Presupposition and Implicature in Compositional Semantics Edited by
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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
Palgrave Studies in Pragmatics, Language and Cognition Series Series Standing Order ISBN 0–333–99010–2 Hardback 0–333–98584–2 Paperback (outside North America only) You can receive future titles in this series as they are published by placing a standing order. Please contact your bookseller or, in case of difficulty, write to us at the address below with your name and address, the title of the series and the ISBN quoted above. Customer Services Department, Macmillan Distribution Ltd, Houndmills, Basingstoke, Hampshire RG21 6XS, England
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
2006047823
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.
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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
26
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
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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
a. Every boy invited his girlfriend. b. Every boy also invited LUISE / HIS CLIMBING PARTNER. c. inference: Luise/his climbing partner is not the girlfriend of any of the boys
(52 )
a. ∀x: also (f(x)) (Luise) (λz. x invited z) b. f: x→ x’s girl friend c. ∀x: x invited Luise & @(x’s girlfriend =Luise & x invited x’s girlfriend) d. PSP: ∀x: x’s girlfriend =Luise & x invited x’s girlfriend
A final example for an anaphoric presupposition I will mention is the one triggered by stop. Consider (53), once more from Heim (1990). (53)
John is cooking now. He will stop cooking when tomorrow’s basketball game starts.
The discourse suggests that John will be engaged in a continuous cooking event from now until tomorrow. If ‘John stopped cooking’ simply presupposed that John had cooked at some immediately preceding time interval, we should not have to interpret the discourse in such an implausible way. Once more, the presupposition is anaphoric in that it refers back to a salient time interval in the discourse, and that is the cooking John is engaged in now. We must suppose that this time interval extends until the basketball game. (53 ) is a quantificational version. (53 )
During the World Championship last year, John would cook the evening before an important match.
Quantifier Dependent Presuppositions 31
Every time / mostly / . . . , he stopped cooking when the match began the next day. We see that there is a class of presuppositions that share with again the property of depending on an anaphoric element, as well as the empirical consequences this property has.
4
Conclusions and consequences
We have investigated a set of data in which the content of the presupposition triggered by again depends on a quantifier. I have proposed an analysis for these data in which the presupposition that again introduces is determined by an anaphoric element. That element is represented in the syntax and makes the first argument of the adverb again. It can be free, (perhaps) bound, or internally complex, like other natural language variables. Thus the quantifier dependent examples receive an analysis parallel to other examples in which the content of a variable depends on a quantifier, for instance quantifier domain restrictions. The quantfier dependent data lend further support to the analysis of again’s presupposition containing a free variable. A similar argument can be made for other anaphoric presuppositions.
Acknowledgements I am grateful to the audiences to whom various parts of this work were presented, and to Irene Heim and Luisa Marti for their help with anaphoric presuppositions and complex variables respectively. Many thanks to an anonymous reviewer for two important comments on the prefinal version.
Notes 1. This can be made more explicit in a dynamic framework in which contexts are sets of world-assignment pairs, but I will not do so here. 2. We tend to take the time immediately preceding the topic time t1 to be a time at which the proposition expressed by the sentence with again is not true. See e.g. Stechow (1996) for discussion. This effect is ignored in our formal lexical entry for again, but would have to be used in a complete account of (25). 3. I have put the non-identity requirement for the associate and the antecedent in the semantics of also. See Beaver (2001) for an argument that this may not be the right place.
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References Beaver, David (2001). Presupposition and Assertion in Dynamic Semantics. Stanford, CSLI. Beck, Sigrid (2005). ‘There and Back Again: A Semantic Analysis’. Journal of Semantics 22, 3–51. Beck, Sigrid (2006). ‘Focus on Again’. Linguistics and Philosophy 29, 277–314. Chierchia, Gennaro (1993). ‘Questions with Quantifiers’. Natural Language Semantics 1, 181–234. Cooper, Robin (1979). ‘The Interpretation of Pronouns’. In: F. Heny & H.S. Schnelle (eds): Selections from the third Groningen Round Table (= Syntax and Semantics 10). New York, Academic Press, 61–92. Fabricius-Hansen, Cathrine (2001). ‘Wi(e)der and Again(st)’. In: Caroline Fery and Wolfgang Sternefeld (eds): Audiatur Vox Sapientiae: A Festschrift for Arnim von Stechow. Akademie Verlag, Berlin, 101–30. von Fintel, Kai (1994). ‘Restrictions on Quantifier Domains’. PhD dissertation, University of Massachusetts Amherst. von Fintel, Kai (2003). ‘Pragmatics; Notes on Presupposition’. Ms, MIT. Heim, Irene (1990). ‘Presupposition Projection’. In: R. van der Sandt (ed.): Presupposition, Lexical Meaning and Discourse Processes. Workshop Reader, University of Nijmegen. Heim, Irene (1991). ‘Artikel und Definitheit’. In: Stechow, Arnim von & Dieter Wunderlich (eds): Handbook of Semantics. De Gruyter. Heim, Irene & Angelika Kratzer (1998). Semantics in Generative Grammar. Blackwell. Jäger, Gerhard & Reinhard Blutner (2003). ‘Competition and Interpretation: The German Adverb wieder (‘again’)’. In: E. Lang, C. Maienborn & C. FabriciusHansen (eds), Modifying Adjuncts. Mouton de Gruyter, 393–416. Kadmon, Nirit (2001). Formal Pragmatics: Semantics, Pragmatics, Presupposition and Focus. Blackwell. Kamp, Hans and Antje Rossdeutscher (1994). ‘DRS-construction and Lexicallydriven Inference’. Theoretical Linguistics 20: 165–235. Klein, Wolfgang (2001). ‘Time and again’. In: Caroline Fery and Wolfgang Sternefeld (eds): Audiatur Vox Sapientiae: A Festschrift for Arnim von Stechow. Akademie Verlag, Berlin, 267–86. Marti, Luisa (2003). ‘Contextual Variables’. PhD dissertation, University of Connecticut. Rooth, Mats (1992). ‘A Theory of Focus Interpretation’. Natural Language Semantics 1, 75–116. Saeboe, Kjell Johan (2004). ‘Conversational Contrast and Conventional Parallel: Topic Implicatures and Additive Presuppositions’. Journal of Semantics 21: 199–217. van der Sandt, Rob (1992). ‘Presupposition Projection as Anaphora Resolution’. Journal of Semantics 9, 333–77. van der Sandt, Rob & Janneke Huitink (2003). Again. Proceedings of the 2003 Amsterdam Colloquium. Soames, Scott (1989). ‘Presupposition’. In: D. Gabbay & F. Günthner (eds): Handbook of Philosophical Logic. Kluwer, Dordrecht.
Quantifier Dependent Presuppositions 33 Stalnaker, Robert (1973). ‘Presuppositions’. Journal of Philosophical Logic 2, 447–57. Stechow, Arnim von (1996). ‘The Different Readings of Wieder “Again”: A Structural Account’. Journal of Semantics 13, 87–138. Westerstahl, D. (1984). ‘Some Results on Quantifiers’. Notre Dame Journal of Formal Logic 25, 152–70. Project Gutenberg official homesite: http://promo.net/pg
3 Licensing or Regine Eckardt University of Göttingen
This chapter addresses the so-called free choice effects of disjunction under existential quantification. The effect has received most attention in modal contexts, specifically as free choice permission. Consequently, a broad range of analyses trace the reason for free choice effects at its interaction with modality. I will argue that free choice effects arise with any kind of existential quantification, and that an analysis should hence not essentially rest on modality. I propose that a Boolean analysis of or, in concert with specific interpretation of existentials, is sufficient to derive the observed effects. It is moreover proposed that the reinterpretation of existential quantifiers is made necessary by a principle of or-licensing which is the second cornerstone of the analysis.
1
Introduction
Our logic classes taught us that the word or denotes Boolean disjunction ∨. However, looking at uses of or in everyday life, it seems that the word rarely ever exhibits its pure meaning. The problem seems to be that disjunctive statements A or B contain the simpler parts A and B. Why did the speaker fail to make one of the simpler statements and chose the longer, and less informative disjunction instead? A survey of the data leads to the following cases: In downward monotone contexts, A or B statements are indeed more informative than simpler statements. In such sentences, or can unproblematically denote Boolean disjunction. In certain other uses, the disjunctive statement may be longer than A alone, or B alone, and less informative than A and B, but gives rise to extra implicatures and hence leads to motivated utterances. We could label such uses as ‘Boolean ∨ plus pragmatic inferences’. 34
Licensing or 35
In a last kind of cases, however, or occurs in a sense that is hard to explain as the result of Boolean or plus pragmatic inferences. These are the so-called free choice use of or in the scope of existential modals. The following example illustrates the case.
(1.1) (1.2)
Judy may take coffee or juice. Judy may take coffee, and Judy may take juice.
The puzzle is this. The sentences in (1.1) and (1.2) seem intuitively equivalent. However, a simple Boolean analysis of or, together with a simple possible-world analysis of may as existential quantification over deontically accessible worlds (‘worlds that show what Judy is allowed to do’), fails to predict this intuition. The failure rests on the well-known fact that, in predicate logic, formula (1.3) does not imply (1.4). Kamp (1973) is the classical reference which brought the free choice puzzle on the agenda of formal semantics.
(1.3) (1.4)
∃x( A(x) ∨ B(x) ) ∃x( A(x) ) ∧ ∃x( B(x) )
In recent years, several strategies to solve this puzzle have been explored. As the effect arises predominantly in modal contexts, some authors attribute it to a revised interpretation of modal existentials (plus, possibly, further pragmatic effects). This line was followed, for example, by Schulz (2002), Aloni (2003a,b), or Simons (2005a,b). The more radical kind of rescue, however, consists in the claim that the word or did not denote Boolean disjunction in the first place. Zimmermann (2000) develops an analysis of or as conjoined epistemic alternatives and derives free choice effects in modal contexts from this analysis. The more recent Geurts (2005), while deviating from Zimmermann’s proposal in detail, can be seen as a conservative extension of this kind of approach. The authors leave it somewhat open whether they would allow for a reading of or as Boolean disjunction in addition to their analyses. However, Zimmermann seems to defend a maximal position in that the chapter lists several examples where his denotation for or is problematic; a second use in a Boolean sense is never his proposed solution. I will therefore at some points refer to his approach as the most consequently non-Boolean analysis.
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Presupposition and Implicature in Compositional Semantics
Apart from free choice examples, any analysis of or should be able to cope with the following range of cases. (1.5)
a. Nobody was sick or on holiday. b. Nobody was sick, and nobody was on holiday.
Sentence (1.5) illustrates the use of or in a downward entailing context (here: the scope of negation). Whatever the exact delimitations of contexts may be, elementary predicate logic tells us that the disjunction (a) logically entails the conjunction in (b.). Semantic intuition suggests that Boolean ∨ is a fully adequate denotation of or in these examples. (1.6) (1.7)
Joe is drunk or sick. (As far as I can see,) Joe might be drunk, and Joe might be sick (and I don’t know which)
In positive contexts, epistemic uncertainty appears to be the standard reason to use or. If no other reason can be thought of, the hearer will assume that the speaker makes an unspecific assertion because he does not know any better. (1.8)
Everybody ordered a beer or a pizza.
This sentence shows or in an upwards monotone context. If or is taken to denote Boolean disjunction, then (1.8) is true if everyone ordered a beer (and no pizza), if everybody ordered a pizza (and no beer), or in mixed cases. In fact, our semantic competence tells us that (1.8) should only be used in mixed cases (unless the speaker has imperfect knowledge). For instance, it can felicitously be uttered by the waitress who has just taken the corresponding order. We can assume that she has perfect knowledge about the order; e.g. having noted it as a list. In such a situation, she does not seem to express a list of epistemic possibilities, neither globally (‘possibly everybody ordered a beer, and possibly everybody ordered a pizza, and I don’t know which’) nor locally (‘for each customer, it is possible that he ordered beer, and its possible that he ordered pizza’). In these cases, however, a simple Gricean argument can account for this fact. If the speaker knew that everybody in fact ordered a beer, he could have said so and been briefer and more informative. Similarly for a homogeneous order for pizzas. Hence, the mixed cases are the only ones that warrant possible utterances. (Matters change, of course, as soon as or is justified by the
Licensing or 37
speaker’s imperfect knowledge.) Analogous examples arise in necessity statements (i.e. for modal universal quantification). The cases listed so far (including free choice examples) are the common stock in the literature. The last two types of examples, to my knowledge, have not yet received extensive attention. (1.9)
The whole school was posing in the yard to welcome the queen. Everybody was dressed in nice clothes for the great day. a. Some children waved little flags or threw flowers. b. Some children waved little flags. And some children threw flowers.
The sentence in (1.9.a) seems to be uttered by the speaker with a certain group of children in mind. He might vaguely intend to talk about those children who took part in cheerful activities. No epistemic uncertainty is expressed, and we understand that the disjunction is used because among the active children, there were some who waved and some who threw flowers. The conjunction in (b.) follows. Note that (1.9) is the analogue of the classical free choice constellation in the domain of nominal quantification. Klinedinst (2005) is another source where such examples were discussed.1 I sympathize with his findings, which, however, need to be sharpened to do justice to the data. Finally, consider (1.10). (1.10)
What new privileges does Judy gain when she’s 18 years old? # Judy may drive a car, or marry without her parents’ consent or vote in elections.
The striking fact about (1.10) is that it does not offer an instance of the free choice pattern. Specifically, the disjunct does not imply the conjoined list of privileges of those over-age in (1.11). (1.11)
Judy may drive a car, and Judy may marry without her parents’ consent, and Judy may vote in elections.
Free choice or essentially occurs in just those cases where the disjunction lists deontic alternatives with respect to one specific decision. (1.10) in a free choice interpretation sounds as if the three things depended on each other, somehow as if Judy’s driving a car would exclude her voting in elections. I will come back to the no list of privileges example (1.10) at several places. Specifically, I will use it to explore the nature of deontic alternatives that are addressed by true free choice sentences (Section 4).
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Presupposition and Implicature in Compositional Semantics
Note that Zimmermann (2000) predicts that it should be a natural free choice example and imply (1.11) (Section 2). This chapter is organized as follows:2 In Section 2, I will recapitulate uses of Boolean and ‘ill-behaved’ or and offer a brief review of the most recent literature. It will be concluded that or requires licensing in most contexts, and that licensing or can require a non-standard use of other parts of the sentence (specifically existential quantifiers). In Section 3, I will elaborate my analysis of examples like (1.9). I propose that these examples rest on quasi-specific existential quantification. The hearer will understand that the speaker has a certain group of individuals in mind, and in order to be truthful has to use disjunction. Section 4 shows how this analysis can be carried over to the modal case, i.e. free choice examples of the type in (1.1). Section 5 discusses some examples where various kinds of licensing or interact. It highlights the program underlying the present chapter (as many others before): The word or can show unexpected effects in various ways. It is preferable to assume one uniform semantic contribution, namely Boolean disjunction, which interacts with other parts of the sentence in different ways which, in turn, lead to different side messages.
2
Boolean and mis-behaved ‘or’
Boolean disjunction is potentially problematic in terms of pragmatics. Disjunction offers us a means to denote a weaker property by using a more complex expression. This constellation, in many contexts, posits a contradiction to the combined M- and I-principle (Levinson 2000) or classically, Grice’s maxims of manner and quantity. Such conflicts arise already in the simplest possible disjunctions, the disjunction of two positive atomic sentences. (2.1) offers an example. (2.1)
Joe is drunk or sick
Instead of one of two possible, more specific statements (‘Joe is drunk’, ‘Joe is sick’), the speaker chooses to attribute the broader property of ‘being drunk or sick’ to Joe. Of course, it is not principally problematic to utter sentences with general properties. A sentence like ‘Joe is German’ is pragmatically unproblematic, even though the speaker might know that Joe is in fact from Bavaria. The speaker did not mention Bavaria, and if the context does not render the German counties relevant, the sentence Joe is German does not implicate Joe is not from Bavaria or The speaker does not know whether Joe is from Bavaria. Disjunctions, however,
Licensing or 39
are different. In using a disjunction, the speaker necessarily has to mention two properties which are usually more specific. These properties are presented as salient and relevant. The simpler sentences are salient alternative utterances in context. The hearer hence will look for a reason why the speaker chose a more complex expression in order to give less information. Going back to example (2.1), it is a textbook case in pragmatics to infer that (2.1) implicates that (2.2). (2.2)
Speaker does not know that Joe is drunk, and speaker does not know that Joe is sick.
Let me call a surrounding sentence in which a disjunction may be embedded a sentence frame. Then we can posit a general requirement on uses of or: A sentence frame does not pragmatically license disjunction if the simpler sentence(s) entail the frame plus disjunction . (2.3)
unlicensed disjunction: (A) → (A ∨ B)
The use of disjunction is pragmatically licensed if the simple sentence does not entail disjunction (2.4.a), and specifically if sentence frame with disjunction entails the simple sentence (2.4.b). Moreover, or is licensed if there are implicatures such that disjunction plus its implicatures are not entailed (2.4.c). (2.4)
a. licensed disjunction: (A) −/→ (A ∨ B) b. licensed disjunction: (A ∨ B) → (A) c. licensed disjunction: (A) −/→ (A ∨ B) ∧ with implicature .
It can be seen easily that disjunctions in downward entailing contexts instantiate the (b.) case. Negation as well as the antecedent of a conditional, or the restrictor of universal quantifiers, are good pragmatic licensing contexts for Boolean disjunction. (2.5) (2.6)
If you get an A or a B in the exam, I will take you out for dinner. (Either condition will be sufficient) Nobody was bored or annoyed. Gordon is the youngest man who ever climbed the Chimborazzo or the K2. Gordon eats neither meat nor fish.
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Presupposition and Implicature in Compositional Semantics
Note that the last kind of use under negation must have been perceived so genuinely a useful or pattern in English that the original construction not either . . . or together with negative concord n- was lexicalized as neither . . . nor. I therefore take the neither nor construction as a particularly clear use of or under negation. A disjunction in the antecedent of a conditional is likewise useful because it allows the speaker to express two conditionals in one. Let us now turn to some cases where a sentence plus a pragmatic inference can license the use of a disjunction. We already saw (1.8) above, but more cases show that the scope of universal quantifiers uniformly give rise to implicatures. Consider the sentence in (2.7). (2.7)
(In order to get a credit,) You have to write a paper or kill a rabbit.
Simple Boolean disjunction under universal modal quantification will lead to a sentence meaning which holds true • if in fact, I intend to hand out a credit for a paper, and under no other circumstances • if in fact, I intend to hand out a credit for a dead rabbit, and under no other circumstances • if in fact, I intend to hand out a credit exactly if one or the other requirement is fulfilled. Our everyday understanding of (2.7) suggests that it only should be true in the third case. Neither case should be mentioned spuriously (even though practical reasoning would strongly suggest the first scenario!). Like in (1.8), we can argue that the author of the announcement, having full control over matters, should have used a simpler and more informative sentence in the first and second scenario. Similar observations hold for or in the scope of proportional quantifiers with a strict ratio (e.g. ‘exactly half’). All these contexts allow the use of or plus implicatures. None of these cases needs to involve epistemic uncertainty. Once again, epistemic uncertainty could be the reason for the speaker to utter (2.7) – for instance for a student who can not remember the announcement very well. But the point is that epistemic uncertainty need not be understood. A third class of sentences require one further step in order to allow for a motivated use of or. They are such that in their literal interpretation, the use of or would not be licensed (unless expressing epistemic uncertainty). However, such sentences can be improved by resorting
Licensing or 41
to re-interpretations or secondary readings. (2.8) offers an example. Imagine the following report by the class teacher after class: (2.8)
(Today’s math class was just a disaster. I was not able to inspire anyone for the beauty of the subject. The kids just did not react.) Some pupils were sleeping or daydreaming.
If all parts of (2.8) are understood in their normal, common way, we get an existential statement that is weaker than the simpler statements without disjunction. (2.9.a) is entailed by b. and c. (I use capital variables for plural objects. Predicates are assumed to apply to pluralities in a distributive manner. The details are given in the next section.) (2.9)
a. ∃X( PUPIL(X) ∧ [ SLEEP(X) ∨ DAYDREAM(X) ] ) b. ∃X( PUPIL(X) ∧ [SLEEP(X)] ) c. ∃X( PUPIL(X) ∧ [DAYDREAM(X)] )
Hence we would expect that (2.8) is pragmatically marked. One way to remedy this markedness could consist in an implicature about epistemic uncertainty. In this reading, the speaker is not sure whether the pupils were asleep or awake, daydreaming. However, under normal circumstances the sentence intuitively seems a shorter way to express (2.10). (2.10)
(My class today was just a disaster.) Some pupils were sleeping, and some pupils were daydreaming.
This stronger statement seems to come about in two subsequent steps. First, the indefinite ‘some’ is not interpreted as a mere existential quantification. The speaker appears to have a specific group of pupils X in mind that she wants to talk about. Using ‘some pupils’ in a specific sense, she can refer to this group. Secondly, given that the referent is fixed, the speaker appears to have reason not to use one of the simpler sentences ‘some pupils were sleeping’ or ‘some pupils were daydreaming’. The hearer will hence infer that among the pupils that the speaker intends to talk about, some were sleeping and not daydreaming, and some were daydreaming and not sleeping. Sentence (2.10) is entailed by the overall information conveyed by (2.8), but crucially, the groups of ‘some pupils’ in (2.10) are not the larger group that the speaker was talking about in (2.8). Note that the pattern corresponds to the free choice inference.
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The free choice puzzle has received renewed attention in the last years, starting with the analysis by Zimmermann (2000), followed by Geurts (2005), Aloni (2003b), Schulz (2002), Simons (2005a,b) and Klinedinst (2005). A very detailed and insightful discussion of earlier treatments, including Kamp (1973) and (1979), is given in Schulz (2002). The majority of papers rest on a modified analysis for or. Zimmermann 2000 (and Geurts, elaborating on Zimmermann 2000) claims that or does not contribute logical disjunction, but presents a series of epistemic alternatives which the speaker conjoinedly entertains. The paradigm case of this pattern is shown by sentences like (2.11) which comes down to the statement in (2.12): (2.11) (2.12)
Joe is drunk or sick. (As far as I can see,) Joe might be drunk, and Joe might be sick (and I don’t know which)
Zimmermann assumes that (a) all alternatives mentioned as a disjunct have non-empty intersection with the epistemic background of the speaker; that (b) there is no subset of epistemic alternatives of the speaker which supports none of the alternatives mentioned, and (c) there is an implicature about ‘independence’ of the alternatives mentioned. Assumption (a) is designed to derive genuineness: no disjunct is uttered spuriously. Assumption (b) predicts exhaustivity under normal circumstances. No life option should remain unmentioned. Condition (c) is motivated by the observation that the hearer usually seems to understand that the alternatives are mutually exclusive in some sense. The examples discussed in this chapter rest on logical independence, but the author states that more general (topological) notions of non-overlap are operant in the general case. Free choice effects for epistemic might follow straightforwardly from the analysis. In order to generalize the analysis to deontic modality, Zimmermann proposes the authority principle. If the speaker can be assumed to be an authority in the issue in question, epistemic possibility (‘maybe’) can be strengthened to epistemic certainty (‘in fact’). In spite of its initial plausibility, Zimmermann (2000) has problems in those cases where or does not show modal flavour. Among the problematic cases are those without modal component (e.g. (2.8) and (2.6)), but problems arise also for deontic must as well as the no-list-of-privileges case. Consider once more the announcement in (2.7). If we interpret (2.7) as
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a list of epistemic possibilities, we get something like (2.13)
Possibly, you have to write a paper, and possibly, you have to kill a rabbit. ♦((KILL-A-RABBIT) ) ∧ ♦((WRITE-A-PAPER))
Given that the author of the requirement has full knowledge about it, we can apply the authority principle in order to go beyond the ‘ignorant student’ reading of (2.7). The authority principle leads to (2.14)
(KILL-A-RABBIT) ∧ (WRITE-A-PAPER)
This states that the requirement for a credit consists of two parts: killing a rabbit and writing the paper. This does not match the natural understanding of (2.7). Zimmermann’s prediction for example (1.10), repeated here as (2.15), is likewise problematic. Remember that the sentence was not an acceptable way to state the conjunction in (2.16). (2.15)
(2.16)
(What new privileges does Judy gain when she’s 18 years old?) # Judy may drive a car, or marry without her parents’ consent or vote in elections. Judy may drive a car, and Judy may marry without her parents’ consent, and Judy may vote in elections.
