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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: Wed, 25 Jun 2025 10:26:52 +0300
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On 2025-06-24 14:55:11 +0000, olcott said:

> On 6/24/2025 3:47 AM, Mikko wrote:
>> On 2025-06-23 15:16:14 +0000, olcott said:
>> 
>>> 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.
>> 
>> If the set of the premises is not the same it is not the same proof.
> 
> When a proof has known facts all of its premises thenn
> its conclusion is proven definitely true when it is proven.

Nevertheless, the proofa are not the same if their sets of premises
are not the same.

-- 
Mikko