From: holmes@opal.idbsu.edu (Randall Holmes)
Newsgroups: sci.logic
Subject: Re: The Mathematical Universe
Keywords: inconsistent multiplicities
Date: 5 Oct 92 21:50:56 GMT
Organization: Boise State University

In article <BvnGy0.BH0@unx.sas.com> sasghm@theseus.unx.sas.com (Gary Merrill) writes:
>
>In article <1992Oct2.231700.5065@guinness.idbsu.edu>, holmes@opal.idbsu.edu (Randall Holmes) writes:
>
>|> >
>|> >What more specifically worries me is that mathematicians in recent
>|> >decades have adopted a way of talking about "universes", as if this
>|> >relieved them of the obligation of attending to the mathematical
>|> >structure of *the* universe in which their "universes" exist.
>|> 
>|> It certainly is an appalling semantic breach to refer to several
>|> universes!  It does seem that there should be at most one.
>
>This puzzles me Randall.  Having confessed (to me at least) that you
>are a possible worlds realist, you surprise me with this apparent
>denial of multiple universes (which under at least one common interpretation
>would mean the same as multiple possible worlds).  Could you clarify
>this a bit?  Do you mean, for example, to countenance multiple possible
>universes (all of which you concede the "reality" of), but assert the
>existence of only one *actual* universe?
>
>How is reference to several universes more appalling than reference
>to several possible worlds?  Or is your view that there is only *one*
>universe and this comprises all the possible worlds (only one of which
>is actual)?

On the issue of "possible worlds": a better way to state my position
is that I hold that models of the notion of "possible world" actually
exist (models of Kripke's semantics for modal logic).  Suitable parts
of these models may reasonably be called "possible worlds" (especially
alternate versions of the physical world we live in, which I view as a
samll corner of the logical universe).  But my underlying logic is not
modal; "possible" is not a qualification of the existence of these
objects, which are simply real, like everything else.  Of course,
inside a model of Kripke's semantics, there are notions of possibility
and necessity which may qualify the "existence" of objects, but these
notions of "possibility", "necessity", and "existence" are internal to
the model.  Now there may be room in the logical universe for models
of a notion of "possible world" in which one of the "possibilities" is
a model of the actual logical universe and the other "possibilities"
are models of alternate complete logical universes.  In this case, I
would say that the "possible worlds", as objects, all exist, but that
the "possibilities" which they purport to represent are not all
realized.  Note that in this case the "actual" logical universe is not
the whole logical universe (which includes all the objects under
discussion) but a representation of the whole using a proper part of
the whole.

I think I said very clearly in our earlier discussion that I
countenance no distinction between actuality and existence.  But it
may be that by your definition I am not really a "possible worlds
realist".


[...]

>
>
>-- 
>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 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
Xref: sparky sci.logic:1642 sci.math:12589 rec.games.chess:8453