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From: kube@cogsci.berkeley.edu (Paul Kube)
Newsgroups: sci.philosophy.tech
Subject: Re: Simplicity and truth (was: Re: Science and Aesthetics)
Message-ID: <20297@ucbvax.BERKELEY.EDU>
Date: Tue, 25-Aug-87 22:15:08 EDT
Article-I.D.: ucbvax.20297
Posted: Tue Aug 25 22:15:08 1987
Date-Received: Thu, 27-Aug-87 04:25:14 EDT
Sender: usenet@ucbvax.BERKELEY.EDU
Reply-To: kube@cogsci.berkeley.edu.UUCP (Paul Kube)
Organization: University of California, Berkeley
Lines: 41
Summary: sketch of an argument for Ockham's razor

References:


In article <132@snark.UUCP> eric@snark.UUCP (Eric S. Raymond) writes:
>There is no *formal* argument for Occam's Razor. It's a heuristic, based on
>experience of what kinds of theory-building practices yield the most predictive
>and robust theories. The argument for it, like the argument for scientific
>method itself, is simply that it works.

If by `formal' you mean `deductive', I'd guess you're certainly right.
Ockham's razor isn't a truth of logic.  If you mean `rigorous', I don't see
what its being a heuristic has to do with it.  It's certainly possible to
give a rigorous justification for a heuristic.

I'd believe a strong inductive argument for Ockham's razor along the
lines you sketch, but I'm not optimistic about there being one.  For
one thing, the clearest sorts of violation of the razor--where a
theory is complexified *without any change in observational
consequences*--exactly preserve predictiveness and robustness.  For
another, I'd bet that application of the razor without regard to
observational consequences does at least as much harm as good; I'd
offhand expect complexification to work just as well.  But I'm
prepared to be convinced by a careful study of the history of science
that shows otherwise.  

I'd also believe an argument that goes along the folowing lines, but
I'm not optimistic about it being extendable in the appropriate ways.
Maybe you can suggest something: As I've characterized it, Ockham's
razor is a claim about the relative likelihoods of the truth of
theories, viz.  that the simpler of two is more likely to be true.  So
suppose there are two theories, T1 and T2, and let W1 and W2 be the
sets of possible worlds in which they are respectively true.  Suppose
T1 and T2 have all the same observational consequences; then W1 and W2
are both subsets of the set of possible worlds that, for all we can
tell by observation, the actual world is in.  The question is: Is the
actual world in W1 or W2?, and we want to maximize the likelihood of
making the right guess.  Well, the rational thing seems to be to pick
the bigger of W1 and W2 (and so the least restrictive, i.e. simplest,
of T1 and T2).  But it seems to me that for lots of cases we care
about, W1 and W2 are going to have the same cardinality; and a
natural measure will assign them both the same measure; and then I
don't know how to say one is more likely than the other.

--Paul kube@berkeley.edu, ...!ucbvax!kube