 12/29/2025 11:49 PM, Tristan Wibberley wrote:

On 30/12/2025 04:35, olcott wrote:

...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

Correctly paraphrased as:
a sequence of inference steps from axioms
that assert that they themselves do not exist.

No they don't. That's an interpretation outside the system. The
axioms
merely force you to conclude that some symbol or other is not
negation
and/or another one is not a reference to the system itself when fools >>>>>> think they both /are/ those things.

G := (F re4 G)

That isn't the statement of G, so you start with a lie.

a sequence of inference steps in F from the axioms
of F that assert that they themselves do not exist in F.

(F re4 G)
"re4" means that a sequence of inference steps from
F to G do not exist.

Right, and there is, it is just an infinite sequence of steps.

You are stupidly saying that something that does not exist
at all infinitely exists.

????

What doesn't exist:
A finite sequence in F

What does exist:
An infinite sequence if F, and
A finite sequence in Meta

Thus, your claim LIES by comparing the finite sequence to the infinte sequence, or sequences in different systems with different rules.

So, either finite == infinite or F == M by your logic,

Both are LIES, so you are just a LIAR.

And a stupid one at that as I have lost track of how many times it has
been explained to you, and you have shown an inability to learn it.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/25 2:13 PM, olcott wrote:

On 12/30/2025 1:10 PM, Richard Damon wrote:

On 12/30/25 2:01 PM, olcott wrote:

On 12/30/2025 12:57 PM, Richard Damon wrote:

On 12/30/25 11:15 AM, olcott wrote:

On 12/30/2025 9:14 AM, Richard Damon wrote:

On 12/30/25 9:52 AM, olcott wrote:

On 12/30/2025 8:32 AM, Richard Damon wrote:

On 12/30/25 12:33 AM, olcott wrote:

On 12/29/2025 10:50 PM, Richard Damon wrote:

On 12/29/25 11:35 PM, olcott wrote:

On 12/29/2025 9:51 PM, Richard Damon wrote:

On 12/29/25 6:28 PM, olcott wrote:

On 12/29/2025 5:06 PM, Richard Damon wrote:

On 12/29/25 4:38 PM, olcott wrote:

There exists a sequence of inference steps from
the axioms of a formal system that prove that
they themselves do not exist.

Right, there is an INFININTE string of inference steps in >>>>>>>>>>>>>> the base theory that shows that no FINITE string of >>>>>>>>>>>>>> inference steps to show it.

Rene Descartes said: "I think therefore I never existed". >>>>>>>>>>>>>
There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

There is no sequence of inference steps that
prove they themselves do not exist.

That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.
That is all that G||del ever proved.

In other words, you are just showing that you don't know >>>>>>>>>>>> what you are talking about and thus going into non-sense, >>>>>>>>>>>>

...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41) >>>>>>>>>>

Yes, you have said this before, and I have explained it, but >>>>>>>>>> apparently you can't read.

Correctly paraphrased as:
a sequence of inference steps from axioms
that assert that they themselves do not exist.

Nope, as I have pointed out, you have missed the context, >>>>>>>>>> because you are so stupid.

a proposition which asserts its own unprovability.

a proposition who has a meaning in the meta-system talking about >>>>>>>> its provability in the base system.

This sentence is not true: "This sentence is not true"
the outer sentence is true because the inner sentence
is semantically incoherent.

You just ignore context as that is just to complicated for you. >>>>>>>>

I focus on the details that everyone else has been
indoctrinated to ignore.

The proof of such an propostion within the same
formal system would require a sequence of inference
steps that prove that they themselves do not exist.

Which just shows you don't understand the concept of Formal
Systems, and their meta-systems.

This sentence is not true: "This sentence is not true"
the outer sentence is true because the inner sentence
is semantically incoherent.

In other words, you can't talk about the sentence you want to talk >>>>>> about, so you do to soething irrelevent.

Exactly the opposite Incompleteness and Undefinability
dishonestly dodge the fact the their actual sentences
are incoherent by using the meta-level.

And what is incoherent about using a meta-level.

All a mete-level is, is to build a new Formal System, based on the
base system that knows the basic properties of the base system.

For instance, the Rational Numbers can be considers a "meta" of the
Integeres.

This meta-level is correct to state that these sentences
are not provable and not true.

The meta-level never looks at why they are unprovable
and untrue. They are unprovable and untrue BECAUSE they
are semantically incoherent.

No, the sentence of G was specifically constructed to have a
coherent meaning in the base system, but you just are too stupid to
understand that.

Why do you lie about this? Does lying give you cheap thrill?

...We are therefore confronted with a proposition which asserts its
own unprovability. 15 rCa (G||del 1931:40-41)

And where does this say that is what the sentence is in the base system?

That <is> the summation of his whole proof dip shit.

In may be a "summation", but doesn't show an error.

Your problem is you just don't understand what you are talking about
since you chose to make yourself ignorant.

You are just as bad as the flat-earthers, but at least they TRY to use
real logic,
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 30/12/2025 14:32, olcott wrote:

G := (F re4 G)
a sequence of inference steps in F from the axioms
of F that assert that they themselves do not exist in F.

You suppose that's what the symbols mean. Yet you know that supposition
is inadmissible per-Se. Cognitive dissonance in action.

You rely on the delusion that the internal sensation of defining a
symbol actually has that effect on your mindspace and also on the
continued hallucination that the symbol is then stably so defined when
you later introspect your mind-space.
--
Tristan Wibberley

The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/2025 2:22 PM, Tristan Wibberley wrote:

On 30/12/2025 14:32, olcott wrote:

G := (F re4 G)
a sequence of inference steps in F from the axioms
of F that assert that they themselves do not exist in F.

You suppose that's what the symbols mean. Yet you know that supposition
is inadmissible per-Se. Cognitive dissonance in action.

The symbols *mean* a self-contradictory expression of language
the same sort of thing as: "this sentence is not true".

You rely on the delusion that the internal sensation of defining a
symbol actually has that effect on your mindspace and also on the
continued hallucination that the symbol is then stably so defined when
you later introspect your mind-space.

--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/25 3:35 PM, olcott wrote:

On 12/30/2025 2:22 PM, Tristan Wibberley wrote:

On 30/12/2025 14:32, olcott wrote:

G := (F re4 G)
a sequence of inference steps in F from the axioms
of F that assert that they themselves do not exist in F.

You suppose that's what the symbols mean. Yet you know that supposition
is inadmissible per-Se. Cognitive dissonance in action.

The symbols *mean* a self-contradictory expression of language
the same sort of thing as: "this sentence is not true".

But it doesn't, as it is satisfiable by a statement that is true but unprovable, which just mean the statement is established true by an
infinite chain of infernce, but there is no finite chain of inference
that establishes it.

Yes, it can also be satisfied by making the statement not have a truth
value, so we have two options.

Your problem is that since that WASN'T the actual statement of G, but
just an interpreation of it, and the ACTUAL statement for G must have a
truth value, as it is asking about the existance of a number with a
computable property, we can show that the non-truth-bearing option must
be incorrect.

Of course, when you only think things half way, you can try to argue otherwise, but that just shows your ignornace.

You only reject the fact that it can be statisifed by a true statement
that can't be proven, because you don't want such a thing to exist. But
they do, at least if you allow mathematics to exist.

So, unless you want to insist that civilization regress back to
primative times without higher logic, you are just living a lie.

Your "world" is built on the lie that we can know all truths, when the
world is actually more complicated than that, which just breaks you ideas.

You rely on the delusion that the internal sensation of defining a
symbol actually has that effect on your mindspace and also on the
continued hallucination that the symbol is then stably so defined when
you later introspect your mind-space.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 30/12/2025 20:35, olcott wrote:

The symbols *mean* a self-contradictory expression of language
the same sort of thing as: "this sentence is not true".

Not per-Se. Formally, it depends on the full nature of the system
they're in.
--
Tristan Wibberley

The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 30/12/2025 20:59, Richard Damon wrote:

On 12/30/25 3:35 PM, olcott wrote:

On 12/30/2025 2:22 PM, Tristan Wibberley wrote:

On 30/12/2025 14:32, olcott wrote:

G := (F re4 G)
a sequence of inference steps in F from the axioms
of F that assert that they themselves do not exist in F.

You suppose that's what the symbols mean. Yet you know that supposition
is inadmissible per-Se. Cognitive dissonance in action.

