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

From: Simon G Best (s.g.best_at_btopenworld.com)
Date: 08/06/04 

Date: Fri, 6 Aug 2004 14:54:19 +0000 (UTC)

Peter Olcott wrote:
>
> Would I have spent $70.00 on www.Halting-Problem.com
> for the domain name and domain name forwarding service
> if I was just kidding around?

Investing money in it doesn't make it correct.

> So far no one has correctly refuted anything at all that I have
> said of consequence. The closest that anyone has come to
> correctly refuting anything that I have said of consequence
> was exactly what is meant by the same algorithm using the
> same input data, must always produce the same results.

Which does indeed refute what you've claimed.

Now, however, you're stuck on the idea that somehow a Turing Machine can
tell whether or not the program its analyzing was the program that
invoked it to do that analysis. It can't. It only has itself and the
tape, which are both identical in both cases. Therefore, its behaviour
is identical in both cases. That's why "what is meant by the same
algorithm using the same input data, must always produce the same
results" disproves your claims.

> Once the definitions of these terms were precisely specified
> the conclusion was clearly correct. When I refer to my own
> blunders, this is what I am referring to. I am fairly certain that
> every other error that I made was essentially syntactical,
> thus of little consequence.

The error you keep making at the moment is a thunderously significant
error. That's why I've been reposting my thought experiment, so that
you can see *why* it's a significant error.

> There were very many claims
> that I am incorrect, but, most of these claims were merely
> empty and unsupported.

On the contrary, most such claims (explicitly or implicitly) referred
back to properly substantiated claims that your claims were incorrect.

> Those claims that were supported
> were clearly incorrect. The most significant attempt at refuting
> my statements was based on an ill-conceived notion of the
> capabilities of Turing Machines.

No. It's based on the fact that Turing Machines are completely
deterministic.

> These attempts at refutation
> would appear to an outside observer to be the most correct.
> Of course this assumes that this outside observer knows little
> to nothing about Turing Machines.

No, it assumes that outside observers can find out for themselves what a
Turing Machine is, and see for themselves that they're inevitably,
completely deterministic.

You're not fooling anyone, you know.

Relevant facts:-

1. Turing Machines are completely deterministic. Same input, same
output - *always*. This /obviously/ follows from the definition of a
Turing Machine. (You seem to think otherwise, which only demonstrates
that you're willfully ignoring the definition of Turing Machines.)

2. Turing Machines have no way of knowing who or what invoked them.
(Even if a Turing Machine finds information on its tape which says that
it was invoked by program P, it does not know whether this is true, or
someone or something else was lying to it. (We can easily construct a
diagonal case where LoopIfHalts lies to WillHalt.))

1 and 2 are enough for Turing's proof to be irrefutable, and your claims
to the contrary disproven.

However, the Church-Turing Thesis is still (as far as I know)
/unproven/. You really should have moved on to that issue, instead of
ignorantly wasting even more of your time trying to refute an
irrefutable proof.

Simon

Relevant Pages