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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: A different perspective on undecidability
Date: Wed, 16 Oct 2024 20:47:28 -0400
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On 10/16/24 1:55 PM, olcott wrote:
> On 10/16/2024 12:31 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. 
>>
>> When the question: Is finite string X a theory of L?
>> has no correct answer from YES and NO, then the question
>> is rejected as not a truth bearer.
>>
> 
> I did not say that exactly correctly.
> 
> When the question:
> Is finite string X a theory of L?
> has no correct answer from YES and NO,
> 
> then the statements:
> (a) Finite string X is a theory of L
> and
> (b) Finite string X is NOT a theory of L
> 
> are rejected as not a truth bearers.
> 
> 

How can there not be a Yes or No answer?

Either X IS or it IS NOT a theory of L, as either a proof exists or it 
doesn't.

If X is non-sense, then it isn't a theory of L, as you can't prove 
non-sense to be true in a non-contradictory L.

So, how can THOSE questions not be a truth bearers?

You don't seem to understad what Truth actually is.

I guess your logic is that there is no such thing as a non-contradictory 
field of study.

But that is just because you don't seem to understand how logic actually 
works.

>>> 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.
>>>
>>
>>
> 
>