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

On 11/05/2025 02:00, olcott wrote:

On 5/10/2025 6:56 PM, Mr Flibble wrote:

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.
>
/Flibble

>
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.
>

 That is correct. A running program and an input finite
string ARE NOT THE SAME.

According to the language in which you chose to implement HHH(), your input is not a string. 7.1.1(1) reads: "A string is a contiguous sequence of characters terminated by and including the first null character."

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

>
Such composition is invalid.
>

 Richard is trying to get away with saying that a
finite string THAT IS NOT A RUNNING PROGRAM
<IS> A RUNNING PROGRAM

When you try to simulate it step by step you are trying to run it. If you are suggesting that you are failing to do so, I would have to agree with you.
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
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