Re: What is the Result from Invoking this Halt Function?

From: Peter Olcott (olcott_at_worldnet.att.net)
Date: 08/07/04 

Date: Sat, 07 Aug 2004 03:30:21 GMT

"David C. Ullrich" <ullrich@math.okstate.edu> wrote in message news:f7v6h0dmtd1strl0ftldjh6njr8oonvuns@4ax.com...
> On Fri, 06 Aug 2004 01:47:34 GMT, "Peter Olcott"
> <olcott@worldnet.att.net> wrote:
>
> >
> >"Marc Goodman" <marc.goodman@comcast.net> wrote in message news:ibgQc.246159$Oq2.130858@attbi_s52...
> >> Peter Olcott wrote:
> >> > All that Turing proved was that it is impossible to construct a Halt
> >> > Analyzer that always returns the correct result of the Halt Analysis
> >> > to the program (or TM) being analyzed.
> >>
> >> No. What he showed is that if a Halt determiner existed,
> >> it could be used to construct a paradox.
> >
> >Yet this paradox that he constructed can only possibly exist under
> >one specific circumstance and no others. If the halt analyzer simply
> >refrains from ever providing its result to any program that is being
> >analyzed, then this paradox becomes completely impossible to construct.
> >That's exactly all that it takes, it takes nothing at all more than this.
> >It really is just as simple as that.
> >
> >Before leaping into yet another round of incorrect refutation, try to first
> >derive a single counter-example that correctly refutes the statement that
> >I just made immediately above.
>
> it's amazing how you seem unable to follow the simple proof that this
> is not possible, regardless of how many times it's explained. one
> more time:
>
> suppose that P is a program that does what you say - a correct halt
> analyzer that refrains from returning the result under some
> circumstances. now let Q be a program that does exactly what P
> does, except that Q always does return 1 or 0. the proof shows
> that Q cannot exist. hence P cannot exist. qed.

Slight little error here that makes all the difference.
You say that the conclusion that Q can't exist entails that P can't exist.
Yet it is not that Q can't exist. Merely that Q sometimes reports results
that are not correct.

This is a perfect example of a (otherwise) very well formed refutation,
that just happens to be incorrect. I think that this is the basic form of
all of the official and published refutations.

This is either the key most crucial point that I am missing, or the key
crucial point that everyone else (except me) has missed for sixty eight
years.

Let's take this ALL THE WAY. Please explain to me exactly and precisely
how is it that Q can not exist? The way that I see it can perfectly well
exist, yet sometimes provide incorrect results. I see nothing at all about
Q that would in any possible way, by any stretch of the imagination
prevent it from existing.

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