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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: Thu, 25 Apr 2024 07:32:40 -0400
Organization: i2pn2 (i2pn.org)
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On 4/24/24 11:56 PM, olcott wrote:
> On 4/24/2024 10:38 PM, Richard Damon wrote:
>> On 4/24/24 10:16 PM, olcott wrote:
>>> On 4/24/2024 9:00 PM, Richard Damon wrote:
>>>> On 4/24/24 8:57 PM, olcott wrote:
>>>>> On 4/24/2024 7:49 PM, Richard Damon wrote:
>>>>>> On 4/24/24 8:17 PM, olcott wrote:
>>>>>>> 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.
>>>>>>
>>>>>> And what you don't seem to understand is that it *IS*.
>>>>>>
>>>>>> The DEFINITION of a Halt Decider is to decide on the program 
>>>>>> described by it input.
>>>>>>
>>>>>> What else could that mean but the program described by the input?
>>>>>>
>>>>>>>
>>>>>>> All these same people also know the computable functions only
>>>>>>> operate on their inputs and are not allowed to consider anything
>>>>>>> else.
>>>>>>
>>>>>> First, we don't know that a Halt Decider is a "Computable 
>>>>>> Function" and in fact, that is the question, is the Halting 
>>>>>> Function computable?
>>>>>>
>>>>>> Second, the input IS a "Description of the program" to be decided 
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