Re: Yet another Attempt at Disproving the Halting Problem

From: Jerry Coffin (jcoffin_at_taeus.com)
Date: 08/10/04 

Date: 9 Aug 2004 22:21:36 -0700

"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.

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.

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. ...
    (comp.theory)
  • 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. ...
    (comp.lang.cpp)
  • 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. ...
    (sci.logic)
  • Re: Yet another Attempt at Disproving the Halting Problem
    ... >>Only deduction can guarantee that it always provides correct results. ... >>considered to be valid inductive inference, ... Deduction can not err, induction can err. ... > An inductive proof can be just as much of a proof as a deductive ...
    (comp.theory)
  • Re: Yet another Attempt at Disproving the Halting Problem
    ... >>Only deduction can guarantee that it always provides correct results. ... >>considered to be valid inductive inference, ... Deduction can not err, induction can err. ... > An inductive proof can be just as much of a proof as a deductive ...
    (sci.logic)
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