naturalness of the entities that correspond to the constituents of these sentences. The
properties that correspond to sentential operators are properties of propositions,
whereas the properties that correspond to quantifiers are properties of properties.
On the property-realist construal, some higher-order properties are more natural
than others.
A more intriguing form of realism might deny that the ontological correlates of
sentence operators are properties but rather belong to a different ontological category
altogether; this is the view of Mulligan (2010: 583, fn. 24), for example, who calls the
ontological correlates“connectors.”Similarly, one might hold that the ontological
correlates of quantifiers are not properties but rather are modes of being understood
assui generisentities. Provided that this more intriguing form of realism counten-
ances the ranking of such entities on the same naturalness scale, what I say about the
less intriguing version of realism holds also for the more intriguing.
Let’s provisionally be realists about properties; we’ll examine later in this
section how much rides on this provisional move. Here is an interesting question:
to what extent do non-natural properties exist? Here are two plausible but competing
answers. Answer one: all properties, natural or unnatural, exist to the same degree,
whatever that degree is. Answer two: more natural properties exist to a higher degree
than less natural properties.
I think that the second answer is better than thefirst, and that some prominent
metaphysicians who work on the metaphysics of properties have implicitly commit-
ted themselves to this view. One slogan championed by nominalists is that properties
are mere shadows cast by predicates. I disagree: perfectly natural properties have a
glow of their own. However, less than natural properties are mere shadows, although
they are cast by the perfectly natural properties rather than by linguistic entities.
Shadows are real, but they are less real than that which is their source.
Let us consider the work of D. M. Armstrong (1997), who is a full-blooded realist
about perfectly natural properties, which he identifies with universals. But his
attitude towards the less than perfectly natural properties is harder to discern.
Consider the following puzzling remarks:
Thefirst-class properties of particulars are the universals they instantiate. The second-class
properties of particulars have the following necessary and sufficient condition. They are not
universals, but when truly predicated of a particular, the resultant truth is a contingent
one.... What is their status? Will it be said that they do not exist? That will be a difficult
saying, since it can hardly be denied that innumerable statements in which these property- and
relation-words appear aretrue. [Armstrong 1997: 44]
To this is added the thesis of the ontological free lunch. What supervenes in the strong sense
is not something that is ontologically anything more than what it supervenes upon.... The
second-class properties are not ontologically additional to the first-class properties....
The second-class properties are not properties additional to thefirst-class properties. But it
is to be emphasized that this does not make the second-class properties unreal. They are real
and cannot be talked away. [Armstrong 1997: 45]