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

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:

>
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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>

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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).
>
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.
>

>
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.
>

  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

 Formalized as:

NO!!
That is what it reduces to in the metalangugae, but not what it is in the language, which is where it counts.

x ∉ True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_275_276.pdf
 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.

No, Tarski's syntax

 He does not formalize most important part:
"where the symbol 'p' represents the whole sentence x"
 If he did formalize that most important part it would
be this: x ∉ True if and only if x
 

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.
This is your problem, you just don't understand logic and its systems, so you don't understad the difference between the language/system and the metalanguage/metasystem, because you idea of "logic" doesn't follow the same sort of rules, it seems because you don't understand how rules actually work.