From: sasghm@theseus.unx.sas.com (Gary Merrill)
Subject: Re: The Mathematical Universe
Originator: sasghm@theseus.unx.sas.com
Date: Tue, 6 Oct 1992 13:48:13 GMT
Organization: SAS Institute Inc.
Keywords: inconsistent multiplicities


In article <1992Oct5.203643.17540@guinness.idbsu.edu>, holmes@opal.idbsu.edu (Randall Holmes) writes:

|> No, my view is that there is only one universe, and this includes all
|> of the "possible worlds", _all_ of which are actual.  I am a possible

But certainly there *is* a distinguished world (which we normally refer
to as the "actual" one).  You may say that *all* of the possible worlds
are actual (or real, or whatever), but if you wish to retain a distinction
between what *is* and what *might be*, then *some* distinction must be
made.  No?  If not, I don't see how to distinguish between fact and fiction.

|> words realist with regard to the physical world, which I regard as
|> being a small corner of the logical universe.  I don't think that
|> there is more than one possible logical universe (although I do admit
|> that it can be described in different ways).

I don't have a good grasp of the distinctions you are making here.  Are
there many possible physical worlds?  Or when you speak of the "physical
world" do you take this to select a single one of the possible worlds.
Possible, then, in what sense?  Physically possible?  Logically possible?

Is yourview that there is one possible logical universe (and I'm not sure
what this means) reflected by the modal principle

	Pp -> Np

(where 'P' is the possibility operator and 'N' the necessity operator).
If so, when you speak of the "logical universe" to you mean to exclude
objects of which empirical assertions can be made and restrict your domain
to objects (mathematical/logical in nature) of which only logical (or
necessary) assertions may be made?

|> I'm actually guilty of the same appalling offense myself :-) since I
|> will quite regularly refer to the "physical universe" (which is not
|> _the_ universe) as opposed to the logical universe (which is).  I'm
|> speaking somewhat tongue-in-cheek; I think that the use of "universe"
|> to mean "current domain of discourse" is defensible, and explains the
|> uses of the term of which the original posting was complaining.

Okay, but the "current domain of discourse" may or may not in *fact*
match up with *our* world.  I guess it's not clear to me what the scope
of 'world' and 'universe' has here.  By 'universe' do you mean to encompass
all time (or more generally, all indexicals)?  Or are you willing to
speak of "the universe at time t" as being "the universe".

|> 
|> I do not make the distinction between "actuality" and "existence".

Okay.  But some things *do* exists, some things *might* exists (but don't),
and some things *can't* exist.  So there are some distinctions that need
to be made -- unless you want to deny just this.  If so, you may end up
denying any distinction between empirical and other kinds of truths.
I think this is more than just the denial of the analytic/synthetic
dogma attacked by Quine et al., but I'm not clear on the details of your
view.
Xref: sparky sci.logic:1601 sci.math:12358 rec.games.chess:8222