[ Followup-To: set ]% This sentence is not true.
In comp.theory olcott <polcott333@gmail.com> wrote:On 4/28/2026 5:22 AM, Alan Mackenzie wrote:[ .... ]In comp.theory olcott <polcott333@gmail.com> wrote:On 4/27/2026 4:03 PM, Alan Mackenzie wrote:
Peter Olcott has never read and understood such a proof. Although not
particularly difficult, it is beyond his understanding.After all these years where I have repeatedly proven ....You have spent years demonstrating you don't understand the concept of a
mathematical proof. You haven't proven anything..... that Gödel himself says that his proof does have pathological self
reference you repeatedly deny this because you and everyone else here
only cares about denigration rather than truth.I care deeply about the truth. Gödel's theorem is part of the truth.Prolog detects [and rejects] pathological self reference in the Gödel
sentenceThis suggests Prolog is not up to the job. Or more likely, the
programmer of that piece of Prolog isn't up to the job.BEGIN:(Gödel 1931:39-41)...there is also a close
...We are therefore confronted with a proposition which asserts its own
unprovability. 15[ Spam snipped ]Yes. You have not read and understood this proof. You have merely
extracted and misunderstood an off the cuff motivational remark from it.So you are trying to get away with saying ....Please stop lying about what I wrote.
that Gödel did not say: ...We are therefore confronted with aYes, Gödel wrote that.
proposition which asserts its own unprovability. 15
I don't see how that is not dishonest.What is dishonest (or more likely ignorant) is your trying to construe
that sentence as being the same as the liar paradox. It's not the same,
as you have been told countless times.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog finally once and for all resolves the Liar Paradox as semantically incoherent within the analytical framework of Proof Theoretical Semantics. It does this on the basis that the LP specifies a cycle in the directed graph of its evaluation sequence, thus not a well founded justification tree.
F ⊢ GF ↔ ¬ProvF(⌜GF⌝)
https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
Olcott's Minimal Type Theory
G ↔ ¬Prov_PA(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔ 01 02
01 G
02 ¬ 03
03 Prov_PA 04
04 Gödel_Number_of 01 // cycle
% 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.
The first incompleteness theorem sentence
has a cycle in the directed graph of its
evaluation sequence making it semantically
incoherent.
This kind of semantically incoherence is
foundational in proof theoretic semantics.
[ .... ]Model Theoretic Semantics is stupidly incorrect
And please note, this theorem is _TRUE_. It has been proven
rigorously and verified by millions of students and academics over
a very long time period.Within the wrong kind of semantics.The theorem is true.
Yet never once examined within the alternative foundation of
proof theoretic semantics utterly replacing foundation of model
theoretic semantics.Whatever proof theoretic semantics is. It would appear it is
insufficiently powerful to do maths with - that it is insufficiently
powerful to express anything it cannot prove.You are a mere sheep that follows the herd.I am an educated person. You are the wilfully ignorant outsider trying
to spread falsehood.
It is not about math, it is about meaning. unprovable essentiallyYou are objectively wrong. Unprovable and untrue are two different
means untrue. Going outside of PA in a separate model of PA has always
been cheating.
things, again, as has been pointed out to you countless times.
You are mistaking your own ignorance of proof theoreticI have no interest in "proof theoretic semantics". It has no relevance,
semantics for my ignorance of Gödel.
whatever it might be. You are, as you admit, ignorant about Gödel's
theorem.
Proof Theoretic Semantics corrects that error.
That I disagree with what you carefully memorized
by rote does not mean that I do not understand what
you carefully memorized by rote.
[ .... ]--
-- Copyright 2026 Olcott
Copyright 2026 Olcott
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.
This required establishing a new foundation
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