The sentence in (2.15) will be assigned the meaning in (2.17). Following Zimmermann, I use for deontic possibility here. (2.17)
♦((DRIVE-JANE-CAR)) ∧ ♦((MARRY-JANE)) ∧ ♦((VOTE-JANE))
This list of epistemic possibilities is subject to Zimmermann’s requirements to lists, (a)–(c). In particular, logical incompatibility (c) could, but need not necessarily, be required for (DRIVE–JANE–CAR), (MARRY–JANE) and (VOTE–JANE). In actual practice, however, no form of incompatibility (or non-overlap) is intended in deontic free choice examples. This chapter proposes to apply the authority principle to (2.17). If the speaker has full knowledge about Jane’s privileges, he will not only hold all three alternatives as possible, but as actual facts. Specifically, they can hence not be mutually exclusive. (2.18)
(DRIVE–JANE–CAR) ∧ (MARRY–JANE) ∧ (VOTE–JANE)
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(2.18) however expresses exactly the list of privileges that Jane (as well as any 18 year old person) will enjoy. The analysis, far from explaining that (2.15) is unacceptable, will predict that it is a perfect statement of lists of privileges. Schulz (2003) argues in favour of a pragmatic basis for the modal approach in Zimmermann (2000). Going back to Gazdar’s seminal work on implicature, Schulz assumes a systematic set of possible implicatures of disjunctions under modal operators which are evaluated in context. The remaining implicatures are then fed into a highly developed modal logic framework and give rise to the desired entailments. Schulz’ analysis moreover extends to obligation sentences and puts a wide range of data into a coherent common framework. While the present proposal shares Schulz’ perspective of a modular semantic-pragmatic setup, Schulz once again offers an analysis which focusses on modal quantification and is inherently designed to cover free choice effects in those, and only those examples. Schulz’ division of labour into pragmatics and semantics will avoid modal readings for those sentences where Boolean disjunction plus Gricean inferencing is sufficient (see (1.8) Everybody ordered beer or pizza), but the setup is unsuited to capture free choice effects in nonmodal contexts. The following example replicates the effects shown in (2.8) and (1.9). (2.19)
(Gordon is not as strict a vegetarian as he wants to make you believe. I have observed him for quite a while and. . .) Gordon sometimes DID eat meat or fish. → Gordon sometimes ate meat. And Gordon sometimes ate fish.
Two recent proposals by Simons (2005a,b) rest on a modified analysis for or but do not posit a modal component. The core idea of both proposals lies in the assumption that the disjuncts in the sentence should be collected in a set which is then available for further semantic computation. In Simons (2005b), the set of disjuncts is moreover exploited for a scoping mechanism in that, at an appropriate place, set union will be performed, reflecting the semantic contribution of or. Simons’ proposal so far rests on a classical boolean view of or which can not explain the free choice puzzle. At this point, both accounts stipulate semantic requirements on the set of disjuncts which yield the desired entailments. Simons (2005a) discusses the requirement of being a supercover, while Simons (2005b) resorts to the weaker symmetry condition. Let me concentrate on this more recent proposal. The symmetry condition states that there should be some
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salient property P which is shared by all disjuncts. Simon illustrates the idea on basis of examples like (2.20). (2.20)
Judy may take coffee or juice.
The condition refers to the set of disjuncts { Judy take coffee, Judy take juice} and requires one salient common property for all these disjuncts. In absence of any common property which is entailed logically at this point, Simons stipulates that the requirement could be ‘that both propositions have nonempty intersection with the deontically accessible worlds’. With this extra requirement, the free choice entailment follows. While the symmetry condition offers the correct results, it remains a convenient mystery that hearers always resort to the right kind of common property. Simons explicitely refrains from discussing the motivation underlying symmetry. The following kind of abuse can therefore not be excluded so far: (2.20 )
Judy may take coffee or juice. Salient common property: Judy take coffee and Judy take juice are both desirable options for Judy. (They have nonempty intersection with Judy’s buletic alternatives.) Fact: In fact, Judy is only allowed to take juice.
(2.20’) is predicted to be acceptable by Simons’ symmetry condition. In fact, it is not a good situation for the sentence to be true. I suspect that a pragmatic motivation of the symmetry condition would reveal it to summarize the pragmatic inferences that will be at the heart of the approach in the present chapter. One important aspect in Simons (2005b) consists in that she acknowledges the existence of pure Boolean disjunction in downward entailing contexts. She quotes the observation that or with modals, if negated, is absolutely well-behaved. I will evaluate her solution in section five, where interacting licensing factors are discussed. A recent proposal which is very close in spirit to the present chapter was made by Klinedinst (2005). He is the only author, as far as I can see, who has ever pointed out free choice effects in nonmodal contexts. Consequently, any analysis of these effects should not rest on modality in a way which can not be transferred to ordinary existential quantification. It is this criticism that stands, in Klinedinst’s as well as my opinion, against all approaches that were reviewed so far (as well as related ones), in spite of their sophistication and adequate predictions in the modal domain. While Klinedinst’s examples, as well as (1.8), (1.9), are essential in the
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understanding of free choice effects, he does not explore explicit existential quantification in sufficient detail and therefore fails to understand free choice effects as the consequence of semantic re-interpretations plus pragmatic inferencing. He does not discuss specificity effects, and related effects in the modal domain which lead to the no-list-of-privileges facts. The present approach to the free choice puzzle is very conservative in its analysis of or and modality. I propose that or is Boolean disjunction, and that existential statements are interpreted as specific under suitable circumstances. If a disjoint property is attributed to a specific set of objects, we can derive an implicature that all disjuncts must be exhibited by some elements of this set. The implicature arises by simple allusion to the Gricean maxims of manner (‘be brief – comparing the salient alternative utterances’) and quality (‘do not say what you believe to be false’). The analysis will receive initial support from data with explicit existential quantification. They give us clear access to the discourse pragmatics of the effects under investigation. We can then proceed to the generalization to the modal case.
3
Explicit existential quantification and ‘or’
In the present section, I will investigate free choice effects with explicit nominal or adverbial existential quantification in more detail. I will use the term ‘explicit existentials’ for these quantifiers, because unlike modal existentials, they allow us to specify restrictions on the domain of quantification, and to investigate its status in discourse. Explicit existentials offer a test case for free choice effects where the interacting interpretive and pragmatic mechanisms are easier to access than in the modal case. After revisiting some phenomena, I will offer a semantic analysis for free choice effects for explicit existentials which will be applied to modal existentials in Section four. Let me start by illustrating the free choice effects for explicit existentials with some more examples. All examples are given with an appropriate context. The ties between free choice existentials and the discourse context will be discussed below. (3.1)
(3.2)
(Our class visited the Zoo yesterday. After watching animals in the morning, we took a break near the kiosk at noon.) Some pupils had chips or ice cream. (Others went to the playground.) (Discussing whether our friend Gordon is a vegetarian or not: No, I don’t think that he is. We visited a summer school together, and I remember clearly that . . . ) Gordon sometimes DID eat meat or fish.
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The conjoined statements in (3.3 ) and (3.4) are intuitively entailed by the respective disjunctions. (3.3) (3.4)
Some pupils had chips, and some pupils had ice cream. Gordon sometimes ate meat, and Gordon sometimes ate fish.
The examples hence exhibit an entailment pattern for existential quantification over individuals and times which is analogous to free choice effects. Some other, more subtle intuitions could be explicated as follows: The speaker wants to talk about some specific people, things or occasions. The specific persons, things or occasions that she wants to talk about exemplify a general property which is exemplified by the disjuncts. In the pupil-example, the speaker could announce her intentions as follows: ‘Among the ways that children can amuse themselves in a zoo, let me now name those which have to do with food.’ In the Gordon-example: ‘Among the occasions of Gordon eating, let me talk about those which violate his strict vows as a vegetarian.’ Let me now try to delineate the pragmatics of free choice effects with explicit existentials. I characterized them as ‘specific’ so far. Several observations suggest that, in fact, a partitive use of the existential seems crucial in order to elicit free choice effects. This is evidenced by several kinds of examples where the respective word order patterns do not support partitive readings very well, or where the context definitively excludes such a reading. In order to come to a richer spectrum of data, I will consider both English and German data in this section. The free choice effects for German explicit existentials exactly mirror the English effects, but due to greater freedom in word order, we can look at a broader spectrum of data. As a first example, let us passive sentences. Examples like (3.5) do not easily give rise to free choice effects. The resulting sentences have a very odd ring to them. It seems extremely hard to pinpoint the pragmatic side messages, and hence the intended overall information conveyed by (3.5). Here, as well as below, we see sentences with unlicensed and hard-to-license uses of disjunctions. There is as yet no technical term for the kind of interpretive puzzlement that befalls the hearer in view of sentences like (3.5), (3.7), or (3.8). (3.5)
a. Beer or pizza was ordered by some pupils. b. Bier oder Pizza wurde von manchen Schülern bestellt.
Whatever (3.5) may mean, we do not understand a free choice effect easily. If we compare (3.5) with other, good partitive uses of existentials,
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we observe that the quantifier does not precede the property that is attributed to the NP referents. In common partitive uses of quantifiers, however, the stressed quantifier should precede the property in question (see e.g. Jäger, 1996, Eckardt 1998). We can hence conlude that free choice effects arise only when the explicit existential precedes the disjunctive property. More minimal pairs which illustrate word order effects are those in (3.6) which rest on verb pairs like get/bring, and (3.7) in German where changes in word order can turn an odd disjunction into a good disjunction. (3.6) (3.7)
(3.8)
√
Some children get their presents from the Christkindl or Santa Claus. # The Christkindl or Santa Claus bring the presents to some children. √ Manche Kinder bekommen die Geschenke some kids get the presents vom Christkind oder dem Nikolaus from-the Christkind or the Santa Claus. # Vom Christkind oder dem Nikolaus bekommen from-the Christkind or the Santa Claus get manche Kinder die Geschenke. some children the presents √ Manchen Kindern bringt das Christkind oder der Nikolaus die Geschenke. to-some children brings the Christkind or the Santa Claus the presents # Das Christkind oder der Nikolaus bringt manchen Kindern die Geschenke. The Christkind or the Santa Claus brings to-some children the presents.
Note that ‘specific use’ of an explicit existential does not exclude generic uses. The following example seems to be talking about kinds of guests rather than a specific group of persons present. The example could elaborate a remark like ‘you know how hard it is to run a pizzeria which meets all customers’ ideas of Italian food’. (3.9)
There are some guests who want pizza or beer. There are OTHER guests who want bruscetti or saltimbocca.
What seems to be crucial is that the disjuncts are understood as representative for a more overarching property, one which the speaker does not want to use explicitely (‘underclass food’ in contrast to ‘refined food’). In other cases, the property might not even have a good name, like in the Gordon-example in (3.2). ‘exhibiting non-vegetarian eating behaviour’
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seems an extremely clumsy paraphrase for the property of ‘eating meat or fish’. The above example morevoer shows that resentational sentences with there is do not impede free choice effects. However, if we take (3.9) as an utterance in a different kind of situation (and with a different kind of message in the speaker’s mind), we can test that the partitive use of some is necessary in order to derive free choice effects. In the scenario in (3.10) where a partitive use is definitively excluded, or will be understood as epistemically licensed: ‘and I don’t know which’: (3.10)
The owner of the local pizza hut is shaken awake by his wife at 3 am: ‘Get up, man! There are some guests at the door who want pizza or beer!’ (undertone: I didn’t quite understand which.)
In sum, a partitive use of the explicit existential seems crucial for free choice effects. Sentences with word orders which impede partitive use, as well as utterances in situations where partitive uses are blocked do not give rise to free choice effects. Free choice effects for explicit existentials can be captured by the following, simple kind of analysis. Let me stress that the exact nature of specificity in (i) might require further investigation. (i) partitive/specific use of an explicit existential [[ Some N ]] = P . ∃X( [[N]](X) ∧ P(X) ) Presupposition: The hearer understands that the speaker has an intended instantiation A for the existential X in mind. A is a true subset of a group B of known objects with property [[N]]: A ⊂ B. Notational comment: I assume that properties P are defined for atomic and plural objects. Predication over plural objects (for non-collective properties) is defined as in (ii). (ii) plural predication: A property P holds for some given plurality X, P(X) iff for all x ≤ X: P(x) (iii) Pragmatics of or in plural predication over group of objects A: 1. Speaker uses (P or Q)(A) and has sufficient knowledge of the situation. 2. Speaker did not use the simpler P(A), nor the simpler Q(A), and hence violated the maxim of manner: be brief. 3. He must have reason to do so. The reason could be the maxim of quality: The speaker seems to believe that neither P(A) nor Q(A) are true.
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4. Hence, speaker knows that for some x1 , x2 ≤ A : P(x1 ) ∧ ¬Q(x1 ), ¬P(x2 ) ∧ Q(x2 ) The present analysis of free choice effects is essentially pragmatic. Before moving on to the modal case, I will briefly review some related data that offer evidence about the semantics–pragmatics interface. There is an ongoing debate about the interaction of pragmatic inferencing with semantic composition. Specifically, work like Chierchia (2004) or Sauerland (2004, forthcoming) raise the possibility that the pragmatic evaluation of subconstituents might precede the completion of semantic composition. Explicit existentials with or show interesting effects in the antecedent of conditionals. Consider the sentence pattern in (3.11). (3.11)
If any/some N do A or B, then S.
It offers the opportunity to study the semantics–pragmatics interface. Specifically, if free choice effects arise in the antecedent of a conditional, the present account will require pragmatic inferencing before semantic composition has been completed. If, however, free choice effects do not arise in this constellation, this would lend support to the traditional sequential picture of semantic composition preceding pragmatic inferencing. The actual data are intricate. In the bulk of examples, it seems impossible to understand free choice effects with nominal existential quantifiers plus disjunction in the if -clause. Consider the sentence in (3.12). (3.12)
If any pupils take drugs or steal jewellery, then the teacher will be fired.
The sentence intuitively seems equivalent to the conjunction in (3.13). This equivalence is predicted by classical logic. (3.13)
If any pupils take drugs then the teacher will be fired, and if any pupils steal jewellery, then the teacher will be fired.
Note that or is in a downward-entailing context in (3.12). We would therefore expect that the sentence (3.12) has a reading which rests on Boolean disjunction, and shows no further implicatures. According to my intuition, this expectation is borne out. In the present example, it is very implausible to understand that only the conjoined vices will get
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the teacher sacked, while he may stay if only one or the other kind of criminal activity has been reported. (3.14)
If some pupils take drugs, and some pupils steal jewellery, then (and only then) the teacher will be fired.3
If we take sentence (3.12) as a typical exemplar of the scheme (3.11), we will conclude that antecedents of conditionals block free choice effects. This supports a pragmatic analysis of the effect, plus the traditional view of a strictily sequential modus operandi of semantics and pragmatics. This observation is challenged by similar modal examples like in (3.15), discussed in Zimmermann (2000). He points out that free choice effects can arise in (3.15).4 (3.15)
If Mr X might be in Chelsea or Hyde Park, then we can as well give up. understood: Neither possibility alone would be reason to give up, but the joined possibilities set Mr X in such a strong stragetic position as to be invincible.
At this point, we could either conclude that the analysis of free choice effects with modals should be substantially different from the one for explicit existentials (contra the aim of my chapter). Or we could resort to some unnamed difference between the pragmatics for modals in contrast to explicit existentials (not very attractive). Or we can look for more examples with explicit existentials in if-clauses. Indeed, it seems that with a suitable preceding context, we can reinforce free choice effects. The sentence in (3.16) plausibly is a free choice example, as wittnessed in (3.17) and (3.18). (3.16) (3.17) (3.18)
If Gordon sometimes drinks beer or wine, we could offer him a good bottle of Bordeaux as a present. If Gordon sometimes drinks wine, then we could offer him a good bottle of Bordeaux. Not implied: If Gordon sometimes drinks beer, then we could offer him a good bottle of Bordeaux.
We seem to read ‘Gordon sometimes drinks beer or wine’ as ‘Gordon appreciates mild alcohol abuse’. The implication certainly does not distribute over the disjuncts in the antecedent. Beer drinking is not a good indication that someone will appreciate expensive Bordeaux wines. With
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a bit of goodwill, the same effect can even be achieved with nominal quantifiers. (3.19)
If some visitors started talking or fell asleep during the concert, then the performance must have been awful.
Again, it is plausible to understand the disjunction in (3.19) as an exemplaric list of the property of ‘not concentrating on the presentation’. If this is in fact the speaker’s point, he would insist that neither sleeping nor wispering audience alone is sufficient to indicate a poor concert. Yet, if several indicators coincide, certain conclusions about the quality of the concert are legitimate. The data are puzzling so far. Free choice effects seem to arise in some, but not all embedded uses in if -clauses. Does this mean that pragmatic inferencing can sometimes, but not always, take place during semantic composition? A closer look at the examples in question might help to resolve the paradox. To my intuition, the conditionals above (including the Zimmermann examples) are not the law-like uses of conditionals like in ‘if it rains, then the street gets wet’. The conditionals in question seem to take up an asserted fact of previous utterances (‘It seems that Mr X might be in Chelsea or Hyde Park’). In such a plain assertion, plain Boolean disjunction would not be licensed and pragmatic strengthening has to take place in order to motivate the use of or. If I am right in this intuition, then the antecedent takes up a fact that was estabished in discourse, and the consequent names the conclusion the speaker wants to draw. A case without disjunction is given in (3.20). (3.20)
A: I do not feel well today. B: Too bad. If you don’t feel well, you won’t want to try my homebaked cream cake I guess.
This kind of conditionals can be used in discourse in order to present an assertion of the speaker as a natural consequence of previous assertions. What is important here is that the content of the if -clause is taken up anaphorically from the discourse. Let me therefore call these conditionals anaphoric conditionals. Upon closer inspection, it turns out that free choice effects in the antecedent of a conditional can be systematically provoked in anaphoric conditionals. If that is true, the role of pragmatics is quite different than in an all-new utterance. While the details of a copying mechanism of literal content plus implicatures are still highly unexplored, we may expect
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that the free choice effects are copied effects from an antecedent root sentence rather than pragmatic inferencing dove-tailed with semantic composition. The analysis so far suggests that pragmatics indeed follows semantic evaluation. If no appropriate antecedent sentence (plus implicatures) is available, free choice effects in the antecedent of conditionals are very hard to understand. This holds true at least for free choice effects for explicit existentials. Let me now turn to the modal case.
4
Modal existentials
In this section, I will pursue the question whether the analysis for free choice effects for nominal and adverbial quantifiers can be generalized to the case of modal existential quantification. Let me briefly repeat the essential characteristics of the former: • The existential quantifier was used partitively, refering to a subset of a set of objects that is salient in context. • The existential quantifier was used in a specific sense: The hearer will understand that the speaker has a certain set of referents in mind. • The disjoint property is loosely understood as the case-by-case exemplification of a more general property.5 Evidently, these characteristics can not be directly translated into characteristics of modal existentials. First, there is no clear notion of partitive modal quantification. It is unclear (to me) how one would present a set of worlds as salient, and which modal statements could convey meanings like: ‘In some of these worlds, Jane takes coffee, but there are others left.’ Likewise, it is very difficult to verify whether the speaker had some specific set of worlds in mind. We can not point at worlds and ask: did you mean this one? or that one? or yet another one? The last characteristic will turn out to be easiest to rediscover in the modal domain. In summary, it seems likely that a transfer of the analysis in Section 3 will have to rely on slightly different versions of these characteristics of free choice modal existentials. I will first discuss deontic modals (Section 4.1) and then turn to epistemic possibility (in 4.2). Epistemic possibility will be closely compared to Zimmermann 2000 where this is taken to be the basic case. 4.1
Deontic possibility
Deontic may, in the simplest case, conveys an existential statement about the set of worlds which are deontic alternatives for some subject (as seen from the real world w∗ ). Semantic modelling usually assumes that the
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existential statement states the existence of one world at least. A sentence like (4.1) states that there is a deontic alternative where Jane takes coffee. (4.1)
Jane may take coffee.
However, as Klinedinst (2005) points out, it would be more realistic to assume that such a statement asserts the existence of a plurality of worlds of a certain kind. He argues that every permission sentence leaves many things unmentioned that Jane may do or not do, as well as irrelevant side aspects. Hence, there is not only one but many deontic alternatives w (for Jane at w∗ ) which exemplify her taking coffee. The semantic analysis of modal existentials does not lose its strength if we allow quantification over pluralities of worlds: there are some deontic alternatives for Jane where Jane takes coffee. Next, let me discuss which part of a person’s deontic alternatives is described with a free choice disjunction. Two scenarios come to mind. In some cases, the preceding context makes it clear that the full space of deontic alternatives is covered. The subject has several options but has to chose one of them. (4.2) offers an example. (4.2)
a. You must choose a password. b. You may choose your old one, or a new one.
Such examples are very close in meaning to imperatives like you must choose your old one or a new one. The fact that each disjunct denotes a genuine alternative is derived like in Section 2 above, and the pertinent conjunction follows. We will come back to such cases below. Usually, however, permission sentences are true permissions in that the subject also has the option to do nothing. (4.3)
Jane may take tea or coffee.
This sentence, intuitively, has a threefold message. First, Jane has permission to take tea and she has permission to take coffee. Second, it is her choice which one to take. And third, she may as well choose not to take either one. In free choice permission sentences, • the speaker decides to talk specifically about all and only those deontic alternatives which exemplify one among several possible actions that the subject may take in one specific choice • the possible actions are losely understood as excluding each other (which is, however, not strictly necessary)
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• logical independence is not sufficient for mutual exclusion; the possible actions must be tied together as being all possible outcomes of one decision of the subject. The last observation is important. Remember that disjoint lists of mutually independent privileges do not give rise to free choice effects. I repeat the crucial example (1.10) for convenience. (1.10)
What new privileges does Judy gain when she’s 18 years old? # Judy may drive a car, or marry without her parents’ consent or vote in elections.
In sum, the speaker has indeed a specific subset of the set of all deontic alternatives (of the subject) in mind. The subset is the one which exemplifies all possible decisions that the subject is allowed to take in one given case. A sentence like (4.3) expresses: ‘The speaker wants to inform you about Jane’s range of deontic alternatives as far as the choice of hot restaurative beverages is concerned.’ While we will turn to more complex examples below, I will take this paraphrase as the base line for the semantic analysis of modal existential quantification if licensing for ‘or’ is required. I have no conclusive views on other ‘neutral’ cases. The following points generalise the analysis of Section 2 to deontic modals. (i) may S refers to some specific intended subset W of all deontic alternatives Wdeont for some subject a at world w∗ . It is the subset W which exemplifies all possible decisions that the subject is allowed to take in one given case.6 (ii) Plural predication over worlds: A property P holds for some given plurality W of worlds, P(W) iff for all w ≤ W: P(w).7 (iii) Pragmatics of or in plural predication: 1. Speaker uses (A or B)(W) and has sufficient knowledge of the situation. 2. Speaker did not use the simpler A(W), nor the simpler B(W), and hence violated the maxim of manner: be brief. 3. He must have reason to do so. The reason could be the maxim of quality: The speaker seems to believe that neither A(W) nor B(W) are true. 4. Hence, speaker knows that for some w1 , w2 ∈ W: A(w1 )∧¬B(w1 ), ¬A(w2 ) ∧ B(w2 )
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If we apply this analysis to sentence (4.3), it yields the following. (4.5)
a. ∃W( [TAKE(JANE, TEA) ∨ TAKE(JANE, COFFEE) ](W) ) where speaker has a certain set W of alternatives in mind. b. . . .that is, for all w∈W: [TAKE(JANE, TEA)∨TAKE(JANE, COFFEE)](w) c. As speaker uses (A or B)(W) instead of the simpler A(W), or B(W), he implicates that the simpler statements would not hold true for the set of worlds W he has in mind. Hence, there are w1 , w2 ∈ W such that TAKE(JANE, TEA)(w1 )∧¬TAKE(JANE, COFFEE) (w1 ) and ¬TAKE(JANE, TEA)(w2 )∧TAKE(JANE, COFFEE) (w2 ). In other words: Jane may take tea. And: Jane may take coffee.
This shows that the desired free choice effects follow from the analysis of this basic case. Let us come back to those cases where may A or B is tantamount to must A or B. Geurts (2005) points out that the preceding discourse can specify the quantificational domain. I repeat the crucial example in (4.2). (4.2)
a. You must choose a password. b. You may choose your old one, or a new one.
The first sentence characterizes the deontic alternatives in total. In this context, it is completely clear that the may quantification in b. refers to the range of deontic worlds described in a. In this case, an analysis as in (i)–(iii) is fully convincing, as the set of alternatives that the speaker must have in mind is the set of all those where the addressee adheres to the obligation in a. This totality of worlds W is characterized by the disjunctive property in (4.6), and as above the free choice conjunction in (4.7) is implicated. (4.6) (4.7)
[ CHOOSE(YOU, OLDPASSWORD) ∨ CHOOSE (YOU, NEWPASSWORD) ](W) ∃w(CHOOSE(YOU, OLDPASSWORD) (w))∧∃w(CHOOSE(YOU, NEWPASSWORD) (w))
Note that the sentence ‘You must choose your old password, or a new password.’ is logically equivalent to (4.2.b) in the given context. An explanation of the ‘friendlier’ undertone of the may statement remains to be developed. Even though the range of options that the speaker has in mind in modal existentials is more difficult to pinpoint than for explicit existentials, a closer look at the data can reveal some conventions. Let us
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turn back to example (4.3). There is some tacit suggestion that the disjunct in (4.3) exhausts the options of Jane as far as hot beverages with restorive quality are concerned. The speaker restricts attention to these cases and remains tacit about cold drinks, food, and any other activity. The speaker would not be uncooperative if it turned out that Jane has more unrelated options in addition: the choice between soft drinks, the choice between wine/beer, the choice between vegetarian and nonvegetarian lunch etc. The speaker has just that set of deontic alternatives in mind that exemplify the hot beverages choice. To see this point more clearly, imagine an air flight where the stewardess approaches passengers and offers: (4.8)
You may take coffee or ham sandwich.
In this context (passenger and stewardess both informed about conventional refreshments) the utterance strongly suggests that the stewardess has run out of any other food or drink. She is cooperatively listing the remaining options and leaves for you to choose. If there were in fact more kinds of drink or food available, the passenger would be justly annoyed and have the feeling that the stewardess did not exhaust the full range of deontic alternatives that sentence (4.8) suggests she has in mind. Further examples can serve to illustrate this intuition: (4.9)
Samantha may take up her studies at Stanford or Harvard. possible intended deontic alternatives: worlds that exemplify all possible universities S. may go to worlds that exemplify all possible ivy league universities S. may go to
Hence, the utterer of (4.9) would not be uncooperative if it turned out that Samantha also has the possibility to go to Mayor Chesterton College at Sheperd’s Hill, say. In that case, the speaker would just have the second set of deontic alternatives in mind. Matters are different in (4.10). (4.10)
Frederick may take up his studies at Stanford or at Major Chesterton College at Sheperd’s Hill. possible intended deontic alternatives: worlds that exemplify all possible universities F. may go to
In (4.10) the two disjuncts that describe Frederick’s options are disparate enough not to exemplify any sub-class of universities. Hence, we’ll tend to understand the list in (4.10) as exhaustive list of Frederick’s options.
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Let me finally briefly mention modal disjunctions like the following, as discussed in Geurts (2005): (4.11) (4.12)
You may do A, or you must do B. You must do A, or you must do B.
I think that these require a more refined analysis of deontic space and discourse. An example like the schematic (4.11) suggests that the first A option is more agreeable than the second, B option. Hence, (4.13) seems a natural instantiation for (4.11) while (4.14) is not (according to my own preferences): (4.13) (4.14)
You may do the shopping, or you must clean the toilet. You may clean the toilet, or you must do the shopping.
The pattern in (4.12), in contrast, has been disputed as illogical (e.g. Schulz 2003 as reported in Geurts 2005). How can there be, logically thinking, an alternative of two equally binding obligations? (Note that (4.12) is not understood as an epistemic alternative here ‘. . . and I don’t remember which’.) I think that the criticism is well taken, even though the examples are valid and existant. Yet, the contribution of or seems to be dynamic-temporal and beyond the range of phenomena that I want to address here. Consider a classical instantiation of (4.12): (4.15)
(4.16)
Your money, or your Life! (Geld oder Leben!) (You must pass me your money, or you must die.) Hands up, or I’ll shoot you! (You must take your hands up, or you must die) You have to take away your car now. Or you’ll have to pay a fine of 50 Euro.
As before, the options are again ordered according to the degree of unpleasantness of the requirements. But secondly, there is a clear temporal dimension in the contribution of or in such examples. You must do A. And if you have not done A in due time, B will follow. Hence, the disjunction of obligations like in (4.12) does not present an alternative of obligations now but a sequence of ever more unpleasant obligations in the future. (This is the essence of all threats for punishment). I will not consider such uses of or in more detail here.
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4.2
Epistemic possibility
Let us take a natural example of epistemic free choice as our starting point. We observe our friend John late at night, pale, leaning at a lamp post. We conclude: (4.17)
John might be drunk or ill.
In cases like this, there is one clear issue, pieces of evidence or some fact and we present a list of possibilities that we hold compatible with this fact. At this point, it might be useful to recapitulate Zimmermann’s acceptability conditions on lists. Relating the listed propositions p1 , . . . pn to the epistemic alternatives of the speaker Hw,c it is assumed that i. pi ∩ Hw,c = Ø for 1 ≤ i ≤ n (each disjunct is a genuine alternative) ii. there is no set M such that M ∩ Hw,c = Ø and M ∩ pi = Ø for 1 ≤ i ≤ n. (the disjuncts together exhaust the epistemic space) iii. the disjunctions do not overlap, in the sense of a suitable topology. (independence; a violable pragmatic requirement) Condition ii. amounts to the assumption that the speaker designs the list of alternatives with the intention to exhaust his epistemic space. In order to remain realistic, Zimmermann allows for a tacit elsewhere disjunct in order to account for open ended lists of irrelevant cases. This assumption could be rephrased as follows: (A) The speaker intends to make a modal existential statement about his full epistemic space; or: that part of the epistemic space where the relevant, realistic options that he wants to list are exemplified.8 The intention in uses like (4.17) can be paraphrased as follows: ‘I want to talk about the set W of all reasonable epistemic alternatives – even though I use specific existential quantification to address them – and I attribute the property [ DRUNK(JOHN)∨ILL(JOHN) ](W) to this set of worlds.’ Epistemic alternatives which might be excluded from this statement are those remote possibilities the speaker has bad eyesight, it is in fact a lifesize doll of John that is leaning at the lamp post, etc. Note that the resulting constellation is parallel to the permission sentence in (4.5): ‘You must choose a password. You may choose your old password or a new one’. Like in that earlier case, (4.17) could be replaced by John must be drunk or ill. The quantification expressed, and the set of worlds refered
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to, therefore do not exhibit the standard neutral case of existential quantification. However, (4.5) and (4.17) can be captured as one limit case of specific existential quantification where some are practically all. Like in Section 4.1, the genuineness of each disjunct follows by pragmatic inference. This, in turn, again entails the free choice conjunction. (4.18)
John might be drunk. And: John might be ill.
One very nice illustration of the tension between (a) the desire to exhaust all possibilities, (b) the fact that this might require an endless list, and (c) the systematic neglect of certain epistemic possibilities, is exhibited by the German children’s book Schachtelmonster (Monster in a Box). A little boy finds a cardboard box and explores the possibility that there might be some Schachtelmonsters (cardboard box monsters) in that box. The hidden premise of the reflections in (4.19) is ‘assume that there are monsters in that box’ (i.e. let’s devise this list of disjuncts with that set of epistemic alternatives in mind where there are actually monsters in the box). (4.19)
Vielleicht sind sie gelb mit blauen Tupfen, oder blau mit gelben, perhaps are they yellow with blue spots or blue with yellow oder vielleicht sind es Mumienmonster, oder ein paar or perhaps they are mummy-monsters or a pair Fledermausmonster, oder ganz viele . . . bat-monsters or a-whole many ‘Perhaps they are yellow with blue spots, or blue with yellow spots, or perhaps they are mummy monsters, or some bat monsters, or a terrible lot of them . . .’
The possibilities listed here do not cover the whole epistemic space of the little boy (because, luckily, there is still the possibility that there are no monsters in the box at all). The disjuncts listed do not seem to cover the full range of possible monsters either. Who can think of all possible monsters there could be? The epistemic alternatives rather seem to address the set of worlds which exemplify types of monsters the little boy can think of. Finally, further explorations will have to settle the extent to which or in epistemic statements can sometimes share the dynamic quality of the disjunctions at the end of Section 4.1. It might be plausible to assume that or in an open list refers dynamically to sequences of epistemic states of the speaker: Or, if the previous possibilities I could think
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of are not true, this new set of possibilities is another option. I will leave such uses of contemplative or untreated here. At the beginning of the section, I suggested that modal free choice examples arise most easily in contexts where the speaker addresses one clear issue, pieces of evidence or fact. He lists, so to speak, all resulting possibilities that are compatible with a certain kind of evidence, fact, observation etc. (It is perhaps not an accident that Zimmermann 2000 rests entirely on examples from a detective mystery game.) To what degree is such a context not only ‘natural’ but even necessary? To check this, consider an example where the speaker in fact reports unrelated possibilities. (4.20)
(On the ride to a wedding, the family discusses what the ceremony might be like.) The bride might wear a fancy white dress, or there might be children with flowers, or a band might be playing, or there might be a big cream cake.
A disjunction like this has an odd ring to it. If we understand it as disjoint possibilities – and a suitable prosodic pattern may enhance this – then the speculations seem to imply that under normal circumstances, only one of these possibilities is expected to hold. (The couple could have just enough money to buy either a dress, or flowers, or hire a band, or buy a cake.) Compare a list of possibilities as in (4.21). (4.21)
The bride might wear a fancy white dress and there might be children with flowers and a band might be playing and there might be a big cream cake.
(4.21) is a good way to speculate about a wedding in its various, unconnected aspects. In this sense, it does not follow from (4.20). Zimmermann 2000 could, of course, capture this fact by appeal to condition (iii), the mutual non-overlap of alternatives. (4.20) illustrates that non-overlap is not a requirement about logical non-redundancy (as his examples could suggest) but about mutual exclusiveness.9 In sum, the analysis of epistemic free choice examples mirrors the previous cases in the following manner. (i) might S expresses existential quantification over epistemic alternatives. The speaker has in mind a subset W of all epistemic alternatives
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Wepist (for speaker, in context c at world w∗ ). It is the subset W which exemplifies all possible conclusions or options that the speaker can think of in view of a certain piece of evidence, facts, situations, or reflection. (ii) Plural predication over worlds: A property P holds for some given plurality W of worlds, P(W) iff for all w ≤ W: P(w). (iii) Pragmatics of or in plural predication: (a) Speaker uses (A or B)(W) and has sufficient knowledge of the situation. (b) Speaker did not use the simpler A(W), nor the simpler B(W), and hence violated the maxim of manner: be brief. (c) He must have reason to do so. The reason could be the maxim of quality: The speaker seems to believe that neither A(W) nor B(W) are true. (d) Hence, speaker knows that for some w1 , w2 ∈ W : A(w1 ) ∧ ¬B(w1 ), ¬A(w2 ) ∧ B(w2 ) The only assumption that one could find problematic, (A), has been shown to mirror analogous assumptions that are inherent in earlier work, and in that sense, the present proposal is as good or as bad as these. However, the present analysis for epistemic free choice has been developed as an instantiation of a more general pattern that arguably also covers deontic free choice examples, and extensional free choice examples. Moreover, the analysis rests on the assumption that the word or denotes Boolean disjunction, and that all other effects are due to pragmatic inferencing, if necessary enhanced by reinterpretation of other parts of the sentence (here: existential quantification). This leaves the option of devising individual analyses for different kinds of implicatures for different kinds of disjunctive sentences. The final section will briefly but non-exhaustively highlight this issue.
5
Interactions between different licensers
The present approach presents a modular semantic-pragmatic analysis of free choice effects of or. The connective or uniformly denotes boolean disjunction. The word or (hence) offers a systematic means to convey a weaker property (A or B) instead of two stronger properties (A, B). This weakening requires pragmatic licensing: why say less, in more words? In many uses, we may have simple and perspicuous reasons to use weaker
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properties instead of stronger ones, e.g.: downward entailing contexts: antecedents of conditionals, restrictors of universal quantification, negation with certain implicatures: Scope of universal quantification (every guest received a rose or a hat) and necessity operators (epistemic, deontic, etc.) Other uses would, in their literal meaning, trade a weaker statement for a stronger one. In such uses, speakers/hearers can use conventional reinterpretations of other parts of the sentence in order to come to a content where or is pragmatically meaningful. This option was elaborated for explicit and modal existential quantification. Finally, if no other explicit reason to use or is given in the sentence, epistemic might serves as a default licenser, as in (5.1). It was demonstrated in the previous section how we can derive the conjoined possibilities in (5.2).
(5.1) (5.2)
John is a buddhist or a hindu ( . . . and I don’t remember which) John might be a buddhist. And John might be a hindu.
I argued that epistemic uncertainty can not be the only way to license or. Many uses of or patently lack any flavour of epistemic uncertainty or insufficient knowledge. The modular analysis of or can explain why or has very different flavours in different contexts of use. Consider the following list of examples. None of these seems to indicate uncertainties on the side of the speaker. (Of course, all examples can be interpreted as involving epistemic alternatives, but this will not be the only, nor the most natural interpretation.)
(5.3) (5.4) (5.5)
(5.6)
All applicants are buddhists or hindus (implicature: and both possibilities occur) If you get an A or a B in the exam, I’ll take you out for dinner (implies: either precondition is sufficient) You must take a written exam or present three times in class. (implicature: which describes all your possible options; either one is a life option.) Nobody was bored or annoyed. Gordon never eats meat or fish. Gordon eats neither meat nor fish.
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All the examples in (5.3) to (5.6) have in common that a plain boolean analysis of or, together with a simple application of the maxims of manner and quality, are sufficient to describe the information content of the examples in question. If the strategy pursued in the present chapter is correct, then a simple boolean analysis of or is likewise sufficient in other cases, specifically those that give rise to free choice effects.10 The observed logical strengthenings arise, I claimed, by a reinterpretation of existential quantification rather than by a nonstandard analysis of or. This will lead to the prediction that such reinterpretations will become superfluous if other licensers are present in the sentence. I will discuss two constellations, negation and conditionals as licensers. Simons (2005b) points out that the negation of a disjoint permission behaves strangely. She states that ‘when we embed or under both a modal and negation, it stops misbehaving and starts acting like a well-behaved Boolean operator’. The following example is discussed in detail: (5.7)
Jane may not sing or dance.
Simons diagnoses the following readings of (5.7): (5.8) (5.9)
Either Jane is not permitted to sing, or Jane is not permitted to dance. Jane isn’t permitted to do either, sing or dance (‘neither nor reading’)
Simons uses a modal re-interpretation of or (close to Zimmermann (2000)) to attribute the pertinent free-choice reading to the unnegated sentence (5.10). (5.10)
Jane may sing or dance. ♦( jane sing ) ∧ ♦( jane dance )
Negation then leads to reading (5.8). (5.11)
¬(♦( jane sing ) ∧ ♦( jane dance ) ) ≡ ¬ ( jane sing ) ∨ ¬ ( jane dance )
Yet, as argued in Simons (2005b), the more salient reading in (5.9) remains unanalysable in Zimmermann (2000). Simons herself can capture the second reading because her symmetry condition, posited on the disjuncts, is satisfied in negated uses. (The shared property of both disjuncts is to have empty intersection with jane’s deontic space.) While
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this technically leads to the correct results, the basis for Simons’ condition remains unanalysed, which turns it into an austere – and easily violable – stipulation. Under the present account, we’d say that a specific interpretation of existential quantification (may) is essentially driven by the need to license the use of or as a longer way to say less. An analysis of (5.7) can proceed as follows: The material in the scope of the modal operator amounts to the disjunction11 (5.12)
jane sing ∨ jane dance.
The modal applies, and we can assume that it does so under the standard existential analysis. (5.13)
♦ (jane sing ∨ jane dance)
Finally, the result is combined with negation. (5.14)
¬ ♦ (jane sing ∨ jane dance)
The disjunction in (5.14) is in a downward entailing context, and hence the resulting statement is logically stronger than the competing simpler forms. (5.15)
¬ ♦ (jane sing), ¬ ♦ (jane dance)
The use of disjunction is pragmatically licensed here because it leads to a stronger statement in a simpler way than by using two separate sentences ( Jane may not sing, and Jane may not dance). In this case, the boolean interpretation of or does not need any further interpretative or pragmatic processes to make sense. The epistemic reading (5.8) comes about in a different manner. In the present approach, the free choice effects for deontic may . . . or . . . are derived without any reference to epistemic modality. In whatever way negation, modality and conjunction distribute out, this will not bring us from deontic to epistemic modality. However, I assume that epistemic possibility is the default licensing mechanism for or. The epistemic disjunction will be derived directly, by assigning wide scope to or and licensing it epistemically. (Note that wide scope or is not in a downward entailing context.)
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(5.16)
Possibly, Jane may not sing or Jane may not dance. ‘It is not allowed for Jane to sing, or it is not allowed for Jane to dance, and I don’t know which.’
If we analyse epistemic ‘possibly’ as shown in Section 4, we can also derive the corresponding conjunction. (5.17)
Possibly, Jane may not sing, and possibly, Jane may not dance.
Going back to the preceding accounts, note that Simons (2005b) and Zimmermann (2000) (as in Simons 2005b) derive the disjunction in (5.11) by boolean distribution of negation over two conjuncts. The connective in (5.11) (as copied from Simons (2005b)) is simple Boolean or without any further modal force. Hence, (5.17) can not be derived from (5.11). Of course, both authors could resort to a Gricean argument here, but this would be at odds with the general program pursued in both papers, namely to derive free choice effects in the use of or as part of the literal content. Note that there is a third scoping possibility for or in sentence (5.7), leading to the logical structure ¬ (♦ (jane sing) ∨ ♦(jane dance)). Under the present analysis all logical operators and quantifiers get their standard interpretation unless more is required for pragmatic reasons, which is not the case here. (Negation of two disjuncts is stronger than negation of either disjunct alone). Therefore this option is logically equivalent to (5.14). It seems a natural assumption that the scope of or determines the pragmatic repair strategies and implicatures – if necessary – which warrant its use. Specifically, epistemic possibility appears to occur only with wide scope or. Exceptions from this observation can arise in contexts where a previous wide scope epistemic modality gets copied into an embedded context from previous discourse.12 This happens in the second kind of example that I will look into, or in the antecedent of conditional clauses. Antecedents of conditionals provide a good reason to use or. Consider the conditional in (5.18). It is intended as equivalent to the conjoined conditionals in (5.19). The two sentences are indeed logically equivalent under a Boolean analysis of or. The example is taken from Zimmermann (2000:275). (5.18)
If Mr X is in Regents Park or in Bloomsbury, he cannot take a boat.
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(5.19)
If Mr X is in Regents Park, he cannot take a boat, and if Mr X is in Bloomsbury, he cannot take a boat.
Consequently, there is no further need to re-interpret any part of the sentence in order to come to a statement that warrants the use of disjunction. Specifically, note that an epistemic interpretation of or, while still possible, is at best marginal in such an example. (5.20)
If Mr X is in Regents Park or in Bloomsbury, he cannot take a boat. If Mr X is in Regents Park, he cannot take a boat, or if Mr X is in Bloomsbury, he cannot take a boat, and I don’t remember which.
This observation suggests that the different ways to make sense of or are not mutually exclusive. The presence of one does not lead to a principled unavailability of the other (even though ‘innocent’ speakers of English tend to refute (5.20) on stylistic grounds). The epistemic use of or as paraphrased in (5.20) requires the following steps in the semantic evaluation: (i) Disjunction is interpreted with highest scope above the conditional, (ii) the resulting literal meaning contains a disjunction which lacks motivation, (iii) the hearer grants a modal possibly in the specific sense discussed in section three and (iv) derives the net information of literal content plus implicatures.
6
Summary
In the present chapter, I proposed a modular semantic-pragmatic analysis of free choice effects for or. The account rests on the following assumptions: • Uses of or are tendentially pragmatically unmotivated, specifically where the speaker would use more words to convey less information. The hearer will infer some reason why the speaker used or. • Uses of or can be motivated by implicatures of the literal content of the sentence, by re-interpretation of the original sentence (plus implicatures), and by tacit epistemic modality. • Existential quantification can be re-interpreted as specific existential quantification. This possibility is available in general. It is exploited in motivating uses of or. • The semantics of specific existential quantification allows to derive the free choice effects which have been observed for or. Most importantly,
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it can explain free choice effects in all quantificational domains. Hence, the approach extends naturally to free choice effects for explicit existentials, data which have not received much attention in the literature.13 I argued that core examples like those discussed in the chapter can be captured maintaining a strict sequential order between semantic evaluation and pragmatic inferencing. It should be kept in mind, however, that more elaborate cases of embeddings could require a more refined picture. A sentence like (5.1) has no anaphoric quality, and yet free choice effects in the embedded context are possible. (5.1)
The detective believes that Mr X is in Regents Park or in Bloomsbury.
The proposed analysis hence delineates a new broad range of data which can help us to get a better understanding of the systematic interactions at the semantics-pragmatics interface.
Notes 1. The online version of his SuB 10 talk came to my attention while I was elaborating the core ideas of the chapter. 2. I want to thank an anonymous reviewer whose comments helped me to sharpen and clarify an earlier version of the chapter. 3. I am aware of the less-than arbitrary switch between any and some, but can not spot its exact relevance so far. 4. For all those who are not acquianted with the original paper, it might help to know that the sentence relies on a situation where the interlocutors are engaged in the German board game Scotland Yard in which a single player, Mr X, making hidden moves in London has to be hunted by a team of cooperating detectives. From time to time, Mr X gives clues about his movements which lead to hypotheses about his position. 5. This last observation is less easily explicable than the first two. However, the free choice effects arise most saliently when the preceding context leads the hearer to expect that this-or-that general property will be addressed next (e.g. non-vegetarian behaviour; amusing-by-buying-food and sweets; showing signs of boredom, etc.) 6. There may be more than one set of worlds that serves this purpose. This does not matter for the core of the analysis. It will be sufficient (see below) to assume that the speaker wants to talk about any one subset of deontic alternatives which is large enough to exemplify all options. The pragmatics of or would then implicate that any such subset can only be truthfully described by resorting to a disjoint property. Conjunctions of permissions will follow.
Licensing or 69 7. We could assume here that we are talking about atomic parts of the plurality of worlds, i.e. single possible worlds. Hence, a simpler notation might be w ∈ W. 8. As before, we can weaken this requirement to ‘some sufficiently large part of the epistemic space where all options are exemplified’. 9. At least under normal circumstances. The offer ‘tea or coffee?’ can always be exploited by the request ‘both, please!’ 10. Excluding the dynamic or in Section 4. 11. I follow Simons here in taking the scoping facts of negation relative to must and may for granted. Hence, may not is analysed as ‘negated permission’, while must not denotes ‘obligation not to . . . ’. 12. I do not have any independent proposals to make about scoping of or. In particular, I appreciate Simons’ scoping mechanism for or which allows scopetaking without any syntactic movement operations (dubious or not). My claim is that the scoping mechanism does not require further modifications of the semantics of or which are intended to yield free choice effects. The scoping mechanism in Simons is very strong, as it can potentially give any scope to or. The proposal that I defend here may lead to contentful restrictions to this scoping mechanism. It might turn out that a narrowly defined set of or licensers restricts the possible scopes of or. A systematic exploration remains to be conducted. 13. Klinedinst (2005) poses a welcome exception to this claim. The present chapter shares his perspective and the core analysis. However, the material which is accessible at present does not discuss specificity effects in the explicit domain, nor the interaction of several different ways to make pragmatic sense of or.
References Aloni, Maria (2003a). ‘On choice-offering imperatives’. In P. Dekker and R. van Rooij (eds): Proceedings of the Fourteenth Amsterdam Colloquium, 2003. ILLC, University of Amsterdam. Aloni, Maria (2003b). ‘Free Choice in Modal Contexts’. In M. Weisgerber (ed.): Proceedings of SuB 7. (Arbeitspapier 114, FB Sprachwissenschaft, Konstanz). University of Konstanz. URL: http://www.ub.uni-konstanz.de/kops/volltexte/ 2003/1103/ Chierchia, Gennaro (2004). ‘Scalarity Implicatures, polarity phenomena, and the syntax/pragmatics interface’. In: A. Beletti (ed.): Structures and Beyond. Oxford: Oxford University Press. Eckardt, Regine (1998). ‘Focus and nominal quantifiers’. In P. Bosch, R. van der Sandt (eds): The Focus Book. Cambridge: Cambridge University Press. Geurts, Bart (2005). ‘Entertaining Alternatives. Disjunctions as Modals’. In Natural Language Semantics 13: 383–410. Jäger, Gerhard (1996). ‘Topics in Dynamic Semantics’. PhD thesis, HumboldtUniversity Berlin, published as CIS-Bericht Nr. 96–92, Centrum für Informations- und Sprachverarbeitung LMU München. Kamp, Hans (1973). ‘Free choice permission’. In Proceedings of the Aristotelian Society, N.S. 74: 57–74.
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Kamp, Hans (1979). ‘Semantics versus Pragmatics’. In F. Guenthner, S.J. Schmidt (eds): Formal Semantics and Pragmatics of Natural Languages, Dordrecht, Reidel: 255–87. Klinedinst, Nathan (2005). ‘Freedom from Authority’. Talk presented at SuB 10, Berlin. Kratzer, Angelika and Junko Shimoyama (2002). ‘Indeterminate Pronouns: the View from Japanese’. In Proceedings of the Third Tokyo Conference on Psycholinguistics, 1–25. Longer version at Semantics Archive: http://semanticsarchive.net/. Levinson, Stephen (2000). Presumptive Meanings. Boston: MIT Press. Sauerland, Uli (2004). ‘Scalar implicatures in complex sentences’. Linguistics and Philosophy 27: 367–91. Sauerland, Uli (forthcoming). ‘On embedded implicatures’. Journal of Cognitive Science. Schulz, Katrin (2002). ‘You may read it now or later: A case study on the paradox of free choice permission’. Masters Thesis, ILLC, Amsterdam. Simons, Mandy (2005a). ‘Dividing Things Up. The Semantics of “or” and the Modal/“or” interaction’. In Natural Language Semantics 13: 271–316. Simons, Mandy (2005b). ‘Disjunction and Symmetry’. In E. Georgala, J. Howell (eds): Proceedings of SALT 15. Zimmermann, Thomas Ede (2000). ‘Free Choice Disjunction and Epistemic Possibility’. In Natural Language Semantics 8: 255–90.
4 Free Choice and the Theory of Scalar Implicatures∗ Danny Fox MIT
This chapter will be concerned with the conjunctive interpretation of a family of disjunctive constructions. The relevant conjunctive interpretation, sometimes referred to as a ‘free choice effect,’ (FC) is attested when a disjunctive sentence is embedded under an existential modal operator. I will provide evidence that the relevant generalization extends (with some caveats) to all constructions in which a disjunctive sentence appears under the scope of an existential quantifier, as well as to seemingly unrelated constructions in which conjunction appears under the scope of negation and a universal quantifier. Alonso-Ovalle (2005), following Kratzer and Shimoyama (2002), has presented important evidence arguing that free choice effects should be derived by the system that accounts for Scalar Implicatures (SIs). However, we will see that deriving a free choice implicature is not a simple matter within standard approaches to implicature computation. More specifically, FC directly contradicts neo-Gricean attempts to deal with another observation about disjunction due to Chierchia (2004): Sauerland 2004, Spector 2006. In response to this predicament, I will argue for a system that derives SIs within the linguistic system, though in a somewhat different manner from Chierchia (2004). Specifically, I will argue for a covert exhaustivity operator with meaning somewhat akin to that of only (in the spirit of Chierchia (2004), but more directly following suggestions by Groenendijk and Stokhof (1984), Krifka (1995), Landman (1998), and van Rooij (2002)). We will see that all of our observations about FC, as well as Chierchia’s observations about disjunction, follow from a novel (though fairly natural) approach to the meaning of the exhaustivity operator. It is often claimed that the neo-Gricean account of SIs follows from basic truisms about the nature of communication. However, as is well 71
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known, one assumption is crucial, and far from trivial, namely the assumption that Grice’s Maxim of Quantity should be stated with reference to a formally defined set of alternatives. There is clearly no escape from formally defined alternatives. However, if the perspective argued for here is correct, access to these alternatives should be limited to grammar. A quantity maxim which is not contaminated by syntactic stipulations (together with appropriately placed syntactic stipulations, i.e., within grammar) derives better empirical results.
1
Some background on scalar implicatures
Consider a simple disjunctive sentence such as that in (1). When we hear such a sentence we draw a variety of inferences. (1)
Sue talked to John or Fred.
First, we conclude that (if the speaker is correct) Sue talked to John or to Fred, a conclusion, in and of itself, consistent with the possibility that Sue talked to both (Basic Inference). However, we typically also conclude (again assuming that the speaker’s utterance is correct) that this latter possibility was not attested (Scalar Implicature, SI). Finally, we infer that the speaker’s beliefs don’t determine which person (i.e. John or Fred) Sue talked to (Ignorance Inferences).1 (2)
Inferences we draw from (1): a. Basic Inference: Sue talked to John or Fred (or both). b. Scalar Implicature, SI: Sue didn’t talk to both John and Fred. c. Ignorance Inferences: The speaker doesn’t know that Sue talked to John. The speaker doesn’t know that Sue talked to Fred.
The nature of the inferences in (2a) and (2c) seems rather straightforward. The Basic Inference, (2a), is derived quite directly from the basic meaning of the sentence. The Ignorance Inferences, (2c), are not as direct, but, nevertheless, receive a fairly natural explanation. They are derived straightforwardly from a general reasoning process about the belief states of speakers, along lines outlined by Grice (1975). The source of the inference in (2b), SI, is, at least in my opinion, less obvious. The standard, neo-Gricean, approach captures this inference
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by enriching the set of assumptions that enter into the derivation of Ignorance Inferences, while various competing proposals attribute the inference to a particular enrichment of the basic meaning. Before we see what is at stake, let’s start with a formulation of what might be uncontroversial, namely the account of (2c).2 The basic idea is that communicative principles require speakers to contribute as much as possible to the conversational enterprise. This idea is further elaborated when it is assumed that the goal of certain speech acts is to convey information, and that if all information is to be relevant, more is better. So, assume that two sentences are true and both contribute information that is completely relevant to the topic of conversation. If one contains more information than the other (i.e. is logically stronger),3 use of the more informative one would constitute a greater contribution: (3)
Maxim of Quantity (basic version): If S1 and S2 are both relevant to the topic of conversation and S1 is more informative than S2 , if the speaker believes that both are true, the speaker should utter S1 rather than S2 .
Typically, when (1) is uttered, the information conveyed by each of the disjuncts is relevant. Furthermore, each disjunct is more informative than the entire disjunction. (p entails p or q, but not vice versa.) The fact that the speaker, s, uttered the entire disjunction rather than just a disjunct, therefore, calls for an explanation. If we, the people who interpret the utterance, assume that s obeys the Maxim of Quantity, we conclude, for each disjunct, p, that it is false to claim that s believes that p is true, or if we keep to our convention of using the verb know instead of believe (see note 1), we can state this as a conclusion that s does not know that p is true. If we assume that s believes that her utterance of the disjunction is correct, we derive the Ignorance Inferences. But one logical property of the situation is worth focusing on. When we conclude that s does not believe that p is true, that is, in principle, consistent with two different states of affairs. s might believe that p is false, or, alternatively, she might have no (conclusive) opinion. The reason we infer the latter is that the former would be inconsistent with our other inferences. Under normal circumstances, we infer that s believes that her utterance of p or q is true (Maxim of Quality). If we were to assume that s believes that p is false, we would have to conclude that she believes that q is true. But that would conflict with our inference about q (based on the Maxim of
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Quantity). Hence we must conclude, for each disjunct, that the speaker has no opinion as to whether or not it is true. 1.1
The symmetry problem4
Consider now whether we could extend this line reasoning to account for the SI in (2b). Since we’ve already concluded that the speaker does not know that p is true and that the speaker does not know that q is true, it follows that the speaker does not know that the conjunction p and q is true. This, again, is consistent with two different states of affairs. s might believe that p and q is false, or, alternatively, she might have no (conclusive) opinion. If this time we could exclude the latter possibility, we would derive the SI. The problem is that basically the same line of reasoning we’ve employed above leads us exactly to the opposite conclusion, namely to the exclusion of the possibility that s believes that p and q is false. The idea is fairly simple. The information that p and q is false, if true, would be relevant to the topic of conversation, hence the fact that s did not provide us with this information calls for an explanation.5 Once again, the natural explanation is that s did not have the information, i.e. that s did not know that p and q is false. In other words, instead of an SI, we derive, once again, an Ignorance Inference: we conclude that s does not know that p and q is true, and (exactly by the same type of reasoning) that s does not know that p and q is false, i.e. we conclude that s does not know whether or not p and q is true. As far as I know, a version of this problem was first noticed in Kroch (1972), and stated in its most general form in class notes of Kai von Fintel and Irene Heim. To appreciate the problem in its full generality, consider a general schema for deriving SIs in response to s s utterance of p (of, say, I have 3 children). We start by considering a more informative relevant utterance, p (say, I have 4 children), and reason that if p were true, and if s knew that p were true, the Maxim of Quantity would have forced s to utter p instead of p. We then might reason that it is plausible to assume that s knows whether or not p is true (say, that it is reasonable to assume that s knows how many children she has), and hence that s knows that p is false. The problem, however, is that there is always an equally relevant more informative utterance than p, namely p and not p (in our case, I have exactly 3 children), call it p . By the same reasoning process, if p were true and if s knew that p were true, the communicative principles would have forced s to utter p instead of p.6 Furthermore, if s knows the truth value of p, and of p , then s knows the truth value
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of p . So, the same reasoning process leads to the conclusion that s knows that p is false. The assumption that the speaker knows whether or not p is true, thus, leads to a contradiction and must, therefore, be dropped. This problem was dubbed the symmetry problem in class notes of Kai von Fintel and Irene Heim. Whenever p is uttered, and fails to settle the truth value of a relevant proposition, q, there will be two symmetrical ways of settling it, leading necessarily to an Ignorance Inference. Stated somewhat differently, p is equivalent to the following disjunction (p ∧ q) ∨ (p ∧ ¬q), and therefore should lead to Ignorance Inferences parallel to those stated in (2c). 1.2
The neo-Gricean approach
The neo-Griceans respond to this problem by a revision of the Maxim of Quantity. Specifically, they suggest that the maxim doesn’t require speakers to utter the most informative proposition that is relevant to the topic of conversation, but is more limited in scope. The Maxim merely requires speakers to choose the most informative relevant proposition from a formally defined set of alternatives. It does not require speakers to consider all relevant propositions. The common way to work this out, pioneered by Larry Horn (1972), starts out with the postulation of certain sets of lexical items, Scalar Items, and sets of alternatives to which the scalar items belong, which we will call Horn-Sets:7 (4)
Examples of Horn-Sets a. b. c. d.
{or, and} {some, all} {one, two, three, . . .} {can, must}
These sets of lexical alternatives determine the set of (Horn) alternatives for a sentence by a simple algorithm. The set of alternatives for S, Alt(S), is defined as the set of sentences that one can derive from S by successive replacement of Scalar Items with members of their Horn-Set.8 (5)
Alt(S) = {S : S is derivable from S by successive replacement of scalar items with members of their Horn-Set}
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The Maxim of Quantity can now be stated as follows: (6)
Maxim of Quantity (Neo-Gricean version): If S1 and S2 are both relevant to the topic of conversation, S1 is more informative than S2 , and S1 ∈Alt(S2 ), then, if the speaker believes that both are true, the speaker should prefer S1 to S2 .
Consider the sentence in (1). The postulated scalar item in this sentence is disjunction, for which conjunction is lexically specified as the only alternative, (4a). (1), thus, has just one alternative (other than (1) itself): (7)
Alt(1) = {(1), Sue talked to John and Fred }
When s utters (1), his addressee, h (for hearer), typically concludes (on the assumption that s obeys the revised Maxim of Quantity) that s does not know that the conjunctive sentence in Alt(1) is true, since this alternative sentence is more informative than s s utterance, and is typically relevant. If h assumes, further, that s has an opinion as to whether or not the conjunctive sentence is true, h would conclude that s believes that it is false. The neo-Griceans, thus, attribute a general tendency to addressees, namely the tendency to assume that speakers are opinionated. I state Sauerland’s formulation of this assumption in (8). (8)
Opinionated Speaker (OS): When a speaker, s, utters a sentence, S, the addressee, h, assumes, for every sentence S ∈Alt(S), that the beliefs of s determine the truth value of S , unless this assumption about S leads to the conclusion that the beliefs of s are contradictory.
Under the basic version of the Maxim of Quantity in (3), B-MQ, there was no way to maintain the assumption that the speaker is opinionated about any relevant sentence S (not entailed by S). To repeat, B-MQ derived the symmetric results (a) that the speaker does not know that S and S is true, and (b) that the speaker does not know that S and not S is true. This, together with the assumption that the speaker knows that S is true (Quality), derived the conclusion that the speaker is not opinionated about S . By contrast, under the Neo-Gricean version of the Maxim of Quantity in (6), NG-MQ, the assumption that the speaker is opinionated about various sentences (not entailed by S) is innocuous. NG-MQ does not always derive the inference that the speaker does not know that S and S is true. It derives such an inference only when S and S (or some equivalent
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sentence) is a member of Alt(S). Under such circumstances, the speaker could be opinionated about S as long as Alt(S) does not have S and not S as a member (nor some equivalent sentence). If S and not S is not a member of Alt(S), NG-MQ does not derive the inference that the speaker does not know that S and not S is true, and the assumption that the speaker believes that S and S is false could be made consistently. To summarize, assume that a speaker s utters the sentence in (1), Sue talked to John or Bill. The addressee, h, assumes that s obeys the Maxim of Quality as well as the revised Maxim of Quantity, NG-MQ. Based on this assumption, h reasons in the following way: 1. Given NG-MQ, there is no X∈Alt(1), such that X is logically stronger than (1), and s thinks that X is true. 2. Alt(1) contains the conjunctive sentence Sue talked to John and Bill, which is logically stronger than s s utterance. Hence, given 1, it’s not the case that s thinks that this conjunctive sentence is true. 3. Given OS, the default assumption is that s has an opinion as to whether Sue talked to John and Bill is true or false. Given 2 (the conclusion that it’s not the case that s thinks that the sentences is true), we can conclude that s thinks that it is false. So, by modifying the set of assumptions that derive Ignorance Inferences (replacing B-MQ with NG-MQ) one can account for the SI in (2b). I would like at this point to discuss a possible alternative that keeps B-MQ in tact but instead enriches the set of syntactic representations available for (1). But it is worth pointing out first that, as things stand right now, our account of the Ignorance Inferences in (2c) is in jeopardy. Specifically, it is incompatible with NG-MQ and our assumption in (4a) about the Horn-Set for disjunction. The account was crucially dependent on the assumption that the Maxim of Quantity would prefer the utterance of a disjunct to the utterance of a disjunction, an assumption incompatible with the way Alt(1) is defined on the basis of (4a). One might respond to this problem with an independent (pragmatic) account for (2c) (Gazdar 1979) or by enriching the Horn-Set for disjunction (Sauerland 2004). The latter will be discussed in greater detail in Section 4. 1.3
An alternative syntactic approach
The alternative syntactic approach that I would like to defend is guided by the intuition that a principle of language use (such as the Maxim of Quantity) should not be sensitive to the formal (and somewhat arbitrary)
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definition of Alt(S).9 If this intuition is correct, B-MQ is to be preferred to NG-MQ. However, as pointed out in Section 1.1, B-MQ derives Ignorance Inferences that contradict attested SIs. Therefore, if B-MQ is correct, something else is needed to derive SIs. More specifically, SIs must be derived from the basic meaning of the relevant sentences; otherwise the symmetry situation would yield unwanted Ignorance Inferences. Following proposals by Groenendijk and Stokhof (1984), Krifka (1995), Landman (1998), van Rooij (2002), and to some extent Chierchia (2004), I would like to suggest that the syntax of natural language has a covert operator which is optionally appended to sentences, and that this operator is responsible for SIs.10 The guiding observation is that there is a systematic way to state the SI of a sentence, using the focus sensitive operator only. Consider the sentence in (9), which has the SI that John didn’t buy 4 houses. (9)
John bought three houses.
This SI could be stated explicitly using the focus sensitive particle only in association with the numeral expression three. (10)
John only bought THREE houses.
This observation extends to all SIs; SIs can always be stated explicitly with the focus sensitive particle only, as long as the relevant scalar items bear pitch accent: (11)
(12)
a. John did some of the homework. b. Implicature: John only did SOME of the homework. For all of the alternatives to ‘some’, d, if the proposition that John did d of the homework is true, then it is entailed by the proposition that John did some of the homework. a. John talked to Mary or Sue. b. Implicature: John only talked to Mary OR Sue. For all of the alternatives to ‘or’, con, if the proposition that John talked to Mary con Sue is true then it is entailed by the proposition that John talked to Mary or Sue.
Sentence that generates SIs usually contain scalar items,11 and in such cases it is always possible to state the SIs explicitly, by appending the
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operator only to the sentence and placing focal accent on the relevant scalar item: (13)
The only implicature generalization (OIG): A sentence, S, as a default, licenses the inference/implicature that (the speaker believes) only S’, where S’ is a modification of S with focus on scalar items.
From the neo-Gricean perspective discussed in Section 1.2, it is pretty clear why (9)–(12) should obey the OIG. As is commonly assumed, and as indicated by the italic paraphrases, the role of only is to eliminate alternatives. Furthermore, when focus is placed on scalar items, the relevant alternatives are precisely the Horn-alternatives that NG-MQ refers to. However, the OIG suggests yet another possibility, namely that B-MQ is the right conversational maxim and SIs are derived within the grammar, namely by of a covert exhaustivity operator with a meaning somewhat a kin to that of only. Assume, for the moment, the semantics for only suggested by the paraphrases in (9)–(12). Specifically, assume that only combines with a sentence (the prejacent), p, and a set of alternatives, A, (determined by focus). The result of this combination is a sentence which presupposes that p is true and furthermore asserts that every true member of A is already entailed by p (i.e. that all non-weaker alternatives, all ‘real alternatives’, are false): (14)
[[only]] (A<st,t> )(pst ) = λw: p(w) = 1. ∀q∈NW(p,A): q(w) = 012 NW(p,A) = {q∈A: p does not entail q}
The exhaustivity operator, exh, should mean the same, with one small modification. While with only the requirement that the prejacent be true is a presupposition, with exh this requirement should be part of the assertive component: (15)
[[Exh]] (A<st,t> )(pst )(w) ⇔ p(w) & ∀q∈NW(p,A): ¬q(w)
Assume that natural language has exh as a covert operator. Assume, further, that this operator can append to a sentence, S, thereby yielding a stronger sentence S+ = Exh(Alt(S))(S).13 It is easy to see that such a representation would derive both the ‘basic meanings’ and the SIs of the sentences in (9)–(12). This would allow us to keep to the non-stipulative quantity maxim (B-MQ). The cost lies, of course, in the stipulation of exh. There is a clear trade-off here, one that suggests that no decision will be justifiable
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on a priori grounds. The goal of this chapter is to provide an empirical argument in favor of a theory in which B-MQ is at the heart of pragmatic reasoning and exh is responsible for SIs. If such a theory is correct, we might think of exh as a syntactic device designed (‘by a super-engineer’) to facilitate communication in a pragmatic universe governed by B-MQ. Every conversational situation, C, can be characterized by a set of sentences that are relevant at C, QC (for question). An utterance of S at C will be associated with a set of Ignorance Inferences determined by the set of sentences QS,C ⊆QC , whose truth value is not determined by S. B-MQ will derive the set of Ignorance Inferences that correspond to QS,C , i.e., I-INF(S,C) = {¬Ks ϕ: ϕ ∈QS,C }. Furthermore, if ϕ is relevant to the topic of conversation, it seems that same would be true of ¬ϕ (see note 5). Hence I-INF(S,C) = {¬Ks ϕ: ϕ ∈ QS,C } = {¬Ks ϕ and ¬Ks ¬ϕ : ϕ ∈QS,C } Sometimes the set of Ignorance Inferences will be implausible and this would motivate a new parse of the linguistic stimuli, one that involves an exhaustive operator on top of S, i.e. S+ . If no further stipulations are added, the procedure should be able to apply recursively leading to S++ , S+++ , etc. As we will see, this possibility will empirically distinguish our syntactic perspective from the Neo-Gricean alternative. In the next section, I will present the core empirical phenomena that I will use to motivate exh, namely the conjunctive interpretation of disjunction under existential modal constructions (free choice, FC). Furthermore, I will present an argument, due to Kratzer and Shimoyama (2002) (K&S) and Alonso-Ovalle (2005), that FC should be derived by the system that derives SIs. In Section 3, I will present evidence that FC arises in additional circumstances: when disjunction is embedded under certain other existential quantifiers and when conjunction is embedded under negation and universal quantifiers (under the sequence ¬∀). In Section 4, I will discuss a relevant observation about disjunction due to Chirchia (204), and in Section 5 I will present the Neo-Gricean response to Chierchia’s observation (Sauerland 2004) and its failure to predict FC phenomena. Finally, in Section 6–10, I will propose a resolution based on recursive exhaustification which extends to the phenomena discussed in Sections 2 and 3.
2
The problem of free choice permission
Consider the sentence in (16) when uttered by someone who’s understood to be an authority on the relevant rules and regulations, for example, a parent who is accustomed to specifying limits pertaining to the consumption of sweets.
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(16)
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You’re allowed to eat the cake or the ice-cream.
In such a context, (17) would be an immediate inference (Kamp 1973). This inference, sometimes referred to as an inference of free choice permission, is not an expected entailment of obvious candidates for the logical form of (16). (17)
You’re allowed to eat the cake and you are allowed to eat the ice-cream.
For example, (17) is not entailed by (18).14 (18)
Plausible LF for (17): allowed [[you eat the cake] or [ you eat the ice-cream]]
What (18) states is that the relevant rules do not prohibit the disjunctive sentence (the complement of allowed), or, in the terms of possible world semantics, that there is a world consistent with the rules in which one of the disjuncts is true. (18) is thus equivalent to (19), which is clearly weaker than (17). (19)
You are allowed to eat the cake or you are allowed to eat the ice-cream.
The problem is to understand how a disjunctive LF such as (18) can be strengthened to yield the conjunctive inference in (17). In other words, we need to understand how a sentence that should receive the modal logic formalization in (20a) – which is equivalent to (20b) – justifies the FC inference in (20c). (20)
a. ♦(p ∨ q) b. ♦p ∨ ♦q (a ≡ b) c. Free Choice: ♦p ∧ ♦q
2.1 Downward entailing operators, evidence that free choice is an implicature K&S studied FC effects that arise when certain indefinite expressions are embedded under existential modals, and presented a fairly strong argument that the effect should be derived by the system that yields SIs.15 The argument, which has been elaborated and extended to disjunctive
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constructions by Alonso-Ovalle (2005), is based on the observation that there are no traces of FC in certain downward entailing contexts. Consider the sentence in (21). If FC were to follow from the basic meaning of (16), we would expect (21) to have a fairly weak meaning; it should be able to assert that no one is both allowed to eat the cake and allowed to eat the ice-cream, (21 a). We would thus predict (21) to be true in a situation in which everyone is allowed to eat one of the two disserts but no one has free-choice, i.e. in situations in which no one is allowed to decide which of the two deserts to eat. Such an interpretation, if available, is extremely dispreferred.16 To derive the natural interpretation, (21 b), we must factor out whatever is responsible for FC. (21) No one is allowed to eat the cake or the ice-cream. (21)’ a. *negation of FC: ¬∃x[♦P(x) ∧ ♦Q(x)] b. negation of standard meaning: ¬∃x♦(P(x) ∨ Q(x)) As pointed out by Alonso-Ovalle (following K&S), the natural interpretation, (21 b), is expected if FC were to be derived as an SI. Although it is not yet clear how to derive FC as an SI, it is clear that if a derivation were available for the basic case, it would, nevertheless, not be available (at least not necessarily) for (21). This is seen most clearly under the neo-Gricean approach to SIs. Under this approach, an SI is derived as a pragmatic strengthening of the basic meaning of a sentence. The meaning in (21 a) is weaker than the basic meaning in (21 b), and, therefore, cannot be derived along neo-Gricean lines. Under the syntactic alternative, the preference for (21 a) would be stated as a preference for stronger interpretations (See Chierchia 2004, 2005). More specifically, assume, contrary to what you might think at this point, that an exhaustive operator can somehow derive the basic FC effect. We might then suggest that exh can only be introduced if the overall result is a stronger proposition. This could be motivated by the observation that as propositions get stronger fewer Ignorance Inferences are derived by B-MQ. We might, thus, suggest that the introduction of exh is subject to an economy condition related to its functional motivation, namely to the elimination of Ignorance Inferences (i.e. a sentence with exh must lead to fewer Ignorance Inferences than its counterpart without exh, see note 37). Alternatively, we might suggest, in line with the neo-Griceans, that exh must be introduced in matrix position.17 Be that as it may, it is reasonable to assume that the preference for (21 b) would be predicted if FC could be derived as an SI, but not otherwise. Quite independently of particular proposals, it is well known that
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SIs tend to disappear in downward entailing environments (Gazdar 1979, Chierchia 2004). The fact that FC appears to share this property with SIs seems to be a good incentive to search for a theory that would derive the effect as an SI. 2.2
Deriving an FC implicature: the nature of the problem
The projection properties of FC seem to suggest that the effect should be derived as an SI. But how could we derive such a result? K&S made a very interesting proposal which is the basis for the proposal that I will make in Sections 6–10. But this will require quite a bit of ground work. At this point, it is worth understanding what one might say in order to derive SIs based on the neo-Gricean maxim of quantity (NG-MQ). Quite generally, suppose that ϕ is the basic meaning of a sentence, S, and that our goal is to derive a stronger meaning, ϕ , based on NG-MQ. The result could be achieved if we proposed a set of alternatives of the following sort: ALT(S) := {S, S & not Sϕ }, where the meaning of Sϕ is ϕ . If s was to utter S, the addressee, h, would conclude, based on NG-MQ, that s does not believe that not Sϕ is true. Furthermore, based on the assumption that s is an opinionated speaker, h, would conclude that s believes that Sϕ is true. More specifically, suppose that the alternatives of the sentence in (16), repeated below, are the sentences in (22). This is slightly different from the general scheme for deriving implicatures characterized above, but the basic idea is the same.18 (16) (22)
You’re allowed to eat the cake or the ice-cream. Alternatives needed to derive FC for (16) based on NG-MQ: a. You are allowed to eat the cake or the ice-cream. b. You are allowed to eat the cake but you are not allowed to the ice-cream c. You are allowed to eat the ice cream but you are not allowed to eat the cake.
Based on NG-MQ, we would now derive the SI that (22b) and (22c) are both false, which, together with (22a), yields the FC inference. To see this, assume (22a) is true. Now assume that one of the conjuncts in (17) is false, say that you cannot eat the ice-cream. From this it follows that (22b) is true, contrary to the SI. But of course this is not intended as a serious proposal. It follows from a general algorithm that allows us to derive, on a case by case basis, any
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SI that we would like to, and, hence, does not explain the particular SIs that are actualized (See Saeboe 2004). The obvious way to turn this into a serious proposal is to show that the alternatives in (22) are needed on independent grounds. K&S, and in particular Alonso-Ovalle, propose a more natural set of alternatives, namely the one in (23). (23)
Alternatives proposed by K&S/Alonso-Ovalle: a. You are allowed to eat the cake or the ice-cream. b. You are allowed to eat the cake. c. You are allowed to eat the ice cream.
The set of alternatives in (23), in contrast to the one in (22), is consistent with a general constraint on alternatives proposed in Matsumoto (1995).19 Furthermore, as we will see in Section 4, there is independent evidence for the type of Horn-Sets that would derive (a super-set of) the alternatives in (23). The problem, however, is that NG-MQ can not derive the FC effect on the basis of (23). In fact, as we will see in greater detail in Section 5.2, it derives Ignorance Inferences that directly conflict with FC. K&S suggest, however, that FC should be derived from (23) based on a novel principle, which they call anti-exhaustivity. When h interprets s s utterance of (23a), s needs to understand why it is that s preferred this sentence to any of the alternatives. The standard Neo-Gricean reasoning, which relates to the basic meaning of the alternatives, would lead to the conclusion that s does not know/believe that any of the alternatives is true. K&S, however, suggest that h might reason based on the strong meaning (basic meaning + implicatures) of the alternatives. Specifically, K&S suggest that h would attribute the choice of s to the belief that the strong meanings of (23b) and (23c) are both false. Furthermore they assume that the strong meaning of (23b) and (23c) is the basic meaning of (22b) and (22c) respectively. As pointed out by Aloni and van Rooij (forthcoming), this line of reasoning raises a question pertaining to simple disjunctive sentences, such as (1). We would like to understand why such sentences don’t receive a conjunctive interpretation via an anti-exhaustivity inference of the sort outlined above. If each disjunct is an alternative to a disjunctive sentence, why doesn’t the speaker infer that the exhaustive implicature of each disjunct is false? K&S provide an answer this question by postulating a covert modal operator for any disjunctive sentence. I will not go over this proposal
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and the way it might address Aloni and van Rooij’s objection. I would like, instead, to raise another challenge to K&S s basic idea. I think it is important to try to understand how the anti-exhaustive inference fits within a general pragmatic system that derives Ignorance Inferences (as well as SIs). Specifically, I think it is important to understand why NG-MQ does not lead to the Ignorance Inferences in (24) (see Section 4.2 for details). (24)
Predicted inferences of (16), based on (23) and NG-MQ: a. s doesn’t know whether or not you can eat the cake. b. s doesn’t know whether or not you can eat the ice cream.
This is a challenge that this chapter attempts to meet. The idea, in a nut-shell, is to eliminate NG-MQ in favor of the non-stipulative alternative B-MQ. However, understanding how this is to work requires the introduction of a proposal made in Sauerland (2004), which would be extracted from its neo-Gricean setting in order to meet our goals. But before I get there, I would like to introduce an additional challenge. Specifically, I would like to present a few other surprising inferences that are intuitively similar to FC, and should, most likely, be derived by the same system.
3
Other free choice inferences
In this section we will see effects that are very similar in nature to FC, but arise in somewhat different syntactic contexts. These effects will argue for a fairly general explanation of the basic phenomenon, one that is not limited to modal environments or to disjunction. 3.1
FC Under negation and universal modals
Consider the sentence in (25) when uttered by someone who is understood to be an authority on the relevant rules and regulations, for example, a parent who is accustomed to assigning after-dinner chores. (25)
You are not required to both clear the table and do the dishes.
In such a context, (26) would normally be inferred by the addressee. (26)
You are not required to clear the table and you are not required to do the dishes.
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This inference seems very similar to the FC inference drawn in (17) based on (16). To see the similarity, notice that the basic meaning of (25) is predicted to be equivalent to the disjunctive statement that you are allowed to either avoid clearing the table or evade doing the dishes, (27a), and that (26) is equivalent to the conjunction of two possibility statements. (You are allowed to avoid clearing the table and you are allowed to avoid doing the dishes, (27b).) (27)
a. Standard Meaning of (25) ¬(p ∧ q) ≡ ♦¬ (p ∧ q) ≡ ♦(¬p ∨ ¬q) ≡ ♦(¬p) ∨ ♦(¬q) b. Free Choice Inference ♦(¬p) ∧♦(¬q)
Just as in (16), the basic meaning does not explain the inference, and the gap is formally identical. Once again, we have to understand how a sentence that is equivalent to a disjunctive construction can be strengthened to something equivalent to the corresponding conjunction. 3.2
More generally under existential quantifiers
In the basic FC permission sentence in (16), disjunction appears in the scope of the existential modal allowed. Furthermore, as is well-known, FC extends to all constructions in which or is in the scope of an existential modal: (28)
a. The book might be on the desk or in the drawer. (= The book might be on the desk and it might be in the drawer) b. He is a very talented man. He can climb Mount Everest or ski the Matterhorn. (= He can climb Mount Everest and he can ski the Matterhorn.)
What has not been discussed in any systematic way is that this type of conjunctive interpretation extends also to some non-modal constructions:20 (29)
a. There is beer in the fridge or the ice-bucket. (= There is beer in the fridge and there is beer in the ice-bucket.) b. Most people walk to the park, but some people take the highway or the scenic route. (Irene Heim, pc attributed to Regine Eckardt, pc) (= Some people take the highway and some people take the scenic route.)
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c. This course is very difficult. In the past, some students waited 3 semesters to complete it or never finished it at all. (Irene Heim, pc) (= Some students waited 3 semesters to complete the course and some students never finished it at all.) It is thus tempting to suggest that conjunctive interpretations for disjunction are available whenever disjunction is in the scope of an existential quantifier (with the domain of quantification, worlds or individuals, immaterial). However, there are limitations: (30)
a. There is a bottle of beer in the fridge or the ice-bucket. ( = There is a bottle of beer in the fridge and there is a bottle of beer in the ice-bucket.) b. Someone took the highway or the scenic route. ( = Someone took the highway and someone took the scenic route.) c. This course is very difficult. In the past, some student waited 3 semesters to complete it or never finished it at all. ( = some student waited 3 semesters to complete the course and some student never finished it at all.)
As pointed out in Klindinst (2005), the relevant factor seems to be number marking on the indefinite. We might, therefore, suggest the following generalization: (31)
Existential FC: A sentence of the form ∃x [P(x) ∨ Q(x)] can lead to the FC inference, ∃xP(x) ∧ ∃xQ(x), as long as the existential quantifier, ∃x, is not marked by singular morphology.
3.3 More generally, under negation and universal quantifiers In (25) we saw an FC effect arising when conjunction is under the scope of negation and a universal modal (under the sequence, ¬). As illustrated in (32), and stated in (33), the effect arises also when is replaced by an ordinary universal quantifier: (32)
We didn’t give every student of ours both a stipend and a tuition waiver. 1. basic meaning: ¬∀x[P(x) ∧ Q(x)] ≡ ∃x¬ [P(x) ∧ Q(x)] ≡
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∃x [¬P(x) ∨¬Q(x)] ≡ ∃x ¬P(x) ∨∃x¬Q(x) 2. Free Choice: ∃x ¬P(x) ∧∃x¬Q(x) (33)
Conjunctive FC: A sentence of the form ¬∀x[P(x) ∧ Q(x)] can lead to the FC inference ∃x ¬P(x) ∧ ∃x¬Q(x).
In Sections 7–10 we will provide an account of our two generalizations ((31) and (33)) within a general theory of SIs that we will introduce in Section 6, based on a discussion, in Section 5, of Sauerland’s approach to SIs. But before we move on, it is important to rule out an alternative explanation of (25) and (32), in terms of wide scope conjunction. To understand the concern, focus on (25). One might think that this sentence has a logical form in which conjunction takes wide scope over the sequence ¬. If such a logical form were available, the inference in (26) would follow straightforwardly from the basic meaning, and would thus be unrelated to the FC effects that are distributed according to (31). But wide scope conjunction is not a probable explanation. One argument against such an explanation is based on the sentences in (34). If conjunction could take scope over the sequence ¬ in (25) (and over ¬∀ in (32)), we would expect it to be able to outscope negation in (34), an expectation that is not born out.21 (34)
a. I didn’t talk to both John and Bill. b. We didn’t give both a stipend and a tuition waiver to every student.
What I think we learn from (34) is that conjunction can appear to outscope negation only when a universal quantifier intervenes.22 This is expected if conjunction never outscopes negation, and the generalization in (33) is real. Another argument against wide scope conjunction comes from an additional inference we draw from sentences such as (25) and (32). In both cases we draw the inference that the alternative sentence with disjunction instead of conjunction is false. That is, we would tend to draw (35a) as an inference from (25), and (35b) from (32). These inferences are not expected if conjunction receives wide scope, but, as we will see later on, are expected if the phenomenon is derived along with other FC effects. (35)
a. You are required to clear the table or do the dishes. b. We gave every student of ours a stipend or a tuition waiver.
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Chierchia’s puzzle
The account of FC that I will develop will be based on a modification of a proposal made in Sauerland (2004) to deal with a puzzle discovered in Chierchia (2004).23 To understand the puzzle in greater detail, consider first (36) and its implicature that (36) is false. (36) John did some of homework. (36)’ John did all of the homework. As outlined in Section 1.2, this implicature can be derived by NG-MQ under the assumption that some and all are members of the same Horn-Set, (4b),24 from which it follows that (36) is an alternative to (36). NG-MQ, together with the assumption of an opinionated speaker, lead to the conclusion that the speaker believes that (36) is false. Consider next what happens when (36) is embedded as one of two disjuncts: (37)
John did the reading or some of homework.
This type of embedding was presented by Chierchia (2004) as a challenge to the neo-Gricean derivation of implicatures. As Chierchia points out, (37) should be an alternative to (37), and it would therefore seem that (with the assumption that the speaker is opinionated) we should derive the implicature that (the speaker believes that) (37) is false. (37)
John did the reading or all of homework.
This implicature, however, is clearly too strong. If a disjunctive sentence is false, then each of the disjuncts is false. When (37) is uttered, we do derive the inference that the second disjunct of (37) is false. However, we clearly do not derive a similar inference for the first disjunct (which is also the first disjunct of (36)). Chierchia’s challenge for the Neo-Griceans is to avoid the implicature that the first disjunct of (36) is false while at the same time to derive the implicature that the stronger alternative to the second disjunct is false: (38)
Let U be an utterance of p or q where q has a stronger alternative, q . a. Problem 1: to avoid the implicature of ¬p b. Problem 2: to derive the implicature of ¬q’
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Chierchia provides an account for the relevant generalization based on a recursive definition of strengthened meanings. I will not discuss his account, since I can’t figure out how to extend it to FC. Instead, I will discuss the neo-Gricean alternative, which also fails to account for FC, but, which can, nevertheless, be modified in order to provide a syntactic (non-Gricean) alternative that successfully extends to FC.25
5
Sauerland’s proposal26
As pointed out at the end of Section 1.2, the Horn-Set for disjunction in (4a) ({or, and}) cannot account for the Ignorance Inferences that are attested when a simple disjunctive sentence such as (1) is uttered. Sauerland suggests a remedy for this problem which also resolves Chierchia’s puzzle. To derive the appropriate Ignorance Inferences for (1), Sauerland suggests that the alternatives for a disjunctive statement include each of the disjuncts in addition to the corresponding conjunction: p
(39) Alt(p∨q) = p∨q
p∧q q
These alternatives, which are plotted to represent logical strength,27 derive (based on NG-MQ) the following inferences with respect to a speaker, s, who utters p or q, inferences which Sauerland calls Primary (or weak) Implicatures, PIs: (40)
PIs for p or q (based on NG-MQ) a. s does not believe that p is true. b. s does not believe that q is true. c. s does not believe that p and q is true. both a and b.
Already follows from
Given that s is assumed to believe that her utterance of p or q is true (Quality), we derive the Ignorance Inferences discussed in Section 1, that is, for each disjunct, we derive the inference that the speaker does not know whether or not it is true. To derive SIs, the principle of an Opinionated Speaker is employed, (8): (8)
Opinionated Speaker (OS): When a speaker, s, utters a sentence, S, the addressee, h, assumes, for every sentence S ∈Alt(S), that the
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beliefs of s determine the truth value of S , unless this assumption would lead to the conclusion that the beliefs of s are contradictory. This principle asks us to scan the set of alternatives that are stronger than S, and to identify those for which the assumption that the speaker is opinionated is consistent with our prior inferences based on Quality and NG-MQ. For each such alternative, the speaker is assumed to be opinionated, and given the relevant PI, a stronger inference is derived, namely that the speaker believes that the relevant alternative is false, an inference which Sauerland calls a Secondary Implicature (an SI, conveniently). As mentioned above, (40a,b) together with Quality, lead to ignorance with respect to p and to q. Hence, p and q is the only alternative for which the assumption that the speaker is opinionated is consistent with prior inferences. Therefore, only one SI is derived based on OS, namely the inference that the speaker believes that p and q is false: (41)
SI for p or q (based on OS) s believes that p and q is false.
Sauerland, thus, derives the following definition for the two relevant sets of implicatures: (42)
When a speaker s utters a sentence A, the following implicatures are derived: a. PIs = {¬Bs (A’): A’∈ ALT(A) and A’ is stronger than A} b. SIs = {Bs (¬A’): A’∈ ALT(A), A’ is stronger than A, and Bs (A)∧∩PI ∧ Bs (¬A’) is not contradictory}
Based on these definitions, a PI is derived for every alternative stronger than the assertion and an SI for a subset of the stronger alternatives for which an Ignorance Inference hasn’t already been derived (based on NG-MQ and Quality):28 (43)
Implicatures for p ∨q: p Alt(p∨q) = p∨q
p∧q q
a. PIs: ¬Bs (p), ¬Bs (q) b. SI: Bs ¬(p∧q)
The rest, ¬Bs (p∧q), follows
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Sauerland shows that this rather principled approach solves Chierchia’s puzzle once the lexical alternatives that derive the sentential alternatives in (39) are specified. The basic intuition is fairly straightforward. An utterance of p or q derives Ignorance Inferences that are inconsistent with the assumption that the speaker is opinionated about p, thereby solving problem (38a). Problem (38b) is solved as well, but seeing this requires precision about the relevant lexical alternatives and the way they determine sentential alternatives for complex disjunctions, such as (37). The starting point is the observation that in order to derive (39) the alternatives for disjunction must contain two lexical entries that are never attested:29
(44)
Horn-Set(or) = {or, L, R, and}, where pLq = p and pRq = q.
