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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Halting Problem: How my refutation differs to Peter Olcott's
Date: Sat, 10 May 2025 23:21:50 -0500
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On 5/10/2025 11:09 PM, Mr Flibble wrote:
> On Sat, 10 May 2025 23:05:17 -0500, olcott wrote:
> 
>> On 5/10/2025 10:45 PM, Mr Flibble wrote:
>>> On Sat, 10 May 2025 22:16:21 -0500, olcott wrote:
>>>
>>>> On 5/10/2025 10:11 PM, Mr Flibble wrote:
>>>>> On Sat, 10 May 2025 22:00:26 -0500, olcott wrote:
>>>>>
>>>>>> On 5/10/2025 9:51 PM, Mr Flibble wrote:
>>>>>>> On Sat, 10 May 2025 21:49:41 -0400, Richard Damon wrote:
>>>>>>>
>>>>>>>> On 5/10/25 9:18 PM, Mr Flibble wrote:
>>>>>>>>> On Sat, 10 May 2025 21:07:34 -0400, Richard Damon wrote:
>>>>>>>>>
>>>>>>>>>> On 5/10/25 9:00 PM, olcott wrote:
>>>>>>>>>>> On 5/10/2025 6:56 PM, Mr Flibble wrote:
>>>>>>>>>>>> On Sat, 10 May 2025 18:40:53 -0400, Richard Damon wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>> On 5/10/25 4:38 PM, Mr Flibble wrote:
>>>>>>>>>>>>>> How my refutation differs to Peter's:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> * Peter refutes the halting problem based on pathological
>>>>>>>>>>>>>> input manifesting in a simulating halt decider as infinite
>>>>>>>>>>>>>> recursion, this being treated as non-halting.
>>>>>>>>>>>>>> * Flibble refutes the halting problem based on patholgical
>>>>>>>>>>>>>> input manifesting as decider/input self-referencial
>>>>>>>>>>>>>> conflation, resulting in the contradiction at the heart of
>>>>>>>>>>>>>> the halting problem being a category (type) error, i.e.
>>>>>>>>>>>>>> ill-formed.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> These two refutations are related but not exactly the same.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> /Flibble
>>>>>>>>>>>>>
>>>>>>>>>>>>> And the problem is that you use incorrect categories.
>>>>>>>>>>>>>
>>>>>>>>>>>>> The decider needs to be of the category "Program".
>>>>>>>>>>>>>
>>>>>>>>>>>>> The input also needs to be of the category "Program", but
>>>>>>>>>>>>> provided via a representation. The act of representation lets
>>>>>>>>>>>>> us convert items of category Program to the category of
>>>>>>>>>>>>> Finite String which can be an input.
>>>>>>>>>>>>
>>>>>>>>>>>> Those two categories you have identified are different hence
>>>>>>>>>>>> the category error.
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>> That is correct. A running program and an input finite string
>>>>>>>>>>> ARE NOT THE SAME.
>>>>>>>>>>
>>>>>>>>>> But there is a direct relationship between the two.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>>>> The "Pathological Input" *IS* a Program, built by the simple
>>>>>>>>>>>>> rules of composition that are allowed in the system.
>>>>>>>>>>>>
>>>>>>>>>>>> Such composition is invalid.
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>> Richard is trying to get away with saying that a finite string
>>>>>>>>>>> THAT IS NOT A RUNNING PROGRAM <IS> A RUNNING PROGRAM
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>> But they are related to each other,
>>>>>>>>>
>>>>>>>>> Even if there is some perceived relationship between the two
>>>>>>>>> different categories it doesn't mean there still isn't a category
>>>>>>>>> error.
>>>>>>>>
>>>>>>>> So, what is the error, since the input *IS* the finite string that
>>>>>>>> was built by the program representation operation, and thus *IS*
>>>>>>>> what an input needs to be.
>>>>>>>>
>>>>>>>>
>>>>>>>>> Why relationship doesn’t rescue the mistake:
>>>>>>>>>
>>>>>>>>> * Shared context ≠ shared type.
>>>>>>>>> – A pupil and a teacher are clearly related (one teaches, one
>>>>>>>>> learns), but the question “Who is taller, the lesson?” commits a
>>>>>>>>> category error because a lesson isn’t the kind of thing that has
>>>>>>>>> height, regardless of its pedagogical ties to people.
>>>>>>>>
>>>>>>>> Which doesn't apply here, and you are just indicationg you don't
>>>>>>>> understand what a representation is.
>>>>>>>>
>>>>>>>> The input is a finite string that represents a program.
>>>>>>>
>>>>>>> A program and a finite string representing a program are different
>>>>>>> categories ergo we have a category error.
>>>>>>>
>>>>>>> /Flibble
>>>>>>
>>>>>> This made no difference difference until my simulating termination
>>>>>> analyzer discovered they they don't always have the same behavior as
>>>>>> was merely presumed for 90 years.
>>>>>>
>>>>>> A halt decider was "defined" to report on the behavior of the direct
>>>>>> execution of the input ONLY because no one knew that it could
>>>>>> possibly be different behavior than what the input finite string
>>>>>> specifies.
>>>>>>
>>>>>> Everyone here takes this false assumption as the infallible word of
>>>>>> God.
>>>>>> A textbook says it therefore it must be infallible.
>>>>>
>>>>> Yes, the reason why these two different categories cause a category
>>>>> error is because of the self-referential dependency between them,
>>>>> which manifests as infinite recursion in your simulating halt decider
>>>>> case.
>>>>>
>>>>> /Flibble
>>>>
>>>> Yes exactly !!!
>>>> It is great that some people are not so indoctrinated by dogma that
>>>> they can actually think for themselves and not merely follow the herd.
>>>
>>> Not sure about following the herd: I do have a computer science degree
>>> (BSc (Hons)) but I don't recall us covering the halting problem in any
>>> lectures although to be fair I skipped quite a few lectures to write a
>>> MUD, learning C in the process.
>>>
>>> /Flibble
>>
>> The Halting Problem was only covered in the comp theory course that is
>> no longer offered. I learned C back when K & R was the official
>> standard. Been doing mostly C++ for the last 25 years.
> 
> Been doing mostly C++ for the last 33 years.
> 
> /Flibble

I love it. I use it as C with classes.
I never needed anything besides this and the
standard template library. I use std::vector
for every array. Never had to deal with the
tedium of memory management in my life.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer