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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: A different perspective on undecidability --- incorrect question
Date: Sat, 26 Oct 2024 16:57:33 -0500
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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:
>>>
>>>> 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. 
>>
>> Pathological self reference causes an issue in both cases.
>> This issue is resolved by disallowing it in both cases.
> 
> 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.



-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer