Re: The key undecidable instance that I know about

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

 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.
 

"the antinomy of the liar in the metalanguage"
<is>
{the antinomy of the liar in 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.
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.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer