Re: A different perspective on undecidability

On 2024-10-16 17:55:55 +0000, olcott said:

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.

I noticed. You should have said "Is finite string X a theorem of T?".
The letter L usually denotes the language of the theory of T, i.e. the
set of all syntactically correct formulas. The letter T is used for a
theory including its language, logic, and postulates.
--
Mikko