Atoms and Sets: A Characterization of Semantic Number

This article analyzes the interactionsof semantic number, morphological number, and quantification. It argues that the traditional typology of distributive and collective predicates is unsuitable for a truth-conditional theory of plurality. A new test is proposed for classifying the semantic number of predicates according to their behavior with singular/plural quantificational noun phrases such as every/all student(s) and no teacher(s). Predicates that are (in)sensitive to such number variations are called atom/set predicates, respectively, and it is shown that this distinction cuts across the traditional distributive/ collective typology. The processes that govern the semantic number of sentences are reanalyzed in these terms.