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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception ---
 Ultimate Foundation of Truth
Date: Sat, 1 Mar 2025 14:33:49 -0600
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On 3/1/2025 3:10 AM, Mikko wrote:
> On 2025-02-28 23:41:09 +0000, olcott said:
> 
>> On 2/28/2025 4:46 AM, Mikko wrote:
>>> On 2025-02-25 21:10:10 +0000, olcott said:
>>>
>>>> On 2/25/2025 9:35 AM, Mikko wrote:
>>>>> On 2025-02-24 21:44:10 +0000, olcott said:
>>>>>
>>>>>> On 2/24/2025 2:58 AM, Mikko wrote:
>>>>>>> On 2025-02-22 18:42:44 +0000, olcott said:
>>>>>>>
>>>>>>>> On 2/22/2025 3:25 AM, Mikko wrote:
>>>>>>>>> On 2025-02-22 04:44:35 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>> On 2/21/2025 7:05 PM, Richard Damon wrote:
>>>>>>>>>>> On 2/21/25 6:19 PM, olcott wrote:
>>>>>>>>>>>> On 2/20/2025 2:54 AM, Mikko wrote:
>>>>>>>>>>>>> On 2025-02-18 03:59:08 +0000, olcott said:
>>>>>>>>
>>>>>>>>
>>>>>>>>>>>> Tarski anchored his whole proof in the Liar Paradox.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> By showing that given the necessary prerequisites, The 
>>>>>>>>>>> equivalent of the Liar Paradox was a statement that the Truth 
>>>>>>>>>>> Predicate had to be able to handle, which it can't.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> It can be easily handled as ~True(LP) & ~True(~LP), Tarski just
>>>>>>>>>> didn't think it through.
>>>>>>>>>
>>>>>>>>> No, it can't. Tarski requires that True be a predicate, i.e, a 
>>>>>>>>> truth
>>>>>>>>> valued function of one term.
>>>>>>>>
>>>>>>>> It does not matter a whit what the Hell his misconceptions
>>>>>>>> required.
>>>>>>>
>>>>>>> It is not required by any misconception. It is required by the
>>>>>>> meanings of the words and symbols, in particular "predicare"
>>>>>>> and "~".
>>>>>>
>>>>>> That none of modern logic can handle expressions
>>>>>> that are not truth bearers is their error and
>>>>>> short-coming.
>>>>>
>>>>> Why should any logic permit formulas that are not truth-bearers?
>>>>> (Of course, term expressions are not truth-bearers.)
>>>>
>>>> Undecidable expressions are only undecidable because they
>>>> are not truth bearers. Logic ignores this and faults the
>>>> system and not the expression
>>>
>>> An undecidable expression is a thruth bearer.
>>
>> Truth bearer means unequivocally divided into exactly
>> one of true or false.
> 
> In a particular application. Even then the truth value, althogh known
> to exist, may be unknown.
> 

When an expression X has a cycle in the directed graph
of its evaluation sequence then X is not a truth bearer.

LP := ~True(LP) expands to
~True(~True(~True(~True(~True(~True(~True(...)))))))

The exact same thing as Clocksin and Mellish on page 6:
Y will stand for ... foo(foo(foo(Y))), and so on.

https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence 


-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer