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NNTP-Posting-Date: Sun, 28 Apr 2024 14:31:15 +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 07:31:05 -0700
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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.
>>>>>>>>>
>>>>>>>>> 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
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