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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: Sun, 23 Feb 2025 22:39:52 -0600
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On 2/23/2025 8:50 PM, Richard Damon wrote:
> On 2/23/25 1:08 PM, olcott wrote:
>> On 2/22/2025 9:56 PM, Richard Damon wrote:
>>> On 2/22/25 1:42 PM, olcott wrote:
>>>> 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. We simply toss his whole mess out the window and
>>>> reformulate a computable Truth predicate that works correctly.
>>>
>>> But his logic follows from the premises.
>>>
>>> Maybe your logic just can't handle that level of system.
>>>
>>>>
>>>> It is all ultimately anchored relations between finite
>>>> strings even if we must toss all of logical out the window
>>>> to do this correctly.
>>>
>>> And to do what you want, you have to limit your logic system to not 
>>> be able to define the full Natural Number system, as that is what 
>>> allows Tarski to do what he does (like Godel does).
>>>
>>>>
>>>> We are answering the question:
>>>> What are the relationships between arbitrary finite strings
>>>> such that the semantic property of True(L, x)
>>>> (where L and x are finite strings) can always be correctly
>>>> determined for every finite string having a truth value that is
>>>> entirely verified by its relation to other finite strings.
>>>>
>>>
>>> And, if the logic system can support the properties of the Natural 
>>> Number system, and a definition of the predicate True, it can be 
>>> shown that you can create the equivalent of
>>>
>>> Let P be defined as Not( True(L, P))
>>>
>>> in that system, and thus P is a semantically valid, 
>>
>> Not at all. That is the same as saying you know
>> that it is true that all squares are always round.
>>
> 
> Really, then where is the error in his derivation?
> n

You clearly have no idea what "semantically sound" means.
The only correct rebuttal to this is you proving that
you do know this by providing the details of exactly what
"semantically sound" means.

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