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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: Wed, 24 Apr 2024 20:49:57 -0400
Organization: i2pn2 (i2pn.org)
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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"

> 
> 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

Right, so *IF* you can create the algorithm that can compute the mapping 
defined by the Halting Function, for EVERY input, then you can show it 
to be computable.

> 
> When the definition of a halt decider contradicts the definition of
> a computable function they can't both be right.
> 

But sincd the question is if the Halting Function is, in fact, 
computable, the fact that you can't create a function that meets the 
definition is just a proof that the answer to the question is NO, the 
Halting Function is not computable.

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