Summary |
Several
natural languages contain a grammatical distinction between singular and plural
expressions. The distinction also concerns quantification. Alongside singular
quantifiers (‘something’, ‘everything’), we can find plural quantifiers (‘some
things’, ‘all things’). Plural logic is a formal system that regiments plural
quantification as a sui generis form of quantification, distinct from singular
quantification. When treated
as sui generis, plural quantification and plural logic have been thought to be
philosophically significant and have found a number of applications especially
in philosophy of mathematics and metaphysics. For the most part, these
applications can be traced back to two of the virtues that plural
quantification is alleged to have, i.e. ontological innocence and expressive
power. On the one hand, it is assumed that plural quantifiers range in a special plural way over the entities in the range of the singular quantifiers and not over special plural entities (e.g. sets, collections, or any kind of set-like
entities). Thus they do not incur
ontological commitments exceeding those of the singular quantifiers. On the
other hand, as shown by Boolos, plural quantification can interpret monadic second-order
logic. As a result, plural quantification has been thought to provide more
expressive power than singular quantification as captured by first-order logic. While the
growing philosophical literature focuses primarily on the logical and
foundational features of plural quantification, research in natural
language semantics targets the meaning-theoretic and compositional features of
plurals, often from an algebraic perspective. These two strands of research
appear largely unreconciled. |