Presupposition and Implicature in Compositional Semantics (Palgrave Studies in Pragmatics, Languages and Cognition)

Presupposition and Implicature in Compositional Semantics Edited by

Uli Sauerland and Penka Stateva

Palgrave Studies in Pragmatics, Language and Cognition Series Editors: Noël Burton-Roberts and Richard Breheny Series Advisors: Kent Bach, Anne Bezuidenhout, Robyn Carston, Sam Glucksberg, Francesca Happé, François Recanati, Deirdre Wilson Palgrave Studies in Pragmatics, Language and Cognition is a new series of high quality research monographs and edited collections of essays focusing on the human pragmatic capacity and its interaction with natural language semantics and other faculties of mind. A central interest is the interface of pragmatics with the linguistic system(s), with the ‘theory of mind’ capacity and with other mental reasoning and general problem-solving capacities. Work of a social or cultural anthropological kind will be included if firmly embedded in a cognitive framework. Given the interdisciplinarity of the focal issues, relevant research will come from linguistics, philosophy of language, theoretical and experimental pragmatics, psychology and child development. The series will aim to reflect all kinds of research in the relevant fields – conceptual, analytical and experimental. Titles include: Anton Benz, Gerhard Jäger and Robert van Rooij (editors) GAME THEORY AND PRAGMATICS Reinhard Blutner and Henk Zeevat (editors) OPTIMALITY THEORY AND PRAGMATICS María J. Frápolli (editor) SAYING, MEANING AND REFERRING Essays on François Recanati’s Philosophy of Language Corinne Iten LINGUISTIC MEANING, TRUTH CONDITIONS AND RELEVANCE The Case of Concessives Ira Noveck and Dan Sperber (editors) EXPERIMENTAL PRAGMATICS Uli Sauerland and Penka Stateva (editors) PRESUPPOSITION AND IMPLICATURE IN COMPOSITIONAL SEMANTICS Christoph Unger ON THE COGNITIVE ROLE OF GENRE Forthcoming titles: Hans-Christian Schmitz OPTIMAL ACCENTUATION AND ACTIVE INTERPRETATION

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Presupposition and Implicature in Compositional Semantics Edited by

Uli Sauerland and

Penka Stateva

© Selection and editorial matter © Uli Sauerland and Penka Stateva 2007 Chapters © their authors 2007 All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission. No paragraph of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright, Designs and Patents Act 1988, or under the terms of any licence permitting limited copying issued by the Copyright Licensing Agency, 90 Tottenham Court Road, London W1T 4LP. Any person who does any unauthorised act in relation to this publication may be liable to criminal prosecution and civil claims for damages. The authors have asserted their rights to be identified as the authors of this work in accordance with the Copyright, Designs and Patents Act 1988. First published in 2007 by PALGRAVE MACMILLAN Houndmills, Basingstoke, Hampshire RG21 6XS and 175 Fifth Avenue, New York, N.Y. 10010 Companies and representatives throughout the world. PALGRAVE MACMILLAN is the global academic imprint of the Palgrave Macmillan division of St. Martin’s Press, LLC and of Palgrave Macmillan Ltd. Macmillan® is a registered trademark in the United States, United Kingdom and other countries. Palgrave is a registered trademark in the European Union and other countries. ISBN-13: 978–0–230–00533–4 hardback ISBN-10: 0–230–00533–0 hardback This book is printed on paper suitable for recycling and made from fully managed and sustained forest sources. Logging, pulping and manufacturing processes are expected to conform to the environmental regulations of the country of origin. A catalogue record for this book is available from the British Library. Library of Congress Cataloging-in-Publication Data Presupposition and implicature in compositional semantics / edited by Uli Sauerland and Penka Stateva. p. cm.—(Palgrave studies in pragmatics, language, and cognition) Includes bibliographical references and index. ISBN-13: 978–0–230–00533–4 (cloth) ISBN-10: 0–230–00533–0 (cloth) 1. Semantics. 2. Presupposition (Logic) 3. Implication (Logic) 4. Pragmatics. I. Sauerland, Uli. II. Stateva, Penka, 1965– P325.P655 2007 401 .43—dc22 10 9 8 7 6 5 4 3 2 1 16 15 14 13 12 11 10 09 08 07 Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham and Eastbourne

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Contents

Notes on Contributors

viii

1 Introduction

1

Uli Sauerland and Penka Stateva

2 Quantifier Dependent Readings of Anaphoric Presuppositions

12

Sigrid Beck 1 2 3 4

Introduction The presupposition of again Quantifier dependent again Conclusions and consequences

3 Licensing or

12 14 22 31 34

Regine Eckardt 1 2 3 4 5 6

Introduction Boolean and mis-behaved ‘or’ Explicit existential quantification and ‘or’ Modal existentials Interactions between different licensers Summary

4 Free Choice and the Theory of Scalar Implicatures

34 38 46 53 62 67 71

Danny Fox 1 2 3 4 5 6 7 8 9

Some background on scalar implicatures The problem of free choice permission Other free choice inferences Chierchia’s puzzle Sauerland’s proposal An alternative perspective Recursive exhaustification and FC Other existential quantifiers Singular indefinites v

72 80 85 89 90 95 102 105 106

vi

Contents

10 Other FC effects 11 Remaining issues 12 Conclusion

5 Partial Variables and Specificity

108 109 111 121

Gerhard Jäger 1 2 3 4 5 6

Introduction Specificity and scope Solution strategies Partial variables Partial variables and presuppositions Conclusion

6 Negated Antonyms: Creating and Filling the Gap

121 122 125 136 150 154 163

Manfred Krifka 1 Double negatives 2 Attempts to explain double negatives 3 Pragmatic strengthening within an epistemic theory of vagueness 4 Conclusion

7 A Pragmatic Constraint on Adverbial Quantification

163 165 168 175

178

Orin Percus 1 A possible line of argumentation, and reasons to reject it 2 A constraint on the use of sentences with adverbial quantifiers 3 Some consequences of this constraint 4 Consequences for ‘semantic partition’ 5 Concluding remarks

8 Transparency: An Incremental Theory of Presupposition Projection

178 183 191 201 206

214

Philippe Schlenker 1 The dynamic turn and the Transparency theory 2 The projection problem: basic results of the Transparency theory 3 The triggering problem: against a lexical treatment 4 Problems and prospects

215 223 232 236

Contents

9 Aspects of the Pragmatics of Plural Morphology: On Higher-Order Implicatures

vii

243

Benjamin Spector 1 2 3 4 5

A puzzle about plural indefinites Sketch of the analysis The proposal More complex cases An enigma that confirms the hypothesis: the modal presupposition induced by plural indefinites 6 Sauerland’s alternative 7 Conclusion

Index

243 245 251 257 264 267 271

282

Notes on Contributors Sigrid Beck is Professor of Linguistics at the University of Tübingen. She studied linguistics, computer science and psychology at Tübingen and Edinburgh. Her 1996 University of Tübingen dissertation is on Intervention Effects in questions. She has taught at the Universities of Massachusetts, Connecticut, and Potsdam. Her current work is on semantics and its interfaces to syntax and pragmatics, and addresses topics such as questions, plural predication, reciprocals, comparison constructions, and decomposition adverbs. Regine Eckardt is Professor of English at Göttingen University. She is working on topics in semantics and pragmatics, specifically focus semantics, events, aspect, and discourse particles. Her interests extend to historical linguistics and semantic reanalysis. The monographs Adverbs, Events, and Other Things and Meaning Change in Grammaticalization as well as the collected volume Words in Time reflect her work in these fields. In addition, Eckardt published several research articles and is Coeditor of the Journal of Semantics. Danny Fox is currently Associate Professor at the Massachusetts Institute of Technology, where he received his PhD in 1998. From 1998 to 2001, he was a junior fellow at the Harvard Society of Fellows. Among his publications are Economy and Semantic Interpretation, ‘Antecedent Contained Deletion and the Copy Theory of Movement’ (Linguistic Inquiry), and ‘Cyclic Linearization of Syntactic Structure’ (with David Pesetsky, Theoretical Linguistics). Gerhard Jäger is Professor of Linguistics at the University of Bielefeld in Germany. He received his PhD from Humboldt University in 1996, with a thesis on dynamic semantics. He is the author of Anaphora and Type Logical Grammar. Together with Anton Benz and Robert van Rooij, he co-edited Game Theory and Pragmatics (Palgrave Macmillan, 2005). Manfred Krifka is Professor of General Linguistics at Humboldt University, Berlin, and director of ZAS (Center for General Linguistics, viii

Notes on Contributors

ix

Berlin). He has taught at the University of Tübingen and the University of Texas, Austin. He is the author of two books and many other publications on the semantics and pragmatics of aspect, mass nouns and measure constructions, polarity items, and information structure. Orin Percus recently joined the faculty of the University of Nantes. He received his PhD from MIT in 1997 with a thesis on the semantics of indefinites. Since then he worked in Amherst, Milan, and Tübingen. His work investigated general principles that constrain the semantic contribution of embedded clauses, the way in which lexical material contributes to the contextual requirements of sentences, and the semantic composition of copular sentences. He is a founding editor of the journal Snippets. Philippe Schlenker is currently Professor of Linguistics at UCLA, and is affiliated with Institut Jean-Nicod (CNRS) in Paris. He studied philosophy and linguistics in Paris and Boston (PhD in linguistics, MIT, 1999; PhD in philosophy, EHESS, Paris, 2002; Habilitation, EHESS, 2005). His initial work was concerned with the semantics of indexicals and attitude reports (‘A Plea for Monsters’, Linguistics and Philosophy, 2002). His current interests include issues in natural language semantics (intensional phenomena, anaphora, presuppositions) and in philosophical logic (paradoxes). Benjamin Spector is currently a Junior Fellow at the Harvard Society of Fellows. He has presented his PhD dissertation in 2006 (University of Paris 7). From 2003 to 2006, he has been teaching linguistics and logic at Ecole Normale Supérieure in Paris. His work’s main focus is formal pragmatics, especially scalar implicatures and the semantics and pragmatics of questions and answers.

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1 Introduction Uli Sauerland and Penka Stateva Zentrum f ür Allgemeine Sprachwissenschaft (ZAS), Berlin

A speaker of a language can quickly judge the grammaticality, truth and felicity of a sentence on the basis of his beliefs about what is the case and who is talking. A basic goal of semanticists is to model what we do when we judge a sentence to be true. A basic goal of pragmaticists, on the other hand, is to model what we do when we judge a sentence to be felicitous. Semanticists and pragmaticists have each proposed explicit formal models of these mental mechanisms. These models map a pair of a sentence and a model-theoretic representation of what we may believe to be the case onto a truth value and a measure of felicity. Semantics and Pragmatics have both established themselves as independent fields in the 1970s and 1980s. During that period, the distribution of labor between semantics and pragmatics was intensively debated. (Davis (1991) and Kasher (1998) have collected much of the relevant literature in useful volumes.) The separation of semantics and pragmatics has made enormous progress possible in both fields. At the same time though, it has had the unfortunate consequence that interconnections between semantics and pragmatics may have not received enough attention. To begin, we briefly survey the main lines of inquiry in semantics and pragmatics that this volume builds on. For the computation of truth conditions, the dominant view is that this process involves at least three things: One is the structured mental representation of a sentence that syntax provides. The second are the interpretations of the primitive parts of the sentence, which are provided by their lexical entries. The third is the compositional interpretation procedure: A recursive procedure that assigns an interpretation to any sub-structure of the syntactic representation on the basis of the interpretations of the immediate parts of this sub-structure. Recursive application of the interpretation function then successively builds up the 1

2 Presupposition and Implicature in Compositional Semantics

interpretation of larger and larger sub-structures, until the interpretation of the entire sentence results. This view can be attributed to Montague (1974) and Lewis (1970) and has been developed much further since. In the following, we assume the formal model of the interpretation function laid out in the textbook by Heim and Kratzer (1998). For the computation of felicity conditions, the dominant view distinguishes at least two kinds of felicity conditions: Presuppositions (Frege 1879, Strawson 1952) and Implicatures (Grice 1989). Here and in the following, we follow Karttunen and Peters (1979), Horn (1990) and others in assuming that Grice’s Conventional Implicatures are to be identified with presuppositions, and use the term Implicatures to exclusively refer to Grice’s Conversational Implicatures. The mechanisms giving rise to the presuppositions and implicatures of a sentence are also thought to be fundamentally different. We consider first presuppositions, then implicatures. Presuppositions are represented as felicity conditions in the lexical entries of certain morphemes. The computation of the presuppositions of a sentence proceeds in a compositional fashion analogous to the computation of the sentences truth conditions. Technically, presuppositions can be represented as domain restrictions of the functions that represent the meanings of lexical entries, constituents, and sentences (Blau 1978, Heim 1992). A presupposition failure then arises when the value of a function–argument combination is undefined. For example, the domain of the definite determiner the is restricted to properties P such that at least one individual has property P. Therefore, the sentence (1) leads to a presupposition failure if there are no books.

(1)

I didn’t see the books.

Implicatures, on the other hand, are generally held to arise from the interaction of sentence meaning and conditions on felicitous discourse. Grice (1989) proposed one view of the computation of implicatures that continues to be very influential. Consider, for example, the analysis of (2). (2) is true in a situation where I know that the Philharmonic played all Beethoven symphonies this season, however, it is infelicitous because the more informative sentence The Philharmonic played all symphonies by Beethoven is also true.

(2)

The Philharmonic played some symphonies by Beethoven this season.

Introduction 3

Therefore, (2) implicates that the Philharmonic did not play all nine symphonies by Beethoven this season. Horn (1972) observes that not all sentences that are more informative than what is said are considered for implicature computation. For example, They played only some Beethoven symphonies this season is more informative than (2), but (2) does not implicate that they didn’t play only some Beethoven symphonies Horn amends Grice’s proposal with a restriction to scalar alternatives; for example, many and all are scalar alternatives, but not many and only many. Horn (1989), Gazdar (1979), Hirschberg (1985), Matsumoto (1995), Sauerland (2004) have developed this view further, in particular for the analysis of scalar implicatures. In the literature cited above, the three components of sentence interpretation have been considered separately. This separation is justified on theoretical and methodological grounds and has made substantial progress in all three areas possible. However, the separate treatment of the truth conditions, implicatures, and presuppositions, while it was important to make progress, bears certain risks because of the narrow view adopted: It may overlook important interactions between the three components. Furthermore, it may induce researchers to focus on phenomena that fit neatly into one of the three components. This reasoning provides the motivation for the present volume: The contributions concern, on the one hand, empirical phenomena that do not fit neatly into one of the three components and, on the other hand, the interaction of the three components. Specifically, three of the contributions (those by Eckardt, Fox, and Percus) focus on the question of which component should best provide the explanation for a specific empirical phenomenon. Questions of this type are pertinent to the other chapters too, but the other chapters concern directly the interaction between the different components. Two of them concern the interaction between implicatures and truth conditions (those of Krifka and Spector). Three other chapters focus on the interaction between presuppositions and truth conditions (those by Beck, Jäger, and Schlenker). Percus reconsiders the analysis of restrictions on the use of individual level predicates. As is well known, many examples that contain both a temporal adverbial and an individual level predicate are judged ungrammatical, as is illustrated by (3). (3)

*Ingrid was always Swedish.

Percus establishes a parallel between (3) and sentences like (4), which have the same relevant properties and same status but become acceptable if used under suitable pragmatic conditions.

4 Presupposition and Implicature in Compositional Semantics

(4)

(*)The student who finished first was always Swedish.

If, for example, (4) is uttered in a situation in which a number of exams are held during the past week, and different people finish first each time, the speaker can successfully use that sentence to inform the audience of the nationality of the winners. (4) crucially shows that these restrictions on the use of individual level predicates have pragmatic, rather than grammatical origin (pace Kratzer 1995). To identify these pragmatic factors, Percus considers pairs of situations tied to examples like (4). One member of each pair renders the sentence fully acceptable while in the other the sentence gets a much worse status. Examining the relations within these pairs of situations Percus concludes that the status of sentences containing individual level predicates and temporal quantifiers depend on two additional factors: (i) the time intervals that context makes salient and (ii) what the parties to conversation think is being taken for granted. He argues that given standard assumptions about (ii) if the truth of a quantified statement is implied by a variant of it which involves a subset of the time intervals the original involves the original sentence is predicted to sound bizarre. This idea is made precise by establishing a general pragmatic principle which precludes the usage of otherwise legitimate logical forms and is tested in examining related phenomena. Percus’s contribution targets mainly the division of labor between grammar and pragmatics but it also gives an intriguing twist to the study of the interaction between sentence meaning and conditions on felicitous discourse. As he notes, the principle he argues for, has a very specific status among other familiar pragmatic principles since it involves comparison among propositions that are equally informative. It would fall therefore into the Gricean category of Manner, however, unlike other Manner maxims Percus principle does not apply to a surface form. Both Eckardt’s and Fox’s chapters concern the free choice effect with disjunction. The basic problem discovered by Kamp (1973) is that (5a) and (5b) are perceived to be equivalent, but this is not predicted on the basis of the standard logical meanings of permissive modality, conjunction, and disjunction. (5)

a. You may have coffee or tea. b. You may have coffee and you may have tea.

Recent work on the topic has therefore claimed that the standard logical meanings of permissive modality and disjunction are not correct for

Introduction 5

natural language (Zimmermann 2000 and others). But this conclusion is challenged by Eckardt’s and Fox’s chapters. Both chapters independently make the novel observation that plural indefinites also give rise to something akin to a freeehoice effect in examples like (6). (6)

a. Some linguists were having coffee or tea. b. Some linguists were having coffee and some linguists were having tea.

Such examples show that the free choice effect should not be analyzed as tied to an analysis of the interaction of disjunction and existential modality. Fox strengthens this point further by showing that the logical duals of existential quantification and disjunction give rise to the same effect if negated. All these facts argue for an analysis based on the pragmatics of existentials and disjunction. Specifically what Eckardt and Fox both pursue is an analysis of the free choice effect as a conversational implicature. However, the two chapters pursue two different lines of analysis from this point on. Eckardt pursues the intuition that the implicature leading from (6a) to (6b) has the same basis as that from (7) to (6b). The core of her proposal is the claim that (6a) involves distributive quantification over a specific set of linguists. This predicts that the indefinites should behave like the plural definite or universal in (7). (7)

The/All linguists were having coffee or tea.

Eckardt then goes on to extend this account to other cases of free choice effects. Fox’s contribution presents in detail the conflict between the free choice effect and the neo-Gricean approach to scalar implicatures. The neo-Gricean account in the version developed by Sauerland (2004), as Fox shows, predicts that (8) should be an implicature of (5a), but this would contradict (5b). (8)

The speaker is not sure whether you may have coffee and the speaker is not sure whether you may have tea.

Fox develops a new account for scalar implicatures that does not derive them in the same way as other conversational implicatures. Rather, Fox argues that scalar implicature computation must precede the computation of other conversational implicatures and therefore places them in

6 Presupposition and Implicature in Compositional Semantics

the compositional semantic system (cf. Chierchia 2004). Fox shows then that free choice effects can be derived in this architecture on the basis of a novel proposal for exhaustification that can apply recursively. In example (6a), exhaustification at the second level involves a comparison among the three propositions in (9). (9)

a. You may have tea or coffee but not both. b. You may have tea but no coffee. c. You may have coffee but no tea.

Because (9a) is entailed by (9b) and (9c), Fox predicts as the result of the second level of exhaustification the free choice effect: You may have tea or coffee, but not both, and neither tea nor coffee is forbidden. The chapter by Spector is one of the two that concerns the interaction between implicatures and truth conditions. His chapter also presents a second application of Fox’s idea to apply exhaustification recursively; namely, to plural noun phrases. Plural noun phrases in many cases require plural reference, but there are exceptions as recently summarized by Sauerland et al. (2005). Spector asks whether the plurality requirement of plural noun phrases is part of the truth conditions, presuppositions or an implicature, arguing in favor of the latter. Strong initial support for the implicature analysis is provided by the observation that in the scope of negation the plurality requirement does not apply. This is illustrated by the fact that (10b) does not express the negation of (10a). (10)

a. The homework contains difficult problems. b. The homework doesn’t contain difficult problems.

The difference between (10a) and (10b) follows if we assume that the plural does not exclude singular reference. Outside the scope of negation, however, use of the plural implicates that the uniqueness implication of the singular would have been too strong. The result is a plurality implicature. This effect has been observed in previous work in semantics, but all previous attempts of explaining it have been unsatisfactory as Spector argues. The difficulty arises from the assumed logical relation of singular and plural sentences: The implicature analysis assumes that the singular example (11a) entails the plural example (10a) as long as implicatures are put aside. But, then the negated plural example (10b) is predicted to entail the negated singular example (11b). The standard implicature analysis predicts therefore that there should be a clear difference in interpretation between (10b) and (11b). However,

Introduction 7

the two sentences are more or less equivalent – Spector derives what difference there exists in the final section of his chapter. (11)

a. The homework contains a difficult problem. b. The homework doesn’t contain any difficult problem.

Spector elegantly solves this problem by applying the idea of recursive exhaustification from Fox’s chapter. On Spector’s proposal, the first level of exhaustification only compares the plural (10a) to the proposition expressed by (12a) which is equivalent to (10a). At the second level, however, (10a) is compared to (12b), which is the exhaustified version of (12a), and since (12b) entails (10a), the plurality implicature is predicted. For the negated plural in (10b), however, this line of argumentation does not go through since the negation of (12b) is not the exhaustified version of (12a). In this way, Spector provides an nice account of the plurality requirement of the plural. (12)

a. The homework contains at least one difficult problem. b. The homework contains exactly one difficult problem.

The chapter by Krifka discusses another case where the application of negation does not lead to the logical inverse. Consider (13): (13)

a. John is happy. b. John is not unhappy.

Contrary to expectation, the double negative in (13b) is not synonymous with the positive predicate in (13a). Krifka offers a solution to this puzzle by appealing to a process of pragmatic strengthening within an epistemic theory of vagueness (cf. Williamson 1994). This process involves an intricate interplay of a number of pragmatic principles which are applied in the use of negated antonyms. The final three chapters concern presuppositions and their relation to truth conditions. Beck focuses on an observation due to Soames (1989) and Heim (1992) that presuppositions triggered by again are tied to an anaphoric element. Speakers relate Heim’s (14a), for example, but not (14b) to an inference that John’s birthday precedes in time Mary’s birthday. (14)

a. We will have pizza on John’s birthday, so we shouldn’t have pizza again on Mary’s birthday.

8 Presupposition and Implicature in Compositional Semantics

b. We will have pizza on John’s birthday, so we shouldn’t have pizza on Mary’s birthday. It is clear that again triggers a presupposition that there is some time interval preceding Mary’s birthday in which we have already had pizza. But among the many possible previous pizza-eating occasions only one is relevant: that which involves John’s birthday, hence the inference pattern. This intuition points to the fact that the presuppositions of again in (14) involve a specific time period. Beck takes this fact to suggest that again must be related to an anaphoric temporal element for which the assignment gives John’s birthday as a value that satisfies the presuppositions of again. In other words, this temporal element has the properties a free variable in (14). The parallel between this anaphoric element and natural language variables like pronouns, restrictions on quantifier domains and traces is not accidental: Beck proposes that again comes with a lexical entry which specifies that its most internal argument is that anaphoric element, represented as a temporal variable. She further argues that like other variables, it is discernable in syntax and comes in the same varieties: it can be free, bound, or involve a complex structure. Beck tracks original examples of each kind addressing in most detail the interaction of again with quantifiers and the resulting anaphoric presuppositions. It is shown that the proposed logical forms lead to definedness and truth conditions that are in concord with speakers’ intuitions. The chapter concludes with an extention of the proposal to the anaphoric presuppositions of too and also. Jäger’s chapter is concerned with the analysis of specific indefinites. The topic is familiar from the numerous discussions in the literature of their notorious scopal properties. Unlike other quantified expressions, specific indefinites can escape scope islands: (15)

a. If most experiments succeed, John will be happy. b. If an experiment succeeds, John will be happy.

