On 04/15/2026 10:18 AM, olcott wrote:
On 4/15/2026 11:35 AM, Ross Finlayson wrote:
On 04/15/2026 09:17 AM, olcott wrote:
On 4/15/2026 11:06 AM, Ross Finlayson wrote:
On 04/15/2026 08:49 AM, olcott wrote:
On 4/15/2026 10:15 AM, Ross Finlayson wrote:
On 04/14/2026 05:09 AM, Ross Finlayson wrote:
On 04/13/2026 11:34 PM, Mikko wrote:
On 13/04/2026 17:52, olcott wrote:
On 4/13/2026 2:05 AM, Mikko wrote:
On 12/04/2026 16:22, olcott wrote:
On 4/12/2026 4:32 AM, Mikko wrote:
On 11/04/2026 17:27, olcott wrote:
On 4/11/2026 3:06 AM, Mikko wrote:
On 09/04/2026 16:35, olcott wrote:
On 4/9/2026 4:08 AM, Mikko wrote:
On 08/04/2026 14:52, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 05/04/2026 14:25, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 4/5/2026 2:05 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 04/04/2026 19:23, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 4/4/2026 2:53 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 03/04/2026 16:35, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/3/2026 2:13 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 02/04/2026 23:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> To be able to properly ground this in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> existing
That's mainly true. However, in como.lang.prolog >>>>>>>>>>>>>>>>>>>>>>>>> thefoundationalDo you think 100 years would be enough, or at >>>>>>>>>>>>>>>>>>>>>>>>>>>>> least
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
some finite time?
I have to carefully study at least a dozen >>>>>>>>>>>>>>>>>>>>>>>>>>>> papers
that may average 15 pages each. The basic >>>>>>>>>>>>>>>>>>>>>>>>>>>> notion
of a "well founded justification tree" >>>>>>>>>>>>>>>>>>>>>>>>>>>> essentially
means the Proof Theoretic notion of >>>>>>>>>>>>>>>>>>>>>>>>>>>> reduction to
a Canonical proof.
% This sentence is not true. >>>>>>>>>>>>>>>>>>>>>>>>>> ?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you >>>>>>>>>>>>>>>>>>>>>>>>>>> should
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>>>>>>>>>
have two examples:
one with a negative result (as above) and one >>>>>>>>>>>>>>>>>>>>>>>>>>> with a
positive one.
So the above example should be paired with one >>>>>>>>>>>>>>>>>>>>>>>>>>> that
has someting
else in place of not(provable(F, G)) so that the >>>>>>>>>>>>>>>>>>>>>>>>>>> result will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING >>>>>>>>>>>>>>>>>>>>>>>>>
discussion should
be restricted to Prolog specific things, in this >>>>>>>>>>>>>>>>>>>>>>>>> case
to the Prolog
example above and the contrasting Prolog example >>>>>>>>>>>>>>>>>>>>>>>>> not
yet shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>>>>>>>>>> are the options that I have been considering. >>>>>>>>>>>>>>>>>>>>>>>>
The notion of how a well-founded justification tree >>>>>>>>>>>>>>>>>>>>>>>> eliminates undecidability is a key element of my >>>>>>>>>>>>>>>>>>>>>>>> system.
Prolog shows this best.
It is not Prolog computable to determine whether a >>>>>>>>>>>>>>>>>>>>>>> sentence of Peano
arithmetic has a well-founded justification tree in >>>>>>>>>>>>>>>>>>>>>>> Peano
arithmetic.
A formal language similar to Prolog that can >>>>>>>>>>>>>>>>>>>>>> represent
all of the semantics of PA can be developed so that >>>>>>>>>>>>>>>>>>>>>> it detects and rejects expressions that lack >>>>>>>>>>>>>>>>>>>>>> well-founded
justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>> is a function of the Prolog language that >>>>>>>>>>>>>>>>>>>> implements the algorithm.
No, it is not. The question whether a sentence has a >>>>>>>>>>>>>>>>>>> well-founded
justification tree is a question about one thing so it >>>>>>>>>>>>>>>>>>> needs an
algrotim that takes only one input but
uunify_with_occurs_check
takes two.
The number of inputs does not matter.
It certainly does. You can't use
unify_with_occurs_check to
determine
whether reCx reCy (x + y = y + x) has a well-founded >>>>>>>>>>>>>>>>> justification
tree.
[00] reCx
-a roe
-a rooroCroCroCroCroC> [01] reCy
-a-a-a-a-a-a-a-a-a-a roe
-a-a-a-a-a-a-a-a-a-a rooroCroCroCroCroC> [02] Equals >>>>>>>>>>>>>>>> -a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roLroCroCroCroCroC> [03] add (Left)
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a roe >>>>>>>>>>>>>>>> -a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a roLroCroCroCroCroC> [05] x-a <roE
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a rooroCroCroCroCroC> [06] y-a <ro+roCroE
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe roe (Shared
Pointers)
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a rooroCroCroCroCroC> [04] add (Right)-a roe roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roLroCroCroCroCroCroC> [06] y roCroy roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a rooroCroCroCroCroCroC> [05] x roCroCroCroy
There are no cycles in this tree
Can we interprete this to mean that you admit that the >>>>>>>>>>>>>>> predicate
unify_with_occurs_check is not useful for determination >>>>>>>>>>>>>>> whether
reCx reCy (x + y = y + x) has a well-founded justification >>>>>>>>>>>>>>> tree ?
My example was to merely prove that the Liar Paradox >>>>>>>>>>>>>> has never been anything besides incoherent nonsense. >>>>>>>>>>>>>> I showed this in an existing well understood logic >>>>>>>>>>>>>> programming language.
I.e., yes, we can interprete your diagram to mean that you >>>>>>>>>>>>> admit
that
the predicate unify_with_occurs_check is not useful for >>>>>>>>>>>>> determination
whether reCx reCy (x + y = y + x) has a well-founded justification
tree.
Consequently, you agree that your claims to the contrary were >>>>>>>>>>>>> false.
I started with the most salient case within
the most well-known language that can prove
my point. T^he above case if my own Minimal Type
Theory.
Olcott's Minimal Type Theory
G rao -4Prov[PA](riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov[PA]-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle
Nice to see that you don't disagree.
When you understand proof theoretic semantics well
enough then you understand that within the coherent
foundation of PTS G||del 1931 Incompleteness becomes
an instance of incoherent semantics.
An ad-hominem with an unproven premise disqualifies your comment. >>>>>>>>> Though an ad-hominem would disqualify it even if the premise were >>>>>>>>> proven.
Wikipedia has a page about rhetorical fallacies.
https://en.wikipedia.org/wiki/Fallacy
https://en.wikipedia.org/wiki/List_of_fallacies
These are parts of greater accounts of deductive inference
to allay and prevent failures or sabotage of inductive inference, >>>>>>>> the "invincible" ignorance of inductive inference.
This then makes for "two wrongs does not make a right".
The usual account of "axioms" must be distinguished into
at least two kinds: those that "expand comprehension",
and those that "restrict comprehension". Basically one has
that under expansion-of-comprehension, that alternatives
or inverses exist, the other restriction-of-comprehension,
that one or the other doesn't exist.
"Inductive inference" isn't a lie, though, given a lie,
it can't tell the truth.
Then, Wikipedia also has a page about paradox.
https://en.wikipedia.org/wiki/Paradox
https://en.wikipedia.org/wiki/List_of_paradoxes
Then, paradoxes are usually enough given as results of
logic, here about logical paradoxes that would find themselves >>>>>>>> in any theory, not about conflicting theories tangentially
relevant each other, those just being a model of conflicting
theories.
So, about resolving the paradoxes of logic, like Russell
and Burali-Forti and Cantor the paradoxes, these being
references to modern accounts of logic, and about the
Barber and the Heap and the Liar, these being references
to classical expositions of logic, has that eventually any
sort of restriction of comprehension in the universe of
logical objects may thusly be found by expansion of comprehension >>>>>>>> in the universe of logical objects to be contradicted.
So, it's known since antiquity that any sort of inductive
account can be broken.
Then, these "inductive impasses", must need make for
"analytical bridges", where there's a very particular
account of the primeval of the primary, about a universe
of truth already, else any sort of account of axiomatics
with restriction-of-comprehension is broken, instead of
merely being an example of perspective and thus limited
perspective.
So, the account of Pete Olcott is just a crank's/troll's/bot's >>>>>>>> account, adding more restriction-of-comprehension above a
perceived "foundation" that's a false floor, futile and
doomed to fail, while yet simply enough making a claim
that "if it's not wrong it's not wrong", then furthermore
more or less saying "can't tell the difference between
fallacy and paradox and truth".
Here then we may have a modal temporal relevance logic
and a theory where classical logic is modal and excludes
the "material implication" since Chrysippus, and to re-name
the usual account of 20'th century "classical logic" as instead >>>>>>>> along the lines of "Philo's Plotinus' Occam's Compte's Boole's >>>>>>>> Russell's Carnap's nominalist fictionalist logicist positivist >>>>>>>> Tarski's Goedel's quasi-modal account of logic and truth", that >>>>>>>> "Olcott's Goedel's" is yet another account of the quasi-modal. >>>>>>>>
So, it's a crank's/troll's/bot's, sometimes easier just
not to feed it. That said, it's a ready interpretation from
something like modern accounts of inference that simply employ >>>>>>>> quasi-modal logic throughout and suggest thusly tabulating fact >>>>>>>> after fact as truth, and making the fallacy of calling that
"monotonicity" and "entailment", which would be a lie, or as
with regards to contradicting either the competency or veracity, >>>>>>>> of such accounts.
So, PO's futile flailings are just a reflection on the current >>>>>>>> intellectual inertia about the quasi-modal logic, which taking >>>>>>>> a partial account of a partial account, wronged itself twice.
"The notion of a well-founded justification tree
will be fully elaborated."
A finite back-chained inference from the expression
to its axioms. As shown below in MTT the absence of
cycles in the directed graph of the expressions
evaluation sequence.
% This sentence cannot be proven in F
?- G = not(provable(F, G)).
G = not(provable(F, G)).
?- unify_with_occurs_check(G, not(provable(F, G))).
false.
https://www.swi-prolog.org/pldoc/man?
predicate=unify_with_occurs_check/2
Olcott's Minimal Type Theory
G rao -4Prov[PA](riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov[PA]-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle
No, a deductive account about the possibilities and limits of
inductive inference, helping explain any super-classical result,
not just a rule-sniffing dog that follows its own brown nose.
Goedel's incompleteness result is much simpler after a simple
sort of account of quantification and the old "sputniks of
quantification", that readily demonstrate something like
Russell's paradox in account of ordinary arithmetic, for
what somebody like Mirimanoff calls the "extra-ordinary",
and Skolem constructs for fragments and extensions in the
ordinary account of usual model theory about models of integers,
then that Goedel's incompleteness basically gives limits of
applicability of _claims_, here emphasized the _claims_ as
being the proper word for accounts of inference over usual
sorts of nominalist fictionalist logicist positivists' theories.
Otherwise anybody can just come along and prove Russell wrong,
prove Cantor wrong, and otherwise without a paradox-free reason
its account thereof overall, has that "the notion of a well-founded
justification tree", about e-minimality usually enough, to
be _elaborated_, involves the _diligence_ and the _thoroughness_
of a conscientious account of the extra-ordinary, the super-standard, >>>>> and the reasoning for _continuity_, and, _infinity_.
This PO account used to be a bit more open-minded, now it's
quite firmly retro-finitist, the hall-mark of the crank and troll.
So, PO, if there is to be elaborated "well-founded justification
trees",
they live in a domain of discourse with other rulialities
than
well-foundedness/e-minimality/no-infinite-descending-epsilon-chains, >>>>> and
somehow in reality and in logic they _do_ all get along.
"E-laborated" means the diligent work was done,
the work was worked out of it, not just "defined" done.
You need an account that rejects quasi-modal logic or
else anyone can easily give innocuous non-facts that
define themselves "true".
It is best understood within the essential framework
of Prolog of back-chained inference from expressions
using Rules to reach Facts.
Prolog itself is far too weak to generalize this,
none-the-less the infrastructure of expressions
anchored in Facts and Rules does provide the complete
essence.
When we do it this way much of what has been misconstrued
as "undecidability" becomes expressions that are rejected
because they remain ungrounded in Facts.
This is not merely the foundations of math and logic
it is alternative foundations for math and logic that
reject and replace the conventional views.
I'd suggest not using the word "understood", with regards
to reasoning about _closures_ and furthermore _completions_,
with regards to things like "infinite limits" the completions.
Facts and rules for rules-engines and the like are very old-hat,
and contradictory rules
Are excluded.
in such accounts given un-true stated
"facts", besides that "facts" in such accounts are stipulated,
with regards to "verum" vis-a-vis "certum" and that it's only
conscientiously a _scientific_ account, con-scient-ious.
I don't speak Latin. These stipulated Facts are actually true
that is all that need be known about them.
The usual account of quasi-modal logic assumes that
_time has stopped and there is no change_,
the quasi-modal account itself is _not_ a temporal logic
and thusly _not_ a modal logic. Furthermore, the quasi-modal
logic's account of "monotonicity" fails, then that also
the "entailment" is not an apropos term, and besides usual
accounts of "garbage-in/garbage-out" is "crazy-in/crazy-out".
All we need to know that that the Facts are true Facts about general
knowledge.
So, math and logic have _infinity_ and _infinitary reasoning_,
they are _not_ going away.
Not when restricted to the finite list of true (atomic) Facts of general
knowledge.
What you got there is, at best, a calculus of closed-categories,
and if it's not extra-ordinary and super-standard, then it's not.
When closed-categories is referring to the Frege compositional meaning
and not some idiomatic term-of-the-art then yes closed-categories.
About "un-decide-ability", there's furthermore an even stronger
account of _independence_, the mathematical independence, since
I don't need to yet into the nuances of of terms-of-the-art
idiosyncrasies. Either an expression can be resolved to true
or false or it is not a member of the body of knowledge
expressed in language.
there are multiple laws of large numbers, and that measure theory
makes for quasi-invariant measure theory, since doubling/halving
spaces/measures make for the re-Vitali-ization of measure theory
about Vitali and Hausdorff and equi-decomposability, and for
analysts about competing accounts of _convergence_ and _emergence_,
that it is _real_ that some accounts of naive uniqueness instead
are ascribed particular distinctness, about real completions in
the objects of mathematics, beyond "not enough information".
If expressions cannot reach Facts using Rules then they
are out-of-scope. In this case the Rules are full natural
language semantics specified syntactically.
So, your usage of the words is unfortunately poisoned by the
fact that quasi-modal logic makes you think "material implication"
is a thing and that it does the thing, when it is not and does not.
My whole system is constructed entirely on the
basis of A is a necessary consequence of B.
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
Disjunction introduction is totally rejected.
Material implication may be entirely rejected.
Your somewhat convoluted language seems to mostly miss the
point of the barest essence of
"true on the basis of meaning expressed in language"
That's a usual account of "true" in common sense,
then though _all_ the mathematics and logic of
the infinite and infinitary bring _all_ their
matters of rigor resolving paradox for _any_
sorts formal accounts.
Or, "math is hard".
"True on the basis of meaning is true" is a sort
of coherent, pragmatist, correspondence definition
of truth, while though here there's always that
"is" is what "is" is.
Saying that a system is "whole" does not give that
it's "complete". Furthermore, matters of the
continuous and infinite must make for the "replete".
On 4/15/2026 12:33 PM, Ross Finlayson wrote:
On 04/15/2026 10:18 AM, olcott wrote:
On 4/15/2026 11:35 AM, Ross Finlayson wrote:
On 04/15/2026 09:17 AM, olcott wrote:
On 4/15/2026 11:06 AM, Ross Finlayson wrote:
On 04/15/2026 08:49 AM, olcott wrote:
On 4/15/2026 10:15 AM, Ross Finlayson wrote:
On 04/14/2026 05:09 AM, Ross Finlayson wrote:
On 04/13/2026 11:34 PM, Mikko wrote:
On 13/04/2026 17:52, olcott wrote:
On 4/13/2026 2:05 AM, Mikko wrote:
On 12/04/2026 16:22, olcott wrote:
On 4/12/2026 4:32 AM, Mikko wrote:
On 11/04/2026 17:27, olcott wrote:
On 4/11/2026 3:06 AM, Mikko wrote:
On 09/04/2026 16:35, olcott wrote:
On 4/9/2026 4:08 AM, Mikko wrote:
On 08/04/2026 14:52, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 4/6/2026 3:27 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 05/04/2026 14:25, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 4/5/2026 2:05 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 04/04/2026 19:23, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/4/2026 2:53 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 03/04/2026 16:35, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/3/2026 2:13 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 02/04/2026 23:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> To be able to properly ground this in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> existing
That's mainly true. However, in como.lang.prolog >>>>>>>>>>>>>>>>>>>>>>>>>> thefoundationalDo you think 100 years would be enough, or at >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> least
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
some finite time?
I have to carefully study at least a dozen >>>>>>>>>>>>>>>>>>>>>>>>>>>>> papers
that may average 15 pages each. The basic >>>>>>>>>>>>>>>>>>>>>>>>>>>>> notion
of a "well founded justification tree" >>>>>>>>>>>>>>>>>>>>>>>>>>>>> essentially
means the Proof Theoretic notion of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> reduction to
a Canonical proof.
% This sentence is not true. >>>>>>>>>>>>>>>>>>>>>>>>>>> ?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you >>>>>>>>>>>>>>>>>>>>>>>>>>>> should
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>>>>>>>>>>
have two examples:
one with a negative result (as above) and one >>>>>>>>>>>>>>>>>>>>>>>>>>>> with a
positive one.
So the above example should be paired with one >>>>>>>>>>>>>>>>>>>>>>>>>>>> that
has someting
else in place of not(provable(F, G)) so that >>>>>>>>>>>>>>>>>>>>>>>>>>>> the
result will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING >>>>>>>>>>>>>>>>>>>>>>>>>>
discussion should
be restricted to Prolog specific things, in this >>>>>>>>>>>>>>>>>>>>>>>>>> case
to the Prolog
example above and the contrasting Prolog example >>>>>>>>>>>>>>>>>>>>>>>>>> not
yet shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning >>>>>>>>>>>>>>>>>>>>>>>>> Postulates,
the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>>>>>>>>>>> are the options that I have been considering. >>>>>>>>>>>>>>>>>>>>>>>>>
The notion of how a well-founded justification >>>>>>>>>>>>>>>>>>>>>>>>> tree
eliminates undecidability is a key element of my >>>>>>>>>>>>>>>>>>>>>>>>> system.
Prolog shows this best.
It is not Prolog computable to determine whether a >>>>>>>>>>>>>>>>>>>>>>>> sentence of Peano
arithmetic has a well-founded justification tree in >>>>>>>>>>>>>>>>>>>>>>>> Peano
arithmetic.
A formal language similar to Prolog that can >>>>>>>>>>>>>>>>>>>>>>> represent
all of the semantics of PA can be developed so that >>>>>>>>>>>>>>>>>>>>>>> it detects and rejects expressions that lack >>>>>>>>>>>>>>>>>>>>>>> well-founded
justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>>> is a function of the Prolog language that >>>>>>>>>>>>>>>>>>>>> implements the algorithm.
No, it is not. The question whether a sentence has a >>>>>>>>>>>>>>>>>>>> well-founded
justification tree is a question about one thing so it >>>>>>>>>>>>>>>>>>>> needs an
algrotim that takes only one input but >>>>>>>>>>>>>>>>>>>> uunify_with_occurs_check
takes two.
The number of inputs does not matter.
It certainly does. You can't use
unify_with_occurs_check to
determine
whether reCx reCy (x + y = y + x) has a well-founded >>>>>>>>>>>>>>>>>> justification
tree.
[00] reCx
roe
rooroCroCroCroCroC> [01] reCy
roe
rooroCroCroCroCroC> [02] Equals
roe
roLroCroCroCroCroC> [03] add (Left) >>>>>>>>>>>>>>>>> roe roe
roe roLroCroCroCroCroC> [05] x <roE
roe roe roe >>>>>>>>>>>>>>>>> roe rooroCroCroCroCroC> [06] y <ro+roCroE
roe roe roe (Shared
Pointers)
rooroCroCroCroCroC> [04] add (Right) roe roe
roe roe roe >>>>>>>>>>>>>>>>> roLroCroCroCroCroCroC> [06] y roCroy roe
roe roe >>>>>>>>>>>>>>>>> rooroCroCroCroCroCroC> [05] x roCroCroCroy
There are no cycles in this tree
Can we interprete this to mean that you admit that the >>>>>>>>>>>>>>>> predicate
unify_with_occurs_check is not useful for determination >>>>>>>>>>>>>>>> whether
reCx reCy (x + y = y + x) has a well-founded justification >>>>>>>>>>>>>>>> tree ?
My example was to merely prove that the Liar Paradox >>>>>>>>>>>>>>> has never been anything besides incoherent nonsense. >>>>>>>>>>>>>>> I showed this in an existing well understood logic >>>>>>>>>>>>>>> programming language.
I.e., yes, we can interprete your diagram to mean that you >>>>>>>>>>>>>> admit
that
the predicate unify_with_occurs_check is not useful for >>>>>>>>>>>>>> determination
whether reCx reCy (x + y = y + x) has a well-founded >>>>>>>>>>>>>> justification
tree.
Consequently, you agree that your claims to the contrary were >>>>>>>>>>>>>> false.
I started with the most salient case within
the most well-known language that can prove
my point. T^he above case if my own Minimal Type
Theory.
Olcott's Minimal Type Theory
G rao -4Prov[PA](riLGriY)
Directed Graph of evaluation sequence
00 rao 01 02
01 G
02 -4 03
03 Prov[PA] 04
04 G||del_Number_of 01 // cycle
Nice to see that you don't disagree.
When you understand proof theoretic semantics well
enough then you understand that within the coherent
foundation of PTS G||del 1931 Incompleteness becomes
an instance of incoherent semantics.
An ad-hominem with an unproven premise disqualifies your comment. >>>>>>>>>> Though an ad-hominem would disqualify it even if the premise were >>>>>>>>>> proven.
Wikipedia has a page about rhetorical fallacies.
https://en.wikipedia.org/wiki/Fallacy
https://en.wikipedia.org/wiki/List_of_fallacies
These are parts of greater accounts of deductive inference
to allay and prevent failures or sabotage of inductive inference, >>>>>>>>> the "invincible" ignorance of inductive inference.
This then makes for "two wrongs does not make a right".
The usual account of "axioms" must be distinguished into
at least two kinds: those that "expand comprehension",
and those that "restrict comprehension". Basically one has
that under expansion-of-comprehension, that alternatives
or inverses exist, the other restriction-of-comprehension,
that one or the other doesn't exist.
"Inductive inference" isn't a lie, though, given a lie,
it can't tell the truth.
Then, Wikipedia also has a page about paradox.
https://en.wikipedia.org/wiki/Paradox
https://en.wikipedia.org/wiki/List_of_paradoxes
Then, paradoxes are usually enough given as results of
logic, here about logical paradoxes that would find themselves >>>>>>>>> in any theory, not about conflicting theories tangentially
relevant each other, those just being a model of conflicting >>>>>>>>> theories.
So, about resolving the paradoxes of logic, like Russell
and Burali-Forti and Cantor the paradoxes, these being
references to modern accounts of logic, and about the
Barber and the Heap and the Liar, these being references
to classical expositions of logic, has that eventually any
sort of restriction of comprehension in the universe of
logical objects may thusly be found by expansion of comprehension >>>>>>>>> in the universe of logical objects to be contradicted.
So, it's known since antiquity that any sort of inductive
account can be broken.
Then, these "inductive impasses", must need make for
"analytical bridges", where there's a very particular
account of the primeval of the primary, about a universe
of truth already, else any sort of account of axiomatics
with restriction-of-comprehension is broken, instead of
merely being an example of perspective and thus limited
perspective.
So, the account of Pete Olcott is just a crank's/troll's/bot's >>>>>>>>> account, adding more restriction-of-comprehension above a
perceived "foundation" that's a false floor, futile and
doomed to fail, while yet simply enough making a claim
that "if it's not wrong it's not wrong", then furthermore
more or less saying "can't tell the difference between
fallacy and paradox and truth".
Here then we may have a modal temporal relevance logic
and a theory where classical logic is modal and excludes
the "material implication" since Chrysippus, and to re-name
the usual account of 20'th century "classical logic" as instead >>>>>>>>> along the lines of "Philo's Plotinus' Occam's Compte's Boole's >>>>>>>>> Russell's Carnap's nominalist fictionalist logicist positivist >>>>>>>>> Tarski's Goedel's quasi-modal account of logic and truth", that >>>>>>>>> "Olcott's Goedel's" is yet another account of the quasi-modal. >>>>>>>>>
So, it's a crank's/troll's/bot's, sometimes easier just
not to feed it. That said, it's a ready interpretation from
something like modern accounts of inference that simply employ >>>>>>>>> quasi-modal logic throughout and suggest thusly tabulating fact >>>>>>>>> after fact as truth, and making the fallacy of calling that
"monotonicity" and "entailment", which would be a lie, or as >>>>>>>>> with regards to contradicting either the competency or veracity, >>>>>>>>> of such accounts.
So, PO's futile flailings are just a reflection on the current >>>>>>>>> intellectual inertia about the quasi-modal logic, which taking >>>>>>>>> a partial account of a partial account, wronged itself twice. >>>>>>>>>
"The notion of a well-founded justification tree
will be fully elaborated."
A finite back-chained inference from the expression
to its axioms. As shown below in MTT the absence of
cycles in the directed graph of the expressions
evaluation sequence.
% This sentence cannot be proven in F
?- G = not(provable(F, G)).
G = not(provable(F, G)).
?- unify_with_occurs_check(G, not(provable(F, G))).
false.
https://www.swi-prolog.org/pldoc/man?
predicate=unify_with_occurs_check/2
Olcott's Minimal Type Theory
G rao -4Prov[PA](riLGriY)
Directed Graph of evaluation sequence
00 rao 01 02
01 G
02 -4 03
03 Prov[PA] 04
04 G||del_Number_of 01 // cycle
No, a deductive account about the possibilities and limits of
inductive inference, helping explain any super-classical result,
not just a rule-sniffing dog that follows its own brown nose.
Goedel's incompleteness result is much simpler after a simple
sort of account of quantification and the old "sputniks of
quantification", that readily demonstrate something like
Russell's paradox in account of ordinary arithmetic, for
what somebody like Mirimanoff calls the "extra-ordinary",
and Skolem constructs for fragments and extensions in the
ordinary account of usual model theory about models of integers,
then that Goedel's incompleteness basically gives limits of
applicability of _claims_, here emphasized the _claims_ as
being the proper word for accounts of inference over usual
sorts of nominalist fictionalist logicist positivists' theories.
Otherwise anybody can just come along and prove Russell wrong,
prove Cantor wrong, and otherwise without a paradox-free reason
its account thereof overall, has that "the notion of a well-founded >>>>>> justification tree", about e-minimality usually enough, to
be _elaborated_, involves the _diligence_ and the _thoroughness_
of a conscientious account of the extra-ordinary, the super-standard, >>>>>> and the reasoning for _continuity_, and, _infinity_.
This PO account used to be a bit more open-minded, now it's
quite firmly retro-finitist, the hall-mark of the crank and troll. >>>>>>
So, PO, if there is to be elaborated "well-founded justification
trees",
they live in a domain of discourse with other rulialities
than
well-foundedness/e-minimality/no-infinite-descending-epsilon-chains, >>>>>> and
somehow in reality and in logic they _do_ all get along.
"E-laborated" means the diligent work was done,
the work was worked out of it, not just "defined" done.
You need an account that rejects quasi-modal logic or
else anyone can easily give innocuous non-facts that
define themselves "true".
It is best understood within the essential framework
of Prolog of back-chained inference from expressions
using Rules to reach Facts.
Prolog itself is far too weak to generalize this,
none-the-less the infrastructure of expressions
anchored in Facts and Rules does provide the complete
essence.
When we do it this way much of what has been misconstrued
as "undecidability" becomes expressions that are rejected
because they remain ungrounded in Facts.
This is not merely the foundations of math and logic
it is alternative foundations for math and logic that
reject and replace the conventional views.
I'd suggest not using the word "understood", with regards
to reasoning about _closures_ and furthermore _completions_,
with regards to things like "infinite limits" the completions.
Facts and rules for rules-engines and the like are very old-hat,
and contradictory rules
Are excluded.
in such accounts given un-true stated
"facts", besides that "facts" in such accounts are stipulated,
with regards to "verum" vis-a-vis "certum" and that it's only
conscientiously a _scientific_ account, con-scient-ious.
I don't speak Latin. These stipulated Facts are actually true
that is all that need be known about them.
The usual account of quasi-modal logic assumes that
_time has stopped and there is no change_,
the quasi-modal account itself is _not_ a temporal logic
and thusly _not_ a modal logic. Furthermore, the quasi-modal
logic's account of "monotonicity" fails, then that also
the "entailment" is not an apropos term, and besides usual
accounts of "garbage-in/garbage-out" is "crazy-in/crazy-out".
All we need to know that that the Facts are true Facts about general
knowledge.
So, math and logic have _infinity_ and _infinitary reasoning_,
they are _not_ going away.
Not when restricted to the finite list of true (atomic) Facts of general >>> knowledge.
What you got there is, at best, a calculus of closed-categories,
and if it's not extra-ordinary and super-standard, then it's not.
When closed-categories is referring to the Frege compositional meaning
and not some idiomatic term-of-the-art then yes closed-categories.
About "un-decide-ability", there's furthermore an even stronger
account of _independence_, the mathematical independence, since
I don't need to yet into the nuances of of terms-of-the-art
idiosyncrasies. Either an expression can be resolved to true
or false or it is not a member of the body of knowledge
expressed in language.
there are multiple laws of large numbers, and that measure theory
makes for quasi-invariant measure theory, since doubling/halving
spaces/measures make for the re-Vitali-ization of measure theory
about Vitali and Hausdorff and equi-decomposability, and for
analysts about competing accounts of _convergence_ and _emergence_,
that it is _real_ that some accounts of naive uniqueness instead
are ascribed particular distinctness, about real completions in
the objects of mathematics, beyond "not enough information".
If expressions cannot reach Facts using Rules then they
are out-of-scope. In this case the Rules are full natural
language semantics specified syntactically.
So, your usage of the words is unfortunately poisoned by the
fact that quasi-modal logic makes you think "material implication"
is a thing and that it does the thing, when it is not and does not.
My whole system is constructed entirely on the
basis of A is a necessary consequence of B.
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
Disjunction introduction is totally rejected.
Material implication may be entirely rejected.
Your somewhat convoluted language seems to mostly miss the
point of the barest essence of
"true on the basis of meaning expressed in language"
That's a usual account of "true" in common sense,
then though _all_ the mathematics and logic of
the infinite and infinitary bring _all_ their
matters of rigor resolving paradox for _any_
sorts formal accounts.
Or, "math is hard".
"True on the basis of meaning is true" is a sort
of coherent, pragmatist, correspondence definition
of truth, while though here there's always that
"is" is what "is" is.
It took me 27 years to come up with this bridge between coherence/correspondence analytic/synthetic unifying
them into on single exact and precise perspective.
"true on the basis of meaning expressed in language"
expressed in language
expressed in language
expressed in language
Saying that a system is "whole" does not give that
it's "complete". Furthermore, matters of the
continuous and infinite must make for the "replete".
every single detail of general knowledge
"EXPRESSED IN LANGUAGE" can be encoded in my system
thus as complete as complete can possibly be.
Much of this must be algorithmically compressed
to make it finite.
On 04/15/2026 10:43 AM, olcott wrote:
On 4/15/2026 12:33 PM, Ross Finlayson wrote:
On 04/15/2026 10:18 AM, olcott wrote:
On 4/15/2026 11:35 AM, Ross Finlayson wrote:
On 04/15/2026 09:17 AM, olcott wrote:
On 4/15/2026 11:06 AM, Ross Finlayson wrote:
On 04/15/2026 08:49 AM, olcott wrote:
On 4/15/2026 10:15 AM, Ross Finlayson wrote:
On 04/14/2026 05:09 AM, Ross Finlayson wrote:
On 04/13/2026 11:34 PM, Mikko wrote:
On 13/04/2026 17:52, olcott wrote:
On 4/13/2026 2:05 AM, Mikko wrote:
On 12/04/2026 16:22, olcott wrote:
On 4/12/2026 4:32 AM, Mikko wrote:
On 11/04/2026 17:27, olcott wrote:
On 4/11/2026 3:06 AM, Mikko wrote:
On 09/04/2026 16:35, olcott wrote:
On 4/9/2026 4:08 AM, Mikko wrote:
On 08/04/2026 14:52, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 06/04/2026 14:21, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 4/6/2026 3:27 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 05/04/2026 14:25, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 4/5/2026 2:05 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 04/04/2026 19:23, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/4/2026 2:53 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 03/04/2026 16:35, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/3/2026 2:13 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 02/04/2026 23:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> To be able to properly ground this in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> existing
That's mainly true. However, in como.lang.prolog >>>>>>>>>>>>>>>>>>>>>>>>>>> theI have to carefully study at least a dozen >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> papersfoundationalDo you think 100 years would be enough, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or at
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
least
some finite time? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
that may average 15 pages each. The basic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> notion
of a "well founded justification tree" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> essentially
means the Proof Theoretic notion of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> reduction to
a Canonical proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
% This sentence is not true. >>>>>>>>>>>>>>>>>>>>>>>>>>>> ?- LP = not(true(LP)). >>>>>>>>>>>>>>>>>>>>>>>>>>>> LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you >>>>>>>>>>>>>>>>>>>>>>>>>>>>> should
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
have two examples:
one with a negative result (as above) and one >>>>>>>>>>>>>>>>>>>>>>>>>>>>> with a
positive one.
So the above example should be paired with one >>>>>>>>>>>>>>>>>>>>>>>>>>>>> that
has someting
else in place of not(provable(F, G)) so that >>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
result will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING >>>>>>>>>>>>>>>>>>>>>>>>>>>
discussion should
be restricted to Prolog specific things, in this >>>>>>>>>>>>>>>>>>>>>>>>>>> case
to the Prolog
example above and the contrasting Prolog example >>>>>>>>>>>>>>>>>>>>>>>>>>> not
yet shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning >>>>>>>>>>>>>>>>>>>>>>>>>> Postulates,
the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>>>>>>>>>>>> are the options that I have been considering. >>>>>>>>>>>>>>>>>>>>>>>>>>
The notion of how a well-founded justification >>>>>>>>>>>>>>>>>>>>>>>>>> tree
eliminates undecidability is a key element of my >>>>>>>>>>>>>>>>>>>>>>>>>> system.
Prolog shows this best.
It is not Prolog computable to determine whether a >>>>>>>>>>>>>>>>>>>>>>>>> sentence of Peano
arithmetic has a well-founded justification >>>>>>>>>>>>>>>>>>>>>>>>> tree in
Peano
arithmetic.
A formal language similar to Prolog that can >>>>>>>>>>>>>>>>>>>>>>>> represent
all of the semantics of PA can be developed so that >>>>>>>>>>>>>>>>>>>>>>>> it detects and rejects expressions that lack >>>>>>>>>>>>>>>>>>>>>>>> well-founded
justification trees.
A language does not detect. For detection you >>>>>>>>>>>>>>>>>>>>>>> need an
algorithm.
unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>>>> is a function of the Prolog language that >>>>>>>>>>>>>>>>>>>>>> implements the algorithm.
No, it is not. The question whether a sentence has a >>>>>>>>>>>>>>>>>>>>> well-founded
justification tree is a question about one thing so it >>>>>>>>>>>>>>>>>>>>> needs an
algrotim that takes only one input but >>>>>>>>>>>>>>>>>>>>> uunify_with_occurs_check
takes two.
The number of inputs does not matter.
It certainly does. You can't use
unify_with_occurs_check to
determine
whether reCx reCy (x + y = y + x) has a well-founded >>>>>>>>>>>>>>>>>>> justification
tree.
[00] reCx
-a roe
-a rooroCroCroCroCroC> [01] reCy
-a-a-a-a-a-a-a-a-a-a roe
-a-a-a-a-a-a-a-a-a-a rooroCroCroCroCroC> [02] Equals >>>>>>>>>>>>>>>>>> -a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe >>>>>>>>>>>>>>>>>> -a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roLroCroCroCroCroC> [03] add (Left)
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a roe >>>>>>>>>>>>>>>>>> -a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a roLroCroCroCroCroC> [05] x-a <roE
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a rooroCroCroCroCroC> [06] y-a <ro+roCroE
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe roe (Shared
Pointers)
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a rooroCroCroCroCroC> [04] add (Right)-a roe roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roLroCroCroCroCroCroC> [06] y roCroy roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a rooroCroCroCroCroCroC> [05] x roCroCroCroy
There are no cycles in this tree
Can we interprete this to mean that you admit that the >>>>>>>>>>>>>>>>> predicate
unify_with_occurs_check is not useful for determination >>>>>>>>>>>>>>>>> whether
reCx reCy (x + y = y + x) has a well-founded justification >>>>>>>>>>>>>>>>> tree ?
My example was to merely prove that the Liar Paradox >>>>>>>>>>>>>>>> has never been anything besides incoherent nonsense. >>>>>>>>>>>>>>>> I showed this in an existing well understood logic >>>>>>>>>>>>>>>> programming language.
I.e., yes, we can interprete your diagram to mean that you >>>>>>>>>>>>>>> admit
that
the predicate unify_with_occurs_check is not useful for >>>>>>>>>>>>>>> determination
whether reCx reCy (x + y = y + x) has a well-founded >>>>>>>>>>>>>>> justification
tree.
Consequently, you agree that your claims to the contrary >>>>>>>>>>>>>>> were
false.
I started with the most salient case within
the most well-known language that can prove
my point. T^he above case if my own Minimal Type
Theory.
Olcott's Minimal Type Theory
G rao -4Prov[PA](riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov[PA]-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle
Nice to see that you don't disagree.
When you understand proof theoretic semantics well
enough then you understand that within the coherent
foundation of PTS G||del 1931 Incompleteness becomes
an instance of incoherent semantics.
An ad-hominem with an unproven premise disqualifies your >>>>>>>>>>> comment.
Though an ad-hominem would disqualify it even if the premise >>>>>>>>>>> were
proven.
Wikipedia has a page about rhetorical fallacies.
https://en.wikipedia.org/wiki/Fallacy
https://en.wikipedia.org/wiki/List_of_fallacies
These are parts of greater accounts of deductive inference >>>>>>>>>> to allay and prevent failures or sabotage of inductive inference, >>>>>>>>>> the "invincible" ignorance of inductive inference.
This then makes for "two wrongs does not make a right".
The usual account of "axioms" must be distinguished into
at least two kinds: those that "expand comprehension",
and those that "restrict comprehension". Basically one has >>>>>>>>>> that under expansion-of-comprehension, that alternatives
or inverses exist, the other restriction-of-comprehension, >>>>>>>>>> that one or the other doesn't exist.
"Inductive inference" isn't a lie, though, given a lie,
it can't tell the truth.
Then, Wikipedia also has a page about paradox.
https://en.wikipedia.org/wiki/Paradox
https://en.wikipedia.org/wiki/List_of_paradoxes
Then, paradoxes are usually enough given as results of
logic, here about logical paradoxes that would find themselves >>>>>>>>>> in any theory, not about conflicting theories tangentially >>>>>>>>>> relevant each other, those just being a model of conflicting >>>>>>>>>> theories.
So, about resolving the paradoxes of logic, like Russell
and Burali-Forti and Cantor the paradoxes, these being
references to modern accounts of logic, and about the
Barber and the Heap and the Liar, these being references
to classical expositions of logic, has that eventually any >>>>>>>>>> sort of restriction of comprehension in the universe of
logical objects may thusly be found by expansion of comprehension >>>>>>>>>> in the universe of logical objects to be contradicted.
So, it's known since antiquity that any sort of inductive
account can be broken.
Then, these "inductive impasses", must need make for
"analytical bridges", where there's a very particular
account of the primeval of the primary, about a universe
of truth already, else any sort of account of axiomatics
with restriction-of-comprehension is broken, instead of
merely being an example of perspective and thus limited
perspective.
So, the account of Pete Olcott is just a crank's/troll's/bot's >>>>>>>>>> account, adding more restriction-of-comprehension above a
perceived "foundation" that's a false floor, futile and
doomed to fail, while yet simply enough making a claim
that "if it's not wrong it's not wrong", then furthermore
more or less saying "can't tell the difference between
fallacy and paradox and truth".
Here then we may have a modal temporal relevance logic
and a theory where classical logic is modal and excludes
the "material implication" since Chrysippus, and to re-name >>>>>>>>>> the usual account of 20'th century "classical logic" as instead >>>>>>>>>> along the lines of "Philo's Plotinus' Occam's Compte's Boole's >>>>>>>>>> Russell's Carnap's nominalist fictionalist logicist positivist >>>>>>>>>> Tarski's Goedel's quasi-modal account of logic and truth", that >>>>>>>>>> "Olcott's Goedel's" is yet another account of the quasi-modal. >>>>>>>>>>
So, it's a crank's/troll's/bot's, sometimes easier just
not to feed it. That said, it's a ready interpretation from >>>>>>>>>> something like modern accounts of inference that simply employ >>>>>>>>>> quasi-modal logic throughout and suggest thusly tabulating fact >>>>>>>>>> after fact as truth, and making the fallacy of calling that >>>>>>>>>> "monotonicity" and "entailment", which would be a lie, or as >>>>>>>>>> with regards to contradicting either the competency or veracity, >>>>>>>>>> of such accounts.
So, PO's futile flailings are just a reflection on the current >>>>>>>>>> intellectual inertia about the quasi-modal logic, which taking >>>>>>>>>> a partial account of a partial account, wronged itself twice. >>>>>>>>>>
"The notion of a well-founded justification tree
will be fully elaborated."
A finite back-chained inference from the expression
to its axioms. As shown below in MTT the absence of
cycles in the directed graph of the expressions
evaluation sequence.
% This sentence cannot be proven in F
?- G = not(provable(F, G)).
G = not(provable(F, G)).
?- unify_with_occurs_check(G, not(provable(F, G))).
false.
https://www.swi-prolog.org/pldoc/man?
predicate=unify_with_occurs_check/2
Olcott's Minimal Type Theory
G rao -4Prov[PA](riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov[PA]-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle
No, a deductive account about the possibilities and limits of
inductive inference, helping explain any super-classical result, >>>>>>> not just a rule-sniffing dog that follows its own brown nose.
Goedel's incompleteness result is much simpler after a simple
sort of account of quantification and the old "sputniks of
quantification", that readily demonstrate something like
Russell's paradox in account of ordinary arithmetic, for
what somebody like Mirimanoff calls the "extra-ordinary",
and Skolem constructs for fragments and extensions in the
ordinary account of usual model theory about models of integers, >>>>>>> then that Goedel's incompleteness basically gives limits of
applicability of _claims_, here emphasized the _claims_ as
being the proper word for accounts of inference over usual
sorts of nominalist fictionalist logicist positivists' theories. >>>>>>>
Otherwise anybody can just come along and prove Russell wrong,
prove Cantor wrong, and otherwise without a paradox-free reason
its account thereof overall, has that "the notion of a well-founded >>>>>>> justification tree", about e-minimality usually enough, to
be _elaborated_, involves the _diligence_ and the _thoroughness_ >>>>>>> of a conscientious account of the extra-ordinary, the super-
standard,
and the reasoning for _continuity_, and, _infinity_.
This PO account used to be a bit more open-minded, now it's
quite firmly retro-finitist, the hall-mark of the crank and troll. >>>>>>>
So, PO, if there is to be elaborated "well-founded justification >>>>>>> trees",
they live in a domain of discourse with other rulialities
than
well-foundedness/e-minimality/no-infinite-descending-epsilon-chains, >>>>>>> and
somehow in reality and in logic they _do_ all get along.
"E-laborated" means the diligent work was done,
the work was worked out of it, not just "defined" done.
You need an account that rejects quasi-modal logic or
else anyone can easily give innocuous non-facts that
define themselves "true".
It is best understood within the essential framework
of Prolog of back-chained inference from expressions
using Rules to reach Facts.
Prolog itself is far too weak to generalize this,
none-the-less the infrastructure of expressions
anchored in Facts and Rules does provide the complete
essence.
When we do it this way much of what has been misconstrued
as "undecidability" becomes expressions that are rejected
because they remain ungrounded in Facts.
This is not merely the foundations of math and logic
it is alternative foundations for math and logic that
reject and replace the conventional views.
I'd suggest not using the word "understood", with regards
to reasoning about _closures_ and furthermore _completions_,
with regards to things like "infinite limits" the completions.
Facts and rules for rules-engines and the like are very old-hat,
and contradictory rules
Are excluded.
in such accounts given un-true stated
"facts", besides that "facts" in such accounts are stipulated,
with regards to "verum" vis-a-vis "certum" and that it's only
conscientiously a _scientific_ account, con-scient-ious.
I don't speak Latin. These stipulated Facts are actually true
that is all that need be known about them.
The usual account of quasi-modal logic assumes that
_time has stopped and there is no change_,
the quasi-modal account itself is _not_ a temporal logic
and thusly _not_ a modal logic. Furthermore, the quasi-modal
logic's account of "monotonicity" fails, then that also
the "entailment" is not an apropos term, and besides usual
accounts of "garbage-in/garbage-out" is "crazy-in/crazy-out".
All we need to know that that the Facts are true Facts about general
knowledge.
So, math and logic have _infinity_ and _infinitary reasoning_,
they are _not_ going away.
Not when restricted to the finite list of true (atomic) Facts of
general
knowledge.
What you got there is, at best, a calculus of closed-categories,
and if it's not extra-ordinary and super-standard, then it's not.
When closed-categories is referring to the Frege compositional meaning >>>> and not some idiomatic term-of-the-art then yes closed-categories.
About "un-decide-ability", there's furthermore an even stronger
account of _independence_, the mathematical independence, since
I don't need to yet into the nuances of of terms-of-the-art
idiosyncrasies. Either an expression can be resolved to true
or false or it is not a member of the body of knowledge
expressed in language.
there are multiple laws of large numbers, and that measure theory
makes for quasi-invariant measure theory, since doubling/halving
spaces/measures make for the re-Vitali-ization of measure theory
about Vitali and Hausdorff and equi-decomposability, and for
analysts about competing accounts of _convergence_ and _emergence_,
that it is _real_ that some accounts of naive uniqueness instead
are ascribed particular distinctness, about real completions in
the objects of mathematics, beyond "not enough information".
If expressions cannot reach Facts using Rules then they
are out-of-scope. In this case the Rules are full natural
language semantics specified syntactically.
So, your usage of the words is unfortunately poisoned by the
fact that quasi-modal logic makes you think "material implication"
is a thing and that it does the thing, when it is not and does not.
My whole system is constructed entirely on the
basis of A is a necessary consequence of B.
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
Disjunction introduction is totally rejected.
Material implication may be entirely rejected.
Your somewhat convoluted language seems to mostly miss the
point of the barest essence of
"true on the basis of meaning expressed in language"
That's a usual account of "true" in common sense,
then though _all_ the mathematics and logic of
the infinite and infinitary bring _all_ their
matters of rigor resolving paradox for _any_
sorts formal accounts.
Or, "math is hard".
"True on the basis of meaning is true" is a sort
of coherent, pragmatist, correspondence definition
of truth, while though here there's always that
"is" is what "is" is.
It took me 27 years to come up with this bridge between
coherence/correspondence analytic/synthetic unifying
them into on single exact and precise perspective.
"true on the basis of meaning expressed in language"
expressed in language
expressed in language
expressed in language
Saying that a system is "whole" does not give that
it's "complete". Furthermore, matters of the
continuous and infinite must make for the "replete".
every single detail of general knowledge
"EXPRESSED IN LANGUAGE" can be encoded in my system
thus as complete as complete can possibly be.
Much of this must be algorithmically compressed
to make it finite.
The use of the words "anchor" or "Goedelian anchor"
or any mention of "delve" or "crucial" and recently
enough "compression" sure sounds like a bot to me.
The compression has at least two kinds:
loss-less and loss-y.
"Methods of exhaustion" are _not_ the completions themselves,
and naive inductive accounts do _not_ complete themselves.
Making "claims" absent "proofs" isn't quite use-less,
though it is illogical.
Perhaps it would help if you posted all your ramblings
with your bot bros instead of just posting the same
snippet a hundreds times and since it's malformed
saying that it's profound.
On 4/15/2026 12:51 PM, Ross Finlayson wrote:
On 04/15/2026 10:43 AM, olcott wrote:
On 4/15/2026 12:33 PM, Ross Finlayson wrote:
On 04/15/2026 10:18 AM, olcott wrote:
On 4/15/2026 11:35 AM, Ross Finlayson wrote:
On 04/15/2026 09:17 AM, olcott wrote:
On 4/15/2026 11:06 AM, Ross Finlayson wrote:
On 04/15/2026 08:49 AM, olcott wrote:
On 4/15/2026 10:15 AM, Ross Finlayson wrote:
On 04/14/2026 05:09 AM, Ross Finlayson wrote:
On 04/13/2026 11:34 PM, Mikko wrote:
On 13/04/2026 17:52, olcott wrote:
On 4/13/2026 2:05 AM, Mikko wrote:
On 12/04/2026 16:22, olcott wrote:
On 4/12/2026 4:32 AM, Mikko wrote:
On 11/04/2026 17:27, olcott wrote:
On 4/11/2026 3:06 AM, Mikko wrote:
On 09/04/2026 16:35, olcott wrote:
On 4/9/2026 4:08 AM, Mikko wrote:
On 08/04/2026 14:52, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:It certainly does. You can't use
On 07/04/2026 17:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 4/7/2026 3:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 06/04/2026 14:21, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 4/6/2026 3:27 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 05/04/2026 14:25, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/5/2026 2:05 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 04/04/2026 19:23, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/4/2026 2:53 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 03/04/2026 16:35, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/3/2026 2:13 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 02/04/2026 23:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> To be able to properly ground this in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> existing
That's mainly true. However, in >>>>>>>>>>>>>>>>>>>>>>>>>>>> como.lang.prologI have to carefully study at least a dozen >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> papersfoundational >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Do you think 100 years would be enough, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or at
least
some finite time? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
that may average 15 pages each. The basic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> notion
of a "well founded justification tree" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> essentially
means the Proof Theoretic notion of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> reduction to
a Canonical proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
% This sentence is not true. >>>>>>>>>>>>>>>>>>>>>>>>>>>>> ?- LP = not(true(LP)). >>>>>>>>>>>>>>>>>>>>>>>>>>>>> LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> should
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
have two examples: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> one with a negative result (as above) and one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with a
positive one.
So the above example should be paired with >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> one
that
has someting
else in place of not(provable(F, G)) so that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the
result will not be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> false.
THIS IS NOT A PROLOG SPECIFIC THING >>>>>>>>>>>>>>>>>>>>>>>>>>>>
the
discussion should
be restricted to Prolog specific things, in >>>>>>>>>>>>>>>>>>>>>>>>>>>> this
case
to the Prolog
example above and the contrasting Prolog >>>>>>>>>>>>>>>>>>>>>>>>>>>> example
not
yet shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>>>>>>>>>>>>> I require some way to formalize natural >>>>>>>>>>>>>>>>>>>>>>>>>>> language.
Montague Grammar, Rudolf Carnap Meaning >>>>>>>>>>>>>>>>>>>>>>>>>>> Postulates,
the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>>>>>>>>>>>>> are the options that I have been considering. >>>>>>>>>>>>>>>>>>>>>>>>>>>
The notion of how a well-founded justification >>>>>>>>>>>>>>>>>>>>>>>>>>> tree
eliminates undecidability is a key element of my >>>>>>>>>>>>>>>>>>>>>>>>>>> system.
Prolog shows this best.
It is not Prolog computable to determine >>>>>>>>>>>>>>>>>>>>>>>>>> whether a
sentence of Peano
arithmetic has a well-founded justification >>>>>>>>>>>>>>>>>>>>>>>>>> tree in
Peano
arithmetic.
A formal language similar to Prolog that can >>>>>>>>>>>>>>>>>>>>>>>>> represent
all of the semantics of PA can be developed so >>>>>>>>>>>>>>>>>>>>>>>>> that
it detects and rejects expressions that lack >>>>>>>>>>>>>>>>>>>>>>>>> well-founded
justification trees.
A language does not detect. For detection you >>>>>>>>>>>>>>>>>>>>>>>> need an
algorithm.
unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>>>>> is a function of the Prolog language that >>>>>>>>>>>>>>>>>>>>>>> implements the algorithm.
No, it is not. The question whether a sentence has a >>>>>>>>>>>>>>>>>>>>>> well-founded
justification tree is a question about one thing >>>>>>>>>>>>>>>>>>>>>> so it
needs an
algrotim that takes only one input but >>>>>>>>>>>>>>>>>>>>>> uunify_with_occurs_check
takes two.
The number of inputs does not matter. >>>>>>>>>>>>>>>>>>>>
unify_with_occurs_check to
determine
whether reCx reCy (x + y = y + x) has a well-founded >>>>>>>>>>>>>>>>>>>> justification
tree.
[00] reCx
roe
rooroCroCroCroCroC> [01] reCy
roe
rooroCroCroCroCroC> [02] Equals >>>>>>>>>>>>>>>>>>> roe
roLroCroCroCroCroC> [03] add (Left) >>>>>>>>>>>>>>>>>>> roe roe
roe roLroCroCroCroCroC> [05] x <roE
roe roe roe >>>>>>>>>>>>>>>>>>> roe rooroCroCroCroCroC> [06] y <ro+roCroE
roe roe roe >>>>>>>>>>>>>>>>>>> (Shared
Pointers)
rooroCroCroCroCroC> [04] add (Right) roe roe
roe roe roe >>>>>>>>>>>>>>>>>>> roLroCroCroCroCroCroC> [06] y roCroy roe
roe roe >>>>>>>>>>>>>>>>>>> rooroCroCroCroCroCroC> [05] x roCroCroCroy
There are no cycles in this tree
Can we interprete this to mean that you admit that the >>>>>>>>>>>>>>>>>> predicate
unify_with_occurs_check is not useful for determination >>>>>>>>>>>>>>>>>> whether
reCx reCy (x + y = y + x) has a well-founded justification >>>>>>>>>>>>>>>>>> tree ?
My example was to merely prove that the Liar Paradox >>>>>>>>>>>>>>>>> has never been anything besides incoherent nonsense. >>>>>>>>>>>>>>>>> I showed this in an existing well understood logic >>>>>>>>>>>>>>>>> programming language.
I.e., yes, we can interprete your diagram to mean that you >>>>>>>>>>>>>>>> admit
that
the predicate unify_with_occurs_check is not useful for >>>>>>>>>>>>>>>> determination
whether reCx reCy (x + y = y + x) has a well-founded >>>>>>>>>>>>>>>> justification
tree.
Consequently, you agree that your claims to the contrary >>>>>>>>>>>>>>>> were
false.
I started with the most salient case within
the most well-known language that can prove
my point. T^he above case if my own Minimal Type >>>>>>>>>>>>>>> Theory.
Olcott's Minimal Type Theory
G rao -4Prov[PA](riLGriY)
Directed Graph of evaluation sequence
00 rao 01 02
01 G
02 -4 03
03 Prov[PA] 04
04 G||del_Number_of 01 // cycle
Nice to see that you don't disagree.
When you understand proof theoretic semantics well
enough then you understand that within the coherent
foundation of PTS G||del 1931 Incompleteness becomes >>>>>>>>>>>>> an instance of incoherent semantics.
An ad-hominem with an unproven premise disqualifies your >>>>>>>>>>>> comment.
Though an ad-hominem would disqualify it even if the premise >>>>>>>>>>>> were
proven.
Wikipedia has a page about rhetorical fallacies.
https://en.wikipedia.org/wiki/Fallacy
https://en.wikipedia.org/wiki/List_of_fallacies
These are parts of greater accounts of deductive inference >>>>>>>>>>> to allay and prevent failures or sabotage of inductive
inference,
the "invincible" ignorance of inductive inference.
This then makes for "two wrongs does not make a right".
The usual account of "axioms" must be distinguished into >>>>>>>>>>> at least two kinds: those that "expand comprehension",
and those that "restrict comprehension". Basically one has >>>>>>>>>>> that under expansion-of-comprehension, that alternatives >>>>>>>>>>> or inverses exist, the other restriction-of-comprehension, >>>>>>>>>>> that one or the other doesn't exist.
"Inductive inference" isn't a lie, though, given a lie,
it can't tell the truth.
Then, Wikipedia also has a page about paradox.
https://en.wikipedia.org/wiki/Paradox
https://en.wikipedia.org/wiki/List_of_paradoxes
Then, paradoxes are usually enough given as results of
logic, here about logical paradoxes that would find themselves >>>>>>>>>>> in any theory, not about conflicting theories tangentially >>>>>>>>>>> relevant each other, those just being a model of conflicting >>>>>>>>>>> theories.
So, about resolving the paradoxes of logic, like Russell >>>>>>>>>>> and Burali-Forti and Cantor the paradoxes, these being
references to modern accounts of logic, and about the
Barber and the Heap and the Liar, these being references >>>>>>>>>>> to classical expositions of logic, has that eventually any >>>>>>>>>>> sort of restriction of comprehension in the universe of
logical objects may thusly be found by expansion of
comprehension
in the universe of logical objects to be contradicted.
So, it's known since antiquity that any sort of inductive >>>>>>>>>>> account can be broken.
Then, these "inductive impasses", must need make for
"analytical bridges", where there's a very particular
account of the primeval of the primary, about a universe >>>>>>>>>>> of truth already, else any sort of account of axiomatics >>>>>>>>>>> with restriction-of-comprehension is broken, instead of
merely being an example of perspective and thus limited
perspective.
So, the account of Pete Olcott is just a crank's/troll's/bot's >>>>>>>>>>> account, adding more restriction-of-comprehension above a >>>>>>>>>>> perceived "foundation" that's a false floor, futile and
doomed to fail, while yet simply enough making a claim
that "if it's not wrong it's not wrong", then furthermore >>>>>>>>>>> more or less saying "can't tell the difference between
fallacy and paradox and truth".
Here then we may have a modal temporal relevance logic
and a theory where classical logic is modal and excludes >>>>>>>>>>> the "material implication" since Chrysippus, and to re-name >>>>>>>>>>> the usual account of 20'th century "classical logic" as instead >>>>>>>>>>> along the lines of "Philo's Plotinus' Occam's Compte's Boole's >>>>>>>>>>> Russell's Carnap's nominalist fictionalist logicist positivist >>>>>>>>>>> Tarski's Goedel's quasi-modal account of logic and truth", that >>>>>>>>>>> "Olcott's Goedel's" is yet another account of the quasi-modal. >>>>>>>>>>>
So, it's a crank's/troll's/bot's, sometimes easier just
not to feed it. That said, it's a ready interpretation from >>>>>>>>>>> something like modern accounts of inference that simply employ >>>>>>>>>>> quasi-modal logic throughout and suggest thusly tabulating fact >>>>>>>>>>> after fact as truth, and making the fallacy of calling that >>>>>>>>>>> "monotonicity" and "entailment", which would be a lie, or as >>>>>>>>>>> with regards to contradicting either the competency or veracity, >>>>>>>>>>> of such accounts.
So, PO's futile flailings are just a reflection on the current >>>>>>>>>>> intellectual inertia about the quasi-modal logic, which taking >>>>>>>>>>> a partial account of a partial account, wronged itself twice. >>>>>>>>>>>
"The notion of a well-founded justification tree
will be fully elaborated."
A finite back-chained inference from the expression
to its axioms. As shown below in MTT the absence of
cycles in the directed graph of the expressions
evaluation sequence.
