🚀 go-pugleaf

In the following, OR = Occam's Razor.

In article <20297@ucbvax.BERKELEY.EDU>, kube@cogsci.berkeley.edu (Paul Kube) writes:
> [quotes my claim that OR is just a heuristic, not formally demonstrable]
>
> 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.
>
> [Argument that says we should trust weaker theories because they describe
>  larger subsets of the set of all possible universes, so our universe is
>  more likely to be in the set]

That's a really interesting way to think about the problem which hadn't
occurred to me at all. It's no kind of 'demonstration' of OR but it seems to
translate our intuitive notion of 'theory strength' into terms that may make
it easier to think about.

>   But it seems to me that for lots of cases we care about, [the truth sets
> of the theories being compared] 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.

Well, then...don't. There are situations like this in the real world where
scientists work with several predictively-equivalent but distinct formalisms. I
understand, for example, that there are three distinct formalism, very
different in style, in which you can do quantum mechanics. One of them is
called S-matrix theory, I think the second one is based on systematic use of
Feynman diagrams, and the I think the third involves trying to solve the
time-dependent Schrodinger equations by analytic means.

I may have those three flavors wrong (physicists be gentle with me, I am
merely a defrocked mathematician) but I hope this makes the point. Nobody
says that you *have* to choose one out of a bunch of predictively-equivalent
theories and swear allegiance to it...

> --Paul kube@berkeley.edu, ...!ucbvax!kube
-- 
      Eric S. Raymond
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