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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: A different perspective on undecidability --- incorrect question
Date: Thu, 24 Oct 2024 17:06:08 +0300
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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.

-- 
Mikko