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

On 3/16/2025 8:19 AM, Mikko wrote:

On 2025-03-15 17:15:39 +0000, olcott said:
 

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

On 2025-03-11 03:23:51 +0000, olcott said:
>

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.

>
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.

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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.
>

>
bool True(X)
{
   if (~unify_with_occurs_check(X))
     return false;
   else if (~Truth_Bearer(X))
    return false;
   else
    return IsTrue(X);
}
>
LP := ~True(LP)
True(LP) resolves to false.

>
~True(LP) resolves to true

>
It may seem that way if you fail to understand
Clocksin & Mellish explanation of
>
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.
>
ON PAGE 3
https://www.researchgate.net/ publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence

>
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".

 The above is irrelevant to the fact that you didn't say anothing about
the text you quoted.
 

LP := ~True(LP) expanded to infinite recursion
~True(~True(~True(~True(~True(~True(...))))))
The same way that Clocksin and Mellish do on their example
that you dishonestly keep ignoring.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer