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

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

On 2025-03-17 15:56:38 +0000, olcott said:
 

On 3/17/2025 6:26 AM, Richard Damon wrote:

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

 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"
 The self-reference is only in the English and not
encoded n the formalism thus cannot be directly
evaluated in the formalism.
 This does say: LP := ~True(LP)
"This sentence is not true"

 But that sentence you started with is only in the METALANGUAGE, so your "Formalism" isn't a statement in the LANGUAGE.
 x is a fully defined expression in the language developed per that earlier proof.
 So, x doesn't NEED to be "formalized" as it IS formalized.
 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.
 Sorry, you are just showing that you don't understand what you are talking about.
 

 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...

 That very much depends on what does "correctly" mean about "True(X)".
 

 The common meaning of True on the basis of the meaning
of words such as "cats are animals" for all words
and all meanings.