Re: Truthmaker Maximalism and pathological self-reference

On 5/12/2025 6:28 PM, wij wrote:

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]

>
Of course, there are no pathological inputs like this because H does not
exist.

>
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 time is
very dubious.
>
Tradition logic is insufficient for math/logic, the foundation of science.
The implication is profound and goes beyond most people thought.
>
https://sourceforge.net/projects/cscall/files/MisFiles/RealNumber2-en.txt/download
...
Peano's axioms, which are the basis of mathematical logic, have a serious flaw:
Without a termination condition, it is impossible to explain "∞∉ℕ" (if the
definition of numbers relies on Peano's axioms).
This has led to many theories related to infinity, including density and 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 procedual
description)...
>
So, in some POOH's rebuttal (just olcott's text, he don't understand what logic
'if' means) that uses logic (Tarski,Sisper,Russell,PL,...), that logic
themselves are invalid (I should save the long ellaberation).
>
In short, my opinion is that TM/algorithm (C/C++/Assembly could and should 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–Turing thesis: TM cannot be proved to be
exceeded simply because (current) axiomized system is less powerful than TM.
>
Back to POOH's pathological input theory:
The pathological input exists is because POOH exists.
>

>
"This sentence is false" is proven by Prolog
to be semantically incorrect because of its
pathological self-reference. Prolog sees this
as infinitely recursive.
>
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.
>
{Truthmaker Maximalism} is the sub-field of philosophy
that should have the answer to this.
>
"This sentence is not true" has no truthmaker.
"This sentence has no truthmaker" has no truthmaker.
>
There is no sequence of truth preserving operations
from Basic Facts that derives either sentence.
>

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

I already have all this stuff figured out.
I never wasted the time to see what all the opinions
are I simply directly reverse-engineered the answers
from their first principles.

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

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer