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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 14:57:40 +0200
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On 2025-03-17 13:18:42 +0000, olcott said:

> On 3/17/2025 4:04 AM, Mikko wrote:
>> 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.
>> 
> 
> *It seems to me that you are dishonest abut that*

Doesn't matter. Hopefully readers can see that you are dishonest but
that is their problem, not yours or mine.

> BEGIN:(Clocksin & Mellish 2003:254)
> Finally, a note about how Prolog matching sometimes differs from the 
> unification used in Resolution. 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. In this example, foo(Y) is matched against Y, which 
> appears within it. As a result, Y will stand for foo(Y), which is 
> foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))), 
> and soon. So Y ends up standing for some kind of infinite structure.
> END:(Clocksin & Mellish 2003:254)

The above quote is irrelevant to the question whether ~True(LP) resolves
to true.

-- 
Mikko