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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: A different perspective on undecidability --- incorrect question
Date: Fri, 25 Oct 2024 09:37:19 -0500
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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.


> Ae also know
> that a good foundation to computability does not eliminate
> undecidablility but proves it, and also proves uncomputablility
> of various functions.
> 
> Whether some foundation can be correct or what it would mean to
> call it so is a different problem.
> 
>> It does eliminate undecidability
>> and not bothering to look at it is no actual rebuttal.
> 
> You may say so but you don't offer any good argument to support
> that claim. Instead you offer various indications that you will
> never present a good argument about anything.
> 


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