From: sasghm@theseus.unx.sas.com (Gary Merrill)
Subject: Re: The Mathematical Universe
Originator: sasghm@theseus.unx.sas.com
Date: Tue, 6 Oct 1992 14:17:20 GMT
Organization: SAS Institute Inc.
Keywords: inconsistent multiplicities


I have had terrible problems this morning with AFS on our network, and this
has caused my mail and news to behave rather oddly.  I *tried* an earlier
post, but do not think it succeeded.  So here is a response to two of
Randalls's ...


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.


In article <1992Oct5.215056.17908@guinness.idbsu.edu>, holmes@opal.idbsu.edu (Randall Holmes) writes:

|> 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

It appears to me from this that you wish to assert only the reality of
our *representation* of possible worlds and not go any further in the
direction of whether this is a representation *of* anything that exists.
(It seems to me this interpretation is similar to the approach I took
in the paper I sent you.)

|> the whole logical universe (which includes all the objects under
|> discussion) but a representation of the whole using a proper part of
|> the whole.

Again, this seems only to even more directly concede the reality of
our *representations*.  It is not obvious to me what are the intended
"objects under discussion" (the representations or the things represented).
This has a very nominalistic flavor.

|> 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".

Well, I'm still trying to get a grip on what this means -- particularly
since I thought you were holding a realist or Platonist position arrayed
against the sort of anti-realist position I have espoused.  At this point,
I'm having trouble distinguishing your position from my own.



-- 
Gary H. Merrill  [Principal Systems Developer, C Compiler Development]
SAS Institute Inc. / SAS Campus Dr. / Cary, NC  27513 / (919) 677-8000
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Newsgroups: sci.logic