Re: A different perspective on undecidability

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.

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.
>

 

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