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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: ChatGPT totally understands exactly how I refuted the conventional halting problem proof technique
Date: Mon, 23 Jun 2025 10:37:34 +0300
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On 2025-06-22 14:38:56 +0000, olcott said:

> On 6/21/2025 11:01 PM, Alan Mackenzie wrote:
>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>> int DD()
>>> {
>>> int Halt_Status = HHH(DD);
>>> if (Halt_Status)
>>> HERE: goto HERE;
>>> return Halt_Status;
>>> }
>> 
>>> https://chatgpt.com/s/t_6857335b37a08191a077d57039fa4a76
>>> ChatGPT agrees that I have correctly refuted every
>>> halting problem proof technique that relies on the above
>>> pattern.
>> 
>> That's neither here nor there.  The plain fact is you have NOT refuted
>> any proof technique.  How could you, you don't even understand what is
>> meant by proof?
> 
> A proof is any sequence of steps such that its conclusion
> can be correctly determined to be necessarily true.

False. There are other requirements. Every sentence of the sequence,
not just the last one, must either be a premise or follow from
earlier ones with an acceptable inference rule. Most commonly
accepted rules are modus ponens and substitution of equals. Modus
tollens and reduction are often accepted, too.

The usual purpose of a proof is to convince. Therefore, what is not
convincing is not a proof or at least not a useful proof.

-- 
Mikko