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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic,comp.theory
Subject: Re: Undecidability based on epistemological antinomies V2 --H(D,D)--
Date: Mon, 29 Apr 2024 09:28:55 -0500
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On 4/29/2024 4:17 AM, Mikko wrote:
> On 2024-04-28 13:10:29 +0000, olcott said:
> 
>> On 4/28/2024 3:36 AM, Mikko wrote:
>>> On 2024-04-27 13:39:50 +0000, olcott said:
>>>
>>>> On 4/27/2024 3:24 AM, Mikko wrote:
>>>>> On 2024-04-26 13:54:05 +0000, olcott said:
>>>>>
>>>>>> On 4/26/2024 3:32 AM, Mikko wrote:
>>>>>>> On 2024-04-25 14:15:20 +0000, olcott said:
>>>>>>>
>>>>>>>> On 4/25/2024 3:16 AM, Mikko wrote:
>>>>>>>>> On 2024-04-25 00:17:57 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>> On 4/24/2024 6:01 PM, Richard Damon wrote:
>>>>>>>>>>> On 4/24/24 11:33 AM, olcott wrote:
>>>>>>>>>>>> On 4/24/2024 3:35 AM, Mikko wrote:
>>>>>>>>>>>>> On 2024-04-23 14:31:00 +0000, olcott said:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> On 4/23/2024 3:21 AM, Mikko wrote:
>>>>>>>>>>>>>>> On 2024-04-22 17:37:55 +0000, olcott said:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> On 4/22/2024 10:27 AM, Mikko wrote:
>>>>>>>>>>>>>>>>> On 2024-04-22 14:10:54 +0000, olcott said:
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> On 4/22/2024 4:35 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>>> On 2024-04-21 14:44:37 +0000, olcott said:
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> On 4/21/2024 2:57 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>>>>> On 2024-04-20 15:20:05 +0000, olcott said:
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> On 4/20/2024 2:54 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 2024-04-19 18:04:48 +0000, olcott said:
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> When we create a three-valued logic system that 
>>>>>>>>>>>>>>>>>>>>>>>> has these
>>>>>>>>>>>>>>>>>>>>>>>> three values: {True, False, Nonsense}
>>>>>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Three-valued_logic
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Such three valued logic has the problem that a 
>>>>>>>>>>>>>>>>>>>>>>> tautology of the
>>>>>>>>>>>>>>>>>>>>>>> ordinary propositional logic cannot be trusted to 
>>>>>>>>>>>>>>>>>>>>>>> be true. For
>>>>>>>>>>>>>>>>>>>>>>> example, in ordinary logic A ∨ ¬A is always true. 
>>>>>>>>>>>>>>>>>>>>>>> This means that
>>>>>>>>>>>>>>>>>>>>>>> some ordinary proofs of ordinary theorems are no 
>>>>>>>>>>>>>>>>>>>>>>> longer valid and
>>>>>>>>>>>>>>>>>>>>>>> you need to accept the possibility that a theory 
>>>>>>>>>>>>>>>>>>>>>>> that is complete
>>>>>>>>>>>>>>>>>>>>>>> in ordinary logic is incomplete in your logic.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> I only used three-valued logic as a teaching 
>>>>>>>>>>>>>>>>>>>>>> device. Whenever an
>>>>>>>>>>>>>>>>>>>>>> expression of language has the value of {Nonsense} 
>>>>>>>>>>>>>>>>>>>>>> then it is
>>>>>>>>>>>>>>>>>>>>>> rejected and not allowed to be used in any logical 
>>>>>>>>>>>>>>>>>>>>>> operations. It
>>>>>>>>>>>>>>>>>>>>>> is basically invalid input.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> You cannot teach because you lack necessary skills. 
>>>>>>>>>>>>>>>>>>>>> Therefore you
>>>>>>>>>>>>>>>>>>>>> don't need any teaching device.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> That is too close to ad homimen.
>>>>>>>>>>>>>>>>>>>> If you think my reasoning is incorrect then point to 
>>>>>>>>>>>>>>>>>>>> the error
>>>>>>>>>>>>>>>>>>>> in my reasoning. Saying that in your opinion I am a 
>>>>>>>>>>>>>>>>>>>> bad teacher
>>>>>>>>>>>>>>>>>>>> is too close to ad hominem because it refers to your 
>>>>>>>>>>>>>>>>>>>> opinion of
>>>>>>>>>>>>>>>>>>>> me and utterly bypasses any of my reasoning.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> No, it isn't. You introduced youtself as a topic of 
>>>>>>>>>>>>>>>>>>> discussion so
>>>>>>>>>>>>>>>>>>> you are a legitimate topic of discussion.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> I didn't claim that there be any reasoning, incorrect 
>>>>>>>>>>>>>>>>>>> or otherwise.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> If you claim I am a bad teacher you must point out 
>>>>>>>>>>>>>>>>>> what is wrong with
>>>>>>>>>>>>>>>>>> the lesson otherwise your claim that I am a bad 
>>>>>>>>>>>>>>>>>> teacher is essentially
>>>>>>>>>>>>>>>>>> an as hominem attack.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> You are not a teacher, bad or otherwise. That you lack 
>>>>>>>>>>>>>>>>> skills that
>>>>>>>>>>>>>>>>> happen to be necessary for teaching is obvious from you 
>>>>>>>>>>>>>>>>> postings
>>>>>>>>>>>>>>>>> here. A teacher needs to understand human psychology 
>>>>>>>>>>>>>>>>> but you don't.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> You may be correct that I am a terrible teacher.
>>>>>>>>>>>>>>>> None-the-less Mathematicians might not have very much 
>>>>>>>>>>>>>>>> understanding
>>>>>>>>>>>>>>>> of the link between proof theory and computability.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Sume mathematicians do have very much understanding of 
>>>>>>>>>>>>>>> that. But that
>>>>>>>>>>>>>>> link is not needed for understanding and solving problems 
>>>>>>>>>>>>>>> separately
>>>>>>>>>>>>>>> in the two areas.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> When I refer to rejecting an invalid input math would 
>>>>>>>>>>>>>>>> seem to construe
>>>>>>>>>>>>>>>> this as nonsense, where as computability theory would 
>>>>>>>>>>>>>>>> totally understand.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> People working on computability theory do not understand 
>>>>>>>>>>>>>>> "invalid input"
>>>>>>>>>>>>>>> as "impossible input".
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> The proof then shows, for any program f that might 
>>>>>>>>>>>>>> determine whether
>>>>>>>>>>>>>> programs halt, that a "pathological" program g, called 
>>>>>>>>>>>>>> with some input,
>>>>>>>>>>>>>> can pass its own source and its input to f and then 
>>>>>>>>>>>>>> specifically do the
>>>>>>>>>>>>>> opposite of what f predicts g will do. No f can exist that 
>>>>>>>>>>>>>> handles this
>>>>>>>>>>>>>> case, thus showing undecidability.
>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Halting_problem#
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> So then they must believe that there exists an H that does 
>>>>>>>>>>>>>> correctly
>>>>>>>>>>>>>> determine the halt status of every input, some inputs are 
>>>>>>>>>>>>>> simply
>>>>>>>>>>>>>> more difficult than others, no inputs are impossible.
>>>>>>>>>>>>>
>>>>>>>>>>>>> That "must" is false as it does not follow from anything.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Sure it does. If there are no "impossible" inputs that entails
>>>>>>>>>>>> that all inputs are possible. When all inputs are possible then
>>>>>>>>>>>> the halting problem proof is wrong.
>>>>>>>>>>>>
>>>>>>>>>>>> *Termination Analyzer H is Not Fooled by Pathological Input D*
>>>>>>>>>>>> https://www.researchgate.net/publication/369971402_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D
>>>>>>>>>>>>
>>>>>>>>>>>> Everyone that objects to the statement that H(D,D) correctly 
>>>>>>>>>>>> determines the halt status of its inputs say that believe 
>>>>>>>>>>>> that H(D,D) must report on the behavior of the D(D) that 
>>>>>>>>>>>> invokes H(D,D).
>>>>>>>>>>>
>>>>>>>>>>> Right, because that IS the definition of a Halt Decider.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Everyone here takes the definition of a halt decider to be
>>>>>>>>>> required to determine the halt status of the program that
>>>>>>>>>> invokes this halt decider, knowing full well that the program
>>>>>>>>>> that invokes this halt decider IS NOT ITS INPUT.
>>>>>>>>>>
>>>>>>>>>> All these same people also know the computable functions only
>>>>>>>>>> operate on their inputs and are not allowed to consider anything
>>>>>>>>>> else.
>>>>>>>>>>
>>>>>>>>>> Computable functions are the formalized analogue of the 
>>>>>>>>>> intuitive notion
>>>>>>>>>> of algorithms, in the sense that a function is computable if 
>>>>>>>>>> there
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