Flexibility Principles in Boolean Semantics: The Interpretation of Coordination, Plurality, and Scope in Natural Language (review)

Based on some of the main chapters of Winter’s 1998 dissertation, this book takes the Boolean approach to natural language semantics, an extension of Montague grammar. The main objective is to examine how suitable these assumptions are for the linguistic theory of coordination, plurality, and scope. It is argued that the Boolean framework needs to be augmented by flexibility principles—semantic operations that have no phonological realization.

Three kinds of flexibility principles have been identified as necessary for the analysis of coordination, plurality, and scope in Boolean semantics: (1) logical principles such as ‘function application’, (2) type fitting principles or ‘last resort’ principles, and (3) category shifting principles. New flexible treatments of collective noun phrase coordination, the scope of indefinites, and plural quantification are proposed. This system eliminates ad hoc assumptions about syntax and lexical semantics that were previously needed. Ch. 1 (1–27) gives a general overview of the problems of coordination, plurality, and scope that are the focus of this book. It outlines the central foundational assumptions of the semantic theory and introduces the notion of flexibility. Ch. 2, ‘Coordination and collectivity’ (29–75), describes the problem of collectivity and noun phrase coordination in general terms. It critically reviews previous treatments and focuses on the proposal to treat conjunction using non-Boolean operators. The proposed flexible Boolean approach is introduced there.

Ch. 3, ‘The choice-function treatment of indefinites’ (77–134), gives an overview of the general problem of NP scope and the scope problem of indefinites in particular. ‘Choice functions’ are proposed as the ‘uniform’ mechanism for interpreting indefinites. Plural indefinites motivate the use of a ‘distributivity operator’. Ch. 4, ‘Predicate-quantifier flexibility’ (135–89), unifies the two mechanisms proposed in Chs. 2 and 3 by adopting a more general conception of semantic flexibility. Noun phrases have different semantic functions: While all noun phrases can be interpreted as generalized quantifiers, some NPs can also function as predicates.

Ch. 5, ‘Plural quantification and the atom/set distinction’ (191–249), deals with the problems of plurality. The first problem concerns the general parameters that determine whether a sentence gets a collective interpretation. The second concerns the collective interpretation when the nominal involved is a plural quantificational nominal. A novel typology of predicates, ‘set’ vs. ‘atom’ predicates, is proposed based on their behavior with quantificational nominals. Ch. 6, ‘On distributivity’ (251–66), summarizes the general approach to distributivity phenomena that emerges from the proposals in the previous chapters. It claims that only cases where a plural nominal takes scope over another element in the sentence constitute relevant evidence about the formal semantic nature of distribution. Quantificational distributivity, which is more restricted, shows only atomic behavior and hence atomic distributivity operators are advantageous. It is proposed that distributivity operators should be located both on the nominal and on the predicate. Ch. 7 (267–69) presents the conclusions. In short, the flexibility paradigm reveals further advantages of the Boolean approach to language, natural as well as artificial.