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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: Mon, 12 May 2025 09:31:58 -0500
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On 5/12/2025 2:19 AM, Mikko wrote:
> On 2025-05-11 03:11:43 +0000, Mr Flibble said:
> 
>> 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.
> 
> That is contradicto in adiecto: a refertial dependncy between two entities
> of different categories cannot be self-referential. An entity can have a
> self-referential dependncy only to itself and it is always of the same
> category as it is itself.
> 

Referential dependency.

void bar()
{
   foo();
}

void foo()
{
   bar();
}

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