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

On 5/10/25 9:00 PM, 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.
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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.

But there is a direct relationship between the two.

 

>
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
 

But they are related to each other,
I guess you think computers can't process numbers, text or an image, after all, computers just work on memory cells that are set one way or another. That isn't the same thing a "number", "text", or an image.
The key is we need to have a way to create the representation from our item, be it Number, character, or Program, and we need a way to interprete the representation to allow us to reconstruct the original item.
Of course, this requires the understanding of an abstraction, which seems beyond you. After all, you don't even understand the concept of a pure function in computer science meaning it can't just access anything in the computer that it wants, but only the data supplied as its input.

>
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

 Like the question: What time is it (yes or no)?
I came up with that 20 years ago during my work on the HP.