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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory
Subject: Re: Unpartial Halt Deciders --- category error 2
Date: Sun, 20 Apr 2025 11:18:42 +0200
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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.