Formal Properties of Measurement Constructions

Formal Properties of Measurement Constructions

≥

Interface Explorations 12

Editors

Artemis Alexiadou T. Alan Hall

Mouton de Gruyter Berlin · New York

Formal Properties of Measurement Constructions

by

Kimiko Nakanishi

Mouton de Gruyter Berlin · New York

Mouton de Gruyter (formerly Mouton, The Hague) is a Division of Walter de Gruyter GmbH & Co. KG, Berlin.

앝 Printed on acid-free paper which falls within the guidelines 앪 of the ANSI to ensure permanence and durability.

Library of Congress Cataloging-in-Publication Data Nakanishi, Kimiko, 1975⫺ Formal properties of measurement constructions / by Kimiko Nakanishi. p. cm. ⫺ (Interface explorations ; 12) Includes bibliographical references and index. ISBN 978-3-11-018598-0 (cloth : alk. paper) 1. Grammar, Comparative and general ⫺ Syntax. 2. Semantics. 3. Grammar, Comparative and general ⫺ Quantifiers. 4. Grammar, Comparative and general ⫺ Comparative clauses. 5. Compositionality (Linguistics) I. Title. P291.N265 2007 415⫺dc22 2007042912

ISBN 978-3-11-018598-0 ISSN 1861-4167 Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.d-nb.de. ” Copyright 2007 by Walter de Gruyter GmbH & Co. KG, 10785 Berlin All rights reserved, including those of translation into foreign languages. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Cover design: Christopher Schneider, Berlin. Printed in Germany.

Acknowledgements

This book is a revision of my University of Pennsylvania Ph.D. thesis, completed in 2004. Although technical details have been changed and improved, the conceptual core of the thesis is the same. First, I should like to thank the people who contributed to the thesis. My deepest thanks go to Maribel Romero, who was my thesis supervisor and who introduced me to the field of formal semantics. Without her advice, encouragement, and friendship, I could not have come this far. I admire her enthusiasm as a linguist and her warm heart as a person. Thanks are also due to Satoshi Tomioka. In discussing Japanese data with Satoshi, I began to see how to examine the anatomy of the language. His guidance led me to some of the semantic issues discussed in this book. I always enjoyed having (linguistic and non-linguistic) discussions with him in my mother tongue. It was Tony Kroch who encouraged me to look at German saying ‘Japanese and German belong to different language families, but there are striking similarities between the two.’ Tony was right! I found that some constructions in Japanese and German share some semantic properties in common (as reported in this work), which made me seek an explanatory tool that applies to different linguistic phenomena. It was very fortunate that Roger Schwarzschild came to give a talk at Penn in 2002 when I was looking for a thesis topic. The material that Roger presented at that time turned into one of the core arguments of my thesis, which survives in this book. I am grateful for the numerous discussions (and great sushi) that we had in New Brunswick. I would like to thank Artemis Alexiadou, one of the editors of the Interface Explorations series, for encouraging me to publish my thesis as a book. My gratitude also goes to an anonymous reviewer from Mouton de Gruyter, whose extensive commentary lead to substantial improvements in the content of this work. I am grateful to Judith Alexander for proof-reading manuscripts and providing me with many helpful comments. My thanks also go to Ursula Kleinhenz, my editor at Mouton de Gruyter, who was very patient and supportive throughout the publication process. I would also like to thank Wolfgang Konwitschny, my production editor at Mouton de Gruyter, for editorial assistance at the final stage.

vi Acknowledgements I have benefited greatly from discussions with Irene Heim, Chris Kennedy, Angelika Kratzer, and Manfred Krifka. Their invaluable comments played a crucial role in developing central components of the book. Numerous other people have given feedback and comments on various aspects of the work presented here. Thanks are due to Klaus Abels, Artemis Alexiadou, Rajesh Bhatt, Jonathan Bobaljik, Christine Brisson, Benjamin Bruening, Daniel Büring, Dave Embick, Cornelia Endriss, Jane Grimshaw, Takao Gunji, Heidi Harley, Nobuko Hasegawa, Stefan Hinterwimmer, Pauline Jacobson, Elsi Kaiser, Makoto Kanazawa, Richard Kayne, Yoshihisa Kitagawa, Heejeong Ko, Bill Ladusaw, Richard Larson, Howard Lasnik, Luisa Martí, William McClure, Martha McGinnis, Jason Merchant, Shigeru Miyagawa, Yoichi Miyamoto, Bill Poser, Norvin Richards, Mamoru Saito, Uli Sauerland, Peter Sells, Yael Sharvit, Andrew Simpson, Anna Szabolcsi, Shoichi Takahashi, Yukinori Takubo, Chris Tancredi, Akira Watanabe, Alexander Williams, and Susi Wurmbrand. For help with German, I would like to thank Klaus Abels, Martin Kappus, Angelika Kratzer, Beatrice Santorini, Uli Sauerland, Tatjana Scheffler, and Augustin Speyer. I wish to thank Beatrice and Augustin in particular for spending so much of their time giving me their judgments. The following people provided me with the cross-linguistic data I needed: Judith Alexander, Dave Embick, Tom McFadden, James Mesbur, Marjorie Pak, and Alexander Williams for English; Josep Quer and Maribel Romero for Catalan; Artemis Alexiadou for Greek. Thanks are also due to Masahiko Aihara, Yukinori Go, Ken Hiraiwa, Yukiko Kambara, Sachie Kotani, Yuko Maki, Shoichi Takahashi, and Satoshi Tomioka for providing judgments of Japanese. Since August 2005, the University of Calgary Linguistics Department has been my home. I am grateful to my colleagues John Archibald, Susanne Carroll, Suzanne Curtin, Michael Dobrovolsky, Darin Flynn, Martha McGinnis, Robert Murray, Amanda Pounder, and Elizabeth Ritter for their moral support. I would also like to thank Elizabeth Mullaney and Linda Toth for assisting me in many ways. The University of Calgary has provided travel assistance and other research support. I am fortunate to have great friends, linguists and non-linguists. I wish to thank each one of them for their love and support. Thanks to Machiko and Tomoki Akazawa, Ayako and Jason Chan, Bridget Copley, Mutsuko Deguchi, Yoshihito Dobashi, Scott Douglas, Misato and Mitsuru Hara, Hazel (my dear cat in Philly), Shinichiro Ishihara, Takayuki Itoga, YoonKyoung Joh, Myuncheol Kim, Kazuaki Maeda, Tom McFadden, Michael

Acknowledgements vii

McKinlay, Emi and James Mesbur, Masashi Nomura, Keisuke Ogawa, Marjorie Pak, Peter Park, Bill Poser, Rocky (my dear cat in Calgary), Tatjana Scheffler, Etsuro Shima, Akiko Shimizu, Toshiro Takamiya, Alexander Williams, and Yoshihiro Yamada. For having made my life in Philly colorful and cheerful, I am grateful to Maciej Baranowski, John Bell, Yukinori Go, Elsi and Ryan Kaiser, Alan Lee, and Shining and TsanKuang Lee. Special thanks go to my dear friends Ken Hiraiwa, Yukiko Kambara, Sachie Kotani, Yuko Maki, Sayaka Nishikawa, and Makoto Tamua, and to my Tunisian friends Tarek Cherichi, Mohamed Tlaies, Youssef Rokhaimi, and Mohamed Elabidi. They were always there for me whenever I needed them. Finally, I would like to thank my parents Yasuko and Hisao Nakanishi, my younger sister Fumiko Nakanishi, my grandmother Utako Kuroda, and our new member of the family Masahiko Aihara, for their love, encouragement, and support. This book is dedicated to them. Kimiko Nakanishi Calgary, Alberta November, 2007

Contents

Acknowledgements 1. 1. 1.1. 1.2. 1.3. 2. 3. 3.1. 3.2. 4. 4.1. 4.2. 4.3. 4.4. 5. 2. 1. 2. 2.1. 2.2. 2.3. 2.4. 2.5. 2.6. 3. 3.1. 3.1.1. 3.1.2. 3.1.3. 3.1.4.

v

The semantic parallelism between the nominal and verbal domains Issues Formal properties of measurement constructions Measurement in the verbal domain and compositionality Cross-categorial distribution of measure phrases Overview Classification in the nominal domain The mass-count distinction and plurality of individuals Classifier languages Classification in the verbal domain The atelic-telic distinction Introducing Davidsonian event arguments Event theories and argument structure Plurality of events Summary of chapter 1

1 1 3 5 7 10 13 13 17 21 21 24 26 32 34

The semantic properties of non-split and split measure phrase constructions Split measure phrase constructions Monotonicity in the nominal domain The data Schwarzschild’s (2002, 2006) monotonicity constraint The application to Japanese and German data Pragmatic considerations Notes on non-monotonic constructions Summary of section 2 Monotonicity in the verbal domain The data Single-occurrence events Individual-level predicates Collective readings Summary of section 3.1

35 35 40 40 41 46 48 50 51 52 52 53 54 57 60

x Contents 3.2. 3.2.1. 3.2.2. 3.2.3. 3.3. 4. 4.1. 4.2. 4.2.1. 4.2.2. 4.2.3. 4.2.4. 4.3. 4.4. 5. 5.1. 5.1.1. 5.1.2. 5.1.3. 5.2. 5.2.1. 5.2.2. 5.2.3. 5.2.4. 5.3. 5.4. 5.5. 5.6. 6. 7. 3. 1. 2. 3.

The monotonicity constraint in the verbal domain (initial attempt) On single-occurrence events On individual-level predicates On collective readings Summary of section 3 Mechanism of event measurement (revised attempt) The proposal The analysis of the data The monoticiy constraint and single-occurrence events The monoticiy constraint and individual-level predicates The monoticiy constraint and collective readings Notes on the numeral one Monotonicity as a formal property of measurement constructions Summary Plurality and distributive-collective readings Previous studies on distributivity Distributive and collective predicates Distributivity as semantic plurality Excursion: “Temporal” distributivity Case 1: Collectivity with progressives The data The analysis Supporting evidence Notes on atelic predicates Case 2: Collectivity with together Case 3: Collectivity with collective predicates Case 4: Collectivity with internal arguments Summary of section 5 Notes on homomorphisms Summary of chapter 2

78 80 80 81 81 83 89 90 91 92 94 96 98 100 103 106 106 108

The syntax and compositional semantics of non-split and split quantifier constructions Introduction The syntax of non-split quantifier constructions The syntax of split quantifier constructions

109 109 110 116

60 61 64 66 67 67 69 73 74 74 75 77

Contents xi

3.1.

5.1. 5.2. 5.3. 6.

Stranding vs. adverbial analyses of floating quantifier constructions Distribution of FQs Morphology of FQs Semantics of FQs The adverbial analysis of FQs Summary The syntax of the floating quantifier construction in Japanese Problems with the transformational analysis Floating quantifiers as adjuncts of verbal predicates The structure of the floating quantifier construction Excursion: Notes on prosodic effects The syntax of Split NP Topicalization in German Summary of section 3 The compositional semantics of non-split and split measure phrase constructions Schwarzschild’s (2002, 2006) analysis of pseudopartitives Non-split measure phrase constructions Split measure phrase constructions Homomorphisms and argument structure: Internal and external split measure phrase constructions The formal properties of homomorphisms Homomorphisms in internal split measure phrase constructions The specification of a homomorphism Summary of chapter 3

4. 1. 2. 2.1. 2.2. 2.3. 2.4. 3. 3.1. 3.2. 3.3. 3.3.1. 3.3.2.

Comparatives and measure phrases as differentials Introduction Comparative constructions Adjectival comparatives Comparative quantification in the nominal domain The semantics of too Adjectival comparatives in Japanese The semantics of -sugiru ‘to exceed’ as a comparative quantifier Syntactic assumptions Adjectival comparatives Comparative quantification in the verbal domain Cardinality of events Homomorphism

3.1.1. 3.1.2. 3.1.3. 3.1.4. 3.1.5. 3.2. 3.2.1. 3.2.2. 3.2.3. 3.2.4. 3.3. 3.4. 4. 4.1. 4.2. 4.3. 5.

117 118 120 122 123 125 126 127 132 135 140 141 146 146 147 149 154 159 159 161 165 169 172 172 175 175 180 183 186 188 188 192 194 195 201

xii Contents 3.3.3. 3.3.4. 3.3.5. 3.4. 3.4.1. 3.4.2. 3.4.3. 3.4.4. 3.5. 4. 5.

Homomorphism to individuals Monotonicity in the verbal domain Summary of section 3.3 -Sugiru with overt degrees Gradable verbs Gradable adverbs and secondary predicates Adjectival modifiers Summary of section 3.4 Summary of section 3 Extension to too many / too much in English Summary of chapter 4

204 211 215 215 216 218 223 224 225 227 233

5.

Cross-linguistic aspects of quantification and compositionality 1. Introduction 2. Universality of monotonicity 3. Pragmatics of split quantifier constructions 3.1. Pragmatics of split NP topicalization in German 3.2. Reconsideration of the semantic properties 3.2.1. Type I contexts 3.2.2. Type II contexts 3.3. Summary of section 3 4. Quantification and compositionality 4.1. For the most part in English and hotondo ‘most’ in Japanese 4.2. Pluractional markers 4.3. Cross-categorial quantification 4.4. Summary of section 4 5. Quantification over events and over situations

235 235 236 239 239 244 244 246 248 249 249 251 253 254 255

6.

258

Concluding remarks

References Index

261 281

Chapter 1 The semantic parallelism between the nominal and verbal domains

1. Issues One of the most important problems for linguistics is describing how speakers produce and interpret sentences. Since Frege, it has been generally assumed that the meaning of a sentence depends on the meanings of the words in the sentence and on the ways in which they are combined: there is a set of syntactic rules in grammar that combines words to form complex expressions and further combines complex expressions to form even more complex expressions. For example, given the words all, the, students, and danced, syntactic rules combine the quantificational expression all and the noun phrase the students to form the complex expression all the students, they then combine the complex expression and the verb danced to form the sentence All the students danced. Along with syntactic rules, it is assumed that there is a set of semantic rules that interpret the whole by combining the interpretations of the corresponding words and phrases. Semantic rules apply when elements are combined by syntactic rules, that is, semantic rules apply in accord with syntactic rules. In the above example, when all and the students are combined by a syntactic rule, a corresponding semantic rule combines the denotation of all with the denotation of the students. The resulting complex denotation all the students then combines with the denotation of danced, yielding the denotation of the sentence All the students danced. In this way, the two components of grammar — syntax and semantics — are intimately related. In this book, I address the issue of how these two components interact with each other. The empirical data examined are the syntax and semantics of non-split quantifier constructions (where a quantifier is adjacent to the noun phrase that it quantifies over) and split quantifier constructions (where a quantifier appears apart from the noun phrase that it quantifies over) in various languages, focusing mainly on Japanese and German. Examples (1) (Japanese) and (2) (German) show that numerals in Japanese

2 The semantic parallelism between nominal/verbal domains and German can be adjacent to a noun phrase (NP), or they can be separated from the NPs that they seem to be associated with. The constructions in (1b) and (2b) are often referred to as the floating quantifier construction and Split NP Topicalization, respectively.1 (1)

a. Gakusei san-nin-ga kinoo odot-ta.2 student three-CL-NOM yesterday dance-PAST ‘Three students danced yesterday.’ b. Gakusei-ga kinoo san-nin odot-ta. student-NOM yesterday three-CL dance-PAST Roughly: ‘Three students danced yesterday.’

(2)

a. Drei Studenten haben gestern getanzt. three students have yesterday danced ‘Three students danced yesterday.’ b. Studenten haben gestern drei getanzt. students have yesterday three danced Roughly: ‘Three students danced yesterday.’

Given such examples, the questions arise: what is the semantic difference, if any, between split and non-split quantifier constructions? Further, what does this difference tell us about the interaction of the syntactic and semantic components of grammar? In the non-split quantifier constructions in (1a) and (2a), the quantificational expression three syntactically combines with, and thus semantically expresses measurement of, the nominal predicate students. This naturally leads us to ask whether the split quantifiers in (1b) and (2b) measure in the nominal domain in the same way as their nonsplit counterparts. The analysis demonstrates that, indeed, split quantifier constructions display certain semantic properties that non-split constructions lack. A second construction of interest to us is the Japanese comparative construction formed with -sugiru ‘to exceed’, which attaches to a verb and 1. The following abbreviations are used in this book: ACC = accusative case marker, ASP = aspectual marker, CL = classifier, COMP = complementizer, COP = copula, GEN = genitive, NM = nominalizer, NOM = nominative, PASS = passive, PAST = past tense, PROG = progressive, TOP = topic marker 2. Numerals in Japanese must be followed by a classifier, which semantically agrees with the nominal predicate. See section 3.2 for further details.

Issues 3

expresses excessiveness just as too much or too many does in English. In (3), although three does not directly combine with the nominal predicate book (at least on the surface), it necessarily denotes the excessive number of books (e.g., John was supposed to read two books, but he read five). (3)

John-ga hon-o kinoo san-satu John-NOM book-ACC yesterday three-CL ‘John read three books too many yesterday.’

yomi-sugi-ta. read-exceed-PAST

By examining the semantics and syntax of non-split/split quantifier constructions in Japanese and German and of comparative constructions in Japanese and English, this book investigates the following three larger issues in the fields of semantics and the syntax/semantics interface: 1) the formal properties of measurement constructions and of language universals, 2) a mechanism of measurement in the verbal domain and compositionality, and 3) a cross-categorial distribution of measure phrases. In the following, I describe these three issues in more detail.

1.1. Formal properties of measurement constructions Under the theory of generalized quantifiers, a classification of determiners has been achieved in terms of their formal properties (Barwise and Cooper 1981, Keenan and Stavi 1986, Keenan 1996). Such a classification gives a satisfactory explanation of several linguistic phenomena such as the distribution of expressions with negative polarity items (Ladusaw 1979), there-insertion (Higginbotham 1987, Keenan 1987, 2003), etc. Extending this approach, the book starts a new investigation of the formal properties of certain syntactic constructions, namely, measurement constructions in various languages. I begin the inquiry by examining the properties of nonsplit and split quantifier constructions in Japanese and German. Natural languages typically count or measure elements using quantificational expressions (numerals, measure phrases, classifier phrases, and quantifiers). Many languages allow a quantificational expression to combine syntactically with a nominal predicate to measure it, as shown in (1a) and (2a), satisfying a general assumption of compositionality that semantic rules apply in accord with syntactic rules. Some languages also have a syntactic configuration where a quantificational expression is split from its host NP, as in (1b) and (2b). As one of the core semantic properties of non-split and

4 The semantic parallelism between nominal/verbal domains split quantifier constructions, I make use of Schwarzschild’s (2002, 2006) notion of monotonicity: a measure function is monotonic relative to the denotation of some entity if and only if a measure obtained for that entity is larger than a measure obtained for proper subparts of it, and is smaller than a measure obtained for proper superparts of it. For example, the measure function “volume” is monotonic to the denotation of water, since, if a given quantity of water has a certain volume, proper subparts of it have lower volumes and superparts of it have higher volumes. The Japanese floating quantifier construction and German Split NP Topicalization, both of which will be shown to involve measurement of verbal predicates, pattern alike with respect to monotonicity in the verbal domain (Chapter 2). Specifically, I show that these two constructions have at least three semantic properties in common: (4)

a. (In)compatibility with single-occurrence events b. Incompatibility with individual-level predicates c. (Un)availability of collective interpretations

These properties can be uniformly explained by monotonicity with respect to verbal predicates. In contrast, the non-split quantifier constructions in (1a) and (2a) show properties uniformly explained by monotonicity with respect to nominal predicates. Since Japanese and German belong to different language families, the finding suggests that monotonicity is a universal property of measurement constructions that extends to related measurement constructions in other languages. The proposal that monotonicity is a property of measurement constructions is further supported by the Japanese -sugiru comparative construction in (3) and by the English comparative construction with too much (e.g., John slept too much), which also involves measurement in the verbal domain (Chapter 4). These constructions share with split quantifier constructions some semantic properties that are captured by monotonicity in the verbal domain. In this way, monotonicity categorizes various measurement constructions in different languages. Such a categorization is useful in that it enables us to explain the linguistic phenomena described in (4) (Chapter 2) and to make further predictions on some properties of related measurement constructions in other languages (Chapter 5).

Issues 5

1.2. Measurement in the verbal domain and compositionality It has been proposed that there are analogies between the mass-count distinction of nominal predicates and the atelic-telic distinction of verbal predicates (ter Meulen 1984, Bach 1986, Krifka 1989). By introducing event arguments (Davidson 1967), we are able to capture this intuition by expressing the parallelism algebraically: a lattice of individuals in the nominal domain and a lattice of events in the verbal domain (Link 1983, Bach 1986, Krifka 1989, Landman 2000). This book provides empirical data where this semantic parallelism has an explanatory power. Specifically, the data from split quantifier constructions in Japanese and German (Chapters 2 and 3) and from comparative constructions in Japanese and English (Chapter 4) illustrate that a semantic mechanism based on parallelism provides a satisfactory account of how the grammar of measurement works. Thus, by examining these data, we are able to establish the theoretical and empirical validity of the semantic parallelism between nominal and verbal predicates. The discussion begins with Schwarzschild’s (2002, 2006) claim that measure functions in pseudopartitives (e.g., three liters of water) measure individuals in the nominal domain and that this measurement must obey monotonicity with respect to nominal predicates. I show that the same mechanism and monotonicity requirement of the measurement in the nominal domain can be observed in non-split quantifier constructions (Chapter 2). That is, non-split quantifiers express measurement of individuals denoted by the host NP. As non-split quantifiers combine directly with their host NP in the syntax (Chapter 3), we see that the syntax and semantic of non-split quantifier constructions operate in tandem: a non-split quantifier syntactically combines with, and thus semantically expresses measurement of, a nominal predicate. Turning to split quantifier constructions, san-nin ‘three-CL’ in Japanese (1b) and drei ‘three’ in German (2b) specify the number of relevant students, roughly meaning the same as their non-split counterparts in (1a) and (2a). This may make sense if we assume that split quantifier constructions are transformationally derived from their non-split counterparts. Specifically, the NP initially forms a nominal constituent with the split quantifier as in (1a) and (2a), and then moves higher in the structure, stranding the quantifier, which yields (1b) and (2b). However, based on the semantic restrictions in (4) that split quantifier constructions impose on the verbal predicate, I argue that split quantifiers differ from their non-split counter-

6 The semantic parallelism between nominal/verbal domains parts in that they express measurement of events in the extension of the VP (and also of individuals in the extension of the NP) (Chapter 2). Furthermore, I present some problems with the transformational account for split quantifier constructions and show that, in the syntax, a split quantifier may first combine with a verbal predicate, and not directly with a nominal predicate (Chapter 3). If we adopt this syntactic structure, we obtain the following simple picture: a split quantifier syntactically combines with, and thus semantically expresses measurement of, a verbal predicate. The generalization is that, in non-split and split quantifier constructions, a quantificational element measures the predicate with which it combines in the syntax. Although there have been a large number of studies on measurement in the nominal domain, not as much is known about measurement in the verbal domain. This book attempts to provide a formal mechanism for measurement in the verbal domain. As discussed above, a split quantifier syntactically combines with, and semantically operates on, a verbal predicate, yet there is a strong intuition that it somehow measures a nominal predicate as well. For instance, the split quantifiers in (1b) and (2b) necessarily express the number of students. In this respect, a split quantifier is different from other linguistic devices that express measurement only of a verbal predicate (e.g., n-times in I saw Mary three times (Chapter 2: section 4), morphemes for verb pluralization in some languages (Chapter 5: section 4.2)). Thus, split quantifier constructions pose a larger question of how the compositionality of grammar can be maintained. I argue that, in split quantifier constructions, there is a semantic mapping — a homomorphism — from events to individuals, and that the measure function applies to individuals mapped from events (Chapter 2). In this way, split quantifiers indirectly measure events by measuring individuals. The proposed mechanism, i.e., direct measurement of individuals mapped from events, amounts to direct measurement of events (see Chapter 2: section 4 for details). Thus, we can maintain a tight link between syntactic and semantic components: a split quantifier syntactically combines with, and thus semantically operates on, a verbal predicate with the help of a homomorphism from events to individuals. The current mechanism enables us to account satisfactorily for some characteristic semantic properties of the split quantifier constructions in Japanese and German (summarized in (4) above). Moreover, the proposed analysis makes a strong case that event arguments exist in the grammar and that there is a semantic correlation between individuals in the nominal domain and events in the verbal domain. I argue further that some comparative constructions in Japanese and

Issues 7

English also involve measurement in the verbal domain (Chapter 4). Specifically, I show that split quantifier constructions in Japanese and German and comparative constructions in Japanese and English have some semantic properties in common, which are uniformly captured by monotonicity with respect to verbal predicates. I claim that measurement in the verbal domain, namely, the measurement process that makes use of a homomorphism, imposes the monotonicity restriction on these constructions, and that this accounts for why they share some semantic properties. A homomorphism is not an ad hoc mechanism that applies only to split quantifier constructions and to some comparative constructions. For instance, two types of homomorphism h, namely, the temporal trace function (h from events to times) and the spatial trace function (h from events to paths), have been used as a powerful explanatory tool in studies by Krifka (1989, 1992, 1998) and by Lasersohn (1995), most notably (Chapter 2: section 6 and Chapter 5: section 4.2). These functions are independently required to explain a variety of cross-linguistic phenomena. I show that comparative constructions make extensive use of these two types of homomorphisms as well as a homomorphism from events to individuals (Chapter 4).

1.3. Cross-categorial distribution of measure phrases The grammar of measurement is closely tied to so-called measure phrases (MPs) such as two feet, three liters, etc. It has been noted that MPs in English have a wide distribution; they can co-occur with various syntactic categories, as illustrated in (5) (Jackendoff 1977). Examples (6) and (7) show that MPs in German and Japanese are also cross-categorial. (5)

a. b. c. d. e.

two feet long two feet longer two feet of rope two feet away walk two feet

(6)

a. zwei Meter lang two meter long ‘two meters long’

8 The semantic parallelism between nominal/verbal domains b. zwei Meter länger two meter longer ‘two meters longer’ c. zwei Meter Seil two meter rope ‘two meters of rope’ d. zwei Meter entfernt two meter removed ‘two meters away’ e. zwei Meter laufen two meter walk ‘walk two meters’ (7)

a. ni meetoru nagai3 two meter long ‘two meters longer’ b. roopu ni meetoru rope two meter ‘two meters of rope’ c. ni meetoru hanarete two meter away ‘two meters away’ d. ni meetoru aruku two meter walk ‘walk two meters’

Schwarzschild (2002, 2006) proposes that, despite the seemingly crosscategorial syntactic distribution of MPs, all instances of MPs have exactly the same semantics: MPs are always predicates of scalar intervals. His proposal is based on Schwarzschild and Wilkinson’s (2002) analysis of comparatives: MPs in comparatives are predicates of parts of scales. For instance, in this table is two feet longer than that table, two feet is a property of an interval of a certain length. If MPs are predicates of intervals, the question is how to obtain intervals in examples such as two feet of rope, where the existence of intervals is not as transparent as in the case of comparatives. Schwarzschild (2002, 2006) claims that, by examining the relation between a MP and the element to 3. In Japanese, the combination of a MP and an adjective is always interpreted as a comparative. See Chapter 4: section 2.4 for details.

Issues 9

which the MP is related to, we obtain a measure function µ, which is a measurement scheme. This measure function maps a member in the extension of the measured element to an interval on a scale. For instance, in two feet of rope, the measure function “length” obtains by examining how two feet is related to rope. This measure function maps an individual x in the extension of rope to an interval on the length scale which has the property [[two feet]], that is, two-feet(µ(x)). The denotation of two feet of rope under Schwarzschild’s analysis is given in (8a). Assuming that there is a parallelism between nominal and verbal predicates (see section 1.2 above), we can carry this analysis over to examples such as walk two feet, where the MP applies to an event. The denotation is provided in (8b) (see Chapter 3: section 4 for details). (8)

a. [[two feet of rope]] = λxe. rope(x) ∧ two-feet(µ(x)), where µ: length 4 b. [[walk two feet]] = λev. walk(e) ∧ two-feet(µ(e)), where µ: spatial length 5

In this book, I add another occurrence of MPs to the paradigms in (6) and (7), that is, MPs in split quantifier constructions, repeated in (9) ((a) for Japanese, (b) for German). (9)

a. Gakusei-ga kinoo san-nin odot-ta. student-NOM yesterday three-CL dance-PAST Roughly: ‘Three students danced yesterday.’ b. Studenten haben gestern drei getanzt. students have yesterday three danced Roughly: ‘Three students danced yesterday.’

(= (1a))

(= (2a))

I show that MPs in these constructions have the same semantics as the MPs occurring in different environments, supporting Schwarzschild’s (2002, 2006) claim for uniform semantics of MPs. I further show that the analysis 4. In the following, I follow Montague’s notation for type theory: e (the type of individuals) and t (the type of truth values) are the basic types. I also make use of d (the type of degrees) and v (the type of events). If σ and τ are semantic types, then <σ,τ> is a semantic type. Nothing else is a semantic type. 5. More precisely, there needs to be a homomorphism h (structure-preserving mapping) from events to their paths, hence the measure function µ applies to h(e), yielding the sub-formula µ(h(e)). See Chapter 2: section 4 for details.

10 The semantic parallelism between nominal/verbal domains proposed in (8) extends to (9) (Chapter 3: section 4). In particular, the MP in (9) as well as the ones in (8) first combines with a measure function µ, and then the complex predicate consisting of the MP and µ combines with a measured predicate P, as in (10). (10) P (NP, VP, …) MP

µ

The denotations of measure functions combining with a NP and with a VP are proposed in (11a, b).6 Based on these denotations, we can obtain the schema in (11c) that captures the cross-categorial nature of measure functions. Thus, while MPs have a uniform semantics regardless of where they occur, measure functions are cross-categorial, as in (11). (11) a. [[µNP]] = λD.λP<e,t>.λxe. P(x) ∧ D(µ(x)) b. [[µVP]] = λD.λP.λev. P(e) ∧ D(µ(e)) c. [[µ]] = λD.λP<σ,t>.λzσ. P(z) ∧ D(µ(z))

2. Overview In the rest of this chapter, I review previous studies on the parallelism between the nominal and verbal domains and further examine the algebraic parallelism between the two. A common way to represent the extension of a NP is to use a lattice of individuals (Link 1983) (see section 3.1 for the definition of a lattice). Krifka (1989) proposes that, by introducing event arguments (Davidson 1967), a lattice of events can be defined in a fashion analogous to the definition of a lattice of individuals. In this way, we can assume that there is an algebraic parallelism between nominal and verbal domains. Chapter 2 examines the semantic properties of non-split and split quantifier constructions in Japanese and German. The central claim of this chapter is that the two constructions differ in their domains of measurement: non-split quantifier constructions involve measurement of individuals in the 6. In Chapters 3 and 4, I assume that MPs are names for degrees, rather than predicates of scalar intervals. Thus, the variable D of type in (11) should be replaced by the variable d of type d (where d is the type of degrees). However, the choice between the two is not crucial for the discussion here.

Overview 11

nominal domain, while split quantifier constructions involve measurement of events in the verbal domain as well as of individuals. This claim is based on the observation that, while both constructions are subject to semantic restriction in the nominal domain, only the split measure phrase constructions are sensitive to restrictions in the verbal domain. These semantic restrictions can be explained by a uniform semantic constraint on the measure function, namely, Schwarzschild’s (2002, 2006) monotonicity constraint. Specifically, I argue that the measure function in the two constructions at issue is subject to the monotonicity constraint, and that we observe different semantic restrictions depending on whether the measure function applies to a nominal or to a verbal domain. I further argue that the mechanism of event measurement requires a semantic mapping from events to individuals, and thus the measure function may apply to individuals mapped from events. This mechanism enables us to account for at least three characteristic semantic properties of the split quantifier construction: (in)compatibility with single-occurrence events, incompatibility with individual-level predicates, and (un)availability of collective readings. Chapter 3 examines the syntax and compositional semantics of non-split and split quantifier constructions. I propose that non-split and split quantifiers can be analyzed as adjuncts to nominal predicates and to verbal predicates, respectively. That is, in the syntax, non-split quantifiers directly combine with nominal predicates, while split quantifiers directly combine with verbal predicates. I then propose compositional semantics for the two constructions and show how their syntactic structures give rise to their semantic properties explained by monotonicity. While MPs are semantically uniform, measure functions are cross-categorial (as in (11)), which accounts for a wide distribution of MPs (as in (5)–(7)). Furthermore, this chapter discusses the formal properties of a homomorphism from events to individuals, which leads us to the question of which function serves as a homomorphism from events to individuals. In Chapter 4, I extend the analysis of non-split and split quantifier constructions to the comparative construction in Japanese formed with -sugiru ‘to exceed’. I argue that -sugiru involves comparative quantification over events, which requires a homomorphism from events to other domains (individuals, paths, etc.). Thus, the -sugiru comparative construction and split quantifier constructions discussed in Chapters 2 and 3 make use of the same mechanism of measurement in the verbal domain: the relevant measure function applies to events, where there is a homomorphism from events to other domains. This analysis is supported by the fact that the -sugiru

12 The semantic parallelism between nominal/verbal domains comparative is also subject to restrictions in the verbal domain just as split quantifier constructions are. The analysis proposed for the -sugiru comparative in Japanese further extends to the comparative construction in English involving too much or too many (e.g., John read too many books). Chapter 5 examines cross-linguistic aspects of quantification and compositionality. Since Japanese and German are typologically distinct languages, the similarities between the two discussed in Chapter 2 suggest that the categorization of measurement constructions based on monotonicity may be universal. This point is enforced by further cross-linguistic data on monotonicity. In particular, I show that the monotonicity analysis applies to split quantifier constructions in Greek and Catalan. However, crosslinguistic split quantifier constructions are not uniform in every respect: the German Split NP Topicalization, but not the Japanese floating quantifier construction, is subject to a specific pragmatic constraint. I examine whether the semantic properties of the German Split NP Topicalization initially explained by monotonicity follow from this pragmatic constraint. Another issue discussed in this chapter is whether there are any other constructions in different languages to which the proposed analysis extends. I examine data from for the most part in English and pluractional verbs in some languages, and show that these constructions also involve a homomorphism from events to other domains. Lastly, I briefly compare the quantification over events discussed in this book and quantification over situations discussed in the previous literature on the so-called quantificational variability effect with adverbs of quantification (e.g., A blue-eyed bear is always intelligent). I show that these two types of quantification differ in important aspects. Throughout the book, following general practice, I adopt the model of grammar assumed in the Government and Binding Theory (Chomsky 1981), schematized in (12). (12)

DS SS LF

PF

The two levels of syntactic representation — DS (deep structure) and SS (surface structure) — are related to each other by transformations. For instance, the sentence Will John come? is represented as in [IP John will [VP

Classification in the nominal domain 13

come]] at DS, and the surface order [CP will1 [IP John t1 [VP come]]] at SS is obtained by applying the movement of will (which leaves a trace t at its original position). SS is the input for both Phonetic Form (PF) and Logical Form (LF), the two levels that constitute the interface between language and other congnitive systems. PF is the phonetic realization of a sentence derived from its surface structure. LF, on the other hand, is a level of representation that serves as the input to semantic interpretation (May 1977, 1985). LF is crucial to account for a variety of linguistic phenomena; for instance, a semantic ambiguity (namely, scope ambiguity) of a sentence such as Someone loves everyone. In the surface order, someone takes scope over everyone, which yields the reading that there is a person who loves everyone. The sentence has another reading where everyone takes scope over someone, i.e., for everyone, there is someone who loves him. The second reading can be explained by assuming that there is a transformation between SS and LF. Specifically, everyone, which is below someone at the SS representation, undergoes Quantifier Raising to a position above someone leaving a trace, as in [IP everyone1 [IP someone [VP loves t1]]]. This representation yields the desired interpretation, but crucially it is not realized phonetically. This is because LF is independent from PF, which is a fundamental assumption in the model (12). Specifically, transformations applied between SS and LF are invisible on the surface. In this book, I take the existence of the LF for granted.

3. Classification in the nominal domain Before we examine the empirical data on non-split and split quantifier constructions, I first review the previous studies on classifications in the nominal domain, i.e., the mass-count distinction (this section), and classifications in the verbal domain, i.e., the atelic-telic distinction (section 4). We will see that the parallelism between the two domains can be achieved by introducing a part-whole structure of individuals and that of events.

3.1. The mass-count distinction and plurality of individuals It is well known that nouns can be divided into two categories, mass and count. From the syntactic point of view, the two categories differ in their distribution (see Chierchia 1998a for a review). For instance, count nouns

14 The semantic parallelism between nominal/verbal domains can take a plural morpheme, while mass nouns cannot (e.g., chairs vs. *furnitures). Another grammatical difference is that count nouns, but not mass nouns, can occur with numerals (e.g., one chair, two chairs, … vs. *one furniture, *two furniture(s), …). Furthermore, mass and count nouns are compatible with a different set of determiners; some determiners such as many and few are compatible only with count nouns (e.g., many chairs vs. *many furniture(s)) and others such as much and little only with mass nouns (e.g., much furniture vs. *much chair(s)). From a semantic point of view, mass and count nouns are distinguished by what they denote. Intuitively, count nouns denote a set of discrete or individuated elements, while mass nouns denote a set without specifying how the elements in that set are divided or individuated. Based on this intuition, two criteria — cumulative reference and divisive reference — have been proposed to distinguish mass and count nouns. On cumulative reference, Quine (1960) states that “so-called mass terms like ‘water’, and ‘footwear’ have the semantic property of referring cumulatively: any sum of parts which are water is water” (p. 91). That is, if we add some part to another part in the extension of a mass noun, the sum of these is also in the extension of the mass noun. On divisive reference, Cheng (1973: 286–287) states that “any part of something which is water is also water”. That is, if a noun is mass, properties that hold for the whole should also hold for its parts. Bunt (1979, 1985) attempts to unify the two criteria, and proposes the homogeneity reference hypothesis. The basic idea behind this hypothesis is that a predicate has homogeneous reference if it is both cumulative and divisive (see also Parsons 1970, Lønning 1987, Schubert and Pelletier 1987, Pelletier and Schubert 1989, Gillon 1992, Higginbotham 1994). Through these properties emerge similarities between plural count nouns and mass nouns. In particular, Link (1983) points out that plural count nouns are cumulative just like mass nouns, as in (13) (1983: 303). (13) a. If a is water and b is water then the sum of a and b is water. b. If the animals in this camp are horses, and the animals in that camp are horses, then the animals in both camps are horses. Based on these examples, Link proposes to capture the similarities between the two model-theoretically using a lattice, which is a partially ordered set, i.e., a set of objects ordered by a reflexive, anti-symmetric and transitive relation. Assuming that the denotation of nouns is a set of (singular and/or plural) individuals, it is possible to express the cumulative reference of

Classification in the nominal domain 15

mass nouns as well as of plural count nouns by ordering the individuals in their extension. For example, take a set containing elements in (14), where x, y, and z are singular individuals, ∪ I is an individual sum operator, and the lines indicate the ordering part-of relation ≤. (14)

x∪Iy∪Iz x∪Iy

x∪Iz

y∪Iz

x

y

z

Mass, Plural count Singular count

Suppose if x, y, and z are water, then their sums (x∪Iy, x∪Iz, y∪Iz, x∪Iy∪Iz) are also water, that is, [[ water]] is {x, y, z, x∪Iy, x∪Iz, y∪Iz, x∪Iy∪Iz}.7 We can order these members by the part-of relation, as in (14), i.e., the extension of a mass noun can be modeled as a lattice of individuals. Suppose now that x∪Iy and x∪Iz are cats. Then the sum of the two, that is, x∪Iy∪Iz, is also cats, showing cumulative property. Thus, in the denotation of cats, namely, {x∪Iy, x∪Iz, x∪Iy∪Iz}, members can be ordered by the part-of relation just as in the denotation of mass nouns. There have been discussions on whether plural count nouns take a set of atomic individuals in their extension. In this book, following Link (1983) but contra Hoeksema (1983), I assume that a set of atomic individuals is included in the extension of a plural count noun. One of the arguments for this view comes from the interpretation of the determiner no (Lasersohn 1988, Schwarzschild 1991). In No cats meowed, for example, if the denotation of cats does not include a set of atomic individuals, the sentence is predicted to be true in the situation where a single cat meowed. However, the intuition is that the sentence is false under the described situation, which is predicted by Link’s view. Thus, the denotation of cats is {x, y, z, x∪Iy, x∪Iz, y∪Iz, x∪Iy∪Iz}. It follows that the extension of a plural count noun as well as that of a mass noun can be expressed as a lattice of individuals in (14). We saw that the denotations of a plural count noun and of a mass noun may be considered to be the same, as in (15b) and (15c). These nouns have the property of cumulative reference, which is expressed by a part-of relation in a lattice of individuals. In contrast, the denotation of a singular count 7. Mass nouns are different from plural count nouns in that their minimal parts are somewhat vague (see Bunt 1985 for this issue). I simply assume here that all nouns, including mass nouns, have minimal parts in their extension (Chierchia 1998b). This assumption does not affect the analysis proposed in this book.

16 The semantic parallelism between nominal/verbal domains noun is a set of singular individuals, as in (15a), where no member is a subpart of other members. Specifically, singular count nouns are subject to the restriction in (16), which says ‘y has no proper parts’. That is, unlike the extensions of mass and plural count nouns, the extension of singular count nouns has no part-of relation. (15) a. [[cat]] = { x, y, z } b. [[cats]] = { x, y, z, x∪Iy, x∪Iz, y∪Iz, x∪Iy∪Iz } c. [[water]] = { x, y, z, x∪Iy, x∪Iz, y∪Iz, x∪Iy∪Iz } (16) ∀x∀y [ x≤y → x=y ]

(Schwarzschild 2006: 76)

Let us now introduce the operation of semantic pluralization * (Link 1983). The *-operator (the “star”-operator) applies to a one-place predicate P and generates all the individual sums of members in the extensions of P.8 With this operator, the denotation of a plural count noun is a set of atomic elements plus a set of non-atomic elements. For instance, if the denotation of cat is (15a), the denotation of *cat or cats would be (15b). *P has the same cumulative reference property as mass nouns, in that it is closed under sum formation: any sum of parts that are *P is also *P, as in (17). (17) a. x and y are cats and x and z are cats iff x, y, and z are cats. b. *cat(x∪Iy) ∧ *cat(x∪Iz) ↔ *cat(x∪Iy∪Iz) Note that a part-whole relation of nouns stays the same for NPs.9 For instance, the extension of old cats or hot water is a lattice of individuals exactly in the same way as that of cats or water is. Similarly, the extension of old cat as well as that of cat has no part-of relation. In the next section, I show that the mass-count distinction is analogous to the atelic-telic distinction in the verbal domain and that the atelic-telic distinction is tied to a VP (a verb plus its internal argument) rather than to a verb by itself. Thus, the 8. In Link (1983), besides singular individuals such as John, there are also plural individuals or individual sums of type e such as John∪IMary that are different from sets such as {John, Mary}. For alternative approaches, see Schwarzschild (1996), among others. 9. I assume here that the highest projection in the nominal structure is DP, not NP (Abney 1987, among others). In this view, the extension of a DP is an individual (or a generalized quantifier), while the extension of a NP is a set of individuals just like the extension of a noun.

Classification in the nominal domain 17

analogies will be made between NPs and VPs, not between nouns and verbs. For this reason, in the following, the mass-count distinction is tied to NPs. The following table summarizes the algebraic properties of NPs: Table 1. Algebraic properties of NPs

With proper parts Mass NPs (water, hot water)

Without proper parts Plural Count NPs (cats, old cats)

Singular Count NPs (cat, old cat)

3.2. Classifier languages Not all languages have syntactic distinctions between mass and count nouns; it has been argued that classifier languages such as Chinese and Japanese lack the mass-count distinction (Chierchia 1998b, among others). In this section, I examine some Japanese examples in detail. Japanese lacks obligatory grammatical markings of plurality, and thus a bare noun can be interpreted as singular or plural. Moreover, there are no definite and indefinite articles. Thus, bare nouns are four-way ambiguous, as shown in (18).10 (18) John-ga hon-o yon-da. John-NOM book-ACC read-PAST ‘John read {a book / books / the book / the books}.’ When a noun occurs with a numeral, the numeral is obligatorily followed by a classifier.11 A classifier is a morpheme that indicates a semantic class of the host noun in terms of shape, size, animacy, and so forth (Downing 1996). The classifier -hon (or -pon when attached to the numeral 10. It has been claimed that some classifier languages have a plural morpheme just like other languages without a classifier system (Li 1999, Chung 2000, Kurafuji 2002, Nakanishi and Tomioka 2004). Even if we accept this claim, these languages still remain peculiar in that plural markings are not obligatory. 11. There are some examples where a numeral is used without a classifier, as in (i). These examples are very limited in their distribution. (i) Sono heya-ni-wa isu-ga zyuunana{-ko/-∅} aru. the room-in-TOP chair-NOM 17{-CL/-∅} exist ‘There are 17 chairs in the room.’ (Zubin and Shimojo 1993: 499)

18 The semantic parallelism between nominal/verbal domains one) in (19a) carries some information about the semantics of pen ‘pen’, such as being inanimate, thin, and long. In (19b), the classifier -hiki indicates that the associated noun neko ‘cat’ is a relatively small animal. (19) a. pen {ip-pon / *iti} pen {one-CL / one} ‘one pen’ b. neko {go-hiki / *go} cat {five-CL / five} ‘five cats’ Mass-like nouns must also occur with classifier phrases: the classifiers in (20) carry some semantic information about the associated noun. (20) a. pan {iti-mai / *iti} bread {one-CL / one} ‘(lit.) one bread’ b. mizu {go-hai / *go} water {five-CL / five} ‘(lit.) five water’ For example, -mai in (20a) indicates that the associated noun is a thin, paper-like entity, and -hai in (20b) is used only with liquid in a container (such as a glass). In these examples, classifiers create individual units that can be counted (Krifka 1995). In this sense, they are analogous to measure phrases in English such as one slice in one slice of bread and five glasses in five glasses of water, which are used to individuate mass nouns in languages without a classifier system. This analogy has led some researchers to claim that all nouns in classifier languages have mass extensions, and thus nouns can be counted only when they are individuated by classsifiers.12 In the remainder of this section, I examine this claim in more detail. Under the canonical view of the syntax and semantics of NPs, NPs denote a property of individuals (type <e,t>), which cannot occur in argument positions. By projecting DP, they can become arguments of type e. For 12. Cheng and Sybesma (1999) claim that Chinese encodes the mass-count distinction at the classifier level, which led them to the conclusion that Chinese has count and mass nouns contra Chierchia (1998a, 1998b) (see also Doetjes 1997). However, what they call “count nouns” and “mass nouns” in Chinese are semantically different from ones in languages without classifiers.

Classification in the nominal domain 19

instance, in English, the NP cat is a property of individuals, hence it cannot appear in argument position (e.g., the sentence Cat is meowing is ungrammatical). In contrast, the DP the cat denotes a specific individual (type e), thus it can be an argument (e.g., the sentence The cat is meowing is grammatical). Then the question arises as to what the status of bare nominal arguments is (e.g., cats in Cats are meowing, which is grammatical). Carlson (1977) proposes that they refer to kinds. A kind is considered to be the totality of its instances. For example, a cat-kind is identified with the totality of cats. Any natural kind has a corresponding property, and any natural property has a corresponding kind. To capture this correspondence between properties and kinds, Chierchia (1984) proposes the “down” operator and the “up” operator, as in (21). What will later become relevant to us is the up operator, which predicativizes kinds and shifts them to predicative common nouns. The definition is given in (22). (21)

PROPERTIES

KINDS down

P <e,t>

up ∪

∩

K e

(Chierchia 1998b: 349)

(22) Let d be a kind. Then for any world/situation s, ∪ d = λx [ x ≤ ds ], if ds is defined λx [FALSE], otherwise where ds is the plural individual that comprises all of the atomic members of the kind. (Chierchia 1998b: 350) The property of being an instance of a kind does not differentiate between singular and plural instances. In other words, the property corresponding to a kind comes out as being mass. For example, both Rocky (singular) and Rocky and Hazel (plural) can be an instance of the cat-kind. In this sense, ∪CAT (the property of being the cat-kind), which corresponds to CAT (the cat-kind), is mass. With these assumptions about kinds, Chierchia (1998b) extends Carlson’s proposal and argues that, in classifier languages where noun phrases are always bare in argument positions, all noun phrases denote kinds. Since the type-shifting ∪-operator assigns a mass denotation to the predicate counterpart of a kind, the extension of nominal predicates is always mass in classifier languages. Something needs to be said about examples where kinds appear as arguments of non-kind taking predicates. For instance, in (23a) in Japanese,

20 The semantic parallelism between nominal/verbal domains John could not have chased the cat-kind, but rather, he chased some object(s) which has/have the property of the cat-kind. Chierchia solves this problem by introducing an operation called Derived Kind Predication (DKP), which is defined in (24). Whenever a non-kind argument slot in a predicate is filled by a kind argument, DKP automatically adjusts the type of the predicate by introducing a local existential quantification over instances of the kind. With DKP, the denotation of (23a) would be (23b). (23) a. John-ga neko-o oikake-ta. John-NOM cat-ACC chase-PAST ‘John chased {a cat / cats / the cat(s)}.’ b. ∃x[ ∪cat(x) ∧ chase(John, x) ] (24) Derived Kind Predication (DKP) If P applies to objects and k denotes a kind, then P(k) = ∃x[ ∪k(x) ∧ P(x) ] (Chierchia 1998b: 364) Following Chierchia’s proposal, I assume that NPs in Japanese denote kinds, hence they always have mass properties. Put differently, I assume that Japanese lacks a mass-count distinction. For one thing, there does not seem to be any syntactic diagnostics in Japanese to tease apart the two classes of NPs. Recall the discussion in section 3.1 that grammatical differences between mass and count NPs include compatibility with the plural morpheme (e.g., *furnitures vs. chairs) and with a numeral (e.g., *one furniture vs. one chair). In Japanese, as shown above, there is no obligatory plural morpheme, and all NPs are compatible with a numeral with the help of a classifier. Moreover, even from a semantic perspective, there does not seem to be any apparent evidence for the mass-count distinction. In Chapter 2: section 2.4, I examine some semantic examples that seemingly corroborate a mass-count distinction in Japanese. However, I show that these examples do not necessarily serve as evidence for the distinction. Before concluding this section, I introduce an additional type-shifting rule that will be used later in this book. Partee (1987) proposes a restricted number of type-shifting operations illustrated in (25), assuming that, depending on context, a nominal predicate can be an argument of type e, a predicate of type <e,t>, or a generalized quantifier of type <<e,t>,t>. Chierchia’s (1984) down and up operators link an argument and a predicate. Another rule that becomes relevant is the ∃-operator that shifts a predicate to a generalized quantifier, as defined in (26).

Classification in the verbal domain 21

(25)

Lift e

<et,t> ∪

Lower BE

∩

∃ <e,t>

(26) ∃: <e,t> → <et,t>

∃X = λP<e,t>. ∃y[X(y) ∧ P(y)]

4. Classification in the verbal domain This section provides a brief overview of earlier studies of aspectual classes of verbal predicates. In section 4.1, I introduce Vendler’s (1957) aspectual categories, which can be reduced to the atelic-telic distinction. This distinction is claimed to be parallel to the mass-count distinction in the nominal domain. In section 4.2, to capture the parallelism between the two, Davidsonian event arguments (Davidson 1967) are introduced. Section 4.3 discusses the association between a verb and its nominal arguments at the level of the conceptual structure and in the syntax under event theories. With event arguments, I show in section 4.4 that we are able to define pluralization in the verbal domain and further capture the algebraic parallelism between the nominal and verbal domains.

4.1. The atelic-telic distinction Vendler (1957) proposes that verbal predicates can be classified into four aspectual classes, namely, states, activities, accomplishments, and achievements, as in (27) (cf. Kenny 1963, Verkuyl 1972, 1993, Dowty 1979, Smith 1991). (27) States know believe desire love

Activities run walk push a cart drive a car

Accomplishments paint a picture make a chair draw a circle recover from illness

Achievements recognize spot lose die (Dowty 1979: 54)

22 The semantic parallelism between nominal/verbal domains Numerous studies have been made of the formal properties underlying these classes. Most notably, depending on whether an event described by the verbal predicate has a terminal point, it is possible to put together states and activities on the one hand, and accomplishments and achievements on the other. Verbal predicates in the first group are called atelic predicates, and in the second group telic predicates. The denotation of atelic predicates has no set terminal point. For instance, in John believes Mary, there is no description of whether John will come to stop believing Mary. Similarly, the sentence John ran does not say whether the event of John’s running ended. In contrast, the denotation of telic predicates includes a terminal point. If John made a chair, John must have terminated the event of making a chair. In John died, we know that the event of John’s dying has terminated. One of the diagnostics for determining the telicity of verbal predicates is to combine the verbal predicate with a durative adverb such as for two hours and with a time span adverb such as in two hours (Dowty 1979). Atelic verbal predicates are compatible with durative adverbs, but not with time span adverbs. The opposite holds for telic verbal predicates. For example, this test shows that run in (28a) is an atelic predicate, whereas die in (28b) is a telic predicate. (28) a. John ran {for ten minutes / *in ten minutes}. b. John died {*for ten minutes / in ten minutes}. Aspectual properties of a verbal predicate are not determined by the verb alone: PPs or internal arguments can influence aspectual properties of the entire expression (Garey 1957, Verkuyl 1972, 1993, Dowty 1979, Platzack 1979, Tenny 1987, 1994, Krifka 1989, 1992, Jackendoff 1996, Rothstein 2004). For instance, while run by itself is atelic, as in (28a), run to the store is telic, as in (29). Moreover, as in (30), a complex verbal predicate is telic when the internal argument is a singular count noun, and atelic when the internal argument is a plural count noun or a mass noun.13

13. It is not always the case that the mass-count distinction of the internal argument correlates with the atelic-telic distinction of the complex verbal predicate: (i) a. John saw a zebra {for an hour / *in an hour}. b. John saw zebras {for an hour / *in an hour}. (Krifka 1992: 31) Krifka (1992) claims that the lexical semantics of the verb plays a crucial role in the way the nominal arguments affect the telicity of the entire verbal expression. Suffice it to say here that telicity needs to be determined by examining a

Classification in the verbal domain 23

(29) John ran to the store {*for ten minutes / in ten minutes}. (30) a. John ate an apple {*for ten minutes / in ten minutes}. b. John ate apples {for ten minutes / *in ten minutes}. c. John drank wine {for ten minutes / *in ten minutes}. Thus, telicity needs to be determined by examining the entire complex verbal expression and not just the verb by itself. A complex verbal expression here corresponds to a VP, assuming a PP such as to the store is adjoined to the VP-level.14 It has been claimed that there are analogies between the mass-count distinction in the nominal domain and the atelic-telic distinction in the verbal domain: mass nouns are like atelic predicates, and count nouns are like telic predicates (ter Meulen 1984, Bach 1986, Krifka 1989). Intuitively, mass nouns and atelic predicates lack a clear limitation, while count nouns and telic predicates come with a precise limit. This intuition leads us to the property of cumulativity discussed in section 3.1: for any given property with cumulative reference, any sum of parts having a property expressed by a cumulative reference also has the same property. Vendler (1967: 101) indicates that atelic predicates, but not telic predicates, have cumulative reference. Recall that, in the nominal domain, mass NPs and plural count NPs, but not singular count NPs, have a cumulative reference. Hence, the cumulative reference property captures the correlation between the masscount and the atelic-telic distinction. Roughly, atelic VPs and mass/plural count NPs are cumulative, whereas telic VPs and singular count NPs are not. In the following, I show that it is possible to distinguish between plural and singular telic VPs, and this distinction makes the parallelism between nominal and verbal predicates complete.

complex verbal predicate, and the status of internal arguments often but not always influences telicity. 14. See Rothstein (2004: Chapter 1) for discussion on the relation between Vendler’s aspectual classes and the atelic-telic distinction. The upshot of her claim is that, while Vendler’s aspectual classes are properties of verbs, telicity and atelicity are properties of VPs.

24 The semantic parallelism between nominal/verbal domains 4.2. Introducing Davidsonian event arguments We saw in section 4.1 that there is an intuitive correlation between the mass-count distinction and the atelic-telic distinction. We also saw in section 3.1 that the extension of nominal predicates can be expressed algebraically by a lattice of individuals. It has been claimed that, by introducing event arguments, the extension of verbal predicates can be expressed by a lattice of events (Krifka 1986, 1989, 1992, 1998, Landman 1996, 2000, in particular). To achieve the algebraic parallelism between a lattice of individuals and a lattice of events, we first need to establish the existence of event arguments. In the following, I present some evidence for their existence. Davidson (1967) proposes that verbs have an implicit event argument besides the explicit arguments in a sentence. Instead of the standard denotation of the verb see in (31a), he proposed (31b), where see(x,y,e) is read as ‘an event which is a seeing event of x by y’. (31) a. [[see]] = λxe.λye. see(y,x) b. [[see]] = λxe.λye.λev. see(y,x,e) One of the most widely accepted motivations for an implicit event argument comes from adverbial modification. Let us first examine adjectival modification in the nominal domain, and compare it with adverbial modification in the verbal domain. It is generally assumed that many adjectives are intersective (female, green, pretty, etc.) (Heim and Kratzer 1998, Landman 2000, among others). Intersective adjectives are combined with nominal predicates by Predicate Modification, defined in (32): if α of type <e,t> has two daughters, β and γ, both of which are of type <e,t>, the denotation of α is the property resulting from the conjunction of β and γ (i.e., [[β]] (x) = 1 ∧ [[γ]] (x) = 1). (32) Predicate Modification If α is a branching node, {β, γ} is the set of α’s daughters, and [[β]] and [[γ]] are both in D<e,t>, then [[α]] = λx ∈ De . [[β]](x) = [[γ]](x) = 1. (Heim and Kratzer 1998: 65) With this rule, the denotation of (33a) will be (33b). This treatment of adjectives correctly predicts that adjectival modifiers can be permutated or

Classification in the verbal domain 25

dropped.15 Since adjectives are treated as predicates connected to a nominal predicate by conjunction, we can freely change the order of adjectives (Permutation in (34a)) or drop some adjectives (Drop in (34b)). (33) a. fluffy, friendly, orange cat b. λx. cat(x) ∧ fluffy(x) ∧ friendly(x) ∧ orange(x) (34) a. Permutation: friendly, fluffy, orange cat λx. cat(x) ∧ friendly(x) ∧ fluffy(x) ∧ orange(x) b. Drop: friendly orange cat λx. cat(x) ∧ friendly(x) ∧ orange(x) It has been observed that the same properties hold for adverbial modifiers. For instance, given John slept for one hour in the room, we can say John slept in the room for one hour (Permutation) and John slept for one hour (Drop). The parallelism becomes more explicit with the so-called diamond entailments in (35). The adjectival modifiers in (35) and the noun itself are predicates of the same argument. The sentence in (a) entails (bi) and (bii), and both (bi) and (bii) entail (c). However, (c) does not entail (bi) or (bii), and neither (bi) nor (bii) entails (a). (35) a. Rocky is a friendly orange cat: cat(r) ∧ friendly(r) ∧ orange(r) b. i. Rocky is a friendly cat: cat(r) ∧ friendly(r) c.

ii. Rocky is an orange cat: cat(r) ∧ orange(r)

Rocky is a cat: cat(r)

Consider now the adverbial modifiers in (36), where the same entailment pattern as (35) holds. We can assume that the adverbial modifiers in (36) are predicates of an event argument.

15. Adjectival modifiers cannot always be permutated: there are some ordering restrictions depending on their sorts (e.g., size, color, quality). For instance, an adjective expressing size comes before an adjective expressing color (e.g., small orange cat, but not orange small cat).

26 The semantic parallelism between nominal/verbal domains (36) a.

John read the book carefully yesterday: ∃e[read(j,the.book,e) ∧ carefully(e) ∧ yesterday(e)]

b. i. J read the book carefully: ∃e[read(j,b,e)∧carefully(e)] c.

ii. J read the book yesterday: ∃e[read(j,b,e)∧yesterday(e)]

J read the book: ∃e[read(j,the.book,e)]

Additional evidence for event arguments comes from anaphoric dependencies (Davidson 1967). By introducing event arguments, we can claim that it in (37) refers to the event argument; it in (37a) refers to the event of Mary’s swimming the channel, and it in (37b) to the event of exploding. (37) a. Mary swam the channel last week. It took a long time. b. We are sitting in my living room in Tel Aviv and there is a loud explosion. I say: “Don’t worry: it was just a plane breaking the sound barrier.” (Rothstein 1998: 5) Event argument has been used to account for a wide variety of empirical data such as resultative constructions, scope interpretations, focus structure, and plurality (see, for instance, Krifka 1989, 1992, 1998, Schein 1993, Lasersohn 1995, Herburger 2000, Landman 2000, Rothstein 2001, 2004). In the rest of this book, I present further empirical data that can be satisfactorily analyzed by positing an event argument. More specifically, I show that the event argument can be a powerful explanatory tool that provides straightforward accounts for some semantic properties of split quantifier constructions and comparative constructions.

4.3. Event theories and argument structure As briefly discussed above, Davidson (1967) argues that verbs have an extra slot for the event argument. For example, the transitive verb see in (38) denotes a three-place relation between the nominal arguments and an implicit event argument, as in (39a). The denotation of (38) under this analysis is (39b). In the original Davidsonian approach, the difference between arguments and adjuncts is encoded in the semantic representation: the arguments have ordered positions in the argument structure of the verb

Classification in the verbal domain 27

(e.g., see(r,h,e) in (39b)), and the adjuncts are modifiers of the event argument (e.g., in(p,e) in (39b)). (38) Rocky saw Hazel in Philadelphia. (39) a. [[see]] = λx.λy.λe. see(y,x,e) b. [[(38)]] = 1 iff ∃e[ see(r,h,e) ∧ in(p,e) ] Alternatively, Castañeda (1967), whose ideas were further developed by Parsons (1990), claims that both arguments and adjuncts are predicates of the event. As in (40), verbs are one-place predicates of events, while arguments and adjuncts are expressed by two-place predicates denoting thematic relations (Carlson 1984, Higginbotham 1985, Dowty 1989, Parsons 1990, Schein 1993, Landman 2000).16 This approach is generally referred to as neo-Davidsonian, as opposed to the traditional Davidsonian approach in (39). (40) a. [[see]] = λx.λy.λe. see(e) ∧ Theme(x,e) ∧ Agent(y,e) b. [[(38)]] = 1 iff ∃e[ see(e) ∧ Theme(h,e) ∧ Agent(r,e) ∧ in(p,e) ] The two theories agree that see is a three-place predicate in the syntax, but they differ in their assumptions at the level of logical-conceptual structure: in the Davidsonian theory, see is a three-place predicate, whereas, in the neo-Davidsonian theory, it is a predicate with one argument, namely, the event argument. Kratzer (1996, forthcoming), in contrast, argues that some neo-Davidsonian argument association is present in the syntax of verbs: external arguments are introduced by a neo-Davidsonian method both at the level of the conceptual structure and in the syntax. Kratzer’s denotations of see and of the sentence (38) are given in (41). The internal argument Hazel is in the denotation of the verb, wheras the external argument Rocky is introduced by a secondary predicate. (41) a. [[see]] = λxe.λev. see(x,e) b. [[(38)]] = 1 iff ∃e[ see(h,e) ∧ Agent(r,e) ∧ in(p,e) ] Kratzer’s proposal for severing the external argument in the syntax is built on previous work pointing out some asymmetries between external 16. I show later in this section that thematic roles should be represented as functions, since each thematic role is assigned only once per event.

28 The semantic parallelism between nominal/verbal domains and internal arguments. Most notably, Marantz (1984) argues that external arguments are not true arguments of their verbs. Evidence for this comes from the fact that an internal, but not an external, argument can trigger a particular interpretation of a verb, as in (42) (take meaning ‘grab’, ‘ride’, ‘have’, etc.). (42) a. b. c. d.

take a book from the shelf take a bus to New York take an aspirin take a nap

(Kratzer 1996: 113)

Kratzer (1996, forthcoming) then addresses the following question: if external arguments are not true arguments of their verbs, where do they come from? She proposes that the agent argument is introduced by a nonovert functional head, namely Voice (see Kratzer forthcoming for the relevance of a theory of voice). Evidence for this proposal comes from the properties of nominalizations and participles, and the range of possible voice alternations, and so on. For details, I refer the reader to Kratzer (1996, forthcoming). Turning now to the independence of external arguments at the level of the conceptual structure, we have evidence from the asymmetry between external and internal arguments in terms of cumulativity, defined in (43). If x and y of the sort S have a property P, the sum of x and y has the same property (cf. cumulative reference discussed in section 3.1). (43) ∀P ∀x,y∈DS[ [P(x) ∧ P(y)] → P(x∪Sy) ] It has been proposed by Krifka (1986, 1989, 1992, 1998) and pursued by Landman (1996, 2000) that the denotations of all thematic relations are cumulative, which Kratzer (forthcoming) refers to as the Cumulativity Universal. Cumulativity as a property of relations between individuals and events is defined in (44). (44) ∀R<e,vt>∀x,y∈DI∀e,e’∈DE[ [R(x)(e)∧R(y)(e’)] → R(x∪Iy)(e∪Ee’) ] Kratzer (forthcoming) shows that the agent relation, but not the putative theme relation, is cumulative.17 Let us examine a slightly modified example 17. Strictly speaking, neo-Davidsonian thematic roles are functions (see shortly below). The Cumulativity Universal concerns the denotation of simple predi-

Classification in the verbal domain 29

taken from Kratzer (forthcoming): suppose that John dug a hole, Mary placed a tree in the hole, and Bill covered the roots with soil, and that the entire planting-a-tree event is the sum of these three subevents. The agents of these subevents are John, Mary, and Bill, respectively. It is true to say that the sum of these three individuals planted the tree, i.e., the sum of the individuals is the agent of the planting-a-tree event. Thus, the agent relation is cumulative, as in (44).18 In this example, if there were a theme relation Theme(x,e), cumulativity would require that the sum of a hole, a tree, and the roots is the theme of the planting event. However, intuitively, the theme of the planting event is the tree alone. Thus, themes are different from agents in that they are not summed. Kratzer’s assumption is that, if arguments of verbs are introduced by secondary predicates denoting general thematic relations such as the agent relation, then there should be a conceptual property shared by all the relations. Krifka’s work shows that cumulativity can be such a property. Then, based on the Cumulativity Universal, the fact that the putative theme relation is not cumulative indicates that there is no theme relation to begin with at the level of the logicalconceptual structure. That is, themes are not introduced by the neoDavidsonian theme relation.19 cates, which are generally represented as relations. Since the main goal here is to examine whether thematic roles satisfy cumulativity, I represent thematic roles as relations. See Chapter 3: section 5.1 for cumulativity as a property of functions. 18. The agent function does not seem to be cumulative in the following scenario: the doctor examined the patient, where the examination has subevents such as the patient lifts his arm, the patient breathes heavily, etc. If the agent function were cumulative, we should mistakenly predict that both the doctor and the patient are the agents. The problem here seems to lie in how to determine relevant subevents. In this case, I assume that the events of the patient’s lifting-the-arm and breathing-heavily are caused by the doctor, i.e., the doctor made the patient lift the arm or breath heavily, and thus the doctor is the agent of these subevents. 19. There is another piece of evidence for the neo-Davidsonian association of external arguments at the level of the conceptual structure. Kratzer (forthcoming: Chapter 2) takes Schein’s (1993) data for neo-Davidsonian association of verb arguments. She carefully teases apart the consequences of Schein’s data for argument association at the level of the conceptual structure and those for argument association in the syntax. The result shows that, while Schein’s case comes out strongly for a neo-Davidsonian association of external arguments at the level of the logical-conceptual structure, the case does not come out as

30 The semantic parallelism between nominal/verbal domains So far, neo-Davidsonian argument associations have been represented as relations. It has been claimed that thematic roles of a certain event must be uniquely specified, as clearly defined in (45) taken from Landman (1996, 2000) (see also Carlson 1984, Parsons 1990). Following Landman (and many others), I henceforth represent thematic roles as functions (e.g., Agent(e)=r), rather than as relations (e.g., Agent(r,e)). (45) The Unique Role Requirement: if a thematic role is specified for an event, it is uniquely specified. Realization: thematic roles are partial functions from events to individuals. (Landman 2000: 38) In sum, Kratzer’s (1996, forthcoming) claim is that external arguments are associated with their verbs by the neo-Davidsonian method both at the level of the conceptual structure and in the syntax. As an illustration of her analysis, the syntactic structure and the semantic computation of the sentence Rocky saw Hazel are provided in (46). The neo-Davidsonian agent head of type <e,vt> and the VP of type are combined by Event Identification in (47), which is one type of Predicate Modification defined in (32). The event argument gets existentially closed at TP. (46)

TP T

VoiceP DP

Voice’

Rocky Voice Agent

VP V’

DP

saw Hazel [[see]] = λye.λev. see(y,e) [[VP]] = λev. see(h,e) [[Agent]] = λxe.λev. Agent(e)=x [[Voice’]] = λxe.λev. Agent(e)=x ∧ see(h,e) [[VoiceP]] = λev. Agent(e)=r ∧ see(h,e) [[TP]] = 1 iff ∃e[Agent(e)=r ∧ see(h,e)]

(by (47))

strongly for agent arguments in the syntax, nor for theme arguments (both at the level of the conceptual structure and in the syntax).

Classification in the verbal domain 31

(47) Event Identification f g <e,>

→

h <e,> λxe.λev. f(x)(e) ∧ g(e) (Kratzer 1996: 122)

As mentioned in section 1, this book examines properties of non-split and split quantifier constructions in Japanese and German, and of comparative constructions in Japanese and English. Hence, it is crucial for our purposes to examine whether the argument structure proposed by Kratzer for English extends to Japanese and German. In the syntax, the following examples indicate that external arguments in Japanese (examples (48)) and in German (examples (49)) are not true arguments of their verbs just as external arguments in English are not (see (42)): (48) a. ie-o tubusu house-ACC smash ‘to smash the house’ b. keikaku-o tubusu plan-ACC smash ‘to ruin one’s plan’ c. zikan-o tubusu time-ACC smash ‘to kill time’ d. koe-o tubusu voice-ACC smash ‘to lose one’s voice’ (49) a. Abschied nehmen farewell take ‘to say goodbye’ b. Anteil nehmen portion take ‘to be interested in’ c. etwas in die Hand nehmen something in the hand take ‘to pick something up’ d. ein Bad nehmen a bath take ‘to bath’

32 The semantic parallelism between nominal/verbal domains Semantically, I assume that the asymmetry between external and internal arguments with respect to cumulativity can be taken to be universal. Thus, Japanese and German behave like English in terms of asymmetries between external and internal arguments both in the syntax and semantics. Following Kratzer (1996, forthcoming), I assume that external arguments are associated with verbs in a neo-Davidsonian fashion both in the syntax and at the level of the logical-conceptual structure.

4.4. Plurality of events We are now ready to go back to the parallelism between the mass-count and the atelic-telic distinctions. In the nominal domain, we saw in section 3.1 that there is a distinction between mass and count NPs. Furthermore, the similarities between mass NPs and plural count NPs on the one hand and singular count NPs on the other are captured model-theoretically by using a lattice of individuals (Link 1983). With the event argument, we can represent the denotation of verbal predicates by using a lattice of events (Krifka 1989, Landman 1996, 2000, among others). Recall the discussion in section 4.1 that telicity and atelicity are properties of VPs, not of verbs by themselves, and that the semantic parallelism holds between NPs and VPs. In this sense, the event argument of a lattice is associated with a VP, i.e., a lattice of events is denoted by a VP. Our task now is to examine what kind of VP can denote a lattice of events. Consider a set containing elements in the figure in (50), where e1, e2, and e3 are singular events, ∪ E is an event sum operator, and the lines indicate the ordering part-of relation ≤. This structure is completely parallel to that which we saw for individuals in (14). e1 ∪ E e2 ∪ E e3

(50) e1 ∪ E e 2

e1 ∪ E e3

e2 ∪ E e3

e1

e2

e3

Atelic, Plural telic Singular telic

Classification in the verbal domain 33

Suppose that e1, e2, and e3 are hitting-Peter events.20 Then, the sums of these events, i.e., e1∪Ee2, e1∪Ee3, e2∪Ee3, and e1∪Ee2∪Ee3, are also hittingPeter events. That is, [[ hit Peter]] is {e1, e2, e3, e1∪ Ee2, e1∪Ee3, e2∪Ee3, e1∪Ee2∪Ee3}. Since the members of this set can be ordered by the part-of relation, the extension of this atelic VP is a lattice of events, as in (50). Telic VPs are analogous to count NPs; in the same way as a singular count NP such as cat denotes a set of atomic individuals, a singular telic VP such as break a car denotes a set of atomic events. The difference is that, unlike NPs, VPs in most languages are not overtly marked for plurality.21 Even without overt plural marking, however, telic VPs can be semantically pluralized by applying the pluralization operation * used for pluralization in the nominal domain (see section 3.1, see also Landman 1989a, b, 2000). A plural telic VP denotes a set containing atomic events and their sums, just as a plural count NP denotes a set containing atomic individuals and their sums. For instance, when [[break a car]] is {e1, e2, e3 }, [[*break a car]] is {e1, e2, e3, e1∪Ee2, e1∪Ee3, e2∪Ee3, e1∪Ee2∪Ee3}, which can be modeled as a lattice of events, as in (50).22 To sum up, the nominal and verbal domains are parallel with respect to algebraic lattice formation. As discussed above, NPs and VPs differ in that VPs in most languages, unlike NPs, lack an overt plural marker. When a VP lacks a plural marker, there is no way of telling whether the VP is semantically pluralized by the covert *-operator. Put differently, a VP without a plural marker can always be understood as being semantically pluralized. An exception to this generalization is a telic VP that denotes a singleoccurrence event such as kill Peter: assuming that Peter may die only once, the killing-Peter event can occur only once. That is, the extension of kill

20. Just like mass NPs, minimal parts of atelic VPs are somewhat vague (see Rothstein 2004, for instance). I simply assume here that bottom elements in a lattice of an atelic VP are events that have the same property as the atelic VP. 21. There are some languages that overtly pluralize verbs as well as nouns by using so-called pluractional markers (morphemes for pluralization), although it is not always the case that pluractional markers reflect the plurality of verbs. See Chapter 5: section 4.2 for further discussion. 22. For lack of a better notation, I use the symbol * to refer to verbal pluralization also in natural language, not just in formal language. For example, cat pluralizes into cats, and break a car pluralizes into *break a car.

34 The semantic parallelism between nominal/verbal domains Peter is a singleton. The parallelism between the nominal and verbal domains is summarized below: 23 Table 2. Algebraic parallelism between the nominal and the verbal domain

With proper parts

Without proper parts

Mass NPs (water, hot water)

Plural Count NPs (cats, old cats)

Singular Count NPs (cat, old cat)

Atelic VPs (drive a car)

Plural Telic VPs (*break a car )

Singular Telic VPs (break a car, kill Peter)

5. Summary of chapter 1 In this chapter, I first discussed the three larger issues in the fields of semantics and the syntax-semantics interface examined in this book, and provided an overview of the book. Then I summarized previous studies on the classifications of predicates in the nominal domain (i.e., the mass-count distinction) and in the verbal domain (i.e., the atelic-telic distinction). The intuitive parallelism between the two distinctions is formally captured by introducing an event argument and by defining lattice structures of events. We shall see in the rest of the book how this formal parallelism between the two domains enables us to capture a wide variety of linguistic phenomena. In particular, I examine the syntax and semantics of non-split and split quantifier constructions in Japanese and German (Chapters 2 and 3) and of comparative constructions in Japanese and English (Chapter 4). Further cross-linguistic constructions are presented in Chapter 5.

23. VPs do not have overt realizations of plurality (but see footnote 21), hence, presumably, atelic VPs can be pluralized as well as telic VPs, as in (i). In contrast, mass NPs cannot be pluralized: although pluralization of nominal predicates must be morphologically marked in general (e.g., -s in English), mass NPs can never be marked with plural morphology. (i) Plural atelic VPs: [[*drive a car]] = {e1, e2, e3, e1∪Ee2, e1∪Ee3, e2 ∪Ee3, e1∪Ee2 ∪Ee3}

Chapter 2 The semantic properties of non-split and split measure phrase constructions

1. Split measure phrase constructions We saw in Chapter 1 that there is a parallelism between the nominal and verbal domains: just as the extension of a nominal phrase may have a partwhole structure of individuals, the extension of a verbal phrase may have a part-whole structure of events. This chapter presents some empirical data for which this parallelism gives a satisfactory account. In particular, I examine the semantic properties of the floating quantifier construction in Japanese and Split NP Topicalization in German, and argue that measure phrases in these constructions express measurement of events as well as of individuals, while their non-floating or non-split counterparts express measurement of individuals only. It is well known that, in English, quantifiers such as all, both, and each can “float” in that they can appear apart from the DPs that they seem to modify, as shown in (1b). Such a quantifier has been traditionally called a floating quantifier (FQ). I refer to all in (1a) as a non-floating quantifier (non-FQ). Example (2) shows that quantifiers in Japanese can also float.1 (1)

a. All the students have gone home. b. The students have all gone home.

1. Besides (2), quantifiers can also appear in prenominal position, as in (i). (i) [Subete-no gakusei]-ga ie-ni kaet-ta. [all-GEN student]-NOM home-to go-PAST ‘All (the) students went home.’ I put aside the configuration in (i), since it does not show the semantic restrictions relevant to the current discussion. See section 2.5 and Chapter 3: section 3.2 for further discussion.

36 The semantic properties of non-split/split MP constructions (2)

a. [Gakusei subete]-ga ie-ni [student all]-NOM home-to ‘All (the) students went home.’ b. Gakusei-ga ie-ni subete student-NOM home-to all

kaet-ta.2 go-PAST kaet-ta. go-PAST

Japanese is strikingly different from English in that it also allows numerals and measure phrases to float, as in (3b) and (4b). As discussed in Chapter 1: section 3.2, numerals in Japanese must be followed by a classifier, yielding a classifier phrase (e.g., san-nin ‘three-CLASSIFIER’), or by a measure word, yielding a measure phrase (e.g., san-rittoru ‘three liters’). In the following, the term measure phrases (MPs) refers to both classifier phrases and genuine measure phrases. (3)

(4)

a. [Gakusei san-nin]-ga ie-ni [student three-CL]-NOM home-to ‘Three students went home.’ b. Gakusei-ga ie-ni san-nin student-NOM home-to three-CL

kaet-ta. go-PAST kaet-ta. go-PAST

a. [Mizu san-rittoru]-ga tukue-nouede [water three-liter]-NOM table-on ‘Three liters of water spilled on the table.’ b. Mizu-ga tukue-nouede san-rittoru water-NOM table-on three-liter

kobore-ta. spill-PAST kobore-ta. spill-PAST

Before we proceed further, a brief terminological note is in order. In this book, I use the term quantifier to refer to expressions such as all, each, as 2. Matrix sentences in Japanese are subject to a certain pragmatic restriction (i.e., a preference of having a topic of the sentence that is marked by the topic marker -wa), althuogh this restriction is not applicable to embedded clauses. To avoid pragmatic complexity, researchers of Japanese linguistics conventionally create an embedded environment by adding koto ‘the fact that’. Throughout the book, I assume that Japanese examples (except for some limited cases) appear in the koto clause, although koto is omitted from the examples. For instance, (2a) is a simlified version of (i). (i) [Gakusei subete]-ga ie-ni kaet-ta koto [student all]-NOM home-to go-PAST the.fact.that ‘the fact that all (the) students went home’

Split measure phrase constructions 37

well as to MPs (numerals, classifier phrases, and measure phrases). The definition here is different from the one in the theory of generalized quantifiers (Barwise and Cooper 1981), where a “quantifier” refers to a quantified noun phrase such as all students, and an expression like all is referred to as a “determiner”. Another well-known construction that allows MPs to appear separated from the associated NP is the so-called Split Topicalization (ST), which occurs in many languages (e.g., Germanic languages, Chinese, Greek, Hungarian, Catalan, etc.). In this chapter, I focus on examples from German (see Chapter 5 for cross-linguistic data). In ST, a noun phrase is separated from the expression that seems to modify it, as in (5b) where the adjective rote is split from the NP Bücher.3 Examples (6) and (7) show that ST can involve MPs (numerals and genuine measure phrases). (5)

(6)

a. Hans hat [rote Bücher] Hans has [red book] ‘Hans bought red books.’ b. Bücher hat Hans rote books has Hans red

gekauft. bought gekauft. bought

a. [Drei Studenten] haben gestern [three students] have yesterday ‘Three students danced yesterday.’ b. Studenten haben gestern drei students have yesterday three

getanzt. danced getanzt. danced

3. The topicalized element in ST is not necessarily a NP; other categories such as PP or VP can also be topicalized, as in (i) and (ii) (cf. de Kuthy 2002, among others). This book exclusively deals with Split NP Topicalization, excluding other types of ST. (i) Split PP Topicalization Von den Büchen hat Hans drei gekauft. of the books has Hans three bought ‘Hans bought three of the books.’ (ii) Split VP Topicalization (or VP Fronting) [Drei Bücher kaufen] will Hans. [three books buy] wants Hans ‘Hans wants to buy three books.’

38 The semantic properties of non-split/split MP constructions (7)

a. Hans hat [drei Liter Wasser] Hans has [three liter water] ‘Hans drank three liters of water.’ b. Wasser hat Hans drei Liter water has Hans three liter

getrunken. drunk getrunken. drunk

The Japanese FQ construction in (3b) and (4b) and the German ST in (6b) and (7b) have the same configuration: the MP is split from the NP that they seem to be associated with. The main goal of this chapter is to show that these two constructions have several semantic properties in common.4 In what follows, the term split M(easure)P(hrase) construction is used to refer to the two constructions together. Their non-split counterparts are called non-split MP constructions. Furthermore, MPs in non-split and split MP constructions are called split MPs and non-split MPs, respectively. The term host NP refers to the NP that a split MP or a non-split MP is associated with.5 Non-split MPs are generally used in noun phrases to express quantity. For example, in (3a) and (6a), the number of relevant students is indicated by the classifier phrase san-nin ‘three-classifier’ or by the numeral drei ‘three’. In (4a) and (7a), the denotation of water is measured by the MP san-rittoru ‘three liters’ or by drei Liter ‘three liters’. In this way, these languages allow a non-split MP to combine syntactically with a nominal predicate to express nominal measurement, satisfying the general assumption of compositionality that semantic rules apply in accord with syntactic rules. On the surface, however, a split MP does not form a nominal constituent with its host NP. The question naturally arises as to whether a split MP measures in the nominal domain in the same way as its non-split counterpart. I claim that non-split and split MP constructions differ in their domains of measurement: non-split MP constructions involve measurement of indi4. Independently, Bobaljik (2003) suggests a possible similarity between the FQ construction in Japanese and Split NP Topicalization in other languages based on some data on the scope of quantifiers. Moreover, in Chapter 5, I show that ST in other languages (Greek and Catalan) has the same semantic properties as the Japanese FQ construction and German ST. 5. Note that the term host NP has no syntactic implications. Specifically, the term should not be taken to mean that a split or non-split MP syntactically combines with the NP. Indeed, in Chapter 3, I argue that a non-split MP, but not a split MP, directly combines with the host NP.

Split measure phrase constructions 39

viduals in the nominal domain, while split MP constructions involve both measurement of events in the verbal domain as well as of individuals in the nominal domain. This claim is based on the observation that, while both constructions are subject to some semantic restrictions in the nominal domain, only split MP constructions are sensitive to restrictions in the verbal domain. It is shown that these semantic restrictions can be explained by a uniform semantic constraint on the measure function, namely, Schwarzschild’s (2002, 2006) monotonicity constraint. In particular, I argue that the measure function of the two constructions at issue is subject to the monotonicity constraint, and that we observe different semantic restrictions depending on whether the measure function applies to a nominal or verbal domain. I further argue that the mechanism of event measurement requires a semantic mapping from events to individuals, and thus the measure function in the end applies to individuals mapped from events. This mechanism enables us to account for at least three characteristic semantic properties of split MP constructions: (i) (in)compatibility with single-occurrence events, (ii) incompatibility with individual-level predicates, and (iii) (un)availability of collective readings. Moreover, the proposed analysis makes a strong case that event arguments exist in the grammar and that there is a semantic correlation between individuals in the nominal domain and events in the verbal domain. It must be noted that, although the Japanese FQ construction and the German ST have several semantic properties in common, they are different in that only the German ST is subject to the pragmatic constraints that the host NP must be a contrastive topic and that the split MP must be a focus. Chapter 5 discusses a possible explanation for the semantic properties of the German ST by appealing to these constraints. Until then, the pragmatic characteristics of the German ST will be suppressed. Moreover, syntactic differences between the two are also suppressed until Chapter 3. The organization of this chapter is as follows. In section 2, I examine the relation between MPs and their host NPs in non-split and split MP constructions, and argue that both non-split and split MP constructions are subject to semantic restrictions in the nominal domain. In section 3, I examine how these MPs are related to verbal predicates, and argue that only split MP constructions are sensitive to semantic restrictions in the verbal domain. Section 4 presents the mechanism of measurement involved in split MP constructions. Section 5 shows that the proposed mechanism is able to account for a wide range of data on distributive-collective readings. Section 6 concludes this chapter.

40 The semantic properties of non-split/split MP constructions 2. Monotonicity in the nominal domain This section first presents some examples indicating that non-split and split MP constructions are semantically restricted with respect to nominal measurement. Then I give a formal definition of Schwarzschild’s (2002, 2006) monotonicity constraint and show that this can account for the semantic restrictions on the two constructions.

2.1. The data I present two sets of data indicating that both non-split and split MPs are subject to some semantic restrictions in the nominal domain. First, not all MPs can be used in these constructions. The examples in (4) and (7) above show that MPs such as three liters can appear both in non-split and split MP constructions. In contrast, three degrees is inappropriate, as shown in (8) (Japanese) and (9) (German). (8)

a.* [Mizu san-do]-ga tukue-nouede kobore-ta. [water three-degree]-NOM table-on spill-PAST ‘Three degree water spilled on the table.’ b.* Mizu-ga tukue-nouede san-do kobore-ta. water-NOM table-on three-degree spill-PAST

(9)

a.* Hans hat [drei Grad Wasser] getrunken. Hans has [three degree water] drunk ‘(lit.) Hans drank three degrees of water.’ b.* Wasser hat Hans drei Grad getrunken. water has Hans three degree drunk

Second, in German, not all NPs can be the host NP of non-split and split MPs. Specifically, a mass NP or a plural count NP, but not a singular count NP, can be the host NP in non-split and split MP constructions. For instance, the mass NP Traubenmarmelade ‘grape jam’ in (10) and the plural count NP Trauben ‘grapes’ in (11) can be host NPs, whereas the singular count NP Traube ‘grape’ in (12) cannot.

Monotonicity in the nominal domain 41

(10) a. Hans hat [drei Kilo Traubenmarmelade] Hans has [three kilo grape jam] ‘Hans bought three kilos of grape jam.’ b. Traubenmarmelade hat Hans drei Kilo grape jam has Hans three kilo (11) a. Hans hat [drei Kilo Trauben] Hans has [three kilo grapes] ‘Hans bought three kilos of grapes.’ b. Trauben hat Hans drei Kilo grapes has Hans three kilo

gekauft. bought gekauft. bought

gekauft. bought gekauft. bought

(12) a.?? Hans hat [drei Gramm Traube] gekauft.6 Hans has [three gram grape] bought ‘(lit.) Hans bought three grams of grape.’ b.??Traube hat Hans drei Gramm gekauft. grape has Hans three gram bought Note that this contrast cannot be attested in Japanese, since Japanese generally lacks an overt grammatical marking of nominal plurality or of a masscount distinction (see Chapter 1: section 3.2 for more discussion; see also section 2.4 below). The question to be addressed now is why there are such restrictions.

2.2. Schwarzschild’s (2002, 2006) monotonicity constraint The same restrictions are observed in English pseudopartitives (e.g., five inches of cable, two days of work).7 To refer to water whose volume is three liters, English uses a pseudopartitive, as in (13a). However, Schwarzschild (2002, 2006) points out that the same construction cannot be used to

6. ‘A grape whose weight is three grams’ needs to be expressed as follows: (i) eine drei Gramm schwere Traube a three gram heavy grape 7. Pseudopartitives differ syntactically from partitives in the use of the definite article: pseudopartitives occur with a bare NP as in three pounds of apples, whereas partitives occur with a definite NP as in three pounds of the/those/her apples (see Selkirk 1977).

42 The semantic properties of non-split/split MP constructions express water whose temperature is three degrees, as in (13b). Similarly, Krifka (1989) shows that it is possible to say (14a), but not (14b).8 (13) a. three liters of water b.* three degrees of water (14) a. five ounces of gold b.* twenty carats of gold

(Krifka 1989: 82)

Schwarzschild (2002, 2006) identifies another restriction on pseudopartitives: mass NPs and plural count NPs, but not singular count NPs, can be used in pseudopartitives, as in (15). (15) a. seven pounds of meat b. seven pounds of marbles c.?? seven pounds of baby Schwarzschild accounts for these restrictions by examining how a measure function µ applies to a measured NP.9 For him, a measure function is a measurement scheme (e.g., volume, temperature, depth) obtained from a relation between a MP and the element to which it applies.10 This is partly

8. Besides expressing the purity of gold, carat may denote a measure of weight (1 carat = 200 mg). When expressing weight, carat can be used in pseudopartitives, as in 23 carats of amethyst (Schwarzschild 2006: 74). 9. Schwarzschild (2006) adopts the term “dimension” rather than “measure function”. 10. Schwarzschild’s (2002, 2006) analysis departs from the standard analysis of MPs where a measure function is lexically denoted by a measure word (e.g., liter in three liters of water) and the measure function is a function from individuals to numbers, preserving certain structures in the object domain, as in (i) (Krifka 1989, Higginbotham 1994, Chierchia 1998a). (i) [[three liters of water]] = ∃x[water(x) ∧ liter(x)=3] Schwarzschild makes this change, noting that the standard analysis of MPs is subject to the following three problems. First, the standard analysis does not extend to other occurrences of MPs such as three feet longer or three feet away (see Chapter 3: section 4). Second, it faces difficulties in examples without numerals such as several liters of water. Presumably, the measure function denoted by liter maps an individual to a number denoted by several. However, several cannot be used in contexts where numbers are called for (e.g., *four

Monotonicity in the nominal domain 43

based on the observation that, in constructions involving measurement, the relevant measure function is determined by different factors such as world knowledge, context, and so forth (see Schwarzschild 2006: section 3.1 for this point). For instance, in John bought five ounces of gold, the measure function is “weight”, since five ounces specifies how much the gold weighs. The function is “length” in John bought three feet of rope, and “depth” in three feet of snow piled up. In the following, a measure function µ under Schwarzschild’s analysis is indicated as µ: measurement scheme (e.g., µ: volume). Schwarzschild argues that the relation between a measure function and a measured NP is not uniform, as illustrated by the following comparison between µ: volume and µ: temperature. If a quantity of water has a certain volume, proper subparts of it will have lower volumes and superparts of it will have higher volumes. In this sense, µ: volume tracks part-whole relations. µ: temperature, however, does not, since if the water has a certain temperature, it is not necessarily true that proper subparts of it have lower temperatures or that superparts have higher temperatures. Schwarzschild calls a measure function monotonic relative to the denotation of an entity if and only if it tracks the part-whole structures of the entity.11 That is, a measure obtained for that entity is larger than a measure obtained for proper subparts of it, and is smaller than a measure obtained for proper superparts of it. I formulate this notion of monotonicity as in (16), where (16i) serves as a pre-condition for (16ii). (16) A measure function µ is monotonic relative to domain I iff: (i) there are at least two individuals x, y in I such that x is a proper subpart of y (i.e., x < y), and (ii) for all x, y in I such that x < y, µ(x) < µ(y)

plus several is less than ten). Third, it cannot account straightforwardly for plural agreement on measure words. See Schwarzschild (2002: 233) for details. 11. Schwarzschild’s monotonicity here is based on Lønning’s (1987) notion of monotonicity. Lønning is concerned with “how much of mathematics should be part of the semantics” (Schwarzschild 2002: 227), and proposes “monotonicity” as an alternative to “additivity”. His definitions of these two notions are cited below: (i) ADD: if a and b do not overlap then µ(a+b) = µ(a)+µ(b) (Lønning 1987: 39) (ii) MON: if a ≤ b then µ(a) ≤ µ(b) (Lønning 1987: 41)

44 The semantic properties of non-split/split MP constructions Let us now go back to the examples in (13). µ: volume is monotonic to the denotation of water, or [[water]], while µ: temperature is not monotonic to it. Schwarzschild captures the contrast in (13) by claiming that the measure function in pseudopartitives must be monotonic relative to the partwhole structure given by the meaning of the noun phrase. Since µ: volume, but not µ: temperature, is monotonic to [[ water]] , three liters of water is acceptable, but not three degrees of water. Regarding (14), the relevant measure functions for five ounces of gold and *twenty carats of gold are µ: weight and µ: purity, respectively. µ: weight, but not µ: purity, can be monotonic to part-whole relations of gold.12 Schwarzschild provides the example three inches of cable to support his analysis. This means that the length of the cable is three inches, but cannot mean that the diameter of the cable is three inches. Schwarzschild claims that, although both µ: length and µ: diameter are equally relevant dimensions, only the former can be monotonic to [[cable]], and thus only the length interpretation is available in the pseudopartitive. While it is easy to see the part-whole relation of a cable in terms of linear segments, a cable is not usually considered to have subparts whose diameters are smaller than that of the whole. Schwarzschild further discusses some cases where a seemingly unnatural monotonic interpretation becomes salient with the help of the context. For instance, ten inches of oil may sound odd initially, since oil is not usually measured in inches. However, if we can find a measurement scheme which applies to [[ oil]] in a monotonic fashion, the monotonicity account predicts that this example would be acceptable. This prediction is borne out, as discussed in Schwarzschild (2002: 226); when there is a growing pool of

12. See Krifka (1989) for an alternative analysis appealing to the extensivity of measure functions. For Krifka, measure functions are lexically denoted by measure words and measure functions are functions from individuals to numbers (see footnote 10 above). Krifka argues that in pseudopartitives measure functions must be extensive, satisfying additivity; if there are two objects whose weights are two ounces and three ounces, respectively, an extensive measure function yields five ounces. In five ounces of gold, the measure function ounces is extensive (e.g., two ounces plus three ounces will give us five ounces), while carats in *twenty carats of gold is not (e.g., we cannot obtain twenty carats by adding five carats and fifteen carats).

Monotonicity in the nominal domain 45

oil seeping out of the ground, oil is measured by µ: diameter, hence ten inches of oil is acceptable.13 The proposed monotonicity analysis is capable of accounting for the contrast in (15). Meat is a mass NP, and the extension of a mass NP has a part-whole relation; if you have a chunk of meat, any smaller chunk of that piece is still meat, and, if there are two chunks of meat, their sum is also meat. Thus, the measure function such as µ: weight can be monotonic relative to the denotation of mass NPs. The same argument holds for the plural count NP marbles. Plural count NPs come with a non-trivial part-whole structure given by the plural-part structure (e.g., if x and y are marbles, the sum of x and y are marbles as well).14 In contrast, baby is a singular count NP, and the extension of a singular count NP is atomic, that is, it has nothing but a trivial part-whole relation (Chapter 1: section 3.1). According to (16), for the measure function to be monotonic relative to a domain, that domain must contain at least two members in a part-whole relation. This is not met, hence the measure function fails to be monotonic with respect to [[baby]]. We could manipulate a part-whole structure by interpreting baby like meat, but that would evoke a gruesome interpretation.15 In sum, Schwarzschild (2002, 2006) argues that pseudopartitives in English must satisfy what I call the monotonicity constraint in the nominal domain: the measure function µ must be monotonic relative to the partwhole structure given by the meaning of the host NP (the definition of monotonicity is given in (16)). The monotonicity constraint accounts for the contrast between µ: volume and µ: temperature, and between mass/plural count NPs and singluar count NPs.

13. Elsi Kaiser (p.c.) suggests that a more natural context could be constructed with µ: depth. For example, in a room where the floor is covered with ten inches of oil, the layer of oil is ten inches deep. 14. Pseudopartitives with plural count nouns are not always acceptable. I discuss this issue in section 2.4 below. 15. Schwarzschild’s monotonicity analysis faces a serious problem with the numeral one; in one dog, which is fully acceptable, µ: cardinality cannot be monotonic to [[dog]] , since [[dog]] does not come with a non-trivial part-whole structure. We may be able to dismiss this problem by adopting the claim that one is different from other numbers both syntactically and semantically (see, for instance, Borer 2005).

46 The semantic properties of non-split/split MP constructions 2.3. The application to Japanese and German data I now show that the monotonicity approach extends straightforwardly to the Japanese and German data presented in section 2.1. First, we have seen that, just like the English pseudopartitive, the Japanese and German non-split and split MP constructions show the contrast between three liters and three degrees: the former, but not the latter, is acceptable in the two constructions ((4) and (8) for Japanese, (7) and (9) for German). Extending Schwarzschild’s (2002, 2006) analysis to Japanese and German data, I claim that the measure function µ in the non-split and split MP constructions must obey the monotonicity constraint, that is, µ must be monotonic relative to the part-whole structure of the host NP. The measure function µ for three liters + water is µ: volume and it is monotonic relative to [[water]]. In contrast, µ: temperature, which is the measure function for three degrees + water, is not. Hence, only µ: volume satisfies the monotonicity constraint. This analysis can also account for examples (17) and (18). (17) a. John-ga [keeburu san-senti]-o kinoo kat-ta. John-NOM [cable three-centimeter]-ACC yesterday buy-PAST OK length: ‘John bought three centimeters of cable yesterday.’ *diameter: ‘John bought a three centimeter cable yesterday.’ b. John-ga keeburu-o kinoo san-senti kat-ta. John-NOM cable-ACC yesterday three-centimeter buy-PAST OK length, *diameter (18) a. Hans hat [drei Zentimeter Kabel] Hans has [three centimeter cable] OK length, *diameter b. Kabel hat Hans drei Zentimeter cable has Hans three centimeter OK length, *diameter

gekauft. bought gekauft. bought

Presumably, when the MP three inches combines with cable, we should be able to obtain the following two readings: the reading that the length of cable is three inches and the reading that the diameter of cable is three inches. However, in both non-split and split MP constructions, only the length reading is available. We can easily imagine a cable having a partwhole structure in terms of length, but it is hard to imagine a context where

Monotonicity in the nominal domain 47

a cable has a non-trivial part-whole relation in terms of diameter. Thus, µ: length, but not µ: diameter, can be monotonic to [[cable]], which accounts for why only the length interpretation is available. The monotonicity approach applies to numerals as well (Schwarzschild 2006:92, see also Krifka 1989). Numerals express the cardinality of the relevant entity. For example, in drei Studenten ‘three students’ in German, drei specifies that the cardinality of a group of students is three. Thus, I assume that the measure function associated with numerals is µ: cardinality. This measure function is always monotonic to [[NP]] . For instance, if a set of Studenten ‘students’ has a certain cardinality (three in drei Studenten ‘three students’), every proper subpart of that set of students will have a lower cardinality (e.g., ‘two students’ is a subpart of ‘three students’ and has a lower cardinality, namely, two). Furthermore, superparts of that set will have a higher cardinality (e.g., ‘five students’ is a superpart of ‘three students’ and has a higher cardinality, namely, five). Recall that numerals in Japanese must be followed by a classifier, yielding a classifier phrase (ClP) such as san-nin ‘three-CL ’. ClPs necessarily express the cardinality of individuals of a certain kind, while numerals denote the cardinality of any type of entity (individuals, events, etc.) (cf. Krifka 1995). It follows that the measure function associated with ClPs is µ: cardinality-of-individuals. Just like µ: cardinality, µ: cardinality-of-individuals is always monotonic relative to [[NP]] . In fact, the example of µ: cardinality illustrated above is on µ: cardinality-of-individuals (or more specifically, cardinality of students). Since the measure function associated with numerals or with ClPs is always monotonic to the denotation of NP (as long as the NP has a part-whole structure in terms of cardinality), we would predict that numerals and ClPs can be used both in non-split and split MP constructions, which is the case. Recall the restriction on the host NP observed for German in (10), (11), and (12): a mass NP Traubenmarmelade ‘grape jam’ and a plural count NP Trauben ‘grapes’ are acceptable in both non-ST and ST, whereas a singular count NP Traube ‘grape’ is not. This is because the extensions of a mass NP and of a plural count NP are lattices of individuals with part-whole relations, while the extension of a singular count NP lacks non-trivial partwhole relation, so there is no way of applying a measure function in a monotonic fashion. That is, with a singular count NP, (16i) cannot be met. Additional examples of the contrast between mass NPs and plural count NPs on the one hand and singular count NPs on the other are given below:16 16. I thank an anonymous reviewer for suggesting the examples in (19), (20), and (21). Ziegenkopf ‘goat head’ in (21) is a delicacy in many Turkish food stores.

48 The semantic properties of non-split/split MP constructions (19) a. [Drei Kilo Butter] lagerten im Kühlschrank. [three kilo butter] stored in.the fridge ‘Three kilos of butter were stored in the fridge.’ b. Butter lagerten drei Kilo im Kühlschrank. butter stored three kilo in.the fridge (20) a. [Drei Kilo Kaffeebohnen] lagerten im Kühlschrank. [three kilo coffee beans] stored in.the fridge ‘Three kilos of coffee beans were stored in the fridge.’ b. Kaffeebohnen lagerten drei Kilo im Kühlschrank. coffee beans stored three kilo in.the fridge (21) a.?? [Drei Kilo Ziegenkopf] lagerten im Kühlschrank. [three kilo goat.head] stored in.the fridge ‘(lit.) Three kilos of goat head were stored in the fridge.’ b.??Ziegenkopf lagerten drei Kilo im Kühlschrank. goat.head stored three kilo in.the fridge

2.4. Pragmatic considerations There is a potential problem with the monotonicity analysis: English pseudopartitives with plural count NPs are not always acceptable. Consider, for instance, twenty kilos of babies in English, which seems to be odd. The plural count NP has a non-trivial part-whole relation (Chapter 1: section 3.1), hence the monotonicity constraint can technically be met. I propose that the oddness of this example derives from pragmatics. In general, individual babies are not measured by µ: weight, but by µ: cardinality using numerals (e.g., three babies). Thus, when µ: weight is used to measure babies, we tend to imagine a situation where some parts of babies are measured, which leads us to a gruesome interpretation. If we create a context where individual babies can be measured by µ: weight, twenty kilos of babies should sound better. For instance, suppose that a nurse moved babies to a doctor’s room using a big cart and that the cart could carry up to twenty kilos. Then we might be able to say A nurse carried twenty kilos of babies on a cart. Thus, besides the monotonicity constraint on the host NP, there must be a pragmatic constraint on selecting an appropriate measurement scheme for the host NP (e.g., for babies, µ: cardinality rather than µ: weight).

Monotonicity in the nominal domain 49

The same observation obtains with non-split and split MP constructions in German: examples (22) are infelicitous without appropriate contexts. Given that German and English have the same mass-count distinction, we can account for the infelicity in (22) by applying the pragmatic explanation. (22) a. # Hans hat [zwanzig Kilo Babys] Hans has [twenty kilo babies] ‘Hans carried twenty kilos of babies.’ # b. Babys hat Hans zwanzig Kilo babies has Hans twenty kilo

getragen. carried getragen. carried

Interestingly, Japanese shows the same contrast between akanboo ‘baby’ in (23) and niku ‘meat’ in (24). (23) a. # John-ga kinoo [akanboo nizyuk-kiro]-o John-NOM yesterday [baby twenty-kilo]-ACC ‘John lifted twenty kilos of babies yesterday.’ b. # John-ga akanboo-o kinoo nizyuk-kiro John-NOM baby-ACC yesterday twenty-kilo

motiage-ta. lift-PAST

(24) a. John-ga kinoo [niku nizyuk-kiro]-o John-NOM yesterday [meat twenty-kilo]-ACC ‘John lifted twenty kilos of meat yesterday.’ b. John-ga niku-o kinoo nizyuk-kiro John-NOM meat-ACC yesterday twenty-kilo

motiage-ta. lift-PAST

motiage-ta. lift-PAST

motiage-ta. lift-PAST

Note that examples (23) are unacceptable even with MPs such as san-kiro ‘three kilo’, which leads us to a singular interpretation of akanboo ‘baby’ (since three kilos is a plausible weight for one baby). This may suggest that Japanese as well as English and German has a mass-count distinction, contra Chierchia’s (1998b) claim that all nouns in classifier languages such as Japanese are mass (see Chapter 1: section 3.2). However, as discussed above for English and German, the oddness of (23) can be explained by a pragmatic constraint. Thus, the contrast in (23) and (24) may have nothing to do with the mass-count distinction. That is, the contrast here does not necessarily serve as evidence for the mass-count distinction in Japanese. For lack of better evidence, I continue to assume that Japanese makes no grammatical distinction between mass and count NPs.

50 The semantic properties of non-split/split MP constructions In sum, besides the monotonicity constraint on the host NP, a pragmatic constraint is also needed to account for the distribution of non-split and split MP constructions (as well as of pseudopartitives). In particular, objects must be measured by an appropriate measurement scheme.

2.5. Notes on non-monotonic constructions Before concluding this section, I briefly comment on constructions that show non-monotonic effects. Schwarzschild (2002, 2006) compares the pseudopartitive two inches of cable with two inch cable, calling the latter attributive, because he considers the MP in two inch cable to be in the position of an attributive adjective. He argues that a measure function in attributives is required to be non-monotonic to the relevant part-whole relation. For instance, we may think of the measure functions µ: length and µ: diameter as possible ways of measuring cable by using the expression two inches. The two differ in that µ: length is monotonic to [[cable]], whereas µ: diameter is non-monotonic to it. Only the diameter interpretation obtains in the attributive two inch cable. In the same vein, although “water whose temperature is three degrees” cannot be expressed by a pseudopartitive (because of the monotonicity constraint), it can be expressed by an attributive, as in three degree water. German and Japanese have examples that may be considered as attributives. In German, the measure function associated with the prenominal modifier n-prozentig ‘n-percent’ must be non-monotonic to [[NP]] . In (25), the percentage of alcohol is non-monotonic to [[Schnaps]] : if the percentage of alcohol in a certain body of liquid is 30%, the percentage of alcohol in any subpart of this liquid is also 30%, neither more nor less.17,18 17. I thank an anonymous reviewer for providing (25) as an example of a nonmonotonic construction. 18. More non-monotonic examples in German (and one of its dialects) can be found in Schwarzschild (2006: 84) (cited in (i) and (ii)). (i) Adjectival affix on measure phrase foif-gred-igs Wasser five-degree-ADJ water ‘five degree water’ (Swiss German) (ii) Stress on measure phrase 2 Milliméter Kabel ‘2 millimeter cable’ (German)

Monotonicity in the nominal domain 51

(25) Hans hat [30-prozentigen Schnaps] Hans has [30-percent schnapps] ‘Hans drank 30% alcohol schnapps.’

getrunken. drunk

In Japanese, the configuration in (26) lets three degrees combine with water to yield the reading “water whose temperature is three degrees”. (26) [San-do-no mizu]-ga tukue-nouede kobore-ta. [three-degree-GEN water]-NOM table-on spill-PAST ‘Three degree water spilled on the table.’ Following Schwarzschild’s analysis of attributives, we may claim that the measure function must be non-monotonic relative to [[ NP]] in German and Japanese prenominal modifiers, whereas it must be monotonic in nonsplit and split MP constructions. However, Japanese prenominal modifiers can be used even when the measure function is monotonic relative to [[NP]] , as in (27). Similarly, (28) allows both length and diameter readings. (27) [San-rittoru-no mizu]-ga tukue-nouede [three-liter-GEN water]-NOM table-on ‘Three liters of water spilled on the table.’

kobore-ta. spill-PAST

(28) John-ga kinoo [san-senti-no keeburu]-o kat-ta. John-NOM yesterday [three-centimeter-GEN cable]-ACC buy-PAST OK length: ‘John bought three centimeters of cable yesterday.’ OK diameter: ‘John bought a three centimeter cable yesterday.’ Thus, at least in Japanese, it seems that no construction is exclusively nonmonotonic. For this reason, I do not discuss non-monotonicity any further, and continue to focus on monotonicity of non-split and split MP constructions. For an extensive discussion on non-monotonicity, see Schwarzschild (2002, 2006).

2.6. Summary of section 2 This section demonstrated that Japanese and German non-split and split MP constructions are subject to some semantic restrictions in terms of nominal predicates. Following Schwarzschild (2002, 2006), I accounted for the

52 The semantic properties of non-split/split MP constructions restrictions by appealing to the monotonicity constraint in the nominal domain: the measure function must be monotonic relative to the part-whole structure given by the meaning of the host NP (as defined in (16)).

3. Monotonicity in the verbal domain We saw in section 2 that the non-split and split MP constructions in Japanese and German behave alike in terms of monotonicity in the nominal domain. This section demonstrates that they differ in at least three respects: compatibility with single-occurrence events, compatibility with individuallevel predicates, and availability of collective readings. The data are explained by extending the monotonicity constraint in the nominal domain to the verbal domain. In particular, I argue that, while non-split MP constructions are sensitive to the monotonicity constraint in the nominal domain, split MP constructions obey the constraint in the verbal domain.19 There is a caveat: in the examples in this section, the host NP is always syntactically the subject (or more precisely, the external argument). Examples where the host NP is an object (or an internal argument) are discussed in section 5.5, where I present asymmetries between MPs associated with external arguments and MPs associated with internal arguments.

3.1. The data The previous section revealed that non-split and split MP constructions are equally sensitive to the monotonicity constraint in the nominal domain. If we turn our attention to the verbal domain, however, we observe some differences. Specifically, the distribution of split MP constructions is more restricted than that of their non-split counterparts: split MP constructions are incompatible with single-occurrence events (section 3.1.1), they cannot co-occur with individual-level predicates (section 3.1.2), and they generally disallow collective interpretations (section 3.1.3). 19. In section 4, I argue that the measure function in split MP constructions indirectly measures events by measuring individuals mapped from events and that the monotonicity constraint is imposed on individuals mapped from events. In other words, the monotonicity constraint does not directly apply to the verbal domain. Rather, the monotonicity effect in the verbal domain is a side-effect of the monotonicity constraint applied to individuals mapped from events.

Monotonicity in the verbal domain 53

3.1.1. Single-occurrence events The first difference between non-split and split MP constructions relates to the sorts of VPs that they occur with. The Japanese examples in (29a) and (30a) show that non-split MP constructions are compatible with any VP, but not all VPs can be used in split MP constructions, as illustrated by the contrast between (29b) with hit Peter and (30b) with kill Peter. The same contrast holds for German, as shown in (31) and (32).20 (29) a. [Gakusei san-nin]-ga kinoo Peter-o [student three-CL]-NOM yesterday Peter-ACC ‘Three students hit Peter yesterday.’ b. Gakusei-ga kinoo san-nin Peter-o student-NOM yesterday three-CL Peter-ACC

tatai-ta. hit-PAST

(30) a. [Gakusei san-nin]-ga kinoo Peter-o [student three-CL]-NOM yesterday Peter-ACC ‘Three students killed Peter yesterday.’ b.??Gakusei-ga kinoo san-nin Peter-o student-NOM yesterday three-CL Peter-ACC

korosi-ta. kill-PAST

(31) a. [Drei Studenten] haben [three students] have ‘Three students hit Peter.’ b. Studenten haben Peter students have Peter

tatai-ta. hit-PAST

korosi-ta. kill-PAST

Peter geschlagen. Peter hit drei geschlagen. three hit

(32) a. [Drei Studenten] haben Peter [three students] have Peter ‘Three students killed Peter.’ b.??Studenten haben Peter drei students have Peter three

umgebracht. killed umgebracht. killed

The observation here is that split MP constructions are subject to a restriction in the verbal domain, whereas there is no restriction for non-split MP constructions. More precisely, split MP constructions are incompatible 20. In the case of German, the contrast in (31b) and (32b) may result from the pragmatics of the sentences. This issue will be discussed in Chapter 5: section 3.

54 The semantic properties of non-split/split MP constructions with VPs denoting an event that can occur only once such as kill Peter. Indeed, (30b) and (32b) with kill Peter are acceptable in the context where Peter is a zombie who can possibly die multiple times. The following examples further confirm the validity of this observation ((33) and (35) for Japanese, (34) and (36) for German): a single-occurrence event such as break that table and build that statue is compatible with non-split MP constructions, but not with split MP constructions. (33) a. [Gakusei san-nin]-ga kinoo sono tukue-o [student three-CL]-NOM yesterday that table-ACC ‘Three students broke that table yesterday.’ b.??Gakusei-ga kinoo san-nin sono tukue-o student-NOM yesterday three-CL that table-ACC (34) a. [Drei Studenten] haben gestern dieses Buch [three students] have yesterday this book ‘Three students destroyed this book yesterday.’ b.??Studenten haben gestern dieses Buch drei students have yesterday this book three

kowasi-ta. break-PAST

vernichtet. destroyed vernichtet. destroyed

(35) a. [Geizyutuka san-nin]-ga kinoo sono doozoo-o [artist three-CL]-NOM yesterday that statue-ACC ‘Three artists built that statue yesterday’ b.??Geizyutuka-ga kinoo san-nin sono doozoo-o artist-NOM yesterday three-CL that statue-ACC (36) a. [Drei Studenten] haben es gestern [three students] have it yesterday ‘Three students built it yesterday.’ b.??Studenten haben es gestern drei students have it yesterday three

kowasi-ta. break-PAST

tukut-ta. make-PAST tukut-ta. make-PAST

gebaut. built gebaut. built

3.1.2. Individual-level predicates The second difference is found in stage-/individual-level predicates. Carlson (1977) argues that predicates can be classified into two classes, namely, stage-level (S-level) and individual-level (I-level) predicates. The former correspond more or less to temporal states, and the latter to permanent sta-

Monotonicity in the verbal domain 55

tes. In previous studies on the Japanese floating quantifier (FQ) construction (or split MP construction in our term), it has been noted that FQs (or split MPs) are incompatible with I-level predicates (Fukushima 1991, Nishigauchi and Uchibori 1991).21 In (37), for instance, there is a contrast in acceptability between the S-level predicate genki-da ‘be healthy’ and the Ilevel predicate osu-da ‘be male’. In contrast, (38) shows that the corresponding non-split MP construction is compatible with both kinds of predicates. (37) a. Uti-no doobutuen-de-wa kaba-ga mada san-too genki-da. our zoo-at-TOP hippo-NOM still three-CL healthy ‘In our zoo, three hippos are still healthy.’ b.* Uti-no doobutuen-de-wa kaba-ga zannennakotoni our zoo-at-TOP hippo-NOM unfortunately san-too osu-da. three-CL male ‘In our zoo, unfortunately, three hippos are male.’ (Mihara 1998: 110–111) (38) a. Uti-no doobutuen-de-wa [kaba san-too]-ga mada genki-da. our zoo-at-TOP [hippo three-CL]-NOM still healthy b. Uti-no doobutuen-de-wa [kaba san-too]-ga our zoo-at-TOP [hippo three-CL]-NOM zannennakotoni osu-da. unfortunately male More examples are provided below. Examples (39) show that both nonsplit and split MP constructions can co-occur with S-level predicates such as byooki-dearu ‘be sick’. In contrast, as in (40), only non-split MP constructions are compatible with I-level predicates such as kasikoi ‘be smart’. The examples in (41) and (42) indicate that the same contrast is observed with genuine MPs, assuming kusatteiru ‘be rotten’ is an S-level predicate and kokusan-dearu ‘be domestic’ is an I-level predicate.

21. Some studies claim that FQs (or split MPs) are compatible with active predicates, but not with stative predicates (Harada 1976, Ohki 1987, Mihara 1998). This kind of analysis fails, however, to capture the contrast in (37), where both predicates are stative. Thus, it is the distinction between S-level and I-level predicates that matters, not the distinction between active and stative predicates.

56 The semantic properties of non-split/split MP constructions (39) a. Kono kurasu-de [gakusei san-nin]-ga this class-in [student three-CL]-NOM ‘Three students are sick in this class.’ b. Gakusei-ga kono kurasu-de san-nin student-NOM this class-in three-CL

byooki-dearu. sick

(40) a. Kono kurasu-de [gakusei san-nin]-ga this class-in [student three-CL]-NOM ‘Three students are smart in this class.’ b.??Gakusei-ga kono kurasu-de san-nin student-NOM this class-in three-CL

kasikoi. smart

(41) a. [Koko-ni aru gyuuniku go-kiro]-ga [here-at be beef five-kilo]-NOM ‘Five kilos of beef here are rotten.’ b.??Koko-ni aru gyuuniku-ga go-kiro here-at be beef-NOM five-kilo

kusatteiru. rotten

(42) a. [Koko-ni aru gyuuniku go-kiro]-ga [here-at be beef five-kilo]-NOM ‘Five kilos of beef here are domestic.’ b.??Koko-ni aru gyuuniku-ga go-kiro here-at be beef-NOM five-kilo

kokusan-dearu. domestic

byooki-dearu. sick

kasikoi. smart

kusatteiru. rotten

kokusan-dearu. domestic

Let us now turn to German. Independently of the observations made for the Japanese FQ construction, it has been observed that German Split Topicalization is compatible with S-level predicates, but not with I-level ones, as shown in (43) (Diesing 1992, Pafel 1995). Examples (44) and (45) show that, as in Japanese, the non-split MP construction in German is acceptable with both types of predicates, while the corresponding split MP examples are compatible only with S-level predicates. (43) a. Wildschweine sind viele verfügbar. wild boars are many available ‘As for wild boars, many are available.’ b.* Wildschweine sind viele intelligent. wild boars are many intelligent ‘As for wild boars, many are intelligent.’

(Diesing 1992: 40)

Monotonicity in the verbal domain 57

(44) a. [Drei Feuerwehrleute] sind [three firemen] are ‘Three firemen are available.’ b. Feuerwehrleute sind drei firemen are three

verfügbar. available

(45) a. [Drei Feuerwehrleute] sind [three firemen] are ‘Three firemen are intelligent.’ b.* Feuerwehrleute sind drei firemen are three

intelligent. intelligent

verfügbar. available

intelligent. intelligent

3.1.3. Collective readings The third difference between non-split and split MP constructions lies in the availability of collective interpretations. Sentences with plural subjects are known to evoke a semantic ambiguity that is not available with singular subjects, as in (46). While (46a) simply states that John lifted the piano, (46b) could mean that John and Peter together lifted the piano (collective reading) or that they each lifted the piano (distributive reading) (see section 5.1 for more discussion). (46) a. John lifted the piano. b. John and Peter lifted the piano. It has been observed that the FQ construction (or split MP construction in our term) in Japanese allows for a distributive, but not a collective, reading (Terada 1990, Kitagawa and Kuroda 1992, Ishii 1999, Kobuchi-Philip 2003, among others: see also section 5 below for more discussion). For example, the non-split MP construction in (47a) has the collective reading that three boys together built one boat and the distributive reading that each of the three boys built a boat, yielding three boats.22 In contrast, the split MP construction in (47b) allows only for the distributive reading.

22. Note that (47a) has another collective reading where a group of three boys together built a boat multiple times, which yields multiple boats. Example (47b) lacks this collective reading as well as the collective reading yielding one boat. For the sake of simplicity, in this section and section 3.2.3, I consider only the

58 The semantic properties of non-split/split MP constructions (47) a. [Otokonoko san-nin]-ga kinoo [boy three-CL]-NOM yesterday ‘Three boys built a boat yesterday.’ OK distributive, OKcollective b. Otokonoko-ga kinoo san-nin boy-NOM yesterday three-CL OK distributive, ??collective

booto-o tukut-ta. boat-ACC make-PAST

booto-o tukut-ta. boat-ACC make-PAST

Similarly, (48b) means that each of three students found a ten dollar bill, but it does not mean that three students together found one bill. Example (49b) can involve two friends, each of whom got married to someone, i.e., there were two couples, but it cannot mean that two friends married each other, which involves only one couple. The non-split MP construction in (48a) and (49a) has both distributive and collective readings. (48) a. [Gakusei san-nin]-ga mitibata-de zyuu-doru-satu-o [student three-CL]-NOM roadside-by ten-dollar-bill-ACC hirot-ta. find-PAST ‘Three students found a ten dollar bill by the roadside.’ OK distributive, OKcollective b. Gakusei-ga mitibata-de san-nin zyuu-doru-satu-o student-NOM roadside-by three-CL ten-dollar-bill-ACC hirot-ta. find-PAST OK distributive, ??collective (49) a. [Tomodati huta-ri]-ga kinoo [friend two-CL]-NOM yesterday ‘Two friends got married yesterday.’ OK distributive, OKcollective b. Tomodati-ga kinoo huta-ri friend-NOM yesterday two-CL OK distributive, ??collective

kekkonsi-ta. marry-PAST

kekkonsi-ta. marry-PAST

The corresponding German non-split and split MP constructions show the same contrast, as in (50)–(52). reading where a group of three boys together built one boat. In section 4.2.3, I consider both collective readings and explain why (47b) lacks these readings.

Monotonicity in the verbal domain 59

(50) a. [Drei Jungen] haben ein Modellboot [three boys] have a model boat ‘Three boys built a model boat.’ OK distributive, OKcollective b. Jungen haben drei ein Modellboot boys have three a model boat OK distributive, ??collective

gebaut. built

gebaut. built

(51) a. [Drei Kinder] haben einen Zehn-Euro-Schein [three children] have a ten-Euro-bill im Straβengraben gefunden. in street-ditch found ‘Three children found a ten Euro bill in the gutter.’ OK distributive, OKcollective b. Kinder haben drei einen Zehn-Euro-Schein children have three a ten-Euro-bill im Straβengraben gefunden. in street-ditch found OK distributive, ?*collective (52) a. [Zwei Bekannte] haben gestern [two acquaintances] have yesterday ‘Two acquaintances married yesterday.’ OK distributive, OKcollective b. Bekannte haben gestern zwei acquaintances have yesterday two OK distributive, ?*collective

geheiratet. married

geheiratet. married

Note that the degree of unacceptability of collective interpretations seems to vary slightly among speakers. A possible source of this variation is discussed in section 5.3. Meanwhile, I continue to assume that collective readings with split MP constructions are unacceptable. There is another important observation that will be put off until section 5.4: split MP constructions are compatible with collective predicates such as surround and gather. In short, I will argue that collectivity in the examples presented above and collectivity in collective predicates are different in nature, and thus the occurrence of split MP constructions with collective predicates is not problematic for the monotonicity analysis presented in sections 3 and 4.

60 The semantic properties of non-split/split MP constructions 3.1.4. Summary of section 3.1 Summing up, we have observed that, unlike non-split MP constructions, split MP constructions are semantically more restricted at least in terms of the three properties summarized in Table 1. Table 1. Semantic properties of non-split / split MP constructions

Single-occurrence events S-/I-level predicates Distributive/collective

Non-split MP

Split MP

OK OK S-level, OKI-level OK distr, OKcollective

* OK OK

S-level, *I-level distr, *collective

3.2. The monotonicity constraint in the verbal domain (initial attempt) We are now faced with the following question: why are split MP constructions subject to semantic restrictions that are not observed with non-split MP constructions? In this section, I attempt to answer this question by extending Schwarschild’s (2002, 2006) monotonicity analysis in the nominal domain to the verbal domain. In section 3.1.1, we saw that a single-occurrence event such as kill Peter is incompatible with split MP constructions. This reminds us of a restriction observed in terms of the nominal domain in section 2, namely, a predicate without a non-trivial part-whole structure (e.g., baby) is not compatible with non-split and split MP constructions. This similarity opens up the possibility of extending the monotonicity constraint in the nominal domain to the verbal domain. In particular, I claim that split MP constructions are subject to the monotonicity constraint in the verbal domain. Recall that, in the nominal domain, the measure function applies to an individual in the extension of the host NP, and that the measure function µ must be monotonic relative to the part-whole structure given by the meaning of the NP. Given the parallelism between nominal and verbal domains discussed in Chapter 1, the measure function in the verbal domain should apply to an event in the extension of the VP. Then the measure function µ must be monotonic to the part-whole structure given by the meaning of the VP (see (16) for the definition of monotonicity). Although the current proposal is able to account for the properties of split MP constructions, as shown shortly, it fails to capture the fact that a

Monotonicity in the verbal domain 61

split MP is also associated with a NP (e.g., the MP in (50b) as well as (50a) expresses the number of boys). I discuss this extensively in section 4, where I revise the current proposal and argue that the monotonicity constraint applies not to events directly, but to individuals mapped from events. The goal of this section is, however, to show that split MP constructions, but not non-split MP constructions, involve measurement of events. Thus, for ease of exposition, the discussion in this section is restricted to the measurement of events, without considering the measurement of individuals.

3.2.1. On single-occurrence events The working hypothesis is that split MP constructions, but not non-split MP constructions, obey the monotonicity constraint in the verbal domain. Let us examine first the examples given in section 3.1.1 for the restriction on single-occurrance events. Take the contrast between hit Peter and kill Peter, repeated in (53) (Japanese) and (54) (German). (53) a. Gakusei-ga kinoo san-nin Peter-o student-NOM yesterday three-CL Peter-ACC ‘Three students hit Peter yesterday.’ b.??Gakusei-ga kinoo san-nin Peter-o student-NOM yesterday three-CL Peter-ACC ‘Three students killed Peter yesterday.’ (54) a. Studenten haben Peter drei students have Peter three ‘Three students hit Peter.’ b.??Studenten haben Peter drei students have Peter three ‘Three students killed Peter.’

tatai-ta. hit-PAST (= (29b)) korosi-ta. kill-PAST (= (30b))

geschlagen. hit (= (31b)) umgebracht. killed (= (32b))

As discussed in Chapter 1: section 4.1, a verbal predicate can be categorized into atelic and telic predicates depending on whether an event described by the predicate has a terminal point. Telicity of verbal predicates may be determined by combining them with durative adverbs (e.g., for ten minutes) and with time span adverbs (e.g., in ten minutes) (Dowty 1979). Examples (55) (Japanese) and (56) (German) show that hit Peter is atelic, while kill Peter is telic both in Japanese and German.

62 The semantic properties of non-split/split MP constructions (55) a. John-ga Peter-o {zyup-pun-kan / *zyup-pun-de} tatai-ta. John-NOM Peter-ACC {ten-minute-for / ten-minute-in} hit-PAST ‘John hit Peter {for ten minutes / *in ten minutes}.’ b. John-ga Peter-o {*zyup-pun-kan / zyup-pun-de} korosi-ta. John-NOM Peter-ACC {ten-minute-for / ten-minute-in} kill-PAST ‘John killed Peter {*for ten minutes / in ten minutes}.’ (56) a. Hans hat Peter {zehn Minuten lang / *in zehn Minuten} Hans has Peter {ten minutes long / in ten minutes} geschlagen. hit ‘Hans hit Peter {for ten minutes / *in ten minutes}.’ b. Hans hat Peter {*zehn Minuten lang / in zehn Minuten} Hans has Peter { ten minutes long / in ten minutes} umgebracht. killed ‘Hans killed Peter {*for ten minutes / in ten minutes}.’ Recall that the atelic-telic distinction in the verbal domain can be viewed as parallel to the mass-count distinction in the nominal domain (see Chapter 1: section 4). Then, we could say that hit Peter has a mass-like property and kill Peter has a count-like property. Put differently, the denotation of hit Peter has at least two members where one is a proper subpart of the other; a hitting-Peter event has a subevent that counts as a hitting-Peter event. The relevant measure function in (53a) and (54a) is considered to be µ: cardinality, and this function can be monotonic to the part-whole structure of the VP hit Peter. In contrast, kill Peter does not seem to provide anything but a trivial part-whole structure; a killing-Peter event does not have a subevent that is considered to be a killing-Peter event. For the measure function to be monotonic relative to the verbal domain, there needs to be (at least) two events with one a subevent of the other (see (16)). Thus, the measure function cannot be monotonic with respect to the VP kill Peter. In contrast, nonsplit MP constructions are immune to the monotonicity constraint in the verbal domain, and thus not sensitive to a part-whole structure of the VP. The current analysis predicts that a telic VP is compatible with the split MP construction so long as its denotation has a non-trivial part-whole structure. This prediction is borne out in (57) ((a) for Japanese, (b) for German). Kill a mouse is a telic VP (John killed a mouse {*for / in} one hour), but, unlike kill Peter, it can occur multiple times (since there are multiple mice,

Monotonicity in the verbal domain 63

as in John killed a mouse many times last year) (cf. Zucchi and White 2002). In this sense, kill a mouse in (57) is pluralized and thus has the plural-part structure. (57) a. Gakusei-ga kinoo san-nin nezumi-o korosi-ta. student-NOM yesterday three-CL mouse-ACC kill-PAST ‘Three students killed a mouse/mice yesterday.’ b.(?)Studenten haben drei eine Maus umgebracht. students have three a mouse killed ‘Three students killed a mouse.’ Regarding (57b), some informants with whom I consulted judged it to be a little awkward. I suspect that this may be caused by the interaction between scrambling and the information structure of Split Topicalization (ST). While the definite object can freely undergo scrambling to the higher position, as in (58), indefinite objects do not seem to undergo scrambling as freely as definite objects, as in (59) (Grewendorf and Sternefeld 1990). (58) a. Hans hat gestern Peter geschlagen. Hans has yesterday Peter hit ‘Hans hit Peter yesterday.’ b. Hans hat Peter1 gestern t1 geschlagen. Hans has Peter yesterday hit (59) a. Hans hat gestern einen Mann geschlagen. Hans has yesterday a man hit ‘Hans hit a man yesterday.’ b. ? Hans hat einen Mann1 gestern t1 geschlagen. Hans has a man yesterday hit In ST, there seems to be a preference of placing the focused split MP at the position preceding the sentence final non-finite verb, as in (60) (see Chapter 5: section 3 for more discussion on focus of ST). (60) a. ? Studenten haben drei Peter geschlagen. students have three Peter hit ‘Three students hit Peter yesterday.’ b. Studenten haben Peter1 drei t1 geschlagen. students have Peter three hit

64 The semantic properties of non-split/split MP constructions Consider now examples (61), which are parallel to (60) except the object is indefinite. (61a) is awkward for the same reason as (60a). Example (61b) is awkward because the scrambling of the indefinite object is restricted, as in (59b). Thus, the ST with an indefinite object always ends up to be awkward. (61) a. ? Studenten haben drei einen Mann geschlagen. students have three a man hit ‘Three students hit a man yesterday.’ b. ? Studenten haben einen Mann1 drei t1 geschlagen. students have a man three hit

3.2.2. On individual-level predicates The monotonicity analysis is also capable of accounting for the second set of data in section 3.1.2 regarding I-level and S-level predicates. Kratzer (1995) argues that S-level and I-level predicates differ in that the latter, but not the former, lack event arguments in their denotations. One of the strongest arguments comes from data on variable binding. Assuming that a when-clause introduces the quantifier always, the sentences in (62) are expressed by tripartite structures consisting of always, a restrictive clause, and a nuclear scope, as in (63) (see Heim 1982 for tripartite structures). Suppose that the S-level predicate speak, but not the I-level predicate know, has an event argument, expressed as ‘l’ in (63).23 Then the data in (62) is explained by the prohibition against vacuous quantification in (64). In (63b), the event argument serves as a free variable to be bound by the quantifier, which satisfies (64). Other examples violate (64). (62) a.* When Mary knows French, she knows it well. b. When Mary speaks French, she speaks it well. c.* When Mary speaks French, she knows it well. d. *When Mary knows French, she speaks it well. (Kratzer 1995: 129)

23. Kratzer (1995: 128) notes that she does not commit herself to a particular view of the precise nature of the Davidsonian argument. In fact, she mentions that what I-level predicates lack may not be an event argument, but may simply be an argument for a spatiotemporal location. Thus, ‘l’ in (62) is for a variable ranging over spatiotemporal locations.

Monotonicity in the verbal domain 65

(63) a.* Always [know(Mary, French)] [know-well(Mary, French)] b. Always [speak(Mary, French, l)] [speak-well(Mary, French, l)] c.* Always [speak(Mary, French, l)] [know-well(Mary, French)] d.* Always [know(Mary, French)] [speak-well(Mary, French)] (64) Prohibition against vacuous quantification For every quantifier Q, there must be a variable x such that Q binds an occurrence of x in both its restrictive clause and its nuclear scope. (Kratzer 1995: 131) Going back to the data on split MP constructions, we observed that they are incompatible with I-level predicates. This restriction naturally follows from the present monotonicity analysis in conjunction with Kratzer’s (1995) claim that I-level predicates lack event arguments. Without event arguments, the VP cannot provide a part-whole relation of events where the measure function applies monotonically.24,25 Supporting evidence comes from Mihara’s (1998) observation that the Japanese split MP construction with I-level predicates becomes acceptable when the split MP is followed by emphatic particles such as -dake ‘only’ and -tomo ‘all’, as shown in (65).

24. Diesing (1992) accounts for the data on ST with S-/I-level predicates in a different way. Assuming that ST involves extraction of the NP, extraction is possible when the subject is VP-internal, while it is prohibited when the subject is VP-external. The subjects of S-level predicates allow extraction, yielding ST, since they are VP-internal. In contrast, ST is impossible with I-level predicates, since the subjects of I-level predicates are VP-external, which disallows extraction (see also Kratzer 1995). This line of explanation, though, does not extend to the other two restrictions of ST on verbal predicates, namely, the incompatibility with single-occurrence events and the lack of collective readings. 25. We could consider I-level predicates as denoting a lattice other than a lattice of events. Indeed, some researchers argue that I-level predicates take an extra argument (e.g., a state argument) (Parsons 1990, Chierchia 1995), which makes it possible for the VP to have a part-whole structure (e.g., a lattice of states). If we claim that split MP constructions require just any part-whole structure of the VP, then we cannot explain the incompatibility with I-level predicates. Thus, for the current analysis to work, it is crucial to assume that split MP constructions require a lattice of events, and not just any lattice denoted by the VP.

66 The semantic properties of non-split/split MP constructions (65) Uti-no doobutuen-de-wa kaba-ga our zoo-at-TOP hippo-NOM zannennakotoni san-too{-dake / -tomo} osu-dearu. unfortunately three-CL{-only / -all} male ‘In our zoo, unfortunately, {only/all} three hippos are male.’ Mihara’s argument goes as follows: the emphatic particles signal that the counting of events described by the sentence is ended, which turns I-level predicates into eventive predicates. In (65), we can imagine that the speaker was counting the number of male hippos, and -dake ‘only’ or -tomo ‘all’ indicates that the speaker has finished counting. In this sense, (65) does not describe a permanent state. This analysis supports the claim that split MP constructions require the existence of event arguments. In contrast, the monotonicity constraint in the verbal domain is not imposed on non-split MP constructions. Thus, the constructions are compatible both with S-level and I-level predicates.

3.2.3. On collective readings Finally, the proposed analysis extends to the observation in section 3.1.3 that split MP constructions permit distributive, but not collective readings. One way of obtaining a distributive reading is to posit multiple events taking a different individual as an agent (see sections 4 and 5 for details). For instance, under the distributive reading of the boys built a boat, we can assume that there are multiple building-a-boat events and that each event takes a different boy as an agent. To put it differently, the VP build a boat is pluralized, and if so, it should have a part-whole structure just as plural NPs do. In contrast, the collective reading of the sentence obtains when a single building-a-boat event takes the boys as a group as an agent. Crucially, members of the group do not act as an agent, but the whole group does, and the group is the agent for a single building-a-boat event. In this sense, build a boat under the collective reading is analogous to kill Peter; the denotations of these predicates do not have a part-whole structure to which the measure function applies monotonically. As has been argued above, nonsplit MP constructions are not subject to the monotonicity constraint in the verbal domain. Hence, we expect them to allow both distributive and collective readings, which they do.

Mechanism of event measurement 67

3.3. Summary of section 3 In this section, I first showed that split MP constructions are semantically more restricted than their non-split counterparts at least in three respects: compatibility with single-occurrence events, compatibility with individuallevel predicates, and availability of collective readings. Then I argued that the monotonicity constraint in the verbal domain is capable of accounting for the differences. In particular, split MP constructions, but not non-split MP constructions, must obey the monotonicity constraint in the verbal domain, and this difference is responsible for the different semantic properties with respect to verbal predicates.

4. Mechanism of event measurement (revised attempt) The discussion in the previous section revealed that split MP constructions differ from non-split MP constructions in that the former, but not the latter, are sensitive to the monotonicity constraint in the verbal domain. This implies that the measure function in split MP constructions applies to a verbal predicate. Crucially, however, split MP constructions such as (66) are semantically different from constructions involving measurement in the verbal domain such as (67) with twice ((a) for Japanese, (b) for German). (66) a. Gakusei-ga kono zyup-pun-de huta-ri seki-o si-ta. student-NOM this ten-minute-in two-CL cough-ACC do-PAST ‘Two students coughed in the last ten minutes.’ b. Studenten haben in den letzten zehn Minuten zwei gehustet. students have in the last ten minutes two coughed ‘Two students coughed in the last ten minutes.’ (67) a. Gakusei-ga kono zyup-pun-de ni-kai seki-o si-ta. student-NOM this ten-minute-in two-times cough-ACC do-PAST ‘A student/students coughed twice in the last ten minutes.’ b. Studenten haben in den letzten zehn Minuten zweimal gehustet. students have in the last ten minutes twice coughed ‘Students coughed twice in the last ten minutes.’ While (66), with the split MP two, must involve two students, (67) with twice does not have to: (67) means that students whose cardinality is

68 The semantic properties of non-split/split MP constructions unspecified coughed twice, that is, ni-kai ‘twice’ or zweimal ‘twice’ is simply counting the number of events without expressing the number of students (cf. Doetjes 1997). This difference indicates that the measure function in (66) is not applying to events directly, unlike the measure function in (67). Furthermore, recall that the discussion in section 2 concluded that both split and non-split MP constructions are subject to semantic restrictions in terms of nominal predicates. Our assumption there was that the measure function in both constructions applies to individuals denoted by the host NP, and that this application must be carried out monotonically. Indeed, both split and non-split MPs in Japanese contain a classifier or a measure word that correlates with the host NP. In German, they contain a measure word that correlates with the host NP. For instance, in the Japanese example (66a), the MP contains a classifier -ri, which semantically agrees with the host NP gakusei ‘student’, indicating that huta-ri ‘two-CLASSIFIER’ must express the cardinality of the students. In this sense, the measure function µ: cardinality in (66a) applies to individuals denoted by the host NP. Regarding non-split MP constructions, we can simply claim that the measure function must apply to the host NP in a monotonic fashion, and thus the constructions are subject to restrictions in the nominal domain, but not to restrictions in the verbal domain. When it comes to split MP constructions, however, we face a dilemma. On the one hand, these constructions show the same nominal restrictions as their non-split counterparts. On the other hand, they also show verbal restrictions, which are not observed in nonsplit constructions. Thus, it appears that the measure function in split MP constructions applies to both nominal and verbal predicates. This section explores the question of resolving this dilemma. In section 4.1, I propose a mechanism that maps events in the verbal domain to individuals in the nominal domain, and claim that the measure function in split MP constructions applies to individuals mapped from events. Section 4.2 shows that the proposed mechanism is capable of accounting for the restrictions in the verbal domain discussed in sections 3. In section 4.3, I argue that monotonicity can be viewd as a formal property of measurement constructions. Section 4.4 provides a summary.

Mechanism of event measurement 69

4.1. The proposal The dilemma we face is this: the measure function in split MP constructions clearly applies to a VP, but at the same time, it seems to apply to a NP as well. To resolve this dilemma, I propose a mechanism that maps events to individuals and argue that, with the help of this mapping, the measure function in the split MP construction applies to individuals mapped from events. In this way, the split MP construction indirectly measures events by measuring individuals. This mechanism is similar to Krifka’s (1989), which he uses to analyze temporal adverbials such as for two hours in John slept for two hours (see also Lasersohn 1995). Krifka claims that temporal adverbials cannot apply directly to events, but can apply to entities that bear a relation to events, most notably times. That is, for two hours indirectly measures the sleeping event by measuring the run time of the event. Formally, Krifka assumes that there is a homomorphism from events E to event run times T. A homomorphism h is a function that preserves a structural relation defined on its domain in a similar relation defined on the range, as in h(e1∪Ee2) = h(e1)∪Th(e2), where ∪E and ∪T are sum operators for events and times, respectively (see also section 6 below).26 Krifka claims that, given a measure function µ for times and h from E to T, we can construe a derived measure function µ’ for events, as in (68). (68) ∀e[ µ’(e) = µ(h(e)) ]

(Krifka 1989: 97)

That is, a derived measure function is a measure function used for a domain that is different from the original domain of application (e.g., a measure function for times used as a measure function for events). In (68), the measure function for times µ’ is defined by µ and h: for all events, the amount of the event e measured by µ’ in E is equal to the amount of h(e) measured by µ in T. Extending Krifka’s analysis to our Japanese data, I argue that there is a homomorphism h from events in E denoted by the VP to individuals in I denoted by the host NP, satisfying h(e1∪Ee2) = h(e1)∪Ih(e2). From the data on non-split MPs, it is clear that there is a measure function that applies to individuals (e.g., in three liters of water, µ: volume applies to water). Following Krifka, given a measure function µ for individuals and h from E to I, 26. A homomorphism of the semilattice S1 ＝ <S1, °> into the semilattice S2 ＝ <S2, °> is a mapping F: S1 → S2 such that F(a°b) = F(a)°F(b), where ‘°’ denotes a composition of two functions (Partee, ter Meulen, and Wall 1990: 286).

70 The semantic properties of non-split/split MP constructions we can derive a measure function µ’ for events. In (69), a measure function µ associated with a non-split MP directly applies to individuals in the greyshaded area in (69) and returns measured amounts. Thus, the monotonicity constraint applies to a lattice of individuals. (69) A measure function associated with a non-split MP I x µ(x) µ In contrast, the measure function µ’ associated with a split MP in (70) applies to events in the grey-shaded area in (70) and returns measured amounts. As in (68), since µ’ for events in (70) amounts to µ(h(e)), the same measurement as (70) can be represented as in (71); µ’(e) in (70) (the measured amount obtained by µ’ applying to events) is equal to µ(h(e)) in (71) (the measured amount obtained by µ applying to individuals mapped from events). In other words, µ’ for events is a combination of h and µ for individuals. The measure function µ in (71) associated with a split MP applies to individuals mapped from events by h, i.e., individuals in the range of h (the grey-shaded area in (71)), indicating that µ indirectly measures events by measuring individuals mapped from events by h and that µ needs to be monotonic to the domain of individuals mapped from events. (70) A measure function associated with a split MP E e µ’(e) µ’ (71) A measure function associated with a split MP E I e h(e) h

µ(h(e)) µ

Let us now apply the proposed mechanism to actual examples and show how it works. In (66) above, for example, a homomorphism h maps coughing events to relevant individuals, namely, the agents of coughing.27 E-

27. In Chapter 3: section 5.1, I discuss extensively why the neo-Davidsonian agent function can serve as a homomorphism from events to individuals.

Mechanism of event measurement 71

xamples (72) and (73) illustrate a legitimate h from a lattice of coughing events to a lattice of students.28,29 e1 ∪ E e2 ∪ E e3

(72) e1 ∪ E e2 e1

e1 ∪ E e3 e2

h

x∪Iy∪Iz

e2 ∪ E e3

x∪Iy

x∪Iz

e3

x

y

y∪Iz z

[[*cough]] = { e1, e2, e3, e1∪Ee2, e1∪Ee3, e2∪Ee3, e1∪Ee2 ∪Ee3 } [[*student]] = { x, y, z, x∪Iy, x∪Iz, y∪Iz, x∪Iy∪Iz } (73)

h e1 ∪ E e2 e1

e2

x∪Iy∪Iz x∪Iy

x∪Iz

y∪Iz

x

y

z

[[*cough]] = { e1, e2, e1∪Ee2 } [[*student]] = { x, y, z, x∪Iy, x∪Iz, y∪Iz, x∪Iy∪Iz } The measure function µ: cardinality in (66) then applies to individuals in the range of h. This leads to the following monotonicity constraint: µ must be monotonic to individuals mapped from events, that is, a lattice con-

28. A lattice of coughing events can be much larger than the ones in (72) and (73) in that these events can take individuals who are not in the denotation of *student as an agent. Since only individuls who are students and who coughed are relevant for the denotation of (66), I consider only the relevant portion of the lattice of coughing events. 29. A question arises as to whether the atomic coughing events e1, e2, and e3 can be mapped to the sums of individuals x∪Iy, x∪Iz, y∪Iz, and x∪Iy∪Iz. Landman (1989a), unlike Link (1983), assumes that atomic verbal predicates never take sums in their extensions. With this simple assumption, Landman successfully reduces distributivity to pluralization of a verbal predicate (see Landman 1989a, 2000 for details). As shown in section 5.1.2, the current analysis also reduces distributivity to pluralization. Thus, following Landman, I assume here that h must map atomic events to atomic (singular or group) individuals.

72 The semantic properties of non-split/split MP constructions sisting of x, y, z, x∪Iy, x∪Iz, y∪Iz, x∪Iy∪Iz in (72) and a lattice consisting of x, y, x∪Iy in (73). These two lattices have members that are ordered by the part-of relation (e.g., x ≤ x∪Iy), and µ: cardinality is able to apply in a monotonic fashion with respect to the two lattices (e.g., the cardinality of x is lower than the cardinality of x∪Iy). Thus, the monotonicity constraint is met both in (72) and (73). The definition of h permits a one-to-many mapping. That is, multiple atomic events may be mapped to the same atomic individual, as in (74), where y corresponds to two events. Indeed, (66) is compatible with a scenario in which, between two students who coughed within the last ten minutes, one of them coughed twice and other other once. In this scenario, the number of students who coughed is two, but the number of atomic coughing events is three. The monotonicity constraint is met in (74), just as in (73): the measure function needs to be monotonic to a lattice consisting of x, y, x∪Iy, and the measure function µ: cardinality can be monotonic with respect to this lattice. e1 ∪ E e2 ∪ E e3

(74) e1 ∪ E e2 e1

e1 ∪ E e3 e2

h

x∪Iy∪Iz

e2 ∪ E e3

x∪Iy

x∪Iz

y∪Iz

e3

x

y

z

Before revisiting the examples presented in section 3.1, I briefly examine event-related readings discussed in Krifka (1990). In (75), besides the obvious reading that presupposes the existence of four thousand ships, Krifka argues that there is an additional reading where four thousand refers to a number of events, i.e., there could be fewer than four thousand ships. (75) Four thousand ships passed through the lock last year. In the event-related reading in (75), the numeral combining with ship measures a number of passing-through-the-lock events. This might be similar to the semantics of a split MP, where a MP that is clearly associated with individuals actually measures events. Hence, the mechanism of deriving event-related readings proposed in Krifka (1990) might be able to account for the semantic properties of split MP constructions. However, Krifka’s mechanism must be different from the mechanism of a homomorphism for

Mechanism of event measurement 73

split MP constructions, since event-related readings are available in nonsplit MP constructions as well as in split MP constructions. For example, in Japanese (76) and German (77), both non-split and split sentences permit the event-related reading. For this reason, I assume that the grammar contains both Krifka’s mechanism for event-related readings and the current mechanism of a homomorphism for split MP constructions. (76) a. [Fune yonsen-soo]-ga kyonen kono suimon-o tuukasi-ta. [ship 4000-CL]-NOM last year this lock-ACC pass-PAST ‘Four thousand ships passed through this lock last year.’ b. Fune-ga kyonen yonsen-soo kono suimon-o tuukasi-ta. ship-NOM last year 4000-CL this lock-ACC pass-PAST (77) a. [Viertausend Schiffe] haben letztes Jahr die Schleuse passiert. [4000 ships] have last year the lock passed ‘Four thousand ships passed through the lock last year.’ b. Schiffe haben letztes Jahr viertausend die Schleuse passiert. ships have last year 4000 the lock passed

4.2. The analysis of the data I have argued so far that the measure function in non-split and split MP constructions must obey the monotonicity constraint: the measure function must be monotonic relative to the given part-whole structure. This constraint applies to the domain where the measure function applies. In the case of non-split MP constructions, the measure function applies to a domain of individuals, thus the constraint must be met in terms of a nominal domain. In contrast, in split MP constructions, the measure function applies to individuals mapped from events by a homomorphism h, and thus the monotonicity constraint must be met in the range of h, or in a nominal domain mapped from a verbal domain. But when I first introduced semantic restrictions on split MP constructions in section 3, I argued that they are caused by the monotonicity constraint in the verbal domain, that is, the measure function in split MP constructions must be monotonic relative to the part-whole structure given by the meaning of the VP. In the following, I show how the refined proposal where the constraint applies to the range of h deals with the semantic restrictions of split MP constructions.

74 The semantic properties of non-split/split MP constructions 4.2.1. The monoticiy constraint and single-occurrence events The first set of data indicates that split MP constructions are incompatible with single-occurrence events such as kill Peter. The relevant examples are repeated below ((a) for Japanese, (b) for German): (78) a.?? Gakusei-ga kinoo san-nin Peter-o korosi-ta. student-NOM yesterday three-CL Peter-ACC kill-PAST ‘Three students killed Peter yesterday.’ (= (30b)) b.??Studenten haben Peter drei umgebracht. students have Peter three killed ‘Three students killed Peter.’ (= (32b)) The incompatibility is now explained as a side-effect of the monotonicity constraint relative to the range of a homomorphism h. In split MP constructions, the measure function applies to individuals mapped from events by h, and the monotonicity constraint must be satisfied there. In particular, individuals mapped from events by h must have a part-whole structure to which the measure function applies monotonically, that is, in the range of h, there must be two or more members that are ordered by the part-of relation and the measure function must track that ordering relation. With singleoccurrence events, the domain of h (that is, the denotation of the VP) is a singleton, thus the range of h is also a singleton, given that h is a structurepreserving function. For this reason, the measure function cannot be monotonic relative to the range of h.

4.2.2. The monoticiy constraint and individual-level predicates The second observation is that split MP constructions are incompatible with I-level predicates such as be smart in (79a) (Japanese) and be intelligent in (79b) (German). (79) a.?? Gakusei-ga kono kurasu-de san-nin kasikoi. student-NOM this class-in three-CL smart ‘In this class, three students are smart.’ b.* Feuerwehrleute sind drei intelligent. firemen are three intelligent ‘Three firemen are intelligent.’

(= (40b))

(= (45b))

Mechanism of event measurement 75

Taking Kratzer’s view (1995), an I-level predicate does not have an event argument to begin with. Then there is no h from events. Hence, the measure function does not have an appropriate domain of application.

4.2.3. The monoticiy constraint and collective readings The third set of data shows that split MP constructions allow for distributive readings, but not for collective readings. Let us examine examples (80) ((a) for Japanese, (b) for German), taken from section 3.1.3. (80) a. Otokonoko-ga kinoo san-nin booto-o tukut-ta. boy-NOM yesterday three-CL boat-ACC make-PAST ‘Three boys built a boat yesterday.’ (= (47b)) b. Jungen haben drei ein Modellboot gebaut. boys have three a model boat built ‘Three boys built a model boat.’ (= (50b)) Suppose that, in (80), the VP build a boat is pluralized and forms a lattice of building-a-boat events, and that there is a homomorphism h from that event lattice to a lattice of boys, as illustrated in (81). Then µ: cardinality applies to a range of h, i.e., a lattice consisting of x, y, z, x∪Iy, x∪Iz, y∪Iz, x∪Iy∪Iz. The monotonicity constraint requires µ to be monotonic to this lattice. Since h preserves the part-whole structure of events, the monotonicity constraint is met. What is relevant in (80) is an individual mapped from events whose cardinality is three, namely, x∪Iy∪Iz. The individual x∪Iy∪Iz consists of x, y, z, each of whom is an agent of an atomic building-a-boat event e1, e2, e3, which yields a distributive interpretation. e1 ∪ E e2 ∪ E e3

(81) e1 ∪ E e2 e1

e1 ∪ E e3 e2

h

x∪Iy∪Iz

e2 ∪ E e3

x∪Iy

x∪Iz

e3

x

y

y∪Iz

[[*build a boat]] = {e1, e2, e3, e1∪Ee2, e1∪Ee3, e2∪Ee3, e1∪Ee2∪Ee3} [[*boy]] = { x, y, z, x∪Iy, x∪Iz, y∪Iz, x∪Iy∪Iz }

z

76 The semantic properties of non-split/split MP constructions The question now is why split MP constructions lack collective readings. In section 3.2.3, I informally assumed that a collective reading of (80) obtains when a single building-a-boat event takes the boys as a group as an agent. Let us formalize this assumption by introducing Landman’s (1989a, 1989b, 1996, 2000) group-forming operation ↑ that maps a sum of individuals (e.g., the sum of the boys x, y, and z; x∪Iy∪Iz) to an atomic group individual (e.g., the boys as a group; ↑(x∪Iy∪Iz)) (see section 5.1.2 for further discussion). A collective reading obtains when the denotation of a predicate is a singleton, as in kill Peter, and the atomic event in the singleton takes a group of three boys, as in build.a.boat(↑(x∪Iy∪Iz)). In particular, there is a homomorphism h from a singleton containing an atomic building-a-boat event e to the group of three boys ↑(x∪Iy∪Iz), as in (82). The measure function applies to the range of h, and the range of h is a singleton containing ↑(x∪Iy∪Iz). Since ↑(x∪Iy∪Iz) has no part-whole structure to which the measure function applies monotonically, the monotonicity constraint is not satisfied. (82)

↑(x∪Iy∪Iz)

e h

Note that (80) has the additional collective reading, that a group of three boys built a boat several times (see footnote 22). In this case, multiple building-a-boat events take the same group of three boys as the agent, as in (83). This case fails as did the case in (82): the measure function applies to the range of h, namely, a singleton containing ↑(x∪Iy∪Iz), and thus the monotonicity constraint cannot be satisfied. In this way, the monotonicity analysis successfully accounts for the lack of a collective reading in split MP constructions.

e1 ∪ E e2 ∪ E e3

(83)

h e1 ∪ E e2

e1 ∪ E e3

e 2 ∪ E e3

e1

e2

e3

↑(x∪Iy∪Iz)

Note that split MP constructions permit collective readings in some environments: when they are in progressive form (that is, in constructions corresponding to the -ing construction in English), when a collectivizer is

Mechanism of event measurement 77

present (e.g., the adverb together), when they occur with collective predicates (e.g., surround), and when the host NP is an internal argument with a predicate that requires a plural internal argument (e.g., collect). These cases are discussed in detail in section 5.

4.2.4. Notes on the numeral one Before moving on, I briefly discuss the observation that the Japanese split MP construction permits the numeral one to split, as in (84). (84) Gakusei-ga kinoo hito-ri student-NOM yesterday one-CL ‘One student hit Peter yesterday.’

Peter-o Peter-ACC

tatai-ta. hit-PAST

This may appear to be problematic for the current monotonicity analysis in that the split MP one does not seem to call for a part-whole structure (cf. footnote 15). It is not the split MP, however, that determines the existence of a part-whole structure, but the relevant verbal and nominal predicates. In (84), the relevant predicates are the VP Peter-o tataku ‘hit Peter’ and the NP gakusei ‘student(s)’. Since hitting-Peter events can occur muptiple times, the denotation of the VP can have a non-trivial part-whole structure. Recall that NPs in Japanese are mass (see Chapter 1: section 3.2), and thus [[gakusei]] in (84) can also have a non-trivial part-whole structure. In split MP constructions, the monotonicity constraint requires the measure function to be monotonic relative to the range of a homomorphism from [[VP]] , that is, [[NP]] mapped from [[VP]] . Since both [[VP]] and [[NP]] in (84) can have a part-whole structure, the monotonicity constraint can be met in (84). In contrast, the German ST with one is generally ungrammatical, as in (85), except for the examples in some special contexts (e.g., es gibt construction in (86)). (85) * {Student / Studenten} hat {student / students} has ‘One student(s) hit Peter.’

Peter ein Peter one

geschlagen. hit

(86) Kopiergeräte gibt es hier nur eines. photocopiers.ACC there is here only one.ACC ‘There is only one photocopier here.’

(Nolda 2000: 3)

78 The semantic properties of non-split/split MP constructions The problem with (85) lies in a conflict between a morphological requirement and a semantic requirement. On the one hand, the host NP must be morphologically singular to be compatible with the split NP one. On the other hand, the monotonicity constraint requires the measure function to be monotonic with respect to the denotation of the host NP mapped from the VP. That is, the host NP must have a part-whole structure. However, when the host NP is singular, its extension lacks a non-trivial part-whole structure. The Japanese split MP construction in (84) is acceptable because there is no morphological requirement: NPs in Japanese lack markings for plurality, hence they are freely interpreted either as singular or as plural.

4.3. Monotonicity as a formal property of measurement constructions The discussion so far has revealed that both non-split and split MP constructions are subject to semantic restrictions in the nominal domain and that only split MP constructions are sensitive to restrictions in the verbal domain, as summarized in Table 2. Table 2. Restrictions on non-split and split MP constructions

Non-split MP constructions Split MP constructions

Nominal domain

Verbal domain

with restrictions with restrictions

no restrictions with restrictions

In non-split MP constructions, the measure function measures the number of individuals in the extension of the host NP, hence we observe the monotonicity constraint in the nominal domain. In contrast, the measure function does not measure events, so no restrictions are observed in the verbal domain. In Chapter 3, I show that this semantic analysis correlates with the syntactic structure of non-split MP constructions, where a non-split MP combines directly with the host NP in the syntax. A non-split MP syntactically combines with the NP, and thus semantically expresses measurement of individuals denoted by the host NP. As for split MP constructions, we saw in section 3.1 that they show some restrictions with respect to verbal predicates, leading to the claim that the measure function must be monotonic to [[VP]] . They are also subject to semantic restrictions in the nominal domain. I showed in section 4.1 that the direct measurement of events is equivalent to the measurement of indi-

Mechanism of event measurement 79

viduals mapped from events by a homomorphism h (see (68)). Based on this equivalence, I argued that the measure function in split MP constructions applies to the range of h, i.e., individuals mapped from events (see (71)). Thus the measure function must be monotonic with respect to the individuals mapped from events. A measure function such as µ: temperature cannot satisfy this constraint because it cannot keep track of the partwhole structure of the individuals. Moreover, NPs lacking a non-trivial part-of relation (e.g., a singular count NP such as baby) cannot satisfy the monotonicity constraint. In this way, the proposed analysis accounts for the semantic restrictions in terms of both nominal and verbal domains in split MP constructions. The discussion in the next chapter reveals that a split MP can be analyzed as an adjunct that syntactically combines with a verbal predicate. Then, by compositionality, a split MP should express the measurement of events, which it does. Thus, the present semantic claim correlates with the syntactic structure, just as in non-split MP constructions. As a result, a simple picture emerges: the measure function in non-split and split MP constructions is sensitive to the monotonicity constraint in the domain to which the measure function applies. The two constructions differ in that, while non-split MP constructions measure in the nominal domain, split MP constructions measure in the verbal domain (which is equivalent to measurement of individuals mapped from events). Hence, these constructions show semantic restrictions on, respectively, the nominal and verbal domains. Furthermore, in split MP constructions, there is a homomorphism from events to individuals, thus these constructions show semantic restrictions in the nominal domain as well. Based on this finding, I propose that monotonicity can be considered as a semantic property governing several different measurement constructions. It is well-known that, under the theory of generalized quantifiers, determiners are classified according to their formal properties, such as reflexivity, conservativity, and upward or downward entailment. This classification provides convincing accounts for several linguistic phenomena, such as the distribution of negative polarity items (Ladusaw 1979) and the restrictions of there-insertion (Higginbotham 1987, Keenan 1987, 2003). Extending this approach, I argue that different measurement constructions can be classified according to their formal properties, monotonicity being one of them. Non-split and split MP constructions belong to different categories: the former is monotonic to [[ NP]] , and the latter is monotonic to [[ VP]] . This classification gives an explanation for several semantic properties of these constructions (see sections 2.1 and 3.1). Other syntactic constructions can

80 The semantic properties of non-split/split MP constructions be evaluated using the property of monotonicity. Based on the data in section 2.2, pseudopartitives in English belong to the same category as non-split MP constructions in Japanese and German. In Chapter 4, I show that some comparative constructions in Japanese and English belong to the same category as non-split MP constructions, and others to the same caterogy as split MP constructions. The cross-linguistic aspect of this novel approach should be also emphasized. Since Japanese and German belong to different language families, the finding in this chapter suggests that monotonicity is a universal property of measurement constructions that extends to related measurement constructions in other languages. In Chapter 5, I elaborate on this point.

4.4. Summary Summing up, I argued that the measure function in split MP constructions indirectly measures events by measuring individuals mapped from events. Formally, I proposed that there is a homomorphism h from a lattice of events to a lattice of individuals, and that the monotonicity constraint must be met with respect to the range of h. The proposed analysis successfully accounts for the sensitivity of split MP constructions to restrictions in the nominal as well as the verbal domain (incompatibility with singleoccurrence events and with I-level predicates, unavailability of collective readings). I further argued that monotonicity can be considered a formal property of measurement constructions and that the categorization of constructions based on monotonicity is useful when accounting for various semantic properties of these constructions.

5. Plurality and distributive-collective readings One of the characteristic properties of split MP constructions is that they lack collective readings (section 3.1.3), although these are not alway unavailable. In this section, I discuss the following four cases where split MP constructions seem to allow collective readings: when a VP is in a progressive form (section 5.2), when a collectivizer (e.g., the adverb together) is present (section 5.3), when a collective predicate such as gather is used (section 5.4), and when the host NP is an internal argument (section 5.5). I show that the monotonicity analysis presented in the previous section is

Plurality and distributive-collective readings 81

capable of accounting for all these cases. Before examing these, I present in section 5.1 a brief overview of previous studies on distributivity.

5.1. Previous studies on distributivity This section briefly summarizes the literature on distributivity. First, I introduce the lexical distinction between distributive and collective predicates, and then I move on to Landman’s theory of distributivity as semantic plurality (Landman 1989a, b, 1996, 2000).

5.1.1. Distributive and collective predicates As shown in section 3.1.3, sentences with plural subjects may evoke semantic ambiguity between distributive and collective interpretations. For example, in the students lifted the piano, there are two readings: a distributive reading that each student lifted the piano by himself and a collective reading that the students together cooperatively lifted the piano. Sentences with plural subjects may also be unambiguous, allowing either only a collective reading, as in (87a, b), or only a distributive reading, as in (87c, d). (87) a. b. c. d.

The students are numerous. John and Mary are a couple. The babies are asleep. Ann and Beth are pregnant.

As summarized in Dowty (1987), there are two main approaches to the collective-distributive distinction. The first approach holds that the distinction results from the interpretation of plural subjects (Hausser 1974, Bennett 1974, Scha 1981). In particular, under distributive readings, plural subjects refer to individuals, and under collective readings, they refer to groups. The second approach holds that the distinction results from a lexical property of the verbal predicate (Link 1983, Dowty and Brodie 1984, Dowty 1987, Roberts 1990, Schwarzschild 1991, 1996, Lasersohn 1995, Brisson 1998, 2003). Under this approach, it is assumed that there are inherently collective, inherently distributive, and ambiguous predicates. One of the strongest arguments for the second approach comes from examples with conjoined VPs in which distributive and collective readings coexist (Link

82 The semantic properties of non-split/split MP constructions 1984, Dowty 1987, Roberts 1990, Lasersohn 1995: Chapter 7, in particular). For instance, in (88a), the collective-distributive distinction cannot arise from the denotation of the NP John and Mary, since it does not make sense to say that John and Mary is interpreted as a group with met in a bar and distributively with had a drink. In the second approach, sentences (88) simply involve a conjunction of collective and distributive VPs. (88) a. John and Mary met at the bar and had a drink. b. John and Mary are a happy couple and are well-adjusted individuals too. c. The students closed their notebooks, left the room, and then gathered in the hall after class. (b, c: Dowty 1987: 98) With examples such as (88), it has been widely accepted that a distributive reading arises when a distributive operator is present on the VP, while a collective reading arises when there is no such operator. The distributive operator D is defined in (89), where the predicate ATOM stands for the property of being an atomic element (see Link 1983, 1987b).30 (89)

D

P(x) = ∀y [ y ≤ x ∧ ATOM(y) → P(y) ]

This operator makes the relevant verbal predicate P apply to all atomic members of the plural subject x. Let us illustrate how the D-operator accounts for the distributive interpretations in (90). (90) a. John and Bill lifted the piano. b. The students lifted the piano. The extension of plural subjects is the sum of individuals. In (90a), the extension of John and Bill is j∪Ib. In (90b), if there are three relevant students Ann, Beth, and Colin, the extension of the students would be the maximum member of a lattice of those students, i.e., a∪Ib∪Ic. With the Doperator, we obtain (91) as the truth conditions of (90) under distributive readings: (91a) says that all atomic members of j∪Ib, namely, John and Bill, lifted the piano, yielding the distributive reading that John and Bill each lifted the piano. A collective reading obtains when there is no distributive operator. The same analysis holds for (90b). 30. Link’s original definition is given below: (i) Distr(P) ↔ ∀x ( P(x) → ATOM(x) )

(Link 1983: 309)

Plurality and distributive-collective readings 83

(91) a.

D

lift.the.piano(j∪Ib) = ∀y [ y ≤ j∪Ib ∧ ATOM(y) → lift.the.piano(y) ] b. Dlift.the.piano(a∪Ib∪Ic) = ∀y [ y ≤ a∪Ib∪Ic ∧ ATOM(y) → lift.the.piano(y) ]

5.1.2. Distributivity as semantic plurality Landman (1989a, 1989b, 1996, 2000) proposes a novel analysis where distributivity is reduced to a semantic pluralization of verbal predicates: “the grammar contains a single operation that forms semantically plural predicates out of semantically singular predicates: in the nominal domain, pluralization leads to plural nouns; in the verbal domain, the same operation creates distributive interpretations” (Landman 2000: 152). In particular, Landman shows that distributive readings obtain by applying Link’s (1983) pluralization operator * proposed for nominal predicates to verbal predicates. Link (1983) treats plural nominal predicates as inherently distributive, based on the assumption that their interpretation is the same as the plural noun that they are based on. For instance, the denotation of the plural predicate are boys in (92a) is the same as that of the plural noun boys, i.e., *boy. * is a pluralization operator, where *P is the closure of the singular predicate P under sum (see Chapter 1: section 3.1). Then the denotation of (92a) would be (92b). (92) a. John and Bill are boys. b. *boy(j∪Ib) Landman shows that the fact in (93) is guaranteed by the definition of * and by the fact that the domain D is an atomic part-of structure. This in turn guarantees that the predicate in (92) is distributive; for all a that is an atomic member of [[boys]] , a is a boy, i.e., John is a boy and Bill is a boy. (93) FACT: if P is a set of atoms then: α ∈ *P iff ∀a ∈ AT(α): a ∈ P

(Landman 2000: 148)

Intuitively, the same paraphrase obtains with a distributive reading of the sentence John and Bill carried the piano, as in (94). Formally, the fact in (93) is equivalent to (95a). Then Link’s (1983) D-operator, repeated in (95b), should be definable in terms of the *-operator.

84 The semantic properties of non-split/split MP constructions (94) John carried the piano and Bill carried the piano iff John and Bill carried the piano (on the distributive interpretation of carry the piano). (Landman 1996: 427) (95) a. *P(x) iff ∀y [ y ≤ x ∧ ATOM(y) → P(y) ] b. DP(x) = ∀y [ y ≤ x ∧ ATOM(y) → P(y) ]

(= (89))

In this way, Landman’s analysis yields distributive readings when a verbal predicate is pluralized. Based on this analysis, Landman argues that the traditional lexical distinction between collective and distributive predicates is incorrect. Specifically, he shows that predicates that are considered to have only collective readings (e.g., meet, gather) may allow distributive readings, as in (96). The intended reading is salient when the sentence The boys and the girls meet is followed by but not in the same room. (96) The boys meet and the girls meet iff the boys and the girls meet (on the distributive interpretation of meet). (Landman 1996: 427) This shows that the putative collective predicate meet permits a distributive reading so long as it can distribute to collections. Then “predicates are lexically specified for what kinds of things they take in their extension, not for whether they are distributive or collective” (Landman 2000: 153). Distributive predicates in the traditional sense can take individual atoms in their extension, while so-called collective predicates take group atoms, not individual atoms. In (96), the predicates distribute over the group of the boys and the group of the girls, and not all the way down to the individuals. Landman proposes the group-forming operation ↑ that maps a sum of individuals (x∪Iy) to an atomic group individual (↑(x∪Iy)) (cf. section 4.2.3). ↑ is considered to be a type-shifting operator that applies freely to turn a sum into a group. This operator becomes relevant later in section 5.3 for the analysis of together. The denotation of the sentence The boys and the girls meet under the distributive reading is given in (97) (when the atomic members of [[boys]] and [[girls]] are {a, b, c, d, e} and {f, g, h}, respectively). (97) *meet( ↑(a∪Ib∪Ic∪Id∪Ie) ∪I ↑(f∪Ig∪Ih) ) In sum, under Landman’s framework, distributive interpretations arise if and only if the relevant predicate is true of each atomic member (individual

Plurality and distributive-collective readings 85

atom or group atom) of the plural subject, but not of the plural subject itself. In the case of a putative distributive predicate (e.g., walk, breathe), the predicate is true of each atomic individual. For example, in The students walked, each student must have walked. In contrast, a putative collective predicate cannot be true of each atomic individual: in The students met, it is not the case that each individual student met (e.g., John met is ungrammatical). However, a putative collective predicate may have a distributive interpretation when the plural subject denotes multiple groups each of which is not an atomic individual (e.g., boys as a group and the girls as a group in (96)). In this way, Landman’s work disagees with the standard view that predicates are lexically specified as being distributive or collective. Rather, distributivity arises when the relevant predicate is pluralized (e.g., a plural distributive predicate with individual atoms in its extension, a plural collective predicate with group atoms in its extension). That is, distributivity is not a lexical specification on certain predicates, but rather a predicate operation. Landman’s analysis is not, however, entirely free from a lexical property of verbal predicates: verbal predicates need to be distinguished by the kinds atoms they take in their extensions. This distinction correlates with the traditional distinction between a distributive and a collective predicate: predicates such as walk (i.e., so-called distributive predicates) take only individual atoms and predicates such as meet (i.e., so-called collective predicates) take only group atoms. In this sense, the traditional claim that there are two types of predicates seems to be valid. The distinction may be made between distributive predicates and collective predicates, or between predicates with individual atoms and predicates with group atoms.31 In this book, I continue to use the terms distributive predicate and collective predicate for convenience. Following Landman, I assume that the two differ in that the agent of the former is an individual atom and that of the latter is a group atom. This assumption allows a collective predicate such as meet to have a distributive interpretation when the predicate is pluralized and takes group atoms in its extension. Turning now to a collective reading, Landman claims that it obtains when a singular predicate takes a group in its extension, as in (98a). As

31. See Winter (2001) for a possibly relevant distinction between atom predicates and set predicates, which is proposed as an alternative for the distinction between distributive and collective predicates.

86 The semantic properties of non-split/split MP constructions discussed above, a distributive interpretation obtains when a semantically plural predicate applies to a sum, as in (98b).32 (98) John and Bill carried the piano upstairs. a. carry(↑(j∪Ib)) b. *carry(j∪Ib)

(Landman 2000: 156)

Landman later incorporates event arguments into his analysis of distributivity as semantic plurality. Assuming that all arguments are introduced by a neo-Davidsonian method (Chapter 1: section 4.3), Landman proposes that thematic roles are defined only for atomic events, not for sums of events, and that they take only atoms (individuals or groups) as values. He further defines plural roles: if e is an event in E, and if for every atomic part a of e, a thematic role R is defined for a, then a plural role *R is defined for e, and maps e onto the sum of the R-values of the atomic parts of e (Landman 2000: 184).33 Landman assumes that, for any predicate P, the plural form *P is the unmarked form, since the singular form P is a subset of the plural form. For example, the denotation of John walked would be ∃e[*walk(e)∧*Ag(e)=j], which can be reduced to ∃e[walk(e)∧Ag(e)=j]. With these assumptions, the interpretations of (98) with event arguments would be (99). In the collective interpretation in (99a), the thematic role can be reduced to a singular form, since it applies to an atom, namely, the group ↑(j∪Ib). Then the verbal predicate is also reduced to the singular. As for the distributive interpretation, the definition of plural roles guarantees the semantic equivalence in (100): if x is a plural agent of an event e, then each atomic part of x is the agent of an atomic part of e, and vice versa. Then the formula in (99b) yields the distributive interpretation. 32. Although Landman disagrees with researchers who claim that the distributivecollective distinction is a lexical property of a verbal predicate, he shares with them the insight that distributivity is derived from a verbal predicate, not from a nominal predicate. Thus, his analysis is capable of handling the examples in (88). The interpretation of (88a) under his analysis is given in (i). (i) meet(↑(j∪Im)) ∧ *drink(j∪Im) 33. This means that all thematic roles are cumulative: if the agent of an event e is x, and the agent of an event e’ is y, then the agent of the sum of e and e’ would be the sum of x and y, that is, Agent(e)∪IAgent(e’) = *Agent(e∪Ee’). Landman and also Krifka (1989) claim that all thematic roles have this property, which Kratzer (forthcoming) argues against. See Chapter 1: section 4.3 and Chapter 3: section 5 for further discussion.

Plurality and distributive-collective readings 87

(99) a. ∃e[*carry(e)∧*Ag(e)=↑(j∪Ib)] ≡ ∃e[carry(e) ∧ Ag(e)=↑(j∪Ib)] b. ∃e[*carry(e) ∧ *Ag(e)=j∪Ib] (100) ∃e[*carry(e) ∧ *Ag(e)=x] iff ∃e∀y[y ≤ x ∧ ATOM(y) → P(e) ∧ Ag(e)=y]34 Let us quickly show that Landman’s theory is compatible with the analysis of distributive and collective readings proposed in section 4.2.3. We saw that, while non-split MP constructions have both collective and distributive readings, split MP constructions have only distributive readings. Some relevant examples are repeated below ((101) for Japanese and (102) for German): (101) a. [Otokonoko san-nin]-ga kinoo [boy three-CL]-NOM yesterday ‘Three boys built a boat yesterday.’ OK distributive, OKcollective b. Otokonoko-ga kinoo san-nin boy-NOM yesterday three-CL OK distributive, ??collective

booto-o tukut-ta. boat-ACC make-PAST

booto-o tukut-ta. boat-ACC make-PAST (= (47))

(102) a. [Drei Jungen] haben ein Modellboot [three boys] have a model boat ‘Three boys built a model boat.’ OK distributive, OKcollective b. Jungen haben drei ein Modellboot boys have three a model boat OK distributive, ??collective

gebaut. built

gebaut. built (= (50))

34. Landman’s (2000: 198) proof is cited below: (i) ∃e ∈ *CARRY: *Ag(e)=x iff ∀a ∈ AT(x): ∃e ∈ CARRY: Ag(e)=a a) If there is a sum of carrying events e (in *CARRY) whose plural agent is a sum of individuals x, then — by definition of plural agent — each atomic part of x is the agent of some atomic part of e. But each atomic part of e is in CARRY. b) If every atomic part of x is the agent of some carrying event (some event in CARRY), then — by definition of plural agent — x is the plural agent of the sum of those carrying events. That sum is in *CARRY.

88 The semantic properties of non-split/split MP constructions I accounted for the distributive reading of split MP constructions by using a homomorphism h from events to individuals. The homomorphism h guarantees a one-to-one mapping from events to individuals, and the monotonicity constraint on the range of h requires the VP to be pluralized, as in (103). For the monotonicity constraint to be met on the range of h, there has to be a non-trivial part-whole structure in the domain of h. Under Landman’s theory, the pluralization of the VP yields a distributive interpretation.

e1 ∪ E e2 ∪ E e3

(103) e1 ∪ E e2 e1

e1 ∪ E e3 e2

h

x∪Iy∪Iz

e2 ∪ E e3

x∪Iy

x∪Iz

y∪Iz

e3

x

y

z (= (81))

Collective readings of split MP constructions obtain only when an atomic member is involved, as in (104) and (105), but these mappings are prohibited by the monotonicity constraint on the range of h. (104)

↑(x∪Iy∪Iz)

e h

(= (82))

e1 ∪ E e2 ∪ E e3

(105)

h e1 ∪ E e2

e1 ∪ E e3

e 2 ∪ E e3

e1

e2

e3

↑(x∪Iy∪Iz)

(= (83)) In contrast, non-split MPs express measurement of individuals only, and they have nothing to do with measurement of events. Thus, there is no need to posit a homomorphism from events to individuals. With no restriction in the verbal domain, a verbal predicate is freely interpreted as singular or plural, which yields both collective and distributive interpretations.

Plurality and distributive-collective readings 89

5.1.3. Excursion: “Temporal” distributivity Before examining more examples of split MP constructions, I make some remarks on studies that use a different notion of distributivity. Kitagawa and Kuroda (1992) (K&K) make a distinction between distributive and non-distributive readings: “the distributive construal necessarily implies the occurrence of multiple events while the non-distributive construal implies the occurrence of only a single event” (1992: 88–89). For example, (106a) has only a distributive reading forced by the temporal expression kono issyuukan-no aida-ni ‘during this week’, while (106b) has only a nondistributive reading forced by sono toki totuzen ‘then suddenly’. (106) a. Kono issyuukan-no aida-ni syuuzin-ga san-nin nigedasita. this week during prisoner-NOM three-CL escaped ‘There have been three jailbreaks this week.’ b. Sono toki totuzen syuuzin-ga san-nin abaredasi-ta. then suddenly prisoner-NOM three-CL started to act violently ‘Then suddenly, three prisoners started to act violently.’ (Kitagawa and Kuroda 1992: 89) In contrast, the distributive-collective distinction discussed above has nothing to do with a temporal relation (see sections 5.1.1 and 5.1.2). A distributive reading obtains when each individual in the extension of the plural subject is the agent of the relevant event, and a collective reading obtains when a group denoted by the plural subject is the agent. While there are many cases where the distinction based on a temporal relation correlates with the distinction based on agenthood, there are also many cases where the two diverge. For instance, (107a) is distributive both in K&K’s sense (forced by so far) and in terms of agenthood. In contrast, (107b) is nondistributive in K&K’s sense (forced by suddenly), but it is ambiguous between distributive and collective readings in terms of the agenthood. (107) a. So far, five students have lifted a desk. b. Five students suddenly lifted a desk. Ishii (1999) argues that the Japanese FQ construction permits only distributive readings in K&K’s sense.35 His analysis predicts that the FQ const35. More specifically, Ishii (1999) argues that there are two types of FQ constructions (one transformationally derived from the non-FQ counterpart and the

90 The semantic properties of non-split/split MP constructions ruction in (108a) is grammatical precisely because it permits a distributive reading (forced by so far). However, his analysis wrongly predicts that (108b) is infelicitous because it has only a non-distributive reading (forced by suddenly). (108) a. Kono kurasu-de-wa koremadeni gakusei-ga tukue-o this class-in-TOP so far student-NOM desk-ACC go-nin motiage-teiru. five-CL lift-have ‘In this class, so far, five students have lifted a desk.’ b. Sono toki totuzen gakusei-ga tukue-o go-nin motiage-ta. then suddenly student-NOM desk-ACC five-CL lift-PAST ‘Then suddenly, five students lifted a desk.’ In contrast, the distributive-collective distinction based on agenthood yields the generalization that the FQ construction lacks collective readings; example (108b) permits a distributive, but not a collective reading. For this reason, to examine the properties of the Japanese FQ construction, it is crucial to adopt the distributive-collective distinction discussed above and not K&K’s distinction between distributive and non-distributive reading.

5.2. Case 1: Collectivity with progressives We are now ready to examine novel data on collective readings of split MP constructions. As mentioned at the beginning of section 5, there are four cases where split MP constructions seem to allow collective readings. The first case to be discussed is the following: collective interpretations are available with progressive forms of VPs.

other involving a FQ that is a VP-adjoined adverb), and that the second type permits only a distributive reading in K&K’s sense (Nakanishi in press for details). I put aside this claim because the purpose of this section is simply to show that distributivity of the FQ construction should be defined in terms of agenthood, and not in terms of a temporal relation.

Plurality and distributive-collective readings 91

5.2.1. The data Japanese has a morpheme -teiru, which attaches to a verb and expresses that the relevant event is progressing, analogous to -ing in English (Ogihara 1998, among others). Examples (109) illustrate that the VP build a boat with -teiru permits a collective reading even in the split MP construction. (109) a. [Otokonoko san-nin]-ga kinoo booto-o [boy three-CL]-NOM yesterday boat-ACC ‘Three boys were building a boat yesterday.’ OK distributive, OKcollective b. Otokonoko-ga kinoo san-nin booto-o boy-NOM yesterday three-CL boat-ACC OK distributive, OKcollective

tukut-tei-ta. make-PROG-PAST

tukut-tei-ta. make-PROG-PAST

In German, the progressive aspect can be expressed by a construction with the preposition an ‘(lit.) at’. For example, in (110), the an construction roughly translates as the -ing progressive in English.36 In this progressive context, both non-split and split MP constructions allow ambiguity between a distributive reading that three boys were separately building a model boat and a collective reading that they were building it together, as in (111). (110) a. Die Jungen haben an einem Modellboot gebaut. the boys have PREP a model boat built ‘The boys were building a model boat.’ 36. The distributions of the German an construction and that of the English -ing construction are not exactly the same. First, the former is much more restricted than the latter; the predicate read a chapter or eat a cake is not permitted in the an construction, but the corresponding -ing sentences are grammatical, as in (i). (i) a.* Die Studenten haben an einem Kapitel gelesen. the students have PREP a chapter read ‘The students were reading a chapter.’ b.* Die Studenten haben an einem Kuchen gegessen. the students have PREP a cake eaten ‘The students were eating a cake.’ Second, an anonymous reviewer pointed out that there are some cases where the an construction, but not the -ing construction, is possible, as in (ii). (ii) Jede Woche bauen wir in der Klasse an einem Modellboot. each week build we in the class PREP a model boat *‘Each week we are building a model boat in class.’

