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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Undecidability based on epistemological antinomies V2 --H(D,D)--
Date: Fri, 26 Apr 2024 11:32:48 +0300
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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 some ordinary proofs of ordinary theorems are no longer valid and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 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*

That "Wrong" is wrong as it refers to a true statement.

> 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

That is correct but not relevant.

> 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
> *That one is correct*

Yes, except that the analogue is not very analogous. For every computable
function there is an algorithm to compute it but there may be more than
one. An algorithm can differ from another one in a way that is not related
to the function it computes.

> 01 int D(ptr x)  // ptr is pointer to int function
> 02 {
> 03   int Halt_Status = H(x, x);
> 04   if (Halt_Status)
> 05     HERE: goto HERE;
> 06   return Halt_Status;
> 07 }
> 08
> 09 void main()
> 10 {
> 11   D(D);
> 12 }
> 
> That H(D,D) must report on the behavior of its caller is the
> one that is incorrect.

What H(D,D) must report is independet of what procedure (if any)
calls it.

-- 
Mikko