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

On 10/21/2024 9:48 PM, Richard Damon wrote:

On 10/21/24 10:04 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.
>

>
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.

 Only if "can not be determined" means that there isn't an actual answer to it,
 Not that we don't know the answer to it.
 For instance, the Twin Primes conjecture is either True, or it is False, it can't be a non-truth-bearer, as either there is or there isn't a highest pair of primes that differs by two.
 

Sure.

The fact we don't know, and maybe can never know, doesn't make the question incorrect.
 Some truth is just unknowable.
 

Sure.

>
An incorrect question is an expression of language that
is not a truth bearer translated into question form.

 Right, and a question that we don't know (or maybe can't know) but is either true or false, is not an incorrect question.
 

Sure.

>
When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.
>
>
>

 Does D halt, is not an incorrect question, as it will halt or not.
 

Tarski is a simpler example for this case.
His theory rightfully cannot determine whether
the following sentence is true or false:
"This sentence is not true".
Because that sentence is not a truth bearer.
That does not mean that True(L,x) cannot be defined.
It only means that some expression ore not truth bearers.

That the H that it was built from won't give the right answer is irrelevent.
 You just don't understand what the terms mean, because you CHOSE to make youself ignorant, and thus INTENTIONALY made yourself into a pathetic ignorant pathological lying idiot.
 Sorry, but that is the facts.
 

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