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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: Wed, 24 Apr 2024 19:57:21 -0500
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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 on, so 
> that IS the input.
> 
> You don't seem to understand the meaning of the word "description"
> 

Everyone else is wrong about this when they allow a description
to include the program that invokes the halt decider.

These same people already know that the program that invokes
the decider is definitely not its input.

These same people also know that computable functions only
operate on their inputs.

So they are simply contradicting their own views by not paying attention.

>>
>> 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
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