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

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

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

On 5/10/25 4:38 PM, Mr Flibble wrote:

How my refutation differs to Peter's:
* Peter refutes the halting problem based on pathological input
manifesting in a simulating halt decider as infinite recursion, this
being treated as non-halting.
* Flibble refutes the halting problem based on patholgical input
manifesting as decider/input self-referencial conflation, resulting in
the contradiction at the heart of the halting problem being a category
(type) error, i.e. ill-formed.
These two refutations are related but not exactly the same.

 
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.

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.

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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.