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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: Sat, 22 Mar 2025 18:14:34 +0200
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On 2025-03-21 12:56:43 +0000, olcott said:

> On 3/21/2025 4:06 AM, Mikko wrote:
>> 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.
> 
> It is self-evident that both expressions specify infinite recursion.
> You denied this so many times in so many ways it was as if you
> formed your rebuttals without ever even glancing at any of my words.

It is self-evident that neither that nor your previous comment is
relevant to the fact that you quoted a text witout saying anything
about it.

-- 
Mikko