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From: dbush <dbush.mobile@gmail.com>
Newsgroups: sci.logic
Subject: Re: The key undecidable instance that I know about --- Truth-bearers
 ONLY
Date: Mon, 10 Mar 2025 22:49:19 -0400
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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.