life), not the other way around. Recall that Heidegger holds that an adequate account
of the generic sense of“being”will explain how the various specific senses of“being”
are unified.
If the restricted quantifiers are prior in meaning to the unrestricted quantifier, then
they must besemantically primitive. A semantically primitive restricted quantifier is
not a complex phrase that“breaks up”into an unrestricted quantifier and a restrict-
ing predicate. I borrow the idea of a semantically primitive restricted quantifier from
Eli Hirsch (2005: 76):
It seems perfectly intelligible to suppose that there can also besemantically restricted quanti-
fiers, that is, quantifiers that, because of the semantic rules implicit in a language, are restricted
in their range in certain specific ways. If the quantifiers in a language are semantically
restricted, they are always limited in their range, regardless of the conversational context.
The phrase“semantically primitive restricted quantifier”is not one with which I am
entirely happy. There is a sense in which any semantically primitive quantifier is an
unrestrictedquantifier. If a speaker had grasped and internalized the meaning of
exactlyone of these semantically primitive quantifiers (and had no other quantifier in
her language), this speaker would not be in a position to say or even to believe that
there is anything more than what is ranged over by that quantifier. (Keep in mind
that the meanings for the semantically primitive restricted quantifiers Hirsch intro-
duces are taken by him to be possible meanings for the unrestricted quantifier.)
Consider, for example, the subsistential quantifier, which ranges over all and only
abstract entities such as numbers or propositions. A language equipped with only the
subsistential quantifier is a language that is not only unable to express facts about
material objects, but is also unable to express the fact that it is unable to express facts
about material objects. From the perspective of someone who speaks only this
language, it will seem as though the subsistential quantifier is unrestricted.
Moreover, we can envision that these restricted quantifiers are equipped with a
character that allows them to be tacitly restricted by contexts, so that, for example,
one could say truthfully while using the subsistential quantifier that everything is
divisible by one, but nothing is divisible by zero. (The tacit restriction in play in this
context is that the subsistential quantifier has been restricted to numbers, which form
only a subset of that which subsists.) This fact seems to help bring home the thought
that these quantifiers are, in an important sense,“unrestricted.”They are not to be
understood as expressions that are either explicitly or implicitly“defined up”from a
more general quantifier and special predicates or special operators.
Heidegger recognizes van Inwagen’s genuinely unrestricted quantifier as a legit-
imate philosophical notion. However, Heidegger holds that the generic unrestricted
quantifier is somehow to be defined in terms of the semantically primitive restricted
quantifiers. How it is to be defined is not at all obvious, given that Heidegger does not
seem to think that the generic sense of“being”is merely the disjunction of the various
specificsensesof“being.”Recall that“being”is instead, on his view,“unified by analogy.”