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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: A different perspective on undecidability --- incorrect question
Date: Sat, 26 Oct 2024 10:52:35 +0300
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On 2024-10-25 14:37:19 +0000, olcott said:

> On 10/25/2024 3:14 AM, Mikko wrote:
>> On 2024-10-24 16:07:03 +0000, olcott said:
>> 
>>> 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.
>> 
>> No, but we already know that you don't offer anything interesting
>> about foundations to computability or undecidabilty.
> 
> 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.

No, not in the same way. ZFC is a useful set theory for many purposes.
You don't offer any useful theory for any purpose.

-- 
Mikko