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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 09:32:54 -0500
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On 5/12/2025 2:32 AM, Mikko wrote:
> On 2025-05-11 11:52:05 +0000, Mr Flibble said:
> 
>> On Sun, 11 May 2025 11:49:50 +0000, joes wrote:
>>
>>> Am Sat, 10 May 2025 23:56:36 +0000 schrieb Mr Flibble:
>>>> 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.
>>>>>
>>>>> 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.
>>> No. HHH has a string representation, like every program.
>>
>> No. Conflating a program with a string representation of the same program
>> in the manner of a self-referential dependency is a category (type) 
>> error.
> 
> There are several meanings for the word "program" but a common one is a
> string that specifies what shall happen when the program is executed.
> One possible string representation of that string is the string itself.
> 

A better name is computational unit.

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