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

From: Peter Olcott (olcott_at_worldnet.att.net)
Date: 08/13/04 

Date: Fri, 13 Aug 2004 12:19:42 GMT

"Karl Heinz Buchegger" <kbuchegg@gascad.at> wrote in message news:411C83AA.312A268D@gascad.at...
> Peter Olcott wrote:
> >

> > In order to show that my method does not work it must be shown
> > that for each and every possible circumstance there does not exist
> > even one single circumstance where my method would work.
>
> No, we don't have to do that.

It a form of proving a negative. Have you every heard of
the difficulty of proving a negative? If you want to prove
that fairies don't exist anywhere in the universe you can not
simply look in your closet, and after failing to find a fairy
conclude that fairies don't exist in the universe.

The proof that there can be no possible halt analyzer that
works for the universal set of TM's is a form of proving
a negative. Your proof must be much more comprehensive
that this.

> In order to show that your method is flawed we just need to find a way
> around it. Then we are back at the 'original' proof and all things
> remain the same.
>
> >
> > Since selectively refraining from returning a result is one single circumstance
> > whereby my method works, the only possible refutation would entail
> > finding a way such that there can not possibly exist any possible means
> > for my program to every selectively refrain from returing a result.
>
> Nonsense. Your method still produces a result. And we can find ways
> (always) to use that result to construct the paradox. To use the
> return value is just one way to do it, the simplest in the case
> of C++. But it need not be so.
> Just by refraining to do something, paradoxes don't vanish into thin air.
>
> >
> > Not Returning A result Is Not Impossible
>
> It is. It may not look like a 'return' statement (and you know this
> otherwise you would not have included the reference to 'read only
> screen memory and such things), but the end effect is the same.
> There are always ways to feed back the result to LoopIfHalts. And
> that is all that we need to show that your 'proof' is based on
> something that dosn't exist in reality.
> Note: We are in a better situation then you. Whatever you come
> up with to make this 'return' impossible, all we need is just
> one way that circumvents this. You on the other hand have to
> show that there is no way to construct that loop. No way - as in
> never, under no circumstances. Just claiming: 'And what if there
> is no web cam around' is not enough. You have to show that we
> cannot use the output of your machine (program) to construct
> a paradox, under no circumstances, no matter what we do.
>
> > The Halt Analyzer could ask the UTM to determine its invocation
> > context before it even begins processing.
>
> And it has already been shown that his is beyond the cpabilities
> of a TM. So this is not an option. I already have invited you
> to include this code in a C++ WillHalt function in a framework
> I have provided (since I am not that fluent with TM, but I am
> fluent in C++), but you refrained from doing so (pun intended).
>
> --
> Karl Heinz Buchegger
> kbuchegg@gascad.at

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