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

On 10/26/24 5:57 PM, olcott wrote:

On 10/26/2024 10:48 AM, Richard Damon wrote:

On 10/26/24 8:59 AM, olcott wrote:

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.

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Nope, because is set theory, the "self-reference"

 does exist and is problematic in its several other instances.
Abolishing it in each case DOES ELIMINATE THE FREAKING PROBLEM.
 

Yes, IN SET THEORY, the "self-reference" can be banned, by the nature of the contstruction.
In Computation Theory it can not, without making the system less than Turing Complete, as the structure of the Computations fundamentally allow for it, and in a way that is potentially undetectable.
You don't seem to understand that fact, but the fundamental nature of being able to encode your processing in the same sort of strings you process makes this a possibility.
Dues to the nature of its relationship to Mathematics and Logic, it turns out that and logic with certain minimal requirements can get into a similar situation.
Your only way to remove it from these fields is to remove that source of "power" in the systems, and the cost of that is just too high for most people, thus you plan just fails.
Of course, you understanding is too crude to see this issue, so it just goes over your head, and your claims just reveal your ignorance of the fields.
Sorry, that is just the facts, that you seem to be too stupid to understand.