% This sentence cannot be proven in F
?- G = not(provable(F, G)).
G = not(provable(F, G)).
?- unify_with_occurs_check(G, not(provable(F, G))).
false.
https://www.swi-prolog.org/pldoc/man?
predicate=unify_with_occurs_check/2
Olcott's Minimal Type Theory
G rao -4Prov[PA](riLGriY)
Directed Graph of evaluation sequence
00 rao 01 02
01 G
02 -4 03
03 Prov[PA] 04
04 G||del_Number_of 01 // cycle
No, a deductive account about the possibilities and limits of
inductive inference, helping explain any super-classical result, >>>>>>>> not just a rule-sniffing dog that follows its own brown nose.
Goedel's incompleteness result is much simpler after a simple
sort of account of quantification and the old "sputniks of
quantification", that readily demonstrate something like
Russell's paradox in account of ordinary arithmetic, for
what somebody like Mirimanoff calls the "extra-ordinary",
and Skolem constructs for fragments and extensions in the
ordinary account of usual model theory about models of integers, >>>>>>>> then that Goedel's incompleteness basically gives limits of
applicability of _claims_, here emphasized the _claims_ as
being the proper word for accounts of inference over usual
sorts of nominalist fictionalist logicist positivists' theories. >>>>>>>>
Otherwise anybody can just come along and prove Russell wrong, >>>>>>>> prove Cantor wrong, and otherwise without a paradox-free reason >>>>>>>> its account thereof overall, has that "the notion of a well-founded >>>>>>>> justification tree", about e-minimality usually enough, to
be _elaborated_, involves the _diligence_ and the _thoroughness_ >>>>>>>> of a conscientious account of the extra-ordinary, the super-
standard,
and the reasoning for _continuity_, and, _infinity_.
This PO account used to be a bit more open-minded, now it's
quite firmly retro-finitist, the hall-mark of the crank and troll. >>>>>>>>
So, PO, if there is to be elaborated "well-founded justification >>>>>>>> trees",
they live in a domain of discourse with other rulialities
than
well-foundedness/e-minimality/no-infinite-descending-epsilon-chains, >>>>>>>>
and
somehow in reality and in logic they _do_ all get along.
"E-laborated" means the diligent work was done,
the work was worked out of it, not just "defined" done.
You need an account that rejects quasi-modal logic or
else anyone can easily give innocuous non-facts that
define themselves "true".
It is best understood within the essential framework
of Prolog of back-chained inference from expressions
using Rules to reach Facts.
Prolog itself is far too weak to generalize this,
none-the-less the infrastructure of expressions
anchored in Facts and Rules does provide the complete
essence.
When we do it this way much of what has been misconstrued
as "undecidability" becomes expressions that are rejected
because they remain ungrounded in Facts.
This is not merely the foundations of math and logic
it is alternative foundations for math and logic that
reject and replace the conventional views.
I'd suggest not using the word "understood", with regards
to reasoning about _closures_ and furthermore _completions_,
with regards to things like "infinite limits" the completions.
Facts and rules for rules-engines and the like are very old-hat,
and contradictory rules
Are excluded.
in such accounts given un-true stated
"facts", besides that "facts" in such accounts are stipulated,
with regards to "verum" vis-a-vis "certum" and that it's only
conscientiously a _scientific_ account, con-scient-ious.
I don't speak Latin. These stipulated Facts are actually true
that is all that need be known about them.
The usual account of quasi-modal logic assumes that
_time has stopped and there is no change_,
the quasi-modal account itself is _not_ a temporal logic
and thusly _not_ a modal logic. Furthermore, the quasi-modal
logic's account of "monotonicity" fails, then that also
the "entailment" is not an apropos term, and besides usual
accounts of "garbage-in/garbage-out" is "crazy-in/crazy-out".
All we need to know that that the Facts are true Facts about general >>>>> knowledge.
So, math and logic have _infinity_ and _infinitary reasoning_,
they are _not_ going away.
Not when restricted to the finite list of true (atomic) Facts of
general
knowledge.
What you got there is, at best, a calculus of closed-categories,
and if it's not extra-ordinary and super-standard, then it's not.
When closed-categories is referring to the Frege compositional meaning >>>>> and not some idiomatic term-of-the-art then yes closed-categories.
About "un-decide-ability", there's furthermore an even stronger
account of _independence_, the mathematical independence, since
I don't need to yet into the nuances of of terms-of-the-art
idiosyncrasies. Either an expression can be resolved to true
or false or it is not a member of the body of knowledge
expressed in language.
there are multiple laws of large numbers, and that measure theory
makes for quasi-invariant measure theory, since doubling/halving
spaces/measures make for the re-Vitali-ization of measure theory
about Vitali and Hausdorff and equi-decomposability, and for
analysts about competing accounts of _convergence_ and _emergence_, >>>>>> that it is _real_ that some accounts of naive uniqueness instead
are ascribed particular distinctness, about real completions in
the objects of mathematics, beyond "not enough information".
If expressions cannot reach Facts using Rules then they
are out-of-scope. In this case the Rules are full natural
language semantics specified syntactically.
So, your usage of the words is unfortunately poisoned by the
fact that quasi-modal logic makes you think "material implication" >>>>>> is a thing and that it does the thing, when it is not and does not. >>>>>>
My whole system is constructed entirely on the
basis of A is a necessary consequence of B.
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
Disjunction introduction is totally rejected.
Material implication may be entirely rejected.
Your somewhat convoluted language seems to mostly miss the
point of the barest essence of
"true on the basis of meaning expressed in language"
That's a usual account of "true" in common sense,
then though _all_ the mathematics and logic of
the infinite and infinitary bring _all_ their
matters of rigor resolving paradox for _any_
sorts formal accounts.
Or, "math is hard".
"True on the basis of meaning is true" is a sort
of coherent, pragmatist, correspondence definition
of truth, while though here there's always that
"is" is what "is" is.
It took me 27 years to come up with this bridge between
coherence/correspondence analytic/synthetic unifying
them into on single exact and precise perspective.
"true on the basis of meaning expressed in language"
expressed in language
expressed in language
expressed in language
Saying that a system is "whole" does not give that
it's "complete". Furthermore, matters of the
continuous and infinite must make for the "replete".
every single detail of general knowledge
"EXPRESSED IN LANGUAGE" can be encoded in my system
thus as complete as complete can possibly be.
Much of this must be algorithmically compressed
to make it finite.
The use of the words "anchor" or "Goedelian anchor"
or any mention of "delve" or "crucial" and recently
enough "compression" sure sounds like a bot to me.
The compression has at least two kinds:
loss-less and loss-y.
"Methods of exhaustion" are _not_ the completions themselves,
and naive inductive accounts do _not_ complete themselves.
Making "claims" absent "proofs" isn't quite use-less,
though it is illogical.
Perhaps it would help if you posted all your ramblings
with your bot bros instead of just posting the same
snippet a hundreds times and since it's malformed
saying that it's profound.
In other words you are merely another learned-by-rote
guy and find philosophical underpinnings to be complete
nonsense within your rote memorization of the conventional
view perspective.
On 4/15/2026 11:51 AM, Andr|- G. Isaak wrote:
On 2026-04-15 06:02, olcott wrote:
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
You've said this (or something similar) to several different posters
now; but bear in mind that you yourself only became aware of the
existence of proof-theoretic semantics a few months ago which means
that you have hardly had enough time to become an expert in PTS.
It turns out that all of my ideas have been fully anchored
in exactly proof theoretic semantics the whole time.
Also
my current ideas have taken the exact PTS basis and extended
them much more.
The current state of PTS seems to still be anchored in
what is essentially propositional logic whereas my system
has been anchored in formalized natural language semantics
for a long time.
So you're really not in a position to tell people what an expert in
PTS might claim about any particular issue.
Andr|-
On 2026-04-15 11:24, olcott wrote:
On 4/15/2026 11:51 AM, Andr|- G. Isaak wrote:
On 2026-04-15 06:02, olcott wrote:
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
You've said this (or something similar) to several different posters
now; but bear in mind that you yourself only became aware of the
existence of proof-theoretic semantics a few months ago which means
that you have hardly had enough time to become an expert in PTS.
It turns out that all of my ideas have been fully anchored
in exactly proof theoretic semantics the whole time.
They really haven't been.
You stumbled upon a framework which, in your mind, bore some vague resemblance to your own ideas, and then you projected your own ideas
onto that framework. But it's very clear from what you've posted here
that you don't really understand PTS as used by, e.g. Schroeder-Heister
or Francez as you keep attributing things to PTS which they very clearly don't endorse.
Also
my current ideas have taken the exact PTS basis and extended
them much more.
Well, until you actually clarify what *you* think that PTS basis is
(referring to the works of others here won't cut it since as I point out above you seem to have a very different interpretation of PTS than its proponents hold), and until you actually lay out what your "extensions"
are, no one is in any position to discuss your ideas.
Andr|-
The current state of PTS seems to still be anchored in
what is essentially propositional logic whereas my system
has been anchored in formalized natural language semantics
for a long time.
So you're really not in a position to tell people what an expert in
PTS might claim about any particular issue.
Andr|-
On 4/15/2026 2:13 PM, Andr|- G. Isaak wrote:
On 2026-04-15 11:24, olcott wrote:
On 4/15/2026 11:51 AM, Andr|- G. Isaak wrote:
On 2026-04-15 06:02, olcott wrote:
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
You've said this (or something similar) to several different posters
now; but bear in mind that you yourself only became aware of the
existence of proof-theoretic semantics a few months ago which means
that you have hardly had enough time to become an expert in PTS.
It turns out that all of my ideas have been fully anchored
in exactly proof theoretic semantics the whole time.
They really haven't been.
You stumbled upon a framework which, in your mind, bore some vague
resemblance to your own ideas, and then you projected your own ideas
onto that framework. But it's very clear from what you've posted here
that you don't really understand PTS as used by, e.g.
Schroeder-Heister or Francez as you keep attributing things to PTS
which they very clearly don't endorse.
Try to explain the details of this.
I am referring to aspects where Professor Dag Prawitz
and professor Peter Schroeder-Heister may have divergent
views. My perspective unifies these divergent views.
Also
my current ideas have taken the exact PTS basis and extended
them much more.
Well, until you actually clarify what *you* think that PTS basis is
I cannot teach my reviewers the entire PTS basis.
(referring to the works of others here won't cut it since as I point
out above you seem to have a very different interpretation of PTS than
its proponents hold), and until you actually lay out what your
"extensions" are, no one is in any position to discuss your ideas.
Andr|-
The current state of PTS seems to still be anchored in
what is essentially propositional logic whereas my system
has been anchored in formalized natural language semantics
for a long time.
So you're really not in a position to tell people what an expert in
PTS might claim about any particular issue.
Andr|-
On 04/15/2026 01:37 PM, olcott wrote:
On 4/15/2026 2:13 PM, Andr|- G. Isaak wrote:
On 2026-04-15 11:24, olcott wrote:
On 4/15/2026 11:51 AM, Andr|- G. Isaak wrote:
On 2026-04-15 06:02, olcott wrote:
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
You've said this (or something similar) to several different posters >>>>> now; but bear in mind that you yourself only became aware of the
existence of proof-theoretic semantics a few months ago which means
that you have hardly had enough time to become an expert in PTS.
It turns out that all of my ideas have been fully anchored
in exactly proof theoretic semantics the whole time.
They really haven't been.
You stumbled upon a framework which, in your mind, bore some vague
resemblance to your own ideas, and then you projected your own ideas
onto that framework. But it's very clear from what you've posted here
that you don't really understand PTS as used by, e.g.
Schroeder-Heister or Francez as you keep attributing things to PTS
which they very clearly don't endorse.
Try to explain the details of this.
I am referring to aspects where Professor Dag Prawitz
and professor Peter Schroeder-Heister may have divergent
views. My perspective unifies these divergent views.
Also
my current ideas have taken the exact PTS basis and extended
them much more.
Well, until you actually clarify what *you* think that PTS basis is
I cannot teach my reviewers the entire PTS basis.
(referring to the works of others here won't cut it since as I point
out above you seem to have a very different interpretation of PTS than
its proponents hold), and until you actually lay out what your
"extensions" are, no one is in any position to discuss your ideas.
