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From: wij <wyniijj5@gmail.com>
Newsgroups: comp.theory
Subject: Re: Truthmaker Maximalism and pathological self-reference
Date: Tue, 13 May 2025 07:28:35 +0800
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In-Reply-To: <vvtveo$1bfib$3@dont-email.me>

On Mon, 2025-05-12 at 18:15 -0500, olcott wrote:
> On 5/12/2025 5:57 PM, wij wrote:
> > On Mon, 2025-05-12 at 17:32 +0100, Ben Bacarisse wrote:
> > [cut]
> > >=20
> > > Of course, there are no pathological inputs like this because H does =
not
> > > exist.
> >=20
> > That is the key point.
> > The 'pathological' input D exists only when the assumed halting decider=
 H exists.
> > D exists AFTER H does, so putting them together to discuss (or to form =
logical
> > expression or even 'theorem', maybe) as though both exist at the same t=
ime is
> > very dubious.
> >=20
> > Tradition logic is insufficient for math/logic, the foundation of scien=
ce.
> > The implication is profound and goes beyond most people thought.
> >=20
> > https://sourceforge.net/projects/cscall/files/MisFiles/RealNumber2-en.t=
xt/download
> > ...
> > Peano's axioms, which are the basis of mathematical logic, have a serio=
us flaw:
> > Without a termination condition, it is impossible to explain "=E2=88=9E=
=E2=88=89=E2=84=95" (if the
> > definition of numbers relies on Peano's axioms).
> > This has led to many theories related to infinity, including density an=
d other
> > laws and logical inferences, to have the same blind spots and mistakes =
(Personal
> > opinion: The reasoning/axiomatic system may need to be changed to a pro=
cedual
> > description)...
> >=20
> > So, in some POOH's rebuttal (just olcott's text, he don't understand wh=
at logic
> > 'if' means) that uses logic (Tarski,Sisper,Russell,PL,...), that logic
> > themselves are invalid (I should save the long ellaberation).
> >=20
> > In short, my opinion is that TM/algorithm (C/C++/Assembly could and sho=
uld be
> > the language for building theorys of math/CS/..), is the foundation of =
science
> > better than contemporary, what-so-called 'strict, consistent/complete' =
axiomized
> > system.
> > Also, this idea can prove Church=E2=80=93Turing thesis: TM cannot be pr=
oved to be
> > exceeded simply because (current) axiomized system is less powerful tha=
n TM.
> >=20
> > Back to POOH's pathological input theory:
> > The pathological input exists is because POOH exists.
> >=20
>=20
> "This sentence is false" is proven by Prolog
> to be semantically incorrect because of its
> pathological self-reference. Prolog sees this
> as infinitely recursive.
>=20
> Here we are 2000 years after the Liar Paradox
> https://en.wikipedia.org/wiki/Liar_paradox#History
> And the best minds in the world are at most pretty
> sure that it isn't true.
>=20
> {Truthmaker Maximalism} is the sub-field of philosophy
> that should have the answer to this.
>=20
> "This sentence is not true" has no truthmaker.
> "This sentence has no truthmaker" has no truthmaker.
>=20
> There is no sequence of truth preserving operations
> from Basic Facts that derives either sentence.
>=20

Google for "contingency" (maybe a 3rd state of logic)

As said previously, 'math/logic' is less powerful than TM.
Traditional logic is limited for CS theories.