The Space of Nominal Reference

			   Almerindo Ojeda
		  University of California at Davis

Tradition has it that a noun is the name of a person, a place, or a thing.
But what persons, places, or things, can a noun name? What, indeed, is the
space of nominal reference?

For every set of entities one may talk about individually there is a
distinct set of entities one may talk about collectively. It is the very
set of entities in question, *but taken as a whole*. Thus, if we can talk
individually about five birds in a tree, then we can also talk collectively
about the five birds in the tree. Similarly, if we can talk about the
coffee each of us is now drinking, then we can talk about the coffee all of
us are now drinking.

Let us say that a *universe of discourse* is the set of entities one may
talk about, be it individually or collectively, on a particular occasion of
linguistic use. Let us furthermore say that the *partitive relation* on a
universe of discourse is the relation which holds between two elements of
the universe whenever one of the elements is a collective whole having the
other element as part. The partitive relation thus holds between each of
the five birds in a tree and the five birds taken as a whole. It likewise
holds between the coffee each of us is now drinking and the coffee all of
us are now drinking.

Partitive relations on universes of discourse have become commonplace in
the semantics of nonsingular reference--see for example the work of Massey,
Wald, Link, Krifka, Landman, Barker, Eschenbach, and Ojeda. In this talk,
partitive relations will be used to define thirty or so families of subsets
of a universe of discourse in terms of notions like individuation,
discreteness, magnitude, variety, and reciprocity. The claim is then made
that every noun must pick its reference from within the families in
question--or that the space of nominal reference is contained in the union
of these families. It is then noted that this claim may lead to a drastic
reduction of the powerset of a universe of discourse, which is the *a
priori* space of nominal reference. The membership of these families will
be illustrated with data from a wide variety of languages.