92 The semantic properties of non-split/split MP constructions b. Die Studenten haben an eine Kapitel {gearbeitet / geschrieben}. the students have PREP a chapter {worked / wrote} ‘The students were {working on / writing} a chapter.’ (111) a. [Drei Jungen] haben an einem Modellboot [three boys] have PREP a model boat ‘Three boys were building a model boat.’ OK distributive, OKcollective b. Jungen haben drei an einem Modellboot boys have three PREP a model boat OK distributive, OKcollective

gebaut. built

gebaut. built

In sum, non-split MP constructions always permit both distributive and collective readings. In contrast, split MP constructions always allow distributive readings, and the availability of collective readings depends on the aspect of verbal predicates. Specifically, collective readings are available with progressive VPs.

5.2.2. The analysis The question to be addressed now is why split MP constructions with progressive VPs permit collective readings. It has been noted that verbal predicates in progressives are tied to a notion of partiality, as informally defined in (112) (Bennett and Partee 1972, Krifka 1992; but see also Dowty 1979, Parsons 1989, Landman 1992). (112) PROG = λPλe’v. ∃e[ P(e) ∧ e’≤ e ∧ e’ is not the final subevent of e] With this definition, the extension of progressive VPs is considered to be a lattice of subevents. For instance, the building-a-boat event in a progressive form may have subparts e’, e”, e”’, where e’, e”, e”’ are subparts of a singular building-a-boat event e. These subparts and their sums form a lattice, where e’∪Ee”∪Ee”’ corresponds to e, as in (113).

Plurality and distributive-collective readings 93

(113)

e’∪Ee”∪Ee”’ (= e) e’∪Ee”

e’∪Ee”’

e”∪Ee”’

e’ e” e”’ [[be building a boat]] = {e’, e”, e”’, e’∪Ee”, e’∪Ee”’, e”∪Ee”’, e’∪Ee”∪Ee”’} In section 4.2.3 (as well as in section 5.1.2), I discussed why split MP constructions lack collective interpretations. In split MP constructions, the monotonicity constraint is imposed on the range of a homomorphism h (i.e., individuals mapped from events), and thus the range of h needs to have a part-whole structure. This requirement excludes the possibility of having a group as an agent, i.e., collective readings are disallowed. One of the legitimate cases is given in (114), which necessarily yields a distributive interpretation: each building-a-boat event e1, e2, e3 is mapped to its agent x, y, z, respectively. e1 ∪ E e2 ∪ E e3

(114) e1 ∪ E e2 e1

e1 ∪ E e3 e2

h

x∪Iy∪Iz

e2 ∪ E e3

x∪Iy

x∪Iz

y∪Iz

e3

x

y

z

[[*build a boat]] = {e1, e2, e3, e1∪Ee2, e1∪Ee3, e2∪Ee3, e1∪Ee2∪Ee3} [[*boy]] = { x, y, z, x∪Iy, x∪Iz, y∪Iz, x∪Iy∪Iz } (= (81)) Extending this approach to split MP constructions with progressive VPs, we could postulate h in (115); each subpart e’, e”, e”’ is mapped to its respective agent x, y, z. Crucially, a singular building-a-boat event e (= e’∪Ee”∪Ee”’) is mapped to x∪Iy∪Iz, which yields a collective reading, although (115) is still distributive in that each individual is an agent of a different subpart of a single building-a-boat event.37

37. An anonymous reviewer pointed out that different subevents of a progressive event may be linked to a unique agent. For example, consider (i), which is constructed by using another progressive form in German, namely, Rheinische Verlaufsform ‘Rhinelandic progressive’.

94 The semantic properties of non-split/split MP constructions

(115)

e’∪Ee”∪Ee”’ e’∪Ee” e’

e’∪Ee”’ e”

h e”∪Ee”’ e”’

x∪Iy∪Iz x∪Iy

x∪Iz

x

y

y∪Iz z

[[ be building a boat]] = {e’, e”, e”’, e’∪Ee”, e’∪Ee”’, e”∪Ee”’, e’∪Ee”∪Ee”’} [[*boy]] = { x, y, z, x∪Iy, x∪Iz, y∪Iz, x∪Iy∪Iz }

5.2.3. Supporting evidence There are two pieces of supporting evidence for the proposed analysis. First, recall the observation in section 3.1.1 that split MP constructions are incompatible with VPs denoting a single-occurrence event. The relevant Japanese examples are given in (116a) and (117a). This is because, when the extension of such VPs is a singleton, the range of a homomorphism h ends up to be a singleton as well. Without a non-trivial part-whole structure, the monotonicity constraint on the range of h cannot be met. The Japanese split MP construction, however, is compatible with a single-occurrence event in a progressive form, as shown in (116b) and (117b).

(i)

Jungen waren drei ein Klavier am tragen. boys were three a piano at.the carrying ‘Three boys were carrying a piano.’ Example (i) permits a collective reading, and intuitively, the group of three boys, but not each individual, is the agent. But the monotonicity constraint cannot be satisfied in such a mapping, which wrongly predicts (i) to be unacceptable. Then we may be obliged to say that, unlike the mapping from events to agents, the mapping from subevents to agents is immune to the monotonicity constraint. This may not be surprising since plurality of events and plurality of subevents are different in nature. For instance, the subparts of a single progressive event cannot be counted, while the subparts of a plurality of events with different agents can (cf. Zimmermann 2002). I leave this issue for future research. See section 5.2.4 for a related discussion.

Plurality and distributive-collective readings 95

(116) a.?? Gakusei-ga kinoo san-nin sono tukue-o kowasi-ta. student-NOM yesterday three-CL that table-ACC break-PAST ‘Three students broke that table yesterday.’ (= (33b)) b. Gakusei-ga kinoo san-nin sono tukue-o kowasi-tei-ta. student-NOM yesterday three-CL that table-ACC break-PROG-PAST ‘Three students were breaking that table yesterday.’ (117) a.?? John-wa [gootoo-ga sokode san-nin Mary-o John-TOP [robber-NOM there three-CL Mary-ACC korosi-ta]-to itta. kill-PAST]-COMP said ‘John said that three robbers killed Mary over there.’ b. John-wa [gootoo-ga sokode san-nin Mary-o John-TOP [robber-NOM there three-CL Mary-ACC korosi-tei-ta]-to itta. kill-PROG-PAST]-COMP said ‘John said that three robbers were killing Mary over there.’ In (116b) and (117b), the monotonicity constraint on the range of a homomorphism h can be satisfied. The extension of a progressive VP is a lattice of subevents, thus the range of h is capable of having a part-whole structure. We further predict that these sentences allow a collective reading. In fact, since the events of breaking-that-table and killing-Mary can occur only once, the collective reading is the only reasonable interpretation. The same observation holds for German. Examples (118) show that the split MP construction with the single-occurrence event build Tokyo Tower is not permitted, but the corresponding an construction is permitted. (118) a.?*Arbeiter haben 10,000 den Tokio-Tower in Tokio gebaut. workers have 10,000 the Tokyo-Tower in Tokyo built ‘Ten thousand workers built Tokyo Tower in Tokyo.’ b. Arbeiter haben 10,000 an den Tokio-Tower in Tokio gebaut. workers have 10,000 PREP the Tokyo-Tower in Tokyo built ‘Ten thousand workers were building Tokyo Tower in Tokyo.’ German has another progressive form, namely, Rheinische Verlaufsform ‘Rhinelandic progressive’ (see footnote 37). Using this construction, it is possible to construct an example of a split MP construction with the single-

96 The semantic properties of non-split/split MP constructions occurrence event kill Peter, as in (119b), which is aceptable unlike nonprogressive (119a).38 (119) a.?? Räuber haben drei Maria umgebracht. robbers have three Mary killed ‘Three robbers killed Mary.’ b. Räuber waren drei Maria am umbringen. robbers were three Mary at.the killing ‘Three robbers were killing Mary.’ The second piece of evidence comes from the suffix -teiru in Japanese. This suffix could yield other interpretations than progressive, such as “experience” in (120) (Ogihara 1998, in particular). Under this reading, the collective reading is unavailable. This is because, unlike the progressive reading, the experience reading does not bring in a notion of partiality. (120) Sono kaisya-de-wa syain-ga kyonen san-nin that company-at-TOP worker-NOM last year three-CL ie-o tate-tei-ru. house-ACC build-TEI-PRES ‘At that company, three workers built a house last year.’

5.2.4. Notes on atelic predicates Before moving on to the second case of collectivity, I briefly discuss the relation between progressive aspect and the atelic-telic distinction. A progressive predicate is always atelic in that the event that it expresses has no set terminal point. For example, the telic predicate build a boat in (121a) is considered to be atelic when it is in progressive form, as in (121b). (121) a. John built a boat {*for ten minutes / in ten minutes}. b. John was building a boat {for ten minutes / *in ten minutes}. 38. The an construction corresponding to (119) is unacceptable, as in (i). This is probably because the distribution of the an construction is very restricted in the first place, as mentioned in footnote 36. (i) * Räuber haben drei an Maria umgebracht. robbers have three PREP Mary killed ‘Three robbers were killing Mary.’

Plurality and distributive-collective readings 97

This leads us to the following question: do split MP constructions permit collective readings with atelic predicates, not just with progressive predicates? The answer to this question seems to be positive. Let us consider the predicate push a cart, which is atelic (e.g., John pushed a cart {for ten minutes / *in ten minutes}) and has both distributive and collective readings (e.g., Three students pushed a cart could mean that each of the three students pushed a cart or that three students together pushed a cart). In Japanese (122) and German (123), both non-split and split MP constructions allow distributive and collective readings with the atelic VP push a cart. In contrast, the examples presented in section 3.1.3 include only telic predicates (build a boat, find a ten dollar bill, and marry), and split MP constructions with those predicates disallow collective readings. (122) a. [Gakusei san-nin]-ga kinoo kaato-o [student three-CL]-NOM yesterday cart-ACC ‘Three students pushed a cart yesterday’ OK distributive, OKcollective b. Gakusei-ga kinoo san-nin kaato-o student-NOM yesterday three-CL cart-ACC OK distributive, OKcollective (123) a. [Drei Studenten] haben einen [three students] have a ‘Three students pushed a cart.’ OK distributive, OKcollective b. Studenten haben drei einen students have three a OK distributive, OKcollective

osi-ta. push-PAST

osi-ta. push-PAST

Karren cart

geschoben. pushed

Karren cart

geschoben. pushed

The question then is why split MP constructions permit collective readings when the VP is atelic. Presumably, we could extend the analysis proposed for progressives: atelic predicates may be considered to have subevents and there is a mapping from a lattice of subevents to a lattice of individuals. While this may open up a new avenue to pursue, there is apparently a problem. The atelic VP push a cart becomes telic with the PP to the store, as in John pushed a cart to the store {*for ten minutes / in ten minutes}. Examples (124) ((a) for Japanese, (b) for German) show that, even with the PP to the store, split MP constructions still permit collective readings.

98 The semantic properties of non-split/split MP constructions (124) a. Gakusei-ga kinoo san-nin kaato-o mise-made osi-ta. student-NOM yesterday three-CL cart-ACC store-to push-PAST ‘Three students pushed a cart to the store yesterday’ OK distributive, OKcollective b. Studenten haben drei einen Karren zum Laden geschoben. students have three a cart to.the store pushed OK distributive, OK/?collective If the observation that both (122b)/(123b) and (124) allow collective readings is correct, then we lose the generalization that split MP constructions permit collective readings with atelic, but not telic, predicates. Unfortunately, there seem to be differences among speakers about the acceptability of the examples, and thus I leave this issue unresolved.

5.3. Case 2: Collectivity with together The second case involves so-called “collectivizing” adverbials such as together (also as a group, collectively, jointly, etc.) (Lasersohn 1995, in particular). When these adverbs appear in sentences that are otherwise ambiguous between distributive and collective readings, only a collective reading is available. For example, while (125a) is ambiguous between the two readings, (125) has a collective reading only. (125) a. John and Mary built a boat. b. John and Mary built a boat together. Similarly, in Japanese and German, when collectivizing adverbs co-occur with split MPs, as in (126), only collective readings are available ((a, b) for Japanese, (c) for German). (126) a. Otokonoko-ga kinoo san-nin issyoni booto-o boy-NOM yesterday three-CL together boat-ACC ‘Three boys built a boat together yesterday.’ b. Otokonoko-ga san-nin(-hito-kumi)-de booto-o boy-NOM three-CL(-one-CL)-COP boat-ACC ‘Boys built a boat by three (as a group).’

tukut-ta. make-PAST tukut-ta. make-PAST

Plurality and distributive-collective readings 99

c. Jungen haben drei zusammen ein Modellboot gebaut. boys have three together a model boat built ‘Three boys built a model boat together.’ The question arises as to why the collective reading in (126), but not in the examples in section 3.1.3 (repeated in (127)), is acceptable. (127) a. Otokonoko-ga kinoo san-nin booto-o tukut-ta. boy-NOM yesterday three-CL boat-ACC make-PAST ‘Three boys built a boat yesterday.’ OK distributive, ??collective (= (47b)) b. Jungen haben drei ein Modellboot gebaut. boys have three a model boat built OK distributive, ??collective (= (50b)) I propose that the collectivizing adverbs in (126) rely on Landman’s (1989a, 1989b, 1996, 2000) group formation operator ↑.39 As discussed in section 5.1.2, ↑ is a type-shifting operator that maps a sum of individuals (e.g., x∪Iy∪Iz) to an atomic group individual (e.g., ↑(x∪Iy∪Iz)). For instance, in (126), ↑ forms a group of three boys, yielding the interpretation that one group consisting of three boys built a model boat. In this case, examples (126) mean that a group of three boys built a boat, where there was only one agent, namely, a group of three boys. I should like to point out here that the collective readings in (126) and (127) are somewhat different in nature; while examples (126) are compatible with the situation where there are other groups of three boys who built a boat, examples (127) are incompatible with such a situation. Then, in (126), we could imagine a homomorphism h from a lattice of building-a-boat events to a lattice of groups of three boys, as shown in (128). Thus, a seemingly collective reading with a collectivizer is not “collective”; it is distributive in that each building-aboat event is mapped to each group of three boys.

39. See Chapter 3: footnote 41 for the denotation of split MPs occurring with together.

100 The semantic properties of non-split/split MP constructions

(128)

e1 ∪ E e2 ∪ E e3

h

↑(a∪Ib∪Ic)∪I↑(d∪Ie∪If)∪I↑(g∪Ih∪Ii)

e1∪Ee2 e1∪Ee3 e2∪Ee3 ↑(a∪Ib∪Ic)∪I↑(d∪Ie∪If) e1

e2

e3

↑(a∪Ib∪Ic)

…

↑(d∪Ie∪If)

… ↑(g∪Ih∪Ii)

Note that the analysis proposed here is analogous to Landman’s analysis of collective predicates such as meet. He points out that these predicates allow distributive readings; e.g., the boys and girls met has a reading where a group of boys and a group of girls met independently (see section 5.1.2). This is because the extension of the boys and girls can be a lattice consisting of two group atoms, i.e., a group of boys and a group of girls. In the same vein, in split MP constructions with collectivizers, the extension of agents can be a lattice consisting of group atoms, as illustrated in (128). I mentioned in section 3.1.3 that there seem to be be differences among speakers about how acceptable collective interpretations are in split MP constructions. Indeed, some informants with whom I consulted said that collective readings were not completely unacceptable. I suggest that this is because informants manipulate the existence of collectivizing adverbs. This is especially plausible for Japanese. As in (126b), collective interpretations obtain by simply putting -de ‘-COPULA’ after the split MP. Hence, even when a split MP is not followed by -de, speakers may obtain “illusive” collective readings by positing a covert -de.

5.4. Case 3: Collectivity with collective predicates Let us now turn to the third case, namely, split MP constructions with a collective predicate. In section 3.1.3, we saw that split MP constructions with an ambiguous predicate such as build a boat disallow collective readings. The following examples show that both non-split and split MP constructions are compatible with the collective predicates surround the city and gather (Japanese: (129) and (131), German: (130) and (132)). (129) a. [Heisi 500-nin]-ga kinoo mati-o torikakon-da. [soldier 500-CL]-NOM yesterday city-ACC surround-PAST ‘Five hundred soldiers surrounded the city yesterday.’

Plurality and distributive-collective readings 101

b. Heisi-ga kinoo soldier-NOM yesterday

500-nin 500-CL

mati-o city-ACC

torikakon-da. surround-PAST

(130) a. [500 Soldaten] umzingelten die Stadt. [500 soldiers] surround the city ‘Five hundred soldiers surrounded the city.’ b. Soldaten umzingelten 500 die Stadt. soldiers surround 500 the city (131) a. [Gakusei zyuu-nin]-ga kinoo [student ten-CL]-NOM yesterday ‘Ten students gathered yesterday.’ b. Gakusei-ga kinoo zyuu-nin student-NOM yesterday ten-CL

atumat-ta. gather-PAST atumat-ta. gather-PAST

(132) a. [Zehn Studenten] haben sich gestern [ten students] have REFL yesterday ‘Ten students gathered yesterday.’ b. Studenten haben sich zehn gestern students have REFL ten yesterday

versammelt. gathered versammelt. gathered

That examples (129)–(132) are grammatical appears to be problematic for monotonicity analysis because, as discussed in section 4.2.3, the monotonicity constraint should exclude collective readings (except for some special cases discussed in sections 5.2 and 5.3). However, I argue that the examples above are indeed compatible with motonicity analysis. Specifically, I claim that, unlike ambiguous predicates such as build a boat, the collective predicates surround the city and gather do not give rise to a genuine collective reading. Compare the sentences Ten students gathered and Ten students made a boat (under its collective reading). The former, but not the latter, has entailments regarding the part-whole relation of the students. For instance, if Ten students gathered is true, then Nine students gathered is also true. More generally, n students gathered entails n–1 students gathered. In contrast, the truth under a collective reading of Ten students made a boat does not gurantee the truth of Nine students made a boat, that is, n students made a boat under a collective reading does not necessarily entail n–1 students made a boat. In this way, although gather is “collective” in that it cannot distribute down to an atomic individual (e.g., One student gathered is ungrammatical), its collective reading is different from a genuine collec-

102 The semantic properties of non-split/split MP constructions tive reading of build a boat that lacks the entailments with respect to a partwhole structure of a plural subject. Consider further the unambiguously distributive predicate sleep. If the sentence Ten boys slept is true, then nine boys must have slept, eight boys must have slept, and so on. This suggests that the collective reading that obtains with gather is not genuinely collective, but rather distributive. The claim that predicates such as gather are not genuinely collective is not new: Dowty (1987) argues that collective predicates such as gather and surround the city have what he calls distributive sub-entailments. Although the collective predicate gather does not distribute down to the individual members of a group, it distributively entails a property of the members of the group (e.g., each undergoing a change of location).40 Compare now (129)–(132) with Japanese (133) and German (134), where split MP constructions are infelicitous. The VP build Tokyo Tower is genuinely collective in that it lacks the entailments of the kind discussed above: if Ten thousand workers built Tokyo Tower is true, it does not necessarily guarantee that One hundred workers built Tokyo Tower is true. (133) a. [Sagyooin itiman-nin]-ga Tokyo-ni Tokyo Tower-o [worker 10,000-CL]-NOM Tokyo-in Tokyo Tower-ACC ‘Ten thousand workers built Tokyo Tower in Tokyo’ b.* Sagyooin-ga Tokyo-ni itiman-nin Tokyo Tower-o worker-NOM Tokyo-in 10,000-CL Tokyo Tower-ACC

tateta. built tateta. built

(134) a. [10,000 Arbeiter] haben den Tokio-Tower in Tokio gebaut. [10,000 workers] have the Tokyo-Tower in Tokyo built ‘Ten thousand workers built Tokyo Tower in Tokyo.’ b.?*Arbeiter haben 10,000 den Tokio-Tower in Tokio gebaut. workers have 10,000 the Tokyo-Tower in Tokyo built 40. There is another interpretation relevant to the discussion here, namely, cover readings, defined in (i) (Gillon 1987, Schwarzschild 1991, 1996, van der Does 1992, Verkuyl and van der Does 1996, Brisson 1998, 2003). (i) X covers Y iff: a. X is a set of nonempty subsets of Y b. ∀y∈Y ∃x∈X [y∈x] For instance, a cover reading is the most plausible reading of the sentence Four hundred firefighters put out the fires in Colorado (Landman 2000: 125): different groups of firefighters (maybe overlapping) put out fires, and those groups together make up four hundred firefighters.

Plurality and distributive / collective readings 103

In sum, if we take the view that predicates such as gather and surround the city are not genuinely collective but rather distributive, examples (129)– (132) do not challenge the current monotonicity analysis.

5.5. Case 4: Collectivity with internal arguments The fourth case comes from the split MP construction where the host NP is an internal argument. So far, when monotonicity in the verbal domain was at issue (sections 3, 4, and 5), examples of split MP constructions were restricted to those where the host NP was a subject, or more specifically, an external argument. The host NP, however, is not restricted to external arguments; as shown in Japanese (135a) and German (135b), the host NP can be an internal argument. (135) a. John-ga hon-o kinoo san-satu yon-da. John-NOM book-ACC yesterday three-CL read-PAST ‘John read three books yesterday.’ b. Bücher hat Hans gestern drei gelesen. books has Hans yesterday three read In the following, depending on whether a split MP is associated with an external or an internal argument, the split MP construction is referred to as an external split MP construction or internal split MP construction.41 In this section, I first show that internal split MP constructions seem to allow a collective reading. Then I argue that this reading is different in nature from the collective reading in external split MP constructions, and that semantic asymmetry between external and internal arguments is responsible for the difference in collectivity. The categorization of predicates based on distributivity is generally made with respect to plural subjects, or more precisely, external arguments (see section 5.1.1), while not much has been said on distributivity with respect to plural objects (or internal arguments) (see Lasersohn 1998 for a relevant discussion). Dowty (1987) categorizes enumerate and count as collective and summarize as ambiguous, and Landman (2000) lists combine as a collective predicate. The verb mix in the internal split MP constructions 41. The host NP must be either an external or an internal argument. To put it differently, the split MP cannot be associated with a PP because of syntactic constraints. See Chapter 3: section 3 for details.

104 The semantic properties of non-split/split MP constructions in (136) ((a) for Japanse, (b) for German) is interpreted both as distributive and collective in terms of the plural internal argument three cocktails. The distributive reading is that John made three different cocktails separately, say, a martini, a margarita, and a piña colada. The collective reading is that John put together three cocktails and made a mysterious drink. (136) a. John-ga kakuteru-o syeikaa-de san-bai maze-ta. John-NOM cocktail-ACC shaker-by three-CL mix-PAST ‘John mixed three cocktails in a shaker.’ b. Getränke hat Hans drei gemischt. drinks has Hans three mixed ‘Hans mixed three drinks.’ Examples (137) ((a) for Japanse, (b) for German) show that internal split MP constructions are compatible with a collective predicate such as pile up. (137) a. John-ga hako-o heya-ni zyuk-ko tumikasane-ta. John-NOM box-ACC room-in ten-CL pile up-PAST ‘John piled up ten boxes in the room.’ b. Kasten häufte Hans gestern zehn an. boxes heaped Hans yesterday ten on ‘Hans piled up ten boxes yesterday.’ I argue that collective readings obtained with internal split MP constructions are the same as those obtained with predicates such as gather and surround the city (see section 5.4). Specifically, collective readings with respect to a plural internal argument are inherently different from genuine collective readings with respect to a plural external argument. For instance, in (137), if John piled up ten boxes, then he must have piled up nine boxes, eight boxes, and so on. That is, the truth of examples (137) entails the truth of the sentences with the smaller number of boxes (but not down to one since John piled up one box is ungrammatical). This is the same entailment pattern as that observed with gather in section 5.4. Thus, neither pile up nor gather is genuinely collective, but rather distributive in that they share the same entailment pattern as distributive predicates such as sleep. The same argument seems to hold for all other putative collective predicates with respect to internal arguments (e.g., mix (under its collective reading), collect, gather, assemble, sum, accumulate, separate, divide).

Plurality and distributive / collective readings 105

Supporting evidence for this generalization comes from the observation that the distributive quantifier every is inappropriate in the subject position of collective predicates (Roberts 1990), but not in the object position (Landman 2000), as in (138). (138) a. ? Every boy meets. b. In this class I will try to combine every semantic theory that has been proposed in the literature. (Landman 2000: 83) If the generalization that internal split MP constructions lack genuine collective readings is on the right track, then the next step would be to ask why this is so. I suggest that this is because there is an inherent incremental relationship between an event and its internal argument, but not between an event and its external argument.42 For instance, in eat an apple, there is an incremental relationship between the eating event and its internal argument an apple in that, as the eating event proceeds, the amount of apple consumed increases. In contrast, it has been claimed that there is no such incremental relationship between an event and its external argument (Tenny 1987, 1994, in particular).43 Let us now go back to the data on distributivity.

42. Various types of incremental relationships can be found in the literature: “ADD-TO” property (Verkuyl 1972, 1993), “measuring out” (Tenny 1987, 1994), “graduality” (Krifka 1989, 1992), “incremental theme” (Dowty 1991), and “structure-preserving binding relations” (Jackendoff 1996) (see Krifka 1998: 198–199 for a summary). 43. Dowty (1991) and Krifka (2001) argue that there can be an incremental relationship between an event and its external argument, as in (i) and (ii). (i) a. John entered the icy water (very slowly). b. John crossed the desert in a week. (Dowty 1991: 570‒571) (ii) Fifty customers complained about the product in two days. (Krifka 2001: 7) These examples, however, are not strong counter-examples to the generalization that the incremental relationship holds only between an event and its internal argument. For (i), we could say that the external argument of a movement verb is special in that it has a double role of being an agent and a moved object, as claimed in Krifka (2001: 7). As for (ii), the incrementality found with quantified NPs such as fifty customers is different in nature from the incrementality with singular NPs, in that, in the former case, the incrementality can be forced by pluralizing both individuals and events, yielding a homomorphic relation between the two (cf. Dowty 1991: 570). Thus, a singular external argument is

106 The semantic properties of non-split/split MP constructions In John piled up ten boxes, there is an incremental relation between the piling up event and boxes, that is, as the piling up event proceeds, the number of boxes increases. This amounts to the entailment described above. In contrast, in ten boys built the statue, there is no incremental relationship between ten boys and the building-the-statue event, hence there is no entailment of the kind found with pile up ten boxes. Summing up, since an internal argument always has an incremental relationship with an event, it never allows a genuine collective reading without entailment. I take this to mean that the seemingly collective readings in (136) and (137) are not genuinely collective, hence they are not problematic for the present monotonicity analysis.

5.6. Summary of section 5 This section presented empirical data on collective and distributive interpretations of split MP constructions. The summary is given in (139). I showed that the monotonicity analysis is capable of handling the whole range of data. (139) a. Case 1: Split MP constructions allow special collective readings with a progressive VP. b. Case 2: Split MP constructions allow special collective readings with a collectivizer. c. Case 3: Split MP constructions with collective predicates lack genuine collective readings. d. Case 4: Internal split MP constructions always lack genuine collective readings.

6. Notes on homomorphisms The analysis of split MP constructions presented in this chapter made a crucial use of a homomorphism from events to individuals. I would like to briefly comment on previous studies that use a homomorphism from events to other domains for the analysis of some empirical phenomena.

different from a singular internal argument in that it does not have an incremental relationship with an event.

Notes on homomorphisms 107

Besides a homorphism from events to individuals proposed in section 4.1, at least two types of homomorphisms have been proposed in previous work, most notably by Krifka (1986, 1989, 1992, 1998, 2001) and by Lasersohn (1988, 1995).44 Recall the discussion in section 4.1 that the measure function associated with the temporal adverb for three hours in John slept for three hours applies to the run time of John’s sleeping event, rather than applying to the event directly. This is because an event cannot be directly measured by a temporal scheme. Instead, for three hours indirectly measures the sleeping event by measuring a run time of the event. Krifka (1989) proposes the temporal trace function τ, which is, a function from events (the extension of E) to their run times (the extension of T), as defined in (140). (140) Temporal trace function τ (homomorphism from events to their run times) τ(e1∪Ee2) = τ(e1)∪Tτ(e2) (Link 1987a, Krifka 1989, 1992, 1998) The same analysis extends to paths of events. For example, in John walked two feet, the measure function associated with the MP two feet indirectly measures John’s walking event by measuring the path of the event, rather than directly measuring it. This is done by the path trace function σ, that is, a function from events (the extension of E) to their paths (the extension of L), as in (141).45 44

45

Additional arguments for homomorphic relations between events and individuals can be found in series of work by Hana Filip (1999, 2000, 2004). Her main arguments come from definiteness in Slavic languages. There seems to be an ontological difference between a homomorphism to paths and one to individuals. Suppose that John ran a one-mile track three times. In this context, (i) is true. In contrast, (ii) cannot mean that John visited a particular friend three times. In other words, three different friends must be involved. (i) a. John-ga kinoo san-mairu hasit-ta. John-NOM yesterday three-mile run-PAST ‘John ran three miles yesterday.’ (Japanese) b. John hat drei Meilen gestern geführt. John has three miles yesterday run (German) (ii) a. John-ga tomodati-o kinoo san-nin tazune-ta. John-NOM friend-ACC yesterday three-CL visit-PAST ‘John visited three friends yesterday.’ (Japanese) b. Freunde hat John gestern drei besucht. friends has John yesterday three visited (German)

108 The semantic properties of non-split/split MP constructions (141) Path trace function σ (homomorphism from events to their paths) σ(e1∪Ee2) = σ(e1)∪Lσ(e2) (Lasersohn 1995, Krifka 1998) Krifka’s and Lasersohn’s work shows that these two functions are independently required to account for a variety of empirical data, such as the semantics of the temporal together (e.g., John and Bill stood up together, where together contributes the meaning ‘at the same time’), of pluractional markers (see Chapter 5: section 4.2), and so forth. Thus, aside from the semantics of split MP constructions, we need a homomorphism from events to other domains, namely, to their temporal traces or to their paths.

7. Summary of chapter 2 In this chapter, I examined the semantic properties of non-split and split MP constructions in Japanese and German. Through empirical studies of these constructions, I strengthened or established the following points: (142) a. The need for variables over events b. The semantic parallelism between the nominal and verbal domains c. Monotonicity as a formal property of non-split and split MP constructions d. The mechanism of measurement in the verbal domain: i) Plurality of events ii) Homomorphism from events to individuals The core argument is that non-split and split MP constructions differ in that the former measure individuals denoted by the host NP in the nominal domain, while the latter measure events denoted by the VP in the verbal domain (as well as individuals). The difference in their domains of measurement is reflected by the difference in their sensitivity to the monotonicity constraint. I further proposed a mechanism of measurement in the verbal domain that makes use of a homomorphism from events to individuals, successfully accounting for characteristic properties of split MP constructions (i.e., (in)compatibility with single-occurrence events and with individual-level predicates, (un)availability of collective readings).

Chapter 3 The syntax and compositional semantics of non-split and split quantifier constructions

1. Introduction The last chapter examined semantic properties of non-split and split MP constructions in Japanese and German. I argued that non-split MP constructions involve measurement of individuals in the nominal domain, whereas split MP constructions involve measurement of events in the verbal domain (and also of individuals via homomorphisms). The goal of this chapter is to seek syntactic structures of the two constructions that allow us to achieve compositionally the semantic properties discussed in Chapter 2. I show that non-split and split MPs in Japanese and German can be analyzed syntactically as adjuncts that combine with, respectively, nominal and verbal predicates. These syntactic structures provide a compositional semantics of the two constructions. Specifically: 1) a non-split MP combines syntactically with, and correspondingly expresses measurement of, a nominal predicate, and 2) a split MP combines syntactically with, and correspondingly expresses measurement of, a verbal predicate (see Chapter 2: section 4.3 for a related discussion). Note that the major contribution of this chapter is to provide a compositional analysis of non-split and split MP constructions, it is not to rule out other competing syntactic accounts. Thus, the discussion in this chapter is by no means a complete survey of the vast literature on the two constructions. For a general overview of non-split MP constructions, see Vos (1999) and Alexiadou, Haegeman, and Stavrou (2007). See Bobljik (2003) for cross-linguistic split MP constructions, and see Nakanishi (in press) for Japanese split MP construction. In the following, I often make use of examples involving quantifiers other than MPs, so I use the more general terms non-split / split quantifier (Q) construction interchangeably with non-split / split MP constructions. In section 2, I examine the syntax of non-split Q construction. Section 3 is devoted to the syntax of split Q constructions, where split Qs are analyzed

110

Syntax and compositional semantics of (non-)split constructions

as adjuncts combining syntactically with verbal predicates. Section 4 provides a compositional semantics of the two constructions. Section 5 discusses some issues regarding a homomorphism involved in split Q constructions. Section 6 is a summary.

2. The syntax of non-split quantifier constructions This section examines the syntax of non-split Q constructions in Japanese and German. Cross-linguistically, there are two types of non-split Q constructions: one with a linking morpheme (e.g., English of in three liters of water) and another without it (e.g., German drei Liter Wasser ‘(lit.) three liter water’, Japanese mizu san-rittoru ‘(lit.) water three-liter’). 1 Since German and Japanese non-split Q constructions belong to the second type, I limit the discussion in this section to the second type. One of the central questions posed in earlier studies is the syntactic status of the two nominal heads in these constructions (Jackendoff 1977, Selkirk 1977, Abney 1987, Löbel 1989, 2001, Kubo 1996, Corver 1998, van Riemsdijk 1998, Vos 1999, Borer 2005, Grimshaw 2005, Alexiadou, Haegeman, and Stavrou 2007). Consider the German non-split Q construction, that is, drei Liter Wasser ‘three liters of water’, where there are two nominal heads the first noun Liter (henceforth, N1) and the second noun Wasser (henceforth, N2). The question arises as to the syntactic relation between these two nominal heads. To put it differently, do they belong to the same or different extended projections (see Grimshaw 2005 for the definion of extended projection)? One could argue that there are two extended projections, and Liter and Wasser belong to different ones. Alternatively, one could claim that a non-split MP construction consists of a single extended projection.2 1. Japanese has a construction that uses the genitive marker -no to connect a MP and the host NP, as in (i). For the reason discussed in Chapter 2: section 2.5, I ignore this construction throughout this chapter (but see section 3.2 below). (i) san-rittoru-no mizu three-liter-GEN water 2. Van Riemsdijk (1998) categorizes non-split MP constructions into six types based on the properties of N1, as shown in the Dutch examples (i). There may be some syntactic variations among different types (see, for instance, Vos 1999). Since the syntax of these constructions is not the main focus of this chapter, I ignore this classification.

The syntax of non-split quantifier constructions 111

Based on data from Dutch and German, van Riemsdijk (1998) and Vos (1999) argue that there is only one projection in non-split MP constructions. The strongest argument for their claim comes from case agreement. As shown in the German examples (1), the two nouns (N1 and N2) always share the same case, which is expected if they are in a single projection and are assigned case by the same case assigner. If they belong to different projections, they could have different cases, which is unattested in non-split MP constructions in Dutch and German. (1)

a. nach [zwei Flaschen rotem Wein] after [two bottles.DAT red.DAT wine.DAT] b. Ich habe [eine Kiste Kubanische Zigarren] bestellt. I have [a.ACC case.ACC cuban.ACC cigars.ACC] ordered (van Riemsdijk 1998: 14-15)

Alexiadou, Haegeman, and Stavrou (2007) illustrate the same point using Greek data, cited in (2). In (2a), the quantifier is in the same case as the following NP, since they are in the same extended projection. Thus, the shared case morphology of N1 and N2 in (2b) indicates that N1 and N2 are in the same extended projection. (2)

a. Tis her.DAT b. Tis her.DAT

(i)

prosfere offered.3SG prosfere offered.3SG

[polus iakinthus]. [many.PL.ACC hyacinths.PL.ACC] [ena buketo iakinthus]. [a.SG.ACC bunch.SG.ACC hyacinths.PL.ACC]

a. Quantifier noun: een a b. Measure noun: drie three c. Container noun: die that d. Part noun: een a e. Collective noun: een a f. Kind noun: vijf five

aantal voorbeelden number examples liter melk liter milk krat bier case beer snee brood slice bread kudde olifanten herd elepants soorten zoogdieren types mammals (van Riemsdijk 1998: 13)

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Syntax and compositional semantics of (non-)split constructions

Additional evidence for the monoprojectional view comes from the fact that N2 cannot take a functional head such as a determiner or a quantifier, as shown in the Dutch examples (3). If N2 were the head of an independent extended projection, it should be able to take any functional head. (3)

a. mijn my b. een a c. drie three

collectie (*de) Duitse klassieken collection (the) German classics stapel (*alle) publicities van Halle pile (all) publications by Halle kisten (*25) sigaren boxes (25) cigars (van Riemsdijk 1998: 15)

Following these arguments, I assume that there is only one projection in non-split MP constructions in German and Dutch, that is, the non-split MP and the host NP are in the same extended projection. The next task is to figure out the internal structure of this projection. One of the widely accepted structures is presented in (4a) (see Löbel 2001, Alexiadou, Haegeman, and Stavrou 2007).3 This structure is especially appealing in that it captures the semantic and syntactic similarities between nominal projections in German/Dutch and in classifier languages. The structure in (4b), taken from Li (1999) with some modification, has been proposed for classifier languages such as Chinese (see also Cheng and Sybesma 1999, Borer 2005, Watanabe 2006).

3. There have been discussions on whether N1 is lexical or functional. Van Riemsdijk (1998) argues that, although N1 and N2 are part of a single extended projection, N1 cannot be analyzed simply as a functional head. In particular, he argues that N1 is a semi-lexical head by showing that N1 has properties of lexical heads. See also Vos (1999), Cover and van Riemsdijk (2001), and Alexiadou, Haegeman, and Stavrou (2007) for further discussion on this issue.

The syntax of non-split quantifier constructions 113

(4)

a.

NumP Spec

b. Num’

drei Num ‘three’

NumP

Spec MP

(cf. Li 1999: 87) Num’

san Num ‘three’

ClP

M

NP

Cl

NP

Liter ‘liter’

Wasser ‘water’

ge ‘CL’

xuesheng ‘student’

Although structures (4) seem to capture the parallelism between German and Japanese (which is a classifier language), adopting them leads us to some problems. First, structure (4b) proposed for Chinese does not extend straightforwardly to Japanese. The intuition behind (4b) is that NPs in Chinese are mass and that classifiers make NPs countable (see Chapter 1: section 3.2). A classifier first combines with a NP, which creates the countable unit [Cl + NP], then this constituent combines with a numeral. In Chinese, [Cl + NP] is a legitimate constituent in that it can occur as an argument, as in (5a). In contrast, a classifier in Japanese must appear with a numeral, hence [Cl + NP] is never possible in the surface syntax, as shown in (5b). (5)

a. Wo xiang mai [ben shu]. I would-like buy [CL book] ‘I would like to buy a book.’ (Cheng and Sybesma 1999: 511) b. Watasi-wa [hon *(is-)satu]-o ka-itai. I-TOP [book (one-)CL]-ACC buy-would like

Another problem is that the structures in (4) do not seem to be capable of accounting for the distribution of MPs: MPs appear in various environments, as illustrated in the English examples (6) (Jackendoff 1977, see also Chapter 1: section 1.3). German (7) and Japanese (8) show that MPs in these languages also have a wide distribution. (6)

a. b. c. d. e.

AP: DegP: NP: PP: VP:

two feet long two feet longer two feet of rope two feet away walk two feet

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Syntax and compositional semantics of (non-)split constructions

(7)

a. zwei two b. zwei two c. zwei two d. zwei two e. zwei two

(8)

Meter meter Meter meter Meter meter Meter meter Meter meter

lang long länger longer Seil rope entfernt removed laufen walk

a. ni meetoru two meter b. ni meetoru two meter c. roopu ni rope two d. ni meetoru two meter e. ni meetoru two meter

nagai4 long naga-sugiru5 long-exceed meetoru meter hanarete away aruku walk

‘two meters long’ ‘two meters longer’ ‘two meters of rope’ ‘two meters away’ ‘walk two meters’

‘two meters longer’ ‘two meters too long’ ‘two meters of rope’ ‘two meters away’ ‘walk two meters’

This distribution of MPs follows naturally if we assume that a MP is an adjunct to maximal projections (e.g., AP in (7a), DegP in (7b), NP in (7c), PP in (7d), VP in (7e)), as schematized in (9). (9)

AP/DegP/NP/PP/VP MP

AP/DegP/NP/PP/VP

two meters In this structure, a numeral and a measure word (or N1) form a constituent, yielding a MP, and then the MP combines with the host NP (or N2).6 For 4. In Japanese, when MPs occur with gradable adjectives, the sentence is always interpreted as a comparative construction, as reflected in the translation in (8a). In Chapter 4: section 2.4, I discuss why this is the case. 5. The Japanese verb -sugiru following adjectives means roughly ‘too’. Chapter 4 discusses the semantics and syntax of -sugiru.

The syntax of non-split quantifier constructions 115

instance, in (7c), zwei ‘two’ and Meter ‘meter’ form a MP, and the MP combines with the host NP Seil ‘rope’. Note that, in Japanese, the surface order [NP + MP] in (8c) does not follow from the structure (9), which would yield the order [MP + NP] (assuming that adjuncts appear on the left side). To derive the correct surface order, I assume that the NP obligatorily moves to a specifier of the higher projection, say, Spec DP, as illustrated in (10) (see Saito and Murasugi 1999 for evidence for the existence of DP in Japanese).7 (10)

DP NP

D’

ropei

NP

D

MP

NP

two meters

ti

A similar argument for the adjunct analysis can be found in Doetjes’ (1997) work on degree quantifiers in French. Degree quantifiers in French such as beaucoup ‘many/much’ or combien ‘how many/much’ can combine with different categories (NPs, VPs, etc.). She argues that, as in (11), combien is an adjunct which can combine with any category and that the whextraction of combien can leave behind the lexical category it modifies. 6. In his analysis of pseudopartitives such as two feet of rope, Schwarschild (2006) also proposes a structure where the MP two feet is a constituent and it combines with the host NP rope, as in (i). His structure, however, differs substantially from the one proposed in (9). Specifically, he proposes a functional head called Mon that is occupied by of (or a null head in the case of German), and the MP is at Spec MonP. See section 4.1 for further discussion. (i) [MonP two feet [Mon of [ NP rope]]] 7. The main concerns in this section are to capture the parallelism between the German and Japanese non-split MP constructions and to account for the crosscategorial distribution of MPs. Thus, I ignore several issues widely discussed in the literature on Japanese nominal phrases (e.g., syntactic differences between MPs and ClPs, the location of case markers). I refer the reader to studies such as follows: Fukui 1986, Tateishi 1989, Terada 1990, Kitahara 1993, Kawashima 1998, Muromatsu 1998, Saito and Murasugi 1999, Fukui and Takano 2000, and Watanabe 2006.

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(11) a. Combieni as-tu lu [NP ti de how many have-you read of ‘How many books did you read?’ b. Combieni les enfants ont-ils how much the children have-they ‘How much did the children laugh?’ c. Vous verrez combieni il est you will see how much he is ‘You will see how evil he is.’

livres]? books [VP ri ti]? laughed [AP ti méchant]. evil (Doetjes 1997: 94)

In this section, I presented an analysis of non-split MP constructions where a non-split MP is adjoined to the host NP. The next section defends the analysis of split MP constructions where a split MP is adjoined to a VP, which makes non-split and split MP constructions syntactically parallel.

3. The syntax of split quantifier constructions In section 3.1, I introduce a stranding analysis of FQs in various languages, where FQ constructions are generated by moving the host DP higher in the structure, stranding a quantificational element (Sportiche 1988, among others). I present some problems of this analysis, and introduce an adverbial analysis, in which FQs are base-generated where they appear (Dowty and Brodie 1984, among others). In sections 3.2 and 3.3, I turn to Japanese FQ construction and German ST, and argue that the adverbial account extends to these constructions. Specifically, split Qs can be analyzed as adjuncts to verbal predicates. As mentioned in section 1, the main goal is to present a structure that allows us to account compositionally for the semantic properties of the split MP constructions discussed in Chapter 2. As will become clear in section 4, the adverbial analysis allows us to achieve this goal, so the discussion is mainly concerned with arguments for the adverbial analysis. For a more complete comparison of transformational and adverbial analyses, see Bobaljik (2003) and Nakanishi (in press), among others.

The syntax of split quantifier constructions 117

3.1. Stranding vs. adverbial analyses of floating quantifier constructions8 It is well known that, in many languages, a quantificational element (often restricted to universal quantifiers) may appear apart from the DP that it seems to modify (henceforth, the host DP), as in (12). (12) a. All the students have gone home. b. The students have all gone home. Over the past few decades, this paradigm has attracted a great deal of attention. Amongst different issues discussed in the literature, the syntactic derivation of the configuration in (12b) is especially important and controversial. One account is to derive transformationally (12b) from (12a) by positing a rightward movement of the quantifier in (12a) (Kayne 1975, in particular). Sportiche (1988) replaced this account with stranding analysis. Based on the intuition that there is a syntactic dependency in (12b) between the quantifier all and the host DP the student, Sportiche claims that “Qs may appear in DP-initial position” (1988: 427).9 Then (12b) is derived as follows: the quantifier all appears in the DP-initial position, as in (13a), and the DP following the quantifier moves to a higher position, stranding the quantifier, as in (13b) (see also Giusti 1990a, b, c). Under this view, the quantifier in (13b) is “floated” in that it is left behind after the movement of the host DP, hence it has been traditionally called a floating quantifier (FQ). (13) a. [IP ___ have [VP [DP all [DP the students]] gone home]] b. [IP [DP the students]i have [VP [DP all ti] gone home]] One of the strongest assets of Sportiche’s analysis (at least at the time it was introduced) is its consistency with the VP-internal subject hypothesis. It has been independently argued that the subject is base-generated within the VP and that it moves to a higher position (Kitagawa 1986, Speas 1986, Speas and Fukui 1986, Kuroda 1988, Koopman and Sportiche 1991). Under Sportiche’s analysis, the FQ construction in (12b) is derived simply by

8. The content of this section benefited greatly from Bobaljik’s (2003) overview of FQs. 9. Sportiche’s (1988) original claim is the following: “Qs may appear in NP-initial position”. “NP” here should be replaced by “DP” in the more recent framework (Abney 1987, among others).

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Syntax and compositional semantics of (non-)split constructions

adopting this hypothesis and assuming that Qs in the DP-initial position may be stranded, as shown in (13). Moreover, Sportiche argues that his analysis is capable of accounting for the three properties of FQs in (14) (see Bobaljik 2003 for details). (14)

a. Distribution of FQs: FQs occur only in positions through which the host DP has passed in the course of its movement. (section 3.1.1) b. Morphology of FQs: FQs display morphological agreement with the host DP. (section 3.1.2) c. Semantics of FQs: FQ and non-FQ constructions are semantically the same. (section 3.1.3)

In the following, I consider these properties in more detail and make the following two points: first, there are counter-examples to (14a) and (14c), and second, not all instances of morphological agreement can be explained by Sportiche’s analysis.

3.1.1. Distribution of FQs Regarding (14a), as pointed out by Bobaljik (1995: 194), Sportiche’s (1988) stranding analysis predicts that FQs occur only in positions through which the host DP has passed in the course of its movement (see also McCloskey 2000 for this point). Bobaljik convincingly shows that examples exist that do not bear out this prediction (see Bobaljik 1995: Chapter IV for details). One prediction following from the stranding analysis is that it is possible for FQs to appear after a passive or an unaccusative verb, since the surface subject of these verbs is originated as an internal argument. These sentences are, however, ungrammatical (see (15)).10 (15) Passive: *The boysi were arrested [ all ti ] Unaccusative: *The boysi have arrived [ all ti ] Another problem appears in those FQ constructions that may be acceptable even though there are no corresponding non-floating counterparts. 10. Sportiche (1988) himself is aware of this problem and suggests a solution. His solution is not as convincing as one would hope in that it must adopt a rather particular analysis of passives and unaccusatives.

The syntax of split quantifier constructions 119

Sportiche’s analysis says that FQ constructions are derived from their nonfloating counterparts. However, it is not clear how we could derive the FQ construction in (16a) from its non-floating counterpart in (16b) if (16b) is ungrammatical to begin with. The same point can be made with examples (17), whose non-floating counterparts are ungrammatical. (16) a. Some (of the) students might all have left in one car. b.?*[All (of) some (of the) students] … (Bobaljik 2003: 124) (17) a. Tom, Dick and Harry have each had a sandwich. b. Fred, Ed and Ned have all been to Paris. (Hoeksema 1996: 65) Similarly, there are complex quantifying expressions that appear in floated, but never prenominal, positions, as in (18). Further examples from Dutch are given in (19) (see also (26) and (28)). (18) a. We have all three of us completed the assignment on time. a’.*[All three of us we] … (Bobaljik 2003: 124) b. These guys were neither of them very smart. (Hoeksema 1996: 66) (19) a. De vrouwen waren geen van allen verlegen. the women were none of all shy ‘The women were none of them shy.’ b.* [Geen van allen de vrouwen] waren/was verlegen. (Hoeksema 1996: 67) Lastly, in some languages, putative examples of FQs are lexically distinct from their prenominal counterparts (Dowty and Brodie 1984, Hoeksema 1996, Doetjes 1997). For instance, allemaal ‘all’ in Dutch (20) and dou ‘all’ in Chinese (21) can never function as prenominal quantifiers and always appear in a “floated” position. These languages have different prenominal quantifiers (alle in Dutch and suo you in Chinese). (20) a. De boeren hadden allemaal hooikoorts. the farmers had all hay-fever ‘The farmers all had hay-fever.’ b.* [Allemaal de boeren] hadden hooikoorts. (Hoeksema 1996: 70)

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Syntax and compositional semantics of (non-)split constructions

(21) a. ren dou zou le people all left ASP ‘The people have all left’ b. suo you de ren zou all PRT people left ‘all the people have left’

le ASP

(Dowty and Brodie 1984: 82)

3.1.2. Morphology of FQs Let us now turn to the second property in (14b), concerning morphological agreement. In languages with a rich agreement system (in terms of case, number, gender, and so on), FQs agree morphologically with the host DP (Sportiche 1988, Shlonsky 1991, Merchant 1996). For example, French examples (22) show that the FQ as well as the non-FQ must agree with the host DP in terms of gender (and also number). (22) a. [{Toutes / *tous} les filles] ont [{all.F.PL / all.M.PL} the girls.F.PL] have ‘All the girls have seen this movie.’ b. Les filles ont {toutes / *tous} the girls.F.PL have {all.F.PL / all.M.PL}

vu ce film. seen this movie vu ce film. seen this movie

It is well known that, when multiple elements which may show morphological argreement occur in the same nominal projection, they must morphologically agree with each other. The agreement between an adjective and a modified noun is a good example; in the French example (23), there must be a morphological marking on the adjective indicating that it is feminine and plural. (23) {petites / *petit /*petits} filles {small.F.PL / small.M.S / small.M.PL} girls.F.PL The morphological agreement between a FQ and the host DP is one of the strongest arguments for stranding analysis. Specifically, we could argue that the FQ is in the same nominal projection as the host DP in the underlying structure, and that the morphological agreement between them is achieved there.

The syntax of split quantifier constructions 121

This is the line of argument taken by Shlonsky (1991). Building on Sportiche’s work, Shlonsky proposes a mechanism that accounts for the agreement between a FQ and its host DP. His proposal is based on Hebrew data, where FQs must host a clitic pronoun that agrees with the host DP in number and gender. In contrast, non-FQs cannot host such a pronoun. Examples are given in (24). (24) a. Katafti ʔet [{kol / *kul-am} ha-praxim] bi-zhirut. (I) picked ACC {all / all-3MPL} the-flowers with-care ‘I picked all the flowers carefully.’ b. Katafti ʔet ha-praxim {kul-am / *kul-o / *kol} bi-zhirut. (I) picked ACC the-flowers {all-3MPL / all-3MS / all} with-care (Shlonsky 1991: 160–161) Shlonsky argues that the quantifier kol- ‘all’ is a functional head that selects a DP complement (which I call the host DP), as in (25). The DP complement moves first to the specifier of QP, where it triggers agreement, and moves further out of the QP to a higher position in the main clause, generating the FQ construction. (25) [QP [DP ha-praxim]i [Q’ kol ti ]] There are some examples of morphological agreement that are problematic for stranding analysis. In particular, there are cases, as discussed in section 3.1.1, where FQ constructions without corresponding non-floating counterparts are acceptable. For instance, German examples (26) show that all- drei ‘all three’ can be split from the host DP diese Studenten ‘these students’, but cannot appear in the prenominal position. (26) a. Diese Studenten haben gestern alle drei protestiert. these.NOM students have yesterday all.NOM three protested ‘(lit.) All these three students protested yesterday.’ b.* [Alle drei diese Studenten] haben gestern protestiert. [all.NOM three these.NOM students] have yesterday protested Crucially, all- ‘all’ in all- drei must agree with the case of the host DP. In stranding analysis, the agreement of all- obtains when all- is in the same nominal projection as its host DP. The surface order obtains by moving the host DP out of the nominal projection, stranding the inflected all-. Such a derivation is untenable in (26a), since (26b) is ungrammatical. Note that

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Syntax and compositional semantics of (non-)split constructions

all- can be in the same nominal projection as diese drei Studenten ‘these three students’, as in (27). However, it is not clear whether (26a) and (27) are transformationally related at all. (27) [Alle diese drei Studenten] haben gestern protestiert. [all.NOM these.NOM three students] have yesterday protested Independently, Bobaljik (2003: 124), using French examples (28), points out the same problem of agreement. (28) a. Elles sont toutes les trois they.F are all.F.PL the three b.* [Toutes les trois elles] sont [all.F.PL the three they.F] are

intelligentes. intelligent intelligentes. intelligent (Kayne 1975: 44)

Lastly, another set of agreement examples poses problems for stranding analysis. Hoeksema (1996) shows that, in the non-FQ construction (29a), the verb is marked as singular, agreeing with the subject each of these men, whereas, in the FQ construction (29b), the verb is marked as plural, agreeing only with these men. If (29b) were derived from (29a), the two sentences should have the same verbal agreement, which they do not. (29) a. Each of these men shaves himself. b. These men each shave themselves.

(Hoeksema 1996: 64)

In sum, the examples of nominal agreement in (26) and (28) and also the examples of verbal agreement in (29) suggest that morphological agreement is not necessarily a strong argument for stranding analysis.

3.1.3. Semantics of FQs Finally, we turn to the observation in (14c) concerning the semantic interpretation of FQ constructions. Sportiche claims that, intuitively, examples with FQs mean the same thing as their counterparts with non-FQs (1988: 426), although a number of studies have presented data showing that nonFQ and FQ constructions are not semantically equivalent (Dowty and Brodie 1984, Bobaljik 1995, Junker 1995, Hoeksema 1996, Doetjes 1997, among others). I present some of these examples here.

The syntax of split quantifier constructions 123

It has been observed that FQs take scope in their surface position, while non-FQs interact with other scope-bearing elements (Dowty and Brodie 1984, Williams 1991, Déprez 1994). For instance, while the non-floated all takes both narrow and wide scope with respect to the modal verb can, as in (30a), the floated all in (30b) takes scope only in its surface position. (30) a. All the contestants can win. b. The contestants all can win.

OK

all>can, OKcan>all all>can, *can>all (Dowty and Brodie 1984: 77) OK

Another semantic difference comes from Junker’s (1990, 1995) observation that the floated each in English and chacun ‘each’ in French differ from their non-floating counterparts in their expression of “simultaneous” and “sequential” events. Simultaneous events occur at the same time, while sequential events occur one after the other. Examples (31) and (32) show that non-FQ constructions express simultaneous but not sequential events, while FQ constructions express sequential, but not simultaneous events. This is shown by their (in)compatibility with the phrases at the same time (for the simultaneous reading) and one after the other (for the sequential reading). (31) a. [Each of the children] took the bus at the same time. a’. [Chacun des enfants] prit l’autobus en même temps. b.???The children each took the bus at the same time. b’.???Les enfants prirent chacun l’autobus en même temps. (Junker 1990: 211) (32) a.???[Each of the children] called his mother one after the other. a’.???[Chacun des enfants] téléphona à sa mère l’un après l’autre. b. The children each called his mother one after the other. b’. Les enfants téléphonèrent chacun à leur mère l’un après l’autre. (Junker 1990: 212)

3.1.4. The adverbial analysis of FQs So far, I have briefly examined three properties of FQ constructions in (14) — namely, syntactic distribution, morphological agreement, and semantic interpretation — and pointed out that stranding analysis faces problems

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Syntax and compositional semantics of (non-)split constructions

with respect to all three properties. An alternative proposal has been made: FQs are not derived by syntactic movement, but are base-generated in VPadjoined positions just as adverbs are, as illustrated in (33) (Klein 1976, Williams 1980, Dowty and Brodie 1984, Junker 1990, 1995, Roberts 1990, Bobaljik 1995, Hoeksema 1996, Doetjes 1997, Brisson 1998).11 I refer to this family of proposals as the adverbial analysis. Although, under the adverbial analysis, the FQ is not floated but rather base-generated in situ, I continue to use the term “FQ” simply to refer to the quantifier that appears apart from its host DP. This terminology does not imply a stranding analysis. (33) the students have [VP all [VP gone home]] Let us examine how the adverbial view fares with the properties of FQ constructions in (14). First, if non-FQ and FQ constructions are transformationally unrelated, FQs are not restricted to occurring only in positions through which the DP has passed in the course of its movement (see examples (16)–(21)).12 Second, as we saw above, morphological agreement between FQs and their host DPs is not necessarily an argument for the stranding approach. Although it is generally assumed that adverbials do not carry agreement (Merchant 1996), we could presumably propose a nonlocal agreement system compatible with the adverbial analysis. For instance, Benmamoun (1999), who argues against Shlonsky’s (1991) analysis summarized in section 3.1.2, proposes that heads of adverbial phrases (but not bare adverbials themselves) carry agreement depending on the internal structure of the constituents they head. Third, earlier studies show that the semantic differences between the two constructions in section 3.1.3 can be accounted for by the adverbial analysis (see Dowty and Brodie 1984, Junker 1990, 1995, Roberts 1990, Doetjes 1997, in particular). Regarding scope, Dowty and Brodie (1984) propose that the floated all is a determiner of type <et,<et,t>> that combines first with the VP and then with the DP. In (30b), all takes can win as an argument, and thus all always takes scope over can. Following Dowty and Brodie, Junker (1990, 1995) argues that the floated each in English and chacun ‘each’ in French are determiners that combine first with the VP. Furthermore, she proposes that each and chacun 11. In (33), I set aside the question of where the students is base-generated. 12. The distribution of FQs is not completely unconstrained. Thus, it is probably necessary to implement a locality restriction under the adverb view (see, for instance, Doetjes 1997, Fitzpatrick 2006: see also sections 3.2.3 and 5.3).

The syntax of split quantifier constructions 125

are distributive operators that set the first argument as the domain of distributivity. Then the domain of distributivity for the FQ is the VP, and distributivity in this case is manifested as the sequential reading.13

3.1.5. Summary In this section, I showed that FQs are analyzable as adverbs. A separate question remains as to whether FQs and split MPs are of the same nature. FQs in most of the languages discussed in this section are restricted to universal Qs (e.g., English FQs are restricted to all, each, and both). In this sense, they may be syntactically and semantically different from split MPs (i.e., split numerals and split measure phrases) in Japanese and German. For example, in German, there are at least two differences between the FQ all in (34a) and the split MP in (34b). First, while the nominal predicate associated with the FQ all may be a DP, the split MP is always associated with a NP. Second, the host DP of a FQ does not necessarily appear in the intial position in a sentence, whereas the host NP of a split MP must appear there. (34) a. Der Lehrer hat die Studenten gestern the teacher has the students yesterday ‘The teacher saw all the students yesterday.’ b. Studenten hat der Lehrer gestern students has the teacher yesterday ‘The teacher saw three students yesterday.’

alle all

gesehen. seen

drei gesehen. three seen

Nonetheless, I show in the following that split MPs in Japanese and German can also be analyzed syntactically as adjuncts to verbal predicates, as illustrated in (33).

13. Note that Junker’s (1990, 1995) notion of distributivity is different from the notion of distributivity used in Chapter 2. For Junker, a distributive interpretation corresponds to sequential events, as described in (32). In contrast, a distributive reading discussed in Chapter 2 obtains when each individual in the extension of the plural subject is the agent of the relevant events. That is, the temporal relation between plural events is irrelevant to the distributivity discussed in Chapter 2 (see Chapter 2: section 5.1.3 for details).

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3.2. The syntax of the floating quantifier construction in Japanese As briefly discussed at the beginning of Chapter 2, MPs and quantifiers in Japanese can appear in various positions in a sentence, as shown in (35). (35) a. [San-nin-no gakusei]-ga kinoo [three-CL-GEN student]-NOM yesterday ‘Three students danced yesterday.’ b. [Gakusei san-nin]-ga kinoo [student three-CL]-NOM yesterday c. Gakusei-ga kinoo san-nin student-NOM yesterday three-CL

odot-ta. dance-PAST odot-ta. dance- PAST odot-ta. dance-PAST

A question arises as to whether these sentences are transformationally related. Although researchers agree that the numeral and the host NP gakusei ‘student’ are in the same nominal projection in (35a) and (35b), opinions vary as to their status in (35c), where the numeral appears apart from its host NP. Some researchers argue that the form in (35c) is derived from (35a) (Kamio 1983, 1977, Haig 1980, among others) or from (35b) (Okutsu 1969, Kitahara 1993) by some syntactic movement.14 Under these transformational analyses, the numeral in (35c) is “floated” in that it is left behind after moving the host NP higher in the structure, much like under Sportiche’s (1988) stranding analysis. For this reason, the same terminology floating quantifier (FQ) is adopted here. Recall that, in Chapter 2, (35b) but not (35a) is treated as the nonfloating counterpart of (35c). This is because the numerals in (35b) and (35c) are both subject to a monotonicity constraint, while the numeral in (35a) is immune to that constraint. For example, san-do ‘three-degree’ cannot be used in the form in (35b) and (35c) because of the monotonicity constraint, although it is fine in the form in (35a) (see Chapter 2: section 2.5). Hence, I focus on the comparison between (35b) and (35c), putting aside (35a). I continue to address (35b) and (35c) as non-FQ and FQ constructions, respectively.

14. More recently, Watanabe (2006) argued that all forms in (35) are transformationally related: the forms in (35) are drived from the same underlying structure by applying massive phrasal movements within DPs. For this analysis to work, we need to posit the existence of various intermediate functional projections within DPs.

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The last section presented the problems with the stranding (or transformational) analysis of FQ constructions in various languages, leading us to an alternative adverbial analysis. In section 3.2.1, following the same reasoning, I present problems with the transformational analysis of the Japanese FQ construction, then, in section 3.2.2, I move on to the alternative adverbial analysis. Adopting the adverbial analysis, section 3.2.3 examines where FQs are adjoined.

3.2.1. Problems with the transformational analysis This section presents two arguments, one syntactic and the other semantic, against the transformational analysis of FQs. The syntactic argument is based on examples where the FQ construction lacks a corresponding nonFQ construction. If the FQ construction is derived from its non-floating counterpart, then the non-FQ construction should be acceptable. I present here four sets of data where only the floating version is acceptable. First, there are some quantifiers in Japanese that can be used only as a FQ (Inoue 1978, Haig 1980, Takano 1984): sorezore ‘each’ in (36) and minna ‘all’ in (37) are acceptable in the FQ construction, but not in the non-FQ construction.15 (36) a.* [Kotosi sotugyoosuru gakusei sorezore]-wa [this year graduate student each]-TOP sangatu-kara syuusyokusaki-de kensyuu-o ukeru. March-from new job-at training-ACC get ‘Each student who is graduating this year will get training at a new job from March.’

15. In Inoue (1978), the form “Q-GEN NP-CASE” in (35a) is compared with the FQ construction in (35c). Thus, (i) and (ii) are used instead of (36a) and (37a). (i) * [Sorezore-no kotosi sotugyoosuru gakusei]-wa sangatu-kara [each-GEN this year graduate student]-TOP March-from syuusyokusaki-de kensyuu-o ukeru. new job-at training-ACC get (ii) * Watasi-ga ronbun-o sidoosita [minna-no Katoo-kun, Yamada-kun, I-NOM paper-ACC supervised [all-GEN Kato-Mr. Yamada-Mr. Kawakami-kun, Itoo-kun]-wa sudeni daigaku-ni syuusyokusiteiru. Kawakami-Mr. Ito-Mr.]- TOP already university-at found-job

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b. Kotosi this year sorezore each

sotugyoosuru gakusei-wa sangatu-kara graduate student-TOP March-from syuusyokusaki-de kensyuu-o ukeru. new job-at training-ACC get ((b) from Inoue 1978: 180)

(37) a.* [Katoo-kun, Yamada-kun, Kawakami-kun, Itoo-kun [Kato-Mr. Yamada-Mr. Kawakami-Mr. Ito-Mr. minna]-wa sudeni daigaku-ni syuusyokusiteiru. all]-TOP already university-at found-job ‘Mr. Kato, Mr. Yamada, Mr. Kawakami, and Mr. Ito have all already found jobs at universities.’ b. Katoo-kun, Yamada-kun, Kawakami-kun, Itoo-kun-wa Kato-Mr. Yamada-Mr. Kawakami-Mr. Ito-Mr.-TOP sudeni minna daigaku-ni syuusyokusiteiru. already all university-at found-job ((b) from Inoue 1978: 180) The second set of examples involves a complex host NP: when the host NP contains a quantificational element, only the FQ construction is acceptable (Inoue 1978, among others). For instance, in (38) and (39), when the host NP contains suu-dai several-CL’ and takusan ‘many’, the non-FQ construction is ungrammatical.16,17

16. Inoue’s (1978) original examples are given below: (i) * [San, yon-dai-no narande hasitteita suu-dai-no torakku]-ga [3, 4-CL-GEN driving in a cavalcade several-CL-GEN truck]-NOM butukatta. struck (ii) * [Suu-wa-no tesuri-ni tomatteita takusan-no suzume]-ga [several-CL-GEN handrail-at staying many-GEN sparrow]-NOM tyuttyu-to naita. tweeted 17. Examples (38b) and (39b) are slightly modified from Inoue’s (1978) original examples; the PPs gaadoreeru-ni ‘against the guardrail’ and go-hun-maeni ‘five minutes ago’ are inserted in order to split the host NP and the Q on the surface. This modification does not affect the acceptability of the sentences.

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(38) a.* [Narande hasitteita suu-dai-no torakku [driving in a cavalcade several-CL-GEN truck san, yon-dai]-ga gaadoreeru-ni butukatta. 3, 4-CL]-NOM guardrail-against struck ‘Three or four of the several trucks driving in a cavalcade struck the guardrail.’ b. Narande hasitteita suu-dai-no torakku-ga driving in a cavalcade several-CL-GEN truck-NOM gaadoreeru-ni san, yon-dai butukatta. guardrail-against 3, 4-CL struck ((b) from Inoue 1978: 175) (39) a.* [Tesuri-ni tomatteita takusan-no suzume suu-wa]-ga [handrail-at staying many-GEN sparrow several-CL]-NOM go-hun-maeni tyuttyu-to naita. five-minute-ago tweeted ‘Five minutes ago, several of the many sparrows at the handrail were tweeting.’ b. Tesuri-ni tomatteita takusan-no suzume-ga handrail-at staying many-GEN sparrow-NOM go-hun-maeni suu-wa tyuttyu-to naita. five-minute-ago several-CL tweeted ((b) from Inoue 1978: 175) The third set of examples involves cases where the host NP is a whphrase. Examples (40) and (41) show that itu-tu ‘five-CL’ can be associated with the wh-phrases dono kudamono ‘which fruit’ or with nani ‘what’ in the FQ construction, but not in the non-FQ construction. (40) a.* John-wa [dono kudamono itu-tu]-o John-NOM [which fruit five-CL]-ACC suupaa-de kat-ta-no? supermarket-at buy-PAST-Q b. John-wa dono kudamono-o suupaa-de John-NOM which fruit-ACC supermarket-at itu-tu kat-ta-no? five-CL buy-PAST-Q ‘At the supermarket, which fruit did John buy five of?’

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Syntax and compositional semantics of (non-)split constructions

(41) a.* John-wa [nani itu-tu]-o suupaa-de John-NOM [what five-CL]-ACC supermarket-at b. John-wa nani-o suupaa-de itu-tu John-NOM what-ACC supermarket-at five-CL ‘What did John buy five of at the supermarket?’

kat-ta-no? buy-PAST-Q kat-ta-no? buy-PAST-Q

Examples (40) and (41) raise an interesting question of how the wh-phrase and the FQ are related to each other. The classifier -tu in these examples is often used as a default classifier for inanimate entities. For example, in (41b), the speaker does not know what John bought, thus he uses the default classifier -tu. The closest translation would be ‘five pieces of what’. Moreover, -tu has a wide distribution; (42) shows that -tu can be used for the kind term kudamono ‘fruit’ as well as for most kinds of fruits such as apples, oranges, peaches, pears, and watermelons. (42) itu-tu-no {kudamono / ringo / mikan / momo / nasi / suika} five-CL-GEN {fruit / apple / orange / peach / pear / watermelon} ‘five {fruits / apples / oranges / peaches / pears / watermelons}’ Then itu-tu ‘five-CL ’ in (40b) should allow the interpretation where -tu is associated with pieces of fruit, that is, ‘which five fruits did John buy?’. This interpretation is unavailable, which is reflected in the trunslation for (40b); as an answer to (40b), we cannot list five different kinds of fruits. Instead, (40b) is asking about fruit that was bought in a certain quantity. The sentence is most appropriately uttered when the speaker knows that John bought various types of fruit, but does not know the quantity of each fruit. Suppose that John bought three apples, two oranges, and five peaches, then the answer to (40b) would be ‘peaches’. If he bought five apples, five oranges, two peaches, and one pear, the answer would be ‘apples and oranges’. In this sense, the FQ must be associated with sub-kinds of the host NP dono kudamono ‘which fruit’. The same story applies to (41b) in that you are expected to list those that John bought five of. This issue may be related to the partitive interpretation created by FQs (Inoue 1978, Kitagawa and Kuroda 1992, Fujita 1994, Hamano 1997, Watanabe 2006). As shown in (43), a partitive interpretation obtains with the FQ, but not with the non-FQ (see section 3.2.4 for more discussion). Although following up on this would be an interesting task, I leave the details open for future research.

The syntax of split quantifier constructions 131

(43) a. [Sokoni iawase-ta otoko go-nin]-ga tero-ni [there be- PAST man five-CL]-NOM terrorism-by makikom-are-ta. involve-PASS-PAST ‘Five (and only five) men who were there got involved in terrorism.’ b. Sokoni iawase-ta otoko-ga tero-ni go-nin there be- PAST man-NOM terrorism-by five-CL makikom-are-ta. involve-PASS-PAST ‘Five of the men who were there got involved in terrorism.’ (Fujita 1994: 35–36) Lastly, the fourth set of examples shows that, under some circumstances, numeral classifier phrases occur only in floating positions (Fukushima 1991: 73). In (44), the classifier -hatu does not agree semantically with the host NP pisutoru ‘pistol’. (44) a.* John-ga [pisutoru ni-hatu]-o John-NOM [pistol two-CL ]-ACC b. John-ga pisutoru-o kinoo John-NOM pistol-ACC yesterday ‘John shot a pistol twice yesterday.’

kinoo yesterday ni-hatu two-CL

ut-ta. shoot-PAST ut-ta. shoot-PAST

Pisutoru ‘pistol’ is counted by the classifier -tyoo, but not by -hatu, as shown in (45a). -Hatu can be used to count the bullets in the pistol, as in (45b). Thus, (44b) expresses that the shooting-a-pistol event done by John involved two bullets, i.e., John shot a pistol twice. This example seems to be similar to the previous examples with the host wh-phrase where the FQ must be associated with sub-kinds of the host NP. In this case, the FQ is associated with the bullets in the pistol. (45) a. ni-{*hatu / tyoo}-no two-CL-GEN b. ni-{hatu / *tyoo}-no two-CL-GEN

pisutoru pistol tama bullet

Regarding semantic interpretations of the FQ construction, I showed in Chapter 2: section 3 that the FQ construction is semantically different from

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its non-floating counterpart in at least three respects: (i) (in)compatibility with single-occurrence events, (ii) incompatibility with individual-level predicates, and (iii) (un)availability of collective interpretations. Note that the semantic properties of FQs per se do not rule out a transformational analysis. Indeed, we might expect to observe some semantic differences as a result of transformations involved in the stranding view. For example, Watanabe (2006, in press) discusses another semantic difference between the FQ and the non-FQ, namely, partitivity (the FQ, but not the non-FQ, evokes a partitive interpretation; see (43)), and argues that this semantic difference can be captured under the transformational analysis. It is not clear, however, how syntactic movements can be the source of semantic differences in terms of (i)–(iii).

3.2.2. Floating quantifiers as adjuncts of verbal predicates In the last section, I showed that there are syntactic and semantic problems with the transformational analysis of FQs. Alternatively, several studies advocate treating FQs as adverbs (Fukushima 1991, Fujita 1994, Gunji and Hashida 1998, Kobuchi-Philip 2003, see also Ishii 1999). The intuition behind this is that FQs seem to be somehow related to verbal predicates, while non-FQs exhibit no such relation. For instance, in (44b), Fukushima (1991) notes that it is not the number of objects (i.e., guns), but rather the number of shooting events that is at issue. Furthermore, Fujita (1994) claims that, while the non-FQ takusan ‘a lot’ in (46a) modifies the host NP niku ‘meat’, the FQ takusan ‘a lot’ indirectly restricts the quantity of niku ‘meat’ via modification of the verb, suggesting that FQs behave just like VP-adverbs in terms of their semantic function.18

18. In the adverbial account proposed by Fukushima (1991) (and also by Fujita (1994)), a FQ in Japanese is a determiner of type <et,<et,t>> that combines with the VP, and then the NP. This is originally proposed by Dowty and Brodie (1984) for the analysis of the floated all in English (see section 3.1.4). However, this account runs into a problem with non-intersective quantifiers such as most. Let us examine the semantics of the non-floated and floated hotondo ‘most’ in (i). The denotation of hotondo in set denotation is given in (ii). (i) a. [Amerikazin hotondo]-ga kyonen utyuu-ni it-ta. [American most]-NOM last year spece-to go-PAST ‘Most Americans went to space last year.’

The syntax of split quantifier constructions 133

(46) a.* proi

sukosi sika-nai noni, little only-PRES although John-wa [nikui takusan]-o isoide tabete-simat-ta. John-TOP [meat a lot]-ACC quickly eat-end up-PAST b. proi sukosi sika-nai noni, little only-PRES although John-wa nikui-o isoide takusan tabete-simat-ta. John-TOP meat-ACC quickly a lot eat-end up-PAST ‘John ended up eating most of the meat quickly, although there was only a little of it to eat.’ ((b) from Fujita 1994: 68)19

Similarly, compare the FQ construction (47) with the non-FQ constructions (48) and (49) ((47) and (48) are taken from Chapter 2). The former is sensitive to the VP that occurs with it, whereas the latter are not. (47) a. Gakusei-ga kinoo san-nin Peter-o student-NOM yesterday three-CL Peter-ACC ‘Three students hit Peter yesterday.’

tatai-ta. hit-PAST

b. Amerikazin-ga kyonen hotondo utyuu-ni it-ta. American-NOM last year most space-to go-PAST (ii) [[most]] = { : A∩B > 1/2 A } In (ia), the set A is the denotation of the NP (i.e., {x: American(x)}) and the set B the denotation of VP (i.e., {y: go.to.space(y)}). Then we obtain the reading that the cardinality of individuals who are American and went to space is more than half of the cardinality of Americans. In (ib), the sets A and B are the denotations of VP and of the NP, respectively. Then (ib) should mean that the cardinality of individuals who went to space and are American is more than half of the cardinality of individuals who went to space, which is not the case: (ib) as well as (ia) mean that most Americans went to space. Nakanishi and Romero (2004) propose the semantics of for the most part in English under event theories, which is immune to this problem. Nakanishi and Romero’s analysis extends naturally to the semantics of the floated hotondo ‘most’ in Japanese (see also footnote 32 and Chapter 5: section 4.1). 19. Fujita’s (1994: 68) original example of a non-FQ construction is given in (i). In the FQ construction in (46b), I added isoide ‘quickly’ to separate the host NP and the FQ. (i) * proi sukosi sikana-i noni, John-wa [takusan-no nikui]-o little only-PRES although John-TOP [a lot-GEN meat]-ACC tabete-simat-ta. eat-end up-PAST

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b.??Gakusei-ga kinoo san-nin Peter-o student-NOM yesterday three-CL Peter-ACC ‘Three students killed Peter yesterday.’ (48) a. [Gakusei [student b. [Gakusei [student

san-nin]-ga three-CL]-NOM san-nin]-ga three-CL]-NOM

(49) a. [San-nin-no [three-CL-GEN b. [San-nin-no [three-CL-GEN

kinoo yesterday kinoo yesterday

korosi-ta. kill-PAST

Peter-o Peter-ACC Peter-o Peter-ACC

tatai-ta. hit-PAST korosi-ta. hit-PAST

gakusei]-ga kinoo Peter-o student]-NOM yesterday Peter-ACC gakusei]-ga kinoo Peter-o student]-NOM yesterday Peter-ACC

tatai-ta. hit-PAST korosi-ta. hit-PAST

As briefly mentioned at the beginning of section 3.2, researchers agree that the numerals in (48) and (49) quantify over the nominal predicate. The difference between the FQ and the non-FQ suggests that the FQ quantifies over something besides this. More specifically, we may be able to argue that a range of semantic restrictions on FQs indicates semantic dependency between FQs and verbal predicates. The shortcomings of the transformational analysis presented in section 3.2.1 are not problematic for the adverbial account. First, if non-FQ and FQ constructions are base-generated independently, it is not surprising to find the FQ construction that lacks a non-floating counterpart. Second, I show in section 4 below that the semantic properties of FQ constructions can be made to follow from the structure where FQs are adjoined to verbal predicates. Another important consequence of the adverbial analysis is that we can unify the syntax of FQs with the analysis of non-split MP constructions presented in section 2. Recall that MPs in Japanese have a wide distribution, as in (50). I proposed that MPs are adjuncts to different maximal projections (AP, DegP, NP, PP, and VP). Under the adverbial account, a FQ is adjoined to a verbal projection, as in (50e). In sections 4 and 5, I show that the FQ, but not the non-FQ, construction requires a homomorphism from events to individuals. (50) a. ni meetoru nagai two meter long ‘two meters longer/too long’

The syntax of split quantifier constructions 135

b. ni meetoru naga-sugiru two meter long-exceed ‘two meters too long’ c. roopu ni meetoru rope two meter ‘two meters of rope’ d. ni meetoru hanarete two meter away ‘two meters away’ e. ni meetoru aruku two meter walk ‘walk two meters’

(= (8))

Studies advocating the adverbial analysis argue that FQs are adverbs because FQs and adverbs have similar syntactic distributions (see Fukushima 1991, Fujita 1994, and Kobuchi-Philip 2003 for details). It is not crucial, however, for our purpose that FQs be categorized as adverbs, so long as they are adjoined to verbal predicates (see section 4). Thus, in the following, I do not emphasise the link between FQs and adverbs.

3.2.3. The structure of the floating quantifier construction Our task now is to figure out the exact syntactic structure of FQs under the assumption that they are adjoined to verbal predicates. It has been argued that there are certain locality restrictions on the dependency between a FQ and the host NP, that is, the host NP must c-command the FQ, as in (51) (Kayne 1981, Belletti 1982).20 Example (52) shows that the Japanese FQ construction is also subject to this constraint. The classifier -nin in the FQ semantically agrees with tomodati ‘friend’, but not with kuruma ‘car’. The sentence is ungrammatical because the host NP tomodati ‘friend’, being embedded, cannot c-command the FQ.21

20. The definition of c-command is given below (Chomsky 1986: 8): (i) α c-commands β iff α does not dominate β and every γ that dominates α dominates β. 21. It has been pointed out that, for inalienable possessions, the embedded NP can be associated with the FQ, as in (i) and (ii) (Kikuchi 1994, Takami 2001, among others).

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Syntax and compositional semantics of (non-)split constructions

(51) a.* [The mother of my friendsi] has alli left. (English) b.* [La mere de mes amisi] est tousi partie. (French) [the mother of my friends] is all left (Kayne 1981: 196) (52) * [Tomodati-no kuruma]-ga san-nin kosyoosi-ta. [friend-GEN car]-NOM three-CL break down-PAST ‘Three friends’ car(s) broke down.’ (Miyagawa 1989: 29) Miyagawa (1989) analyzes a FQ as a secondary predicate (see also Ueda 1986, Miyamoto 1994), and proposes the c-commanding requirement in (53), which takes care of the ungrammaticality of (52). (53) Mutual c-command requirement For a predicate to predicate of a NP, the NP or its trace and the predicate or its trace must c-command each other. (Miyagawa 1989: 30) Note that Miyagawa’s requirement is based on a ternary-branching structure where the FQ, its host NP, and the VP are sisters. Although such a structure was permitted at the time of Miyagawa’s proposal, in recent syntactic theory all structures are considered to have binary branching nodes, assuming that structures are built by an operation called Merge (Chomsky 1995). To accommodate this, we need to recast Miyagawa’s requirement in syntactic structures with binary branching.22 Based on (52), we know that (i)

Yamada Sensei-ga [gakusei-no kami]-o san-nin kit-ta. Yamada Professor-NOM [student-GEN hair]-ACC three-CL clip-PAST ‘Prof Yamada cut three the hair of three students.’(Takami 2001: 137) (ii) Hanako-wa [kodomotati-no tume]-o san-nin kit-ta. Hanako-TOP [children-GEN nail]-ACC three-CL clip-PAST ‘Hanako clipped the nail(s) of three children.’ (Kikuchi 1994: 82) My informants’ and my own judgments vary depending on the example. While judgments varied from acceptable to a little awkward for (i), the informants agreed that (ii) is much worse than (i). It seems that the acceptability of the examples improves when a one-to-one correspondence between the possessor and his body part is clear from the context. For instance, in (i), each child has one head with hair being cut, while, in (ii), it is not clear how many nails were clipped per child. Given this special status with inalienable possessions, I contiue to assume that an embedded NP can must be associated with a FQ. 22. Miyagawa and Arikawa (2007) modify Miyagawa’s (1989) original proposal and assume that the FQ and its host NP form a nominal constituent (such as a Number phrase), following some previous work (Kamio 1977, 1983, Terada

The syntax of split quantifier constructions 137

the host NP must c-command the FQ. There does not seem to be, however, an empirical argument showing that the FQ must c-command the host NP.23 For this reason, I reduce Miyagawa’s requirement to one direction. In particular, the host NP must c-command the FQ, which is the same requirement as the one independently proposed for FQ constructions in other languages (see (51)). The requirement that the host NP must c-command the FQ can account for the well-known observation that the FQ in Japanese is associated with an argument but not an adjunct (Okutsu 1969, Harada 1976, Shibatani 1977, Inoue 1978, Kuno 1978). Specifically, whereas subjects, objects, and what Inoue (1978) calls “quasi-objects” (such as the dative object in (54c)) are possible antecedents of the FQ, as in (54), PPs cannot host the FQ, as in (55).24

1990, Kawashima 1998, Watanabe 2006, among others). This modification makes it possible to maintain the mutual c-command analysis even without ternary-branching structures. But, as pointed out in section 3.2.1, there are a number of problems with such an analysis. 23. Miyagawa (1989) presents (i) to argue that the FQ must c-command its host NP. (i) a. Tomodati-ga huta-ri Sinzyuku-de at-ta. friend-NOM two-CL Sinzyuku-in meet-PAST ‘Two friends met in Sinzyuku.’ b.* Tomodati-ga Sinzyuku-de huta-ri at-ta. friend-NOM Sinzyuku-in two-CL meet-PAST (Miyagawa 1989: 28) Assuming that subjects are generated outside the VP and that Sinzyuku-de is VP-internal, Miyagawa obtains (iia) as the structure for (ia), where the host NP, the FQ, and the VP are sisters. In this structure, the FQ c-commands its host NP (and vice versa). In contrast, in (ib), if Sinzyuku-de is VP-internal, the FQ must also be VP-internal, yielding the structure in (iib). Because the FQ in this structure does not c-command the host NP, (iib) is ungrammatical. (ii) a. [S Tomodati-ga huta-ri [VP Sinzyuku-de at-ta ] ] b. [S Tomodati-ga [VP Sinzyuku-de huta-ri at-ta ] ] There are two points to make. First, my informants found (ib) as (almost) acceptable as (ia). Second, even if we adopt the judgements reported in (i), Miyagawa’s analysis based on ternary-branching structures is untenable under binary-branching structures. 24. There are counterexamples to the generalization that the PP cannot host the FQ, as in (i) and (ii) (Katagiri 1991, Hamano 1997, Mihara 1998, Ishii 1999, Takami 2001). I put aside these examples and assume that the FQ in principle cannot be associated with the PP. See Nakanishi (in press) for further discussion.

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Syntax and compositional semantics of (non-)split constructions

(54) a. Gakusei-ga san-nin hon-o kat-ta. student-NOM three-CL book-ACC buy-PAST ‘Three students bought the book.’ (Miyagawa 1989: 24) b. Hanako-ga pen-o san-bon kat-ta. Hanako-NOM pen-ACC three-CL buy-PAST ‘Hanako bought three pens.’ (Miyagawa 1989: 24) c. Boku-wa yuumeina gakusya-ni san-nin at-ta. I-TOP famous scholar-DAT three-CL meet-PAST ‘I met three famous scholars.’ (Miyagawa 1989: 35) (55) a.* Gakuseitati-wa kuruma-de ni-dai ki-ta. students-TOP car-in two-CL come-PAST ‘Students came in two cars.’ (Miyagawa 1989: 31) b. *Kyonen, Hanako-wa paatii-ni mit-tu ki-ta. last year Hanako-TOP party-to three-CL come-PAST ‘Last year Hanako came to three parties.’ (Miyagawa 1989: 36) Miyagawa (1989) claims that there is a structural difference between arguments and adjuncts; the particles in (54) are cliticized onto the NP, whereas the particles in (55) have their own projection. With these structures, the difference in grammaticality between (54) and (55) naturally follows from the c-command requirement. In (54), assuming that the host NP is higher in the structure than the FQ, the host NP c-commands the FQ. In (55), however, assuming that the host NP is embedded in the PP whose head is -de ‘in’ or -ni ‘to’, the host NP cannot c-command the FQ.25 We saw that FQs are adjoined to verbal predicates and that FQs must ccommand their host NPs. We also saw that the host NP must be either an external or an internal argument. Let us now turn to the question of where (i)

Gantan-ni osiego-kara go-nin nengazyo-o moratta. New Year’s Day-on my student-from five-CL card-ACC received ‘(I) received a card from five students of mine on New Year’s Day.’ (ii) Gakusei-kara nizyuu-mei-izyoo okane-o atume-nakerebanaranai. student-from 20-CL-or more money-ACC collect-must ‘(We) must collect money from 20 students or more.’ (Takami 2001: 128–129) 25. Besides the two structural restrictions sketched here (i.e., the host NP cannot be in an embedded NP, as in (52), or within a PP, as in (55)), the c-command requirement can account for some locality restrictions on FQs. See Nakanishi (in press) for details.

The syntax of split quantifier constructions 139

FQs are situated. Among various syntactic diagnostics used to answer this question (e.g., do so replacement, VP pseudo-clefting) (see, for example, Miyagawa 1989, Fujita 1994, Koizumi 1994), I present here the data on VP-preposing, a construction where the VP followed by -sae ‘even’ is moved to sentence-initial position, as shown in (56). If a FQ appears in a preposed constituent, it must be syntactically within the VP. If it appears outside, it must be outside the VP. Examples (57) show that a FQ associated with an external argument must be outside the VP, whereas examples (58) show that a FQ associated with an internal argument must be within the VP. (56) [VP Mary-o home-sae]i John-ga [ Mary-ACC praise-even] John-NOM ‘Even praise Mary, John did.’

ti si-ta. do-PAST

(57) a. [VP Mary-o home-sae]i gakusei-ga san-nin ti si-ta. [ Mary-ACC praise-even] student-NOM three-CL do-PAST ‘Even praise Mary, three students did.’ b.* [VP San-nin Mary-o home-sae]i gakusei-ga ti si-ta. [ three-CL Mary-ACC praise-even] student-NOM do-PAST ‘(lit.) Even praise Mary three, students did.’ (58) a.* [VP Katuo-o tabe-sae]i Taro-ga san-biki ti [ bonito-ACC eat-even] Taro-NOM three-CL ‘(lit.) Even eat bonitos, Taro three did.’ b. [VP Katuo-o san-biki tabe-sae]i Taro-ga ti [ bonito-ACC three-CL eat-even] Taro-NOM ‘Even eat three bonitos, Taro did.’

si-ta. do-PAST si-ta. do-PAST

Putting these together, I propose the structure in (59) for FQs in Japanese, where FQs are adjuncts to verbal predicates just like adverbs. The FQ associated with an external argument is adjoined to the VP, and it is ccommanded by the host NP, which is at the specifier position of a higher projection. Following Kratzer (1996, forthcoming), I assume that the projection above VP is VoiceP, and that the head of VoiceP takes the agent function which introduces an external argument. In this structure, the host NP is at Spec of VoiceP (“External argument” in (59)). The FQ associated with an internal argument is adjoined to V’, and it is c-commanded by the host NP, which is at the spec of VP (“Internal argument” in (59)).

140 (59)

Syntax and compositional semantics of (non-)split constructions

VoiceP External argument

Voice’ VP

External FQ

Voice VP

Agent

Internal V’ argument Internal FQ

V’

3.2.4. Excursion: Notes on prosodic effects Before concluding the discussion on the Japanese FQ construction, I would like to briefly discuss the status of a FQ that is adjacent to its host NP on the surface. Kitagawa and Kuroda (1992), followed by Fujita (1994), claim that when a numeral quantifier immediately follows its host NP, it can be structurally ambiguous between [NP-CASE Q] and [NP-CASE] [Q] (the brackets indicate constituency). Their claim is supported by the data on cardinal and partitive readings. When the numeral and its host NP form a constituent, as in (60a), only a cardinal reading obtains. In contrast, only a partitive reading obtains when they are apart, as in (60b). (60) a. [Sokoni iawase-ta otoko go-nin]-ga tero-ni [there be- PAST man five-CL]-NOM terrorism-by makikom-are-ta. involve-PASS-PAST ‘Five (and only five) men who were there got involved in terrorism.’ b. Sokoni iawase-ta otoko-ga tero-ni go-nin there be- PAST man-NOM terrorism-by five-CL makikom-are-ta. involve-PASS-PAST ‘Five of the men who were there got involved in terrorism.’ (= (43))

The syntax of split quantifier constructions 141

Kitagawa and Kuroda (1992) observe that, when the numeral and its host NP are adjacent to each other, as in (61), the sentence has both cardinal and partitive readings. They further claim that the two readings in (61) can be teased apart by different prosodic patterns. In particular, with a prosodic boundary or a pause between the host NP and the numeral (indicated by //), (61) has a partitive reading only, which implies that the host NP and the numeral are not in the same nominal projection at least on the surface. In contrast, without any pause between them, (61) allows only a cardinal reading, which indicates that the host NP and the numeral form a nominal constituent, just as in (60a). (61) Sokoni iawase-ta otoko-ga (//) go-nin tero-ni makikomareta. there be- PAST man-NOM five-CL terrorism-by were involved Similarly, in (62), the presence of a prosodic boundary seems to influence the interpretation of the sentence. Without a boundary, the sentence is ambiguous between distributive and collective readings, whereas with a boundary it allows only a distributive reading. (62) Otokonoko-ga (//) san-nin booto-o tukut-ta. boy-NOM three-CL boat-ACC make-PAST ‘Three boys built a boat yesterday.’ OK distributive, (OK)ollective Throughout the book, to avoid this complication, I focus on cases where an element intervenes between a FQ and its host NP, putting aside the question of the implications of the prosodic pattern for the theory of FQs (see Miyagawa and Arikawa 2007 for further discussion on prosody).

3.3. The syntax of Split NP Topicalization in German Let us now turn to Split NP Topicalization (ST) in German. The dominant paradigm, in the great deal of work done on the syntax of this construction, is transformational analysis, where a MP is base-generated in the same nominal constituent as its host NP, and ST is derived from this configuration by moving the host NP to the sentence initial position (van Riemsdijk 1989, Diesing 1992, among others). I first raise two problems with such an account, namely, the lack of non-split counterparts and agreement facts —

142

Syntax and compositional semantics of (non-)split constructions

the same problems raised for the stranding / transformational analysis of FQ constructions in sections 3.1 and 3.2.1. Then, I suggest an alternative analysis for treating a split MP as an adjunct to a verbal predicate. It has been pointed out in the literature that some examples of ST lack corresponding non-split counterparts, as shown in (63) (Fanselow 1988, van Geenhoven 1998, Nolda 2000). The ungrammaticality of (63a) suggests that (63b) could not have been derived from (63a). Further examples are presented in (66) and (67). (63) a.* Es gibt hier [nur eines Kopiergeräte]. there is here [only one.ACC photocopiers.ACC] ‘There is only one photocopier here.’ (Nolda 2000: 3) b. Kopiergeräte gibt es hier nur eines. photocopiers.ACC there is here only one.ACC (Nolda 2000: 5) Another problem for transformational analysis comes from morphological agreement. In ST, the host NP and the split MP always agree in terms of number and case in the same way that a non-split MP agrees with the NP (van Riemsdijk 1989). Examples of number agreement and case agreement are given in (64) and (65), respectively. (64) a. [Drei {Männer / *Mann}] haben gestern [three {man.PL / man.SG}] have yesterday ‘Three men danced yesterday.’ b. {Männer / *Mann} haben gestern drei {man.PL / man.SG} have yesterday three

getanzt. danced getanzt. danced

(65) a. Ich habe [vielen {Tieren/*Tiere}] I have [many.DAT {animals.DAT/animals.NOM·ACC}] ‘I helped many animals.’ b. {Tieren/*Tiere} habe ich vielen {animals.DAT/animals.NOM·ACC} have I many.DAT

geholfen. helped geholfen. helped

It has been argued that number and case agreement obtains within a nominal projection (see section 3.1.2). Based on this assumption, data on agreement have been taken as one of the strongest arguments for the transformational approach (van Riemsdijk 1989, among others): agreement obtains when a MP and its host NP form a nominal constituent, and the host NP undergoes movement leaving the MP behind. As a result, non-split MPs

The syntax of split quantifier constructions 143

and split MPs necessarily show the same agreement. However, such an analysis runs into trouble with examples where the ST lacks a non-split counterpart, as in (66). Example (66a) shows that the host NP and the MP must agree in terms of case, and examples (66b, c) show that they cannot form a nominal constituent. Whatever the mechanism of case agreement turns out to be, it is clear that the nominal constituency of kein- and its host NP is not a necessary condition for case agreement in (66a). (66) a. [{Einen / *Ein}] Wagen hat er sich noch keinen gekauft. [{a.ACC / a.NOM}] car has he REFL yet none.ACC bought b.* einen keinen Wagen c.* keinen einen Wagen (van Riemsdijk 1989: 106, 113) Another problematic example of agreement comes from welch-, which means ‘which’ in prenominal position, as in (67a, b) and ‘some’ in split position, as in (67c). Regardless of its interpretation, welch- always agrees with the NP in terms of case. Given the semantic difference between (67a, b) and (67c), it is hard to argue that (67c) is transformationally related to (67a, b). Rather, (67c) shows that case agreement obtains even when welchdoes not form a nominal constituent with its host NP. (67) a. [{Welchen/*Welche} Tieren] hat Hans geholfen? [{which.DAT/which.NOM·ACC} animals.DAT] has Hans helped ‘Which animals did Hans help?’ b. Hans hat [{welchen/*welche} Tieren] geholfen? Hans has [{which.DAT/which.NOM·ACC} animals.DAT] helped ‘Hans helped which animals?’ / *‘Hans helped some animals.’ c. Tieren hat Hans {welchen/*welche} geholfen. animals.DAT has Hans {some.DAT/some.NOM·ACC} helped ‘Hans helped some animals.’ The crucial point in (66) and (67) is that case agreement obtains even when a MP and its host NP do not form a nominal constituent. If so, the assumption taken by the transformational approach that agreement is part of the nominal system is not as well established as it seems. One possible approach to the problem is to propose a non-local system of agreement that does not require nominal constituency (see Benmamoun 1999, for instance). In any case, what is important for us here is that the link between agree-

144

Syntax and compositional semantics of (non-)split constructions

ment and the nominal system does not follow naturally from the transformational approach as originally argued (see also section 3.1.2). So far, I have raised two problems with the transformational analysis of ST, namely, the lack of a corresponding non-ST and case agreement. Let us now direct our attention to the semantic data provided in Chapter 2 showing that ST, unlike non-ST, is subject to constraints on verbal predicates. Since the Japanese FQ construction has the same semantic properties, we may expect these two constructions to have similar structures. For Japanese, I proposed in section 3.2 that FQs are adjuncts of verbal predicates. An important line of work on ST proposes that a split MP and its host NP are base-generated separately (Fanselow 1988, 1993, van Geenhoven 1998, Krifka 1998a, Fanselow and Cavar 2002, de Kuthy 2002). The structure most relevant to our discussion is van Geenhoven’s (1998), schematised in (69), which is the (partial) underlying structure for (68). (68) a. Bücher hat Hans zwei gelesen. books has Hans two read ‘Hans read two books.’ b. [Bücher gelesen] hat Hans zwei. [books read] has Hans two c.* Zwei gelesen hat Hans Bücher. two read has Hans books (69)

VP …

V’ MP zwei

V NP

V

Bücher

gelesen

Following Fanselow (1988), van Geenhoven (1998) argues that a split NP results from expanding the V-node. Unlike Fanselow, however, van Geenhoven proposes that the NP and the quantifier are independently generated, as in (69). Example (68a) obtains if the NP Bücher in (69) undergoes topicalization. Example (68b) is derived when the higher V-node [V NP V] in (69) is topicalized. Note that the word order in (68b) does not follow

The syntax of split quantifier constructions 145

straightforwardly from the standard analysis, where the host NP is basegenerated in the same nominal projection as the numeral. Van Geenhoven’s structure is different from the one proposed for the Japanese FQ construction in that, in the underlying structure, the NP does not c-command the split MP, although, since the NP undergoes obligatory topicalization to a higher location in the structure, it does c-command the MP in the surface structure. Furthermore, if the NP were adjoined higher than the split MP in the underlying form, we should be able to obtain (68c) by moving the higher V-node [V MP V]. The ungrammaticality of (68c) supports the structure in (69). Hence, I adopt van Geenhoven’s arguments that the MP and the NP are independently generated and that the MP is higher than the NP in the underlying structure. To be consistent with the syntax of the Japanese FQ construction, I minimally modify van Geenhoven’s analysis and assume that the internal argument and the verb form a VP-node, rather than a Vnode, and that the MP is adjoined to that VP-node, as in (70) (see also (73)). (70) [VP [MP zwei] [VP [NP Bücher] [V gelesen] ] ] Van Geenhoven does not discuss the structure of ST when the topicalized NP is an external argument. However, it is possible to construct examples parallel to (68), as in (71). (71) a. Studenten haben zwei getanzt. students have two danced ‘Two students danced.’ b. [Studenten getanzt] haben zwei. [students danced] have two c.*[Zwei getanzt] haben Studenten. two read have students Examples (71b, c) show that, just as in (68b, c), the MP must be higher in the structure than the host NP; [NP V] can be topicalized, whereas [MP V] cannot. Assuming that the external NP is base-generated at the specifier of VoiceP, I propose that the MP is an adjunct to VoiceP, as in (72) (see also (73)). (72) [ VoiceP [MP zwei] [ VoiceP [NP Studenten] [ Voice’ getanzt] ] ] In sum, the structure that I propose for German STs is given in (73).

146 (73)

Syntax and compositional semantics of (non-)split constructions

VoiceP External VoiceP split MP External Voice’ argument Voice VP Agent Internal VP split MP Internal argument

V’

3.4. Summary of section 3 In this section, I examined the syntax of split Q constructions, focusing on the Japanese FQ construction and on the German ST. I presented some problems with the transformational analysis of these constructions, and suggested that quantifiers in these constructions can be analyzed as adjuncts to verbal predicates.

4. The compositional semantics of non-split and split measure phrase constructions In sections 2 and 3, I showed that non-split MPs and split MPs combine syntactically with nominal and verbal predicates, respectively. The goal of this section is to derive compositionally the semantic properties of the nonsplit and split MP constructions discussed in Chapter 2. Section 4.1 introduces Schwarzschild’s (2002, 2006) analysis of pseudopartitives. Building on his analysis, section 4.2 provides a compositional semantics of non-split MP constructions. Section 4.3 demonstrates that the same analysis extends to split MP constructions.

The semantics of non-split/split quantifier constructions 147

4.1. Schwarzschild’s (2002, 2006) analysis of pseudopartitives This section briefly discusses Schwarzschild’s (2002, 2006) analysis of pseudopartitives. Although he does not provide a compositional semantics, he presents the syntax of pseudopartitives and the denotations of the MP and of the entire sentence. In the following, I introduce some aspects of his analysis that become important to the discussion in sections 4.2 and 4.3. As discussed in section 2, MPs can co-occur with various syntactic categories (see also Chapter 1: section 1.3). (74) a. b. c. d. e.

AP: DegP: NP: PP: VP:

two feet long two feet longer two feet of rope two feet away walk two feet

(= (6))

Schwarzschild (2002, 2006) argues that, despite the seemingly crosscategorial syntactic distribution of MPs, all instances of MPs have exactly the same semantics. As the basis for this treatment of MPs, he examines the semantics of MPs in comparative constructions (see Chapter 4 for a more detailed discussion of comparatives). I simply introduce here some fundamentals of Schwarzschild and Wilkinson’s (2002) analysis of comparatives. Schwarzschild and Wilkinson claim that MPs in comparatives are predicates of parts of scales. For example, the expression two inches is used to talk about intervals of ruler, as illustrated in (75). There are many intervals on the ruler that count as two inches. (75)

two inches 1

2

3

two inches 4

5

6

7

8

9

10

11

12

To clarify this point, Schwarzschild (2002, 2006) makes the analogy between adverbs of duration and MPs in comparatives: two hours in (76a) is predicated of the interval on a time scale between two shootings, while two inches in (76b) is predicated of the interval on a length scale between the locations of two rods. (76) a. He shot the sheriff two hours before he shot the deputy. b. Rod A is two inches longer than rod B is. (Schwarzschild 2006: 102)

148

Syntax and compositional semantics of (non-)split constructions

Pursuing the uniform semantics of MPs, Schwarzschild argues that the analysis of MPs in comparatives should apply to MPs that occur in other environments. Specifically, he claims that a MP always denotes a predicate of scalar intervals. If MPs are predicates of intervals, the question is how to obtain intervals on a scale. In Chapter 2: section 2.2, I introduced Schwarzschild’s (2002, 2006) claim that the measure function µ is a measurement scheme (volume, temperature, depth, etc.) that is obtained by examining a relation between a MP and the element to which the MP applies. For instance, in the pseudopartitive two feet of rope, since two feet specifies how long the relevant rope is, the measure function is µ: length. In contrast to the standard analysis of measurement where a measure function is a function from an object to a real number, Schwarzschild argues that a measure function is a function from an object to an interval on a scale (see Chapter 1: section 1.3). In two feet of rope, µ: length maps an individual x in the extension of rope to an interval on the length scale, thus µ(x) is an interval. The MP two feet is predicated of this interval, specifying that µ(x) has the property [[ two feet]] , i.e., two-feet(µ(x)). Recall that µ associated with the MP in pseudopartitives must satisfy the monotonicity constraint in the nominal domain (see Chapter 2: section 2). For instance, in two feet of rope, µ: length has to be monotonic to [[ rope]] . Schwarzschild (2002) proposes the denotation in (77) for two feet of rope, where MON(length,rope) means that µ: length is monotonic with respect to [[rope]] . Note that the monotonicity constraint is incorporated into the assertion in (77), which I argue against in section 4.2. (77) [[ two feet of rope]] = λxe. rope(x) ∧ two-feet(length(x)) ∧ MON(length,rope) The next step is to derive compositionally the denotation in (77). For this purpose, we first need to answer the question of where the measure function µ comes from. Schwarzschild (2002: 237) suggests that µ may be grafted onto the meaning of the MP, or that it may be inserted between the MP and the host NP. The second possibility can be easily pursued by adopting the structure in (78) for pseudopartitives proposed by Schwarzschild (2006).26 In (78), µ is at the head of MonP. In English pseudopartitives, it is lexically realized as of. 26. In his 2002 paper, Schwarzschild (2002) adopts the first possibility, that µ is grafted onto the meaning of the MP. In section 4.2, I suggest an analysis that is a combination of the two possibilities.

The semantics of non-split/split quantifier constructions 149

(78) [MonP two feet [Mon of [NP rope]]] In sum, two points are important for our purpose. First, MPs are semantically uniform, and second, µ is introduced as a separate head.

4.2. Non-split measure phrase constructions We saw in section 2 that MPs in Japanese and German are cross-categocial. Following Schwarzschild (2002, 2006), I assume that, in all instances, MPs have the same semantics. According to Schwarzschild, the uniformity is captured by claiming that MPs always denote predicates of scalar intervals. Alternatively, we could say that a MP is interpreted as a name for a degree of type d (e.g., [[ two feet]] = two-feet), following the standard treatment of MPs in comparatives (e.g., two feet in This rope is two feet long: see Chapter 4 for details).27 For our purpose, either option would work.28 For the discussion of comparatives in Chapter 4, the latter view would be simpler in that we can use a standard degree-based analysis of comparatives without introducing a more novel interval-based analysis.29 For this reason, I assume that a MP is a name for a degree. Then it follows that the measure function is a function from an object to a name for a degree, not to a scalar interval. For example, in two feet of rope, µ: length maps x in [[ rope]] to a name for a degree, that is, µ(x)=two-feet. Let us now examine the syntax of non-split MP constructions. In section 2, I proposed the structure in (79).30

27. In general, a MP that denotes a name for a degree may denote a set of degrees, as in (i). See Chapter 4: section 2 for details. (i) [[two feet]] = λdd. d=two-feet 28. See Nakanishi (2004) for a compositional analysis based on interval semantics. 29. Schwarzschild and Wilkinson (2002) show that the standard degree-based analysis cannot account for the semantics of comparatives that contain a quantifier in the than-clause (e.g., John is taller than everyone else). They propose instead an interval-based analysis. Since this book does not contain examples of this kind, I do not discuss the details of their analysis. 30. Recall that non-split MP constructions in Japanese and German have no linking morpheme such as of in the English two feet of rope. For this reason, I ignore the question of where of is in the structure.

150

Syntax and compositional semantics of (non-)split constructions

(79)

NP MP

NP

two feet

rope

Unlike in Schwarzschild’s (2006) structure (78), there is no obvious location in (79) for the measure function µ. Assuming that µ is introduced as a separate head, I propose the structure in (80), where µ first combines with the MP, and then with the host NP.31 (80)

NP NP MP

µ rope

two feet Under the standard theory, where a measure function is denoted by a measure word such as feet (see Chapter 2: footnote 10), we can compute the semantics of pseudopartitives based on the structure in (79), where the MP two feet directly combines with the host NP rope. In (80), it is not the MP alone but the complex predicate consisting of the MP and µ (henceforth, MP+µ) that combines with the host NP. Thus, MPs under the standard theory are equivalent to the MP+µ proposed here. Cardinality quantifiers (e.g., two, two feet) may be considered as a modifier or as a determiner in the sense of the theory of generalized quantifiers. For ease of exposition, I take the former view; in (80), MP+µ is a modifier combining with the NP rope of type <e,t>.32 It is generally assumed that 31. The structure in (80) is based on Schwarzschild’s proposal in his 2002 paper where he assumes that µ is grafted onto the meaning of the MP. That is, the NP combines with the MP that has µ in its denotation. At the same time, (80) inherits the spirit of Schwarzschild’s proposal in his 2006 paper where µ is introduced as a separate head, as in (78). 32. Under the theory of generalized quantifiers, cardinality quantifiers express a relation between the set of individuals denoted by the NP and the set of individuals denoted by the VP. However, this analysis needs some adjustment if an event argument is introduced. When a verb has an additional event argument, the VP no longer denotes a set of individuals. Although, I consider cardinality

The semantics of non-split/split quantifier constructions 151

there are two ways to combine modifiers with modified elements. One is to assume that a modifier is of the same semantic type as the modified element and to combine the two by Predicate Modification (PM), defined in (81). Another is to assume that a modifier is a function that takes a modified element as an argument and to combine them by Functional Application (FA), defined in (82). These two methods are illustrated in (83). In general, the second approach with Functional Application is capable of handling a wider range of modifiers including non-intersective modifiers (see Heim and Kratzer 1998: section 4.3.3 for details). (81) Predicate Modification (PM) If α is a branching node, {β, γ} is the set of α’s daughters, and [[ β]] and [[γ]] are both in D<e,t>, then [[α]] = λx ∈ De . [[β]] (x) = [[γ]] (x) = 1. (Heim and Kratzer 1998: 65) (82) Functional Application (FA) If α is a branching node and {β, γ} is the set of α’s daughters, then α is in the domain of [[ ]] if both β and γ are and [[β]] is a function whose domain contains [[γ]] . In this case, [[α]] = [[β]] ([[γ]] ) (Heim and Kratzer 1998: 49) (83) a. [[ cat]] = λxe. cat(x) [[orange]] = λxe. orange(x) [[orange cat]] = λxe. cat(x) ∧ orange(x) b. [[cat]] = λxe. cat(x) [[orange]] = λP<e,t>.λxe. P(x) ∧ orange(x) [[orange cat]] = λxe. cat(x) ∧ orange(x)

(by PM)

(by FA)

Going back to the compositional semantics of non-split MP constructions, I propose that MP+µ combines with the host NP by Functional Application, rather than by Predicate Modification, for reasons that will become clear shortly. Ignoring the monotonicity constraint for the moment, I propoquantifiers to be modifiers, it is possible to analyze them as determiners with event arguments, and to maintain the mechanism of a homomorphism from events to individuals, following the analysis of for the most part in English proposed in Nakanishi and Romero (2004) (see Chapter 5: section 4.1, see also Herburger 2000, Beaver and Clark 2003). Thus, whether we treat cardinality quantifiers as modifiers or as determiners, we can achieve a compositional analysis of non-split and split MP constructions.

152

Syntax and compositional semantics of (non-)split constructions

se (84) as the denotation of µ in non-split MP constructions. The compositional semantics of two feet of rope is given in (85). (84) [[µNP]] = λdd.λP<e,t>.λxe. P(x) ∧ µ(x)=d (85) a. b. c. d.

(first version)

[[two feet]] = two-feet [[two feet +µ]] = λP<e,t>.λxe. P(x) ∧ length/depth(x)=two-feet [[rope]] = λxe. rope(x) [[two feet of rope]] = λxe. rope(x) ∧ length(x)=two-feet (by FA)

The measure function µ first takes the MP in (85a) as an argument, as in (85b), and MP+µ combines with the NP by FA, as in (85d). The MP signals the kind of measure function available: with two feet, µ must be something like µ: length or µ: depth (but not µ: weight, µ: cardinality, etc.), yielding length(x)=two-feet or depth(x)=two-feet in (85b). Between these possibilities, the NP determines which µ needs to be used; when two feet+µ combines with rope, as in (85d), µ is determined to be µ: length, not µ: depth, since rope can be measured by its length, but not by its depth (because rope does not have depth). Let us now add the monotonicity constraint to the denotation of µ. As shown in (77), Schwarzschild (2002, 2006) assumes that the monotonicity constraint is incorporated into the assertion. This assumption not only predicts that (86a) is grammatical and felicitous, but also predicts incorrectly that it is necessarily true. Consider the denotation in (86b). MON(tmp.,water) is false, since µ: temperature is not monotonic to [[ water]] , which makes the formula under the negation false. With the negation at the top, the entire sentence is felicitous and true, even if all relevant water disappeared, which is contrary to our intuition. (86) a.* 90 degrees of water didn’t disappear. b. ¬∃z [water(z) ∧ 90-degrees(tmp.(z)) ∧ MON(tmp.,water) ∧ disappear(z)] Alternatively, I minimally modify Schwarzschild’s denotation and propose to put the monotonicity constraint in the presupposition. Since a MP is a name for a degree, there is no room to add the monotonicity constraint in the denotation of the MP. Thus, the presupposition must be encoded in the denotation of µ, as in (87), where MON(µ,P) is read as “µ is monotonic with respect to the denotation of P”.

The semantics of non-split/split quantifier constructions 153

(87) [[µNP]] = λdd.λP<e,t>: MON(µ,P).λxe. P(x) ∧ µ(x)=d The measure function µ first combines with the MP, and then MP+µ combines with the host NP by FA. In this analysis, we can elaborate the denotation of µ by incorporating the monotonicity constraint in the nominal domain. Note that, if MP+µ is of the type <e,t> (e.g., λxe. length(x)=two-feet), we are unable to add the monotonicity constraint to the presupposition. The truth condition of (86a) is given in (88), which has the presupposition MON(tmp.,water). Since this presupposition cannot be met, (86a) is predicted to be always infelicitous. (88) ¬∃z [water(z) ∧ tmp.(z)=90-degrees ∧ disappear(z)]33 In Chapter 2: section 2, we saw that the semantic properties of non-split MP constructions in Japanese and German are the same as those of English pseudopartitives. Assuming that the MP, the measure function, and the NP combine in the same way in these constructions, the current proposal on English pseudopartitives should extend to Japanese and German non-split MP constructions. The structure and compositional semantics of (89) ((a) for Japanese, (b) for German) are presented in (90).34 (89) a. [Mizu san-rittoru]-ga kobore-ta. [water three-liter]-NOM spill-PAST ‘Three liters of water spilled.’ b. [Drei Liter Wasser] sind verschüttet worden. [three liter water] are spilled become (90)

VP NP

V’ NP

MP

spilled

µ water

three liters 33. Here, for simplicity, I ignore event arguments. This does not affect the content of the proposed analysis. 34. Strictly speaking, in Japanese, [[water]] should be treated as a kind of type e (see Chapter 1: section 3.2).

154

Syntax and compositional semantics of (non-)split constructions

[[three liter]] = three-liters [[three liter+µ]] = λP<e,t>: MON(volume,P).λxe. P(x) ∧ volume(x)=three-liters [[water]] = λxe. water(x) [[three liter water]] = λxe. water(x) ∧ volume(x)=three-liters ∃ + [[ three liter water]] = λP<e,t>. ∃y[water(y) ∧ volume(y)=three-liters ∧ P(y)]35 [[(89)]] = 1 iff ∃y[water(y) volume(y)=three-liters ∧ spill(y)] Presupposition: µ: volume is monotonic to [[water]]. Assertion: There is water y such that y spilled and the volume of y is three liters.

4.3. Split measure phrase constructions The last section provided an analysis of MPs that occur with NPs, as in two feet of rope. The proposed analysis extends naturally to examples such as walk two feet, where a MP combines with the VP. The denotation of µ for events is proposed in (91), which is parallel to that of µ for individuals in (87). The compositional semantics of walk two feet is given in (92). (91) [[µVP]] = λdd.λP: MON(µ,P). λev. P(e) ∧ µ(e)=d (92) a. b. c. d.

