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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: Mon, 24 Feb 2025 17:11:58 -0600
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On 2/24/2025 6:27 AM, Richard Damon wrote:
> On 2/23/25 11:39 PM, olcott wrote:
>> 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.
>>
> 
> Sure I do.
> 
> A Systems is semantically sound if every statement that can be proven is 
> actually true by the systems semantics,

That is very good.

> in other words, the system 
> doesn't allow the proving of a false statement.
> 

That is not too bad yet ignores that some expressions
might not have any truth value.

> Note, "Semantics" deals with the meaning IN THE SYSTEM, and not just the 
> meaning of the words being used. 

I am referring to the system of ALL knowledge that can be expressed
using language. I  have always only been referring to this system
and you keep forgetting.

> If formal logic, which has been the 
> field you have been discussing in, even if you don't understand it or 
> want it to be, defines semanticly true as any statement that can be 
> reached by (a possibly infinite) chain of valid reasoning steps, and 
> thus a Formal System is always Semantically Sound as long as the given 
> facts in the system are not contradictory, and it is based on consistant 
> logical operators.
> 


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