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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: Fri, 21 Mar 2025 11:06:42 +0200
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On 2025-03-20 22:55:17 +0000, olcott said:

> On 3/20/2025 7:57 AM, Mikko wrote:
>> 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.
>> 
> 
> If ?- equal(foo(Y), Y)
> resolves to foo(foo(foo(foo(foo(foo(...))))))
> 
> then ?- LP = not(true(LP)).
> resolves to not(true(not(true(not(true(not(true(...))))))))

Of cours. But that is irrelevant to the fact that you quoted a text
without saying anything about it.

-- 
Mikko