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

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.

 But is irrelevent to your arguement.
 

 "It would then be possible to reconstruct the antinomy of the liar
  in the metalanguage, by forming in the language itself a sentence"

 Right, the "Liar" is in the METALANGUAGE, not the LANGUAGE where the predicate is defined.
 You are just showing you don't understand the concept of Metalanguage.
 

 Thus anchoring his whole proof in the Liar Paradox even if
you do not understand the term "metalanguage" well enough
to know this.

 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.
--
Mikko