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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: This is how I overturn the Tarski Undefinability theorem
Date: Sat, 31 Aug 2024 15:11:13 -0400
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On 8/31/24 2:48 PM, olcott wrote:
> *This is how I overturn the Tarski Undefinability theorem*
> An analytic expression of language is any expression of formal or 
> natural language that can be proven true or false entirely on the basis 
> of a connection to its semantic meaning in this same language.
> 
> This connection must be through a sequence of truth preserving 
> operations from expression x of language L to meaning M in L. A lack of 
> such connection from x or ~x in L is construed as x is not a truth 
> bearer in L.

Right, so when x in L is defined to be !True(L,x) does such a connetion 
exist?


> 
> Tarski's Liar Paradox from page 248
>     It would then be possible to reconstruct the antinomy of the liar
>     in the metalanguage, by forming in the language itself a sentence
>     x such that the sentence of the metalanguage which is correlated
>     with x asserts that x is not a true sentence.
>     https://liarparadox.org/Tarski_247_248.pdf

Right, he *SHOWS* that in the system, it is possible to create the 
statement that

x (in L) is defined to be ~True(L, x)

PERIOD.

Try to show where is proof of such a statement is wrong.
Your problem is you don't understand what Tarski is doing at all, so you 
can't point to a statement that is in error, just that you think the 
answer must be wrong. THAT is not a "refuation", just proof that it is 
likely that the error is in *YOUR* ideas,

So, if you claim that such a statement x can neither be established or 
refuted in L, then BY THE DEFINITION of the "True" prediciate, that is 
that True is TRUE if the statement is actually true, while FALSE for all 
other cases, either being refutable, or being a non-truth bearer, then 
True(L, x) must be FALSE, but that means that !True(L, x) must be TRUE, 
and thus x *IS* establish as a TRUE statement, derivable from the fact 
that True(L, x) was FALSE, and the definition of negation.

This means that there exist a statement (x) which is TRUE, but True(L,x) 
is FALSE, and thus the predicate True can not meet its definition.

This shows that no such predicate can meet that definition.

Unless you can resolve THAT contradiciton somehow, you have to accept 
the conclusion, or just admit you don't understand how logic works.

> 
> Formalized as:
> x ∉ True if and only if p
> where the symbol 'p' represents the whole sentence x
> https://liarparadox.org/Tarski_275_276.pdf
> 
> *Formalized as Prolog*

But that is invalid, as Prolog doesn't support the needed degree of logic.

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

As Prolog admits here. All you have done here is proven that you don't 
actually understand how logic works.

> 
> When formalized as Prolog unify_with_occurs_check()
> detects a cycle in the directed graph of the evaluation
> sequence proving the LP is not a truth bearer.

Which is meaningless as Prolog doesn't support the needed level of 
logic, and proves that YOU don't support the needed level of logic, and 
thus your "arguement" is just invalid, and you claims just lies.

> 
> The purpose of this work was to show that algorithmic
> undecidability is a misconception providing more details
> than Wittgenstein's rebuttal of Gödel.
> 
> https://www.liarparadox.org/Wittgenstein.pdf
> 

Which was a statement taken from unpublished papers, and was apparently 
from before Wittgenstein had even read the actual Godel paper.

We don't know if Wittgenstein even continued to believe this, with the 
question, if he did, why did he not publish it?