From:  Richard Damon <richard@damon-family.org>
Date:  17 Oct 2024 08:47:26 Hong Kong Time
Newsgroup:  news.alt119.net/sci.logic
Subject:  

Re: A different perspective on undecidability

NNTP-Posting-Host:  null

On 10/16/24 6:34 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.
>>
> 
> *I still said that wrong*
> (1) There is a finite set of expressions of language
> that are stipulated to be true (STBT) in theory L.
> 
> (2) There is a finite set of true preserving operations
> (TPO) that can be applied to this finite set in theory L.
> 
> When formula x cannot be derived by applying the TPO
> of L to STBT of L then x is not a theorem of L.
> 
> A theorem is a statement that can be demonstrated to be
> true by accepted mathematical operations and arguments.
> https://mathworld.wolfram.com/Theorem.html
> 

How can there not be a Yes or No answer to it being a statement that can 
be proven true?

Either X IS or it IS NOT a theory of L, as either a proof of its truth 
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.