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Re: The error of the halting problem

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On 6/4/24 1:28 PM, olcott wrote:
> On 6/4/2024 3:00 AM, Mikko wrote:
>> On 2024-06-03 20:53:01 +0000, olcott said:
>>
>>> For any program H that might determine whether programs halt, a
>>> "pathological" program D, called with some input, can pass its own
>>> source and its input to H and then specifically do the opposite of what
>>> H predicts D will do. No H can exist that handles this case. 
>>> https://en.wikipedia.org/wiki/Halting_problem
>>>
>>> The way that the halting problem is conventionally understood is that H
>>> must correctly answer yes or no to an input that contradicts both
>>> answers, thus H is being asked a question isomorphic to the Liar
>>> Paradox: Is this sentence true or false: "This sentence is not true." ?
>>>
>>> *Two PhD computer science professors agree with this assessment*
>>>
>>> E C R Hehner. Problems with the Halting Problem, COMPUTING2011 
>>> Symposium on 75 years of Turing Machine and Lambda-Calculus, 
>>> Karlsruhe Germany, invited, 2011 October 20-21; Advances in Computer 
>>> Science and Engineering v.10 n.1 p.31-60, 2013
>>> https://www.cs.toronto.edu/~hehner/PHP.pdf
>>>
>>> Bill Stoddart. The Halting Paradox
>>> 20 December 2017
>>> https://arxiv.org/abs/1906.05340
>>> arXiv:1906.05340 [cs.LO]
>>>
>>> E C R Hehner. Objective and Subjective Specifications
>>> WST Workshop on Termination, Oxford.  2018 July 18.
>>> See https://www.cs.toronto.edu/~hehner/OSS.pdf
>>
>> That does not identify which problem is meant by the term "halting 
>> problem",
>> nor does it identify what part of the problemis erroneous or what the
>> word "error" could even mean in this context, let alone how it would 
>> apply
>> to the particular unspecified point.
>>
> 
> For any program H that might determine whether programs halt, a
> "pathological" program D, called with some input, can pass its own
> source and its input to H and then specifically do the opposite of
> what H predicts D will do. No H can exist that handles this case.
> https://en.wikipedia.org/wiki/Halting_problem

Right.

> 
> *Quoted form above*
> The way that the halting problem is conventionally understood is that H
> must correctly answer yes or no to an input that contradicts both
> answers, thus H is being asked a question isomorphic to the Liar
> Paradox: Is this sentence true or false: "This sentence is not true." ?
>

Nope, it only contradict the answer that the particular H gives.

You keep on forgetting that the H is a SPECIFIC program, so from the 
definition of that program, its answer to any question has been fixed, 
so the input only needs to contratradict the answer THAT program gives.

It doesn't need to contradict that other program, that you think of as 
the other H that answers differently, because that other H isn't THIS H 
that it was designed to contradict.

So, what ever answer H DOES give, will be the wrong one and the other is 
right. If somehow H could give that other answer, it wou;d be right, but 
then it wouldn't be the machine that the pathological input was designe 
to make wrong, so there is no progblem with it geting the right answer.

Now, once we have proven that THIS H gives the wrong answer, if you then 
switch to the H that gives the right answer for that contradictory 
input, then we can make a NEW input that contradicts THAT machine, 
showing it also has an input it gets wrong.

You seem to have a blind spot about the fact that a GIVEN program will 
ALWAYS produce exactly the same answer for a given input, and that 
answer was determined from the moment that program was created. Thus 
when you try to talk about "whichever" answer it gives, you are talking 
foolishness, as there is only one answer for a given input that it WILL 
give. And this blind spot is what leads you into your invalid logic.

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The error of the halting problem olcott <polcott333@gmail.com> - 2024-06-03 15:53 -0500
  Re: The error of the halting problem Richard Damon <richard@damon-family.org> - 2024-06-03 20:55 -0400
    Re: The error of the halting problem olcott <polcott333@gmail.com> - 2024-06-03 19:59 -0500
      Re: The error of the halting problem Richard Damon <richard@damon-family.org> - 2024-06-03 21:44 -0400
        Re: The error of the halting problem olcott <polcott333@gmail.com> - 2024-06-03 20:51 -0500
          Re: The error of the halting problem Richard Damon <richard@damon-family.org> - 2024-06-03 21:58 -0400
            Re: The error of the halting problem olcott <polcott333@gmail.com> - 2024-06-03 21:14 -0500
              Re: The error of the halting problem Richard Damon <richard@damon-family.org> - 2024-06-03 22:26 -0400
                Re: The error of the halting problem olcott <polcott333@gmail.com> - 2024-06-03 21:32 -0500
                Re: The error of the halting problem Richard Damon <richard@damon-family.org> - 2024-06-03 22:47 -0400
                Re: The error of the halting problem olcott <polcott333@gmail.com> - 2024-06-03 21:58 -0500
                Re: The error of the halting problem Richard Damon <richard@damon-family.org> - 2024-06-03 23:11 -0400
                Re: The error of the halting problem joes <noreply@example.com> - 2024-06-04 08:29 +0000
                Re: The error of the halting problem --- G is untrue in PA olcott <polcott333@gmail.com> - 2024-06-04 12:45 -0500
                Re: The error of the halting problem --- G is untrue in PA Richard Damon <richard@damon-family.org> - 2024-06-04 21:48 -0400
                Re: The error of the halting problem Mikko <mikko.levanto@iki.fi> - 2024-06-04 12:24 +0300
              Re: The error of the halting problem joes <noreply@example.com> - 2024-06-04 08:27 +0000
      Re: The error of the halting problem Mikko <mikko.levanto@iki.fi> - 2024-06-04 11:09 +0300
  Re: The error of the halting problem Mikko <mikko.levanto@iki.fi> - 2024-06-04 11:00 +0300
    Re: The error of the halting problem olcott <polcott333@gmail.com> - 2024-06-04 12:28 -0500
      Re: The error of the halting problem Richard Damon <richard@damon-family.org> - 2024-06-04 21:48 -0400

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