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

On 2/22/25 1:42 PM, olcott wrote:

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

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

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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.

But his logic follows from the premises.
Maybe your logic just can't handle that level of system.

 It is all ultimately anchored relations between finite
strings even if we must toss all of logical out the window
to do this correctly.

And to do what you want, you have to limit your logic system to not be able to define the full Natural Number system, as that is what allows Tarski to do what he does (like Godel does).

 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.
 

And, if the logic system can support the properties of the Natural Number system, and a definition of the predicate True, it can be shown that you can create the equivalent of
Let P be defined as Not( True(L, P))
in that system, and thus P is a semantically valid, and thus the predicate must handle it.
Of course, all you have shown is that you are too stupid to understand that work, and superstitiously beleive it must be false, not realizing you are just proving your stupidity.

 

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.
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