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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: A different perspective on undecidability --- incorrect question
Date: Thu, 24 Oct 2024 19:46:42 -0400
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On 10/24/24 12:07 PM, olcott wrote:
> On 10/24/2024 9:06 AM, Mikko wrote:
>> On 2024-10-22 15:04:37 +0000, olcott said:
>>
>>> On 10/22/2024 2:39 AM, Mikko wrote:
>>>> On 2024-10-22 02:04:14 +0000, olcott said:
>>>>
>>>>> 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.
>>>>
>>>> There are several possibilities.
>>>>
>>>> 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.
>>>>
>>>> Another possibility is that a theory is poorly constructed: the
>>>> author just failed to include an important postulate.
>>>>
>>>> Then there is the possibility that the purpose of the theory is
>>>> incompatible with decidability, for example arithmetic.
>>>>
>>>>> An incorrect question is an expression of language that
>>>>> is not a truth bearer translated into question form.
>>>>>
>>>>> When "X a formula of theory Y" is neither true nor false
>>>>> then "X a formula of theory Y" is not a truth bearer.
>>>>
>>>> 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.
>>>
>>> See my most recent reply to Richard it sums up
>>> my position most succinctly.
>>
>> We already know that your position is uninteresting.
>>
> 
> 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. It does eliminate undecidability
> and not bothering to look at it is no actual rebuttal.
> 

So, you admit that you haven't actually rebutted any of the errors 
pointed out in your logic, as saying they are not interesting isn't 
actually a rebuttal.

Thus you admit that nothing you have said has any useful basis.