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INTRODUCTION TO MONTAGUE 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 . 2. Semantics(philosophy). 3. . 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 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 141 I. Compositionality and the - 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; and Relative Clauses 203 V. Be, Transitive Verbs, 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 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 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 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 . 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 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. PREFACE xi

As background for this textbook, we presuppose acquaintance with such rudiments of logic and set theory as might be found, for example, in the first five chapters of Wall (1972) and perhaps some familiarity with the basic prin• ciples and goals of generative transformational grammar (see, for example, Baker, 1978; Akmajian and Heny, 1975). For those readers who have no pre• vious knowledge of formal semantics, there is no denying the fact that it will require diligent application to get through it all. Montague Semantics is mani• festly of an intensely formal nature. Yet the ideas involved are not in them• selves really difficult, and the systems considered here are built up pro• gressively and in an orderly way. Furthermore, there are numerous problems and exercises sprinkled throughout, which the reader is encouraged to work through as a check on how well the preceding material has been understood. Answers for many of these are prOVided at the end of the book. By the end of Chapter 7 the reader should be prepared to read the current literature in the field. This book is an outgrowth of a manuscript prepared by Dowty as an intro• duction to his book on word meaning (Dowty, 1979). But the length of that book made it impractical to include the introduction there, and this intro• duction was instead distributed temporarily by the Indiana University Linguistics Club under the title A Guide to Montague's PTQ. Wall and Peters had independently undertaken to write an introduction to Montague Semantics, and they then invited Dowty to join them as collaborator on this project, in which Dowty's Guide could be incorporated. This Guide forms the basis of chapters two through seven of the present textbook. It was revised and expanded by Wall, who added discussions of the languages LOE and LiE as well as other material, and was further emended by the other two authors. Dowty wrote 6-JV and Appendix III, Wall and Peters the Preface and Chapter 1, and Peters Chapter 8. Chapter 9 was assembled by Peters with the aid of students. Barbara Partee generously offered us the exercises she had con• structed for Dowty's Guide; these make up the bulk of the problems and exercises in the book. We are grateful to her for this contribution and for her comments. Those who have made helpful suggestions and/or assisted with the preparation of the manuscript are too numerous to mention individually here, but we would like to single out in particular Jon Barwise, David Cohen, Edit Doron, Will Dowling, Douglas Fuller, Simon Gray, Charles Kirkpatrick, Doug Moran, Marlene Deetz Payha, Joseph Queen, Robert Starr, Gregory Stump, and Hans Uszkoreit.

D.R.D., R.E.W., and S.P.