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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 07:33:25 -0400
Organization: i2pn2 (i2pn.org)
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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.

> 
> 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 
to get to a goal, something that seems to be beyond you.

You are just too stupid to understand the thoughts he is thinking 
because you "logic" isn't correct, and too simple.