Re: The mistake of the Tarski Proof

On 31/05/24 07:01, olcott wrote:

Tarski's Liar Paradox from page 248
    It would then be possible to reconstruct the antinomy of the liar
    in the metalanguage, by forming in the language itself a sentence
    x such that the sentence of the metalanguage which is correlated
    with *x asserts that x is not a true sentence*
    https://liarparadox.org/Tarski_247_248.pdf
 *Formalized as*
x ∉ True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_275_276.pdf
 *adapted to become this*
x ∉ Pr if and only if p // line 1 of the proof
 Here is the Tarski Undefinability Theorem proof
(1) x ∉ Provable if and only if p // assumption (see above)
(2) x ∈ True if and only if p // Tarski's convention T
(3) x ∉ Provable if and only if x ∈ True. // (1) and (2) combined
(4) either x ∉ True or x̄ ∉ True; // axiom: ~True(x) ∨ ~True(~x)
(5) if x ∈ Provable, then x ∈ True; // axiom: Provable(x) → True(x)
(6) if x̄ ∈ Provable, then x̄ ∈ True; // axiom: Provable(~x) → True(~x)
(7) x ∈ True
(8) x ∉ Provable
(9) x̄ ∉ Provable
 The expression forming line (1) of the proof is directly derived from
the liar paradox as shown above.
 

And what is your problem with it? You see the words "liar paradox" and your brain turns off and you write nonsense.