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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: A different perspective on undecidability --- incorrect question
Date: Mon, 21 Oct 2024 22:17:37 -0500
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On 10/21/2024 9:48 PM, Richard Damon wrote:
> On 10/21/24 10:04 PM, olcott wrote:
>> On 10/16/2024 11:37 AM, Mikko wrote:
>>> On 2024-10-16 14:27:09 +0000, olcott said:
>>>
>>>> The whole notion of undecidability is anchored in ignoring the fact 
>>>> that
>>>> some expressions of language are simply not truth bearers.
>>>
>>> A formal theory is undecidable if there is no Turing machine that
>>> determines whether a formula of that theory is a theorem of that
>>> theory or not. Whether an expression is a truth bearer is not
>>> relevant. Either there is a valid proof of that formula or there
>>> is not. No third possibility.
>>>
>>
>> After being continually interrupted by emergencies
>> interrupting other emergencies...
>>
>> If the answer to the question: Is X a formula of theory Y
>> cannot be determined to be yes or no then the question
>> itself is somehow incorrect.
> 
> Only if "can not be determined" means that there isn't an actual answer 
> to it,
> 
> Not that we don't know the answer to it.
> 
> For instance, the Twin Primes conjecture is either True, or it is False, 
> it can't be a non-truth-bearer, as either there is or there isn't a 
> highest pair of primes that differs by two.
> 

Sure.

> The fact we don't know, and maybe can never know, doesn't make the 
> question incorrect.
> 
> Some truth is just unknowable.
> 

Sure.

>>
>> An incorrect question is an expression of language that
>> is not a truth bearer translated into question form.
> 
> Right, and a question that we don't know (or maybe can't know) but is 
> either true or false, is not an incorrect question.
> 

Sure.

>>
>> When "X a formula of theory Y" is neither true nor false
>> then "X a formula of theory Y" is not a truth bearer.
>>
>>
>>
> 
> Does D halt, is not an incorrect question, as it will halt or not.
> 

Tarski is a simpler example for this case.
His theory rightfully cannot determine whether
the following sentence is true or false:
"This sentence is not true".
Because that sentence is not a truth bearer.

That does not mean that True(L,x) cannot be defined.
It only means that some expression ore not truth bearers.

> That the H that it was built from won't give the right answer is 
> irrelevent.
> 
> You just don't understand what the terms mean, because you CHOSE to make 
> youself ignorant, and thus INTENTIONALY made yourself into a pathetic 
> ignorant pathological lying idiot.
> 
> Sorry, but that is the facts.
> 




-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer