On Conditionals

ON CONDITIONALS

On Conditionals provides the first major cross-disciplinary account of conditional (if-then) constructions. Conditional sentences directly reflect the language user's ability to reason about alternatives, uncertainties and unrealized contingencies. An understanding of the conceptual and behavioural organization involved in the construction and interpretation of these kinds of sentences therefore provides fundamental insights into the inferential strategies and the cognitive and linguistic processes of human beings. Nevertheless, conditionals have not been studied in depth until recently, and current research has tended to be compartmentalized within particular disciplines. The present volume brings together studies from several perspectives: (i) philosophical, focusing on abstract formal systems, interpretations based on truth or information conditions and precise notions of inference and entailment; (ii) psychological, focusing on evidence about how people not trained in formal logic use and interpret conditionals in language and everyday reasoning, whether in natural or experimental situations; and (iii) linguistic, focusing on the universals of language that partly constrain the way we reason, and on the relations to other linguistic domains revealed by acquisition and historical change. Readers of On Conditionals - whether their backgrounds are in cognitive science, philosophy of language, linguistics, or indeed artificial intelligence - will find in the book an original and salutary emphasis on the intrinsic connections between the issues that are addressed. The volume points to exciting new directions for interdisciplinary work on the way in which we use form, meaning, interpretation and action in reasoning and in learning from experience.

ON CONDITIONALS EDITED BY

Elizabeth Closs Traugott Alice ter Meulen Judy Snitzer Reilly Charles A. Ferguson

The right of the University of Cambridge to print and sell all manner of books was granted by Henry Vlll in 1534. The University has printed and published continuously since 1584.

CAMBRIDGE UNIVERSITY PRESS Cambridge London New York New Rochelle Melbourne Sydney

CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo, Delhi Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521113274 © Cambridge University Press 1986 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 1986 This digitally printed version 2009 A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data On Conditionals. "Present volume arose out of a Symposium on Conditionals and Cognitive Processes, which was held at Stanford University in December 1983" - Pref. Includes indexes. 1. Grammar, Comparative and general - ConditionalsCongresses. I. Traugott, Elizabeth Closs. II. Symposium on Conditionals and Cognitive Processes (1983: Stanford University) P292.5.05 1986 415 86 9529 ISBN 978-0-521-30644-7 hardback ISBN 978-0-521-11327-4 paperback

CONTENTS

Contributors Preface Acknowledgments

vii ix xi

PARTI: GENERAL STUDIES 1 OVERVIEW Charles A. Ferguson, Judy Snitzer Reilly, Alice ter Meulen, and Elizabeth Closs Traugott 2 CONDITIONALS AND CONDITIONAL INFORMATION Jon Barwise

3 21

3 CONDITIONALS AND MENTAL MODELS

P. N. Johnson-Laird 4 CONDITIONALS: A TYPOLOGY Bernard Comrie

55 77

PARTII: PARTICULAR STUDIES 5 ON THE INTERPRETATION OF 'DONKEY' -SENTENCES Tanya Reinhart

103

6 GENERIC INFORMATION, CONDITIONAL CONTEXTS AND CONSTRAINTS Alice ter Meulen

123

7 DATA SEMANTICS AND THE PRAGMATICS OF INDICATIVE CONDITIONALS Frank Veltman

147

8 REMARKS ON THE SEMANTICS AND PRAGMATICS OF CONDITIONALS Ernest W. Adams

i6g

Contents 9 THE USE OF CONDITIONALS IN INDUCEMENTS AND DETERRENTS Samuel Fillenbaum

179

10 CONDITIONALS AND SPEECH ACTS Johan Van der Auwera

197

11 CONSTRAINTS ON THE FORM AND MEANING OF THE PROTASIS John Haiman

215

12 CONDITIONALS, CONCESSIVE CONDITIONALS AND CONCESSIVES: AREAS OF CONTRAST, OVERLAP AND NEUTRALIZATION Ekkehard Konig

229

13 THE REALIS-IRREALIS CONTINUUM IN THE CLASSICAL GREEK CONDITIONAL Joseph H. Greenberg

247

14 THE HISTORICAL DEVELOPMENT OF SI-CLAUSES IN ROMANCE Martin B. Harris

265

15 FIRST STEPS IN ACQUIRING CONDITIONALS Melissa Bowerman

285

16 THE ACQUISITION OF TEMPORALS AND CONDITIONALS Judy Snitzer Reilly

309

17 CONDITIONALS ARE DISCOURSE-BOUND Noriko Akatsuka

333

18 CONDITIONALS IN DISCOURSE! A TEXT-BASED STUDY FROM ENGLISH Cecilia E. Ford and Sandra A. Thompson

353

Index of names Index of languages Index of subjects

373 377 379

VI

CONTRIBUTORS

Ernest W. Adams Department of Philosophy, University of California, Berkeley Noriko Akatsuka Department of East Asian Languages and Cultures, University of California at Los Angeles Jon Barwise Center for the Study of Language and Information, Stanford University Melissa Bowerman Max-Planck-Institut fur Psycholinguistik, Nijmegen Bernard Comrie Department of Linguistics, University of Southern California Charles A. Ferguson Department of Linguistics, Stanford University Samuel Fillenbaum Department of Psychology, University of North Carolina Cecilia E. Ford Applied Linguistics Program, University of California at Los Angeles Joseph H. Greenberg Department of Linguistics, Stanford University John Haiman Department of Anthropology, University of Manitoba Martin B. Harris Department of Modern Languages, University of Salford P. N. Johnson-Laird MRC Applied Psychology Unit, Cambridge Ekkehard Konig Seminar fur Englische Philologie, Universitat Hannover Judy Snitzer Reilly Salk Institute for Biological Studies, California Tanya Reinhart Department of Poetics and Comparative Literature, Tel Aviv University Alice ter Meulen Department of Linguistics, University of Washington Sandra A. Thompson Department of Linguistics, University of California at Santa Barbara Elizabeth Closs Traugott Departments of Linguistics and English, Stanford University Johan Van der Auwera Department of Linguistics, University of Antwerp Frank Veltman Centrale Interfaculteit, University of Amsterdam

vn

PREFACE

Conditional (if-then) sentences have long been of central concern in the study of reasoning. Because modern academic practice has compartmentalized three distinct disciplines: linguistics, psychology and philosophy, a tremendous variety of different questions and angles of approach have developed, often independently, and without a common focus. The purposes of this book are: (i) to emphasize the intrinsic connections between the issues that have been addressed within the three disciplines; (ii) to show that all share similar concerns with how human beings use conditional constructions in their language to reason and to communicate their thoughts; and (iii) to point to new directions and potential areas of cross-fertilization for future studies. The papers are arranged as follows. Part I presents a broad survey of conditionals, the ways in which they are used to reason, and the ways in which they are structured in language (the overview by the editors, and papers by Barwise, Johnson-Laird, and Comrie from the points of view of philosophy, psychology, and linguistics, respectively). Part II presents approaches to particular aspects of conditionals, starting with papers in the tradition of philosophy and formal syntax and semantics that show how the study of conditionals can lead to the refinement of syntactic and semantic theories (Reinhart, ter Meulen, and Veltman). It moves on to papers that focus on the intentions of speakers in using and understanding conditionals from the different perspectives of philosophy, linguistics and psychology (Adams, Van der Auwera, and Fillenbaum). These are followed by detailed linguistic studies of the interaction of conditionals with other categories of grammar: conjunctive and disjunctive coordinators (Haiman), concessives (Haiman and Konig), modals (Greenberg), tense and aspect (Harris). Three case studies focus on the development of conditional constructions in history (Harris) and in language acquisition (Bowerman, Reilly). The final papers focus on the pragmatics of conditionals used in constructed dialogues (Akatsuka) and in actual expository monologic texts (Ford and Thompson). Each of the papers in Part II is preceded by a brief introductory editorial paragraph pointing to connections with other papers in Part II. Since different terminologies are used in the different traditions and are not always exactly translatable from one tradition to another, no attempt has been made to impose one set of terminology throughout the volume; cross-references in the index should aid the reader in identifying partial equivalences. ix

Preface The present volume arose out of a Symposium on Conditionals and Cognitive Processes, which was held at Stanford University in December 1983. A preparatory workshop in May 1982, summarized in a working paper by Traugott and Ferguson entitled Toward a checklist for conditionals', laid the groundwork for this Symposium. Most of the contributions were extensively rewritten; some were conceived only during the Symposium. We have included widely different perspectives on conditionals, which despite differences in approach and in terminology nevertheless often address the same or very similar data and phenomena, in the hope that it will inspire genuinely interdisciplinary research with an improved understanding of the current state of the art in the various disciplines.

ACKNOWLEDGMENTS

We gratefully acknowledge the support of a number of organizations. Funding for the Symposium on Conditionals and Cognitive Processes that was the inspiration for this book was provided by the National Science Foundation (NSF Grant BNS-8309784) and by the Center for the Study of Language and Information at Stanford University. Elizabeth Traugott's research on conditionals was largely conducted during 1983-4 while she was a Guggenheim Fellow and a Fellow at the Center for Advanced Study in the Behavioral Sciences (supported in part by NSF Grant BNS 76-22943). Special thanks are due to Randa Mulford for her expert help in editing and preparing the indexes, and to Penny Carter for her assistance in bringing the volume to fruition.

XI

PART I

GENERAL STUDIES

1 OVERVIEW • Charles A. Ferguson, Judy Snitzer Reilly, Alice ter Meulen, Elizabeth Closs Traugott If the organism carries a 'small-scale model1 of external reality and of its own possible actions within its head, it is able to try out various alternatives, conclude which is the best of them, react to future situations before they arise, utilize the knowledge of past events in dealing with the present and the future, and in every way to react in a much fuller, safer, and more competent manner to the emergencies which face it. (Craik 1943:61) 1. I N T R O D U C T I O N

Conditional (if-then) constructions directly reflect the characteristically human ability to reason about alternative situations, to make inferences based on incomplete information, to imagine possible correlations between situations, and to understand how the world would change if certain correlations were different. Understanding the conceptual and behavioural organization of this ability to construct and interpret conditionals provides basic insights into the cognitive processes, linguistic competence, and inferential strategies of human beings. The question of what a conditional construction is may be answered in many different ways, and from many different perspectives. The linguistic characterization of conditionals in different languages provides the basis for linguistic universals, which presumably at least in part constrain the way we reason. The diachronic point of view provides knowledge of the possible adaptations that a system of conditionals may undergo, and may detect dependencies on developments in other linguistic domains. Studies of language acquisition provide additional perspectives on a linguistic system, offering not only developmental data but also insights into the basic components and relationships of the adult system. Cognitive psychology presents us with empirical evidence about how people not trained in formal logic use and interpret conditionals in natural language and everyday reasoning. Philosophical logic and philosophy of language both design abstract formal systems of conditionals with interpretations based on truth conditions or information conditions, defining a precise notion of inference or entailment. The linguistic, psychological and philosophical traditions outlined here have been, and will continue to be, developed relatively independently of each other.

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This is inevitable, and even to some extent to be desired. They not only have somewhat different goals, but they use different methods and different types of data, ranging from introspection to text analysis to experimentation. It would be impossible completely to synthesize all the traditions into one research programme. On the other hand, an improved understanding of these various perspectives, their results and their limitations, is essential to the future development of a more genuinely interdisciplinary approach to conditionals in cognitive science. The present volume is the first major attempt at combining the different perspectives and research traditions. This overview is intended to provide a guideline to the papers in the book, giving some further background to the various issues addressed in the papers, and setting the main results in a larger context. It also suggests some possible new lines of research. 2. LINGUISTIC TRADITIONS Linguistic traditions assume that there is some principled correlation between the psychological and semantic properties of conditionals on the one hand and their form on the other. Although there may not be a strict one-to-one relation between meaning and form, the relationship is nevertheless far from arbitrary, and reflects a finite range of conceptual correlates. Insight into the mental representation of conditionals is expected from research on such questions as whether a language has a prototypical conditional construction, what other constructions can be used as conditionals, and what other semantic functions can be expressed by conditionals. Some discussion of conditionals can be found in virtually all descriptive grammars of languages. However, linguists working in the generative tradition have until recently paid surprisingly little attention to conditionals. This may be in part because conditionals interact so extensively with other domains (e.g. causals, temporals, modals) that they pose enormous difficulties for analysis; but it is perhaps largely due to the fact that their syntactic properties tend to be less interesting than their semantic ones, and semantic theory has only within the last decade caught up with advances in syntactic theory. Most recent linguistic work has been either from the perspective of detailed descriptive studies of certain aspects of conditionals in particular languages, or from the broad perspective of universals. In addition, some work has also been done on diachronic aspects of conditionals. We discuss these approaches in turn. 2.1 Descriptive studies The central task of linguistic description is the analysis and presentation of aspects of the grammatical structure of a particular language or language variety, used

Overview by a given speech community located in space and time. Several thousand such grammars or grammatical sketches have been produced, based on different theoretical models and intended for different purposes. Since all natural languages are assumed to have some kind of conditional sentences, any full-scale grammatical description is likely to include an account of conditional constructions, although some models of grammar do not make provision for them and some methods of collecting language data tend not to result in grammars that refer to conditionals. Every human language, it may be assumed, has some way of forming conditional sentences, in which the speaker supposes that such-and-such is (was, might be, had been . . . ) so - the //-clause or 'protasis', also called the 'antecedent' - and concludes that such-and-such is (was, would have been . . . ) so - the then-clause or 'apodosis', also called the 'consequent'. Likewise, every account of human reasoning, every system of logic, has as a key notion an if-then relation between propositions: if p, then q. Yet neither the essential semantics nor the range of possible variation in the form of conditional constructions has been adequately established. The prime purpose of the descriptive linguistic approach is to determine the range of forms and their meanings within and across languages. Such studies show that the ways of expressing conditionals may differ substantially from English if-then markers. Furthermore, they show that people in different societies or different communities within the same society may have different experiences with conditionals and different uses for them (see, for example, Lavandera 1975). It has been argued that preliterate societies do not use overt syllogistic reasoning (Ong 1982: ch. 111). It in no way follows from this that preliterate languages have no conditionals. On the contrary, they clearly do (see much of the data in Haiman's chapter in this volume), but they may be used in other ways and in other contexts. Despite the wealth of descriptive studies, the question of what constitutes a conditional construction in a given language has as yet no adequate theoretical answer. Since material implication has a long history and is the most workedover and best-known logical relation between propositions that corresponds to the conditional sentences of natural languages, linguists are often tempted to use it as the defining basis for conditionals. This is widely recognized as less than satisfactory, in the first instance because users of natural languages tend to reject the validity of false antecedent implying true consequent and often assume some kind of causal connection between the propositions (Geis and Zwicky 1971). Further, the use of material implication for linguistic definition in no way helps to explain the syntactic and etymological ties between conditionals and wish clauses, temporal and causal clauses, imperatives, and so forth. These difficulties have been repeatedly discussed by both philosophers and linguists. Comrie (this volume) accepts the defining role of material implication as a matter of convenience, although acknowledging the familiar objections. Others, such as Smith (1983), preserve the defining value by shifting the

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problems to pragmatics and by modifying the usual meaning of material implication. At the present stage of research it seems likely that if conditionals are in some sense a natural class of linguistic phenomena, the formulation of a universally valid definition will be aided by the accumulation of detailed descriptions of different languages. In practice descriptivists tend to identify conditionals first on the basis of clear semantic equivalence with if-then sentences in a well-known or welldescribed metalanguage, then by the morphological, syntactic, and lexical markers (or 'diacritics') of such sentences, and finally by extension to (a) sentences with such markers that do not agree semantically with conditionals in the metalanguage, and (b) sentences that agree semantically but lack such markers. A language may have one favoured or 'prototype' conditional construction; it may have a small set of such constructions; or it may have no such clear-cut marking of conditionals. Also, the prototypical construction(s) may vary in degrees of use. Thus English if and Latin si unambiguously mark most conditional sentences in those languages, and it is usually possible to use them to paraphrase other sentences generally regarded semantically as conditional sentences. By contrast, conditional sentences in (Classical) Arabic are mostly marked by one of two markers, in 'if (noncounterfactual) or law 'if (counterfactual). In Bengali the two prototypical constructions are with/od/ 'if and with a conditional, nonfinite verb form -/e, the two being generally equivalent semantically but appropriate under different pragmatic conditions. Hua has an unambiguous hypothetical 'if marker, the compound conjunctive suffix -mamo, but many sentences that can be interpreted conditionally do not contain it. Finally, Chinese has no clear prototype conditional construction: although there are some particles translatable as 'if, most conditional sentences are in principle ambiguous and are interpreted as conditional only from the context. Conditional markers are most commonly particles, clitics, or affixes, and these are most commonly placed in or next to the //"-clause. These 'diacritics' may be semantically opaque or in varying degrees transparent (e.g. Russian esli 'if is a form of 'be' plus the interrogative particle //, thus 'be it that . . . ' ) . In some languages the [/marker is related to or identical with 'when' or 'whenever' (see the chapters by ter Meulen and Reilly in this volume), or is closely related to markers of modality (Greenberg in this volume). Other markers also occur, however, most notably intonation and word order, as in the subjectverb inversion which is becoming rare in English but which is still very much alive in German. Many languages have special markers for negative conditionals, again varying from transparent (e.g. Latin nisi) to opaque (English unless). In many languages it will be necessary to describe constructions that specify different degrees of hypotheticality. Various terminological traditions exist: irrealis (unreal), hypothetical, potential, future less vivid, counterf actual, impossible, 'indicative', and 'subjunctive'. Languages vary from almost no dif-

Overview ferentiation, as in Chinese, to such elaborate systems as that of Classical Greek. The distinction may be made by different markers for the protasis, as in the two Arabic words already cited, by a special apodosis marker (e.g. Greek an marking counterfactuals), or by special patterns of tense/aspect forms (e.g. the habitual, noncontinuous Bengali past in -t- when used in a conditional sentence has exclusively counterfactual meaning; see also Harris's discussion of Romance in this volume). In some languages the conditional sentences in which the protasis has the meaning 'whenever' fit formally into the system of hypotheticality as the 'generic' conditional, but in other languages, such as Bengali, 'whenever' may be totally outside the system of conditional sentences, having a syntax parallel to temporal clauses, but not allowing the use of'if. In languages where conditional sentences have been well-described, it is invariably found that some sentences with the formal markers of conditionality are semantically and pragmatically only marginally conditional or not conditional at all. For example, the following political advertisement for a newspaper columnist called Herb Caen: Herb Caen for President. If he doesn't save the country, hell certainly save your day depends on the possible interpretation of /fas the concessive 'although'. In this volume Van der Auwera and Konig address the relation of conditionals to concessives. Another example of the use of a conditional form for nonconditional purposes is provided by such phrases as If you please, which has a wide range of uses, many of them not obviously conditional. To understand the full range of meanings to which conditional forms can be put requires work not only on sentences out of context but also on conditional structures in actual continuous texts, whether spoken or written, monologic or dialogic. One such study is provided in Ford and Thompson's paper (this volume) on expository monologic texts. Here conditional sentences are not used to express material implication, and only rarely to open up new possibilities. Rather, they are used to repeat earlier claims, introduce particular cases illustrating preceding generalizations, establish contrasts with what precedes (see also Akatsuka in this volume), or, when the protasis is in second position, to introduce afterthoughts. The use of conditionals to mark the step-by-step, 'chunked', development of the exposition can also be found in rather different contexts. Marchese (1984) shows that conditionals are used in Godie, a West African Kru language, to mark units in the 'procedural genre' (directions for carrying out a task such as planting rice). She suggests that they mark places where the 'teacher' implies that the 'student' should check whether the appropriate stage in the procedure has actually been understood. To this extent the conditional protasis coheres with other devices for developing information flow, including topic development. In Ford and Thompson's spoken texts, conditionals are also used to form

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polite requests. Presumably, the modality of the conditional allows the speaker to appear less dogmatic or intrusive than would be the case if a nonconditional form were used - hence such formulaic introductions as / thought it might be useful if you knew about yesterday's meeting (note the additional distancing effect of the past tense). An investigation of the extent to which other logical relations such as and, or, and because are used in similar ways in such formulae would add significantly to our understanding of precisely which properties of //"are being selected as politeness markers: irrealis, the use of nonpresent tenses, or even syntactic subordination. Politeness formulae with conditional forms typically involve second person subjects in protases. This ties in with work by Inoue (1983) on the use in Japanese of cleft conditional constructions (those with -(no) nara (ba)- 'if it is that') to convey a sense of uncertainty (hence politeness in some cases, but also impoliteness and scepticism in others) about a situation which the speaker cannot really know or experience, e.g. someone else's (typically the addressee's) emotional or physical feelings. It is striking in this connection that the experiments reported in this volume by Fillenbaum on conditionals used as threats and promises involve exclusively sentences with second person subjects. When Adams reminds us that the reasons may be quite different for saying If you eat the mushroom you will be poisoned and If I eat the mushroom I will be poisoned, although they express basically the same proposition, it is presumably not irrelevant that the formal difference lies in the subjects of the protasis and apodosis. A better understanding of the uses to which conditionals may be put would seem to depend on the development of a theory concerning the interaction of conditionals with first versus second versus third person subjects. Interactions between conditional protases and the person of the subject suggest a further variable worth investigating: that of genre. Expository genres are likely to reveal rather different uses of conditionals from other genres, e.g. strategic planning sessions in which speakers suggest possibilities for people to act on, legal writs versus cross-examining of witnesses, etc. Until the evidence is in, it will be difficult to determine the constraints on possible contexts in which conditionals can be used. What does emerge, however, is that any adequate theory of conditionals must account for the fact that they express relationships between situations. Furthermore, it must be rich enough to motivate the various uses of conditional structures to describe not only relations between situations expressed in propositions but also situations between speakers. 2.2 Universalist studies Research traditions that hold much promise for deeper understanding of conditionals attempt to characterize universal properties of language. One tradition,

Overview often identified with 'universal grammar' and called the 'linguistic universals tradition', is associated with the work of Chomsky and generative grammar. It seeks to identify and predict properties of all languages, with focus on languages as fundamentally rational or computational systems, and on the question of what the mental representations of universal properties of language might be (Chomsky 1975). Most of the work on conditionals in this tradition has been carried out by psychologists and philosophers, and is discussed more fully in sections 3 and 4. Another tradition, often called the 'language universals tradition', is associated with the work of Greenberg, and seeks to identify linguistic generalizations that hold true in many, but not necessarily all, natural languages. The focus here is not so much on language as a rational system but on language as a system that is both rational (propositional) and communicative (functional). The language universals approach (represented in this volume especially in papers by Comrie and Haiman) depends on reliable, valid analyses of particular languages and comparable data from sizeable numbers of unrelated languages. It contributes directly to the characterization of the nature of human language and the range of possible variation among languages. It contributes further, and some might say even more significantly, when researchers examine the relationships between overlapping or conflicting generalizations or attempt to find explanatory principles that account for the generalizations. An early universalist claim about conditionals is Greenberg's Universal of Word Order 14: 'In conditional statements, the conditional clause precedes the conclusion as the normal order in all languages' (Greenberg 1963:66). This stood out among the universals of word order proposed, in that it was held to be valid no matter what the normal or 'basic' order of the simple, active, declarative sentence, e.g. Subject-Verb-Object, or Subject-Object-Verb. Greenberg attempted to explain this universal with reference to iconicity, or parallels between order of elements in language and order of elements in experience, including the order of reasoning. He noted also that logicians always symbolized the order implying-implied exactly as in spoken language. Lehmann (1974) examined this universal and its explanation. He found the universal empirically valid - in other words, he could find no counterexamples: whenever another order occurs it is non-normal or 'marked' in some way (e.g. the //"-clause is an afterthought). He found Greenberg's explanation adequate in so far as it invoked the order of reasoning, but inadequate in so far as it invoked physical experience, and proceeded to analyse the universal and its possible explanatory principles in a manner highly typical of the" universals research tradition. He used evidence from: (a) semantic concepts that figure etymologically or synchronically in //-markers, such as Romance si/se and Latin si(c) 'thus'; (b) syntactic and/or semantic parallels between conditional and other kinds of clauses, e.g. verb inversion in German conditional clauses and questions, or the presupposition of causality in counterfactual conditionals; and (c) homonymy or polysemy of conditional clauses, as in languages where

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the words for 'if and 'or' are homophones. On the basis of these investigations, Lehmann hypothesized a set of semantic constituents of conditionals, including volitional, disjunctive, temporal/locative, and causal elements. Finally, he offered an informal derivation of the Greenberg universal based on a communicative strategy whereby the speaker both engages the addressee in contemplating a potential disjunction and at the same time uses this potential disjunction as the ground for developing an argument. Lehmann attempted to characterize the field of conditionals as a whole. A different kind of approach is to focus on ways in which certain properties of conditionals intersect with properties of other systems.1 Various linguists have claimed, for example, that a protasis is, in some important sense, a kind of sentence topic, and also a kind of prototypical subordinate clause. A sentence topic (as distinguished from a discourse topic - see Brown and Yule 1983: 68-73) is accepted by many linguists as a grammatical unit characterized by certain syntactic, semantic, and often phonological or prosodic properties. When the claim is made that conditional clauses are topics (Haiman 1978) this means that these clauses share critical properties of topics in many languages. It is clear that not all topics are conditional clauses, and not all conditional clauses (at least in the sense of clauses with 'if) are topics, but to the extent that the two structures overlap, generalizations about topics are likely to hold also for conditionals. Thus a whole avenue leading to understanding about conditionals is opened up. Similarly, when the claim is made that the conditional clause is the subordinate clause par excellence, the universals approach would look for crosslinguistic evidence (e.g. the position of clause negation in Bengali discussed in Ferguson 1963). It would also explore the implications of this identification, for example in relation to types of conditional sentences that take the form of coordinated clauses. 2.3 Historical studies Historical studies of conditionals largely address the same questions as descriptive and universalist studies. The difference is primarily one of focus, which in this case is on sources and outcomes, in other words on the processes by which conditionals come to be expressed in new ways and by which they come to express other semantic functions. Questions of directionality and of stability of linguistic elements are central here. Historical linguistics assumes that combinations of linguistic properties that are now impossible and unattested have always been impossible and unattested. This principle, often termed the 'uniformitarian principle' (Weinreich, Labov and Herzog 1968) suggests that, at least for languages as far back as we can reconstruct (which is down to c. 5000 BC), conditional structures in language will have been somewhat similar. Descriptive studies of a wide range of languages are essential for determining what the extent of, and constraints on, possible structures might be. 10

Overview Syntactic questions concerning the development of conditionals range over a number of issues. One is how shifts from coordinate 'paratactic' structure to subordinate 'hypotactic' structure occur, and whether they involve any shift in semantic function - evidence from Modern English and other languages that allow for paratactic conditional structures suggests that they do not. Other questions, which often border more on semantic than syntactic issues, concern changes in the interaction between connectives such as if and tenses or moods. Harris's paper in this volume illustrates the complexities of such a study. Interactions with changes in tense and mood marking have led to radical changes in the details of the verb system of conditionals in the Romance languages. Yet the basic system has remained remarkably stable across several languages and over a thousand years of development. How far other language groups show the same kind of stability remains to be investigated; but, given the constraints on what conditionals are about, and the limited resources in language for expressing such relationships, it may be that the overall characteristics do remain fairly stable, at least when there is a prototypical conditional marker such as Romance si. Semantic questions concerning the development of conditional markers lead to the interesting result that these are derived from a very small set of nonconditionals. Some of the sources have been cited above in connection with Lehmann's study of the universals of conditionals. Traugott (1985) has independently suggested a similar set of main sources, specifically: (i) modals of possibility, doubt and wish, (ii) interrogatives, (iii) copulas, typically of the existential kind, (iv) topic markers and demonstratives and (v) temporals, usually of the nonpunctual type, i.e. usually durative or neutral between durative and punctual (like when). In hypothesizing how the change from modal etc. to conditional could come about, it is plausible to argue that in each case the source marked one of the constraints on the conditional relation. Conditionals raise possibilities on an irrealis continuum, hence the use of modals and interrogatives. Some conditionals presuppose the existence of the situation inp (see Greenberg's discussion of 'particular' conditionals in Greek). Conditionals also treat the situation in p as a constraint on, therefore a frame for, ^ in the actual world i in the case where 0 is not true in any world 7 accessible from i. The most common option, the one followed by Stalnaker and Lewis in their theories, for example, claims that in this case the conditional is true in world i. Call this Option I. On the other hand, one might claim that the conditional is undefined (or perhaps false) in world /. Call this Option II. Virgil's argument is that if either option were correct, 26

Conditionals and conditional information then in order to assign true to his statements (6) and (7) in the actual world, FLT and RH must be true. Here, for the interested reader, is Virgil's argument. Since the natural numbers and other hereditarily finite objects are the same in all possible worlds, talk about them is absolute between possible worlds. That is, a proposition about such objects will have the same truth value in all possible worlds. In particular, being formally provable is absolute between possible worlds, since formal proofs are hereditarily finite objects. Thus RH is formally provable in one world just in case it is formally provable in all. Let's first assume that Option II is right. Then, since (6) is true, there must be a possible world / in which Paul gives a correct proof/? of RH. Similarly, if Option I is right, then since (7) is true, the embedded statement If you could give a correct proof of RH, then I could give a correct proof of not-FLT is false, so again there must be a possible world / in which Paul gives a correct proof p of RH. Now there is no reason to suppose that the actual physical proof p found by Paul exists in worlds other than /, or that, if it does, Paul finds it in other worlds. However, because it exists in/, RH is formally provable in/ and hence formally provable in all worlds. But the RH must be provable in the actual world, and so both RH and FLT must be true.4 Since Virgil has not, in fact, proved FLT, his argument that it is true must be absurd. As Quine says, subjunctive conditionals (I would say all conditionals) express a relationship between the matters spoken of by the antecedent and by the consequent. Intuitively, the reason that (6) is true has to do with a relationship between the type of situations where Paul discovers a proof of a conjecture and the type of situations where his friend Virgil converts Paul's proof into a proof of something he knows to be equivalent to the conjecture. That is, (6) seems to have to do with, or be about, the types of situations described by its antecedent and consequent. The possible worlds framework is too blunt an instrument to let us get our hands on these types of situations and a relationship between them. Note, for example, that the consequents of the conditionals in (6) and (7) played absolutely no role in the above argument, aside from their role in getting us to agree that the statements (6) and (7) were true. Any statements with the same antecedent and same truth value would have done as well, regardless of what the consequent was about. Another example, which is less technical and more persuasive to some people of the point I am trying to make, comes in the discussion in section 3.4. Example C: Bizet and Verdi, Kennedy and Oswald The two previous examples had to do with subjunctive conditionals, a kind of conditional that has, in general, struck logicians as highly problematic, especially because they are frequently used to make counterfactual claims. Consider, for example, the famous pair of sentences that made Quine wonder 'whether 27

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any really coherent theory of the contrafactual conditional of ordinary language is possible at all' (Quine 1959: 15): (8) (9)

If Bizet and Verdi had been compatriots, Bizet would have been Italian If Bizet and Verdi had been compatriots, Verdi would have been French

Much ink has been spilt on this pair of statements. For Quine and many others the inability to decide between them casts doubt on the very existence of a coherent account of the counterfactual. Lewis, on the other hand, argues that since there is nothing to choose between them, they are both false, and uses this to motivate his version of a possible worlds account over Stalnaker's. But why are the problems with this pair only problems about subjunctive or counterfactual conditional statements? It is hard to see what problems about these statements, made by a cultured, twentieth-century logician, would not apply equally to the following pair if either had been made by less knowledgeable contemporaries of Bizet and Verdi: (10) (11)

If Bizet and Verdi are compatriots, then Bizet is Italian If Bizet and Verdi are compatriots, then Verdi is French

On the material conditional account, one can say that both are true, since the common antecedent is false, but one can say nothing about the earlier pair. Look at them informationally, though. Under what conditions could (10) be used to convey information? Imagine someone who knows that Verdi is Italian, knows what it means for two people to be compatriots, but does not know the nationality of Bizet. This person is in circumstances where he can use (10) to make an informative statement. These circumstances would not permit him, though, to use (11) to make an informative statement. Notice that the person who would make an informative claim with (10) needs to know at least two things: a fact about Verdi, that he is Italian, and a general fact about compatriots of Italians, that they are also Italians. The latter fact can be viewed as a relation between two types of situations, one where an individual is a compatriot of some Italian, the other where the individual is himself Italian. Now go back to (8) and (9). Exactly the same can be said of (8) and (9) as we said of (10) and (11), respectively. If a twentieth-century speaker knew that Verdi was Italian, and knew what it meant for two people to be compatriots, but did not know the nationality of Bizet, he could use (8), but not (9), to convey information. Indeed, the information content of the statements (8) and (10) (though not the meanings of the sentences used) is virtually the same. Similarly with (9) and (11). An adequate account should permit of informative (and hence true) statements made with any of (8)-(i 1). It seems dubious, from the perspective of informative communication, that a theory could get things right about one kind of conditional and have virtually nothing to say about the other. And it cuts both ways. The material conditional 28

Conditionals and conditional information does not apply to the subjunctive; the possible worlds approach, in Lewis's version, does not say anything about the indicative. The usual argument (e.g. Lewis 1973: 3) for a radical difference between the semantics of subjunctive (or counterfactual) and indicative conditionals contrasts the following pair, the first of which is true, the second of which is probably false: (12) (13)

If Oswald did not kill Kennedy, then someone else did If Oswald had not killed Kennedy, then someone else would have

The difference in truth value of this pair is supposed to show that we need different sorts of accounts. This seems like a mistake, though. The minimal change in (13) that gives an indicative is not (12) but (10): (14)

If Oswald has not killed Kennedy, then someone else will have

To see that (13) and (14) could be used, from different temporal vantage points, to convey the same information, imagine that one of the various conspiracy theories of Kennedy's assassination is correct, and that the mastermind behind the plot has lined up several would-be assassins along the fateful route in Dallas, with Oswald the first. At the end of the appointed hour, the mastermind looks at his watch and asserts (14). It seems that roughly the same information would be conveyed if, years later, the mastermind asserted (13). The considerations embodied in Examples A-C suggest to me that Thomason and Stalnaker are right in their call for a unified account of subjunctive and indicative conditionals, but that such an account has to be more fine-grained than the possible worlds account, to let us get at those relations between the subject matter of the antecedent and consequent that conditionals are about. The next four examples bring up a different set of problems. Example D: The case of the missing pollen Much of what we know about the world, and how to act in it, is local, or conditional, in that we know how things work as long as certain conditions obtain. I know that if it snows, then the sidewalks will be slippery, and so I must take care. I know that if my 9-month-old daughter Claire rubs her eyes, then she is sleepy, and so will take a nap. I know that if the cat comes into the house, Claire will get bitten by fleas. In describing these pieces of conditional knowledge, I have used conditional statements, but I am not claiming that conditional knowledge amounts to knowing these conditional sentences. And, indeed, I do not think that such knowledge does amount to knowing sentences, but that is beside the point here. When I speak of certain conditions obtaining, I am not referring to the conditions described by the antecedents of these conditionals, but to other, more pervasive, background conditions that generally obtain. 29

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What one has knowledge about, when one has a piece of conditional knowledge of the above form, is a feature of the world - what Perry and I have called a conditional constraint on the world. In the main section of this paper I want to examine how the meanings of conditional sentences are related to these conditional constraints on the world. Now, though, I want to give some examples of how the ordinary reasoning we do using conditional statements is governed by the conditional nature of our knowledge. It is well known that ordinary reasoning using conditional statements is wildly different from the logic of the material conditional. Philosophers have realized this for many years. Recent attention to the problem has arisen in artificial intelligence (AI). AI workers, in attempting to build machines that act intelligently in the real world, have demonstrated the ubiquity of conditional knowledge, and the extent to which the commonsense use of such knowledge is at odds with straightforward applications of traditional logic. Let's briefly review this discrepancy by examining a few examples of the difference between the ordinary use of conditionals and that given by classical logic. First, take the knowledge about what it means when Claire rubs her eyes, expressed by my general conditional statement above: (15)

If Claire rubs her eyes, then she is sleepy

For months this was a sound piece of (conditional) knowledge that Mary Ellen and I used to understand Claire and learn when we should put her to bed. However, in early summer it began to fail us. As conditions changed around us, a frame of mind which in one set of circumstances represented knowledge of Claire came to represent a false belief about her. Combined with other symptoms, we eventually figured out that Claire was allergic to something or other (call it pollen X since we are still not sure what it was) and that X could also cause her to rub her eyes. And so we changed our belief. Suppose one wants to represent knowledge with sentences and sound reasoning with valid deduction. Examples like the above pose a dilemma. Either one cannot use the obvious conditional sentence, one corresponding to what I would have said was the case, to represent what I knew, or else one cannot use a host of inferences that are judged valid in classical logic in representing my reasoning (or both - and this, I fear, is the real moral). For example, I cannot use any inference that would justify concluding / / Claire rubs her eyes in the presence of pollen X, then she is sleepy from / / Claire rubs her eyes, then she is sleepy. For example, I would have to abandon the Hypothetical Syllogism as representing sound reasoning: from [If 0 then y] and [If y then ip] infer [If 0 then xp] 30

Conditionals and conditional information Here is an example of what is called the nonmonotonicity of ordinary reasoning. If the cat had come in the house, Claire would have been bitten by fleas. However, if the cat had not had fleas and had come into the house, Claire would not have been bitten by fleas. Such examples cause one to abandon the rule: from [If 0 then xp] infer [If (p and%, then xp] If I am at all typical, many logicians tend to think of these problems as analogous to friction in classical mechanics. Logic is after frictionless inference. If we can get that right, then surely we should be able to add a parameter later to take care of this problem. After all, isn't the problem straightforward at some level? Isn't it just that one is not being explicit about what the real antecedent of the statement is, the one that makes the conditional true and that the speaker really meant? This intuition, which seems fairly sound, suggests a certain strategy of fleshing out conditionals by adding a syntactic parameter, one that can be used for making background assumptions explicit. The idea would be to find some way to move from a conditional statement: A: If 0 then xp to a 'weaker' statement: A': If£, then if 0 then xp (weaker since it has an additional antecedent), that meets two conditions: (i) /? describes the conditions under which the original conditional A holds; and (ii) the person that claims to know (believe, assert) the original conditional A really knows (believes, intends to assert) the weaker A'. I think that many workers in AI who have confronted these problems now believe this assumption is just plain false. I have come to agree. It seems to me that it is another form of the fleshing out strategy mentioned earlier. Again it seems to be based on the confusion between sentence and statement, and on a reluctance to take the context of an utterance into sufficient account. There is simply no reason to suppose that there is any way to flesh out a conditional statement to incorporate a description of the exact conditions under which the conditional holds, or even the conditions under which the speaker believes it to hold. However, there seems to be something right about the intuitions behind the strategy. In all of these examples there is a none too subtle shift in context that somehow affects the appropriateness of the usual inference schemes. We do need some sort of parameter to take account of this shift in context in

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an explicit way. Within the possible worlds approach to semantics, this is just what Stalnaker and Lewis provide. For Stalnaker, for example, the missing parameter is a selection function / from nonempty sets of worlds to worlds. For Lewis, it is a similarity relation on possible worlds. The failure of the above inference schemes for the logic of ordinary language conditionals, and the fact that they fail in the Stalnaker and Lewis accounts for the right sorts of reasons, is one of the arguments in favour of those theories. However, consider the following:

Example E: A proof that i = —i If you examine statements made by mathematicians in doing mathematics, as opposed to the way it gets formalized in logic, it turns out that the problems from the last section arise there too. Just the same sorts of inferences get you in trouble, for just the same sorts of reasons. Indeed, many of the famous false 'proofs' can be phrased as improper uses of laws like the above. I will give the very simplest here, a 'proof that i = - i , that uses (or rather, misuses) only true conditional statements and the usual laws of equality. I use / for V - i, so that / • / = - 1 . 1 also use the fact that V i = i. (16) (17)

If x = a • b, then Vx = \/a • Vb If x = 1 and a = -1 and b = -1, then

x-a-b

From these true statements, and the laws of equality, we can conclude, using the Hypothetical Syllogism, that: (18)

If x= 1 a n d « = - 1 and/? = - 1 , then* = - 1

There are two, related, ways of looking at this problem, both of which locate the difficulty with a shift in background conditions, but which differ in a way that will prove important. One analysis of the problem would be to say that the sentence used in (16) can be used, in different circumstances, to make radically different statements, statements where there is an implicit universal quantification over a domain of numbers fixed by context. Some such statements would be true, others false. The sentence can be used in high school algebra courses to make a true statement about all positive real numbers. However, this is not the context in which it is being used when combined with (17), where we extract square roots of negative numbers. While there is no problem with taking square roots of negative numbers, (16) does not express a true fact in those circumstances. A somewhat different analysis would be to say that an informative statement of (16) is not a complete proposition, but rather is what one might call a parametric proposition, something that yields a fact when the parameters are appropriately fixed. Just what counts as an appropriate value of the parameters is 32

Conditionals and conditional information determined by context. In the case of (16) the appropriate values of the parameters are positive real numbers. Thus, in combining it with (17) we are fixing the parameters of the parametric proposition described by (16) at inappropriate values. This example is so simple that it is perhaps not as convincing as it might be. A better example uses the following law derived in the study of triangles: (19)

If sin(a) = sin(/?) then a= (3

There is an infamous 'proof (e.g. Maxwell 1959: 10-12) that all acute triangles are isosceles, one that revolves around a misuse of this fact. Law (19) is typically proved in circumstances where one is talking only about angles that are interior angles of acute triangles, and so smaller than 900. In the infamous proof (19) is applied to two angles which are, as it turns out, exactly 1800 apart, so they cannot both be interior angles of such triangles. What is deceptive is the way one strays out of the circumstances where (19) applies quite without knowing it. Anyone who has ever had to formalize mathematical proofs in first-order logic knows that this sort of context relativity pervades ordinary mathematical discourse. The context dependence of mathematical discourse is part of what makes formalizing mathematical proofs so very difficult, since the context has to be formalized too. Of course, in mathematics this is usually (always?) possible, even if difficult. The difference is that in real life it is not just difficult but often simply impossible, because the context may be literally ineffable. What moral should we draw from this? At least one: that however one wants to account for the failures, real or apparent, of classical laws like the Hypothetical Syllogism for natural language conditionals, the failures are not an argument for a clean break between natural language conditionals on the one hand, and mathematical conditionals on the other. A theory that accounts for the facts in one case but misses them in the other is, other things being equal, less satisfactory than one with a unified account. The account I am proposing makes explicit the dependence of the information content of conditional statements on background conditions. It predicts that whenever the Hypothetical Syllogism fails, there is a shift of background conditions involved. Example F: Jack and Jim's quarrel This is a famous example taken from Downing (1959), of a subjunctive conditional that has been argued to be both true and false. The situation is this. Jack and Jim are old friends, prone to helping one another under normal circumstances. Jim is very proud, and so would never ask help of anyone with whom he had recently quarrelled. Jack, on the other hand, is a very unforgiving person, and so wouldn't have helped anyone with whom he had recently quarrelled. Now, in the particular situation, Jim needs help but he and Jack have 33

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quarrelled. The counterfactual in question is: (20)

If Jim had asked Jack for help, then Jack would have helped him

Is this true or false, or both? Given all the facts of the case, Jim could not possibly have asked Jack for help, so if the antecedent is to be seriously entertained some of the facts must be set aside - perhaps because the speaker is ignorant of them. If one sets aside the fact that Jim and Jack have quarrelled, then, it is claimed, (20) seems to be true. On the other hand if you ignore the fact that Jim is stubborn, and so imagine that he might have asked Jack for help, Jack would not have helped because of the quarrel, so (20) seems to be false. Example G: Sly Pete and Mr Stone One last example, this one due to Allan Gibbard (1981), of two indicative conditional statements, each of which seems to be true, but which also seem to be in direct conflict. It has many of the features of the previous example, but seems, initially, more of a challenge to the kind of account I want to give. Sly Pete and Mr Stone are playing poker on a Mississippi riverboat. It is now up to Pete to call or fold. My henchman Zack sees Stone's hand which is quite good, and signals its contents to Pete. My henchman Jack sees both hands, and sees that Pete's hand is rather low so that Stone's is the winning hand. At this point the room is cleared. A few minutes later Zack slips me a note which says 'if Pete called, he won', and Jack slips me a note which says 'if Pete called, he lost. ...' I conclude that Pete folded. (Gibbard 1981, as quoted in Stalnaker 1984: 108) Gibbard uses these examples to argue against the idea that these sorts of indicative conditionals express any sort of proposition at all. His argument is discussed at length in Stalnaker (1984). The example here would seem to present a serious obstacle to any sort of informational account of the conditional. After all, both henchmen seem completely justified by the facts of the situation in asserting what they do, so presumably such an account will have to call both assertions informational, hence true. But how can they both be giving us information about what will happen if Pete in fact calls? While this is rather similar to Example F, our analysis is committed to different claims about the two examples, as we will see later. 3. INFORMATION IN SITUATION SEMANTICS In this section I am going to review some points made in S&A, with some modifications suggested in Barwise and Perry (1985; hereinafter Ss&sa) stressing those parts of the theory that are central to my proposal for the semantics of conditional sentences. 34

Conditionals and conditional information 3.1 Meaning, information, and constraints In Situation Semantics we look at the linguistic meaning within a general theory of meaning and information. The general picture is that a situation s can contain information in virtue of some constraint that holds between types of situations.5 Let us use S, S', . .. for types of situations, and write s:S if s is of type S. A type S of situation is realized if there is a real situation s:S.6 A constraint is a relation holding between types of situations, S=>S\ If this relation holds, then it's a fact that if S is realized, then so is S'. We read S^>S' as S involves Sf. In S&A we indicated such a constraint C by: involves, S, S''; 1 A real situation s contains information relative to such an actual constraint C if s:S. It may contain various pieces of information relative to C, but the most general proposition that s contains, relative to C, is that S' is realized, that is, that there is a real situation s:S'. In order to see how one situation can contain information about specific things, it is important to realize that constraints hold between parameterized types of situations. Here is an example with a single space-time parameter /. Consider the constraint that if Claire rubs her eyes, then she is sleepy. This constraint is a relation between two types of situations, S and S': S = the type of situation where at /, Claire is rubbing her eyes which we write as: [s I in s: at /: rubbing, Claire's eyes, Claire; 1] and, using the same notation; Sr = [s I in s: at /: sleepy, Claire; 1] Assume that S really does involve 5', so that if at some specific space-time location /, s is of type S(l) (the type where the parameter / is anchored to /), then there is a real situation s':S'(l). In other words, at that very location, Claire is sleepy in s'. Thus, the proposition that S'(l) is realized entails the proposition that at /, Claire is sleepy. In general a constraint C or the form S^>S' will have many parameters, and every parameter in S' will also be a parameter of S. Given any such constraint, and any anchor/for some or all of the parameters in 5, that is, any assignment of appropriate values to the parameters, then the result of replacing the parameters by the values will give rise to an actual constraint. That is, if: is actual, then so is:

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We call the latter constraint an instance of the former. If a parameterized constraint is actual, then every appropriate instance of it is also actual. Thus, one who knows a general constraint, and knows that something is an instance of it, has enough information to conclude that the latter is actual. Looking ahead to the use of constraints to interpret conditionals, this is a good place to make a point relating actual constraints C and their instances. Consider the following constraint, where x, a and b are parameters that can be anchored to positive real numbers: x being the product of a and b involves VJC being the product of Va and Vb\ that is: where: S = [s | in s: product, a, b, x; i] S' = [s\ in s: product, Va, V&, VJC; I] This is a general law relating situations with positive real numbers as constituents. The parameters are what Perry and I call roles, indeterminates that can only be anchored to positive real numbers. However, given an anchor /for any or all of these indeterminates, this law gives us a more specific law: For example, if we anchor x to i, then we get a law relating the square roots of positive reals and their reciprocals. In the limiting case, we get a law relating types of situations with no parameters at all. Suppose we anchor x to i, a to 4 and b to 1/4, for example. This still gives us an actual constraint, one that relates the type of situation S containing the fact that 1 = 4 • 1/4 to the type of situation Sf where the square root of 1 is the product of the square roots of 4 and 1/4. Or, if we anchor b instead to 1/3, we would get another actual constraint as an instance of C, this one where the type of situation where 1 = 4 - 1 / 3 involves the type S'(i, 4, 1/3). Of course there are no actual situations where 1 =4-1/3, but the specific constraint is still a legitimate instance of various general actual constraints, and so actual. Consequently, anyone who knew the general law, and that 1,4 and 1/3 were positive real numbers would be justified in concluding the specific instance of it. It might be a way he would come to learn that 4-1/3 is not 1. So far none of this has anything to do with language. It just has to do with things like situations, types of situations, constraints, propositions, and the like. What does it have to do with linguistic meaning and the use of language to convey information? Recall that we began by distinguishing between sentences and statements, where the latter are certain kinds of utterances made with declarative sentences. Similarly, we distinguish between the meaning of a declarative sentence and the interpretation of an utterance of that sentence. 36

Conditionals and conditional information Roughly speaking, the interpretation of an utterance is the fact, situation or event it describes. Thus, at a first approximation, an utterance of Claire is sleeping will describe a real situation s where Claire is sleeping at the spacetime location / referred to by the speaker with the use of the present tense is, one that temporally overlaps the space-time location lu of the utterance: in s: at /: sleeping, Claire; i However, things are not quite so simple. If there are any such situations, there will be many such, containing more or less of the rest of what is going on. And there may be none, if my utterance is false. So we modify this so that the interpretation is a type of situation, the type S of situation where Claire is sleeping. We take the propositional content of the utterance to be that there is a real situation of that type - in other words, that S is realized. Thus, we take the interpretation of an utterance to be the type of situation it describes, and so take the meaning of a sentence to be a relation between types of situations, the type in which the sentence is used to assert something, on the one hand, and the type so described, on the other. That is, the meaning of a sentence is itself a constraint. We analyse linguistic meaning as residing in these sorts of systematic relations between types of situations. In S&A we saw that a great many contextual elements can enter in determining the interpretation of any particular statement from the meaning of the underlying sentence. This is even more pervasive in getting from the meaning of conditionals to their interpretation. As we saw in the examples, even in mathematics, the context greatly affects the interpretation of a given sentence. There are two different sorts of context relativity that need to be distinguished to understand conditionals, distinguished much more clearly than we did in S&A. One might call them features of language that exploit environmental constants, versus features that exploit systematic variation. Indexicals are examples of the latter; the former are a bit harder to identify. Let me give two examples. Consider the difference between the sentences: (21) (22)

It's 4 p.m. It's 4 p.m. here

It seems that under normal circumstances the information conveyed by informational utterances of these sentences is the same, so that the utterances must have the same interpretation, and so the sentences have the same meaning. This is the way we treated them in S&A. However, this glosses over what might appear a minor point, which becomes important in the understanding of conditionals. There is a slight difference in meaning between these two sentences. If you and I are talking about calling New York from here in California, and you ask me what time it is there, I can use (21) but not (22) - at least, not without simultaneously pointing at a map or something similar - to tell you the time 37

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there. This suggests that the interpretation of (22) is complete in a way that (21) is possibly incomplete, in that the interpretation of (21) does not determine the place it is about in quite so definite a way as (22) does. Sentence (21) normally exploits the fact that time is relatively invariant with respect to place. As long as we are in the same time zone, we can simply ignore the fact that time is a function of place. Thus, the interpretation of sentence (21) has a parameter whose exact value is usually irrelevant for the information content. However, it can be set at unusual values by context, as in our talk of calling New York. The use of the word 'here' exploits systematic variation, namely that the place a person can refer to with 'here' varies in a systematic way with where the person is. A speaker can always refer to where he is with 'here', if necessary, and the interpretation of (22) will contain that place as a constituent, rather than containing a parameter that gets set at that place by context. There is an inclination to think that something like the fleshing out strategy should take care of context dependence, that statements like (21) are always telegraphic forms of some more complete utterance, like (22), or It's 4 p.m. in New York, or some such. However, this is just as misguided as the previously mentioned instances of this strategy, and for just the same reason. There is no reason to suppose that the speaker has, in general, any context-independent way of referring to the place he is talking about. Let me be a bit more explicit about the proposal I am making for a difference in meaning for these two statements. For the sentence: (22)

It's 4 p.m. here

when used in a statement u, describes the state of affairs regarding the time, at the location lu where the statement is made, as being 4p.m. Using our notation: at lu: 4p.m.; 1 In terms of types, we have a parameter-free type 5 = [5 I in 5: at lu: 4 p.m.; 1] By contrast, a statement using: (21)

It's 4 p.m.

gives us a parametric type S(l) = [s I in s: at /: 4 p.m.; 1] Under normal circumstances this parameter is filled automatically by context. Once one sees examples of this, they come up everywhere. For example, suppose I say Kansas City is closer than Columbus. There is a three-place relation lurking here, x is closer than y to z, but the third parameter is fairly insensitive and can be filled in by context. Normally it is filled in by the location 38

Conditionals and conditional information of the utterance, but it need not be. I could be talking to my wife about our trip to Minnesota next summer, and arguing that we should go to see my family in Kansas City rather than hers in Columbus, because Kansas City is closer than Columbus, closer to where we will be. Thus, we will distinguish a statement with a parameter-free interpretation from one with an interpretation that gives one only a parametric type of situation, where the parameter must be filled by context in a different way. We will return to this below, in the discussion of parametric information. In general, however, the picture of meaning is basically the same. Meaning consists in constraints between types of situations, and it is such constraints that allow a situation to contain information. There are many different kinds of actual constraints, arising in radically different ways: from laws of nature, from the process of individuating the world, from conventions, from people's intentions, among others. This is not the place to go into this in any detail, so I will assume the reader is familiar with the account of constraints and meaning given in S&A. The interest in the account given below rests entirely on taking constraints seriously. The main thing we need to get started on the semantics of conditionals is the view of constraints as facts relating types of situations, facts which can guide people's actions. They are just the sort of relation between matters that Quine felt were needed for an understanding of subjunctive conditionals. As indicated earlier, such states of affairs are enormously important in everyday life. Consequently, it is important for people to be able to describe them to others. That, I would claim, is why human languages always have a way of forming conditionals. 3.2 Truth conditions versus information conditions There are many ways of classifying competing semantic accounts. One way that makes for strange bedfellows is whether they take sentences (or better, statements) to determine truth values directly or indirectly. Thus, while any self-respecting semantic theory must give some account of the conditions under which a statement is true, there is still a good deal of flexibility as to whether this account is direct or indirect. In accounts of meaning based on Tarski's analysis of truth, as in Davidson's programme, for example, it is assumed that to know the meaning of a sentence just is to know the conditions under which it is true, so this is a direct theory. Mentalistic theories are indirect, in that they factor the interpretation of a statement through something mental, like the idea it expresses, or a sentence of 'mentalese'. Situation Semantics is also indirect in its approach to truth, but in a more radical way. In Situation Semantics, attention shifts from the conditions under which a statement is true, to something stronger, the conditions under which a statement carries information, and what information it carries under those 39

Jon Barwise

conditions.7 The main point can be summed up briefly as follows. If a semantic account is going to explain the role utterances can play in the communication of information between agents, then it has to give an account of the information content of utterances. In Situation Semantics, the interpretation of a statement is a type of situation. If the statement is true, there is a real situation of that type. A key ingredient in understanding the information content of a sentence is understanding the subject matter of statements made with it - that is, understanding what situations it can describe and under what conditions it can describe them. Only if we can get our hands on the subject matter of constituent statements can we express relationships between them of the kind needed to understand conditionals. Neither first-order model theory nor possible world semantics gives us a fine-grained enough stock of things to serve as subject matter to satisfy our current needs - as we have seen above. This move, from truth conditions to strong information conditions, has other consequences, and is more of a departure from the model-theoretic tradition than it might seem at first. It allows us to apply general principles of information flow in the explanation of semantic phenomena. One of the most important such applications is what Perry and I call 'exploitation of environmental constants'. The basic idea is that what stays fixed does not need to be made explicit. This is important enough to deserve a subsection of its own. 3.3 Conditional constraints, environmental constants and parametric information The final piece that we need to review is the discussion of conditional constraints from S&A (pp. 99-100, 112-14, a n d 270-2). I will review this in some detail, taking advantage of some of the changes made in Ss&sa, and some more recent thoughts Perry and I have had on the matter. Most constraints to which we are attuned do not apply to every situation, but only under certain conditions. For example, striking a match means that it will light, but only under appropriate conditions, including the condition that free oxygen be present. It doesn't mean that it will light if you're underwater, for example. This concept of a conditional constraint, and the conditions under which a conditional constraint holds, was a central part of our account of how one can come to know things on the basis of nonfactual constraints, by exploiting environmental factors. For example, it explains how it was that for months I was able to use the conditional constraint about Claire to learn when she was sleepy, until she encountered pollen X. The concept thus turns out to be important in understanding the informational function of conditionals. In order to get the account of conditionals to work out right, though, in terms of fitting the data, we need to modify slightly our earlier account of conditional constraints. To motivate the change, let me step back and discuss a more general issue. 40

Conditionals and conditional information If R is some n + iary relation, then it takes n + i objects ax . . . an + i (one of these may be a space-time location) and a truth value / to determine a proposition, namely the proposition that the objects stand (/= i) or do not stand (z = o) in the relation R; equivalently, the proposition that the parameterfree type: 5 = [5 | in5: R,#i . . ., afran+ \\ i] is realized. However, if one of these objects, an + ] say, is an environmental constant, that is, if an+x is fixed in some way, then it only takes n objects and a truth value to determine the same proposition. If true, this proposition can be a piece of information about R, and the objects in question. Now let's look at it the other way around. What if we are given R and ax, . . . ,an and a truth value / explicitly? We do not have enough for a parameterfree type, and hence a proposition. All we have is a parametric type: S(an4.j) = [s I in s: R, au . . .#n,an

+ l\

i]

Only if the final parameter an + x is anchored to a value an + l in some other way will we have enough to give us a proposition that represents information, or misinformation. Until that is fixed, all we have is parametric information or misinformation - information relative to some assignments, misinformation relative to others. We have already seen some concrete examples of this in the discussion of It's 4 p.m. and Kansas City is closer than Columbus, and back in the discussion of Example E. The interpretation of these statements gives information relative to certain parameters that have to be determined by context. I want to treat the involves relation in a similar way, as a three-place relation between types of situations: S involves S' given that B, which I write as:

We think of B as conditions on the situations we are in such that the constraint between S and S' holds, as long as the situations in question are all of type B.« The important thing to realize is that as long as a given background condition B is in force - that is, as long as all situations that arise are of type B - then there is no reason that one will ever be aware of the dependence on B. It can be treated as an environmental constant. For example, it was only when Claire started rubbing her eyes when she obviously was not sleepy that we had any idea that the constraint that her rubbing her eyes means she is sleepy is conditional on certain background conditions B obtaining, conditions that had held until then but of which we were unaware. The actual constraint was not the constraint S^>S' described earlier, but S^>S' \ B, where B is the type of situation where there is no pollen X present at /. 41

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That is, just as we can think of the relation of being closer than as a two-place relation, as long as a fixed vantage point is maintained, so too we can think of constraints as being absolute relations between types of situations, as long as background conditions stay constant. Problems can arise in communication, when the background conditions are different for speaker and listener. If I am talking to someone around here and explain that Kansas City is closer than Columbus, communication should be straightforward. However, if I am speaking on the phone and say the same thing, communication is problematic. Similarly, when I told a babysitter in March that if Claire rubs her eyes, then she is sleepy, then communication worked, and the sitter obtained useful information about Claire's behaviour. However, if I had written this on a permanent set of instructions and a sitter had read it in June, when conditions had changed, communication would not have worked, in that she would have obtained a piece of misinformation. Similarly, in a class where angles are always interior angles of acute triangles, the students and teacher exploit this environmental constant to convey information with the sentence: if sin(a) = sin(/3), then a — j8 However, if we inadvertently stray out of this environment into one where angles greater than 900 come up, as in Example E, then we may use this sentence to convey misinformation, and so make mistakes. A speaker can affect what sorts of background conditions are appropriate for the interpretation of his utterance. Indeed, the utterance itself can have an effect on the background conditions that are taken as being in effect. If I say Matches struck usually ignite, and if it is interpreted relative to normal background conditions, then it expresses a true fact. However, if I say Matches struck in the presence of free oxygen usually ignite then the presence of free oxygen is not taken as being part of the background conditions of my utterance. 4. I N T E R P R E T I N G CONDITIONAL STATEMENTS With these pieces in place, let's turn to conditionals. To motivate the discussion, and tie it up with constraints, I will start by treating general conditionals. I will first discuss the interpretation of general conditionals, then the interpretation of specific conditionals. 4.1 Interpreting general conditionals Consider a pair of statements as follows: (23) (24)

Snow means that the sidewalks are slippery If it snows, then the sidewalks are slippery 42

Conditionals and conditional information For our purposes, we can take these as synonymous. Moreover, statement (23) is one that attributes information to situations of a certain type, snowy ones, by describing a constraint between types of situations. This being the case, it is only natural to take the interpretation of (23) and (24) to be a single constraint:

2

4

(

2

4

2

4

)

S'24 = [s I in s: at /: snowing; 1] S"24 = [s I in s: at /: slippery, sidewalks; 1] where / is a role restricted to range over sublocations of the present location / referred to by the speaker of (24). Thus, these are the parameterized types assigned as the interpretations of the antecedent and consequent, respectively, with the role / common to both. The constraint means that for every anchoring of / to some real location /', any situation sx of type S'2A (/') is part of some s2: S"2,(l).

Similarly, (25) and (26) describe a single constraint C2: (25) (26)

Claire rubbing her eyes means that she is sleepy If Claire rubs her eyes, then she is sleepy

However, this is not quite right. Neither of these constraints is actual. They do hold quite widely, though, and as long as we are in conditions B where they do hold, we can trust them. Thus, what we assign to these statements is a parametric constraint, where a parameter/? is to be anchored to the prevailing background conditions. Thus, what we want is not C2 but C2\B where B is anchored to the prevailing background conditions, hopefully to B = [s | in s: at /: pollen X; o], or something containing it. Thus, the interpretation of a general conditional statement is a parametric constraint C\B, where B is a parameter anchored to the prevailing background, and where C is S=>5", these types being the interpretations of the antecedent and consequent, respectively. As such, this will not provide a complete proposition, but only a parametric proposition, a proposition relative to the background conditions B - the proposition that C\ B is actual. This may be information, or it may not. This makes the exact information content of a statement of a general conditional highly context-dependent, which seems right. However, it might appear to be too context-dependent, since it could happen that the exact information content is not even determined by what the speaker knows, in that he or she might not know what the relevant conditions B are. This may seem an unpleasant consequence of the account, but, sad to say, it seems right. Moreover, it is just what is needed for many of the puzzling features of the logic of conditionals, as we will see. In any case, it is not restricted to conditionals. After all, I can obviously say of two objects a and b that 43

Jon Barwise

a is closer than b, that is, closer to me - even if I don't know exactly where I am. The information content of my statement is that a is closer than b to me, and so is relative to where I am. Similarly, the speaker's environment determines B, and to the extent that the listener shares B, the statement can function informationally in a more or less straightforward manner. 4.2 Interpreting specific conditionals Let us look at some specific conditionals related to the general conditional discussed above: (27) (28)

If it is snowing, then the sidewalks are slippery If it snowed, then the sidewalks were slippery

These conditionals also describe constraints, but more specific ones, in that the space-time location has been filled out by use of the more specific tense: Q7

=

^23(^27)

^28

=

^23 ('28/

where l21 and /28 are the space-time locations referred to in utterances (27) and (28), respectively. More generally, under what conditions can a specific conditional sentence 0—> t/> convey information, and, under those conditions, what information does it convey? The basic picture is this. The speaker is talking about a specific, highly limited, situation, say su. Usually just a few things and some relations between them are involved. He is saying that this is a situation where a conditional constraint S=$>S' \B applies, where B is anchored to the background conditions. S is the interpretation of 0, S' is the interpretation of ip. Thus, his utterance will be informational relative to B if there is an anchor / for the parameters of B such that su:B(f), and if he has the information, relative to B, that S^>S' \B is actual. He may have such information simply by being in that type of situation and knowing how things work there. The propositional content of his utterance is just that S(f) => S'(f) is actual. Notice that both the specific situation su and the type of situation B play roles in determining when a specific conditional statement is informational, but they are not part of the information content. Of course, some of the constituents of su will be constituents of the types S and 5' and hence be constituents of the information content. For example, the values of the parameters anchored by/will be constituents. Lewis (1973) discusses the annoying vagueness of the truth conditions of counterfactuals. He puts this down to a difficulty in knowing what other worlds are most similar to our own. On our account, the difficulty in deciding whether a given counterfactual statement is true is not due to any vagueness about what the underlying sentence means, or to difficulty in knowing what other 44

Conditionals and conditional information possible worlds are most similar to our own. On the account presented here, the meaning is pretty clear, and there are no other possible worlds. Rather, the difficulty in knowing whether a counterfactual statement is true rests in two other problems:9 knowing just what situation su the speaker is talking about; and knowing whether there is some background type B such that su is of type B and the conditioned constraint C \ B is actual. 4.3 The examples revisited The account I have given, while informal, is rigorous enough to commit us to claims about the examples given earlier. Let's work through some of these examples to see what predictions our theory makes, and how well it stands up. I will take them in a different order. Example D. For a first example, I take one that is true, but where both the antecedent and consequent are false. One of the things that must be accounted for is how a true conditional can carry new information to a listener who already knows that both the antecedent and consequent are false. To see that this can happen, imagine that Mary Ellen and I are going out for the evening, and that a new sitter has arrived. Suppose she happens to see that Claire is annoyed with the cat and fussing at it, that she is not rubbing her eyes, and that she is not the least bit sleepy. From the other room, though, I only hear Claire fussing and say: (29)

If Claire is rubbing her eyes, then she is sleepy

It seems pretty obvious that my statement carries information about Claire to the sitter, and that the information is something about Claire other than the fact that she is not rubbing her eyes. What I am saying is that a certain constraint C29 is actual in a particular situation s29. But just what situation s29 am I talking about? Is it the real world where Claire is not rubbing her eyes and is not sleepy, or is it some fictitious but 'near' world where Claire is rubbing her eyes and is sleepy? Neither; and here is a real advantage of dealing with situations, which are partial, rather than the whole world. I refer to the situation with Claire playing on the floor with some toys. This situation is quite limited in that it does not settle many things, like whether or not Claire is rubbing her eyes, or whether the cat is present. What I say about this situation is that it is one where a certain conditional constraint applies, so that a certain unconditional constraint is actual. As long as there is no pollen X present there, then the constraint is actual, and my communicative act is informative. Let's look at this example in a bit more detail, just to get the feel for what is going on. The constraint I am describing is C29 = S'29 => S"29 where S'29 is: [s I in s: at /: rubbing, Claire, Claire's eyes; 1] andS'^is: 45

Jon Barwise

[s | in s: at /: sleepy, Claire; i] Here / is the particular space-time location referred to in my use of the present progressive. To say that this constraint C29 applies in the particular situation s29 is to say that there is a background type B such that C291 B holds, and s29 is of type B. By assumption, the only sort of constraint of this sort around is where B is the type of there being no pollen X present. Of course the sitter does not know just what that condition is, and I might not either, in making my statement. As regards subjunctives and counterfactuals, notice that if, a few minutes later, I say to the sitter / / Claire had been rubbing her eyes, then she would have been sleepy, I am describing exactly the same constraint, but just from a different point in time and, perhaps, with the knowledge (or false belief) that there was no real situation of the type described by the antecedent. Now let's contrast (29) with a false statement, but one that would seem to follow from it using the Hypothetical Syllogism: (30)

If Claire is rubbing her eyes and there is pollen X present, then she is sleepy

The antecedent of this conditional changes the conditions under which it can be used appropriately. The background type can no longer be one where there is no pollen X present. Whereas (29) was said in a background where it was a fact there was no pollen X present (at /: pollen X; o), the use of (30) is not appropriate in a context where this fact is fixed. In order for S^>S' \B to be a constraint, S f\ B must be coherent if the constraint is to be a constraint on situations at all. More generally, there will be no problem applying the Hypothetical Syllogism if the background conditions B stay constant. It is only as they shift that invalid inferences will get made. Example E. Exactly the same thing is at work here. With (16) we are describing a conditional constraint, one that applies to positive real numbers, that is, in those situations where the numbers being talked of are positive reals. In the 'proof that 1 = - 1 , we have moved out of these conditions and have attempted to apply the constraint where it is not applicable. The same holds for the 'proof that all triangles are isosceles triangles. Example A. Now let's take an example where it is really not clear whether the statement is true or is false - the example of Virgil and the rock. Virgil's (5) was a specific conditional statement. It asserted that a conditional constraint C5 (relating types of situations in which he is attacked and types of situations in which he defends himself) applied in the situation s5 he was in at the demonstration. Was (5) indeed true? It was just if C5 applied in s5. Were there general psychological facts about Virgil, and facts about how things were back then, that applied to give a general constraint, of which this was a special case? Since Virgil had never been in a situation where he was really being attacked, 46

Conditionals and conditional information he simply did not know how he would have reacted. But this is why Virgil's initial puzzlement was in fact entirely appropriate. His answer ought to have been'I don't know'. Example C. What can we now say about the statements that caused Quine to despair? Let's start with the indicative versions: (10) (i i)

If Bizet and Verdi are compatriots, then Bizet is Italian If Bizet and Verdi are compatriots, then Verdi is French

Taking the sentence/statement distinction seriously, let's imagine that these were uttered by different speakers, A and B, to a common listener, C. Consider (10) first. As we saw earlier, the conditions under which this would be informational would be if A were talking about the situation of Verdi's being Italian. In this case, (10) does describe an actual constraint, and it is informationally correct. On the other hand, if B is talking about the situation of Bizet's being French, ( n ) too describes an actual constraint. Both constraints are specific instances of a general conditional constraints: if x is of nationality z, then if x and y are compatriots, then y is of nationality z. So there are circumstances in which (10) and ( n ) both represent true statements, statements about different specific situations, statements that convey different information about these situations to C. What is C's reaction? She might not believe both statements, since they do sound at odds. On the other hand, she might believe both of these true statements and so come to know both facts described. That is, she comes to learn that if Bizet and Verdi had been compatriots, then Bizet would have been Italian and Verdi would have been French. However, the latter is incompatible with Bizet and Verdi being compatriots. Thus, C could, in fact, learn that they were not compatriots, something neither A nor B needed to know to make informational statements. Now let us turn to the subjunctive versions, say (8) as contrasted with (10): (8)

If Bizet and Verdi had been compatriots, Bizet would have been Italian

We can take this to be about the very same situation, of Verdi's being Italian, and describing the same constraint. It might be used in trying to decide whether or not Bizet and Verdi were compatriots. Or, more typically, it would be used as a counterfactual, where one knew that, in fact, there was no real situation extending the one being talked about in which the two men were compatriots. The conclusion, though, is that there is no reason not to say that both (8) and (9) could be used, counterfactually, to make true statements, statements that carry information about a certain specific constraint. While this is in direct conflict with Lewis's account, it seems to square with most people's intuitions. Example F. With this under our belt, let us see what the account would say about Downing's example: (20)

If Jim had asked Jack for help, then Jack would have helped him 47

Jon Barwise

Consider a particular statement u of (20). Such an utterance will determine a constraint C20, one where Jim asking Jack for help involves Jack helping Jim. However, in addition, the statement has to be made about a specific real situation s20, relative to a set of background conditions, B2Q. The background, we will suppose, contains only the fact about Jim and Jack being willing to help one another when asked, provided they have not quarrelled recently. We will leave the rest to the situation being talked about. Given appropriate context, one could imagine the speaker talking about either of two situations, s2o,o which omits the quarrel, or s2(M which includes the quarrel but omits the fact that Jim is stubborn. However, neither of these situations is one where the constraint applies, since neither is the sort of situation where Jim and Jack would help one another. The second is clearly abnormal in that the quarrel is explicitly present. However, the first only leaves the quarrel out. It is still not a situation where they have not quarrelled, that is, one where there is a fact of their not having quarrelled. A speaker who did not know about the quarrel might feel justified in asserting (20) but he would not in fact have had enough information to make a true statement. Only if he had known that there had been no quarrel could he have been in such a position, and he can't have known that. Notice that there is a conditional closely related to (20) that the ignorant speaker might legitimately fall back on, once learning of the quarrel: (31)

If Jim and Jack had not quarrelled and Jim had asked Jack for help, then Jack would have helped Jim

Here the speaker has explicitly moved part of the background into the conditional, so we get a true conditional closely related to the original. Conversational maxims suggest giving the speaker the benefit of the doubt if that is what he claims he really meant. What about the following argument? 'But look, if Jim had asked Jack for help, then they couldn't have recently quarrelled (since then Jim would not have asked), so sure enough Jack would have helped.' This conditional is clearly changing the background conditions, moving the lack of an argument between Jack and Jim out of the background, into the subject matter, so it is not an appropriate defence of the statement in (20) in the original background #20-

Example G. Zack, you will recall, had enough information to assert If Pete called, then he won. Jack, on the other hand, had enough to assert / / Pete called, then he lost. Yet, it seemed, we had conflicting information about what would happen in the case where Pete in fact called. We can assume that the background type for both utterances was the same, including facts about the rules of poker, and about how good players use all available information about their opponents' hands. Zack thinks he has information about a particular situation, one that includes Mr Stone's hand and 48

Conditionals and conditional information about Pete's having information as to what Stone's hand is. Talking about that, he asserts (under the prevailing conditions) that if Pete calls, he will win, because he will only call if he knows his hand is better than Mr Stone's. Jack, on the other hand, is talking about a different situation, one that includes the facts of the matter about both hands. According to the rules of poker, if Pete calls with the hands as they are, he will lose. If Jack and Zack really have the information they think they have, then Pete won't call. What happens if Pete does call? Well, that can only happen if one of them had misinformation about the situation they were talking about, not information. There could be various reasons for this. Perhaps Jack mistook one of the two hands. Or perhaps Zack is wrong about Pete's poker playing ability, or about Pete's having received the information about Mr Stone's hand from Zack's signals. Or perhaps Pete is about to have a sudden change of heart, one that makes him unwilling to use illicitly obtained information. All kinds of things could go wrong. If any of them go wrong, then the situation being talked about does not match the assumed background conditions, so the respective speaker is just plain wrong. The fact that both speakers could be right in no way militates against there being a propositional content to their claims. If both are right, then the propositions combine to yield the right consequence, that Pete will not call. If Pete calls, then one of them was mistaken. That speaker was conveying the propositional content, not as information but as misinformation. Example B. This leaves us only with attempting to understand the information conditions of statements (6) and (7). First, what are the prevailing background assumptions Bl Well, they are certain commonsense facts about actual proofs of conjectures about natural numbers, like the fact that anything that has a correct proof is true, not false. In addition, there is an actual conditional constraint, that if one has a proof that 0 and xp are equivalent, then having a proof of 0 involves being able to obtain a proof of \p. Finally, there is the assumption that we are talking about open conjectures, not about propositions whose truth we already know. The situation being talked about contains two particular statements, FLT and RH, and Virgil's proof that they are equivalent. The statement (6) describes a specific actual constraint obtained from the general conditional constraint. The puzzling case, though, is (7): (7)

It is false that if you could give a proof of RH, then I could give a proof of not-FLT

It seems true, but just why? To answer this, we must examine the informational function of It is false that if 0 then \p, where the embedded conditional is a specific conditional. If the embedded statement says of a certain situation su that some conditional constraint applies, giving a specific constraint, then It is false that if 0 then 49

Jon Barwise

xp asserts that there is no such conditional constraint that applies to su giving the constraint in question. Given the plethora of constraints we recognize, how could it ever happen that a speaker comes to have the information that there is no such conditional constraint that applies in a particular situation to yield some specific actual constraint? Let's look at a couple of examples. Suppose you say / / you were as poor as I am, you would not buy so many books. I may know that you are wrong, because I may know that I am poorer than you. This is just what the material conditional gets at, when it says that a conditional is false if the antecedent is false and the conclusion true. Here is a different sort of example. Suppose we are ready to distribute some candy bars to the children, and you, wanting to be the one to hand them out, say If I give each child one of these bars, every child will get one he likes. However, I notice that all the candy bars have coconut in them, and know that some of these children cannot stand coconut. I know that your conditional statement is false, since there can be no such way of giving the children bars that will make them all happy, no matter how good your intentions. This same idea applies to an example from Stalnaker (1984: 164). Tweedledum and Tweedledee are prevented from tossing a fair coin. Tweedledum says / / we had tossed the coin, then it would have come up heads. Tweedledee disagrees quite strongly, asserting that if they had tossed it, it would have come up tails. I claim that they are both wrong. It is just false to make either claim since general symmetry considerations show that there is no general law which determines the outcome of a fair coin toss before the coin is tossed.10 It is not, as Stalnaker suggests, that the statements are of indeterminate truth value, but rather that they are both false. Notice, though, that either Tweedle would be right in asserting the conditional / / we had tossed this coin, it would have come up heads or tails. However, for understanding (7), the tricky case is when the antecedent of the conditional is necessarily false, something that has not come up in the above examples. Or has it? What if, in the case of the candy bars, there are fewer bars than children? In that case, the antecedent is necessarily false, but it still seems that we would judge the conditional as a whole false, for the observed reason. Now, let's get back to Virgil. How could it be that he has the information needed to assert (7)? That is, how can he have the information that the embedded statement: If you could give a proofofRH, then I could give a proof of not- FLT is false? Paul gives the answer to this. In these circumstances, RH and not-FLT serve not so much to designate particular statements, as to designate parameters anchored to RH and not-FLT. That is, the best way to understand (7) is as denying the existence of a general constraint that gets one from a proof of a conjecture in number theory to a proof of something inconsistent with the conjecture. There can be no such general constraint because any number-theoretic statement that is provable is true. 50

Conditionals and conditional information 5. CONCLUSION What in the world are conditionals about? I have attempted to show that the sort of answer that Quine suggests, that they describe relations between the matters spoken of by the antecedent and consequent, is in fact quite workable, and that it applies to a wide range of conditionals, including mathematical conditionals. The two essential ingredients of my account are constraints as the interpretation of conditionals and the use of a parametric background type that is anchored by context. The former is needed to get at the subject matter of conditional statements, the latter is needed to account for their logic. Both of these are suggested by general considerations having to do with information and its flow. This account is, admittedly, more complicated than the material conditional. I have the feeling, though, that it gets at what people working on truth-conditional accounts of conditionals have really been after. What one really wants is an account that describes the conditions under which a speaker is in a position to assert if 0 then \p, in terms of the conditions under which 0 and ip obtain. Notice the wording here. We assume that there are such things as conditions under which things hold. The conditions are not descriptions, but we can try to describe them. That is, the conditions are not linguistic expressions but things that we can try to describe in our theory by using linguistic expressions. This is just the kind of account we have sketched of the interpretation of conditionals. We have suggested spelling out the conditions under which a speaker can assert a conditional, and the information the conditional carries, in terms of relations between the types of situations described by their antecedents and consequents, much as Quine suggested. The account is compositional to the extent that the meaning of compound sentence (// 0 then \p) is systematically related to that of its parts, even though there is no simple relation between the particular truth value of the whole and its parts. There is another tradition in the study of conditionals, one that takes conditionals as being about dispositions to change beliefs in the light of new evidence. The intuition is that if I believe that if 0 then \p and come to learn that 0, then I will be disposed, in general, to believe that ip. What does our account have to say about such matters? Stalnaker (1984: ch. 6) makes a convincing case for needing to distinguish between what he calls conditional11 belief and belief in conditional propositions. He argues that they should be closely related, in that conditional propositions, whatever they are, are 'propositions about features of the world which justify certain policies for changing one's belief in response to potential new information' (p. 119). But constraints are exactly those features of the world that underwrite information flow, and so are just the sort of thing one needs to 51

Jon Barwise

know about to be in a justified position in changing one's beliefs in response to new information.

NOTES 1 This paper, the second in a series with the general title of The situation in logic', grew out of my reply to Richmond Thomason's papers (1983a, b), which he presented to the Symposium on Conditionals and Cognitive Processes. Reading Stalnaker (1984) inspired me to rewrite the paper and give, I think, a more satisfactory account. I would like to thank the members of the CSLI Logic Group for many helpful comments on both drafts, especially John Etchemendy and David Israel. Daily discussions with John Perry in the course of writing the paper were crucial to its development. Thanks also to Alice ter Meulen, Rich Thomason and Elizabeth Traugott for helpful comments on the earlier draft, and to Ingrid Deiwiks for help with preparation of the paper far beyond the call of duty. The research for, and preparation of, this paper were done at the Center for the Study of Language and Information, supported by an award from the System Development Foundation. 2 These are the questions for declarative sentences. Other sorts of sentences will have other informational functions. Questions, for example, are quests for information. 3 To be definite about what I mean by provable, I will take 'proof to mean a proof in first-order logic from the axioms of some standard true number theory like Peano arithmetic. 4 One heroic measure that might be suggested to avoid this paradoxical situation would be for all different possible worlds to have non-isomorphic natural numbers. However, this will not solve the problem as long as each world satisfies the reflection schema, which asserts that anything provable is true. For in that case, FLT will be true in world j , but since the integers of j must contain the actual integers as an initial segment, FLT will be true in the actual world as well, and hence so will RH, which is equivalent to it. This was why I took FLT to be a universal numbertheoretic conjecture. 5 In S&A we sometimes used classes of situations, and class membership, to represent these types. At other times we used event-types and anchorings to represent them. One of the changes suggested in Ss&sa was to treat these types directly, rather than representing them with sets or classes. I am following that change here, though little harm will come from using the notion of event-type from S&A. I use the notation [s I . . . s ...] for the type of situation that satisfies the conditions . . . 5 . . . . Borrowing a notation from computer science, I write s:S to indicate that s is of type 5. This only makes sense if S has no parameters. There are three operations on types that are important: fl, U, and ~~|. These satisfy the usual laws for a boolean algebra, except for the laws that makes SU~|S a unit element and Sfl~|S a zero element. Rather than there being a zero element, there is a property of being an incoherent type, which is satisfied by a filter of types, in particular, by every type of the form 5fl~|5. There is a partial ordering on the types, SCS', which means that every situation of type S is also of type S'. Thus, if SCS' and s:S, then s:S'. 6 If S has parameters, then S is realized only relative to some anchor for the parameters of S. 7 Any statement will carry some extraneous information, like what language the speaker is using. What really counts is that it should carry its propositional content as information. In S&A we stressed the type of situation a statement describes, and called that the interpretation of the statement. In Ss&sa, however, in reaction 52

Conditionals and conditional information to Soames' commentary (1985), we admitted that there are associated propositions, and called them the propositional content of the statement. In this paper I am taking the propositional content to be the proposition that the type of situation described is realized. 8 In S&A we tried to define this three-place relation in terms of the two-place relation, by BDS'^S". Studying conditionals has convinced me that this particular reduction is incorrect. In this paper I will just treat it as a three-place relation. I will implicitly use the following five assumptions about this relation in what follows: (1) if B is fixed, then the resulting two-place relation is transitive: Sj => S21 B and S2 =>S3\B then S} => S3 \ B. This is why the Hypothetical Syllogism is valid as long as background conditions do not vary. (2) If a conditional constraint holds relative to some B and this background condition is tightened, then the constraint holds relative to the more restrictive type of situation B'\ if S^S' \ B and B'CB, where B' is compatible with S, then S => 5' I B'. (3) If S => S' I B then S is compatible with B, that is, SHB is not incoherent. (4) If S^>S' B and / is a coherent anchor for some of the parameters of B, then 5(/)=^>5'(/) B(f). (5) If S^S' \B where B has no parameters, and if B is realized by some real situation, then S =J> S' is actual. 9 This seems to correspond very well to Stalnaker's intuitions, if not his formal account, when he says (1984: 131): Suppose a speaker says something of the form if A then B and a hearer disagrees. There are two contrasting kinds of explanations for the conflict: (1) it may be that the hearer has not understood what .. . situation the speaker meant . . . or (2) it may be that the speaker and hearer disagree about some relevant fact. In Stalnaker's more formal account, both sorts of facts go into determining a single selection function on possible worlds that determines the proposition. 10 I am assuming that even if some strong form of determinism is true, that fact is not what the Tweedles were getting at with their conditionals. 11 For Stalnaker this use of conditional has to do with dispositions to change beliefs, not with the conditions under which a belief is knowledge, as when I spoke of conditional knowledge.

REFERENCES Barwise, Jon. To appear. The situation in logic. 1: logic, meaning and information. In Proceedings of the ig8$ International Symposium on the Philosophy, Method and History of Science, Salzburg. Amsterdam: North Holland Publishing Company. Barwise, Jon and John Perry. 1983. Situations and attitudes. Cambridge, Mass.: Bradford Books, MIT Press. Barwise, Jon and John Perry. 1985. Shifting situations and shaken attitudes. Linguistics and Philosophy, 8, 1: 105-61. Downing, P. 1959. Subjunctive conditionals, time order, and causation. Proceedings of the Aristotelian Society 59: 149-59. Dretske, Fred. 1981. Knowledge and the flow of information. Cambridge, Mass.: Bradford Books, MIT Press. Gibbard, Allan. 1981. Two recent theories of conditionals. As quoted in Robert Stalnaker, 1984. Inquiry. Cambridge Mass.: Bradford Books, MIT Press, 108-9. 53

Jon Barwise Lewis, David. 1973. Counterfactuals. Cambridge, Mass.: Harvard University Press. Maxwell, E. A. 1959. Fallacies in mathematics. Cambridge: Cambridge University Press. Quine, Willard Van Orman. 1959. Methods of logic, rev. edn. New York: Holt, Rinehart and Winston. Soames, Scott. 1985. Lost innocence. Linguistics and Philosophy, 8,1: 59-71. Stalnaker, Robert. 1984. Inquiry. Cambridge, Mass.: Bradford Books, MIT Press. Thomason, Richmond. 1983a. Conditionals, time and causal independence. MS, University of Pittsburgh. Thomason, Richmond. 1983b. Remarks on mood and conditionals. MS, University of Pittsburgh.

54

CONDITIONALS AND MENTAL MODELS •

P. N. Johnson-Laird 1. INTRODUCTION What would count as a complete theory of conditionals?1 One goal for such a theory is to answer the following two questions: (i) (ii)

What do conditionals mean? What are their logical properties?

These are matters of logical and linguistic analysis: they concern human competence. However, a complete theory of conditionals should also answer two psychological questions: (iii) (iv)

How do people understand them? How do people reason with them?

These are matters of human performance that call for the investigation of mental processes. There are a number of theories that provide answers to some of these four questions. Yet, despite the conceptual analyses of philosophers and logicians, the semantic and syntactic studies of linguists, and the experimental investigations of psychologists, there is no single existing theory that provides a unified and complete account of both competence and performance. My aim in this paper is accordingly to make progress towards such a theory - a theory that concerns the everyday interpretation and use of conditionals, not an idealized philosophical concept, and one that is intended as a contribution to cognitive science. The paper has four parts. The first part considers how ordinary individuals reason with conditionals, and it describes the main approach that psychologists have taken to deductive reasoning - the theory that there are formal rules of inference in the mind. It argues, however, that this view is mistaken and that inference depends instead on a search for 'mental models' of premises that are counterexamples to putative conclusions. A corollary of this theory is that the logical properties of conditionals derive from their interpretation and not from any formal rules associated with them. The second part of the paper takes up this question of how people interpret conditionals. It establishes 55

P. N. Johnson-Laird that they do so in different ways in different contexts. Such interpretations could reflect an intrinsic ambiguity in conditionals, or alternatively the effects of context on an underlying univocal concept. The third part thus considers the attempt by Braine to provide a psychologically plausible univocal analysis, and the theory proposed by Ramsey, and later elaborated by Stalnaker, that conditionals are evaluated by a sort of 'thought experiment'. Braine's theory unfortunately fails to apply to all conditionals; Stalnaker's approach, and recent alternatives to it, relies on a 'possible worlds' semantics. The fourth part treats this approach as the starting point for a new psychological theory based on the notion of mental models.

2. HOW DO PEOPLE REASON WITH CONDITIONALS? 2. i The main empirical phenomena Psychological experiments have shown that people with no training in logic cope reasonably well with arguments in the form of modus ponens (see Wason and Johnson-Laird 1972). Given such premises as: (1)

If the red light is on, the studio is occupied

(2)

The red light is on

(If p then q)

(p)

nearly everyone draws the conclusion: (3) The studio is occupied (•"• q) The only mystery here is the mechanism that selects this particular valid conclusion from the potentially infinite set of other valid conclusions that could be drawn from the same premises. These other conclusions, such as a disjunction or conjunction of the premises, are obviously trivial, but the mechanism that leads to the formulation of nontrivial conclusions has yet to be elucidated definitively. I have argued elsewhere that its operations can be described in terms of the maintenance of semantic information (Johnson-Laird 1983). Ordinary reasoners have greater difficulty with arguments in the form of modus tollendo tollens: (4) (5) (6)

If the red light is on, the studio is occupied The studio is not occupied Therefore, the red light is not on

(If p then q) (~q) (.'. ~p)

Likewise, they make many mistakes, as Wason and his colleagues have shown, in deciding what evidence would in principle controvert a conditional rule (see e.g. Wason and Johnson-Laird 1972). For instance, in order to evaluate the rule: 56

Conditionals and mental models (7)

If there is a vowel on one side of a card, then there is an even number on the other side

the majority of subjects choose to turn over a card bearing a vowel, but they fail to select a card bearing an odd number. They are often less susceptible to this sin of omission if the rules and materials are more realistic, but this manipulation does not always work, and quite why it should work at all remains a matter of active controversy (see Evans 1982; Griggs 1983; Wason 1983; Oakhill and Johnson-Laird 1983). 2.2 The doctrine of mental logic Psychological theories of propositional reasoning have invariably been based on the assumption that the mind contains rules of inference or inferential schemata of the sort postulated in 'natural deduction' systems (see e.g. Inhelder and Piaget 1958; Johnson-Laird 1975; Osherson 1975; Braine 1978; Rips 1983). Mistakes in reasoning are then explained in terms of misinterpretations of the premises, failures in performance, and even the possible existence of 'pathological' rules of inference. The difference in difficulty between modus ponens and modus tollendo tollens is accounted for by assuming that there is a mental rule for the former, but not for the latter - which must therefore depend on a chain of deductions such as a reductio ad absurdum. Alas, this theoretical manoeuvre is intrinsically ad hoc, and so too is the way these theories of mental logic try, if at all, to specify the mechanism that leads to informative rather than to trivial conclusions. The theorist selects one formalization of the calculus rather than another, and lays down otherwise arbitrary constraints on the use of rules of inference. The doctrine that there are mental rules of logic implies that people have at least two sorts of knowledge about conditionals: a knowledge of their logical properties, which is embodied in rules such as modus ponens, and a knowledge of their meaning and, in particular, of their truth conditions. These two sorts of knowledge must of course be compatible with one another. However, there is an important asymmetry between them: a statement of the truth conditions of conditionals constrains the form of inferences that are valid, but a statement of the form of valid inferences leaves conditionals open to a number of distinct semantic interpretations. On the one hand, if the conditional is taken to have the truth conditions of material implication - true unless its antecedent is true and its consequent is false - then both modus ponens and modus tollendo tollens will be valid. On the other hand, if a conditional is taken to be governed by these two rules of inference, it does not follow that it has the truth conditions of material implication. It might instead have 'defective' truth conditions in which no truth value is assigned in those cases where its antecedent is false. Although such a conditional, if p then q, is not equivalent to its contrapositive, if ~q then ~~p, both rules of inference remain valid (see Johnson-Laird and Tagart 1969). 57

P. N. Johnson-Laird 2.3 The theory of mental models and its application to inference The asymmetry between meaning and inferential form naturally suggests that children may acquire a knowledge of truth conditions before they acquire a knowledge of rules of inference. It also suggests a more radical hypothesis: perhaps the only people who ever acquire complete systems of formal rules of inference are logicians, and perhaps the doctrine of mental logic is a complete mistake. Once one knows the truth conditions of propositional connectives (and quantifiers), there are a number of algorithms for reasoning that do not require any access to formal rules. Hence, a logically untutored mind may not contain rules of inference, inferential schemata, or any system for making deductions that depends on the quasisyntactic manipulation of symbols. Reasoning could be based not on formal principles but on the fundamental semantic principle that a valid deduction has no counterexamples: there is no model of the premises in which the conclusion is false. This assumption leads naturally to a quite different conception of human reasoning. At the heart of the theory is the thesis that any deduction about a finite domain can be made using mental models. The following general inferential procedure is only a slight extension of a theory of comprehension. Step 1. Construct a mental model of the state of affairs that the premises describe. Step 2. Formulate, if possible, an informative conclusion that is true in all the models of the premises that have so far been constructed. If there is no informative conclusion but only trivially valid ones, then no conclusion is drawn from the premises. Step 3. Try to construct an alternative model of the premises that renders the conclusion false. If there is such a model, abandon the conclusion and return to step 2. If there is no such model, i.e. the finite possibilities inherent in a finite model have all been examined, then the conclusion is valid. If a given conclusion is to be evaluated, then only this step need be carried out. The theory of mental models can be applied to propositional, relational and quantificational reasoning, though it is restricted to finite domains. It has been implemented in a variety of computer programs, and it has been corroborated by the results of experiments on reasoning (Johnson-Laird 1983). Unlike the theories based on mental logic, its deductive mechanism depends on a search for counterexamples. However, reasoners have to be able to construct mental models of states of affairs described in premises. Indeed, the theory implies that the logical properties of connectives and quantifiers derive from their interpretations and, in particular, from their contribution to the truth conditions of the assertions in which they occur. It is therefore crucial to give an account of how people understand conditionals since, according to the theory, interpretations determine logical properties. 58

Conditionals and mental models 3. HOW DO PEOPLE UNDERSTAND CONDITIONALS? 3. i The interpretation of conditionals Psychologists have discovered one uncontroversial fact about conditionals: they are interpreted in different ways in different situations. In the first experiment on the interpretation of conditionals, Johnson-Laird and Tagart (1969) asked subjects to evaluate a set of cards in the light of a conditional, such as: (8)

If there is an 'A' on the left-hand side of the card, then there is a number '3' on the right-hand side

Thus, a card might have an 'A' on the left and a '4' on the right, and the subjects' task was to decide whether the card indicated that the conditional was true (or false), or was irrelevant to its truth value. Most subjects produced a pattern of judgements consistent with a 'defective' truth table: the conditional was true when its antecedent and consequent were true; it was false when its antecedent was true and its consequent false; but when its antecedent was false of a card, then that card was 'irrelevant' to the truth value of the conditional. This defective truth table for ordinary conditionals had been mooted by various authors, including both Quine (1952) and Wason (1966). An important qualification to these results was demonstrated by Legrenzi (1970). He showed that in a strictly binary situation subjects tend to treat conditionals as having the truth table of material equivalence: true when the antecedent and consequent are both true or both false, but false in any other condition. His subjects watched a ball bearing run down one of two channels, causing one of two lights to be illuminated. Given a conditional of the form: (9)

If the ball rolls to the left, then the green light is lit

the majority of subjects treated trials in which the antecedent and consequent were both true, or both false, as consistent with the rule, and any other combination as inconsistent with it. Some philosophers - notably Grice (1967) - have argued that conditionals correspond to material implications from which certain implicatures are drawn in virtue of conversational conventions. Other philosophers have argued that conditionals never correspond to material implications. For instance, Stalnaker (1968) wrote: 'the falsity of the antecedent is never sufficient reason to affirm a conditional, even an indicative conditional' (but cf. Stalnaker 1975). Yet, certain conditionals with negated antecedents do seem to have truth conditions corresponding to those of material implication, e.g. the assertion: (10)

If the poem isn't by Wordsworth, then it is by Coleridge

seems to be rendered true by the mere fact that the poem is by Wordsworth, i.e. the antecedent is false; or by the mere fact that it is by Coleridge, i.e. the consequent is true. 59

P. N. Johnson-Laird Most traditional theories of conditionals draw a distinction, explicitly or implicitly, between indicative and subjunctive (or counterfactual) conditionals. Even theorists who attempt to treat indicative conditionals truth-functionally concede that counterf actuals such as: (i i)

If the Viennese had three legs, they would march in waltz time

establish some sort of connection between antecedent and consequent, and accordingly transcend any simple truth-functional account. Such conditionals can indeed be true even if both antecedent and consequent are false. They involve further tacit premises which, if taken together with the antecedent, entail the consequent (see Chisholm 1946; Goodman 1947). There is some disagreement among theorists about whether a counterfactual implies that some such argument exists or is itself an elliptical presentation of it. The problem, of course, is to specify which premises should be used with a given antecedent. Philosophers have naturally swept this problem into the pragmatic 'wastepaper basket': it is all a matter of context. Undoubtedly, conditionals are interpreted in many different ways, and the variety of interpretations is even greater, as Fillenbaum (1978) has established, when illocutionary force is taken into account. This diversity in interpretation is perplexing, but it does not necessarily imply that if is polysemous. Several theorists have made ingenious attempts to reconcile a univocal semantics for conditionals with the vagaries of their interpretation, and it is to these attempts that we now turn. 4. WHAT DO CONDITIONALS MEAN? 4.1 A univocal psychological theory Braine (1978) has proposed an ingenious uniform interpretation of conditionals that is consistent with the doctrine that there are inferential schemata in the mind. In part anticipated by Ryle (1949: ch. 5), he argues that assertions of the form: If p then q merely state a rule of inference to the effect that q can be inferred from p: P Therefore, q though they provide in themselves no information about the basis for the inference. Thus, for example, the conditional: (12)

If the red light is on, then the studio is occupied

sanctions the inference: 60

Conditionals and mental models The red light is on Therefore, the studio is occupied Although it is true that whenever q follows from p, the assertion: if p then q, is true, the converse claim is unfortunately false. There are many conditionals that do not have the force of warranting inferences, e.g.: (13) (14) (15)

If you've run out of petrol, there is a garage down the road If you're interested, the world record for the mile has just been broken If the court wants the tapes, Richard has them

Thus, (13) can hardly be said to warrant the inference: You've run out of petrol Therefore, there is a garage down the road In this and the other cases, the consequent of the conditional is true simpliciter (given that the conditional is true), and the antecedent is not a premise but stipulates the conditions in which the truth of the conditional is likely to be of relevance to the addressee (Austin 1961). Many other conditionals can hardly be said to warrant inferences. Indeed, a striking feature of conditionals is that their antecedents always state conditions, whereas their consequents can serve a variety of illocutionary functions: (16) you are married to her I hereby pronounce you married to her If you give her the ring, are you married to her? do marry her if only you would marry her! A conditional that contains a performative utterance hardly states a rule of inference, and a conditional with a question or an exclamation as its consequent certainly cannot serve as a rule of inference. Indeed, any formulation of the semantics of conditionals in terms of truth conditions is, strictly speaking, too restrictive. What is required is an account that accommodates statements, performatives, questions, requests, and the full panoply of illocutions. If conditionals always sanction rules of inference, then their logical properties should be straightforward. In fact, their behaviour in inference seems quite variable. Some conditional premises yield a transitive conclusion; others, as Stalnaker (1968) points out, do not: (17) (18)

If J. Edgar Hoover had been a Communist, then he would have been a traitor If J. Edgar Hoover had been born in Russia, then he would have been a Communist

Braine (1979) argues that such examples are misleading and are not genuine failures in transitivity. If the second premise is true and Hoover became a 61

P. N. Johnson-Laird naturalized American, then transitivity holds. But, if the second premise is true and Hoover did not become a naturalized American, then the first premise is false. In short, either transitivity holds or one of the premises is false in the context of the argument. The following two assertions, however, seem to be true in the same context: (19) (20)

If you need any money, then there is a ten pound note in your wallet If there is a ten pound note in your wallet, then you don't need any money

The first asserts that there is a ten pound note in your wallet and states the conditions in which this information may be relevant; the second states the principle that if there is a ten pound note in your wallet then you do not need any money. Yet, obviously, the transitive inference is invalid: If you need any money, then you don't need any money The only way out appears to be to recognize that not every conditional sanctions an inference, and thus to accept that Braine's theory is only a part of the story and does not apply to all conditionals. 4.2 The Ramsey-Stalnaker 'thought experiment' An alternative approach to a unified semantics for conditionals began with Ramsey's (1931) idea that the way to evaluate a conditional is to add its antecedent to your stock of beliefs, and then to assess whether or not its consequent is true. If you believe that there is a causal or necessary connection from the antecedent to the consequent, then rationally you will infer that the consequent is true, and hence that the conditional as a whole is true. If you already believe that the consequent is true, then it should remain a part of your beliefs, and you will consider the conditional true, too. Hence, a causal or necessary connection may be relevant to your assessment of the conditional, but it is not an indispensable part of the process. This 'thought experiment' triggered by a conditional works only where you have no prior opinion about the truth of the antecedent. Stalnaker (1968) accordingly suggested the following addition to the procedure. Where you believe the antecedent to be true, your evaluation of the conditional is equivalent to your belief about the consequent. Where you believe the antecedent to be false, its addition to your beliefs will require some of them to be modified in order to avoid inconsistency, and which particular modifications you make will be determined on pragmatic grounds (see Rescher 1964). A general procedure for conditionals can thus be summarized as follows: add the antecedent to your stock of beliefs; adjust your other beliefs, where necessary, to maintain consistency; and evaluate the conditional as true or false depending on whether its consequent is true or false. 62

Conditionals and mental models Stalnaker (1968, 1981) went on to propose a set of truth conditions for conditionals congruent with this method of evaluation and based on 'possible world' semantics. Subsequently, Lewis (1973), Pollock (1976) and others have formulated alternative accounts of counterfactual conditionals within the same framework of 'possible worlds'. Undoubtedly, this approach has made a major contribution to elucidating language in general and conditionals in particular. What I want to consider in the next section is a psychological theory partly inspired by it, but also based on the assumption that because the set of possible worlds is infinite in size, it cannot fit directly into an individual's mind (see also Partee 1979; Johnson-Laird 1982). 5. MENTAL MODELS OF CONDITIONALS 5.1 Some assumptions about the interpretation of conditionals The ideal solution to the problem of 'if would be to establish neither a single uniform logic of the term, nor a variety of meanings for it, but a single uniform semantics from which both the diversity of the interpretations of conditionals and the vagaries in their logical behaviour will emerge. In aiming for such a theory, I shall begin with a number of interrelated assumptions that I shall briefly motivate. First, the meaning of conditionals can be grasped by human beings. This principle ought to go without saying, but it has to be made explicit - in part because 'possible world' analyses are too big to fit immediately inside anyone's head, and in part because certain theories lead to the view that, in Putnam's phrase, 'meanings ain't in the head' (see Putnam 1975 for a defence of this view, and Johnson-Laird 1983 for a rejoinder). Since one cannot prove that people understand the proper meaning of conditionals, it is necessary to assume that they do. Second, the semantic interpretations of conditionals can be built up compositionally from the interpretations of their constituents. The principle of compositionality is familiar to students of logical semantics and Montague Grammar, though of course it is not universally accepted (see e.g. Russell 1905; Chomsky 1977). In my view, compositionality is hardly an empirical issue: such is the power of compositional semantics that any noncompositional analysis can probably be mimicked by a compositional one. Third, there is an immediate and striking observation that can be made once one accepts compositionality: the interpretation of the consequent of a conditional is identical to the interpretation of the same main clause if it occurs in isolation but in a context that is known to satisfy the antecedent of the conditional. There are therefore no constraints on the form or illocutionary force of the consequent. Similarly, there is no need to make special provisions for the interpretation of the consequents of conditionals, since the 63

P. N. Johnson-Laird ordinary procedures for coping with main clauses suffice. In particular, the mental model theory of modal auxiliaries such as 'may' and 'will', which assumes that they are unambiguous but depend on epistemic or deontic beliefs for their interpretation (Johnson-Laird 1978), can be directly incorporated within the present account. The third assumption is borne out by the following observation. If both speaker and listener are conscious of the content of an antecedent, i.e. of the imminence of the corresponding state of affairs, then it can be omitted. For example, a mother observing her child about to grab a forbidden cake can assert: (21)

I'll smack you

The force of this utterance is not that the mother will smack the child regardless, but rather that she will do so if the child takes the cake. Indeed, should the mother be uncertain about her child's intentions she could equally well assert: (22)

If you take the cake, I'll smack you

Even with counterfactuals, the antecedent can be omitted where the speaker and the listener are conscious that the antecedent event was imminent but did not occur. Hence the mother, observing instead that her child has mastered the temptation to take the cake, can assert: (23)

I'd have smacked you

where the force of the utterance is that she would have done so if the child had taken the cake. Fourth, it is a corollary of the previous assumption that the function of the antecedent of a conditional is to establish a context, i.e. a state of affairs that should be taken for granted in considering the consequent. When the speaker and listener are conscious that the actual state of affairs does correspond to the antecedent, then indeed it is odd to assert the antecedent. The mother would not say: (24)

If you take the cake ...

in a context where the child has plainly taken it. Here, it would only be appropriate to use an antecedent that designates a generic state of affairs that subsumes what has happened: (25)

If you take cakes ...

Since antecedents function to establish contexts of interpretation, there are corresponding constraints on their form: they must make a statement, and their tense and aspect call for a special interpretation. Finally, although the Ramsey-Stalnaker notion of a 'thought experiment' has been endorsed by some psychologists (Rips and Marcus 1977), it is an 64

Conditionals and mental models idealization: people do not evaluate a conditional by adding its antecedent to their complete stock of beliefs (with minimal modifications) and evaluating its consequent. They do not have ready access to all their beliefs, and it might take hours for them to review even a relevant sample. Armed with these assumptions, let us turn to the theory of mental models to help us to formulate an account of how conditionals are evaluated. The overall, though over-simplified, scheme can be summarized in two steps: Step i. Construct a mental model based on the superficial linguistic representation of the antecedent and on those beliefs triggered during this process. Step 2. Interpret the consequent in the context of the model and general knowledge. There are, of course, many details that need to be spelt out in order to transform this simple picture into a more accurate one, and I will consider, first, the interpretation of the antecedent; second, the nature of the relation between the antecedent and the consequent; and finally, the extent to which the truth conditions of the antecedent specify the situation in which the consequent is evaluated. 5.2 The interpretation of the antecedent What underlies the meaning of conditionals, according to the present theory, is the ability to envisage states of affairs that may or may not correspond to reality, that is, the ability to construct mental models of such states of affairs and to bear in mind their existential status. The metaphysics of English distinguishes between three major classes of states of affairs: actual states, real possibilities and hypothetical states. An actual state is described by a straightforwardly true but contingent assertion, such as: (26)

Elizabeth II is the queen of England

A real possibility is described by an indicative antecedent: (27)

If Elizabeth II abdicates ...

which designates an event that is possible in relation to the current state of affairs. A hypothetical state is described by a subjunctive antecedent: (28)

If Elizabeth II had abdicated ...

which designates a once possible, but now imaginary event, to be taken hypothetically in relation to the then current state of affairs. The distinction between real possibilities and hypothetical states is one between the real history of the world and hypothetical alternatives to it (see Isard 1975 for the description of a computer program that interprets conditionals 65

P. N. Johnson-Laird

about games of tic-tac-toe in very much this way). Hence, there is no difference in the truth conditions of the two sorts of conditional when they refer to future events, e.g.: (29)

If anyone uses nuclear weapons, World War III will occur

and: (30)

If anyone were to use nuclear weapons, World War III would occur

The only distinction here is that (30) suggests that the possibility is more remote. There are, however, differences in the acceptability of certain illocutions depending on whether a reference to the future concerns a real possibility or a hypothetical event. An antecedent expressing a real possibility can be coupled with a performative or a request: (31)

If you give her the ring, I hereby pronounce you married

But an antecedent that expresses a hypothetical event in a history that is an alternative to reality less readily accommodates performatives or requests: (32)

?If you were to give her the ring, I hereby pronounce you married

In referring to past events or to those that are presently occurring, there are genuine differences in the truth conditions of the two sorts of conditional. Adams (1970) provides us with a useful pair of contrasting examples: (33)

If Oswald didn't assassinate Kennedy, then someone else did

and: (34)

If Oswald hadn't assassinated Kennedy, then someone else would have

The antecedent of the first conditional presents a real possibility, namely, that Oswald did not kill Kennedy. This may be the true state of affairs in the actual history of the world. Since Kennedy was indeed assassinated, it follows that someone else must have done the deed, and hence the conditional is true. The antecedent of the second conditional presents a hypothetical possibility, and it therefore invites us to consider, not the actual history of the world (which for the speaker includes Oswald as the murderer of Kennedy), but a hypothetical alternative history in which Oswald did not kill Kennedy. The conditional asserts that in this alternative Kennedy would nevertheless be murdered - an assertion which is, to say the least, debatable. A similar contrast can be drawn for antecedents that refer to events presently occurring. In summary, if is a verbal cue to consider real or hypothetical possibilities, and the content, the grammatical mood of the clause, and the context, usually make clear the intended status of the antecedent. The metaphysics of English is in fact more complicated than I have so far admitted: the contrasting system of actual states, real possibilities and hypothetical states is all relative to the 66

Conditionals and mental models status of the discourse. Hence, the same tripartite division of conditionals applies equally to factual or fictional discourse. There are even conditionals that bridge the gap from the fictional to the real: (35)

If Hamlet had killed the king at once, then the play would have come to an abrupt end

and from the real to the fictional: (36)

If 'Hamlet' had been a soap opera, he would have married Ophelia

5.3 The nature of the relation between antecedent and consequent Once a model of the antecedent has been established, the consequent can be interpreted in relation to that model. As I have already argued, there is nothing particularly special about the process of interpreting the consequent perse, but the nature of the relation between antecedent model and consequent is more problematical. The early philosophical analyses of conditionals (e.g. Chisholm 1946; Goodman 1947) recognized the importance of this relation, but it has tended to be downgraded in the Ramsey-Stalnaker-Lewis approach on the grounds that a conditional is true if its consequent is true in the relevant world(s) in which the antecedent is true, regardless of whether there is any relation between them. From a psychological standpoint, no one asserts a conditional on such grounds alone. One would hardly claim: (37)

If Elizabeth II abdicates, then some dogs have fleas

merely because the consequent is almost certainly true in the state of affairs characterized by the antecedent. Indeed, such an assertion would be interpreted as positing some relation between the antecedent and the consequent, and listeners would attempt to sketch in a plausible scenario that relates them. As we shall see, we can make sense of certain conditionals only by bearing in mind that they are invariably taken to mean that some sort of relation is intended to hold between antecedent and consequent. There are two issues concerning this relation: its nature, and its degree, i.e. the extent to which the antecedent determines the state of affairs in which the consequent is to be evaluated. In this section, I am going to consider the nature of the relation, beginning with its temporal component. If the antecedent of a conditional refers to a specific event or to a temporally bounded state, its consequent may refer to an event or state that occurs earlier, contemporaneously, or later. An indicative antecedent referring to the present can be related to events or states in the past, present, or future: (38)

f was hot yesterday If it is wet now, then it \ is hot now will be hot tomorrow 67

P. N. Johns on-Laird

An antecedent referring to the future can likewise be related to states that occur earlier, at the same time, or later: (39)

[ was hot yesterday . . . . is hot now Tr If it is wet tomorrow, then it < . . is hot tomorrow will be hot the day after

In this case, both the time of the utterance and events prior to it can occur before the antecedent state. Not surprisingly, the analogous possibilities are open for an antecedent referring to the past. And exactly the same possibilities can arise with counterfactual conditionals: (40)

f had been wet yesterday f would have been hot yesterday If it i were wet now it i would be hot now were wet tomorrow [ would be hot tomorrow

where any combination of antecedent and consequent is feasible. Granted these various temporal relations, the consequent event does not necessarily occur at the same time as the antecedent event. It may be necessary to construct a scenario leading from the antecedent model to the consequent event, or from the consequent event to the antecedent model. Consider the assertion: (41)

If it rains in the Sahara, the desert will get wet

An accurate model of the antecedent should represent the fact that the desert gets wet, and the conditional should therefore be evaluated as true without the need to construct a scenario. But now consider the related example: (42)

If it rains in the Sahara, the desert will bloom

A model of the antecedent will not represent the blooming desert since that is not a concurrent event; but it is, of course, a likely consequence in the near future. Hence, the interpretation of the consequent of the conditional calls for the construction of a scenario based on the initial model of the antecedent and on beliefs about the relations between the two. The nature of the beliefs used to develop a scenario will determine the nature of the relation between the antecedent and the consequent. Conditionals such as: (43)

If the match had been struck, it would have lit

(44)

If the match had lit, it would have had to have been struck

elicit beliefs about causal relations. Conditionals such as: (45)

If it had been midday just now, it would have been 11 a.m. an hour ago 68

Conditionals and mental models (46)

If it had been 11 a.m. an hour ago, it would have been midday just now

elicit beliefs about temporal measurement that establish the necessary connection between antecedent and consequent. The role of beliefs in fleshing out the interpretation of conditionals is easily overlooked, as it has been sometimes by theorists who have sought to reduce causal assertions to the assertion of counterfactuals. A comprehensive theory of causal relations should accommodate the fact that, as Miller and Johnson-Laird (1976) have argued, one event (or its non-occurrence) can cause, allow, or prevent another event (or its nonoccurrence). A counterfactual of a given form is indeed indeterminate. Thus, the conditional: (47)

If the match hadn't been struck, it wouldn't have lit

is taken to mean that one event caused the other, whereas the conditional: (48)

If the match hadn't been dry, it wouldn't have lit

is taken to mean that the one state of affairs allowed the other to occur. The interpretation of conditionals depends on beliefs, if only because the interpretation of auxiliaries and tense depends on them, too (see Johnson-Laird 1978).

5.4 Truth conditions and the antecedent-consequent relation The truth conditions of a conditional depend on the extent to which the antecedent specifies the situation in which the extension of the consequent is to be evaluated. In principle, there could be three possible degrees of relation between antecedent and consequent: the antecedent could determine the state of affairs in which the consequent is to be evaluated completely, partially, or not at all. In practice, it turns out that there are conditionals in all three categories, and I will examine each sort in turn. Since it is tedious to have to keep pointing out that the consequent can serve any illocutionary function, I shall assume in what follows that whenever I refer to 'truth conditions' the reader will mentally enlarge this phrase to embrace the meanings of questions, requests, and other illocutions. At one extreme there is the category of conditional in which the antecedent has no bearing on the state of affairs in which the consequent's truth conditions have to be evaluated - it merely stipulates the relevance of the information conveyed by the consequent. This sort of conditional is exemplified by: (49)

If you've run out of petrol, there's a garage down the road

Here, the conditional is simply true or false depending on whether or not there is a garage down the road. The main criterion that distinguishes this class of conditionals is that the antecedent expresses (or implies) a desire, 69

P. N. Johnson-Laird need, predilection or state of mind that in principle cannot be related to the truth of the consequent, but the consequent provides information of potential use to those in that state of mind. The general schema for such conditionals is thus:

If p (where p implies x

needs feels wants

y),

then (x will be interested to know that) q is the case Since the consequent, q, describes some state of affairs that is supposedly relevant to x, it must be either factual or concern real possibilities: (50) If you need money, there \ is

> some in the bank

Granted this analysis, it ought to be possible for a hypothetical need or predilection to be the occasion of referring to some actual state of affairs or to a real possibility. Hence, there should be a category of conditionals with antecedents that refer to alternative histories, and with consequents that refer to actual states or real possibilities. Such conditionals do indeed exist, e.g.: (51)

If you had needed some money, there was some in the bank

which asserts that, relevant to a new imaginary state of affairs (your need of money) at a particular time in the past, there was an actual state of affairs (money in the bank) which obtained at that time. The conditional is thus true provided only that there was some money in the bank at the relevant time. The present theory has thus led to the discovery of a class of conditionals which combine counterfactual antecedents with indicative consequents - a class to which I have been unable to find any reference in the literature. At the other extreme, there is the second category of conditional in which the antecedent completely determines the state of affairs in which the truth conditions of the consequent are to be evaluated. For example, such a conditional as: (52)

If someone is in a room, there is a room that is not empty

is true because its consequent is true in any mental model of its antecedent. This simple class of conditionals illustrates the way in which truth conditions can be stated within the framework of mental models. A conditional in this category with the form: If p, then q 70

Conditionals and mental models is true if and only if q is true in any mental model of p. Hence, in this case there is a ready translation into the framework of possible worlds. A mental model based on the antecedent of a conditional is a fragment of many possible worlds, that is, it is consistent with many alternative complete specifications of how the world might be, because many propositions will be neither true nor false in the fragment. The conditional is true if and only if q is true in all the accessible worlds in which p is true. The third, highly frequent, and most problematical category of conditionals, contains those in which the antecedent provides part, but only part, of the specification of the state of affairs in which the consequent is to be evaluated. An illuminating way in which to consider such conditionals is in the context of everyday reasoning (see Johnson-Laird 1983). Suppose, for example, that evidence at a murder trial establishes that the victim was stabbed to death in a cinema during the afternoon and that the accused was on an express train to Edinburgh when the murder was committed. One might be tempted to assert (like many of the subjects whom Bruno Bara and I have tested informally): (53)

If the accused was on a train when the murder occurred, then he (sic) must be innocent

It is clear from questioning the subjects that they base this claim on a number of implicit assumptions: A person cannot be in two places at once There are no cinemas on trains Express trains do not pass through cinemas It is not possible to stab someone in a cinema if one is travelling on a train These principles are obviously used in constructing a mental model based on the evidence given at the trial. They could, however, all be made explicit in the antecedent of the conditional: If the accused was on a train when the murder occurred, and a person cannot be in two places at once, and there are no cinemas on trains, and ..., then the accused is innocent Thus, the natural way in which to think of such conditionals is that the consequent is evaluated with respect to a model of the state of affairs that is described by the antecedent taken in conjunction with general knowledge. The point of the informal experiment, however, was to demonstrate that there is no simple algorithm by which to discover all the possible conditions that must be fulfilled in order to guarantee innocence: subjects readily raise 71

P. N. Johnson-Laird

a number of feasible scenarios in which, despite the assumptions above, the accused is nevertheless guilty. For example, he may have used an accomplice, or a radio-controlled robot, or a spring-loaded knife hidden in the seat. Of course one can go on adding explicit denials of each of these possibilities to the antecedent (just as we do in the experiment), and of course there comes a point when even the most ingenious of subjects concedes the innocence of the suspect. Yet, there is no way to ensure that all the possibilities of guilt have been exhausted. Two morals follow: first, there is no guarantee of the validity of many everyday inferences, since one cannot be sure that all models of the premises lead to the conclusion; second, many everyday conditionals are incomplete: that is, their utterance, even when context is taken into account, does not suffice to establish precisely what proposition is being expressed. In particular, the antecedent situation may be radically underdetermined. Mental model theory copes with the indeterminacy of discourse in the following way: an initial model is constructed (perhaps even based on arbitrary choices) which can be revised recursively in the light of subsequent information. One obvious source of subsequent information is the consequent of the conditional. This point is brought out by Quine's (i960) revealing pair of examples: (54)

If Caesar had been in command in Korea, he would have used catapults

and: (55)

If Caesar had been in command in Korea, he would have used the atom bomb

In the first case, the consequent suggests an antecedent model representing the military technology of Caesar's day; in the second case, the consequent suggests an antecedent model representing Caesar's hawkish personality. Granted these respective models, then both conditionals are plausible, though their antecedents still remain too underdetermined to yield definite truth values. The major conclusion that follows from this tripartite analysis of conditionals is that the truth conditions of a conditional depend on establishing which category it belongs to: if it is a member of the first category, then it will be true given only that its consequent is true; if it is a member of the second category it will be true provided that its consequent is true in any model of its antecedent; if it is a member of the third category, then it is true if the consequent is true with respect to the model based on the antecedent and any relevant beliefs (including those triggered by the consequent) and there is no such model in which the consequent is false. However, in this third case, the antecedent may lack clear-cut truth conditions, and it will be impossible to establish whether the conditional is true or false. Since it is impossible to determine which of the three categories a conditional belongs to merely from its antecedent, it follows that its truth conditions depend on the relation between antecedent and consequent. 72

Conditionals and mental models 6. CONCLUSIONS This paper began with four questions, which I will now try to answer, treating them in reverse order. How do people reason with conditionals? They do so by setting up mental models of conditionals based on their interpretation of them, formulating informative conclusions, and then searching for alternative interpretations that refute these putative conclusions. They normally make no use of rules of inference, depending instead on their ability to interpret conditionals and to search for counterexamples. How do people interpret conditionals? They set up a mental model based on the meaning of the antecedent, and on their beliefs and knowledge of the context. They then determine the nature and degree of the relation between antecedent and consequent. This process may lead to a recursive revision in the antecedent model. Finally, if need be, they set up a scenario relating the model of the consequent to the antecedent model. The relation may be merely that the consequent state of affairs is relevant to a protagonist in the antecedent model, or it may be a logical, temporal, causal or deontic relation between the two models. What are the logical properties of conditionals? They are many and various. Conditionals are not creatures of a constant hue. Like chameleons, as I once put it, they take on the colour suggested by their surroundings. Their logical properties depend on the relation between antecedent and consequent, and that in turn depends on beliefs. Even where the antecedent specifies completely the state of affairs in which the consequent is to be evaluated, the relation may be an entailment: (56) If a man has a suit, then he has a jacket and trousers or a mutual entailment: (57) If a woman has a husband, then she is married The former supports inferences in the form of modus ponens and modus tollendo tollens; the latter, in addition, supports valid inferences of the form: Mary is married. Therefore, she has a husband Mary does not have a husband. Therefore, she is not married What do conditionals mean? If is a cue to consider a possible or hypothetical state of affairs. Where the relation between antecedent and consequent is one of 'relevance', the conditional is true if and only if its consequent is true. Otherwise, the conditional is true if and only if the consequent is true in the antecedent model and there is no alternative model in which it is false. The majority of conditionals, however, lack clear-cut truth conditions because their antecedents and the beliefs they trigger place insufficient constraints on the set of possible antecedent models. If the consequent is a request, or a question, or some other illocution, then the extension of the conditional is the same 73

P. N. Johnson-Laird mutatis mutandis. The states of affairs in which a request, for instance, should be carried out are those that correspond to the antecedent model. What I have presented in this paper is not, of course, a complete theory of conditionals. That would require a much more detailed and comprehensive account of the compositional semantics of conditionals, of their systemic contrast to other structures based on when, unless, because, and of the mental processes underlying the construction and manipulation of models. Nevertheless, mental models do seem to be one way - the only way that has so far been advanced - to make psychological sense of conditionals in the light of the work on 'possible world' semantics. NOTE i I am very grateful to David Lewis and Bob Stalnaker for criticisms of an earlier draft of this paper. REFERENCES Adams, Ernest. 1970. Subjunctive and indicative conditionals. Foundations of Language 6: 89-94. Austin, J. L. 1961. Ifs and cans. In Philosophical papers of J. L. Austin, ed. J. O. Urmson and G. J. Warnock. Oxford: Oxford University Press. Braine, Martin D. S. 1978. On the relation between the natural logic of reasoning and standard logic. Psychological Review 85: 1-21. Braine, Martin D. S. 1979. On some claims about if-then. Linguistics and Philosophy 3; 35-47Chisholm, Roderick M. 1946. The contrary-to-fact conditional. Mind 55: 289-307. Chomsky, Noam. 1977. Essays on form and interpretation. Amsterdam: North-Holland. Evans, Jonathan St B. T. 1982. The psychology of deductive reasoning. London: Routledge and Kegan Paul. Fillenbaum, Samuel. 1978. How to do some things with IF. In Semantic factors in cognition, ed. John W. Cotton and Roberta L. Klatzky, 169-214. Hillsdale, NJ: Lawrence Erlbaum. Goodman, Nelson. 1947. The problem of counterfactual conditionals. Journal of Philosophy 44:113-28. Grice, H. Paul. 1967. The William James lectures, Harvard University. Published in part in 1975 as Logic and conversation. In Studies in syntax, VOL. 3, Speech acts, ed. Peter Cole and Jerry L. Morgan, 64-75. New York: Academic Press. Griggs, Richard A. 1983. The role of problem content in the selection task and in the THOG problem. In Thinking and reasoning: psychological approaches, ed. Jonathan St B. T. Evans, 16-43. London: Routledge and Kegan Paul. Inhelder, Barbel and Jean Piaget. 1958. The growth of logical thinking from childhood to adolescence. London: Routledge and Kegan Paul. Isard, S. D. 1975. What would you have done if ...? Theoretical Linguistics 1: 233-55. Johnson-Laird, P. N. 1975. Models of deduction. In Reasoning: representation and process in children and adults, ed. Rachel J. Falmagne, 7-54. Hillsdale, NJ: Lawrence Erlbaum. Johnson-Laird, P. N. 1978. The meaning of modality. Cognitive Science 2: 17-26. Johnson-Laird, P. N. 1982. Formal semantics and the psychology of meaning. In Pro74

Conditionals and mental models cesses, beliefs and questions, ed. Stanley Peters and Esa Saarinen. Dordrecht: Reidel. Johnson-Laird, P. N. 1983. Mental models: towards a cognitive science of language, inference, and consciousness. Cambridge, Mass.: Harvard University Press; Cambridge: Cambridge University Press. Johnson-Laird, P. N. and J. Tagart. 1969. How implication is understood. American Journal of Psychology 82: 367-73. Legrenzi, Paolo. 1970. Relations between language and reasoning about deductive rules. In Advances in psycholinguistics, ed. Giovanni B. Flores d'Arcais and Willem J. M. Levelt. Amsterdam: North-Holland. Lewis, David. 1973. Counterfactuals. Oxford: Blackwell. Miller, George A., and P. N. Johnson-Laird. 1976. Language and perception. Cambridge, Mass.: Harvard University Press; Cambridge: Cambridge University Press. Oakhill, J. V. and P. N. Johnson-Laird. 1983. Cognitive load and the search for counterexamples. Laboratory of Experimental Psychology, University of Sussex, MS. Osherson, Daniel N. 1975. Logic and models of logical thinking. In Reasoning: representation and process in children and adults, ed. Rachel J. Falmagne, 81-91. Hillsdale, NJ: Lawrence Erlbaum. Partee, Barbara Hall. 1979. Semantics- mathematics or psychology? In Semantics from different points of view, ed. R. Baiierle, Urs Egli, and Arnim von Stechow, 1-14. Berlin: Springer-Verlag. Pollock, John. 1976. Subjunctive reasoning. Dordrecht: Reidel. Putnam, Hilary, 1975. The meaning of 'meaning1. Language, mind and knowledge, ed. Keith Gunderson, 131-93. Minnesota Studies in the Philosophy of Science, VOL. 7. Minneapolis: University of Minnesota Press. Quine, Willard Van Orman. 1952. Methods of logic. London: Routledge and Kegan Paul. Quine, Willard Van Orman. i960. Word and object. Cambridge, Mass.: MIT Press. Ramsey, Frank Plumpton. 1931. General propositions and causality. In The foundations of mathematics and other logical essays, ed. Frank Plumpton Ramsey. London: Routledge and Kegan Paul. Rescher, Nicolas. 1964. Hypothetical reasoning. Amsterdam: North-Holland. Rips, Lance J. 1983. Cognitive processes in propositional reasoning. Psychological Review 90: 38-71. Rips, Lance J., and Sandra L. Marcus. 1977. Suppositions and the analysis of conditional sentences. In Cognitive processes in comprehension, ed. Marcel Adam Just and Patricia A. Carpenter, 185-220. Hillsdale, NJ: Lawrence Erlbaum. Russell, Bertrand. 1905. On denoting. Mind 14: 479-93. Ryle, Gilbert. 1949. The concept of mind. London: Hutchinson. Stalnaker, Robert C. 1968. A theory of conditionals. In Studies in logical theory, ed. Nicolas Rescher, 98-112. Oxford: Blackwell. Stalnaker, Robert C. 1975. Indicative conditionals. Philosophia 5: 269-86. Stalnaker, Robert C. 1981. A defence of conditional excluded middle. In Ifs: conditionals, belief, decision, chance and time, ed. William L. Harper, Robert C. Stalnaker and Glenn Pearce, 87-104. Dordrecht: Reidel. Wason, Peter C. 1966. Reasoning. In New horizons in psychology, ed. Brian M. Foss. Harmondsworth, Middx.: Penguin. Wason, Peter C. 1983. Realism and rationality in the selection task. In Thinking and reasoning: psychological approaches, ed. Jonathan St B. T. Evans, 44-75. London: Routledge and Kegan Paul. Wason, Peter C , and P. N. Johnson-Laird. 1972. Psychology of reasoning: structure and content. Cambridge, Mass.: Harvard University Press. 75

CONDITIONALS: A TYPOLOGY • Bernard

Comrie

1. INTRODUCTION The aims of this paper are, first, to attempt a characterization of conditionals that has crosslinguistic validity and, second and more important, to try to identify the significant parameters in the crosslinguistic description of conditionals, looking both at properties that are common to all languages and at properties that show significant crosslinguistic variation.1 The claim that a given parameter of variation is significant is, of course, an empirical claim, and it may well be that in further work on this topic other parameters, of which I am unaware or which I consider insignificant, will need to be added to my list. Two general remarks are necessary before embarking on the characterization of conditionals and crosslinguistic variation within conditionals: these relate to the general problem of isolating a given construction, both intralinguistically and interlinguistically, and to the general problem of identifying the meaning of a construction. I assume that a given construction is to be identified, in general, in terms of a prototype rather than in terms of necessary-and-sufficient conditions. Thus, I will not be surprised if some sentences having the form of prototypical conditionals in a given language do not in fact receive the interpretation of conditions (as when English If you do that, I'll hit you is interpreted as a prohibitive), nor if sentences that do not have the form of prototypical conditionals nonetheless receive a conditional interpretation (cf. the parallel interpretations in English of / / he came late, he was punished and Whenever he came late he was punished). Furthermore, I distinguish strictly between the meaning of a construction and its interpretation, claiming that many aspects of interpretation that are traditionally assigned to the semantics of a construction or sentence are in fact conversational implicatures (in the Gricean sense) that are not part of the meaning of the sentence, and can in fact be cancelled in appropriate circumstances. This last point will become particularly important in the discussion of degrees of hypotheticality (section 5). As a simple illustration, we may return to the example (1) If you do that, I'll hit you Under normal circumstances, this will be interpreted as indicating that if the addressee does not carry out the action referred to, then the speaker will not 77

Bernard Comrie

hit the addressee, i.e. the if is interpreted as if and only if; however, other examples show clearly that English // is not necessarily interpreted in this way: (2)

If you buy those stocks, then you'll lose your money, but of course you'll probably lose your money anyway

In terms of the context in which If you do that, I'll hit you is normally uttered, the conversational implicature that if is to be interpreted as 'if and only if falls out naturally: the utterance is intended as a prohibition, giving motivation to comply with the prohibition (namely, not getting hit). If the speaker hits the addressee anyway, or rather, if the addressee assumes that the speaker may hit the addressee anyway, then the motivation behind the prohibition is lost, i.e. the utterance becomes incoherent.2 2. C H A R A C T E R I Z A T I O N OF CONDITIONALS In logic, conditionals (material implications) are defined as a relation between two propositions, the protasis (p) and the apodosis (q), such that either p and q are both true, or p is false and q is true, or p is false and q is false; excluded is the possibility of p being true while q is false. I maintain that this logical characterization is part of the characterization of conditionals in natural language (though, as will be seen below, a further restriction is necessary in natural language). Many conditional sentences in natural language do indeed receive an interpretation congruent with this range of possibilities allowed in logic, e.g. (3)

If today is Sunday, the priest will be in church

(as said by someone who is in fact unsure what day of the week it is - this caveat is not essential, but makes for more plausible interpretations). This allows that today is Sunday, and that the priest is in church. However, should it turn out that today is not in fact Sunday, then the proposition remains true whether or not the priest is in church. All that is excluded is that today should be Sunday and that the priest should not be in church. In examining actual utterances in actual contexts, the interpretation of a conditional may be more restrictive than this, in particular by excluding the possibility of '~p and q\ Thus, if someone says (4)

If you go out without the umbrella, you'll get wet

then the normal interpretation is that if the addressee does take the umbrella (and uses it in the appropriate way), then the addressee will not get wet. In fact, however, this is not part of the meaning of the conditional, but only a conversational implicature, which can be derived from other aspects of the interpretation of the sentence in context. Given Grice's overall injunction to 78

Conditionals: a typology be relevant, and knowing that people in general prefer not to get wet, and that umbrellas are typically used to prevent getting wet, the only coherent interpretation of the utterance is as a warning to take the umbrella to prevent getting wet. If the speaker saying If you go without the umbrella, you'll get wet knows full well that the umbrella has so many holes that it won't keep the addressee dry, then strictly speaking the speaker has not made a false statement, although he has made a misleading one (perversely so). This suggests a universal, which I will now formulate as a hypothesis. If a language has any conditional construction, then it will have one where the logical relation between the two propositions is the same as that given for material implication in the propositional calculus. From this, it follows that a language should not just have a construction with the meaning: '/? if and only if q* (i.e. the conditional is true if p and q are both true or both false, but not otherwise). This does not exclude the possibility that a language might have, in addition, conditionals with this more restricted truth table. Thus, in English the conjunctional phrase provided that encodes just such a biconditional, e.g.: (5)

Provided that no one objects, we'll have the meeting at 4 o'clock

(from which we deduce, without any appeal to conversational implicatures, that if anyone objects the meeting will not be held at 4 o'clock and that if no one objects the meeting will be held at 4 o'clock). English unless has a similar biconditional interpretation, though with negation of the protasis, thus: (6)

Unless you leave immediately, you'll be late

has the interpretation 'If and only if you do not leave immediately, you will be late' (see Quirk etal. 1972: 781).3 One further point that follows from the above characterization of the logical relation between protasis and apodosis is that, in the conditional construction, neither of these propositions is stated to be true. Apparent counterexamples come to mind, as in the following dialogue: A: I'm leaving now B: If you're leaving now, I won't be able to go with you Note that B can say this even fully accepting that A is indeed leaving now. What is crucial, however, is that the truth of 'A is leaving now' is not part of the meaning of the conditional sentence, although it may indeed form part of the overall interpretation of the context of which B's utterance forms only one part. This can be seen from the contrast between B's utterance above and the alternative: (7)

Since you're leaving now, I won't be able to go with you

This alternative states explicitly that A is leaving now, and therefore commits B to not going with A. The conditional version still leaves open, however, 79

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the possibility that, if A changes his mind, then B will in fact go with him. Thus, in a conditional if p then q, there is no statement of the truth of either p or q, although this is of course consistent with the truth of p or q being established elsewhere in the context. The related question of whether conditionals can express the falsity of p or q is crucial to the discussion of counterf actual conditionals, and I will return to this problem in section 5. Most descriptions of English sentences like: (8)

If he had come, I would have been happy

state that it is in fact false that he came and false that I was happy, but in section 5 I suggest that this is not the case in English, and that the comparable data require further investigation for other languages. Thus it is possible that a stronger generalization may be forthcoming, namely: from a conditional neither the truth nor the falsity of either p or q can be deduced (though they may be derived by implicature or from context). One feature of the characterization of material implication in logic is that the only relation that need hold between protasis and apodosis is that expressed in the truth table, so that otherwise totally unrelated propositions may appear as protasis and apodosis, subject only to the condition that they have appropriate truth values, as in: (9)

If Paris is the capital of France, two is an even number

(10)

If Paris is the capital of Spain, two is an odd number

(11)

If Paris is the capital of Spain, two is an even number

This does not carry over to natural language, where conditionals require a stronger link between protasis and apodosis. In most instances (see below for exceptions) this link is causal, i.e. the content of the protasis must be interpretable as a cause of the content of the apodosis. We therefore add this as a second requirement in the characterization of conditionals in natural language. One might hypothesize that the causal relation is a conversational implicature, rather than part of the meaning of the conditional; but, while I have no strict data arguments against this, it does not correspond to my intuitions about the anomaly of sentences of the type given above - they are false because they require a causal relation that is not there. Conditionals are of course still distinct from causal constructions, in that causal constructions involve commitment to the truth of two propositions, thus: (12)

Since you're leaving now, I won't go with you

commits the speaker to believing that the addressee is leaving now and that the speaker will not go with the addressee, whereas: (13)

If you're leaving now, I won't go with you

commits the speaker to neither. 80

Conditionals: a typology The causal relation is from the protasis as cause to the apodosis as effect. In section 6 we will discuss some conditional constructions with an inverse causal relation, i.e. where the apodosis is a cause for the protasis, as in: (14)

If it will amuse you, I'll tell you a joke

where my telling the joke is the cause of your being amused. Note, however, that in such examples there is also a causal relation from protasis to apodosis: your future amusement is the cause for my telling the joke. Thus such constructions are actually bicausal, and therefore consistent with the claim that conditionals necessarily involve a causal relation from protasis to apodosis. Causal relations in language in general may involve not only the literal content of propositions but also the speaker's motivation for making the claim that includes a proposition. Thus, the most usual interpretation of: (15)

John is a thief, because I saw him stealing

is not that my seeing John steal caused him to be a thief, but rather that my seeing John steal is the reason for my believing that he is a thief (epistemic). In the example: (16)

Since you asked, ten isn't a prime number

the addressee's asking provides the reason not for ten being a nonprime number, but rather for the speaker's asserting this (speech act).4 This same kind of causal relation is possible in conditionals. Under normal circumstances the following sentence would be rejected as incoherent: (17)

If Bismarck is the capital of North Dakota, then Pierre is the capital of South Dakota

because there is no causal link between the two propositions. The sentence becomes coherent, however, if embedded in the following dialogue: A: What's the capital of South Dakota? B: I'm not sure. Bismarck and Pierre are the capitals of the two Dakotas, but I'm not sure which is which A: Bismarck is the capital of North Dakota B: If Bismarck is the capital of North Dakota, then Pierre is the capital of South Dakota Here, the causal link is not directly between Bismarck being capital of North Dakota and Pierre being capital of South Dakota but rather between B's knowledge that Bismarck is capital of North Dakota and the epistemic basis of B's claim that Pierre is capital of South Dakota. An example of the speech act type would be: (18)

If you want to know, ten isn't a prime number

An apparent counterexample to the causal link in conditionals is provided by constructions with even if: 81

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(19)

Even if you pay me, I still won't do it

which clearly does not have as part of its meaning 'Since you will pay me, I will do it'.5 In fact, part of the meaning of this sentence is precisely the denial of a causal link between protasis and apodosis. This last observation gives a clue to a possible way to incorporate such constructions into our general characterization of conditionals. Common to all types is reference, in the semantics of the construction, to a causal relation between protasis and apodosis; whether the causal relation is presented positively or negatively simply distinguishes subtypes. One might compare the following example: (20)

I will do this, not because I want to, but because you have forced me to

where the second clause explicitly denies a causal relation between the speaker's wanting to do something and his doing it, even though the second clause is surely still causal. The characterization of conditionals provided so far is purely in conceptual terms, i.e. the logical relation between two propositions and the causal relation between them. To say that a language has a conditional construction or conditional constructions, we need to add to these conceptual criteria a formal criterion, namely that the language must have a formally identifiable syntactic construction whose basic function is to encode conditionals as defined above. The construction may have other uses in addition to that of expressing conditionals, but this must be its basic function. One can weaken the definition slightly, requiring only that encoding conditionals be one of the basic functions of the construction in question, and in what follows I will normally use this weaker characterization. Thus, a German sentence like: (21)

Wenn er kommt, gehe ich weg

will be considered an instance of a conditional in its interpretation 'If he comes, I leave', but not in its interpretation 'When he comes, I leave'.6 The weaker definition has the advantage of encompassing a broader range of constructions crosslinguistically, about which it is possible to make significant crosslinguistic generalizations. It does, of course, also have the disadvantage that it becomes more difficult to isolate conditionals from other constructions: thus, in Mandarin, the sentence: (22)

Zhangsan he jiu, wo ma ta lit. 'Zhangsan drink wine, I scold him'

covers a wide range of possible relations between the two clauses ('If/when/because Zhangsan drinks wine, I scold him'), with little evidence for isolating a separate conditional meaning.7 This characterization also allows that other constructions may receive conditional interpretations, provided that this is not their basic meaning. Thus, appro82

Conditionals: a typology priate modification of the modality in concessive clauses can produce results that receive the same interpretation as conditional clauses with even, as in: (23)

Although he may look a fool, he's actually very intelligent

and (24)

Even if he looks a fool, he's actually very intelligent

Likewise, insertion of indefinite ever into temporal clauses can lead to interpretations identical to those of conditionals: (25)

Whenever he came late, he was scolded

and: (26)

If he came late, he was scolded

Note, incidentally, that neither of the last two sentences: (unlike the parallel version with just when) implies that he did ever come late, although with past time reference the sentences are not particularly coherent if the potential situation of his coming late was never realized; the potentiality is clearer with future time reference: (27)

Whenever/if he comes late, he will be scolded

3. CLAUSE ORDER The definition of the logical relation holding in a conditional construction, as given in section 2, also distinguishes between the two propositions or their linguistic reflection as clauses, i.e. protasis and apodosis: the conditional allows that the protasis may be false and the apodosis true, but not vice versa. (The causal relation from protasis to apodosis reinforces this distinction.) Greenberg (1963: 84-5) states the following Universal of Word Order 14 concerning the linear order of the two clauses: In conditional statements, the conditional clause [=protasis, BC] precedes the conclusion [=apodosis, BC] as the normal order in all languages. Work leading up to the present paper has uncovered no counterexamples to this generalization. Although many languages allow both orders, protasisapodosis and apodosis-protasis, many grammars note explicitly that the usual order is for the protasis to precede, and presumably the same will hold for many languages where the grammars are silent on this point. In some languages the protasis must precede the apodosis, in particular in languages with a rigid rule requiring the finite verb of the main clause to stand sentence-finally (e.g. Turkish). Since the positioning of protases in such languages can be viewed as just a special case of the general rule whereby subordinate clauses must precede main clauses, this does not necessarily say anything specific about conditional 83

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constructions. However, this same restriction to protasis-apodosis order is also found in some languages which do not have a strict subordinate-main clause order restriction, suggesting that there is indeed something special about conditional clauses in this respect, i.e. the preponderance of the protasis-apodosis order in languages with free clause order is not 'just statistical', but does reflect something significant about language. In Mandarin, the protasis must precede the apodosis, irrespective of whether either protasis or apodosis is marked overtly, e.g. (28)

(ruguo) Zhangsan he jiu, wo (jiu) ma ta lit. '(If) Zhangsan drink wine, I (then) scold him' i.e. 'if Zhangsan drinks wine, (then) I will scold him'

In Ngiyambaa, with past tense counterfactuals, both clauses have the same overt marking (with the clitic -ma), and the first must be interpreted as protasis, e.g.: (29)

Nginuu-ma-ni buraay giyi, ngindu-ma-ni yada gurawiyi lit. 'your-counterfactual-this child was, you-counterfactual-this well looked-after' i.e. 'if this child had been yours, you would have looked after it well' (Example from Donaldson 1980: 251-2)8

Given the observational universal that the protasis tends to precede the apodosis, it is interesting to try to come up with possible explanations for this state of affairs. The suggestions below are necessarily speculative, and it is not necessary that only one of them be the correct solution: possibly the interaction of all or some of these factors leads to the observed preferred clause order. Given that it seems to be commoner crosslinguistically for the protasis to be marked overtly as nonfactual than for the apodosis to be so marked (see section 4), placing the overtly marked protasis in front of the unmarked apodosis avoids the apodosis being interpreted as a factual statement. Thus, in English: (30)

If you translate this for me, I'll give you $100

it is clear from the outset that the speaker is not promising outright to give the addressee $100, but that this payment is contingent on the addressee performing the translation task. With the order: (31)

I'll give you $100 if you translate this for me

there is the potential danger that the first clause will be interpreted in isolation, before (or without) hearing the second clause. If this were the whole story, then some interesting predictions would follow. In particular, one would expect that in a language or in a construction where the apodosis is overtly marked as nonfactual it would be more likely for the apodosis to precede than in languages/constructions where the apodosis is not overtly marked for factuality. 84

Conditionals: a typology Unfortunately, I know of no evidence that this prediction is in fact borne out; rather, my current impression is that preposing of the protasis prevails even where the apodosis is marked for factuality. Moreover, in conditionally interpreted sentences where the protasis is not marked overtly as nonfactual, one might expect to find greater frequency of preposing of the apodosis (whether marked or not), since the protasis does not here serve a function of indicating nonfactuality overtly. Note, however, that in Mandarin, as mentioned above, the protasis necessarily precedes the apodosis, whether the protasis alone is marked for nonfactuality (by a conjunction such as ruguo 'if), whether the apodosis alone is marked (for instance by na and/or jlu 'then, in that case'), whether both are marked, or whether neither is marked. Likewise, in English one can have the order: (32)

Do that and I'll smash your face

as an equivalent to: (33)

If y ° u do that, I'll smash your face

even though the protasis in isolation appears to be an instruction to the addressee to carry out the action which it is in fact the speaker's intention to prevent; it is not possible to say: (34)

I'll smash your face and do that

with the same meaning. Thus, if overt indication of nonfactuality is at the root of the observed clause order, then this factor has been grammaticalized to such an extent that its original function is scarcely recognizable. A second possibility would be that the linear order of clauses reflects the temporal reference of the two clauses. It is indeed generally the case that the temporal reference of the protasis is located before, or at least not posterior to, that of the apodosis (see section 6). This explanation would suggest that if the temporal relation is reversed, the clause order should (at least statistically) shift. In section 6 are discussed conditionals where the temporal reference of the protasis follows that of the apodosis, constructions such as: (35)

If it will amuse you, I'll tell you a joke

The prediction is thus that the order: (36)

I'll tell you a joke, if it'll amuse you

should be more likely than: (37)

I'll tell you another joke, if that one amused you

(In (37) the protasis precedes the apodosis temporally.) This prediction now simply requires empirical testing. I doubt whether such testing will be easy, given the low textual frequency of conditionals where the temporal reference of the apodosis precedes that of the protasis, but at least the issue is clear. 85

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Thirdly, the observed linear order may reflect the cause and effect relation between the two clauses: since cause precedes effect (at least in our conceptualization of the world), it could be that this is mirrored iconically in the order of the clauses. Unfortunately for this hypothesis, it does not seem to be the case that causal clauses typically precede rather than follow their main clause (except, of course, in languages that have a syntactic requirement that all subordinate clauses precede their main clause). While the discrepancy between protases and causal clauses may be related to their different characteristic communicative dynamism (conditional clauses are more topical, causal clauses more rhematic), this just pushes the question one stage back: why is it that this communicative difference exists between conditional protases and causal clauses? The fourth suggestion is that made by Lehmann (1974), and relates directly to the structure of discourses containing conditional constructions. Lehmann notes that in any discourse it is necessary for the participants to gain common ground step by step. In this process of establishing common ground, a conditional protasis represents progress in its establishment in a disjunctive situation: there are two possibilities (namely, p and ~/?), and before communication can progress, it is necessary for the speaker to establish which of the disjuncts is to be considered; only then can the argumentation proceed. From this perspective, the linear order of the clauses is iconic to the sequence of steps in the argumentation. A similar idea has been presented and elaborated by Haiman (1978), who claims that conditionals (i.e. protases) are topics. Since topics tend crosslinguistically to occur sentence-initially, it would follow that conditional protases should also occur sentence-initially. In this connection it is worth citing Haiman's characterizations of conditionals and topics: A conditional clause [=protasis, BC] is (perhaps only hypothetically) a part of the knowledge shared by the speaker and his listener. As such, it constitutes the framework which has been selected for the following discourse. The topic represents the entity whose existence is agreed upon by the speaker and his audience. As such, it constitutes the framework which has been selected for the following discourse. (Haiman 1978: 583, 585) If this approach is correct, then it would still be the case that some degree of grammaticalization has taken place, since it is, of course, possible to have conditional protases in discourse that are not topical, as in: (38)

I will leave, if you pay me

in response to: (39)

Under what circumstances will you leave?

where the protasis is focus (and, like focus in general crosslinguistically, tends to occur sentence-finally).9 86

Conditionals: a typology 4. MARKERS OF PROTASIS AND APODOSIS In this section I am concerned with how a construction is marked overtly as being a conditional rather than some other formal or conceptual category. As we have already seen, it is possible for a construction to have a conditional interpretation even in the absence of any overt indication of conditionality, as for instance in Mandarin - but this seems to be quite exceptional across the languages of the world. Most languages mark either the protasis, or the apodosis, or both. It is important to note that what is at issue here is the category of conditional as a whole, irrespective of the degree of hypotheticality of the conditional. Thus, in English: (40)

If he had done that, we would have been all right

the use of the conditional in the apodosis we would have been all right indicates nonfactuality (indeed, the most likely interpretation is counterfactuality). However, (a) this does not in itself indicate explicitly that this proposition is dependent on some other conditional proposition, and, even more importantly, (b) in conditional constructions with lower hypotheticality, verb forms are used which do not in themselves indicate nonfactuality, as in: (41)

If he does that, we will be all right

where we will be all right could in isolation be a factual prediction. In all such examples, however, English indicates conditionality by the conjunction if, therefore this marker (which is part of the protasis) is the overt marker of conditionality. Overt marking of the protasis seems to be the commonest situation crosslinguistically, and languages like Mandarin and Ngiyambaa that do not mark the protasis overtly seem to be the exception rather than the rule.10 I know of no language where it is obligatory to mark the apodosis but impossible to mark the protasis, although Mandarin does allow as one alternative the construction where the protasis is unmarked and the apodosis marked (Zhangsdn he jiu, wd jiu ma ta). Overt marking of the protasis is frequently by means of conjunctions, such as English if, Maltese jekk and kieku (distinguished by degrees of hypotheticality - see section 5), Mandarin ruguo, Haya kd (Salone 1977: 151). But it may also be by verb form, as in Turkish gelirsem 'if I come', gelsem 'if I were to come' (where the verb form also encodes degrees of hypotheticality- Lewis 1967: 130), Hua -mamo and -hipana (distinguished by degrees of hypotheticality - Haiman 1980: 180-7). Other possibilities for marking the protasis seem to be more restricted, e.g. subject-verb (or subject-auxiliary) inversion in German and English: (42)

Hatte er das getan, ware ich gliicklich gewesen 'Had he done that, I would have been happy'

where the initial position of the verb in the first clause indicates conditionality. 87

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Many languages with overt marking of the protasis typically do not mark the apodosis. Although English can mark the apodosis explicitly with then, it is in fact rather unusual to do so; similarly in Russian with to (in Russian, the protasis is marked with esli 'if). In some languages, overt marking of the apodosis is much more frequent, for instance in German (with so) and in Bengali (Ferguson 1982); and overt marking of the apodosis is claimed to be obligatory for some native speakers of New Guinea Pidgin (Sankoff and Laberge 1973), the only language where I am aware of an obligatory apodosis marker. All cases known to me of overt apodosis marking involve particles, often (as pointed out by John Haiman) of pronominal origin, and therefore perhaps analysable as resumptive pronouns. One interesting observation, tying in with the observations in section 3 on the functional pressure to mark conditionals overtly for their nonfactuality, is that there seems to be some interplay between degree of overt marking in the protasis and degree of overt marking in the apodosis. Thus, in German, the use of so in the apodosis is more likely if the protasis uses inversion (less clearly marked for conditionality) than if it uses the conjunction wenn.

5. D E G R E E S OF HYPOTHETICALITY Accounts of conditional constructions, starting with traditional descriptions of the classical languages, typically make use of such oppositions as open versus closed conditions, or real versus unreal, or real (open) versus hypothetical versus counterfactual, referring to different degrees of hypotheticality of the truth of the propositions involved. What is characteristic of most of these accounts is that they assume a neat bipartite or tripartite division (according to language), with a clear-cut boundary between the two or three types. The view that I wish to expound in this section is that, in fact, hypotheticality is a continuum, with (perhaps) no clear-cut divisions, and that different languages simply distinguish different degrees of hypotheticality along this continuum, the choice of form often being determined by subjective evaluation rather than by truth-conditional semantics. This avoids, in particular, the contorted and often empty formulations attempting to distinguish between real (open) and hypothetical conditionals, formulations such as 'nothing is implied about the fulfilment or probability of fulfilment' versus 'only conceded as a supposition and may or may not be fulfilled' (Kennedy 1962: 98), where it is difficult to see any rigid difference between the range of the two definitions. By the term 'hypotheticality', I mean the degree of probability of realization of the situations referred to in the conditional, and more especially in the protasis. I shall use the convention that 'greater hypotheticality' means 'lower probability' and 'lower hypotheticality' means 'greater probability'. Thus a factual sentence would represent the lowest degree of hypotheticality, while a

Conditionals: a typology counterfactual clause would represent the highest degree. In section 21 have already argued that a conditional never involves factuality - or more accurately, that a conditional never expresses the factuality of either of its constituent propositions. That one or other of the propositions is true may be known independently of the conditional, for instance from the rest of the verbal context or from other sources, but this does not alter the crucial fact that the conditional itself does not express this factuality. In context, the sentence: (43)

If it's raining, we won't go to the park

may well receive the interpretation (44)

Since it's raining, we won't go to the park

but this is not part of its meaning. Somewhat more controversially, I will claim that conditionals are also incapable of expressing the counterfactuality of a proposition, despite the apparent counterfactuality of such examples as: (45)

If you had arrived on time, we'd have finished by now

which clearly receives a counterfactual interpretation (at least, under normal circumstances).11 The motivation for my claim will be the consideration of so-called counterfactual conditionals in English. The relevant evidence goes beyond that usually considered in treatments of conditionals in English (although English is one of the most thoroughly investigated languages from this viewpoint), and therefore comparable evidence is difficult to find in grammars of other languages. The provisional nature of the claim, therefore, should be understood: I am claiming that English lacks counterfactual conditionals, i.e. a conditional construction from which the falsity of either protasis or apodosis can be deduced logically. I suspect that the same may be true of other languages where a separate class of counterfactual conditionals is said to exist; this suspicion is, of course, open to disconfirmation, and I am in fact anxious that the relevant detailed work should be carried out on languages other than English which are said to have counterfactuals. In English, there are two candidates for counterfactuals. First, conditionals with the past tense (indicative or subjunctive) in the protasis and the conditional in the apodosis; and second, conditionals with the pluperfect in the protasis and the conditional perfect in the apodosis. For the first type, it is easy to show that counterfactuality can be cancelled. Imagine the following dialogue: A: Will you buy me a beer? B: If you gave me a kiss, I'd buy you a beer With this particular example it is unlikely that B's utterance would be interpreted as counterfactual, i.e. as indicating falsity of a proposition stating that 89

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B will buy A a beer. Indeed, this particular utterance is most likely to be used by B in order to induce A to kiss B, whereupon B will be committed to buying a beer for A. B could, of course, also have said: (46)

If you give me a kiss, I'll buy you a beer

but what is crucial is the possibility of the version cited in the dialogue. (The version in the dialogue is more hypothetical than its alternative, i.e. suggests a lower probability of A's kissing B, which in the given circumstances might be used by B to avoid too negative an aspersion on A's morals.) For the second type, it is easy to show that counterfactuality is not part of the meaning of the apodosis, as can be seen in the following example: (47)

(Even) if I had had a million dollars, I (still) wouldn't have given you the money you asked for

The most plausible interpretation for this sentence (especially if either the even or the still or both are included) is that the speaker did not give the money asked for, i.e. that the apodosis is true. It is harder to find convincing examples where the protasis is not necessarily false, and speaker judgements do seem to vary somewhat. For many speakers, however, the following example will serve: (48)

If the butler had done it, we would have found just the clues that we did in fact find12

The final clause of (48) makes it clear that we did in fact find the clues in question, i.e. the apodosis is true; the sentence also leaves open the possibility that the butler did indeed do it. Thus, this construction does not have counterfactuality as part of the meaning of either protasis or apodosis. It is interesting to speculate on why counterfactuality should be a stronger implicature with conditionals that have past time reference than with those that have future time reference, with those with present time reference occupying an intermediate position. Presumably, it is connected with the expectation that one should have greater certainty about past events than about future events, so that a past situation that is nonfactual will probably be counterfactual, whereas a future situation that is nonfactual is quite likely to be just left open. Given that the construction with the greatest degree of hypotheticality does not imply counterfactuality in its interpretation, one might wonder whether one can perhaps make the inverse correlation, namely that a situation that is interpreted as counterfactual must receive the construction with the highest degree of hypotheticality. Even this seems, however, not to be true, as can be seen in the following dialogue: A: Are we in Bolivia now? B: If Brasilia is the capital of Bolivia, then we're in Bolivia 90

Conditionals: a typology Assume that B's reply is in fact sarcastic, i.e. B knows that they are in Brasilia, therefore in Brazil, and is making fun of A's mistaken belief that they are in Bolivia. Then both the propositions 'Brasilia is the capital of Bolivia' and 'we're in Bolivia' are counterfactual, B knows that they are counterfactual, and moreover B believes that A knows that at least 'Brasilia is the capital of Bolivia' is counterfactual (otherwise the sarcasm would be lost). What is crucial about this example is that B's utterance leaves completely open whether or not Brasilia is the capital of Bolivia, and thus does not express counterfactuality; indeed the sarcasm resides precisely in the conflict between the openness of the protasis and the factual knowledge that Brasilia is not the capital of Bolivia. This example serves to emphasize the point that by choosing a given degree of hypotheticality within conditional constructions, the speaker expresses a certain degree of hypotheticality; this expressed degree of hypotheticality need not correspond to his actual belief, much less to the real world. We may now turn to the positive task of providing a framework for the description of degrees of hypotheticality across languages. It should be noted that there are some languages which make no distinction in terms of degrees of hypotheticality, for instance Mandarin, where Zhangsan he-le jiu, wo jiu ma ta can cover all of 'If Zhangsan has drunk wine, I'll scold him', 'If Zhangsan drank wine, I would scold him', 'If Zhangsan had drunk wine, I would have scolded him' (Mandarin also makes no distinctions of absolute tense). Similarly in Indonesian: (49)

saya mau pergi dengan kamu, kalau kamu naik kapal-terbang lit. 'I future go with you, if you mount airplane'

can mean 'I will go with you if you go by plane', 'I would go with you if you went by plane', or 'I would have gone with you if you had gone by plane', although it is also possible to distinguish different degrees of hypotheticality explicitly (Kahler 1965: 180-1; Dardjowidjojo 1978: 159). At least a two-way distinction in terms of degrees of hypotheticality seems to be common crosslinguistically, however, and some languages make a three-way distinction. First, it is useful to deal with a class of conditionals which are completely open, i.e. where the protasis is simply stated as a hypothesis without any claim whatsoever to the truth, falsity, or probability of the protasis. In actual discourse such conditionals seem to be very rare, but in English, at least, they do have some distinctive properties. In particular, in English such protases can contain a future tense (with will), although normally future tenses do not occur in protases in English, being replaced by the present except in highly restricted circumstances (see further, section 6). Usually, the proposition contained in the protasis has already been entered into the discourse, as in the following dialogue: A: The Universe won't come to an end for several million years yet

Bernard Comrie

B: If it won't come to an end for several million years yet, we'll still be able to go to Florida this winter It is important to note that B is simply accepting, for the purposes of the argument, the hypothesis that A's proposition is true. In fact, the BrasiliaBolivia dialogue above is another example of this kind of completely open conditional, where, however, B does not in fact accept the truth of the proposition 'Brasilia is the capital of Bolivia'. In completely open conditionals of this type, English simply uses the verb form that would be used in an independent clause expressing the same proposition, i.e. with a full range of temporal, aspectual, and modal distinctions. I am not aware of a sufficient range of detailed studies of other languages to be able to make any serious crosslinguistic comments on this construction. For the remaining conditionals, the distinctions come into play relating to the speaker's expressed evaluation of the probability of the situation referred to in the protasis. English here makes a two-way distinction between lower and greater hypotheticality. Lower hypotheticality involves the indicative without any backshifting in tense, i.e. the past tense is used only if there is indeed past time reference, as in: (50a) If you come tomorrow, you'll be able to join us on a picnic or: (50b) If the students come on Fridays, they have oral practice in Quechua or (with past time reference): (51)

If the students came on Fridays, they had oral practice in Quechua

Greater hypotheticality involves backshifting in tense, so that with future time reference one finds the past tense in the protasis (corresponding to the present tense in conditionals with lower hypotheticality) and the conditional in the apodosis (corresponding to the future in conditionals with lower hypotheticality): (52)

If you came tomorrow, you'd be able to join us on a picnic

The same forms are found with present time reference, as in: (53)

If the students came on Fridays, they would have oral practice in Quechua

With past time reference, one finds the pluperfect in the protasis and the conditional perfect in the apodosis, as in: (54)

If the students had come on Friday they would have had oral practice in Quechua.13

Similar, though not identical, distributions are found in many European languages. Thus French, German, Russian, and Latvian have indicative mood 92

Conditionals: a typology without backshifting in tense in the construction with lower hypotheticality, but use the following verb forms in the construction with greater hypotheticality: French employs the imperfect in the protasis and the conditional in the apodosis; German the past subjunctive or the conditional (i.e. form with wurde) in both clauses; Russian and Latvian the conditional in both clauses. In these languages, degrees of hypotheticality are indicated by choice of verb form, but some languages also indicate this by different conjunctions. Thus, in Maltese jekk 'if is used for lower hypotheticality and kieku for greater hypotheticality. Yapese has a distinction between faqdn raa (less hypothetical) and yugu raa or (goo)mangea (described as 'counterfactual' - Jensen 1977: 316-18). In Ngiyambaa, as already noted in section 3, greater hypotheticality (or counterfactuality?) is indicated by the clitic -ma in both clauses. Classical Greek seems to be unusual in having its marker for higher hypotheticality, an, only in the apodosis. Some languages make a three-way distinction in this area, as in the following Latin examples from Cicero: type I (indicative) Si vales, bene est 'If you are in good health, all is well'; type II (subjunctive without shift to past tense) Hanc vlam si asperam esse negem, mentiar 'If I were to deny that this road is rough, I should lie'; type III (subjunctive with shift to past tense) Si ad centensimum annum vixisset, senectutis earn suae paeniteret? 'If he had lived to his hundredth year, would he be regretting his old age?' (Kennedy 1962: 98-9). Similarly in Persian, again arranged in order of increasing hypotheticality: agar miravi, agarberavi, agarmirafti, respectively indicative, subjunctive, conditional (formally, a past tense) 'if you are/were going' (Windfuhr 1979: 92). 6. TIME REFERENCE In this section we shall be concerned with overt expression of time reference in conditionals, concentrating on those instances where the time reference of verb forms is different in a conditional from that found in other constructions. Two sets of time reference turn out to be particularly interesting here: time reference in conditionals with high hypotheticality (especially with nonfuture time reference), and time reference in conditionals with low hypotheticality and future time reference. I suspect that these two sets of conditionals are in fact the most basic, in the sense that they are the most used in actual discourse, and in that grammars of individual languages are more likely to require overt reference to these classes of conditionals. Grammars of many languages discuss only these two sets of conditionals, or at least restrict their examples to these two kinds. One frequent phenomenon crosslinguistically in conditionals with high hypotheticality is loss of tense distinctions. In an extreme form, this can be seen in Russian, which has a three-way tense distinction (past/present/future), but no tense distinction whatsoever in conditionals with high hypotheticality, 93

Bernard Comrie e.g.: (55)

Esli by ty prisel, ja byl by rad 'If you came/had come I would be/have been glad'

A less extreme neutralization is found in Latvian, where the usual three-way tense distinction (past/present/future) is reduced to a two-way opposition between past time reference (conditional perfect) and nonpast time reference (conditional): (56) (57)

Ja es butu aizgajis, jus mani nebutu redzejis 'If I had gone away, you would not have seen me' Es stradatu, ja vins man maksatu 'I would work if he paid me' (Examples from Fennell and Gelsen 1980: 188, 512)

English shows a similar tense reduction. In conditionals with low hypotheticality, the three-way distinction (past/present/future) is maintained - although the present/future opposition is neutralized in the protasis, it is retained in the apodosis, as in: (58)

If he comes (regularly), I run away

versus: (59)

If he comes (tomorrow), I'll run away

However, in the conditional with greater hypotheticality, the present/future opposition is neutralized: (60)

If (ever) he came, I would run away

and (61)

If he came (tomorrow), I would run away

One aspect of time reference that is common in Indo-European and European-area languages in conditionals with high hypotheticality is backshifting of tense, i.e. use of a morphologically past tense with present (or future) time reference and of a pluperfect with past time reference, as in English: (62)

If he came, I would run away

(63)

If he had come, I would have run away

Apparently, some varieties of English can even backshift a pluperfect to 'plupluperfect', a form that does not otherwise occur in English, as in: (64)

If he'd 've come, I'd 've run away

- although the analysis of this verb form in the protasis (had/'would have/of come?) is controversial. Backshifting of tense is not, however, restricted to 94

Conditionals: a typology these languages. Thus in Haya, in conditionals with high hypotheticality, present time reference is expressed by the recent past tense, while past time reference is expressed by a sequential combination of recent past tense and intermediate past tense markers (Salone 1977: 155-7). F ° r a more extended crosslinguistic study, see James (1982). The indication of time reference in protases of conditionals with low hypotheticality and future time reference is particularly complex crosslinguistically, as discussed in Comrie (1982). Basically, four types can be distinguished. In type one, the expected future tense is used, as in Latvian: (65)

Ja tu runasi (future), es tevi dzirdesu 'If you speak, I'll hear you'

In type two, the present indicative is used with future time reference, even in languages where there are heavy restrictions on this use of the present tense, as in English: (66)

If it rains tomorrow, I'll take an umbrella (cf. *it rains tomorrow)

In type three, present tense is used, but in a non-indicative mood, as in Armenian, where the present subjunctive is used: (67)

Yethe du gas (present subjunctive), yes ka-ganam 'If you come, I will go'

In the fourth type, a form is used which is neither present nor indicative, as in Portuguese, where the so-called future subjunctive appears: (68)

Se voce nao vier (future subjunctive), eu vou sair 'If you don't come, I will leave'

Note that in each of these examples, the apodosis remains in the future indicative (or whatever verb form is usual in the given language for expressing future time reference). In fact, the situation is more complex than these straightforward examples suggest, as can be seen by more detailed examination of English (as an example of type two) and Portuguese (as an example of type four). The situation outlined above, with use of the present indicative or the future subjunctive, holds only where the temporal reference of the protasis precedes or overlaps that of the apodosis. This is, as noted in section 3, the usual temporal relation between protasis and apodosis, but conditionals are perfectly possible where the time reference of the apodosis precedes that of the protasis. In this case, Portuguese disallows the future subjunctive, resorting instead either to the compound future indicative (with the auxiliary ir 'to go') or, preferably, to the compound future of the future subjunctive: (69)

Se isso vai/for machucar voce, eu nao fa?o 95

Bernard Comrie

'If this will hurt you, I won't do it' In English, with this temporal relation between the two clauses, the future indicative is used, but only if there is a causal link from the apodosis (as cause) to the protasis (as effect), as in: (70)

If it will amuse you, I'll tell you a joke

where my telling you a joke is the cause of your amusement (in addition to my desire to amuse you being the reason for my telling the joke, i.e. there is a bicausal relation). Where this causal relation is lacking, some means other than the future tense must be used to indicate future time reference, such as the going to construction, as in: (71)

If it's going to rain, I'll take my umbrella

7. CONCLUSIONS In this paper I have tried both to give a definition of conditionals applicable to natural language and to isolate the major parameters that are necessary for the description and typologization of conditionals crosslinguistically. The definition proposed for conditionals combines material implication with the relevance of a causal relation from the protasis to the apodosis. The parameters discussed are clause order, marking of conditionality, degrees of hypotheticality, and time reference. It was noted that the most common clause order both crosslinguistically and within individual languages is for the protasis to precede the apodosis, and that for some constructions this order is obligatory, even in languages which do not have a general rule requiring subordinate clauses to precede main clauses. Although it is possible to have conditionals where neither protasis nor apodosis is explicitly marked as being part of a conditional, it is usual for the protasis to be overtly marked; marking of the apodosis is less common, and marking of the apodosis alone is particularly rare. It was argued that the notion 'degrees of hypotheticality' defines a continuum, with different languages making a different number of overt distinctions along this continuum, and it was hypothesized that no language has a specific form to mark counterfactuals (as opposed to conditionals of high hypotheticality). Concerning time reference, some languages neutralize the range of oppositions of time reference in conditionals, while backshifting of tense (e.g. a formal past tense with present time reference) is found crosslinguistically in conditionals with high hypotheticality; the commonest kinds of conditionals in actual use seem to be those of low hypotheticality with future time reference and those of high hypotheticality with past time reference, and these seem also 96

Conditionals: a typology to be the kinds of conditionals which most often have idiosyncratic rules referring to them in grammars of languages. The examples discussed at the end of section 6, together with some of the other English examples discussed in the text, show how complex the parameters involved in conditionals can become in their interaction. It is to be hoped that more detailed studies of conditionals in a wider range of languages will enable us to see what universals, if any, lurk behind these more complex interactions. NOTES 1 I have benefited greatly from discussion with participants in the Conditionals Workshop, Stanford University, May 1982, and the Symposium on Conditionals and Cognitive Processes, Stanford University, December 1983. I have also benefited, more than citations in the text would suggest, from discussion with Noriko Akatsuka, John Haiman, Eric Kellerman, and Johan Van der Auwera, and from the comments of my panel discussant, Joseph H. Greenberg. 2 Note that distinguishing meaning from interpretation does not mean abandoning the attempt to account for interpretations, but rather that the search for an account of interpretations will appeal to a number of components in addition to meaning - a comprehensive account must incorporate theories of all of these components. I am thus sympathetic to the analysis of interpretations of conditionals (see, for instance, Johnson-Laird in this volume), although I believe this analysis will be more fruitful if meaning and interpretation are distinguished more systematically. 3 As pointed out to me by John Haiman, the meaning of unless (and equivalent conjunctions in other languages) is much narrower than that of 'if and only if ... not'. Contrast the acceptable It'll be dark tomorrow if and only if the sun doesn't rise with the bizarre It'll be dark tomorrow unless the sun rises. However, the characterization given in the text is part of the meaning of unless. 4 I am grateful to Eve E. Sweetser for impressing on me the distinction between the epistemic and speech act types. 5 This point was made by several participants in the Symposium. 6 For a different approach to the relation between conditionals and temporals, see Haiman (1978). While I agree that it is necessary to account for the similarities (up to identity) between conditionals and temporals in many languages, it is also necessary to account for the differences between them in many languages. 7 Mandarin examples throughout are taken from Li and Thompson (1982). Note that in German, unlike Mandarin, the homophony of temporal and conditional constructions does not extend to all tense/aspects; thus, Wenn er gestern ankam, war er zu spat can only be 'If he arrived yesterday he was late' ('When ...' would have to be a/?...). 8 John Haiman informs me, on the basis of unpublished fieldwork by Lee Brandson, that in Gende (East New Guinea Highlands), neither protasis nor apodosis is overtly marked as such, and that either clause order is possible. 9 While I find it plausible that conditional protases are prototypically topics, as claimed by Haiman (or perhaps given, as claimed by Akatsuka in this volume), I find it less plausible that conditional protases should be defined as topics, since, for the reasons given in section 2, I believe that the notion of material implication is also important to the definition of conditionals and to their separation from other clauses 97

Bernard Comrie that may have topic status (such as temporal clauses). 10 Since most grammars available to me of Australian languages do not discuss conditionals, it is possible that Ngiyambaa may evince a more widespread areal trait here. 11 Stephen R. Anderson points out to me that English conditionals with if only are necessarily counterfactual, e.g. If only I had a thousand dollars I'd buy a computer. Further investigation of such constructions may therefore lead to weakening of the claim in the text, unless the counterfactuality can be attributed to some element not part of the expression of conditionality (e.g. be predicted from the semantics of only). 12 For further discussion of such examples, see Davies (1979: 157-62). 13 In fact, English overall seems to have more than two degrees of hypotheticality for nonpast conditionals, since here double backshifting (pluperfect in protasis, conditional perfect in apodosis) may be used, e.g. // you had come next Wednesday, you would have met Grannie, which is more appropriate than If you came ... you would meet... if the addressee has already indicated inability to come on Wednesday (Dudman 1983: 38-9).

REFERENCES Comrie, Bernard. 1982. Future time reference in conditional protases. Australian Journal of Linguistics 2: 143-52. Dardjowidjojo, Soenjono. 1978. Sentence patterns of Indonesian. Honololu: University Press of Hawaii. Davies, Eitian C. 1979. On the semantics of syntax. London: Croom Helm. Donaldson, Tamsin. 1980. Ngiyambaa: the language of the Wangaaybuwan. Cambridge: Cambridge University Press. Dudman, V. H. 1983. Tense and time in English verb clusters of the primary pattern. Australian Journal of Linguistics 3: 25-44. Fennell, T. C. and H. Gelsen. 1980. A grammar of modern Latvian. The Hague: Mouton. Ferguson, Charles A. 1982. Conditionals in Bengali. Paper presented at the Conditionals Workshop, Stanford University, May 21-22. Greenberg, Joseph H. 1963. Some universals of grammar with particular reference to the order of meaningful elements. In Universals of language, ed. Joseph H. Greenberg, 73-113. Cambridge, Mass.: MIT Press. Haiman, John. 1978. Conditionals are topics. Language 54: 564-89. Haiman, John. 1980. Hua: a Papuan language of the Eastern Highlands of New Guinea. Amsterdam: Benjamins. James, Deborah. 1982. Past tense and hypotheticality: a cross-linguistic study. Studies in Language 6: 375-403. Jensen, John T. 1977. Yapese reference grammar. Honolulu: University Press of Hawaii. Kahler, Hans. 1965. Grammatik der Bahasa Indonesia, 2nd ed. Wiesbaden: Harrassowitz. Kennedy, B. H. 1962. The shorter Latin primer, rev. edn. London: Longman. Lehmann, Christian. 1974. Prinzipien fur 'Universal 14'. In Linguistic Workshop II, ed. Hansjakob Seiler, 69-97. Munich: Wilhelm Fink Verlag. Lewis, Geoffrey L. 1967. Turkish grammar. Oxford: Clarendon Press. Li, Charles N., and Sandra A. Thompson. 1982. Conditionals in Mandarin. Paper presented at the Conditionals Workshop, Stanford University, May 21-22. Quirk, Randolph, Sydney Greenbaum, Geoffrey Leech and Jan Svartvik. 1972. A university grammar of English. London: Longman. Salone, Sukari. 1977. Conditionals. In Hay a grammatical structure, ed. Ernest R. Byarushengo, Alessandro Duranti, and Larry M. Hyman, 149-59. Los Angeles: Department 98

Conditionals: a typology of Linguistics, University of Southern California. Sankoff, Gillian and Suzanne Laberge, 1973. On the acquisition of native speakers by a language. Kivung 6: 32-43. Reprinted in Gillian Sankoff. 1980. The social life of language. Philadelphia: University of Pennsylvania Press. Windfuhr, Gernod L. 1979. Persian grammar. The Hague: Mouton.

99

PART II

PARTICULAR

STUDIES

ON THE INTERPRETATION OF 'DONKEY'-SENTENCES •

Tanya Reinhart Editors' note. Conditionals systematically affect the dependencies that may obtain between pronouns and their antecedents when they occur in the two different clauses of conditional sentences. Paradigmatic of such interactions are the 'donkey'-sentences which have preoccupied linguistic theory and philosophical accounts of reference and quantification for a considerable time. Reinhart's paper presents a syntactic and semantic account of such sentences. All indefinite noun phrases are taken to be bound by other quantifiers and operators. This resolves the problem of interaction and shows that the phenomenon can be generalized to a much wider class, including some plurals. 1. THE PROBLEM The so-called 'donkey'-sentences pose well-known problems both to the semantic theory of scope and to the theory of anaphora: u 1i)

a. If Max owns a donkey, he hates it b. If a vampire checks in, Lucie invites him to dinner

The pronoun in sentence (ia) can be anaphoric to a donkey, and the crucial point is that this is a case of bound-variable anaphora, rather than of pragmatic coreference. This can be observed if we compare such sentences with others having adverbial clauses, e.g.: (2)

a. When Max owned a donkey, he hated it b. Since a stranger came in with a donkey, we had to provide some hay for it

In the sentences of (2) the pronoun refers to a specific donkey. Although the antecedent is indefinite, it has a fixed value; hence, this is a case of pragmatic coreference. In the sentences of (1), on the other hand, there is no fixed value for, for example, a donkey that the pronoun can refer to. The value of the pronoun varies with the choice of value for a donkey, i.e. it behaves as a bound variable. The semantic problem is that under a standard interpretation of such sentences, as given in (3) for (ia), the pronoun is not in the scope of the quantifier which appears to bind it, so it cannot be bound: (3)

If (3x (x is a donkey and Max owns x)) then (Max hates x) 103

Tanya Reinhart (4)

*If Max owns every donkey he hates it

That, normally, quantified NPs in the position of a donkey in sentence (ia) cannot bind pronouns outside the (/"-clause, is shown also by the fact that the similar sentence in (4), with a universal quantifier, does not allow anaphora. The problem at issue is restricted to indefinite antecedents, or more generally, as we shall see later, to 'weak' NPs. A peculiar property of 'donkey'-sentences is that an alternative scope analysis exists in which the pronoun is in the scope of the binding quantifier, as in (5),for(ia): (5)

Vx (x is a donkey and Max owns x) (Max hates x) 'For every donkey, if Max owns it, he hates it'

In (5) the indefinite is interpreted as a universal, rather than an existential, quantifier, and this seems to yield correctly the truth conditions of (ia), since the sentence entails that Max hates every donkey he owns, if he owns any. If it turns out that Max has several donkeys and he only hates one of them, the sentence is false. (For a detailed defence of assuming such entailment see Heim 1982.) The same problem shows up also in relative clauses, as in (6): (6) (7) (8)

a. Every man who owns a donkey hates it b. Vx (x is a man and 3y (y is a donkey and x owns y)) (x hates y) Vx, Vy (x is a man and y is a donkey and x owns y) (x hates y) If a man owns a donkey, he hates it

In the standard scope analysis of (6a), given in (6b), the existential quantifier is embedded in the restrictive term of every, hence it cannot bind the pronoun. However, here too the indefinite NP can be interpreted as a universal rather than an existential quantifier, as in (7) (for every man x and every donkey y, if x owns y, x hates y), with the same entailment as before. In (7) the pronoun is bound by this quantifier, so anaphora is permitted. Note that the analysis in (7) also captures the truth conditions of the conditional in (8). Since this conditional contains two indefinite NPs, they are both translated as universal quantifiers. If the logical forms (LFs) (5) and (7) can be assumed for the sentences under consideration, the binding of the pronoun is no longer a semantic problem. However, the crucial problem is how such LFs can be derived from the surface structures of these sentences, as they appear to require operations which violate all known restrictions on semantic interpretation rules. The analysis for the 'donkey'-cases should explain how the indefinite becomes universally quantified, how it gets scope outside its clause, and what conditionals and relative clauses have in common (which explains their similarity in the case of 'donkey'-contexts). 104

On the interpretation of 'donkey'-sentences As we shall see in section 3, the answer to most of these questions is no longer a mystery, due to Heim's (1982) analysis of 'donkey'-contexts. Heim argues that indefinite NPs contain no quantifier, hence they can be bound by another operator, if they occur in its restrictive term at LF, as is the case with indefinites in both relative clauses and //-clauses. The universal force of the indefinites in the examples we examined follows, then, from the fact that they are bound by some other universal operator in the sentence. The LF (7) is, then, a case of pair quantification, where one universal operator binds two variables. However, questions arise when we consider cases where the operator available for binding the indefinite is not a universal, as in (9): (9)

a. Most women who have a dog talk to it b. Almost every woman who has a dog talks to it

A sentence like (9a) still entails that most women talk to every dog they have. However, the indefinite NP a dog here is not bound by a universal quantifier at LF, and the standard interpretation of the pair quantification derived from it does not yield the right truth condition. The universal force of the indefinites in such contexts is, then, independent of the operator in whose restrictive term it occurs. My question in this paper is: what is the source of this universal force? I argue that the answer follows from the set-interpretation of indefinite NPs, or 'weak' NPs in general. The universal entailment, then, is independent of the binding relations assumed by Heim, but this means that her analysis, which is crucial for explaining the anaphora in such cases, can be maintained. Although, as we shall see in section 2, the problem at issue is semantic and not pragmatic, the answer to the interpretation problem will be based on observing the behaviour of such NPs in discourse. 2. IS THE PROBLEM SEMANTIC OR PRAGMATIC? In view of the difficulties in interpreting 'donkey'-anaphora, a tempting move would be to argue that the pronouns in the 'donkey'-cases are not, in fact, bound variables, but are interpreted by some other coreference mechanism. An extensive critical survey of the various proposals along this line can be found in Heim (1982). Here we will consider only Evans's (1980) analysis, which seems the most promising. Evans argues for the existence of E-type pronoun interpretation, under which the pronoun is taken to refer to the object(s) which satisfy the clause containing a quantified NP (QNP). This type may be illustrated with (10): (10)

a. Lucie has many cats and they are so cute b. Every guest brought three bottles to the party. By midnight, they were (all) empty

Since the pronouns here occur outside the sentence containing their quantified 105

Tanya Reinhart antecedent, they cannot be in the QNP's scope. (Evans provides further arguments supporting this which will be mentioned in section 4.) The pronouns are construed, then, as referential, but their reference depends on the choice of value for the QNP in the first sentence. In (10a) the pronoun refers to (all) the cats that Lucie owns. Although Evans does not discuss this, we may assume that the same interpretation is available also when the indefinite is in the scope of another quantifier: in (iob) the pronoun refers to all the bottles which turn out to satisfy the first quantified proposition. In the 'donkey'-contexts, such as (11): (11)

Every guest who brought three bottles put them in the refrigerator

both the QNP antecedent and the pronoun are in the scope of another quantifier {every). The antecedent clause contains a variable bound by every. Hence, the relevant value selected for the pronouns is the bottles satisfying x brought three bottles and this value varies with the choice of value for x. Evans's basic intuition concerning the interpretation of E-type pronouns is, I believe, correct. In section 4 I argue that a way to capture this intuition is to view his E-type pronouns as set-pronouns (denoting maximal sets of their members). This enables us to avoid certain problems with interpreting Evans's proposal that were pointed out by Heim (1982). The crucial question which remains, however, is whether in the 'donkey'-cases the anaphora can be viewed, indeed, as a case of coreference, or whether the set-pronoun must, nevertheless, be interpreted as bound. Note, first, that some notion of binding is implicit in the analysis of why the interpretation of the pronoun is different in the 'donkey'-context (11) from its interpretation in the cross-sentential anaphora in (iob). (The pronouns here denote different sets: if there were ten guests who brought each exactly three bottles the pronoun in (iob) denotes thirty bottles while in (11) it denotes three bottles.) Suppose we assume Evans intends the pronoun to denote in such a case something like all bottles x brought. This pronoun interpretation is still dependent on the choice of value for the quantifier which binds x. What this means is that although the pronoun is clearly not bound by its antecedent, its interpretation, or the set it denotes, is, in some sense, bound by the quantifier every. Probably this is what Evans intends, but this is not a straightforward case of unbound anaphora, and the relevant sense of binding here needs to be explicated. Haik (1984) has observed that the relation between every and the pronoun in the 'donkey'-context obeys also surface structure restrictions typical of bound anaphora, which do not apply in the case of coreference, and these too need to be explained if we view the phenomenon as a case of pragmatic coreference. Two other properties of 'donkey'-type anaphora are not explained by a pragmatic E-type analysis. First, as we saw, this type is permitted only with indefinite NPs (or, as we shall see later, with all NPs with 'weak' determiners), and 106

On the interpretation of 'donkey'-sentences it is not clear how the E-type analysis can explain why the plural QNPs with a strong determiner in (12) do not allow anaphora: (12)

*Every critic who fell asleep during most 1 . i_ • • • i_ „, pieces, wrote enthusiastic reviews about all but two > \ .1 . L them. at least 20 per cent ofr i the (If, for some speakers, anaphora seems to be allowed here, it is only if the pronoun denotes the [common-noun] set of all pieces, or if it denotes a fixed set. This is a different type of anaphora, which need not concern us here.) If all that is going on in the 'donkey'-cases is a selection of objects satisfying the antecedent clause, clearly there are such objects established here and the pronoun should have been able to refer to them. Next, the distribution of 'donkey'-type anaphora is severely restricted and for such anaphora to be possible it is not sufficient that the antecedent and the pronoun be in the scope of another quantifier: (13)

*Every woman thought s[that she'd already met some man] when she saw him

The pronoun in (13) is in the scope of every. The antecedent clause contains a variable bound by every (the pronoun she). Still, the pronoun him cannot refer to the man satisfying x had met some man, varying with the choice of a woman: i.e. the 'donkey'-type anaphora where the choice of the pronoun varies with the choice of a man is impossible here. More generally, 'donkey'type anaphora is possible only when the antecedent is in the restrictive term of another operator. We may conclude that the 'donkey'-problems cannot be reduced to a purely pragmatic analysis of coreference. Haik (1984) provides an extremely interesting syntactic analysis of S-internal E-type anaphora in a wide range of cases. Her analysis keeps, in essence, Evans's intuitions, but introduces a mechanism for treating the pronouns as (indirectly) bound at surface structure by the QNP that has their antecedent in its scope. We should note, however, that this analysis cannot capture the last property of 'donkey'-anaphora we observed above - namely that it is possible only if the antecedent is in the restrictive term. To see that this is a crucial property that needs to be captured let us examine a few more cases: (14)

(15)

a. To show her his love, every knight who courted a lady committed suicide b. *To show her his love every knight sent roses to a lady /courted a lady patiently c. Every man who brought three bottles put them in the refrigerator d. *Every man who brought them put three bottles in the refrigerator e. *If someone brought them, he put three bottles in the refrigerator *Every man assumed that jokes about a lady in the party annoyed her 107

Tanya Reinhart

In all the examples above the indefinite antecedent does not c-command (or bind) the pronoun syntactically. In all of them, however, both the antecedent and the pronoun are in the scope of the every quantifier, or the conditional operator (which will be discussed in section 3). But only in (14a) and (14c) is the antecedent in the restrictive term of this operator, and these are the only cases which allow anaphora. (The specific, or wide-scope interpretation of the indefinite should, of course, be ignored in judging these examples.) The inappropriateness of anaphora in the other cases of (14) cannot be reduced to pragmatic considerations such as linear order (i.e. the fact that the pronoun precedes the antecedent), since on the one hand 'backward' anaphora with an indefinite antecedent is possible in (14a) but on the other hand 'forward' anaphora is blocked in (15). It turns out, however, that Haik's analysis allows anaphora equally in all these sentences, as well as in (13).3 The analysis of the semantic binding of the pronouns in 'donkey'-contexts must capture the two specific properties of the distribution of E-type anaphora S-internally that we observed in this section. As we saw, assuming E-type interpretation alone cannot do that, but in section 41 argue that a more explicit analysis of this type of interpretation explains the apparent universal force of the indefinite NPs in this context, which is independent of the issue of how they are bound. 3. HEIM'S ANALYSIS OF THE LOGICAL FORM OF 'DONKEY'-SENTENCES As we saw, the problem at issue is restricted to indefinite NPs which are traditionally interpreted as existential quantifiers. For this reason, scholarly attention has recently focused on the analysis of indefinite NPs. The most promising solution to the semantic problem stems from the observation that indefinite NPs are not, in fact, inherently existential quantifiers (Heim 1982; Kamp 1984). Heim's work is most explicitly related to surface structure, and I will therefore follow it here, focusing only on her LF analyses. The discussion is restricted to the logical syntax of these sentences. In the next section I examine their interpretation and the extensions necessary for the analysis to apply in the full range of cases. Heim's (1982) point of departure is that the indefinite article is not a quantifier, hence indefinite NPs are not quantified. Rather, they are interpreted as open formulae containing a variable that needs to be bound by some operator (e.g. man(x) for a man). The different interpretations of indefinites follow from the selection of the operator. It can be an available universal operator, an adverbial operator in the sentence, an existential operator introduced by the LF rules to bind the indefinite formula, or a 'discourse' operator. Let us see first how this works in the case of relative clauses, since the analysis of the conditionals is based on the same mechanism. 108

On the interpretation of 'donkey'-sentences Heim assumes LF formation rules similar to those assumed in the government and binding framework, following May (1977), the difference being only that unlike Quantifier-raising (QR), her rule of NP-raising adjoins to S any NP, regardless of its interpretation (excluding pronouns). This operation is restricted syntactically, as assumed for QR. The next rule applies specifically to quantifiers attaching them (out of the raised NP) to the dominating S. Some results are illustrated, with minor changes, in (16)—(18). (For ease of presentation I have written some variables in already at this stage. The binding of variables is obtained in Heim's analysis by an explicit indexing system, which I will not discuss.) Every man who, e} buys a car worships it => I. NP[Every man who} e{ buys a car]! s [e, worships it] =^> II. [Every man who] [a car]2 s[z\ buys e2]]! [ej worships it]

every

car (x) (17)

ey buys ex

Every man worships some car S every

NP,

A man (x) car (y) 109

ex worships ey

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(18)

We saw a man entering

we saw ex entering Sentences (16) and (17) contain a quantifier (every). The way the raising rules are defined, the higher S always dominates, in such cases, three constituents. The second of these is defined as the restrictive term of the quantifier, and the third as its nuclear scope. When a sentence is quantified, as in (16) and (17), a further LF rule named 'existential closure' applies to such structures adjoining a quantifier 3 to the nuclear scope of every quantifier. Applied to (17) it yields (19): (19) every

car (y)

ex worships ey

A structure like (19) yields the existential interpretation of indefinites. The same rule applies vacuously to the nuclear scope of (16, III), but there will be no variable it can bind there, since car(x) occurs in the restrictive term. Since the relative clause in (16) is the restrictive term of every, 3 cannot be inserted there. Hence, the only operator that can bind the indefinite in (16, III) is the universal operator every. This operator, thus, will bind both variables, and the LF-representation (20) (with a universal quantification over pairs) is obtained for the sentence. The system, thus, explicitly determines when an indefinite is interpreted as an existential, and when it is bound by another universal operator. (20)

Every x, y (man(x) & car(y) & x buys y) (x worships y) no

On the interpretation of 'donkey'-sentences In (18) no quantifier is present in the sentence, so neither existential closure nor binding to another quantifier can apply. In this case, it is assumed that the variable in the indefinite is bound by an abstract discourse operator. The indefinite may be viewed, then, as a 'discourse referent' or (roughly) as a specific indefinite. The LF (20) derived for (16) is the one which we examined in (7) of section 1. As we saw, this LF captures correctly the truth conditions of the sentence and allows the pronoun (it) of (16) to be bound. Heim's analysis, then, provides an explicit mechanism for deriving this LF from the surface structure of 'donkey'-sentences. Turning now to conditionals, the question is what binds the indefinite, as there is no overt operator in these sentences. Heim argues that conditionals contain an abstract sentential operator which she labels 'invisible necessity operator' and writes as D. In its force this operator is similar to the necessity operator - though they are not identical, since the conditional operator expresses a pragmatic rather than a logical necessity. It functions similarly to adverbial operators like always, invariably, or universally, which were analysed by Lewis (1975). Such adverbials may force an apparent universal interpretation of indefinite NPs as in (21): *iT . . . [ an old-fashioned critic hates an avant-garde 6 vpiece [Invariably J b. All old fashioned critics hate all avant-garde pieces (22)

a. [ Sometimes 1

,j

r

i_-

J

••

^

1

J

•

I Of an old-fashioned critic attacks an avant-garde piece b. Some old-fashioned critics attack some avant-garde pieces Sentence (21a) is similar in meaning to the universally quantified sentence (21b), though they are not precisely equivalent. Different sentential adverbials may force a different interpretation of the indefinites, as in (22a), where they are interpreted existentially, pretty much like (22b). Like the 'universal' sentential adverbs, the conditional operator forces a universal interpretation of indefinite NPs. In Heim's analysis this is a sentential operator which, like an adverbial operator, has the whole sentence in its scope. If a conditional sentence contains no adverbial operator, the conditional operator is realized as in (23b) (the precise LF of (23a) will be given shortly in (26)). However, other adverbials may fill the operator slot, as in (23d), in which case there is no independent conditional operator:4 (23)

a. If a man is happy, he talks to his dog b. • (if a man is happy, he talks to his dog) . \ if a man is happy, he talks to his dog A. FFJ 5 Almost always J in

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d. J OFTEN

1

r(

. ,

u

u

u ^

A

^

1 ALMOST ALWAYS J 0« a man is happy, he talks to his dog). In this analysis, then (as in Lewis's analysis), the if of the conditional has no interpretation; or, more generally, there is no independent conditional interpretation. The interpretation is dependent upon the sentential operator, and only if no other such operator is available in the sentence is the abstract conditional operator realized. The if in conditionals has, in this analysis, a purely syntactic role: it marks the restrictive term of the operator. The //"-clause of a conditional is always the restrictive term, regardless of its position in the sentence. This distinguishes conditionals from conjunctions (e.g. Always Max comes late and Lucie comes early), where no such requirement holds. The assumption that the conditional operator functions like a sentential adverbial operator, rather than originating in the //"-clause independently of other adverbial operators, is not without problems. One major problem is that the sentential adverbial operators allow indefinites to bind pronouns freely in the adverbial's scope as in (24b): (24)

a. * Lucie throws some dress away after she wears it once b. Always Lucie throws some dress away after she wears it once

In the case of 'bare' conditionals, anaphora is allowed only if the antecedent is in the //"-clause, as in (25b), but not otherwise, as in (25a): (25)

a. *Lucie kisses some guest if /ze talks about Hegel b. If some guest talks about Hegel, Lucie kisses him I Oft

I Lucie kisses some guest if he talks about Hegel

This fact seems to follow from Heim's analysis of the //"-clause as the restrictive term of the conditional operator. However, the problem is that if another sentential adverbial operator is added to (25a), as in (25c), anaphora is permitted. If the conditional operator is identical in interpretation and scope to the sentential adverbials, there is no explanation for why it cannot allow anaphora in the same way when it is realized independently in (25a). I believe that the conditional operator originates in the //"-clause and not in the matrix S-position, and the general condition allowing an operator to bind an indefinite NP is that it c-commands it at SS. In (24b) and (25c) the operator (always) c-commands the whole sentence, including the indefinite NP, but in (25a) it c-commands only the //"-clause, hence it cannot bind the antecedent outside it. This stresses the similarity between conditionals and relative clauses: in both cases the indefinite antecedent can occur only in the restrictive term, since it is only this part of the sentence which is c-commanded by the operator at SS. This would mean that the conditional operator is independent of the other 112

On the interpretation of 'donkey'-sentences adverbial operators, and, in contrast to Lewis's proposal, it is realized even if an adverbial operator is present. The problem of the interaction between this operator and other adverbial operators should be handled by whatever analysis handles similar interactions with universally quantified NPs, as e.g. in Often every guest talks about Hegel, or Sometimes every woman who likes a guest talks to him about Hegel. Heim's analysis of the scope of indefinites in conditionals, to which we now turn, is not crucially dependent upon the assumption. The conditional operator functions like a sentential adverbial operator. The LF assigned in this analysis to (26a) is (26c): (26)

a. If a mant owns a donkey2 hej hates it2 b.

donkey (y)

ej owns e2

c. • Vx y (man(x) & donkey(y) & x owns y) (x hates y) NP2 and NP2 are raised to the initial positions of the //"-clause by the standard NP-raising operation at LF that we observed above. The //-clause is the restrictive term of the necessity operator; hence no quantifier can be inserted there (the 3 in the nuclear scope of this example is vacuous, as it can bind nothing). The only operator that can bind both indefinites is, therefore, the conditional operator, which, as we saw, is similar in force to a universal operator. Hence we derive here the formula in (26c), which is similar to the universal quantification over pairs in (20). If the pronouns in the second clause are co-indexed with a man and a donkey they are translated as the same variables, hence they are both bound by the conditional operator and anaphora is permitted. Note that, unlike the universal quantifier, the conditional operator, or a

Tanya Reinhart sentential operator in general, does not bind independently an NP-variable in the sentence. It can only bind a variable in such sentences because of the specific properties of indefinite NPs which can 'attach themselves' to available operators. The pair quantification in (26c) is obtained because the //-clause happens to contain two indefinite NPs. If there is only one such NP the operator binds only one variable, as in (23a), repeated in (27): (27)

a. If a man is happy, he talks to his dog b . D x (man(x) & happy(x)) (x talks to x's dog)

In conclusion, we may note that Heim's analysis answers the questions raised in section 1, of how the indefinites get wide scope in 'donkey'-contexts, and of why this is possible both in conditional and in relative clauses. (We turn in the next section to the question of the universal entailment.) It also captures the properties of 'donkey'-anaphora we examined in section 2. As we saw in examples (12) and (4), such anaphora is possible only when the antecedent is indefinite, or existential. This is captured in this analysis since only these NPs lack an independent binding quantifier. If a universally quantified NP appears in a relative clause or in an //"-clause, it cannot be bound by the higher operator. Neither can it leave its clause to obtain wider scope, because of the clausal restrictions on QR (or NP-raising). Hence its scope is only this clause, and a pronoun outside this clause cannot be bound by it. The analysis also opens the way for capturing the fact we observed in (13)—(15), that 'donkey'-type anaphora is possible only when the antecedent is in the restrictive term of another operator. In Heim's analysis, whenever the indefinite NP occurs in the nuclear term (i.e. outside the restrictive term), the rule of existential closure inserts an 3 quantifier. The indefinite is, then, bound by this quantifier, and it cannot be bound by the sentential or universal operator. This may be illustrated with a sentence similar to (i4d): (28a) *Every guest who brought itx put a bottle! in the refrigerator (28b)

every N guest (y) who ey brought it ey put ex in the refrigerator In the LF (28b) of this sentence, 3 must be inserted, and since there is an indefinite N {a bottle) in its scope, this NP is bound by it. A bottle, then, 114

On the interpretation of 'donkey'-sentences cannot be bound by every. In the LF obtained, the pronoun it is outside the scope of the operator, hence it cannot be bound by it.5 4. WEAK NPs AND THE SOURCE OF THE UNIVERSAL FORCE Our next question is: what is the precise interpretation of the LFs derived by Heim's analysis? In the case of the LF (20) derived for (16) which is repeated in (29), not much more seems to be needed concerning the interpretation of the formula. Under any interpretation it appears to capture correctly the truth conditions of the sentence. The question arises, however, if we consider other strong quantifiers as binders, as in (30). (29) (30)

a. b. a. b. c. d.

Every man who buys a car2 worships it2 Every x, y (man(x) & car(y) & x buys y) (x worships y) Almost every man who buys a car2 worships it2 Almost every x, y (man(x) & car(y) & x buys y) (x worships y) Almost every (x, y) (man(x) & car(y) & x buys y) (x worships y) Almost every x, Vy (man(x) & car(y) & x buys y) (x worships y)

The LF that would be derived for (30a), if we apply Heim's analysis, is (30b), and the question is what does it mean? A pair interpretation, as in (30c), does not give the right truth conditions here, as has been pointed out in, among others, Kempson (1984). If there are ten car-buying men, one of which bought fifty cars and worshipped all of them, the others of which bought one car each and neglected to worship it, (30c) is true, since most man-car pairs enter the worship relation; but the original sentence (30a) is false under these conditions. What the sentence means, in fact, is that most car-buying men worship all the cars they bought, i.e. the truth conditions of the sentence are captured correctly by an LF like (3od) which contains a universal operator. ((30d) is the 'absorption' structure of Higginbotham and May 1984.) Roughly, a formula of the form almost every x, Vy, {cp, \p) is interpreted as almost every x, s.t. 3y 0:]Vy s.t. 3 x cp :\p].) This is, indeed, the analysis Heim intended for these cases. The puzzle here, however, is what is the source of the apparent universal force of the indefinite in this case, since no standard procedure can derive (3od) from (30b). More generally, it seems that indefinite NPs in the restrictive term of another quantifier always have a universal force, regardless of the semantics of the quantifier which binds them. A sentence with the form Qx who owns a donkeyx hates itx always entails x hates all the donkeys x owns, even if Q itself is not a universal quantifier (replace, e.g., Q with more than half, many or two). It is crucial, therefore, to explain this entailment, especially if we want to maintain that the indefinite (a donkey) here is bound by the Q at issue. Before addressing this question, we should look at another interpretation

Tanya Reinhart

problem which will eventually provide the clues for the answer. So far we have considered, following Heim, only singular indefinites as antecedents in 'donkey'-anaphora. In fact, the relevant distinction determining which NPs can serve as antecedents in 'donkey'-type anaphora is that between weak and strong NPs. This term will be used here to refer to NPs with weak or strong determiners in the sense of Barwise and Cooper (i981) or cardinal versus noncardinal determiners as defined by Keenan (forthcoming).6 All weak NPs can bind pronouns outside of their apparent scope, when they occur in the restrictive term of another quantifier. Some examples are given in (31):

(30

two several a. Every guests for dinner less than five vampire who was through with many invited them by midnight between ten and thirteen as many guests as you can imagine b. If a vampire invites more than fifty guests for dinner, they have a chance to survive

Clearly, in such examples the interpretation of the plural pronoun them varies with the choice of a vampire (each vampire might have invited a different set of guests to which the pronoun refers). Hence, it has the properties of bound anaphora. As we saw in (4) and (12), strong NPs cannot enter this type of anaphora relation. Heim's analysis must be extended, then, to hold for all weak NPs - which means that all weak NPs lack an inherent quantifier and, hence, can be bound by another operator in the sentence (or by an 3 operator). This, in fact, is a plausible extension, since an emerging agreement in studies of weak NPs is that the determiner in such cases is not a quantifier but a cardinality marker for the set defined by the NP. (Such an analysis was proposed originally by Bartsch 1973 and, informally, in Milsark 1974; it was recently developed independently by, for example, Higginbotham 1984; Scha 1984; Cormack and Kempson 1984; Keenan forthcoming; Lobner 1984.) The question, however, is how such NPs can be bound by another operator in the sentence. Once the full range of antecedents is considered, it becomes clear that the quantifier in the derived LFs for 'donkey'-sentences cannot bind an individual variable, as we have so far assumed. Since the NP bound by the universal or the conditional operator in example (31) is interpreted as a set, the quantifier index corresponding to this NP in the LF must be a set-variable. The same would be true in the case of a singular weak NP, as in (29), the only difference being that the cardinality of the set is (at least) 1. Consequently, the pronouns with the same index also refer to sets (or to each of their members). With this, then, we can turn to the question of what explains the apparent 116

On the interpretation of 'donkey'-sentences universal force of weak NPs in 'donkey'-contexts. (The same universal force shows up with plural weak NPs, e.g. Most men who have more than two dogs hate them entails that most of these men hate all the dogs they have.) The answer requires a closer look at the sets defined by weak NPs. A standard set analysis for weak NPs assumes that the weak NP itself denotes a set (which is a subset of the set defined by the noun interpretation). This is consistent with Heim's analysis where the open formula corresponds to the NP. So the NP in a sentence like (32a) can be analysed as in (32b): (32)

a. At least two vampires appeared b. X C {z I vampire (z)} and | X | ^ 2

(X is a subset of a set of individuals z with the vampire property, and the cardinality of X (i.e. the number of its members) is equal to or greater than 2.) The set X may be viewed as bound by something like Heim's discourse 3-operator, or stored at the discourse storage, which enables subsequent discourse to refer back to it. However, a closer look at the behaviour of weak NPs in discourse reveals that something more must be going on. As we saw in section 2, anaphora with weak NPs is possible also across sentences, where the pronoun cannot possibly be bound, as in (33): (33)

a. Two vampires appeared and Lucie chased them away b. Lucie has at least fifteen dogs, and Felix takes care of them

Given the analysis of weak NPs as sets with cardinality, we may say that the pronoun in such sentences refers to a set established in the previous sentence (as a discourse referent). It is clear, however, that in (33a) it does not refer to just any set of (at least) two vampires but, as observed by Evans (1980), to all the vampires argued to have appeared in the first sentence. Similarly, in (33b) Felix takes care of all of Lucie's dogs. As pointed out by Evans, the conjunction in example (33b) does not mean something like There exist (at least) fifteen dogs that Lucie owns and Felix takes care of, since the latter can be true if there are certain dogs which Lucie owns but which Felix does not take care of, while (33b) will be false under these conditions, since it entails that Felix takes care of all of Lucie's dogs. We see then that the apparent universal force of weak NPs in contexts of anaphora is not a peculiar property of 'donkey'-type cases where the antecedent is bound by another operator, but it is a general characteristic of these sorts of NPs and it must follow from their semantic analysis. To capture this, the sets defined by the weak NPs must be determined by their whole clause; for example, for (32a) it is the set in (34) which is stored for future discourse reference, and not just the set in (32b): (34)

X = {z I vampire(z) and z appeared} and | X | ^ 2

(X is the maximal set of individuals z with the vampire property who appeared 117

Tanya Reinhart and its cardinality is equal to or greater than 2.) Since X is defined as a maximal set, i.e. it contains all the vampires which appeared, if a pronoun refers back to this set, as in (33a), it refers to all its members, i.e. to all the objects satisfying the previous clause. I assume, then, that weak NPs are always interpreted as a set defined by the whole clause. In case the clause contains another quantified NP, as in Every neighbour has a dog, the set defined for the weak NP contains a variable bound by that quantifier: {z | dog(z) and x has z}. For this reason a pronoun can refer to this set only if it is in the scope of the operator which binds the variable in it. In other words, such sets are not available for discourse anaphora as, for example in * Every neighbour has a dog and I feed it. This analysis captures Evans's description of E-type pronouns as pronouns referring to all objects satisfying the antecedent's clause. However, it is not the pronouns which have this property: the pronouns here are standard setpronouns, i.e. pronouns referring to sets, and there are many other instances of such pronouns, for example in all cases of plurals. As such, their interpretation is determined by the interpretation of the antecedent, and if the antecedent is weak its interpretation is the set defined by the clause. This interpretation of weak NPs is, then, the source of the universal entailments in cases of anaphora with weak NPs, and the indefinite NP itself need not be universally quantified. The weak NPs in 'donkey'-sentences are analysed in precisely the same way: (35)

a. If Lucie has (any) children, Lucie spoils them b. X = {z children(z) and Lucie has z} and | X | ^ z c. • X(X = {z children(z) and Lucie has z} and | X | ^ z) (Lucie spoils X) d. *If Lucie has children she spoils them, but I can't stand them e. * Every man who owns a donkey left, and Felix had to take care of it The clause containing the NP children in (35a) is the //"-clause {Lucie has children), hence this NP is interpreted as the maximal set determined by this clause, as in (35b). However, the difference between a 'donkey'-sentence, such as (35a), and the case of discourse anaphora we examined in (33), is that this weak NP is bound, as we saw, by the conditional operator. In Heim's analysis, its index is copied into the conditional operator. Since the NP is interpreted as in (35b), this index is a set-index, and the pronoun with the same index is also a set-pronoun; hence the full analysis of (35a) is (35c). The fact that the weak NP in 'donkey'-contexts is bound explains why it cannot serve as an antecedent for discourse anaphora, as witnessed by (35d), a fact observed by Haik (1984). More generally, discourse anaphora with sets is possible only when the antecedent is not locally bound in the previous sentence, though it may be bound by a discourse 3 operator - for example, it 118

On the interpretation of 'donkey'-sentences is impossible also in (35e). This stresses further the point we observed in section 2, that a pragmatic E-type analysis alone is not sufficient to handle 'donkey'contexts.7 We can return now to the interpretation of the LFs derived by Heim's analysis for sentences like (30a), repeated in (36a): (36)

a. (Almost) every man who buys a car2 worhsips it2 b. (Almost) every x,y (man(x) and a car(y) and x buys y) (x worships y)-

c. (a car(y) and x buys y) => (Y = {z | car(z) and x buys z} and | Y | ^ 1) d. (almost) every (x,Y) (man(x) and Y = {z | car(z) and x buys (z)} and YI ^ 1) (x worships Y) (37) a. Most vampires who invited more than three guests2 for dinner were through with them2 by midnight b. most (x,Y) (vampires(x) and Y = {z | guest(z) and x invited z for dinner} and I Y I > 3) (x was through with Y by midnight) Sentence (36b) is just the indexed LF derived for (36a) by Heim's LF rules. What the indices on the quantifier mean is determined by the interpretation of the arguments they bind. First, the clause containing a car is interpreted as in (36c) (that this is a clause at LF can be checked in its derivation-tree (16) above). Y, then, is a set-variable and all other occurrences of y in the formula are replaced with the same set-variable, including the pronoun (we return shortly to what this means for the pronoun). The final analysis is, then, given in (36d) (for almost every pair consisting of a man x and the set of cars he buys Y, it is true that the man x worships the cars in the set Y). Example (37) illustrates the same with plural NPs. This analysis handles the problems with quantifiers like almost every that we observed in the discussion of (30): Y denotes the (maximal) set of cars bought by x, and the quantifier selects almost every pair of an individual x and a set Y (defined on x). If, as in our previous story, a given individual bought fifty cars, (x,Y) in this case still denotes only one pair consisting of one man and a set of fifty cars. The universal entailment that we observed there (that almost every man worships all the cars he buys) follows, then, from the set interpretation of the weakNP. 8 A further note is needed concerning the interpretation of the pronouns. The analysis assigns them set-variables, but it is obvious that each man in example (36d) worships individual cars and not a set of cars. This, however, is a general issue of interpreting set relations, and I will assume the general distributive convention (38) for all cases where an argument is a set-variable: (38)

V(Y) = df(Vz£Y)(iMz))

When the pronoun is plural, the decision whether this convention applies depends on the predicate, i.e. it does not apply when the predicate forces a collective interpretation: (36d) is then to be replaced by (39): 119

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(almost) every (x,Y) (man(x) and Y = {z | car(z) and x buys z} and IYI ^ 1) (VwsY (x worship w))

5. C O N C L U S I O N The results of this paper may be summarized as follows: 1.

Weak NPs can bind pronouns outside their apparent scope, when they occur in the restrictive term of another operator. Weak NPs may themselves be locally bound by other QNPs. Conditional contexts allow a bound-variable interpretation of pronouns with weak NP antecedents, whereas temporal or causal sentential connectives do not allow bound variables but only pragmatic coreference. The source of the universal force of the weak NPs bound by the conditional operator or other QNPs is the maximal set interpretation of the weak NP, determined by the whole restrictive clause, and pronouns refer to that set when in the scope of the binding operator.

2. 3.

4.

NOTES 1 I wish to thank Irene Heim for extensive discussions of ideas related to this paper. 2 I will only illustrate the problem here; for a survey of the extensive literature on this issue, as well as its history, see Heim (1982). 3 An apparent counterexample, cited both by Evans (1980) and by Haik, to my claim that 'donkey'-type anaphora is possible only when the antecedent is in the restrictive term of another operator, is the case of VP-conjunction: (i)

Every villager owns some sheep and feeds them at night (Evans 1980: 39)

This, however, is not a case of 'donkey'-type anaphora, but a straightforward bound anaphora, since the antecedent some sheep is permitted to bind the pronoun: it both has it in its scope and c-commands it. Given either my definition of c-command (e.g. Reinhart 1983) or its more recent statement in terms of maximal projections in Aoun and Sportich (1982), the relevant node for c-command here is the top VP (the maximal VP projection). That this is just a case of bound anaphora is witnessed by the fact that all quantifiers can bind pronouns from this position as in (ii): (ii)

a. Lucie read each book and wrote a review about it b. Felix kissed every woman and invited her to dance

(As we saw in (12) and in (4) 'strong' quantifiers, as in (ii), cannot bind pronouns in 'donkey'-type environments.) 4 In these examples, the capitals in (23d) represent sentential operators, as opposed to actual adverbs, matching the box in (23b). 5 The problem is, however, that an alternative scope analysis is possible for sentence (28) with 3 having wide scope over every (i.e. the NP bottle is raised by QR to the topmost position in the sentence). In this case, anaphora will not be blocked by Heim's analysis, though the sentence clearly has no anaphora interpretation. This, however, is an independent problem for theories assuming that the binding of pronoun variables is captured at LF. In fact, this binding is sensitive to surface structure properties which are lost at LF. In Reinhart (forthcoming) I argue that the binding mechanism 120

On the interpretation of 'donkey'-sentences proposed by Heim must apply at surface structure rather than at LF. Once this mechanism is established, anaphora in (28) will be blocked under any scope analysis by the general surface structure conditions that block binding in e.g. (iii), although QR permits assigning wide scope to every guest: (iii)

*Her husband annoyed every guest

6 As a test for deciding which NPs are weak and which are strong the reader may use f/zere-insertion contexts, which allow only weak NPs: (iv) There are

f five notes than twenty

vampires in the garden

exactly ten (v) f all 1 There are \ most \ vampires in the garden [ half of the J 7 One case of discourse anaphora which remains to be explained is that of (10b) in section 2, repeated in (vi): (vi)

Every guest brought three bottles to the party. By midnight, they were (all) empty

In such cases, where a plural weak antecedent is in the scope of another quantifier (but is not bound by it), the discourse pronoun refers to the union of the weak-NP sets for the values established for x(x is a guest). (So if there were ten guests the pronoun refers to thirty bottles.) 8 More work is needed for the cases where the head NP in the relative clause is, itself, weak, as in (vii). In such cases both weak NPs are bound by the discourse 3 operator: (vii)

Two men who found a vampire chased him away

REFERENCES Aoun, Joseph and Dominique Sportich. 1982. On the formal theory of government. The Linguistic Review 2,3:211-36.

Bartsch, Renate. 1973. The semantics and syntax of number and numbers. In Syntax and semantics 2, ed. John P. Kimball. New York and London: Seminar Press. Barwise, Jon and Robin Cooper. 1981. Generalized quantifiers and natural language. Linguistics and Philosophy 4: 159-219. Cormack, Annabel and Ruth, Kempson. 1984. Are indefinite NPs names, variables, or neither? Paper presented at the Fifth Groningen Round Table, June. Evans, Gareth. 1980. Pronouns. Linguistic Inquiry 11: 337-62. Haik, Isabelle. 1984. Indirect binding. Linguistic Inquiry 15: 185-224. Heim, Irene. 1982. The semantics of definite and indefinite noun phrases. Ph.D. dissertation, University of Massachusetts, Amherst. Higginbotham, Jim. 1984. Indefiniteness and predication. Paper prepared for the Fifth Groningen Round Table (appears in the Abstracts volume). Higginbotham, Jim and Robert May. 1984. Questions, quantifiers and crossing. The Linguistic Review 1: 41-80. Kamp, Hans. 1984. A theory of truth and semantic representation. In Truth, interpretation and information, ed. Jeroen Groenendijk, Theo Janssen and Martin Stokhof. GRASS 2. Dordrecht: Foris Publications. 121

Tanya Reinhart Keenan, Edward. Forthcoming. A (formal) semantic definition of indefinites. In The representation of indefiniteness, ed. Eric Reuland and Alice ter Meulen. Cambridge, Mass.: MIT Press. Kempson, Ruth. 1984. Weak crossover, logical form and pragmatics. Paper delivered at GLOW, Copenhagen, April. Lewis, David. 1975. Adverbs of quantification. In Formal semantics of natural language, ed. Edward Keenan. Cambridge: Cambridge University Press. Lobner, Sebastian. 1984. Indefinites, counting, and the background/foreground distinction. Paper presented at the Fifth Groningen Round Table, June. May, Robert. 1977. The grammar of quantification. Ph.D. dissertation, MIT. Distributed by Indiana Linguistics Club, Bloomington, Ind. Milsark, Gary. 1974. Existential sentences in English. Ph.D. dissertation, MIT. Reinhart, Tanya. 1983. Anaphora and semantic interpretation. London: Croom Helm; and (1985) Chicago: University of Chicago Press. Reinhart, Tanya. Forthcoming. A surface structure analysis of the donkey-problem. In The representation of indefiniteness, ed. Eric Reuland and Alice ter Meulen. Cambridge, Mass.: MIT Press. Scha, Remko. 1984. Distributive, collective and cumulative quantification. In Truth, interpretation and information, ed. Jeroen Groenendijk, Theo Janssen and Martin Stokhof. GRASS 2. Dordrecht: Foris Publications. Stechow, Arnim von. 1980. Modification of noun phrases, a challenge for compositional semantics. Theoretical Linguistics 7: 57-109.

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GENERIC INFORMATION, CONDITIONAL CONTEXTS AND CONSTRAINTS • Alice ter Meulen Editors' note. The semantics of generic statements in conditional contexts is addressed, and a model-theoretic analysis is developed in the framework of Situation Semantics. Context-dependent interpretation, including tense and plural anaphora, is discussed for generic and episodic information. The paper is related to Barwise's by the formal framework, and to Reinhart's by addressing anaphora. It analyses Reilly's protogenerics and formulates some specific conditions for the interchangeability of conditionals and temporal adverbs. 1. INTRODUCTION This paper is concerned with the semantic interpretation of generic expressions in conditionals and with their interaction with temporal adverbs and tense, assuming Situation Semantics as a general framework for a model-theoretic semantics of natural language.1 As a theory of meaning and interpretation which attributes to the context of an utterance an important role in its interpretation, this recently developed semantic theory will provide new and fruitful concepts for analysing the use of generics in natural language and their role in structuring meaning as a relation between expressions and situations in the external world.2 The issues concerning generics are presented as informally as possible at first, to clarify the underlying intuitions. Reilly's notion of 'protogeneric' (this volume) is discussed as a form of contextually restricted generic expression and the general question is addressed of the conditions under which when and whenever are interchangeable with the conditional if-then without distortion of meaning. Conditionals and generics are shown to share an important semantic property: persistence of expressed information, or insensitivity to putative counterexamples. Generic interpretations of sentences result in the most common cases from the interaction between the tense and aspect and the interpretation of the subject noun phrase (NP). Hence the generic interpretation of an expression is not determined, at any lexical level, in isolation from its context. In section 2 I discuss, at first informally, which NPs may occur in a given VP-context when the sentence itself is interpreted as expressing information about a kind of entity but when the VP is neutral to the ontological level of the interpretation of the subject, be it kinds, sets of individuals, or stages of an individual (see 123

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Carlson 1979, 1982). The consequences of the variation of tense are studied subsequently in a context with a fixed subject NP. A model theoretic analysis of generically interpreted sentences is proposed in section 3, introducing some of the central concepts of Situation Semantics. Generic information is shown to be persistent, even in 'recalcitrant' situations, which demonstrates some of the usefulness of this semantics of natural language over the more traditional 'possible world' semantics. In section 4 the interaction of generic information with conditional contexts and various sentential temporal adverbs is discussed, and it is argued that the interchangeability of such adverbs with conditionals is quite restricted. Arguments are presented against the view, advocated by Reilly and many others, that the degree of subjective certainty a speaker may have concerning the truth of the antecedent of a conditional is a relevant condition for this interchangeability. Supposing that the world is one way or another is not the same thing as knowing or believing something about the world as it is, although the relation of conditionals and attitudes remains an interesting area for linguistic and philosophical research: unfortunately this lies outside the scope of the present paper. A brief discussion of conditional generics, i.e. generic interpretations of consequents of conditionals, concludes the paper. 2. WAYS OF EXPRESSING GENERIC INFORMATION NPs in generically interpreted sentences3 may be of four different kinds. Three are exhibited in the following sentences within a neutral VP-context.4 (1) (2) (3)

Donkeys are stubborn A donkey is stubborn The donkey is stubborn

The bare plural NP donkeys, the indefinite NP a donkey and the definite NP the donkey convey generic information when the predicate allows of a kind-level interpretation, denoting a property of kinds. Obviously these three sentences admit an interpretation which attributes a property to, respectively, a set of donkeys (possibly determined by context), any arbitrarily selected donkey to which no prior reference has been made, or to a donkey introduced at an earlier stage of the interpretation of preceding discourse. The point here is merely that sentences (i)-(3) may be used to express information about a kind of animal, rather than about any of the members of that kind. Such generic information is not directly descriptive of what happens to be the case in the situation in which it is used, or in any particular situation. If we assume that a sentence is interpreted by the set of situations in which it is true, not only may situations in which donkeys are manifesting stubborn behaviour be included in the interpretation of (i)-(3), but also situations that do not contain 124

Generic information, conditional contexts and constraints any donkey. Even in a situation in which a particular donkey exhibits unusually complaisant behaviour, we still adhere to the generic information about its kind. Although generic information is not directly descriptive of particular situations, its purpose is to classify such situations as being of a particular type and as entering into relations with other types of situations. The fourth example of a generically interpretable sentence contains a nominalized predicate: (4)

Being stubborn is characteristic of donkeys

in which the property referred to by the nominalization is correlated to the kind. Such correlations are often expressed by nominalizations, and by appealing to such correlations we come to understand metaphorical uses of language. Accepting a meaningful correlation between the property of being stubborn and the kind donkeys, we can call someone 'a donkey', meaning to attribute to him donkey-like stubbornness. The two properties are correlated in such a way that situations of a type fitting the one property are systematically correlated to the situations of a type fitting the other property or kind. This correlation is usually not symmetrical, but there is an anti-symmetrical dependency of the one property on the other.5 The correlations, which I will call 'constraints', may be specified as causal or explanatory connections between types of situations; or, as in (4), as a genetically inherent disposition of members to behave in a certain manner; or, perhaps more imaginatively, as a consequence of our typically Western way of stereotyping, which is inherent to our perspective and understanding of the world. It is difficult for anyone who uses the constraint to give meaning to the language to assess its nature. Getting attuned to a constraint is realizing that the situations we encounter exhibit certain regularities and learning to ignore some of their dissimilarities and variation. Eventually, due to one's lack of imagination of what variation could still be admitted within a pattern of regularities, one may have come to conceive of a constraint as a necessary and nomic connection between parts of the world, assuming that the world could never be otherwise. In this sense our prejudices and predispositions are also constraints upon which we act and which serve us to classify the situations we are in. But an outsider, who is not attuned to the same constraint or is perhaps not as finely attuned to it, mayconceive of the constraint as a merely contingent or accidental correlation, or as a constraint which is subject to special spaito-temporal restrictions. If a discrepancy arises between the understanding two speakers may have of the nature of the constraint they are attuned to, it must have some effects on the interpretation they give to each other's utterances and it must limit their understanding of what they are saying, and of each other's view of the world. Attunement to some constraints may be necessary conditions for knowing a language, whereas other constraints may have to be adhered to if one is considered to behave rationally within the language community. 125

Alice ter Meulen If examples (i)-(4) are interpreted by different sets of situations, they should all be compatible with situations containing donkeys, individuals realizing the kind, which are behaving stubbornly. The episodic or 'ephemeral' (Davidson's word) sentences like: (5) (6)

There are (some) stubborn donkeys Chiquita, Pedro's donkey, is being stubborn again

describe such situations directly. But situations without donkeys are compatible with generic information stated in these sentences. In fact, even when a particular donkey in a situation happens to behave well, which I will call a 'recalcitrant' situation, this remains compatible with the generic information. In general, generic interpretation does not preclude such recalcitrant situations, which render episodic information about individuals true. But recognizing a situation as a recalcitrant one presupposes adherence to the correlation expressed with generics, realizing that the current situation does not fit the general pattern. This is one reason why generic information cannot be expressed by universally quantified expressions about individuals, which convey episodic information about members of a kind. For instance: (7)

Every donkey is stubborn

either describes directly a contextually-determined set of donkeys which are all behaving stubbornly in a situation, which is the case when the universal quantifier is restricted to a contextually fixed domain, or, when there is no such restriction, it describes all situations, actual or otherwise, that contain donkeys, attributing stubbornness to them. But (7) is falsified by a situation in which a donkey does not behave stubbornly, i.e. by any situation which would be a recalcitrant one in the case of generic information. Generic information, contrary to a universal statement such as (7), is persistent in such recalcitrant situations. What it means for information to be persistent will be explained set-theoretically in the next section, when Situation Semantics is introduced and constraints can be defined precisely. The sentences (i)-(4) with the generic interpretations are all in the simple present tense. Indeed, this tense form is often indicative of habits or dispositions of the denotation of the subject NP, expressing these as a state of affairs, a stative situation in which no change occurs. Such generic interpretations of present tense statements are not directly descriptive of a present or actual situation, or of the discourse situation, but describe something in a 'timeless' way, true of no specific past, present or future moment. Of course, this does not mean that generic information cannot be restricted in applying only to particular space-time locations, or in special contexts, as I will discuss later. The progressive tense, indicative of changing situations and evolving time, is seldom used to express generic information. Only with explicit grading 126

Generic information, conditional contexts and constraints adverbs or verbs expressing gradual change can contexts be created which admit generic interpretations. Examples are: (8) (9)

Donkeys are becoming ever more stubborn Donkeys are getting stubborn when you beat them

More commonly, the progressive is used to convey episodic information about individuals (see Carlson 1982). However, sentence (8) may be interpreted generically as expressing the view that in comparing donkeys in the past and the present as to their stubbornness, the latter are more stubborn than the former. This remains true information even when a presently existing donkey is less stubborn than some donkey in the past, or even when one and the same donkey is growing more obedient. Similarly, (9) remains true even when beating a particular donkey does not make it more stubborn than it was before. On their episodic interpretation (8) and (9) state that some situation contains donkeys which are all increasingly stubborn, and the increase must occur in each donkey in that situation for these sentences to be true, i.e. they express universal information. As was remarked above, the timeless or 'eternal' character of generic information does not mean such information remains true for once and for all. As with all other parts of our knowledge about the world, it is permanently up for revision. Meeting too many recalcitrant situations may eventually weaken our attunement to a constraint we once held to be nomic and law-like. We may subsequently revise and refine a constraint, to adjust it to newly discovered special conditions or contextual restrictions, while salvaging the generic, meaning-giving relation between types of situations. Depending on the nature of the correlation, such adjustments may affect the meaning of what we say. Discovering new similarities among situations may also give rise to new constraints which replace older and coarser ones and which reorganize the world by classifying situations into a finer scheme or types (the jade-case). Or, in seeking deeper explanations of the correlations we recognize between types of situations, one, more universal, constraint may reorganize our information more efficiently. Besides the present tense, past and future tenses may well be used to express generic information, but there appears to be a strong preference for bare plural subject NPs in past and future contexts. Indefinite as well as definite NPs, as in (2) and (3), are interpreted episodically in tensed contexts as being about individual donkeys in past or future situations: (10) (11) (12) (13)

Donkeys will be stubborn when they are beaten Donkeys were stubborn A donkey was stubborn Some/all donkeys will be stubborn when they have been beaten

Sentences (10) and (11) are not directly descriptive of a future or past situation, but they express a correlation we now perceive between a kind of animal and 127

Alice ter Meulen future or past types of situations. Sentences (12) and (13), however, express episodic information about individual donkeys. Bare plurals referring to kinds are used in tensed and other intensional contexts for expressing generic information, as kinds are not constituents of particular situations but, rather, abstract objects in types of situations. Kinds serve in the first place to classify particular situations as being of a certain type. This is best illustrated by the fact that sentences (12) and (13) with indefinite determiners, in contrast to (10) and (11), allow a paraphrase with a tensed existential context without distorting their meaning: (14) (15)

There was a stubborn donkey There will be some donkeys which are stubborn when they have been beaten

It should be noticed further that (12) and (13) and their paraphrases (14) and (15) with non-universal, indefinite determiners are symmetrical; in this they contrast with the generic interpretations, which are always anti-symmetrical - as was shown above. Although the following sentences are perfectly acceptable: (16) (17)

There will be donkeys which are stubborn when they are beaten There were donkeys which were stubborn

and (10) and (11) entail them respectively, there is a subtle, but important loss of meaning, which is best brought out by an explicit comparative in their context. The generic information in (11), for instance, modified with an explicit comparative to: (11')

Donkeys were more stubborn than they are these days

implies that donkeys are nowadays less stubborn than donkeys in the past. It admits of an interpretation of the anaphor they as an entirely disjoint set of donkeys with respect to the set of donkeys interpreting its antecedent. None of the donkeys of that past time when they were stubborn may still be in existence. Sentence (17), on the contrary, when modified in a similar way to: (17')

There were donkeys which were more stubborn than they are (?) these days

does not necessarily compare donkeys of the past to our present donkeys, if it is at all acceptable. Here the comparison can only be carried out with respect to each individual donkey for its past and current degree of stubbornness. The anaphor they in (17) is interpreted as dependent upon the interpretation of the bare plural donkeys in such a way that the degree of stubbornness depends on the choice of donkey. For a comparison of kinds across situations 128

Generic information, conditional contexts and constraints the generic bare plural is required, whereas in an existential context the predicatively occurring bare plural NP, just like the other quantifiers which are acceptable in such contexts, is interpreted existentially and is dependent on the temporal location determined by the tense. The same point is supported by the following sentences: (18) (19)

Donkeys are less stubborn than they were There are donkeys which are less stubborn than they were

Only (18) compares at the kind-level, across types of situations. Sentence (19) compares only the stubbornness of some presently existing donkeys with their past behaviour in this respect. The plural pronoun they in (19) depends on the set of donkeys interpreting its antecedent. In (18) the anaphor is interpreted in a way which must take into account that the set of donkeys in a past situation which serves as reference set for the comparison may be completely disjoint from the set of donkeys in the present situation, so it cannot simply pick up its reference from the set interpreting the antecedent. Pending a formal and more explicit and descriptively adequate theory of plural anaphora, the main points that this is intended to demonstrate are that existential contexts never convey generic information and that tense in a generically interpreted sentence has no deictic force and does not serve to locate the interpretation of the subject NP in time. 3. KIND-TYPES, CONSTRAINTS AND CONDITIONALS After this informal exploration of the various ways in which natural language expresses generic information, the central notions need to be given precise content in a model-theoretic framework. For this purpose I adopt the Situation Semantics of Barwise and Perry (1983), which is developed with particular emphasis on context-dependent interpretation, and which employs partial functions and intensional properties as constituents of situations to present a new account of intensional contexts, scope and informational dependencies in natural language. A brief exposition of the theory is in order here (see also Barwise in this volume). Situations, so,Sj..., are sets of triples of the form:

(l,(Rn,Xl,...xn),pot> where / is a location in space-time, Rn an n-place relation, Xj . . . xn individuals (together called a constituent sequence) and pol is a polarity, either yes or no, affirming or denying that the relation holds between the mentioned individuals. Locations, relations, individuals and polarities are the primitives of the theory. Situation-types, S}, S2, . . . , are situations which contain indeterminates /, R, x for location, relation or individual, which are abstract objects that serve as place holders for the real objects. An anchor is a (possibly partial) function 129

Alice ter Meulen assigning real objects to the indeterminates in a situation-type. This provides the means to classify a real situation as being of a certain type. It is defined as: s0 is of type So iff for some anchor/, S0\f] is part of s0 where the 'part of notion between situations is just the inclusion relation between their constituent-sequences, i.e.: Sj is part ofs0 iff all constituent-sequences of Sj are constituent-sequences of s0 (preserving polarity, of course) Situations are organized into structures, which determine a number of important relations between them, according to the following definition. A structure of situations consists of a collection of situations, S, and a non-empty subcollection So satisfying the following conditions: (i) (ii) (iii) (iv)

Every situation in So is coherent (i. e. no polarity conflicts, and everything is identical to itself) If s e So and s0 C s then soe S (parts of actual situations are factual) For any subset X C S there is an s in So such that every sn e X is part of 5 (every factual situation is part of an actual situation) S respects all constraints in S, which are relations between situationtypes in S

The situations in So are actual situations, and the situations in S are factual. This structure defines compatible sets of situations, and constraints determine further structure on these sets, giving rise to meaningful relations between situations in the structure. This general notion of a constraint will be illustrated further below. Persistence of information is analysed as a binary relation on collections of situations, respectively the collection of 'meaningful options' for a particular factual or actual situation and the collection of situations which are not 'precluded' by that situation. These notions are given the following definitions. Let s0 be of type So and s7 be of type Sj, then Sj is a meaningful option for s0 iff. for every anchor / for all indeterminates in So, if S0[f] is part of s0, then Sj\f] is part of s7, given the constraint C which correlates So and Sj in the structure of situations. The collection P of all meaningful options for s0 given C captures the information which is persistent relative to another collection of situations, namely the ones that are not precluded by s0, again given C. The precluded situations may be thought of as situations inaccessible from s0, in the structure of situations. It would require a revision in the structure or in its constraints to make such situations accessible to s0. The definition captures this formally. A situation s0 precludes a situation Sj if they are incompatible, which is a primitive notion in Situation Semantics, or if no anchor/such 130

Generic information, conditional contexts and constraints that S0[f] is part of s0 can be extended to an anchor/ such that Sj\f] is part of Sj. Let X stand for the collection of situations not precluded by s0, then the intersection PC\X= \[so]\c which is persistent in X, as for any s2, s2eX if Sj is part of s2 and s2 e \[so]\c then s2 e \[so]\c. Persistence in this sense is a kind of stability under extensions of the available information. Using this notion of persistence of information to give precise content to the claim, informally argued for above, that generic information is persistent in recalcitrant situations, we need first an appropriate characterization of kinds. Let So be the situation-type: So = at /: donkey, a; yes where /is a location indeterminate, and a indicates an individual indeterminate and let Sj be the situation-type: Sj = I: stubborn, a; yes which each capture similarities across situations at the individual-level. To raise these situation-types to the kind-level required for generic interpretations, Situation Semantics provides the general means to construct complex indeterminates or 'roles' from any situation-type. Let x be an individual indeterminate and Sn be a situation-type which contains x, then (jr, Sn) is a complex indeterminate, called a role. Having such a complex abstract object, a new definition of a kind-type can be formulated along the lines of object-types (Barwise and Perry 1983: 75). Just as situation-types classify situations, kind-types classify kinds which themselves classify situations. A kind-type is a situation-type K((x, Sn)) with exactly one complex indeterminate. This makes the definition of members of a kind which realize the kind-type quite straightforward. A kindtype K((x, Sn)) is realized by an individual a if the situation Sn[a] is factual, and if a realizes K((x, Sn)) then a is a member of the kind K.6 This definition constructs kinds as complex object-types and provides a very general method to abstract from similarities across situations consisting of individuals to the kinds the individuals are members of, giving a purely set-theoretic analysis of the relation of 'realization' between a kind and its members. Obviously, as the situation-types may be arbitrarily complex, this allows a bewildering variety of possible kinds. This should not worry the semanticist, whose task it is to clarify the nature of the objects interpreting natural language and their relations and dependencies, working within a programme to provide a theory of reasoning and inference that explains how information is obtained, preserved or lost in manipulations. Returning to the first example of a generic sentence (1), its interpretation can now be represented as follows. Let So and 57 be the two situation-types as defined above. K0((x, So)) represents the generic interpretation of the bare plural NP donkeys, and Kj((x, S})) the abstract property of being stubborn, i.e. the generic or state-of-affairs interpretation of the VP are stubborn. The

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sentence as a whole expresses a relation between these two kind-types Ko and *,: C = at lu: involve, Ko, Kj\ yes

where lu is taken to be the universal location, which, if we had not required that every situation or situation-type contain a location, could be dropped, making C an unlocated constraint (this is actually allowed in recent modifications of the theory). The primitive relation involve should not be taken to be descriptive in any sense. It merely states the correlation between the two kind-types, as abstract objects satisfying its argument places. Note that there is no requirement in C that Ko and Kj be realized simultaneously. C does not express any correlation at the episodic level, but only an abstract correlation between abstract objects. Constraints determine which situations in a given structure of situations are meaningful options, given a particular situation s0. Take s0 to be the situation in which Jackie, a dog, encounters Chiquita, a donkey, on a narrow mountain trail. If Jackie is attuned to C, i.e. if she has learned the connection between Ko and K} as a meaningful relation which is useful in determining one's actions, and if Jackie rightly assesses s0 to be of type S0, and realizes the applicability of C in this situation, then there are several possibilities she may choose from. First, guided by C, Jackie may return on her path, not even testing out whether Chiquita who realizes Ko will actually realize K} as well (situation s2). Or Jackie may start barking to see whether Chiquita will realize K} or not (situation s3). If, however, a recalcitrant situation arises, and Chiquita is not stubbornly standing on the path but moves away, then Jackie may pursue her way (situation s4). Now s2 and s3 are clearly meaningful options for Jackie in s0, given C. Even though Jackie draws two different conclusions from the situation s0 and her attunement to C, the two courses of action are equally employing the meaningful relation stated by C. Other constraints, but also moods or irrational preferences, may determine which course of action is to be followed, given such a choice. On the other hand, when s4 arises Jackie remains attuned to C; the generic information she adheres to is in no sense invalidated by this particular episode of complaisant donkey behaviour. In s4 Chiquita realizes Ko but not /C7, so it cannot be a meaningful option for s0. But s4 is not precluded by s0 either; the information that Chiquita is a donkey and that she is not stubborn is compatible at an episodic level. So in this case s0 is part of s4, s0 e U^]] c trivially, and by persistence of [[s^Hc in the collection of situations not precluded by C, s4 e \[so]\c. A general characterization of the important notion of a recalcitrant situation relative to a constraint is now straightforward. Let C be of the form: C = at lu: involve, S, Sf; yes

then a situation s is recalcitrant with respect to C when for some anchor / S[f] is part of s but for no extension f of/ S'\f] is part of s. When S and 132

Generic information, conditional contexts and constraints S' are kind-types, as in the above example, this means that s is recalcitrant with respect to C when some individual a realizes S in s but does not realize

S' ins. Similarly, conditionals generally persist in recalcitrant situations. They express information which is formalized as a constraint on a structure of situations, correlating particular situation-types without requiring that every situation which realizes the antecedent situation-type also realizes the consequent situation-type. This is discussed below under the nature of 'unless' conditions and nonmonotonic reasoning.

4. CONDITIONAL CONTEXTS AND TEMPORAL ADVERBIALS A conditional sentence expresses a particular correlation between the information contained in its antecedent //"-clause and its consequent then-clause. In this section I discuss generic interpretations of antecedents, illustrating how generic information can be put into conditionals, and how further conditions and contextual restrictions may determine special conditional constraints. The temporal adverbs when and whenever are shown to be used for locating the interpretation of sentences in time, thus conveying episodic information about what is happening, something for which conditionals are not ordinarily used. Putting sentence (2) into a conditional context: (20)

If a donkey is stubborn, Pedro beats it

the generic interpretation of the indefinite NP a donkey seems to be lost when (20) is interpreted as stating that every time something that realizes the donkeykind and realizes stubborness, i.e. an episode of a particular donkey behaving stubbornly, Pedro beats the donkey (not necessarily temporally overlapping situations). Under that interpretation (20) conveys universal episodic information correlating two situation-types in such a way that when a situation of the first type occurs, i.e. a particular episode of stubborn donkey behaviour, the second situation-type is instantiated as well. In general, episodic information in conditional contexts correlates all instantiations of two types of situations. This is often expressed by indicating the universal force of indefinite NPs in a conditional context, i.e. sentence (20) is about all donkeys which are stubborn and the anaphor refers to each one. This has provided the major motivation for the introduction of reference markers or discourse-referents in DRS-theory (seeKamp 1984). In contrast to the relation between (2) and (20), the generic interpretation of (1) is preserved when the sentence is put into a conditional context, as in(2i) 7 : (21)

If donkeys are stubborn, Pedro beats them 133

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Such conditionals may, however, have two quite different interpretations. Either (21) is interpreted episodically as expressing that all donkeys which behave stubbornly (once, twice, often or constantly) are beaten by Pedro. Or, when the antecedent is interpreted generically, Pedro beats donkeys no matter whether each donkey actually behaves stubbornly or not. Generic information in the antecedent of a conditional may serve to set special conditions on the types of situations which may interpret the consequence. The difference between the two interpretations of (21) may be clarified by considering their interaction with universal episodic sentences and temporal adverbs. Information equivalent to the first interpretation of (21) is expressed by the universal sentence: (22)

Every donkey that behaves stubbornly is beaten by Pedro

which, due to its present tense, still leaves open how often each donkey manifests stubborn behaviour and, furthermore, does not require that the stubborn behaviour occur as often or in any temporal relation to Pedro's beatings. The use of a temporal adverb as in (23), instead of the conditional in (20), does seem to require that the manifestations of stubborn behaviour and the beatings are in some way temporally related. (23)

When a donkey is stubborn, Pedro beats it

This would equally be required with a universal temporal adverb such as whenever, independently of the tense in the sentence. This shows that conditionals with indefinite NPs in subject position may be paraphrased with temporal adverbs, which only add the requirement of temporal relations to the situations described by the antecedents and consequents. The second, generic interpretation of (21) cannot be paraphrased by a universal sentence like (22), nor by temporal adverbs which universally quantify over situations at an episodic level. In accordance with the observations made in section 2 about existential contexts, (20) and (22) and the nongeneric interpretation of (21) convey the same information as the conditional existential in

(24)

IftherJ i s are

1 [ * d °" k e y l being stubborn, Pedro beats [ \ tnem

donkeys

The generic interpretation of (21) is not reducible to such a conditional existential expression, since the antecedent expresses a correlation between kindtypes, which is itself a condition which must be met by the structure of situations before the situation-type interpreting the consequent can be determined. Hence the conditional in (21) states a correlation between a constraint C, as formalized in the previous section, and a situation-type 57 of the form:

Sj = at/: beat,p,x; yes 134

Generic information, conditional contexts and constraints where the individual indeterminate x is anchored to any individual that realizes the kind-types in the antecedent. The conditional expresses a condition on possible extensions of anchors which determine the members of the kinds constructed by interpreting the antecedent. So on its generic interpretation (21) is of the form 'if C, then S/, where the antecedent constrains the situations of type Sj to respect the anchors and the correlation expressed by C. Suppose, for instance, that s7 is a situation in which Pedro is beating a donkey: 57[[beats, Pedro, a]\ yes [donkey, a]\ yes where a is a real individual, and Sj is of type S}, and for some anchor/, K0[f] is part of s7, since a is a member of the donkey-kind in s7. Notice that a does not have to behave stubbornly in s7, as the constraint C only correlates kindtypes and makes a situation like s2 a meaningful option for s7, which is not precluded by it, whereas s2 is: [stubborn, a]\ no So, on this generic interpretation of (21), Pedro does not beat a donkey just when it is behaving stubbornly, and the situations which interpret the consequent do not have to realize both kind-types correlated by the antecedent expressing the constraint - as long as it does not conflict with the anchors previously established. The atemporal character of generic information is analysed as a lack of temporal relation between the kind-types in C or between their realizations. Sentences with temporal adverbs, however, not only locate situations with respect to each other in time, but also seem to require overlap in time between each situation of the antecedent-type and a situation of the consequent-type, thus establishing a particular mapping between episodic situations. When sentences like (20) and (21) are used for counterfactuals, similar observations can be made: (25) (26)

If a donkey were stubborn, Pedro would beat it If donkeys were stubborn, Pedro would beat them

where (25) states an individual-level counterfactual and allows a paraphrase with temporal adverbs, and expresses information equivalent to a conditional existential with a counterfactual tense: 2 v( 7) u

xr.L f a stubborn donkey 1 _ , ... . If there were , , , . \. , Pedro would beat it a donkey being stubborn

But (26), on its generic interpretation, expresses in its antecedent a counterfactual constraint, presupposing that the structure of situations in which the current situation is contained does not respect the constraint: i.e. the discourse situation 135

Alice ter Meulen

is here not of the type described by the constraint, or it cannot provide an anchor for the situation-types in the constraint. Such information cannot be expressed by temporal adverbials, since they always locate the situations in time and impose a particular mapping between situations or dependencies between anchors for situation-types. Neither can conditional existential sentences convey such generic information, as they force predicative interpretations of bare NPs. From these observations and theoretical considerations the following conclusions can be drawn: 1.

2.

3. 4.

/ / i n a conditional: if S then Sf is interchangeable under preservation of its meaning with a temporal adverb when/whenever used as a sentential connective, if the head NP in S is an indefinite NP, independently of the tense in S or S'. Universal NPs with a restrictive relative clause that S express the same information as ifS' then S", where S' is S except for having an indefinite head NP, instead of the universal NP in S, living on the same head-noun interpretation, and S" contains an anaphor dependent on it. Conditional existential sentences convey only conditional episodic information. Generic interpretations of antecedents in conditionals are never reducible to sentences connected by temporal adverbials when or whenever.

Obviously, the interchangeability of conditionals and temporal adverbs used as sentential connectives is entirely independent of the degree of subjective certainty a speaker may have concerning the truth of the antecedent, or concerning the question whether the situation described by the antecedent actually occurs or will occur later. To discredit the surprisingly common idea that there is such a connection between certainty and conditionals, the following examples may suffice:8 (28) (29)

If two and two are four, Pedro beats a stubborn donkey When Chiquita is stubborn, Pedro beats her

In (28) a relatively uninformative sentence puts a liberal constraint on the situation-type described by the consequent. Such a sentence may be used to say that Pedro always beats stubborn donkeys, as the supposition in the antecedent is supposedly an 'eternal' truth of arithmetic, which most, if not all, structures of situations will respect. Sentence (29), on the other hand, might be considered true even though Chiquita never in her life behaves stubbornly. Contrary to Reilly's claim (this volume) that the interchangeability of conditionals and temporal adverbs increases with the degree of certainty a speaker has concerning the antecedent, (28) and (29) demonstrate that even the most certain of things may be supposed in the antecedent of a conditional, whereas situations which may never arise - and the speaker may well be aware of 136

Generic information, conditional contexts and constraints that - can be described in sentences connected with temporal adverbs. However, it may very well be the case that the order of acquisition of conditionals and temporal sentential adverbs is partly determined by the child's subjective certainty concerning the antecedent or first sentence. If this is the case, an explanation must be offered as to why and how eventually a child comes to recognize the irrelevance of this subjective factor in adult speech. Reilly introduces the interesting notion of a 'protogeneric', which is a general statement about familiar objects in distinctive contexts. The following sentences are given as examples of such protogenerics: (30) (31) (32) (33)

When rain comes, we put an umbrella on top of us We go to bed when it's dark When men have beards they look so handsome You eat medicine when you're sick

First, it should be noted that the antecedents and consequents in these sentences all state some more or less causal or reason-giving connection, requiring some temporal connection between the situations so described, further supported by the use of temporal adverbs. Also, all examples are in the present indicative tense, most commonly interpreted as habituals. Sentences (30) and (31) are clearly about a contextually determined set of individuals, the interpretation of the indexical we in the discourse situation. The correlation expressed is thus restricted to a particular contextual setting, which could be formalized by an additional restriction on anchors. If the correlation C between the antecedent and consequent of (30) is of the form: C = at /; involve, Sj, S2', yes the situation-types Sj and S2 must be anchored within the contextual setting, anchoring we to the speakers in the discourse situation. Given the temporal relation suggested by the content of the antecedents and consequents in (30) and (31), it is hard to give them a genuinely generic interpretation in which the temporal connection is not playing an important role. Instead, the correlation expressed seems to be of a universal nature: i.e. all rain-occasions are situations in which we put an umbrella up; or all darkness-situations make us go to bed. If this interpretation is correct, these sentences do not allow for recalcitrant situations, like the generic information in constraints. Protogenerics are in this respect lacking the force of generics, which correlate kindtypes and serve an important function in determining meaningful options and are preserved in recalcitrant situations. If we wear a raincoat and do not need an umbrella, or when we stay up late are situations which seem precluded by the temporal adverbs in (30) and (31), just as conditionals with indefinites would preclude them. In this context I would like to discuss briefly how the 'unless' conditions, which indicate what situations are precluded by a given correlation between 137

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situation-types, serve the function of constraining counterexamples to the universal sentences and conditionals, and how they are related to constraints which preclude situations. In more logical literature, and more recently in artificial intelligence research, it has frequently been pointed out that antecedents cannot be strengthened by arbitrary sentences while preserving the correlation between antecedent and consequent. Stalnaker (1975), among others, has developed a conditional logic in which addition of antecedents does not generally preserve validity (see also Barwise in this volume). The phenomenon is called 'nonmonotonic reasoning' and the much cherished example is: (34)

If I put sugar in my coffee, it will taste nice

Hence: (35)

If I put sugar and diesel oil in my coffee, it will taste nice

The antecedent in the first conditional determines on the one hand what situation-types may serve to interpret the consequent, by restricting the class of possible ones to the ones which are compatible with the antecedent situationtype in polarities and anchors. Putting sugar in my coffee to make it taste nice precludes a host of situations, not only adding diesel oil, but also situations in which I am allergic to sweetening, or in which the coffee is cold and bitter. Setting an antecedent for a conditional is introducing a new situation, and indicating what background assumptions should be maintained in using that antecedent in reasoning towards a new conclusion or in determining what situation-types may be correlated to its interpretation. Background assumptions most often play the role of precluding situations, and precluding other constraints or correlations between situation-types, or of determining a hierarchy of constraints which apply in a certain order to the current situation. Universal sentences do not admit of any exceptions, as I have argued above. But a conditional sentence determines a universal correlation between the situations conforming to its antecedent and its consequent. A counterexample to a conditional can only be accepted as such if it conforms not only to the situationtype of the antecedent but also to all the other assumptions and background constraints. Generic information, as a correlation between kind-types, tolerates putative counterexamples, since it does not require a universal correlation between realizations of each kind-type. It is adhered to even when its kind-types are not realized, or when some of their realizations do not provide instances of the correlation. In defending a conditional against a counterexample, one seeks to understand the situation described by the counterexample, to find reasons for precluding it as not conforming to the background assumptions. A constraint, however, does not need to be defended against recalcitrant situations, as it is persistent. To modify one's constraints requires much more than a simple counterexample which conforms to the antecedent and all of its background assumptions. It requires a change in the entire structure of situations 138

Generic information, conditional contexts and constraints in which one operates, and I doubt that constraints may be modified in isolation, as they form a closely knit network of meaningful relations which we impose on the situation in which we find ourselves. Contrary to the diesel oil example, we are all too often not aware of what situations are precluded by the constraints we go by. Perhaps the best strategy to convince someone to employ another constraint, or to modify his constraints, is to show that there are significant situations included in one's new constraint that are precluded by his and, furthermore, that the new constraint makes more sense or fits better with other constraints which are already shown to work well. Conditional statements are in general monotone in compatible situations which preserve background and anchors. Sentence (21), for instance, may be strengthened to: (36)

If donkeys are stubborn and slow, Pedro beats them

Also spatio-temporal restrictions may determine contextual settings for conditionals and for generic information that must be preserved in additional antecedents or new information. Witness: (37)

If donkeys are stubborn in Spain, Pedro beats them

which does not entail (21); nor does: (38)

If Spanish donkeys are stubborn, Pedro beats them

This indicates that the information contained in the generic interpretation of an antecedent is not in general preserved, i.e. is not persistent under arbitrary supersets of the interpretation of the VP or subject NP.9 To return to Reilly's examples of protogenerics, sentences (32) and (33) are importantly different from (30) and (31). Sentence (32) contains a bare plural NP as head, and (33) is based on the indexical you, but used in the sense of one, any arbitrary person. The correlation between men and the beards they grow, stated in (32), may be interpreted as generic information with a restrictive condition, to which I will return in the next section on conditional generics.

5. CONDITIONAL GENERICS In this section generic interpretations of consequents in conditionals are discussed, and a brief outline is presented of how nongeneric antecedents may serve to restrict such generic information in consequents, information which often is supported by anaphoric dependencies. The correlation between antecedent and consequent in conditional generics is importantly different from the constraints which generic antecedents may impose on the situation-types interpreting the consequent, as was discussed in the previous section. Again the 139

Alice ter Meulen

question of interchangeability of conditionals and temporal adverbs is considered, and it turns out that in conditional generics with only generically interpreted consequents the interchange is more liberal, due to their nongeneric antecedents. The following example is adopted from Carlson (1979), with a slight variation. (39)

Donkeys are stubborn, if they have green eyes

This is a conditional generic, in which the antecedent presents a condition for the generic interpretation of the consequent. In this example, the consequent, which, as it contains the head NP, must precede the antecedent containing the dependent anaphor, conveys generic information. In line with the analysis of generics proposed earlier, (39) is of the form: (39')

C, if So

where C is a constraint, correlating kind-types based on donkey and stubborn as properties in situation-types, and So is here a situation-type: So = at /: green eyes, x; yes have,y, x; yes where y is an individual indeterminate to be anchored by extending the anchors of individuals which realize the kind-type Ko, i.e. donkeys. So provides an additional restriction on individuals which realize the kind-types correlated in the constraint. This is why C in (39) is a conditional constraint. In Carlson (1979) it is argued that sentences like (39) with bare plural NPs as heads are interpreted as equivalent to: (40)

Donkeys that have green eyes are stubborn

where the restriction expressed in the antecedent is put into the relative clause restricting the head NP. Carlson also argues that (39) cannot be equivalent to a universal sentence or to an indefinite NP in a conditional existential context, as these would impose too strong interpretations on generics, which would not admit of recalcitrant situations. In the analysis in Situation Semantics it is easy to build this restriction directly into the kind-type, as follows: K2((x, S2))

where S2 is a situation-type S2 = at /: donkey, x; yes green eyes, y; yes have, x,y; yes with the constraint C, which represents the generic information in (40) as a correlation between kind-types K2 and Kh as defined above. This is a general method to construct kind-types out of any complex situation-type. lfs0 contains a particular green-eyed donkey which realizes both K2 and Kj, there are meaningful options to s0 in which it behaves stubbornly; but also, situations in which 140

Generic information, conditional contexts and constraints the donkey does not behave stubbornly are meaningful options to s0, since C would persist in such recalcitrant situations. In Farkas and Sugioka (1983) an interesting argument is put forward against Carlson's analysis, which also bears on the analysis outlined here, constructing kind-types from any complex situation-type. They show that, though the restrictive relative clause analysis seems to have an initial plausibility for simple sentences like (39), it cannot easily generalize to conjoined sentences with dependent anaphors: (41) (42)

Donkeys are stubborn, if/when they have green eyes and they are stupid if/when they have brown eyes *Donkeys that have green eyes are stubborn, and they are stupid, if/when they have brown eyes

When the restriction is in the antecedent of a conditional sentence, or in its temporal when-dause, a conjoined sentence S' with an anaphor dependent on the plural head NP in S is acceptable. But when the restriction is contained within a restrictive relative clause belonging to the head NP in S, no such coreferential dependency is possible if S' contains an incompatible restriction (assuming that donkeys cannot have both green and brown eyes). Farkas and Sugioka use this argument to support a translational semantic analysis of generics, with an adverbial generally quantifying over cases or instantiations of unbound variables of open formulae, containing the restriction in the antecedent of a nonmaterial conditional. Although I cannot subscribe to their analysis, as it makes episodic information bear on the truth of generic statements and I favour a direct semantic interpretation in set-theoretic models, their argument shows convincingly that anaphoric dependencies on kind-types should be independent of restrictions on the individuals realizing the kind-type for the interpretation of (41). Of course, the unacceptability of (42) is accounted for by the general requirement that in order to be interpretable conjoined expressions must contain compatible information. Note that the intended anaphoric dependency on the NP with the restrictive relative clause would be perfectly acceptable if the restriction in S' were compatible with S, as in: (43)

and they get worse, if/when you beat them

For the interpretation of (41) a method is needed for constructing entities by addition of simpler ones, which allows the joining of the kind-type and the situation-type of the restricting condition as independent constituents in a complex entity. Addition is defined in Barwise and Perry (1983) for situationtypes by their union of constituents. It is noticed (p. 91) that even though a situation s may be of type S and of type S", s is not necessarily of type S + S' as the anchors of the two situation-types may conflict on some value assigned to the common indeterminates. Since kind-types have been defined as special situation-types, the addition of a kind-type and a situation-type is 141

Alice ter Meulen simply their union of constituents: K + S. This can be a first argument in a constraint C, which represents the generic information about green-eyed donkeys and their stubbornness without having to appeal to complex kind-types. C = at /: involve, K0((x, So)) + S2, Kj((x, S 7 »; yes where So = at /: donkey, JC; yes S7 = at /: stubborn, JC; yes 52 = at /: donkey, JC; yes green eyes, y; yes have, JC, y;yes Similarly, the second conjunct of (41) expresses generic information restricted by an additional condition: C = at /: involve K0((x, So)) + S3, K4((x, S4)); yes where So is as defined above and 53 = at /: donkey, JC; yes brown eyes,y\ yes have,x,y\ yes 54 = at /: stupid, JC; yes (The co-indexing of the kind-type and the situation-type on which it is based is only a mnemonic aid, which has no further semantic significance.) Sentence (41) is now interpreted by a conjunction of C and C, and expresses generic information, persistent in recalcitrant situations; i.e., green-eyed donkeys that are never stubborn, or smart brown-eyed donkeys, cannot be counterexamples to (41). Although the difficult issues concerning the interpretation of the anaphora remain outside the scope of the present paper, the fact that C and C" have Ko as a constituent in common may serve as a first step towards a more satisfactory account of the interaction of the conditionals and plural anaphora for which Kamp (1984) provides the essential analytic tools (cf. Reinhart in this volume). In a conditional generic statement the generic NP is usually part of the consequent, as in (39). When it is contained in the antecedent the whole expression is interpreted more easily as a generic conditional, expressing a constraint on complex kind-types as in: (44)

If donkeys have green eyes, they are stubborn

The condition expressed in the antecedent of (44) can be represented by a complex kind-type (green-eyed donkeys) which serves as an antecedent for the anaphor in the consequent. This preferred generic interpretation of (44) is even stronger in the counterfactual: (45)

If donkeys had green eyes, they would be stubborn 142

Generic information, conditional contexts and constraints which, according to my intuitions, does not admit of a nongeneric interpretation of the antecedent, restricting the first argument in the constraint correlating donkeys and stubbornness by a situation-type. In conditional generics temporal adverbs can replace if in the antecedent without loss of meaning, as the antecedent expresses a universal condition ('all the ones that have green eyes'), which is episodic. This use of when in a restrictive condition on generics is often called the atemporal use (Carlson 1979). Especially when used with stative VPs it does not locate the situationtypes in space-time. In the case the restrictive clause with the temporal adverb expresses episodic information, the consequent, if it is to be interpreted generically, must contain a verb denoting gradual change: (46)

^Donkeys , I become 1 stubborn, ,, f when 1 they , get A * *.. older

Sentence (46) expresses a generic correlation, a constraint, between the degree of stubbornness and age. One could argue, however, that when here is not so much atemporal as omnitemporal. The conditional if is clearly unacceptable in such contexts of gradual change. The episodic antecedent of conditional generics hardly admits of existential paraphrase, as it prohibits the necessary anaphoric dependency. Sentence (39) is equivalent to the questionable: (39")

Donkeys are stubborn, if they are (the) ones with green eyes

Returning once more to Reilly's example (32) of a protogeneric: When men have beards, they look so handsome, it is, on a generic reading, a conditional generic analysed as: C = at /: involve, K0((x, So)) + S2, * , « * , S,»; yes where So = at /: man, x; yes S1; = at /: man,x; yes beard, y; yes have, x,y; yes S2 = at /: look handsome, x; yes So bearded men that do not look handsome are not precluded by C, but handsome looks are said to be meaningful options for any given bearded man. 6. CONCLUSIONS I have argued that there are various ways in natural language to express generic information. Generics serve primarily to form the basis of explanations, expectations of what the present situation may evolve into, and to determine the meaningful options for a given situation. Generic information can be represented set-theoretically as constraints on situation-types and kind-types. The initially guiding idea that generic information serves to classify parts of the 143

Alice ter Meulen world as being similar and stable under changes, even when the world does not conform to it and the fit is quite loose, was analysed by defining persistence of generic information in recalcitrant situations. Similarly, conditionals express information which persists in recalcitrant situations, if their antecedent admits of a generic interpretation. It was shown that conditional contexts differ from tensed contexts or temporal adverbials connecting sentences. The dynamics of interpretation consist not only of the more often studied cumulative gathering of information on a stable domain or a fixed world (see Veltman in this volume), but also, and equally important, of the preservation of information about the similarities in the world as it is changing. This paper has attempted to show how generic information and generics in conditional contexts serve the latter purpose. NOTES 1 This paper has profited from the comments and criticism of Greg Carlson, Elizabeth Traugott, Frank Veltman and Henk Zeevat, for which I am duly grateful. It has also profited much from Carlson's work on bare plurals and generic NPs, and from the insights of DRS-theory developed by Hans Kamp on anaphora and informational dependencies across discourse (Carlson 1979,1982; Kamp 1984). Of course, the views I outline remain entirely my own responsibility. 2 See Barwise and Perry (1983) and the issue of Linguistics and Philosophy of March 1985 for a valuable source of comments and criticism of Situation Semantics. 3 Sometimes, for example in Carlson (1982), nomic (or gnomic) sentences are distinguished from the generic NPs occurring in them. The terminology is somewhat simpler here: expression of any syntactic category may be interpreted generically, and hence convey generic information. Episodic information is contrasted with generic information in a close analogy to the individual-level and stage-level versus kind-level predicates of Carlson's analysis. 4 A VP-context is neutral if it is interpreted as a property that may be equally attributed to kinds, individuals or stages of individuals: e.g. be stubborn may describe a 'dispositional' property of kinds or individuals, which is not necessarily actually manifested in behaviour (stages). The argument in this paper does not hinge on so-called dispositional properties, since a nondispositional predicate like be grey would equally allow generic interpretations of (i)-(3). 5 This anti-symmetry concerns the following relation between properties. Let R be the intended correlation, and A be the subject NP being stubborn, and B the other NP donkeys in (4) then: R(A, B) and R(B, A) => A = B Predicative relations are generally not symmetric; neither are, obviously, conditional dependencies. 6 It is perhaps useful to compare this 'type-free' construction of new semantic entities from simpler ones with the atomic type-theory of Montague Grammar, which is also Carlson's framework. A detailed comparison of a fragment in both semantic theories would be required to convince anyone of the claimed advantages of Situation Semantics, but this must await another occasion. For the purposes of this paper, let me point out the following connections. In Situation Semantics properties are constituents of situation-types, whereas in PTQ, the fragment of Montague Grammar most often 144

Generic information, conditional contexts and constraints employed as a model, properties are extensionally interpreted to be sets of individuals or functions from possible worlds to these. The individuals in Situation Semantics are just the individuals of type e of PTQ; atomic entities and the polarities yes /no are identical to the truth values assigned to propositions of type t. Roles are doing the job of lambda-abstracts of PTQ, and anchoring roles amounts to lambda-conversion. The construction of kind-types might be comparable to type-lowering in Chierchia (1984), since it treats the complex indeterminate based on an 'individual-level' situation-type as if it were an individual-level entity itself. Situation Semantics allows entities of any complexity as constituents of situations, which is inherent to its type-free model theory. I argue in another paper that the fundamental distinction between properties and individuals that Situation Semantics adheres to is not necessary if one constructs individuals from properties, resulting in an even more type-free model theory. The complex issues concerning self-application and the avoidance of paradoxes cannot be addressed in this paper; but see Chierchia (1984) for detailed analysis. 7 The analysis of (1) assumes that sentences are interpreted as relations between the subject NP interpretation and the VP interpretation, rather than taking the latter to be the argument to the functor interpreting the former. I have in mind that the INFL node establishes this relation configurationally. 8 See Reilly (this volume) and also Stockwell, Schachter and Partee (1973) in support of this mistaken idea. 9 These facts about generics can be rendered as: (i) (ii)

DABandACA'J^DA'B D AB and B C B' £> D AB'

which tell those familiar with Generalized Quantifiers that the context-dependency of generics sets them apart from proper names or definite NPs as being neither (i) persistent, nor (ii) monotone-increasing. See van Benthem and ter Meulen (1985) for recent research in Generalized Quantifier Theory.

REFERENCES Barwise, Jon and John Perry. 1983. Situations and attitudes. Cambridge, Mass.: Bradford Books, MIT Press. Benthem, Johan van and Alice ter Meulen (eds.) 1985. Generalized quantifiers in natural language. GRASS 4, Dordrecht: Foris Publications. Carlson, Gregory. 1979. Generics and atemporal when. Linguistics and Philosophy 3: 49-98. Carlson, Gregory. 1982. Generic terms and generic sentences. Journal of Philosophical Logic 11: 145-81. Chierchia, Gennaro. 1984. Topics in the syntax and semantics of infinitives and gerunds. Ph.D. dissertation, University of Massachusetts. Farkas, Donka and Y. Sugioka. 1983. Restrictive if/when clauses. Linguistics and Philosophy 6: 225-58. Kamp, Hans. 1984. A semantic theory of truth and interpretation. In Truth, interpretation and information, ed. Jeroen Groenendijk, Theo Janssen and Martin Stokhof. GRASS 2, Dordrecht: Foris Publications. Stalnaker, Robert C. 1975. Indicative conditionals. Philosophia 5: 269-86. Stockwell, Robert, Paul Schachter and Barbara Partee. 1973. The major syntactic categories of English. New York: Holt, Rinehart and Winston. Linguistics and Philosophy. March 1985. Special issue on Situation Semantics.

145

DATA SEMANTICS AND THE PRAGMATICS OF INDICATIVE CONDITIONALS •

Frank Veltman Editors' note. This chapter proposes a clear criterion for a demarcation between the semantics and pragmatics of indicative conditionals, based on a dynamic logic known as data semantics and a relative notion of truth (for which it is criticized by Adams). Gricean maxims are given a central explanatory role in accounting for conditionals. As a model for information processing, data semantics shows similarities to Situation Semantics (see the chapters by Barwise and ter Meulen). Discussion of the interaction between modals and conditionals is also to be found in Greenberg's contribution. 1. INTRODUCTION Some arguments are logically valid but pragmatically incorrect.1 Others are pragmatically correct but logically invalid. Grice's Logic and conversation (1975) taught us to draw these distinctions, but unfortunately most of us draw them differently. What one calls a logically valid argument form with a few pragmatically incorrect instances is for another a logically invalid argument form with many pragmatically correct instances. For example, if you believe that indicative conditionals behave like material or strict implications, you will be ready to point out that the intuitively absurd argument.2 (1)

If Jones wins the election, Smith will retire to private life If Smith dies before the election, Jones will win it .'. If Smith dies before the election, he will retire to private life

is just a pragmatically incorrect instance of the logically valid Hypothetical Syllogism: (2)

If B then C If A then B .-.If A t h e n C

If, on the other hand, your favourite semantic theory attributes the logical properties of variably strict implications to indicative conditionals, in which 147

Frank Veltman case you will find the Hypothetical Syllogism logically invalid, you will maintain that the intuitively sound argument: (3)

If Jones wins the election, Smith will have to leave the White House If Smith goes on antagonizing his supporters, Jones will win the election .'. If Smith goes on antagonizing his supporters, he will have to leave the White House

is at best a pragmatically correct instance of this inference pattern.3 The literature on conditionals is full of examples like (1), put forward by one author as a clear-cut counterexample to a putative logical principle, only to be explained away by another author as an innocent pragmatic exception to an otherwise faultless semantic rule. The strategy described in connection with (3) is less frequently followed. Still, every now and then some author feels called upon to explain why a given inference pattern, in most cases a classical logical principle which 'as recent investigations show' is 'nevertheless' logically invalid, has for so long kept out of harm's way. Usually, the explanation offered involves a partial rehabilitation of the inference pattern concerned: although not logically valid, most of its instances turn out pragmatically sound. The issue is not just verbal. In most cases the 'pragmatic' arguments put forward by the one party are quite different in character from the 'semantic' arguments put forward by the other. That does not mean, however, that both parties put forward the same kind of pragmatic arguments, much less that they need have the same conception of semantics. Actually, the pragmatic differences are the least pronounced: most people working on conditionals agree that pragmatic theories begin where semantic theories end and that they should take the form of a theory of conversation a la Grice. But then - and this is typical for the field of conditionals - there is no consensus at all as to what form a semantic theory should take: that of a theory of truth? According to the majority of logicians, who take the classical standard of logical validity as the starting point of their investigations, yes. (Roughly: an argument is valid if and only if it is impossible for all its premises to be true while its conclusion is false.) No, answer the relevance logicians:4 truth preservation may be a necessary condition for the logical validity of an argument, but it is by no means sufficient (the premises of the argument must in addition be relevant to the conclusion). No, answer Adams et al.5, believing as they do that the proper explanation of validity is to be given in terms of probability rather than truth. (Roughly: an argument is valid if and only if it is impossible for all its premises to be probable while its conclusion is improbable.) And no, I shall answer in this paper. The proper explication of logical validity is this: an argument is valid if and only if it is impossible for all its premises to be true on the basis of the available evidence while its conclusion is not 148

Data semantics and the pragmatics of indicative conditionals true on that basis. Consequently, a semantic theory should supply an explication of what it means for a statement to be true on the basis of the available evidence. In this paper I will sketch such a semantic theory. The above remarks should have made clear, however, that there is little sense in discussing a semantic theory - if, at least, it presents a semantics for conditionals - without paying any attention to its ramifications for pragmatics. Therefore a good deal of this paper is devoted to pragmatic questions: if indicative conditionals do have the semantic properties ascribed to them here, what will their pragmatic properties be? Which logically invalid arguments will become pragmatically correct and which logically valid arguments will on pragmatic grounds become absurd? The answer to this question can be much less arbitrary than the literature suggests. Indeed, semantics and pragmatics can be so attuned that the dividing line between logical validity and pragmatic correctness is drawn exactly as a criterion of cancellability prescribes. 2. INFORMATION MODELS What does it mean for an English sentence, in particular an English conditional sentence, to be true on the basis of the available evidence? Following usual logical practice, I shall not try to answer this question directly but introduce a logical language L, the sentences of which will serve as formal 'translations' of English sentences. L is given by: (i)

a vocabulary consisting of countably many atomic sentences, two parentheses, three one-place operators ~~|, must, and may and three two-place operators A , v, and —>

(ii)

the formation rules that one would expect for a language with such a vocabulary

As usual the operators ~~|, v and A are meant as formal counterparts of English negation, disjunction and conjunction respectively. If A and B are formal translations of the English sentences A' and B', then (A-»B) is meant to be a formal translation of the indicative conditional with antecedent A' and consequent B'. The operator may represents the English expression 'it may be the case that', in its epistemic sense, and the operator must the expression 'it must be the case that', also in its epistemic sense. It will appear that the"semantic and pragmatic properties of indicative conditionals are closely tied up with the properties of these expressions. In presenting the semantics for L, I shall again follow usual practice and first specify the admissible models for L. Definition i. An information model (for L) is a triple (S, ^ , V) with the following properties:

(i)

S± 149

Frank Veltman (ii) (iii)

^ is a partial ordering of S; each maximal chain in (S, ^ ) contains a maximal element V is a function with domain S; (a) for each seS, Vs is a partial function assigning at most one of the values i or o to the atomic sentences of L; (b) if s ^ s ' , V s c Vs>; (c) if sis a maximal element of (S, ^ ) , Vs is total

The basic entities of an information model,6 the elements of S, are called (possible) information states: the speakers of the language L - one speaker at different times, or different speakers at the same time - can have different information about reality. For our purposes, all there is to know about any information state is covered by the relation ^ and the function V. V tells for each atomic sentence A and each information state s whether A is true on the basis of the evidence available at s, in which case VS(A) = i, or whether A is false on that basis, in which case VS(A) = o, or whether the evidence available at s does not allow any definite conclusion about the truth value of A, in which case VS(A) is undefined. The relation ^ determines the position of each information state among the others. In this connection it is particularly important to know, given the evidence at a certain information state, what the outcome of any further investigations might be. Whenever s ^ s', we say that it is possible for s to grow into s'. So understood, it will be clear why ^ is taken to be a partial order. The requirement that K s c ^ if s ^ s ' constrains the semantic properties of atomic sentences considerably: once an atomic sentence A has turned out to be true (or false) on the basis of the evidence, it will remain true (or false) whatever additional data may come to light. As we shall see in the next section, not every sentence of L is stable in this sense. Notice that it may very well be that s < s ' while V s = Vs>: accumulation of evidence need not necessarily mean that more atomic sentences get a definite truth value. (Suppose it is possible for s to grow into an information state where both the atomic sentence A and the atomic sentence B are true. It may very well be that this possibility is excluded once s has grown into s\ That does not mean, however, that it must be clear at s' which of the atomic sentences A and B is false.) If s is a maximal element of (S, ^ ) s is called a complete information state. The choice of terminology will do here as an explanation for the requirement that at maximal elements s the function Vs must assign a definite truth value to every atomic sentence. The requirement that each maximal chain in (S, ^ ) must contain a maximal element implies that every incomplete state can grow into a complete information state7 - in principle that is, not necessarily in practice. One of the maximal elements of (S, ^ ) is rather special. At that point, say s0, the information is not only complete, but also correct: the evidence available at s0 is derived from the actual world. Since the speakers of the language L cannot but get their data from the actual world, they will always be in an information state that can grow into s0.8 However, as long as their 150

Data semantics and the pragmatics of indicative conditionals data are incomplete, they do not exactly know what the actual world is like. That is where the information states that cannot grow into s0 come in: a speaker may at a given point have to reckon with the possibility that further investigations will bring him in such an information state even if this does not in fact happen. Notice that the information models (5, ^ , V) are so defined that it may very well occur that for a given atomic sentence A and an information state s the following holds: (i)

f o r n o s ' ^ s , VS.(A) = o

(ii)

VS(A) is undefined

From (i) it follows that VS>(A) = i for every complete s' ^ s . So it may very well occur that a certain atomic sentence A is not true on the basis of the evidence available at s, while on the other hand it is impossible for s to grow into an information state at which A will turn out false. Indeed, s will inevitably grow into an information state at which A is true. One may wonder whether we should allow this. Wouldn't it be plausible to call A true on the basis of the evidence available at s? Shouldn't we demand that VS(A) = i if for no s' ^ s, VS.(A) = o? I do not think so. I think it would blur an important distinction - that between direct and indirect evidence - if one were to maintain that it is solely on the basis of the evidence available at s that the sentence A is true. Someone in the information state s is not directly aquainted with the state of affairs described by A. His data at best constitute indirect evidence for the truth of A: A must be true, all right, but it may take quite some time before this is definitely shown. 3. SEMANTIC STABILITY AND INSTABILITY Let M = (S, ^ , V) be an information model, s an information state in S and A a sentence of L. In the sequel 'Mlh5A' abbreviates 'A is true (in M) on the basis of the evidence available at s', and 'MSHI A' abbreviates 'A is false (in M) on the basis of the evidence available at s.' Definition 2. Let M = {S, ^ , V) be a model and s an information state. If A is atomic, then Aflh5AiffVs(A) = i Ms-UAiffVs(A) = o Mlh s nAiffM s HIA Af s HnAiffMI|- s A M\\-Smay A iff for some information state s' ^ s, M\\-s> A Mf\\ may A iff for no information state s' ^ s, M||-s< A M\\-Smust A iff for no information state s' ^ s, M SHIA M fWmust A iff for some information state s' ^ s, MSHIA

Frank Veltman Mlh s AABiffM|h s AandMlh 5 £ M s HIAABiffM s HIAorM s HIB Mlh s AvBiffMlh s AorMlh s B M s HIAvBiffM s HIAandM_||B Mlhs A—>B iff for no information state s' ^ s , M\\-s> A and MSHIB Ms-\\ A—>B iff for some information state s' ^ s , M\\-s> A andM s HIB In discussing this definition I shall often refer to the following information states: Information state i. You are presented with two little boxes, box i and box 2. The boxes are closed but you know that together they contain three marbles, a blue one, a yellow one and a red one, and that each box contains at least one of them. Information state 2. As 1, except that in addition you know that the blue marble is in box 1. (Where the other two marbles are remains a secret.)

3.1 May Suppose you are in information state 1. Somebody says: 'The blue marble may be in box 2.' Would you agree? Suppose you are in information state 2. Somebody says: 'The blue marble may be in box 2.' Would you still agree? According to definition 2, your answer to the first question should be 'Yes', and to the second question 'No'. Definition 2 says that a sentence of the form may A is true on the basis of the evidence available at a given information state s as long as it is possible for s to grow into an information state s' where, on the basis of the then available evidence, A is true; and that such a sentence is false on the basis of the evidence available at s if and only if this possibility is excluded. In information state 1 you must still reckon with the possibility that the blue marble will turn out to be in box 2. Therefore the sentence The blue marble may be in box 2 is true on the basis of the evidence available there. In information state 2 you do not have to reckon with this possibility anymore. Once you know that the blue marble is in box 1, it is wrong to maintain that it may nevertheless be in box 2. At most, you can say that it might have been in box 2. Unlike atomic sentences, the truth of sentences of the form may A need not be stable. They will often be true on the basis of limited evidence only to become false as soon as new evidence becomes available. Once their falsity has been established, however, it has been established for good. In terms of the following definition: sentences of the form may A, though in general not T-stable, are at least F-stable. Definition 3. Let A be a sentence. 152

Data semantics and the pragmatics of indicative conditionals A is T-stable iff for every model M = (S, ^ , V) and information state s € S, if M lhs A then M lhS' A for every information state s' ^ s A is F-stable iff for every model M = (S, ^ , V) and information state s € S, if MSHIA then MSHIA for every information state s' ^ s A is stable iff A is both T-stable and F-stable The theory of may developed here differs widely from those developed within the framework of possible world semantics. It renders the sentence: (4) The blue marble is in box 1 and it may not be there contradictory, just like: (5)

The blue marble is in box 1 and it isn't

According to all other theories (4) is a pragmatic absurdity rather than a logical contradiction: (4) can be perfectly true although nobody can ever sincerely assert it. Is there any evidence in favour of this claim, that sentences like (4) are pragmatically rather than logically absurd? I am afraid not. The only empirical support which it could conceivably get should consist in an informal example which shows that the apparent inconsistency of sentences of the form A/\may~~\A can sometimes be cancelled. I am pretty sure, however, that no such example will ever be found. Anyone asserting a sentence like (4) fails to fulfil the conversational maxim of quality, as for example Groenendijk and Stokhof (1975) are ready to explain. (Roughly: by asserting the right-hand conjunct The blue marble may not be in box /, the speaker indicates that the sentence The blue marble is not in box 1 is consistent with everything he believes. But according to the maxim of quality he is not allowed to assert the left-hand conjunct if he does not believe that the blue marble is in box 1.) So if there is any example showing that the apparent inconsistency of these sentences can really be cancelled, it must be one in which the speaker indicates (either explicitly or implicitly, but at least in a way clear enough to the hearer) that he is stating something he does not himself believe, but that he is doing so for some good reason, i.e. one which can be reconciled with the overall Cooperative Principle. I am afraid that no hearer will ever be found who is able to detect what good reason that might be. That it is impossible to breach the maxim of quality and yet observe the overall Cooperative Principle has been noticed before.9 For example, Gazdar (1979: 46) notices that an implicature arising from the maxim of quality 'differs from those arising from the other maxims because it cannot be intelligibly cancelled'. Yet the only conclusion which is usually drawn is that the maxim of quality has a privileged position among the other maxims. Everybody seems to accept, if reluctantly, that the criterion of cancellability offers at best a sufficient condition for calling something pragmatic instead of logical. 153

Frank Veltman The one argument I have to offer in favour of the position that sentences of the form A A may ~~|A are logically rather than pragmatically absurd is highly theoretical. Consider the following (re)formulation of the maxim of quality: Do not assert a sentence A unless A is true on the basis of the evidence at your disposal. Notice that every sentence which owes its pragmatic absurdity simply and solely to the fact that it can never be asserted without violating this maxim is also absurd for semantic reasons - for dflta-semantic reasons at least. Hence the question of cancellability need not arise. By doing data semantics instead of the usual truth-conditional semantics, we have, so to speak, annexed part of what was always called pragmatics. As a consequence, the border between logical and pragmatic-but-not-logical inconsistency and that between logical and pragmatic-but-not-logical validity has been redrawn. Actually, it seems that now cancellability can serve as a condition which an argument must satisfy in order to be classified as pragmatically but not logically valid. 3.2 Must I already hinted at the truth condition for the operator must near the end of section 2. According to definition 2, a sentence of the form must A is true on the basis of the available evidence if and only if no additional evidence could make A false. Hence, if one keeps on gathering more information, A will inevitably, sooner or later, turn out true. As long as A could yet turn out false, must A is false. It is worth noting that in many cases this analysis renders a sentence of the form must A weaker than A itself. If an atomic sentence A is true on the basis of the available evidence, then must A is true on that basis as well. But must A can be true on the basis of the evidence without A being true on that basis. In the latter case the data constitute at best indirect evidence for A, in the first case direct evidence. That must A is weaker than A on many occasions has been noticed by a number of authors. Karttunen (1972: 12) illustrates this with the following examples: (6)

John must have left

(7)

John has left

His informal explanation fits in neatly with my formal analysis: Intuitively, (6) makes a weaker claim than (7). In general, one would use (6), the epistemic must, only in circumstances where it is not yet an established fact that John has left. In (6), the speaker indicates that he has no first hand evidence about John's departure, and neither has it been reported to him by trustworthy sources. Instead (6) seems to say that the truth of John has left in some way logically follows from other facts the speaker knows and some reasonable assumptions that he is willing to 154

Data semantics and the pragmatics of indicative conditionals entertain. A man who has actually seen John leave or has read about it in the newspaper would not ordinarily assert (6), since he is in the position to make the stronger claim in (7). Similar remarks can be found in Groenendijk and Stokhof (1975), Kratzer (1977), and Lyons (1977).10 Still, despite the unanimity on this point, no theory has yet been proposed which actually predicts that on many occasions must A is a logical consequence of A. Most theories treat may and must as epistemic modalities and, depending on whether the underlying epistemic notion is knowledge or belief, must A turns out to be either stronger than A or independent of it. Notice that sentences of the form must A are T-stable though they are not in general F-stable. Consider, for example, the sentence: (8)

Either the yellow or the red marble must be in box 2

For all you know in information state 1 it may very well be that the blue marble is in box 2 while both the yellow and the red marble are in box 1. Hence it is not the case that either the yellow or the red one must be in box 2. But as soon as you are told that the blue marble is in box 1 this is different. At least one of the marbles is in box 2 and it cannot be the blue one. So it must be the yellow one or the red one.

3-3 K According to definition 2, a sentence of the form A—>B is true on the basis of the evidence available at a given information state s if and only if s cannot grow into an information state s' at which A is true on the basis of available evidence and B is false. If, by any chance, further investigations should reveal that A is true, they will also reveal that B is true. Furthermore, it is stated that A—> B is false on the basis of the evidence available at a certain information state s if and only if it is still possible for s to grow into an information state at which A is true and B false on the basis of the available evidence. As a consequence, we find that sentences of the form A—>B are not in general F-stable. Consider the sentence: (9)

If the yellow marble is in box 1, the red one is in box 2

Again, the evidence available in information state 1 allows for the possibility that both the yellow and the red marble are in box 1. So on the basis of the limited evidence available there, (9) is false: it is not so that if the yellow marble is in box 1, the red one is in box 2. In information state 2, however, (9) is not false any more. Once you know that the blue marble is in box 1, you can be sure that if the yellow marble happens to be in box 1, the red one will turn out to be in box 2. 155

Frank Veltman Now consider the negation of (9): (10)

It is not so that if the yellow marble is in box 1, the red one is in box 2

This sentence is true on the basis of the evidence available at information state 1 - at least if we apply definition 2 to it. Suppose you are in information state 1 and somebody - Mrs S. - asserts (9): 'If the yellow marble is in box 1, the red marble is in box 2.' Would it be appropriate, then, to reply like this: 'No, you are wrong, it may very well be that both the yellow and the red marble are in box 1. So it is not the case that if the yellow marble is in box 1, the red one is in box 2'? Such a reply would only under very special circumstances be correct. Only when you know for certain that Mrs S. is not better informed than yourself, because only then can you be sure that she is mistaken. Certainly, for all you know (in information state 1), sentence (9) is false and sentence (10) is true, but sentence (9) is not F-stable and sentence (10) is not T-stable. If by any chance the blue marble should be in box 1 and if Mrs S. should know this, then what she says is true on the basis of the evidence available to her. So perhaps she is better informed than yourself; perhaps she is telling you something about the marbles you did not yet know. Therefore, instead of denying the truth of her statement you'd better ask her on what evidence it is based. In normal conversation every statement is meant to convey some new information, and only when this new information is incompatible with some T-stable sentence that is true on the basis of the evidence gathered may one raise doubts about it - as when you are in information state 2 and Mrs S. says, 'Maybe the yellow marble is in box 1 and if so, the red one is in box 1 too.' However, even in this case it would be inappropriate to reply with a simple denial: 'No, it may very well be that the yellow marble is in box 1 and the red one is in box 2.' Again, such a sentence is not T-stable; it might owe its truth to a lack of information on your part - that is certainly what Mrs S. will think. So what you will have to reply is something much stronger: 'No, it cannot be that the yellow and the red marble are both in box 1. So if the yellow marble is in box 1, the red one isn't.' These considerations may help us to understand some of the peculiarities of negated conditionals. For one thing, they explain why a conditional statement A—> B is so often refuted with a counterconditional A—»~~|B rather than with a negated conditional ~1(A—>B). But they do so without thereby equating sentences of the form A—»~|B with sentences of the form ~~|(A—» B). On the account given here, ~~|(A—>B) is not logically equivalent to A—>~~|B, as it would be if —> behaved as Stalnaker (1968) and Adams (1975) predict. Nor is it equivalent to A A ~~|B as it would be if —• behaved like material implication. We find that ~~|(A—»B) is equivalent to may (A A ~]B). There 156

Data semantics and the pragmatics of indicative conditionals is nothing wrong in believing both (n)

It is not the case that if Jones wins the election, Smith will retire to private life

(suppose Smith dies before the election) and (12)

It is not the case that if Jones wins the election, Smith won't retire

(suppose Smith does not die before the election) Moreover, neither of these beliefs would commit one to the belief that (13)

Jones will win the election

Jones may win the election, that is the only thing one can say about it. Let A be F-stable and suppose that A is false on the basis of the available evidence. Then according to definition 2, A—>B is true on the basis of the evidence for any sentence B. Similarly, if B is T-stable and true on the basis of the available evidence then A—»B is true on the basis of the evidence for any sentence A. In other words, the present treatment of conditionals does not meet the requirement that a sentence of the form A—>B should never be true unless the antecedent A is somehow 'relevant' to the consequent B. The well-known 'paradoxes' of material implication turn out logically valid. We find, for example, that from a logical point of view, there is nothing wrong with: (14)

The blue marble is in box 1 .'. If the blue marble is in box 2, it is in box 1

If you do find it difficult to accept the validity of this argument, please read the conclusion once more without losing sight of the premise. The argument does not run like: (15)

The blue marble is in box 1 .'. If the blue marble had been in box 2, it would have been in box 1

Or perhaps it helps to compare (14) with: (16)

The blue marble is in box 1 '. The blue marble is in box 1, if it is anywhere at all

(Anywhere . . . , then why not try box 2?) If this does not help either, the reader is referred to section 4.2 where I shall argue that (14), though logically valid, is nevertheless pragmatically incorrect. By now it will be clear that the logic attributed to indicative conditionals by the theory presented here cannot easily be fitted into the spectrum formed by the theories proposed so far. One more example: the principle of modus 157

Frank Veltman tollens, which holds both in classical and in intuitionistic logic, and also in the systems of strict and variably strict implication, and even in such a weak system as the system of relevance logic, fails. It is not generally so that one can conclude ~~|A from A—»B and ~~1B. The closest approximation available is this: if B is F-stable then must ~|A follows from A—>B and ~~|B. If B is not F-stable even this weakened version of modus tollens fails. Consider, for example, the premises A—>(B—>C) and ~1(B—>C), where A, B and C are three distinct atomic sentences. Neither A nor must ~~|A follow from these sentences, we only have that may "~|A is true on the basis of the available evidence if A—> (B—> C) and ~~|(B—> C) are. (Suppose you are in information state i. Then for all you know it may very well be that neither the yellow nor the blue marble is in box 2. So it is not the case that if the yellow marble isn't in box 2, the blue one is. However, if the red marble happens to be in box 1 things are different. Indeed, if the red marble is in box 1, then if the yellow marble isn't in box 2 the blue one is. Now, by an application of modus tollens, it would follow from the italicized sentences that the red marble isn't in box 1, but obviously it may very well be there.) So we find that in certain respects data logic is weaker than the weakest logic in the literature: modus tollens is not always valid. In other respects, however, it is at least as strong as any of the others: we saw that A—> B follows from B, at least if B is T-stable. In yet other respects it lies somewhere inbetween: we saw that ~1(A—> B) is equivalent to may (A A "IB), which is exactly what one would find if —> were the implication and may the possibility operator of one of the Lewis systems.11 The arguments which on my account are logically invalid cannot easily be explained away as 'just' pragmatically unsound. Notoriously difficult (for those who believe that indicative conditionals behave like material implications) are, for example, the schemes ~~|(A—»B)/.'. A and ( A A B ) — » C / . ' . (A—>C) v (B—>C). So far, no satisfactory pragmatic explanation has been offered for the fact that many instances of these inference patterns seem anomalous. On the other hand, those who think that my theory is too strong, that too many of the wrong arguments come out valid, can produce a lot of intuitive counterexamples to make their point. Here I am the one who has to produce the good reasons for saying that these are 'just' pragmatically unsound instances of valid argument forms. I shall turn to this in section 4.2. (For more information on the logic of —> the reader is referred to Veltman 1985.) 3.4 Conjunction, disjunction and negation I trust that the truth and falsity conditions for sentences of the form ~~|A, A A B, and A v B do not need any further explanation.12 The reader will have noticed that sentences of the form A v ~~1A are not always true on the basis of the available evidence: the Principle of Excluded Middle does not generally 158

Data semantics and the pragmatics of indicative conditionals hold. That does not mean, however, that sentences of the form A v ~~|A can be false on the basis of the available evidence: must (A v ~~]A) is logically valid. Besides, we get a Principle of Excluded Muddle in return. No matter what the exact evidence is, the sentence must A v must ~~]A v (may A A may ~~|A) is always true on the basis of it. In the sequel, I shall sometimes discriminate between the sentences which contain no operators other than ~1, v and A, and the other ones by calling the former descriptive and the latter nondescriptive. All descriptive sentences are stable, most nondescriptive sentences are not. Intuitively, the difference between these two kinds of sentence amounts to this: by uttering a descriptive sentence a speaker only informs his audience of the evidence he already has. By uttering a nondescriptive sentence he also expresses his expectations about the outcome of further investigations. Notice that at complete information states s the following holds: Mlh 5 AorM s HIA Aflr- s A->BiffMI|- s AorMlh s B

M\\-smayAif£M\\-sA M\\-smustAffiM\\-sA In other words, it does not make much sense to use the phrases if-then, must and may in a context where the information is complete. If-then gets the meaning of the material implication while the meaning of both must and may boils down to that of the empty operator. However, in such a context there is no need to use nondescriptive sentences; the information is complete, so what good could speculations on the outcome of further investigations possibly be? A few remarks are due here on the relation between the relative notions 'true/false on the basis of the available evidence' and the absolute notions 'true' and 'false'. Indeed, the reader may have wondered whether these notions are related at all. Wouldn't it be better to say that definition 2 deals with the notions of verification and falsification rather than the notions of truth and falsity? After all, it is obvious that nothing is verified or falsified except on the basis of evidence. But it is far from obvious that this evidence, or rather the availability of it, could make a difference to the truth value of the sentence concerned. Truth and falsity depend only on the facts of the case and not on information one may have gathered.13 The absolute notions of truth and falsity can be defined in terms of the relative notions as follows: a sentence is true/false if and only if it is true/false on the basis of the evidence that will be available when the data are complete. In formulae: MH-AiffMlhSoA MHIAiffMSoHIA 159

Frank Veltman Here s0 is the rather special information state discussed near the end of section 2: the information state in which any speaker, if he should ever get there, would be acquainted with all the facts that constitute reality. Hence, it is indeed the facts and nothing but the facts that determine whether a sentence is true or false in the absolute sense. We saw, however, that there are many sentences for which the absolute notions of truth and falsity make little sense. There is a lot to learn from what is in fact the case, but not which sentences may be true or must be true or will be true if only . . . . There is no way to decide the question whether the red and the yellow marble may both be in box 1 by just opening the boxes. A question like that can only be judged in the light of what may be the case: the possibilities left open by the facts as far as they are known. Given the possibilities left open by the facts known in information state 2, the yellow and the red marbles cannot both be in box 1. The sentence The yellow and red marbles may both be in box 1 is false on the basis of the evidence available in information state 2. Now, I have no objections against replacing this phrase by another one - 'falsified by the available evidence' or 'refutable in information state 2', whatever you like. The real issue is, I think, which notions are fundamental: the absolute notions of truth and falsity or the relative ones, whatever you call them. In this paper we are exploring the idea that the relative notions are fundamental. So far it has proved fairly fruitful: it has enabled us to draw the distinction between direct and indirect evidence and that between stable and unstable sentences - important distinctions it would seem, even in purely logical matters. 4. PRAGMATIC CORRECTNESS AND INCORRECTNESS Recall the Principle of Excluded Muddle: must B v must "~|B v (may B A may ~~|B) is a logical law. This means that the possible contexts in which a conditional with antecedent A and consequent C can be uttered all fall into the nine categories in table 1. Claim: Assume that A and C are descriptive sentences. Then the only contexts in which a speaker can assert A—> C without violating any conversational maxim are the ones in category 5. In other words, an indicative conditional statement with a descriptive antecedent and consequent will normally implicate that neither the truth nor the falsity of its antecedent or consequent are definitely established. The claim itself is not new.14 What is new is the straightforward proof of it. Consider first the contexts fitting into category 2, 3 or 6. In such contexts the sentence A—> C is false on the basis of the evidence available to the speaker - it is left to the reader to check this with the help of definition 2. So anyone who says A—>C in one of these contexts is saying something for which he lacks adequate evidence, which according to the maxim of quality (the one 160

Data semantics and the pragmatics of indicative conditionals Table 1. The square of modal possibilities i. must A mustC

3. must A

2. must A mayC

must ~"|C

may ~~|C

4. may A may ~lA mustC 7. must ~|A mustC

5. may A may ~lA may C may ~\C 8. must~\A mayC may i C

6. may A may ~\A must ~|C 9. must~\A must ~\C

Note: Read the table as follows: in category 1 must A is true on the basis of the evidence available to the speaker and must C, too, etc.

formulated in section 3.1) he is not supposed to do. Anyone who knows, or at least could have known, that A cannot be true, and who therefore falls within one of the categories 7, 8 or 9 could, according to definition 2, truthfully assert that A—>C. But if he did so he would be sinning against the maxims of quantity and manner. By definition 2, must ~~|A is stronger and therefore more informative than A—>C. Apart from that, it is also less wordy. So if he said must ~~\A he would be being more helpful. The only remaining categories are 1 and 4, in both of which the speaker knows that C must be the case. Again: must C is both stronger and less wordy than A—>C. If the speaker were to state A—>C, he would not be telling us all he knows, and that in too many words. So, indicative conditionals are typically uttered in contexts fitting in category 5, the centre of table 1. This is not to say, of course, that any conditional statement will automatically be correct when uttered in such a context. For one thing, in such a context the sentence A—>C cannot be true on the basis of the available evidence unless the antecedent A is somehow 'relevant' to the consequent C. Let C be any descriptive sentence - for example, The red marble is in box 1. Suppose you do not know whether C - maybe the red marble is in box 1, maybe not. Likewise, let A be any descriptive sentence - It is raining in Ipanema. Again, you do not know whether A - maybe it is raining in Ipanema, maybe not. Now consider A—>C: If it is raining in Ipanema, the red marble is in box 1. Clearly, there must be some noncoincidental connection between A and C if it is really to be so that no additional evidence can establish the truth of A without establishing that C must be true; how on earth could the weather condition in Ipanema have anything to do with the position of the marbles? In section 2.2 we noted that definition 2 itself does not guarantee that a conditional is true on the basis of the available evidence only if its antecedent is relevant to its consequent. We can now see why this does not matter too much. Pragmatic constraints ensure that an indicative conditional will normally 161

Frank Veltman be asserted only in circumstances where this requirement is fulfilled. Those contexts in which definition 2 makes a conditional true without the antecedent being relevant to the consequent are contexts in which so much is known about the truth and falsity of either of these that it cannot be asserted without violating some conversational maxim. 4.1 Odd conditionals Should conditionals never be uttered in other circumstances than the ones fitting in category 5, just because this violates one or the other conversational maxim? Of course not. There are plenty of good occasions for doing just this, only it must be clear to the hearer that a maxim has been overruled and why. Contexts fitting into 2, 3 and 6 are not among these occasions. There the conditional is false on the basis of the evidence available to the speaker and, as we noticed in section 3.1, any violation of the maxim of quality is incompatible with the overall Cooperative Principle.15 But the literature is full of ifs and thens with the most eccentric things in between and all those I know fit quite neatly in that part of table 1 formed by the categories 1, 4, 8 and 9. In fact this categorization is of great help when we want to classify the figures of speech beginning with if. All of the examples which go (17)

If..., I'll eat my hat

belong to category 9: the speaker is clearly not intending to eat his hat and the hearer is expected to complete the (weakened version of) modus tollens for himself, which gives (18)

It cannot be the case t h a t . . .

Why say (17) rather than (18)? Surely in order to make the claim that the antecedent is as definitely false as the applied modus tollens is valid. The same rhetoric occurs in constructions like: (19)

If..., I am a Dutchman

(20)

If..., I am the Empress of China16

(21)

I'll be hanged, if . . .

which all implicate the falsity of their antecedents (unless of course the speaker could be a Dutchman, or the Empress of China, or sentenced to death). There are also plenty of examples of which the antecedent is trivially true and the hearer is supposed to apply modus ponens:17 (22)

She is on the wrong side of thirty, if she is a day

(23)

If there is one thing I cannot stand, it is getting caught in the rush-hour traffic 162

Data semantics and the pragmatics of indicative conditionals It will be clear that these examples belong to category i. Category 4 is the most diverse. In addition to examples where if is used for purely rhetorical reasons, as in: (24)

This is the best book of the month, if not of the year

it also contains examples where //"serves as an opting out device: (25)

There is coffee in the pot, if you want some

(26)

If there is anything you need, my name is Marcia

(27)

I paid back that fiver, if you remember

(28)

If I may interrupt you, you're wanted on the telephone

Let us first discuss (24). The speaker supposes that the hearer is well aware of the trivial truth that this book will certainly be the best of the month if it is the best of the year. In formulae, the hearer is supposed to know that B ^ C. From this, together with what the speaker tells him, ~~|B-^ C, he could (by data-logical means), conclude must C: this must be the best book of the month. Just as in the above examples the speaker intends the hearer to draw this conclusion. Example (25) works differently. The hearer knows that the speaker is not in a position to know whether he (the hearer) wants some coffee or not. From this he can infer that the conditional is asserted in one of the categories 4, 5 or 6. It cannot be category 6, for then the statement would be false on the basis of information available to the speaker. For the same reason it cannot be category 5 (unless the speaker happens to be a genie who could just make coffee in the pot on command - but let us assume that the hearer knows he is not). So the only possibility left is category 4: there must be coffee in the pot. To what good purpose - if any - does the speaker prefer the if-iorm to the statement that there is coffee in the pot? I think that the speaker in simply asserting the consequent would run the risk of defying the maxim of relevance, by saying something which does not interest the hearer at all. With the antecedent the speaker indicates that he is well aware of this: it provides a condition under which the consequent will be interesting. The examples (27) and (28) show that it is not always the maxim of relevance that is involved. In (27) the speaker indicates with the antecedent that he is opting out of the maxim of quantity;18 to account for (28) we must appeal to a maxim of politeness.19-20 Also in category 8 one can breach the conversational maxims to good effect: (29)

If it does not rain tomorrow, then it is going to pour (given as a summary of a dismal weather forecast)

(30)

If I don't beat him, then I'll thrash him (a boxer boasting before his fight) 163

Frank Veltman Both (29) and (30) convey that their antecedent will turn out false, but they leave their consequent undecided. The reader will be able to work out these implicatures himself ((29) and (30) both mirror example (24)). I have not been able to find any good (idiomatic) conditionals fitting into category 7. Nor can I offer a satisfactory explanation why there aren't any. A rather unsatisfactory explanation runs like this: saying A—> C and conveying by this both the more informative must ~|A and the more informative must C involves violating the maxim of quantity not once but twice. It could be asking too much of a hearer to expect him to work this out. The examples discussed above must look odd, if not perplexing, to those who hold the view that a conditional statement cannot be true unless the antecedent and the consequent are in some sense 'causally' connected. How could any causal chain ever bridge the gap between the antecedent she is a day and the consequent she is on the wrong side of thirty of (22); or that between the antecedent there is anything you need and the consequent my name is Marcia of (26)? Given that how the dots are filled in is irrelevant to the truth of if . . . , I'll eat my hat as long as they are filled in with something which is false, what could such a sentence express if not a simple truth-functional connection between the antecedent and the consequent? These examples suggest that the ifoi natural language could be ambiguous: usually it expresses a causal connection, but in some exceptional cases it does not. I do not think that this is the right way to see it. One of the advantages of the data-semantic approach is that we can uphold the idea of an unambiguous if. The //"that enables a speaker (in information state 1) to formulate the general constraint that the blue marble is in box 2 if the other two are in box 1 is the very same if that enables him (in information state 2) to say that the blue marble is in box 1 if it is anywhere at all. 4.2 A test for pragmatic correctness Consider the following well-known example. (31)

If there is sugar in the coffee, then it will taste good .'. If there is sugar in the coffee and diesel-oil as well, then it will taste good

This argument sounds suspicious. In fact, it is often claimed that it is quite possible to accept the premise while rejecting the conclusion. So it would seem that (31) provides a clear-cut counterexample to the Principle of Strengthening the Antecedent. But is it really so clear-cut? Compare (31) with (32): (32)

Maybe there is diesel-oil in the coffee If there is sugar in the coffee, then it will taste good •". If there is sugar in the coffee and diesel-oil as well, then it will taste good 164

Data semantics and the pragmatics of indicative conditionals Would those speakers who accept the premise of (31) while rejecting its conclusion also be prepared to accept the premises of (32)? I do not think so. Sugared coffee which may contain diesel-oil as well does not in general taste good. Yet the difference between (31) and (32) is very small: it is a conversational implicature of the conclusion of (31) that the coffee may well contain diesel-oil (along with other things you usually take in your coffee). All we did to get (32) was to add this implicature as a second premise to the original argument. The same trick can be applied to example (1). There the conclusion implicates that Smith may die before the election: (33)

Maybe Smith dies before the election If Jones wins the election, Smith will retire to private life If Smith dies before the election, Jones will win it .'. If Smith dies before the election, he will retire to private life

Again, once you reckon with the implicatures of the conclusion, the premises of the original argument turn out unacceptable. Given the possibility of Smith's demise, it is not the case that if Jones wins the election Smith will retire. It may very well be that Jones wins the election and that Smith does not retire because he died. From a data-logical point of view (31) and (1) are perfectly in order: if the premises are true on the basis of the available evidence, then so is the conclusion. But unfortunately the premises of these arguments cannot be true on the basis of the available evidence if one takes the pragmatic implicatures of the conclusion into account. That is why they lack any cogency. I would suggest generalizing these examples as a test for the pragmatic correctness of an argument: any argument of which the premises cannot hold if one takes the implicatures of the conclusion into account is pragmatically unsound. The purpose of an argument is to convince others of its conclusion. You want to persuade someone to accept something he would perhaps rather not accept by showing that it logically follows from something he is willing to accept. In a way the conclusion comes first, together with all its implicatures, and the premises are brought in later when it appears that the conclusion is not taken for granted. But then, of course, it will not help if you bring in premises that are incompatible with the implicatures of the conclusion - unless you also say that in asserting the conclusion you have violated the conversational maxims. There is one more argument which I have claimed to be pragmatically incorrect rather than logically invalid, and for which the above test yields the right result:21 consider (14) on page 157. The conclusion implicates that The blue marble may not be in box 1. If we add this to the premise The blue marble is in box 1 we get a data-semantic contradiction. Hence (14) is pragmatically incorrect. But (16), which is of the same form as (14), is without fault. For its conclusion The blue marble is in box 1, if it is anywhere at all does not 165

Frank Veltman implicate that the blue marble may not be in box i (the conclusion belongs to category i rather than category 5). Note that no instance of the argument form C/.'. A—>C will pass our test unless its conclusion is an odd conditional belonging to category 1 or category 4. In this respect the argument form C/A •". A—>C differs from argument forms like the Hypothetical Syllogism B^> C, A-+ B / . \ A-> C and the Principle of Strengthening the Antecedent A-> C/.*. (A A B ) ^ C , which have many pragmatically correct instances with conclusions belonging to category 5. Yet, even if this so-called paradox of implication had no correct instances at all, it would still not follow that it is logically invalid rather than pragmatically unsound.

NOTES 1 This paper overlaps in some passages with Veltman (1981). I am grateful to Ernest Adams, Mark Cobler, Jon Dorling, Fred Landman, Michael Morreau, Stanley Peters, Marjorie Pigge and Alice ter Meulen for comments, corrections, suggestions, discussions, translations, criticism, and help. Throughout this paper I shall assume that the reader is familiar with Grice (1975). 2 This example is drawn from Adams (1975). 3 This strategy is followed in Stalnaker (1976). 4 See in particular Anderson and Belnap (1975). 5 See Adams (1975) and also Cooper (1978). 6 The information models defined here closely resemble the Kripke models for intuitionistic logic. See Kripke (1965). Formally, the main difference with intuitionistic logic lies in the treatment of negation. See Thomason (1969) for still another treatment of negation within this framework. 7 Actually, the assumption is somewhat stronger; it excludes the possibility of there being any sequence of successive information states that does not ultimately end in an information state that is complete. I have made this stronger assumption just for technical convenience. As far as logic is concerned, it does not make any difference which one you make. In fact, from a logical point of view, you might even make the still weaker assumption that for each seS and each atomic sentence A there is an s' ^ s such that Vs> (A) is defined. 8 I am ready to admit that the word information as it occurs in the phrase 'information state' is not used in its ordinary sense. Perhaps it would be better to speak of 'evidence states'. 9 Cases of irony and metaphor will perhaps be considered as counterexamples to this claim. But I think these phenomena are best explained as involving an apparent infringement of the maxim of quality. In short: since a literal interpretation of an ironical or metaphorical statement is out of the question, as it would immediately lead to the conclusion that the speaker is breaching the maxim of quality, the hearer tries to reinterpret the words of the speaker in such a way that they can yet be reconciled with this maxim - the maxim of quality itself. Cases like these must be clearly distinguished from cases where the hearer ultimately concludes that a maxim - any maxim other than the maxim of quality - has really been overruled, albeit in a manner that can be reconciled with the supposition that at least the overall Cooperative Principle - but not the maxim in question - has been observed. 166

Data semantics and the pragmatics of indicative conditionals 10 A nice illustration of the differences between must A and A is given by Akatsuka (this volume). Compare / am hungry with / must be hungry and you are hungry with you must be hungry. 11 I mean the C. I. Lewis systems here: see Hughes and Cresswell (1972). 12 This does not mean that they are above suspicion; for a defence, see Veltman (1981). 13 These critical remarks were made by Stanley Peters in his discussion of my talk at the Stanford Symposium on Conditionals. 14 Already in Strawson (1952: 88) we find the remark that 'the hypothetical statement carries the implication either of uncertainty about, or disbelief in, the fulfilment of both the antecedent and consequent'. See also Stalnaker (1976) and Gazdar (1979). 15 The statement He is a fine friend, if he is really telling all these lies belongs - after reinterpretation - to category 5. Compare note 9. 16 Unlike Akatsuka (this volume), I do not think that a special truth value must be introduced to account for the rhetorical force of sentences like this one. 17 Note that within our framework modus ponens takes the form A, A—»C/.'. must C. (A conditional sentence A - » C with descriptive A and C is true on the basis of the available evidence if and only if any further data which supply direct evidence for A supply at least indirect evidence for C.) 18 Admittedly, this remark leaves a lot of questions concerning the example (27) open. For one thing, it is unclear why English speakers prefer (27) to the sentence I paid back that fiver, if you don't remember. Given our explanation for (25), one would expect things to be the other way round - as they are when one uses in case instead of if. {In case you don't remember, I paid back that fiver sounds better than In case you remember, . . . ) Only if the antecedent contains a negation can one safely say that it provides a condition under which the consequent would be informative. 19 Many of the examples discussed in this section have been taken from Lauerbach (1979). For a further discussion of, in particular, examples involving a maxim of politeness, the reader is referred to pp. 240-50 of Lauerbach's book. 20 English allows both clause orders antecedent-consequent and consequent-antecedent. From the examples given so far, it appears that this is so even for conditionals that implicate the truth of their consequent. Notice, however, that one cannot overtly mark the consequent with then in some of these conditionals without affecting their original impact. This is particularly so for conditionals where if is used as an opting out device, witness // / may interrupt you, then you are wanted on the telephone. In Dutch and German changing the word order in the consequent has the same effect: it seems obligatory to give the consequent the word order of a single main clause (finite verb second) when 'if is used as an opting out device, while in all other cases with the antecedent preceding the consequent the verb of the consequent gets second position with respect to the antecedent clause and thus precedes the subject of the consequent. This means that the whole conditional construction is treated as a single main clause with the antecedent taking the front adverbial position. 21 See Cooper (1978: ch. 8) for many other examples. REFERENCES Adams, Ernest W. 1975. The logic of conditionals: an application of probability to deductive logic. Dordrecht: Reidel. Anderson, Alan R. and Nuel D. Belnap, Jr. 1975. Entailment, VOL. I. Princeton: Princeton University Press. Cooper, WilliamS. 1978. Foundations of logico-linguistics. Dordrecht: Reidel. Gazdar, Gerald. 1979. Pragmatics. New York: Academic Press. 167

Frank Veltman Grice, H. Paul. 1975. Logic and conversation. Syntax and semantics, VOL. 3, Speech acts, ed. Peter Cole and Jerrold M. Morgan, 64-75. New York: Academic Press. Groenendijk, Jeroen and Martin Stokhof. 1975. Modality and conversational information. Theoretical Linguistics 2: 61-112. Hughes, G. E. and M. J. Cresswell. 1972. An introduction to modal logic, 2nd edn. London: Methuen. Karttunen, Lauri. 1972. Possible and must. In Syntax and semantics /, ed. John P. Kimball, 1-20. New York: Seminar Press. Kratzer, Angelika. 1977. What 'must' and 'can' must and can mean. Linguistics and Philosophy 1:337-55. Kripke, Saul A. 1965. Semantical analysis of intuitionistic logic 1. In Formal systems and recursive functions, ed. J. N. Crossley and M. A. E. Dummett, 92-130. Amsterdam: North-Holland. Lauerbach, Gerda. 1979. Form und Funktion englischer Konditionalsdtze mit 'if. Tubingen: Niemeyer. Lyons, John. 1977. Semantics, VOL. 2. Cambridge: Cambridge University Press. Stalnaker, Robert C. 1968. A theory of conditionals. In Studies in logical theory, ed. N. Rescher, 98-112. American Philosophical Quarterly monograph series, no. 2. Oxford: Blackwell. Stalnaker, Robert C. 1976. Indicative conditionals. In Language in focus, ed. A. Kasher, 179-96. Dordrecht: Reidel. Strawson, P. F. 1952. Introduction to logical theory. London: Methuen. Thomason, Richmond H. 1969. A semantical study of constructible falsity. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 15: 247-57. Veltman, Frank. 1981. Data semantics. Reprinted 1984 in Information, interpretation and inference, ed. Jeroen Groenendijk, Theo Janssen and Martin Stokhof, 43-65. Dordrecht: Foris Publications. Veltman, Frank. 1985. Logics for conditionals. Doctoral dissertation, University of Amsterdam.

