Re: ChatGPT totally understands exactly how I refuted the conventional halting problem proof technique

On 6/23/2025 2:37 AM, Mikko wrote:

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.

There is a subset of proofs that have this requirement.
They typically are of the form that a conclusion is
proved definitely true within a set of assumptions.
Another form of this same proof only has expressions
of language known to be true as its premises.
*This is the kind of proof that ChatGPT outputs*
A more generic proof of this form is any set of expressions
of language that proves that an expression of language is
definitely true. This more generic proof can be much more
powerful because it can fully integrate natural language
semantics into its inference steps.

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.
 

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