Re: Unpartial Halt Deciders --- category error 2

Op 19.apr.2025 om 22:58 schreef olcott:

On 4/19/2025 3:27 PM, Keith Thompson wrote:

Mr Flibble <flibble@red-dwarf.jmc.corp> writes:

On Sat, 19 Apr 2025 13:34:40 -0400, Richard Damon wrote:

On 4/19/25 8:05 AM, Mr Flibble wrote:

On Sat, 19 Apr 2025 07:55:55 -0400, Richard Damon wrote:

[...]

On 4/18/2025 2:32 PM, Keith Thompson wrote:

Mr Flibble <flibble@red-dwarf.jmc.corp> writes:

On Fri, 18 Apr 2025 12:25:36 -0700, Keith Thompson wrote:

Mr Flibble <flibble@red-dwarf.jmc.corp> writes:

I, aka Mr Flibble, have created a new computer science term, the
"Unpartial Halt Decider".  It is a Halt Decider over the domain
of all program-input pairs excluding pathological input (a
manifestation of the self referencial category error).

[...]
>
Do you have a rigorous definition of "pathological input"?
>
Is there an algorithm to determine whether a given input is
"pathological" or not?
>
I could define an is_prime() function like this:
>
       bool is_prime(int n) {
           return n >= 3 && n % 2 == 1;
           // returns true for odd numbers >= 3, false for
           all others
       }
>
I'll just say that odd numbers that are not prime are pathological
input, so I don't have to deal with them.

>
Pathological input:
>
Self-referencial to the decider.

>
OK.
>
Do you have a *rigorous* definition of "pathological input"?
>
Is there an algorithm to determine whether a given input is
"pathological" or not?

[...]

Examples are not definitions.
>
And the problem is that the above example is itself a category error
for the problem, as the DD provided above isn't a complete program, as
it doesn't include the code for HHH as required, and when you include
Halt7.c as part of the input, your HHH isn't a seperate program of its
own, and thus doesn't have a Turing Complete range of inputs it can
accept.
>
Sorry, you are just showing you don't understand what it means to
DEFINE something.

>
Ah, the fundamental mistake you have been making all this time, Damon!
The self-referencial category error doesn't magically disappear by
providing source code rather than a run-time function address to the
decider; you are simply transforming the same input without affecting
the result.
>
/Flibble

>
And WHAT is the category error?  You stil can't show the difference in
CATEGORY between what is allowed and what isn't, and in fact, you can't
even precisely define what is and isn't allowed.
>
Now, you also run into the issue that the "Olcott System" begins with an
actual category error as we do not have the required two seperate
programs of the "Decider" and the "Program to be decided on" given via
representation as the input, as what you want to call that program to be
decided isn't one without including the code of the decider it is using,
and when you do include it, the arguments about no version of the
decider being able to succeed is improper as it must always be that
exact program that we started with, and thus it just FAILS to do a
correct simulation, while a correct simulation of this exact input
(which includes the ORIGINAL decider) will halt.
>
Sorry, YOU are the one stuck with the fundamental mistake, or is it a
funny mental mistake because you don't understand what you are talking
about.

>
The category error is extant over the domain of pathological inputs, no
matter what form those inputs take.

>
That certain is a lot of words.
>
Do you have a rigorous definition of "pathological input"?
>
Is there an algorithm to determine whether a given input is
"pathological" or not?
>
"Yes" and "No" could be valid answers to either of those questions.
Nothing you have written above is an answer to either of those
questions.
>
Are you able to answer those questions?
>

 Objective and Subjective Specifications
Eric C.R. Hehner
Department of Computer Science, University of Toronto
 (6) Can Carol correctly answer “no” to this (yes/no) question?
https://www.cs.toronto.edu/~hehner/OSS.pdf
 Pathological inputs are such that
Does the input halt on its input?
Both yes and no are the wrong answer.

We are discussion inputs that describe a program. A specific input describes a specific program.
For a specific program, one answer is always correct and the other one is wrong. If not, give an example of a specific program that both halts and does not halt.
With this definition, pathological input does not exist.