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

On 2/28/2025 4:59 AM, Mikko wrote:

On 2025-02-26 05:02:13 +0000, olcott said:
 

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.

 No, it is not. The decider is no way a part of a specific problem
instance unless it is a part of that finite string expression.
 

Is the term decider/input pair over your head?
A unique finite string of integers combined
with a specific decider is a SPECIFIC PROBLEM INSTANCE.
A decider is itself a unique finite string of integer
values for any 100% specific system of Turing Machine
descriptions.

That a specific problem instance is a single finite string expression
is true about formal problems but usually not about practical problems.
 

Like how to get your wife to quit yelling at you?
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer