Re: A different perspective on undecidability --- incorrect question

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.
An incorrect question is an expression of language that
is not a truth bearer translated into question form.
When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer