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

On 10/21/24 11:17 PM, olcott wrote:

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:
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The whole notion of undecidability is anchored in ignoring the fact that
some expressions of language are simply not truth bearers.

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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.
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After being continually interrupted by emergencies
interrupting other emergencies...
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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.

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Only if "can not be determined" means that there isn't an actual answer to it,
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Not that we don't know the answer to it.
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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.
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 Sure.

So, you agree your definition is wrong

 

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

And again.

 

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

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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.
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 Sure.

So you argee again that you proposition is wrong.

 

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When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.
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Does D halt, is not an incorrect question, as it will halt or not.
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 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.

No, that isn't his statement, but of course your problem is you can't understand his actual statement so need to paraphrase it, and that loses some critical properties.

 That does not mean that True(L,x) cannot be defined.
It only means that some expression ore not truth bearers.

His proof does, the fact that you don't undetstand what he is talking about doesn't make him wrong.
You asserting he is wrong becuase you don't understand his proof makes you wrong, and STUPID.

 

That the H that it was built from won't give the right answer is irrelevent.
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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.
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Sorry, but that is the facts.
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