The symbols *mean* a self-contradictory expression of language
the same sort of thing as: "this sentence is not true".

But it doesn't, as it is satisfiable by a statement that is true but unprovable, which just mean the statement is established true by an
infinite chain of infernce

Are you using a finite derivation in the meta-system of the limit of a converging sequence of finite derivations of increasing length (whose
terminals may or may not be the statement being proved but the limit of
whose terminals /is/)?

And thus you say the statement is true thereby exemplifying a point from
which we may inductively infer a meaning for "true"? Is that "true of
the system in the meta-system" ?
--
Tristan Wibberley

The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/2025 3:26 PM, Tristan Wibberley wrote:

On 30/12/2025 20:35, olcott wrote:

The symbols *mean* a self-contradictory expression of language
the same sort of thing as: "this sentence is not true".

Not per-Se. Formally, it depends on the full nature of the system
they're in.

Sure and we could define a "black cat" as a
{fifteen story office building eating a sandwich}

Within the pure semantics of the actual underlying
meanings any expression of language that means:

{a sequence of inference steps in F from the axioms
of F that assert that they themselves do not exist in F}

is semantically incoherent.
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/2025 3:34 PM, Tristan Wibberley wrote:

On 30/12/2025 20:59, Richard Damon wrote:

On 12/30/25 3:35 PM, olcott wrote:

On 12/30/2025 2:22 PM, Tristan Wibberley wrote:

On 30/12/2025 14:32, olcott wrote:

G := (F re4 G)
a sequence of inference steps in F from the axioms
of F that assert that they themselves do not exist in F.

You suppose that's what the symbols mean. Yet you know that supposition >>>> is inadmissible per-Se. Cognitive dissonance in action.

The symbols *mean* a self-contradictory expression of language
the same sort of thing as: "this sentence is not true".

But it doesn't, as it is satisfiable by a statement that is true but
unprovable, which just mean the statement is established true by an
infinite chain of infernce

Are you using a finite derivation in the meta-system of the limit of a converging sequence of finite derivations of increasing length (whose terminals may or may not be the statement being proved but the limit of
whose terminals /is/)?

And thus you say the statement is true thereby exemplifying a point from which we may inductively infer a meaning for "true"? Is that "true of
the system in the meta-system" ?

True in the system can only really mean provable
from the axioms of this same system any other
meaning is nonsense.
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/25 4:41 PM, olcott wrote:

On 12/30/2025 3:34 PM, Tristan Wibberley wrote:

On 30/12/2025 20:59, Richard Damon wrote:

On 12/30/25 3:35 PM, olcott wrote:

On 12/30/2025 2:22 PM, Tristan Wibberley wrote:

On 30/12/2025 14:32, olcott wrote:

G := (F re4 G)
a sequence of inference steps in F from the axioms
of F that assert that they themselves do not exist in F.

You suppose that's what the symbols mean. Yet you know that
supposition
is inadmissible per-Se. Cognitive dissonance in action.

The symbols *mean* a self-contradictory expression of language
the same sort of thing as: "this sentence is not true".

But it doesn't, as it is satisfiable by a statement that is true but
unprovable, which just mean the statement is established true by an
infinite chain of infernce

Are you using a finite derivation in the meta-system of the limit of a
converging sequence of finite derivations of increasing length (whose
terminals may or may not be the statement being proved but the limit of
whose terminals /is/)?

And thus you say the statement is true thereby exemplifying a point from
which we may inductively infer a meaning for "true"? Is that "true of
the system in the meta-system" ?

True in the system can only really mean provable
from the axioms of this same system any other
meaning is nonsense.

True doesn't need to be PROVEN, only ESTABLISHED

True in the system F *IS* established as it is just a fact that no
number will satisfy the relationship, which can be established by
testing all of that countably infinite set.

We happen to be able to prove in the meta-system that all numbers will
fail to meet the relationship. In the system we just need to test that
whole infinite set, so the testing arguemnt isn't a proof, but does
establish the fact.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/25 4:34 PM, Tristan Wibberley wrote:

On 30/12/2025 20:59, Richard Damon wrote:

On 12/30/25 3:35 PM, olcott wrote:

On 12/30/2025 2:22 PM, Tristan Wibberley wrote:

On 30/12/2025 14:32, olcott wrote:

G := (F re4 G)
a sequence of inference steps in F from the axioms
of F that assert that they themselves do not exist in F.

You suppose that's what the symbols mean. Yet you know that supposition >>>> is inadmissible per-Se. Cognitive dissonance in action.

The symbols *mean* a self-contradictory expression of language
the same sort of thing as: "this sentence is not true".

But it doesn't, as it is satisfiable by a statement that is true but
unprovable, which just mean the statement is established true by an
infinite chain of infernce

Are you using a finite derivation in the meta-system of the limit of a converging sequence of finite derivations of increasing length (whose terminals may or may not be the statement being proved but the limit of
whose terminals /is/)?

And thus you say the statement is true thereby exemplifying a point from which we may inductively infer a meaning for "true"? Is that "true of
the system in the meta-system" ?

The fact that it is true in the meta system comes out of the interpretation

We KNOW, from the basic nature of the statement G, that it is asseeting
the non-existance of a number meeting a computable relationship that it
must have a truth value, as either such a number exists or not.

From the interpretation in the meta, we know that if a number exists
that stisfies the relationship, from such a number we can create a proof
that no number can exist that satisfies that relationship, there by
given the comment he makes that we have a statement that asserts its one unprobability. That is the "meaning" of any number that statisfies the relationship, and thus such a number can not exist.

Since such a number can not exist, that proves (in the meta system) that
the original statement was true.

It also allows us to look into the base system, and thus say that in the
base system, we can show that every number will just fail the
relationship, and thus we can show an (infinite) sequence of steps in
the base system that establishes the truth of the statement in the system.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/25 4:39 PM, olcott wrote:

On 12/30/2025 3:26 PM, Tristan Wibberley wrote:

On 30/12/2025 20:35, olcott wrote:

The symbols *mean* a self-contradictory expression of language
the same sort of thing as: "this sentence is not true".

Not per-Se. Formally, it depends on the full nature of the system
they're in.

Sure and we could define a "black cat" as a
{fifteen story office building eating a sandwich}

Sure, just can't do that in a system that already defines those other
terms differently.

It may be that is such a system, you just can't have black cats.

Within the pure semantics of the actual underlying
meanings any expression of language that means:

{a sequence of inference steps in F from the axioms
-aof F that assert that they themselves do not exist in F}

is semantically incoherent.

But that isn't what the statement means, as you lost the context of
where each sequence is in, and what steps are allowed in the sequence.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

In sci.logic Richard Damon <Richard@damon-family.org> wrote:

On 12/29/25 2:21 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

On 29/12/2025 13:37, Richard Damon wrote:

Incompleteness is a property of a given Formal System, it says that
there exist a statement that is true in that system, but can not be
proven in that system.

What do you mean by "proven" here. Do you mean "derived" ?

I think Richard misspoke slightly. The undecidable statement is
true *in the intended interpretation* of the formal system
(In Goedel's case, the natural numbers with addition and multiplication).

Truth "in the formal system" isn't really defined. You need an interpretation.

By the way when I wrote "Richard misspoke slightly" I should have
added "but that doesn't invalidate his argument". Sorry about that.

No, statements in a formal system are DEFINED to be true, if that
statement, referencing object defined in the system model, and related
by relationships defined in the system can be established starting with
the initial "facts" (axioms) of the system, and following the allowed logical operations of the system.

That's provability, not truth.

THus in the formal system of addition of Natural Numbers, the statement
2 + 3 = 5 is a true statement, as it can be derived from the operations
in the system.

A statement provable in the system, and a true statement about natural
numbers.

Some Formal System include a "model" that define
interpreations, though another layer above can be added (as Godel did).

I dunno, I always saw the models as separate from the formal system.
(That said, an intended model often provides the motivation for the
formal system.)
--
pa at panix dot com
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/30/25 6:14 PM, Pierre Asselin wrote:

In sci.logic Richard Damon <Richard@damon-family.org> wrote:

On 12/29/25 2:21 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

On 29/12/2025 13:37, Richard Damon wrote:

Incompleteness is a property of a given Formal System, it says that
there exist a statement that is true in that system, but can not be
proven in that system.

What do you mean by "proven" here. Do you mean "derived" ?

I think Richard misspoke slightly. The undecidable statement is
true *in the intended interpretation* of the formal system
(In Goedel's case, the natural numbers with addition and multiplication). >>>
Truth "in the formal system" isn't really defined. You need an
interpretation.

By the way when I wrote "Richard misspoke slightly" I should have
added "but that doesn't invalidate his argument". Sorry about that.

No, statements in a formal system are DEFINED to be true, if that
statement, referencing object defined in the system model, and related
by relationships defined in the system can be established starting with
the initial "facts" (axioms) of the system, and following the allowed
logical operations of the system.

That's provability, not truth.

No, provability requires a FINITE sequence to be showable.

Truth can be established by an INFINITE sequence.

THus in the formal system of addition of Natural Numbers, the statement
2 + 3 = 5 is a true statement, as it can be derived from the operations
in the system.

A statement provable in the system, and a true statement about natural numbers.

And thus a true statement in a system that defines Natural Numbers.

Some Formal System include a "model" that define
interpreations, though another layer above can be added (as Godel did).

I dunno, I always saw the models as separate from the formal system.
(That said, an intended model often provides the motivation for the
formal system.)

Models CAN be seperate, or can be assumed part of the system.

For instance, Geometery needs a model to be able to be used for
anything. The basic system defines the basic truths of the system, and
derives a lot of transforms. You need to add a model into the system to
define what points, lines, etc you are going to be starting from, to
actually get a result. The theories talk about points, lines, etc as
formal parameters to the theory, but doesn't create any to work with.
You need to add a model to it.

Mathematics is somewhat similar. While the bases system will define the numbers that we can work with, a lot of the theories in the system
reference values, and we can add a model to provide meaningful values to operate on. Some facts, like 2 + 3 = 5 don't need a model, but others
are only really meaningful if we have a model to give us specific values
to work with,
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

In sci.logic Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

[ ... ]
Then he defines a new system "P" which he uses to get even more muddled, leaves out the crucial elements of his proof because it's too easy to
get wrong,

G%del, muddled? He was the most meticulous sonovabitch that ever
lived!

and Stephen Meyer says he does get it wrong; he seems to be
the only person in the world that ever checked.

People have misunderstood G%del and proved it by their comments.
I don't know who Stephen Meyer is; my money is on G%del.
--
pa at panix dot com
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

In sci.logic Richard Damon <Richard@damon-family.org> wrote:

No, provability requires a FINITE sequence to be showable.

Truth can be established by an INFINITE sequence.

You're going off the beaten paths. Does that work
if you quantify over real numbers? Just curious.
--
pa at panix dot com
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/29/25 3:20 PM, Tristan Wibberley wrote:

On 29/12/2025 19:53, Richard Damon wrote:

On 12/29/25 2:32 PM, olcott wrote:

On 12/29/2025 1:21 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

On 29/12/2025 13:37, Richard Damon wrote:

Incompleteness is a property of a given Formal System, it says that >>>>>> there exist a statement that is true in that system, but can not be >>>>>> proven in that system.

What do you mean by "proven" here. Do you mean "derived" ?

I think Richard misspoke slightly. The undecidable statement is
true *in the intended interpretation* of the formal system
(In Goedel's case, the natural numbers with addition and
multiplication).

Truth "in the formal system" isn't really defined. You need an
interpretation.

Unless (as I have been saying for at least a decade)
the formal language directly encodes all of its
semantics directly in its syntax. The Montague
Grammar of natural language semantics is the best
known example of this.

But it can't, as any system that defines symbols, can have something
outside it assign additional meaning to those symbols.

Ontology suggests ways to *apply* a system. The system itself works
without additional meaning just as it does with. That's the point of
formal systems.

There may be SOME meaning within the system, but, with a sufficiently
expressive system, additional meaning can be imposed.

additional meaning is given to an embedding or extension (which is pretty-much a special-case of embedding) of a system, not to the system itself.

In the case of G||del's preamble, he defines an extension of PM (I should suppose he was using 2nd ed. in 1931 from his untruths about PM if
applied to 1st. ed.) That extension is inconsistent (or, better, I
think, indiscriminate). his referent there for PM slides between PM and
the derived system as he writes and he gets muddled taking a half-formed conclusion about one, assuming and completing it for the other.

Then he defines a new system "P" which he uses to get even more muddled, leaves out the crucial elements of his proof because it's too easy to
get wrong, and Stephen Meyer says he does get it wrong; he seems to be
the only person in the world that ever checked.

I would suggest, if you find an actual ERROR in what he said, that you
can prove, you write a paper and publish it to make a name for yourself.

Of course, if you show that your error is you don't actually understand
what you claim to be talking about, you will make the fool of yourself.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/31/25 4:18 PM, Pierre Asselin wrote:

In sci.logic Richard Damon <Richard@damon-family.org> wrote:

No, provability requires a FINITE sequence to be showable.

Truth can be established by an INFINITE sequence.

You're going off the beaten paths. Does that work
if you quantify over real numbers? Just curious.

Why not?

It says the steps may not be enumerable, but the inenumerable path exists.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/31/2025 3:16 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

[ ... ]
Then he defines a new system "P" which he uses to get even more muddled,
leaves out the crucial elements of his proof because it's too easy to
get wrong,

G||del, muddled? He was the most meticulous sonovabitch that ever
lived!

and Stephen Meyer says he does get it wrong; he seems to be
the only person in the world that ever checked.

People have misunderstood G||del and proved it by their comments.
I don't know who Stephen Meyer is; my money is on G||del.

G||del proved that there cannot possibly exist any
sequence of inference steps in F prove that they
themselves do not exist.

He admitted this himself:
...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/31/25 4:52 PM, olcott wrote:

On 12/31/2025 3:16 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

[ ... ]
Then he defines a new system "P" which he uses to get even more muddled, >>> leaves out the crucial elements of his proof because it's too easy to
get wrong,

G||del, muddled? He was the most meticulous sonovabitch that ever
lived!

and Stephen Meyer says he does get it wrong; he seems to be
the only person in the world that ever checked.

People have misunderstood G||del and proved it by their comments.
I don't know who Stephen Meyer is; my money is on G||del.

G||del proved that there cannot possibly exist any
sequence of inference steps in F prove that they
themselves do not exist.

No *FINITE* sequence of inference steps.

He also proves there *IS* an infinite sequence of steps

He admitted this himself:
...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

And proofs are finite.

And that statement is made in the Meta System, and is talking about the
base system.

All you are doing is proving that you are an idiot, and maybe in your
case there isn't a difference between You and a deterministic machine,
as you are stuck in your bad programming.

It seems you hae a broken CPU.

G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/29/2025 2:20 PM, Tristan Wibberley wrote:

On 29/12/2025 19:53, Richard Damon wrote:

On 12/29/25 2:32 PM, olcott wrote:

On 12/29/2025 1:21 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

On 29/12/2025 13:37, Richard Damon wrote:

Incompleteness is a property of a given Formal System, it says that >>>>>> there exist a statement that is true in that system, but can not be >>>>>> proven in that system.

What do you mean by "proven" here. Do you mean "derived" ?

I think Richard misspoke slightly. The undecidable statement is
true *in the intended interpretation* of the formal system
(In Goedel's case, the natural numbers with addition and
multiplication).

Truth "in the formal system" isn't really defined. You need an
interpretation.

Unless (as I have been saying for at least a decade)
the formal language directly encodes all of its
semantics directly in its syntax. The Montague
Grammar of natural language semantics is the best
known example of this.

But it can't, as any system that defines symbols, can have something
outside it assign additional meaning to those symbols.

Ontology suggests ways to *apply* a system. The system itself works
without additional meaning just as it does with. That's the point of
formal systems.

There may be SOME meaning within the system, but, with a sufficiently
expressive system, additional meaning can be imposed.

additional meaning is given to an embedding or extension (which is pretty-much a special-case of embedding) of a system, not to the system itself.

In the case of G||del's preamble, he defines an extension of PM (I should suppose he was using 2nd ed. in 1931 from his untruths about PM if
applied to 1st. ed.) That extension is inconsistent (or, better, I
think, indiscriminate). his referent there for PM slides between PM and
the derived system as he writes and he gets muddled taking a half-formed conclusion about one, assuming and completing it for the other.

Then he defines a new system "P" which he uses to get even more muddled, leaves out the crucial elements of his proof because it's too easy to
get wrong, and Stephen Meyer says he does get it wrong; he seems to be
the only person in the world that ever checked.

G||del proved that there cannot possibly exist any
sequence of inference steps in F prove that they
themselves do not exist.

He admitted this himself:
...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/31/2025 3:56 PM, Richard Damon wrote:

On 12/31/25 4:52 PM, olcott wrote:

On 12/31/2025 3:16 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

[ ... ]
Then he defines a new system "P" which he uses to get even more
muddled,
leaves out the crucial elements of his proof because it's too easy to
get wrong,

G||del, muddled? He was the most meticulous sonovabitch that ever
lived!

and Stephen Meyer says he does get it wrong; he seems to be
the only person in the world that ever checked.

People have misunderstood G||del and proved it by their comments.
I don't know who Stephen Meyer is; my money is on G||del.

G||del proved that there cannot possibly exist any
sequence of inference steps in F prove that they
themselves do not exist.

No *FINITE* sequence of inference steps.

Nothing can prove that itself does not
exist because that forms proof that it
does exist, dumbo.

He also proves there *IS* an infinite sequence of steps

He admitted this himself:
...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

And proofs are finite.

And that statement is made in the Meta System, and is talking about the
base system.

All you are doing is proving that you are an idiot, and maybe in your
case there isn't a difference between You and a deterministic machine,
as you are stuck in your bad programming.

It seems you hae a broken CPU.

G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems

--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/31/25 4:57 PM, olcott wrote:

On 12/29/2025 2:20 PM, Tristan Wibberley wrote:

On 29/12/2025 19:53, Richard Damon wrote:

On 12/29/25 2:32 PM, olcott wrote:

On 12/29/2025 1:21 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

On 29/12/2025 13:37, Richard Damon wrote:

Incompleteness is a property of a given Formal System, it says that >>>>>>> there exist a statement that is true in that system, but can not be >>>>>>> proven in that system.

What do you mean by "proven" here. Do you mean "derived" ?

I think Richard misspoke slightly. The undecidable statement is
true *in the intended interpretation* of the formal system
(In Goedel's case, the natural numbers with addition and
multiplication).

Truth "in the formal system" isn't really defined. You need an
interpretation.

Unless (as I have been saying for at least a decade)
the formal language directly encodes all of its
semantics directly in its syntax. The Montague
Grammar of natural language semantics is the best
known example of this.

But it can't, as any system that defines symbols, can have something
outside it assign additional meaning to those symbols.

Ontology suggests ways to *apply* a system. The system itself works
without additional meaning just as it does with. That's the point of
formal systems.

There may be SOME meaning within the system, but, with a sufficiently
expressive system, additional meaning can be imposed.

additional meaning is given to an embedding or extension (which is
pretty-much a special-case of embedding) of a system, not to the system
itself.

In the case of G||del's preamble, he defines an extension of PM (I should
suppose he was using 2nd ed. in 1931 from his untruths about PM if
applied to 1st. ed.) That extension is inconsistent (or, better, I
think, indiscriminate). his referent there for PM slides between PM and
the derived system as he writes and he gets muddled taking a half-formed
conclusion about one, assuming and completing it for the other.

Then he defines a new system "P" which he uses to get even more muddled,
leaves out the crucial elements of his proof because it's too easy to
get wrong, and Stephen Meyer says he does get it wrong; he seems to be
the only person in the world that ever checked.

G||del proved that there cannot possibly exist any
sequence of inference steps in F prove that they
themselves do not exist.

No *FINITE* sequence, as that is what a proof is.

He also proved the existance of the INFINITE sequence that made the
statement true.

He admitted this himself:
...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

Which you don't understand,

This is an interpreation of the statement in the meta system that is
talking about its provability in the base system.

So yes, the statement is TRUE and unprovable.

If it was FALSE, then that says we can prove a false statement to be
true, which is just a contradiction.

Of course, you are just showing your stupidity and inability to
understand things,

It sounds like you have burnt out your CPU and lost the ability to
think, and are stuck in a trap loop.

G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/31/25 4:59 PM, olcott wrote:

On 12/31/2025 3:56 PM, Richard Damon wrote:

On 12/31/25 4:52 PM, olcott wrote:

On 12/31/2025 3:16 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

[ ... ]
Then he defines a new system "P" which he uses to get even more
muddled,
leaves out the crucial elements of his proof because it's too easy to >>>>> get wrong,

G||del, muddled? He was the most meticulous sonovabitch that ever
lived!

and Stephen Meyer says he does get it wrong; he seems to be
the only person in the world that ever checked.

People have misunderstood G||del and proved it by their comments.
I don't know who Stephen Meyer is; my money is on G||del.

G||del proved that there cannot possibly exist any
sequence of inference steps in F prove that they
themselves do not exist.

No *FINITE* sequence of inference steps.

Nothing can prove that itself does not
exist because that forms proof that it
does exist, dumbo.

So you are just ignoring context because you are stupid.

The statement, with the added information of the meta-system proves (by
a proof in the meta system) that the statment is true.

Because, the statement is just a statement of arithmatic in the base
system, that means it is also must be true in the base system.

A result of the statement being true, it shows (with its interpreation
in the meta system) that there can not be a proof in the base system for it,

So, all you are doing is saying you can't tell the difference between different system and think they are all the same.

That is like saying your cat can be a dog.

You really are THAT stupid.

So
G + Meta proves G
G without Meta can't prove G

No contradiction, as Meta provides the information that allows the proof
to be formed.

He also proves there *IS* an infinite sequence of steps

He admitted this himself:
...We are therefore confronted with a proposition
which asserts its own unprovability. 15 rCa (G||del 1931:40-41)

And proofs are finite.

And that statement is made in the Meta System, and is talking about
the base system.

All you are doing is proving that you are an idiot, and maybe in your
case there isn't a difference between You and a deterministic machine,
as you are stuck in your bad programming.

It seems you hae a broken CPU.

G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/31/2025 4:09 PM, Richard Damon wrote:

On 12/31/25 4:59 PM, olcott wrote:

On 12/31/2025 3:56 PM, Richard Damon wrote:

On 12/31/25 4:52 PM, olcott wrote:

On 12/31/2025 3:16 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

[ ... ]
Then he defines a new system "P" which he uses to get even more
muddled,
leaves out the crucial elements of his proof because it's too easy to >>>>>> get wrong,

G||del, muddled? He was the most meticulous sonovabitch that ever
lived!

and Stephen Meyer says he does get it wrong; he seems to be
the only person in the world that ever checked.

People have misunderstood G||del and proved it by their comments.
I don't know who Stephen Meyer is; my money is on G||del.

G||del proved that there cannot possibly exist any
sequence of inference steps in F prove that they
themselves do not exist.

No *FINITE* sequence of inference steps.

Nothing can prove that itself does not
exist because that forms proof that it
does exist, dumbo.

So you are just ignoring context because you are stupid.

The statement, with the added information of the meta-system proves (by
a proof in the meta system) that the statment is true.

Something else can prove that X cannot prove that
X does not exist, AKA your meta-system.

Nothing can directly prove that itself does not
exist because this forms proof that it does exist.
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/31/25 5:42 PM, olcott wrote:

On 12/31/2025 4:09 PM, Richard Damon wrote:

On 12/31/25 4:59 PM, olcott wrote:

On 12/31/2025 3:56 PM, Richard Damon wrote:

On 12/31/25 4:52 PM, olcott wrote:

On 12/31/2025 3:16 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

[ ... ]
Then he defines a new system "P" which he uses to get even more >>>>>>> muddled,
leaves out the crucial elements of his proof because it's too
easy to
get wrong,

G||del, muddled? He was the most meticulous sonovabitch that ever
lived!

and Stephen Meyer says he does get it wrong; he seems to be
the only person in the world that ever checked.

People have misunderstood G||del and proved it by their comments.
I don't know who Stephen Meyer is; my money is on G||del.

G||del proved that there cannot possibly exist any
sequence of inference steps in F prove that they
themselves do not exist.

No *FINITE* sequence of inference steps.

Nothing can prove that itself does not
exist because that forms proof that it
does exist, dumbo.

So you are just ignoring context because you are stupid.

The statement, with the added information of the meta-system proves
(by a proof in the meta system) that the statment is true.

Something else can prove that X cannot prove that
X does not exist, AKA your meta-system.

Nothing can directly prove that itself does not
exist because this forms proof that it does exist.

