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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Unpartial Halt Deciders
Date: Sat, 19 Apr 2025 13:34:40 -0400
Organization: i2pn2 (i2pn.org)
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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.