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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception ---
 Ultimate Foundation of Truth
Date: Sat, 1 Mar 2025 16:58:38 -0500
Organization: i2pn2 (i2pn.org)
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On 3/1/25 3:33 PM, olcott wrote:
> 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
> 

Except that they aren't looking at the ACTUAL definition of G, just the 
approximation derived from its meaning in the Meta system.

I don't think Prolog can handle the ACTUAL definition of G that Godel 
derives.