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

On 2/26/25 12:02 AM, olcott wrote:

On 2/25/2025 10:21 PM, Richard Damon wrote:

On 2/25/25 4:10 PM, olcott wrote:

On 2/25/2025 9:35 AM, Mikko wrote:

On 2025-02-24 21:44:10 +0000, olcott said:
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On 2/24/2025 2:58 AM, Mikko wrote:

On 2025-02-22 18:42:44 +0000, olcott said:
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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.

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It is not required by any misconception. It is required by the
meanings of the words and symbols, in particular "predicare"
and "~".

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That none of modern logic can handle expressions
that are not truth bearers is their error and
short-coming.

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Why should any logic permit formulas that are not truth-bearers?
(Of course, term expressions are not truth-bearers.)
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Undecidable expressions are only undecidable because they
are not truth bearers. Logic ignores this and faults the
system and not the expression
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Nope. And "expressions" are not "undecidable", but "Problems" are.
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 A specific problem instance is a single finite string expression input
to a specific decider.

And there is not an issue with getting the answer to that particular problem. Note, it isn't the decider that defines the value of the expression, it is the problem statement that the instance is from.
For instance, for a Halt Decider, the question is does the program the input represent Halt when it is run, and that ALWAYS has an answer, so that instance is "decidable". We may not know the answer, but it has one, and since non-halting can't always be finitely determinable, we find we can't compute the answer.
For instance, the halting of DD is NOT "undecidable", as HHH1 was able to simulate it to the end, showing it halts. The HHH you have provided just has a "bug" in it that misunderstands the nature of HHH.
You are just showing that you fundamentally are ignorant of important aspects of the field, and too stupid to see that error.

 

You seem to have a fundamental problem with the meaning of the words, likely because you can't handle the needed abstractions.
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Of course, since you don't understand what a "program" is, you never were on a good track.