John Burgess

This work, the first book-length study of its topic, is an important contribution to the literature of philosophical logic and philosophy of language, with implications for other branches of philosophy, including philosophy of mathematics. However, five of the book's ten chapters, including many of the author's most original contributions, are devoted to issues about natural language, and lie pretty well outside the scope of this journal, not to mention that of the reviewer's competence. For this reason I will here largely confine my attention to the other half of the book, and so will be far from doing full justice to the book as a whole; indeed, there is such a wealth of detail in the book that I will be unable to do full justice even to the five chapters selected for comment.Non-distributive predicates.To begin with some points that have often been remarked, formulas in classical first-order logic are built up from predicates by means of a limited range of logical operators. Natural language involves many other such operators, beginning with temporal and modal operators, that are of great philosophical interest, but these are ignored by classical first-order logic. The reasons why it ignores them are surely that classical first-order logic was developed primarily for analyzing mathematical arguments, and that such grammatical categories as tense and mood play no significant role in mathematics.It has been less often remarked that the range of predicates considered in classical first-order logic is also limited. From Frege onwards, predicates have been taken to be essentially sentences with one or more gaps or places suitable to be filled in by singular noun phrases. Natural language involves also plural predicates, as well as mixed predicates with some …