Thomas Hofweber (2009: 275–9) argues that natural language quantificational
expressions are polysemous. He distinguishes between two readings of quantifica-
tional expressions: an inferential reading, in which they are characterized by infer-
ential role, and a second reading in which they are characterized in terms of domains
of entities. Consider the question,“are there numbers?”According to Hofweber, if
the quantifier in question has the meaning characterized by inferential role, the
question is trivially answered with a yes. (Interestingly, Hofweber also has an
argument that the answer is“no”if the quantifier expression is intended in the
second sense.)
There are many apparent points of conflict between Hofweber’s views and
my own. First, for me, quantifier expressions are all primarily characterized by
their syntactic and inferential roles—a quantifier is something that behaves syntac-
tically and inferentially like the unrestricted existential quantifier of ordinary lan-
guage. (I am happy to talk in terms of domains as well; but since there are ways
ofbeing, there are also ways ofbeing a domain, and hence the syntactic and
inferential characterizations seem more fruitful.) This characterization presupposed
that there is one thing that can be identified astheunrestricted existential quantifier
of ordinary language.^64
This leads to the second point of difference: as discussed in section 2.2, it
is ultimately a matter of indifference to me whether ontological locutions in
ordinary language are polysemous or univocal. I am happy to accept that, in ordinary
language,“being,”“some,”“there is,”“exist,”are basically interchangeable and that
all are to be understood in terms of an unrestricted existential quantifier. Whether or
not this is the case is to be settled more by linguistics than metaphysics, but it is
ultimately an orthogonal issue to what most concerns me: whether there are modes of
being and whether some modes are“superior”in some way to others. Linguistic
inquiry is relevant to this metaphysical project only in the following ways. First, our
patterns of language usemighttrack intuitions about modes of being, and insofar as
this is a possibility, it would be good to have insight into what those patterns are.
Second, philosophical linguistics can provide us with descriptions of possible struc-
tures for languages to consider, and some of these structures might be exemplified
by metaphysically better languages than English even if they are not exemplified in
English itself.
But for Hofweber, it is important that,“there are more numbers than there are
planets in the galaxy”is semantically ambiguous, and that on one of its disambigu-
ations, it is false. Maybe that’s the case, but the sentence doesn’t seem ambiguous.
(This isnotto say that numbers and planets exist in the same way!) Again, this is a
matter for linguistics to settle, provided that the linguistics is not constrained by
antecedent ontological qualms. I’dbefine if ontological expressions are polysemous
(^64) This is a presupposition I am happy to accept, but as we will see shortly, I am also in principle willing
to reject.