consequences, they are unintuitive in themselves. I would prefer to develop a theory
that does not imply them. (Understandably, Westerhoff’s preferences are different.)
Let us turn to worries that Westerhoff does not address. First worry: it is hard
to see howsetorclasscould be ontological categories on Westerhoff’s account.
Consider, for example, the two-category ontology articulated by David Lewis (1991)
that consists of individuals and classes of individuals.^7 Trivially, every set of individ-
uals is constructed out of individuals via set-formation, and, on Lewis’s view, every
other set is constructed out of sets that ultimately are constructed from sets of
individuals.^8 Therefore, no set of sets is a base set, since the form set of individuals
suffices to construct any set of sets via the operation of set-formation. Since no set of
sets is a base set, sets do not form an ontological category. Similar remarks apply to
classes. So Lewis’s (1991) ontology, which recognizes two ontological categories,
individualandclass, is a one-category ontology on Westerhoff’s account. This is
odd. It is not clear to me how to revise Westerhoff’s account so that this oddity
does not arise.^9
More generally, it appears to be a consequence of Westerhoff’s account that
entities with structure never form an ontological category. Is the formation of states
of affairs from properties and universals a constructive operation? If so, then states of
affairs do not form an ontological category, contrary to the views of many meta-
physicians.^10 Smith (2004: 252–5) discusses a“modified Aristotelian”system accord-
ing to which one of the top-level ontological categories iscombinations, which has as
subcategoriesset,whole, andstate of affairs. Grossman (1973: 149) defends the view
that“the notion of structure... has to be ranked as one of the ontological categories.”
Westerhoff’s account implies that such ontological schemes are incoherent.
The second worry is a converse of thefirst: it is not clear how Westerhoff
can accommodate an ontology containingstuff.^11 Westerhoff’s meta-ontological
machinery might be suitable for ontologies with various categories of individuals—
things that can be counted or be members of sets, for example—but how to include
stuff in addition to (or rather than) things is less clear. (By contrast, we discussed a
version of ontological pluralism with things and stuff in section 2.5.2.)
A third worry is that Westerhoff’s account seems to implySommer’s Law.^12
Sommer’s Law is that no ontological categoriesmerely overlap: category C1 merely
overlaps category C2 just in case there is somexthat is a member of both C1 and C2,
(^7) Although, as noted earlier, Lewis does not use the term“ontological category,”this description is not
inapt. Compare with Nolan (2011: 278). 8
According to Lewis (1991), every singleton is“derived”from an individual via a singleton formation
operation and classes are simply mereological sums of singletons. 9
Perhaps on a more standard version of set theory, Westerhoff could say that the null set is the sole
form set for the category of sets. Thanks to Mike Rea for discussion here. 10
Westerhoff does not presuppose that states of affairs are“made of”their constituents, but it would be
problematic were this to be inconsistent with his account of ontological categories. 11
12 Thanks to Mike Rea for this worry.
Sommer’s Law is named after Fred Sommers, and is defended in Sommers (1963) and (1965).