These four alternatives, when combined with the alternatives for some ({some, all}), yield 8 alternatives to (37), based on (5) above:30
(45)
Alt(r or sh) =
a. r ∨ sh b. r L sh ≡ r c. r R sh ≡ sh d. r ∧ sh e. r ∨ ah f. r L ah ≡ r g. r R ah ≡ ah h. r ∧ ah
To see what PIs and SIs are derived, it is useful to plot the alternatives in a way that indicates relative strength. But it is already easy to see how the two problems in (38) are solved. To repeat, problem (38a) is solved based on the observation that the speaker cannot believe that r is false if a PI ensures that she does not believe that sh is true and Quality ensures that she believes that r or sh is true. Problem (38b) is solved based on the observation that ah is a member of the alternative set (alternative g), and that an SI can be derived for this alternative (consistent with prior
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inferences): (46)
Implicatures for r ∨ sh: ALT(r ∨ sh) = r r∨ah
r∧ah ah
r∨sh
r∧sh sh
PI = ¬Bs (r∨ah), ¬Bs (sh), SI = Bs (¬ah), Bs (¬(r∧sh))
(the rest follow) (the rest, Bs ¬(r∧ah), follows)
5.1 Advantage of Sauerland’s proposal: embedding under universal quantifiers The Horn-Set in (44) plays two independent roles for Sauerland. It provides NG-MQ with the alternatives needed to derive the Ignorance Inferences for p ∨ q. These inferences explain (within the Neo-Gricean paradigm) the lack of certain SIs when scalar items are embedded within one of the disjuncts (problem (38)a). Furthermore, given (5), we can generate alternatives for complex disjunctive sentences (e.g. q for the sentence in (38)) that derive otherwise surprising SIs (problem (38b)). However, the system makes a further prediction. Specifically, it predicts that in certain contexts the two basic alternatives p and q will generate SIs rather than Ignorance Inferences. The relevant case involves embedding of disjunction under an upward monotone operator O such that O(p ∨ q) does not entail the disjunctive sentence O(p) ∨ O(q). For such an operator, the following is not contradictory. (47)
O(p∨q) ∧¬O(p) ∧¬O(q) ∧¬O(p∧q)
Hence, if s utters O(p ∨ q), an SI would be generated for each of the stronger alternatives (O(p), O(q), and O(p∧q)). Evidence that this prediction is correct comes from (48) and (49), which naturally yield the implicatures in (a) and (b).31
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Presupposition and Implicature in Compositional Semantics
You’re required to talk to Mary or Sue. Implicatures: a. You’re not required to talk to Mary. b. You’re not required to talk to Sue.
(49)
Every friend of mine has a boy friend or a girl friend. Implicatures: a. It’s not true that every friend of mine has a boy friend. b. It’s not true that every friend of mine has a girl friend.
These facts follow straightforwardly from the Sauerland scale:
(50)
Alt(∀x(P(x)∨Q(x)) = ∀x(P(x)∨Q(x))
∀xP(x) ∀x(P(x)∧Q(x)) ∀xQ(x)
PIs = ¬Bs (∀xP(x)), ¬Bs (∀xQ(x)) (the rest, ¬Bs ∀x(P(x)∧Q(x)), follows) SIs = Bs (¬∀xP(x)), Bs (¬∀xQ(x)) (the rest, Bs ¬∀x(P(x)∧Q(x)), follows) 5.2
But . . . what about FC?
Sauerland’s system makes yet another prediction about disjunction embedding, a prediction which is in direct conflict with FC. If disjunction is embedded under an upward monotone operator O such that O(p∨q) entails the disjunctive sentence O(p) ∨ O(q), the system predicts Ignorance Inferences with respect to O(p) and O(q). The reasoning is exactly identical to the basic case of unembedded disjunction: there is no way to assume that the speaker is opinionated about one of the alternatives O(p) and O(q) without contradicting the Primary Implicature that the speaker does not know that the other disjunct is true (given Quality). This does not seem to be the correct prediction for existential modals and plural existential DPs (generalization (31)). These operators, under their basic meaning, are both commutative with respect to disjunction (♦(p∨q) ≡ (♦p∨♦q); ∃x(P(x)∨Q(x)) ≡ ∃xP(x)∨∃xQ(x)). Hence Ignorance Inferences are predicted.
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95
You may eat the cake or the ice-cream.
Alt(51) = ◊(p∨q)
◊p ◊q
◊(p∧q)
PIs = ¬Bs (♦p), ¬Bs (♦q), ¬Bs ♦(p∧q) SIs = Bs ¬♦(p∧q) We’ve seen good arguments that FC should be derived as an implicature. However, under Sauerland’s system we derive Primary Implicatures (in bold) that contradict FC. The situation is quite interesting. The alternatives that K&S and Alonso-Ovalle appeal to in order to derive FC derive contradictory Ignorance Inferences in Sauerland’s system. If K&S are right, Sauerland’s system needs to change. However, K&S’s insight, if correct, needs to be embedded in a general system for implicature computation, one that can account for Chierchia’s puzzle, as well as for the emergence of Ignorance Inferences.
6
An alternative perspective
There are two problems with Sauerland’s system. On the one hand, it derives Ignorance Inferences that directly contradict the attested FC effect. On the other hand, it does not provide the basis for antiexhaustivity, which, if K&S are correct, is at the heart of FC. I will argue that the first problem teaches us that, contrary to the neo-Gricean assumption, Primary Implicatures do not serve the foundation for the computation of SIs. Instead, SIs are derived in the syntactic/semantic component via an exhaustive operator, as suggested in Section 1.3. Once a semantic representation is chosen, Ignorance Inferences are computed by the pragmatic system, based on the non-stipulative maxim of quantity (B-MQ). Without an exhaustive operator, incorrect Ignorance Inferences are computed in FC environments. However, once we modify the meaning of exh, based on Sauerland’s insights, the inferences can be avoided by a sequence of two exhaustive operators, which yield, in effect, antiexhaustivity, thereby solving the second problem. Furthermore, it turns out that FC is predicted in all the environments discussed in Section 3. 6.1
A new lexical entry for the exhaustive operator
Let’s start by reviewing our lexical entry for only and exh from Section 1.3. These entries ((14) and (15), repeated below) derive strong meanings that
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are in most cases equivalent to the basic meaning conjoined with the SIs derived by the neo-Gricean system. (52)
a. [[only]] (A<st,t> )(pst ) = λ w: p(w) = 1. ∀q∈NW(p,A): q(w) = 0 NW(p,A) = {q∈A: p does not entail q} b. [[Exh]] (A<st,t> )(pst )(w)⇔ p(w) & ∀q∈NW(p,A): ¬q(w)
However, predictions are sometimes different when the alternatives are not totally ordered by entailment. In particular, for the sets of alternatives that Sauerland has postulated, the lexical entries in (52) can derive contradictory results. To see this, consider the following dialogue: (53)
A: John talked to Mary or Sue. B: Do you think he might have spoken to both of them? A: No, he only spoke to Mary OR Sue.
Under (52)a, A’s final sentence should presuppose that the prejacent, John spoke to Mary or Sue, is true and that this is not the case for any of the (non-weaker) alternatives. Thus, if Sauerland is right about the lexical alternatives for disjunction, the two alternatives in (54) would both have to be false for the utterance to be true, which would, of course, contradict the presupposition. (54)
a. John talked to Mary. b. John talked to Sue.
This is a wrong result, which means that if Sauerland is right about the alternatives for disjunction, the lexical entries in (52) probably need to be revised.32 A revision of this sort is also needed based on much older observations due to Groenendijk and Stokhof (1984): (55)
a. Who did John talk to? Only Mary or SUE b. Who did John talk to? Only Some GIRL Groenendijk and Stokhof (1984)
Let’s focus on (55a). If (52a) is correct, the answer to the question should assert that every alternative not entailed by the prejacent, John talked to Mary or Sue, is false. This time the set of alternatives consists (most likely) of every proposition of the form John talked to x based on the denotation
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of the question, and the fact that the whole DP Mary or Sue is focused. In other words, the answer to the question in (55a) should entail the propositions that John didn’t talk to Mary and that he didn’t talk to Sue, which should contradict the presupposed prejacent. Groenendijk and Stokhof (1984), who noticed the problem, suggested a modification to the standard lexical entry for only, which was accommodated in Spector (2006) to the syntax we are assuming (based on Schultz and van Rooij (2006)): (56)
a. [[only]] (A<st,t> )(pst ) = λw: p(w) = 1. Minimal(w)(A)(p) b. [[Exh]](A<st,t> )(pst )(w) ⇔ p(w) & Minimal(w)(A)(p) Minimal(w)(A)(p) ⇔ ¬∃w’p(w’) = 1(Aw ⊂ Aw ) Aω = {p∈A: p(ω) = 1}
As pointed out by Spector (again, based on van Rooij and Schultz), this lexical entry can solve Chierchia’s problem. However, it yields results that contradict FC (see note 41). For this reason, I would like to suggest an alternative, one that is linked in a very direct way to Sauerland’s proposal. What we learn from Groenendijk and Stokhof is that there is something in the meaning of only ‘designed’ to avoid contradictions: only takes a set of alternatives A and a prejacent p, and attempts to exclude as many propositions from A in a way that would be consistent with the requirement that the prejacent be true. I would like to suggest that the basic algorithm is Sauerland’s, i.e. that propositions from A are excluded as long as their exclusion does not lead (given p) to the inclusion of some other proposition in A: (57)
a. [[only]] (A<st,t> )(pst ) = λw: p(w) = 1. ∀q∈NW(p,A) [q is innocently excludable given A→q(w) = 0] b. [[Exh]] (A<st,t> )(pst )(w)⇔ p(w) & ∀q∈NW(p,A) [q is innocently excludable given A→ ¬q(w)]
q is innocently excludable given A if ¬∃q’∈ NW(p,A) [p∧¬q⇒ q’] To see how this is supposed to work, consider an utterance of the disjunction p or q. Consider first what happens without an exhaustive operator, under the basic syntactic representation. Under such a representation, the sentence would assert that the disjunction is true and would be consistent with the truth of the conjunction (inclusive or). By
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B-MQ this would yield a variety of Ignorance Inferences, which might be implausible in a particular context, and if so, would motivate the introduction of an exhaustive operator, Exh(Alt(p or q))( p or q). Under this alternative parse the sentence would assert that the prejacent p or q is true and that every innocently excludable alternative is false. Assuming the Sauerland alternatives, we derive the simple ExOR meaning. None of the disjuncts is innocently excludable, since the exclusion of one will lead to the inclusion of the other, given the prejacent. Once again, we will circle the innocently excludable alternatives.
(58)
p Alt(p∨q) = p∨q
p∧q q
Excluding p will necessarily include q while excluding q will necessarily include p. p∧q is thus the only proposition in NW(p∨q, Alt(p∨q)) that can be innocently excluded given the set of alternatives in (58). Thus, it is the only proposition that is excluded and the derived meaning is the familiar ExOR. Before moving to FC, I would like to show how the lexical entries in (57b) replicates Sauerland results. But even before that, I would like to point out that Sauerland’s algorithm is not totally contradiction free, and that his assumptions should therefore be modified slightly. This modification would motivate a corresponding modification in (57). Consider the question answer pair in (59) from Groenendijk and Stokhof. Assume that the alternatives for A is the Hamblin denotation of Q, Alt((59)A), in (60). (59) (60)
Q: Who did Fred talk to? A: Some GIRL Alt((59)A) = {that Fred talked to x: x is a person or a set of people}
Assume also that there are more than two girls in the domain of quantification. If all these assumptions are correct, it would be possible (by
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Sauerland’s algorithm) to introduce an SI of the form Bs ¬ϕ, for every ϕ in Alt((59)A). Each SI of this sort is consistent with the set of PIs and Quality. However, once all the SIs are collected, the result is contradictory. The problem extends to the lexical entry for exh in (57) (and for only, if we look back at (55b)). Every member of Alt((59)A) is innocently excludable. Hence, if we were to append exh to (59)A, the result would be contradictory. One way to deal with this problem is to assume that the set of alternatives is always closed under disjunction (see Spector 2005, as well as note 29). An alternative, which is available when exh is assumed, is to eliminate additional elements from the set of innocently excludable propositions for a prejacent, p, given a set of alternatives A, I-E(p,A):
(61)
a. [[only]] (A<st,> )(pst ) = λw: p(w) = 1. ∀q∈I-E(p,A)→ q(w) = 0 b. [[Exh]] (A<st,t> )(pst )(w)⇔ p(w) & ∀q∈ I-E(p,A)→ ¬ q(w) I-E(p,A) = ∩{A’⊆A: A’ is a maximal set in A, s.t., A’¬ ∪{p} is consistent} A¬ = {¬ p: p∈A}
To see if a proposition q is innocently excludable, we must look at every maximal set of propositions in A such that its exclusion is consistent with the prejacent. Every such set could be excluded consistently as long as nothing else in A is excluded. Hence the only propositions that could be excluded non-arbitrarily are those that are in every one of these sets (the innocently excludable alternatives). Every proposition which is not in every such set would be an arbitrary exclusion, since the choice to exclude it, will force us to include a proposition from one of the other maximal exclusions (if the result is to be consistent), and the choice between alternative exclusion appears arbitrary.33 To see what results are derived by this lexical entry, it is probably best to go through the various cases we’ve discussed. Let’s first see how we would exhaustify p∨q given the Sauerland alternatives. The first step would be to identify the maximal consistent exclusions given the prejacent p∨q. If p is excluded, q must be true and vice versa. Hence, one maximal exclusion is {p, p∧q}, and the other is {q, p∧q}. The intersection is p∧q, hence, Exh(Alt(p∨q))(p∨q) = (p∨q) ∧¬(p∧q) = p∇q.
100 Presupposition and Implicature in Compositional Semantics
(62)
p p∧q
Alt(p∧q) = p∨q q
We circle (with dotted-lines) the maximal exclusions consistent with the prejacent, and we circle the intersection, the set of innocently excludable alternatives, with a completed line. Exh(Alt(p∨q))(p∨q) = (p∨q) ∧¬(p∧q) = p∇q. Consider now the exhaustification of (59)A under the assumption that the set of alternatives is the Hamblin-denotation of the question, (60). Assume that there are three girls in the domain of quantification, Mary, Sue, and Jane, and that there are no non-girls.34 Every maximal exclusion will include every member of the Hamblin-set but one of the following: (m) Fred talked to Mary, (s) Fred talked to Sue, and (j) Fred talked to Jane. So the intersection of all-maximal exclusions, the set of innocentlyexcludable alternatives, is the set of propositions of the form Fred talked to X, where X is a plurality of girls: (63)
Alt((59)A) = {Fred talked to x: x a person or a set of people} =
m
m&s
s
m&j
j
m&s&j
s&j
Exh(Alt((59)A))((59)A) = Fred talked to some girl ∧¬(m& s) ∧ ¬ (m& j) ∧¬ (s& j) = Fred talked to exactly one girl. 6.2
Replicating Sauerland’s results
Consider again Chierchia’s sentence r ∨ sh and its Sauerland alternatives. To see which alternative can be innocently excluded we have to identify the maximal (consistent) exclusions. The set of innocently excludable alternative is the intersection. The reader can consult the diagram in (64) to see that Sauerland’s results are replicated.
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(64)
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Alt(r ∨ sh) =
r r∨ah r∨sh
r∧ah ah r∧sh
sh
ah, r ∧ sh, r∧ah are the proposition in Alt(ss∨b) that can be innocently excluded given the set of alternatives: Exh(Alt(r∨sh))(r∨sh) = (r∨sh)∧¬ ah ∧¬(r∧sh) Consider next embedding under universal quantifiers. As discussed in Section 5.1, such embedding allows for the consistent exclusion of all the Sauerland-alternatives (other than the prejacent). Hence, there is only one maximal exclusion, which is excluded by exh:35 (65)
You’re required to talk to Mary or Sue. Implicatures: a. You’re not required to talk to Mary. b. You’re not required to talk to Sue.
(66)
Every friend of mine has a boy friend or a girl friend. a. It’s not true that every friend of mine has a boy friend. b. It’s not true that every friend of mine has a girl friend. ∀xP(x)
(67) Alt(∀x(P(x)∨Q(x)) = ∀x(P(x)∨Q(x))
∀x(P(x)∧Q(x)) ∀xQ(x)
Exh (Alt(∀x(P(x)∨Q(x)))(∀x(P(x)∨Q(x))) = ∀x(P(x)∨Q(x)) ∧¬∀xP(x) ∧¬∀xQ(x)
So the exhaustive operator as defined in (61)b, based on what’s needed for only, (61)a, derives the same results as Sauerland’s system (with the
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exception of cases such as (59) for which Sauerland’s system can derive contradictory implicatures). This is not surprising. The set of innocently excludable proposition is (modulo (59)) precisely the set of propositions for which Sauerland’s system yields SIs – for which SIs can be introduced innocently. However, there is an important architectural difference between the two systems, one that relates to the division of labor between syntax/ semantics and pragmatics. Under Sauerland’s neo-Gricean system, NG-MQ (and the PIs that it generates) is the underlying source of SIs. Under the syntactic alternative that we are considering, SIs have a syntactic source, and can serve to avoid Ignorance Inferences, which are computed post syntactically based on B-MQ. This architectural difference has empirical ramifications for FC. We’ve already seen that Sauerland’s system predicts Ignorance Inferences that contradict FC. We will see that under our syntactic alternative, the problem can be avoided by recursive exhaustification.
7
Recursive exhaustification and FC36
Suppose that exh is a covert operator which can append to any sentence. It is reasonable to assume that, in parsing (or producing) a sentence, exh will be used whenever the result fairs better than its counterpart without exh. One way in which a sentence with exh would be better than its exh-less counterpart is if the latter generates implausible Ignorance Inferences based on B-MQ. We thus predict the following recursive parsing strategy: (68)
7.1
Recursive Parsing-Strategy: If a sentence S has an undesirable Ignorance Inference, parse it as Exh(Alt(S))(S).37 Simple disjunction
Consider the disjunctive sentence in (69) (69)
I ate the cake or the ice-cream.
If this sentence is parsed without an exhaustive operator, B-MQ will generate the Ignorance Inference that the speaker doesn’t know what she ate (only that it included the cake or the ice-cream or both). This inference might seem implausible, and the hearer might therefore prefer the following parse, where C is the set of Sauerland-alternatives to the disjunctive sentence.
Free Choice and Scalar Implicatures
(70)
103
Exh(C)(I ate the cake or the ice-cream)
As we’ve seen already, the meaning of (70) is the ExOR meaning of (69). This meaning will now generate (given B-MQ) the Ignorance Inference that the speaker doesn’t know what she ate (only that, whatever it was, it included the cake or the ice-cream but not both). This, again, might seem implausible, and the hearer might employ the parsing strategy, again: (71)
Exh(C’)[Exh(C)(I ate the cake or the ice-cream)] where C’=Alt[Exh(C)(I ate the cake or the ice-cream)] = {Exh(C)(p) : p∈C}38
However, (71) ends up equivalent to (70). And further application of the parsing strategy is not helpful either. It will, thus, follow that there is no way to avoid the (sometimes undesirable) Ignorance Inference. To see this, we need to compute the set of alternatives, C’: (72)
C’ = {1. Exh(C) (p∨q), 2. Exh(C)(p), 3. Exh(C)(q), 4. Exh(C)(p∧q)} 1. Exh(C) (p∨q) = (p∨q) ∧¬ (p∧q) = (p ∧¬q)∨(q ∧¬p) 2. Exh(C)(p)= p∧¬q 3. Exh(C)(q)= q∧¬p 4. Exh(C)(p∧q) = p∧q (can be ignored since already excluded by the prejacent) Exh(C) (p∨q) = Exh(C)(p)∨Exh(C)(q)
Two simple observations are worth making. The first alternative, the prejacent of (71), is equivalent to the disjunction of the second and third alternative, and the fourth alternative is already excluded by the prejacent, and hence can be ignored. The relevant alternatives are thus the following: 2.Exh(C)(p)
(73)
C= Alt(Exh(p∨q)) = Exh(C)(p) ∨ Exh(C)(q) 3. Exh(C)(q) Exh(C)[Exh(C)(p ∨ q)] = Exh(C) (p ∨ q) = (p ∨ q) ∧ ¬ (p ∧ q)
If 2 is excluded, 3 must be true, and vice versa. Hence, meaning does not change with a second level of exhaustification, nor will it change when
104 Presupposition and Implicature in Compositional Semantics
exh is appended yet another time.39 There is thus no way to avoid what might be an undesirable Ignorance Inference. 7.2
The basic free choice effect
Consider now (74). (74)
You may eat the cake or the ice-cream.
Without an exhaustive operator, this sentence will generate the Ignorance Inference that the speaker doesn’t know what one is allowed to eat (only that the allowed things include the cake or the ice-cream or both). This might seem implausible, and the hearer might opt for another parse: (75)
Exh(C)(You may eat the cake or the ice-cream)
Given the Sauerland alternatives for disjunction, the set of alternatives, C, would be the following:40 (76)
Alt(74)
C = ◊(p ∨ q)
◊p ◊q
◊(p∧q) Notice ◊(p ∨ q) ⇔ ◊p ∨ ◊q but (crucially) ◊(p∧q) <≠> ◊p ∧ ◊q
♦(p∧q) is the only proposition in Alt(♦(p∨q)) that can be innocently excluded given the set of alternatives (excluding ♦p will necessarily include ♦q while excluding ♦q will necessarily include ♦p). Hence, the meaning of (75) in our modal logic formalization is ♦(p∨q)∧¬♦(p∧q). Crucially (75) is consistent with the free choice possibility, ♦p∧♦q, though it, of course, does not assert free choice.41 This new meaning will now generate the Ignorance Inference that the speaker doesn’t know what one is allowed to eat (only that the allowed things include the cake or the ice-cream but not both). This might seem implausible, and the hearer might employ the parsing strategy again: (77)
Exh(C’)[Exh(C)(You may eat the cake or the ice-cream)] where C’={Exh(C)(p): p∈C}
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This time, second exhaustification has consequences. To see this, we need to compute the meanings of the various alternatives: (78)
C’= {1. Exh(C) (♦(p∨q)), 2. Exh(C)(♦p), 3. Exh(C)(♦q), 4. Exh(C) (♦(p∧q))} 1. Exh(C) (♦(p∨q)) = ♦(p∨q) ∧¬♦(p∧q), crucially = (♦p ∧¬♦q)∨ (♦q∧¬♦p) 2. Exh(C)(♦p)= ♦p ∧¬♦q 3. Exh(C)(♦q)= ♦q ∧¬♦p 4. Exh(C) ♦(p∧q) = ♦(p∧q) (can be ignored since already excluded by the prejacent)
C9 = ◊(p∨q) ∧¬ ◊(p ∧ q)
◊p ∧¬ ◊q ◊p ∧¬ ◊q
There are now two propositions in C’ that can be innocently (and nontrivially) excluded. (Excluding Exh(C)(♦p) will not necessarily include Exh(C)(♦q), and excluding Exh(C)(♦q) will not necessarily include Exh(C)(♦p).) Hence, (79)
Exc(C’)(Exh(C) (♦(p∨q))) = ♦(p∨q))∧¬♦(p∧q) ¬(♦p ∧¬♦q) ¬(♦q ∧¬♦p) = ♦(p) ∧ ♦(q) and ¬♦(p∧q)
and and
We thus derive the FC effect for cases in which disjunction is embedded under existential modals.42
8
Other existential quantifiers
The key to the distinction between disjunction embedded under an existential modal and unembedded disjunction is that in the latter case the strongest alternative ♦(p ∧ q) is stronger than the conjunction of the two other alternatives ♦p and ♦q. Hence, the first layer of exhaustification is consistent with the later exclusion of Exh(C)♦p and Exh(C)♦q.43 This answers Aloni and van Rooij’s (2005) objection
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Presupposition and Implicature in Compositional Semantics
to Kratzer and Shimoyama (Section 2.2), and extends to account for embedding under existential quantifiers: (80)
a. There is beer in the fridge or the ice-bucket. b. People sometimes take the highway or the scenic route (Irene Heim, pc attributing Regine Eckardt, pc) c. This course is very difficult. Last year, some students waited 3 semesters to complete it or never finished it at all. (Irene Heim, pc)
Here, too, first exhaustification will be fairly weak ∃x(Px ∨ Qx)∧¬∃x(Px ∧ Qx) consistent with later exclusion of Exh(C)∃xPx and Exh(C)∃xQx, the cumulative effect of which entails ∃xPx ∧ ∃xQx.
9
Singular indefinites
At the moment the system makes wrong predictions for embedding under singular indefinites: (81)
a. There is a bottle of beer in the fridge or the ice-bucket. b. This course is very difficult. Some student waited 3 semesters to complete it or never finished it at all.
Right now, an FC effect is expected for this case as well. However, the expectation changes once an independently needed difference between plural and singular indefinites is factored in. Consider the sentences in (82). These sentences have the indicated implicature that the alternative assertion involving quantification over plural individuals is false: (82)
a. There is a bottle of beer in the fridge. Implicature: there aren’t two bottles of beer in the fridge. b. Some student talked to Mary Implicature: It’s not true that two students talked to Mary.
This implicature leads to the conclusion that a singular indefinite is a scalar item, with a plural (or dual) indefinite as an alternative: (83)
Horn-Set(Some NP-sing) = {Some NP-sing (henceforth ∃1), two NPs (henceforth ∃2)}
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With this Horn-Set, exh would, of course, derive the correct implicature for (82). But, interestingly, we also explain the lack of FC in (81). To see this consider (81a), and the set of alternatives derived by (5), (84). The alternative-set includes alternatives of the sort we’ve considered in (76) (upper diamond of (84)). But it also includes alternatives generated by replacing ∃1 with ∃2 (lower diamond of (84)). (84)
Alt((82)a) ∃1xP(x) ∃1x(P(x)∧Q(x)) ∃1xQ(x) ∃2xP(x)
C = ∃1x(P(x) ∨ Q(x))
∃2x(P(x) ∧ Q(x))
∃2x(P(x)∨Q(x)) ∃2xQ(x)
The set of innocently-excludable alternatives contains ∃1x (P(x)∧Q(x)) as well as ∃2x(P(x)∧Q(x)). Hence the exhaustification of (82a) is the following:44 (85)
Exh(C)( ∃1x(P(x)∨ Q(x))) = ∃1x(P(x)∨ Q(x)) & ¬∃1x(P(x)∧Q(x)) & ¬∃2x(P(x)∨ Q(x)) ⇒ ¬(∃1xP(x)∧∃1x Q(x))
This representation already contradicts the FC effect, a situation which, of course, cannot change by further exhaustification. We thus derive the generalization in (31). It is of course important to return to our computation of basic FC and make sure that nothing changes when universal quantifiers are introduced as alternatives to existential quantifiers (4b,d) (see note 40). I leave this as a task for the interested reader, though an equivalent computation will be carried out in (87) and (88), below, and the appendix will
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contain a theorem that will make all of our results transparent with fewer computations.
10
Other FC effects
Multiple exhaustification also accounts for the generalization in (33), i.e., it generates FC effects for the sequences ¬∧ and ¬∀∧ (introduced in Sections 3.1 and 3.3.) I will illustrate this for ¬∧, and allow the reader to verify that nothing changes when is replaced with ∀. Consider (25), repeated below as (86), with its FC inference, which (to repeat) is not predicted by the basic meaning. (86)
You are not required to both clear the table and do the dishes. 1. basic meaning: ¬(p∧q) ≡ ♦¬ (p∧q) ≡ ♦(¬p∨¬q) ≡ ♦(¬p) ∨♦(¬q) 2. Free Choice: ♦(¬p) ∧♦(¬q)
Once again, FC will follow after two layers of exhaustivity are computed. Let’s start with the first layer, which we compute based on the alternatives generated by Sauerland’s Horn-Set {∧, L, R, ∧} and the traditional Horn-Set {♦, }, (8d).
(87)
Alt((86))
¬ p ¬ (p ∨ q) ¬ q ¬◊p C = ¬ (p ∧ q))
¬ ◊(p ∨ q)
¬ ◊(p ∧ q) ¬◊p
Exh(C) (¬ (p ∧ q)) = ¬ (p ∧ q)) & (p ∨ q) & ◊(p ∧ q)
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If we decide to add another layer of exhaustification, we get the following result: (88)
Exh(C’)[Exh(C)(¬(p ∧ q)] = ¬(p ∧ q)) & (p ∨q) & ♦(p ∧ q) & ¬(¬p ∧ q) & ¬(¬q ∧ p) This yields the FC effect, based on the following equivalences: ¬(p ∧ q)) ≡ ♦¬p ∨ ♦¬q ¬(¬p ∧ q) ≡ ¬(♦¬p ∧ ¬♦¬q) ¬(¬q ∧ p) ≡ ¬(♦¬q ∧ ¬♦¬p)
11
Remaining issues
In Sections 6–10 we have seen how our two generalizations about the distribution of FC ((31) and (33)) can be derived based on recursive exhaustification under a Sauerland-inspired meaning for exh. But before concluding, I would like to discuss two apparent predictions of the account which are somewhat problematic. 11.1 ¬♦(p ∧ q) The lack of a conjunctive interpretation for p ∨ q was derived in Section 7 on the basis of the observation that the first layer of exhaustification excludes p∧q, an exclusion which cannot be overridden at the second level of exhaustification. The situation changes in FC environments, by the introduction of appropriate operators. When p∨q is embedded under an existential quantifier, e.g. ♦ (p ∨ q), the first level of exhaustification excludes ♦ (p ∧ q), a relatively weak exclusion, i.e. consistent with ♦ p ∧ ♦q. Hence it is possible (at the second level of exhaustification) to innocently exclude the exhaustive interpretation of ♦p and of ♦q. This proposal makes a clear prediction, or at least so it seems. Specifically, it predicts that FC will always be accompanied by the anticonjunctive inference ¬♦(p ∧ q). However, Simons (2005) claims that
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this prediction is false. Specifically, she presents (89) as a sentence that can produce FC while lacking an anti-conjunctive inference. (89)
Jane may sing or dance. (Simons 2005) Possible Reading: Jane may sing and Jane may dance, compatible with permission to do both.
I think I agree with Simons judgments, and the speakers I’ve consulted with also seem to agree. Interestingly, people seem to have a different feelings when asked about the FC effect that arises for the sequence ¬∀∧. Consider, again, (86). (86)
You are not required to both clear the table and do the dishes.
It seems quite hard to get rid of the inference that you are required to either clear the table or do the dishes. More specifically, although judgments of this sort are notoriously difficult, there doesn’t seem to be an interpretation which involves FC (i.e. entails that each chore is such that you are allowed to avoid it), which does not, at the same time, entail that at least one of the chores is requited.45 I will try to explain these facts on the assumption that in (89) each of the disjuncts could be exhaustified separately. Assume, as we have assumed above, that the alternatives for Exh could be determined (at least in the absence of scalar items) based on focus. (89) might now receive the following parse, where C and C are determined based on scalar items (as outlined above), and C1 , C2 are determined based on the focus value of the relevant prejacent. (89)
Exh(C )(Exh(C )(♦(Exh(C1 )(Jane sing) or Exh(C2 )(Jane dance)))).
Assume, further, that sing and dance are focused so that C1 = C2 . To simplify the exposition (but with no loss of generality) let’s assume that C1,2 has only two members {p = Jane sing, q = Jane dance}, with the following result: p! := Exh(C1 )(p) = p ∧ ¬q q! := Exh(C2 )(q) = q ∧ ¬p As we see in (90), we derive Simons’ reading.
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(90)
Exh(C )(Exh(C )(♦(p!∨q!))) = ♦(p!∨q!) ∧¬♦(p!∧ q!) ∧ ♦(p!) ∧♦(q!) = ♦(p!∨q!) ∧ ♦(p!) ∧ ♦(q!)
11.2
The scope of disjunction
The analysis of FC crucially depends on the assumption that in the relevant sentences disjunction receives narrow scope relative to the relevant existential quantifier. This assumption is corroborated by the contrast in (91). (91)
a. We may either eat the cake or the ice-cream. (+FC) b. Either we may eat the cake or the ice-cream. (−FC)
Larson (1985) has pointed out that either marks the scope of disjunction in constructions such as (91). The fact that FC is present only for (91a) thus corroborates the scopal assumptions made in this chapter. However, as pointed out in Zimmerman (2002), FC seems to be available in (92). (92)
You may eat the cake or you may eat the ice-cream.
I leave this as an unresolved problem, noting that the behavior with indefinites is different. (See Simons 2005, Alonso-Ovalle (2005), and Klindinst (2005) for relevant discussion.)46 (93)
12
a. Some students waited 3 semester to complete this course or never finished it at all. (+FC) b. Some students either waited 3 semester to complete this course or never finished it at all. (+FC) c. (Either) Some students waited 3 semester to complete this course or some students never finished it at all. (−FC)
Conclusion
In this chapter I’ve argued that Free Choice effects arise in two seemingly unrelated contexts: when disjunction is embedded under non-singular existential quantifiers, (31), and when conjunction is embedded under a universal quantifier which is, itself, c-commanded by negation, (33). Both FC effects follow from a method for exhaustification inspired by Sauerland’s solution for Chierchia’s puzzle, a method in which the notion of an innocently excludable alternative plays a central role.
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However, the proposal can work only if Sauerland’s basic idea is removed from its Neo-Gricean setting. The reason for this is rather plain. Under the Neo-Gricean assumptions, SIs are derived as strengthenings of inferences that follow from NG-MQ, a maxim which would derive Ignorance Inferences based on the symmetric alternatives generated by disjunction. Hence the Neo-Gricean assumptions derive Ignorance Inferences that conflict with the empirically attested Free Choice effects. A necessary conclusion, given the alternatives for disjunction, is that NG-MQ cannot be correct, and that there can be no primary implicatures which are computed on the basis of the relevant alternatives. The conclusion, itself, is an immediate consequence of a system in which pragmatic reasoning is based on all relevant alternative assertions (B-MQ), i.e. a pragmatic system which can only derive Ignorance Inferences. If B-MQ is correct, SIs must be derived within grammar, as argued for on independent grounds in Chierchia (2004) and Fox (2004). The grammatical mechanism needed for FC seems to be an exhaustive operator, along the lines of Groenendijk and Stokhof (1984), and Krifka (1995), which can apply recursively to a single linguistic expression (based on a Sauerland-inspired lexical entry). If this is correct, it might be useful to ask questions about possible external/functional motivations for exh. I hinted at the possibility that exh is needed to solve a communication problem that will arise very often in a pragmatic universe governed by B-MQ.
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Appendix In this appendix, I prove a rather simple theorem which should allow the reader to understand the results described in this chapter with fewer computations. I define an FC interpretation which I call AnEx (for Antiexhaustivity), and prove that this interpretation, if consistent, is the result of the 2nd layer of exhaustification. Let C be a set of propositions with p∈C. I = I-E(p,C) = Ø I’= (C\ I\{p}) = Ø AnEx = ∩{¬ExhC (q):q∈I’}∩ ExhC (p) Claim If AnEx = Ø (is consistent), Exh2 C (p) = AnEx. Proof ExhC (p) entails ¬q, for all q∈I Hence, ExhC (p) entails ¬ ExhC (q), for all q∈I Hence, AnEx entails ¬ExhC (q), for all q∈I
(by definition of Exh) (¬q entails ¬ ExhC (q)) (AnEx has ExhC (p) as a conjunct) Hence, AnEx = ∩{¬ExhC (q):q∈I’}∩{¬ExhC (q):q∈I}∩ExhC (p) = ∩{¬ExhC (q): q∈ C\ {p}} ∩ ExhC (p).
Hence, If AnEx is consistent, I-E(ExhC (p), C’) = C’ \{ExhC (p)} (where C’:= {ExhC (q):q∈C}) Hence, Exh2 C (p) = ∩{¬ExhC (q):q∈ C’ \{ExhC (p)}} ∩ ExhC (p) = AnEx (by definition of exh)
Notes ∗ This work is very much inspired by earlier proposals of Kratzer and Shimoyama,
Alonso-Ovalle, Gennaro Chierchia, an in particular by Kai von Fintel’s class presentation of’ Kratzer and Shimoyama. Special thanks go to Gennaro Chierchia, Kai von Fintel, and Irene Heim. I’ve also benefited from discussions with Luis Alonso-Ovalle, Jon Gajewski, Nathan Klindinst, Ezra Keshet, Angelika Kratrer, Fred Landsman, Philippe Schlenker, Benjamin Spector, and from comments and questions at the 2005 LSA summer institute (MIT and Harvard), and at colloquia at Umass Amherst, SUNY Stony Brook, Tel-Aviv University, and Tuebingen University.
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1. Following Gazdar (1979) and Sauerland (2004), I will sometimes use the verb know to describe Ignorance Inferences. This choice is problematic because of factivity inferences associated with know, which are clearly inaccurate. However, it’s not clear that there is a better choice: believe is problematic because of neg-raising. When I will find factivity particularly disturbing (or neg-raising sufficiently innocuous), I will favor belief-talk. My choices will, however, be far from systematic. The reader should bear all of this in mind and ignore factivity inferences associated with know, as well as the neg-raising property of believe. 2. Although I think that there is agreement that (2c) ought to be derived from principles of communication, there have been conflicting proposals concerning the precise derivation. As we will see below, the complications could be argued to follow from the neo-Gricean perspective on SIs. See our discussion in p. 12 of Gazdar (1979) and Sauerland (2004). 3. The relevant notion of informativity for a pragmatic account should probably be that of contextual-strength (i.e. logical strength given contextual presuppositions). For the consequence of this distinction to the theory of SIs, with a potential argument against (neo-)Gricean accounts, see Fox (2004), and Magri (2005). 4. The discussion in this section relies heavily on the introduction to pragmatics taught by Kai von Fintel and Irene Heim at MIT. 5. The assumptions made here about ‘relevance’ are the following: 1. If p and q are both relevant, so is ‘p and q.’ 2. if p is relevant, so is ‘not p.’ (To say that p is relevant is to say that the question Is p true or false? relevant.) 6. It is sometimes suggested that Grice’s Maxim of Manner (M) could be used to explain s s avoidance of p. Such a suggestion requires an ordering of linguistic expressions by which p would be more optimal than p from M’s perspective. For arguments against obvious orderings (various measures of complexity), see Matsumoto (1995), as well as Fox and Hackl (forthcoming). 7. Usually called Horn-Scales for bad reasons, as discussed in Sauerland (2004). 8. This definition, which comes from Sauerland (2004), is implicit in much earlier work, and is of course very similar to the definition of alternative sets in Rooth (1985). 9. This consideration would be weakened significantly if one could make sense of Alt(S) from the perspective of a general theory of language use. For efforts along these lines, See Spector (2006). 10. For a collection of some of the arguments in favor of this covert operator, see Fox (2004) and Chierchia (2005). 11. This statement is not always true, nor is it predicted to be. Scalar Items generate alternatives, but alternatives could be specified in other ways as well: by pitch-accent or by an explicit question. See the discussion of (59) below, as well as notes 29, 32, and 46. 12. λχ:ψ(χ).φ is a function defined only for objects of which ψ is true (convention from Heim and Kratzer 1998). 13. This assumption is most natural if Alt(S) is the focus value of S, which could follow if scalar items are assumed to be inherently focused, see Krifka (1995) for a possible implementation.
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14. In (18) the subject is reconstructed into both disjuncts, and to is omitted. This is done for expository purposes and, of course, does not affect meaning. 15. Although this chapter focuses on disjunction, the basic proposal can derive FC for the relevant indefinites as long as we assume (along the lines of Chierchia (2005)) that the relevant indefinites have the following alternatives: ALT(irgendein NP)= {irgendein NP’: NP’⊆ NP}∪{all NP’: NP’⊆ NP}. 16. I think that the interpretation is available in contexts that, more generally, allow for ‘intrusive’ implicatures of the relevant sort (See Cohen 1971, Horn 1989, Levinson 2000, Recanati 2003, among others): i. None of my students did SOME of the homework, They all did ALL of it. ii. No one is allowed to eat the cake OR the ice-cream. Everyone will be told what to eat.
17.
18. 19.
20.
21.
22.
23. 24. 25.
However, Kamp(1973) points out that it is easier for FC to ‘intrude’ into the antecedent of a conditional: If you are allowed to eat the cake or the ice-cream, you are pretty lucky. If K&S are correct, the FC interpretation of the antecedent would require an analysis involving an embedded implicature, as pointed out by Alonso-Ovalle, but without the ‘meta-linguistic’ feel that is sometimes associated with such intrusion. Unfortunately, I have nothing interesting to add. The latter possibility seems less plausible given the accumulation of evidence for ‘intrusive’ or ‘embedded’ implicatures (at least in non-downward entailing environments), see Chierchia (2004). The discussion in note 16 is of course, problematic, and more so from the Neo-Gricean perspective. It would instantiate the scheme if b and c were replaced by a single alternative, namely the disjunction of the two. Matsumoto argues that lexical items can be members of the same Horn-Set only if they denote functions of the same monotonicity. ∨ is upward monotone with respect to both arguments, but ∧¬ is downward monotone with respect to its right-hand argument. Skipping ahead to Sauerland’s Horn-set, L and R are upward (as well as downward) monotone with respect to their immaterial arguments. While working on this chapter, I have learned about two new papers about FC that make this same observation: KIindinst (2005) and Eckardt (this volume). If the distributor both is omitted the resulting interpretation is equivalent to wide scope conjunction. The correct account relies most likely on a ‘homogeneity’ presupposition (Fodor 1976, Gajewski 2005). In order to account for the difference between (32) and (34b), we would also have to say that inversion of the surface scope of conjunction and universal quantification is impossible in (34b), a consequence of Scope Economy, a principle I’ve argued for in Fox (2000). See also Lee (1995), and Simons (2002). And that the set does not include the ‘symmetric alternative’ to all, some but not all. Chierchia himself developed an account of FC which is quite similar to the account proposed here and is to some extent independent of his recursive procedure for implicature computation. Specifically, his account, like mine, is based on operators that apply to a prejacent and a set of alternatives. However,
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26. 27. 28. 29.
30. 31.
32.
33.
34.
35.
Presupposition and Implicature in Compositional Semantics the crucial operator for him is an ‘anti-exhaustivity’ operator, distinct from what might be responsible for implicature computation. Benjamin Spector made the same proposal, in a somewhat different (more generalized) format. A related proposal can be found in Lee (1995). If x is to the left of y with a connecting line, then x is weaker than y. From now on, I will circle those alternatives for which an SI can be derived consistently with Quality and NG-MQ. Spector (2003, 2006) suggests a different perspective. Specifically, he suggests that alternative sets are defined as the closure under ∧ and ∨ of the set of positive answers to a given question. The Sauerland alternatives for John talked to Mary or Bill would, thus, be derived (along with other useful alternatives) if the relevant question was who did John talk to? What FC teaches us, if my proposal is correct, is that there is no closure under ∧. Some of what I say could work if Sauerland’s alternatives were replaced by basic answers to a Hamblin-question closed under ∨. (Conjunction in unembedded cases will be part of the basic Hamblin denotation, derived from quantification over pluralities). One would still have to make sense of second layers of exhaustivity (see Section 11.2, note 46). r := John did the reading; sh := John did some of the homework; ah := John did all of the homework. In Fox (2003) I pointed out this prediction, but was not sure about the empirical facts. I was convinced by conversations with Benjamin Spector and the discussion in Sauerland (2005). Gennaro Chierchia (p.c.) points out that in the dialogue in (53) or might be receiving contrastive focus with conjunction, with the other alternatives (L and R) inactive. This possibility will not be helpful in explaining the avoidance of a contradiction in Groenendijk and Stokhof’s examples in (55). As pointed out to me by Angelika Kratzer and Fred Landman, the proposed mechanism for exhaustification is reminiscent of what is needed for counterfactuals in the premise semantics developed by Veltman (1977) and Kratzer (1981). In particular, the set of propositions that can be added as premises to a counter factual antecedent p is ∩{A⊆C: A is a maximal set in C, s.t., A ∪ {p} is consistent} where C is the set of all true propositions. Without non-girls, the answer is somewhat strange. That’s probably because questions presuppose that at least one answer (in the Hamblin sense) is true, and, thus, without non-girls, the answer just repeats the presupposition. Adding non-girls is thus crucial, but, it is trivial to see that it will not affect the result, in any interesting way; propositions related to non-girls will be excluded and things will be more difficult to draw, but other than that, it’s all the same. In conversation with Gennaro Chierchia, we’ve noticed that things are a little more complicated. As things stand right now, Alt(∀x(P(x)∨Q(x)) contains additional members: ∃x(P(x)∨Q(x)), ∃x(P(x)), and ∃x(Q(x)). The latter two make it impossible to innocently exclude ∀xP(x) and ∀xQ(x). There are various simple ways to correct for this problem. The obvious thing that comes to mind is to define Alt(S) so that it includes only stronger sentences than S. However, this would be a problematic move given data that is not discussed in this chapter. Here’s another possibility: Alt(S) is the smallest set, s.t. (a)
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S∈ Alt(S), and (b) If S ∈ Alt(S) and S can be derived from S by replacement of a single scalar item with an alternative, and S does not entail S , S ∈ Alt(S). 36. The core idea was developed during conversations with Ezra Keshet. 37. This should be modified to allow introduction of exh in a non-matrix position. (i) Recursive Parsing-Strategy: If a sentence S has an undesirable Ignorance Inference, try to append exh to some constituent X in S, i.e. modify the parse [S . . . X . . .] as follows: [S . . . Exh(Alt(X))(X) . . .]. We could also incorporate an economy condition of the sort alluded to in Section 2.1: (ii) Condition on exh-insertion: exh can be appended to a constituent X, only if the resulting sentence generates fewer Ignorance Inferences (based on B-MQ). 38. By the algorithm in (5). 39. The theorem in 1 is completely trivial, and the one in 2 (due to Benjamin Spector, p.c.) is less so: 1. Let C be a set of alternatives, Si , such that for each i exhaustification is trivial (i.e., Exh(C)(Si )⇔ Si ), then for each i, 2nd exhaustification is trivial (i.e., Exh(C’)(Exh(C)(Si )) ⇔ Exh(C)(Si ), where C’ = {Exh(C)(S): S∈C}) 2. due to Spector: Let C be a set of finite alternatives, Si , then there is an n∈N, s.t. ∀m>n, Exhn (C)(Si ) = Exhm (C)(Si ) Exhn (C)(Si ) := Exh(C’)Exhn−1 (C)(Si ), where C’ = {Exhn−1 (C)(S): S∈C}, and Exh1 (C)(S) = Exh(C)(S). 40. The set of alternatives is actually larger, including a variant of each alternative in C with a universal modal replacing the existential modal. This does not affect our results as the reader can verify. See the appendix, as well as (84) and (85) where a parallel computation is carried out with the full set of alternatives. 41. This exemplifies the difference between the lexical entry we are considering and the Groenendijk and Stokhof-type alternative in (56). Under (56), (75) would express a stronger proposition ♦(p ∨ q) ∧¬ (♦p∧♦q), which will be inconsistent with FC. 42. As pointed out in Simons (2005), ♦(p ∨ q) sometimes yields FC without the inference that ♦ (p∧q) is false. A solution to this problem will be discussed in Section 11.1. 43. The following is easily verifiable: Let C= {w, s, n, e} be a diamond set of alternatives going stronger from w to e (w is weaker than s, n, and e; s and n are logically independent and weaker than e), where w entails (s∨n). With such alternatives, 2nd exhaustification of w is vacuous (Exh2 (C)(w) ⇔ Exh(C)(w)) iff e ⇔ s&n. Furthermore, when 2nd exhaustification of w is not vacuous, Exh2 (C)(w) ⇔ s∧n∧¬e. 44. This explanation, however, depends on the assumption that the alternatives for ∃1 cannot be inactive when exh associates with ∨. An assumption of this sort was argued for on independent grounds in Chierchia (2005). 45. Note that both is crucial. See note 21.
