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

On 2025-03-17 13:24:24 +0000, olcott said:
 

On 3/17/2025 4:08 AM, Mikko wrote:

On 2025-03-15 17:08:33 +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
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.

>
Prolog does not prove anything other than what you ask. I don't think
you can ask Prolog whether there is a cycle in LP after LP = not(true(LP)).

>
?- LP = not(true(LP)).
LP = not(true(LP)).

 Meaning that LP = not(true(LP)) is accepted as a valid query and evalated
as true with the implication that LP is the same as not(true(LP)).
 

?- unify_with_occurs_check(LP, not(true(LP))).
false.

 Meaning that unify_with_occurs_check(LP, not(true(LP))) is accepted as a
valid query and evaluated as false.