Re: [PO] Re: Proving a negative is hard

From: Peter Olcott (olcott_at_worldnet.att.net)
Date: 08/23/04 

Date: Mon, 23 Aug 2004 02:47:45 GMT

"Daryl McCullough" <daryl@atc-nycorp.com> wrote in message news:cgauts0147t@drn.newsguy.com...
> Peter Olcott says...
>
> >The problem is not that the standard proof does not apply in my
> >case.
>
> Yes, it is. The standard proof is about computable *functions*,

The standard proof arbitrarily restricts itself the mathematical
functions. It is possible for software functions to selectively
refuse the provide a result. It is not possible for mathematical
function to do this. This is the specific gap between the mathematical
abstraction, and the actual Turing Machine implementation.

> where the output is a deterministic function of the inputs. So
> H(x,y) *always* halts and *always* returns the same value for
> the same inputs x and y. You are proposing a program that doesn't
> have those properties. So the proof doesn't apply. That doesn't
> mean that an *analogous* proof won't work. I gave you a proof
> that works for your modified conventions.

I saw no possible way that you could make creating a TM
that can actually implement the behavior of LoopIfHalts in
the case where my method is implemented. I did have to
augment my method to accommodate your excellent objections.
This slightly revised method sure seems airtight to me.
Can you find a leak anywhere?

>
> --
> Daryl McCullough
> Ithaca, NY
>

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