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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic,comp.ai.philosophy
Subject: Re: Title: A Structural Analysis of the Standard Halting Problem
 Proof
Date: Tue, 22 Jul 2025 08:43:50 -0500
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On 7/22/2025 5:33 AM, Mikko wrote:
> On 2025-07-21 13:57:04 +0000, olcott said:
> 
>> On 7/21/2025 4:10 AM, Mikko wrote:
>>> On 2025-07-20 15:36:51 +0000, olcott said:
>>>
>>>> On 7/20/2025 8:05 AM, Alan Mackenzie wrote:
>>>>> [ Followup-To: set ]
>>>>>
>>>>> In comp.theory Mr Flibble <flibble@red-dwarf.jmc.corp> wrote:
>>>>>> On Sun, 20 Jul 2025 07:13:43 -0400, Richard Damon wrote:
>>>>>
>>>>>>> On 7/20/25 12:58 AM, olcott wrote:
>>>>>>>> Title: A Structural Analysis of the Standard Halting Problem Proof
>>>>>
>>>>>>>> Author: PL Olcott
>>>>>
>>>>>>>> Abstract:
>>>>>>>> This paper presents a formal critique of the standard proof of the
>>>>>>>> undecidability of the Halting Problem. While we do not dispute the
>>>>>>>> conclusion that the Halting Problem is undecidable, we argue 
>>>>>>>> that the
>>>>>>>> conventional proof fails to establish this conclusion due to a
>>>>>>>> fundamental misapplication of Turing machine semantics. 
>>>>>>>> Specifically,
>>>>>>>> we show that the contradiction used in the proof arises from 
>>>>>>>> conflating
>>>>>>>> the behavior of encoded simulations with direct execution, and from
>>>>>>>> making assumptions about a decider's domain that do not hold 
>>>>>>>> under a
>>>>>>>> rigorous model of computation.
>>>>>
>>>>>
>>>>>
>>>>>>> Your problem is you don't understand the meaning of the words you 
>>>>>>> are
>>>>>>> using.
>>>>>
>>>>>> This is an ad hominem attack, not argumentation.
>>>>>
>>>>> Maybe it was you wanting to create that impression by dishonestly
>>>>> snipping the substance of Richard's post, where he illustrated some of
>>>>> the words whose meaning PO fails to understand.
>>>>
>>>> It never has been that I do not understand
>>>> the definitions of words it is that I have
>>>> proven that some of these definitions are incorrect.
>>>
>>> That you think a definition is incorrect does not change the defined
>>> meaning. If you don't accept the definition the best you can do is
>>> that you don't use the term.
>>
>> That I prove that a definition is derived from provably
>> false assumptions proves that this definition is incorrect.
> 
> No, it does not. Definitions are what they are. How they are derived
> does not matter. It is a category error to say that a defintion is
> incorrect.
> 

*Yes this is a strange and rare case*
When the halting problem proof requires reporting on
the behavior of a directly executing machine and no
Turing machine based halt decider can take another
directly executing Turing machine as an input then
this is an error.

To correct this error we redefine the halting problem
to report on the behavior that its input specifies.

>> No one here is capable of paying enough attention to my
>> proof that the halting problem definition is incorrect
>> because my proof requires two steps and no one here can
>> even pay attention to one step.
> 
> It is sufficient to note that "definition is incorrect" is a category
> error and consequently a "proof" of that is bogus.
> 


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