Re: Halting Problem: What Constitutes Pathological Input

On 5/7/25 12:17 PM, Mr Flibble wrote:

On Wed, 07 May 2025 11:35:07 +0100, Richard Heathfield wrote:
 

On 07/05/2025 11:26, Fred. Zwarts wrote:

Op 07.mei.2025 om 03:39 schreef olcott:

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<snip>
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There must be an algorithm having a specified sequence of steps that
are applied to the input to derive the output.
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Your 'must' has no basis.

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Not only that, but he is literally begging the question - i.e. assuming
as true that which he hopes to prove. "All questions must be decidable,
therefore all questions are decidable."
>
Turing assumed the same thing: "All questions are decidable." But he
went on to demonstrate that if the assumption is true, it must be false
- a patent absurdity that shows that his original assumption was false.

 Wrong. All *well-formed* questions are decidable; the question the halting
problem asks is not *well-formed*; if is *ill-formed* as it is predicated
on a category (type) error.
 /Flibble

Nope.
What isn't "well formed" about the halting question?
DO you think that some complete program as defined by computation theory doesn't have a correct answer to the question of does it halt?
YOUR logic is predicated on a category error, as you forget that "deciders" are Programs, and their domain of input is the representation of *ALL* programs.