Atom Predicates and Set Predicates: Towards a General Theory of Plural Quantification

The interpretation of sentences with plural determiners and collective predicates is a highly complex problem that has not been sufficiently investigated, despite many advances in theories of plurality and quantification. This paper proposes a new typology of predicates that serves as a basis for a general treatment of singular and plural noun phrases within generalized quantifier theory. Section 2 proposes that instead of the traditional distinction between “distributive”, “collective” and “mixed” predicates, a binary classification of predicates should be used according to their behaviour with plural determiners like all and exactly five. Predicates that allow collectivity with such determiners are referred to as set predicates. These are predicates like meet, gather, surround the castle or praise each other, which are traditionally classified as collective/mixed. However, following Dowty (1987) it is shown that some intuitively “collective” predicates like be numerous, be a good team or vote do not show collectivity when combined with plural quantificational noun phrases. Together with “distributive” predicates, these are classified as atom predicates. It is proposed that the difference between atom predicates and set predicates lies in their type. Atom predicates range over singularities – members of an arbitrary domain of individuals E. Set predicates range over pluralities – non-empty subsets of E. This does not mean that atom predicates cannot show collectivity effects, but only that these effects are restricted to “set-denoting” noun phrases like the students or Mary and Sue. Following previous works it is proposed that collectivity with set denoting NPs may appear due to a mapping from sets to “impure” atoms in E: singularities of the same sort as the denotation of NPs like the committee or the team. Section 3 substantiates the quantificational mechanism that accounts for the meaning of sentences like all the students met, where a plural determiner appears with a set predicate. Determiners standardly range over atoms. Plural nouns, unlike singular nouns, range over sets. This type mismatch between the determiner and the plural noun triggers a type shifting principle that fits the determiner to quantification over sets. The relations between this process and the conservativity of quantification in natural language are briefly examined.