plural and primitive singular quantifiers appear in the metaphysically ideal language.
If the metaphysically ideal language has both plural and singular quantifiers with
non-identical domains, then there is no especially tricky issue: we can straightfor-
wardly say that there are at least two different modes of being. But suppose the
metaphysically ideal language has exactly one singular quantifier and exactly one
plural quantifier, and that the domains of the two kinds of fundamental quantifiers
are the same. Then should we say that there are two modes of being, and that
everything enjoys the same modes of being?
In such a case, I think this is what we should say.^62 Modes of being correspond
with fundamental quantifier expressions, and such expressions may be plural or
singular. The result generated in this case is surely odd, but I think that we are in the
kind of situation in which a sensible criterion yields a silly result when applied to
something that is in itself silly. I can’t see what might justify claiming that the
metaphysically ideal language is like this. Either the ideal language has a plural
quantifier ranging over a given domain, or a singular quantifier, but not both. And
though I actually incline towards the idea that the fundamental quantifiers are plural,
in what follows here and in the successive chapters I will speak as though they are
singular. By and large, my doing so will make it easier for me to state and argue for
various positions and nothing in what follows will turn on my talking this way for
reasons of convenience.
More interesting is what one should say about higher-order quantification. First-
order quantifiers and names, broadly construed, are connected in the following way.
Given a sentence of the form“aisF,”in which“a”is a name and“F”is the predicate,
one can replace the name with a variable, such as“x”, and then bind that variable
with afirst-order quantifier, such as“some.”This procedure yields the quantified
sentence“somexis F.”One kind of second-order quantifier, which I’ll call a
predicate-quantifier, is connected with predicates in an analogous way: one can
replace the predicate with a different kind of variable, such as“ḟ”, and bind that
variable with a predicate-quantifier, also called“some.”This procedure yields the
sentence“a is someḟ,”which could be taken to say that a is some way or other.
Some philosophers have argued that higher-order quantification is really singular
quantification over“higher-order entities,”such as sets or properties.^63 A natural
extension of such a view is that, although in the metaphysical ideal language all
quantifiers arefirst-order quantifiers, the domain of some of those quantifiers
includes sets or properties. On the other hand, some philosophers have argued that
some (and perhaps all?) higher-order quantifiers can be treated as special plural
quantifiers over“first-order”individuals such as tables and chairs.^64 Obvious cases
are easy:“there is some way that all tables and chairs are”can be understood as“there
(^62) One lesson of Caplan (2011: 97–100) is that it would be very hard for me to not say this without also
ruling out other versions of ontological pluralism that I would prefer not to rule out. 63
Most famously, Quine (1970).^64 Most famously, Boolos (1984, 1985).