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

On 2025-05-11 11:52:05 +0000, Mr Flibble said:

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:

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.

 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 are several meanings for the word "program" but a common one is a
string that specifies what shall happen when the program is executed.
One possible string representation of that string is the string itself.
--
Mikko