Re: Can you find anything wrong with this solution to the Halting Problem?

From: Peter Olcott (olcott_at_worldnet.att.net)
Date: 07/13/04 

Date: Tue, 13 Jul 2004 11:32:48 GMT

> He may or may not be, but his argument is correct. The whole
> point and effect of mathematical proofs is that once they
> have been done there's no need to worry about the question
> any more. It's faintly possible that there may be an error
> in Turing's proof (but how come none of us computer
> scientists and mathematicians has spotted it?), or an

http://home.att.net/~olcott/halts.html
Maybe because you quit looking, and assumed that it
was fruitless. In any case since this does not address any
of the points that I made it is not any form of valid refutation.

> inconsistency in the mathematical foundations. If you want
> to refute Turing's (or any other for that matter) proof --
> that the there is no Turing machine that can take any other
> machine + data and determine whether or not it will halt --
> the /easiest/ way would be to point to the error in that
> proof, or point to the inconsistency in the underlying
> mathematics.
>
> If you can't do either of those easier things we can safely
> ignore your attempts to disprove it on the grounds that it
> is far more probable that there is an error in your proof
> than in Turing's. Note that when I say "far more probable"
> here I'm referring to the fact that there is no proof of
> absolute consistency of mathematics, so there is no
> /absolute/ guarantee that any proof is meaningful. I'm not a
> gambling man, but at those odds I'd wager the whole universe
> against an atom. Be warned that if you did succeed in
> finding such a flaw, you wouldn't be able to argue that with
> confidence that 1+1=2 any more.
>
> If you want to elicit a response other than scorn, ridicule
> and ire, you would be best served by learning the nature of
> mathematical proof. Start with learning first-order
> predicate calculus, and then Peano arithmetic or some other
> formal system that includes induction and perhaps reductio
> ad absurdam. When you can prove a few things formally come
> back and ask what to try next.
>
> --
> Jón Fairbairn Jon.Fairbairn@cl.cam.ac.uk
>

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