From: holmes@opal.idbsu.edu (Randall Holmes)
Subject: Re: The Mathematical Universe
Keywords: inconsistent multiplicities
Organization: Boise State University
Date: Thu, 8 Oct 1992 05:03:25 GMT

In article <Bvr8tF.D99@unx.sas.com> sasghm@theseus.unx.sas.com (Gary Merrill) writes:
>
>In article <1992Oct6.155930.2363@guinness.idbsu.edu>, holmes@opal.idbsu.edu (Randall Holmes) writes:
>
>|> Where I do find talk of possible worlds reasonable is in the
>|> discussion of the physical world that we live in.  Since I think that
>|> the physical world is a subset of the logical universe, I find it
>|> reasonable to suppose that alternate physical worlds (all possible
>|> ones) _actually exist_ (in exactly the same sense that ours does).
>
>It's this "same sense" that bothers me a bit.
>
>Can I get to another one of them?  How?  Or am *I* already in (some of)
>them?  Is it really *me*?  Can we communicate with the populations of
>these possible worlds (as we can with the populations of our own)?

No access to most of them.  But see the role of alternate worlds in
the many-worlds model of QM (which is _not_ why I think alternate
worlds exist).  You might recognize some individuals in some of them
as versions of yourself; exactly where to draw the line is a
question...


>
>|> Such worlds provide an actual model for Kripke's semantics for modal
>|> logic, for discussions restricted to the physical world; in the
>|> internal language of this model, they are "possible worlds".  It is
>|> probably an abuse of terminology to call them "possible worlds"
>|> without reference to this model.  I don't think that one of them is
>|> especially worthy of notice, except for the fact that I (and all of
>|> _us_) are in it.
>
>But isn't this a big "except"?  As in "The difference between P and -P
>is not worthy of notice except for the fact that P is true and -P is
>false"?

The other ones aren't "false".  They are just as real as this one.
But this conversation is taking place in this one.  Now, in the
internal language of the Kripke model of possible-worlds semantics
made up of the "possible physical worlds", it is the case in our world
that some states of affairs obtaining in the other possible worlds are
false.  But this is a different sense of "false".  Again, in the
interanl sense for this model, each possible world is actual for
itself, while all the others are merely possible.  But none of them
is privileged.

>
>|> In an absolute sense (relative to the _logical_ universe) I am _not_ a
>|> possible worlds realist; I think that there is one actual logical
>|> universe.  However, there are various ways to describe the actual
>
>I think the word "actual" is then a no-op here.  What is its sense?
>

I shouldn't have used it, since you use it as a technical term...  The
logical universe is real; by definition, it is the only logical
universe.


>
>-- 
>Gary H. Merrill  [Principal Systems Developer, C Compiler Development]
>SAS Institute Inc. / SAS Campus Dr. / Cary, NC  27513 / (919) 677-8000
>sasghm@theseus.unx.sas.com ... !mcnc!sas!sasghm

The reason why I maintain that alternate physical universes exist is
that I also maintain that the physical world is a "mathematical
object" (say, for the sake of argument, a function with domain R^{4}
and values expressing the intensities of various fields at given
places and times; I am not committed to a specific description of this
kind).  There are, of course, many other functions of the same general
kind as the one to be identified with the physical universe, some of
which satisfy the same "natural laws" as ours.  These latter ones are
the "possible worlds" to which I am referring.

The reason why I propose this viewpoint is that mathematical realism
provides one with more than enough objects; one does not _need_
-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu