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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: Mon, 17 Mar 2025 11:04:30 +0200
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On 2025-03-16 14:38:16 +0000, olcott said:

> On 3/16/2025 8:19 AM, Mikko wrote:
>> On 2025-03-15 17:15:39 +0000, olcott said:
>> 
>>> On 3/11/2025 5:50 AM, Mikko wrote:
>>>> On 2025-03-11 03:23:51 +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
>>>>> 
>>>>> It may seem that way if you fail to understand
>>>>> Clocksin & Mellish explanation of
>>>>> 
>>>>> Most Prolog systems will allow you to
>>>>> satisfy goals like:
>>>>>    equal(X, X).
>>>>>    ?- equal(foo(Y), Y).
>>>>> 
>>>>> that is, they will allow you to match a
>>>>> term against an uninstantiated subterm of itself.
>>>>> 
>>>>> ON PAGE 3
>>>>> https://www.researchgate.net/ 
>>>>> publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence 
>>>>> 
>>>> 
>>>> That you can quote some text but don't say anything about it supports the
>>>> hypthesis that you don't understand the text you quoted.
>>> 
>>> I said that unify_with_occurs_check() detects
>>> cycles in the directed graph of the evaluation
>>> sequence of an expression that does explain
>>> everything even if it seems like I said
>>> blah, blah, blah to everyone not knowing the
>>> meaning of these words: "cycle", directed graph"
>>> "evaluation sequence".
>> 
>> The above is irrelevant to the fact that you didn't say anothing about
>> the text you quoted.
>> 
> 
> LP := ~True(LP) expanded to infinite recursion
> ~True(~True(~True(~True(~True(~True(...))))))
> The same way that Clocksin and Mellish do on their example
> that you dishonestly keep ignoring.

They don't say so in the above quoted text. What they do say is essentially
what I have said in another context but not relevant here.

-- 
Mikko