Re: The mistake of the Tarski Proof

On 5/31/24 1:01 AM, 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

And, he is pointing out that it has been SHOWN that this can be done, because we have assumed the existance of the Truth Predicate, and other theorems previously proven (which I don't think you understand)

 *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)

NOT ASSUMED, but from a PROVEN STATEMENT

(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.

Nope, you are just showing you are not reading.
Perhaps because of your admitted mental deficiencies.

 When Line (2) is combined with line (1) then line (3) derived. Line (3)
partially derived from the Liar Paradox directly contradicts the axiom
on line (5).
 Since Line (3) partially derived from the Liar Paradox directly
contradicts the axiom at line (5) this proves the Line(3) is based on a
false assumption. That false assumption was line (1).
 

Nope, line (1) was proven from previous work. The assumption we go back to is the assumption of the eistance of the Truth Predicate.