I wish to submit the following abstract. I am sorry that I am two days
late with it, but with the university closed and so much to do this time of
year, you know how it is. Anyway, here is the abstract: (Please put a
LaTeX preamble on it.)
Title: Disjunctive Information
Author: Edwin D. Mares
Victoria University of Wellington
Some situations carry the information that a disjunction $A\vee B$ obtains,
but do not carry the information that $A$ obtains nor the information that
$B$ obtains. In such cases, I call $A\vee B$ an {\it unresolved
disjunction}. Any theory which postulates that denies Laplacian determinism
will, by virtue of this, postulate situations in which there are unresolved
disjunctions. Quantum physics, for example, postulates cases in which there
is disjunctive information. In addition, in order to deal adequately with
what Barwise and Perry call {\it resource situations} we need to treat
unresolved disjunctions. In some circumstances we have available to us the
information that $A\vee B$ without having the information that $A$ or the
information that $B$.
The purpose of this paper is to give a semantics for disjunction that takes
seriously the problem of disjunctive information. I postulate a relation
of {\it Possibly determining} ($D$) between an abstract situation, $s$, and
sets of abstract situations. These sets of situations represent
possible extensions, given the information in $s$. Limiting ourselves to
temporal cases, for the moment, we can think of these sets of situations as
representing possible futures for $s$. I utilize the relation $D$
to give a truth condition for disjunction. That is, $s\models A\vee B$ if
and only if, for each set of situations $X$ such that $DsX$, there is a
situation $s\prime$ for which $s\prime\models A$ or $s\prime\models B$.
Thus, for example, a sea battle will occur on the following day or it will
not, according to $s$, if and only if, for each future possibly determined
by $s$, there is a situation in which the sea battle occurs or a situation
in which the sea battle does not occur.
The formal sections of the paper are concerned with showing that the
desired properties of disjunction hold in the model theory. Having
developed this model theory formally, we apply it to the problems of the
interpretation of quantum physics -- drawing on a comparison between it and
Storres McCall's recent work -- and more generally on the problem of
formally representing indeterminism. Moreover, we suggest ways in which
this way of thinking about disjunction suits verificationism better than
the intuitionistic treatment of disjunction, according to which all
disjuncts are resolved in all evidential situations.
Ed Mares
Department of Philosophy
Victoria University of Wellington
PO Box 600
Wellington, New Zealand
TEL. [04] 471 5368 FAX [04] 495 5130