(first version)

[[two feet]] = two-feet [[two feet+µ]] = λP.λev.P(e) ∧ spatial-length/depth(e)=two-feet [[walk]] = λev. walk(e) [[walk two feet]] = λev. walk(e) ∧ spatial-length(h(e))=two-feet

As in (85), when µ combines with the MP two feet, we obtain the subformula µ(e)=two-feet, indicating that the measurement of an event e by µ yields two-feet. This signals that µ must be something like µ: spatial-length or µ: depth, which yields spatial-length(e)=two-feet or depth(e)=two-feet.36 35. ∃ is a type-shifting operation proposed by Partee (1987) (see Chapter 1: section 3.2). The definition is given in (i). (i) ∃: <e,t> → <et,t> ∃X = λP<e,t>. ∃x[X(x) ∧ P(x)] 36. I use µ: spatial-length instead of the more general measure function µ: length. This is to dintinguish between length with respect to the path of the event and length with respect to the temporal time span of the event. For example, in John walked two feet and John walked for one hour, John’s walking event can be

The semantics of non-split/split quantifier constructions 155

Nevertheless, an event per se does not have spatial length or depth, but its path does. This is analogous to the fact that temporal adverbials such as for three hours do not apply to events directly, but to temporal traces of events (see Chapter 2: sections 4.1 and 6). Thus, we need a homomorphism h from events to their paths to make µ: spatial-length or µ: depth applicable to events (Lasersohn 1995, Krifka 1998b, in particular). The measure function µ associated with a split MP also requires h, namely, h from events to individuals. In this case, the measure function must be monotonic to the range of h. Thus, instead of (91), I propose (93) as a denotation of the µ associated with MPs combining with a VP (e.g., two feet in walk two feet, three hours in sleep three hours, a split MP in split MP constructions). MON(µ,RangeP(h)) is read as “the measure function µ is monotonic to the range of h from a set of events in P”. In the case of split MP constructions, RangeP(h) is a set of all individuals mapped by h from an event in P, that is, {x: ∃e∈P[h(e)=x]}. (93) [[µVP]] = λdd.λP: MON(µ,RangeP(h)).λev . P(e) ∧ µ(h(e))=d The general picture is that a MP signals the kind of measure function µ that is needed for events, which in turn determines the kind of h called for. In the case of the split MPs discussed in Chapter 2, h is from events to individuals, since split MPs carry a measure word or a classifier that agrees semantically with its host NP.37 Consider first the Japanese FQ construction in (94), whose LF and semantics are provided in (95). (94) Otokonoko-ga huta-ri boy-NOM two-CL ‘Two boys danced.’

odot-ta. dance-PAST

measured by its spatial length and by temporal length, respectively. See Chapter 4 for more examples involving µ: spatial-length and µ: temporal-length. 37. In split MPs, a homomorphism h is always from events to individuals, since split MPs usually carry a measure word or a classifier that agrees semantically with its host NP. For this reason, we could include this information in the presupposition of the denotation of split MPs. Furthermore, the required homomorphism from events to individuals must be natural (cf. Kratzer forthcoming: Chapter 3 for natural relations). The modified lexical entry of split MPs is given in (i). (i) [[µVP]] = λdd. λP: MON(µ,P) ∧ [∃h:{ev:P(e)=1}→De∧natural<,t>(h)]. λev. P(e) ∧ µ(e)=d

156

Syntax and compositional semantics of (non-)split constructions

(95)

TP VoiceP NP boy

T Voice’

VP+

Voice VP

MP

Agent

µ danced

two-CL [[two-CL +µ]] = λP: MON(cardinality-of-ind.,RangeP(h)).λev. P(e) ∧ cardinality-of-ind.(h(e))=two-individuals [[dance]] = λev. *dance(e)38 [[ VP+]] = λev. *dance(e) ∧ cardinality-of-ind.(h(e))=two-individuals [[ Voice ]] = λxe.λev. Agent(e)=x [[ Voice’ ]] = λye.λev. Agent(e)=y ∧ *dance(e) ∧ cardinality-of-individuals(h(e))=two-individuals39 [[ NP]] = BOY type e (kind) (Chapter 1: section 3.2) [[ VoiceP]] = [λye.λev. Ag(e)=y ∧ *dance(e) ∧ cardinality-of-individuals(h(e))=two-individuals](BOY) DKP40 → λev. ∃x[∪boy(x) ∧ Ag(e)=x ∧ *dance(e) ∧ cardinality-of-individuals(h(e))=two-individuals] [[TP]] = 1 iff ∃e∃x[∪boy(x) ∧ Ag(e)=x ∧ *dance(e) ∧ cardinality-of-individuals(h(e))=two-individuals]

38. * is the operation of semantic pluralization (Chapter 1: sections 3.1 and 4.4). 39. This step is done by Kratzer’s Event Identification in (i) (Kratzer 1996: 122). (i) Event Identification: f g → h <e,> <e,> λxe.λev. f(x)(e) ∧ g(e) 40. The semantic rule of Derived Kind Predication (DKP) discussed in Chapter 1: section 3.2 is repeated in (i) and rendered as a corresponding schema in (ii). (i) Derived Kind Predication (DKP) If P applies to objects and k denotes a kind, then P(k) = ∃x[ ∪k(x) ∧ P(x) ] (Chierchia 1998: 364) (ii) P(k) = λyσ. … λzτ. ∃x[ ∪k(x) ∧ P(x)(y) … (z) ]

The semantics of non-split/split quantifier constructions 157

Presupposition: µ: cardinality-of-individuals is monotonic to the range of h. Assertion: There is a plural dancing event e by x and there is x such that x is a boy/boys. µ applied to h(e) yields two individuals. By combining µ for VPs and the MP two-CL, we obtain the sub-formula µ(h(e))=two-individuals. This signals that µ must be µ: cardinality-ofindividuals, yielding cardinality-of-individuals(h(e))=two-individuals, where h is from events to individuals. Since there is a presupposition that µ is monotonic to the range of h, we can account for the properties of the split MP construction discussed in Chapter 2: section 3 ((in)compatibility with single-occurrence events and with I-level predicates, (un)availability of collective readings).41 Turning now to German Split Topicalization, the structure and compositional semantics of (96) are given in (97). (96) Jungen haben zwei getanzt. boys have two danced ‘Two boys danced.’ (97)

TP T

VoiceP+ VoiceP

MP

µ NP

Voice’

two boys

Voice

VP

Agent

danced

41. In Chapter 2: section 5.3, I showed that split MP constructions with a collectivizer such as together allow collective interpretations. The denotation of MP+µ occurring with together is given in (i), where “one-mp-group” corresponds to one group consisting of the number of individuals expressed by the MP. (i) [[ MP+µ … together ]] = λP: MON(µ,RangeP(h)).λev. P(e) ∧ µ(e)=one-mp-group

158

Syntax and compositional semantics of (non-)split constructions

[[ dance]] = λev. *dance(e) [[ Voice]] = λye.λev. Agent(e)=y [[ Voice’]] = λye.λev. Agent(e)=y ∧ *dance(e) (footnote 39) [[ boys]] = λxe. *boy(x) ∃ + [[boys]] = λP<e,vt>.λev. ∃x[*boy(x) ∧ P(x)(e)]42 [[ VoiceP]] = λev. ∃x[*boy(x) ∧ Agent(e)=x ∧ *dance(e)] [[ two]] = two [[ two+µVoiceP]] = λP: MON(cardinality,RangeP(h)).λev. P(e) ∧ cardinality(h(e))=two [[VoiceP+]] = λev. ∃x[*boy(x) ∧ Ag(e)=x ∧ *dance(e)] ∧ cardinality(h(e))=two [[ TP]] = 1 iff ∃e∃x[*boy(x) ∧ Ag(e)=x ∧ *dance(e) ∧ cardinality(h(e))=two] Presupposition: µ: cardinality is monotonic to the range of h. Assertion: There is a plural dancing event e by x and there is x such that x is a boy/boys. µ applied to h(e) yields two. The German ST is different from the Japanese FQ in that the split MP is adjoined to VoiceP instead of to VP. However, the denotation of µ stays the same as the one proposed in (93) because VoiceP is of type , which is the same as the type of VP. By combining µ and the MP zwei ‘two’, we obtain the sub-formula µ(h(e))=two, which signals that µ must be µ: cardinality and yields cardinality(h(e))=two. In German, events must be counted by an expression such as zweimal ‘(lit.) two times’, but not by a bare numeral such as zwei ‘two’. Thus, µ: cardinality here does not apply to events, but to individuals. Then there must be a homomorphism h from events to individuals, where cardinality(h(e)) yields two individuals. As a result, we obtain the same semantics as in (95). Thus, we can account for the various semantic properties captured by the monotonicity constraint (discussed in Chapter 2) in both the German ST and the Japanese FQ construction. In this way, a MP in split MP constructions specifies the measure function and the homomorphism involved. In Chapter 4, I show that a MP in some comparative constructions does exactly the same job, suggesting that the proposed analysis for split MP constructions extends to a wide range of constructions. 42. The definition of ∃ is given in (i), which is like Partee’s (1987) type-shifting rule in (ii) except that (i) is with event arguments. (i) ∃: <e,t> → <<e,vt>,vt> ∃X = λP<e,vt>.λev. ∃x[X(x) ∧ P(x)(e)] (ii) ∃: <e,t> → <et,t> ∃X = λP<e,t>. ∃x[X(x) ∧ P(x)]

Homomorphism and argument structure 159

5. Homomorphisms and argument structure: Internal and external split measure phrase constructions I have assumed so far that, when a split MP takes a subject (or more specifically, an external argument) as its host NP, the relevant homomorphism is the agent function. For example, in (94) and (96), a homomorphism h maps a set of dancing events to a set of students. There are two issues that arise from this assumption. First, recall that, besides an external argument, an internal argument can serve as a host NP, as in (98) ((a) for Japanese, (b) for German). (98) a. Peter-ga ki-o kinoo san-bon Peter-NOM tree-ACC yesterday three-CL ‘Peter planted three trees yesterday.’ b. Bäume hat Peter gestern drei trees has Peter yesterday three

ue-ta. plant-PAST gepflanzt. planted

In the following, I use the terms external split MP constructions and internal split MP constructions depending on whether the split MP is associated with an external argument or an internal argument (cf. Chapter 2: section 5.5). In (98), the internal argument is not an agent, and thus the agent function cannot be the relevant homomorphism. If it is not the agent function that relates events to individuals, then we must seek another appropriate function that serves as a homomorphism in internal split MP constructions. Second, notice that nothing in the denotation of µ in (99) (repeated from (93)) says that h is the agent function, that is, nothing forces us to use the agent function as a homomorphism even in external split MP constructions. We need to find a way to specify the function that plays this role. (99) [[µVP/VoiceP]] = λdd.λP: MON(µ,RangeP(h)).λev. P(e) ∧ µ(h(e))=d

5.1. The formal properties of homomorphisms Before addressing the two issues raised above, let us examine formal properties of a homomorphism. A homomorphism h is a function that preserves a structural relation defined on its domain in a similar relation defined on the range. Suppose that there are two elements of the sort S. Then h

160

Syntax and compositional semantics of (non-)split constructions

from S to S’ maps the sum of x and y in S, i.e., x∪Sy, to the sum of h(x) and h(y) in S’, i.e., h(x)∪S’h(y), as defined in (100). That is, h must be a function and it must be structure preserving. (100) ∀h ∀x,y∈DS[ h(x∪Sy) = h(x)∪S’h(y) ] The structure preserving nature of h is reminiscent of the property of cumulativity, which is defined in (101): if x and y of the sort S have a property P, the sum of x and y has the same property (see Chapter 1: section 4.3). For example, suppose if a mass NP milk has two parts x and y, then x∪Iy must be milk as well. In the same vein, if an atelic VP drive a car has two parts e1 and e2, e1∪Ee2 must also be a driving-a-car event. (101) P is cumulative iff: ∀x,y∈DS[ [P(x) ∧ P(y)] → P(x∪Sy) ] Cumulativity can be defined as a property of relations between two sorts, as in (102): given that there are two elements a, b in the sort S and two elements x, y in the sort S’ and that a relation R holds between a and x and between b and y, the same relation R holds between a∪ Sb and x∪ S’y. (102) Relational Cumulativity ∀R ∀a,b∈DS ∀x,y∈DS’[ [R(a)(x) ∧ R(b)(y)] → R(a∪Sb)(x∪S’y) ] We can further define cumulativity as a property of functions from elements in the sort S to elements in the sort S’, as in (103): suppose that a, b are in S, x, y are in S’, and F maps a to x and b to y; then F maps a∪Sb to x∪S’y. (103) Functional Cumulativity ∀F ∀a,b∈DS ∀x,y∈DS’[ [F(a)=x ∧ F(b)=y] → F(a∪Sb)=x∪S’y ] Functional cumulativity in (103) essentially expresses the defining property for h in (100), i.e., F(a∪Sb)=F(a)∪ S’F(b). Thus, any relation that is functional and cumulative can serve as h. I now examine whether the agent association is functional and cumulative. First, it is functional because the agent role of a certain event must be uniquely specified (see Chapter 1: section 4.3, see also Carlson 1984, Parsons 1990, Landman 2000). Second, it is cumulative in that, if x and y are agents of e and e’, respectively, the sum of x and y is the agent of the sum

Homomorphism and argument structure 161

of e and e’, as in (104a) (Krifka 1986, 1989, 1992, 1998b, Landman 1996, 2000, Kratzer forthcoming). Let us revisit Kratzer’s (forthcoming) example presented in Chapter 1: section 4.3; the planting-a-tree event is the sum of three subevents — John dug a hole, Mary placed a tree in the hole, and Bill covered the roots with soil. We can say that the sum of the agents of the subevents, namely, j∪Im∪Ib, is the agent of the planting-a-tree event. Thus, the agent function is cumulative, as in (104a). Since (104a) is equivalent to (104b), it follows that, when the host NP of a split MP is an external argument, the agent function serves as h from events to individuals. (104) a. ∀e,e’∈DE ∀x,y∈DI[ [Agent(e)=x ∧ Agent(e’)=y] → Agent(e∪Ee’)=x∪Iy ] b. Agent(e∪Ee’) = Agent(e)∪IAgent(e’)

5.2. Homomorphisms in internal split measure phrase constructions Let us now turn to one of the questions at issue: in internal split MP constructions such as in (98), what function maps events to individuals? The obvious candidate is the theme function. As discussed in Chapter 1: section 4.3, however, Kratzer (forthcoming) argues that the theme function is not cumulative. For instance, in the above example of a planting-a-tree event, the theme of this event is not the sum of the themes of the subevents, namely, hole∪Itree∪Iroots. She takes the non-cumulativity of the putative theme function to mean that there is no theme function to begin with (see Chapter 1: section 4.3 for details). If there is no theme function, how are themes introduced, and furthermore, what serves as a homomorphism from events to themes in (98)? What becomes relevant here is Kratzer’s (forthcoming) claim that verb denotations, which are relations between events and their internal argument individuals, are cumulative. Under Kratzer’s theory, the denotation of verbs with internal arguments includes an event argument and an internal argument, but not an external argument (see Chapter 1: section 4.3). For example, the denotation of the transitive verb plant would be λxλe.plant(x,e). These verbs denote relations between individuals and events. Kratzer argues that these relations are cumulative. For example, if e1 is a plantingroses event and e2 is a planting-tulips event, the sum of these two events is an event of planting roses and tulips, satisfying the definition of cumulativity in (105).

162

Syntax and compositional semantics of (non-)split constructions

(105) ∀x,y∈DI ∀e1,e2 ∈DE[ [plant(x,e1) ∧ plant(y,e2)] → plant(x∪Iy, e1∪Ee2) ] For our purpose it does not seem problematic to treat a relation between individuals denoted by the internal argument and events as a function from events to individuals, as in plant(e)=x.43 The only change that this move requires is the assumption that each event is associated with a unique theme individual. In fact, this is exactly what Krifka’s (1986, 1989, 1992) notion of uniqueness of objects (UNI-O) in (106) expresses: each event associates with a unique individual. Krifka claims that the relation between events and their themes must satisfy the uniqueness of objects. For instance, in plant a tree, each planting event is related to a unique tree, and to nothing else. (106) ∀R[ UNI-O(R) ↔ ∀e∀x∀y[R(x,e) ∧ R(y,e) → x=y] ] (Krifka 1989: 92) Following Kratzer’s claim, I assume that denotations of transitive verbs are relations between individuals and events, and that these relations are cumulative. Furthermore, based on (106), these relations can be represented as functions, as in (107a), which is equivalent to (107b). Hence, denotations of transitive verbs are functional and cumulative, which satisfies the conditions for a legitimate homomorphism from events to individuals. (107) a. ∀x,y∈DI ∀e1,e2 ∈DE[ [plant(e1)=x ∧ plant(e2)=y] → plant(e1∪Ee2)=x∪Iy ] b. plant(e1∪Ee2) = plant(e1)∪Iplant(e2) Assuming that the homomorphism from events to individuals in (98) is the denotation of plant, I propose the structure in (108) as the structure of the Japanese FQ construction in (98a). In (108), the complex predicate MP+µ combines with plant of type <e,vt>. Then the denotation of a measure function µ in the verbal domain needs to be modified accordingly. I propose the denotation in (109) for µ associated with internal split MPs. The compositional semantics of (98a) is given in (110). 43. Kratzer’s (1996, forthcoming) denotation of plant, a function f of type <e,>, can be viewed as the right-to-left Schönfinkelization of the function f’ of type <,t>. This last function, in turn, is mathematically equivalent to the characteristic set {<xe,ev>: f’(x,e)=1}. This final set of pairs is the function from events to individuals that we need.

Homomorphism and argument structure 163

(108)

VoiceP DP Peter

Voice’ VP

Voice V’+

NP trees

Agent V’

MP

µ planted

three-CL (109) [[µV’]]= λdd.λP<e,vt>:MON(µ,RangeP(h)).λxe.λev.P(x)(e) ∧ µ(h(e))=d (110) [[three-CL +µV’]]= λP<e,vt>: MON(cardinality-of-ind.,RangeP(h)).λxe. λev.P(x)(e) ∧ cardinality-of-ind.(h(e))=3-individuals [[ plant]] = λxe.λev. *plant(e)=x [[V’+]] = λxe.λev.*plant(e)=x ∧ cardinality-of-ind.(h(e))=3-individuals [[ NP]] = TREE type e (kind) [[ VP]] = [λxe.λev.*plant(e)=x ∧ cardinal.-of-ind.(h(e))=3-ind.](TREE) DKP → λev.∃x[∪tree(x) ∧ *plant(e)=x ∧ cardinality-of-individuals(h(e))=3-individuals] (footnote 40) [[ Voice’ ]] = λye.λev. Ag(e)=y ∧ ∃x[∪tree(x) ∧ *plant(e)=x ∧ cardinality-of-ind.(h(e))=3-individuals] (footnote 39) [[ VoiceP]] = λev. Ag(e)=peter ∧ ∃x[∪tree(x) ∧ *plant(e)=x ∧ cardinality-of-individuals(h(e))=3-individuals] [[ TP]] = 1 iff ∃e∃x[Ag(e)=peter ∧ ∪tree(x) ∧ *plant(e)=x ∧ cardinality-of-individuals(h(e))=3-individuals] Presupposition: µ: cardinality-of-individuals is monotonic to the range of h. Assertion: There is a plural event e of Peter’s planting x and there is x such that x is a tree/trees. µ applied to h(e) yields three individuals. Just like the external split MP in (95), the internal split MP signals that we need µ: cardinality-of-individuals, which calls for a homomorphism h from events to individuals, hence we obtain the sub-formula cardinality-ofindividuals(h(e))=three-individuals.

164

Syntax and compositional semantics of (non-)split constructions

In the German ST in (98b), the internal split MP is adjoined to VP, as in (111) (see (73)). Thus, we can simply use the denotation of µ proposed in (93) (repeated in (112)). The compositional semantics in (112) demonstrates that the denotation of (98b) is basically the same as that of the Japanese FQ construction in (110). (111)

TP T

VoiceP DP

Voice’ VP+

Peter Voice Agent MP

VP µ NP

V’

trees

planted

three

(112) [[ plant]] = λxe.λev. *plant(e)=x ∃ + [[ NP]] = λP<e,vt>.λev. ∃x[*tree(x) ∧ P(x)(e)] (footnote 42) [[ VP]] = λev. ∃x[*tree(x) ∧ *plant(e)=x] [[ µVP]] = λdd.λP: MON(µ,RangeP(h)).λev. P(e) ∧ µ(h(e))=d [[ three-CL +µVP ]] = λP: MON(cardinality,RangeP(h)).λev. P(e) ∧ cardinality(h(e))=three [[ VP+]] = λev. ∃x[*tree(x) ∧ *plant(e)=x] ∧ cardinality(h(e))=three [[ Voice’]] = λye.λev. Ag(e)=y ∧ ∃x[*tree(x) ∧ *plant(e)=x] ∧ cardinality(h(e))=three (footnote 39) [[VoiceP]] = λev. Ag(e)=peter ∧ ∃x[*tree(x) ∧ *plant(e)=x] ∧ cardinality(h(e))=three [[ TP]] = 1 iff ∃e∃x[Ag(e)=peter ∧ *tree(x) ∧ *plant(e)=x ∧ cardinality(h(e))=three] Presupposition: µ: cardinality is monotonic to the range of h. Assertion: There is a plural event e of Peter’s planting x and there is x such that x is a tree/trees. µ applied to h(e) yields three. Under the proposed analysis, any relation that is functional and cumulative should be able to serve as a homomorphism h. Suppose that there is a

Homomorphism and argument structure 165

planting-a-tree event consisting of three subevents; John dug a hole with a shovel, Mary carried a tree with a cart, and Bill covered the roots with a scoop. Then we can say that the sum of a shovel, a cart, and a scoop is the instruments of the planting event. This example illustrates that the instrument function is cumulative. An instrument NP cannot, however, host a split MP, as shown in the Japanese example (113). (113)*Peter-ga sono ki-o syoberu-de kinoo mit-tu ue-ta. Peter-NOM that tree-ACC shovel-with yesterday three-CL plant-PAST ‘Peter planted that tree with three shovels yesterday.’ It is not the lack of a homomorphism, but the lack of a c-command relation that renders this sentence infelicitous. As discussed in section 3.2.3, in Japanese, a split MP must be c-commanded by its host NP. Thus, (113) is unacceptable, not because the instrument function cannot be a homomorphism, but because the split MP cannot be c-commanded by the host NP syoberu ‘shovel’. In (113), the host NP is embedded in a PP, and thus cannot c-command the split MP. Given this syntactic constraint, split MPs are observed with arguments (agents and themes), but not with adjuncts.

5.3. The specification of a homomorphism Let us now turn to the question of how to specify which function serves as a homomorphism h. In particular, we need to make sure that h is the agent function when the host NP is an external argument, and that it is the verb denotation when the host NP is an internal argument. The analysis proposed in section 4 requires h from events to individuals, but there is no specification as to which function is involved. For instance, in the Japanese example (114a), the split MP indicates that we need µ: cardinality-ofindividuals, which calls for h from events to individuals, yielding the subformula cardinality-of-individuals(h(e))=two-individuals, as in (114b). Since it does not specify the function involved, h from events could be to individuals in the extension of the external argument sensei ‘teacher’ (when h is the agent function) or to individuals in the extension of the internal argument gakusei ‘student’ (when h is the verb denotation). Empirically, only the second option is available for (114a) (cf. Nakanishi in press).

166

Syntax and compositional semantics of (non-)split constructions

(114) a. Sensei1-ga gakusei2-o huta-ri*1/2 nagut-ta. teather-NOM student-ACC two-CL hit-PAST ‘A teacher/teachers hit two students.’ b. ∃e∃x∃y[Ag(e)=x ∧ ∪teacher(x) ∧ ∪student(y) ∧ *hit(e)=y ∧ cardinality-of-individuals(h(e))=two-individuals] To account for this, the syntactic constraint discussed in section 3.2.3 becomes relevant: the split MP must be c-commanded by the host NP. Based on this constraint and the structures of the split MP construction proposed in (95) and (108) (repeated in (115a, b)), we may claim that the measure function µ associated with the split MP must bear the same index as the closest c-commanding NP and that µ applies to the co-indexed NP. (115) a.

TP VoiceP NP boy

T Voice’

VP VP

MP

b.

µ

VoiceP DP Peter

Voice

NP

Agent

trees

Voice’ VP

V’ Agent V’ MP

danced two-CL

Voice

µ planted

three-CL

In (114a), for example, the internal argument gakusei ‘student’ is the closest c-commanding NP of the split MP, hence µ bears the same index as the internal argument, predicting that µ applies to elements in the denotation of the internal argument. This analysis cannot, however, account for (116a), whose denotation is given in (116b). (116) a. Gakusei1-ga gakusei2-o huta-ri*1/2 nagut-ta. student-NOM student-ACC two-CL hit-PAST ‘A student/students hit two students.’ b. ∃e∃x∃y[Ag(e)=x ∧ ∪student(x) ∧ ∪student(y) ∧ *hit(e)=y ∧ cardinality-of-individuals(h(e))=two-individuals]

Homomorphism and argument structure 167

The proposed analysis predicts that µ applies to the denotation of the internal argument gakusei ‘student’. But note that in (116a), the denotations of the internal and external arguments are identical, namely, [[*student]] (e.g., if the extension of the internal argument is {x, y, z, x∪Iy, x∪Iz, y∪Iz, x∪Iy∪Iz}, then the extension of the external argument is also {x, y, z, x∪Iy, x∪Iz, y∪Iz, x∪Iy∪Iz}). The current analysis would certainly guarantee that µ: cardinality-of-individuals applies to students, that is, for all relevant events e, h(e) in cardinality-of-individuals(h(e)) is a member of [[ *student]] . This still allows for ‘two-CL ’ in (116a) to be linked to the external argument, yielding the reading ‘two students hit a student/students’. Contrary to this prediction, (116a) lacks such a reading. I suggest that, alternatively, the measure function µ associated with a split MP must bear the same index as the head taking the closest ccommanding NP as its argument and that the co-indexed head serves as h, as schematized in (117). (117) a.

VoiceP NP

b. Voice’

VP

VP NP

V’

Voice MP VP

MP

Agenti

V’ µi planti/hiti

µi

In (115a) with an external split MP, for instance, the closest c-commanding NP for the split MP is the external argument otokonoko ‘boy’ and the head taking this NP as its argument is the Voice head dominating the agent function, as in (117a). Thus, the relevant h must map from events to agents. In (115b) with an internal split MP, the closest c-commanding NP for the split MP is the internal argument ki ‘tree’ and the head taking this NP as its argument is the transitive verb ueru ‘plant’, as in (117b). It follows that the relevant h is the denotation of plant. Example (116) involves an internal split MP, hence the relevant homomorphism is the denotation of hit, as in (117b). Even though the extensions of the internal and external argument gakusei ‘student’ are identical, the students y in the range of *hit(e)=y differ from the students x in the range of Agent(e)=x. Thus, the proposed analysis correctly predicts the interpretation in (116).

168

Syntax and compositional semantics of (non-)split constructions

Note that the German ST is structurally different from the Japanese FQ construction in that the split MP is higher in the structure than its host NP. The relevant structures are repeated in (118). (118) a.

TP T

VoiceP VoiceP

MP

µ NP

Voice’

two boys

b.

Voice

VP

Agent

danced

(= (97))

TP T

VoiceP DP

Voice’

Peter Voice Agent MP

VP VP µ NP

V’

trees

planted

three (= (111))

In (118), the host NP does not c-command the split MP. However, we can carry over the analysis proposed for Japanese by adopting the notion of mcommand (m for maximal projection) instead of c-command.44 Under the 44. The definition of m-command is given below (Chomsky 1986): (i) α m-commands β iff α does not dominate β, β does not dominate α, and the maximal projection of α dominates β. Note that, for our purposes, we need to assume that the upper segment of VoiceP in (118a) or of VP in (118b) dominates the adjoined MP, that is, dominatoin need not be complete, but can be partial instead.

Summary of chapter 3 169

notion of m-command, what matters is the first maximal projection rather than the first branching node. For example, in (119a), the NP m-commands the MP. Hence, I suggest that, in the German ST, the measure function µ associated with the split MP must bear the same index as the head taking the closest m-commanding NP as its argument and that the co-indexed head serves as a homomorphism. In (118a) with the external split MP, the closest m-commanding NP for the split MP is the external argument Jungen ‘boys’ and the head taking this NP as its argument is the Voice head dominating the agent function, as in (119a). Thus, the relevant homomorphism is the agent function. In (118b) with the internal split MP, the closest mcommanding NP for the split MP is the internal argument Bäume ‘trees’ and the head taking this NP as its argument is the transitive verb pflanzen ‘plant’, as in (119b). Then the relevant homomorphism is [[plant]] . (119)

a.

VoiceP

b.

VP

VoiceP MP

µi

VP MP

NP

Voice’ Voice

µi NP

VP

V’ planti

Agenti

6. Summary of chapter 3 The points established in this chapter are summarized below: (120) a. Mechanism of measurement and compositionality: i) Measurement in the nominal domain ii) Measurement in the verbal domain (homomorphism from events to other domains (individuals, paths, etc.)) b. Semantics of measure phrases and measure functions: i) Measure phrases as names for a degree ii) Measure functions as a cross-categorial measurement scheme c. Validity of a homomorphism

170

Syntax and compositional semantics of (non-)split constructions

Regarding (120a), I presented syntactic structures of non-split and split MP constructions: in the syntax, non-split MPs combine with nominal predicates and split MPs combine with verbal predicates. Based on the proposed syntactic structures, I showed that we can derive compositionally the semantic interpretations of the constructions discussed in Chapter 2. The discussion in Chapters 2 and 3 may be considered as an example of how the consideration of semantic facts can provide arguments for particular syntactic structures in the tradition of Partee’s (1975) semantically-based treatment of restrictive relative clauses.45 Specifically, a non-split MP combines syntactically with, and correspondingly expresses measurement of, a nominal predicate. Moreover, a split MP combines syntactically with, and correspondingly expresses measurement of, a verbal predicate. Regarding (120b), I proposed that, while MPs are semantically uniform (i.e., they always denote names for a degree), measure functions µ are cross-categorial. The denotations of µ associated with non-split MPs, with external split MPs, and with internal split MPs are given in (121).46 The schema in (122) captures the cross-categorial nature of µ. (121) a. [[µNP]] = λdd.λP<e,t>: MON(µ,P).λxe. P(x) ∧ µ(x)=d b. [[µVP/VoiceP]] = λdd.λP: MON(µ,P).λev. P(e) ∧ µ(e)=d c. [[µV’]] = λdd.λP<e,vt>: MON(µ,P).λxe.λev. P(x)(e) ∧ µ(e)=d (122) [[µ]] =λdd.λP<σ…,<τ,t>>:MON(µ,P).λxσ…λyτ. P(x)…(y) ∧ µ(y)=d The measure function µ applies to an element y of type τ (i.e., an individual of type e in (121a), an event of type v in (121b, c), and yields a degree denoted by the MP. Moreover, µ is monotonic to the predicate P. In the syntax, the complex predicate MP+µ combines with P, as in (123). (123) P (e.g., NP, VP, V’, …) MP

µ

The schema in (122) together with the structure in (123) captures the fact that µ associated with a non-split or a split MP is sensitive to the monotonicity constraint in the domain with which the MP combines in the syntax. 45. I thank an anonymous reviewer for discussions related to this matter. 46. In (121b, c), I put aside a homomorphism h for simplicity. See (93) and (109) for the denotations incorporating h.

Summary of chapter 3 171

In the next chapter, I show that the proposed analysis extends to comparative constructions involving comparative quantification in the nominal and verbal domains.

Chapter 4 Comparatives and measure phrases as differentials

1. Introduction Chapters 2 and 3 examined the syntax and semantics of non-split and split MP constructions in Japanese and German. The central argument was that, while non-split MP constructions involve measurement of individuals, split MP constructions involve measurement of events as well as of individuals. This chapter examines other constructions, namely, certain comparative constructions in Japanese and English, and demonstrates that some comparatives compare degrees associated with individuals (comparatives in the nominal domain), and others compare degrees associated with events (comparatives in the verbal domain). Regarding comparatives in the verbal domain, I argue that the same mechanism as that proposed for split MP constructions applies to them. Specifically, they make use of a homomorphism from events to other domains (including to individuals). Moreover, I show that both types of comparatives are subject to the same monotonicity constraint as the one proposed for non-split and split MP constructions. A large part of this chapter is devoted to the investigation of the Japanese comparative construction formed with -sugiru. Sugiru is an intransitive verb meaning ‘to pass, to exceed’, as shown in (1). (1)

a. Simekiri-ga sugi-ta. deadline-NOM pass-PAST ‘The deadline has passed.’ b. Joodan-ga sugi-ta. joke-NOM exceed-PAST ‘(I) took a joke too far.’

It can also attach to an adjective or a verb, as in (2), and function as a degree morpheme that expresses excessiveness, analogous to English too.

Introduction 173

(2)

a. Kono ana-ga huka-sugi-ru. this hole-NOM deep-exceed-PRES ‘This hole is too deep.’ b. John-ga ne-sugi-ta. John-NOM sleep-exceed-PAST ‘John slept too much.’

When -sugiru occurs with a measure phrase (MP), as in (3), we observe strikingly different semantic interpretations depending on where the MP appears. While (3a) means that John overdid the reading of three particular books (i.e., John read them too many times or for too long), (3b) means that John read three more books than he was supposed to (e.g., he was supposed to read five, but ended up reading eight). One of the core questions addressed in this chapter is how to obtain these two readings. I show that -sugiru in examples (3) involves comparative quantification in the verbal domain, which calls for a homomorphism from events to other domains just as split MP constructions do. The two examples differ in that the MP in (3b), but not the one in (3a), specifies that the relevant homomorphism is from events to individuals (namely, from reading events to books) (see section 3.3.3 for details). (3)

a. John-ga [hon san-satu]-o kinoo yomi-sugi-ta. John-NOM [book three-CL]-ACC yesterday read-exceed-PAST ‘John read (the) three books too much yesterday.’ b. John-ga hon-o kinoo san-satu yomi-sugi-ta. John-NOM book-ACC yesterday three-CL read-exceed-PAST ‘John read three books too many yesterday.’

The organization of this chapter is as follows. Section 2 presents a brief summary of the studies on comparative constructions. In section 3, I propose that -sugiru is a comparative quantifier that is analogous to too in English. A close scrutiny of the data reveals that the reading in (3b) is derived by treating the MP as a differential MP (e.g., one inch in John is one inch taller than Mary).1 In contrast, the MP in (3a) is not a differential MP, but it is a non-split MP that modifies the NP that it combines with. In section 4, I extend the proposed analysis to the comparative construction in English 1. Differential MPs in a comparative are syntactically different from split MPs, as shown in section 3.3.3. They are, however, similar on the surface in that they both appear appart from the NP with which they are associated.

174 Comparatives and measure phrases as differentials with too many or too much and show that this construction involves comparative quantification in the nominal and verbal domains. Section 5 is the summary of this chapter. Before examing comparatives, let us introduce some semantic rules used in this chapter. I assume that quantificational elements such as everyone undergo quantifier raising at the LF, as in (4a) (Chapter 1: section 4). As an alternative to this structure, Heim and Kratzer (1998) propose the structure in (4b), where the trace is a variable of type e and the adjoined index right below the moved phrase is a variable binder. (4)

a.

IP+

QP1

IP+

b. IP

everyone John

QP VP

loves

1

IP

everyone John t1

VP loves

t1

For the semantic interpretation, we require the Predicate Abstraction Rule defined in (5) and the Trace and Pronouns Rule defined in (6). In (5), [[α]] g is read as “the denotation of α under a variable assignment g” and g x/i is read as “g modified so as to assign x to index i”. (5)

Predicate Abstraction Rule Let α be a branching node with daughters β and γ, where β dominates only a numerical index i. Then, for any variable assignment g, [[α]] g = λx ∈ D. [[γ]] g x/i. (Heim and Kratzer 1998: 186)

(6)

Traces and Pronouns Rule If α is a pronoun or a trace, g is a variable assignment, and i ∈ dom(g), then [[αi]] g = g(i) (Heim and Kratzer 1998:111)

The compositional semantics of (4b) based on (5) and (6) is given in (7). (7)

[[t1]] g = g(1) (by (6)) [[ IP]] g = 1 iff love(j,g(1)) [[1 IP]] g = λxe.[[ IP]] g x/1 = λxe. love(j,gx/1(1)) = λxe. love(j,x) (by (5)) [[everyone]] g = λP<e,t>. ∀y[ person(y) → P(y) ] [[ IP+]] g = [[everyone]] g ([[ 1 IP]] g) = 1 iff ∀y[ person(y) → love(j,y) ]

Comparative constructions 175

2. Comparative constructions Over the past few decades, a considerable number of studies have been made on comparative constructions, with the main emphasis on adjectival comparatives such as John is taller than Mary (Cresswell 1976, Hellan 1981, Hoeksema 1983, Seuren 1984, von Stechow 1984a, b, Heim 1985, 2000, Klein 1991, Rullmann 1995, Kennedy 1999, Schwarzschild and Wilkinson 2002). Section 2.1 introduces some background assumptions on adjectival comparatives that are adopted in this chapter. In section 2.2, I introduce Hackl’s (2000) analysis of complex quantifiers such as more than six, which involves comparative quantification in the nominal domain. In section 2.3, I present a simplified semantics of too that later becomes relevant for the semantics of -sugiru. Section 2.4 presents a brief summary of adjectival comparatives in Japanese. Comparative constructions are known to be complex in both their syntax and their semantics. Despite the large number of studies on the topic, many problems are still in controversy (especially regarding the discrepancy between syntactic and semantic treatments of the constructions). For this reason, in this section, I simply introduce some theoretical assumptions that I adopt from the literature, without providing an overall summary of the topic.

2.1. Adjectival comparatives It is generally assumed that gradable adjectives such as tall, deep, and expensive denote relations between individuals and degrees (see Kennedy 1999 for a general discussion). For example, in John is tall, tall denotes a relation between John and his degree of height. I assume here that a gradable adjective such as tall denotes a function of type , as in (8) (where tall(x,d) is read as “x is tall to degree d”), and that this function is monotone in the sense of (9). (8)

[[tall]] = λdd.λxe. tall(x,d)

(9)

A function f of type is monotone iff ∀x∀d∀d’[ f(d)(x) = 1 ∧ d’
(Heim 2000: 41)

176 Comparatives and measure phrases as differentials A gradable adjective can co-occur with a MP such as six feet, as in (10a). Given the denotation of gradable adjectives in (8), the truth condition of this sentence is (10b), which is read as “John is tall to six feet”. I assume here that a MP is a name for a degree (of type d).2 (10) a. John is six feet tall. b. tall(j,6’) Compositionally, following Heim (2000), I assume that a degree adjective first combines with a degree argument of type d (labeled DegP). For instance, the structure of (10a) is considered to be the one in (11). The degree adjective of type combines with DegP of type d, then the AP of type <e,t> combines with the subject John (is is semantically vacuous), yielding the truth condition in (10b). (11)

IP DP John

I

VP V is

AP DegP

A’

six feet

tall

[[tall]] g = λdd.λxe. tall(x,d) [[six feet]] g = 6’ [[six feet tall]] g = λxe. tall(x,6’) [[John (is) six feet tall]] g = 1 iff tall(j,6’) Let us now consider a comparative construction with -er, such as (12). (12) John is taller than six feet. I adopt (13) as the semantics of -er: -er is a determiner of type >, which takes two sets of degrees and compares their maximal values (von Stechow 1984a). max is a function from a set D of degrees to the degree d 2. Alternatively, a MP can be treated as a predicate of scalar intervals. See Schwarzschild and Wilkinson (2002) for details.

Comparative constructions 177

in D such that, for all other degrees d’ in D, d is greater or equal to d’, as defined in (14) (the definition taken from Heim 2000: 42).3 (13) [[-er]] = λD.λD’. max(D’) > max(D) (14) max(D) := ιd. D(d) = 1 ∧ ∀d’[D(d’) = 1 → d’≤ d] The LF structure of (12) is given in (15) (based on Heim 2000). IP+

(15) DegP Deg

1

IP DP

I

VP

than 6’ -er

John

V is

AP DegP

A’

t1

tall

I assume that a MP may be interpreted either as a name for a degree, as shown above, or as a set of degrees, as in (16) (see, for instance, Hackl 2000). With (16), the denotation of the DegP -er than six feet is (17). Note that {d:d=6’} is a singleton {6’}, and thus max{d:d=6’} is equal to 6’. (16) [[six feet]] = λdd. d=6’ (17) [[-er than six feet]] = λD’. max(D’) > max{d:d=6’} = λD’. max(D’) > 6’

3. Von Stechow (1984a) provides some arguments against an alternative analysis where a comparative clause is treated as a definite description of degrees (Russell 1905). For instance, in (i), assuming that linguists vary in their degrees of richness, there is no unique degree such that linguists can be d-rich. See Rullmann (1995) for various arguments that support von Stechow’s maximality analysis. (i) John is richer than a linguist can be. (Rullmann 1995: 54)

178 Comparatives and measure phrases as differentials The DegP of type in (17) cannot directly combine with tall, which is of type . As a generalized quantifier, it can undergo quantifier raising, leaving a trace of type d. The moved DegP adjoins to IP, creating a λabstract of type . This allows the DegP to combine with [[1 IP]] , yielding the truth condition that the maximal degree d such that John is d-tall is greater than six feet, as in (18). (18) [[1 IP]] g = λdd. [[IP]] g d/1 = λdd. tall(j,gd/1(1)) = λdd. tall(j,d) [[ IP+]] g = [[ DegP]] g ([[1 IP]] g) = 1 iff max{d: tall(j,d)} > 6’ The same analysis extends to examples such as (19). Specifically, (19) is a comparison between the maximal degree to which John is tall and the maximal degree to which Mary is tall. (19) John is taller than Mary is. I simply assume here that the than-clause in (19) involves a gradable predicate, which is deleted under indentity with the matrix clause (i.e., than Mary is tall). With this assumption and a degree abstraction within the thanclause, the denotation of the than-clause is a set of degrees such that Mary is d-tall (i.e., λdd.tall(m,d)). Just as in (15), -er takes two sets of degrees as arguments, where the first argument is denoted by the than-clause and the second by the λ-abstract of the main clause. Then, based on the LF analogous to (15), the truth-condition of (19) is computed as in (20). (20) [[(19)]] g = [[-er]] g ([[than Mary is]] g)([[1 IP]] g) = [λD.λD’. max(D’) > max(D)](λdd. tall(m,d))(λdd. tall(j,d)) = 1 iff max{d: tall(j,d)} > max{d: tall(m,d)} The -er comparative construction may have a differential MP (von Stechow 1984b), such as one inch in (21a). While the sentence expresses a comparison between two maximal degrees just as (19) does, it additionally expresses that the difference between the two is one inch. The truth condition of (21a) can be stated as in (21b). (21) a. John is one inch taller than Mary is. b. max{d: tall(j,d)} − max{d: tall(m,d)} = 1”

Comparative constructions 179

The truth condtion in (21b) is obtained by assuming the denotation of -er in (22).4 Note that, in (22), the mathematical operations of subtraction (−) and equalization (=) require the three relevant degrees, namely, max(D’), max(D), and d, to be of the same sort. This requirement successfully excludes deviant examples such as John is two pounds taller than Mary, where degrees are not of the same sort. (22) [[-er]] = λD.λdd.λD’. max(D’) − max(D) = d 5 At the LF, -er is the head of DegP, which takes the than-clause as a complement, and has the differential MP at the specifier position, as in (23). The DegP adjoins to IP and combines with the λ-abstract of the main clause, yielding the truth condition that the difference between the maximal degree to which John is tall and the maximal degree to which Mary is tall is one inch. IP+

(23) DegP MP

1 Deg’

one inch Deg -er

IP John is t1 tall

CP than Mary is

[[-er than Mary is]] g = λdd.λD’. max(D’) − max{d: tall(m,d)}= d [[DegP]] g = λD’. max(D’) − max{d: tall(m,d)} = 1” [[1 IP]] g = λdd. [[IP]] g d/1 = λdd. tall(j,gd/1(1)) = λdd. tall(j,d) [[(21a)]] g = 1 iff max{d: tall(j,d)} − max{d: tall(m,d)} = 1” 4. We may assume that -er is ambiguous between the denotation without a differential MP in (13) and with a differential MP in (22). Alternatively, we could assume that there is only one denotation of -er, namely, (22), and that, when there is no overt differential MP, the degree argument d in (22) may be saturated by a contextually specified positive value. The choice between the two is not crucial here. 5. Assuming that a MP may be interpreted as a set of degrees, as in (16), we could adopt (i) instead of (22). (i) [[-er]] = λD.λD’.λD”. max(D”) − max(D) = max(D’)

180 Comparatives and measure phrases as differentials 2.2. Comparative quantification in the nominal domain This section examines a comparative quantification in the nominal domain. It has been proposed that a complex determiner such as more than six is decomposed into MANY followed by the DegP -er than six, assuming that more is the morphological spell-out of MANY + -er (Ross 1967, Bresnan 1973, Hackl 2000). Hackl (2000) proposes the denotation of MANY in (24), where MANY takes a degree argument and yields the characteristic function of a set of individuals that are numerous to degree d.6 In this analysis, MANY associates a degree argument with the cardinality of a (pluralized) individual x, and sentence (25) is interpreted as in (26). (24) [[ MANY]] = λdd.λxe. |x|=d

(Hackl 2000: 53)

(25) More than six boys danced. IP+

(26) DegP

1

-er than 6

IP DP

I

VP

NP danced DegP

MANY boys

t1 [[ t1 MANY]] g = λxe. |x|=g(1) [[ NP]] g = λxe. *boy(x)7 [[ DP]] g = λxe. *boy(x) ∧ |x|=g(1) ∃: <e,t> → <et,t> ∃X = λP<e,t>. ∃y[X(y) ∧ P(y)] (Partee 1987, see also Chapter 1: section 3.2) g ∃ + [[DP]] = λP. ∃y[*boy(y) ∧ |y|=g(1) ∧ P(y)] [[ VP]] g = λxe. *dance(x) 6. Hackl (2000) later proposes that MANY is a gradable determiner, i.e., a degree function that takes a degree argument and returns a determiner meaning: (i) [[MANY]] = λdd.λP<e,t>.λQ<e,t>. ∃x[ P(x) ∧ Q(x) ∧ |x| = d ] 7. Recall that * is Link’s (1983) operation of semantic pluralization (Chapter 1: sections 3.1 and 4.4).

Comparative constructions 181

[[ IP]] g = 1 iff ∃y[*boy(y) ∧ |y|=g(1) ∧ *dance(y)] [[1 IP]] g = λdd. [[ IP]] g d/1 = λdd. ∃y[*boy(y) ∧ |y|=d ∧ *dance(y)] [[ -er than six]] g = λD’. max(D’) > 6 [[ IP+]] g = 1 iff max{d: ∃y[*boy(y) ∧ |y|=d ∧ *dance(y)]} > 6 “The maximal degree d such that d-many boys danced exceeds six.” Presumably, the same analysis should extend to examples such as (27), where a MP and a mass NP are involved instead of a numeral and a count NP. (27) More than six pounds of gold disappeared. The semantics of (27) can be easily captured by adopting a more general denotation of MANY (or MUCH when the host NP is mass) given in (28). (28) [[MANY/MUCH]] = λdd.λxe. µ(x)=d

(first version)

This function is exactly the same as the one in (24) except that the measure function µ is used insted of cardinality. Assuming that cardinality is one type of measure function (see, for instance, Chapter 2: section 2.3), (24) is a sub-type of (28). The LF and compositional semantics of sentence (27) then are the same as those of sentence (25) that are provided in (26). The only difference is that the more general denotation of MANY/MUCH in (28) needs to be used instead of (24). This is shown in (29). (29) LF: [IP [DegP -er than 6 pounds] [1 [IP [DP t1 MUCH gold] [VP disappeared]]]] [[ t1 MUCH]] g = λxe. µ(x)=g(1) [[ DP]] g = λxe.[[gold]] g(x) ∧ [[ t1 MUCH]] g(x) = λxe.gold(x) ∧ µ(x)=g(1) ∃ + [[DP]] g = λP. ∃y[gold(y) ∧ µ(y)=g(1) ∧ P(y)] [[ IP]] g = 1 iff ∃y[gold(y) ∧ µ(y)=g(1) ∧ *disappear(y)] [[1 IP]] g = λdd.[[IP]] g d/1 = λdd. ∃y[gold(y) ∧ µ(y)=d ∧ *disappear(y)] [[ DegP]] g = λD’. max(D’) > 6-pounds (see (17)) [[(27)]] g=1 iff max{d:∃y[gold(y)∧µ(y)=d∧*disappear(y)]}> 6-pounds “The maximal degree d such that d-much gold disappeared exceeds six pounds.” In (29), MANY/MUCH first combines with a degree argument, namely, the trace of DegP, and the complex predicate MANY/MUCH+t combines

182 Comparatives and measure phrases as differentials with the NP. This composition is reminiscent of that of a non-split MP construction discussed in Chapter 3: section 4.2. The structure of six pounds of gold and the semantics of the measure function µ are repeated in (30) and (31) (where MON(µ,P) is read as “µ is monotonic with respect to the denotation of P”). (30)

NP NP MP

µ gold

six pounds (31) [[µNP]] = λdd.λP<e,t>: MON(µ,P).λxe. P(x) ∧ µ(x)=d In this construction, µ has to be monotonic to [[NP]] , and this constraint is encoded as the presuppostion of µ. The definition of monotonicity is repeated in (32) (see Chapter 2: section 2.2 for details). (32) A measure function µ is monotonic relative to domain I iff: (i) there are at least two individuals x, y in I such that x is a proper subpart of y (i.e., x < y), and (ii) for all x, y in I such that x < y, µ(x) < µ(y) In section 2.3 below, I show that the comparative construction involving MANY/MUCH is also sensitive to monotonicity. Specifically, the measure function associated with MANY/MUCH must be monotonic to [[NP]] . Thus, I argue that the denotation of MANY/MUCH is parallel to that of the measure function in the nominal domain, as proposed in (33). The compositional semantics of sentence (27) based on (33) is provided is provided in (34). We obtain the same truth condition as (29), plus the presupposition that µ is monotonic to [[gold]] (cf. Chapter 3: section 4.2). (33) [[MANY/MUCH]] = λdd.λP<e,t>: MON(µ,P).λxe. P(x) ∧ µ(x)=d (34) [IP [DegP -er than 6 pounds] [1 [IP [DP t1 MUCH gold] [VP disappeared]]]] [[t1 MUCH gold]] g = [[ MUCH]] g([[t1]] g)([[gold]] g) = [λdd.λP<e,t>: MON(µ,P).λxe. P(x) ∧ µ(x)=d](g(1))(λxe. gold(x)) = λxe. gold(x) ∧ µ(x)=g(1)

Comparative constructions 183

[[ IP]] g = 1 iff ∃y[gold(y) ∧ µ(y)=g(1) ∧ *disappear(y)] (with Predicate Modification and existential-closure) [[(27)]] g=1 iff max{d:∃y[gold(y)∧µ(y)=d∧*disappear(y)]}> 6-pounds

2.3. The semantics of too This section provides a simplified semantics of too that is parallel to the semantics of -er presented in section 2.1. In sections 3 and 4 in this chapter, I show that the proposed semantics of too provides an adequate tool to capture the parallelism between comparatives in the nominal and verbal domains. This parallelism has exactly the same nature as the parallelism between measurements in the nominal and verbal domains observed in nonsplit and split MP constructions in Chapters 2 and 3. Furthermore, I show that comparative constructions can be sensitive to monotonicity with respect to [[ NP]] or [[ VP]] , depending on the domain in which comparative quantification applies. This result leads to the claim that monotonicity is a formal property of different measurement constructions (non-split and split MP constructions, comparative constructions). By simplifying the semantics of too, we can straightforwardly express systematic properties of grammar that run across different measurement constructions. Although it should be possible to add the monotonicity requirement to a more adequete denotation of too (such as Meier’s (2003) in footnote 8), this introduces complications that are particular to comparatives. For this reason, I adopt in this chapter a simplified semantics of too, although this approach is too simplistic to account for the full range of properties of the comparative with too. Heim (2000) and Meier (2003) consider the too construction as a comparison between two values, where the standard of comparison is modalized. For example, John is too tall informally means that John’s actual height is greater than the contextually given height at which he is expected or desired to be. Heim (2000) proposes the denotation of too in (35), according to which we obtain the meaning “the maximal degree such that John is d-tall in the actual world w is greater than the maximal degree such that John is d-tall in a possible world”, as in (36).8 8. Meier (2003) articulated a more elaborate semantics of too, as in (i), which takes a sentential complement (e.g., to throw it away in (ii)) into account. She proposes that the sentential complement contains an implicit or explicit modal expression. For example, the denotation of (ii) would be (iii).

184 Comparatives and measure phrases as differentials (35) [[too]] w = λP<s,dt>. max(P(w)) > max{d: ∃w’∈ Acc(w): P(w’)(d) = 1} (Heim 2000: 59) (36) [[John is too tall]] w = 1 iff max{d: tall(j,d,w)} > max{d: ∃w’∈ Acc(w): tall(j,d,w’)} I pursue here Heim’s and Meier’s idea that too is a comparison between two sets of degrees, but I simplify their analysis by not modalizing the standard of comparison. Recall that -er expresses a comparison between two maximal values, one associated with a main clause and the other with a than-clause (see section 2.1). Like -er, too is a comparison between two maximal values. However, instead of the maximal value associated with a than-clause, too takes a context-sensitive value C provided by context, as in (37).9 (37) a. [[ too]] = λD. max(D) > C b. [[ too]] = λdd.λD. max(D) − C = d

(with a differential MP)

The LF and compositional semantics of John is too tall, which are analogous to those of -er comparatives, are given in (38). The sentence is true (i)

[[too]] = f: D<s, <<s,<st,t>>, <, t>>> For all w ∈ W, Q ∈ D<s,<st,t>> and P ∈ D : f(w)(Q)(P) = 1 iff MAX(λe.P(e)(w)) > MAX(λe*.Q(w)(P(e*))) (Meier 2003: 92) (ii) The food is too good to throw (it) away. (iii) [[too(@)(λw. canR(w)(h)(λw. PRO1 is thrown away in w)) (λe.λw. the food1 is e-good in w)]] g = 1 iff the maximal e such that food is e-good is greater than the maximal e* such that, if the food is e*-good, it can be thrown away given what is allowed. (Meier 2003: 93) The examples of too comparatives (including Japanese -sugiru comparatives) examined in this chapter do not involve sentential complements of the kind discussed in Meier, and thus I disregard them here for simplicity. Examples analogous to (ii) can be constructed with -sugiru, as in (iv). In this case, the semantics of -sugiru needs to be elaborated, as suggested by Meier. I leave this issue for future study. (iv) Kono tabemono-wa suteru-ni-wa yo-sugi-ru. this food-TOP throw-to- TOP good-exceed-PRES ‘This food is too good to throw away.’ 9. Just as in the case of -er, we are not required to posit two denotations of too (see footnote 4).

Comparative constructions 185

if and only if the maximal degree d such that John is d-tall is greater than C (i.e., a standard degree of tallness salient in the context). (38) LF: [IP [DegP too] [1 [IP John t1 is tall]]] [[ IP]] g = [[ too]] g([[1 IP]] g) = [λD. max(D) > C](λdd. tall(j,d)) = 1 iff max{d: tall(j,d)} > C The too construction may take a differential MP, as in John is one inch too tall. The LF and the compositional semantics of this sentence is spelled out in (39) (cf. -er comparative in (23)). (39) LF: [IP [DegP one inch too] [1 [IP John t1 is tall]]] [[ IP]] g = [[ DegP]] g([[1 IP]] g) = [λD. max(D) − C = 1”](λdd.tall(j,d)) = 1 iff max{d: tall(j,d)} − C = 1” Just like -er, too can appear in the nominal domain, as in (40). (40) Too much gold disappeared. We saw in section 2.2 that more than six (pounds) is decomposed to MANY/MUCH and the DegP -er than six (pounds). In the case of the too comparative, this decomposition is obvious from the surface syntax (e.g., too much gold, too many boys). I assume that the overt many/much in the too comparative has the same denotation as the covert MANY/MUCH proposed in (33), repeated in (41). The distinction between many and much is made depending on whether the combined NP is a count or a mass noun. (41) [[many/much]] = λdd.λP<e,t>: MON(µ,P).λxe. P(x) ∧ µ(x)=d Based on (41), the semantics of sentence (40) is computed as follows: (42) LF: [IP+ [DegP too] [1 [IP [DP t1 much gold] [VP disappeared]]]] [[ t1 much gold]] g = [[ much]] g([[t1]] g)([[gold]] g) = [λdd.λP<e,t>: MON(µ,P).λxe. P(x) ∧ µ(x)=d](g(1))(λxe. gold(x)) = λxe. gold(x) ∧ µ(x)=g(1) [[1 IP]] g = λdd. ∃y[gold(y) ∧ µ(y)=d ∧ *disappear(y)] (see (34)) g [[(40)]] = 1 iff max{d: ∃y[gold(y) ∧ µ(y)=d ∧ *disappear(y)]} > C

186 Comparatives and measure phrases as differentials This yields the presupposition that µ is monotonic to [[gold]]. The question now is whether the too comparative of the form in (40) manifests any monotonicity effects. Schwarzschild (2002, 2006) shows that the answer to this question is positive. He cites Parsons’ (1970) observation that too much gold could mean gold that is too heavy or gold whose volume is excessive, but it cannot mean gold whose color is too dark. This is because, while measure functions such as µ: weight or µ: volume can be monotonic to [[gold]] , µ: darkness cannot. In (42), this restriction is incorporated in the presupposition. In section 4, I examine the too comparative in the verbal domain (e.g., John slept too much), and show that monotonicity is in effect there as well.

2.4. Adjectival comparatives in Japanese Before examining the -sugiru comparative, I briefly discuss some properties of Japaense adjectives and comparatives exemplified in (43). (43) a. Kono ana-ga hukai. this hole-NOM deep ‘This hole is deep.’ b. Kono ana-ga ano ana-yori hukai. this hole -NOM that hole-than deep ‘This hole is deeper than that hole.’ c. Kono ana-ga ano ana-yori zyuu-inti hukai. this hole-NOM that hole-than ten-inch deep ‘This hole is ten inches deeper than that hole.’ Interestingly, unlike English comparatives that require adjectives to be marked by the comparative morpheme -er, adjectives in Japanese comparative constructions are not overtly marked with a comparative morpheme.10 10. The adverb motto, which is often translated as ‘more’, may come close to -er, as in (i). However, unlike -er, motto in comparatives is not obligatory. Moreover, as in (ii), motto cannot co-occur with a differential MP. Thus, motto cannot be a simple comparative morpheme (see also Beck, Oda, and Sugisaki 2004: section 5.2). (i) Kono ana-ga ano ana-yori (motto) hukai. this hole-NOM that hole-than (MOTTO) deep ‘This hole is deeper than that hole.’

Comparative constructions 187

In (43b), a comparative interpretation arises by having a phrase led by yori. A yori-phrase or -clause in Japanese is generally considered to have the same function as a than-phrase or -clause in English (Kikuchi 1987, Ishii 1991).11,12 Example (43c) show that a yori-phrase can co-occur with a differential MP. When a MP is used with an adjective, the MP is interpreted as a differential in a comparative construction even without a yori-phrase or -clause (Kikuchi 2002). For example, this hole in (44a) can be interpreted as being ten inches deeper than something else salient in the context, but not as being ten inches deep. Under the first interpretation, I assume that the comparison is between the maximal degree to which this hole is deep and the maximal degree to which some salient element x is deep, as in (44b). (44) a. Kono ana-ga zyuu-inti hukai. this hole-NOM ten-inch deep ‘This hole is ten inches deeper.’ b. max{d: deep(this.hole,d)} − max{d: ∃x[deep(x,d)]} = 10” Sentence (44a) is strikingly different from its English counterpart in (45a), where the MP denotes a name for a degree that saturates the degree argument of deep (see (11)). In English, the comparative reading (44b) obtains only when an adjective is morphologically marked with -er, as in (45b).

(ii)

Kono ana-ga ano ana-yori zyuu-inti (*motto) hukai. this hole-NOM that hole-than ten-inch (MOTTO) deep ‘This hole is ten inches deeper than that hole.’ 11. Beck, Oda, and Sugisaki (2004) argue against the standard assumption that the Japanese yori-clause corresponds to the English than-clause. They claim instead that the yori-clause provides a context setter which allows the inference of a standard of comparison just as English compared to phrase does. For example, in Sam is tall compared to Joe, compared to Joe provides the size standard made salient by the utterance context, which is most likely to be Joe’s height. Thus, the sentence denotes that the degree d such that Sam is d-tall is greater than Joe’s height, as in (i). (i) ∃d[Sam is d-tall ∧ d>c], where c is Joe’s height In this chapter, I adopt the traditional analysis of treating yori as than. 12. I assume that phrasal comparatives are analyzed in the same way as clausal comparatives. See Bhatt and Takahashi (2007) for the comparison of competing analyses.

188 Comparatives and measure phrases as differentials (45) a. This hole is ten inches deep. b. This hole is ten inches deeper than that one.

3. The semantics of -sugiru ‘to exceed’ as a comparative quantifier We are now ready to examine examples with -sugiru in Japanese. As described in section 1, -sugiru attaches to an adjective or a verb and expresses excessiveness, as in (46). In the following, I refer to the two instances of -sugiru in (46) as A(djective)-sugiru and V(erb)-sugiru, respectively. (46) a. Kono ana-ga huka-sugi-ru. this hole-NOM deep-exceed-PRES ‘This hole is too deep.’ b. John-ga ne-sugi-ta. John-NOM sleep-exceed-PAST ‘John slept too much.’

(= (2))

Section 3.1 introduces syntactic assumptions on -sugiru. Section 3.2 examines the semantics of A-sugiru. I show that the correct interpretation of sentences with A-sugiru is obtained by assuming that the denotation of -sugiru is analogous to that of too in English. Section 3.3 investigates the semantics of V-sugiru. I claim that V-sugiru is decomposed into two parts: a part that expresses excessiveness just as too does and a part that relates a degree with an event (cf. MANY/MUCH in (33)). I further argue that there is a homomorphism from events to other domains such as times, paths, and individuals. Thus, V-sugiru provides further evidence for the homomorphism proposed in Chapters 2 and 3. Section 3.4 introduces additional examples of V-sugiru, where the denotation of -sugiru is the same as that of -sugiru in A-sugiru. Section 3.5 is a summary.

3.1. Syntactic assumptions Before examining the semantics of -sugiru, some syntactic assumptions need to be stated. It has been assumed that -sugiru in V-sugiru is a raising verb that takes a sentential complement (Sugioka 1985, Kageyama and Yumoto 1997, Koizumi 1998, among others). The subject of a raising verb starts out as the subject of that verb’s nonfinite complement clause and

The semantics of -sugiru as a comparative quantifier 189

becomes the matrix subject by subject raising. For instance, seem in English is a raising verb: in the sentence John seemed to be happy, John is understood to be the subject of be happy, which undergoes subject raising to become the syntactic subject of seemed. In Japanese, honorification is used to determine whether a verb is a raising verb (Sugioka 1985, Kageyama and Yumoto 1997). When the subject is someone to be respected, a verb can be morphologically marked for honorification, as in (47). In (47), -sugiru can be added after the honorific morpheme -ninarare, as in (48a), but not immediately after the main verb hasiri- ‘run’, as in (48b). (47) Yamada sensei-ga o-hasiri-ninarare-ta. Yamada professor-NOM HONOR-run-HONOR-PAST ‘Professor Yamada ran.’ (48) a. Yamada sensei-ga o-hasiri-ninarare-sugi-ta. Yamada professor-NOM HONOR-run-HONOR-exceed-PAST ‘Professor Yamada ran too much.’ b.??Yamada sensei-ga o-hasiri-sugi-ninarare-ta. Yamada professor-NOM HONOR-run-exceed-HONOR-PAST If Yamada sensei ‘Professor Yamada’ were the subject of hasiri-sugiru ‘run too much’, the honorific morpheme would attach to hasiri-sugiru, as in (48b). The unacceptability of (48b) suggests that Yamada sensei cannot be the subject of V-sugiru. Moreover, the acceptability of (48a) shows that Yamada sensei is the subject of the main verb hasiri- ‘run’ just as in (47). These examples suggest that -sugiru is a raising verb with a sentential complement, as in (49). Yamada sensei is the subject of the embedded clause, and it undergoes subject raising.

190 Comparatives and measure phrases as differentials TP13

(49) VP VoiceP DP

T V

Voice’

Yamada VP

Voice

run

Agent

-sugiru

Further evidence supporting the claim that -sugiru is a raising verb comes from Koizumi’s (1998) data on scope. Koizumi shows that the object in a raising construction may have either narrow or wide scope with respect to the raising verb, as in (50), whereas the object in a control construction cannot have narrow scope, as in (51). -Sugiru behaves like a raising verb in this respect, as in (52). (50) John-wa Emi-dake-o home-kake-ta. John-TOP Emi-only-ACC praise-be about to-PAST ‘John was about to praise only Emi.’ OK only>be about to (It is only Emi that John was to praise) OK be about to>only (It is to praise only Emi that John was about to do) (Koizumi 1998: 5) (51) John-wa ringo-dake-o tabe-wasure-ta. John-TOP apple-only-ACC eat-forget-PAST ‘John forgot to eat only apples.’ OK only>forget (Among many things John was supposed to eat, it is only apples that he forgot to eat) * forget>only (It is eating only apples that John forgot to do) (Koizumi 1998: 5)

13. In section 3.3, I show that V-sugiru involves a comparison of degrees associated with events. To compute the meaning of V-sugiru, the relevant event argument needs to be bound. In Chapter 1: section 4.3, I assumed that the event argument is existentially closed at TP. Thus, I use TP instead of IP for the structure of V-sugiru.

