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

On 10/22/2024 10:02 PM, Richard Damon wrote:

On 10/22/24 10:56 AM, olcott wrote:

On 10/22/2024 6:22 AM, Richard Damon wrote:

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.

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So, you agree your definition is wrong
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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.

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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.

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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.

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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.
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Haskell Curry species expressions of theory {T} that are
stipulated to be true:
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    Thus, given {T}, an elementary theorem is an
    elementary statement which is true.
https://www.liarparadox.org/Haskell_Curry_45.pdf
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When we start with the foundation that True(L,x) is defined
as applying a set of truth preserving operations to a set
of expressions of language stipulated to be true Tarski's
proof fails.
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We overcome Tarski Undefinability the same way that ZFC
overcame Russell's Paradox. We replace the prior foundation
with a new one.
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https://liarparadox.org/Tarski_275_276.pdf

 So, DO THAT then, and show what you get.
 So, just as Z and F did, and went through ALL the logical proofs to show what you could do with there rules, write up your complete set of rules and then show what can be done with it.
 

They could have accomplished the same thing by merely
adding the rule that no set can be a member of itself.
This by itself eliminates Russell's Paradox.

You have been told this for years, but don't seem to understand, perhaps because you don't understand the basics well enough to actually do that.
 Note, it isn't just the summary you will find on the informal sites that you need to do, but the FORMAL PROOF that is in their academic papers.
 Papers you probably can't understand.
 And not, that since you are moving to a more basic level, of changing the fundamental rules of the logic, you can't just assume any of the existing logic principles still work.
 

What would stop working in Naive Set theory if we simply
added the axiom that no set can be a member of itself?

This may well be the sort of thing where it takes 20 pages to show that 2 + 3 = 5 at the fundamental level of defining what + means.
 

Not when the algorithm for doing first-grade arithmetic
on ASCII digit strings is provided.

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

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His proof does, the fact that you don't undetstand what he is talking about doesn't make him wrong.
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You asserting he is wrong becuase you don't understand his proof makes you wrong, and STUPID.
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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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--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer