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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 23:05:17 -0500
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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.

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