Re: The key undecidable instance that I know about --- Truth-bearers ONLY

On 2025-03-19 01:36:33 +0000, olcott said:
 

On 3/18/2025 9:08 AM, Mikko wrote:

On 2025-03-17 15:56:38 +0000, olcott said:
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On 3/17/2025 6:26 AM, Richard Damon wrote:

On 3/17/25 12:36 AM, olcott wrote:

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x ∉ True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_275_276.pdf
That does not say: "This sentence is not true"
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The self-reference is only in the English and not
encoded n the formalism thus cannot be directly
evaluated in the formalism.
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This does say: LP := ~True(LP)
"This sentence is not true"

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But that sentence you started with is only in the METALANGUAGE, so your "Formalism" isn't a statement in the LANGUAGE.
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x is a fully defined expression in the language developed per that earlier proof.
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So, x doesn't NEED to be "formalized" as it IS formalized.
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The issue is that the "self-reference" isn't anything expressed in the LANGUAGE, so isn't part of x itself, but is based on properties established in the METALANGUAGE that can be expressed in the language.
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Sorry, you are just showing that you don't understand what you are talking about.
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There is no counter-example in the set of human general
knowledge that can be expressed using language such that
True(X) does not work correctly...

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That very much depends on what does "correctly" mean about "True(X)".
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The common meaning of True on the basis of the meaning
of words such as "cats are animals" for all words
and all meanings.

 Not possible (althogh a partial soultion could be useful).