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

On 2/23/25 11:39 PM, olcott wrote:

On 2/23/2025 8:50 PM, Richard Damon wrote:

On 2/23/25 1:08 PM, olcott wrote:

On 2/22/2025 9:56 PM, Richard Damon wrote:

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:

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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.

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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.

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But his logic follows from the premises.
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Maybe your logic just can't handle that level of system.
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It is all ultimately anchored relations between finite
strings even if we must toss all of logical out the window
to do this correctly.

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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).
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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.
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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
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Let P be defined as Not( True(L, P))
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in that system, and thus P is a semantically valid,

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Not at all. That is the same as saying you know
that it is true that all squares are always round.
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Really, then where is the error in his derivation?
n

 You clearly have no idea what "semantically sound" means.
The only correct rebuttal to this is you proving that
you do know this by providing the details of exactly what
"semantically sound" means.
 

Sure I do.
A Systems is semantically sound if every statement that can be proven is actually true by the systems semantics, in other words, the system doesn't allow the proving of a false statement.
Note, "Semantics" deals with the meaning IN THE SYSTEM, and not just the meaning of the words being used. If formal logic, which has been the field you have been discussing in, even if you don't understand it or want it to be, defines semanticly true as any statement that can be reached by (a possibly infinite) chain of valid reasoning steps, and thus a Formal System is always Semantically Sound as long as the given facts in the system are not contradictory, and it is based on consistant logical operators.