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

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 false.
X = "A box of rocks"
True(X) resolves to false.
True(~X) resolves to false.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer