From: holmes@opal.idbsu.edu (Randall Holmes)
Newsgroups: sci.logic
Subject: Re: The Mathematical Universe
Keywords: inconsistent multiplicities
Date: 5 Oct 92 20:36:43 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)?

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
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'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.


>
>|> >
>|> >Thus, if "universes" are things, and U is one of these things,
>|> >and x is something which "exists in" U, then there *is* really
>|> >something there, which could be denoted by, e.g., "U.x" - and
>|> >which simply exists, period.
>|> >
>|> 
>|> This is not a paradoxical situation.  It is perfectly consistent for
>|> the universe (the set of all x such that x = x, i.e., everything) to
>|> exist and be a member of itself.  (Just not in ZFC!)
>
>This raises some interesting questions about just what *does* exist.
>First, I suppose, the *actual* things exist (one is tempted to say,
>"The things that really exist exist").  Then there are the mere possibilia
>(which under most semantics sastisfy reflexivity of identity).  However,
>it can be (has been) argued that *impossibilia* satisfy this principle as
>well.  One *might* want to block existential generalization in this case,
>or one (Meinong?) might not.  But if you are going to allow quantification
>over possibilia, why not impossibilia as well?  Of course, this does
>change the sense that we normally attach to "there is ...".  And then
>there is the annoying problem of principles of individuation for
>impossibilia.

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

>
>|> >
>|> >But it is for this very reason that religion is not, nor ever
>|> >can be, part of science. But mathematics, whatever it is, gets
>|> >whatever respect it has by being, or pretending to be, part of
>|> >science.
>|> 
>|> Be careful.  Mathematics is _older_ than natural science (in the
>|> modern sense) and it is ___NOT___ part of it.  Attempts to incorporate
>|> mathematics into the natural sciences do neither math nor science any
>|> good.
>
>Be careful again.  Distinguish "is a tool used in science" with "is part
>of science", "is a tool that may be applied to empirical domains" with
>"has direct empirical content" or "derives its meaning from its empirical
>applications."
>
>|> 
>|> >
>|> >So the contents of mathematical "universes" ought to be open
>|> >to the scrutiny even of those who do not (in whatever sense one
>|> >can) "live" or "work" in those universes: otherwise they are simply 
>|> >not scientific concepts, but more like religious or artistic ideas,
>
>Certainly there are similarities between Platonism in mathematics and
>various aspects of religious faith -- particularly if one wants to
>countenance the "existence" of possibilia or impossibilia.  Was it
>Augustine who said something like "I believe *because* it is absurd"?

It was Tertullian, I believe.

>
>
>
>
>
>-- 
>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
Newsgroups: sci.logic,sci.math,rec.games.chess