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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: Sun, 16 Mar 2025 09:32:34 -0500
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On 3/16/2025 6:33 AM, Richard Damon wrote:
> On 3/15/25 10:37 PM, olcott wrote:
>> On 3/15/2025 9:12 PM, Richard Damon wrote:
>>> On 3/15/25 9:19 PM, olcott wrote:
>>>> On 3/15/2025 3:44 PM, Richard Damon wrote:
>>>>> On 3/15/25 1:15 PM, olcott wrote:
>>>>>> 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".
>>>>>>
>>>>>
>>>>> Except for the fact that you aren't giving it the actual x that 
>>>>> Tarski creates (or the G for Godel) as expressed in the language, 
>>>>> in part because it uses logic that can't be expressed in Prolog.
>>>>>
>>>>
>>>>
>>>> Tarski's Liar Paradox from page 248
>>>>     It would then be possible to reconstruct the antinomy of the liar
>>>>     in the metalanguage, by forming in the language itself a sentence
>>>>     x such that the sentence of the metalanguage which is correlated
>>>>     with x asserts that x is not a true sentence.
>>>>     https://liarparadox.org/Tarski_247_248.pdf
>>>
>>>
>>>
>>>>
>>>> Formalized as:
>>>
>>> NO!!
>>>
>>> That is what it reduces to in the metalangugae, but not what it is in 
>>> the language, which is where it counts.
>>>
>>>> x ∉ True if and only if p
>>>> where the symbol 'p' represents the whole sentence x
>>>> https://liarparadox.org/Tarski_275_276.pdf
>>>>
>>>> Not all all. It is merely that Tarski's somewhat clumsy
>>>> syntax does not encode the Liar Paradox where its
>>>> pathological self-reference can be directly seen.
>>>
>>> No, Tarski's syntax
>>>
>>>>
>>>> He does not formalize most important part:
>>>> "where the symbol 'p' represents the whole sentence x"
>>>>
>>>> If he did formalize that most important part it would
>>>> be this: x ∉ True if and only if x
>>>>
>>>
>>>
>>> Nope, you are just not understanding that 'x' is a fairly complecated 
>>> sentence in the language, for which in the metalanguge, it can be 
>>> reduced to the symbol p.
>>>
>>
>> When Tarski formalized the Liar Paradox
>> HE DID IT INCORRECTLY.
> 
> We wasn't "Formalizing" the Liar Paradox.
> 
     reconstruct the antinomy of the liar
     in the metalanguage, by forming in the language itself a sentence
     x such that the sentence of the metalanguage which is correlated
     with x asserts that x is not a true sentence.

>>
>> LP := ~True(LP) <is> "This sentence is not true"
>> Tarski GOT THIS WRONG.
>>
> 
> Nope, you don't understand what he is doing, because he is using thought 
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