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REMARKS ON THE SEMANTICS AND PRAGMATICS OF CONDITIONALS Ernest W. Adams Editors' note. Emphasizing truth as a property of sentences, Adams criticizes relative conceptions of truth such as are developed in Veltman's contribution, for overemphasizing the distinction between semantics and pragmatics. A probabilistic semantics for conditionals that includes pragmatic considerations and maxims can account for the kinematics of belief and model the dynamics of belief change appropriately, without relying on relativized truth definitions. Some similar aspects of the dynamics of belief are also discussed by Akatsuka, Fillenbaum and Greenberg. The first part of this chapter will discuss aspects of Veltman's chapter in this volume 'Data semantics and the pragmatics of indicative conditionals', and particularly his semantics for conditionals, while the second will comment on more general methodological issues having to do with relations between three seemingly disparate theories: (i) Grice's theories of meaning and conversational implicature, (2) the Bayesian theory of decision making, and (3) my own probabilistic theory of conditionals. The discussion of Veltman's chapter will presuppose familiarity with technical aspects of the theory presented there. The central concept of Veltman's theory is that of a sentence being true in an information state in an information model, which is a ternary relation between sentences, information states, and information models. What we want to ask is how this ternary relation is related to the property of truth, which is what Tarski (1944) insists the sort of truth that satisfies Convention T must be. Looking ahead to pragmatic matters, to be commented on later, we shall also want to insist that what is important for those purposes is the property of truth, and not truth relative to this or that abstractly defined model. The usual way of transforming relative definitions of truth, such as truth in a model or truth in a possible world, into definitions of truth simpliciter is to stipulate that sentences (or propositions or statements, these distinctions need not concern us here) have the property of truth if and only if they are true in the actual model or possible world. There is nothing to object to in this, assuming that we can distinguish clearly between atomic and non-atomic sentences, that we are only interested in the truth conditions of non-atomic sentences, and that these can be defined recursively in terms of the truth 169

Ernest W. Adams conditions of their parts (i.e., we are only concerned with the recursive clauses of truth definitions). It should be kept in mind, however, that taking these things for granted begs a myriad of logical questions which have concerned most of the leading logicians from Aristotle to the present day. But let them be begged: we must still ask how Veltman's definition of truth in an information state in an information model might be 'derelativized' to yield a definition of truth simpliciter. I would suggest the following as a natural generalization of the method of defining truth as a property from relativized truth definitions, which might apply to Veltman's theory: a sentence may be stipulated to be true simpliciter if and only if it is true in some information state in the actual information model. To explain this suggestion in detail would not only require us to enter into the complexities of the information state and model concepts, but also to explain how what I have here called the 'actual' information model might be distinguished among all possible such models. There is not space for such a discussion here, and I will confine myself to suggesting that the actual information model (or an actual information model) must be one whose valuation function only assigns the value i to true atomic sentences and the value o to false ones. This stipulation would at least imply that atomic sentences must satisfy Convention T, and hence the most basic 'criterion of material adequacy' would be satisfied by Veltman's theory of truth in its application to atomic sentences. The question of whether this criterion of adequacy is also satisfied in application to non-atomic sentences is more delicate, but I am now going to argue, not that Tarski's criterion is not satisfied, but rather that Veltman's theory does not meet what might be called a 'pragmatic criterion of adequacy' when it applies to conditionals. The following example is described in embryo in Adams (1975). A diner, D, is seated at a table with a plate of nonpoisonous mushrooms before him that he is thinking of eating (D is not sure that the mushrooms are nonpoison ous) and an observer, O, who thinks the mushrooms are poisonous, is standing looking at him. O has a 'thought' that he expresses to himself as: Ot: If D eats the mushrooms he will be poisoned and wishing to inform D he says to him the sentence: Os: If you eat the mushrooms you will be poisoned Hearing this in turn instils in D's mind the thought which he expresses to himself as: D t : If I eat the mushrooms I will be poisoned and in virtue of coming to believe this, D decides not to eat the mushrooms. It is intuitively evident that as formulated here all of the conditional sentences O t , O s , and D t express the same proposition, though it will later be important 170

Remarks on the semantics and pragmatics of conditionals that O's and D's reasons for thinking and saying these things may be quite different. However, let us now consider their truth as characterized in Veltman's theory, augmented by my stipulation concerning the derelativization of the truth concept. It follows immediately from the truth conditions of conditionals that are assumed in Veltman's theory that the three conditionals just described would have to be true. This is because D did not eat the mushrooms, and because in application to conditionals whose parts are atomic sentences, Veltman's theory yields the same truth conditions as apply to the material conditional. The fact is that by a not uninteresting circuitous route Veltman arrives at the same conclusions about simple conditionals (ones whose parts are atomic formulae or boolean combinations of them) as does Grice (1975) and which Lewis (1976) also accepts for indicative conditionals. Now I want to argue that any theory of truth such as Veltman's that entails that the proposition which D expresses to himself as D t is true, fails to satisfy a requirement of adequacy which I would hold to be part of the rationale of logic: for specifiable reasons and in specifiable circumstances, persons should wish to accept propositions held to be true and to avoid accepting ones held to be false. Vague as this is - and I will not attempt a more careful statement here - it is at least intuitively plausible that this requirement is not met in D's situation. Whatever other requirements of adequacy may be met in defining truth in such a way that D t turns out to be true in this situation, D certainly would not have wished to accept D t , since accepting it led him not to eat the mushrooms when in fact they were not poisonous. One may argue that meeting the foregoing pragmatic requirement should be part of the rationale of logic as a normative theory, which purports to explain how persons ought to reason. Logic formulates principles whose rationale is to guide persons who follow them to true conclusions and to help them to avoid falsehood. But what if the conclusions like D t that are baptized 'true' in some logical theory are ones which persons would in fact not wish to accept? In such a case I would say that persons will be well advised to ignore theory, since it has no rationale. To follow theory in such circumstances would be like following prescriptions for playing a game, the following of which could be expected to lead to unwanted consequences. The foregoing applies to a much wider range of theories than Veltman's. Orthodox logic's material conditional analysis of conditionals clearly fails to satisfy the pragmatic requirement of adequacy, and I suspect that it is the intuitive recognition of this by students and teachers alike that leads them to treat the theory as no more than an artificial formalism, not to be applied to the practical problems of life. A similar, though somewhat weaker, criticism applies to many non-orthodox theories of conditionals, such as ordered possible worlds theories, 'relevance' theories, causal or necessary condition theories, and most of the amazing host of ad hoc theories that have been excogitated 171

Ernest W. Adams to try to account for the unwelcome counterexamples to the orthodox theory. It is not so much that these theories fail to meet the pragmatic requirement as that no effort has been made to demonstrate that they do meet it. In the absence of such an effort, the presumption is against them. (Can it be argued that it is to the diner's interest to reject D t on the grounds that in the nearest possible world in which he eats the mushrooms he will not be poisoned?) Note too that the pragmatic requirement explains the importance of insisting that truth should be a property. It is to D's interest to accept D t if it is true simpliciter, and it will be of no concern to him which models or possible worlds or information models it is true in unless he knows which among them is the actual one. In fact, one may wonder what practical interest D could have in any world other than the actual one. This could have to do with logical validity, which leads to a couple of asides on Veltman's characterization of this concept before we turn to the more important topic of pragmatics. In a generalized sense, Veltman's is a kind of truth value gap theory in that it allows that sentences may be neither true nor false in certain information states and models. This means that the definitions of logical validity must be modified to take this into account. Veltman's definition closely parallels that of three-valued logic in which the only 'designated' truth value is 'truth' (as against truth together with neither truth nor falsehood): i.e., an inference is valid in this theory if its conclusion is true in all information states and models in which all of its premises are true. Given trivalence together with this definition of logical validity, we have the standard consequence that the Principle of the Excluded Middle is not valid: i.e., 'A v - A ' is not a logical consequence of the empty set of premises. Without attempting to develop this point in detail, I want to raise a query as to whether this definition meets another pragmatic requirement of adequacy, this time not for definitions of truth but rather for definitions of validity. The requirement is that persons should have good reason to reason in accord with principles held to be valid. In particular, when they have good reason to accept the premises of such inferences and they know that the inferences are valid, this knowledge should give them good reason to accept their conclusions. The requirement defined here is not the same as the pragmatic criterion of adequacy for truth definitions and I have no argument to show that Veltman's definition fails to meet the requirement. However, I feel that it is desirable that an argument be given that such a non-orthodox validity definition as Veltman's does meet the requirement, for if it fails to do so it loses its rationale as a characterization of how persons should reason. But now we must turn to pragmatics. As will by now be evident, I use 'pragmatics' in an enlarged sense, according to which the distinction between semantics and pragmatics is an artificial one because definitions of key semantic notions such as truth are required to meet pragmatic criteria of adequacy. Of course, this merely returns to the more traditional philosophical sense of pragmatism, which stresses the practical 172

Remarks on the semantics and pragmatics of conditionals utility of holding true beliefs and which relates it to the 'contextual factors' that are currently regarded as specifically pragmatic because it is dependent on the contexts in which beliefs are held and acted upon or uttered. The current usage of 'pragmatics' focuses on utterance largely independent of belief and acceptance, but I can't be sure how important that is so far as concerns the interpretation of Veltman's theory, and it may be that I have been unduly critical in the above comments on the 'semantical' aspect of the theory in tacitly assuming that is the only aspect of the theory that has to do with belief and action. In any event, interpreting his 'pragmatics' as having implications for belief and action, i.e., as having utilitarian implications, there is much in that aspect of the theory which seems to me extremely good. I will point out just one of what I regard as the theory's excellences in this respect, and raise a methodological query. It seems to me absolutely right to relate the conditions of correct utterance of conditionals to what I would call 'practical modalities', namely the musts and mays that are discussed in their connection with conditionals in section 3 of Veltman's paper. These are intrinsically epistemic ideas, as Veltman stresses, and I am inclined to regard the expression of a practical may as describing a possibility that can't be neglected under given circumstances. Veltman's theory admirably captures Strawson's intuition that the expression of a hypothetical carries the implication of uncertainty concerning its antecedent, and I see it as having great potential for dealing with the sadly neglected topic of enthymemes involving conditionals, which are common patterns of reasoning which don't conform to this or that formal theory of validity. This leads to the methodological query. Why, given that the practical modalities in Veltman's theory are epistemic notions, as is indeed the whole theory since it is based on the idea of an information state, are these ideas not quantified probabilistically in the way that is now usual? The probabilistic formulation would also naturally accommodate two things which don't fit in so easily with the 'static' approach to semantics. One is that for the so-called unstable sentences of Veltman's theory their truth values may change within a single information model. Value change is something more commonly associated with probability than with truth, and this suggests that what Veltman labels 'truth' may really be something like 'qualitative probability' by another name. But making the probabilities explicit and quantitative would have several advantages, one of which for me would be to make it possible to link Veltman's theory with my efforts to account for enthymematic reasoning involving conditionals along probabilistic lines (Adams 1983). The other, and I think greater, advantage of an explicit probabilistic formulation would be that it would link up the theory more naturally with the actions whose practical utility is involved in pragmatic criteria of adequacy of definitions of truth and validity. In what follows I will turn from explicit consideration of Veltman's theory to unsystematic speculations on the 173

Ernest W. Adams link between utterance, acceptance and action, which I am suggesting the quantitative formulation would make possible and which involves aspects of Gricean theory, of Bayesian decision theory, and my own theory of conditionals. This will be discussed primarily with reference to the 'semiotic situation' (with apologies to Professors Barwise and Perry) involving the Diner, the Observer and the mushrooms previously described. I think an adequate semiotics should be able to account for, and link, each of four stages in the 'process' involving the Observer, the Diner and the mushrooms, as follows: (I) O having the thought he expresses to himself as Ot: If D eats the mushrooms he will be poisoned (II) O uttering the sentence Os: If you eat the mushrooms you will be poisoned (III) D 'accepting' O's statement and coming to the belief he expresses to himself as D t : If I eat the mushrooms I will be poisoned (IV) D deciding not to eat the mushrooms. Of course there is more to the story than this - for instance, D might initially have asked the question D q : If I eat the mushrooms will I be poisoned? and D's decision will in turn have consequences; but we may for now concentrate just on the four given stages. It is in explaining their causal connections that the different theories mentioned above are involved, and we work backwards, beginning with the link between D's thinking D t and his deciding not to eat the mushrooms. Bayesian decision theory (see Jeffrey 1983) is involved in explaining how D's thinking D t led him to decide not to eat the mushrooms. Very roughly, this decision is determined by two factors: D's desires, particularly those for the pleasant experience of eating nonpoisonous mushrooms and for not being poisoned by poisonous ones, and his 'conditional degrees of belief as to the chances of any of these consequences following if he eats the mushrooms. In this case we can assume that being poisoned is overwhelmingly undesirable, and the most important degree of belief 'factor' is D's regarding the chances of his being poisoned if he eats the mushrooms as high. Though it would be overly simple to hold that the sentence that D expresses as D t means that this probability is high, the two are clearly connected, since D's coming to hold the belief he expresses as D t also led him to regard the chances in this way and not eat the mushrooms. It is in explaining the connection between the 'content' of D t and the probability, that my own theory of conditionals (Adams 1975,1981) enters, though I cannot pursue this matter in detail here. The next causal link, moving backwards, is between O's utterance expressed by Os and D's coming to the belief D t , and it is in explaining this that Grjce's 174

Remarks on the semantics and pragmatics of conditionals theory of meaning (Grice 1969) comes into play. O's utterance is an assertive speech act, the primary intention of which is to elicit a 'response' in D, and which employs certain means to achieve this end. Here we may assume that O's intention was just to induce D to hold the belief expressed as D t . According to Grice's analysis, part of the means employed to bring this about is that D should come to realize that this is what O intends him to think. This of course is the point at which the meaning of the sentence Os comes into play, since D's understanding of it is what enables him to recognize what it is that O wants him to think (of course the sentence Os has various nonstandard usages, such as in irony and so on, but we can put those aside here). However, just getting D to recognize that O wants him to come to accept Dt is not enough by itself to explain D's acceptance (that doesn't give D a 'reason' for holding this belief), and to complete the explanation we must bring in other factors. Very generally, we must take into account belief kinematics such as is discussed in Jeffrey (1983: ch. 11), since that is what is involved when D changes from not thinking D t to thinking it. Passing over issues of great complexity, the sort of belief change described in this theory must be brought about by giving the believer 'rational reasons' for changing his or her mind, and in D's case they could not be his recognition of O's intentions alone. What might provide such 'sufficient reasons' would be D's coming to think that O himself holds the belief expressed as O t , and moreover for reasons that D would accept. One supposes that what O hopes for in uttering Os is that D will come to think that O believes Ot and for good reasons: O hopes that D will think he is sincere and 'well-informed'. Of course it is extremely difficult to explain what it is that might make D think O is sincere and well-informed, and I will only say that it seems to me most likely that this involves D's general belief that O values his credibility - the very thing O needs if the primary intentions of his speech acts are to have a chance of being realized - and O wouldn't risk that in a situation in which a lie or rash assertion could easily be found out. Moving back to the step from O's having the thought he expresses to himself as Ot to his asserting O s, we may not say that the thought causes the utterance, but it is clearly part of the explanation for it. We may imagine that another important factor in the explanation is O's desire to be helpful (e.g. by responding to the question D q ), and it is here that Grice's conversational maxims enter the picture. Again issues of great complexity are involved, and the only one I will select to comment on has to do with the nature of the help that D seeks and O offers. We might be inclined to think that what D really wants is just to be told what to do - to eat or not to eat the mushrooms - and that O is helping him by telling him in an oblique way not to eat the mushrooms. That might be the case in this situation, but there is a more interesting possibility. What D wants is to be placed in possession of information that will enable 175

Ernest W. Adams him to make up his own mind whether or not to eat the mushrooms, and that is what O provides him with in asserting Os. Though D presumably wants to avoid being poisoned, O cannot be certain of this (D might be hoping to experience some sort of ritual purification involving a bit of mushroom poisoning), and whichever result D wants - to be poisoned or not - O helps him to choose between eating the mushrooms or not when he offers him the information Os. The way in which this 'ethically neutral' information helps D to make his decision has already been commented on (in the step from stage III to stage IV), but a special remark may be made about the character of this sort of information, which is not of the 'ruling out of possibilities' type. What is essential to the help that is given D in telling him Os is that D comes to think that the chances of his being poisoned if he eats the mushrooms are high. A conditional probability becomes high, though nothing is ruled out with complete certainty, and that isn't important so far as concerns D's decision. Reflecting on this shows the mistakenness of Grice's claim that asserting the conditional Os in circumstances in which O has good reason to think that D won't eat the mushrooms (in fact what gives O good reason to think it is that he knows he is going to assert Os) violates a maxim of quality. This is because, though both are true, saying to D that he wouldn't eat the mushrooms would give information of a much poorer quality than the conditional, since it wouldn't provide what D wants, namely information that will help him make up his own mind whether or not to eat the mushrooms. Factual claims may function to provide information of the conventionally conceived 'ruling out of possibilities' sort (and that is what Grice presupposes in his theory of conversation), but here I am at least in general agreement with the ordered possible worlds theorists that conditionals are not factual in any simple sense. All of the foregoing is terribly sketchy and I would not want to have to defend it in any of its details. However, I feel more confident of the Tightness of the general approach, and in particular of the claim that an adequate semiotic theory must involve aspects of speech act theory and of Bayesian decision and belief change theory - and this must involve the probabilities of conditionals when assertions and thoughts are expressed by them. The problem is to work out the details, for as I see it, it is only by doing so that we will put ourselves in a position to choose between rival analyses of conditionals and other controversial forms. That is the fundamental import of the view that the distinction between semantics and pragmatics is an artificial one, and the test of such a composite theory of speech and action must be its ability to account for semiotic processes such as those just discussed. This cannot be further developed here, but I will end by describing a kind of 'test' semiotic situation due to Vann Mcgee (1984), which involves a striking counterexample to modus ponens, and which an adequate theory should be able to explain. Except for noting that the situation shows the untenability of the 'inference warrant' theory of conditionals (Toulmin 1958: 99), I will eschew comment. 176

Remarks on the semantics and pragmatics of conditionals Imagine two persons, A and B, looking into the murky waters of a shallow lake whose depth they cannot judge. They dimly make out two forms swimming near the bottom and A says to B There are two large fish. B agrees and adds Yes, and if they are fish then if they have lungs they are lungfish. But neither concludes by modus ponens that If they have lungs they are lungfish. Whatever the formulists may claim, modus ponens is not the universal bedrock of reasoning that many have supposed it to be.

REFERENCES Adams, Ernest. 1975. The logic of conditionals: an application ofprobability to deductive logic. Dordrecht: Reidel. Adams, Ernest. 1981. Truth, proof, and conditionals. Pacific Philosophical Quarterly 10:340-53. Adams, Ernest. 1983. Probabilistic enthymemes. Journal of Pragmatics 7: 283-95. Grice, H. Paul. 1969. Utterers' meanings and intentions. Philosophical Review 78: 147-77Grice, H. Paul. 1975. Logic and conversation. In Syntax and semantics, VOL 3, Speech acts, ed. Peter Cole and Jerry Morgan. New York: Academic Press. Jeffrey, Richard. 1983. The logic of decision, 2nd edn. Chicago: University of Chicago Press. Lewis, David. 1976. Probabilities of conditionals and conditional probabilities. Philosophical Review 85: 297-315. Mcgee, Vann. 1984. A counterexample to modus ponens. Journal of Philosophy 82: 462-71. Tarski, Alfred. 1944. The semantic conception of truth. Philosophy and Phenomenological Research 4. Toulmin, Stephen. 1958. The uses of argument. Cambridge: Cambridge University Press.

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THE USE OF CONDITIONALS IN INDUCEMENTS AND DETERRENTS •

Samuel Fillenbaum Editors' note. Using data from a variety of experimental tasks, Fillenbaum discusses threats, bribes, and promises phrased both conditionally and disjunctively in terms of interrelations between propositional content, speaker attitude, speech act and linguistic structure. These topics are also of concern to Akatsuka, Greenberg, Haiman, Konig, and especially Van der Auwera. 1. INTRODUCTION I shall be concerned with the use of conditionals in inducements, conditional promises and bribes, and their use in deterrents, conditional threats and warnings.1 This paper will examine the logic and possible phrasing of such conditionals the principal function of which is purposive, i.e., constitutes an attempt on the part of the speaker to get the addressee to do something (// you fix the car I'll give you $100) or to refrain from doing something (// you come any closer I'll shoot). It is hoped that the account to be developed here will provide an analysis for this special class of speech act conditionals, and serve in some measure as a model for approaching the study of other sorts of conditionals; also that some of the kinds of considerations that emerge as critical here, e.g. the importance of knowledge of the contents of the p and q propositions involved in the conditional, will be of more general relevance. Conditional promises and threats clearly involve something more than the statement of a contingency between the p and q propositions involved, more even than the statement of some causal connection between these propositions. Conditional promises and threats are essentially tied to their perlocutionary effects on the addressee (Ad). The point of a conditional promise is not merely to inform Ad of the good consequences to Ad of some action, but, rather, to try to enforce that action by a (tacit) offer of these consequences. The point of a conditional threat is not merely to tell Ad of the negative consequences to Ad resulting from action on his or her part, but, rather, to deter Ad from that action by warning of such consequences. An inducement or deterrent really amounts to a speaker's request to Ad to do or not do certain things, together with information spelling out consequences for Ad designed to enforce the request. Principally, I shall be interested in determining when inducements 179

Samuel Fillenbaum and deterrents may or may not be phrased with if, and and or. It is hoped that this will reveal how these operators are used, as well as exhibiting something of the role of incentives in persuasive communication. In the frame If p, q we may represent recognition of incentives starkly by a 'plus' or 'minus' sign on the q proposition, thus symbolizing something that the Ad wants or does not want to happen. If, indeed, recognition of the incentives offered is critical to the understanding of conditional promises and threats, this suggests that recognition of the content of the q proposition is indispensable because, among other things, this will permit Ad to determine the signing and extremity of signing of the q proposition. While most attention here will be directed to the role of the rewards and punishments offered, knowledge of the p proposition that permits the Ad to assess its signing and the extremity of that signing is also highly relevant. Indeed, the relation between the p and q propositions with regard to sign and degree will determine the plausibility of any attempt at inducing or deterring action, and therefore presumably the outcome of any such attempt. From the perspective of the psychologist, let me make two kinds of comments, first something substantive and then something more methodological. The role of rewards and punishments as 'regulators of human conduct' has a long history outside of psychology proper. Within psychology, substantively and conceptually, there has been enormous concern with the ways in which rewards and punishments may be used in seeking to control and modify action and behaviour. And, in so far as incentives are verbally offered, psychologists, although hardly any would use the terminology, have been concerned with what speech act theorists might call the perlocutionary effects of an utterance on the target or addressee. So, in this area the substantive concerns of the psychologist and of the speech act philosopher readily come together (although the conceptual frameworks within which they work may differ). I have already pointed out that Ad's ability to recognize the nature and extremity of the incentive being offered requires - indeed takes for granted - an understanding of the content of the q proposition. Knowledge of semantic content is thus absolutely essential if Ad is to be able to determine whether the speaker is trying to get him to do something (the content of/?) or is trying to deter him from doing that. Very likely, propositional content figures in additional ways in the proper understanding of these and other conditionals.2 Historically, in the study of conditionals by psychologists, especially with regard to the understanding of conditionals in reasoning and inferential tasks, the dominant tendency has been to purge conditionals of semantic content as much as possible. Attempts have been made to come as close as possible to the syntactic frame If p, q, with p and q often quite arbitrary and unrelated, as if they were almost dummy propositions. More recently, even in this domain, matters of substantive semantic content have been addressed, and, more generally, there has come to be much concern with semantic memory, world know180

The use of conditionals in inducements and deterrents ledge and assumptions about communicative conventions which affect understanding (on these matters see Fillenbaum 1977b, 1978). The present chapter, as will be obvious, is in this latter mode. Now to the methodological comment: I think it is part of the professional formation, or perhaps deformation, of psychologists that they try to get data or information in various ways from subjects other than themselves. Psychologists want to fiddle with things experimentally, to manipulate things, to see what does or does not make a difference, and so on. Indeed, with regard to the study of conditionals, there are all sorts of ways to investigate how such sentences are understood and used. It is perfectly possible to ask people to make judgements of equivalence - whether or not two sentences are the same in meaning. It is perfectly possible to give people sentences, ask them for paraphrases, and to examine properties of their productions. It is perfectly possible to give people sentences and ask them to classify or categorize them, specifying the kinds of categories to be employed. It is perfectly possible to give people pairs of sentences and to ask whether, under normal circumstances, given the first one would infer the second. It is perfectly possible to have people memorize sentences and then to look at their performance on a recognition task, with particular attention to the systematic errors made. All of the above tasks, as well as others (e.g. procedures looking at response latencies) have indeed been used in the study of conditionals (see Fillenbaum 1978). I want to consider the overall shape of the results yielded by such techniques with regard to inducements and deterrents in particular, and to see what sort of an account these results demand. The analysis will seek to interpret the phenomena in terms of pragmatic factors such as the context in which inducements and deterrents are offered, as well as their communicative function as attempts to control the behaviour of Ad, a function which depends on certain assumptions held in common between the speaker (Sp) and Ad. Some suggestions will be made about inferences that may be drawn from inducements and deterrents phrased as conditionals, and the relation holding between inducements and deterrents phrased as conditional sentences, conjunctive sentences and disjunctive sentences. Essentially, all this concerns the relation between the logical form and the illocutionary force of certain kinds of sentences that figure importantly in attempts at manipulating the behaviour of others. I shall be concerned with one class of purposive uses of the conditional. What is said explicitly appears to involve a causal connection. Given If p, q, p on your part will be the cause of q on my part. What is implicit and primary, however, is a purposive or an intentional notion because q on my part is really being 'offered' to get something done or not done with regard to p on your part. This purposive or intentional notion is what defines an inducement or deterrent as such. I shall try to show that the relations holding among propositions phrased with if, and, and or are systematically affected 181

Samuel Fillenbaum as a function of whether a conditional promise or conditional threat is involved. Further, while proper understanding of both inducements and deterrents requires inferences that go beyond what is said explicitly, deterrents appear to require additional inferences at yet one extra remove. The data to be mentioned briefly are based mainly on the use of an inference task, a paraphrasing task, a judgement task where subjects were required to decide whether or not sentences were equivalent in meaning and, finally, a sentence classification or description task. A full account of the tasks, analyses, and results may be found in Fillenbaum (1976, 1978); here only the barest summary is given. 2. DATA AND INTERPRETATION 2.1 Inferences: proposition and obverse First a word about the results yielded by the inference task. Subjects were required to indicate whether or not the second of a pair of sentences was 'a reasonable, natural sort of inference' given the first sentence. The relation between the sentences in a pair was always that between a sentence and its obverse, i.e. between If p, q {If you fix the car I'll give you $100) and If not p, not q {If you don t fix the car I wont give you $100) or / / not p, q {If you don't shut up I'll scream) and If p, not q {If you shut up I won't scream). The inferences subjects draw from inducements and deterrents reveal their understanding of such statements and their appreciation of various consequences of different actions on their part. With regard both to conditional promises and conditional threats, subjects very readily accepted the 'fallacious' inference from a proposition to its obverse, with average acceptance values ranging between 80 per cent and 90 per cent. It did not seem to make any real difference whether an inducement or deterrent was involved - subjects were very prone to commit the fallacy of the denied antecedent in both cases. How may we account for such results? A Gricean explanation (Grice 1967, 1975) in terms of conversational assumptions readily suggests itself and appears plausible. Why, offered an inducement of the form Ifp, q+, might Ad believe that If notp, notq-\- follows? Consider that the inducement q+ is being offered to get Ad to do p. In so far as obtaining q+ is contingent upon doing p, the inducement would lose all force if that contingency were eliminated. If q+ were to come about whether or not Ad did p, the conditionally of the inducement which defines it as such, rather than as a simple straightforward offer of a good outcome, would be lost, and the statement would have no point. If Sp is going to give Ad $100 regardless of what Ad does, then there is no reason for Ad to modify his or her behaviour one way or the other. The argument concerning deterrents is exactly parallel. In so far as Ad believes that Sp is sincere, Ad must assume that the outcomes offered will be differential 182

The use of conditionals in inducements and deterrents and contingent upon his or her own action, which Sp is seeking to control through the inducement or deterrent offered. The 'conversational implicature' follows quite directly if Ad assumes that Sp is conforming to the maxim of quantity in saying no less than is appropriate to the circumstances. So in this context, the 'fallacious' invited inference is not only plausible, but not to make it would appear at best foolish, if not perverse. 2.2 Inferences: if not and unless We have just seen that in the case of a proposition and its obverse (e.g. the relation between Ifp, q and If not p, not q) inducements and deterrents behave in a very similar fashion, the invited inference being accepted overwhelmingly; and I have indicated why this ought to be so in terms of a Gricean conversational analysis. Now I want to look at another case involving inducements and deterrents, those phrased with if not and unless, where they behave rather differently with regard to the acceptability of invited inferences. For deterrents (conditional threats), if not and unless propositions are seen as very tightly related (following from each other 86 per cent and 90 per cent of the time, respectively). For inducements (conditional promises), the relationship is considerably weaker {if not and unless propositions follow from each other only 52 per cent and 59 per cent of the time, respectively).3 How can one explain these results, which reveal substantial and significant differences between deterrents and inducements? Propositions phrased with if not and unless often appear intimately related, if not equivalent. However, compelling arguments have been offered by Geis (1973) against the identification of unless with if not. Rather, Geis offers as a gloss for Unless p, q something like 'under all circumstances except p, q' or 'in any event other than p, q\ Why should if not and unless statements, nevertheless, often appear to be intimately related? Recourse to a principle of invited inference may help toward providing an explanation. Start with: (1)

Ifnotp,q

which readily invites the inference of its obverse: (2)

Ifp,notq

Taken together (1) and (2) license: (3)

Only if p, not q

and: (4)

Only if not p,q

both of which are consistent and compatible with Geis's gloss of unless as: (5)

'under all circumstances except p, q' 183

Samuel Fillenbaum with (4) doing this directly and (3) doing it indirectly by focusing on the only circumstance,/?, under which q would not result. Which of these is the preferred understanding of unless propositions? Fillenbaum (1976) gives some reasons in terms of behaviour under sentence negation for choosing (3) Only if p, not q, whereas Clark and Clark (1977: 457) opt for (4) Only if not p, q. Perhaps consideration of the results from the invited inference task may allow us to decide between these alternatives, and also reveal something about the kinds of knowledge involved in, and necessary for, understanding. First consider conditional threats or warnings (If notp, q-) where an utterance such as If you don't give me your money I'll kill you can readily be paraphrased as, or license the inference to, Unless you give me your money I'll kill you. On the rendering of unless as: (3')

Only if p, not q -

the unless phrasing leads to such an interpretation as Only if you give me your money, I won't kill you which quite directly specifies what Sp wants Ad to do and also indicates this as the unique condition under which q- will not occur. On this account the unless version is indeed very close to the original phrasing with if not, where Sp is trying to get Ad to do p and seeks to enforce that action by the threat of q—. On the rendering of Unless p, q— as: (4')

Only if not p, q -

the unless phrasing leads to such an interpretation as Only if you don't give me your money, I will kill you. Sp would seem to be concerned with the variety of circumstances where q— will hold rather than the unique circumstance under which it doesn't hold, which in fact Sp is trying to bring about. So on this rendering, the if not and unless versions do appear different in some respects, and should not overwhelmingly be regarded the one as leading to the other. The fact that they are so regarded therefore argues against (4') Only if not p, q- and supports (3') Only if p, not q-, on which account the results are as expected, as the more appropriate rendering of unless. Next consider inducements or conditional promises (If not p, q+), where a sentence such as / / you don't give me a ticket I'll give you $20 does not seem to be quite properly paraphrased by Unless you give me a ticket I'll give you $20. The latter sentence seems to suggest that in the ordinary run of things Sp would give Ad the $20 and only a ticket could prevent Sp from doing that, something strange and not to be expected, given our knowledge of the ways of the world. In contrast, the source promise makes it clear that the bribe is being offered just to avoid a ticket and has very much the force of Only if you don't give me a ticket will I give you $20, rather than Only if you give me a ticket won't I give you $20. On the Clarks' account where Unless p,q+ is glossed as; (4")

Only if not p, q+ 184

The use of conditionals in inducements and deterrents the unless sentence should be understood as Only if you don't give me a ticket will I give you $20 which does indeed appear to be a proper or close rendering of the original or source inducement. Hence, if this is right, one might expect inducements phrased as Unless p,q+ and If not p, q+ to be acceptable inferences from each other. The fact that this is often not the case would thus seem to tell against the Clarks' account. On Fillenbaum's account where Unless p,q+ is glossed as (3")

Only if p, not q+

the unless sentence should be understood as Only if you give me a ticket won't I give you $20 which I have suggested above in important respects misrepresents the source inducement. So, on this account, one might expect inducements phrased as Unless p, q+ and If not p, q+ often not to be acceptable inferences from each other. This is what was found, and may be taken as providing some measure of support for Fillenbaum's account. Thus in the context both of threats and promises as attempts to control or manipulate behaviour, the rendering of unless as (3) Only ifp, not q seems to be the more appropriate one.4 The main point of the foregoing is not that it provides any definitive grounds for choosing the one account for unless over the other, although it may be of some suggestive value on that score, nor that it provides any sort of adequate or complete analysis of why the relation between if not and unless is much closer for deterrents than inducements, although the findings are consistent with the suggestions that I have offered. Rather, it should be of interest because it again highlights the role of our knowledge of the ways of the world in interpretation and understanding. One does not generally assume that good things will be offered without special reason, and that only some action on the part of Ad might choke off the flow from the cornucopia (the traffic ticket example). Further, it suggests that communicative strategies may affect both phrasing and understanding. Thus, if Unless p, q is glossed as 'in all circumstances other than/?, q, and if 'all circumstances other than/?' would characteristically constitute a much larger set than p, then given the choice between Only if p, not q and Only if not p, q as renderings of unless, the former may come to be preferred just because it specifies things more precisely and specifically by using the language of (the unique) exception. 2.3 The phrasing of inducements and deterrents with if, and, and or Now consider the relations holding among inducements and deterrents phrased with if, and and or, and how these relations are systematically affected, depending on whether an inducement or deterrent is involved. To justify this interest in the phrasing of inducements and deterrents as conjunctives and disjunctives, a word is first needed on the results yielded by the paraphrase task for all sorts of conditionals. Both conditional promises and conditional threats were 185

Samuel Fillenbaum Table I. The phrasing of inducements and deterrents Promises

Threats

If you fix the car I'll give you $100

If you come any closer I'll shoot

(2)pANDq+ (3) p OR not q+ (4) *not p OR q+

(2)pANDq(3) *p OR not q (4) not p OR q -

Note: The ' + ' or ' —' sign indicates desirability or undesirability of q for the addressee and * indicates that the paraphrase is not acceptable and in some ways strange.

quite commonly paraphrased with arcd-statements, and were just about the only kinds of conditionals that elicited such paraphrases. Conditional promises were very rarely paraphrased with or-sentences, while conditional threats were very often paraphrased as disjunctives. This was especially common if they involved a negatively stated antecedent proposition (thus statements like / / you don't shut up, I'll hit you were more often than not paraphrased as something like Shut up or I'll hit you). A conditional promise phrased with if (If you fix the car I'll give you $100) can readily be paraphrased with and (Fix the car and I'll give you $100). The same holds for a conditional threat (// you come any closer Fll shoot may be paraphrased with and as Come any closer and Fll shoot). But what happens when one attempts to phrase or paraphrase these as disjunctives? In the case of the conditional promise, one might paraphrase If you fix the car I'll give you $100 as Fix the car or I won't give you $100. While this is acceptable and coherent as an attempt to elicit a particular action, it appears to differ from its source sentence in one important respect: the source sentence is a conditional promise while the disjunctive paraphrase above is really a sort of conditional threat, involving the conditional withholding of an incentive as contrasted with its conditional offer in the //"phrasing. If, on the other hand, one negates the first proposition in an attempt at a disjunctive paraphrase, one gets Don't fix the car or I'll give you $100 which is not an acceptable paraphrase of the source //"sentence. Moreover, it is strange and almost incoherent to boot (why this should be will be discussed below). Now, how about phrasing a deterrent disjunctively? Negating the first proposition yields Don't come any closer or I'll shoot which is coherent and a perfectly acceptable paraphrase of / / you come any closer I'll shoot. On the other hand, negating the second proposition leads to Come any closer or I won't shoot which is both unacceptable as a paraphrase and a somewhat strange and puzzling statement. Thus, in paraphrases with or, inducements and deterrents behave very differently. This is laid out for reference in table 1. The results from the equivalence judgement task are completely consistent 186

The use of conditionals in inducements and deterrents with expectation. In this task subjects were given pairs of sentences, the first one always phrased with if and the second phrased with either and or or, and if the latter, either the first or second proposition was negated. For both inducements and deterrents, conjunctive sentences were overwhelmingly judged equivalent to their partners phrased with if. The results with disjunctives were very different, depending on whether an inducement or deterrent was involved. For inducements, a version with or which negated the second proposition was characteristically accepted as equivalent to the //"version, while one that negated the first proposition was characteristically judged to differ in meaning from the if version. On the other hand, for deterrents, a version with or which negated the second proposition was characteristically rejected as different in meaning from the //"version, while one that negated the first proposition was overwhelmingly judged as equivalent in meaning to its //"version. The results from the description or sentence classification task yielded findings consistent with those noted above. Subjects were given a series of sentences and asked to classify each as a threat, warning, promise, or none of these (NOT). The sentences which involved inducements and deterrents were phrased as //"-sentences, as awd-sentences and as or-sentences with negation on either the first or second proposition. Phrased as conditionals or conjunctives, inducements were characteristically described as promises, and deterrents as threats or warnings. However, in the disjunctive phrasings the sign of the consequences came to have a striking, differential effect. For inducements phrased as disjunctives, if the first proposition is negated, sentences are classified as NOT over half the time; if the second proposition is negated then these sentences are characteristically regarded as threats or warnings, seldom as promises. Deterrents phrased as disjunctives with the first proposition negated are characteristically classified as threats or warnings; if the second proposition is negated over half of the descriptions fall into the NOT category. Overall, the results yielded by the various procedures are consistent and sensible. Clearly, the sign of the q proposition can make a critical difference. Inducements and deterrents behave very similarly when phrased with if and and, but differ consistently in some important respects when phrased with or. It seems difficult to phrase a conditional promise with or. When one attempts to phrase it disjunctively, with negation on the second proposition, it becomes a sort of conditional threat of the withdrawal of a positive incentive. It is perhaps worth noting that an inducement statement phrased as a conditional (// you fix the car I'll give you $100) is characteristically judged equivalent in meaning to a disjunctive version with the second proposition negated (Fix the car or I won't give you $100). At the same time, the former statement is generally regarded as a promise and the latter as a threat or warning. A considerable semantic and pragmatic subtlety is revealed in these judgements. It is as though our subjects are saying that If p, q+ and p or not q+ are equivalent because they both amount to attempts to get Ad to do p, but that

Samuel Fillenbaum they differ in that the if version tries to do this by promising an incentive while the or version seeks to do it by threatening the withdrawal of that incentive. Here I have presented some data or phenomena; what is needed now is an analysis that accounts for the ways in which inducements and deterrents may or may not be phrased, and which exhibits some of the implicit rules that govern the purposive use of conditionals as well as revealing how expectations about consequences affect the form and phrasing of such conditionals. I shall try to sketch out such an analysis, working mainly from the point of view of Ad, just because inducements or deterrents are 'essentially tied' to perlocutionary effects. They constitute attempts to get Ad to do something or refrain from doing something via 'enforcers', positive or negative incentives which are explicitly spelt out. Begin with the simple (perhaps tautological) assumption that Ad wants to get good outcomes and to avoid bad outcomes. Assume further that Ad has the requisite knowledge that allows him or her to recognize the properties of the outcome that is actually being offered (i.e. to determine the sign and extremity of signing of the q proposition). Then an inducement will be effective in so far as Ad wants q+ enough to do something, /?, in exchange (with p not too costly, or at least less costly than q+ is valuable). A deterrent will be effective in so far as Ad wants to avoid q— enough to not do something, p, in exchange (with p not too valuable, or at least less valuable than q— is costly). With this in mind, consider the phrasing of inducements and deterrents with if, and, and or. 2.4 Interpretation of inducements and deterrents phrased as conditionals First consider the if phrasing. An inducement phrased with if will have the form If p, q+. Recognizing q+ for what it is, viz. that it is positively signed and is therefore desirable, Ad might employ a legitimate argument form, modus ponens, and affirm the antecedent; Ad wants g+, Ad has just been told that tf P* (I'll kill you))) Is (28'") ad hoc? Perhaps not. A speech act such as (28) is a little special. So one could expect the analysis to be a little special too. I do not think that (28'") is too special. It is not miraculous, for example, that (28) is associated with two kinds of speech acts, an imperative and an assertion. Remember (from section 3.2) that if-then speech acts consist of two speech acts, too: one about the sufficiency of protasis for apodosis, and one an assertion about the possibility of protasis and apodosis. Another special feature of (28'") is that both p and q are within the scope of an imperative, while only the 208

Conditionals and speech acts protasis verb has imperative form.9 Again, this is not really bizarre. 'Normal' ifp, then q imperatives only have one imperative form, too: (38)

If he opens the window, kill him

Of course, in (38) it is the apodosis verb that has imperative form, while in (28) it is the protasis verb. In (38) Ad is impered to do q, given /?, and Ad should not worry about p. In (28) we find the exact opposite: Ad is impered to dop and not to worry about q, which, given/?, will come about automatically. A point of interest is that the double speech act analysis of (28'") is compatible with the fact that some speech acts of the form of (28) seem to be primarily imperative, while others seem primarily conditional. Sentence (28), for example, is first and foremost an imperative. 'General imperatives', however, such as (39): (39)

Scratch a Russian and you'll find a Tartar

(due to Jespersen 1940: 475) capitalize on the conditional meaning. This is also the case when the q verb has a past tense. Sentence (40) is again due to Jespersen (1940: 476-7, 1963: 314-15): (40)

Give him time, and he was generally equal to the demands of suburban customers

5-3 The ( ! ( / ? A ^ ) ) & (!-(/?—•