The semantics of -sugiru as a comparative quantifier 191

(52) John-wa niku-dake-o tabe-sugi-ta. John-TOP meat-only-ACC eat-exceed-PAST ‘John overdid eating only meat.’ OK only>exceed (Among many things John ate, it is only meat that he overate) OK exceed>only (For too long time, John ate nothing but meat) (Koizumi 1998: 5) Other supporting evidence comes from examples such as (53), where the excessiveness introduced by -sugiru is not associated with the matrix verb. (53) a. John-ga *(hayaku) oki-sugi-ta. John-NOM (early) get up-exceed-PAST ‘John got up too early.’ b. John-ga kami-o *(mizikaku) kiri-sugi-ta. John-NOM hair-ACC (shortly) get up-exceed-PAST ‘John cut his hair too short.’ These sentences are unacceptable without the presence of the adverbs hayaku ‘early’ and mizikaku ‘shortly’, respectively (see sections 3.3.4 and 3.4 for further discussion). This observation suggests that the scope of -sugiru cannot be restricted to the matrix verb. More specifically, in (53), the adverbs must be in the scope of -sugiru. In structure (49), the adverbs in (53) are embedded within the complement of -sugiru, thus they are in the scope of -sugiru. Compare now examples of V-sugiru (48) with those of A-sugiru (54). (54) a. Yamada sensei-ga o-yasasiku-teirassyaru. Yamada professor-NOM HONOR-kind-HONOR ‘Professor Yamada is kind.’ b. Yamada sensei-ga o-yasasi-sugi-teirassyaru. Yamada professor-NOM HONOR-kind-exceed-HONOR ‘Professor Yamada is too kind.’ b’.*Yamada sensei-ga o-yasasiku-teirassyari-sugiru. Yamada professor-NOM HONOR-kind-HONOR-exceed Contrary to (48), the honorific morpheme in (54) must attach to -sugiru. It follows that the subject Yamada sensei ‘Professor Yamada’ is the subject of

192 Comparatives and measure phrases as differentials A-sugiru. Specifically, in the syntax, -sugiru first combines with an adjective, and the complex predicate A-sugiru combines with the subject, as in (55a). This is analogous to the too comparative in English, whose structure is given in (55b). The structural similarities between the two suggest that -sugiru in A-sugiru is semantically the same as too in English. This is discussed in the next section. (55) a. -Sugiru comparative IP DP

b. Too comparative IP

I’

Yamada VP

I

AP

V

kind

-sugiru

DP

I

Yamada

V is

VP AP DegP

A’

too

kind

3.2. Adjectival comparatives Let us now examine the semantics of A-sugiru. In (55), I showed that there is a syntactic parallelism between the use of A-sugiru and English too with an adjective. Intuitively, they both express excessiveness associated with a gradable adjective. This suggests that the analysis of too presented in section 2.3 extends directly to the analysis of A-sugiru. Specifically, the denotation of -sugiru in (56) is the same as that of too in (37). (56) a. [[-sugiru]] = λD. max(D) > C b. [[-sugiru]] = λdd.λD. max(D) − C = d

(with a differential)14

Although -sugiru and too are syntactically different in that -sugiru is a verb and too is a degree expression, this difference does not affect the semantic parallelism between the two. The LF and semantic computation of the sentence John is too tall are provided in (57). 14. Alternatively, as suggested in footnote 4, we could assume that there is only one denotation of -sugiru, namely, (56b), and that, when there is no overt differential MP, d in (56b) may be saturated by a contextually specified positive value.

The semantics of -sugiru as a comparative quantifier 193

(57) LF: [IP [DegP too] [1 [IP John t1 is tall]]] [[ IP]] g = [[ too]] g([[ 1 IP]] g) = [λD. max(D) > C](λdd. tall(j,d)) = 1 iff max{d: tall(j,d)} > C (= (38)) As shown in (55a), -sugiru is the head of a VP that takes an AP as a complement. Since -sugiru of type cannot combine with the AP of type , it moves to a higher position. I assume that there is a functional projection FP above IP. Then -sugiru moves to F at the LF, as in (58). This make -sugiru combinable with the λ-abstract of the main clause. The semantic computation based on (58) yields the same truth condition as that based on the LF in (57). (58)

FP

DP

IP

1

VP

I

John AP kind

F -sugiru

V t1

[[ FP]] g = [[-sugiru]] g([[1 IP]] g)= [λD. max(D) > C](λdd. kind(j,d)) = 1 iff max{d: kind(j,d)} > C Note that -sugiru is not fully acceptable with differential MPs, as shown in (59a). My informants’ judgments varied from a little awkward to quite awkward, but the informants agreed that the awkwardness came from the apparent redundancy of -sugiru in this context, since the comparative interpretation obtains even without -sugiru, as in (59b) (see section 2.4).15 15. Besides introducing comparative quantification as too does in English, -sugiru has a kind of negative implication in the same way as the English adverb excessively or prefix over- (in the case of excessiveness in the verbal domain; e.g., overeat, oversleep). For instance, (58) implies that it is inconvenient that John is more kind than he is expected to be. Hence, presumably, when the negative implication evoked by -sugiru is meaningful, -sugiru should be able to co-occur with a differential MP. -Sugiru in this case is not redundant because, besides introducing comparative quantification, it evokes pragmatic implications that are otherwise unavailable. This prediction is borne out, as shown in (i),

194 Comparatives and measure phrases as differentials (59) a.?/??Kono ana-ga zyuu-inti huka-sugi-ru. this hole-NOM ten-inch deep-exceed-PRES ‘This hole is ten inches too deep.’ b. Kono ana-ga zyuu-inti hukai. this hole-NOM ten-inch long ‘This hole is ten inches deeper.’

(= (44))

3.3. Comparative quantification in the verbal domain Let us now turn to examples of -sugiru occurring with verbs, as in (60). (60) John-ga kinoo hasiri-sugi-ta. John-NOM yesterday run-exceed-PAST ‘John ran too much yesterday.’ This sentence has three readings. First, suppose that John is a 100 meter sprinter and he usually practices running a race ten times a day. Sentence (60) can mean that he practiced running a race more than ten times yesterday. Second, suppose that John generally runs ten miles a day. In this case, (60) can mean that he ran more than ten miles yesterday. Third, imagine that John usually runs for an hour, then (60) can be used when he ran more than an hour yesterday. Under these three readings, excessiveness of -sugiru is tied to different aspects of events, that is, the cardinality of events, the spatial length of events, and the temporal length of events, respectively. I argue in this section that the V-sugiru comparative exemplified in (60) is an instance of comparative quantification in the verbal domain. Extending the analysis of A-sugiru, I argue that -sugiru in V-sugiru is a comparative quantifier like too in English. V-sugiru differs from A-sugiru in that the degree at issue is associated with an event, not with an adjective. Since where -sugiru evokes the negative implication that the unfortunate rejection was caused by John’s abstract being one page too long. In footnote 29, I discuss another context where -sugiru is not redundant. (i) John-no abusutorakuto-wa iti-peezi naga-sugi-te John-GEN abstract-TOP one-page long-exceed-because kyakka-sare-ta. reject-PASS-PAST ‘Since John’s abstract was one page too long, it was rejected.’

The semantics of -sugiru as a comparative quantifier 195

an event does not have a degree argument, we need a component relating an event to a degree. For this, I claim that, just as there is a hinge between an individual and a degree in the nominal domain (namely, MANY/MUCH introduced in section 2.2), there is a hinge between an event and a degree in the verbal domain. This parallelism is schematized in (61). (61) a. In the nominal domain

DegP ()

b. In the verbal domain

NP (<e,t>) VoiceP () MANY/MUCHx DegP MANY/MUCHe (>) () (>)

In the following, I examine cases where degree is associated with cardinality of events (section 3.3.1), temporal or spatial length (section 3.3.2), and cardinality of individuals (section 3.3.3). I argue that, to express excessiveness of temporal length, of spatial length, or of cardinality of individuals, we need to use the homomorphism from events to the relevant domain that was developed for split MP constructions in Chapater 2. Moreover, I show that the V-sugiru comparative is sensitive to a monotonicity constraint just as split MP constructions are (section 3.3.4). This is not surprising given that the two constructions use the same mechanism of measurement in the verbal domain.

3.3.1. Cardinality of events As shown above, V-sugiru triggers different interpretations depending on the lexical meaning of the verb and the context where it occurs. For instance, in (62), the excess lies in the number of times that John went shopping. (62) John-ga kaimono-ni iki-sugi-ta. John-NOM shopping-to go-exceed-PAST ‘John went shopping too many times.’ How do we compositionally calculate the semantics of (62)? Recalling that -sugiru is a raising verb that takes a nonfinite clause as a complement (see section 3.1), the structure of (62) should be as follows:

196 Comparatives and measure phrases as differentials (63)

TP VP VoiceP DP John VP

T V

Voice’

-sugiru

Voice

go shopping Agent In the last section, we saw that -sugiru in A-sugiru is a comparative quantifier over degrees of type , as in (64). (64) [[-sugiru]] = λD. max(D) > C

(= (56a))

If we adopt (63) and (64), there is a type mismatch between -sugiru and the complement VoiceP John-ga kaimono-ni iki- ‘(lit.) John go shopping’. While -sugiru takes a set of degrees as an argument, VoiceP lacks a degree argument; it simply denotes a set of John’s-going-shopping events (i.e., λev . Agent(e)=j ∧ *go.shopping(e)). To obtain the relevant interpretation, we need to somehow express ‘(lit.) John go shopping d-many times’. I argue that this is possible by introducing a component that associates a degree with an event denoted by a sentential complement. In section 2.2, we saw that a complex determiner such as more than six is decomposed into the comparative quantifier -er than six and MANY/MUCH in (33) that associates a degree with an individual. With this hinge, the comparative quantifier can combine with a nominal predicate, as in more than six boys. Extending this analysis to the verbal domain, I propose that -sugiru is semantically decomposed into two parts, as in (65): the implicit function MANY/MUCH in (66) that relates an event with a degree, and -sugiru in (64) that expresses excessiveness in the same way as too does. Hereafter I use the subscript e for MANY/MUCH that connects a degree and an event, and the subscript x for MANY/MUCH that connects a degree and an individual.

The semantics of -sugiru as a comparative quantifier 197

(65)

V16 MANY/MUCHe

V -sugiru

(66) [[ MANY/MUCHe]] = λdd.λP: MON(µ,P).λev. P(e) ∧ µ(e)=d (first version) One difference between a complex determiner such as more than six in the nominal domain and -sugiru in the verbal domain is that, while a decomposition in the nominal domain in English is morpho-syntactically transparent (more = many + -er and too many/much = too + many/much), there is no overt realization of the decomposition of -sugiru. Specifically, MANY/MUCHe in (66) is never lexically realized in the -sugiru comparative. However, cross-linguistically, a morpho-syntactic decomposition and a semantic decomposition are not always correlated with each other. For example, Spanish demasiado in (67a) is considered to be a comparative quantifier similar to the English too. The same lexical element can combine with a nominal predicate, as in (67b), or with a verbal predicate, as in (67c). (67) a. Esta falda es demasiado larga. this skirt is too much long ‘This skirt is too long.’ b. Bailaron demasiados chicos.17 danced too many boys ‘Too many boys danced.’

16. We may consider MANY/MUCHe + -sugiru an instance of a V-V compound. Independently, Japanese is known to have vibrant instances of V-V compounds (Kageyama 1993, Nishiyama 1998, Fukushima 2005). For this analysis to work, however, we need to assume that MANY/MUCHe is a verb. This may be a viable option given that MANY/MUCHe is never overtly realized in Japanese, and thus we are not obliged to use the lexical items many and much. However, I do not pursue this option because of the lack of evidence. I leave the exact internal structure of (65) for future research. See footnote 19 for a related issue. 17. When demasiado ‘too much’ is a nominal modifier, it has to agree morphologically with the following nominal predicate in terms of gender and number.

198 Comparatives and measure phrases as differentials c. Juan sale de juerga demasiado. Juan goes out of party too much ‘Juan goes out partying too much.’ The semantics of demasiado can be captured by extending the present analysis for Japanese -sugiru: demasiado is a comparative quantifier that combines directly with an adjective in (67a), and, in (67b, c), it requires a presence of a hinge between a degree and an individual (in (67b)) or an event (in (67c)). More specifically, demasiado in (67b, c) is semantically decomposed to a part expressing excess, like too, and a part relating a degree with an individual or an event. In contrast, some languages always lexically realize a hinge. Consider, for example, the English translations in (67): the hinge many/much is present in (67b, c) (see section 4 for further discussion on English too many / too much). Thus, there may be some cross-linguistic variation in the correlation between semantic and morpho-syntactic decomposition. It is no surprise that the Japanese -sugiru is semantically decomposed to two parts without being morpho-syntactically decomposed. We have now established the analysis of -sugiru as a comparative quantifier in the verbal domain. The LF and compositional semantics of example (62) are spelled out in (68). Since -sugiru of type cannot combine directly with MANY/MUCHe of type >, it moves to a position where it can combine with the λ-abstract of the main clause (cf. (26)). The event argument of the main clause is existentially closed at TP, thus -sugiru must move to a position above TP. Ignoring syntactic details, I assume that -sugiru is interpreted at the head of FP.18

18. Technically, -sugiru as a verb should move through every relevant head, which means that it moves from V to T to F. For ease of exposition, I omit the movement to T in (68), although the computation with this movement would give the same result as in (68).

The semantics of -sugiru as a comparative quantifier 199

(68)

FP TP VP+

John VP

T

F -sugiru

V+

VoiceP DP

1

Voice’

MANY/MUCHe V

Voice

t1

go shopping Agent [[V+]] g = λP: MON(µ,P).λev. P(e) ∧ µ(e)=g(1) [[ VoiceP]] g = λev. Agent(e)=j ∧ *go.shopping(e) [[VP+]] g = λev. Agent(e)=j ∧ *go.shopping(e) ∧ µ(e)=g(1) [[ TP]] g = 1 iff ∃e[Agent(e)=j ∧ *go.shopping(e) ∧ µ(e)=g(1)] [[1 TP]] g =λdd.[[TP]] g d/1= λdd.∃e[Ag(e)=j ∧ *go.shopping(e) ∧ µ(e)=d] [[FP]] g = [[-sugiru]] g([[1 TP]] g) = 1 iff max{d: ∃e[Ag(e)=j ∧ *go.shopping(e) ∧ µ(e)=d]} > C Presupposition: µ is monotonic to [[ VoiceP]] . Assertion: The maximal degree d such that there is a plural John’sgoing-shopping event e whose cardinality (of atomic events) is dmany exceeds C. The relevant measure function µ is determined by contextual factors just as µ in non-split and split MP constructions is (see Chapters 2 and 3). In (68), µ applies to John’s going-shopping events. Such events are reasonably measured by cardinality (i.e., how many times John went shopping), hence we readily obtain the interpretation that excessiveness is associated with cardinality of events. Note that the compositional semantics in (68) yields the presupposition that µ: cardinality-of-events is monotonic to [[VoiceP]]. Although I continue to include the presupposition in the semantics of the V-sugiru comparative, the discussion of this presupposition is supressed until section 3.3.4. I show there, that the V-sugiru comparative is sensitive to the monotonicity constraint which is realized as the presupposition.

200 Comparatives and measure phrases as differentials One could object to the compositional semantics in (68) on the basis of a discrepancy between morpho-syntax and semantics. In particular, -sugiru in (68) does not combine directly with the verb at the LF, even though -sugiru attaches directly to the verb in the surface syntax. Indeed, nothing can intervene between the verb and -sugiru. Although I do not have a solution for this problem, I would like to point out that the same problem obtains with English -er: -er does not combine directly with an adjective at the LF (see (15)), even though -er morphologically attaches to the adjective, as in taller. Thus, the issue of this discrepancy is not particular to the Vsugiru comparative, and a solution for the -er comparative should carry over to the V-sugiru comparative (see Bhatt and Pancheva 2004 for a discussion of this issue based on English comparatives). The -sugiru comparative in (62) can occur with a MP such as san-kai ‘three times’, as shown in (69a). Sentence (69a) is strikingly different from the non-comparative sentence in (69b): while the MP in (69a) expresses the cardinality of John’s excessive going-shopping events, the MP in (69b) simply expresses the cardinality of John’s going-shopping event. (69) a. John-ga konsyuu kaimono-ni san-kai iki-sugi-ta. John-NOM this week shopping-to three-time go-exceed-PAST ‘John went shopping three times too many this week.’ b. John-ga konsyuu kaimono-ni san-kai it-ta. John-NOM this week shopping-to three-time go-PAST ‘John went shopping three times this week.’ This contrast indicates that the MP in (69a) is a differential MP just as one inch is in John is one inch taller than Mary. One may wonder why Vsugiru in (69a) is compatible with a differential MP, as opposed to Asugiru in (59a) which is incompatible with a differential. I argued in section 3.2 that the incompatibility of A-sugiru with a differential is due to redundancy: a comparative interpretation obtains even without the presence of -sugiru, as in (59b). In contrast, (69b) without -sugiru does not give rise to a comparative interpretation. Thus, -sugiru in (69a) is not taken to be redundant, contra (59a) (see also footnote 28). The LF and compositional semantics of (69a) are given in (70).19 19. The denotation of -sugiru with a differential is given in (i). (i) [[-sugiru]] = λdd.λD. max(D) − C = d (= (56b)) In (i), -sugiru first combines with a differential, hence the structure (70). However, it is not clear how the differential three times syntactically combines

The semantics of -sugiru as a comparative quantifier 201

(70)

FP TP

1

John went shopping t1 MANY/MUCHe

F 3 times

-sugiru

[[1 TP]] g = λdd.[[TP]] g d/1= λdd. ∃e[Ag(e)=j∧*go.shopping(e)∧µ(e)=d] [[F]] g = [[-sugiru]] g([[three times]] g) = λD. max(D) − C = 3-times [[FP]] g = [λD. max(D) − C = 3-times]([[1 TP]] g) = 1 iff max{d: ∃e[Ag(e)=j ∧ *go.shopping(e) ∧ µ(e)=d]} − C = 3-times Presupposition: µ is monotonic to [[ VoiceP]] . Assertion: The maximal degree d such that there is a plural John’sgoing-shopping event e whose cardinality (of atomic events) is dmany exceeds C by three times.

3.3.2. Homomorphism The previous section examined the case where excessiveness in the Vsugiru comparative is associated with the cardinality of events. As mentioned at the beginning of section 3.2 (see (60)), this is not the only interpretation available with V-sugiru; excessiveness may be tied to the spatial length, as in (71a), or to the temporal length, as in (71b). (71) a. John-ga san-mairu oyogi-sugi-ta. John-NOM three-mile swim-exceed-PAST ‘John swam three miles too far.’

with the verb -sugiru. In (70), three times may be viewed as an affix that moves with the verb, but this view is inconsistent with the general distribution of a differential in the V-sugiru comparative. In particular, as shown in (ii), the differential can appear in different positions in the sentence, which is inconsistent with its being an affix. Furthermore, three times is a complex nominal predicate, and thus it is unreasonable to treat the entire predicate as an affix. However, for the lack of a better alternative, I continue to use the structure (70). (ii) (San-kai) John-ga (san-kai) konsyuu (san-kai) kaimono-ni iki-sugi-ta. (3 times) J-NOM (3 times) this week (3times) shopping-to go-exceed-PAST ‘John went shopping three times too many this week.’

202 Comparatives and measure phrases as differentials b. John-ga san-zikan ne-sugi-ta. John-NOM three-hour sleep-exceed-PAST ‘John slept three hours too long.’ In (71) as well as in (69a), the differential MPs (san-mairu ‘three miles’, san-zikan ‘three hours’, and san-kai ‘three times’) signal the available interpretation. For example, (71a) without the differential may be about excessive temporal length (i.e., John swam an excessively long time), just as in (71b) (see (76a) below). With the differential san-mairu ‘three miles’, the temporal reading becomes unavailable because san-mairu cannot be expressing a temporal length. Recall that, in the denotation of MANY/MUCHe in (72), the relevant degree (with which the excessiveness of -sugiru is associated) is determined by applying a measure function µ to an event (the sub-formula µ(e)=d). (72) [[MANY/MUCHe]] = λdd.λP:MON(µ,P).λev. P(e)∧µ(e)=d (=(66)) In (71a), the MP san-mairu ‘three miles’ indicates that the relevant measure function is µ: spatial-length, and it cannot be a function such as µ: temporal-length or cardinality-of-events. In (72), µ: temporal-length applies to an event (the sub-formula spatial-length(e)=d). An event per se does not have a spatial length, but its path does, as discussed in Chapter 2: sections 4.1 and 6. To resolve this discrepancy, I propose to incorporate a homomorphism h into the denotation of MANY/MUCHe in (72). The revised version is given in (73), where MON(µ,RangeP(h)) means that the measure function µ is monotonic to the range of h from a set of events in P.20 This denotation is exactly the same as the one of the measure function in (74) associated with split MP constructions (taken from Chapter 3: section 4.3). (73) [[MANY/MUCHe]] = λdd.λP: MON(µ,RangeP(h)).λev. P(e) ∧ µ(h(e))=d (revised version) (74) [[µVP]] = λdd.λP: MON(µ,RangeP(h)).λev . P(e) ∧ µ(h(e))=d Thus, the analysis proposed for split MP constructions should extend to the V-sugiru comparative: a MP signals what kind of measure function µ for 20. Alternatively, one may claim that a homomorphism h from events to paths is introduced by a type-mismatch rule: since the sub-formula spatial-length(e)=d in (72) is infelicitous, we insert h, as in spatial-length(h(e))=d.

The semantics of -sugiru as a comparative quantifier 203

events is needed, which in turn determines what kind of h is called for. In (71b), the differential MP san-zikan ‘three hours’ signals that the relevant measure function is µ: temporal-length, which specifies the relevant homomorphism to be the one from events to their run times. We saw that, in (69a) with the MP san-kai ‘three times’, µ: cardinality-of-events is relevant. In that case, a homomorphism is not required because events have cardinality. Let us examine the compositional semantics of (71a) spelled out in (75). (75)

FP TP John swam t1 MANY/MUCHe

1

F 3 miles

-sugiru

[[1 TP]] g =λdd.[[TP]] g d/1= λdd. ∃e[Ag(e)=j ∧ *swim(e) ∧ µ(h(e))=d] [[ F]] g = [[-sugiru]] g([[three miles]] g) = λD. max(D) − C = 3-miles [[FP]] g = [λD. max(D) − C = 3-miles]([[1 TP]] g) = 1 iff max{d: ∃e[Ag(e)=j ∧ *swim(e) ∧ µ(h(e))=d]} − C = 3-miles Presupposition: µ is monotonic to the range of h. Assertion: The maximal degree d such that there is John’s swimming event e whose spatial length is d exceeds C by three miles. In this case, the relevant measure function is µ: spatial-length, which is signaled by the differential san-mairu ‘three miles’. Then the relevant homomorphism must be from an event to its path, namely, from John’s swimming event to its path. It is predicted that the V-sugiru comparative without a differential MP may be interpreted ambiguously, as suggested above. If the measure function is not specified by a differential MP, then there should be some flexibility in choosing the relevant measure function. This prediction is borne out in (76), which corresponds to (71). For instance, (76a) can express excessiveness of cardinality of events, of temporal length, or of spatial length. Any measure function can be used so long as it is compatible with the relevant event (in this case, John’s swimming event). This explains why (76b) lacks a spatial length interpretation: it does not make sense to talk about the spatial length of John’s sleeping event.

204 Comparatives and measure phrases as differentials (76) a. John-ga oyogi-sugi-ta. John-NOM swim-too much-PAST ‘John swam too much.’ (too many times, too long, too far) b. John-ga ne-sugi-ta. John-NOM sleep-exceed-PAST ‘John slept too much.’ (too many times, too long) In sum, I showed that the mechanism proposed for split MP constructions applies to the V-sugiru comparative. The generalization is that a MP (a split MP discussed in Chapters 2 and 3 or a differential MP discussed in this section) signals what kind of measure function µ for events is required, which in turn determines what kind of homomorphism h is called for. The relation between µ and h is schematized in (77). (77) µσ(hτ(e)) µ1, µ2, µ3, µ4, … , µσ h1, h2, h3, h4, … , hτ

(temporal-length, spatial-length, cardinality) (from events to times, to paths, to individuals)

Possible combinations of the two are not random. We first obtain a measure function, which is signalled by a MP, if there is one, or is specified by the context. Then µ restricts the available h. In the next section, I examine in detail the case where the V-sugiru comparative involves µ: cardinality-ofindividuals and h from events to individuals.

3.3.3. Homomorphism to individuals There is yet another possible interpretation of the V-sugiru comparative. Besides the temporal reading that John read a book or books for too long, sentence (78a) has the reading that John read too many books. 21 The availability of this reading becomes apparent in (78b), where san-satu ‘three-CL’ specifies the number of books that were excessive.

21. Sentence (78a) also permits the reading where the excess lies in the number of times that John read a book or books, which becomes salient with expressions such as san-kai ‘three times’, as in (i) (see section 3.3.1). (i) John-ga hon-o kinoo san-kai yomi-sugi-ta. John-NOM book-ACC yesterday three-time read-exceed-PAST ‘John read a book/books three times too many.’

The semantics of -sugiru as a comparative quantifier 205

(78) a. John-ga hon-o kinoo yomi-sugi-ta. John-NOM book-ACC yesterday read-exceed-PAST ‘(lit.) John read a book/books too much yesterday.’ b. John-ga hon-o kinoo san-satu yomi-sugi-ta. John-NOM book-ACC yesterday three-CL read-exceed-PAST ‘John read three books too many yesterday.’ (= (3b)) I propose an analysis of (78) parallel to that of the examples presented in section 3.3.2. In particular, the MP san-satu ‘three-CL’ in (78b) is treated as a differential MP. The semantics of (78b) is calculated as follows: (79)

FP TP

1

John read book(s) t1 MANY/MUCHe

F three-CL

-sugiru

[[1 TP]] g = λdd.∃e[Ag(e)=j ∧ ∃x[∪book(x)∧*read(e)=x] ∧ µ(h(e))=d]22 [[ F]] g = [[-sugiru]] g([[three-CL]] g)= λD.max(D) − C = 3-individuals [[FP]] g = [λD.max(D) − C = 3-individuals]([[1 TP]] g) = 1 iff max{d: ∃e[Ag(e)=j ∧ ∃x[∪book(x) ∧ *read(e)=x] ∧ µ(h(e))=d]} − C = 3-individuals Presupposition: µ is monotonic to the range of h. Assertion: The maximal degree d such that there is a plural John’s reading event e which is mapped to d-many individuals (namely, books) exceeds C by three individuals. San-satu ‘three-CL’ as a differential MP expresses the measure function called for, namely, µ: cardinality-of-individuals. This measure function cannot apply directly to events, and thus a homomorphism h from events to individuals, as proposed in Chapter 2: section 4.1, is needed. Moreover, verb denotations that are functional relations between individuals and events can serve as a homomorphism from events to individuals (see Chapter 3: section 5.2). In this case, the denotation of yomu ‘to read’ is the relevant homomorphism, which may be treated as a function from reading events to individuals denoted by the internal argument hon ‘book(s)’. Then µ: cardinality-of-individuals applies to a set of books mapped from events.

22. See Chapter 1: section 3.2 for the definition of the “up” operator ∪.

206 Comparatives and measure phrases as differentials We are now ready to return to the question posed at the beginning of this chapter: how can we account for the semantic difference between (3b), repeated in (78b), and (3a), repeated in (80)? (80) John-ga [hon san-satu]-o kinoo yomi-sugi-ta. John-NOM [book three-CL]-ACC yesterday read-exceed-PAST ‘John read (the) three books too much yesterday.’ (= (3a)) I propose that the two sentences differ in how the MP san-satu ‘three-CL’ is combined syntactically with the rest of the sentence. As shown in (79), the MP in (78b) is a differential MP, which signals that the relevant measure function is µ: cardinality-of-individuals. Thus, the MP refers to an excessive number of books. In contrast, in (80), the MP forms a nominal constituent with its host NP, as in (81). (81)

FP TP VP+

1 T

VoiceP

V+

John read [three-CL books]

MANY/MUCHe t1

F -sugiru

[[ VoiceP]] g = λev. Ag(e)=j ∧ ∃x[∪book(x) ∧ |x|=3 ∧ *read(e)=x] [[V+]] g = λP: MON(µ,RangeP(h)).λev. P(e) ∧ µ(h(e))=g(1) [[VP+]] g = [[ V+]] g ([[ VoiceP]] g) = λev. Ag(e)=j ∧ ∃x[∪book(x) ∧ |x|=3 ∧ *read(e)=x] ∧ µ(h(e))=g(1) [[1 TP]] g = λdd. ∃e[Ag(e)=j ∧ ∃x[∪book(x) ∧ |x|=3 ∧ *read(e)=x] ∧ µ(h(e))=d] [[FP]] g = [[-sugiru]] g([[1 TP]] g) = 1 iff max{d:∃e[Ag(e)=j∧∃x[∪book(x)∧|x|=3∧*read(e)=x]∧µ(h(e))=d]}> C In (81), -sugiru combines with the nonfinite non-split MP construction ‘John read (the) three books’ (corresponding to VoiceP) (cf. Chapter 3: section 4.2). If there is no overt differential MP, the excessiveness of -sugiru can be associated with any degree compatible with John’s reading-three-books event, as discussed in section 3.3.2. For instance, the rele-

The semantics of -sugiru as a comparative quantifier 207

vant measure function µ can be µ: cardinality-of-events, in which case a homomorphism is not necessary, yielding the interpretation that John read three books too many times. It can be µ: temporal-length, which involves a homomorphism from events to their run times, yielding the reading that John read three books for too long. Crucially, it cannot be µ: cardinality-ofindividuals because cardinality of books is already specified by the nonsplit MP san-satu ‘three-CL’ which is contained in the complement of -sugiru. Under the current analysis, the MP in (78b) is treated as a differential MP, which is an argument of -sugiru, as in (79). Alternatively, can we assume that -sugiru takes the nonfinite version of the split MP construction in (82) as a complement, as in (83) (cf. Chapter 3: sections 4.3 and 5.2)? (82) John-ga hon-o kinoo John-NOM book-ACC yesterday ‘John read three books yesterday.’

san-satu yon-da. three-CL read-PAST

(83)

FP TP VP+

Voice’

John VP NP books MP three-CL

T

F -sugiru

V+

VoiceP DP

1

MANY/MUCHe V

Voice

t1

V’ Agent V read

The answer to this question is negative. That is, san-satu ‘three-CL’ in (78b) cannot be a split MP, as in (83), but must be a differential MP, as shown in (79). This point becomes clear by examining the semantic computation of sentence (78b) based on the LF (83), which is given in (84).

208 Comparatives and measure phrases as differentials (84) [[VoiceP]] g = λev. Ag(e)=j ∧ ∃x[∪book(x) ∧ *read(e)=x ∧ µ(h(e))=3-individuals] [[ VP+]] g = [[ V+]] g ([[ VoiceP]] g) = λev.Ag(e)=j ∧ ∃x[∪book(x) ∧ *read(e)=x ∧ µ(h(e))=3-ind] ∧ µ(h(e))=g(1) g [[FP]] = [[-sugiru]] g([[ 1 TP]] g) = 1 iff max{d: ∃e[Ag(e)=j ∧ ∃x[∪book(x) ∧ *read(e)=x ∧ µ(h(e))=3-individuals] ∧ µ(h(e))=d]} > C Based on the compositional semantics of split MP constructions discussed in Chapter 3: section 5.2, the sentential complement VoiceP in (83) denotes a plural event e of John’s reading books and µ: cardinality-of-individuals applied to h(e) yields three individuals, where h is [[read]] . This means essentially that the cardinality of books that John read is three, which is semantically indistinguishable from VoiceP in (81) (namely, the non-split MP construction). Then sentence (78b) should allow a cardinality-of-events reading or a temporal-length reading as sentence (80) does. However, the only reading available in (78b) is the cardinality-of-individuals reading, which follows from the semantics in (79). Hence, the MP in (78b) should be treated as a differential MP introduced by -sugiru, as in (79), and not as a split MP in the split MP construction, as in (83). In sum, in the V-sugiru comparative, a MP that appears apart from the NP with which it is associated, as in (78b), is a differential MP. The differential MP is syntactically different from a MP in split MP constructions, as demonstrated by the comparison between (79) and (83). Supporting evidence for this view lies in the different syntactic distributions of differential and split MPs. In the V-sugiru comparative, a differential MP can be associated with an internal argument, as exemplified in (78b), whereas it cannot be easily associated with an external argument, as in (85).23 23. The following examples show that the contrast is between internal and external arguments, and not between objects and subjects: a MP in the V-sugiru comparative can be associated with subjects of unaccusative verbs, i.e., internal arguments, as in (i) (cf. Kageyama and Yumoto 1997: 106–107). (i) a. Arubaito-o bosyuusi-ta tokoro kiboosya-ga san-nin ki-sugi-ta. recruited part time job when applicant-NOM three- CL come-exceeded ‘When (I) recruited people for a part time job, three too many applicants came.’ b. Bokin-o sita tokoro okane-ga sen-doru atumari-sugi-ta. raised funds when money-NOM 1000-dollar gather-exceed- PAST ‘When (I) raised funds, 1000 dollars too much money gathered.’

The semantics of -sugiru as a comparative quantifier 209

(85) a.?? Gakusei-ga kinoo san-nin sono miitingu-ni student-NOM yesterday three-CL that meeting-in sankasi-sugi-ta. participate-exceed-PAST ‘Three too many students participated in that meeting yesterday.’ b.??Kyoozyu-ga John-ni huta-ri suisenzyoo-o professor-NOM John-for two-CL letter-ACC kaki-sugi-ta. write-exceed-PAST ‘Two too many professors wrote a letter of recommendation for John.’ In contrast, in split MP constructions, there is no such restriction, as we saw in Chapters 2 and 3. Some of the relevant examples are repeated in (86). These examples show that the host NP of split MP constructions can be either an external (in (86a)) or an internal argument (in (86b)). (86) a. Gakusei-ga kinoo san-nin odot-ta. student-NOM yesterday three-CL danced-PAST ‘Three students danced yesterday.’ b. Peter-ga ki-o kinoo san-bon ue-ta. Peter-NOM tree-ACC yesterday three-CL plant-PAST ‘Peter planted three trees yesterday.’ A question arises as to why differential MPs cannot be easily associated with external arguments. Kageyama and Yumoto (1997) claim that the reading where -sugiru expresses excessiveness of quantity obtains only when the relevant quantity is tied to an incremental element. In Chapter 2: section 5.5, I showed that, while the internal argument has an inherent incremental relationship with events, the incremental relationship between the external argument and events must be manipulated by some operation such as pluralization. This further accounts for example (87), which shows that the V-sugiru comparative with the MP associated with a PP is unacceptable. (87) * John-ga konsaato-de sensyuu mit-tu utai-sugi-ta. John-NOM concert-at last week three-CL sing-exceed-PAST ‘John sang at three too many concerts last week.’

210 Comparatives and measure phrases as differentials Example (87) as well as examples (85) are infelicitous because excessiveness expressed by -sugiru is not tied to an incremental element, assuming that the NP within PP and the external argument do not have any inherent incremental relationship with events. Note that split MP constructions are also unacceptable when the host NP is in PP, as in (88). However, this restriction is explained purely on a syntactic ground: a split MP must be c-commanded by the host NP (see Chapter 3: section 3.2.3). The host NP cannot c-command the split MP when it is embedded in PP. (88) * Gakuseitati-wa kuruma-de ni-dai students-TOP car-in two-CL ‘Students came in two cars.’

ki-ta. come-PAST (Miyagawa 1989: 31)

In contrast, as clear from the structure in (79), a differential MP is not ccommanded by the NP with which it is associated. Then, the analysis proposed for split MP constructions in Chapter 3: section 5.3 is inapplicable for the V-sugiru construction. Specifically, I argued there that the relevant homomorphism h is determined by the structural relation between the split MP and its host NP. A question arises then as to how to specify the function that serves as the relevant h from events to individuals in the V-sugiru construction. In (85) and (87), I showed that a differential MP cannot be associated with an external argument or a NP within PP. Then an internal argument is the only feasible host NP for a differential MP. It follows that h from events to individuals in the V-sugiru construction is always from the relevant events to individuals denoted by the internal argument. Summing up, I argued that differential MPs and split MPs are syntactically different: a differential MP is the argument of a comparative quantifier (namely, -er, too, -sugiru), while a split MP is the argument of a measure function. Despite of this syntactic difference, I assumed that they are both names for degrees, following Schwarzschild’s (2002, 2006) claim that MPs have a uniform semantics (Chapter 3: sections 4.1 and 4.2). Recall now that a MP in non-split and split MP constructions first combines with a measure function µ at the LF, and then with the relevant predicate, as in (89) (Chapter 3: section 4). Given that the MP is always a name for a degree, µ must be cross-categorial, as in (90) (Chapter 3: section 6).

The semantics of -sugiru as a comparative quantifier 211

(89) P (e.g., NP, VP, V’, …) MP

µ

(90) [[µ]] = λdd.λP<σ…,<τ,t>>: MON(µ,P).λxσ…λyτ. P(x)…(y) ∧ µ(y)=d a. [[µNP]] = λdd.λP<e,t>: MON(µ,P).λxe. P(x) ∧ µ(x)=d b. [[µVP/VoiceP]] = λdd.λP: MON(µ,P).λev. P(e) ∧ µ(e)=d c. [[µV’]] = λdd.λP<e,vt>: MON(µ,P).λxe.λev. P(x)(e) ∧ µ(e)=d This cross-categorial nature of the measure function is observed with MANY/MUCH in comparative constructions as well. I proposed (91) as the denotations of MANY/MUCH for comparative quantification in the nominal and verbal domain.24 It is possible to draw from (91) a schema in (92) that captures the cross-categorial nature of MANY/MUCH. (91) a. [[ MANY/MUCHx]] = λdd.λP<e,t>: MON(µ,P).λxe. P(x) ∧ µ(x)=d b. [[ MANY/MUCHe]] = λdd.λP: MON(µ,P).λev. P(e) ∧ µ(e)=d (92) [[ MANY/MUCH]] = λdd.λP<σ…, <τ,t>>: MON(µ,P). λxσ…λyτ. P(x)…(y) ∧ µ(y)=d In this way, the analysis of the V-sugiru comparative proposed here is parallel to that of split MP constructions proposed in Chapters 2 and 3. In the next section, I provide further evidence for the parallelism between the two sets of constructions. In particular, I show that the V-sugiru comparative is sensitive to the monotonicity constraint much as split MP constructions are.

3.3.4. Monotonicity in the verbal domain We saw that the V-sugiru comparative makes use of the same mechanism proposed for split MP constructions, that is, a homomorphism from events to other domains. In Chapter 2, I argued that split MP constructions are sensitive to the monotonicity constraint in the verbal domain, and that the monotonicity constraint is encoded in the denotation of the measure function associated with a split MP. Up to this point, based on the parallelism between V-sugiru and split MP constructions, I have simply assumed that

24. For ease of exposition, I ignore the presence of a homomorphism in (91b).

212 Comparatives and measure phrases as differentials the denotation of MANY/MUCHe also encodes the monotonicity constraint. In the following, I present empirical evidence to support this assumption. Specifically, I show that the V-sugiru comparative is also sensitive to the monotonicity constraint in the verbal domain. One of the properties of split MPs explained by monotonicity in the verbal domain is that split MP constructions are incompatible with singleoccurrence events.25 Examples (93) show that the V-sugiru comparative is also incompatible with such events. (93) a.* John-ga sono hon-o kai-sugi-ta. John-NOM that book-ACC buy-exceed-PAST ‘John bought that book too much.’ b.* NASA-ga Aporo 15-o utiage-sugi-ta. NASA-NOM Apollo 15-ACC launch-exceed-PAST ‘NASA launched Apollo 15 too much.’ c.* John-ga sono koppu-o kowasi-sugi-ta. John-NOM that cup-ACC smash-exceed-PAST ‘John smashed that cup too much.’ Recall the structure of the V-sugiru comparative and the denotation of MANY/MUCHe given below: (94)

VP VoiceP

V MANY/MUCHe -sugiru

(95) [[MANY/MUCHe]] = λdd.λP: MON(µ,RangeP(h)).λev. P(e) ∧ µ(h(e))=d

(= (73))

25. In split MP constructions, there are two more sets of data explained by monotonicity in the verbal domain: incompatibility with individual-level predicates and unavailability of collective readings (Chapter 2: section 3). Recall that these are the properties of MPs associated with external arguments. Since -sugiru cannot be easily associated with external arguments (see (85)), we are unable to attest these properties with the V-sugiru comparative. See section 4 for a discussion on distributive and collective readings.

The semantics of -sugiru as a comparative quantifier 213

The monotonicity constraint is encoded as a presupposition of the V-sugiru comparative: the measure function µ is monotonic to the range of a homomorphism h from a set of events in P. Based on (94), µ must be monotonic to the range of h from a set of events denoted by VoiceP (or by any node under VoiceP that is of type ). In all the examples in (93), the extension of VoiceP (namely, nonfinite clauses John buy that book, NASA launch Apollo 15, and John smash that cup) is a singleton. Then, regardless of what h is at work, the range of h is also a singleton. For µ to be monotonic to the range of h, there has to be two or more members at the range of h (see definition (32) above; see also Chapter 2: section 4.2.1). It follows that the monotonicity constraint cannot be met in (93): in these examples, µ can never be monotonic to the range of h. As shown in section 3.3.3, the domain of h is not restricted to a set of events denoted by VoiceP. In particular, it may be a set of events denoted by V under VoiceP (namely, a verb that -sugiru is attached to). For instance, in (93a), there may be h from events to individuals, that is, from a set of buying events to a set of individuals denoted by the internal argument. The internal argument is that book, which is of type e. If we take a set-theoretic view and consider [[that book]] as a set of individuals, it denotes a singleton set {that.book}. Thus, the monotonicity constraint is not satisfied. Presumably, in (93a), we could posit that -sugiru is associated with some excessiveness relevant to the event of John’s buying that book, of NASA’s launching Apollo 15, or of John’s smashing that cup. For example, in (93a), we could imagine that John bought that book at an excessively high price. Similarly, in (93b), it may be the case that the NASA launch of Apollo 15 was too high or too low.26 However, in these examples, there is no monotonic relation (or structure-preserving homomorphism) between John’s buying-that-book event and the price of the book, and between NASA’s launching-Apollo event and the height of Apollo. For this reason, positing a possible source of excessiveness does not help to satisfy the monotonicity constraint. When an internal argument of examples (93) is an indefinite NP, as in (96), the V-sugiru comparative is acceptable. 26. The described situations can be expressed by using adverbs or secondary predicates, such as takaku ‘expensively’ and hikuku ‘low’ (see (114) and (115)). As is discussed in section 3.4.2, the adverbs or secondary predicates in (114) and (115) have a degree argument in their denotation that can be associated with -sugiru. Thus, we do not need to make use of MANY/MUCHe. Without MANY/MUCHe, (114) and (115) are immune to the monotonicity constraint.

214 Comparatives and measure phrases as differentials (96) a. John-ga hon-o kai-sugi-ta. John-NOM book-ACC buy-exceed-PAST ‘John bought books too much.’ b. NASA-ga roketto-o utiage-sugi-ta. NASA-NOM rocket-ACC launch-exceed-PAST ‘NASA launched rockets too much.’ c. John-ga koppu-o kowasi-sugi-ta. John-NOM cup-ACC smash-exceed-PAST ‘John smashed cups too much.’ In these examples, unlike in (93), the denotation of VoiceP is not a singleton. Consider (96a), which is ambiguous between two readings depending on what measure function µ is chosen. One reading obtains with µ: cardinality-of-individuals. Example (97a) shows the existence of this reading with the help of the differential MP yon-satu ‘four-CL’, which specifies that µ is cardinality-of-individuals. Another reading obtains with µ: cardinality-ofevents. This reading becomes salient with differential MP yon-kai ‘four times’ that calls for µ: cardinality-of-events, as in (97b). (97) a. John-ga hon-o yon-satu kai-sugi-ta. John-NOM book-ACC four-CL buy-exceed-PAST ‘John bought four books too many.’ b. John-ga hon-o yon-kai kai-sugi-ta. John-NOM book-ACC four-time buy-exceed-PAST ‘John bought a book/books four times too many.’ Under the first reading, the relevant h is from a set of events denoted by the verb buy to a set of events denoted by book(s). Since the denotations of buy and of book(s) are not singletons, we can easily construct a homomorphism h that allows us to satisfy the monotonicity constraint. Under the second reading, we do not need to make use of h from events to another domain, because µ: cardinality-of-events can directly apply to events (see section 3.3.1 for details). Then µ must be monotonic to the denotation of VoiceP, namely, the nonfinite clause John buy book(s). This is not a singleton; John’s buying-book(s) event can occur many times. Thus, the monotonicity constraint is satisfied here as well. The data in this section demonstrated that the V-sugiru comparative is sensitive to the monotonicity constraint in the verbal domain in the same way as split MP constructions. This finding supports the core argument of

The semantics of -sugiru as a comparative quantifier 215

the present analysis that both of these constructions involve the mechanism of measurement in the verbal domain.

3.3.5. Summary of section 3.3 In section 3.2, we saw that the Japanese -sugiru is semantically analogous to the English too. Section 3.3 presented examples of the V-sugiru comparative where -sugiru expresses excessiveness of events. -Sugiru is decomposed into two parts: -sugiru that expresses excessiveness in the same way as too does, and the implicit function MANY/MUCHe, as in (98). MANY/MUCHe associates a degree with an event that may be mapped to another domain by a homomorphism h. When a differential MP is present, it signals the measure function µ needed, and further determines the h called for. (98)

V MANY/MUCHe

V -sugiru

(= (65))

[[-sugiru]] = λD. max(D) > C [[-sugiru]] = λdd.λD. max(D) − C = d (= (56)) [[MANY/MUCHe]] = λdd.λP:MON(µ,RangeP(h)).λev. P(e) ∧ µ(h(e))=d (= (73))

3.4. -Sugiru with overt degrees In this section, I show that the distribution of V-sugiru is wider than has been suggested. Specificallly, I present cases where the relevant degree comes from gradable verbs such as cool and love (section 3.4.1) and gradable adverbs such as early and expensively (section 3.4.2). In these cases, since gradable verbs and adverbs have a degree argument in their denotations, the excessiveness expressed by -sugiru can be directly associated with that degree argument, just as in A-sugiru in section 3.2. Hence, there is no need to introduce the component MANY/MUCHe, which associates an

216 Comparatives and measure phrases as differentials event with a degree. In section 3.4.3, I discuss cases where a degree adjective is present in a sentential complement of -sugiru.

3.4.1. Gradable verbs Some verbs seem to be inherent gradable just as gradable adjectives such as tall. So-called degree achievement verbs (Dowty 1979) such as lengthen, cool, and widen provide clear examples. These verbs are considered to have a degree argument in their denotations, as in (99) (cf. Hay, Kennedy, and Levin 1999); (100a) denotes the event of making the soup d-cool, and (100b) is about the event of making that skirt d-short. I propose that, in (100), the excessiveness expressed by -sugiru is directly associated with the degree argument of the verb, just as in the case of A-sugiru (section 3.2). (99) a. [[cool]] = λxe.λdd.λev. cool(x,e,d) b. [[shorten]] = λxe.λdd.λev. shorten(x,e,d) (100) a. John-ga suupu-o samasi-sugi-ta. John-NOM soup-ACC cool-exceed-PAST ‘John cooled the soup too much.’ b. Mary-ga sono sukaato-o mizikakusi-sugi-ta. Mary-NOM that skirt-ACC shorten-exceed-PAST ‘Mary shortened that skirt too much.’ The V-sugiru comparative with degree achievements is, however, syntactically different from the A-sugiru comparative: while -sugiru in the A-sugiru comparative combines directly with an adjective, -sugiru in the V-sugiru comparative combines with a sentential complement VoiceP (see section 3.1). Hence, we need a mechanism to percolate the degree argument of the verb within VoiceP up to VoiceP, and to saturate it with the trace of the comparative quantifier -sugiru. For this purpose, I propose the rule in (101), which passes the degree argument in VP up to Voice’. With this rule, we obtain the desired interpretation, as in (102) (corresponding to (100a)). (101)

Voice’ VP

Voice <e,vt>

λxe.λdd.λev.[[ Voice]](x)(e) ∧ [[ VP]] (d)(e)

The semantics of -sugiru as a comparative quantifier 217

(102)

FP TP VP+ VoiceP DP John VP

1 T

F -sugiru

V

Voice’

t1

Voice

cool the soup Agent [[cool the soup]] g = λdd.λev. cool(the.soup,d,e) [[Voice]] g = λxe.λev. Ag(e)=x [[Voice’]] g = λxe.λdd.λev. Ag(e)=x ∧ cool(the.soup,d,e) (by (101)) [[VoiceP]] g = λdd.λev. Ag(e)=j ∧ cool(the.soup,d,e) [[ VP+]] g = λev. Ag(e)=j ∧ cool(the.soup,g(1),e) [[1 TP]] g = λdd. [[ TP]] g d/1 = λdd. ∃e[Ag(e)=j ∧ cool(the.soup,d,e)] [[ FP]] g = max{d: ∃e[Ag(e)=j ∧ cool(the.soup,d,e)]} > C “The maximal degree d such that John cooled the soup d-much exceeds C.” Verbs with a degree argument are not limited to degree achievements. For instance, Tsujimura (2001) presents a wide range of verbs in Japanese that are considered to be degree verbs, as summarized in (103). (103) a. Psych verbs: komaru ‘be troubled’, yorokobu ‘be pleased’ b. Verbs of emission: hikaru ‘shine’, kirameku ‘sparkle’, niou ‘stink’ c. Change of state verbs: kawaru ‘change’, tizimaru ‘shrink’, tokeru ‘melt’ (Tsujimura 2001: 34) -Sugiru, which can co-occur with all of these verbs, expresses excessiveness of a degree expressed by the verbs. Assuming that the denotation of these verbs has a degree argument just as that of degree achievements does, the desired interpretation obtains in the same way as in (102). For instance,

218 Comparatives and measure phrases as differentials (104a) means that that light shone excessively. The truth-condition of this sentence is given in (104b). (104) a. Sono raito-ga hikari-sugi-ta. that light-NOM shine-exceed-PAST ‘That light shone too much.’ b. max{d: ∃e[shine(that.light,d,e)]} > C27 “The maximal degree d such that that light shone d-much exceeds C.” Other verbs relevant here are those that introduce intensity, such as aisuru ‘to love’ and siru ‘to learn’. These verbs involve some gradability as in ‘John loved Mary d-much’, hence they are considered to have a degree argument in their denotation. The example with aisuru ‘to love’ and its denotation are given in (105). (105) a. John-ga Mary-o aisi-sugi-ta. John-NOM Mary-ACC love-exceed-PAST ‘John loved Mary too much.’ b. max{d: ∃e[Ag(e)=j ∧ love(m,d,e)]} > C “The maximal degree d such that John loved Mary d-much exceeds C.”

3.4.2. Gradable adverbs and secondary predicates The V-sugiru comparative can also be licensed when it co-occurs with adverbs such as hayaku ‘early’, as in (106a). Sentence (106b) is unacceptable because John’s getting-up event cannot be naturally associated with any degree; it has no temporal or spatial length, and it usually occurs once a day (unless we set up a context where John gets up multiple times a day). (106) a. John-ga kinoo hayaku oki-sugi-ta. John-NOM yesterday early get up-exceed-PAST ‘John got up too early yesterday.’ b.* John-ga kinoo oki-sugi-ta. John-NOM yesterday get up-exceed-PAST

(= (53))

27. I assume that hiraru ‘shine’ (as well as other verbs in (103)) is an unaccusative verb.

The semantics of -sugiru as a comparative quantifier 219

This construction, as with -sugiru with adjectives, disallows differential MPs, as in (107a). In adjectival comparatives, the unacceptability of -sugiru occurring with MPs is explained by redundancy: a comparative interpretation exists without -sugiru, hence -sugiru is redundant (see (59)). The same explanation holds in (107): the sentence without -sugiru in (107b) has a comparative interpretation, where iti-zikan ‘one hour’ is interpreted as a differential MP, thus -sugiru in (107a) is redundant.28 (107) a.?? John-ga iti-zikan hayaku oki-sugi-ta. John-NOM one-hour early get up-exceed-PAST ‘John got up one hour too early.’ b. John-ga iti-zikan hayaku oki-ta. John-NOM one-hour early get up-PAST ‘John got up one hour earlier.’ The current approach is further supported by (108). As discussed in section 2.4, a yori-phrase is analogous to a than-phrase in English, which is used in the -er comparative construction. Adjectives in Japanese do not have an overt marking for -er, thus an -er comparative interpretation is induced by having a yori-phrase. In the same vein, (108a) with the yoriphrase has an -er comparative interpretation, which leads us to claim that adverbs in Japanese also lack an overt marking for -er. Since (108a) is already a comparative, (108b) is odd, having a redundant comparative quantifier -sugiru.

28. Unlike in (107a), the V-sugiru comparative discussed in section 3.3 seems to be able to co-occur with a differential MP and a gradable adverb such as nagaku ‘long’, as in (i). Nevertheless, not all gradable adverbs can be so used; for instance, mizikaku ‘shortly’ is unacceptable in (i). I argue that nagaku in (i) is a lexical realization of MANY/MUCHe: just as we can say ‘John slept too much’ as well as ‘John slept too long’, the MANY/MUCHe component of -sugiru can be optionally overtly spelled out. (i) John-ga san-zikan {nagaku / *mizikaku} ne-sugi-ta. John-NOM three-hour {longly / shortly} sleep-exceed- PAST ‘John slept three hours too long/short.’

220 Comparatives and measure phrases as differentials (108) a. John-ga Bill-yori hayaku John-NOM Bill-than early ‘John got up earlier than Bill.’ b.??John-ga Bill-yori hayaku John-NOM Bill-than early

oki-ta. get up-PAST oki-sugi-ta.29 get up-exceed-PAST

The parallelism between adjectives and adverbs indicates that the denotation of adverbs such as early must be analogous to that of gradable adjectives in that a degree argument is present in both. The difference is that, while a degree argument with an adjective denotes a relation between individuals and degrees, the one with an adverb denotes a relation between events and degrees. I propose a denotation such as (109) for gradable adverbs. (109) [[early]] = λdd.λev. early(e,d) With the denotation in (109), we are able to derive compositionally the meaning of sentence (108a). Assuming that gradable adjectives are adjoined to VP, the LF of (108a) is (110). The VP of type and the gradable adverb of type are combined by the rule given in (111).

29. Some informants accepted (108b) under the following interpretation: John and Bill both got up too early, and between the two of them, John got up even earlier. That is, the -er comparative indicated by the yori-phrase compares the maximal degree to which John got up earlier than C (i.e., [[ John got up too early]]) and the maximal degree to which Bill got up earlier than C (i.e., [[Bill got up too early]] ). In this context, comparative quantifications introduced by -sugiru and by the yori-phrase target different degrees, thus there is no redundancy. The same explanation holds for examples with adjectives, as in (i). Some informants accepted (i) under the reading that the maximal degree to which this skirt is longer than C is greater than the maximal degree to which that skirt is longer than C. In this reading, the comparative quantification evoked by -sugiru is not redundant. (i) (?) Kono sukaato-ga ano sukaato-yori naga-sugi-ru. this skirt-NOM that skirt-than long-exceed-PRES ‘The excessive length of this skirt is greater than the excessive length of that skirt.’

The semantics of -sugiru as a comparative quantifier 221

(110)

FP TP VP+ VoiceP DP

AdvP early

T

F -sugiru

V

Voice’

John VP

1

t1

Voice VP Agent get up

[[get up]] g = λev. get.up(e) [[early]] g = λdd.λev. early(e,d) [[ VP]] g = λdd.λev. get.up(e) ∧ early(e,d) (by (111)) [[ VoiceP]] g = λdd.λev. Ag(e)=j ∧ get.up(e) ∧ early(e,d) [[ VP+]] g = λev. Ag(e)=j ∧ get.up(e) ∧ early(e,g(1)) [[1 TP]] g = λdd.[[ FP]] g d/1 = λdd. ∃e[Ag(e)=j ∧ get.up(e) ∧ early(e,d)] [[FP]] g = 1 iff max{d: ∃e[Ag(e)=j ∧ get.up(e) ∧ early(e,d)]} > C “The maximal degree d such that John got up d-early exceeds C.” (111)

λdd.λev. [[AdvP]] (d)(e) ∧ [[VP]] (e)

VP AdvP



VP

The proposed analysis for gradable adverbs extends to secondary predicates. This makes sense, since secondary predicates in Japanese exemplified in (112) are morphologically indistinguishable from adverbs. (112) John-ga sono ie-o akaku John-NOM that house-ACC redly ‘John painted that house red.’

nut-ta. paint-PAST

222 Comparatives and measure phrases as differentials The V-sugiru comparatives in (113)–(115) are acceptable only in the presence of some gradable secondary predicate such as konagonani ‘to pieces’, takaku ‘expensively’, and hikuku ‘(lit.) lowly’. (113) a. John-ga sono koppu-o konagonani kowasi-sugi-ta. John-NOM that cup-ACC to pieces smash-exceed-PAST ‘John smashed that cup too finely.’ b.* John-ga sono koppu-o kowasi-sugi-ta. John-NOM that cup-ACC smash-exceed-PAST ‘John smashed that cup too much.’ (= (93c)) (114) a. John-ga sono hon-o takaku kai-sugi-ta. John-NOM that book-ACC expensively buy-exceed-PAST ‘(lit.) John bought that book too expensively.’ b. *John-ga sono hon-o kai-sugi-ta. John-NOM that book-ACC buy-exceed-PAST ‘John bought that book too much.’ (= (93a)) (115) a. NASA-ga Aporo 15-o hikuku utiage-sugi-ta. NASA-NOM Apollo 15-ACC low launch-exceed-PAST ‘(lit.) NASA launched Apollo 15 too lowly.’ (= NASA’s launch of Appollo 15 was too low.) b. *NASA-ga Aporo 15-o utiage-sugi-ta. NASA-NOM Apollo 15-ACC launch-exceed-PAST ‘NASA launched Apollo 15 too much.’ (=(93b)) Example (116a) shows that, just like (107a), -sugiru in this context is unacceptable when it occurs with MPs. This is caused by the redundancy of -sugiru: a comparative interpretation obtains without -sugiru, as in (116b). (116) a.??NASA-ga Aporo 15-o go-meetoru hikuku utiage-sugi-ta. NASA-NOM Apollo 15-ACC five-meter low launch-exceeded ‘(lit.) NASA launched Apollo 15 five meters too lowly.’ (= NASA’s launch of Apollo was 15 five meters too low.) b. NASA-ga Aporo 15-o go-meetoru hikuku utiage-ta. NASA-NOM Apollo 15-ACC five-meter low launch-PAST ‘(lit.) NASA launched Apollo 15 five meters lower.’ (= NASA’s launch of Apollo was 15 five meters lower.)

The semantics of -sugiru as a comparative quantifier 223

Based on these data, I assume that the examples with secondary predicates in (113)–(115) are semantically similar to the examples with gradable adverbs in (106). I propose (117) as the denotations of secondary predicates. Just as with -sugiru with gradable adverbs, -sugiru with secondary predicates expresses excessiveness associated with a degree argument of a secondary predicate.30 (117) a. [[ to pieces]] = λdd.λev. to.pieces(e,d) b. [[ expensively]] = λdd.λev. expensively(e,d) c. [[ low]] = λdd.λev. low(e,d)

3.4.3. Adjectival modifiers Lastly, I discuss cases where V-sugiru occurs with a gradable adjective that is embedded in the complement clause of -sugiru. Consider (118) taken from Kikuchi (2001). (118) John-ga hukai ana-o hori-sugi-ta. John-NOM deep hole-ACC dig-exceed-PAST ‘(lit.) John dug a deep hole(s) too much.’ Aside from the reading that John dug too many deep holes, which obtains with a homomorphism from events to individuals by the mechanism proposed in section 3.3.3, there is another reading which some informants allow: John dug a hole that is too deep, where the excessiveness is tied to the degree argument of the gradable adjective hukai ‘deep’. The reading where -sugiru is associated with the degree argument of an embedded adjective is, however, not always available (Kageyama and Yumoto 1997: section 2.3.4). For instance, (119) seems to lack such a reading (i.e., “John had soup that was too hot” and “John read a book that was too difficult”). (119) a. John-ga atui suupu-o nomi-sugi-ta. John-NOM hot soup-ACC drink-exceed-PAST ‘(lit.) John had hot soup too much.’

30. See Rothstein (2001, 2004) for further details of the semantics of secondary predicates.

224 Comparatives and measure phrases as differentials b. John-ga muzukasii hon-o yomi-sugi-ta. John-NOM difficult book-ACC read-exceed-PAST ‘(lit.) John read a difficult book(s) too much.’ I suspect that, in general, the degree argument of an adjectival modifier in a sentential complement cannot be associated with -sugiru because the adjectival modifier is too deeply embedded in the syntactic structure to percolate up to VoiceP. Then, a question remains as to why (118) permits the adjectival excessiveness reading. I propose that the reading at issue obtains when the verb horu ‘to dig’ is interpreted as a gradable verb (see section 3.4.1). Suppose that horu ‘to dig’ has a degree argument in its denotation, as in λxe.λdd.λev.dig(x,e,d). This degree argument can then be associated with -sugiru. There is an obvious correlation between John’s digging-a-hole event and the depth of the hole: the more you dig a hole, the deeper the hole becomes. Hence, there is a correlation between excessiveness associated with the degree argument of horu ‘to dig’ and excessiveness associated with the degree argument of hukai ‘deep’. This analysis would predict that, when there is no such correlation, the adjectival comparative reading at issue is not available. This prediction is borne out in (119); there is no correlation between a degree associated with John’s drinkingsoup event and the temperature of the soup, and between a degree associated with John’s reading-a-book event and the difficulty of the book. The validity of the present analysis is further supported by example (120), which is identical to (118) except for the adjective. This sentence lacks the adjectival excessiveness reading that John dug a hole that is too narrow. This is because there is no correlation between John’s digging-a-hole event and the narrowness of the hole. (120) John-ga hosoi ana-o hori-sugi-ta. John-NOM narrow hole-ACC dig-exceed-PAST ‘(lit.) John dug a narrow hole(s) too much.’

