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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: The key undecidable instance that I know about --- Truth-bearers
 ONLY
Date: Tue, 18 Mar 2025 20:52:01 -0500
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On 3/18/2025 9:20 AM, Mikko wrote:
> 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.
> 

I have been saying "cycles" all along and it has always been cycles.
https://www.swi-prolog.org/pldoc/man?predicate=unify_with_occurs_check/2

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer