On Tue, Jan 20, 1998 at 10:14:24AM -0800, Robin Hanson wrote:
> I need to get back to even more basic basics.  
> 
> 1) There's a certain elegant simplicity to the claim "all possible universes 
> exist", at least if "possible" is interpreted as broadly as possible, i.e.,
> "not logically inconsistent".  But if you start substituting other meanings 
> for "possible", I think the elegance quickly disappears.  You'd then still
> have to explain why other non-logically-inconsistent universes don't exist,
> and you'd have a bunch more weird universes to explain why we don't easily 
> observe them.   

The problem is coming up with a definition of "possible" that actually
leads to a useful theory. Otherwise we're left with "All possible
universes exist, so what?" I think the set of all Turing machines is
broad enough and simple enough to be considerably more elegant than
assuming that only one specific universe exists. It's not a problem to
explain why we don't observe other universes. This is simply because TMs
are independent of each other. I agree that it would be nice to either
have a broader useful definition of "possible" or a strong justification
of why non-computable universes do not exist, but I don't think it is
necessary. 

> I find the many worlds theory of quantum mechanics elegant, but not because
> it can be thought of as equally the above claim with a certain odd quantum
> definition of "possible".  I find it elegant because it seems simpler than
> the known alternatives which account for the empirical data.
> 
> 2) I can see why you might want some sort of prior over universes, so you
> can make inferences about what universe you are in.  But why should your
> difficulty in choosing such a prior be an argument against universes 
> existing?  Just because you have trouble thinking about a universe doesn't 
> mean it doesn't exist.

I think one of the main reasons for considering the idea that all possible
universes exist is to establish a rigorious basis for induction, and for
that we need a prior over universes.

> 3) My basic problem with the "all possible universes exist" claim is that
> I find it hard to figure out whether my actions have any consequences.  
> If all possible universes exist, then for any me in one universe choosing 
> one action, there is another me in another universe choosing another action.
> In a global sense I can't choose actions anymore.  All possible actions get
> chosen.  

But isn't this also a problem with the many-worlds interpretation of
quantum mechanics? I'm not sure what the solution is but I assume there is
one, since the many-worlds interpretation seems to be fairly widely
accepted.

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