Re: The key undecidable instance that I know about

On 3/10/2025 5:45 PM, 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.

 But showing depth isn't my job, as it doesn't require depth to point out your error.
 

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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.

 Why should I try to show an error in Tarski's argument, I think it is sound.
 YOU are the one claiming he is wrong, so YOU have the burden of proof to show that.
 

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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.

 But I have, you are just too stupid to understand it.
 AS I have said, the statement where you say Tarski is making a bad assumption, isn't a statement of assumption, but a pulling forward of a previous result, which you just fail to even try to address, or even indicate you understand what he is trying to say.
 Is seems the problem is he is using theory beyond your ability to understand, so you just assume he is wrong, which is just invalid logic,
 

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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,

 I didn't say I didn't understand what you said, I was pointing out that you never pointed out an actual error in logic, just said the results were illogical by your understand and thus you reject it.
 That isn't how logic works, and just shows your ignorance of the field.
 

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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.
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LP := ~True(LP)  DOES SPECIFY INFINITE RECURSION.

 WHich is irrelevent, as that isn't the statement in view, only what could be shown to be a meaning of the actual statement.
 

The Liar Paradox PROPERLY FORMALIZED <is> Infinitely recursive
thus semantically incorrect.
"It would then be possible to reconstruct the antinomy of the liar
  in the metalanguage, by forming in the language itself a sentence"
Thus anchoring his whole proof in the Liar Paradox even if
you do not understand the term "metalanguage" well enough
to know this.

Since that statement was shown to be a valid statement under just the added assumption that a Truth Predicate Existed,

NOT AT ALL.
We assume that True(X) exists and X = "a box of rocks"
that does not  mean that True() does not exist. It means
that we must reject all Not_Truth_Bearer(X).
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer