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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic,comp.theory
Subject: Re: Undecidability based on epistemological antinomies V2 --H(D,D)--
Date: Sun, 28 Apr 2024 12:13:27 -0400
Organization: i2pn2 (i2pn.org)
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On 4/28/24 11:27 AM, olcott wrote:
> On 4/28/2024 10:10 AM, Richard Damon wrote:
>> On 4/28/24 10:48 AM, olcott wrote:
>>> On 4/28/2024 9:31 AM, Ross Finlayson wrote:
>>>> On 04/28/2024 06:10 AM, olcott wrote:
>>>>> 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.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
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