Re: The key undecidable instance that I know about

On 3/9/25 6:28 PM, olcott wrote:

On 3/9/2025 4:43 PM, Richard Damon wrote:

On 3/9/25 4:08 PM, olcott wrote:

On 3/9/2025 2:24 PM, Richard Damon wrote:

On 3/9/25 1:15 PM, olcott wrote:

Is the Liar Paradox True or False?
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LP := ~True(LP)
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?- LP = not(true(LP)).
LP = not(true(LP)).
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?- unify_with_occurs_check(LP, not(true(LP))).
false.
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Its infinitely recursive structure makes it neither true nor false.
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The liar's paradox isn't an "undecidable" instance, as "undecidable" is about a problem that has a true or false answer that can not be computed for every case.
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Tarski thought that is was undecidable and anchored his
whole proof in it.
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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

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Note, he says to construct the antinomy of the liar in the METALANGUAGE representing the statement x in the LANGUAGE. Thus "x" is *NOT* the liar, but something that with the additional information of the metalanguage can be reduced to it.
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 "the antinomy of the liar in the metalanguage"
<is>
{the antinomy of the liar in the metalanguage}

So, you admit you don't understand what that means?
Do you understand the differene between the metalanguage and the language?
You do understand that the whole proof is about the Truth Predicate in the LANGUAGE, not the Metalanguage.

 And my understanding of his metalanguage that I have
had for several years and just refreshed from the
original source material does seem to prove that
this does mean that Tarski did anchor his whole
proof in the antinomy of the liar.

And clearly you don't understand the meaning of the metalanguage.
Note, the antinomy of the liar in the metalanguage is a result that comes from the actual statement "x", that is in the language gets manipulated based on new concepts from the metalanguage allowing it to be simplifed.
Your ignorance of how that is done is NOT an error on Tarski's part, just stupidity on yours.

 Until you provide ALL OF THE REASONING PROVIDING
ALL OF THE DETAILS OF EXACTLY HOW I AM WRONG
it seems reasonable to conclude that you do not
have any of these details and only have pure bluster.
 

Not my job.
You need to point to the actual logical step you think Tarski got wrong, not a conclusion you disagree with.
In particular, you need to show a claim he makes that is not supported by what he has shown or from valid logical reasoning. Note, you can't alter the rules of logic to be something different than what Tarski is using, or you are just admitting that you don't know what you are talking about.
Note, the paragraph you quote from page 248 isn't making a new claim, but is pulling forward from his previous work, so if you disagree with that step, you need to show how it doesn't follow from that previous work, or the error in that previous work. Your not understanding it is n0t finding an error in it.