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

From: Simon G Best (s.g.best_at_btopenworld.com)
Date: 08/05/04 

Date: Thu, 5 Aug 2004 14:34:22 +0000 (UTC)

Peter Olcott wrote:
>
> If a task can be accomplished in C++, (and I have already shown that)
> therefore a task can be accomplished by a TM.

And any proof about TMs is also a proof about 'C++' programs (assuming
that the Church-Turing Thesis is correct). Therefore, /assuming that
the Church-Turing Thesis is correct/, your claim of what you've
"accomplished in C++" was disproven in 1936.

> To state that a task
> that can be accomplished in C++ can not be accomplished by a TM,
> is to show a fundamental lack of understanding of TM's.

No. What it /would/ mean is that whoever makes such a statement is
disagreeing with the Church-Turing Thesis.

If you /had/ proved that there is a general solution to the Halting
Problem (HP) for Turing Machines (TMs), then what you'd have proved is
that the Church-Turing Thesis is incorrect, *not* that a TM can be a
halt analyzer.

(As far as I know,) The Church-Turing Thesis is unproven. The fact that
no TM could ever be a halt analyzer for TMs is most certainly proven.
So, if your 'C++' 'solution' to the HP for TMs really worked, then what
you'd've done is to /disprove/ the Church-Turing Thesis.

I should emphasise, however, that I'm not in any way conceding that you
have proved that a general solution to the HP for TMs could exist. I'm
just pointing out that it really makes no sense to refer to the
(unproven) Church-Turing Thesis to try to defend your claimed refutation.

In other words: I'm trying to nudge you in the direction of trying to
disprove the Church-Turing Thesis, rather than continue to waste even
more time trying to refute an irrefutable proof. The /reason/ I'm doing
this is because I'm getting bored of the same stuff being repeated over
and over and over again, and I'd like to move on to the Church-Turing
Thesis. I'm confident that you'll make a complete hash of it as well,
but I'd like to learn more about the Church-Turing Thesis from your many
respondents. So, yes, my motivation is quite selfish :-)

Simon