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46. FC depends on the nature of the alternatives (e.g. E must be stronger than the conjunction of N and S, see note 43, or the appendix for a more general statement). The correlation with scope is predicted on the basis of the algorithm that determines alternatives, (5): at every level of exhaustfication, alternatives are determined on the basis of the structure of the prejacent. If (92) turns out to be indicative (rather than (91) and (93)), i.e. if it turns out that FC is possible even when disjunction has scope over the relevant existential quantifies, it would be possible to capture the facts with a relatively simple modification of the system I’ve proposed. In this chapter I’ve assumed that Alt(S) is determined either contextually or by the algorithm in (5), where the algorithm was crucial for the recursive step (see note 38). However, we could define a special rule for recursive exhaustification which would allow the rule to apply even when alternatives are contextually determined. Suppose that a sentence S is uttered in a context in which Q is the salient set of alternatives. If S were to be exhaustified (relative to Q), the syntactic representation would be Exh(Q)(S). We could now define the 2nd layer of Exhaustification, as follows: Exh2 (S):= Exh(C)[Exh(Q)(S)], where C= {Exh(Q)(ϕ): ϕ ∈Q}. Now (92) could receive an FC interpretation if Q could be the set of sentences of the form You can eat x, where x denotes a singular or plural individuals (perhaps with closure under disjunction, see note 29).
References Aloni, M. & R. van Rooij (forthcoming) ‘Free Choice Items and Alternatives’, Proceedings of KNAW Academy Colloquium: Cognitive Foundations of Interpretation. Alonso-Ovalle, L. (2005) ‘Disjunction in a Modal Space’, handout of a paper presented at NYU Polarity Workshop, http://www.people.umass.edu/luisalo/ alonso_ovalle_NYU_handout.pdf Cohen, L.J. (1971) ‘The Logical Particles of Natural Language’, in Y. Bar-Hillel (ed.), Pragmatics of Natural Language, 56–68. Dordrecht: D. Reidel. Chierchia, G. (2004) ‘Scalar Implicatures, Polarity Phenomena, and the Syntax/ Pragmatics Interface’, in A. Belletti (ed.), Structures and Beyond. Oxford: Oxford University Press. Chierchia, G. (2005) ‘Broaden your Views: Implicatures of Domain Widening and the “Logicality” of Language’, unpublished ms. University of MilanBicocca/Harvard University. Fodor, J. D. (1970) ‘Linguistic Description of Opaque Contexts’, MIT Dissertation. Fox, D. (2000) Economy and Semantic Interpretation, Linguistic Inquiry Monographs, 35, Cambridge, MA: MITWPL and MIT Press. Fox, D. (2003) ‘Implicature Calculation, Only, and Lumping: Another Look at the Puzzle of Disjunction’, handout, Yale University, http://web.mit.edu/linguistics/ www/fox/Yale.pdf. Fox, D. (2004) ‘Back to the Theory of Implicatures, Class 4 of Implicatures and Exhaustivity’, handouts from a class taught at USC, http://mit.edu/linguistics/ www/fox/pdf/class_4.pdf Fox, D. and M. Hacke (forthcoming) ‘The Universal Density of Measurement’, Linguistics and philosophy.
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Gajewski, J., (2005) ‘Neg-Raising, Polarity and Presupposition’, MIT Dissertation. Gazdar (1979) Pragmatics: Implicature, Presupposition, and Logical Form. New York: Academic Press. Grice, P. (1975) ‘Logic and Conversation’, in Cole, P. and J. Morgan (eds), Syntax and Semantics 3: Speech Acts. New York: Academic Press. Groenendijk, G., and Stokhof, M. (1984) ‘Studies on the Semantics of Questions and the Pragmatics of Answers’, PhD dissertation, University of Amsterdam. Hamblin, C. (1973) ‘Questions in Montague Grammar’, Foundations of Language 10: 41–53. Heim, I. and A. Kratzer (1998) Semantics in Generative Grammar. Malden, MA: Blackwell. Horn, L. (1969) ‘A Presuppositional Analysis of Only and Even’, CLS 5: 97–108. Horn, L. (1972) ‘On the Semantic Properties of Logical Operators in English’, PhD thesis, UCLA. Horn, L. (1989) A Natural History of Negation. Chicago: University of Chicago Press. Klindinst (2005) ‘Plurals, Modals, and Conjunctive Disjunction’, handout from SuB 10. Kratzer, A. (1981) ‘Partition and Revision: the Semantics of Counterfactuals’, Journal of Philosophical Logic 10: 242–58. Kratzer, A. and Shimoyama, J. (2002) ‘Indeterminate Pronouns: The View from Japanese’, in Y. Otsu (ed.), Proceedings of the Third Tokyo Conference on Psycholinguistics. Tokyo: Hituzi Syobo. Krifka, M. (1995) ‘The Semantics and Pragmatics of Polarity Items’, Linguistic Analysis 25: 209–57. Kamp (1973) ‘Free Choice Permission’, Proceedings of the Aristotelian Society, vol. 74, pp. 57–74. Kroch, A. (1972) ‘Lexical and inferred meanings for some time adverbs’, Quarterly Progress Report of the Research Laboratory of Electronics 104. MIT. Landman, F. (1998) ‘Plurals and Maximalization’, in S. Rothstein (ed.), Events and Grammar. Dordrecht: Kluwer. Larson R. K. (1985) ‘On the Syntax of Disjunction Scope’, Natural Language and Linguistic Theory 3: 217–64. Lee, Y. S. (1995) ‘Scalar Information and Semantics of Focus Operators’, PhD dissertation, U. T. Austin. Levinson, S. (2000) Presumptive Meanings. Cambridge, Mass: MIT Press. June 2003. Magri (2005) ‘Constraints on the Readings of Bare Plural Subjects: Syntax or Semantics’, ms MIT. Matsumoto, Y. (1995) ‘The Conversational Condition on Horn Scales’, Linguistics and Philosophy 18: 21–60. Recanati, F. (2003) ‘Embedded Implicatures’, ms, Institut Jean Nicod, Paris. Rooth, M. (1985) ‘Association with Focus’, PhD dissertation, University of Massachusetts, Amherst. van Rooij, R. (2002) ‘Relevance Only’. Proceedings of Edilog. van Rooij, R., and Schulz, K. (2004) ‘Exhaustive Interpretation of Complex Sentences’, Journal of Logic, Language and Information 13: 491–519.
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Saeboe, Kjell Johan (2004) ‘Optimal Interpretation of Permission Sentences, in Asatiani et al. (eds), Proceedings of the 5th Tbilisi Symposium on Language, Logic and Computation, Amsterdam and Tbilisi, 137–44. Sauerland, U. (2004) ‘Scalar Implicatures in Complex Sentences’, Linguistics and Philosophy, 27: 367–91. Sauerland, U. (2005) ‘The Epistemic Step’, talk presented at Experimental Pragmatics, Cambridge University, Cambridge, UK, April 2005. Schulz, K. and van Rooij (2006) ‘Pragmatic Meaning and Non-monotonic Reasoning: The Case of Exhaustive Interpretation’, Linguistics and Philosophy, 29:2, 205–50. Simons (2000) Issues in the Semantics and Pragmatics of Disjunction, NY: Garland Publishing. Simons (2005) Dividing Things Up: the Semantics of or and the Modal/or Interaction, Natural Language Semantics 13: 271–316. Spector, B. (2003) ‘Scalar Implicatures: Local or Global?’, paper presented at the workshop ‘Polarity, Scalar Phenomena, and Implicatures’, University of Milan – Bicocca. Spector, B. (2006) ‘Aspects de la pragmatique des opérateurs logiques’, PhD thesis, University of Paris 7. Veltman F. (1976) ‘Prejudices, Presuppositions and the Theory of Counterfactuals’, in Groenendijk, J. and Stokhof, M. (eds), Amsterdam Papers in Formal Grammar. Proceedings of the 1st Amsterdam Colloquium, pp. 248–81. University of Amsterdam. Zimmermann, E. (2000) ‘Free Choice Disjunction and Epistemic Possibility’, Natural Language Semantics 8: 255–90.
5 Partial Variables and Specificity Gerhard Jäger University of Bielefeld
In this chapter I propose a novel analysis of the semantics of specific indefinites. Following standard DRT, I assume that indefinites introduce a free variable into the logical representation, but I assume the the descriptive content of an indefinite DP is interpreted as a precondition for the corresponding variable to denote. Formally this is implemented as an extension of classical predicate logic with partial variables – variables that come with a restriction. This leads to a reconception of restricted quantification: the restriction is tied to the variable, not to the quantifier. After an overview over the major existing theories of the scope of indefinites, the central part of the chapter is devoted to develop a model-theoretic semantics for this extension of predicate logic. Finally the chapter argues that the notion of partial variables lends itself to the analysis of other linguistic phenomena as well. Especially presuppositions can be analyzed as restrictions on variables in a natural way.
1
Introduction
This chapter deals with the peculiar scope taking properties of indefinite DPs, which differ massively from other scope bearing elements. The theory that I am going to propose can be seen as a variant of the DRT approach in the version of Heim (1982), according to which the semantic contribution of an indefinite is basically a free variable, while its scope is determined by a non-lexical operation of existential closure. The crucial innovation lies in the treatment of the descriptive material of indefinites. While DRT analyzes it as part of the truth conditions, I will argue that it is to be considered as a precondition for the accompanying variable to denote. Existential closure serves a double 121
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function in my analysis: it binds a variable, and it turns its definedness conditions into truth conditions. While the basic idea of my analysis is taken from DRT, it also adopts crucial features of two other current approaches to the scope of indefinites, Tanya Reinhart’s choice function approach (Reinhart (1997), see also Winter (1997) and Kratzer (1998)), and the analysis of specificity as a presuppositional phenomenon that was independently proposed by several authors in recent years (among others by Cresti (1995); Reniers (1997); van Geenhoven (1998); Krifka (1998); Yeom (1998); Geurts (1999b)). So my proposal can be seen as an attempt to a synthesis. The structure of the chapter is as follows: in Section 2 I will briefly review the empirical phenomena we are going to deal with. Section 3 discusses the most important proposals from the literature. In Section 4 the idea of indefiniteness and partial interpretation will be presented, and I will show how this strategy overcomes the main problems that were discussed in the preceding sections. Section 5 explores the connection between partial variables and presuppositions, and Section 6 summarizes the findings.
2
Specificity and scope
The scope of quantifiers is usually clause bounded. This is illustrated in the following examples: (1)
a. If most experiments succeed, Jones will be happy. b. Jones thanked the student that had conducted experiments.
most
In (la) the quantifier most experiments is embedded in an if-clause. Its scope is restricted to this clause; there is no reading according to which it holds for most experiments x that Jones would be happy if x succeeds. Likewise, the quantifier is embedded in a relative clause in (b) and cannot take scope over the matrix clause. Most quantifiers – actually all strong quantifiers, as well as various weak quantifiers like exactly three students or at most three students – behave in a way similar to most experiments in this respect.1 Singular indefinites like an experiment and plain cardinal quantifiers like three experiments are exceptional though. They can escape scope islands. (2)
a. If an experiment succeeds, Jones will be happy. b. If three experiments succeed, Jones will be happy.
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(2a) has a reading according to which there is a certain experiment whose success would make Jones happy, and likewise for (b), where there are three specific experiments. The same applies to the example with a relative clause. (3a) has a reading where there is a specific experiment such that Jones thanked the students who had conducted it, and analogously for (b). (3)
a. Jones thanked the students that had conducted an experiment. b. Jones thanked the students that had conducted three experiments.
These facts were first discussed in Fodor and Sag (1982). They proposed that indefinites are ambiguous between a quantificational and a referential reading. According to them, apparent wide scope indefinites are not scope bearing at all, and the illusion of global scope arises through their referential interpretation. However, already Farkas (1981) showed that indefinites can take scope outside their local clause without having global scope, and the same point was made again in Abusch (1994). (4)
a. Every writer overheard the rumor that she didn’t write a book she wrote. (∀ > ∃ > ¬) (from Diesing (1992)) b. Every professor got a headache whenever there was a student he hated in class. (∀ > ∃ > whenever) (from Abusch (1994))
In the most prominent reading of (4a), the indefinite a book she wrote takes narrow scope with respect to every writer, but wide scope with respect to the rumor and the negation. In (b) a student he hated has scope over the matrix clause even though it is embedded in a when-clause, but it is outscoped by every professor. These intermediate scope readings do not depend on the presence of a bound pronoun inside the indefinite in question (as the previous examples might suggest). In (5) we have a reading where a boy is outscoped by every town, but outscopes every girl. (5)
In every town, every girl that a boy was in love with married an Albanian. (∀ > ∃ > ∀ > ∃) (from Cresti (1995))
It has occasionally been suggested (most recently by Dekker (2002); the idea can be traced back to Hintikka (1986), who confines this approach to indefinites modified by certain though) that these readings are referential
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despite appearance to the contrary. According to this view, referential indefinites can refer either to individuals or to Skolem functions, and the latter option leads to the illusion of non-global scope. Applied to (5) this means that a boy refers to a specific function f from towns to boys, and the relevant reading can be paraphrased as In every town t, every girl that f (t) was in love with married an Albanian. The intermediate scope reading is true if and only if there is a boy-valued function f which makes this paraphrase true. However, this strategy does not extend to cases where an indefinite with non-local scope is outscoped by a downward monotonic quantifier.2 Consider (6)
(Some centuries ago, many countries were monarchies, and you could cause a major crisis or even a civil war just by killing the king. Nowadays most countries are republics.) Less than one out of fifty states will cease to function if a particular person is killed.
In the most prominent reading of the last sentence, the indefinite a particular person takes scope over the if-clause, but is outscoped by less than one out of fifty states. Suppose the indefinite has a Skolem function reading. This means that a particular person refers to a Skolem function from states to persons, and the sentence can be paraphrased as Less than one out of fifty states s will cease to function if f(s) is killed. Now suppose that each state would cease to function if the head of the secret police gets killed, while the presidents and prime ministers are entirely unimportant. In this scenario, (6) would be false in the intermediate scope reading. However, there is a Skolem function f , mapping each state to its president, that would make the above paraphrase true. So the Skolem function reading is certainly not equivalent to the intermediate scope reading. In the above example, intuitions are fairly robust that the intermediate scope reading exists. The crucial point here is that specificity cannot be reduced to Skolem function readings in the general case. This is not to deny that indefinites can range over Skolem functions, as for instance in (7)
Most professors recommend a certain book, namely their PhD thesis.
The prominent reading of this sentence can be paraphrased as ‘There is a book valued Skolem function f , and most professors x recommend f (x), and f is the function that maps people to their PhD thesis.’ So Skolem
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function readings are possible, but this issue is orthogonal to the problem of specificity, and I will not consider it any further in this chapter.3 From this kind of consideration, Chierchia (2001) and Schwarz (2001), inter alia, concluded that the readings in question are genuine scope readings that cannot be reduced to referentiality. At this point a note on terminology is necessary: indefinites with exceptional scoping behavior are sometimes called ‘specific’, and I will follow this convention. Some authors, however, assume that specificity is more than just non-local scope. It has been suggested that the speaker has to have a particular individual ‘in mind’ which the indefinite in question refers to, or that some other relation of cognitive contact holds between the denotation of the indefinite and some agent. I leave these issues open as orthogonal to the problems I am concerned with in this article. For the time being, when I use the term ‘specific’, it simply means ‘having non-local scope’.
3
Solution strategies
The discussion of the last example shows that a standard scoping mechanism like Quantifier Raising or Cooper storage is not sufficient to account for the peculiarities of specific indefinites. Even if the empirical problem pertaining to the collective/distributive distinction could be overcome within such a framework, we would still be left with the conclusion that there are two versions of the scoping mechanism, one of which is clause bounded and the other unrestricted. This would be a conceptually unsatisfactory state of affairs. Alternatively one might conjecture that the scope of specific indefinites is not derived via the standard scoping mechanism but via some entirely different process. This assumption is only conceptually attractive though if this alternative process can be independently motivated and is not just stipulated for the analysis of specificity. The literature contains three families of proposals for unbound scoping mechanisms that are applicable to specificity. In this section I will briefly review them and point out their merits as well as their disadvantages. 3.1
Scope by existential closure
The literature on Discourse Representation Theory (most notably Heim (1982) and Kamp and Reyle (1993)), contains plenty of evidence that indefinites are non-quantificational. According to this theory, indefinites introduce a free variable into the semantic representation. This variable can be bound by some super-ordinate unselective binder (like an adverb of quantification). If the variable is not bound by such an
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operator, a default operation of existential closure applies that amounts to existential quantification over the else free variable. Existential closure in the sense of DRT is an obvious candidate for a mechanism to assign scope to indefinites. However, it leads to incorrect predictions if the indefinite has a non-trivial descriptive content. The following example from Reinhart (1995) illustrates this point. (8)
a. If we invite some philosopher, Max will be offended. b. ∃x((PHILOSOPHER’(x) ∧ INVITE’(WE’, x)) → OFFENDED’(MAX’))
Analyzing (8a) in a DRT-style way without employing any further scoping mechanisms leads to a semantic representation like (8b) for the specific reading of (a), where the existential impact of the indefinite some philosopher takes wide scope while the descriptive content remains in the antecedent of the conditional. As already observed in Heim (1982) for an analogous example, (8b) does not represent the truth conditions of the specific reading of (8a). The former is true if there is one non-philosopher, while (8a) in the wide-scope reading requires the existence of a philosopher x with the property that Max will be offended if we invite x. Since the existence of the non-philosopher Donald Duck is sufficient to verify (8b) but not (8a), this problem is sometimes called the Donald Duck problem in the literature. 3.2
Indefinites and choice functions
To overcome this and related problems, several authors proposed to employ choice functions for the analysis of indefinites (see for instance Reinhart (1992, 1995, 1997), Winter (1997), Kratzer (1998)). To cut a long story short, according to these theories, the semantic counterpart of an indefinite determiner is a variable over a choice function, i.e. a function that maps non-empty sets to one of their elements. This variable is subject to existential closure in a way akin to the treatment of free individual variables in DRT. (8a) would therefore come out as (9)
∃f (CH(f ) ∧ (INVITE’(WE’, f (PHILOSOPHER’)) → OFFENDED’(MAX’)))
The extension of the predicate constant CH is the set of choice function of type e, t, e, i.e. ∀f (CH(f ) ↔ ∀P(∃x.P(x) → P(f (P))))
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(9) in fact represents the truth conditions of (8a) in an adequate way. Generally speaking, the choice function approach solves several problems in one stroke. Since it uses unselective binding to assign scope to indefinites, it covers the fact that the scope of indefinites is structurally unrestricted. Also, the choice function mechanism makes sure that the existential impact of an indefinite is not unduly divorced from its descriptive content. (The interested reader is referred to Reinhart (1997) for details.) On the other hand, the choice function approach faces at least two serious problems. This has been pointed out at several places, for instance in Reniers (1997), Geurts (2000) and Endriss (2001). First, what happens if the extension of the descriptive content of an indefinite is empty? Consider (10)
If you push a certain red button on your computer, the electricity in the whole building will turn off.4
Suppose I’m just kidding – your computer is not connected to the power supply. There aren’t even any red buttons on your computer. It is, however, possible to switch off the electricity in the building by pushing a certain button in the basement. In this case the sentence is certainly false. The choice function approach predicts it to be true though. The extension of red button at your computer is the empty set. There are no restrictions about what kind of value a choice function returns when applied to the empty set. It could as well be the central switch in the basement, which would make the sentence true. Let us call this problem the empty set problem. The second problem arises if the descriptive content of an indefinite contains a pronoun that is bound by some super-ordinate quantifier. The following example (from Abusch (1994)) can serve to discuss this point. (11)
Every professori rewarded every student who read some book hei had recommended.
According to the choice function approach, the sentence should have a reading which can be represented as (12)
∃f (CH(f ) ∧ ∀x(PROFESSOR’(x) → ∀y(STUDENT’(y)∧ READ’(f (λz.BOOK’(z) ∧ RECOMMEND’(x, z))) → REWARD’(x, y))))
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Presupposition and Implicature in Compositional Semantics
Suppose two professor, a and b, happened to recommend exactly the same books to their students. Then the expressions λz.BOOK’(z) ∧ RECOMMEND’(a, z) and λz.BOOK’(z) ∧ RECOMMEND’(b, z) denote the same set, and thus the terms f (λz.BOOK’(z) ∧ RECOMMEND’(a, z)) and f (λz.BOOK’(z) ∧ RECOMMEND’(b, z)) denote the same individual. So the reading that is described in (12) can be paraphrased as follows: Every professor has a favorite book. He recommends this book (possibly along with other books), and he awards students that read his favorite book. Furthermore, if two professors recommend the same books, they have the same favorite book. It might be argued that this reading is actually there but hard to detect, because it is logically stronger than the ordinary narrow-scope reading (12). This is not the case anymore though if we use a downward monotonic quantifier in subject position, as in (13)
At most three girls visited a boy that they fancied.
According to the choice function approach, this sentence should have the reading given in (14a), which – ignoring the empty set problem for the moment – is truth-conditionally equivalent to (14b).5 (14)
a.