Jäger proposes a theory of specific indefinites from which these properties naturally follow while he avoids the pitfalls of other influential proposals. His theory is a synergy of ideas from DRT, the choice function approach, and theories that associate specificity with presuppositions. Indefinites are proposed to be analyzed as partial variables: local assignments determine the value of the variable which, however, comes with definedness conditions and only if these are fulfilled the indefinite can refer. Since

Introduction 9

indefinites are translated as variables, they can be bound by existential closure which can apply at every sentential level thus providing for the observed scopal freedom of specific indefinites. The core proposal in the chapter follows a trend in the literature to view specificity as a kind of presupposition phenomenon. Furthermore, it is extended to suggest that in general presuppositions are restrictions on partial variables. This view elegantly accounts for presupposition projection and accommodation. Specific indefinites are treated on a par with standard pesupposition triggers but, in addition, they are subject to the Novelty Condition (Heim 1982). Schlenker’s contribution is concerned with basic issues of presupposition triggering and presupposition projection. He does not accept the notion of presupposition as basic, but seeks to derive it from general pragmatic principles. Specifically, Schlenker proposes a new pragmatic principle, Be Articulate, that constrains the use of lexical items that express more than one separate truth-conditional contribution simultaneously. Namely, Be Articulate requires that only one of these components of the meaning must introduce new information. He shows that this straightforwardly derives the principles of presupposition projection: For example, assume that to stop Q-ing expresses two separate truth-conditional contributions: not doing Q and having done Q in the past. Then the use of stop in (16) satisfies Be Articulate when either one of the contributions of to stop smoking is part of the common ground. (16)

Sue stopped smoking.

If the sentential context in which stop occurs, however, establishes that one of the contributions of stop is redundant, nothing is required of the common ground. This provides an explanation for examples of presupposition filtering like (17a). Schlenker’s account, furthermore, straightforwardly extends to examples like (17b), where it is the other contribution of stop that is redundant. (17)

a. If Sue ever smoked, she has stopped smoking. b. If Sue isn’t smoking, she has stopped smoking.

The work presented in this volume is one of the results of a research network on Semantics and Pragmatics called the Semantiknetzwerk. The network has been funded by the German research council DFG (grants SA 925/2-1 and SA 925/2-2, principal investigator Uli Sauerland), and we are very grateful for this financial support. The support has allowed

10

Presupposition and Implicature in Compositional Semantics

us to hold five meetings up to now with a sixth meeting planned for September 2006. Four of the meetings were held in Berlin at the Centre for General Linguistics, and one was held in Nijmegen, Holland. Many of the chapters contained in this volume have been presented and discussed at one of the five meetings. In addition to the authors and editors of the present volume, the following researchers took part in these meetings regularly: Richard Breheny Irene Heim, Graham Katz, Cecile Meier, Doris Penka, and Ede Zimmermann. Furthermore the following researchers took place in some of the meetings: Bridget Copley, Cornelia Endriss, Bart Geurts, Beáta Gyuris, Andreas Haida, Elke Kasimir, Jason Mattausch, Robert van Rooij, Katrin Schulz, Magdalena Schwager, Yael Sharvit, Arnim von Stechow, Kazuko Yatsushiro, and several others. We would like to thank all participants for making the meetings of the Semantiknetzwerk a lively and stimulating forum for the discussion and exchange of ideas leading to this book and several other publications.

References Blau, U.: 1978, Die dreiwertige Logik der Sprache. Ihre Syntax, Semantik und Anwendung in der Sprachanalyse. de Gruyter, Berlin, Germany. Chierchia, G.: 2004, ‘Scalar implicatures, polarity phenomena, and the syntax/pragmatics interface’, in A. Belletti (ed.), Structures and Beyond, pp. 39–103. Oxford University Press, Oxford, UK. Davis, S. (ed.): 1991, Pragmatics. A Reader. Oxford University Press, Oxford, UK. Frege, G.: 1879, Begriffsschrift. Eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Neubert, Halle, Germany. Gazdar, G.: 1979, Pragmatics: Implicature, Presupposition, and Logical Form. Academic Press, New York, N.Y. Grice, P.: 1989, Studies in the Way of Words. Harvard University Press, Cambridge, Mass. Heim, I.: 1982, ‘The semantics of definite and indefinite noun phrases’, PhD dissertation, University of Massachusetts, Amherst. Heim, I.: 1992, ‘Presupposition projection and the semantics of attitude verbs’, Journal of Semantics 9, 183–221. Heim, I. and A. Kratzer: 1998, Semantics in Generative Grammar. Blackwell, Oxford, UK. Hirschberg, J.: 1985, ‘A theory of scalar implicature’, PhD dissertation, University of Pennsylvania, Philadelphia, Penn. Horn, L. R.: 1972, ‘On the semantic properties of logical operators in English’, PhD dissertation, University of California, Los Angeles. Horn, L. R.: 1989, A Natural History of Negation. University of Chicago Press, Chicago, Ill. Horn, L. R.: 1990, ‘Hamburgers and truth: why Gricean explanation is Gricean’, in K. Hall et al. (eds), Proceedings of the Sixteenth Annual Meeting of the Berkeley Linguistics Society, pp. 454–71. Berkeley Linguistics Society, Berkeley, Calif.

Introduction 11 Kamp, H.: 1973, ‘Free choice permission’, Proceedings of the Aristotelian Society, New Series 74, 57–74. Karttunen, L. and S. Peters: 1979, ‘Conventional Implicature’, in C. Oh and D. Dinneen (eds), Presupposition (Syntax and Semantics 11), pp. 1–56. Academic Press, New York, NY. Kasher, A. (ed.): 1998, Pragmatics: Critical Concepts. Routledge, London, UK. Kratzer, A.: 1995, ‘Stage-level and individual-level predicates’, in G. N. Carlson and F. J. Pelletier (eds), The Generic Book, pp. 125–75. University of Chicago Press, Chicago, Ill. Lewis, D.: 1970, ‘General semantics’, Synthese 22, 18–67. Matsumoto, Y.: 1995, ‘The conversational condition on Horn scales’, Linguistics and Philosophy 18, 21–60. Montague, R.: 1974, ‘The proper treatment of quantification in ordinary English’, in R. Thomason (ed.), Richard Montague: Selected Papers, pp. 247–70. Yale University Press, New Haven, Conn. Sauerland, U.: 2004, ‘Scalar implicatures in complex sentences’, Linguistics and Philosophy 27, 367–91. Sauerland, U., J. Andersen, and K. Yatsushiro: 2005, ‘The plural is semantically unmarked’, in S. Kepser and M. Reis (eds), Linguistic Evidence – Empirical, Theoretical, and Computational Perspectives, vol. V, pp. 413–34. Mouton d’Gruyter, Berlin, Germany. Soames, S.: 1989, ‘Presupposition’, in D. Gabbay and F. Guenthner (eds), Handbook of Philosophical Logic, vol. IV, pp. 553–16. Reidel, Dordrecht, Netherlands. Strawson, P.F.: 1952, Introduction to Logical Theory. Methuen, London, UK. Williamson, T.: 1994, Vagueness. Routledge, London. Zimmermann, T. E.: 2000, ‘Free choice disjunction and epistemic possibility’, Natural Language Semantics 9, 255–90.

2 Quantifier Dependent Readings of Anaphoric Presuppositions Sigrid Beck Universität Tübingen

It has been observed (e.g. Cooper (1979), Chierchia (1993), von Fintel (1994), Marti (2003)) that the interpretation of natural language variables (overt or covert) can depend on a quantifier. The standard analysis of this phenomenon is to assume a hidden structure inside the variable, part of which is semantically bound by the quantifier. In this chapter I argue that the presupposition of the adverb ‘again’ and other similar presuppositions depend on a variable that gives rise to the same phenomenon.

