Re: The error of the halting problem

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." ?
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*Two PhD computer science professors agree with this assessment*
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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
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Bill Stoddart. The Halting Paradox
20 December 2017
https://arxiv.org/abs/1906.05340
arXiv:1906.05340 [cs.LO]
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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

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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.