This is an ambitious book, which claims that the theory of plurality and event structure it develops 'is the only game in town in the semantics of plurals' (5). It comprises twelve chapters, two appendices, extensive notes, references, and indices. The first chapter elegantly summarizes the entire book, and points to the specific sections in which the arguments are fully developed. The core theory is laid out in the next three chapters, with the remaining chapters providing detailed analysis of the semantics of plurality and quantification, including first- and second-order quantification, semidistributivity, and cumulative quantification. The first appendix is a short postscript on the ambiguity of logical form, while the second provides a comprehensive listing of variable symbols and notational conventions, and restates all the crucial definitions and examples in the text. Given the intricacy of the argumentation, the layout of the book could hardly be better.
S argues for Boolos' 1984 analysis of definite plural noun phrases as predicates, each of which denotes each object it is true of. Thus 'the elms ... does not denote [a plural] object that comprehends all elms. Rather it denotes each elm' (37). Like Boolos, S avoids the postulation of plural objects in order to prevent Russell's paradox from arising within a semantics for natural languages which is rich enough to account for certain entailments. However, Boolos' analysis introduces a discrepancy between the syntactic form of definite noun phrases and their logical forms. A singular like the elm denotes an object directly, whereas a plural like the elms denotes a predicate, which in turn denotes objects. [NOTE 1]
I am not convinced of the need to analyze definite plural noun phrases differently from singular ones. The now standard view of plural definites as denoting plural objects leads to paradox only under certain assumptions which strike me as dubious. Chief among them is an assumption of which 1 is a special case (29).
(1) There exists an elm |= The elms exist
First, the conclusion has a peculiar grammatical form, in which the subject of exist is definite. Second, the inference in 1, even if the conclusion is grammatical, is invalid. It ignores the plurality of the elms. This can be seen sharply if an indefinite phrase replaces the definite one in the conclusion, as in 2.
(2) There exists an elm |= There exist elms
Reversing the premise and conclusion in 2, of course, does result in a valid inference.
(3) There exist elms |= There exists an elm
The inference in 3 is a consequence of the axiom 4 in which N is a singular common noun predicate, and Ns is its plural counterpart, and ≤ and O are the part-whole and overlap relations of the calculus of individuals (Goodman 1951).
(4) $x(Ns(x)) Û $y(N(y)) Ù $z(N(z)) Ù y ≤ x Ù z ≤ x Ù ~(y O z)
The plural definite description the elms is related to the plural predicate elms exactly as the singular definite description the elm is related to the singular predicate elm, and picks out the appropriate plural object as its denotation. Axiom 4, unlike the 'comprehension axiom' that S provides (31, formula 62) for the relation between singulars and plurals, does not lead to Russell's paradox. [NOTE 2]
S's central thesis is a 'radical Davidsonian decomposition' of any natural-language predication into a conjunction of predications in which each theta-role is a two-place predicate relating an event argument and a participant, and the main predicate holds just of an event argument (10). The various predications are connected by anaphoric relations that are reminiscent of those that hold between pronouns and antecedents. For example, he proposes that 5 has the logical form 6, paraphrasable as 7 (8-13). [NOTE 3]
(5) Three video games taught every quarterback two new plays.