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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: The key undecidable instance that I know about --- Truth-bearers ONLY
Date: Thu, 20 Mar 2025 11:59:41 +0200
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On 2025-03-19 23:22:53 +0000, olcott said:

> On 3/19/2025 10:57 AM, Mikko wrote:
>> On 2025-03-19 01:52:01 +0000, olcott said:
>> 
>>> 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.
>> 
>> Not all along, just occasionally. What you did say that Prolog proves
>> that there is a cycle in the directed graph of their evaluation sequence.
>> I said that Prolog does not prove that. Then you posted some examples of
>> prolog not proving that and didn't mention "cycles" any more.
>> 
>>> https://www.swi-prolog.org/pldoc/man?predicate=unify_with_occurs_check/2
>> 
>> That link confirms what I said above. It also said that one of the arguments
>> already has a cycle then that cycle does not prevent unification and does
>> not cause infinite execution.
> 
> Clearly you have no idea what a cycle in a directed graph means.

It is a sin to present a false claim about another person.

-- 
Mikko