Re: Unpartial Halt Deciders --- category error

On 4/19/25 4:57 PM, Mr Flibble wrote:

On Sat, 19 Apr 2025 15:44:31 -0500, olcott wrote:
 

On 4/19/2025 1:06 PM, Mr Flibble wrote:

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 4/18/25 11:52 PM, olcott 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.
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Do you have a *rigorous* definition of "pathological input"?
>
Is there an algorithm to determine whether a given input is
"pathological" or not?
>
>

int DD()
{
      int Halt_Status = HHH(DD);
      if (Halt_Status)
        HERE: goto HERE;
      return Halt_Status;
}
>
Patterns isomorphic to the above when simulated by HHH.
>
>
>

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.
>
/Flibble

>
The category error in the halting problem proof is to define an input D
that is able to actually do the opposite of whatever value that H
reports.
>
Now the question: Does the input D halt becomes self-contradictory for
H.
>
So it is asking a yes/no question where both yes and no are the wrong
answer that is the category error.
>
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
>
Richard Damon found a loophole in the original question.
I inserted (yes/no) to close the loophole.

 No, the category error is conflating the decider with the input through
self-reference.
 /Flibble

No, the input is clearly defined by what it is. Note that the Olcott presentation is in error, as the input to actually be a program needs to contain its own copy of the decider that it is built on, and not be "mixed together" in one space. His result *IS* a category error as his D/DD/DDD isn't a prgram as it is incomplete and when we include that code into the definition of D/DD/DDD then his arguments about H/HH/HHH are incorrect as you can't change them "in place" without changing the input, and his algorith definition can't handle being translated in memory as show by the HHH/HHH1 difference.
Note, The input in the Linz proof doesn't HAVE a "self-reference", the program just references (by copying) the decider it is to refute, and it is given an input that just happens to be a representation of itself, which is a valid input. The input doesn't "Reference" the contray-program, it just has a description/copy of it.
Note, Turing Machines don't HAVE "References" as a fundamental elelement, so can't be self-referenential