Re: Halting Problem: How my refutation differs to Peter Olcott's

Am Sun, 11 May 2025 11:52:05 +0000 schrieb Mr Flibble:

On Sun, 11 May 2025 11:49:50 +0000, joes wrote:

Am Sat, 10 May 2025 23:56:36 +0000 schrieb Mr Flibble:

On Sat, 10 May 2025 18:40:53 -0400, Richard Damon wrote:

And the problem is that you use incorrect categories.
The decider needs to be of the category "Program".
The input also needs to be of the category "Program", but provided
via a representation. The act of representation lets us convert items
of category Program to the category of Finite String which can be an
input.

 
Those two categories you have identified are different hence the
category error.

No. HHH has a string representation, like every program.

No. Conflating a program with a string representation of the same
program in the manner of a self-referential dependency is a category
(type) error.

There is no conflation. HHH is passed a representation of a program.

The "Pathological Input" *IS* a Program, built by the simple rules of
composition that are allowed in the system.

Such composition is invalid.

No. DDD has only a function call, a condition, and an infinite loop.

No. It is ill-formed due to the category error.

Nothing is ill-formed about these three things.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.