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NNTP-Posting-Date: Sun, 28 Apr 2024 15:41:48 +0000
Subject: Re: Undecidability based on epistemological antinomies V2 --H(D,D)--
Newsgroups: sci.logic,comp.theory
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sun, 28 Apr 2024 08:41:50 -0700
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On 04/28/2024 07:48 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.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> 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.
>>>>>>>>>>>
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