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

On 3/15/2025 1:08 PM, olcott wrote:

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
LP := ~True(LP) resolves to true
>
Therefore the assumption that a correct True() predicate exists is proven false.

 When you stupidly ignore Prolog and MTT that
both prove there is a cycle in the directed graph
of their evaluation sequence. If you have no idea
what "cycle", "directed graph" and "evaluation sequence"
means then this mistake is easy to make.
 

That doesn't change the fact that since True(LP) evaluates to false, that ~True(LP) evaluates to true.
And since ~True(LP) is the same as LP, that shows that LP is true.  That means True(LP) was wrong, which is a contradiction, therefore the assumption that a correct True() exists is proven false.