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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: Mon, 17 Mar 2025 08:18:42 -0500
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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*

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)


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