I imagine that that happens because you learn from there. I find nonsense there all the time. The people who run it are oligophrenic. So I avoid it like a plague. — Lionino

Most people can't understand his original proof
https://liarparadox.org/Tarski_275_276.pdf
so I use the Wikipedia simplification.

This is where Tarski anchors his proof in the actual Liar Paradox
https://liarparadox.org/Tarski_247_248.pdf

I have no dog in the fight. I don't know if the article on Tarski is correct or not, I don't have much of a way to judge myself. Mine was just an off-the-cuff comment.

Before the reply to my post, I deleted "To see that, you just need to read the article that you yourself say is "clear and accurate"", as I thought it would be better not to invite referencing that article again.

But to address that article, here are the proofs without ""liar"" (scare quotes in original), "ask", "truth bearer" or anything else extraneous to the mathematical proofs:

In this context, 'formula' and 'sentence' mean 'formula in the language of first order arithmetic' and 'sentence in the language of first order arithmetic'.

In this context, 'true' and 'false' mean 'true in the standard model for the language of first order arithmetic' and 'false in in the standard model for the language of first order arithmetic'.

For every formula M, let g(M) be the numeral for the Godel number of M.

/

Theorem: There is no formula T(x) such that for every sentence S, T(g(S)) is true if and only if S is true.

Proof:

Toward a contradiction, suppose there is such a T(x).

So, there is a formula D(x) such that for every numeral m, D(m) is true if and only if m is the numeral for the Godel number of a formula P(x) such that P(m) is false. (The steps in obtaining this line from the previous line are not included in the article.)

D(g(D(x))) is true
if and only if
g(D(x)) is the numeral for the Godel number of a formula P(x) such that P(g(D(x))) is false.

Toward a contradiction, suppose D(g(D(x))) is true.
So g(D(x)) is the numeral for the Godel number of a formula P(x) such that P(g(D(x))) is false.
g(D(x)) is g(P(x)), so D(x) is P(x), so D(g(S(x))) is P(g(S(x))), so D(g(S(x))) is false. Contradiction.

Toward a contradiction, suppose D(g(D(x))) is false.
So it is not the case that g(D(x)) is the numeral for the Godel number of a formula P(x) such that P(g(D(x))) is false.
So D(g(D(x))) is true. Contradiction.

So there is no formula T(x) such that for every sentence S, T(g(S)) is true if and only if S is true.

/

Theorem: There is no formula T(x) such that for every sentence S, S is true if and only if T(g(S)) is true.

Proof:

Lemma: For every formula P(x) there is a sentence D such that D <-> P(g(D)) is true.

Toward a contradiction, suppose there is a formula T(x) such that for every sentence S, S is true if and only if T(g(S)) is true.

So, for every sentence S, S <-> T(g(S)) is true.

By the lemma, there is a sentence D such that D <-> ~T(g(D)) is true. But also, D <-> T(g(D)) is true. Contradiction.

So there is no formula T(x) such that for every sentence S, S is true if and only if T(g(S)) is true.

I don't think they're stupid. Rather, I find that there is complacency and sloppiness in the writing of certain articles, sometimes to the extent that there are plain falsehoods in them. But in the case of the article being discussed, I'm not pointing out falsehoods, but rather the confusions the article opens.

↪PL Olcott I have no dog in the fight. I don't know if the article on Tarski is correct or not, I don't have much of a way to judge myself. Mine was just an off-the-cuff comment. — Lionino

Personally I love Wikipedia it always gives me a succinct clear gist of the whole idea in the first couple of sentences. When used this way it seems to be a very high quality standard.

I always go on the basis that his true predicate struggles with the Liar Paradox.
and concludes that no True (Language, Expression) can exists because would
have to handle the Liar Paradox incorrectly.

This is how I propose to handle the Liar Paradox correctly
LP = "This sentence is not true."
Boolean True(English, LP) is false
Boolean True(English, ~LP) is false

I would estimate that the users use ordinary English and the Cyc lexical analyzer converts words into GUIDs. — PL Olcott

That sounds like a cumbrous task for normal users to go through for using the system. They would want just type in the expressions in their ordinary use of the language or words into the system, and expect to get the correct definitions for their queries. Somehow the Cyc Project must be able to convert the expressions or words into the unique GUID to narrow down and select the correct definitions for them. Would you agree?

I don't think they're stupid. — TonesInDeepFreeze

I personally think so. I am convinced Wik***dia and Reddit have the same userbase.

Personally I love Wikipedia it always gives me a succinct clear gist of the whole idea in the first couple of sentences. When used this way it seems to be a very high quality standard. — PL Olcott

That is always the excuse given by users of that site. It is either "a good summary", when there are often mistakes right in the header and the site itself is rotten to the core, or to "check the sources on the bottom". Nobody who says that actually checks the sources on the bottom of course, otherwise they would notice the users there frequently misquote the sources they use. Especially because they have little understanding of the topic they are writing about.

That sounds like a cumbrous task for normal users to go through for using the system. They would want just type in the expressions in their ordinary use of the language or words into the system, and expect to get the correct definitions for their queries. Somehow the Cyc Project must be able to convert the expressions or words into the unique GUID to narrow down and select the correct definitions for them. Would you agree? — Corvus

The Cyc project converts the words of the users into multiple GUIDs and then from context narrows down to list to the intended meanings.

That is always the excuse given by users of that site. It is either "a good summary", when there are often mistakes right in the header and the site itself is rotten to the core, or to "check the sources on the bottom". — Lionino

I examine many original sources and then quote Wikipedia as a verified summation of the technical ideas involved. The key point here is that the Tarski Undefinability theorem is anchored in the Liar Paradox and that by itself is its big mistake. Tarski himself shows that his proof is anchored in the Liar Paradox yet does this in a somewhat convoluted way that would be too difficult for most people to follow.

I directly understand his actual proof.
https://liarparadox.org/Tarski_275_276.pdf