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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic,comp.ai.philosophy
Subject: Re: The halting problem as defined is a category error
Date: Tue, 22 Jul 2025 08:56:36 -0500
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On 7/22/2025 5:51 AM, Mikko wrote:
> On 2025-07-21 14:07:27 +0000, olcott said:
> 
>> On 7/21/2025 4:38 AM, Mikko wrote:
>>> On 2025-07-20 15:04:34 +0000, olcott said:
>>>
>>>> On 7/20/2025 3:46 AM, Mikko wrote:
>>>>> On 2025-07-19 14:59:41 +0000, olcott said:
>>>>>
>>>>>> On 7/19/2025 4:02 AM, Mikko wrote:
>>>>>>> On 2025-07-18 22:11:50 +0000, Mr Flibble said:
>>>>>>>
>>>>>>>> On Thu, 17 Jul 2025 13:01:31 -0500, olcott wrote:
>>>>>>>>
>>>>>>>>> Claude.ai agrees that the halting problem as defined is a category
>>>>>>>>> error.
>>>>>>>>>
>>>>>>>>> https://claude.ai/share/0b784d2a-447e-441f-b3f0-a204fa17135a
>>>>>>>>>
>>>>>>>>> This can only be directly seen within my notion of a simulating 
>>>>>>>>> halt
>>>>>>>>> decider. I used the Linz proof as my basis.
>>>>>>>>>
>>>>>>>>> Sorrowfully Peter Linz passed away 2 days less than one year 
>>>>>>>>> ago on my
>>>>>>>>> Mom's birthday July 19, 2024.
>>>>>>>>
>>>>>>>> I was the first to state that the halting problem as defined is 
>>>>>>>> a category
>>>>>>>> error and I stated it in this forum.
>>>>>>>
>>>>>>> Indeed you stated that but failed to identify the actual error. You
>>>>>>> did not say which word in the problem statement is wrong or what is
>>>>>>> the wrong category or what would be the right one.
>>>>>>
>>>>>> I conclusively proved the actual category error yet
>>>>>> people that are only interested in rebuttal want no
>>>>>> part of any proof that I am correct.
>>>>>
>>>>> Is it the same error as Flibble found?
>>>>
>>>> Flibble's category error is stated abstractly.
>>>> My version is stated concretely.
>>>
>>> Could you post a pointer to your version?
>>
>> The category error is a type mismatch error where
>> a Turing Machine decider is required to report on
>> the behavior of a directly executed machine yet
>> cannot take a directly executed machine as an input.
> 
> That is not a category error. A category error is a word or phrase
> of some category in a context that requires a word or phrase of a
> different category.
> 

The category error is the mistake of assuming that
a directly executing Turing machine is in the category
of input to a Turing machine halt decider.

The category error is typically stated indirectly by
requiring a Turing machine based halt decider to report
on the behavior of a directly executed Turing machine.

It can be easily corrected by changing the requirement
to report on the behavior that its finite string input
specifies.

*I have conclusively proven that these behaviors diverge*
That people cannot understand this proof does not mean that
it is not a proof.

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer