Introduction

This introduction presents an overview of key concepts discussed in the subsequent chapters of this book. The book examines that categorial grammars (CGs) are distinctive, though, for their direct representation of semantics in syntax- which endears them to philosophers of language, and to some linguists- and for their arithmetical transparency- which endears them to logicians, and especially to formal and computational linguists. CG offer a 'quasi-arithmetical notation for syntactic description', or 'computable linguistic description', combining explicit and precise algebraic characteristics with a close correspondence to the observed semantic and syntactic patterns of natural languages. The book covers debates over issues of underlying principle, such as word order and psychological plausibility, and areas of perhaps peripheral interest to the theoretical linguist, such as logic, algebra and computational parsing. The non-triviality of notational variance is of course a very general point, not restricted to CG or indeed to formal linguistics, and one which is all too commonly ignored in scientific argument.