Nope, got a source for that?

Why does my explanation not work?

Can you even put my explaination imto your own words to show that you understand it.

The statement G, under the interpreation provided by M certainly can
prove that the system without M can't prove it.

It seems you think that X is as big as X+1

Sorry, you are just showing that you brain has self-distructed itself
and left you with no ability to reason.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/31/2025 4:48 PM, Richard Damon wrote:

On 12/31/25 5:42 PM, olcott wrote:

On 12/31/2025 4:09 PM, Richard Damon wrote:

On 12/31/25 4:59 PM, olcott wrote:

On 12/31/2025 3:56 PM, Richard Damon wrote:

On 12/31/25 4:52 PM, olcott wrote:

On 12/31/2025 3:16 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

[ ... ]
Then he defines a new system "P" which he uses to get even more >>>>>>>> muddled,
leaves out the crucial elements of his proof because it's too >>>>>>>> easy to
get wrong,

G||del, muddled? He was the most meticulous sonovabitch that ever >>>>>>> lived!

and Stephen Meyer says he does get it wrong; he seems to be
the only person in the world that ever checked.

People have misunderstood G||del and proved it by their comments. >>>>>>> I don't know who Stephen Meyer is; my money is on G||del.

G||del proved that there cannot possibly exist any
sequence of inference steps in F prove that they
themselves do not exist.

No *FINITE* sequence of inference steps.

Nothing can prove that itself does not
exist because that forms proof that it
does exist, dumbo.

So you are just ignoring context because you are stupid.

The statement, with the added information of the meta-system proves
(by a proof in the meta system) that the statment is true.

Something else can prove that X cannot prove that
X does not exist, AKA your meta-system.

Nothing can directly prove that itself does not
exist because this forms proof that it does exist.

Nope, got a source for that?

Why does my explanation not work?

It is not that your explanation doesn't work.
It is that it ignores the root cause of why
G is unprovable in F.

If you disagree then provide a correct
proof that you yourself never existed.

If you can't see how this is impossible
you must by very dumb.

Since you have proved that you are quite
smart then any disagreement would most
likely be a lie, a mere head game.

Can you even put my explaination imto your own words to show that you understand it.

The statement G, under the interpreation provided by M certainly can
prove that the system without M can't prove it.

It seems you think that X is as big as X+1

Sorry, you are just showing that you brain has self-distructed itself
and left you with no ability to reason.

--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/31/25 6:08 PM, olcott wrote:

On 12/31/2025 4:48 PM, Richard Damon wrote:

On 12/31/25 5:42 PM, olcott wrote:

On 12/31/2025 4:09 PM, Richard Damon wrote:

On 12/31/25 4:59 PM, olcott wrote:

On 12/31/2025 3:56 PM, Richard Damon wrote:

On 12/31/25 4:52 PM, olcott wrote:

On 12/31/2025 3:16 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

[ ... ]
Then he defines a new system "P" which he uses to get even more >>>>>>>>> muddled,
leaves out the crucial elements of his proof because it's too >>>>>>>>> easy to
get wrong,

G||del, muddled? He was the most meticulous sonovabitch that ever >>>>>>>> lived!

and Stephen Meyer says he does get it wrong; he seems to be
the only person in the world that ever checked.

People have misunderstood G||del and proved it by their comments. >>>>>>>> I don't know who Stephen Meyer is; my money is on G||del.

G||del proved that there cannot possibly exist any
sequence of inference steps in F prove that they
themselves do not exist.

No *FINITE* sequence of inference steps.

Nothing can prove that itself does not
exist because that forms proof that it
does exist, dumbo.

So you are just ignoring context because you are stupid.

The statement, with the added information of the meta-system proves
(by a proof in the meta system) that the statment is true.

Something else can prove that X cannot prove that
X does not exist, AKA your meta-system.

Nothing can directly prove that itself does not
exist because this forms proof that it does exist.

Nope, got a source for that?

Why does my explanation not work?

It is not that your explanation doesn't work.
It is that it ignores the root cause of why
G is unprovable in F.

So, how do you think you can prove it in F?

If you disagree then provide a correct
proof that you yourself never existed.

Not the same.

You are ignoring the effect of different context.

And, since I exist, I can't prove a false statement that I don't exist.

Also, G isn't the proof, it is the thing being proven or not.

If you can't see how this is impossible
you must by very dumb.

Your arguement is just stupid, and invalid.

Showing that likely you are both STUPID yourself, and a liar.

Since you have proved that you are quite
smart then any disagreement would most
likely be a lie, a mere head game.

Why? How is it a lie to disagree with a falsehood?

You just continue to prove that you are nothing but a totally ignorant pathological liar that just doesn't understand logic, but doesn't care.

Can you even put my explaination imto your own words to show that you
understand it.

The statement G, under the interpreation provided by M certainly can
prove that the system without M can't prove it.

It seems you think that X is as big as X+1

Sorry, you are just showing that you brain has self-distructed itself
and left you with no ability to reason.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/31/2025 5:27 PM, Richard Damon wrote:

On 12/31/25 6:08 PM, olcott wrote:

On 12/31/2025 4:48 PM, Richard Damon wrote:

On 12/31/25 5:42 PM, olcott wrote:

On 12/31/2025 4:09 PM, Richard Damon wrote:

On 12/31/25 4:59 PM, olcott wrote:

On 12/31/2025 3:56 PM, Richard Damon wrote:

On 12/31/25 4:52 PM, olcott wrote:

On 12/31/2025 3:16 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

[ ... ]
Then he defines a new system "P" which he uses to get even >>>>>>>>>> more muddled,
leaves out the crucial elements of his proof because it's too >>>>>>>>>> easy to
get wrong,

G||del, muddled? He was the most meticulous sonovabitch that ever >>>>>>>>> lived!

and Stephen Meyer says he does get it wrong; he seems to be >>>>>>>>>> the only person in the world that ever checked.

People have misunderstood G||del and proved it by their comments. >>>>>>>>> I don't know who Stephen Meyer is; my money is on G||del.

G||del proved that there cannot possibly exist any
sequence of inference steps in F prove that they
themselves do not exist.

No *FINITE* sequence of inference steps.

Nothing can prove that itself does not
exist because that forms proof that it
does exist, dumbo.

So you are just ignoring context because you are stupid.

The statement, with the added information of the meta-system proves >>>>> (by a proof in the meta system) that the statment is true.

Something else can prove that X cannot prove that
X does not exist, AKA your meta-system.

Nothing can directly prove that itself does not
exist because this forms proof that it does exist.

Nope, got a source for that?

Why does my explanation not work?

It is not that your explanation doesn't work.
It is that it ignores the root cause of why
G is unprovable in F.

So, how do you think you can prove it in F?

Nothing can prove that itself does not exist.
Any such proof would be self-refuting.
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/31/25 7:23 PM, olcott wrote:

On 12/31/2025 5:27 PM, Richard Damon wrote:

On 12/31/25 6:08 PM, olcott wrote:

On 12/31/2025 4:48 PM, Richard Damon wrote:

On 12/31/25 5:42 PM, olcott wrote:

On 12/31/2025 4:09 PM, Richard Damon wrote:

On 12/31/25 4:59 PM, olcott wrote:

On 12/31/2025 3:56 PM, Richard Damon wrote:

On 12/31/25 4:52 PM, olcott wrote:

On 12/31/2025 3:16 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote: >>>>>>>>>>

[ ... ]
Then he defines a new system "P" which he uses to get even >>>>>>>>>>> more muddled,
leaves out the crucial elements of his proof because it's too >>>>>>>>>>> easy to
get wrong,

G||del, muddled? He was the most meticulous sonovabitch that ever >>>>>>>>>> lived!

and Stephen Meyer says he does get it wrong; he seems to be >>>>>>>>>>> the only person in the world that ever checked.

People have misunderstood G||del and proved it by their comments. >>>>>>>>>> I don't know who Stephen Meyer is; my money is on G||del.

G||del proved that there cannot possibly exist any
sequence of inference steps in F prove that they
themselves do not exist.

No *FINITE* sequence of inference steps.

Nothing can prove that itself does not
exist because that forms proof that it
does exist, dumbo.

So you are just ignoring context because you are stupid.

The statement, with the added information of the meta-system
proves (by a proof in the meta system) that the statment is true.

Something else can prove that X cannot prove that
X does not exist, AKA your meta-system.

Nothing can directly prove that itself does not
exist because this forms proof that it does exist.

Nope, got a source for that?

Why does my explanation not work?

It is not that your explanation doesn't work.
It is that it ignores the root cause of why
G is unprovable in F.

So, how do you think you can prove it in F?

Nothing can prove that itself does not exist.
Any such proof would be self-refuting.

But it isn't the PROOF that does the proving, it is the statement.

THe statement G exist, and it is True.

Because it is true, and can be proven with the additional knowledge and
tools of the meta-system, it shows that without the addtional knowledge
and tools you can't make the proof.

It seems you don't understand that the base system and the meta system
are different.

Boy, are you stupid.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/31/2025 6:35 PM, Richard Damon wrote:

On 12/31/25 7:23 PM, olcott wrote:

On 12/31/2025 5:27 PM, Richard Damon wrote:

On 12/31/25 6:08 PM, olcott wrote:

On 12/31/2025 4:48 PM, Richard Damon wrote:

On 12/31/25 5:42 PM, olcott wrote:

On 12/31/2025 4:09 PM, Richard Damon wrote:

On 12/31/25 4:59 PM, olcott wrote:

On 12/31/2025 3:56 PM, Richard Damon wrote:

On 12/31/25 4:52 PM, olcott wrote:

On 12/31/2025 3:16 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote: >>>>>>>>>>>

[ ... ]
Then he defines a new system "P" which he uses to get even >>>>>>>>>>>> more muddled,
leaves out the crucial elements of his proof because it's >>>>>>>>>>>> too easy to
get wrong,

G||del, muddled? He was the most meticulous sonovabitch that ever >>>>>>>>>>> lived!

and Stephen Meyer says he does get it wrong; he seems to be >>>>>>>>>>>> the only person in the world that ever checked.

People have misunderstood G||del and proved it by their comments. >>>>>>>>>>> I don't know who Stephen Meyer is; my money is on G||del. >>>>>>>>>>>

G||del proved that there cannot possibly exist any
sequence of inference steps in F prove that they
themselves do not exist.

No *FINITE* sequence of inference steps.

Nothing can prove that itself does not
exist because that forms proof that it
does exist, dumbo.

So you are just ignoring context because you are stupid.

The statement, with the added information of the meta-system
proves (by a proof in the meta system) that the statment is true. >>>>>>>

Something else can prove that X cannot prove that
X does not exist, AKA your meta-system.

Nothing can directly prove that itself does not
exist because this forms proof that it does exist.

Nope, got a source for that?

Why does my explanation not work?

It is not that your explanation doesn't work.
It is that it ignores the root cause of why
G is unprovable in F.

So, how do you think you can prove it in F?

Nothing can prove that itself does not exist.
Any such proof would be self-refuting.

But it isn't the PROOF that does the proving, it is the statement.

THe statement G exist, and it is True.

...We are therefore confronted with a proposition which
asserts its own unprovability. 15 rCa (G||del 1931:40-41)

When we name this proposition G then a proof of G
would be a sequence of inference steps that prove
that they themselves do not exist.

Anything that asserts its own non-existence
is necessarily incorrect.

Because it is true, and can be proven with the additional knowledge and tools-a of the meta-system, it shows that without the addtional knowledge and tools you can't make the proof.

It seems you don't understand that the base system and the meta system
are different.

Boy, are you stupid.

--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/31/25 8:04 PM, olcott wrote:

On 12/31/2025 6:35 PM, Richard Damon wrote:

On 12/31/25 7:23 PM, olcott wrote:

On 12/31/2025 5:27 PM, Richard Damon wrote:

On 12/31/25 6:08 PM, olcott wrote:

On 12/31/2025 4:48 PM, Richard Damon wrote:

On 12/31/25 5:42 PM, olcott wrote:

On 12/31/2025 4:09 PM, Richard Damon wrote:

On 12/31/25 4:59 PM, olcott wrote:

On 12/31/2025 3:56 PM, Richard Damon wrote:

On 12/31/25 4:52 PM, olcott wrote:

On 12/31/2025 3:16 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote: >>>>>>>>>>>>

[ ... ]
Then he defines a new system "P" which he uses to get even >>>>>>>>>>>>> more muddled,
leaves out the crucial elements of his proof because it's >>>>>>>>>>>>> too easy to
get wrong,

G||del, muddled? He was the most meticulous sonovabitch that >>>>>>>>>>>> ever
lived!

and Stephen Meyer says he does get it wrong; he seems to be >>>>>>>>>>>>> the only person in the world that ever checked.

People have misunderstood G||del and proved it by their >>>>>>>>>>>> comments.
I don't know who Stephen Meyer is; my money is on G||del. >>>>>>>>>>>>

G||del proved that there cannot possibly exist any
sequence of inference steps in F prove that they
themselves do not exist.

No *FINITE* sequence of inference steps.

Nothing can prove that itself does not
exist because that forms proof that it
does exist, dumbo.

So you are just ignoring context because you are stupid.

The statement, with the added information of the meta-system
proves (by a proof in the meta system) that the statment is true. >>>>>>>>

Something else can prove that X cannot prove that
X does not exist, AKA your meta-system.

Nothing can directly prove that itself does not
exist because this forms proof that it does exist.

Nope, got a source for that?

Why does my explanation not work?

It is not that your explanation doesn't work.
It is that it ignores the root cause of why
G is unprovable in F.

So, how do you think you can prove it in F?

Nothing can prove that itself does not exist.
Any such proof would be self-refuting.

But it isn't the PROOF that does the proving, it is the statement.

THe statement G exist, and it is True.

...We are therefore confronted with a proposition which
asserts its own unprovability. 15 rCa (G||del 1931:40-41)

You keep on repeating that, but show you don't know what it means,
proving your stupidity.

When we name this proposition G then a proof of G
would be a sequence of inference steps that prove
that they themselves do not exist.

Right, we name the proposition G.

Then we form a set of steps in M, the Meta-system that proves that G is
True.

And, the steps they prove do not exist, are those that live in the base
system F.

It is quite possible to travel at a speed in the "Meta-System" "Car"
that would be impossible to do in the base system "Tricycle".

Or, to life a 10 Ton block with a hydrolic crane that you could not life
with your bear hands.

You don't seem to understand the simple fact that there are two
different but related systems being talked about, because you are just
too stupid.

Sorry, you are just proving your stupidity, and the fact you don't even
try to answer the problem being pointed out, that you KNOW you are too
stupid, so you are just going to repeat your know lies because that is
all you can think of.

Anything that asserts its own non-existence
is necessarily incorrect.

Because it is true, and can be proven with the additional knowledge
and tools-a of the meta-system, it shows that without the addtional
knowledge and tools you can't make the proof.

It seems you don't understand that the base system and the meta system
are different.

Boy, are you stupid.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/31/2025 7:29 PM, Richard Damon wrote:

On 12/31/25 8:04 PM, olcott wrote:

On 12/31/2025 6:35 PM, Richard Damon wrote:

On 12/31/25 7:23 PM, olcott wrote:

On 12/31/2025 5:27 PM, Richard Damon wrote:

On 12/31/25 6:08 PM, olcott wrote:

On 12/31/2025 4:48 PM, Richard Damon wrote:

On 12/31/25 5:42 PM, olcott wrote:

On 12/31/2025 4:09 PM, Richard Damon wrote:

On 12/31/25 4:59 PM, olcott wrote:

On 12/31/2025 3:56 PM, Richard Damon wrote:

On 12/31/25 4:52 PM, olcott wrote:

On 12/31/2025 3:16 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote: >>>>>>>>>>>>>

[ ... ]
Then he defines a new system "P" which he uses to get even >>>>>>>>>>>>>> more muddled,
leaves out the crucial elements of his proof because it's >>>>>>>>>>>>>> too easy to
get wrong,

G||del, muddled? He was the most meticulous sonovabitch that >>>>>>>>>>>>> ever
lived!

and Stephen Meyer says he does get it wrong; he seems to be >>>>>>>>>>>>>> the only person in the world that ever checked.

People have misunderstood G||del and proved it by their >>>>>>>>>>>>> comments.
I don't know who Stephen Meyer is; my money is on G||del. >>>>>>>>>>>>>

G||del proved that there cannot possibly exist any
sequence of inference steps in F prove that they
themselves do not exist.

No *FINITE* sequence of inference steps.

