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

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.
The "Pathological Input" *IS* a Program, built by the simple rules of composition that are allowed in the system.
What is the category error?
Note, the decider can not be an "oracle" or something more powerful than a program, as Turing Complete programs are the most powerful thing we can build, and the decider needs to be something at least theoretically buildable to be a solution.