Introduction to Montague Semantics Studies in Linguistics and Philosophy
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INTRODUCTION TO MONTAGUE SEMANTICS STUDIES IN LINGUISTICS AND PHILOSOPHY formerly Synthese Language Library Managing Editors: GENNORO CHIERCHIA, Cornwell University PAULINE JACOBSON, Brown University Editorial Board: EMMON BACH, University of Massachusetts at Amherst JON BARWISE, CSLI, Stanford JOHAN VAN BENTHEM, Mathematics Institute, University of Amsterdam DAVID DOWTY, Ohio State University, Columbus GERALD GAZDAR, University of Sussex, Brighton EWAN KLEIN, University of Edinburgh BILL LADUSA W, University of California at Santa Cruz SCOTT SOAMES, Princeton University HENRY THOMPSON, University of Edinburgh VOLUM E 11 INTRODUCTION TO MONTAGUE SEMANTICS by DA VID R. DOWTY Dept. of Linguistics, Ohio State University, Columbus ROBERT E. WALL Dept. of Linguistics, University of Texas at Austin and STANLEY PETERS CSLI, Stanford KLUWER ACADEMIC PUBLISHERS DORDRECHT I BOSTON I LONDON library of Congress Cataloging in Publication Data Dowty, David R. Introduction to Montague semantics. (Syn these language library; v. 11) Bibliography: p. Includes index. 1. Montague grammar. 2. Semantics(philosophy). 3. Generative grammar. 4. Formal languages-Semantics. I. Wall, Robert Eugene, joint author. II. Peters, Stanley, 1941- joint author. III. Title. IV. Series P158.5D6 415 80-20267 ISBN-13: 978-90-277-1142-7 e-ISBN-13978-94-009-9065-4 DOl: 10.1007/978-94-009-9065-4 Published by Kluwer Academic Publishers, P.O. Box 17,3300 AA Dordrecht, The Netherlands. Kluwer Academic Publishers incorporates the publishing programmes of D. Reidel, Martinus Nijhoff, Dr W. Junk and MTP Press. Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. Box 322,3300 AH Dordrecht, The Netherlands. Printed all acid-free paper First published 1981 Reprinted 1983, 1984, 1985 Reprillled with corrections 1985, 1988, 1989, 1992 All Rights Reserved © 1981 Kluwer Academic Publishers, Dordrecht, The Netherlands No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner. TABLE OF CONTENTS PREFACE ix 1. INTRODUCTION 1 2. THE SYNTAX AND SEMANTICS OF TWO SIMPLE LANGUAGES 14 I. The Language Lo 14 1. Syntax of Lo 14 2. Semantics of Lo 16 II. The Language LOE 23 1. Syntax of LOE 23 2. Semantics of LOE 25 3. Alternative Fonnulations of LOE and Lo 35 III. A Synopsis of Truth-Conditional Semantics 41 IV. The Notion of Truth Relative to a Model 44 V. Validity and Entailment Defined in Terms of Possible Models 47 VI. Model Theory and Deductive Systems 50 Exercises 53 Note 54 3. FIRST-ORDER PREDICATE LOGIC 56 I. The Language L I 56 1. Syntax of LI 56 2. Semantics of LI 59 II. The Language LIE 66 1. Syntax of LIE 69 2. Semantics of LIE 72 Exercises 81 Notes 82 v vi TABLE OF CONTENTS 4. A HIGHER-ORDER TYPE-THEORETIC LANGUAGE 83 I. A Notational Variant of L1 83 II. The Language L type 88 1. Syntax of Ltype 91 2. Semantics of L type 92 III. Lambda Abstraction and the Language L", 98 Exercises 110 Notes 111 5. TENSE AND MODAL OPERATORS 112 I. Tense Operators and Their Interpretation 112 II. The Other Varieties of Modal Logic; the Operators 0 and 0 121 III. Languages Containing Both Tense and Modal Operators: Coordinate Semantics 131 Exercises 139 Notes 139 6. MONTAGUE'S INTENSIONAL LOGIC 141 I. Compositionality and the Intension-Extension Distinction 141 II. The Intensional Logic of PTQ 154 1. Syntax of IL 155 2. Semantics of IL 157 III. Examples of 'Oblique Contexts' as Represented in IL 162 IV. Some Unresolved Issues with Possible Worlds Semantics and Propositional Attitudes 170 Notes 175 7. THE GRAMMAR OF PTQ 179 I. The Overall Organization of the PTQ Grammar 179 1. The Syntactic Categories of English in the PTQ Grammar 181 2. The Correspondence Between Categories of English and Types of IL 184 II. Subject-Predicate and Determiner-Noun Rules 190 III. Conjoined Sentences, Verb Phrases, and Term Phrases 198 IV. Anaphoric Pronouns as Bound Variables; Scope Ambiguities and Relative Clauses 203 V. Be, Transitive Verbs, Meaning Postulates, and Non-Specific Readings 215 VI. Adverbs and Infmitive Complement Verbs 232 VII. De dicto Pronouns and Some Pronoun Problems 237 TAB LE OF CONTENTS vii VIII. Prepositions, Tenses, and Negation 243 Exercises 245 Notes 248 8. MONTAGUE'S GENERAL SEMIOTIC PROGRAM 252 9. AN ANNOTATED BIBLIOGRAPHY OF FURTHER WORK IN MONTAGUE SEMANTICS 269 APPENDIX I: Index of Symbols 277 A P PEN D I X I I: Variable Type Conventions for Chapter 7 278 A P PEN D I X I I I : The Temperature Is Ninety and Rising 279 Notes 286 REF ERE N C E S '287 ANSWERS TO SELECTED PROBLEMS AND EXERCISES 294 INDEX 307 PREFACE 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. Previous introductions to Montague's framework, e.g., Partee (1975a) and Thomason (i 974a), have served very well to bring Montague's ideas to the attention of linguists and philosophers generally, but within the relatively brief space they occupy they could not provide the detailed account that seems ,0 be required for a thoroughgoing understanding of these ideas. The increasing interest in Montague Semantics thus seemed to call for a textbook that wouln start from a minimal basis of set theory and logic and proceed stepwise toward the goal of the PTQ system and a view of Montague's overall program. This book is an attempt to provide what is necessary for ix x PREFACE understanding Montague's work itself as well as the recent literature based on this approach. The plan of the book is as follows. In Chapter I we sketch some of the basic assumptions underlying the truth-conditional, model-theoretic, and "possible worlds" approaches to semantics and attempt to justify these assumptions in very general terms. In Chapter 2 we illustrate the truth conditional and model-theoretic methods using a formal language which is essen tially the propositional calculus and a small fragment of an analogous language bearing some resemblance to English. In the next three chapters the complexity of the languages is gradually increased - first by the addition of variables and quantifiers, and then by the addition of tense-, modal-, and A-operators - and the model-theoretic semantics is correspondingly augmented to take account of the :lew constructions. A number of notational alterations along the way prepare the reader gradually for the rather intricate and some times confusing system used by Montague. In Chapter 6 the language under consideration is the Intensional Logic which Montague employs in PTQ as an intermediate translation language con necting English to its model-theoretic interpretation. The PTQ system itself is the subject of Chapter 7. Chapter 8 contains a discussion of Montague's general semiotic program as set forth in his paper 'Universal Grammar' (Montague I 970c), and Chapter 9 consists of an annotated bibliography of publications in which Montague's framework has been extended and applied to other problems in the domain of natural language. From a certain point of view, it would have been desirable to include a detailed discussion of many of the extensions of Montague's system in this textbook. For while the syntax of the original PTQ fragment is relatively rudimentary, these extensions show that Montague's original program is com patible with a syntax that achieves the degree of sophistication found in current transformational theory, and that it allows a precise examination of the interconnection of syntax and semantics in a way that is rarely achieved in other semantic frameworks. Thus it is really these extensions rather than the PTQ grammar itself which justify Montague Grammar as an interesting and productive paradigm for linguistic research. Unfortunately, a detailed dis cussion of this work would have lengthened this book to ungainly propor tions; and in any event, such a discussion should not be absolutely essential since this book will equip the reader to attack the original articles quite easily. We simply issue the warning here that the reader should examine this literature before drawing any final conclusions about the usefulness of Montague's program for linguistics.