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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 20:22:59 -0500
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On 10/26/2024 8:04 PM, Richard Damon wrote:
> On 10/26/24 5:57 PM, olcott wrote:
>> 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.
>>
> 
> Yes, IN SET THEORY, the "self-reference" can be banned, by the nature of 
> the contstruction.
> 

That seems to be the best way.

> In Computation Theory it can not, without making the system less than 
> Turing Complete, as the structure of the Computations fundamentally 
> allow for it, 

Sure.

> and in a way that is potentially undetectable.
> 

I really don't think so it only seems that way.

> You don't seem to understand that fact, but the fundamental nature of 
> being able to encode your processing in the same sort of strings you 
> process makes this a possibility.
> 

It does not make these things undetectable, it merely
allows failing to detect.

> Dues to the nature of its relationship to Mathematics and Logic, it 
> turns out that and logic with certain minimal requirements can get into 
> a similar situation.
> 

I think that I can see deeper than the Curry/Howard Isomorphism.
Computations and formal systems are in their most basic foundational 
essence finite string transformation rules.

> Your only way to remove it from these fields is to remove that source of 
> "power" in the systems, and the cost of that is just too high for most 
> people, thus you plan just fails.
> 

Detection then rejection.

> Of course, you understanding is too crude to see this issue, so it just 
> goes over your head, and your claims just reveal your ignorance of the 
> fields.
> 
> Sorry, that is just the facts, that you seem to be too stupid to 
> understand.

In other words you can correctly explain every single detail
conclusively proving how finite string transformation rules
are totally unrelated to either computation and formal systems.

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