1

Introduction

Von Fintel (1994), following Heim (1991), notes that (1a) has the reading paraphrased in (1b) and proposes the analysis sketched in (1 ). (1)

(1 )

a. Only one class was so bad that no student passed. b. Only one class was so bad that no student in that class passed. a. [[noC ]](A)(B) = 1 iff (g(C) ∩ A) ∩ B = { } b. [[only one class] [λx[ tx was so bad that [IP [DP nof(x) student ] [ passed]]]] c. only one class x: x was so bad that nof(x) student passed d. f: x → {y: y is in x}

The crucial property of the analysis is that the quantifier is assumed to have a covert restriction variable (cf. e.g. Westerstahl (1984), Rooth (1992), von Fintel (1994)), its resource domain variable (C in (1 a)). The value of this restriction varies depending on the quantifier ‘only one class’. Hence it is proposed that the resource domain variable itself 12

Quantifier Dependent Presuppositions 13

has a hidden internal structure, consisting of a variable x bound by ‘only one class’ and a free function variable that assigns to x the set of students in x. The suggestion that an expression of natural language that normally functions as a variable (this is meant in the following when I say ‘natural language variable’) is internally complex and can for this reason covary with a quantifier (without being bound by it) is not new. It has been made by Cooper (1979) to analyze certain pronouns, and extended to traces by Chierchia (1993). Interesting consequences especially for the theory of Logical Form have been investigated by Marti (2003). Thus a natural language variable can be free, bound or internally complex. In this chapter I argue that the adverb again gives rise to interpretations that similarly show covariation with a quantifier, and that the analysis sketched for the resource domain variable case can be extended to again. To give an example, consider (2), (3). (2) Bill was sick on his birthday. He was sick again on Thanksgiving. (2 ) Bill’s birthday is before Thanksgiving. (3) In 1995, 1996 and 1998, Bill was sick on the day of the department party. In each of these years, he was sick again on Thanksgiving. (3 ) In each of these years the department party was before Thanksgiving. Intuitively, the adverb again makes reference to a time preceding the time that the sentence with again talks about. Thus (2) triggers the inference (2 ), because the use of again in the second sentence requires there to be a previous time at which Bill was sick, and the only relevant time in the context is the one mentioned in the first sentence, Bill’s birthday. The example in (3) shows that which earlier time is picked can depend on a quantifier – here: ‘in each of these years’. Example (3) triggers the inference (3 ). The use of again requires that for each of the years 1995, 1996 and 1998, the department party that year precedes Thanksgiving that year. I will extend the analysis of (1) to (3) and related examples. The next section of this chapter introduces again and the theory of again’s presupposition I will use. In the subsequent Section 3 I examine the quantifier dependent cases and develop an analysis for them. Conclusions are presented in Section 4.

14

Presupposition and Implicature in Compositional Semantics

2

The presupposition of again

2.1

Basics

The adverb again indicates repetition, as illustrated by the simple example below. (4a) is only appropriate if (4b) holds. Thus it is standardly assumed that (4a) presupposes (4b). (4b) is given slightly more formally in (4c). t1 stands for the time interval that the sentence (4a) is about. (4)

a. John snored again. b. John had snored before. c. ∃t [t < t1 & John snored at t ]

I adopt a view of presuppositions according to which they are restrictions on appropriate contexts (compare Stalnaker (1973), Heim (1990), Kadmon (2001) among others). The restriction that (4a) imposes on contexts in which it can be uttered is given in (5a) (informally) and (5b) (more precisely); c is Stalnaker’s context set; c entails p iff c is a subset of p. (5)

a. (4a) is only felicitous in a context that entails that John had snored before. b. c ⇒ λw.∃t [t < t1 & John snored in w at t ]

Again triggers this presupposition. It is associated with a lexical entry like the one in (6) (see for example Stechow (1996), Fabricius-Hansen (2001), Jäger and Blutner (2003), van der Sandt and Huitink (2003) for recent discussion; the entry in (6) will serve as a starting point for present purposes). The definition (6) entails that the truth value of a sentence containing again may be undefined in a world. I take it that a sentence S is felicitous in a context c only if the presuppositions of S are true in all worlds in c; or in other words, S can only be added to c if c entails the presuppositions of S (cf. (7 )). This is how presupposition as undefinedness in simple sentences is mapped to appropriateness in a context (von Fintel (2003) calls (7 ) ‘Stalnaker’s Bridge’). The application to the example is illustrated in (7); t1 is a free time variable that is assigned a time interval by the variable assignment function g; in the example, suppose that is the interval t1. Thus (4a) can only be uttered felicitously in context c if (5b) is the case, as desired. (6)

[[again]] (p<τ , <s,t)(t)(w)

=1 if p(t)(w) & ∃t [t
Quantifier Dependent Presuppositions 15

(7)

(7 )

[[ [[[ John snored] again ] t1 ]]]g (w) is defined only if ∃t [t < g(t1) & John snored in w at t ] If defined, it is true iff John snored in w at g(t1). S is only felicitous in c if for all w ∈ c: [[S]]g (w) is defined.

As a general notational convention, I try to use boldface t1, t2 etc for free metavariables over time intervals and regular t1, t2 etc as time pronouns in the object language (the linguistic structures of English). Later on, the notation in (7 ) for the information in (7) will be handy, where @ marks presupposed material (cf. Beaver (2001)). (7 )

John snored in w at g(t1) & @(∃t’[t’
While (6) is (roughly) what is standardly used, it seems upon closer inspection that we need a more sophisticated version of again’s presupposition. It has been argued by Soames (1989) (who refers to unpublished work by Kripke), and by Heim (1990) that the presupposition introduced by again is about a specific time, not existential. An example I take from Heim (1990) is given below. (8)

a. We will have pizza on John’s birthday, so we shouldn’t have pizza again on Mary’s birthday. b. We will have pizza on John’s birthday, so we shouldn’t have pizza on Mary’s birthday.

In (8a) but not in (8b) one infers that John’s birthday precedes Mary’s birthday. This must come from the presence of again in (8a). But as long as we take the appropriateness constraint imposed by again to be (9a), there is no explanation for the inference: presumably, we had pizza plenty of times in the past, so this presupposition would be met, independently of John’s birthday. Intuitively, however, one takes John’s birthday to be the relevent prior time at which we had pizza. This follows if the appropriateness condition imposed on the context is as in (9b): of a particular earlier time, the context must entail that we had pizza at that time. The presupposition of again is thus specific rather than existential: (10a). In the example, the prior time is assumed to be the time of John’s birthday (since this is the only time relevant in the context), hence the inference that John’s birthday is earlier than Mary’s. (9)

a. c ⇒ λw.∃t [t
16

(10)

Presupposition and Implicature in Compositional Semantics

a. that we have pizza at t & t
This argument amounts to the claim that the content of the presupposition triggered by again depends on an anaphoric element (as pointed out by Kripke and emphasized in the semantic discussion of Kamp and Rossdeutscher (1994)). I will follow the argument and represent that element, like other implicit anaphoric elements, as a free variable, to be assigned a value by the contextually relevant variable assignment. A revised lexical entry for again is given in (11). The free variable is the first argument of again in (11) and shows up as a subscript in the syntactic structure in (12) (see also Beck (2006)). (12) gives the interpretation of the example. We try to choose a variable assignment function g such that the presupposition triggered by again is met. The only salient candidate is the time talked about in the first sentence in (8a), John’s birthday. Thus the anaphor is resolved to that − g(t )=John’s birthday.1 Note that the fact that the content of the presupposition again gives rise to depends on an anaphoric element makes it necessary to give again that variable as another argument. This was not necessary in the old version (6). The analysis in (11)–(12) assumes that again’s first argument is represented in the syntactic structure. (11)

[[again]] (t ) (p) (t) (w)

= 1 if p(t)(w) & p(t )(w) & t
(12)

[[ [[[we have pizza] againt ] t1 ] ]]g (w) is defined only if we have pizza in w at g(t ) and g(t ) < g(t1). If defined, it is true iff we have pizza in w at g(t1).

On this analysis, notice, there is no relevant difference between the variable called t in (11) and natural language variables like pronouns, traces and quantifier domain restrictions. They all show up in the syntactic structure that is the input to compositional interpretation, and should have similar properties. We will exploit this to provide an analysis of examples like (3) from the introduction. For completeness, I will mention an aspect of the interpretation of again that has attracted much attention in the literature. Sentences with again often exhibit the so-called repetitive/restitutive ambiguity illustrated in (13).

Quantifier Dependent Presuppositions 17

(13)

Otto opened the door again.

(13 )

a. (13) presupposes that Otto had opened the door before. Then, it is true iff Otto opened the door. = Otto opened the door, and he had done that before. (repetitive) b. (13) presupposes that the door had been open before. Then, it is true iff Otto opened the door. = Otto opened the door, and the door had been open before. (restitutive)

(14)

a. Jack opened his lips to speak, but shut them again, [. . .] (Jack and Jill, by Luisa May Alcott; from the Project Gutenberg offical homesite http://promo.net/pg/) b. ‘shut them again’ is appropriate because there is a previous time at which Jack’s lips were shut (namely the beginning of the opening).

I will assume a structural analysis of this ambiguity in the style of von Stechow (1996) (see Stechow (1996), Fabricius-Hansen (2001), Jäger and Blutner (2003), Beck (2005), among others, for discussion). Application of the structural theory to our example in (13) is illustrated informally in (15)–(17). Crucial is the decomposition of the transitive verb open into the adjective open and an empty verb expressing a change of state. (15)

a. Otto opened the door. b. underlying structure: [VP Otto [ ØV [SC openAdj [the door]]]] c. surface structure: [VP Otto [ [Ø + openAdj ]V [SC t [the door]]]]

(16)

a. [[ØV ]] = λpλxλtλw.x does something in w at t that causes that p comes to be in w at t b. [[SC]] = λtλw.the door is open in w at t

(17)

λtλw.Otto does something in w at t that causes that the door comes to be open in w at t

Decomposition creates two possible adjunction sites for the adverb again, above and below the empty verb: (18a,b). The two structures lead to two different interpretations, paraphrased in (19a,b), which correspond to the repetitive and the restitutive reading respectively. The

18

Presupposition and Implicature in Compositional Semantics

ambiguity is thus analysed as a scope ambiguity between again and the empty verb. (18)

a. b.

[VP [VP Otto [ ØV [SC openAdj [the door]]]] again] [VP Otto [ ØV [SC [SC openAdj [the door]] again]]]

(19)

a. Once more, Otto did something that caused the door to become open. b. Otto did something that caused the door to become once more open.

Under this analysis, the semantics of again remains the same on the restitutive reading as on the repetitive reading, and whatever effects we find regarding the presupposition should show up on both readings. 2.2

Anaphoricity

Again on both the repetitive and restitutive reading should be recognizably anaphoric, given the analysis above. That is, we should always be able to identify the relevant prior time of an occurance of again in discourse. It has been observed (Fabricius-Hansen (2001), Kamp and Rossdeutscher (1994), Klein (2001), and following them Beck (2006)) that this is indeed a property of again. Below are some of Fabricius-Hansen’s examples as well as some that I myself collected that illustrate this. I italicise the predicate that again combines with as well as the preceding predicate that causes again’s presupposition to be satisfied. The relevant prior time that the presupposition triggered by again refers to would be the time interval associated with the first predicate. The context provides an appropriate salient antecedent for again’s first argument. (20)

Fabricius-Hansen (2001): a. Er konnte sich an nichts erinnern, nicht einmal daran, dass ich ihn gebeten hatte, sich diese drei Dinge zu merken. Ich wiederholte den Test und liess ihn diesmal die Bezeichnungen der drei Gegenstaende aufschreiben; wieder hatte er sie vergessen [. . .] He remembered none of them or indeed that I had even asked him to remember. I repeated the test, this time getting him to write down the names of the three objects; again he forgot [. . .] b. Elias hoerte nicht bloss, er sah das Toenen. Sah, wie sich die Luft unaufhoerlich verdichtete und wieder dehnte. Elias not only heard the sounds, he also saw them. He saw the air incessantly contracting and expanding [again; SB].

Quantifier Dependent Presuppositions 19

(21)

Project Gutenberg – repetitive uses: a. She rather suspected it to be so [. . .] from his listening to her so attentively while she sang to them; and when the visit was returned by the Middletons’ dining at the cottage, the fact was ascertained by his listening to her again. (Sense and Sensibility, Jane Austen) b. [. . .] the old lady shook the bottle with the air of a general who had routed the foe before and meant to do it again. ( Jack & Jill, Louisa May Alcott)

(22)

Project Gutenberg – restitutive uses: a. As she said this, she sunk into a reverie for a few moments; – but rousing herself again, [. . .] (Sense and Sensibility, by Jane Austen) b. And away she went; but returning again in a moment, [. . .] (Sense and Sensibility, by Jane Austen)

I should point out that while Fabricius-Hansen (2001) also calls the presupposition of again anaphoric, there is a difference in what we mean by this. According to her, the presupposition of again is anaphoric in the way that all presuppositions are anaphoric – in the sense of van der Sandt (1992). This is not what is meant here. I do not regard the presupposition triggered by again itself as an anaphor. For me, it is an admittance condition. But its content depends on an anaphoric element – i.e. what presupposition precisely is triggered depends on the context. This is not a property of all presuppositions. The content of the presupposition triggered by the definite article, for example, does not (necessarily) depend on an anaphor. 2.3

Discourse inferences

The data we have seen show that anaphoric presuppositions play an important role for discourse coherence. They guide us in organizing the information provided by individual sentences into a coherent whole. This becomes most obvious when they lead to inferences that would not otherwise have been justified. The pizza example repeated below illustrates this. (23)

We will have pizza on John’s birthday, so we shouldn’t have pizza again on Mary’s birthday.

20

Presupposition and Implicature in Compositional Semantics

The observation is that (23) supports the inference (24a). Why does it do that? The context to which the second sentence of (23) is added entails of a time t that we had pizza at t ((24b)). We take t to be the antecedent of again’s first argument. The use of again then imposes on the context the requirement (24c). The context does not entail that t
a. b. c. d.

John’s birthday precedes Mary’s c ⇒ that we have pizza at t c ⇒ that we have pizza at t & t
The pizza example is not unique in supporting such inferences, and is therefore not unique as an illustration of the anaphoric nature of the presupposition that again gives rise to. Both of the following examples support inferences that are partial presupposition accommodations, and both times the key to what is accommodated is the anaphoric first argument of again. In neither of the examples would this particular inference arise if again were not anaphoric, i.e. did not make reference to a particular time. Kamp and Rossdeutscher (1994) call such effects ‘presupposition justification’. (25)

A group from Jehova’s witnesses was on my doorstep at 1pm. An hour later, they were there AGAIN.

(25 )

a. (25) ⇒ they left in between 1pm and 2pm b. c ⇒ that a group from Jehova’s witnesses was on my doorstep at t c. c ⇒ that a group from Jehova’s witnesses was on my doorstep at t and t
(26)

In January 2000, we were skiing in Grafton. In January 2001, we were skiing in Vermont AGAIN.

