In this book we hope to acquaint the reader with the fundamentals of truth conditional model-theoretic semantics, and in particular with a version of this developed by Richard Montague in a series of papers published during the 1960's and early 1970's. In many ways the paper 'The Proper Treatment of Quantification in Ordinary English' (commonly abbreviated PTQ) represents the culmination of Montague's efforts to apply the techniques developed within mathematical logic to the semantics of natural languages, and indeed it is the system outlined there that people generally have in mind when they refer to "Montague Grammar." (We prefer the term "Montague Semantics" inasmuch as a grammar, as conceived of in current linguistics, would contain at least a phonological component, a morphological component, and other subsystems which are either lacking entirely or present only in a very rudi mentary state in the PTQ system. ) Montague's work has attracted increasing attention in recent years among linguists and philosophers since it offers the hope that semantics can be characterized with the same formal rigor and explicitness that transformational approaches have brought to syntax. Whether this hope can be fully realized remains to be seen, but it is clear nonetheless that Montague semantics has already established itself as a productive para digm, leading to new areas of inquiry and suggesting new ways of conceiving of theories of natural language. Unfortunately, Montague's papers are tersely written and very difficult to follow unless one has a considerable background in logical semantics."

The most general goal of this book is to propose and illustrate a program of research in word semantics that combines some of the methodology and results in linguistic semantics, primarily that of the generative semantics school, with the rigorously formalized syntactic and semantic framework for the analysis of natural languages developed by Richard Montague and his associates, a framework in which truth and denotation with respect to a model are taken as the fundamental semantic notions. I hope to show, both from the linguist's and the philosopher's point of view, not only why this synthesis can be undertaken but also why it will be useful to pursue it. On the one hand, the linguists' decompositions of word meanings into more primitive parts are by themselves inherently incomplete, in that they deal only in distinctions in meaning without providing an account of what mean ings really are. Not only can these analyses be made complete by a model theoretic semantics, but also such an account of these analyses renders them more exact and more readily testable than they could ever be otherwise."

The most general goal of this book is to propose and illustrate a program of research in word semantics that combines some of the methodology and results in linguistic semantics, primarily that of the generative semantics school, with the rigorously formalized syntactic and semantic framework for the analysis of natural languages developed by Richard Montague and his associates, a framework in which truth and denotation with respect to a model are taken as the fundamental semantic notions. I hope to show, both from the linguist's and the philosopher's point of view, not only why this synthesis can be undertaken but also why it will be useful to pursue it. On the one hand, the linguists' decompositions of word meanings into more primitive parts are by themselves inherently incomplete, in that they deal only in distinctions in meaning without providing an account of what mean ings really are. Not only can these analyses be made complete by a model theoretic semantics, but also such an account of these analyses renders them more exact and more readily testable than they could ever be otherwise."

In this book we hope to acquaint the reader with the fundamentals of truth conditional model-theoretic semantics, and in particular with a version of this developed by Richard Montague in a series of papers published during the 1960's and early 1970's. In many ways the paper 'The Proper Treatment of Quantification in Ordinary English' (commonly abbreviated PTQ) represents the culmination of Montague's efforts to apply the techniques developed within mathematical logic to the semantics of natural languages, and indeed it is the system outlined there that people generally have in mind when they refer to "Montague Grammar." (We prefer the term "Montague Semantics" inasmuch as a grammar, as conceived of in current linguistics, would contain at least a phonological component, a morphological component, and other subsystems which are either lacking entirely or present only in a very rudi mentary state in the PTQ system. ) Montague's work has attracted increasing attention in recent years among linguists and philosophers since it offers the hope that semantics can be characterized with the same formal rigor and explicitness that transformational approaches have brought to syntax. Whether this hope can be fully realized remains to be seen, but it is clear nonetheless that Montague semantics has already established itself as a productive para digm, leading to new areas of inquiry and suggesting new ways of conceiving of theories of natural language. Unfortunately, Montague's papers are tersely written and very difficult to follow unless one has a considerable background in logical semantics."