can say that there are exactly two Fs by asserting that∃x∃y(Fx&Fy&~x=y&
( 8 zFz!z=xorz=y)). So if there is some sense in which certain things are not to
be counted, we should also expect that there is some sense in which certain things are
not there at all.
Let us develop such a view. There are at least two possible quantifiers in play: a
perfectly natural one,“∃n,”that includes all natural properties but no less than
natural ones in its domain, and a less than perfectly natural one,“∃i,”that includes
all the properties in its domain. One candidate for being“∃i”is the unrestricted
quantifier of ordinary English. For the sake of a simple example, suppose that there
are exactly two perfectly natural properties, P1 and P2, and one less natural property,
namely the disjunction of them, P1∨P2. On this view, the following sentences
are true:
- (^8) nz[zis a property!(z=P1orz= P2)]
- (^8) iz[zis a property!(z=P1orz=P2orz=P1∨P2)]
We respect the intuition that P1∨P2 is no addition of being by endorsing 1. Given 1,
there is a straightforward and metaphysically important sense of“being”according to
which there are exactly two properties. P1∨P2 would be an addition of being if it were
a false-maker for 1, for then, fundamentally speaking,it would have to be counted.
That which is anontologicaladdition to being is that which is to be found in the
domain of“∃n.”But we also respect the intuition that P1∨P2 exists by endorsing 2 as
well. P1∨P2 must be counted among what there is, but it counts for less in virtue of
being less than fully real. The denial of 2 is the difficult saying that Armstrong warns
us not to utter, but the denial of 2 must not be confused with the affirmation of 1. By
accepting both 1 and 2 we accommodate both intuitions in a clean way. Second-class
properties really are second-class—they exist merely degenerately—but they are
nonetheless within the range of the unrestricted quantifier of ordinary English and
hence are real.
The solution to Armstrong’s troubles made use of two possible meanings for the
existential quantifier, one of which was more natural than the other. One might
wonder how essential to the solution the disparity of naturalness is. Would it suffice if
both quantifiers were equally natural, given that one does not include the second-
class properties that the other includes? In short, would a solution that appeals to
levels of beingrather thandegrees of beingbe equally adequate? (The idea is that
perfectly natural properties would enjoy two fundamental modes of being, one of
which it shares with the second-class properties, whereas the second-class properties
enjoy merely one fundamental mode.)
I think appealing to levels of being here is inapt, and for the same reason that
appealing to levels of being in the case of almost nothings proved inapt (in section
5.2). The nature and existence of second-class properties arefixed by the nature and
existence offirst-class properties. That’s a given and unsurprising provided that second-
class properties do not fully exist. But it would be very surprising if second-class