Re: The key undecidable instance that I know about --- Truth-bearers ONLY

On 3/17/25 12:36 AM, olcott wrote:

On 3/16/2025 9:52 PM, Richard Damon wrote:

On 3/16/25 8:22 PM, olcott wrote:

On 3/16/2025 5:50 PM, Richard Damon wrote:

On 3/16/25 10:32 AM, olcott wrote:

On 3/16/2025 6:33 AM, Richard Damon wrote:

On 3/15/25 10:37 PM, olcott wrote:

On 3/15/2025 9:12 PM, Richard Damon wrote:

On 3/15/25 9:19 PM, olcott wrote:

On 3/15/2025 3:44 PM, Richard Damon wrote:

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

On 3/11/2025 5:50 AM, Mikko wrote:

On 2025-03-11 03:23:51 +0000, olcott said:
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On 3/10/2025 9:49 PM, dbush wrote:

On 3/10/2025 10:39 PM, olcott wrote:

On 3/10/2025 9:21 PM, Richard Damon wrote:

On 3/10/25 9:45 PM, olcott wrote:

On 3/10/2025 5:45 PM, Richard Damon wrote:

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

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

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WHich is irrelevent, as that isn't the statement in view, only what could be shown to be a meaning of the actual statement.
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The Liar Paradox PROPERLY FORMALIZED <is> Infinitely recursive
thus semantically incorrect.

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But is irrelevent to your arguement.
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"It would then be possible to reconstruct the antinomy of the liar
  in the metalanguage, by forming in the language itself a sentence"

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Right, the "Liar" is in the METALANGUAGE, not the LANGUAGE where the predicate is defined.
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You are just showing you don't understand the concept of Metalanguage.
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Thus anchoring his whole proof in the Liar Paradox even if
you do not understand the term "metalanguage" well enough
to know this.

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Yes, there is a connection to the liar's paradox, and that is that he shows that the presumed existance of a Truth Predicate forces the logic system to have to resolve the liar's paradox.
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bool True(X)
{
   if (~unify_with_occurs_check(X))
     return false;
   else if (~Truth_Bearer(X))
    return false;
   else
    return IsTrue(X);
}
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LP := ~True(LP)
True(LP) resolves to false.

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~True(LP) resolves to true

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It may seem that way if you fail to understand
Clocksin & Mellish explanation of
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Most Prolog systems will allow you to
satisfy goals like:
   equal(X, X).
   ?- equal(foo(Y), Y).
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that is, they will allow you to match a
term against an uninstantiated subterm of itself.
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ON PAGE 3
https://www.researchgate.net/ publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence

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That you can quote some text but don't say anything about it supports the
hypthesis that you don't understand the text you quoted.
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I said that unify_with_occurs_check() detects
cycles in the directed graph of the evaluation
sequence of an expression that does explain
everything even if it seems like I said
blah, blah, blah to everyone not knowing the
meaning of these words: "cycle", directed graph"
"evaluation sequence".
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Except for the fact that you aren't giving it the actual x that Tarski creates (or the G for Godel) as expressed in the language, in part because it uses logic that can't be expressed in Prolog.
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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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Formalized as:

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NO!!
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That is what it reduces to in the metalangugae, but not what it is in the language, which is where it counts.
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x ∉ True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_275_276.pdf
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Not all all. It is merely that Tarski's somewhat clumsy
syntax does not encode the Liar Paradox where its
pathological self-reference can be directly seen.

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No, Tarski's syntax
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He does not formalize most important part:
"where the symbol 'p' represents the whole sentence x"
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If he did formalize that most important part it would
be this: x ∉ True if and only if x
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Nope, you are just not understanding that 'x' is a fairly complecated sentence in the language, for which in the metalanguge, it can be reduced to the symbol p.
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When Tarski formalized the Liar Paradox
HE DID IT INCORRECTLY.

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We wasn't "Formalizing" the Liar Paradox.
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     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.

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Apparently you don't understand what it means to "reconstruct" something.
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Incorrectly reconstruct "the antinomy of the liar"
by some incorrect means. Tarski stupidly forgot to
include self-reference.
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Nope, you don't understand what he did.
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Where is the error in the previous proof that shows how to construct that x?
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 x ∉ True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_275_276.pdf
That does not say: "This sentence is not true"
 The self-reference is only in the English and not
encoded n the formalism thus cannot be directly
evaluated in the formalism.
 This does say: LP := ~True(LP)
"This sentence is not true"

But that sentence you started with is only in the METALANGUAGE, so your "Formalism" isn't a statement in the LANGUAGE.
x is a fully defined expression in the language developed per that earlier proof.
So, x doesn't NEED to be "formalized" as it IS formalized.
The issue is that the "self-reference" isn't anything expressed in the LANGUAGE, so isn't part of x itself, but is based on properties established in the METALANGUAGE that can be expressed in the language.
Sorry, you are just showing that you don't understand what you are talking about.

 

I guess you are just going to need to admit you are too stupid to understand what he did.
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He didn't "forget" to include self-reference, he just shows that you can build references indirectly with mathematics in a way that it isn't there in the logical form, Just like Godel did.
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Perhaps the problem with Tarski is that his proof gets abstract enough that it is harder to understand how he does it, but it is still done correctly, unless you can point to an actual error.
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As opposed to saying the answer doesn't match your OPINION of what it should be, for which you have NO PROOF that your OPINION has any real basis other than your admitted lies.