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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 21:50:02 -0400
Organization: i2pn2 (i2pn.org)
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On 4/25/24 10:15 AM, olcott wrote:
> 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
>>> of algorithms, in the sense that a function is computable if there
>>> exists an algorithm that can do the job of the function, i.e. given an
>>> input of the function domain it can return the corresponding output.
>>> https://en.wikipedia.org/wiki/Computable_function
>>>
>>> When the definition of a halt decider contradicts the definition of
>>> a computable function they can't both be right.
>>
>> When the definitions of a term contradicts the definition of another term
>> then both of them are wrong. A correct definition does not contradict
>> anything other than a different definition of the same term.
>>
> 
> *Wrong*
> In logic, the law of non-contradiction (LNC) (also known as the law of
> contradiction, principle of non-contradiction (PNC), or the principle of
> contradiction) states that contradictory propositions cannot both be
> true in the same sense at the same time
> https://en.wikipedia.org/wiki/Law_of_noncontradiction
> 
> Computable functions are the formalized analogue of the intuitive notion
> of algorithms, in the sense that a function is computable if there
> exists an algorithm that can do the job of the function, i.e. given an
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