(26 )

a. (26) ⇒ Grafton is in Vermont b. c ⇒ that t
Quantifier Dependent Presuppositions 21

d. accommodate: we were in Vermont at t hence: Grafton is in Vermont When there are no additional inferences, the role of the anaphoric presupposition seems to be to confirm an interpretation arrived at on independent grounds. The example below illustrates that. The relevant aspects of the interpretation of (27) are given in (27 a). The temporal order of the events can be derived from the use of the expression ‘return the visit’. The use of again confirms that this is the temporal organization of the events described (cf. (27 b)). (27)

She rather suspected it to be so [. . .] from his listening to her so attentively while she sang to them; and when the visit was returned by the Middletons’ dining at the cottage, the fact was ascertained by his listening to her again. (Sense and Sensibility, Jane Austen)

(27 )

a. that he listened to her at t1 that he listened to her at t2 & t1
Compare Fabricius-Hansen (2001), Klein (2001), van der Sandt and Huitink (2003), Saeboe (2004) and Beck (2006) for further comments on various aspects of the behaviour of again in discourse. We will assume the analysis in (11), in which again combines with a free variable first that determines the content of its presupposition. That analysis has received further support in this and the previous subsection. 2.4

Bound occurences of again’s first argument?

All the examples we have considered so far were cases in which the variable that is the first argument of again occurs free. Can it also occur bound? Perhaps. The following example may be a case in point: the temporal quantifier ‘every time’ would be the binder (I omit the world parameter in these examples for simplicity). Given the general facts of presupposition projection in the scope of a quantifier illustrated by example (29), the analysis makes the prediction that the presupposition of the sentence with again is as in (28b). (28)

a. Last semester, Bill was sick on Tuesday three times. Every time he was sick again two days later.

22

Presupposition and Implicature in Compositional Semantics

b. ∀t[ t is one of the three Tuesdays → [[again]] (t) (λt . Bill was sick at t )(t + 2 days)] Assertion: ∀t[ t is one of the three Tuesdays → Bill was sick at t + 2 days] PSP: ∀t[ t is one of the three Tuesdays → Bill was sick at t & t
a. Every player brought her TV Derendingen warm-up t-shirt. b. PSP: Every player had a TV Derendingen warm-up t-shirt.

Some support for such an analysis of (28) comes from the variant in (28 a), which licenses the inference in (28 b). (28 )

a. Last semester, Bill was sick on Tuesday three times. Every time he was sick again on the day of the colloquium. b. Every time, the (relevant) colloquium was after Tuesday. c. PSP: ∀t[ t is one of the three Tuesdays → Bill was sick at t and t < the (relevant) colloquium]

In general, I find it hard to identify conclusively a bound reading as opposed to a more indirectly quantifier dependent reading, to which we turn in the next section. Note that if again’s first argument can be bound, it behaves like pronouns and traces; if it cannot be bound, it is, as far as I know, like a quantifier’s resource domain variable in that respect. I have no particular expectation either way.

3

Quantifier dependent again

3.1 E-type pronouns, complex traces, quantifier domain restrictions To my knowledge, the first proposal that natural language variables can have a hidden internal complexity concerns pronouns; a relevant early reference is Cooper (1979). A Cooper-style analysis for the example in (30) is given in (30 ) (example and details taken from Heim and Kratzer (1998)). (30)

a. Every host bought just one bottle of wine and served it with dessert. b. For every host x: x bought just one bottle of wine and x served the bottle that x had bought with dessert.

Quantifier Dependent Presuppositions 23

(30 )

a. For every host x: x bought just one bottle of wine and x served [the [R x]] with dessert b. "it" = [ the [R x]] R : = λu.λv.u had bought v and v is a bottle of wine

Chierchia (1993) applies a similar strategy to traces in so-called functional wh-questions. An example and its analysis is given in (31)–(31 ). (31)

a. Who does every Italian love? b. example answer (functional reading): his greengrocer

(31 )

a. [whoi [ every Italiank loves ti,k ]] b. which f: for every Italian x, x loves f(x)? c. ti,k = [ t> pro > ]] [[ ti,k ]]g = g(ti) (g( prok)) = f(x)

We are already familiar with example (1)–(1 ) from the introduction, in which the variable – the domain restriction of the quantifier – is itself covert. It seems to be a general properties of the expressions that appear function as variables in natural language that they permit an analysis in which they consist of a free variable part combining with a part that can be bound. (1)

a. Only one class was so bad that no student passed. b. Only one class was so bad that no student in that class passed.

(1 )

a. [[noC ]] (A)(B) = 1 iff (g(C) ∩A) ∩B = { } b. [ [only one class] [lx [ tx was so bad that [IP [DP nof(x) student ] [ passed]]]] c. only one class x: x was so bad that nof(x) student passed d. f: x → {y: y is in x}

Marti (2003) provides arguments to the effect that such covert variables, while invisible, are nonetheless syntactically real. This supports an analysis that assumes additional internal structure including a bound variable as in (1 ). The view that emerges from this discussion is that quite generally, natural language variables can be more complex than appearance would indicate, and that that complexity is reflected in their syntactic structure.

24

Presupposition and Implicature in Compositional Semantics

3.2 Again and quantifiers We are now ready to consider the interaction of again and quantifiers. We established above that the presupposition of again contains an anaphoric variable, and also showed that variables in natural language can be quantifier dependent. We expect that again’s anaphoric variable should be able to depend on a quantifier as well, and this is going to be our view of example (3) from the introduction and related data. We begin with a slightly simpler example, (32) below. (32)

In 1995, 1996 and 1998, Bill was sick on Labour Day. In each of these years, he was sick again on Thanksgiving.

Intuitively, the earlier time that again makes reference to in (32) is the time of illness on the relevant Labour Day. Thus there is not one earlier time, but three. In other words, the anaphoric variable in the semantics of again depends on the quantifier ‘in each of these years’. In contrast to example (28) on the analysis discussed above, the earlier time is not itself in the domain of the quantifier, but depends on it indirectly. I propose the analysis in (33) for the slightly simplified version (33a). (33)

a. Every year, Bill was sick again on Thanksgiving that year. b. ∀t[ year(t) & C(t) → [[again]] (f(t)) (λt .Bill was sick at t )(Thanksgiving in t)] c. f: t → the Labour Day in t C = {1995, 1996, 1998} d. ∀t[ year(t) & C(t) → Bill was sick on Thanksgiving in t & @(Bill was sick on Labour Day in t & (Labour Day in t < Thanksgiving in t))] e. ∀t[ year(t) & C(t) → Bill was sick on Labour Day in t & (Labour Day in t < Thanksgiving in t)]

Given the general facts of presupposition projection in the scope of a quantifier already mentioned, the analysis makes the prediction that the presupposition of the sentence with again is as in (33e). This seems right, and the presupposition can be assumed to be met in (32) by virtue of the first sentence plus world knowledge. (34) would be the presupposition of (33a) using the semantic analysis of again in (11) but without a functional analysis of the anaphoric variable. This amounts to the claim that Bill was sick at a time preceding 1995 - which strikes me as counterintuitive. (35) would be the result of using the original semantics of again in (6), with the predicted presupposition (35b) from (35a). This looks perhaps

Quantifier Dependent Presuppositions 25

a little better, even if it is still weaker than (33e). But of course it uses an analysis of again that we had retired for independent reasons already. (34)

∀t[ year(t) & C(t) → Bill was sick at t & t
(35)

a. ∀t[ year(t) & C(t) → Bill was sick at t & @(∃t [t
I think that the analysis in (33) is the most intuitive view of what happens in (32). The case for functional anaphoric variables in again’s presupposition can be strengthened when we consider examples that require partial presupposition accommodation (like the pizza example), hence give rise to additional inferences. I have constructed a quantificational version of the pizza example below. The sentence intuitively supports the inference in (36b). It is analysed in (37). Following the same steps as in the previous example, we arrive at (37d) as the presupposition of (37a). The context establishes that we had pizza at Johns birthday every year, but it is not asserted that John’s birthday preceded the department picnic. In the same way as in the non-quantificational version, we assume that this part of the presupposition is in fact true. The assumption surfaces as an inference. (36)

a. Every year, we had pizza on John’s birthday, and decided that we shouldn’t have pizza again at the department picnic. b. Every year, John’s B-day preceded the department picnic

(37)

a. ∀t[we have pizza at John’s B-day in t & we decide that shouldn’t [again(f(t)) (λt . we have pizza at t )(the picnic in t)]] b. f: t → John’s B-day in t c. ∀t[we have pizza at John’s B-day in t & we decide that shouldn’t [we have pizza at the picnic in t] & @(we have pizza at John’s B-day in t & John’s B-day in t < the picnic in t)] d. PSP: ∀t[we have pizza at John’s B-day in t & John’s B-day in t
Suppose that we had used a standard, simple first argument of again. The predicted presupposition is then (38): that a particular time t precedes all annual picnics, and we had pizza at t . That would be John’s birthday

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Presupposition and Implicature in Compositional Semantics

in the first of the years talked about. The presupposition is not suitable to support the intuitive inference. (38)

∀t[we have pizza at t & t < the picnic in t]

Similarly, the existential analysis of the presupposition of again (given below) is not suitable to support that inference – it is too weak. Thus we can conclude that we have found further support for an analysis of the presupposition of again as involving an anaphoric element. The support comes from the additional, quantificational data themselves as well as from the general fact that our hidden variable in the semantics of again behaves like other hidden variables. (39)

a. ∀t[we have pizza at John’s B-day in t & we decide that shouldn’t [we have pizza at the picnic in t] & @(∃t [we have pizza at t & t < the picnic in t)]] b. PSP: ∀t[∃t [we have pizza at t & t < the picnic in t)]]

Example (3) from the introduction is of course just the pizza example in disguise. I add example (40) as a plausible case of quantifier dependent restitutitve again. The verb forget is decomposed into BECOME + ‘not know’. Once more the presupposition in (41e) seems more appropriate to me than the one in (42). (40)

a. She has told me her name three times. b. Every time / mostly /. . . I forgot it again five minutes later.

(41)

a. ∀t[t is one of the three times → I forgot it again at t+5min] b. ∀t[t is one of the three times → BECOME (t+5) ([[again]] (f(t)) (λt .I do not know it at t ))] c. f: t → t−1 (the time immediately preceding t) d. ∀t[t is one of the three times → BECOME (t+5) (λt .I do not know it at t ) & @(I do not know it at t−1)] e. PSP: ∀t[t is one of the three times → I do not know it at t−1]

(42)

∀t[t is one of the three times → I do not know it at t & t
Quantifier Dependent Presuppositions 27

The phenomenon discussed here is natural enough; an informal search via Google turned up the following two instances: (43)

From the diary of a cat owner:

Heute haben unsere Schätzchen Besuch gehabt. Wir haben Nachbarskater Thommy herein gelassen. Erstes Problem war, dass Merlin in der Zeit, bis Thommy sich bequemt hat, reinzuhüpfen, schon 3x nach draußen geflitzt ist. Otto hat ihn dann jedes Mal wieder geschnappt und hineingetragen. Today our darlings had a visitor. We let in the neighbours’ cat Thommy. The first problem was that until Thommy agreed to hop in, Merlin had run out three times. Otto cought him again every time and carried him inside. http://www.janko.at/WM/Tagebuch2004_09.htm (44)

Description of a grassroots group party event:

Höhepunkt war für viele das Modell der Castor-Strecke von Lüneburg nach Dannenberg. Die mehr als sechs Meter lange Modellbahnstrecke, mit unendlicher Liebe zum Detail gebaut, hatte alles, worauf man sich schon mal wieder vorbereiten sollte: Jede Menge bunte protestierende Leute, viel Polizei, ein rollender Castorzug, ein als Hochsicherheitstrakt ausgebauter Verladekran, [. . .] und als Höhepunkt eine Brücke die rechtzeitig vor dem Zug zusammenbricht. Das machte sie während des Festes 471-mal. Der Zug musste jedes Mal wieder zurückfahren. For many the highlight was the model of Castor’s train line from Lüneburg to Dannenberg. The model railway was longer than six meters, constructed with endless love for detail, and had everything one ought to be prepared for: loads of colorful protesting people, a lot of police, a rolling Castor train, a high security crane, [. . .] and as the highlight a bridge that collapses in time in front of the train. It did that 471 times during the party. The train had to go back again every time. http://www.graswurzel.net/281/castor.shtml An anonymous reviewer points out that these examples might involve bound first arguments of again rather than complex ones. I think the uncertainty stems from the fact that the restriction of the relevant quantifier (‘every time’) is largely pragmatic and there may be more than one plausible candidate for what is quantified over; this makes it difficult

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Presupposition and Implicature in Compositional Semantics

to decide whether the ‘earlier’ time depends on the quantifier directly (through binding) or indirectly (via internal complexitiy). Data like (3), (32) and (36) are clearer in that respect. A final remark: I think that there are data that receive a natural analysis in terms of again’s hidden variable being dependent on a nominal quantifier. A candidate is given below (let the notation tx stand informally for the time at which x is told x’s password). I leave the details of the analysis for another occasion. (45)

a. The principal called us into the study and told us our individual password. b. Everyone forgot it again immediately/within the hour.

(45 )

a. ∀x[BECOME (tx +1hour) (again f(x) (λt.x does not know x’s password at t))] b. f: x → the time just before x was told x’s password c. PSP: ∀x[x does not know x’s password at f(x)]

3.3

Some further instances: also, stop

The adverb again is not the only expression in natural language that has been suggested to trigger a presupposition dependent on an anaphoric element. The literature (once more Soames (1989) following Kripke, and Heim (1990); see also Beaver (2001)) points out that a similar argument can be made for too/also and stop. Let’s look at too/also. Standardly, it is assumed that (46a) (in which Laura associates with too) has the presupposition in (46b). According to our understanding of presupposition, this means (46c). A semantics for too/also in this spirit is given in (46d), where I combine directly with the associate for simplicity (instead of using a focus semantics). (46)

a. b. c. d.

LAURA was at the conference, too. ∃x[x =Laura and x was at the conference] c ⇒ λw.∃x[x =Laura and x was at the conference in w] [[also]] (y)(P)(t)(w) is defined only if ∃x[x =y and P(x)(t)(w). If defined, it is true iff P(y)(t)(w).

This analysis runs into a problem with the contrast in (47a) vs. (47b). It is not clear why (47b) should be bad, since the first sentence states that the conference was well-attended.

Quantifier Dependent Presuppositions 29

(47)

a. Peter was at the well-attended recent conference in Mount Kisco. LAURA was at the conference, too. b. # Peter wasn’t at the well-attended recent conference in Mount Kisco. LAURA was at the conference, too.

Intuitively, the problem in (47b) is Peter. We just stated that Peter was NOT at the conference, and Peter seems to be what too wants to relate to. This can be captured once we recognize that the presupposition triggered by too/also is specific rather than existential, as described in (48). The context must provide a particular person of which it implies that that person was at the conference. The only person specifically mentioned is Peter, but Peter was not at the conference. The presupposition is thus met in (47a) but not in (47b), and (47b) is correctly predicted to be infelicitous. Thus we revise our (simplified) lexical entry for too/also to (48c), in which it first combines with a hidden anaphor.3 The analysis of the example is given in (49). The same point is usually made on the basis of the infelicity of examples like (50) out of the blue. (48)

a. ∃x[x =Laura and c ⇒ λw.x was at the conference in w] b. that x was at the conference & x =Laura c. [[also]] (x)(y)(P)(t)(w) is defined only if x=y and P(x)(t)(w). If defined, it is true iff P(y)(t)(w).

(49)

[[ LAURA t1 be at the conference, too(x) ]]g (w) is defined only if g(x) =Laura and g(x) was at the conference in w at g(t1). Then, it is true iff Laura was at the conference in w at g(t1).

(50)

Sam is having dinner in New York tonight, too.

The similarity of again to too/also is particularly clear when we consider examples like (51). Assume that too associates with with ‘in the fall of 1997’. (51)

a. In the fall of 1997, the conference was in Mount Kisco again. b. In the fall of 1997, the conference was in Mount Kisco, too.

The only difference between the two sentences is that (51a) requires a context that establishes for some other time than fall 1997 that the

30

Presupposition and Implicature in Compositional Semantics

conference had been in Mount Kisco, whereas in (51b) the other time has to be earlier than fall 1997. So in the semantics of again, we have ti