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From: mclean%NRL-CSS@sri-unix.UUCP
Newsgroups: net.sf-lovers
Subject: alternate universes
Message-ID: <4282@sri-arpa.UUCP>
Date: Wed, 17-Aug-83 10:26:27 EDT
Article-I.D.: sri-arpa.4282
Posted: Wed Aug 17 10:26:27 1983
Date-Received: Fri, 19-Aug-83 17:29:08 EDT
Lines: 25

From:  John McLean <mclean@NRL-CSS>


Another use of alternate universes besides the "many world" interpretation
of quantum mechanics is in semantics. For example in modal logic (the logic
of necessity and possibility), Saul Kripke formalized Leibniz's suggestion to
treat "necessarily p" as meaning that p is true in every universe accessible
from this one and "possibly p" as meaning that p is true in some universe
accessible from this one.  Depending on the different requirements one places
on the "accessibility" relation, different logical laws are true of necessity.
For example, if accessibility is transitive (i. e., if w2 is accessible from w1
and w3 is accessibly from w2, then w3 is accessibly from w1), then anything
that is necessary is necessarily necessary; and if accessibility is symmetric
(i. e., if w2 is accessible from w1, then w1 is accessibly from w2), then
anything that is possible is necessarily possible.

The use of alternate universes has also been suggested for a semantics of
counterfactuals (i. e., contrary to fact conditionals such as "if I were you,
I would have not done that").  David Lewis has suggested that such statements
are true if they are true in the universe that is most similar to ours in which
the antecedent of the conditional is true.  This leads us back to quantum
mechanics since one suggested interpretation of probability statements of the
kind found in quantum mechanics is in terms of counterfactuals.

John