Re: Foundation for a Formal Refutation of the Original Halting Problem?

From: Peter Olcott (olcott_at_worldnet.att.net)
Date: 08/05/04 

Date: Thu, 05 Aug 2004 01:49:50 GMT

"Mitch Harris" <harrisq@tcs.inf.tu-dresden.de> wrote in message news:2nbh8hFult03U1@uni-berlin.de...
> Peter Olcott wrote:
> >
> > A program that halts iff it goes into an infinite loop or goes into
> > an infinite loop iff it halts is not one of them.
> >
> > A program that can correctly determine if the set of all programs
> > (or TM's) will halt is one of them. (as least as far as the proof that
> > it can't be done is concerned).
>
> To me, this sounds like you -got- it. You finally
> understand. Such a program is in effect non-existent.

What I don't see is how when I explained step-by-step
detail-by-detail how this could be done, that you don't
get what I am saying?

Preconceived notions hardwired to brain, need rewiring?
You assume that it can be done with such attachment, that
any evidence to the contrary is never seen.

> Now for the next step. Because this program (Diag or
> LoopIfHalts) doesn't exist, but it was constructed in a
> legal manner. then some component of it must also not exist.
> The only assumed component was Halt(M,w). Therefore, it is
> this component that causes the problem. The assumption of
> the existence of Halt(M,w) must be wrong. So, Halt(M,w)
> doesn't exist. QED.
>
> Can we break out the champagne now?
>
> --
> Mitch Harris
> (remove q to reply)
>

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