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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: The key undecidable instance that I know about --- Truth-bearers
 ONLY
Date: Sun, 16 Mar 2025 18:50:05 -0400
Organization: i2pn2 (i2pn.org)
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On 3/16/25 10:32 AM, olcott wrote:
> 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.

Apparently you don't understand what it means to "reconstruct" something.

Or the difference between the "Langauge" and the "Metalanguage"


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