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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception --- Ultimate Foundation of Truth
Date: Mon, 3 Mar 2025 17:30:06 +0200
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On 2025-03-01 20:33:49 +0000, olcott said:

> 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.

A directed graph of an evaluation sequence is not a part of X. Whether
X is true may be known from other considerations.

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

It can but needn't be expanded that way.

-- 
Mikko