Re: Mathematical incompleteness has always been a misconception --- Ultimate Foundation of Truth

On 2/22/2025 3:25 AM, Mikko wrote:

On 2025-02-22 04:44:35 +0000, olcott said:
 

On 2/21/2025 7:05 PM, Richard Damon wrote:

On 2/21/25 6:19 PM, olcott wrote:

On 2/20/2025 2:54 AM, Mikko wrote:

On 2025-02-18 03:59:08 +0000, olcott said:

Tarski anchored his whole proof in the Liar Paradox.
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By showing that given the necessary prerequisites, The equivalent of the Liar Paradox was a statement that the Truth Predicate had to be able to handle, which it can't.
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It can be easily handled as ~True(LP) & ~True(~LP), Tarski just
didn't think it through.

 No, it can't. Tarski requires that True be a predicate, i.e, a truth
valued function of one term.

It does not matter a whit what the Hell his misconceptions
required. We simply toss his whole mess out the window and
reformulate a computable Truth predicate that works correctly.
It is all ultimately anchored relations between finite
strings even if we must toss all of logical out the window
to do this correctly.
We are answering the question:
What are the relationships between arbitrary finite strings
such that the semantic property of True(L, x)
(where L and x are finite strings) can always be correctly
determined for every finite string having a truth value that is
entirely verified by its relation to other finite strings.

Therefore LP must be a term. But the
argument of ~ must be a formula, not a term. Therefore the expression
~True(LP) & ~True(~LP) is not syntactiaclly valid and therefore does
not mean anything.
 

--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer