Re: Analysis of Flibble’s Latest: Detecting vs. Simulating Infinite Recursion ZFC

On 21/05/2025 21:28, olcott wrote:

On 5/21/2025 3:13 PM, Richard Heathfield wrote:

On 21/05/2025 20:28, olcott wrote:

<snip>

I have only been talking about the ACTUAL
conventional proof of the halting problem.

>
The ACTUAL conventional proof of the Halting Problem goes something like this:
>
1) assume that it is possible to devise an algorithm that can determine in finitely many steps ascertain whether an arbitrary program applied to arbitrary data does or does not stop.
>
2) given such an algorithm, imagine incorporating it into a program that ascertains whether a supplied program with supplied data halts, loops if it does, and halts if it doesn't.
>

 This step is impossible.

Correct. We have derived an impossible consequence of our assumption, thus proving that the assumption is false.

It only seemed possible

No. It never seemed possible. It always seemed like the impossible contradiction that it is.

because no one ever
tried to completely encode every detail.

Why would they? One would have to be pretty stupid to try.

This screwy mistake came about

It's not screwy, and it's not a mistake. It's a proof that there is at least one thing which we'd like a computer to be able to do but which it will never be able to do.
Like you said, it's impossible. QED.

because fools thought
that a halt decider H is supposed to report on the behavior
of the program that itself is contained within rather
than the behavior that its actual input actually specifies.

What your halt decider reports on is entirely up to you, but thanks to Turing we know that it will not be able to act as a /universal/ termination analyser that always gets the answer right regardless of the input.
Sometimes? Sure. bool decide(whatever){return true;} will get it right sometimes. But for some inputs your decider will get it wrong.

int main()
{
   DDD(); // No HHH can report on the behavior of its caller.
}

That's irrelevant to the Halting Problem.
<snip>
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
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