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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 13:26:12 -0500
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On 4/28/2024 1:12 PM, Ross Finlayson wrote:
> On 04/28/2024 10:10 AM, olcott wrote:
>> On 4/28/2024 11:13 AM, Richard Damon wrote:
>>> 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.
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