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

On 2024-10-26 12:59:33 +0000, olcott said:
 

On 10/26/2024 2:52 AM, Mikko wrote:

On 2024-10-25 14:37:19 +0000, olcott said:
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On 10/25/2024 3:14 AM, Mikko wrote:

On 2024-10-24 16:07:03 +0000, olcott said:
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On 10/24/2024 9:06 AM, Mikko wrote:

On 2024-10-22 15:04:37 +0000, olcott said:
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On 10/22/2024 2:39 AM, Mikko wrote:

On 2024-10-22 02:04:14 +0000, olcott said:
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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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There are several possibilities.
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A theory may be intentionally incomplete. For example, group theory
leaves several important question unanswered. There are infinitely
may different groups and group axioms must be true in every group.
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Another possibility is that a theory is poorly constructed: the
author just failed to include an important postulate.
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Then there is the possibility that the purpose of the theory is
incompatible with decidability, for example arithmetic.
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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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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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Whether AB = BA is not answered by group theory but is alwasy
true or false about specific A and B and universally true in
some groups but not all.

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See my most recent reply to Richard it sums up
my position most succinctly.

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We already know that your position is uninteresting.
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Don't want to bother to look at it (AKA uninteresting) is not at
all the same thing as the corrected foundation to computability
does not eliminate undecidability.

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No, but we already know that you don't offer anything interesting
about foundations to computability or undecidabilty.

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In the same way that ZFC eliminated RP True_Olcott(L,x)
eliminates undecidability. Not bothering to pay attention
is less than no rebuttal what-so-ever.

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No, not in the same way.

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Pathological self reference causes an issue in both cases.
This issue is resolved by disallowing it in both cases.

 There is no self reference in a formal theory. Expressions of a formal
theory don't refer.