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

On 5/10/25 7:56 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.
 

"Program" and "Program"?

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

 Such composition is invalid.

I guess you don't understand what programming is.

 

>
What is the category error?

 A category error (also called a category mistake) happens when we talk
about something as if it belonged to a logical or ontological class it
simply doesn’t fit. In other words, we mis-sort an object, property, or
question into the wrong “bin,” so the statement can’t possibly be true or
false—it’s just confused. -- ChatGPT
 /Flibble

Right, and the class of both is "Program"
The Program to be decided on is transformed by the mechanical process of "Representation" to convert it to the category "Finite String"
I guess you don't understand what these mean.