Re: Yet another Attempt at Disproving the Halting Problem

From: Peter Olcott (olcott_at_worldnet.att.net)
Date: 08/10/04 

Date: Tue, 10 Aug 2004 06:40:41 GMT

"Jerry Coffin" <jcoffin@taeus.com> wrote in message news:b2e4b04.0408092121.7c5bbb89@posting.google.com...
> "Peter Olcott" <olcott@worldnet.att.net> wrote in message news:<dLWPc.381367$Gx4.219217@bgtnsc04-news.ops.worldnet.att.net>...
>
> [ ... ]
>
> > Within deduction it is never valid.
> > Only deduction can guarantee that it always provides correct results. It is
> > considered to be valid inductive inference, yet inductive inference can not
> > guarantee correct results. Deduction can not err, induction can err.
>
> You should really quit while you're ahead -- or in this case, before
> you get further behind.
>
> An inductive proof can be just as much of a proof as a deductive
> proof.
>
Logical induction depends upon a crucial assumption that might not be
true, whereas deduction does not.

> What you're (apparently) thinking of is not induction. Just to give an
> example, I could look at a bunch of odd primes, and conclude from it
> that all odd numbers are primes.

Like I said mathematical induction is an entirely different process
than inductive inference. They just happen to share the same name.

> That's not induction though. In a real inductive proof, the first part
> is usually fairly trivial: prove the result for the most trivial case
> you can -- in the example above, I'd prove that 3 is prime. Then comes
> the part that's usually harder: I have to prove that if it's true for
> N, then it's also true for whatever's needed to generate the rest of
> the applicable values. In the case above, I'd have to prove that for
> any odd N, if N is prime then N+2 is also prime. Since I can't do
> that, the inductive proof doesn't err.
>
> --
> Later,
> Jerry.
>
> The universe is a figment of its own imagination.

Relevant Pages

  • Re: Yet another Attempt at Disproving the Halting Problem
    ... >> Only deduction can guarantee that it always provides correct results. ... Deduction can not err, induction can err. ... > An inductive proof can be just as much of a proof as a deductive ... > that all odd numbers are primes. ...
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  • Re: Yet another Attempt at Disproving the Halting Problem
    ... >> Only deduction can guarantee that it always provides correct results. ... Deduction can not err, induction can err. ... > An inductive proof can be just as much of a proof as a deductive ... > that all odd numbers are primes. ...
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