3.4.4. Summary of section 3.4 In this section, I presented a wide variety of examples of the V-sugiru comparative that has a degree argument somewhere in the sentential complement of -sugiru. The degree argument in the complement is saturated by the trace of -sugiru (except for the degree argument of an embedded

The semantics of -sugiru as a comparative quantifier 225

adjective discussed in section 3.4.3), which is analogous to the process observed with A-sugiru in section 3.2. The overall generalization then is that the V-sugiru comparative of the kind discussed in this section is licensed only if there is a degree argument in the complement clause of -sugiru.

3.5. Summary of section 3 Let us now put together the analysis of -sugiru presented in sections 3.2, 3.3 and 3.4. In section 3.2, I analyzed -sugiru in A-sugiru as having the same compositional semantics as English too. In this case, the degree argument of an adjective is saturated by the trace of -sugiru, as in (121), hence the excessiveness is tied to the degree expressed by the adjective. (121)

FP

DP AP

IP

1

VP

I

F -sugiru

V t1

d

Extending this analysis, I argued that -sugiru in V-sugiru also expresses excessiveness just as too does. There are two types of V-sugiru comparatives depending on whether a degree argument is present in a sentence. In section 3.4, I discussed cases where some element in a complement clause has a degree argument in its denotation (gradable verbs, gradable adverbs, secondary predicates). The degree argument in the complement percolates up to VoiceP, and combines with the trace of -sugiru. That is, the degree argument is saturated by the trace of -sugiru, as in (122). This is the same process as the one we saw with gradable adjectives in (121).

226 Comparatives and measure phrases as differentials (122)

FP TP VP

1



VoiceP

-sugiru

T V t1

d

When there is no degree argument in a complement clause, -sugiru is decomposed into two parts, as discussed in section 3.3: a part that expresses excessiveness as English too does and a part that associates a degree with an event introduced by the complement (MANY/MUCHe). Besides the interpretation where cardinality of events is excessive, there are interpretations referring to excessive temporal length, spatial length, and cardinality of individuals. This is captured by assuming that there is a homomorphism from events to other domains (times, paths, and individuals). The degree argument introduced by MANY/MUCHe is saturated by the trace of -sugiru, as in (123); hence the excessiveness is tied to the degree expressed by MANY/MUCHe, which is associated with an event denoted by VoiceP. (123)

FP TP VP VoiceP

1



-sugiru

T V

MANY/MUCHe >

V t1

d

In sum, it is possible to categorize the -sugiru comparative into two types: one with and one without an inherent degree argument. The first type is represented by A-sugiru (section 3.2) and by V-sugiru with degree verbs, gradable adverbs, or secondary predicates (section 3.4). Redundancy guarantees that this type of -sugiru comparative cannot co-occur with differen-

Extension to too many / too much in English 227

tial MP (a comparative interpretation is available without having -sugiru). The second type involves MANY/MUCHe introducing a degree argument into the higher V-node in (123). In this type, -sugiru can freely take a differential MP as an argument, which specifies the measurement scheme (i.e., a measure function µ) and the homomorphism.

4. Extension to too many / too much in English In this section, I extend the analysis of the V-sugiru comparative to too many / too much in English. As in (124), too much can express excessiveness of cardinality of events, of spatial length, or of temporal length. Hence, I assume that the analysis of -sugiru as comparative quantification in the verbal domain proposed in section 3.3 straightforwardly extends to too much in English (124). The denotations of (124) are given in (125). (124) a. John went shopping too much. b. John swam too much. c. John slept too much. (125) a. max{d: ∃e[Ag(e)=j∧*go.shopping(e)∧µ(e)=d]} > C b. max{d: ∃e[Ag(e)=j∧*swim(e)∧µ(h(e))=d]} > C c. max{d: ∃e[Ag(e)=j∧*sleep(e)∧µ(h(e))=d]} > C My main interest in this section is in too many / too much occurring in the nominal domain, as in John bought too many apples. Based on the analysis proposed in section 2.3, the LF and compositional semantics of this sentence are presented in (126).

228 Comparatives and measure phrases as differentials TP+

(126) DegP

1

too

T

TP VoiceP DP

Voice’

John Voice Agent

VP V

DP

bought

NP t1

many apples

[[many]] g = λdd.λP<e,t>: MON(µ,P).λxe. P(x) ∧ µ(x)=d (= (33)) [[ t1 many]] g = λP<e,t>: MON(µ,P).λxe. P(x) ∧ µ(x)=g(1) [[DP]] g = λxe. *apple(x) ∧ µ(x)=g(1) ∃: <e,t> → <<e,vt>,t> ∃X = λP<e,vt>.λev. ∃y[X(y) ∧ P(y)(e)] ∃ + [[ DP]] g = λP<e,vt>.λev. ∃y[*apple(y) ∧ µ(y)=g(1) ∧ P(y)(e)] [[VP]] g = λev. ∃y[*apple(y) ∧ µ(y)=g(1) ∧ *buy(e)=y] [[VoiceP]] g = λev. Ag(e)=j ∧ ∃y[*apple(y) ∧ µ(y)=g(1) ∧ *buy(e)=y] [[ TP]] g = 1 iff ∃e[Ag(e)=j ∧ ∃y[*apple(y) ∧ µ(y)=g(1) ∧ *buy(e)=y]] [[1 TP]] g = λdd.[[TP]] g d/1 = λdd.∃e[Ag(e)=j ∧ ∃y[*apple(y) ∧ µ(y)=d ∧ *buy(e)=y]] [[ TP+]] g = [[too]] g ([[1 TP]] g) =1 iff max{d:∃e[Ag(e)=j ∧ ∃y[*apple(y)∧µ(y)=d∧*buy(e)=y]]} > C Presupposition: µ: cardinality is monotonic to [[apples]] . Assertion: The maximal degree d such that John bought d-many apples exceeds C. Too in comparative quantification in the nominal domain can take a differential MP, as in John bought three too many apples. As proposed above, a differential MP is considered to be an argument of the comparative quantifier too. Then the compositional semantics of this sentence can be spelled out as in (127).31

31. The analysis proposed in (127) will be slightly modified in (131).

Extension to too many / too much in English 229

TP+

(127) DegP

1

MP

Deg’

three

too

TP

John bought t1-many apples (see (126))

[[1 TP]] g = λdd. ∃e[Ag(e)=j ∧ ∃y[*apple(y) ∧ µ(y)=d ∧ *buy(e)=y]] [[DegP]] g = λD. max(D) − C = 3 [[ TP+]] g = [[ DegP]] g ([[1 TP]] g) = 1 iff max{d: ∃e[Ag(e)=j ∧ ∃y[*apple(y) ∧ µ(y)=d ∧ *buy(e)=y]]} − C = 3 Presupposition: µ: cardinality is monotonic to [[apples]] . Assertion: The maximal degree d such that John bought d-many apples exceeds C by three. I now direct our attention to an intriguing semantic difference between too many and too much. In (128a), we obtain the reading spelled out in (127), that is, John exceeded the number of apples that he was supposed to buy by three.32 In contrast, (128b) has an additional reading that John exceeded the amount of stuff that he was supposed to buy by three apples, which I call the stuff reading.33 (128) a. John bought three apples too many. b. John bought three apples too much. How can we obtain the stuff reading of (128b)? The fact that too much can appear in argument position, as in John bought too much, indicates that it must be a nominal predicate of some sort that can serve as an argument. 32. Later in this section, I discuss how (128a) is related to John bought three too many apples. 33. Judith Alexander (personal communication) pointed out that there needs to be enough context to evoke the stuff reading, and suggested the context in (i). Under this context, sentence (ii) naturally gives rise to a stuff reading. (i) Suppose that we are given a recipe for apple cake, which we try. The resulting cake is not very good and we adjust the ingredients by reducing the apples by three and the flour by one cup. The cake made with the new recipe is better. (ii) The original recipe had three apples and one cup of flour too much.

230 Comparatives and measure phrases as differentials Moreover, too much can take an overt NP, as in too much wine. Thus, I assume that, when too much appears in argument position, it has a NP that is elided on the surface. Since John bought too much roughly means that John bought too much stuff, I assume that the NP stuff exists at the LF. I further claim that too much can take a differential MP such as three apples. The intuition behind this claim is that apples functions in the same way as a classifier in Japanese (section 3.3.3). The LF of (128b) is given in (129), which is similar to the LF in (127). TP+

(129) DegP MP 3 apples

1

TP

Deg’ T too

VoiceP DP

Voice’

John Voice Agent

VP V

DP

bought

NP t1

much stuff

[[ t1 much]] g = λP<e,t>: MON(µ,P).λxe. P(x) ∧ µ(x)=g(1) [[ t1 much stuff]] g = λxe. stuff(x) ∧ µ(x)=g(1) ∃ + [[ t1 much stuff]] g = λP<e,vt>.λev. ∃y[stuff(y) ∧ µ(y)=g(1) ∧ P(y)(e)] [[VP]] g = λev. ∃y[stuff(y) ∧ µ(y)=g(1) ∧ *buy(e)=y] [[VoiceP]] g = λev. Ag(e)=j ∧ ∃y[stuff(y) ∧ µ(y)=g(1) ∧ *buy(e)=y] [[ TP]] g = 1 iff ∃e[Ag(e)=j ∧ ∃y[stuff(y) ∧ µ(y)=g(1) ∧ *buy(e)=y]] [[1 TP]] g = λdd.[[TP]] g d/1 = λdd. ∃e[Ag(e)=j ∧ ∃y[stuff(y) ∧ µ(y)=d ∧ *buy(e)=y]] [[DegP]] g = λD. max(D) − C = 3-apples [[ TP+]] g = [[DegP]] g ([[ 1 TP]] g) = 1 iff max{d:∃e[Ag(e)=j∧∃y[stuff(y)∧µ(y)=d∧*buy(e)=y]} − C = 3-apples Presupposition: µ: amount is monotonic to [[stuff]] . Assertion: The maximal degree d such that John bought d-much stuff exceeds C by three apples.

Extension to too many / too much in English 231

The question now is why the stuff reading is unavailable in (128a). Recall that the interpretation of (128a) is the same as the one of John bought three too many apples. Given the semantic similarity between the two sentences, I propose that these two sentences are derived by a NP-deletion from the same underlying structure, as in (130). Too many is a complex comparative quantifier that combines with a NP, as in too many apples in (126). Moreover, as we saw in (129), we can consider three apples to be a differential MP. Then the LF of these sentnece is (131). (130) a. John bought three apples too many apples. b. John bought three apples too many apples. TP+

(131) DegP

1

MP

Deg’

three apples

too

TP

John bought t1-many apples (see (126))

[[ 1 TP]] g = λdd.∃e[Ag(e)=j ∧ ∃y[*apple(y) ∧ µ(y)=d ∧ *buy(e)=y]] [[TP+]] g = 1 iff max{d:∃e[Ag(e)=j∧∃y[*apple(y)∧µ(y)=d∧*buy(e)=y]]}−C=3-apples Presupposition: µ: cardinality is monotonic to [[ apples]] . Assertion: The maximal degree d such that John bought d-many apples exceeds C by three apples. Although (131) differs from (127) in that the differential is three apples, not three, the denotations in (131) and in (127) are almost identical. Hence, it is natural to assume the underlying structure [John bought three apples too many apples]. I suggest that there is a constraint that prohibits having two identical NPs in the surface form. Depending on which NP is deleted, we obtain either John bought three apples too many or John bought three too many apples, as in (130).34 34. I claimed above that the underlying structure of (128b) with too much contains the NP stuff, as shown in (129), and that this NP is deleted on the surface. Although I do not have an anlaysis for how this deletion proceeds, I point out that this deletion is different in nature from NP-deletion by identity proposed for (130) with too many. Specifically, NP deletion by identity is possible with too

232 Comparatives and measure phrases as differentials As with too many in English, the V-sugiru comparative lacks the stuff reading. For example, (132a) has the same reading as (128a), that is, John exceeded the number of apples that he was supposed to buy by three. The denotation of this sentence is given in (132b), based on the mechanism proposed in section 3.3.3. (132) a. John-ga ringo-o san-ko kai-sugi-ta. John-NOM apple-ACC three-CL buy-exceed-PAST ‘John bought three apples too many.’ b. max{d: ∃e∃x[Agent(e)=j ∧ *apple(x) ∧ *buy(x,e) ∧ µ(h(e))=d]} − C = 3 individuals Presupposition: µ: cardinality-of-individuals is monotonic to [[VoiceP]] . Assertion: The maximal degree d such that there is a plural John’s buying event e which is mapped to d-many individuals (namely, apples) exceeds C by three individuals. Example (132a) is analyzed as comparative quantification in the verbal domain, where san-ko ‘three-CL ’ as a differential MP expresses that the relevant measure function is cardinality-of-individuals, which requires a homomorphism h from events to individuals. The lack of the stuff reading then is the result of this homomorphism: since h is a verb denotation buy(e)=x, the differential MP must necessarily be associated with the internal argument of a buying event, namely, apples. In this way, although the English too many comparative and the Japanese V-sugiru comparative both lack the stuff reading, the absence is explained by different systems: while too many involves comparative quantification in the nominal domain, -sugiru involves comparative quantification in the verbal domain. There is a potential difference between the English too many and the Japanese -sugiru, which indicates that the two involve comparative quantification in different domains. As shown in (133a), the too many comparative can be ambiguous between distributive and collective readings. As discussed in section 3.3.3, differential MPs in the V-sugiru comparative cannot generally be associated with external arguments. For this reason, the acceptability of (133b) is controversial. However, some informants accepmany, but not with too much. This is shown by the following examples provided me by Jason Merchant (personal communication). (i) a. John revealed too many of his secrets. Bill concealed too many. b.* John revealed too much of his background. Bill concealed too much.

Summary of chapter 4 233

ted it, and judged that only a distributive reading is available. Recall the discussion in Chapter 2 that split MP constructions lack a collective reading because of the monotonicity constraint in the verbal domain. Since the Vsugiru comparative is also sensitive to the monotonicity constraint in the verbal domain, as shown in section 3.3.4, it lacks a collective reading. In contrast, the too many construction involves quantification in the nominal domain, hence it is immune to the constraint in the verbal domain. (133) a. Three too many boys carried the piano. OK distributive, OKcollective ? b. Otokonoko-ga san-nin piano-o hakobi-sugi-ta. boy-NOM three-CL piano-ACC carry-exceed-PAST ‘Three too many boys carried the piano.’ OK distributive, *collective

5. Summary of chapter 4 In this chapter, I examined the syntax and semantics of comparative constructions. Some of the issues discussed here are summarized in (134). (134) a. Monotonicity as a formal property of comparative constructions b. The mechanism of comparative quantification: i) Quantification in the nominal domain ii) Quantification in the verbal domain (homomorphism from events to other domains (individuals, times, paths)) c. The semantics of measure phrases and of measure components (MANY/MUCH) The first issue concerns monotonicity as a formal property of measurement constructions. The data presented in this chapter revealed that some comparative constructions, namely, the English too many / too much comparative and the Japanese-sugiru comparative, are sensitive to the monotonicity constraint. This result indicates that monotonicity unifies seemingly unrelated measurement constructions, namely some comparative constructions and non-split / split MP constructions. The second issue concerns the compositional semantics of comparative quantification in the nominal and verbal domains. A particular emphasis is put on quantification in the verbal domain. I proposed in section 3.3 that the

234 Comparatives and measure phrases as differentials V-sugiru comparative in Japanese makes use of a homomorphism from events to another domain, just as split MP constructions do. Thus, this mechanism is needed not just for one particular construction, but applies to a range of empirical data. The third issue concerns the semantics of measurement expressions. I adopted Schwarzschild’s (2002, 2006) claim that MPs are semantically uniform. I further proposed that, just as measure functions are crosscategorial, some components of comparative quantifiers (i.e., MANY/MUCH) are cross-categorial, which enables us to capture the similarity between non-split / split MP constructions and comparative constructions.

Chapter 5 Cross-linguistic aspects of quantification and compositionality

1. Introduction A very important question for any linguistic analysis is how well it stands up when applied to different languages. The goal of this chapter is to investigate two issues that arise with cross-linguistic data. The first issue is whether the proposed analysis of non-split / split MP constructions in Japanese and German (and also of some comparatives in Japanese and English) applies to other languages. In section 2, I present data on non-split and split MP constructions in Greek and Catalan and show that these constructions are sensitive to the same semantic restrictions as the ones of the corresponding Japanese and German constructions, which can be captured by the monotonicity constraint (Chatper 2). This finding suggests that monotonicity is a universal formal property of measurement constructions, although cross-linguistic split MP constructions are not uniform in every respect. In section 3, I show that the German Split NP Topicalization (ST), but not the Japanese floating quantifier (FQ) construction, is subject to a specific pragmatic constraint — namely, the German ST must have a special topic-focus structure. I examine whether the semantic properties of the German ST initially explained by monotonicity follow from this pragmatic constraint. The second issue concerns whether the proposed analysis (or parts of it) can be extended to other constructions in other languages. In section 4.1, I present data on for the most part in English (Nakanishi and Romero 2004) and on hotondo ‘most’ in Japanese. I show that these constructions involve a homomorphism from events to other domains just as split MP constructions do. Furthermore, in section 4.2, I examine some data on pluractional markers, i.e., morphemes that overtly express plurality of events. These data support the present analysis which appeals to plurality of events and mapping functions. In section 4.3, I briefly discuss cross-categorial quanti-

236 Cross-linguistic aspects of quantification and compositionality fication observed with particles that can occur both with nominal and with verbal predicates. Before concluding, I discuss briefly in section 5 some differences between quantification over events and quantification over situations. In Chapters 2 and 3, we saw that a split quantifier measures events denoted by a verbal predicate, but that at the same time it is associated with individuals denoted by a nominal predicate. This is reminiscent of the so-called quantificational variability effect with adverbs of quantification. For example, A blue-eyed bear is always intelligent has the reading that ‘all blue-eyed bears are intelligent’, where always has the effect of semantically quantifying over a blue-eyed bear, although syntactically it is an adverb. It has been argued that this phenomenon involves quantification over situations. I show that quantification over events and quantification over situations differ in some important aspects.

2. Universality of monotonicity In Chapter 2, we saw that in Japanese and German, split MP constructions, but not non-split MP constructions, are subject to some semantic restrictions in the verbal domain, that is, incompatibility with single-occurrence events, incompatibility with individual-level predicates, and the lack of collective readings. In the following, I show that split MP constructions in Greek and Catalan also have these properties, while their non-split counterparts do not. These properties can be consistently accounted for by the monotonicity constraint in the verbal domain. The first property to be considered is the compatability of the relevant construction with single-occurrence events. While non-split MP constructions are always acceptable, split MP constructions are compatible with hit Peter, but not with kill Peter. Examples (1)–(2) are from Greek, and examples (3)–(4) are from Catalan. (1)

a. [Tris fitites] htipisan ti mitera [three students] hit.3PL the mother ‘Three students hit Peter’s mother.’ b. Fitites htipisan tris ti mitera students hit.3PL three the mother

tu Petru. the Peter.GEN tu Petru. the Peter.GEN

Universality of monotonicity 237

(2)

a. [Tris fitites] skotosan ti mitera [three students] kill.3PL the mother ‘Three students kill Peter’s mother.’ b.??Fitites skotosan tris ti mitera students kill.3PL three the mother

tu Petru. the Peter.GEN tu Petru. the Peter.GEN

(3)

a. [Tres estudiants] han colpejat el Pere. [three students] have hit the Peter ‘Three students hit Peter.’ b. D’estudiants, han colpejat el Pere tres. of-students have hit the Peter three

(4)

a. [Tres estudiants] han matat el Pere. [three students] have killed the Peter ‘Three students killed Peter.’ b.???D’estudiants, han matat el Pere tres. of-students have killed the Peter three

The second property is the compatability of the constructions at issue with stage- and individual-level predicates. In Greek, non-split MP constructions are compatible with both types of predicates, whereas split MP constructions are compatible only with stage-level predicates, as shown in (5)–(6). In Catalan, it is not possible to construct an appropriate minimal pair, because, whether or not MPs are involved, stage-level predicates are best expressed with hi ha ‘there is’, as in (7a). Thus, (7b) is not completely acceptable. (5)

(6)

a. S’afti tin poli, [tris pirosvestes] ine in this the town [three firemen] are ‘In this town, three firemen are available.’ b. S’afti tin poli, pirosvestes ine tris in this the town firemen are three

diathesimi. available

a. S’afti tin poli, [tris pirosvestes] ine in this the town [three firemen] are ‘In this town, three firemen are altruistic.’ b.* S’afti tin poli, pirosvestes ine tris in this the town firemen are three

altruistes. altruistic

diathesimi. available

altruistes. altruistic

238 Cross-linguistic aspects of quantification and compositionality (7)

a. Hi ha bombers disponibles. there is firemen available ‘There are firemen available.’ b. ?Alguns bombers estan disponibles. some firemen are available ‘Firemen are available.’

The last property to be considered is the availability of collective readings with these constructions. Non-split MP constructions are ambiguous between collective and distributive readings, whereas split MP constructions lack collective readings, as shown in (8) from Greek and in (9) from Catalan. (8)

(9)

a. [Tris fitites] vrikan ena hartomisma ton 10 Euro [three students] found a bill 10 Euro.GEN ‘Three students found a ten-Euro bill on the street.’ OK distributive, OKcollective b. Fitites vrikan tris ena hartomisma ton 10 Euro students found three a bill 10 Euro.GEN OK distributive, ??collective

sto dromo. on.the street

sto dromo. on.the street

a. [Tres estudiants] han construït una maqueta. [three students] have built a model ‘Three students built a model.’ OK distributive, OKcollective b. D’estudiants, han construït una maqueta tres. of-students have built a model three OK distributive, ??collective b’.*D’estudiants, han construït aquesta maqueta tres. of-students have built the model three ‘Three students built the model.’

The examples presented above suggest that the same monotonicity analysis should extend to Greek and Catalan. Thus, we have found at least four languages — Japanese, German, Greek, and Catalan — that seem to share the same semantic mechanism based on monotonicity. While the last three languages belong to the Indo-European language family, Japanese does not. The three Indo-European languages are further classified into different language families: German is a Germanic language, Greek is a Greek lan-

Pragmatics of split quantifier constructions 239

guage, and Catalan is a Romance language. This diversity among the four languages at issue suggests that monotonicity is a universal property of measurement constructions that holds for related measurement constructions in different languages. In other words, cross-linguistic measurement constructions can be categorized into different classes based on the formal property of monotonicity (see Chapter 6).

3. Pragmatics of split quantifier constructions The empirical data presented in Chapter 2 and section 2 of this chapter demonstrated that split MP constructions in different languages have several semantic properties explained by the monotonicity constraint in the verbal domain in common. Split MP constructions are not, however, uniform in all respects cross-linguistically. In this section, I point out that there are pragmatic differences among split MP constructions. Specifically, I show that the German ST differs from the Japanese FQ construction in that the former, but not the latter, requires a special topic-focus configuration. This raises the following question: can the semantic properties of the German ST be explained by appealing to the pragmatic constraint on this construction and not to monotonicity? I show that, although the pragmatic analysis is able to account straightforwardly for some properties of the ST, it is unable to capture the full range of examples.

3.1. Pragmatics of split NP topicalization in German It has been argued that, in the German ST, the host NP must be a contrastive topic and the split MP must be a focus (Krifka 1998, among others). For instance, in (10a), the host NP Studenten ‘students’ must be contrasted with other groups of non-students such as professors and office workers. The split MP drei ‘three’ is a focus placed in the pre-verbal focus position. The sentence roughly corresponds to the paraphrase “as for students, the cardinality of students who danced yesterday was three” (and as for professors, the cardinality of ones danced was five, etc.). Unlike the German ST, the Japanese FQ construction is not subject to a marked topic-focus structure.1 1. Some researchers claim that, in the Japanese FQ construction, the host NP is a topic and the FQ is a focus (Takami 2001, in particular). Even under such an analysis, the host NP need not be contrastive. Rather, the host NP is simply a

240 Cross-linguistic aspects of quantification and compositionality For example, (10b) does not evoke a contrastive interpretation; it simply states that the cardinality of students who danced was three. (10) a. Studenten haben gestern drei students have yesterday three ‘Three students danced yesterday.’ b. Gakusei-ga kinoo san-nin student-NOM yesterday three-CL

getanzt. danced odot-ta. dance-PAST

This pragmatic restriction on the German ST is reflected in prosodic structure. It has been claimed that this construction necessarily involves the rise-fall contour, where the rising pitch is on the host NP and the falling pitch is on the split MP, as in (11a) (Krifka 1998). It is independently known that the rising pitch accent is a topic accent, while the falling pitch accent is a focus accent (Féry 1993, Büring 1997). I express the topic-focus structure of (11a) as in (11b), using [ ]T and [ ]F. (11) a. Stu/Denten haben gestern \DREi getanzt. students have yesterday three danced b. [Studenten]T haben gestern [drei]F getanzt. In Chapter 2: section 3.1.1, I showed that a ST is incompatible with single-occurrence events, as in (12), and that the incompatibility is accounted for by the monotonicity constraint: the measure function must apply monotonically to the relevant part-whole structure. Note that the infelicity of (12) also follows naturally from the pragmatic constraint that the host NP must be a contrastive topic.2 The contrastive nature of the host NP implies that there is a group of non-students who killed Peter. Since Peter cannot be killed multiple times, the sentence is infelicitous. (12) ?? Studenten haben Peter drei umgebracht. students have Peter three killed ‘Three students killed Peter.’

thematic topic (see Kuno 1973, for instance, for the distinction between contrastic and thematic topics). 2. I thank Angelika Kratzer and Manfred Krifka for suggesting the alternative pragmatic account.

Pragmatics of split quantifier constructions 241

In this way, the incompatability of STs with single-occurrence events can be explained by either the monotonicity constraint or by the pragmatic constraint. Which analysis should we adopt? If the pragmatic constraint successfully explains the full range of semantic properties of ST, it is certainly better to adopt the pragmatic analysis. The pragmatic constraint is independently needed for ST structure, whereas the monotonicity constraint is proposed precisely to account for the semantic properties at issue. In the following, I examine whether the full range of semantic properties of ST can be captured by the pragmatic constraint. For this purpose, we need to construct scenarios where ST is used naturally, namely, contexts where the host NP is a contrastive topic and the split MP is a focus. The host NP can be a contrastive topic when there are groups contrasted with it. For this, I use a pair such as boys vs. girls or students vs. professors. As for the focus, it is well known that the position in an answer that correlates with the position of a wh-word in a question is a focus (Rooth 1985, 1992, 1996, in particular). The question-answer pair in (13) illustrates this point. A1 is an appropriate answer for Q because a focus is placed in the right position: John in A1 corresponds to the wh-word in Q. In contrast, A2 is inappropriate, since the focus does not correspond to the wh-word. (13) Q: A1: A2:

Who met Mary? [John]F met Mary. # John met [Mary]F.

Based on these methods, the scenario in (14) is constructed for the dialogue in (15). In the ST in (15), the host NPs, Studenten ‘students’, Professoren ‘professors’, and Arbeiter ‘workers’ are contrasted with each other. The split numerals are foci, since they correspond to the wh-word wieviele ‘how many’ in the preceding question. (14) Scenario 1: At the party for the Department of Linguistics held yesterday, three students, two professors, and four office workers danced. (15) Q: Wieviele Leute haben gestern how many people have yesterday ‘How many people danced yesterday?’

getanzt? danced

242 Cross-linguistic aspects of quantification and compositionality A: [Studenten]T haben [drei]F getanzt, students have three danced [zwei]F getanzt, und [Arbeiter]T two danced and workers ‘As for students, three danced, as for as for workers, four danced.’

[Professoren]T haben professors have haben [vier]F getanzt. have four danced professors, two danced, and

As long as the host NP is a contrastive topic and the split MP is a focus, we can create more scenarios that are compatible with ST. Consider (16), for instance. (16) Scenario 2: At the party for the Department of Linguistics held yesterday, people engaged in different activities. As for students, three danced, five sang, and two played the piano. As for professors, four danced and six played the piano. This scenario may give rise to a multiple wh-question, such as the one in (17), which creates multiple foci in the corresponding answer. In (17A), the verbal predicates expressing dancing, singing, and playing the piano are focus as well as the split MPs. (17) Q: Wieviele Leute haben während der Party was gemacht? how many people have during the party what done ‘How many people did what at the party?’ A: [Studenten]T haben [drei]F [getanzt]F, students have three danced [fünf]F [gesungen]F, und [zwei]F [Klavier gespielt]F. five sung and two piano played [Professoren]T haben [vier]F [getanzt]F und professors have four danced and [sechs]F [Klavier gespielt]F. six piano played ‘As for students, three danced, five sang, and two played the piano. As for professors, four danced and six played the piano.’ Another possible scenario is given in (18), which is a variation of (16). This scenario also yields a multiple wh-question, as in (19). In the corresponding ST, the split MP as well as a part of the VP is in the focus.

Pragmatics of split quantifier constructions 243

(18) Scenario 3: At the party for the Department of Linguistics held yesterday, people had different drinks. As for students, three had beer, five had wine, and two had vodka. As for professors, four had wine and six had rum. (19) Q: Wieviele Leute haben während der Party was getrunken? how many people have during the party what drunk ‘How many people drank what at the party?’ A: [Studenten]T haben [Bier]F [drei]F getrunken, [Wein]F [fünf]F students have beer three drunk wine five getrunken, und [Rum]F [zwei]F getrunken. drunk and rum two drunk [Professoren]T haben [Bier]F [vier]F getrunken professors have beer four drunk und [Wein]F [sechs]F getrunken, and wine six drunk ‘As for students, three had beer, five had wine, and two had rum. As for professors, four had beer and six had wine.’ Summing up, in the German ST, the host NP must be a contrastive topic and the split MP must be in the focus. The verbal predicate can be constant, as shown with Scenario 1, or it can vary, as shown with Scenarios 2 and 3. I call the first case Type I and the second case Type II. The following table summarizes the properties of the two types of contexts for ST: Table 1. Two types of contexts for German Split NP Topicalization

Host NP

Split MP

VP

Type I: Scenario 1 ((14), (15))

Contrastive topic

Focus

Constant

Type II: Scenario 2 ((16), (17))

Contrastive topic

Focus

Entirely different

Type II: Scenario 3 ((18), (19))

Contrastive topic

Focus

Partially different

244 Cross-linguistic aspects of quantification and compositionality 3.2. Reconsideration of the semantic properties In Chapter 2, I showed that the German ST is incompatible with singleoccurrence events and that it lacks collective interpretations. In this section, I reexamine these examples by putting them in contexts that elicit the appropriate topic-focus structure. In the following, I consider two types of contexts in turn. I conclude that monotonicity analysis fares better in accounting for the full range of data and for the similarities between the German ST and the Japanese FQ construction.

3.2.1. Type I contexts Let us first examine Type I contexts, where the VP is constant (see (15)). The first semantic property to be considered is incompatibility with singleoccurrence events. The relevant example is repeated in (20). (20) ?? Studenten haben Peter drei umgebracht. students have Peter three killed ‘Three students killed Peter.’

(= (12))

I briefly illustrated in section 3.1 the pragmatic oddity of this example. Let us elaborate this point more carefully by invoking a Type I context. As shown in (21), for Studenten ‘students’ to be contrastive, there must be some group of non-students such as a group of professors who killed Peter. However, this context would suggest that Peter was killed multiple times, which makes (21A) infelicitous. Thus, the pragmatic analysis successfully predicts incompatibility with single-occurrence events. (21) Q: Wieviele Leute haben Peter umgebracht? how many people have Peter killed ‘How many people killed Peter?’ ?? A: [Studenten]T haben ihn [drei]F umgebracht, students have him three killed und [Professoren]T haben ihn [zwei]F umgebracht. and professors have him two killed ‘As for students, three killed him, and, as for professors, two killed him.’

Pragmatics of split quantifier constructions 245

Another property of the ST is the lack of collective readings, as in (22). (22) Jungen haben drei ein Modellboot boys have three a model boat ‘Three boys built a model boat.’ OK distributive, ??collective

gebaut. built

When (23Q) is answered by a bare numeral, as in (23A), or by a non-split MP construction, as in (23A’), both distributive and collective readings are available. In contrast, the ST in (24), as an answer to (23Q), lacks a collective reading. The unavailability of the collective reading in (24) cannot result from the focus on the numeral, since (23A), where the numeral is in the focus, allows the collective reading. It cannot result from the topic status of the host NP since (25), where the host NP is a topic, allows both distributive and collective readings. Hence, the pragmatic constraint cannot explain the lack of a collective reading in (24). (23) Q: Wieviele Kinder haben ein Modellboot gebaut? how many children have a model boat built A: [Drei]F. three OK distributive, OKcollective A’: [Drei Jungen]F haben ein Modellboot gebaut. three boys have a model boat built ‘Three boys built a model boat.’ OK distributive, OKcollective (24) [Jungen]T haben ein Modellboot [drei]F gebaut. boys have a model boat three built (Und [Mädchen]T haben ein Modellboot [fünf]F gebaut.) ‘As for boys, three built a model boat. (And as for girls, five built a model boat.)’ OK distributive, ??collective (25) Q: Wo haben Kinder ein Modellboot gebaut? where have children a model-boat built ‘Where did children build a model boat?’

246 Cross-linguistic aspects of quantification and compositionality A: [Jungen]T haben ein Modellboot [im Klassenzimmer]F gebaut. boys have a model boat in-the classroom built (Und [Mädchen]T [in der Küche]F.) ‘Boys built a model boat in the classroom. (And girls in the kitchen.)’ OK distributive, OKcollective In sum, pragmatic analysis with a Type I context predicts that the ST cannot occur with single-occurrence events, but it cannot account for why the ST lacks collective readings. In contrast, monotonicity analysis can account for both properties, as shown in Chapter 2.

3.2.2. Type II contexts Let us now turn to the second type of contexts, where the entire verbal predicate or some part of it is in the focus along with the split MP (see (17) and (19)). The first property I evaluate is incompatibility with singleoccurrence events. Example (26) provides a context where the VP is entirely different, and (27) provides a context where the VP is partially different. In these examples, since the VPs are not constant, the pragmatic infelicity observed with the Type I context in (21A) does not arise; the context does not require a single-occurrence event to occur multiple times. Indeed, some informants judged these examples as relatively acceptable. However, most of the informants agreed that these examples are still infelicitous to some degree, which cannot be explained by the topic-focus structure alone. (26) Type II: entirely different VP [The teacher found out that the children were involved in some mischief.] Q: Was haben die Kinder heute angerichtet? what have the children today committed ‘What bad things did the children do today?’ Q’: Wieviele Kinder haben heute was angerichtet? how many children have today what committed ‘How many children did what bad things today?’

Pragmatics of split quantifier constructions 247

A: ?(?)[Jungen]T haben [sechs]F [die Statue zerstört]F, und boys have six the statue destroyed and [Mädchen]T haben [zwei]F [die Vase zerbrochen]F. girls have two the vase broken ‘As for boys, six destroyed the statue, and as for girls, two broke the vase.’ (27) Type II: partially different VP [The statue was found broken and the teacher tracked down 10 children (7 boys and 3 girls) who were involved in this mischief.] Q: Was haben die Kinder mit der Statue angerichtet? what have the children with the statue committed ‘What did the children do to the statue?’ Q’:Wieviele Kinder haben was mit der Statue angerichtet? how many children have what with the statue committed ‘How many children did what with the statue?’ A: [Jungen]T haben sie [zwei]F [getreten]F boys have it two kicked und [fünf]F [geschlagen]F. and five hit ?(?) [Mädchen]T haben sie (dann) [drei]F [zerstört]F. girls have it then three smashed ‘As for boys, two kicked it and five hit it. Then three girls smashed it.’ The second property to be considered is the lack of collective readings. The relevant examples are given in (28) with entirely different VPs and in (29) with partially different VPs. (28) Type II: entirely different VP Q: Wieviele Kinder haben heute was gemacht? how many children have today what do ‘How many children did what today?’ A: [Jungen]T haben [drei]F [ein Modellboot gebaut]F boys have three a model-boat built und [fünf]F [getanzt]F. and five danced [Mädchen]T haben [vier]F [getanzt]F und [zwei]F [gesungen]F. girls have four danced and two sung

248 Cross-linguistic aspects of quantification and compositionality ‘As for boys, three built a model boat and five danced. As for girls, four danced and three sang.’ build a model boat: OKdistributive, ?collective (29) Type II: partially different VP Q: Was haben die Kinder angehoben? what have the children lift ‘What did the children lift?’ A: [Jungen]T haben [die Kiste]F [drei]F angehoben boys have the box three lifted und [den Tisch]F [fünf]F. and the table five [Mädchen]T haben [den Stuhl]F [vier]F angehoben. girls have the chair four lifted ‘As for boys, three lifted the box and five lifted the table. As for girls, four lifted the chair.’ OK distributive, ?(?)collective In these examples, the degree of acceptability of collective readings seems to vary among the informants. That contextual factors influence the acceptability of collective interpretations may suggest that the lack of collective readings does not result from monotonicity, but rather from pragmatics. Nevertheless, the informants who judged the collective readings in (28) and (29) as relatively acceptable still rejected the collective reading in (24) under the Type I context. Thus, it seems that pragmatic factors influence the acceptability of collective readings only when there are multiple foci. I have no explanation for this observation at this point, and thus I leave it for future research.

3.3. Summary of section 3 Table 2 below summarizes the data presented in this section. A pragmatic analysis can account for some semantic properties of STs, but it is unable to account for the full range of data. Furthermore, as mentioned in section 3.1, the Japanese FQ construction does not involve a special topic-focus structure, yet it has the same semantic properties as the German ST. The monotonicity analysis can account for all semantic properties as well as crosslinguistic parallelism.

Quantification and compositionality 249 Table 2. Comparison between pragmatic and semantic accounts

Semantic properties:

Incompatibility with single-occurrence event

Lack of collective readings

Pragmatic account: Type I Type II

explainable not explainable

not explainable (multiple foci?)

Monotonicity account:

explainable

explainable

4. Quantification and compositionality In section 2, we saw that non-split and split MP constructions in Greek and Catalan have the same semantic properties as non-split and split MP constructions in Japanese and German, indicating that monotonicity may be universal in nature. Another question that arises is whether the proposed analysis (or parts of it) can be extended to other constructions in other languages. In this section, I investigate here three sets of empirical data, namely, for the most part in English and hotondo ‘most’ in Japanese (section 4.1), pluractional markers (section 4.2), and cross-categorial particles (section 4.3).

4.1. For the most part in English and hotondo ‘most’ in Japanese It has been claimed that for the most part in English may trigger the effect of quantification over individuals introduced by plural definite NPs (Berman 1991, Lahiri 1991, 2002, Williams 2000). This is referred to as the Quantificational Variability Effect (QVE) (see also section 5 below). In (30), the adverbial expression for the most part quantifies over the definite NP his friends, evoking the interpretation ‘John likes most of his friends’. (30) (For the most part,) John(, for the most part,) likes his friends. In Nakanishi and Romero (2004), we propose that for the most part introduces (focus-sensitive) quantification over the domain of events and that different ways of “cutting” or measuring this domain will yield various readings (the QVE reading in (30), the temporal reading in (32), and the path reading in (34)). The different ways of “cutting” events translate to the

250 Cross-linguistic aspects of quantification and compositionality different homomorphisms (from events to individuals, to times, and to paths) proposed in Chapter 2. For example, (30) involves a homomorphism from the John’s-liking events to [[his friends]] . As a result, for the most part quantifies over [[ his friends]] , yielding the interpretation ‘most of his friends’. Moreover, Nakanishi and Romero show that, under the QVE reading, sentences with for the most part lack collective interpretations, as shown in (31). This is because a homomorphism from events to individuals always yields a distributive reading (see Chapter 2: section 3.2.2 for details). (31) For the most part, the girls built a sand castle. OK distributive, *collective The proposed analysis further extends to other readings of for the most part. For example, Nakanishi and Romero point out that (32) has the reading that Amy spent most of yesterday building a sand castle. This reading obtains when for the most part quantifies over times mapped from events by a homomorphism. Under this temporal reading, a collective reading is permitted, as shown in (33). Recall that the collective reading in (31) is disallowed because of the homomorphism from events to individuals. The homomorphism involved in (33) is from events to times, not to individuals. Hence nothing prohibits the collective reading in (33). (32) Q: What did Amy do yesterday? A: For the most part, she was building a sand castle. (33) Q: What did the boys do yesterday afternoon? A: For the most part, they were building a sand castle. OK distributive, OKcollective In the same vein, the Spanish example in (34) allows both distributive and collective interpretations. This example involves a homomorphism from events to paths, thus the collective reading obtains, just as in (33). (34) Los chichos abrieron la puerta en su totalidad. the boys opened the door in its totality ‘The boys opened the door all the way.’ OK distributive, OKcollective

Quantification and compositionality 251

In sum, the analysis proposed in Nakanishi and Romero (2004) shows that the analysis of split MP constructions proposed in Chapter 2 directly extends to for the most part in English. As additional data, I present examples of the split hotondo ‘most’ in Japanese in (35), where the same range of interpretations obtains. As proposed in Chapter 2, the measure function associated with split MPs applies to events. When there is a homomorphism from events to other domains, the measure function ends up applying to elements mapped from events by the homomorphism. With this mechanism, hotondo ‘most’ is able to quantify over different domains, namely, individuals in (35a), times in (35b), and paths in (35c). (35) a. Gakusei-ga paatii-de hotondo odot-ta. student-NOM party-at most dance-PAST ‘Most (of the) students danced at the party.’ b. John-ga paatii-de hotondo odot-tei-ta. John-NOM party-at most dance-PROG-PAST ‘John was dancing at the party most of the time.’ c. John-ga doa-o isoide hotondo ake-ta. John-NOM door-ACC quickly most open-PAST ‘John quickly opened the door most of the way.’

4.2. Pluractional markers The present analysis also extends to morphological markings for verbal pluralization, which I discuss briefly. Some languages are able to morphologically express plurality of events. For instance, in ǂHoan (a moribund Khoisan language spoken in southeastern Botswana), kí- is attached to a verb to express plurality related to events (Collins 2001). In (36a), when kíis attached to tchi ‘shoot’, it gives the sense of repeated action. In (36b), when kí- is attached to kini ‘want, look for’, it yields the interpretation ‘looking around’. Morphological markers such as kí- in ǂHoan that indicate plurality of events are called pluractional markers (Newman 1990). (36) a. Jefo kí-tchi-tcu-‘a ʘ’u ki ||a’’a-qa Jeff PL-shoot-REP PERF duiker PREP arrow-PL ‘Jeff shot at the duiker with arrows.’

252 Cross-linguistic aspects of quantification and compositionality b. ya ‘a-kí- kini-q||o ʘ’u 3SG PROG-PL-want-around duiker ‘He is looking around for a duiker.’

(Collins 2001: 464)

It is well known that pluractional markers do not simply reflect the plurality of events, but evoke a wide range of interpretations associated with multiplicity of actions (Cusic 1981, Mithun 1988, Newman 1990, Lasersohn 1995, Ojeda 1998, Collins 2001, Yu 2003, and many others). Based on Barker’s (1964) work on pluractional markers in Klamath, Lasersohn (1995) proposes the semantics of V-PA (a combination of a verb V and a pluractional marker PA) in (37), where X ranges over sets of events: “a pluractional verb will hold true of a group of events iff its corresponding ‘singular’ verb holds true of each individual event in the group” (Lasersohn 1995: 241). In (37), card(X) ≥ n means that the cardinality of X is equal to or greater than a pragmatically fixed number n. (37) V-PA(X) ↔ ∀e∈X[V(e)] ∧ card(X) ≥ n

(Lasersohn 1995: 241)

Lasersohn (1995) further identifies several groups of interpretations available with pluractional markers; temporal iteration, spatial scattering, and separate individuals. These interpretations have a notion of distributivity in common, that is, the events in the set denoted by the pluractional verb are distributed over different times, different spaces, or different participants. To capture these interpretations, Lasersohn proposes the semantics of V-PA in (38): f is a function from events to other domains, and ¬f(e) ∘ f(e’) means that f(e) and f(e’) do not overlap. The notion of overlap is defined in (39): two sets overlap iff they have a non-empty intersection. The identity of f determines which interpretation obtains with a pluractional marker. (38) V-PA(X) ↔ ∀e,e’∈X[V(e) ∧ ¬f(e) ∘ f(e’)] ∧ card(X) ≥ n Temporal: f = τ Spatio-temporal: f = K Participant-based: f = θ, where θ is a thematic relation assigned by V (Lasersohn 1995: 256) (39) X ∘ Y iff ∃Z[Z = X ∩ Y ∧ Z ≠ ∅]

(Lasersohn 1995: 223)

The functions in (38) are not ad hoc tools proposed only for pluractional verbs: independently from the semantics of pluractional markers, Lasersohn

Quantification and compositionality 253

uses three types of functions from events, i.e., the temporal function τ, the spatio-temporal function K, and the participant-based function θ, for the analysis of together in English. See Lasersohn (1995) for details. Clearly, the analysis of pluractional markers proposed by Lasersohn (1995) is analogous to the analysis of split MP constructions and verbal comparatives proposed in this book, where there is a homomorphism from events to other domains. In the range of data discussed in Lasersohn (1995) and in this book, the mechanism of a homomorphism plays a crucial role in accounting for various interpretations obtained with a single syntactic configuration.

4.3. Cross-categorial quantification Throughout this book, I emphasized that MPs such as two feet have a wide distribution, as in two feet of rope, walk two feet, two feet long, and so on (Jackendoff 1977). In this section, I show that MPs are not alone in having cross-categorial distribution. For instance, some languages have particles that can occur with both nominal and verbal predicates, as in (40) and (41) from Carrier, an Athabaskan language of the Central Interior of British Columbia. (40) Bet ʌzna ʔʌg ʌs-i ʔi za haninzʌn. washing-machine it only he-wants ‘The only thing he wants is a washing machine.’

(Poser 1999: 109)

(41) Ts’udʌn ʌtso za ʔʌtni.3 child he-cries only he-says ‘The child keeps crying.’

(Poser 1999: 111)

The particle za takes an element on its left in its scope and adds the interpretation ‘only’. In (40), za takes the nominal predicate ʔi ‘it’ (which refers to a washing-machine) in its scope, and yields the interpretation ‘only a washing machine’. In (41), za takes the verbal predicate ʌtso ‘he-cries’ in its scope, and yields the interpretation ‘keep on crying’. We can clearly see the correlation between these two interpretations: za gives a sense of exclusiveness of an element, regardless of what element is in its scope. When the 3. According to Poser (1999), ʔʌtni ‘he-says’ is a dummy verb that is used to create the preferred word order.

254 Cross-linguistic aspects of quantification and compositionality element is a nominal predicate, za adds an implication ‘only that nominal predicate’. When the element is a verbal predicate, we obtain ‘only that verbal predicate’, which naturally gives rise to the interpretation ‘keep on doing’.4

4.4. Summary of section 4 In this section, I presented some data relevant to the analysis proposed for split MP construstions (and also for verbal comparatives). I showed that for the most part in English makes use of the same measurement strategy as that of split MP constructions in that both constructions involve a homomorphism from events to other domains. Then I introduced Lasersohn’s (1995) analysis of pluractional markers and showed that the various interpretations of pluractional markers can be accounted for by making use of a homomorphism. Lastly, I briefly discussed some data on cross-categorial quantification. Before concluding this section, I should like to mention another piece of empirical data possibly related to the present analysis, namely, adverbial readings with DP-internal adjectives (Larson 1999, Zimmermann 2002, 2003). For example, in (42), the DP-internal adjectives occasional and individual can have the DP-external interpretations occasionally and individually. (42a) can mean ‘occasionally, a sailor strolled by’ and (42b) can mean ‘students entered the room individually (i.e., one by one)’. This is reminiscent of the proposed interpretation of split MP constructions, where a NP-external split MP is associated semantically with the NP. How to connect the semantic mechanisms of these two constructions is an open question for future work. (42) a. The/An occasional sailor strolled by. b. Individual students entered the room.

(Zimmermann 2003: 249)

4. Perhaps my point is better illustrated with the following case, brought to my attention by Richard Larson (personal communication). Some languages have a particle that means ‘another’ with a nominal predicate and ‘again’ with a verbal predicate. Another example would be a particle which means ‘whole’ with a nominal predicate and ‘completely’ with a verbal predicate. Unfortunately, I was unable to obtain examples of these quantificational particles.

Quantification over events and over situations 255

5. Quantification over events and over situations Having demonstrated some cross-linguistic extensions of the proposed analysis, I briefly discuss another direction to which the proposed analysis extends, namely, quantification over situations. In Chapter 2, I argued that the measure function in split MP constructions measures events denoted by a VP. More precisely, with a homomorphism from a lattice of events to a lattice of individuals, the measure function applies to individuals mapped from events. In other words, the measure function indirectly measures events by measuring individuals mapped from events. In Chapter 3, I argued that a split MP is an adjunct to a verbal predicate. Thus, a split MP syntactically combines with, and correspondingly semantically measures, a verbal predicate. For example, in (43), the split function associated with the split MP two applies to [[ boys]] mapped from the dancing events by a homomorphism. Although the split MP combines with the VP dance in the syntax, it is semantically associated with boys with the help of this homomorphism. (43) a. Otokonoko-ga kinoo huta-ri boy-NOM yesterday two-CL ‘Two boys danced yesterday.’ b. Jungen haben gestern zwei boys have yesterday two

odot-ta. dance-PAST getanzt. danced

Furthermore, we saw in section 4.1 that this analysis can be extended to for the most part in English, which shows the quantificational variability effect (QVE) over a plural definite NP. For instance, the sentence For the most part, John likes his friends has the interpretation ‘John likes most of his friends’. It is well known that the QVE over an indefinite NP is possible with the presence of so-called adverbs of quantification (e.g., always, usually), as in (44) (von Fintel 1994, among others). Example (44) has the interpretation ‘all blue-eyed bears are intelligent’. Under this interpretation, always has the effect of semantically quantifying over a blue-eyed bear, although syntactically it is an adverb that combines with the verbal predicate. (44) A blue-eyed bear is always intelligent.

256 Cross-linguistic aspects of quantification and compositionality It has been argued that the QVE with adverbs of quantification involves a correspondence between individuals and minimal situations containing each individual. Thus, split MP constructions and the QVE may make use of a similar mapping strategy, although they differ in that the former involves events and the latter situations. I show that quantification over events and quantification over situations are fundamentally different in at least two respects. First, while my analysis of monotonicity imposed on the range of a homomorphism forces a distributive reading, the definition of a situation that exemplifies a proposition p in Kratzer (1998) — an “extended” notion of a minimal situation — does not force distributivity. For example, for Kratzer, a situation s exemplifies the proposition ‘that there are horses’ if and only if s contains horses (possibly more than two) and nothing else. This means that, in sentences like (45a), whose denotation is given in (45b), the situations quantified over by always do not need to contain only two students each but they may each contain more students. Hence, (45) is judged to be true when each situation s contains a team of ten Penn students, who collectively build a raft in s’. (45) a. Students from Penn always build a raft. b. λw0. ∀s[ s≤w0 ∧ s contains Penn students and nothing else → ∃s’[ s’≤s ∧ Penn students build a raft in s’ ] ] Second, as discussed in Nakanishi and Romero (2004), for the most part quantifies over events (see section 4.1). Nakanishi and Romero present examples of for the most part under the QVE reading, as in (46), and the examples of usually / always under the QVE reading, as in (47). Examples (46) show that for the most part can quantify over the many (generic) events, as in (46a), or over parts of one episodic event as in (46b). In contrast, examples (47) show that usually / always, which involves quantification over situations, cannot be used in an episodic context, as the infelicity of (47b) suggests. (46) a. For the most part, the students who sit over there are smart. b. For the most part, the students sitting over there now are smart. (47) a. The students who sit over there are {usually / always} smart. b.# The students sitting over there now are {usually / always} smart.

Quantification over events and over situations 257

In this section, I discussed some differences between quantification over events and quantification over situations. Obviously, the discussion here is far from a complete comparison of the two, and a further investigation is required to reach a fuller understanding of the phenomena.

Chapter 6 Concluding remarks

This book investigated the following three issues in the fields of semantics and the syntax/semantics interface by examining the grammar of measurement constructions: (1)

a. Formal properties of measurement constructions and language universals b. Mechanism of measurement in the verbal domain and compositionality c. Uniform semantics of measure phrases and cross-categorial nature of measure functions

In particular, I examined the formal properties of various measurement constructions, namely, non-split and split MP constructions in Japanese and German, and comparative constructions in Japanese and English. The investigation demonstrated that these constructions can be categorized into two classes depending on whether the construction is sensitive to the monotonicity constraint in the nominal domain or in the verbal domain. Specifically, constructions involving measurement in the nominal domain show semantic properties explained by the monotonicity constraint in the nominal domain, while constructions involving measurement in the verbal domain show semantic properties explained by the monotonicity constraint in the verbal domain. Since Japanese and German are typologically distinct languages, the finding suggests that the categorization of measurement constructions based on monotonicity may be universal. This point is strengthened by the fact that the monotonicity analysis also applies to split MP constructions in Greek and Catalan (Chapter 5: section 2). Table 1 summarizes the domains of measurement and the formal properties of measurement constructions examined in this book.

Concluding remarks 259 Table 1. Domains of measurement and formal properties of measurement constructions

Domains of measurement

Formal properties

Measurement constructions

Nominal domain

Monotonicity in the nominal domain

- Pseudopartitives in English (Ch 2, 3) - Non-split MP constructions in Japanese and German (Ch 2, 3) - Too comparative in English (Ch 4)

Verbal domain

Monotonicity in the verbal domain

- Split MP constructions in Japanese, German, Greek, and Catalan (Ch 2, 3, 5) - V-sugiru comparative in Japanese (Ch 4) - Too comparative in English (Ch 4) - for the most part in English (Ch 5)

I further proposed a mechanism for measurement in the verbal domain which maintains the compositionality of grammar. In Chapter 2, we saw that a split MP syntactically combines with, and semantically operates on, a verbal predicate, yet there is a strong intuition that it somehow measures a nominal predicate as well. This intuition was captured by using a homomorphism (i.e., a structure-preserving mapping) from events to individuals, which makes a split MP indirectly measure events by measuring individuals. I argued that this mechanism is capable of accounting for some semantic properties of constructions involving measurement in the verbal domain ((in)compatibility with single-occurrence events, incompatibility with individual-level predicates, and (un)availability of collective interpretations). The data presented in this chapter showed that the proposed analysis possibly extends to a wider range of cross-linguistic data. The current analysis also captured the cross-categorial distribution of MPs (e.g., two feet of rope, walk two feet, two feet long). A distinction was made between MPs and measure functions. I posited that a measure function µ intervenes between a MP and the measured category, as in (2). I argued that, while MPs are semantically uniform (Schwarzschild 2002, 2006), measure functions are cross-categorial, deriving the wide distribution of MPs.

260

Concluding remarks

(2) P (e.g., NP, VP, V’, …) MP

µ

I hope to have shown that the proposed analysis, which makes use of the notions of monotonicity, homomorphic mappings, and cross-categorial measure functions, provides us with an adequate tool to account for the grammar of the different measurement constructions given in Table 1.

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Index

*-operator (“star”-operator), 16, 33, 83 ∃-operator, 21–22, 154, 158 adjectival comparatives, see comparative constructions adverbial analysis, 123–125, 134–135 agent, 27–28 argument structure, 26, 159 aspectual classes, 21 A(djective)-sugiru comparatives, see comparative constructions atelic predicates, 22, 33–34, see also atelic–telic distinction atelic-telic distinction, 21–23, 33–34, 61–62, 96–98 atomic, 15–16, 33

comparative quantification, 173, 180– 183, 194, 211, 227, 232 compositionality, 5–6, 79, 109, 235 contrastive topic, 239–243 count nouns, 13–17, 34, see also masscount distinction cover readings, 102 cumulative reference, 14, 23, 28 cumulativity, 23, 28–29, 160–162 Cumulativity Universal, 28–29

Davidsonian, 26–27 degree argument, 176, 179–180 degree phrase (DegP), 176 Derived Kind Predication (DKP), 20, 156 differential, 178–179, 184–185, 200– 208, 219 cardinality, 47, 68, 71–72, 157–168, distributive and collective readings, 57– 180, 195–201 59, 66, 75–77, 80–88, 103–106, 233, c-command, 116–117, 135–136 238, 245–248 classifier, 2, 17–20, 36, 47, 68, 112–113, distributive operator, 82–84 130–131 distributive predicates, 84–85 collective predicates, 84–85, 100–103 distributive readings, see distributive collective readings, see distributive and and collective readings collective readings distributive sub-entailments, 102 collectivizers, 98–100, 157 divisive reference, 14 comparative constructions durative adverbs, 22 adjectival comparatives, 175–179, 186–188, 192–194, 223–224 event arguments, 24–26 A(djective)-sugiru comparatives, Event Identification, 30–31, 156 188, 191–194 too comparatives, 183–186, 227–231, event-related reading, 72–73 event sum operator (∪E), 32 233 external argument, 27–32, 138–140, V(erb)-sugiru comparatives, 188, 145–146, 159, 208–209 191–192, 194–195, 232–233 comparative quantifiers, 173, 188, 194– external split measure phrase (MP) construction, 103, 159 198

282 Index floating quantifiers (FQs), 35, 117–118, 126 floating quantifier (FQ) construction, 2, 117–118, 126, 155–157, 162–163 focus, 239–243 for the most part, 249–251 Functional Application, 151 Government and Binding Theory, 12– 13 gradable adjectives, 175–176, 192, 223–224 gradable adverbs, 218–221 gradable verbs, 216 group-forming operation (↑), 76, 84, 99 homomorphism, 6–7, 69–72, 106–108, 155, 159–169, 201–205 host NP, 38 incremental relationship, 105–106, 209–210 individual-level predicates, see stagelevel and individual-level predicates individual sum operator (∪I), 15 internal arguments, 27–28, 103–106, 138–140, 146, 159, 208–209 internal split measure phrase (MP) construction, 103, 159 kinds, 19–20, 32, 156, 163 lattices, 14–17, 32–34, 71–72 Logical Form (LF), 12–13 mass nouns, 13–17, 18–20, 34, see also mass-count distinction mass-count distinction, 13–17, 20, 34, 40–42, 45, 48–49 max, 176–177 m-command, 168–169 measure function, 9–10, 42–45, 152– 155, 168–170, 181–182, 204

measure phrases (MPs), 7–10, 36, 113– 115, 170, 173 measurement construction, 3–4, 259 measurement scheme, 43 monotonicity, 4, 43–45, 78–80, 186, 211–214, 236 monotonicity constraint, 43–45, 60–61, 152–153, 155, 211–214 neo-Davidsonian, 27 non-floating quantifiers (non-FQs), 35 non-split measure phrase (MP) construction, 38, 111–116, 149–154, 206–207, 236–238 non-split measure phrases (MPs), 38 non-split quantifier (Q) construction, 1– 2, 109–110 operation of semantic pluralization, 16, see also *-operator part-of relation (≤), 15–16, 32 path trace function, 108 pluractional marker, 251–253 plurality, 13, 32–33, 80, 83–87 pluralization, 16, 33 Predicate Abstraction Rule, 174 Predicate Modification, 24, 151 presupposition, 152 progressive, 90–96 prosodic effects, 140–141 pseudopartitives, 41–42, 147–149 quantification over situations, 255–257 quantificational variability effect (QVE), 12, 236, 255–256 Quantifier Raising (QR), 13, 174 scrambling, 63–64 secondary predicates, 221–223 single-occurrence event, 53–54, 61–64, 74, 94–96, 212–213, 236–237, 244, 246–247

Index 283 split measure phrase (MP) construction, 38, 154–158, 236–238 split measure phrases (MPs), 38 Split NP Topicalization (ST), 2, 37–38, 141–146, 157–158, 164–165, 239– 243 split quantifier (Q) construction, 1–2, 109 stage-level predicates, see stage-level and individual-level predicates stage-level and individual-level predicates, 54–57, 64–66, 74–75, 237–238 stranding analysis, 117–118 -sugiru, 2–3, 172–173, see also comparative constructions telic predicates, 22, 33–34, see also atelic-telic distinction

telicity, see atelic-telic distinction temporal distributivity, 89–90 temporal trace function, 107 theme, 27–29 time span adverbs, 22 too comparatives, see comparative constructions Trace and Pronouns Rule, 174 type-shifting operation, 20–21 Unique Role Requirement, 30 Uniqueness of Objects, 162 VoiceP, 28, 30 V(erb)-sugiru comparatives, see comparative constructions