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NNTP-Posting-Date: Sun, 28 Apr 2024 18:46:05 +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 11:46:11 -0700
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On 04/28/2024 11:26 AM, olcott wrote:
> 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
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