This book is part of a burgeoning literature on the syntax and semantics of plural noun phrases and of sentences containing them, and 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.
S'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 the latter. According to both theories, singular NPs (the cow) refer to individuals, and 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 two-membered 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. [NOTE 1]
The book consists of ten 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 of references, 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. Chapters 4-9 constitute the core of the book, and contain the main argumentation for the union theory, while exploring some related issues, including the analysis of collective nouns (chapter 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, 155-158), S shows that natural languages do not exploit these riches; there are, for example, no predicates which select arguments which are restricted to particular higher-order 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 of coordination does not provide for the unlimited embedding of coordinate expressions, and thus fails to provide even the syntactic means for expressing the full power of the 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 to appear).
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. 34-5. Suppose that every woman is either an author or an athlete and that all authors and athletes are women, that the men outnumber the authors and also outnumber the athletes, but that the women outnumber the men. Now consider the sentences (1) through (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 situation just 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 refers to the set of women, as it must under the union theory, then (2) and (3) should have exactly the same truth value. Therefore, the sets theorist concludes, the authors and the athletes must refer to something distinct from the set of women, namely to the set of sets consisting of the authors and the athletes.
S's solution is to deny that from the coreference of the authors and the athletes and the women one can conclude that the two phrases make the same contribution to the truth values of the sentences containing them. He develops an analysis of the semantics of plural NPs which handles not only cases like these but also cases involving reciprocal predicates, which have up to now constituted the strongest evidence for the sets theory. His analysis of reciprocity in chapter 6 permits the interpretation of reciprocal sentences to vary depending on contextual factors, much like the strongest meaning account of Dalrymple et al. 1994; Kim and Peters to appear. [NOTE 2]
One of S's central concerns is the relation between distributive and cumulative interpretations of sentences containing plural NPs. Both are interpretations which support inferential relations with other sentences with corresponding NPs of smaller cardinality. For example, if from a sentence of the form (4.a) we can conclude both (4.b) and (4.c), or their conjunction, we say that (4.a) has a distributive interpretation.
(4) a. NP1 and NP2 VP
b. NP1 VP
c. NP2 VP
Similarly, if from (4.b) and (4.c) together, or their conjunction, we can conclude (4.a), we say that (4.a) has a cumulative interpretation. That is, distributivity and cumulativity are converses. The notions were first discussed together by Goodman 1951 in connection with the calculus of individuals, and were defined as specific properties of predicates. [NOTE 3] For example, the predicate is/are red is both distributive and cumulative since (5.a), an instance of (4.a), holds if and only if both (5.b) and (5.c), instances of (4.b) and (4.c), hold.
(5) a. the backpack and the suitcase are red
b. the backpack is red
c. the suitcase is red
On the other hand, the predicate is/are light (in weight) is distributive but not cumulative and the predicate is/are heavy is cumulative but not distributive, since (6.a) implies both (6.b) and (6.c) but not conversely, and (7.b) and (7.c) together imply (7.a) but not conversely.
(6) a. the backpack and the suitcase are light
b. the backpack is light
c. the suitcase is light
(7) a. the backpack and the suitcase are heavy
b. the backpack is heavy
c. the suitcase is heavy
However, both the sentence the backpack and the suitcase are light and the sentence the backpack and the suitcase are heavy may also be understood both cumulatively and distributively just like the sentence the backpack and the suitcase are red.
S follows recent work in obtaining the distributive interpretation of sentences in which the predicate is not inherently distributive by means of a D-operator (sec. 5.2.2), paraphrasable as each, which he further generalizes so as to render the distributive-collective ambiguity a matter of pragmatics rather than of semantics (secs. 5.2.4 and 5.3; see in particular p. 75). He also follows current tradition by assuming that 'cumulativity is independent of the predicates involved' (60). As he immediately notes, this incorrectly predicts that (8.b) and (8.c) together imply (8.a) (as well as incorrectly predicting that (6.b) and (6.c) together imply (6.a)).
(8) a. the boys and the girls look alike
b. the boys look alike
c. the girls look alike
One solution would be to obtain the cumulative interpretation by application of the (generalized) D-operator, which combines with predicates which are not inherently cumulative (such as is/are light and look alike), to yield a cumulative interpretation. In the case of the predicate look alike, which appears to be neither cumulative nor distributive, addition of the D-operator renders it simultaneously cumulative and distributive. That is, (8.a) has either the noncumulative and nondistributive interpretation (9.a) or the cumulative and distributive interpretation (9.b).