Andr|-
The current state of PTS seems to still be anchored in
what is essentially propositional logic whereas my system
has been anchored in formalized natural language semantics
for a long time.
So you're really not in a position to tell people what an expert in
PTS might claim about any particular issue.
Andr|-
If you can't explain it then you don't know it.
On 4/15/2026 2:13 PM, Andr|- G. Isaak wrote:
On 2026-04-15 11:24, olcott wrote:
On 4/15/2026 11:51 AM, Andr|- G. Isaak wrote:
On 2026-04-15 06:02, olcott wrote:
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
You've said this (or something similar) to several different posters
now; but bear in mind that you yourself only became aware of the
existence of proof-theoretic semantics a few months ago which means
that you have hardly had enough time to become an expert in PTS.
It turns out that all of my ideas have been fully anchored
in exactly proof theoretic semantics the whole time.
They really haven't been.
You stumbled upon a framework which, in your mind, bore some vague
resemblance to your own ideas, and then you projected your own ideas
onto that framework. But it's very clear from what you've posted here
that you don't really understand PTS as used by, e.g.
Schroeder-Heister or Francez as you keep attributing things to PTS
which they very clearly don't endorse.
Try to explain the details of this.
I am referring to aspects where Professor Dag Prawitz
and professor Peter Schroeder-Heister may have divergent
views. My perspective unifies these divergent views.
Also
my current ideas have taken the exact PTS basis and extended
them much more.
Well, until you actually clarify what *you* think that PTS basis is
I cannot teach my reviewers the entire PTS basis.
On 2026-04-15 14:37, olcott wrote:
On 4/15/2026 2:13 PM, Andr|- G. Isaak wrote:
On 2026-04-15 11:24, olcott wrote:
On 4/15/2026 11:51 AM, Andr|- G. Isaak wrote:
On 2026-04-15 06:02, olcott wrote:
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
You've said this (or something similar) to several different
posters now; but bear in mind that you yourself only became aware
of the existence of proof-theoretic semantics a few months ago
which means that you have hardly had enough time to become an
expert in PTS.
It turns out that all of my ideas have been fully anchored
in exactly proof theoretic semantics the whole time.
They really haven't been.
You stumbled upon a framework which, in your mind, bore some vague
resemblance to your own ideas, and then you projected your own ideas
onto that framework. But it's very clear from what you've posted here
that you don't really understand PTS as used by, e.g. Schroeder-
Heister or Francez as you keep attributing things to PTS which they
very clearly don't endorse.
Try to explain the details of this.
I am referring to aspects where Professor Dag Prawitz
and professor Peter Schroeder-Heister may have divergent
views. My perspective unifies these divergent views.
So what are these divergent views and how exactly have you unified them?
Also
my current ideas have taken the exact PTS basis and extended
them much more.
Well, until you actually clarify what *you* think that PTS basis is
I cannot teach my reviewers the entire PTS basis.
If you ever realize your plans to publish your work, you would be
expected to do just that.
PTS is not sufficiently well-known that you
could get away with simply assuming it in a published paper; you would
need to lay out the details of this theory.
Doing so here would be good practice since its something you will
eventually have to do anyways.
Andr|-
On 4/15/2026 1:58 AM, Mikko wrote:
On 14/04/2026 16:50, olcott wrote:
On 4/14/2026 12:59 AM, Mikko wrote:
On 13/04/2026 17:52, olcott wrote:
On 4/13/2026 2:05 AM, Mikko wrote:
On 12/04/2026 16:22, olcott wrote:
On 4/12/2026 4:32 AM, Mikko wrote:
On 11/04/2026 17:27, olcott wrote:
On 4/11/2026 3:06 AM, Mikko wrote:
On 09/04/2026 16:35, olcott wrote:My example was to merely prove that the Liar Paradox
On 4/9/2026 4:08 AM, Mikko wrote:
On 08/04/2026 14:52, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 4/3/2026 2:13 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 02/04/2026 23:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> To be able to properly ground this in existing >>>>>>>>>>>>>>>>>>>>>>>>> foundational
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>>Do you think 100 years would be enough, or at >>>>>>>>>>>>>>>>>>>>>>>> least some finite time?
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you should >>>>>>>>>>>>>>>>>>>>>> have two examples:
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>>>>
one with a negative result (as above) and one with >>>>>>>>>>>>>>>>>>>>>> a positive one.
So the above example should be paired with one >>>>>>>>>>>>>>>>>>>>>> that has someting
else in place of not(provable(F, G)) so that the >>>>>>>>>>>>>>>>>>>>>> result will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the >>>>>>>>>>>>>>>>>>>> discussion should
be restricted to Prolog specific things, in this >>>>>>>>>>>>>>>>>>>> case to the Prolog
example above and the contrasting Prolog example not >>>>>>>>>>>>>>>>>>>> yet shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>>>>> are the options that I have been considering. >>>>>>>>>>>>>>>>>>>
The notion of how a well-founded justification tree >>>>>>>>>>>>>>>>>>> eliminates undecidability is a key element of my system. >>>>>>>>>>>>>>>>>>> Prolog shows this best.
It is not Prolog computable to determine whether a >>>>>>>>>>>>>>>>>> sentence of Peano
arithmetic has a well-founded justification tree in >>>>>>>>>>>>>>>>>> Peano arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>>>>>>> all of the semantics of PA can be developed so that >>>>>>>>>>>>>>>>> it detects and rejects expressions that lack well-founded >>>>>>>>>>>>>>>>> justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))).
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well- >>>>>>>>>>>>>> founded
justification tree is a question about one thing so it >>>>>>>>>>>>>> needs an
algrotim that takes only one input but
uunify_with_occurs_check
takes two.
The number of inputs does not matter.
It certainly does. You can't use unify_with_occurs_check to >>>>>>>>>>>> determine
whether reCx reCy (x + y = y + x) has a well-founded
justification tree.
[00] reCx
-a-aroe
-a-arooroCroCroCroCroC> [01] reCy
-a-a-a-a-a-a-a-a-a-a roe
-a-a-a-a-a-a-a-a-a-a rooroCroCroCroCroC> [02] Equals
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roLroCroCroCroCroC> [03] add (Left)
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a roe >>>>>>>>>>> -a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a roLroCroCroCroCroC> [05] x-a <roE
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a rooroCroCroCroCroC> [06] y-a <ro+roCroE
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe roe (Shared
Pointers)
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a rooroCroCroCroCroC> [04] add (Right)-a roe roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roLroCroCroCroCroCroC> [06] y roCroy roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a rooroCroCroCroCroCroC> [05] x roCroCroCroy
There are no cycles in this tree
Can we interprete this to mean that you admit that the predicate >>>>>>>>>> unify_with_occurs_check is not useful for determination whether >>>>>>>>>> reCx reCy (x + y = y + x) has a well-founded justification tree ? >>>>>>>>>
has never been anything besides incoherent nonsense.
I showed this in an existing well understood logic
programming language.
I.e., yes, we can interprete your diagram to mean that you admit >>>>>>>> that
the predicate unify_with_occurs_check is not useful for
determination
whether reCx reCy (x + y = y + x) has a well-founded justification >>>>>>>> tree.
Consequently, you agree that your claims to the contrary were >>>>>>>> false.
I started with the most salient case within
the most well-known language that can prove
my point. T^he above case if my own Minimal Type
Theory.
Olcott's Minimal Type Theory
G rao -4Prov[PA](riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov[PA]-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle
Nice to see that you don't disagree.
When you understand proof theoretic semantics well
enough then you understand that within the coherent
foundation of PTS G||del 1931 Incompleteness becomes
an instance of incoherent semantics.
PTS is irrelevant to G|udel's incompleteness theorem, which is about
formal logic, not about PTS.
PTS replaces the foundation of model theory and this
changes everything.
Only for PTS. It changes nothing for those who use model theory.
Likewise modern medicine changes nothing for
those with the evil spirit theory of disease.
On 4/15/2026 2:07 AM, Mikko wrote:
On 14/04/2026 16:45, olcott wrote:
On 4/14/2026 1:34 AM, Mikko wrote:
On 13/04/2026 17:52, olcott wrote:
On 4/13/2026 2:05 AM, Mikko wrote:
On 12/04/2026 16:22, olcott wrote:
On 4/12/2026 4:32 AM, Mikko wrote:
On 11/04/2026 17:27, olcott wrote:
On 4/11/2026 3:06 AM, Mikko wrote:
On 09/04/2026 16:35, olcott wrote:My example was to merely prove that the Liar Paradox
On 4/9/2026 4:08 AM, Mikko wrote:
On 08/04/2026 14:52, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 4/3/2026 2:13 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 02/04/2026 23:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> To be able to properly ground this in existing >>>>>>>>>>>>>>>>>>>>>>>>> foundational
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>>Do you think 100 years would be enough, or at >>>>>>>>>>>>>>>>>>>>>>>> least some finite time?
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you should >>>>>>>>>>>>>>>>>>>>>> have two examples:
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>>>>
one with a negative result (as above) and one with >>>>>>>>>>>>>>>>>>>>>> a positive one.
So the above example should be paired with one >>>>>>>>>>>>>>>>>>>>>> that has someting
else in place of not(provable(F, G)) so that the >>>>>>>>>>>>>>>>>>>>>> result will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the >>>>>>>>>>>>>>>>>>>> discussion should
be restricted to Prolog specific things, in this >>>>>>>>>>>>>>>>>>>> case to the Prolog
example above and the contrasting Prolog example not >>>>>>>>>>>>>>>>>>>> yet shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>>>>> are the options that I have been considering. >>>>>>>>>>>>>>>>>>>
The notion of how a well-founded justification tree >>>>>>>>>>>>>>>>>>> eliminates undecidability is a key element of my system. >>>>>>>>>>>>>>>>>>> Prolog shows this best.
It is not Prolog computable to determine whether a >>>>>>>>>>>>>>>>>> sentence of Peano
arithmetic has a well-founded justification tree in >>>>>>>>>>>>>>>>>> Peano arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>>>>>>> all of the semantics of PA can be developed so that >>>>>>>>>>>>>>>>> it detects and rejects expressions that lack well-founded >>>>>>>>>>>>>>>>> justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))).
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well- >>>>>>>>>>>>>> founded
justification tree is a question about one thing so it >>>>>>>>>>>>>> needs an
algrotim that takes only one input but
uunify_with_occurs_check
takes two.
The number of inputs does not matter.
It certainly does. You can't use unify_with_occurs_check to >>>>>>>>>>>> determine
whether reCx reCy (x + y = y + x) has a well-founded
justification tree.
[00] reCx
-a-aroe
-a-arooroCroCroCroCroC> [01] reCy
-a-a-a-a-a-a-a-a-a-a roe
-a-a-a-a-a-a-a-a-a-a rooroCroCroCroCroC> [02] Equals
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roLroCroCroCroCroC> [03] add (Left)
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a roe >>>>>>>>>>> -a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a roLroCroCroCroCroC> [05] x-a <roE
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a rooroCroCroCroCroC> [06] y-a <ro+roCroE
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe roe (Shared
Pointers)
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a rooroCroCroCroCroC> [04] add (Right)-a roe roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roLroCroCroCroCroCroC> [06] y roCroy roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a rooroCroCroCroCroCroC> [05] x roCroCroCroy
There are no cycles in this tree
Can we interprete this to mean that you admit that the predicate >>>>>>>>>> unify_with_occurs_check is not useful for determination whether >>>>>>>>>> reCx reCy (x + y = y + x) has a well-founded justification tree ? >>>>>>>>>
has never been anything besides incoherent nonsense.
I showed this in an existing well understood logic
programming language.
I.e., yes, we can interprete your diagram to mean that you admit >>>>>>>> that
the predicate unify_with_occurs_check is not useful for
determination
whether reCx reCy (x + y = y + x) has a well-founded justification >>>>>>>> tree.
Consequently, you agree that your claims to the contrary were >>>>>>>> false.
I started with the most salient case within
the most well-known language that can prove
my point. T^he above case if my own Minimal Type
Theory.
Olcott's Minimal Type Theory
G rao -4Prov[PA](riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov[PA]-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle
Nice to see that you don't disagree.
