quantifier. But since there is no unrestricted quantifier, it is hard to say that some
semantically primitive restricted quantifier is at least as natural as the unrestricted
quantifier.
In order to keep things simple, consider a view that holds that sets enjoy one way
of being whereas concrete entities enjoy another. Consider now an infinite sequence
of quantifiers, indexed to the ordinals, such that thefirst member, Q0, ranges over all
and only concrete objects, Q1 ranges over all and only concrete objects and sets of
concrete objects, Q2 ranges over everything Q1 ranges over as well as sets of things
within Q1’s range, etc. Consider a second infinite sequence of quantifiers, also
indexed to the ordinals, Q0,..., Qn-, which is such that Q0 ranges over all and
only concrete objects, while each of Q1-,..., Qn- rangeover all and only the sets
ranged over by Q1... Qn. (In short, none of the domains of Q1-... Qn- include
concrete objects.) Basically, thefirst sequence is a sequence of increasingly expansive
quantifiers that have both individuals and sets within their domains, whereas the
second sequence is a sequence of increasingly expansive quantifiers that have only
sets within their domains (save Q0). Someone who wants to distinguish the mode of
being of a set from the mode of being of an individual while still denying the
possibility of unrestricted quantification can claim that the perfectly natural quanti-
fiers are Q0 along with Q1-,...,Qn-rather than Q1,... , Qn. So we can make sense of
the view that there are modes of being without believing in the possibility of
absolutely unrestricted quantification.
There is still the worry that, in describing this view, I am quantifying over every-
thing. This is a real worry, but it is an instance of a more general worry: how can the
denier of absolute quantification state her view without quantifying over everything?
I don’t know how this question is to be answered, but I believe that the friend of ways of
being who is also a foe of unrestricted quantification can follow suit, provided that it
can be answered at all. But exploring this further would take us very far afield indeed.
Another view worth considering holds that the domains of the fundamental
quantifiers overlap. This view is interesting, for according to it, there is anxsuch
thatxexists in more than one way. For historical antecedents, consider that Aristotle
(1984a: 17)discusses the possibility that some qualities might also be“relatives”in the
Categoriesat 11a37. Brower (2014: 53) notes a suggestion of Aristotle inPhysicsIII.3
that every entity that falls under the category ofpassionalso falls under the category
ofaction.^53 Furthermore, Brower (2014: 206–10) argues that this is Aquinas’s view as
well. More recently, Bertrand Russell (1964) distinguished betweenbeingandexist-
encebut held that everything that exists has being but not vice versa.^54 And regardless
of its historical antecedents, we can envision how such a view could be motivated:
consider the view that (i) particulars and universals exist in different ways, (ii) the
actual and the possible also exist in different ways, and (iii) these divisions cross-cut.
(^53) See Aristotle’sPhysicsIII.3 (1984a: 344–5); 202b1–10 seem especially relevant.
(^54) See Caplan (2011) for further discussion of Russell’s ontological pluralism.