(9) a. the boys look like the girls and the girls look like the boys
b. the boys look alike and the girls look alike
An adequate analysis of the cumulative and distributive properties of sentences with reciprocal predicates such as look alike requires, however, a further distinction, between what may be called incremental and nonincremental cumulativity and distributivity. [NOTE 4] The relation between (8.a) on the one hand and (8.b) and (8.c) on the other is nonincremental, since plurals and not singulars are put together (cumulated) or taken apart (distributed). However, the relation between (10.a) on the one hand and (10.b), (10.c) and (10.d) on the other is incremental, since singulars and not plurals are put together or taken apart (the examples are taken from Leonard & Goodman 1940; in S's examples on p. 14, the name Bluto has been changed to Brutus).
(10) a. Popeye and Bluto and Wimpy were shipmates
b. Popeye and Wimpy were shipmates
c. Popeye and Bluto were shipmates
d. Bluto and Wimpy were shipmates
The reciprocal predicates were shipmates and look alike are incrementally both cumulative and distributive, but are nonincrementally either both cumulative and distributive or neither cumulative nor distributive. Indeed all reciprocal predicates are nonincrementally either both cumulative and distributive or neither cumulative nor distributive. On the other hand, reciprocal predicates may be incrementally both cumulative and distributive (were shipmates, look alike, are similar to each other), distributive but not cumulative (are similar), or cumulative but not distributive (sat next to each other). Thus the real significance of Leonard and Goodman's (1940) observation concerning the nonequivalence of sentences like they are similar and they are similar to each other, which S discusses on p. 105, n. 30, is not just that both are similar and are similar to each other are reciprocal predicates, but that the former is incrementally distributive but noncumulative, whereas the latter is incrementally both distributive and cumulative. Reciprocal predicates formed with each other are invariably incrementally cumulative, though they may not be incrementally distributive (e.g. sat next to each other). Reciprocal predicates lacking an overt anaphor may or may not be incrementally cumulative (are shipmates and look alike are incrementally cumulative whereas are similar and agree are not), and they may or may not be incrementally distributive (look alike and are similar are incrementally distributive whereas are in equilibrium and are five kilometers apart are not), but they must be one or the other.
Dalrymple, Mary, M. Kanazawa, Sam Mchombo, and Stanley Peters. 1994. What do reciprocals mean? Proceedings of SALT IV, 61-78.
Goodman, Nelson. 1951. The structure of appearance. Cambridge, MA: Harvard University Press.
Kim, Yookyung, and Stanley Peters. to appear. Semantic and pragmatic context-dependence: The case of reciprocals. [Published in Is the best good enough? Optimality and competition in syntax, ed. by Pilar Barbosa, Danny Fox, Paul Hagstrom, Martha McGinnis, and David Pesetsky. Cambridge, MA: MIT Press, 1998, pp. 221-247.]
Langendoen, D. Terence. to appear. Limitations on embedding in coordinate structures. Journal of Psycholinguistic Research. [Published in vol. 27, pp. 235-259, 1998.]
Lasersohn, Peter. 1995. Plurality, conjunction, and events. (Studies in linguistics and philosophy 55). Dordrecht, NL: Kluwer Academic Publishers.
Leonard, Henry, and Nelson Goodman. 1940. The calculus of individuals and its uses. Journal of Symbolic Logic 5: 45-56.
Quine, Willard Van Orman. 1980. Set theory and its logic, rev. ed. Cambridge, MA: Harvard University Press.
Schein, Barry. 1993. Plurals and events (Current studies in linguistics 23). Cambridge, MA: MIT Press.
1. S points out that other theories of plurality are possible, including those based on event semantics, and that Schein 1993 has argued that "a semantics based on the notion of a plurality, such as the one used in this book, is incoherent" (197). S also does not consider the possibility of plural quantification (197-8). [BACK]
2. However, S takes issue with certain aspects of the strongest meaning account (130-1). [BACK]
3. Goodman however used the terms 'dissective' and 'collective' rather than 'distributive' and 'cumulative'. [BACK]
4. The distinction is not needed for sentences with nonreciprocal predicates, which are incrementally cumulative or dissective if and only if they are respectively nonincrementally cumulative or dissective. [BACK]