When you understand proof theoretic semantics well
enough then you understand that within the coherent
foundation of PTS G||del 1931 Incompleteness becomes
an instance of incoherent semantics.
An ad-hominem with an unproven premise disqualifies your comment.
Though an ad-hominem would disqualify it even if the premise were
proven.
You keep arguing on the basis of ignorance of proof
theoretic semantics, like a kindergarten kid that
says I just don't believe in algebra.
You are the one who is like a kindergarten kid that says "I just
don't believe in algebra". Instead of algebra, you just don't
believe in logic.
But it is indeed true that I don't believe in conclusions if it
is not known whether the premises are true. And I don't believe
that ad-hominem can be a part of a valid argument, although it
might be a basis to reject a testimnoy.
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
On 4/15/2026 1:58 AM, Mikko wrote:
On 14/04/2026 16:50, olcott wrote:
On 4/14/2026 12:59 AM, Mikko wrote:
On 13/04/2026 17:52, olcott wrote:
On 4/13/2026 2:05 AM, Mikko wrote:
On 12/04/2026 16:22, olcott wrote:
On 4/12/2026 4:32 AM, Mikko wrote:
On 11/04/2026 17:27, olcott wrote:
On 4/11/2026 3:06 AM, Mikko wrote:
On 09/04/2026 16:35, olcott wrote:My example was to merely prove that the Liar Paradox
On 4/9/2026 4:08 AM, Mikko wrote:
On 08/04/2026 14:52, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 4/3/2026 2:13 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 02/04/2026 23:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> To be able to properly ground this in existing >>>>>>>>>>>>>>>>>>>>>>>>> foundational
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>>Do you think 100 years would be enough, or at >>>>>>>>>>>>>>>>>>>>>>>> least some finite time?
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you should >>>>>>>>>>>>>>>>>>>>>> have two examples:
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>>>>
one with a negative result (as above) and one with >>>>>>>>>>>>>>>>>>>>>> a positive one.
So the above example should be paired with one >>>>>>>>>>>>>>>>>>>>>> that has someting
else in place of not(provable(F, G)) so that the >>>>>>>>>>>>>>>>>>>>>> result will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the >>>>>>>>>>>>>>>>>>>> discussion should
be restricted to Prolog specific things, in this >>>>>>>>>>>>>>>>>>>> case to the Prolog
example above and the contrasting Prolog example not >>>>>>>>>>>>>>>>>>>> yet shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>>>>> are the options that I have been considering. >>>>>>>>>>>>>>>>>>>
The notion of how a well-founded justification tree >>>>>>>>>>>>>>>>>>> eliminates undecidability is a key element of my system. >>>>>>>>>>>>>>>>>>> Prolog shows this best.
It is not Prolog computable to determine whether a >>>>>>>>>>>>>>>>>> sentence of Peano
arithmetic has a well-founded justification tree in >>>>>>>>>>>>>>>>>> Peano arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>>>>>>> all of the semantics of PA can be developed so that >>>>>>>>>>>>>>>>> it detects and rejects expressions that lack well-founded >>>>>>>>>>>>>>>>> justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))).
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well- >>>>>>>>>>>>>> founded
justification tree is a question about one thing so it >>>>>>>>>>>>>> needs an
algrotim that takes only one input but
uunify_with_occurs_check
takes two.
The number of inputs does not matter.
It certainly does. You can't use unify_with_occurs_check to >>>>>>>>>>>> determine
whether reCx reCy (x + y = y + x) has a well-founded
justification tree.
[00] reCx
-a-aroe
-a-arooroCroCroCroCroC> [01] reCy
-a-a-a-a-a-a-a-a-a-a roe
-a-a-a-a-a-a-a-a-a-a rooroCroCroCroCroC> [02] Equals
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roLroCroCroCroCroC> [03] add (Left)
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a roe >>>>>>>>>>> -a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a roLroCroCroCroCroC> [05] x-a <roE
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a rooroCroCroCroCroC> [06] y-a <ro+roCroE
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe roe (Shared
Pointers)
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a rooroCroCroCroCroC> [04] add (Right)-a roe roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roLroCroCroCroCroCroC> [06] y roCroy roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a roe
-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a rooroCroCroCroCroCroC> [05] x roCroCroCroy
There are no cycles in this tree
Can we interprete this to mean that you admit that the predicate >>>>>>>>>> unify_with_occurs_check is not useful for determination whether >>>>>>>>>> reCx reCy (x + y = y + x) has a well-founded justification tree ? >>>>>>>>>
has never been anything besides incoherent nonsense.
I showed this in an existing well understood logic
programming language.
I.e., yes, we can interprete your diagram to mean that you admit >>>>>>>> that
the predicate unify_with_occurs_check is not useful for
determination
whether reCx reCy (x + y = y + x) has a well-founded justification >>>>>>>> tree.
Consequently, you agree that your claims to the contrary were >>>>>>>> false.
I started with the most salient case within
the most well-known language that can prove
my point. T^he above case if my own Minimal Type
Theory.
Olcott's Minimal Type Theory
G rao -4Prov[PA](riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov[PA]-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle
Nice to see that you don't disagree.
When you understand proof theoretic semantics well
enough then you understand that within the coherent
foundation of PTS G||del 1931 Incompleteness becomes
an instance of incoherent semantics.
PTS is irrelevant to G|udel's incompleteness theorem, which is about
formal logic, not about PTS.
PTS replaces the foundation of model theory and this
changes everything.
Only for PTS. It changes nothing for those who use model theory.
Likewise modern medicine changes nothing for
those with the evil spirit theory of disease.
But both are irrelevant to the incompleteness theorem, which is
derived from logic and arithmetic with truth preserving inferences.
On 15/04/2026 15:02, olcott wrote:
On 4/15/2026 2:07 AM, Mikko wrote:
But it is indeed true that I don't believe in conclusions if it
is not known whether the premises are true. And I don't believe
that ad-hominem can be a part of a valid argument, although it
might be a basis to reject a testimnoy.
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
Not quite. I will remain a wonderer. You will remain clueless.
On 4/16/2026 3:33 AM, Mikko wrote:
On 15/04/2026 15:02, olcott wrote:
On 4/15/2026 2:07 AM, Mikko wrote:
But it is indeed true that I don't believe in conclusions if it
is not known whether the premises are true. And I don't believe
that ad-hominem can be a part of a valid argument, although it
might be a basis to reject a testimnoy.
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
Not quite. I will remain a wonderer. You will remain clueless.
It will soon be an easily verified fact that all
my ideas have always been fully anchored in modern
Proof Theoretic Semantics.
I will write a new paper that specifically anchors
each of my ideas point-by-point and item-by-item
in direct quotes from foundational papers in Proof
Theoretic Semantics. This is easy to do, yet takes
time to get it exactly right.
On 16/04/2026 15:52, olcott wrote:
On 4/16/2026 3:33 AM, Mikko wrote:
On 15/04/2026 15:02, olcott wrote:
On 4/15/2026 2:07 AM, Mikko wrote:
But it is indeed true that I don't believe in conclusions if it
is not known whether the premises are true. And I don't believe
that ad-hominem can be a part of a valid argument, although it
might be a basis to reject a testimnoy.
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
Not quite. I will remain a wonderer. You will remain clueless.
It will soon be an easily verified fact that all
my ideas have always been fully anchored in modern
Proof Theoretic Semantics.
Does that "soon" mean less than 50 years ?
I will write a new paper that specifically anchors
each of my ideas point-by-point and item-by-item
in direct quotes from foundational papers in Proof
Theoretic Semantics. This is easy to do, yet takes
time to get it exactly right.
A good paper would not give any reason to think that the author may
be stupid or ignorant.
On 4/17/2026 1:52 AM, Mikko wrote:
On 16/04/2026 15:52, olcott wrote:
On 4/16/2026 3:33 AM, Mikko wrote:
On 15/04/2026 15:02, olcott wrote:
On 4/15/2026 2:07 AM, Mikko wrote:
But it is indeed true that I don't believe in conclusions if it
is not known whether the premises are true. And I don't believe
that ad-hominem can be a part of a valid argument, although it
might be a basis to reject a testimnoy.
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
Not quite. I will remain a wonderer. You will remain clueless.
It will soon be an easily verified fact that all
my ideas have always been fully anchored in modern
Proof Theoretic Semantics.
Does that "soon" mean less than 50 years ?
From one month until the end of Summer.
I have three enormous construction projects
on my house that also must be done in that
same time-frame and my car just broke down
again. Because I am very poor I must do all
this work myself.
I will write a new paper that specifically anchors
each of my ideas point-by-point and item-by-item
in direct quotes from foundational papers in Proof
Theoretic Semantics. This is easy to do, yet takes
time to get it exactly right.
A good paper would not give any reason to think that the author may
be stupid or ignorant.
I am as a matter of objective fact a genius.
The key thing that I have been missing is
a succinct set of terms-of-the-art that refer
to the exact meanings that I intend. Outside
of PTS there is no such set of terms-of-the-art.
On 17/04/2026 17:34, olcott wrote:
On 4/17/2026 1:52 AM, Mikko wrote:
On 16/04/2026 15:52, olcott wrote:
On 4/16/2026 3:33 AM, Mikko wrote:
On 15/04/2026 15:02, olcott wrote:
On 4/15/2026 2:07 AM, Mikko wrote:
But it is indeed true that I don't believe in conclusions if it
is not known whether the premises are true. And I don't believe
that ad-hominem can be a part of a valid argument, although it
might be a basis to reject a testimnoy.
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
Not quite. I will remain a wonderer. You will remain clueless.
It will soon be an easily verified fact that all
my ideas have always been fully anchored in modern
Proof Theoretic Semantics.
Does that "soon" mean less than 50 years ?
-aFrom one month until the end of Summer.
I have three enormous construction projects
on my house that also must be done in that
same time-frame and my car just broke down
again. Because I am very poor I must do all
this work myself.
I will write a new paper that specifically anchors
each of my ideas point-by-point and item-by-item
in direct quotes from foundational papers in Proof
Theoretic Semantics. This is easy to do, yet takes
time to get it exactly right.
A good paper would not give any reason to think that the author may
be stupid or ignorant.
I am as a matter of objective fact a genius.
The key thing that I have been missing is
a succinct set of terms-of-the-art that refer
to the exact meanings that I intend. Outside
of PTS there is no such set of terms-of-the-art.
In such situations it is best to work on problem you want to complete
first, if possible. If somethen prevents working on that problme then
on what you want to complete next.
On 4/18/2026 4:19 AM, Mikko wrote:
On 17/04/2026 17:34, olcott wrote:
On 4/17/2026 1:52 AM, Mikko wrote:
On 16/04/2026 15:52, olcott wrote:
On 4/16/2026 3:33 AM, Mikko wrote:
On 15/04/2026 15:02, olcott wrote:
On 4/15/2026 2:07 AM, Mikko wrote:
But it is indeed true that I don't believe in conclusions if it >>>>>>>> is not known whether the premises are true. And I don't believe >>>>>>>> that ad-hominem can be a part of a valid argument, although it >>>>>>>> might be a basis to reject a testimnoy.
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
Not quite. I will remain a wonderer. You will remain clueless.
It will soon be an easily verified fact that all
my ideas have always been fully anchored in modern
Proof Theoretic Semantics.
Does that "soon" mean less than 50 years ?
-aFrom one month until the end of Summer.
I have three enormous construction projects
on my house that also must be done in that
same time-frame and my car just broke down
again. Because I am very poor I must do all
this work myself.
I will write a new paper that specifically anchors
each of my ideas point-by-point and item-by-item
in direct quotes from foundational papers in Proof
Theoretic Semantics. This is easy to do, yet takes
time to get it exactly right.
A good paper would not give any reason to think that the author may
be stupid or ignorant.
I am as a matter of objective fact a genius.
The key thing that I have been missing is
a succinct set of terms-of-the-art that refer
to the exact meanings that I intend. Outside
of PTS there is no such set of terms-of-the-art.
In such situations it is best to work on problem you want to complete
first, if possible. If somethen prevents working on that problme then
on what you want to complete next.
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
The complete structure of this system is now defined
within ordinary Proof Theoretic Semantics.
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