Re: The key undecidable instance that I know about

On 3/10/25 11:51 AM, olcott wrote:

On 3/10/2025 6:04 AM, Richard Damon wrote:

On 3/9/25 11:39 PM, olcott wrote:

On 3/9/2025 8:57 PM, Richard Damon wrote:

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}

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

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And clearly you don't understand the meaning of the metalanguage.
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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.
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That does not really show any depth of understanding.
You might have greater depth, yet did not show it yet.

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No, your reply, by not addressing *ANY* of
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Your ignorance of how that is done is NOT an error on Tarski's part, just stupidity on yours.
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Yet you never said how it should be done, thus I
have no way to tell what you say is not pure bluster.
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Maybe because what you want to define can't be.
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Tarski shows how to derive that part in the earlier work. It is clear that you just don't have the brains to understand that discussion, and it isn't my job to educate you on that, particularly when you have declared that you idea of logic fundamentally disagrees with the actual rules of logic, so you fundamentally don't understand how to use logic.
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That you refer to my stupidity yet fail to point out any
mistake seems to be strong evidence that you are clueless.

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Sure I have pointed out your error. You are just too stupid to recognize the.
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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.
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Not my job.
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You need to point to the actual logical step you think Tarski got wrong, not a conclusion you disagree with.
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Yu failure to understand what i said is not my mistake,

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I.E. your claim is that you don't understand the error pointed out to you means the error wasn't pointed out to you.
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 You did not point any the details of any error
the most that you did is state your opinion
that I made some mistake somewhere. Even a bot
as stupid as the original bot Eliza could do that.
 http://en.wikipedia.org/wiki/ELIZA
 

I pointed out that your error was not to point out an actual error, but just disagreeing with a conclusion.
Thus, you are showing that you are just too stupid to know what you are talking about.