Nothing can prove that itself does not
exist because that forms proof that it
does exist, dumbo.

So you are just ignoring context because you are stupid.

The statement, with the added information of the meta-system >>>>>>>>> proves (by a proof in the meta system) that the statment is true. >>>>>>>>>

Something else can prove that X cannot prove that
X does not exist, AKA your meta-system.

Nothing can directly prove that itself does not
exist because this forms proof that it does exist.

Nope, got a source for that?

Why does my explanation not work?

It is not that your explanation doesn't work.
It is that it ignores the root cause of why
G is unprovable in F.

So, how do you think you can prove it in F?

Nothing can prove that itself does not exist.
Any such proof would be self-refuting.

But it isn't the PROOF that does the proving, it is the statement.

THe statement G exist, and it is True.

...We are therefore confronted with a proposition which
asserts its own unprovability. 15 rCa (G||del 1931:40-41)

You keep on repeating that, but show you don't know what it means,
proving your stupidity.

It can only mean one thing when taken 100% literally.

a proposition which asserts its own unprovability.
G says that itself is unprovable

G says that itself has no sequence of inference
steps that prove that they themselves do not exist.

It say nothing at all about any meta-system.
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/31/25 9:15 PM, olcott wrote:

On 12/31/2025 7:29 PM, Richard Damon wrote:

On 12/31/25 8:04 PM, olcott wrote:

On 12/31/2025 6:35 PM, Richard Damon wrote:

On 12/31/25 7:23 PM, olcott wrote:

On 12/31/2025 5:27 PM, Richard Damon wrote:

On 12/31/25 6:08 PM, olcott wrote:

On 12/31/2025 4:48 PM, Richard Damon wrote:

On 12/31/25 5:42 PM, olcott wrote:

On 12/31/2025 4:09 PM, Richard Damon wrote:

On 12/31/25 4:59 PM, olcott wrote:

On 12/31/2025 3:56 PM, Richard Damon wrote:

On 12/31/25 4:52 PM, olcott wrote:

On 12/31/2025 3:16 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote: >>>>>>>>>>>>>>

[ ... ]
Then he defines a new system "P" which he uses to get >>>>>>>>>>>>>>> even more muddled,
leaves out the crucial elements of his proof because it's >>>>>>>>>>>>>>> too easy to
get wrong,

G||del, muddled? He was the most meticulous sonovabitch >>>>>>>>>>>>>> that ever
lived!

and Stephen Meyer says he does get it wrong; he seems to be >>>>>>>>>>>>>>> the only person in the world that ever checked.

People have misunderstood G||del and proved it by their >>>>>>>>>>>>>> comments.
I don't know who Stephen Meyer is; my money is on G||del. >>>>>>>>>>>>>>

G||del proved that there cannot possibly exist any
sequence of inference steps in F prove that they
themselves do not exist.

No *FINITE* sequence of inference steps.

Nothing can prove that itself does not
exist because that forms proof that it
does exist, dumbo.

So you are just ignoring context because you are stupid.

The statement, with the added information of the meta-system >>>>>>>>>> proves (by a proof in the meta system) that the statment is true. >>>>>>>>>>

Something else can prove that X cannot prove that
X does not exist, AKA your meta-system.

Nothing can directly prove that itself does not
exist because this forms proof that it does exist.

Nope, got a source for that?

Why does my explanation not work?

It is not that your explanation doesn't work.
It is that it ignores the root cause of why
G is unprovable in F.

So, how do you think you can prove it in F?

Nothing can prove that itself does not exist.
Any such proof would be self-refuting.

But it isn't the PROOF that does the proving, it is the statement.

THe statement G exist, and it is True.

...We are therefore confronted with a proposition which
asserts its own unprovability. 15 rCa (G||del 1931:40-41)

You keep on repeating that, but show you don't know what it means,
proving your stupidity.

It can only mean one thing when taken 100% literally.

The problem is language is not to be taken "100% literally", and thus
you just show you don't understand how words have meaning.

a proposition which asserts its own unprovability.
G says that itself is unprovable

G says that itself has no sequence of inference
steps that prove that they themselves do not exist.

It say nothing at all about any meta-system.

Sure it does, as it is in the section talking about an analysis in the meta-syste

I guess you are just proving you are a total idiot with no understanding
of the structure of language, which is why your goal of trying to base
your logic on words and their meaning is so hilarious, since you neve runderstod the nature of language in the first place.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/31/2025 8:48 PM, Richard Damon wrote:

On 12/31/25 9:15 PM, olcott wrote:

On 12/31/2025 7:29 PM, Richard Damon wrote:

On 12/31/25 8:04 PM, olcott wrote:

On 12/31/2025 6:35 PM, Richard Damon wrote:

On 12/31/25 7:23 PM, olcott wrote:

On 12/31/2025 5:27 PM, Richard Damon wrote:

On 12/31/25 6:08 PM, olcott wrote:

On 12/31/2025 4:48 PM, Richard Damon wrote:

On 12/31/25 5:42 PM, olcott wrote:

On 12/31/2025 4:09 PM, Richard Damon wrote:

On 12/31/25 4:59 PM, olcott wrote:

On 12/31/2025 3:56 PM, Richard Damon wrote:

On 12/31/25 4:52 PM, olcott wrote:

On 12/31/2025 3:16 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote: >>>>>>>>>>>>>>>

[ ... ]
Then he defines a new system "P" which he uses to get >>>>>>>>>>>>>>>> even more muddled,
leaves out the crucial elements of his proof because >>>>>>>>>>>>>>>> it's too easy to
get wrong,

G||del, muddled? He was the most meticulous sonovabitch >>>>>>>>>>>>>>> that ever
lived!

and Stephen Meyer says he does get it wrong; he seems to be >>>>>>>>>>>>>>>> the only person in the world that ever checked. >>>>>>>>>>>>>>>

People have misunderstood G||del and proved it by their >>>>>>>>>>>>>>> comments.
I don't know who Stephen Meyer is; my money is on G||del. >>>>>>>>>>>>>>>

G||del proved that there cannot possibly exist any >>>>>>>>>>>>>> sequence of inference steps in F prove that they
themselves do not exist.

No *FINITE* sequence of inference steps.

Nothing can prove that itself does not
exist because that forms proof that it
does exist, dumbo.

So you are just ignoring context because you are stupid. >>>>>>>>>>>
The statement, with the added information of the meta-system >>>>>>>>>>> proves (by a proof in the meta system) that the statment is >>>>>>>>>>> true.

Something else can prove that X cannot prove that
X does not exist, AKA your meta-system.

Nothing can directly prove that itself does not
exist because this forms proof that it does exist.

Nope, got a source for that?

Why does my explanation not work?

It is not that your explanation doesn't work.
It is that it ignores the root cause of why
G is unprovable in F.

So, how do you think you can prove it in F?

Nothing can prove that itself does not exist.
Any such proof would be self-refuting.

But it isn't the PROOF that does the proving, it is the statement.

THe statement G exist, and it is True.

...We are therefore confronted with a proposition which
asserts its own unprovability. 15 rCa (G||del 1931:40-41)

You keep on repeating that, but show you don't know what it means,
proving your stupidity.

It can only mean one thing when taken 100% literally.

The problem is language is not to be taken "100% literally", and thus
you just show you don't understand how words have meaning.

Formal mathematical specifications are taken literally or incorrectly.

a proposition which asserts its own unprovability.
G says that itself is unprovable

G says that itself has no sequence of inference
steps that prove that they themselves do not exist.

"a proposition which asserts its own unprovability."
says nothing at all about any meta-system.

a proposition which asserts its own unprovability.
G says that itself is unprovable

G says that itself has no sequence of inference
steps that prove that they themselves do not exist.

It say nothing at all about any meta-system.

Sure it does, as it is in the section talking about an analysis in the meta-syste

I guess you are just proving you are a total idiot with no understanding
of the structure of language, which is why your goal of trying to base
your logic on words and their meaning is so hilarious, since you neve runderstod the nature of language in the first place.

--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 31/12/2025 21:16, Pierre Asselin wrote:

In sci.logic Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

[ ... ]
Then he defines a new system "P" which he uses to get even more muddled,
leaves out the crucial elements of his proof because it's too easy to
get wrong,

G||del, muddled? He was the most meticulous sonovabitch that ever
lived!

Have you heard about his musings on God?

and Stephen Meyer says he does get it wrong; he seems to be
the only person in the world that ever checked.

