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From: mmcirvin@world.std.com (Matt McIrvin)
Subject: Re: determinism vs non-determinism, was: Really random? (now back on original topic)
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In article <96351.081748JCA31@MAINE.MAINE.EDU>, <JCA31@MAINE.MAINE.EDU> wrote:

> Not to hopelessly confuse things, but is anyone familiar with Greg Chaitin's
> recent work? The gist of it is that, given a finite set of axioms, one can
> only prove a finite number of theories.

I'm not sure what you mean by this-- from a finite number of axioms, it
is often trivially possible to derive an infinite number of theorems.
For instance, from the Peano axioms you can prove 1+1=2, 2+2=4, 6+8=14...
However, Goedel does say that you *cannot* derive all true statements,
even about positive integer arithmetic, from one set of axioms with one
set of consistent formal manipulations.

> If you bring Goedel into the picture,
> the result is that maybe we shouldn't be wielding Occam's razor quite so
> religiously. The razor is a great tool, no question about that, but it begins
> to look as though we aren't going to be able to extend scientific theory
> forever, without eventually just accepting some unprovable truths as new
> postulates. [...]

Physical theories already have unprovable statements as postulates. If the
predictions of the theory are borne out, that provides some evidence that
the postulates might be on the right track, but it certainly does not prove
their absolute truth, and it is always possible-- and has happened many
times-- that a more correct theory could be based on new and extremely
different postulates, which are equally unprovable.

Occam's razor doesn't say that you can never multiply entities, just that
it's not a good idea to do it unnecessarily.

(I agree with you that the notion of the observer affecting the
observed system is not a *necessary feature* of a scientific theory,
though it certainly occurs in some.)

-- 
Matt McIrvin   <http://world.std.com/~mmcirvin/>
