🚀 go-pugleaf

In article <20297@ucbvax.BERKELEY.EDU> kube@cogsci.berkeley.edu.UUCP (Paul Kube) writes:
>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.

Very interesting idea -- but it seems to me that you are talking about
*another* criterion for desirability in scientific theories, namely: scope.
Of two theories, we will pick the one that has the broadest potential
applicability (something that explains *all* trees, not just grapefruit trees,
for instance -- the biggest W1 or W2, as you say).  And this makes sense, for
the reason you give.  But is it really necessarily the *simpler* theory that
has the wider scope?  That doesn't seem to be necessarily true.  It seems that
sometimes to generate a wider W1 or W2 of applicability, one might have to add
complexities to the theory.  It *might* be the case, but if so, an example or
an argument to demonstrate this would help.

I may have missed the boat totally on what you are trying to say.
-- 
"Absolute knowledge means never having to change your mind."

Sarge Gerbode
Institute for Research in Metapsychology
950 Guinda St.
Palo Alto, CA 94301
UUCP:  pyramid!thirdi!sarge