People have misunderstood G||del and proved it by their comments.
I don't know who Stephen Meyer is; my money is on G||del.

I misremembered, it was James Meyer. He has a website on it http://www.jamesrmeyer.com . He's very angry about people telling him
he's wrong but who never checked like he did because they keep telling
him reasons it's right that he's certain are not reflected in the actual
work.
--
Tristan Wibberley

The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 1/1/26 12:03 AM, olcott wrote:

On 12/31/2025 8:48 PM, Richard Damon wrote:

On 12/31/25 9:15 PM, olcott wrote:

On 12/31/2025 7:29 PM, Richard Damon wrote:

On 12/31/25 8:04 PM, olcott wrote:

On 12/31/2025 6:35 PM, Richard Damon wrote:

On 12/31/25 7:23 PM, olcott wrote:

On 12/31/2025 5:27 PM, Richard Damon wrote:

On 12/31/25 6:08 PM, olcott wrote:

On 12/31/2025 4:48 PM, Richard Damon wrote:

On 12/31/25 5:42 PM, olcott wrote:

On 12/31/2025 4:09 PM, Richard Damon wrote:

On 12/31/25 4:59 PM, olcott wrote:

On 12/31/2025 3:56 PM, Richard Damon wrote:

On 12/31/25 4:52 PM, olcott wrote:

On 12/31/2025 3:16 PM, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote: >>>>>>>>>>>>>>>>

[ ... ]
Then he defines a new system "P" which he uses to get >>>>>>>>>>>>>>>>> even more muddled,
leaves out the crucial elements of his proof because >>>>>>>>>>>>>>>>> it's too easy to
get wrong,

G||del, muddled? He was the most meticulous sonovabitch >>>>>>>>>>>>>>>> that ever
lived!

and Stephen Meyer says he does get it wrong; he seems >>>>>>>>>>>>>>>>> to be
the only person in the world that ever checked. >>>>>>>>>>>>>>>>

People have misunderstood G||del and proved it by their >>>>>>>>>>>>>>>> comments.
I don't know who Stephen Meyer is; my money is on G||del. >>>>>>>>>>>>>>>>

G||del proved that there cannot possibly exist any >>>>>>>>>>>>>>> sequence of inference steps in F prove that they >>>>>>>>>>>>>>> themselves do not exist.

No *FINITE* sequence of inference steps.

Nothing can prove that itself does not
exist because that forms proof that it
does exist, dumbo.

So you are just ignoring context because you are stupid. >>>>>>>>>>>>
The statement, with the added information of the meta-system >>>>>>>>>>>> proves (by a proof in the meta system) that the statment is >>>>>>>>>>>> true.

Something else can prove that X cannot prove that
X does not exist, AKA your meta-system.

Nothing can directly prove that itself does not
exist because this forms proof that it does exist.

Nope, got a source for that?

Why does my explanation not work?

It is not that your explanation doesn't work.
It is that it ignores the root cause of why
G is unprovable in F.

So, how do you think you can prove it in F?

Nothing can prove that itself does not exist.
Any such proof would be self-refuting.

But it isn't the PROOF that does the proving, it is the statement. >>>>>>
THe statement G exist, and it is True.

...We are therefore confronted with a proposition which
asserts its own unprovability. 15 rCa (G||del 1931:40-41)

You keep on repeating that, but show you don't know what it means,
proving your stupidity.

It can only mean one thing when taken 100% literally.

The problem is language is not to be taken "100% literally", and thus
you just show you don't understand how words have meaning.

Formal mathematical specifications are taken literally or incorrectly.

Which only applies to formal mathematical specifications, and not to
just natural language statements made in a paper.

a proposition which asserts its own unprovability.
G says that itself is unprovable

Which is a Natural Language interpretation of the Formal Mathematical statement which G is, based on the additional meaning it obtains from
the mete system M.

G is actually a preposition about the non-existance of a Natural Number
g that satisfies a particular mathematical relationship. That
relationship in F is just some complicated formula that can be evaluated
for any Natural Number, but the meta-system M understands that encoded
into this formula is a proof checker of proofs of the statement G
encoded into a number by rules in M of proofs in F.

G says that itself has no sequence of inference
steps that prove that they themselves do not exist.

Yes, from knowledge obtain in M, we can understand G to mean that there
is no sequence if F that proves it.

You seem to be confusing the sequence of steps which prove a statement
with the statement itself.

Typical of you, as you have shown you don't know what "Proof" means,
amoung your many other misunderstood words.

"a proposition which asserts its own unprovability."
says nothing at all about any meta-system.

Because you are taking the statement out of its context.

I guess you just just don't understand how languages work.

Note, even formal mathematical specifications will depend on context,
and most won't indicate what system they are made in, but that comes out
of the context they were made in.

All you are doing is proving that you are dumber that even the AI LLMs
that you praise, because at least they look at tbe full context of a
sttaement (even if only mechanically).

Thus, you prove that you are just an ignorant pathological liar.

a proposition which asserts its own unprovability.
G says that itself is unprovable

G says that itself has no sequence of inference
steps that prove that they themselves do not exist.

It say nothing at all about any meta-system.

Sure it does, as it is in the section talking about an analysis in the
meta-syste

I guess you are just proving you are a total idiot with no
understanding of the structure of language, which is why your goal of
trying to base your logic on words and their meaning is so hilarious,
since you neve runderstod the nature of language in the first place.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 1/1/26 5:41 AM, Tristan Wibberley wrote:

On 31/12/2025 21:16, Pierre Asselin wrote:

In sci.logic Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

[ ... ]
Then he defines a new system "P" which he uses to get even more muddled, >>> leaves out the crucial elements of his proof because it's too easy to
get wrong,

G||del, muddled? He was the most meticulous sonovabitch that ever
lived!

Have you heard about his musings on God?

and Stephen Meyer says he does get it wrong; he seems to be
the only person in the world that ever checked.

People have misunderstood G||del and proved it by their comments.
I don't know who Stephen Meyer is; my money is on G||del.

I misremembered, it was James Meyer. He has a website on it http://www.jamesrmeyer.com . He's very angry about people telling him
he's wrong but who never checked like he did because they keep telling
him reasons it's right that he's certain are not reflected in the actual work.

In other words, since he doesn't understand it, it must be wrong.


Since his page begins with a rejection of the axiom of Choice, and the
example he gives, it shows a limitation in his ability to understand the nature of infinite systems.

To expect that infinite systems behave just like we see finite systems
work is a funamental error.

Yes, it seems to create paradoxes, but those paradoxes are only apparent
due to the lack of understanding about the actual nature of infinite sets.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 1/1/26 9:34 AM, Richard Damon wrote:

On 1/1/26 5:41 AM, Tristan Wibberley wrote:

On 31/12/2025 21:16, Pierre Asselin wrote:

In sci.logic Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

[ ... ]
Then he defines a new system "P" which he uses to get even more
muddled,
leaves out the crucial elements of his proof because it's too easy to
get wrong,

G||del, muddled? He was the most meticulous sonovabitch that ever
lived!

Have you heard about his musings on God?

and Stephen Meyer says he does get it wrong; he seems to be
the only person in the world that ever checked.

People have misunderstood G||del and proved it by their comments.
I don't know who Stephen Meyer is; my money is on G||del.

I misremembered, it was James Meyer. He has a website on it
http://www.jamesrmeyer.com . He's very angry about people telling him
he's wrong but who never checked like he did because they keep telling
him reasons it's right that he's certain are not reflected in the actual
work.

i tried to talk to that fool. he banned me pretty quickly so obviously
it's a fucking idiot

In other words, since he doesn't understand it, it must be wrong.

Since his page begins with a rejection of the axiom of Choice, and the example he gives, it shows a limitation in his ability to understand the nature of infinite systems.

To expect that infinite systems behave just like we see finite systems
work is a funamental error.

Yes, it seems to create paradoxes, but those paradoxes are only apparent
due to the lack of understanding about the actual nature of infinite sets.

--
a burnt out swe investigating into why our tooling doesn't involve
basic semantic proofs like halting analysis

please excuse my pseudo-pyscript,

~ nick
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 31/12/2025 23:27, Richard Damon wrote:

So, how do you think you can prove it in F?

What does "F" refer to?
--
Tristan Wibberley

The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

--- Synchronet 3.21a-Linux NewsLink 1.2