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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: Sun, 28 Apr 2024 08:10:29 -0500
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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
>>>>>>>> exists an algorithm that can do the job of the function, i.e. 
>>>>>>>> given an
>>>>>>>> input of the function domain it can return the corresponding 
>>>>>>>> output.
>>>>>>>> https://en.wikipedia.org/wiki/Computable_function
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