Pluralities by Roger Schwartzchild (review)

648LANGUAGE, VOLUME 74, NUMBER 3 (1998) Pluralities. By Roger Schwartzchild. (Studies in linguistics and philosophy 61.) Dordrecht: Kluwer, 1996. Pp. xi, 211. Reviewed by D. Terence Langendoen, University ofArizona Part of a burgeoning literature on the syntax and semantics of plural noun phrases and of sentences containing them, this book can profitably be read together with another recently published book in the Studies in linguistics and philosophy series (Lasersohn 1995). The two books complement each other and together provide a comprehensive review of the literature. Schwartzchild's main goals are to compare two theories of the semantics of plurality, which he calls the sets theory and the union theory, and to argue for die latter. According to both theories, singular NPs (the cow) refer to individuals while noncoordinate plural NPs (the cows) and coordinate NPs whose members are all singular (the cow and the pig) refer to sets of individuals. The theories diverge in their interpretation of coordinate NPs at least one of whose members is plural (the cow and the pigs; the cows and the pig; the cows and the pigs). On the sets theory, such NPs refer to sets of sets; for example the cows and the pigs refers to the twomembered set, one of whose members is the set of individual cows and the other is the set of individual pigs. On the union theory, they refer to sets of individuals; in this case to the set made up of the individual cows and pigs.1 The book consists often chapters, an appendix on 'Quine's innovation' (Quine 1980), which eliminates the distinction between singleton sets and their members and which S assumes holds for natural-language semantics, a list ofreferences, and a very short index. The first three chapters provide an initial formalization and discussion of the two theories, survey the recent literature on plurality, identifying who has argued for each of these theories, and preview the relevant data. Chs. 4-9 constitute me core of the book and contain the main argumentation for the union theory while exploring some related issues, including the analysis of collective nouns (Ch. 9). The final chapter provides a concluding summary. As S observes, the sets theory is committed to a richer ontology than the union theory, not just to sets of sets, but also to sets of sets of sets, etc. without limit. In several places (see especially 45-53, 155-58), S shows that natural languages do not exploit these riches; there are, for example, no predicates which select arguments which are restricted to particular higherorder sets. Accordingly, there is no need to invest natural-language semantics with the full power of the sets theory. The argument can be strengthened by observing that the syntax ofcoordination does not provide for the unlimited embedding of coordinate expressions and thus fails to provide even the syntactic means for expressing the full power ofthe sets theory. For example, a coordinate NP of the form A and B and C and D, where A, B, C, and D are noncoordinate NPs, may be understood as having no internal structure or as having two binary coordinates as members ([A and B] and [C and D]) but not as having a more deeply embedded structure (e.g. A and [B and [C and D]]) (Langendoen 1998). Much of the book is taken up with the analysis of examples which have been used to support the sets theory, for example the following from pp. 34-35. Suppose that every woman is either an author or an athlete and that all authors and athletes are women, mat the men outnumber the authors and also outnumber the athletes, but that the women outnumber the men. Now consider the sentences 1-3. (1)the men outnumber the authors and the men outnumber the athletes (2)the men outnumber the authors and the athletes (3)the men outnumber the women In the situationjust described, 1 is true, 2 is either true or false depending on its reading (distributive or collective), and 3 is false. However, if the compound NP the authors and the athletes 1 S points out that other theories of plurality are possible, including those based on...