The Fragmentation of Being

belongs? Do objects necessarily belong to their ontological categories? Are there
fundamental differences betweenontologicalcategories and other kinds of categories,
or just differences of degree? Is there more than one“right way”of dividing the world
into ontological categories?
The account of ontological categories defended here can make sense of these
questions, although it provides little guidance as to how they should be answered.
This is not necessarily a defect of the account. It is one of the jobs of meta-ontology to
tell us what we should mean by“ontological category.”It is the job offirst-order
ontology to tell us what ontological categories there are, and how these categories
relate to one another. To the extent that we are moved by considerations of
neutrality, we should be happy that our account of ontological categories does not
make too many decisions about ontology for us.
In this section, I will focus on some recent work by Jan Westerhoff on ontological
categories, although other views will be discussed along the way. Westerhoff’s
fundamental approach is diametrically opposed to mine. I seek to use the notion of
an ontological category toexplainapparent failures of recombination, whereas, as we
will see, Westerhoff takes failures of recombination as the starting point in his
analysis of ontological categories.
Westerhoff’s (2005: 6–7, 100) preferred account takes as primitive the notion of a
state of affairs. States of affairs have constituents that appear also as members of sets.
Call a set aform setjust in case it is a set of constituents (of states of affairs) that have
the same form; two constituents have the sameformjust in case they areintersub-
stitutablein all states of affairs.
The notion of intersubstitutability in a state of affairs is also primitive for Westerh-
off, but perhaps the following examples illuminate it sufficiently. Consider the state
of affairs of my ball’s being red. My ball could have been blue, which implies that
it is possible that there is a state of affairs in which my ball is blue. Being blue is
substitutable with being red in the state of affairs of my ball’s being red. This is true of
any state of affairs in which something is red, moreover, the converse holds as well.
Being blue and being red are intersubstitutable in the same states of affairs. Just as an
expression is substitutable for another expression in a given sentence only if that
substitution results in a meaningful sentence, a constituent is substitutable for
another constituent only if that substitution would result in a possibly obtaining
state of affairs.
Among the form sets are thebase sets. Westerhoff identifies the ontological
categories with the base sets. The base sets are the minimal form sets that, via
some manner ofconstruction, generate allthe other form sets. According to
Westerhoff (2005: 97) to say that a set B generates a set X is just to say“that there
is a certain set of operations which can be applied to the members of B to obtain any
member of X.”Westerhoff (2005: 118–21, 125) suggests that these operations include
mereological compositionandset-formationand possibly other“constructive”oper-
ations. As an example, Westerhoff (2005: 102) says that the set-nominalist constructs

CATEGORIES OF BEING 