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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: Sat, 15 Mar 2025 22:12:57 -0400
Organization: i2pn2 (i2pn.org)
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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.

This is your problem, you just don't understand logic and its systems, 
so you don't understad the difference between the language/system and 
the metalanguage/metasystem, because you idea of "logic" doesn't follow 
the same sort of rules, it seems because you don't understand how rules 
actually work.