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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Unpartial Halt Deciders --- category error
Date: Sat, 19 Apr 2025 16:02:53 -0500
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On 4/19/2025 3:57 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.
>>>>>>>>
>>>>>>>> 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

Yes that seems to be another way to say it.

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer