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VOLUME 27 NUMBER 3 AUGUST 2010 CONTENTS Chris Cummins and Napoleon Katsos Comparative and Superlative Quantifiers: Prag...

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VOLUME 27 NUMBER 3 AUGUST 2010

CONTENTS Chris Cummins and Napoleon Katsos Comparative and Superlative Quantifiers: Pragmatic Effects of Comparison Type

271

307

Susan Rothstein Counting and the Mass/Count Distinction

343

Short Contributions

399

FORTHCOMING ARTICLES Adrian Brasoveanu: Decomposing Modal Quantification Tamina Stephenson: Control in Centred Worlds Eric Swanson: On Scope Relations between Quantifiers and Epistemic Modals


Jungmee Lee and Judith Tonhauser Temporal Interpretation without Tense: Korean and Japanese Coordination Constructions

Terje Lohndal More on Scope Illusions

JOURNAL OF SEMANTICS

JOURNAL OF SEMANTICS


Journal of

SEMANTICS www.jos.oxfordjournals.org

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issn 0167-5133 (Print) issn 1477-4593 (Online)

JOURNAL OF SEMANTICS A N I NTERNATIONAL J OURNAL FOR THE I NTERDISCIPLINARY S TUDY THE S EMANTICS OF N ATURAL L ANGUAGE MANAGING EDITOR: ASSOCIATE EDITORS:

OF

Philippe Schlenker (Institut Jean-Nicod, Paris; New York University) Danny Fox (Massachusetts Institute of Technology) Rick Nouwen (Utrecht University) Maribel Romero (University of Konstanz) Robert van Rooij (University of Amsterdam) Mats Rooth (Cornell University) Bernhard Schwarz (McGill University) Roger Schwarzschild (Rutgers University) Yael Sharvit (University of Connecticut) Jesse Snedeker (Harvard University) Anna Szabolcsi (New York University) Zoltán Gendler Szabó (Yale University)

ADVISORY BOARD: Gennaro Chierchia (Harvard University) Beth Levin (Stanford University) Bart Geurts (University of Nijmegen) Barbara Partee (University of Massachusetts, Lila Gleitman (University of Pennsylvania) Amherst) Irene Heim (Massachusetts Institute of Technology) François Recanati (Institut Jean-Nicod, Paris) Laurence R. Horn (Yale University) Maribel Romero (University of Konstanz) Hans Kamp (Stuttgart University and University of Bernhard Schwarz (McGill University) Texas, Austin) Arnim von Stechow (University of Tübingen) Manfred Krifka (Humboldt University Berlin; ZAS, Berlin)Thomas Ede Zimmermann (University of Frankfurt)

EDITORIAL BOARD: Maria Aloni (University of Amsterdam) Pranav Anand (University of California, Santa Cruz) Ana Arregui (University of Ottawa) Nicholas Asher (IRIT, Toulouse; University of Texas, Austin) Chris Barker (New York University) Sigrid Beck (University of Tübingen) Rajesh Bhatt (University of Massachusetts, Amherst) Maria Bittner (Rutgers University) Peter Bosch (University of Osnabrück) Richard Breheny (University College London) Daniel Büring (University of California, Los Angeles) Emmanuel Chemla (Institut Jean-Nicod, Paris; LSCP, Paris) Jill G. de Villiers (Smith College) Paul Dekker (University of Amsterdam) Josh Dever (University of Texas, Austin) Regine Eckardt (University of Göttingen) Martina Faller (University of Manchester) Delia Fara (Princeton University) Lyn Frazier (University of Massachusetts, Amherst) Jeroen Groenendijk (University of Amsterdam) Elena Guerzoni (University of Southern California) Martin Hackl (Pomona College) Pauline Jacobson (Brown University) Andrew Kehler (University of California, San Diego) Chris Kennedy (University of Chicago) Jeffrey C. King (Rutgers University) Angelika Kratzer (University of Massachusetts,

Amherst) Peter Lasersohn (University of Illinois) Jeffrey Lidz (University of Maryland) John MacFarlane (University of California, Berkeley) Lisa Matthewson (University of British Columbia) Julien Musolino (Rutgers University) Ira Noveck (L2C2, CNRS, Lyon) Francis Jeffry Pelletier (University of Alberta) Colin Phillips (University of Maryland) Paul M. Pietroski (University of Maryland) Christopher Potts (Stanford University) Liina Pylkkänen (New York University) Gillian C. Ramchand (University of Tromsoe) Uli Sauerland (ZAS, Berlin) Barry Schein (University of Southern California) Benjamin Spector (Institut Jean-Nicod, Paris) Robert Stalnaker (Massachusetts Institute of Technology) Jason Stanley (Rutgers University) Mark Steedman (University of Edinburgh) Michael K. Tanenhaus (University of Rochester) Jos van Berkum (Max Planck Institute for Psycholinguistics, Nijmegen) Rob van der Sandt (University of Nijmegen) Yoad Winter (Utrecht University) Henk Zeevat (University of Amsterdam)

EDITORIAL CONTACT: [email protected] © Oxford University Press 2010 For subscription information please see back of journal.

Editorial Policy Scope Journal of Semantics aims to be the premier generalist journal in semantics. It covers all areas in the study of meaning, and particularly welcomes submissions using the best available methodologies in semantics, pragmatics, the syntax/semantics interface, cross-linguistic semantics, experimental studies of meaning (processing, acquisition, neurolinguistics), and semantically informed philosophy of language. Types of articles Journal of Semantics welcomes all types of research articles–with the usual proviso that length must be justified by scientific value. Besides standard articles, the Journal will welcome ‘squibs’, i.e. very short empirical or theoretical contributions that make a pointed argument. In exceptional circumstances, and upon the advice of the head of the Advisory Board, the Journal will publish ‘featured articles’, i.e. pieces that we take to make extraordinary contributions to the field. Editorial decisions within 10 weeks The Journal aims to make editorial decisions within 10 weeks of submission. Refereeing Articles can only be accepted upon the advice of anonymous referees, who are asked to uphold strict scientific standards. Authors may include their names on their manuscripts, but they need not do so. (To avoid conflicts of interest, any manuscript submitted by one of the Editors will be handled by the head of the Advisory Board, who will be responsible for selecting referees and making an editorial decision.) Submissions All submissions are handled electronically. Manuscripts should be emailed in PDF format to the Managing Editor [[email protected]], who will forward them to one of the Editors. The latter will be responsible for selecting referees and making an editorial decision. Receipt of a submission is systematically confirmed. Papers are accepted for review only on the condition that they have neither as a whole nor in part been published elsewhere, are elsewhere under review or have been accepted for publication. In case of any doubt authors must notify the Managing Editor of the relevant circumstances at the time of submission. It is understood that authors accept the copyright conditions stated in the journal if the paper is accepted for publication.

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JOURNAL OF SEMANTICS A N I NTERNATIONAL J OURNAL FOR THE I NTERDISCIPLINARY S TUDY THE S EMANTICS OF N ATURAL L ANGUAGE MANAGING EDITOR: ASSOCIATE EDITORS:

OF

Philippe Schlenker (Institut Jean-Nicod, Paris; New York University) Danny Fox (Massachusetts Institute of Technology) Rick Nouwen (Utrecht University) Maribel Romero (University of Konstanz) Robert van Rooij (University of Amsterdam) Mats Rooth (Cornell University) Bernhard Schwarz (McGill University) Roger Schwarzschild (Rutgers University) Yael Sharvit (University of Connecticut) Jesse Snedeker (Harvard University) Anna Szabolcsi (New York University) Zoltán Gendler Szabó (Yale University)

ADVISORY BOARD: Gennaro Chierchia (Harvard University) Beth Levin (Stanford University) Bart Geurts (University of Nijmegen) Barbara Partee (University of Massachusetts, Lila Gleitman (University of Pennsylvania) Amherst) Irene Heim (Massachusetts Institute of Technology) François Recanati (Institut Jean-Nicod, Paris) Laurence R. Horn (Yale University) Maribel Romero (University of Konstanz) Hans Kamp (Stuttgart University and University of Bernhard Schwarz (McGill University) Texas, Austin) Arnim von Stechow (University of Tübingen) Manfred Krifka (Humboldt University Berlin; ZAS, Berlin)Thomas Ede Zimmermann (University of Frankfurt)

EDITORIAL BOARD: Maria Aloni (University of Amsterdam) Pranav Anand (University of California, Santa Cruz) Ana Arregui (University of Ottawa) Nicholas Asher (IRIT, Toulouse; University of Texas, Austin) Chris Barker (New York University) Sigrid Beck (University of Tübingen) Rajesh Bhatt (University of Massachusetts, Amherst) Maria Bittner (Rutgers University) Peter Bosch (University of Osnabrück) Richard Breheny (University College London) Daniel Büring (University of California, Los Angeles) Emmanuel Chemla (Institut Jean-Nicod, Paris; LSCP, Paris) Jill G. de Villiers (Smith College) Paul Dekker (University of Amsterdam) Josh Dever (University of Texas, Austin) Regine Eckardt (University of Göttingen) Martina Faller (University of Manchester) Delia Fara (Princeton University) Lyn Frazier (University of Massachusetts, Amherst) Jeroen Groenendijk (University of Amsterdam) Elena Guerzoni (University of Southern California) Martin Hackl (Pomona College) Pauline Jacobson (Brown University) Andrew Kehler (University of California, San Diego) Chris Kennedy (University of Chicago) Jeffrey C. King (Rutgers University) Angelika Kratzer (University of Massachusetts,

Amherst) Peter Lasersohn (University of Illinois) Jeffrey Lidz (University of Maryland) John MacFarlane (University of California, Berkeley) Lisa Matthewson (University of British Columbia) Julien Musolino (Rutgers University) Ira Noveck (L2C2, CNRS, Lyon) Francis Jeffry Pelletier (University of Alberta) Colin Phillips (University of Maryland) Paul M. Pietroski (University of Maryland) Christopher Potts (Stanford University) Liina Pylkkänen (New York University) Gillian C. Ramchand (University of Tromsoe) Uli Sauerland (ZAS, Berlin) Barry Schein (University of Southern California) Benjamin Spector (Institut Jean-Nicod, Paris) Robert Stalnaker (Massachusetts Institute of Technology) Jason Stanley (Rutgers University) Mark Steedman (University of Edinburgh) Michael K. Tanenhaus (University of Rochester) Jos van Berkum (Max Planck Institute for Psycholinguistics, Nijmegen) Rob van der Sandt (University of Nijmegen) Yoad Winter (Utrecht University) Henk Zeevat (University of Amsterdam)

EDITORIAL CONTACT: [email protected] © Oxford University Press 2010 For subscription information please see back of journal.

Editorial Policy Scope Journal of Semantics aims to be the premier generalist journal in semantics. It covers all areas in the study of meaning, and particularly welcomes submissions using the best available methodologies in semantics, pragmatics, the syntax/semantics interface, cross-linguistic semantics, experimental studies of meaning (processing, acquisition, neurolinguistics), and semantically informed philosophy of language. Types of articles Journal of Semantics welcomes all types of research articles–with the usual proviso that length must be justified by scientific value. Besides standard articles, the Journal will welcome ‘squibs’, i.e. very short empirical or theoretical contributions that make a pointed argument. In exceptional circumstances, and upon the advice of the head of the Advisory Board, the Journal will publish ‘featured articles’, i.e. pieces that we take to make extraordinary contributions to the field. Editorial decisions within 10 weeks The Journal aims to make editorial decisions within 10 weeks of submission. Refereeing Articles can only be accepted upon the advice of anonymous referees, who are asked to uphold strict scientific standards. Authors may include their names on their manuscripts, but they need not do so. (To avoid conflicts of interest, any manuscript submitted by one of the Editors will be handled by the head of the Advisory Board, who will be responsible for selecting referees and making an editorial decision.) Submissions All submissions are handled electronically. Manuscripts should be emailed in PDF format to the Managing Editor [[email protected]], who will forward them to one of the Editors. The latter will be responsible for selecting referees and making an editorial decision. Receipt of a submission is systematically confirmed. Papers are accepted for review only on the condition that they have neither as a whole nor in part been published elsewhere, are elsewhere under review or have been accepted for publication. In case of any doubt authors must notify the Managing Editor of the relevant circumstances at the time of submission. It is understood that authors accept the copyright conditions stated in the journal if the paper is accepted for publication.

All rights reserved; no part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without prior written permission of the Publishers, or a licence permitting restricted copying issued in the UK by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1P 9HE, or in the USA by the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923. Typeset by TNQ Books and Journals Pvt. Ltd., Chennai, India. Printed by Bell and Bain Ltd, Glasgow, UK

JOURNAL OF SEMANTICS Volume 27 Number 3

CONTENTS CHRIS CUMMINS AND NAPOLEON KATSOS Comparative and Superlative Quantifiers: Pragmatic Effects of Comparison Type

271

JUNGMEE LEE AND JUDITH TONHAUSER Temporal Interpretation without Tense: Korean and Japanese Coordination Constructions

307

SUSAN ROTHSTEIN Counting and the Mass/Count Distinction

343

Short Contributions TERJE LOHNDAL More on Scope Illusions

Please visit the journal’s web site at www.jos.oxfordjournals.org

399

Journal of Semantics 27: 271–305 doi:10.1093/jos/ffq006 Advance Access publication March 18, 2010

Comparative and Superlative Quantifiers: Pragmatic Effects of Comparison Type CHRIS CUMMINS AND NAPOLEON KATSOS University of Cambridge

It has historically been assumed that comparative (‘more than’, ‘fewer/less than’) and superlative (‘at most’, ‘at least’) quantifiers can be semantically analysed in accordance with their core logical–mathematical properties. However, recent theoretical and experimental work has cast doubt on the validity of this assumption. Geurts & Nouwen (2007) have claimed that superlative quantifiers possess an additional modal component in their semantics that is absent from comparative quantifiers and that this accounts for the previously neglected differences in usage and interpretation between the two types of quantifier that they identify. Their semantically modal hypothesis has received additional support from empirical investigations. In this article, we further corroborate that superlative quantifiers have additional modal interpretations. However, we propose an alternative analysis, whereby these quantifiers possess the semantics postulated by the classical model and the additional aspects of meaning arise as a consequence of psychological complexity and pragmatic implicature. We explain how this model is consistent with the existing empirical findings. Additionally, we present the findings of four novel experiments that support our model above the semantically modal account.

1 INTRODUCTION There is an ever-burgeoning literature in semantics and pragmatics dealing with the interpretation of number terms. At first sight, the natural numbers appear ideal candidates for formalization using classical approaches borrowed from mathematical logic. However, this approach turns out to be fraught with difficulties, which continue to be debated at great length. Until recently, it has been assumed that certain categories of numerically quantified expressions can be formalized in a fairly intuitive way. This article deals with two classes of such expressions, comparative and superlative quantifiers. Comparative quantifiers are those of the form ‘more than’ and ‘fewer/less than’ and have Ó The Author 2010. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected].

Downloaded from jos.oxfordjournals.org by guest on December 31, 2010

Abstract

272 Comparative and Superlative Quantifiers

traditionally been regarded as equivalent to the mathematical symbols > and , respectively. Restricting our attention to cardinalities, it follows from this approach that superlative and comparative quantifiers are interdefinable, as in the following examples. (1) John has at most two cars 4 John has fewer than three cars. (2) Kelly has at least three children 4 Kelly has more than two children. Downloaded from jos.oxfordjournals.org by guest on December 31, 2010

This view is challenged by Geurts and Nouwen (2007), who argue that equivalence does not typically hold between comparative and superlative quantifiers. They observe four differences in the usage and interpretation of these types of quantifier. First, they note that superlative quantifiers admit a specific construal, absent from the comparative quantifier. Secondly, they identify differences in the patterns of inference that arise from the putatively equivalent sentences. Thirdly, they observe distributional differences between comparative and superlative forms. And finally, they claim that certain usages of comparative quantifiers give rise to ambiguity that does not follow from the superlative ‘equivalent’. To address these issues, they develop a proposal in which comparative and superlative quantifiers differ in modality. Geurts and Nouwen’s proposal gives rise to several empirically testable predictions, notably that the superlative quantifiers will be mastered more slowly by acquirers, that they will be disfavoured in processing and that they will give rise to different reasoning patterns. These proposals are investigated by Geurts et al. (2010), in a series of experiments. Broadly, the predictions are borne out, and thus, Geurts and Nouwen’s account is favoured by comparison with the classical approach. In this article, we develop an alternative proposal to that offered by Geurts and Nouwen (2007). Rather than proposing a modal component to the semantics of superlative quantifiers, we propose that there is a fundamental difference in complexity between expressions conveying < and > and those conveying < and >, which we will argue arises from the disjunctive nature of non-strict comparison. We will argue, following Bu¨ring (2007), that the use of superlative quantifiers triggers an implicature. We show that the classical model of quantifier semantics, augmented with this distinction, gives similar predictions to those made by Geurts and Nouwen, and is consistent with the data

Chris Cummins and Napoleon Katsos 273

they use to argue against the classical model. We further demonstrate that the data obtained by Geurts et al. (2010) are compatible with our account. We then conduct additional experiments that demonstrate the availability of inferences predicted to be unavailable by Geurts and Nouwen and the acceptability of statements they predict to be unacceptable. We show that these data are compatible with our augmented classical model. Finally, we argue that on the basis of these data, as well as considerations of parsimony and acquirability, the augmented classical model should be preferred to the semantically modal account.

As outlined above, the classical view of comparative and superlative quantifiers holds them to be interdefinable in a systematic way: ‘at most n’ ¼ ‘fewer than n + 1’, ‘at least n’ ¼ ‘more than n 1’. In addition to providing us with an elegant formal treatment of these entities, this account conforms with our naive intuitions about the truth conditions of numerically quantified statements. These intuitions require that ‘John has at most two children’ is false only in cases where the cardinality of the set {John’s children} is 3 or more, and ‘Kelly has at least three cars’ is false only in cases where the cardinality of the set {Kelly’s cars} is 2 or less. However, Geurts and Nouwen (2007) identify a number of areas in which this account is unsatisfactory. They are suspicious of interdefinability on the grounds that it implies that one set of quantifiers is entirely redundant, given the existence of the other.1 They also specify a number of additional objections to the analysis, as described in the following paragraphs. A key objection is that the inference patterns arising from the superlative quantifiers differ from those admitted by the comparative forms. Geurts and Nouwen argue that a sentence such as (3a) gives rise to the inference (3b) but not to the inference (3c), despite (3b) and (3c) being semantically identical on the classical view. 1

Arguably the quantifiers are not, even on the classical view, interdefinable on non-discrete sets such as are used in measurements: ‘more than 2 metres’ cannot be equivalent to ‘at least x metres’ for any x. This could license the existence of both types of quantifier, although by itself it does not explain why both are actually used in discrete cases. In this article, we follow Geurts and Nouwen (2007) in focusing on these discrete cases but note that our argument will have implications for the analysis of the more general continuous case.


2 PROBLEMS WITH THE CLASSICAL VIEW OF COMPARATIVE AND SUPERLATIVE QUANTIFIERS


(3) a. Dave had (exactly) three Martinis. b. Dave had more than two Martinis. c. Dave had at least three Martinis.

(4) a. There are at most two people who have that authority, namely the Queen and the Prime Minister. b.*There are fewer than three people who have that authority, namely the Queen and the Prime Minister. Geurts and Nouwen (2007: 537f) also note that the superlative quantifiers have a wider range than their comparative counterparts, citing the following examples. (5) a. Betty had three Martinis at most / *fewer than. b. At least / *More than Betty had three Martinis. They note that some contexts permit the comparative but not the superlative quantifier, though the prohibition is less clear-cut, as in (6). (6) Betty didn’t have ?at least / more than three Martinis. Finally, they claim that sentences with comparative quantifiers are sometimes ambiguous in a way that those with superlative quantifiers are not. In particular, they contrast (7a) and (7b). (7) a. You may have at most two beers. b. You may have fewer than three beers. Geurts and Nouwen argue that the latter (comparative) does not necessarily rule out the possibility that the addressee may have more than three beers; it merely grants permission to have a smaller number of beers. Although they admit that ‘this construal may seem far-fetched’ (2007: 539), they contend that this does represent a difference in


They support their intuitions by verifying this claim experimentally. Hence, it appears that the meanings of comparative and superlative quantifiers systematically differ in some profound way. In addition to these, Geurts and Nouwen collate data suggesting that the distribution of comparative and superlative quantifiers differs systematically. They observe that the argument of superlative quantifiers can have a specific construal, which is not licensed by the theoretically equivalent comparative quantifiers. This provides a referent for the ‘namely’ clause in (4a), which is unacceptable in (4b).


meaning between these two sentences that is not captured by the classical account. In summary, there are reasons arising from both the interpretation and distribution of these quantifiers to support the contention that the classical view of their meaning is inadequate. In the following section, we discuss the specific proposal outlined by Geurts and Nouwen (2007) for dealing with these puzzles.

Geurts and Nouwen (2007) propose an account of quantifier meaning in which superlative quantifiers have a modal component of meaning. Specifically, they consider example (8). (8)

Betty drank at least four highballs.

They ascribe to (8) a semantic formula that can be glossed as ‘the speaker is certain that there is a group of four highballs each of which was drunk by Betty, and considers it possible that Betty drank more than four highballs’ (552). For the corresponding ‘at most’ sentence, ‘Betty drank at most four highballs’, they obtain the analysis that ‘it grants the possibility that Betty had four highballs, and it excludes the possibility that she had more than four’ (ibid.). They also propose that comparative and superlative quantifiers differ in argument type. Their conjecture is that superlative quantifiers accept arguments of any Boolean type, that is, both propositional and predicative arguments. In this way, they analyse ‘At least it isn’t raining’ as an assertion ‘that the speaker is sure it isn’t raining, and that he considers it possible that something ‘‘better’’ than non-raining might be the case, as well’ (ibid.). Using their account, Geurts and Nouwen are able to give solutions to all the problems they previously discussed. From the assumption that comparative and superlative quantifiers are not interdefinable, it follows that there is no redundancy in the system. The more substantive issues raised in the preceding section may be resolved as follows.

The inference patterns involving superlative quantifiers are a subset of those arising from comparative quantifiers because of clashes of


3 THE SEMANTICALLY MODAL ACCOUNT OF SUPERLATIVE QUANTIFIER MEANING


In sum, Geurts and Nouwen’s modal theory of superlative quantifier meaning accounts well for the observed findings, modulo some concerns about the treatment of superlative quantifiers in conditional environments (to which we return later). In addition, their theory gives rise to empirically testable predictions. In the following section, we review the work done on investigating these predictions.

4 EMPIRICAL INVESTIGATION OF QUANTIFIER MEANING Geurts and Nouwen (2007) subject some of their intuitions about the inference patterns arising from these quantifiers to empirical investigation. However, their theory gives rise to a broader range of predictions that are also susceptible to testing by experimental means. Geurts et al. (2010) argue that three particular predictions arise from the modal view of superlative quantifier usage: (i) that superlative quantifiers give rise to different inference patterns to comparative quantifiers; (ii) that superlative quantifiers should be harder to learn than comparatives, on the basis of their additional semantic complexity; and (iii) that superlative quantifiers should be harder to process than comparatives, for the same reason.


modality. ‘At most n’ does not imply ‘at most n + 1’, ‘exactly n’ does not imply ‘at most n’ or ‘at least n’ and so on. The specific construal of the argument of the superlative quantifier is possible because its argument (e.g. ‘two people’) may be parsed as an existential quantifier. This is not legitimate in the comparative case because the comparative quantifier does not accept non-predicative arguments. The validity of superlative quantifiers in a broader range of contexts than comparative quantifiers stems from their ability to accept additional argument types. At the same time, the inappropriateness of superlative quantifiers in other contexts—for example, under the scope of negation—reflects their modal semantic content. The ambiguity in the fourth case does not arise in the modal case due to factors involving the semantic combination of modal expressions—Geurts and Nouwen refer to this as modal concord. Put simply, their view appears to be that the superlative quantifier enters unambiguously into a concord reading with the preceding modal, as these both express possibility.


In this section we summarize the work done by Geurts et al. to investigate these predictions, as well as the findings of other research bearing upon these questions.2

4.1 Inference patterns arising from comparative and superlative quantifiers

2 These experiments were conducted using native-speaker participants and in English unless otherwise stated. 3 This controls for informativeness and makes it more legitimate to compare upward- and downward-entailing quantifiers.


Supporting their intuitions, Geurts and Nouwen (2007) performed a pencil-and-paper experiment in which they asked participants to decide whether certain implications were valid. Broadly, their participants concurred that (in Dutch) ‘Beryl had three sherries’ implied both ‘Beryl had more than two sherries’ and ‘Beryl had fewer than five sherries’. By contrast, 78% of their participants rejected the implication ‘Beryl had at most four sherries’, and only about half accepted ‘Beryl had at least three sherries’. This technique was employed for a wider range of premise– conclusion pairs by Geurts et al. (2010), again in Dutch. Instead of using ‘fewer than five’ and ‘at most four’ as Geurts and Nouwen did, Geurts et al. used ‘fewer than four’ (accepted 93% of the time) and ‘at most three’ (accepted 61% of the time).3 They also added three further pairs of conditions: ‘at most two’ / ‘at most three’ (14% acceptance) v. ‘fewer than three’ / ‘fewer than four’ (71% acceptance), ‘at least three’ / ‘three’ (50% acceptance) v. ‘at most three’ / ‘three’ (18% acceptance) and ‘three or four’ / ‘at least three’ (96%) v. ‘two or three’ / ‘at most three’ (93%). As these latter two comparisons do not contrast superlative with comparative quantifiers, but instead explore the effect of entailment direction, we shall not discuss them further here. In summary, these data constitute additional evidence for the nonequivalence of comparative and superlative quantifiers in a reasoning context. Valid arguments involving comparative quantifiers seem to fail, in the opinion of the majority, when recast using superlative quantifiers that are ‘classically’ equivalent. Most strikingly, the inference from ‘at most two’ / ‘at most three’ succeeds in only 14% of cases, where the putatively equivalent ‘fewer than three’ / ‘fewer than four’ achieves 71% acceptance. This concurs with the prediction arising from Geurts and Nouwen’s account and thus offers it empirical support.


4.2 Delay in acquisition of superlative quantifiers Prior to Geurts and Nouwen’s (2007) prediction, the acquisition of comparative and superlative quantifiers had already been compared by Musolino (2004: 26–8). In his experiment, participants are given a selection of cards with zero to four objects on them and asked to select those with ‘exactly 2’, ‘at least/most 2’ or ‘more than 2’. Adults performed at or near ceiling in all conditions. However, while children (aged 4–5) were 100% accurate on ‘exactly 2’ and 88% accurate on ‘more than’, they performed at chance on the superlative quantifiers. By asking the child participants about their understanding of these terms, Musolino demonstrated that their poor performance on the superlative quantifiers was rooted in a profound lack of understanding of these quantifiers’ meanings. Geurts et al. (2010) further develop this line of enquiry, using a different experimental protocol. Their experiment involved presenting participants with a set of six boxes, some of which each contained a toy of a certain kind. They asked the participants to make the situation match the sentence they were about to hear, either by adding toys, removing toys or leaving the boxes as they were. The test sentences were of the form ‘Q of the boxes have a toy’, where Q was a numerical quantifier; the subjects were adults and children aged 11 years. Adults performed at 100% in all conditions, while the children’s performance ranged from 97% on ‘more than three’ to 42% on ‘at most three’. ‘More than’ and ‘at least’ were easier than ‘fewer than’ and ‘at most’, respectively, and comparative quantifiers were privileged over superlative quantifiers. Assuming that these snapshots of development are a reasonable depiction of stages in the process of acquiring comparative and


As Geurts and Nouwen (2007) discuss, there are issues concerning the interpretation of the bare numerals in these items, which might mean ‘exactly n’ or ‘at least n’. This distinction is critical to the validity of several of the inferences under test; for instance, ‘at least three’ / ‘three’ is false under the first reading of ‘three’ but is tautologous under the second. Geurts et al. (2010) address this in a follow-up task using ‘exactly three’, obtaining similar results; however, it could be argued that this modification draws the participants’ attention to the underinformativeness of the non-exact statement and could bias them towards its rejection. Nevertheless, the distinction between comparative and superlative quantifiers is compellingly supported by this experiment.


More than: 1243 Less than: 698 Fewer than: 86 At least: 812 At most: 44

However, this is clearly not the whole story, as we have to account for these frequency trends themselves. From a modal perspective, these could be argued to arise from the difference in core meaning. Later in this article, we will be arguing that the infrequency of superlative quantifiers stems from their complexity. In either case, we do not commit to a view as to whether the order of acquisition is causally modulated by frequency, although this is not implausible.

4.3 Delay in processing of superlative quantifiers Geurts et al. (2010) also test the online processing of comparative and superlative quantifiers by adult participants, as we discussed earlier. Recall that participants were presented with a sentence ‘There are Q As’ or ‘There are Q Bs’ and then a display in which some numbers of the letter A or B are present. They were asked to press a button to indicate whether the sentence is true or false of the situation displayed. Reading times and decision times were measured. Within the decision 4

A reviewer of an earlier draft of this article pointed out that ‘at most’ is much closer to the others in frequency in a Google search, with around 30 million hits as against 450 million for ‘at least’. In the BNC (2007), ‘at most’ occurs 478 times in all, and ‘at least’ 25 090 times. However, many of the Google instances of ‘at most’ are locative + quantifier, for example, 114 000 ‘at most places’, 90 800 ‘at most stores’ and numerous instances of ‘at most of ’. The same holds for the BNC, which is why we restrict the statistics reported to the cases of collocations with numerals.


superlative quantifiers, then this experimental evidence also supports Geurts and Nouwen’s hypothesis. It appears that children first master ‘more than’ and much later develop an understanding of the corresponding superlative quantifier ‘at least’. Similarly, ‘fewer than’ is followed at a distance by ‘at most’, which has typically still not been mastered at the age of 11. Therefore, we can conclude that comparative quantifiers are indeed mastered earlier than superlative quantifiers, as Geurts and Nouwen’s theory predicts. In passing, we note that these experimental data are also coherent with input frequencies, if we take general corpora to be indicative of these. It is clear that comparative quantifiers are used substantially more frequently than superlative quantifiers: for instance, the British National Corpus (BNC) gives the frequency of their occurrence with the numerals 1–20 (in digital form) as follows.


4.4 Interim summary We have seen how Geurts et al.’s (2010) experiments bear out the predictions made by Geurts and Nouwen (2007) and thus constitute evidence in favour of the semantically modal account over the classical model. In the following section, we spell out an alternative proposal that captures the aspects of the interpretation of superlative quantifiers that Geurts and Nouwen highlighted but with a different division of labour between semantics and pragmatics than they envisioned. We further examine how this can account for the empirical data discussed above. 5 A PRAGMATIC ACCOUNT OF SUPERLATIVE QUANTIFIER MEANING In discussing the classical model (attributed to Barwise & Cooper 1981), both Geurts and Nouwen (2007) and Geurts et al. (2010) have drawn no distinction between the comparative and superlative forms. From a formal point of view, this is correct; the classical view predicts that ‘at most n’ is true in exactly the same set of cases for which ‘fewer than n + 1’ is true. In this approach, comparative and superlative quantifiers are also equal in mathematical complexity; each corresponds to one symbol, be it >, . This amounts to the observation that each quantifier maps a pair of arguments to a truth-value. However, here we wish to consider the possibility that the operators > and < are not equivalent to the operators < and > because the latter


times, there were effects of both entailment direction and quantifier type, just as for the acquisition experiment: ‘at most’ was the slowest to be verified, ‘more than’ the quickest. For the reading times, there were no significant effects. This was argued to support the hypothesis of complexity; the task involving deeper processing gave rise to evident delays in the superlative case, as predicted from Geurts and Nouwen’s account. It is also worth remarking upon the correlation between complexity/processing difficulty and age of acquisition for these quantifiers, as demonstrated by the previous experiment. The data from this experiment support a view in which the quantifiers that are acquired later are more difficult to process. Also, although the reading times are statistically not significantly different, they can be seen to pattern with the decision times, though they vary to a much less pronounced effect.


5 As observed by Bu¨ring (2007), this proposal assumes that the implicature is triggered by a property of the expression—namely that it is disjunctive—rather than the expression itself. This is a departure from standard Gricean analyses, in which implicatures are derivable from what is said. If correct, this proposal requires a thorough reconsideration of the notion of implicature. However, note that the implicature we wish to derive could also be based on the manner maxim: a speaker must have a reason to use a complex expression (e.g. ‘at most n’, according to Bu¨ring’s analysis in which this is disjunctive) when a simpler one is available (e.g. ‘fewer than n + 1’, which is analysed as a simplex proposition). In this case, a good reason to use ‘at most n’ is to highlight that ‘exactly n’ is a likely possibility. With this in mind, we leave the question of the precise nature of the implicature involved to future study.


pair can each be regarded as disjunctions, at some non-linguistic level of representation. We suggest that < and > are represented as ‘¼ n or < n’ and ‘¼ n or > n’, respectively. Furthermore, as per the classical model, we wish to propose that the operators < and > provide the semantics of natural language ‘at most’ and ‘at least’, just as the operators < and > provide the semantics of the comparative quantifiers. On this proposal, not only < and > but also natural language ‘at least’ and ‘at most’ are treated as disjunctions. The latter part of this claim is consistent with Bu¨ring’s (2007) analysis whereby ‘at least n’ is interpreted as ‘exactly n or more than n’ and ‘at most n’ is interpreted as ‘exactly n or fewer than n’. This in turn extends the semantic account proposed by Krifka (1999). This proposal has three important implications. First, in accordance with Bu¨ring’s analysis, the use of a superlative quantifier, whose meaning is a disjunction, gives rise to a quantity implicature, as a consequence of Grice’s (1975) first maxim of quantity. ‘At least n’ conveys semantically that > n holds and implicates that the speaker does not know (or is not at liberty to say) whether it is the case that ¼ n or > n holds. Similarly, ‘at most n’ conveys semantically that < n holds and implicates that the speaker does not know (or is not at liberty to say) whether it is the case that ¼ n or < n holds. This is the classical clausal implicature associated with disjunction (e.g. Horn 1972), whereby by asserting that ‘p or q’ the speaker implicates that (s)he is not in a position to make a stronger statement, such as asserting that ‘p’ or that ‘q’.5 This proposal is distinct from that of Geurts and Nouwen (2007) as no specific notion of modality is stipulated as part of the semantics of superlative quantifiers. Indeed, no semantic difference is proposed between comparative and superlative quantifiers (other than the numerical difference in their arguments); the difference in modality is now captured as a pragmatic inference. A second consequence of this proposal is that both the natural language expressions ‘at least n’ and ‘at most n’ and the logical operators < and > may be more difficult to process at a psychological level than


6 EXPERIMENT 1—EMPIRICAL INVESTIGATION OF THE COMPLEXITY OF NON-STRICT COMPARISON To the best of our knowledge, the distinction between strict and nonstrict comparison has not been studied in detail within the domain of the psychology of mathematics. However, we posit that non-strict comparison is more complex, and specifically disjunctive, on the following grounds.


the natural language expressions ‘more than n’ and ‘fewer than n’ and the logical operators < and >, respectively. This is because, at a psychological level, the disjunction ‘¼ n or > n’ could be more complex than either of the disjuncts ‘¼ n’ or ‘> n’ on their own. We would expect the difference in psychological complexity to manifest itself in a usage preference for the less complex option, when both are available. A third consequence of this proposal is that any differences in usage and meaning between superlative and comparative quantifiers are not attached to the specific forms ‘at most’ and ‘at least’ but rather that they arise because of the pragmatic implicatures and psychological complexity associated with expressions whose underlying meaning is a disjunction. Thus, our account predicts that all forms that are semantically expressible as < and > will pattern together and behave distinctively from the forms expressible as < or >. This is coherent with the account offered by Nouwen (2010): his class A modifiers are those traditionally expressible as < or >, and his class B modifiers those expressible as < and >. However, unlike Nouwen, we do not posit a more elaborate semantic difference between these classes of modifier. We will follow Nouwen (2008) in referring to < and > as strict comparison and < and > as non-strict comparison. Thus, we propose that by treating ‘at most’ and ‘at least’ as disjunctions, we can identify two grounds on which superlative and comparative quantifiers differ, namely the clausal implicature and the psychological complexity associated with the former. In section 6, we shall see how these differences can be invoked to explain extant experimental findings on the difference between comparative and superlative quantifiers. In the remainder of this article, we will first present an experimental justification of the analysis of superlative quantifiers as psychologically complex and specifically disjunctive. We will discuss the explanation of extant experimental findings in terms of this proposal. We will then exhibit evidence in support of the classical view of quantifiers, augmented by this disjunctive analysis (and consequent implicatures), against the semantically modal account of Geurts and Nouwen (2007).


(a)

Assuming that the basic means of comparison between two quantities are ‘more/less than’ and ‘equal to’, > and < each correspond to a single simplex operation of comparison. < and > are each obtained by the disjunction of two simplex operations and are thus greater in complexity. (b) The operators > and < are customarily glossed as ‘greater than’ and ‘less than’, while < and > are customarily glossed as ‘less than or equal to’ and ‘greater than or equal to’. The absence of a nondisjunctive expression for these operators in common parlance suggests that they are naturally regarded as complex.

6.1 Methodology In our experiment, we replicated the methodology of Geurts et al. (2010), as described above, with the following change. In place of sentences of the form ‘There are Q N Xs’, our participants read


The above observations suggest that the claim that superlative quantifiers are disjunctive might be plausible but fall far short of making a convincing case for it. However, it is also possible to investigate this claim by adapting a technique applied to comparative and superlative quantifiers by Geurts et al. (2010). In their experiment, Geurts et al. (2010) presented participants with a sentence on a computer screen of the form ‘There are Q N Xs’, where Q denotes a quantifier of the form ‘exactly’, ‘at least’, ‘at most’, ‘more than’ or ‘fewer than’; N denotes a number; and X denotes a letter (either A or B). The participants were instructed to press a key once they had read and understood the sentence. They were then shown a display consisting of some number of instances of the relevant letter, either A or B, and instructed to indicate whether the preceding sentence had been true or false of this situation, by pressing the appropriate key. Over a series of 38 trials, the response times for each participant in each condition were measured and analysed. Geurts et al. (2010) demonstrated a processing preference for comparative over superlative quantifiers, by demonstrating that the former gave rise to a shorter response time. If non-strict comparison is processed as a disjunction, we expect that comparisons involving strict comparison will give rise to longer response times than strict comparisons, even in the absence of any linguistically relevant content (such as comparative or superlative quantifiers). By contrast, if both strict and non-strict comparisons are equally demanding, there should be no significant effect of comparison type.


6.2 Results The participants’ performance across the test conditions was as follows. Condition

No. of observations

Mean response time in ms (SD)

¼

105

982 (314)

>

132

1007 (369)

139

1110 (466)

, ). Each of the 38 items used by Geurts et al. was translated into this form (6 for equality, 8 for each of the other conditions). The display of letters proceeded as in Geurts et al.’s experiment, and participants were given the same instructions (substituting the word ‘statement’ for ‘sentence’). The experiment was administered to 20 subjects, all members of the University of Cambridge, aged between 20 and 36 years. A total of 16 of the subjects were female. The results of two participants were excluded from the following analysis, one for a high error rate (18/38 ¼ 47%, compared with 30/684 ¼ 4.4% for the 18 participants analysed) and one for a slow mean response time (more than twice the mean for the 18 participants analysed). In addition, following Geurts et al. (2010), we excluded incorrect responses from consideration. Also, in order to minimize the effect of outliers arising through lapses in concentration, we further trimmed the data by removing from consideration any responses that exceeded [mean + 2 standard deviation (SD)] for the individual participant.6


6.3 Discussion The findings of this experiment closely parallel those of Geurts et al. (2010). Specifically, the condition of equality is numerically the fastest to be verified. Of the remaining four conditions, the < condition is the slowest and the > condition is the fastest to be verified. There is a statistically significant main effect of non-strict comparison, supporting the hypothesis that non-strict comparison is more complex than strict comparison. In this experiment, the effect of entailment direction was marginally non-significant, but the pattern resembled that of Geurts et al., with < faster than > and < faster than and > and 0.5 for < and and < and 0.5 for > and differed significantly from > (Student’s t-test, t ¼ 2.01, df ¼ 269, P < 0.05 two tailed), while < v. < narrowly failed to reach significance (t ¼ 1.51, df ¼ 251, P ¼ 0.066 one tailed).


7 CONSEQUENCES OF THE COMPLEXITY OF NON-STRICT COMPARISON Having presented empirical evidence for the claim that non-strict comparison is psychologically more complex than strict comparison, and argued that this is consistent with the idea that non-strict comparative forms such as superlative quantifiers are treated as disjunctions, we now consider the consequences of this for the system of numerical quantifiers in general. One such consequence might be that the reasoning patterns arising from superlative quantifiers are not identical to those arising from


superlative quantifiers is being jettisoned during this process (unless we make the ambitious and novel claim that the mathematical operators < and > also possess modal semantic content). Hence, it is no longer clear why superlative quantifiers should give rise to longer decision times than comparative quantifiers, especially if we make the reasonable supposition that this conversion occurs during the reading phase rather than the decision phase. Conversely, if the statements containing the operators < and > are being converted into sentences of the form ‘at most’ and ‘at least’, they appear to be acquiring modal content—on Geurts et al.’s account—which they previously lacked. That is, the conversion is not a semantically appropriate one. The observation that response times in our study are faster than those in Geurts et al.’s study suggests that the conversion is more likely to be proceeding from linguistic to mathematical expressions than vice versa. If this is the case, then the modal semantic explanation for the processing delay is not viable, unless the translation from modal sentence to non-modal statement is happening during the decision phase. However, we should note that variation between participants’ response times is considerable, and it is possible that the faster response times merely reflect higher performance by this set of subjects, by comparison with those who performed Geurts et al.’s version of the task. For the moment, therefore, we do not wish to commit to a view on whether the above descriptions correctly characterize the participants’ process in performing this task. It suffices for our purpose to draw the conclusion—licensed by the same arguments put forward by Geurts et al. (2010)—that non-strict comparison is more complex than strict comparison. This supports the hypothesis that non-strict comparison is treated as disjunctive. In what follows, we explore the consequences of adding this into the classical model of numerical quantifier semantics.



comparative quantifiers, in that the superlative quantifiers obstruct the generation of logically valid inferences. This follows because the disjunction gives rise to an implicature, as set out in Bu¨ring (2007). Recall that, for instance, ‘at most’ can be analysed as ‘less than or equal to’ and hence the use of ‘at most’ in declarative contexts gives rise to the implicatures that ‘less than’ and ‘equal to’ are both possibilities. The latter implicature disrupts the inferential process explored in experiment 1 of Geurts et al. (2010), as described below. Consider the case discussed in section 4.1, where participants are asked whether the implication ‘Beryl had at most three sherries’ / ‘Beryl had at most four sherries’ is legitimate. According to the classical account, this should be acceptable, but it is rejected by the vast majority of participants. By contrast, in our disjunctive account of ‘at most’, the consequent ‘Beryl had at most four sherries’ gives rise to the implicature that it is possible, from the speaker’s point of view, that Beryl had exactly four sherries. This directly contradicts the antecedent, ‘Beryl had at most three sherries’. This has the potential to block participants’ acceptance of the implication under test. Note that this explanation is similar in character to that proposed by Geurts and Nouwen (2007). In their account, the implication ‘at most n’ / ‘at most n – 1’ fails because of a contradiction at the level of semantics, in that ‘at most n’ is held to encompass the explicit possibility of ‘exactly n’. Our account differs only in that this explicit possibility arises through pragmatics rather than semantics; specifically, through the implicature derived from the use of the complex disjunctive non-strict comparison. So far we have seen how the classical account, augmented with a more sophisticated analysis of non-strict comparison, can answer some of the criticisms developed by Geurts and Nouwen (2007) and coheres with their observations about the inference pattern, as supported empirically by Geurts et al. (2010). However, we also need to demonstrate that this account is equally compatible with the other experimental data discussed earlier. Geurts et al.’s (2010) second experiment bore out the prediction that the comparative quantifiers are mastered earlier in acquisition than their superlative counterparts. Here, once again, our enhanced version of the classical account makes the same prediction as the semantically modal account of Geurts and Nouwen (2007). As we argue that superlative quantifiers possess a more complex meaning than comparatives, in that they are represented disjunctively, we also predict that superlative quantifiers are disfavoured in acquisition. Hence, this experiment does not distinguish between the two competing proposals.


8 EXPERIMENT 2—JUDGMENTS OF LOGICAL INFERENCE PATTERNS In our next experiment, we set out to replicate the findings of Geurts et al. (2010) with respect to the inference judgment task. We performed this experiment in order to verify that the patterns observed for Dutch quantifiers were also to be found in English. We also administered a post-test questionnaire to ascertain whether participants had explicit knowledge of any differences between the two types of quantifier.

8.1 Method A total of 15 adult participants were recruited, all of whom were students at the University of Cambridge. None had any university-level


The third experiment conducted by Geurts et al. (2010) shows faster verification times for comparative over superlative quantifiers, as discussed in section 6 of this article. We demonstrated in that section that the same applies for strict v. non-strict comparison, in the absence of the specific linguistic constructs under investigation (comparative and superlative quantifiers). Given this finding, we would predict that the same pattern should be replicated whenever strict and non-strict comparisons are in competition. Therefore, our proposal is compatible with the finding that comparative quantifiers are verified faster than superlative quantifiers. Moreover, we might argue that this proposal is more parsimonious than the semantically modal account of Geurts and Nouwen (2007), in that it explains the outcomes both of Geurts et al.’s (2010) third experiment, for the quantifier case, and our first experiment (section 6), for the comparison case. We have already concluded that the superior performance on strict rather than nonstrict comparison cannot readily be attributed to a semantic difference between comparative and superlative quantifiers, as participants do not appear to be invoking these quantifiers in their verification process. Hence, with reference to the major lines of argument made by Geurts and Nouwen (2007), and the experimental evidence adduced in support of this proposal by Geurts et al. (2010), we have seen that our augmented version of the classical account is equally well supported as the semantically modal account. In the following sections, we present data from a further set of experiments, first replicating Geurts et al.’s findings on the inference judgment task and then obtaining support for our augmented classical account over and above Geurts and Nouwen’s proposal.


8.2 Results The following table presents the acceptance rates for the implication judgment task and compares these rates with those obtained by Geurts et al. (for the eight conditions common to both studies).

1st quantifier

2nd quantifier

3

At least 3

3

More than 2

3

Acceptance (%) Geurts et al. acceptance (%) 62

50

100

100

At most 3

42

61

3

Fewer than 4

84

93

At most 2

At most 3

2

14

Fewer than 3 Fewer than 4

64

71

At least 3

3

90

50

At most 3

3

26

18

More than 3

Fewer than 3

9

N/A

Fewer than 3 More than 3

0

N/A

3

Fewer than 3

13

N/A

3

More than 3

0

N/A


background in mathematics or logic. They were informed that they would see a series of pages, each with two sentences written on them, and that they should circle the answer ‘yes’ if the first sentence implied the second and ‘no’ if it did not. Three sentence pairs were used for each of 12 conditions (36 sentence pairs in all); these included the first eight conditions tested by Geurts et al. (2010) and four additional ‘false’ conditions as controls. The order of these sentence pairs was randomized and the same order used for each participant. As a post-test, participants were asked to write a brief explanation of why they had answered the way they did, for the first instance of each of the 12 conditions.


The metalinguistic judgments elicited from the questionnaire were generally uninformative. These exhibited a degree of uncertainty about some of the conditions but provided no clear indications of any explicit awareness of modality or other semantic effects. We shall not discuss these further in what follows.

8.3 Discussion

9 EXPERIMENT 3—COMPATIBILITY JUDGMENTS OF NUMERICALLY QUANTIFIED EXPRESSIONS Following Geurts et al.’s analysis, the rationale for the failure of ‘at most two’ / ‘at most three’ in experiment 2 was as follows. On the modal view, ‘at most three’ admits the possibility of ‘(exactly) three’. ‘At most two’ uncontroversially excludes this possibility. Therefore, as the possibility of ‘(exactly) three’ cannot follow from ‘at most two’, the implication fails. Following this line of analysis, it is predicted that two such sentences will be judged as logically contradictory. By contrast, the augmented classical view predicts that the two sentences will be logically compatible but pragmatically infelicitous when juxtaposed. We investigated this issue using a method introduced by Katsos (2007: chapter 3; see Katsos 2008 for a review) with the aim of capturing the difference between logical contradiction and pragmatic infelicity for the case of scalar implicature. 7 Note that ‘at least three’ / ‘three’ is valid if and only if the latter ‘three’ is interpreted as existential rather than precise, in which case it is a tautology. In our experiment, the consequent sentences in this case were ‘Anna wrote 3 letters’, ‘There are 3 cities on the map’ and ‘Steve owns 3 suits’, all of which could plausibly be existential statements. For items such as ‘Dave has 3 children’, we might expect lower rates of acceptance.


The results for the conditions common to both this experiment and Geurts et al.’s (2010) were generally very similar, with the exceptions of the ‘three’ / ‘at most three’ and, most strikingly, the ‘at least three’ / ‘three’ pairs. We tentatively attribute this to item effects, arising from the potential ambiguity of the bare numeral.7 Rejection rates for the semantically incorrect control conditions were generally at or near ceiling. Crucially for our purposes, this experiment constitutes a replication of Geurts et al.’s (2010) study as far as the comparative and superlative quantifiers are concerned. We can see that, in English as in Dutch, performance on comparative quantifiers exceeds that on superlatives— judged by traditional standards of logical correctness—in all the cases for which we have comparable data. Thus, we conclude that, as expected, this is not an effect specific to Dutch.


9.1 Methodology A total of 20 participants were recruited, all members of the University of Cambridge, in the age range 20–36 years. Fourteen were female. Participants were presented with a pair of sentences linked by the word ‘specifically’, as in the following example, where Q denotes a quantifier and n and m denote numbers. (9) Jean has Q n houses. Specifically, she has exactly m houses. They were asked to give a judgment on the coherence of the utterance, rating it on a Likert scale ranging from 5 (‘coherent’) to 5 (‘incoherent’). Two types of control items were included. There were items using ‘In fact’, rather than ‘Specifically’, partially to disguise the goal of the experiment and partially to test whether participants’ judgments would differ if the second sentence could be interpreted as a weakening of the speaker’s commitment to the proposition originally expressed. There were also items in which the quantifier and numeral in the first sentence were replaced with the quantifier ‘some’, and the numeral in the second sentence was replaced with ‘none of ’, ‘half of ’ or ‘all of ’.8 This tested the participants’ response to violations of both semantic and pragmatic contradiction, as discussed above. In total, 78 items were used. The value of n was varied over the range 3–5. The results are summarized below. 8

The sentences were chosen in such a way as to license the partitive usage.


In this paradigm, participants are presented with statements and they are asked to give coherence judgments on a scale. Under this methodology, we predicted that semantically self-contradictory statements would be judged as incoherent, while statements that were pragmatically self-contradictory (i.e. in which an implicature is explicitly revised) would be judged more coherent, and statements with neither type of self-contradiction would be judged more coherent still. The modal view of superlative quantifiers, holding that ‘at most n’ semantically conveys the possibility of ‘exactly n’, predicts that a statement containing ‘at most n’ and ‘exactly n 1’ (with reference to the same entities) should pattern with the semantically selfcontradictory statements. Our proposal predicts that a statement containing ‘at most n’ and ‘exactly n 1’ should pattern either with the pragmatically self-contradictory statements (if an implicature is generated) or with the non-self-contradictory statements (if it is not).


9.2 Results The following table shows the mean judgment of coherence, and the corresponding SDs, in each of the experimental conditions. Quantifier Quantifier ‘Specifically’ in second condition in first sentence Mean SD sentence

‘In fact’ Coherent? condition Mean SD

At most n

Exactly n1

1.58 2.57

1.87 2.53 ?

2

At most n

Exactly n

1.90 2.31

1.25 2.60 ?

3

At most n

Exactly n+1

4.08 2.34 4.05 2.10 No

4

At least n

Exactly n1

4.48 1.50 4.27 1.88 No

5

At least n

Exactly n

1.28 2.50

1.33 2.56 ?

6

At least n

Exactly n+1

1.95 2.53

2.55 2.16 ?

7

More than n

Exactly n1

8

More than n

Exactly n+1

3.10 2.18

3.20 1.90 Yes

9

Fewer than n

Exactly n1

3.08 1.80

3.13 1.93 Yes

10 Fewer than n

Exactly n+1

4.75 0.73 4.23 2.05 No

11 Some

None

4.60 1.14 4.07 1.97 No

12 Some

Half

13 Some

All

4.70 0.93 4.28 1.92 No

3.08 2.23 1.08 3.13

3.35 2.00 Yes 0.22 3.10 ?


1


9.3 Discussion Broadly, the trends in both conditions are clear. The statements in which pairs of sentences are semantically compatible, on a classical semantic view, are systematically judged to be coherent. Those in which the sentences are semantically contradictory are judged incoherent. This trend plays out over both the ‘in fact’ and the ‘specifically’ cases, although understandably participants appear to show slightly more leniency to self-contradictory utterances in the ‘in fact’ case. The results for the comparative cases license the assumption that this test is diagnostic for semantic coherence. For our purposes, the critical data are those in which the first sentence contains a superlative quantifier. In these cases, there is once


The global mean across all conditions was 0.64 and the SD 3.88. The semantically self-contradictory cases achieved low ratings in both conditions. The semantically uncontroversially non-contradictory cases (8, 9 and 12) achieved high ratings. The ‘in fact’ condition was regarded as more coherent than the ‘specifically’ condition for 12 out of the 13 cases (significant by the sign test, P < 0.01). We will discuss the ‘specifically’ condition for the following cases. Our first critical case was condition 1, ‘at most n . . . exactly n – 1’. Comparing condition 1 with condition 2, ‘at most n . . . exactly n’, a Student’s t-test gives us t ¼ 0.72, df ¼ 118, P > 0.1. Hence, there is no significant difference between these conditions. Comparing condition 1 with condition 3, the semantically false control ‘at most n . . . exactly n + 1’, we obtain t ¼ 12.6, df ¼ 118, P < 0.01. Thus, condition 1 is highly significantly better than the relevant semantically false control. For the ‘at least’ case, we compared condition 5 with condition 6, and obtained t ¼ 1.46, df ¼ 118, P > 0.1. Again, there is no significant difference between these cases. Both are highly significantly (p < 0.01) more acceptable than the semantically false control condition 4. Comparing the superlative with the comparative quantifiers, we find that the semantically true comparative conditions (8 and 9) yield significantly higher results than the corresponding superlative conditions (again, P < 0.01 for all comparisons). For the control ‘some’ conditions, further pairwise comparisons reveal a significant preference for ‘some . . . half ’ over ‘some . . . all’ and ‘some . . . all’ over ‘some . . . none’ (P < 0.01 for each). ‘Some . . . half ’ also outperforms conditions 1, 2, 5 and 6, which in turn outperform ‘some . . . all’ (all P < 0.01).



again a clear-cut division between the cases that are semantically selfcontradictory and those that are not. Crucially, given a first sentence containing ‘at most n’, participants accept both a continuation ‘exactly n’ and ‘exactly n – 1’, with no statistically significant preference for one or the other. This fails to confirm the predictions arising from the semantically modal account of superlative quantifiers. On this account, the superlative quantifier encodes the possibility of exact equality, a possibility which in our critical cases is then denied by the second sentence. Nevertheless, the participants accept the relevant utterances as clearly coherent rather than incoherent. Under the hypothesis of modality in the semantics, the lack of significant difference between conditions 1 and 2 indicates that revising possibility to certainty is equally incoherent to revising possibility to impossibility, which appears implausible. Notably, revising possibility to impossibility is judged significantly more coherent than revising ‘some’ to ‘all’, which is a case of pragmatic self-contradiction. We therefore consider these data incompatible with the hypothesis that ‘at most’ semantically encodes the possibility of equality. According to our competing proposal, the superlative quantifiers give rise to modal interpretations due to pragmatic implicature. Specifically, we are proposing that the ‘at most n’ first sentence gives rise to an implicature that ‘exactly n’ is possible. Therefore, we would predict that the ‘at most n . . . n – 1’ case should be more comparable to the ‘some . . . all’ case, where such incoherence as exists arises from the second sentence contradicting an implicature of the first, than to the semantically contradictory cases. This is indeed the case in our data: ‘some . . . all’ is judged significantly more acceptable than ‘some . . . none’ and the other contradictory cases, as does ‘at most n . . . n – 1’. Both are judged less acceptable than the non-contradictory cases with the comparative quantifiers (that do not trigger an implicature), as we predicted. Furthermore, our account also suggests that ‘at most n’ should give rise to an implicature that ‘fewer than n’ is possible, which in turn predicts that condition 2 will yield lower ratings than the comparative conditions and similar ratings to those elicited in condition 1. Our results suggest that this is indeed the case. Again, we note that these forms are judged to be significantly more coherent than the ‘some . . . all’ case, even though we are arguing that these are both self-contradictory at a pragmatic level. However, there is a sizeable gulf between these and the control semantically selfcontradictory cases. Put simply, the non-theory-critical cases present


10 EXPERIMENT 4—INFERENCE PATTERNS IN A CONDITIONAL CONTEXT The results of experiment 3 raise the question of whether the inference ‘at most two’ to ‘at most three’, rejected in experiment 2, is available under the right conditions. In experiment 4, we aimed to elicit this inference, using a conditional context. Intuitively, it seems that the superlative quantifiers behave like comparative quantifiers under the scope of conditionals, for example, ‘If Berta had at least/most three drinks . . .’. It was noted by Geurts and Nouwen (2007) that their semantically modal account is unsatisfactory with regard to these and certain other contexts. In this experiment, we investigated whether hearers interpret an utterance such as (10) as a commitment on the part of the speaker to the corresponding proposition (11). (10) ‘If Berta has had at most three drinks, she is fit to drive. Berta has had at most two drinks.’ (11) Berta is fit to drive. This conclusion appears to be licensed by the inference from ‘Berta has had at most two drinks’ to ‘Berta has had at most three drinks’. If


a clear pattern: the semantically self-contradictory cases are rated low, the pragmatically self-contradictory cases towards the middle of the scale and the non-self-contradictory cases are rated higher. If we measure the superlative quantifier cases against this scale, we see them clearly as pragmatically self-contradictory or fully non-self-contradictory. Either way, this contradicts the semantically modal account. Within our pragmatic account, we would suggest that the intermediate status of these results indicates implicature being generated, but less reliably or robustly than in the paradigm case of ‘some’ (‘but not all’). In summary, the coherence judgments elicited in this experiment point to a clear division between semantically self-contradictory and non-self-contradictory utterances, with pragmatically self-contradictory utterances occupying the middle ground. The case of ‘at most n . . . exactly n – 1’, which should be semantically self-contradictory on the semantically modal account, appears to be either pragmatically selfcontradictory or fully coherent, in accordance with our augmented classical account. In fact, as predicted by our account, it patterns similarly to ‘at most n . . . exactly n’. Therefore, we conclude that this experiment favours the augmented classical over the semantically modal account.


10.1 Methodology Eight participants were recruited and were given the test as a questionnaire. There were 14 items in all, three instances of the critical ‘at most two’/’at most three’ case and one instance of each of the other 11 conditions used in experiment 1. Participants were presented with an utterance of the type given above and then asked, ‘Does the speaker believe that . . . ?’ They were invited to respond ‘yes’, ‘no’ or ‘don’t know’. ‘No’ and ‘don’t know’ responses were both treated as negative with regard to the implication being investigated.

10.2 Results 23 of 24 (96%) responses in the ‘at most two’/‘at most three’ case were positive, agreeing that the inference was valid. Responses in the other conditions also patterned with the mathematically valid outcomes.

10.3 Discussion Under the conditions of this experiment, it does appear that the inference from ‘at most two’ to ‘at most three’ (or the inference from ‘if . . . at most three’ to ‘if . . . at most two’) goes through, contrary to the predictions we might expect to draw from the modal hypothesis. This is, however, consistent with the classical account. This outcome is also consistent with our augmented classical account in which ‘at most’ is considered disjunctive (‘less than or equal to’) because the implicature arising from this is clearly different in a conditional environment to that arising in a declarative environment.


the semantically modal account is correct, this inference should not be available and the conclusion cannot be drawn. If the classical account is correct, this inference is available and the conclusion can be drawn unless it is blocked by an implicature. Similarly, the conclusion would be licensed by an inference from ‘If Berta has had at most three drinks, she is fit to drive’ to ‘If Berta has had at most two drinks, she is fit to drive’. If the semantically modal account is correct, this inference is not available either, as a modal interpretation of either ‘at most three’ in the antecedent or ‘at most two’ in the consequent would render it false. If the classical account is correct, then again this inference is available and the conclusion can be drawn unless it is blocked by an implicature.


For instance, the utterance (12) does not give rise to the pragmatic interpretation (13). (12) ‘If Berta has had at most three drinks, she is fit to drive.’ (13) If it is possible that Berta has had at most three drinks and certain that she has had no more than three drinks, then she is fit to drive. Why not? Because (13) is a weakening of the original semantics of the utterances, namely (14).

Therefore, deriving the implicature gives the hearer no additional information. Even if the hearer derives the implicature, this will not supersede the existing semantic content but stands alongside it. Therefore, the pragmatic interpretation of the utterance remains (14), rather than the weaker (13). Rather than triggering a pragmatic enrichment, it seems intuitive to propose that the signal sent by using the ‘at most’ formulation in this case is to draw attention to the upper bound [see Nouwen (2010) for a semantically oriented account along similar lines]. To verify this observation, one can check the parallelism with the paradigmatic case of a possibility implicature arising from disjunction. The declarative ‘There is beef or pork on the menu’ appears to convey the implicature that either is possible. By contrast, this implicature is not available in a conditional context, such as ‘If there is beef or pork on the menu, Max will be happy’. This is presumably because the pragmatic ‘enrichment’ of possibility, when applied to the latter utterance, in fact makes it less informative, in that it imposes an extra condition (possibility of each conjunct) that would have to be satisfied before the conclusion could be drawn. Hence, this implicature does not go through under the scope of a conditional. It might be argued that the materials used in this experiment are slightly awkward from a pragmatic standpoint. A more naturalistic formulation would be along the lines of (15). (15) Anyone who has had at most three drinks is fit to drive. Berta has had at most two drinks. However, in this case, it might conceivably be argued that the inferential process is not clear, as it requires an additional step. The additional step might either be ‘Berta has had at most three drinks’ or ‘Anyone who has had at most two drinks is fit to drive’. We do not believe that anything hinges on this distinction, but we elected to use


(14) If it is certain that Berta has had no more than three drinks, she is fit to drive.


11 EXPERIMENT 5—JUDGMENTS OF LOGICAL INFERENCE PATTERNS IN FELICITOUS CONTEXTS Experiment 2 demonstrated the unavailability of certain classically correct inference patterns involving superlative quantifiers. Under the semantically modal account, this arises for semantic reasons. Under the augmented classical account, we have argued that this stems from the implicatures that arise from consequents containing superlative quantifiers. In experiment 5, we attempt to differentiate these predictions by embedding the reasoning task in experiment 2 within a theoretically more complex task in which the superlative quantifiers are licensed by the context. For example, we ask participants to judge whether (16) implies (17). (16) Anne has three children but Brian has at most two children. (17) Anne and Brian each have at most three children.


the methodology described above in order to allay any concerns arising from this uncertainty. The result of this experiment is not entirely surprising in the light of Geurts and Nouwen’s disclaimer about the legitimacy of the modal interpretation of superlative quantifiers. The results can be explained by assuming that the superlative quantifier under the scope of the conditional has a purely classical meaning: it is not necessary to assume further that the superlative quantifier in the logical antecedent (‘Berta has had at most two drinks’) also lacks modality. However, there does not appear to be any specific proposal to account for the absence of this type of semantic modal meaning within the conditional environment, apart from the classical view, which denies the existence of the modal meaning in toto. It is not impossible to condition on modals, although it is rarely necessary and examples of it are consequently somewhat contrived (e.g. ‘If I think the project might succeed, I’ll fund it for a trial period only’). For this reason, we consider that the outcome of this experiment lends support to an augmented classical account, in which superlative quantifiers are analysed as disjunctions, over the Geurts and Nouwen (2007) account in which these quantifiers possess modal semantics. These results also motivate us to consider whether the same kind of inference might be available in non-conditional contexts, for which Geurts and Nouwen do not identify a problem with their account. This is explored in the following task.


Assuming that this sentence is correctly analysed as predicating ‘having at most three children’ of the two individuals ‘Anne’ and ‘Brian’, we argue that acceptance of this implication requires acceptance that ‘at most two’ implies ‘at most three’ (in addition to acceptance that ‘three’ implies ‘at most three’). Recall that on the semantically modal account this is not available, so the inference should fail. On the augmented classical account, it is available, so the inference should succeed unless it is blocked by implicature.

11.1 Methodology

11.2 Results Acceptance rates for the test conditions (those for which multiple items were tested) were as follows. First sentence

Second sentence

Implication acceptance (%)

1

n . . . at least n + 1

At least n + 1

2

n . . . at least n + 1

At least n

88

3

n . . .at most n 1

At most n

68

4

n . . .at most n 1

At most n 1

7

5

n . . .fewer than n

Fewer than n

3

6

n . . .fewer than n

Fewer than n + 1

7

n . . .more than n

More than n

8

n . . .more than n

More than n 1

0

100 3 95

In addition, results for the filler items were in accordance with semantic expectations. Across all semantically uncontroversial


A total of 20 participants were recruited, members of the University of Cambridge, in the age bracket 20–36 years. 14 were female. The methodology of experiment 2 was replicated using 32 pairs of sentences of the type discussed above, using a range of numerical quantifiers. The numerals and other aspects of the sentential content were varied between conditions.


conditions (i.e. conditions that are not theory-critical for either approach under discussion),9 participants were correct on 488 out of 500 items (97.6%). Crucially, the acceptance rate for the theory-critical implication ‘n . . . at most n – 1’ / ‘at most n’ items is significantly above 50% (41/ 60, P < 0.01 binomial), that is, neither floor nor ceiling.

11.3 Discussion

(17) Anne and Brian each have at most three children. Instead, we would have to hold that the modal possibility applies only to some member of the set {Anne, Brian} and is not binding upon 9

This includes conditions 1 and 4–8 in the table above.


This finding contradicts the prediction of the semantically modal account of superlative quantifier meaning. According to the modal view, as expounded in the interpretation of experiment 1 of Geurts et al. (2010), the implication from ‘at most n – 1’ to ‘at most n’ is unavailable. By contrast, the results of this experiment indicate that this implication is available in certain declarative contexts, albeit less reliably than the corresponding implication with comparative quantifiers. Contrastingly, these data are compatible with our alternative proposal in which ‘at most’ can be analysed as a disjunction and give rise to possible implicatures. According to this proposal, ‘at most three’ serves the function of drawing particular attention to the possibility that ‘exactly three’ holds and has the potential to give rise to an implicature to that effect. However, in this situation, the implicature is not entirely inappropriate because the possibility of equality holds for one of the conjuncts, namely Anne [according to the implicature arising from (21)]. By contrast, on the semantically modal account, this possibility is part of the semantics of ‘at most three’ and should thus be required of both conjuncts. To put it another way, the majority of our participants are able to reason from ‘at most two’ to ‘at most three’ when the implicatures arising from ‘at most’ can be accommodated without a contradiction arising. By contrast, on the semantically modal account, this should not be possible, as the modality renders ‘at most three’ inherently contradictory of ‘at most two’. Is there a way to reconcile these data with the modal hypothesis? We do not think so. To do this, we would have to accept that the modal semantics of ‘at most three’ also does not apply to the individual conjuncts of (17), as repeated below.


the other. In this example, that amounts to saying that (17) is true of a situation in which Anne might have three children, even if Brian cannot possibly have that many. While this analysis is theoretically viable, we find it unsatisfactory. If the above manipulation is accessible to speakers, they should also attest the truth of such statements as (18a), or under the right circumstances even (18b) and (18c), and so on.

As these are intuitively false statements, we submit that ‘each’ does not admit this analysis and therefore that experiment 5 gives evidence against the semantically modal account and in favour of the augmented classical account.

12 GENERAL DISCUSSION Geurts et al. (2010) demonstrate empirical support for the hypothesis that the superlative quantifiers possess a modal component to their semantics, as proposed by Geurts and Nouwen (2007). In this article, we have robustly corroborated the finding that superlative quantifiers possess a modal component. We further proposed that the appropriate locus of the modality is in the pragmatics—and that the differences in the use of superlative quantifiers are due to this implicature as well as the psychological complexity of non-strict comparison relative to strict comparison. In order to document that non-strict comparison is more complex than strict comparison because it is disjunctive, we reported fresh experimental evidence on mathematical quantifier processing. We then argued that the classical account augmented by a disjunctive analysis for the non-strict comparison of the superlative case is equally compatible with the pre-existing empirical data as the semantically modal account. In a further series of experiments, we have elicited data to suggest that our proposal is in fact more satisfactory than Geurts and Nouwen’s semantically modal account of superlative quantification. Again we must mention that Geurts and Nouwen (2007) are aware of their theory’s limitations in its present form, noting in particular the difficulties posed by the conditional context, for example, ‘If Berta has had at most three drinks . . .’. In experiment 4, we provide a practical demonstration of this lacuna and show how the non-modal superlative


(18) a. Anne and Brian each might have three children. b. Anne and Brian each might be a young woman. c. Anne and Brian each might be the only woman named Anne in the village.



quantifier enters into logical relations. However, in experiments 3 and 5, we go further. In experiment 3, we show that participants treat the ‘exactly n is possible’ meaning of superlative quantifiers (with particular reference to ‘at most’, which gives rise to the clearest predictions) as a pragmatic readily revisable inference rather than as part of the logical meaning of the expression. In experiment 5, we show that the superlative quantifiers systematically appear to lack modal semantics but that they give rise to implicatures that are similar but—in certain contexts—distinguishable from this modal semantic meaning. We contend that the pattern of results observed across our set of experiments coheres with the notion that the semantic meaning of superlative quantifiers is fundamentally the classical meaning. The ‘modal’ meaning can instead be analysed as a possibility implicature arising from the use of a superlative quantifier with its disjunctive meaning. This means that there are indeed differences in the inferences that are licensed by superlative and comparative quantifiers, but they follow from the presence or absence of this implicature. Moreover, our demonstration that the online performance preferences for comparative over superlative quantifiers are matched by an online performance preference for strict over non-strict comparison is exactly what one would expect if non-strict comparison is more complex (because it is disjunctive) than strict comparison in general. Under this analysis, we might argue that the communicative effect of ‘at most n’ is to draw particular attention to the number n and the possibility of equality, neither of which are emphasized by the comparative alternative ‘fewer than n + 1’. In declarative contexts, the implicature that the superlative quantifier conveys is very similar to the semantic meaning proposed by Geurts and Nouwen (2007). In downward-entailing contexts, by contrast, the implicature does not arise for standard pragmatic reasons, whereas the semantic meaning proposed by Geurts and Nouwen cannot be explained away in such a principled fashion. Corpus data support the notion that superlative quantifiers achieve this effect. In the BNC, for instance, tokens of ‘at least 20’ outnumber those of ‘more than 19’ by 110 to 6. However, tokens of ‘more than 20’ outnumber ‘at least 21’ by 357 to 23. Similar patterns can be observed for round numbers flanked by non-round numbers, both in the BNC and in other corpora. This is a surprising observation within a modal semantic account of superlative quantifier meaning, as it appears to suggest that the use of superlative quantifiers is sometimes motivated by something other than the wish to express modality. Our augmented classical account is compatible with this notion, given that the use of


(19) a. *Fewer than three people have that authority, namely the Queen and the Prime Minister. ? b. Not fewer than two people have that authority, namely the Queen and the Prime Minister. c. Not more than two people have that authority, namely the Queen and the Prime Minister. (20) a. *Wilma danced with fewer/less than every second man who asked her. b. ? Wilma danced with not less than every second man who asked her. ? c. Wilma danced with not more than every second man who asked her. In (19b) and (19c), explicit reference to ‘two people’ licenses the ‘namely’ continuation; in (20b) and (20c), the possibility of equality seems to license the use of the comparative quantifier in a context in which it is otherwise understood to be forbidden. In both cases, the difference resides in classical semantic properties of the quantifiers. More could be said about this, and indeed its relation to the ‘no more/fewer than’ construction discussed by Nouwen (2008), but


a round number licenses the use of a superlative quantifier, as the value being called attention to is a salient one. By contrast, imputing modality to superlative quantifiers curtails the expressive power of the system, by constraining our choice of number unless we are indifferent to whether or not we use a modal expression. This would explain why, in our experiment 5, the logical implication from ‘at most two’ to ‘at most three’ is accepted, while it was rejected in experiment 2; in experiment 5, ‘at most’ is used (in the consequent) in conjunction with a salient number as determined by the preceding utterance. Under these circumstances, the superlative quantifier in the consequent is licensed and no implicature arises. In the absence of this implicature, the superlative quantifier possesses purely classical meaning and the logically correct inference is drawn. This proposal has implications for the analysis of other expressions. For example, consider the distribution of ‘not more than’ and ‘not fewer/less than’. It could be argued that these are modal, but it seems more plausible, compositionally speaking, to count them as classically semantic comparative quantifiers. The relevant semantic difference between these and their non-negated counterparts is that while ‘more/ fewer than n’ excludes the possibility of n, ‘not more/fewer than n’ admits this possibility. It is simply this difference that appears to underlie the following differences in distribution.


like Geurts and Nouwen (2007: 37f), we take the view that the definitive answer to the question of superlative and comparative quantifier distribution will arise from a more general theory of comparison. Acknowledgements

NAPOLEON KATSOS Research Centre for English and Applied Linguistics University of Cambridge English Faculty Building 9 West Road Cambridge CB3 9DP United Kingdom e-mail: [email protected]

CHRIS CUMMINS Research Centre for English and Applied Linguistics University of Cambridge English Faculty Building 9 West Road Cambridge CB3 9DP United Kingdom e-mail: [email protected]

REFERENCES Barwise, J. & R. Cooper. (1981), ‘Generalized Quantifiers and Natural Language’. Linguistics and Philosophy 4:159–219. The British National Corpus, version 3 (2007), Distributed by Oxford University Computing Services on behalf of the BNC Consortium (http:// www.natcorp.ox.ac.uk/). Bu¨ring, D. (2007), ‘The least "at least" can do’. In C.B. Chang and H.J. Haynie (eds.), Proceedings of WCCFL 26. Cascadilla Press. Somerville, MA. 114–20. Geurts, B. (2006), ‘Take ‘‘five’’: The meaning and use of a number word’.

In S. Vogeleer and L. Tasmowski (eds.), Non-definiteness and Plurality. John Benjamins. Amsterdam. 311–29. Geurts, B, N. Katsos, C. Cummins, J. Moons., & L. Noordman. (2010), ‘Scalar Quantifiers: Logic, Acquisition and Processing’. Language and Cognitive Processes 25:130–48. Geurts, B., & R. Nouwen. (2007), ‘At least et al.: The semantics of scalar modifiers’. Language 83:533–59. Grice, H. P. (1975), ‘Logic and conversation’. In P. Cole and J.L. Morgan (eds.), Syntax and Semantics, Academic Press. New York. 41–58.


We thank Bart Geurts, Rick Nouwen and two anonymous reviewers of the Journal of Semantics for providing substantially helpful comments on the manuscript. Chris Cummins acknowledges the support of a University of Cambridge Domestic Research Studentship and of funding from COST Action A33 for a Short Term Scientific Mission to the University of Nijmegen (COST-STSM-A33-4692). Napoleon Katsos acknowledges the support of the Arts and Humanities Research Council (Ref.: AH/E002358/1).

Chris Cummins and Napoleon Katsos 305 tegrating Linguistic and Developmental Perspectives’. Cognition 93:1–41. Nouwen, R. (2008), ‘Upperbounded No More: The Exhaustive Interpretation of Non-strict Comparison’. Natural Language Semantics 16: 271–95. Nouwen, R. (2010), ‘Two Kinds of Modified Numerals’. Semantics and Pragmatics 3:1–41. R Development Core Team (2008), R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna, Austria. ISBN 3-900051-07-0 (http:// www.R-project.org). First version submitted: 28.05.2009 Second version submitted: 13.10.2009 Third version submitted: 12.02.2010 Accepted: 19.02.2010


Horn, L. (1972), On the Semantic Properties of Logical Operators in English. UCLA dissertation, distributed by Indiana University Linguistics Club. Katsos, N. (2007), Experimental Investigations on the Effects of Structure and Context on the Ph.D. thesis, Generation of Scalar Implicatures. University of Cambridge. Katsos, N. (2008), ‘The Semantics/ Pragmatics Interface from an Experimental Perspective: The Case of Scalar Implicature’. Synthese 165:358–401. Krifka, M. (1999), ‘At least some determiners aren’t determiners’. In K. Turner (ed.), The Semantics/Pragmatics Interface from Different Points of View, Current Research in the Semantics/Pragmatics Interface. Vol. 1. Elsevier. Oxford. 257–92. Musolino, J. (2004), ‘The Semantics and Acquisition of Number Words: In-

Journal of Semantics 27: 307–341 doi:10.1093/jos/ffq005 Advance Access publication March 30, 2010

Temporal Interpretation without Tense: Korean and Japanese Coordination Constructions JUNGMEE LEE AND JUDITH TONHAUSER Ohio State University

Matrix clauses are tensed in Korean and Japanese, but both languages have coordination constructions where any non-final conjunct may or, in the case of Japanese, must be untensed. Building on analyses of the temporal interpretation of tenseless languages such as Yucatec Maya (Mayan: Bohnemeyer 2002) and Kalaallisut (Eskimo-Aleut: Bittner 2005), this article argues that a truly tenseless analysis of the temporal interpretation of these non-final conjuncts is possible once the effects of Aktionsart and the discourse context on temporal interpretation are taken into consideration (cf. Partee 1984; Dowty 1986; Hinrichs 1986). The formal semantic analysis developed here is shown to be empirically and conceptually superior to previous analyses, which claim that the temporal interpretation of tenseless non-final conjuncts is determined either by the tense of the final conjunct (e.g. Yoon 1997; Hirata 2006) or by a tense-like restriction introduced by a zero tense morpheme or the coordination marker (e.g. Nakatani 2004; Chung 2005). The proposed analysis of Korean and Japanese coordination constructions thus provides further evidence that tenseless clauses can be semantically interpreted as such, not just in tenseless languages but even in languages where matrix clauses are otherwise tensed. The article concludes by discussing implications for analyses of cross-linguistic semantic variation.

1 INTRODUCTION A key question in cross-linguistic semantics is how to analyse utterances that have comparable meanings but differ in their morphosyntactic make-up. A case in point is temporality: in some languages, including, for example, English, Korean and Japanese, the temporal interpretation of matrix clauses is affected by tense morphemes, that is, grammaticalized expressions that temporally relate the reference time of an utterance to the speech time, while other languages are tenseless and express comparable meanings without such expressions [e.g. Yucatec Maya (Mayan: Bohnemeyer 2002), Mandarin Chinese (Lin 2005), St’a´t’imcets (Salish: Matthewson 2006), Paraguayan Guaranı´ (Tupı´-Guaranı´: Tonhauser 2006, forthcoming a,b) and Kalaallisut (Eskimo-Aleut: Bittner 2005, 2008, forthcoming)]. This morphosyntactic variation gives rise to the question of whether the analysis of the temporal interpretation of tenseless languages involves covert tense The Author 2010. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected].


Abstract

308 Temporal Interpretation without Tense

(1) Context: My friends went to watch The Matrix yesterday. a. Korean Chelswu-nun ku yenghwa-lul cohaha(-ess)-ko Yenghi-nun Chelswu-TOP that movie-ACC like-PAST-and Yenghi-TOP silheha-ess-ta. dislike-PAST-DECL 1 We refer to the relevant (first) conjunct as the ‘non-final’ conjunct since it is not just the first conjunct that shows this behaviour in the two languages but in fact all non-final conjuncts. We limit our discussion and analysis to coordination constructions with two conjuncts in this article, but believe that our analysis can be straightforwardly extended to examples with more than two conjuncts. We follow, for example, J.H.-S. Yoon (1993, 1994, 1997), J.-M. Yoon (1996), Chung (2005) and Hirata (2006) in analysing these constructions as syntactically coordinate, regardless of whether a tense morpheme is realized or not, but note that other authors treat them as subordinating constructions (e.g. Tokashiki 1989; Kim 1995; Yi 1997, 1998). There are several pieces of evidence for the former analysis. First, if the non-final conjunct was syntactically subordinate to the final conjunct, we would expect a tense morpheme in the non-final conjunct of Korean constructions to be interpreted relative to the event time of the final conjunct (parallel to other subordinate clauses in the language). Thus, we would expect, for example, the past tense morpheme in the non-final conjunct in (i) to be interpreted relative to the past event time of the final conjunct, that is, to temporally locate Chelswu’s going to church prior to his going to the library, contrary to fact.

(i) Chelswu-nun ecey kyohoi-ey ka-ess-ko, kucekkey-nun tosekwan-ey Chelswu-TOP yesterday church-to go-PAST-and the.day.before.yesterday-TOP library-to ka-ess-ta. go-PAST-DECL ‘Chelswu went to church yesterday, and he went to the library the day before yesterday.’ Second, as pointed out by, for example, J.H.-S. Yoon (1997) and Hirata (2006), –ko, –te and –i may connect more than two clauses, as is typical for coordination markers but not for subordination markers. Finally, we follow Kubota and Lee (2008) in assuming that certain syntactic asymmetries between Korean constructions realized with and without tense need not be attributed to a subordination/coordination distinction, as done, for example, in Yi (1997) and Cho (2005). 2 The following glosses are used in the Korean and Japanese examples: ACC ¼ accusative case, COP ¼ copula, DECL ¼ declarative mood, GEN ¼ genitive case, IMP ¼ imperative mood, NOM ¼ nominative case, NPST ¼ non-past tense, PAST ¼ past tense, PL ¼ plural, PROG ¼ progressive aspect, Q ¼ interrogative mood, TOP ¼ topic marker.


morphemes, and hence is parallel to, for example, English in this regard (cf. Matthewson 2006 for St’a´t’imcets), or rather constitutes a case of crosslinguistic semantic variation since the temporal relation between the reference and the utterance time is determined, for example, pragmatically (cf. Bohnemeyer 2002 for Yucatec Maya). This article brings the debate about the formal semantic analysis of tenselessness and its results to bear on temporal interpretation in Korean and Japanese. While matrix clauses in these languages are obligatorily tensed (cf. e.g. Ogihara 1996, Sohn 1999), the non-final conjuncts of particular kinds of coordination constructions are not: in Korean, tense is optional in the non-final conjunct of coordination constructions with –ko ‘and’ [as illustrated in (1a)], and the non-final conjunct of the Japanese constructions with –te ‘and’ or –i ‘and’ cannot be tensed [as in (1b)].1,2

Jungmee Lee and Judith Tonhauser 309

3 The empirical scope of several of the aforementioned papers is wider than the temporal interpretation of the coordination constructions; they also discuss, for example, the interpretation of post-verbal morphemes other than tense (e.g. Fukushima 1999; Chung 2005), negative polarity items and the scope of negation (e.g. Yi 1997; J.H.-S. Yoon 1994, 1997), as well as scrambling, left/right dislocation and whextraction (e.g. Yi 1997; J.H.-S. Yoon 1997; Kwon and Polinsky 2008). While the current paper is limited to temporal interpretation, our results bear on the proper analysis of these constructions more generally since the syntax of tense and temporal interpretation is often argued in these papers to correlate with other syntactic and semantic properties of these constructions.


‘Chelswu liked the movie and Yenghi disliked it.’ b. Japanese Taroo-wa sono eiga-o kiniit(*-ta)-te/-i Hanako-wa Taro-TOP that movie-ACC like-PAST-and/-and Hanako-TOP kirat-ta. dislike-PAST ‘Taro liked the movie and Hanako disliked it.’ In (1a), the Korean past tense morpheme –ess is optional. (The examples give the underlying forms of the Korean and Japanese tenses.) Regardless of its presence, the non-final conjunct receives an interpretation according to which Chelswu’s liking the movie is true (at least) at the time in the past shortly after he and Yenghi watched the movie; Yenghi’s disliking the movie temporally overlaps with Chelswu’s liking the movie. In the Japanese example in (1b), the past tense morpheme –ta cannot be realized in the non-final conjunct. Just as in the Korean example, the (tenseless) non-final conjunct is interpreted in the past of the utterance time in the discourse context given, and Taro’s liking the movie temporally overlaps with Hanako’s disliking the movie at the past reference time. Previous analyses of the temporal interpretation of such constructions uniformly assume that the temporal interpretation of a tenseless non-final conjunct is affected by a (sometimes covert) expression that introduces a tense(-like) restriction. In one set of analyses, it is the tense morpheme of the final conjunct that determines not just the temporal interpretation of the final conjunct but also that of the non-final one (e.g. see J.H.-S. Yoon 1993, 1994, 1997 and B.-M. Kang 1988 for Korean; Hirata 2006 for Japanese); in the other set, the tense(-like) restriction is introduced by a phonologically zero tense morpheme in the non-final conjunct (Chung 2005 for Korean) or by the conjunction marker (cf. Cho 2005 for Korean; Fukushima 1999 and Nakatani 2004 for Japanese).3 In this article, we present novel data to argue that these analyses are not empirically adequate. For example, in the Korean and Japanese examples in (2), the tenseless non-final conjuncts are interpreted in the past of the utterance time, while the final conjuncts, which are marked for non-past tense, have present time reference. The availability of such data is unexpected, if the tense morpheme of the final conjunct determines the


temporal interpretation of the non-final one, as some authors have proposed. Likewise, an analysis according to which the temporal reference of the non-final conjunct is constrained by a phonologically zero tense morpheme would license a present or future interpretation of the non-final conjuncts in (2), contrary to fact.

Furthermore, we present novel evidence that motivates that no such tense(-like) restrictions need to be assumed to temporally interpret the non-final conjuncts since the temporal interpretation of such constructions is fully determined by independently motivated factors not considered by previous analyses, such as Aktionsart and the discourse context (cf. e.g. Partee 1984; Dowty 1986; Hinrichs 1986). In (2), for example, the temporal interpretation of the tenseless non-final conjunct is affected by the contextually given past reference time. Building on the finding that such factors play a key role in the temporal interpretation not just of tensed but also of tenseless languages (cf. e.g. Bohnemeyer 2002; Bittner 2008), we provide a truly tenseless analysis of the temporal interpretation of the (tenseless) non-final conjuncts of Korean and Japanese coordination constructions and show that it is empirically and conceptually superior to previous proposals. Thus, the analysis provides further evidence that tenseless clauses can be semantically interpreted as such, in tenseless languages and in languages where matrix clauses are otherwise tensed, such as Korean and Japanese. The article proceeds as follows. In section 2, we introduce the Reichenbachian framework for the analysis of temporal interpretation and illustrate the role of Aktionsart and discourse context on the temporal interpretation of matrix clauses in Korean and Japanese. Section 3 explores the temporal interpretation of tenseless coordination constructions in the two languages and shows that, besides tense and temporal adverbs, Aktionsart and the discourse context play a key role. The formal semantic analysis (couched in a categorial grammar framework) is developed in section 4 and is compared with previous


(2) Context: John was in a car accident a week ago. He was admitted to the hospital. a. Korean: Ku-nun swuswul-ul pat-ko cikum-un cal cinay-n-ta. he-TOP surgery-ACC receive-and now-TOP well do-NPST-DECL ‘He had surgery and now he is doing well.’ b. Japanese: Kare-wa shujutsu-o uke-te ima-wa daijoobu-da. he-TOP surgery-ACC take-and now-TOP fine-COP.NPST ‘He had surgery and now he is fine.’


proposals in section 5. The article concludes in section 6 with a discussion of implications of this research for analyses of crosslinguistic semantic variation. 2 TEMPORAL INTERPRETATION IN CONTEXT

(3)

Context: Ken was looking into the room. Maria was sitting at the table. Bill got up. Ken greeted him.

The reference time of the first clause of (3) is the (past) time at which Ken was looking into the room. Tense morphemes constrain the relation between the reference time and the utterance time: the past tense auxiliary verb was of was sitting presupposes that the reference time is in the past of the utterance time (e.g. Stone 1997; Kratzer 1998; Bittner 2008), which is the case in this context. The relation between the reference time and the eventuality time, that is, between the time at which Ken was looking into the room and the time of Maria’s sitting at the table, is constrained by Aktionsart, world knowledge and the discourse context (cf. e.g. Dowty 1986; Klein 1994). We distinguish three kinds of Aktionsarten, that is, classes of propositions with distinct aspectual properties: telic ones (e.g. Ken went to the store), processes (e.g. Yesterday it rained all morning long) and statives (e.g. Darla knows Spanish); see, for example, Dowty (1986) for definitions. Propositions denoting telic Aktionsarten and processes are eventive, while propositions denoting a stative Aktionsart are states. We follow, for example, Partee (1984), Dowty (1986) and Hinrichs (1986) in assuming that the effect of Aktionsart and discourse context on temporal interpretation is defeasibly determined by the principle in (4), which is adapted from similar proposals made in the literature: (4)

Temporal interpretation in discourse (TID) principle: Sentences S1, . . ., Sn are temporally interpreted in narrative discourse as follows:


Our exploration of the temporal interpretation of Korean and Japanese coordination constructions is couched in a Reichenbachian framework (Reichenbach 1947): in addition to the utterance time, the time at which an utterance is made, and the eventuality time, the time at which the eventuality is located, the reference time plays a central role in analysing the temporal reference of an utterance. We use the term eventuality as a cover term for events and states (Bach 1986). Following Klein (1994), the reference time is the time an utterance is about, that is, the topical time of the particular part of the discourse. We use the discourse in (3) to illustrate the three times.


a. The reference time of a sentence Si (for 1 i n) is either (i) a time consistent with the temporal adverb(s) of Si or (ii) if no temporal adverb occurs in Si, the reference time provided by the preceding sentence Si–1. b. Event descriptions update the reference time to a new reference time shortly after the original reference time; state descriptions do not update the reference time.

2.1 The temporal interpretation of Korean and Japanese matrix clauses Both Korean and Japanese are typically considered tensed languages since they each have a past tense (which locates the reference time prior to the utterance time) and a non-past tense (which requires the reference time to overlap or follow the utterance time), as illustrated in (5) and (6), respectively.4 (Since this article makes parallel points for Korean and Japanese, the convention we follow in the remainder of this article is to present the Korean version in the a.-example and the Japanese version in the b.-example.) (5) Past tense: a. Chelswu-nun ecey/#cikum/#nayil chwumchwu-ess-ta. Chelswu-TOP yesterday/now/tomorrow dance-PAST-DECL ‘Chelswu danced yesterday/#now/#tomorrow.’ b. Ken-wa kinoo/#ima/#asita ie-ni i-ta. Ken-TOP yesterday/now/tomorrow home-at be-PAST ‘Ken was at home yesterday/#now/#tomorrow.’ 4 In both languages, Aktionsart affects the interpretation of non-past tensed matrix clauses. In Japanese, for example, non-past tense telic eventualities are only compatible with a future-time interpretation (e.g. Kaufmann and Miyachi 2008). These restrictions are not formalized since they are not relevant to the main point of the paper.


In (3), the progressive state of Maria sitting at the table is temporally located at the contextually given reference time [clause (4a.ii)]. Following clause (4b), the reference time is not updated after interpreting the first clause of (3); hence, Bill’s getting up is temporally located at the reference time of the previous clause [clause (4a.ii)], that is, it temporally overlaps with Maria’s sitting at the table. Since the second clause of (3) denotes an event, it updates the reference time [clause (4b)]; this is the reference time at which Ken’s greeting Bill is located, which is hence correctly predicted to temporally follow Bill’s getting up.


(6)

Non-past tense: a. Chelswu-nun #ecey/cikum/nayil chwumchwu-n-ta. Chelswu-TOP yesterday/now/tomorrow dance-NPST-DECL ‘Chelswu is dancing/will dance #yesterday/now/tomorrow.’ b. Ken-wa #kinoo/ima/asita ie-ni i-ru. Ken-TOP yesterday/now/tomorrow home-at be-NPST ‘Ken is/will be at home #yesterday/now/tomorrow.’

(7)

a. Yenghi-ka ecey phathi-lul yel-ess-ta. Chelswu-nun Yenghi-NOM yesterday party-ACC hold-PAST-DECL Chelswu-TOP swul-ey chwiha-ess-ta. alchohol-at get.drunk-PAST-DECL ‘Yenghi had a party yesterday. Chelswu got drunk.’ b. Hanako-wa kinoo paatii-o si-ta. Taroo-wa Hanako-TOP yesterday party-ACC do-PAST Taro-TOP yopparat-ta. get.drunk-PAST ‘Hanako had a party yesterday. Taro got drunk.’

The following examples illustrate that the Aktionsart of a proposition affects the relation of the eventuality to the reference time and whether the reference time is updated or not. The examples in (8) consist of a sequence of two events, whereas the states denoted by the first clauses in (9) are followed by events. As predicted by the discourse-based theory of temporal interpretation outlined above, the two events in (8a) and (8b), respectively, are interpreted to be temporally located one after the other, whereas the states overlap with the events in (9a) and (9b), respectively.


In these examples, the temporal adverbs further constrain the location of the reference time with respect to the utterance time. For example, in the Korean example (5a), Chelswu’s dancing is temporally located within the denotation of the temporal adverb ecey ‘yesterday’. Aktionsart and the discourse context play a key role in the temporal interpretation of Korean and Japanese tensed matrix clauses (e.g. see E.-H. Lee 2007 for Korean; Ogihara 1996 for Japanese; Bittner 2008 cross-linguistically). In the examples in (7), which are modelled after Partee’s (1984) examples, the second clause is interpreted with respect to the reference time of the previous discourse: the individuals’ getting drunk did not occur at just any past time but at the contextually established past time at which the party took place.


The temporal order between eventualities in narrative discourse is not entailed by Aktionsart, that is, not part of the truth-conditional meaning of a discourse but rather implicated. Thus, even though two events in narrative discourse typically receive a sequential interpretation, this implicature can be blocked in a particular discourse context or by world knowledge. Consider the examples in (10): even though two events of riding a bicycle and flying typically are sequentially ordered, they receive an overlapping interpretation in the given discourse context. (10) Context: After watching the ending scene of the movie E.T., Yenghi says: a. E.T.-nun cacenke-lul tha-ess-ta. (Kuliko) pihayng-ul flight-ACC E.T.-TOP bike-ACC ride-PAST-DECL And ha-ess-ta. do-PAST-DECL ‘E.T. rode a bike. (And) he flew.’


(8) Event–event a. Chelswu-ka pang-ey tuleka-ess-ta. Yenghi-nun Chelswu-NOM room-to enter-PAST-DECL Yenghi-TOP ku-eykey keleo-ess-ta. he-to walk.over-PAST-DECL ‘Chelswu entered the room. Yenghi walked over to him.’ b. Taroo-wa heya-ni hait-ta. Hanako-ga kare-no Taro-TOP room-to enter-PAST Hanako-NOM he-GEN hoo-ni aruiteki-ta. direction-to walk.over-PAST ‘Taro entered the room. Hanako walked over to him.’ (9) State–event a. Yenghi-nun khun chayksang aph-ey ancaiss-ess-ta. front-at be.sitting-PAST-DECL Yenghi-TOP large desk Chelswu-ka pang-ey tuleka-ess-ta. Chelswu-NOM room-to enter-PAST-DECL ‘Yenghi was sitting in front of a huge desk. Chelswu entered the room.’ b. Hanako-wa ookina tukue-no mae-ni suwat-tei-ta. Taroo-wa Hanako-TOP large desk-GEN front-at sit-PROG-PAST Taro-TOP heya-ni hait-ta. room-to enter-PAST ‘Hanako was sitting in front of a huge desk. Taro entered the room.’


b. E.T.-wa jitensha-ni not-ta. (Sosite,) ton-da. ride-PAST And fly-PAST E.T.-TOP bike-at ‘E.T. rode a bike. (And) he flew.’ In sum, the temporal interpretation of Korean and Japanese matrix clauses is affected by tense, temporal adverbs, Aktionsart and the discourse context.

2.2 The temporal interpretation of tenseless languages

(11) Ho’liak-e’ t-inw¼il-ah-; Juan. Taán uy¼oók’ot-;. yesterday-TOP PRV-1sg¼see-CMP-3 Juan PROG 3¼dance-INC ‘Yesterday I saw Juan. He was dancing.’ Yucatec Maya is a tenseless language, that is, neither clause in (11) contains a tense morpheme that would constrain the temporal relation between the reference time and the utterance time (Bohnemeyer 2002). The discourse in (11) is nevertheless not temporally unconstrained. In the first clause, the reference time is constrained to a past time interval within the denotation of the temporal adverb ho’liak ‘yesterday’. The eventuality time of the speaker seeing Juan is located at this (past) reference time. The reference time is updated to a time shortly after the reference time of the first clause, and the progressive state denoted by the second clause is located at this new reference time. In this context, we understand Juan’s dancing to temporally overlap with the speaker seeing Juan. Out of context, the interpretation of the second clause of (11) is underdetermined in at least two ways: first, the referent of the third person cross-reference marker uy cannot be determined without a discourse context that makes salient a particular (third person) discourse participant and second, the reference time of the clause is not constrained since the language does not have tense markers. Thus, out of context, the second clause of (11) is compatible with past, present and future reference times (see Bohnemeyer 2002; Tonhauser 2006 for details). Once the discourse context and Aktionsart are taken 5 The following glosses are used in the Yucatec Mayan examples: 1sg ¼ first person singular, 3 ¼ third person, CL ¼ classifier, CMP ¼ completive status, DEF ¼ definite, D2 ¼ deictic marker, INC ¼ incompletive status, PRV ¼ perfective aspect/mood, PREP ¼ preposition, PROG ¼ progressive aspect/ mood, TOP ¼ topic. The perfective connective kaá forces a dynamic interpretation of the perfective event, excluding a resultative interpretation (cf. Bohnemeyer 2002: 413ff).


The temporal interpretation of tenseless languages, too, depends on Aktionsart and the discourse context for determining the temporal relation between eventualities in narrative discourse. Consider the Yucatec Mayan discourse in (11):5


(12) Context: As the little boy was running, . . . kaá h-t’ochpa-;-; t-u¼mots hun-p’eél che’. tree kaá PRV-stumble-CMP-3 PREP-3¼root one-CL Kaá h-luúb-;-; ich le¼ha’¼o’ kaá PRV-fall-CMP-3 in DEF¼water¼D2 ‘. . . he stumbled over the root of a tree. He fell into the water.’ If tenseless languages can receive truly tenseless analyses once the effect of the discourse context and Aktionsart on temporal interpretation are taken into consideration, then, we argue, it might also be possible to give a truly tenseless analysis of the temporal interpretation of tenseless non-final conjuncts in Korean and Japanese coordination constructions. The next section illustrates that the discourse context and Aktionsart play a role in the temporal interpretation of such constructions. 3 THE TEMPORAL INTERPRETATION OF COORDINATION CONSTRUCTIONS As mentioned in the introduction, one set of previous analyses of the Korean and Japanese coordination constructions maintains that the tense of the final conjunct affects the temporal interpretation of both the non-final and the final conjuncts (typically by the tense scoping over both conjuncts). Such analyses are motivated by data where the two conjuncts are interpreted at the same reference time, such as (1a#), the version of (1a) without a tense morpheme in the non-final conjunct:


into consideration, the temporal interpretation of tenseless languages proceeds in a similar fashion as that of tensed languages, with the difference that there are no tense markers that would presuppose a particular temporal relation between the reference time and the utterance time. Thus, just like in English, Korean and Japanese tensed matrix clauses, temporal adverbs and the discourse context establish the reference time for a particular utterance in narrative discourse, and Aktionsart determines the relation between the reference time and the eventuality time and whether the reference time is updated or not. In the naturally occurring discourse in (12), the eventive Aktionsart of the two clauses results in a default sequential interpretation (cf. also Bohnemeyer 2009); as a consequence, the boy’s falling into the water is interpreted to be located shortly after his stumbling.


(1a#)

Context: My friends went to watch The Matrix yesterday. Chelswu-nun ku yenghwa-lul cohaha-ko Yenghi-nun Chelswu-TOP that movie-ACC like-and Yenghi-TOP silheha-ess-ta. dislike-PAST-DECL ‘Chelswu liked the movie and Yenghi disliked it.’

(13) Context: What’s the weather like these days? a. Ecey-nun pi-ka o-ko onul-un nwun-i yesterday-TOP rain-NOM fall-and today-TOP snow-NOM o-n-ta. fall-NPST-DECL ‘It rained yesterday and it is snowing today.’ b. Kinoo-wa ame-ga hut-te kyoo-wa hare-tei-ru. yesterday-TOP rain-NOM fall-and today-TOP shine-PROG-NPST ‘It rained yesterday and the sky is clear today.’ The reverse temporal order between the non-final and the final conjunct is also possible: (14) a. Onul-un nwun-i o-ko ecey-nun pi-ka today-TOP snow-NOM fall-and yesterday-TOP rain-NOM o-ess-ta. fall-NPST-DECL ‘It is snowing today and it rained yesterday.’ 6

Since all of the examples of Japanese coordination constructions presented in this article are compatible and semantically equivalent with both –te ‘–and’ and –i ‘–and’, only the former coordination is given in the examples.


If the tense of the final conjunct determines the temporal interpretation of both conjuncts, it is correctly predicted that the states of Chelswu’s liking the movie and Yenghi’s disliking it are both temporally located at the contextually given past time and temporally overlap. But examples such as (13), pointed to, for example, in Chung (2005) for Korean and Fukushima (1999) for Japanese, present a first piece of evidence that the reference time of the non-final conjunct need not be identical to the reference time of the final conjunct. In these examples, a past time denoting temporal adverb occurs in the tenseless non-final conjunct, and thereby constrains the reference time of the non-final conjunct to a past time, whereas the final conjunct is constrained by a present time denoting temporal adverb and the non-past tense to a time that overlaps with the utterance time.6


(15) Context: How is Chelswu doing in the hospital? a. Cayhoalhwunlyen-ul yelsimhi ha-koiss-ko taum rehabilitation.program-ACC hard do-PROG-and next cwu-ey-nun thoiwuenha-n-ta. week-at-TOP be.discharged-NPST-DECL ‘He is in a tough rehabilitation program and will be discharged next week.’ b. Rihabiri-o sikkari shi-tei-te raishuu-ni-wa rehabilitation-ACC hard do-PROG-and next.week-at-TOP taiinsu-ru. be.discharged-NPST ‘He is in a tough rehabilitation program and will be discharged next week.’ (16) Context: How is Chelswu doing in the hospital? a. Cayhoalhwunlyen-ul yelsimhi ha-koiss-ko swuswul-un rehabilitation.program-ACC hard do-PROG-and operation-TOP cinan cwu-ey pat-ess-ta. last week-at receive-PAST-DECL ‘He is in a tough rehabilitation program and had an operation last week.’ 7

Fukushima’s (1999) analysis predicts that examples like (13b) are not possible but he modifies his original analysis to take into account the effect of temporal adverbs (308). We discuss his proposal in more detail in section 5.


b. Kyoo-wa hare-tei-te kinoo-wa ame-ga hut-ru. today-TOP shine-PROG-and yesterday-TOP rain-NOM fall-NPST ‘The sky is clear today and it rained yesterday.’ Thus, analyses that claim that the temporal interpretation of the nonfinal conjunct is determined by the tense of the final conjunct cannot account for these examples (e.g. see J.H.-S. Yoon 1993, 1994, 1997 and B.M. Kang 1988 for Korean; Fukushima 19997 and Hirata 2006 for Japanese). We argue instead that Aktionsart and the discourse context play a key role in determining the temporal interpretation of the non-final conjuncts. In fact, given the effect of Aktionsart and the discourse context on temporal interpretation that we have outlined in section 2, we predict that temporal adverbs are not necessary in order for the reference time of the non-final conjunct to be distinct from the reference time of the final conjunct. This prediction is borne out, as illustrated by the examples in (15)–(18). In the examples in (15) and (16), the (adverb-free) non-final conjuncts are interpreted at a contextually given present reference time, while the final conjuncts are interpreted at a later and an earlier time, respectively.


b. Rihabiri-o shikkari shi-tei-te shujutsu-wa do-PROG-and operation-TOP rehabilitation-ACC hard senshuu uke-ta. last week receive-PAST ‘He is in a tough rehabilitation program and had an operation last week.’

(17) Context: John was in a car accident a week ago. He was admitted to the hospital. a. Ku-nun swuswul-ul pat-ko cikum-un cal cinay-n-ta. he-TOP surgery-ACC receive-and now-TOP well do-NPST-DECL ‘He had surgery and now he is doing well’ b. Kare-wa shujutsu-o uke-te ima-wa daijoobu-da. he-TOP surgery-ACC take-and now-TOP fine-COP.NPST ‘He had surgery and now he is fine.’ (18) Context: What will you do next week? a. Uimilon hakhoi-ey ka-ko cikum-un palphyo semantics conference-at go-and now-TOP presentation cwunpi-lul ha-n-ta. preparation-ACC do-NPST-DECL ‘I will go to a semantics conference and I am preparing for the presentation now.’ b. Imiron gakkai-ga at-te semantics conference-NOM exist-and ima-wa happyoo-no junbi-o siteiru. now-TOP presentation-GEN preparation-ACC do-PROG-NPST ‘There will be a semantics conference and I am preparing for the presentation now.’ Thus, a temporal adverb (or a tense) need not be realized in the non-final conjunct in order for its reference time to be distinct from that of the final conjunct, contra, for example, Fukushima (1999). The following examples present evidence that the temporal interpretation of the Korean and Japanese coordination constructions is also affected by Aktionsart. Both conjuncts in (19a) and (19b) denote states, and hence receive an overlapping temporal interpretation,


The discourse contexts in (17), repeated from (2), and (18) make salient a past and a future time, respectively, relative to which the nonfinal conjuncts are interpreted. The reference times of the non-final conjuncts are again distinct from those of the final conjuncts, which are constrained by temporal adverbs and tense morphemes to overlap with the utterance time.


whereas the events denoted by the two conjuncts in (20) are correctly predicted to be sequentially ordered.

(20) Context: The president was sitting at his desk in his office. a. Yenghi-ka samwusil-lo tuleo-ko taythonglyeng-un Yenghi-NOM office-to enter-and president-TOP cali-eyse ilese-ess-ta. seat-from stand.up-PAST-DECL ‘Yenghi entered the office and the president stood up.’ b. Hanako-ga ofisu-ni haitteki-te daitooryoo-wa isu-kara Hanako-NOM office-to enter-and president-TOP seat-from tachiagat-ta stand.up-PAST ‘Hanako entered the office and the president stood up.’ The reference times of the two events in both (20a) and (20b) are in the past but not identical. Thus, even if there are no temporal adverbs in either conjunct, and both conjuncts are interpreted in the past, the reference and eventuality times of the two conjuncts need not be identical.8 If Aktionsart affects the temporal interpretation of the coordination constructions, the temporal ordering between two eventualities is not entailed but merely implicated [cf. (10)]. That this is the case is illustrated in (21): in the given discourse context, the default sequential 8 The sequential ordering observed in the examples in (20) arises in this narrative discourse and is due to the particular context and world knowledge. In a non-narrative discourse such as in the Korean example in (i), the question What did they do? can result in a list-like interpretation of the two events denoted by the conjuncts such that any temporal order, including temporal overlap, is possible for the two events.

(i)

Context: Chelswu and Yenghi lost their jobs in Korea. What did they do? Chelswu-nun mikuk-ulo isaka-ko Yenghi-nun tokil-lo isaka-ess-ta. Chelswu-TOP USA-to move-and Yenghi-TOP Germany-to move-PAST-DECL ‘Chelswu moved to the USA and Yenghi moved to Germany.’


(19) Context: What was going on when you were robbed? a. Payntu-nun umak-ul yencwuha-koiss-ko ai-tul-un child-PL-TOP band-TOP music-ACC play-PROG-and nolayha-koiss-ess-ta. sing-PROG-PAST-DECL ‘A band was playing and the children were singing.’ b. Band-ga ongaku-o ensooshi-tei-te kodomotachi-ga band-NOM music-ACC play-PROG-and children-NOM utat-tei-ta. sing-PROG-PAST ‘A band was playing and the children were singing.’


interpretation of riding a bike and flying is overridden (cf. J. Lee 2008 for further examples of this kind). (21) Context: After watching the ending scene of the movie E.T., Yenghi says: a. E.T.-ka cacenke-lul tha-ko, pihang-ul ha-ess-ta. E.T.-NOM bike-ACC ride-and flight-ACC do-PAST-DECL ‘E.T. rode a bike and flew.’ b. E.T.-wa jitensha-ni not-te ton-da. E.T.-TOP bike-at ride-and fly-PAST ‘E.T. rode a bike and flew.’

4 A TENSELESS ANALYSIS OF (TENSELESS) COORDINATION CONSTRUCTIONS The formal analysis of coordination constructions we develop is couched in a combinatoric categorial grammar fragment (cf. e.g. Steedman 1996, 2000; Baldridge 2002). The framework as well as the formal semantic and pragmatic analysis of matrix clauses are introduced in section 4.1. The Korean and Japanese coordination constructions are analysed in sections 4.2 and 4.3, respectively.

4.1 The framework Lexical and phrasal expressions consist of a phonological form, a syntactic category CAT and a meaning (translation) m. They are represented in the form given in (22). (22) form :

CAT

:m

For example, the lexical expression Chelswu-ka ‘Chelswu-NOM’ is represented as in (23): the phonological form is given as Chelswu-ka (rather than in IPA format), the syntactic category is N[NOM], i.e. a nominative case-marked noun phrase, and the expression is translated as the zero-place constant c (non-logical constants are bold-faced).


In sum, the examples in this section provide empirical support for the claim that the discourse context and Aktionsart constrain the temporal interpretation of Korean and Japanese coordination constructions. Previous analyses only considered the effect of tense and temporal adverbs, and proposed a tense(-like) restriction on the interpretation of tenseless non-final conjuncts. The analysis we develop in the next section shows that such a restriction is not needed to temporally interpret coordination constructions. We compare our proposal to previous ones in section 5.


(23) Chelswu-ka :

N[NOM]

:c

(24)

Forward function application

Backward function application

f1 : A = B : a f2 : B : b FA f1 f2 : A : a ðbÞ

f2 : B : b f1 : A n B : a BA f2 f1 : A :a ðbÞ

The lexical entries for the Korean intransitive verb nolayha ‘sing’ and the Japanese uta ‘sing’ are given in (25). The syntactic category of these verbs is S#[–T]\N[NOM], that is, combining these verbs with a nominative noun phrase (category N[NOM]) on their left results in an


The syntactic categories of our fragment are N (for noun phrases), S (for sentences) and S# (for sentence radicals). Case and tense are treated as syntactic features of noun phrases and sentence radicals, respectively: for example, the category N[NOM] is a nominative noun phrase, S#[–T] is an untensed sentence radical and S#[+T] is a tensed sentence radical. If an expression of a category for which a syntactic feature is defined is not specified for the syntactic feature, we assume that the expression is unspecified for that feature (e.g. a sentence radical of category S# could be tensed or untensed). Sentences of category S are always tensed. Following the Montagovian tradition, we translate natural language expression into expressions of a formal language (here, a typed intensional logic with lambdas), which are then semantically interpreted. The basic categories of the formal language are e (for entities), i (for intervals), e (for eventualities) and t (for truth values); we use the variables i, i#, i$, . . . for intervals and x, y, z, . . . for individuals. We assume a tight correspondence between the syntactic categories of natural language expressions and the syntactic categories of the translation language: expressions of the syntactic category N translate into expressions of category e, expressions of category S translate into expressions of category t and sentence radicals (category S#) translate into category Æi, tæ (sets of intervals). We assume the two combinatoric rules given in (24): forward function application (FA) and backward function application (BA). The FA rule combines an expression of form f1, of category A/B (read ‘A forward slash B’) and whose translation is a with an expression to its right of form f2, of category B and whose translation is b. The result of the combination (given below the line) is an expression with the form f1 f2 (i.e. f1 and f2 are concatenated), of category A and with the translation a(b) (i.e. a is applied to b). BA differs from FA only in that the functor expression f1 occurs to the right of its argument f2, that is, the mode of combination is \ (read ‘backward slash’).


untensed sentence radical (category S#[–T]). The translations of both verbs denote a function from individuals x to a set of intervals i such that x sings at i. The constant sing# in the lexical entries is of category Æe, Æe, tææ, that is, denotes a function from individuals to a set of events (of the individual singing). (25) a. Korean: nolayha ‘sing’ : S#[–T]\N[NOM] : kxki[AT(i, sing#(x))] b. Japanese: uta ‘sing’ : S#[–T]\N[NOM] : kxki[AT(i, sing#(x))]

Deictic temporal adverbs and tenses introduce restrictions on the location of the reference time with respect to the utterance time. We illustrate their contribution to temporal interpretation, as well as the framework in general, by analysing the Korean example in (27). (27) Ecey Chelswu-ka nolayha-ess-ta. yesterday Chelswu-NOM sing-PAST-DECL ‘Yesterday Chelswu sang.’ The lexical entries of the words and morphemes used in (27) are given in (23), (25a) and (28a–c). The syntactic category of the temporal adverb ecey ‘yesterday’ is given as S#[–T]/S#[–T] in (28a), that is, the adverb combines with a tenseless sentence radical and returns a tenseless sentence radical. Semantically, the temporal adverb combines with an expression that denotes a set of intervals i and restricts these intervals to those included in the denotation of the constant yday#. The past tense morpheme –ess ‘PAST’ in (28b) combines with an untensed sentence radical (category S#[–T]) and returns a tensed sentence radical (category S#[+T]). Its semantic effect is similar to that of temporal adverbs: it applies to an expression that denotes a set of intervals i and restricts these intervals to those that lie before the now, a distinguished variable that is interpreted as the utterance time. The declarative mood marker –ta


The AT predicate (adopted from Condoravdi 2002) relates an interval i and a formula P that denotes a set of eventualities (category Æe, tæ). The interval i corresponds to the reference time of the utterance. We adopt Krifka’s (1998) trace function s and let s(e) denote the eventuality time of the eventuality e. The temporal relation between the reference time interval i and the eventuality time s(e) depends on the Aktionsart of the expression P: as discussed in section 2, the eventuality time of an event is included in the reference time [s(e) i]; the eventuality time of a state includes the reference time [i s(e)]. de½PðeÞ ^ sðeÞ4i if P is eventive (26) ATði; PÞ ¼ de½PðeÞ ^ i4sðeÞ if P is stative


‘DECL’ in (28c) combines with a tensed sentence radical and returns a sentence (category S), which is of type t, that is, denotes a truth value. (28) a. ecey ‘yesterday’ : S#[–T]/S#[–T] : kPÆi, tæki[P(i) ^ i 4 yday#] b. –ess ‘PAST’ : S#[+T]\S#[–T] : kPÆi, tæki[P(i) ^ i < now]9 c. –ta ‘DECL’ : S\S#[+T] : kPÆi, tæ[P(i)]

(29) Chelswu-ka : N½NOM : c nolaya : s0½T \N½NOM : kxki½ATði; sing0 ðxÞÞ BA ecey : s0½T =s0½T : kPki½PðiÞ ^ i 4 yday0 C:-ka nolayha : s0½T : ki½ATði; sing0 ðcÞÞ FA ecey C:-ka nolayha : s0½T : ki½ATði; sing0 ðcÞÞî 4 yday0 -ess : s0½ + T \ s0½T : kPki½PðiÞî < now BA ecey C:-ka nolayha-ess : s0½ + T : ki½ATði; sing0 ðcÞÞî 4 yday0 ^ i < now -ta : s\s0½ + T : kP½PðiÞ BA Ecey C:-ka nolayha-ess-ta : s : ATði; sing0 ðcÞÞ ^ i 4 yday0 ^ i < now

The unbound variable i in the last line of (29) refers to the reference time, which is contextually provided (and constrained by temporal adverbs and tenses). We assume that the variable assignment function keeps track of the reference time as the interpretation of the discourse proceeds. As discussed above, the AT predicate relates the eventuality time of the eventuality denoted by sing#(c) to the reference time i, resulting in the following translation for (27): (30) Final truth-conditional meaning translation of (27): de[sing#(c, e) ^ s(e) 4 i ^ i < now ^ i 4 yday#] According to (30), (27) is true if and only if the eventuality time of the event of Chelswu’s singing is located in the contextually given reference time i that is prior to now and within the denotation of ecey ‘yesterday’. We return to the question of how reference times are identified and located with respect to each other below, after introducing the analysis of Japanese matrix clauses. 9 For ease of exposition, tense is formally analysed here to assert rather than presuppose a relation between the reference time and the utterance time.


The syntactic and translation derivation of (27) is given in (29). Translation derivations are simplified by lambda conversions whenever applicable. (For reasons of space, Chelswu-ka ‘Chelswu-NOM’ is abbreviated as C.-ka; for readability, the phonological form of an expression is given in a box.)


In contrast to Korean, Japanese matrix clauses do not have a mood marker. We assume that in Japanese the tense morpheme applies to untensed sentence radicals (category S#[–T], type Æi, tæ) to form a tensed sentence (category S, type t). We illustrate the analysis with the example in (31); the relevant lexical entries are given in (31a–d).

The derivation of (31) is given in (32); Hanako-ga ‘Hanako-NOM’ is abbreviated as ‘H.-ga’. (32) H:-ga : N½NOM : h uta : s0½T \N½NOM : kxki½ATði; sing0 ðxÞÞ BA kinoo : s0½T =s0½T : kPÆi;tæ ki½PðiÞ ^ i 4 yday0 H:-ga uta : s0½T : ki½ATði; sing0 ðhÞÞ FA kinoo H:-ga uta : s0½T: ki½ATði; sing0 ðhÞÞ ^ i4yday0 -ta : s \ s0½T: kPÆi;tæ½PðiÞî< now BA Kinoo H:-ga uta-ta : s : ATði; sing0 ðhÞÞ ^ i 4 yday0 ^ i < now

The final translation for (31) is given in (33): (33) Final truth-conditional meaning translation of (31): de[sing#(h, e) ^ s(e) 4 i ^ i < now ^ i 4 yday#] Just like with the Korean example, (31) is true according to (33) if and only if the eventuality time of the event of Hanako singing is located in the contextually given reference time i, which is prior to now and temporally constrained by the past time denoting temporal adverb. Since the effect of Aktionsart on temporal interpretation is not part of the truth-conditional meaning of an utterance, the translations of two successive sentences (or a coordination construction) do not capture the temporal relation between their respective reference and eventuality times. The two clauses of the Korean example (7a), for example, repeated in (34) below, receive translations as in (34a) and (34b), respectively.


(31) Kinoo Hanako-ga uta-ta. yesterday Hanako-NOM sing-PAST ‘Yesterday Hanako sang.’ a. kinoo ‘yesterday’ : S#[–T]/S#[–T] : kPÆi, tæki[P(i) ^ i 4 yday#] b. Hanako-ga ‘Hanako-NOM’ : N[NOM] : h c. uta ‘sing’ : S#[–T]\N[NOM] : kxki[AT(i, sing#(x))] d. –ta ‘PAST’ : S\S#[–T] : kPÆi, tæ[P(i) ^ i < now]


(34) Yenghi-ka ecey phathi-lul yel-ess-ta. Chelswu-nun Yenghi-NOM yesterday party-ACC hold-PAST-DECL Chelswu-TOP swul-ey chuiha-ess-ta. alchohol-at get.drunk-PAST-DECL ‘Yenghi had a party yesterday. Chelswu got drunk.’ a. de[have.party#(y, e) ^ i 4 s(e) ^ i < now ^ i 4 yday#] b. de#[drunk#(c, e#) ^ s(e#) 4 i# ^ i# < now]

(35) Default interpretation of (34) in discourse: dede#[have.party#(y, e) ^ i 4 s(e) ^ i < now ^ i 4 yday# ^ drunk#(c, e#) ^ s(e#) 4 i]

4.2 The interpretation of Korean coordination constructions Recall that tense is optional in the non-final conjunct of Korean coordination constructions. We account for this in the lexical entry of the conjunction marker –ko, given in (36). The suffix first combines with the non-final conjunct to its left, an optionally tensed sentence radical (category S#), and then with the final conjunct to its right, an obligatorily tensed sentence radical (category S#[+T]). The resulting conjunction is also a tensed sentence radical. (36) –ko ‘and’ : (S#[+T]/S#[+T])\S# :kPÆi, tækQÆi, tæki[P(i#) ^ Q(i)] The crucial assumption that accounts for the optionality of the tense morpheme in the non-final conjunct is that both tensed and untensed sentence radicals are of the same syntactic category (S#) and translated by expressions of category Æi, tæ. According to this lexical entry of –ko, the tense morpheme of the final conjunct only affects the temporal interpretation of the final conjunct, which is already tensed when it combines with –ko, and hence the non-final conjunct. The analysis also does not attribute any temporal meaning to the coordination marker (in contrast to, e.g. Cho 2005 and Nakatani 2004, as discussed in section 5). The relevant parts of the syntactic analysis of the Korean example (1a#), repeated in (37), is given in (38).


Since the first sentence of (34) has a stative Aktionsart, it does not update the reference time (clause (b) of the TID in (4)). Hence, the reference time i# of the second sentence of (34) is identical to the reference time i of the first. The default interpretation of (34) is that Chelswu got drunk at Yenghi’s party:


(37) Context: My friends went to watch The Matrix yesterday. Chelswu-nun ku yenghwa-lul cohaha-ko Yenghi-nun like-and Yenghi-TOP Chelswu-TOP that movie-ACC silheha-ess-ta. dislike-PAST-DECL ‘Chelswu liked the movie and Yenghi disliked it.’ For reasons of space, the form, syntactic category and translation of an expression are presented below each other rather than next to each other.

C: ku yenghwa-lul cohaha ko : (s0½ + T /s0½ + T )\s0 : s0½T : ki0 ½AT(i0 ; like:movie0 (c; e)) ^ i0 4s(e) : kPkQki½Pði0 Þ ^ QðiÞ C: ku yenghwa-lul cohaha-ko : s0½ + T /s0½ + T : kQki½ATði0 ; like:movie0 ðc; eÞÞ ^ i0 4sðeÞ ^ QðiÞ

BA Y: silheha-ess : s0½ + T : ki½ATði; dislike:movie0 ðy; e0 ÞÞ^ i4sðe0 Þ ^ i < now

C: ku yenghwa-lul cohaha-ko Y: silheha-ess : s0½ + T : ki½ATði0 ; like:movie0 ðc; eÞÞ ^ i0 4sðeÞ ^ ATði; disike:movie0 ðy; e0 ÞÞ ^ i 4 sðe0 Þ ^ i < now

FA

-ta : s\s0½ + T : kP½PðiÞ

BA Chelswu-nun ku yenghwa-lul cohaha-ko Yenghi-nun silheha-ess-ta : s : ATði0 ; like:movie0 ðc; eÞÞ ^ i0 4sðeÞ ÂTði; dislike:movie0 ðy; e0 ÞÞ ^ i4sðe0 Þ ^ i < now

We assume that the declarative mood marker outscopes the two conjuncts.10 10

Only the final conjunct of a Korean coordination construction is marked for mood. The data in (i) and (ii) motivate that the mood marker affects the interpretation of both conjuncts (see also J. Lee 2008 for discussion). The examples in (i) are felicitous since both conjuncts can be interpreted with the same mood [declarative in (ia), interrogative in (ib)], while (ii) is infelicitous since the non-final conjunct cannot be interpreted as a command. (i)

a. Chelswu-ka chwumchwu-ko Yenghi-ka nolayha-ess-ta. Chelswu-NOM dance-and Yenghi-NOM sing-PAST-DECL ‘Chelswu danced and Yenghi sang’ b. Chelswu-ka chwumchwu-ko Yenghi-ka nolayha-ess-ni? Chelswu-NOM dance-and Yenghi-NOM sing-PAST-Q ‘Did Chelswu dance and Yenghi sing?’ (ii) #Na-nun apu-ko ne-nun na-eykey yak-ul kacikoo-ala. I-TOP sick-and you-TOP I-to medicine-ACC bring-IMP Intended: ‘I am sick, and (thus you) bring me medicine!’


(38) Analysis of the relevant parts of (37): (Y. stands for Yenghi-nun, C. for Chelswu-nun)


(39) Context: rt is a past time shortly after Chelswu and Yenghi saw the movie. dede#[like.movie#(c, e) ^ i# 4 s(e) ^ i# ¼ rt ^ dislike.movie#(y, e#) ^ i# 4 s(e#) ^ i# < now] According to (39), (37) is true if and only if there is a state e of Chelswu liking the movie and a state e# of Yenghi disliking the movie such that the eventuality times of both states are located at the reference time i#, which is in the past of the utterance time at a time shortly after Chelswu and Yenghi saw the movie. Crucially, our analysis correctly predicts that, in the given discourse context, the temporal interpretation of the tenseless version of (37) is equivalent in meaning to that of the version of (37) where a past tense is realized in the non-final conjunct.11 This is the case since the discourse context already constrains the reference time of the non-final conjunct to precede the utterance time; hence, a past tense morpheme in the non-final conjunct does not further constrain the relation between the reference time and the utterance time. Thus, according to our analysis, the two versions of (37) express the same meaning despite morphological differences. The remainder of this section illustrates that the analysis accounts for the other examples discussed in section 3, without further assumptions. Consider first the example in (13a), repeated in (40), where a past time 11 An important question raised by Lisa Matthewson (p.c.) is whether other meaning differences are associated with the presence or absence of the tense morpheme in the Korean constructions. Some authors (e.g. C. Kang 1990; Sohn 1999; Cho 2005) have argued that the tensed and tenseless versions of coordination constructions differ in terms of the discourse relations that can be expressed, for example, that the tensed but not the untensed variant is compatible only with an ‘additive’ discourse relation (which expresses a non-temporal logical conjunction). Kubota and Lee (2008) argue against this on the basis of naturally occurring data.


Since the non-final conjunct of (37) does not have a tense morpheme, the location of the reference time i# at which the eventuality of Chelswu’s liking the movie is temporally located is not fixed relative to the utterance time. Just like with tenseless languages (cf. section 2.2), we assume that the reference time of the non-final conjunct is provided either by a temporal adverb or by the discourse context [clause (a) of the TID principle in (4)]. In (37), the reference time i of the non-final conjunct is contextually provided: it is a past time rt shortly after the time at which Chelswu and Yenghi saw the movie. Since the first clause of (37) is a state, clause (b) of the TID principle specifies that the reference time is not updated. Thus, the reference time i of the second clause of (37) is identified with i#:


denoting temporal adverb occurs in the non-final conjunct and a present time denoting one in the final conjunct. The truthconditional meaning assigned to this example by our analysis is given in (41).

According to clause (a) of the TID principle, the reference times of the two conjuncts are constrained by the times denoted by the temporal adverb realized in each conjunct. Thus, the temporal adverbs of (40) require the reference times of the two conjuncts to be distinct times; according to (41), (40) is correctly predicted to be true if and only if it rained yesterday and it is snowing today. In (17a), repeated in (42), a past reference time is contextually provided for the non-final conjunct. Example (43a) gives the truthconditional meaning and (43b) the default interpretation in context. (42) Context: Chelswu was in a car accident a week ago. He was admitted to the hospital. Ku-nun swuswul-ul pat-ko cikum-un cal cinay-n-ta. he-TOP surgery-ACC receive-and now-TOP well do-NPST-DECL ‘He had surgery and now he is doing well.’ (43) a. Truth-conditional meaning of (42): dede#[have.surgery#(c, e) ^ s(e) 4 i ^ do.well#(c, e#) ^ i# 4 s(e#) ^ i# ¼ now] b. Context: rt is a past time shortly after Chelswu was admitted to the hospital. dede#[have.surgery#(c, e) ^ s(e) 4 rt ^ do.well#(c, e#) ^ i# 4 s(e#) ^ i# ¼ now] The truth conditions of (42) in (43a) again do not specify the location of the reference time i of the non-final conjunct with respect to the utterance time. The reference time rt at which the non-final conjunct is interpreted is a time shortly after Chelswu was admitted to the hospital. Thus, the eventuality time s(e) of the event e of Chelswu having surgery is located at the past reference time rt,


(40) Context: What’s the weather like these days? Ecey-nun pi-ka o-ko onul-un nwun-i yesterday-TOP rain-NOM fall-and today-TOP snow-NOM o-n-ta. fall-NPST-DECL ‘It rained yesterday and it is snowing today.’ (41) Truth-conditional meaning of (40): dede#[rain#(e) ^ s(e) 4 i ^ i 4 yday# ^ snow#(e#) ^ s(e#) 4 i# ^ i# 4 today# ^ i# ¼ now]


(44) Context: The president was sitting at his desk in his office. Yenghi-ka samwusil-lo tuleo-ko taythonglyeng-un cali-eyse seat-from Yenghi-NOM office-to enter-and president-TOP ilese-ess-ta. stand.up-PAST-DECL ‘Yenghi entered the office and the president stood up.’ (45) a. Truth-conditional meaning translation of (44): dede#[enter.office#(y, e) ^ s(e) 4 i ^ stand.up#(p, e#) ^ s(e#) 4 i# ^ i# < now] b. Context: rt is a past time included in the time at which the president sits at his desk. dede#[enter.office#(y, e) ^ s(e) 4 rt ^ stand.up#(p, e#) ^ rt < i# ^ s(e#) 4 i# ^ i# < now] In the discourse context given for (44), clause (a) of the TID principle specifies that the reference time i of the non-final conjunct is a time rt included in the eventuality time of the (progressive) state of the president sitting at his desk. Yenghi’s entering the office is therefore temporally located within this past reference time rt. Since the nonfinal conjunct denotes an event, the reference time is updated to a time i# shortly after rt [per clause (b) of the TID principle in (4)]. The final conjunct is interpreted at this reference time i#, which is constrained by past tense to be prior to the utterance time (i# < now). The analysis thus correctly predicts that the event of the president’s standing up is temporally located after the event of Yenghi entering the office (and both events are located in the past of the utterance time). To conclude, the analysis shows that a truly tenseless (semantic) analysis can be given to constructions where no tense morpheme


as specified in (43b). Since the reference time i# of the final conjunct is located by the temporal adverb cikum ‘now’ [clause (a) of the TID principle], the analysis correctly predicts that (42) is true if and only if there is a past event of Chelswu having surgery and a state of his being fine that overlaps with the utterance time. The temporal interpretation of the examples in (15), (16) and (18) proceeds alike. The final example we discuss is (20a), repeated in (44). In this example, the discourse context and Aktionsart of the two conjuncts give rise to an interpretation where both conjuncts are interpreted at past but non-identical reference times. The truth-conditional meaning of (44) is given in (45a) and the default interpretation in context is in (45b).


is realized in the non-final conjunct once the effect of Aktionsart and the discourse context on temporal interpretation is taken into consideration.

4.3 The interpretation of Japanese coordination constructions

(46) –te/–i ‘and’ :

(S/S)\S#[–T]

: kPÆi, tækQt[P(i) ^ Q]

We illustrate the analysis of Japanese coordination constructions with example (47). (47) Context: My friends went to watch The Matrix yesterday. Taroo-wa sono eiga-o kiniit-te Hanako-wa kirat-ta. Taro-TOP that movie-ACC like-and Hanako-TOP dislike-PAST ‘Taro liked the movie and Hanako disliked it.’ Aside from the requirement that the non-final conjunct not be tensed, the analysis of the temporal interpretation of Japanese coordination constructions is entirely parallel to that of the Korean constructions illustrated in the previous section. (48) Partial syntactic analysis of (47): (T. stands for Taroo-wa, H. stands for Hanako-wa) T: sona eiga-o kiniit : s0½T : ki½AT(i; like:movie0 (t; e)) ^ i4s(e)]

te : (s/s)\s0½T : kPkQ½PðiÞ ^ Q

T: sona eiga-o kiniit-te : s/s : kQ½AT(i; like:movie0 (t; e)) ^ i4s(eÞ ^ Q]

BA H: kirat-ta : s : ½AT(i0 ; dislike:movie0 (h; e0 ))^ i0 4s(e0 ) ^ i0 < now

Taroo-wa sona eiga-o kiniite-te; Hanako-wa kirat-ta : s : ATði; like:movie0 ðt; eÞÞ ^ i4sðeÞ ^ ATði0 ; disike:movie0 ðh; e0 ÞÞ ^ i0 4sðe0 Þ ^ i0 < now

FA


In contrast to their Korean counterparts, the non-final conjuncts of Japanese coordination constructions have to be tenseless. The lexical entries for the Japanese coordination markers –te and –i in (46) guarantee this by requiring the first argument of the coordination markers, the non-final conjunct, to be a tenseless sentence radical (category S#[–T]). Since tensed sentences in Japanese are of category S (cf. section 4.1), this is the category of the second argument of the Japanese coordination markers, as well as the category of the resulting sentence.


The truth-conditional meaning assigned to (47) by the analysis is given in (49a), and (49b) gives the default interpretation given the discourse context where the reference time rt is a past time shortly after Taro and Hanako saw the movie. (49) a. Truth-conditional meaning translation of (47): dede#[like.movie#(t, e) ^ i 4 s(e) ^ dislike.movie#(h, e#) ^ i# 4 s(e#) ^ i# < now] b. Context: rt is a time shortly after Taro and Hanako saw the movie dede#[like.movie#(t, e) ^ rt 4 s(e) ^ dislike.movie#(h, e#) ^ rt 4 s(e#) ^ rt < now]

4.4 Summary The analysis of the temporal interpretation of Korean and Japanese coordination constructions we provided in this section shows that a truly tenseless analysis of tenseless non-final conjuncts is possible once the effects of discourse and Aktionsart on temporal interpretation are taken into consideration. Our analysis borrows insights both from the interpretation of English narrative discourses (e.g. Partee 1984; Dowty 1986; Hinrichs 1986) and from the temporal interpretation of tenseless languages (e.g. Bohnemeyer 2002; Bittner 2008).

5 COMPARISON WITH PREVIOUS PROPOSALS As mentioned above, none of the previous analyses of the temporal interpretation of Korean and Japanese coordination constructions considers the effect of Aktionsart and the discourse context. Instead, they argue that the temporal interpretation of the tenseless non-final conjunct is determined by a tense(-like) meaning restriction introduced by (i) the tense morpheme of the final conjunct, (ii) a zero tense morpheme realized in the non-final conjunct or (iii) the coordination marker. Analyses of type (i), for example, J.H.-S. Yoon (1993, 1994, 1997) and B.-M. Kang (1988) for Korean, and Hirata


Just like in the Korean example, the default interpretation assigned to (47) in the given discourse context is one according to which (47) is true if and only if there are states e and e# of Taro liking the movie and Hanako disliking the movie, respectively, whose eventuality times are located at the contextually given past reference time rt.


(50) Context: Chelswu was in a car accident a week ago. He was admitted to the hospital. Ku-nun swuswul-ul pat-;-ko, cikum-un cal he-TOP surgery-ACC receive-TENSE-and now-TOP well cinay-n-ta. do-NPST-DECL ‘He had surgery, and now he is doing well.’ Chung’s analysis correctly predicts that the non-final conjunct need not be interpreted at the same time as the final conjunct: ‘tense is interpreted in each of the conjuncts, leading to the possibility of an asymmetric tense interpretation’ (558). Although this allows Chung in principle to account for examples like (15)–(18) and (20), where the reference times of the two conjuncts are not identical, his analysis does not have anything to say about how the non-final conjunct or, 12 In contrast to Korean and Japanese, a preliminary investigation of coordination constructions in Turkish suggests that an analysis that assumes that the tense morpheme of the final conjunct plays a role in the temporal interpretation of the final conjunct may be suitable. Just like in Japanese, the non-final conjunct of a Turkish coordination construction with –ip ‘and’ is tenseless (cf. e.g. Kornfilt 1997; Kabak 2007), as illustrated in the examples in (i), where the tense morpheme of the final conjunct is –du¨ ‘PAST’. The Turkish construction, just like that of Korean and Japanese, allows for the reference times of the non-final and final conjuncts to be distinct, as illustrated by the example in (ia), which corresponds to the Korean and Japanese examples in (20). However, our Turkish consultant rejected Turkish variants of examples like (13) and (17), as illustrated in (ib). (Present tense is glossed PRES, dative case is glossed DAT.)

(i) a. Hasan isx-e gid-ip, ev-e do¨n-du¨ Hasan work-DAT go-and home-DAT return-PAST ‘Hasan went to work and returned home.’ (Kornfilt 1997: 110) b.#Hasan isx-e gid-ip, xu s anda uyu-iyor Hasan work-DAT go-and at moment sleep-PROG.PRES (Intended: Hasan went to work and is now sleeping.) One might hypothesize that Turkish differs from Korean and Japanese in that the relation between the reference times of both the non-final and final conjuncts and the utterance time is constrained by the tense of the final conjunct. We leave this question to future research.


(2006) for Japanese, are empirically challenged by examples in which the reference time of the two conjuncts is not identical, such as (15)– (18) and (20).12 Chung’s (2005) analysis of Korean coordination constructions is the only one (as far as we are aware) to propose that the temporal interpretation of a tenseless non-final conjunct is determined by a phonologically zero tense morpheme that is realized in the non-final conjunct. Empirical motivation for the analysis is that overt tense morphemes may occur in the non-final conjunct in Korean. Chung’s analysis is illustrated for the example (17a) in (50), where –; ‘TENSE’ represents the phonologically zero tense morpheme:



for that matter, the entire coordination construction is temporally interpreted. Chung does not, for example, identify any constraints on the interpretation of the phonologically zero tense morpheme, thereby allowing example (50) to receive an interpretation according to which Chelswu has surgery in the future of the utterance time and is now doing well, contrary to native speaker judgments. It is reasonable, of course, to assume that the temporal interpretation of the zero tense morpheme postulated by Chung is restricted by the constraints on temporal interpretation discussed in sections 2 and 3 above. That is, the temporal reference of the zero tense morpheme is either constrained by a temporal adverb in the same clause or identified with the contextually given reference time [cf. clause (a) of the TID principle in (4)]. Assuming that the update of reference times and the relation between the reference time and the eventuality time of an eventuality is governed by principles like those we assume, Chung’s analysis would then make the same predictions as ours, meaning that an analysis where a zero tense morpheme plays a role in the temporal interpretation of Korean and Japanese coordination constructions can succeed. We believe, however, that our approach is preferable to Chung’s for two reasons. First, all other things being equal, there is no need to assume a zero tense morpheme to formally analyse the temporal interpretation of Korean (and Japanese) coordination constructions, as we have shown in section 4. By appealing to Occam’s razor, we argue that our analysis is conceptually superior to Chung’s since it makes the same predictions but makes do with less theoretical constructs. The second argument in favour of our analysis over Chung’s is that the latter is harder to motivate for the Japanese coordination constructions: since Japanese does not allow overt tense morphemes to occur in the non-final conjuncts, it seems less plausible to motivate that a zero tense morpheme occurs and determines the temporal interpretation of nonfinal conjuncts. Our analysis, by contrast, does not require the assumption of zero tense morphemes in an environment where overt tense morphemes cannot occur. The third type of analysis of the Korean and Japanese coordination constructions assumes that a tense-like restriction on a tenseless nonfinal conjunct is contributed by the coordination marker. Cho (2005) assumes that Korean has two homophonous coordination markers –ko, which encode different temporal relations between the two clauses: with –ko1, the non-final conjunct has to be tenseless, is syntactically subordinate to the tensed final conjunct and a sequential temporal interpretation is required of the two clauses; –ko2



coordinates the tensed non-final conjunct with the tensed final conjunct and does not impose a temporal relation. The data discussed in section 3 show that this analysis is not empirically supported since (i) the two conjuncts of example (1a) are interpreted at the same time regardless of whether the non-final conjunct is tensed or not and (ii) the two conjuncts of example (17) are interpreted at distinct times, also regardless of whether the non-final conjunct is tensed or not. Thus, a correlation between the presence of tense in the non-final conjunct and the temporal relation between the two conjuncts is not empirically supported. Following Kuno (1973: 195), Arikawa (1992: 30) and Ogihara (1998: 107) assume that the Japanese coordinator –te ‘and’ is temporal, meaning ‘and then’, and imposes a temporal order on the conjuncts such that the non-final conjunct must precede the final one. A similar proposal is made by Nakatani (2004), who argues that –te is a morphological variant of a relative past tense marker and functions ‘to sequence two intervals’ (168). Japanese examples where the two conjuncts are interpreted at the same time, as in (1b), (19b) and (21b), or the eventuality denoted by the non-final conjunct temporally follows that of the final one, as in (14b), (16b) and (18b), are counterexamples to these proposals. The ‘and then’ meaning observed in some coordination examples is thus better analysed as resulting from the (pragmatic) TID principle than as part of the truth-conditional meaning of the coordinator. Fukushima’s (1999) analysis of Japanese coordination constructions differs from the previously discussed ones in this set in that it does not attribute a particular meaning to the coordination marker. Rather, Fukushima argues that the coordination marker introduces an underspecified functor P that acts as a place holder for the semantic property that determines the temporal interpretation of the tenseless non-final conjunct; the process by which the content of P is recovered is a version of the ellipsis resolution mechanism introduced in Dalrymple et al. (1991). Fukushima assumes that the tense morpheme of the final conjunct determines the interpretation of the tenseless non-final conjunct but he was aware of examples like (13) that pose a problem for his analysis [as for analyses of type (i)]: he argues (308) that in cases where a temporal adverb occurs in the non-final conjunct, the content of P is not recovered from the tense of the final conjunct but instead from the temporal adverb realized in the non-final conjunct. This modification does not, however, account for examples like (15)–(18) where the non-final and final conjuncts are interpreted at distinct times despite no


6 CROSS-LINGUISTIC SEMANTIC VARIATION A feature shared by all of the previous analyses of the Korean and Japanese coordination constructions is that the temporal semantics of a (tenseless) non-final conjunct involves a tense(-like) restriction. The fact that tense morphemes play a role in the temporal interpretation of Korean and Japanese matrix clauses and a variety of subordinate clauses (such as complement and temporal adjunct clauses)13 may have contributed to the assumption that the meaning contributed by tense morphemes is essential to the temporal interpretation of the non-final conjuncts, even when no overt tense morpheme is present. Fukushima (1999) is most explicit about this assumption in his description of Japanese coordination constructions: ‘the tense morpheme required for proper semantic interpretation of the first conjuncts is ‘‘missing’’ on the ‘‘surface’’ level but somehow ‘‘recovered’’ on the semantic level’ (301). By contrast, the analysis we have developed does not rely on tense but only on Aktionsart and the discourse context. This difference between the two types of analyses touches on the larger question regarding the nature and extent of cross-linguistic semantic variation: does morphosyntactic variation in a particular area of grammar correspond 13 Some types of Korean relative clauses have been argued to be tenseless, for example, H. Lee (1991); see J. Lee (2009) for discussion.


temporal adverb occurring in the non-final conjunct. To account for such examples, Fukushima would need to assume that the property of P could be contextually provided. Fukushima, however, falsely assumes that ‘when there is no time adverb . . . in the first conjunct . . ., the first conjunct has to share . . . tense with the second one’ and explicitly argues against ‘a purely contextually/ pragmatically driven recovery method’ (309). Previous analyses of these coordination constructions are not exclusively concerned with the distribution of tense and temporal interpretation (cf. also footnote 3). Often, these analyses correlate the temporal interpretation of these constructions with other syntactic and semantic properties. Since our research has established that previous analyses of the temporal interpretation of these constructions are not empirically adequate, except for the variant of Chung’s analysis of Korean we sketch above, we conclude that the relation between temporal interpretation and the other linguistic properties of coordination constructions proposed in these papers needs to be reassessed.


14 Matthewson (2001) contrasts two hypothesis: (i) the ‘no-variation’ hypothesis according to which ‘there is no cross-linguistic variation in the semantics’ (156) and (ii) the ‘transparent mapping’ hypothesis, which assumes that ‘the semantics transparently reflects the surface syntax’ (155). Matthewson mentions that the latter hypothesis has the advantage of freeing linguists ‘from an anglocentric view of the world’ (156) since it does not lead us to expect that certain structures observed in English are also attested in languages other than English, a position we embrace. Our ‘variation’ hypothesis, however, differs from Matthewson’s transparent mapping hypothesis in the locus and extent of cross-linguistic semantic variation. First, it is not clear whether the transparent mapping hypothesis shares the view that languages express comparable meanings: ‘Since there is no requirement that all languages share the same semantics, this view allows for a wide range of semantic variation’ (Matthewson 2001: 155). Given this characterization of the transparent mapping hypothesis, one may be led to assume that surface differences can lead to languages that cannot express certain meanings, a view we reject. Second, we assume that semantic variation can arise from a number of sources, including differences in lexical meaning; in morpheme inventory; in whether a meaning is entailed, presupposed or implicated; and in the morphosyntactic combinatorics. Matthewson’s characterization of the transparent mapping hypothesis, however, seems to limit the source of variation to the syntax: ‘According to a pure version of the transparent mapping hypothesis, the limits on variation are set by the syntax, and semantic differences result from syntactic differences’ (156).


to variation in how a meaning is expressed? With respect to temporality, does morphosyntactic variation in whether or not a language has tense morphemes correspond to differences in how such languages are temporally interpreted? One hypothesis is that there is no cross-linguistic semantic variation and that morphosyntactic differences between languages only constitute surface-level variation that does not correspond to differences in how a meaning is realized. According to this hypothesis, which Matthewson (2001) calls the ‘no-variation’ hypothesis, ‘there are certain fundamental semantic structures or properties which all languages share; which exactly these are is of course the interesting question’ (156). In the domain of temporal interpretation, evidence for this position is provided in Matthewson (2006): given similarities in the temporal interpretation of English, a tensed language, and St’a´t’imcets, a language without overt tense morphemes, Matthewson argues that the two languages merely differ on the surface and that temporal interpretation in both languages proceeds with tense morphemes, which are overt in English and covert in St’a´t’imcets. A second hypothesis about cross-linguistic semantic variation, which we refer to as the ‘variation’ hypothesis, is that morphosyntactic (surface) differences may reflect differences in how meanings arise.14 Evidence for this position in the domain of temporal interpretation is our analysis of the temporal interpretation of coordination constructions: comparable meanings arise in Korean, Japanese and English despite the fact that the location of the reference time is determined in English non-final conjuncts by tense morphemes, temporal adverbs and/or the discourse context, and only by the latter two in the (tenseless) Korean and Japanese


Acknowledgements We are grateful to Yusuke Kubota and Ai Matsui for providing us with Japanese examples and judgments. Previous versions of this research were presented at the 12th Sinn und Bedeutung conference in Oslo, Norway, and at the workshop ‘Formal Approaches to the Relation of Tense, Aspect and Modality’ at the 18th International Congress of Linguists in Seoul, Korea. We thank our respective audiences as well as Lisa Matthewson, Carl Pollard, Craige Roberts, Yael Sharvit and an anonymous reviewer of the Journal of Semantics for constructive feedback and discussion of the material.

JUNGMEE LEE Department of Linguistics, Ohio State University, 222 Oxley Hall, 1712 Neil Avenue, Columbus, OH 43210 USA e-mail: [email protected]

JUDITH TONHAUSER Department of Linguistics, Ohio State University, 222 Oxley Hall, 1712 Neil Avenue, Columbus, OH 43210 USA e-mail: [email protected]

15 For further evidence of the variation hypothesis, see, for example, Faller (2007) and Murray (2008) on reciprocity and Bittner (2005, 2008, forthcoming) on tense and mood.


counterparts. There is thus variation in how the reference time is temporally located with respect to the utterance time.15 We explored the temporal interpretation of the Korean and Japanese coordination constructions under the variation hypothesis, inspired by recent tenseless analyses of tenseless languages such as Yucatec Maya and Kalaallisut (e.g. Bohnemeyer 2002; Bittner 2008). We would have had to reject the hypothesis if the temporal interpretation of these constructions could not have been analysed purely on the basis of the meanings of the (overt) morphemes, the way they are put together and the discourse context. As discussed in section 5, an analysis of the Korean and Japanese constructions that involves a covert tense morpheme whose interpretation is adequately restricted is possible but conceptually inferior. Thus, adopting the variation hypothesis of cross-linguistic semantics has led us to develop an analysis that does not resort to covert tense morphemes even though the morpheme inventory of Korean and Japanese could be argued to motivate such a move. The fact that the variation hypothesis forces us to examine whether a particular meaning can arise from the meaning of (overt) morphemes, the way they are combined and the discourse context alone is, we argue, a highly desirable effect of the variation hypothesis.


REFERENCES of Meaning. CSLI Publications. Stanford, CA. 59–87. Dalrymple, Mary, Stuart Shieber & Fernando Pereira. (1991). ‘Ellipsis and Higher-Order Unification’. Linguistics and Philosophy 14:399–452. Dowty, David. (1986). ‘The Effects of Aspectual Class on the Temporal Structure of Discourse: Semantics or Pragmatics?’. Linguistics and Philosophy 9:37–61. Faller, Martina. (2007). ‘The Ingredients of Reciprocity in Cuzco Quechua’. Journal of Semantics 24:255–88. Fukushima, Kazuhiko. (1999). ‘Bound Morphemes, Coordination and Bracketing Paradox’. Journal of Linguistics 35:297–320. Hinrichs, Erhard. (1986). ‘Temporal Anaphora in Discourses of English’. Linguistics and Philosophy 9:63–82. Hirata, Ichiro. (2006). ‘Predicate Coordination and Clause Structure in Japanese’. Linguistic Review 23:69–96. Kabak, Barisx. (2007). ‘Turkish Suspended Affixation’. Linguistics 45:311–47. Kang, Beom-Mo. (1988). Functional Inheritance, Anaphora and Semantic Interpretation in a Generalized Categorial Grammar. Ph.D. thesis, Brown University. Kang, Choonwon. (1990). A Study on ‘–ko’-Constructions in Korean. Ph.D. thesis, Georgetown University. Kaufmann, Stefan & Misa Miyachi. (2008). On the Temporal Interpretation of Japanese Temporal Clauses. Unpublished MS, Northwestern University and University of Chicago. Kim, Jong-Bok. (1995). The Grammar of Negation: A Lexicalist, ConstraintBased Perspective. Ph.D. thesis, Stanford University.


Arikawa, Koji. (1992). Binding Domain and Modality: A Case Study of Tense Binding in Japanese. Ph.D. thesis, Madison: University of Wisconsin. Bach, Emmon. (1986). ‘The Algebra of Events’. Linguistics and Philosophy 9:5–16. Baldridge, Jason. (2002). Lexically Specified Derivational Control in Combinatory Categorial Grammar. Ph.D. thesis, University of Edinburgh. Bittner, Maria. (2005). ‘Future Discourse in a Tenseless Language’. Journal of Semantics 22:339–87. Bittner, Maria. (2008). ‘Aspectual universals of temporal anaphora’. In S. Rothstein (ed.), Theoretical and Crosslinguistic Approaches to the Semantics of Aspect. John Benjamins. Amsterdam. 349–85. Bittner, Maria ‘Tense, mood, and centering’. In R. Musan & M. Rathert (eds.), Tense across Languages. Niemeyer. Tu¨bingen, forthcoming. Bohnemeyer, Ju¨rgen. (2002). The Grammar of Time Reference in Yukatek Maya. Lincom. Munich. Bohnemeyer, Ju¨rgen. (2009). ‘Temporal anaphora in a tenseless language’. In W. Klein, and P. Li (eds.), The Expression of Time in Language. Mouton de Gruyter. Berlin. 83–128. Cho, Sae-Youn. (2005). ‘Non-Tensed VP Coordination in Korean: Structure and Meaning’. Language and Information 9:35–49. Chung, Daeho. (2005). ‘What Does BARE –ko Coordination Say about Post-Verbal Morphology in Korean?’. Lingua 115:549–68. Condoravdi, Cleo. (2002). ‘Temporal interpretation of modals: Modals for the present and for the past’. In D. Beaver, L.C. Martıńez, B. Clark, and S. Kaufmann (eds.), The Construction

340 Temporal Interpretation without Tense Lin, Jo-Wang. (2005). ‘Time in a Language without Tense: The Case of Chinese’. Journal of Semantics 23:1–53. Matthewson, Lisa. (2001). ‘Quantification and the Nature of Crosslinguistic Variation’. Natural Language Semantics 9:145–89. Matthewson, Lisa. (2006). ‘Temporal Semantics in a Supposedly Tenseless Language’. Linguistics and Philosophy 29:673–713. Murray, Sarah E. (2008). ‘Reflexivity and reciprocity with(out) underspecification’. In A. Grønn (ed.), Proceedings of Sinn und Bedeutung 12. ILOS. Oslo. Nakatani, Kentaro. (2004). Predicate Concatenation: A Study of the V-te-V Predicate in Japanese. Ph.D. thesis, Harvard University. Ogihara, Toshiyuki. (1996). Tense, Attitude, and Scope. Kluwer. Dordrecht. Ogihara, Toshiyuki. (1998). ‘The Ambiguity of the –te iru Form in Japanese’. Journal of East Asian Linguistics 7:87–120. Partee, Barbara Hall. (1984). ‘Nominal and Temporal Anaphora’. Linguistics and Philosophy 7:243–86. Reichenbach, Hans. (1947). Elements of Symbolic Logic. University of California Press. Berkeley. Sohn, Sung-Ock. (1999). Tense and Aspect in Korean. University of Hawaii Press. Honolulu. Steedman, Mark. (1996). Surface Structure and Interpretation. MIT Press. Cambridge, MA. Steedman, Mark. (2000). ‘Information Structure and the Syntax-Phonology Interface’. Linguistic Inquiry 31:649–89. Stone, Matthew. (1997). The Anaphoric Parallels between Modality and Tense. Technical report IRCS 97-6. University of Pennsylvania. Tokashiki, Kyoko. (1989). On Japanese Coordinate Structures: An Investigation of Structural Differences between the –Te


Klein, Wolfgang. (1994). Time in Language. Routledge. New York. Kornfilt, Jaklin. (1997). Turkish. Routledge. London. Kratzer, Angelika. (1998). ‘More structural analogies between pronouns and tenses’. In D. Strolovitch & A. Lawson (eds.), Proceedings from Semantics and Linguistic Theory (SALT) VIII. CLC Publications. Ithaca, NY. 92–110. Krifka, Manfred. (1998). ‘The origins of telicity’. In S. Rothstein (ed.), Events and Grammar. Kluwer. Dordrecht. 197–235. Kubota, Yusuke & Jungmee Lee. (2008). The Coordinate Structure Constraint as a Discourse-Oriented Principle: Further Evidence from Japanese and Korean. MS under review. Ohio State University. Kuno, Susumu. (1973). The Structure of the Japanese Language. MIT Press. Cambridge, MA. Kwon, Nayoung & Maria Polinsky. (2008). ‘What does coordination look like in a head-final language?’. In B. Lewandowska-Tomaszczyk (ed.), Asymmetric Events. John Benjamins. Amsterdam/Philadelphia. Lee, Eun-Hee. (2007). ‘Dynamic and Stative Information in Temporal Reasoning: Interpretation of Korean Past Markers in Narrative Discourse’. Journal of East Asian Linguistics 16:1–25. Lee, Hyo-sang. (1991). Tense, Aspect and Modality: Pragmatic Analysis of Verbal Affixes in Korean from a Typological Perspective. Ph.D. thesis, University of California, Los Angeles. Lee, Jungmee. (2008). ‘The temporal interpretation of the Korean –ko construction: Aktionsart and discourse context’. In A. Grønn (ed.), Proceedings of Sinn und Bedeutung 12. ILOS. Oslo. Lee, Jungmee. (2009). The Temporal Interpretation of Korean Relative Clauses. Unpublished MS. Ohio State University.

Jungmee Lee and Judith Tonhauser 341 of English and Korean’. In S. Kuno, I.-H. Lee, J. Whitman, J. Maling, Y-S Kang, and Y-j Kim (eds.), Harvard Studies in Korean Linguistics. Harvard University. Harvard. 436–46. Yoon, James Hye-Suk. (1994). ‘Korean verbal inflectional and checking theory’. In The Morphology-Syntax Connection. vol. 22. MIT Working Papers in Linguistics. MIT Press. Cambridge, MA. 251–70. Yoon, James Hye-Suk. (1997). Coordination (a)symmetries. In S. Kuno, J. Whitman, Y.-S. Kang, I.-H. Lee, J. Maling, and Y.-j Kim (eds.), Harvard Studies in Korean Linguistics. Harvard University. Harvard. 251–70. Yoon, Jeong-Me. (1996). ‘Verbal Coordination in Korean and English and the Checking Approach to Verbal Morphology’. Korean Journal of Linguistics 21:1105–35.

First version received: 30.11.2009 Second version received: 01.02.2010 Accepted: 05.02.2010


Form and the –I Form. Master’s thesis. Ohio State University. Tonhauser, Judith. (2006). The Temporal Semantics of Noun Phrases: Evidence from Guaranı´. Ph.D. thesis, Stanford University. Tonhauser, Judith ‘The future marker –ta of Paraguayan Guaranı´: Formal semantics and cross-linguistic comparison’. In R. Musan & M. Rathert (eds.), Tense across Languages. Niemeyer, Tu¨bingen, forthcoming a. Tonhauser, Judith ‘Is Paraguayan Guaranı´ a tenseless language?’. In Proceedings of Semantics of Under-represented Languages of the Americas (SULA) 5. GLSA. Amherst, MA, forthcoming b. Yi, Eun-Young. (1997). De- and Reconstruction Coordination in Korean. Ph.D. thesis, Cornell University. Yi, Eun-Young. (1998). ‘Adjunction, coordination and their theoretical consequences’. In N. Adisasmito-Smith & T. Doeleman (eds.), Cornell Working Papers in Linguistics. Cornell University. Ithaca, NY. Yoon, James Hye-Suk (1993). ‘Tense, coordination and the clausal structures

Journal of Semantics 27: 343–397 doi:10.1093/jos/ffq007 Advance Access publication April 27, 2010

Counting and the Mass/Count Distinction SUSAN ROTHSTEIN Bar-Ilan University

Abstract

1 INTRODUCTION This article offers an account of the semantics of the mass/count distinction, focusing on the semantics of count nouns. The mass/count distinction has interested linguists at least since Jespersen (1924) because it apparently provides a link between cognitive mechanisms of individuation and linguistic mechanisms for counting. In a language that has a mass/count distinction, some nouns can be directly modified by numeral expressions (e.g. three cats) and others cannot (e.g. *three furniture(s)). While the mass/count distinction apparently reflects the fundamental ontological distinction between ‘stuff ’ or ‘substance’ and ‘objects’ or ‘things’, it is nonetheless an independent grammatical distinction that cannot be learned on the basis of the conceptual distinctions between stuff and objects. Count nouns naturally denote individuable entities or bounded entities with stable spatial properties across time (e.g. cat, boy, table, book), while mass nouns are associated The Author 2010. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected].

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This article offers an account of the mass/count distinction and the semantics of count nouns, and argues that it is not based on an atomic/non-atomic nor on a homogeneous/non-homogeneous distinction. I propose that atomicity in the count domain is atomicity relative to a context k, where k is a set of entities that count as atoms (i.e. count as one) in a particular context. Assuming for simplicity Chierchia’s (1998a) and Rothstein’s (2004) theory of mass nouns, in which they denote atomic Boolean semi-lattices closed under the complete join operation, we define an operation COUNTk that applies to the mass noun denotation Nmass and derives the count noun meaning: a set of ordered pairs where d is a member of N \ k and k is the context k relative to which the operation applied. So, there is a typal distinction between mass nouns, which are of type , and count nouns, which are of type . The grammatical differences between count and mass nouns follow from this typal distinction. This allows us to encode grammatically the distinction between semantic atomicity, that is, atomicity relative to a context k, and natural atomicity, that is, inherent individuability. We show a number of ways in which this distinction is grammatically relevant.

344 Counting and the Mass/Count Distinction

(1) a. Three of the books were damaged in transit. b. #Three of the furniture were damaged in transit. c. Three of the pieces of furniture were damaged in transit. (2) a. The curtains and the carpets resemble each other. b. The curtaining and the carpeting resemble each other. Example (2a) is ambiguous between the distributive reading where each curtain and carpet resembles the other curtains and carpets, and the collective reading where the carpets, as a plural entity, resemble the curtains as a plural entity and vice versa. In (2b), only the second reading is possible. There are essentially three ways of trying to characterize a semantic distinction between mass and count nouns: the first, proposed by Link (1983), is to argue that mass nouns and count nouns have their denotations in different domains. The second is to propose that mass and count nouns denote entities of different types but that they are interpreted with respect to the same domain. This is the direction taken by Krifka (1989), who derives count nouns from mass meanings and suggests that count nouns denote extensive measure functions on entities in the mass domain. The third approach is represented by Chierchia (1998a), who argues that mass nouns and count nouns are not distinguished typally and


with substances that take their spatial dimensions from containers (e.g. water, mud), or whose physical boundedness varies over time or depends on the artefact constructed from it (e.g. wood, gold). Soja et al. (1991) have shown that infants are sensitive to the difference between individual objects and substance, and Prasada et al. (2002) have shown that children are aware that count nouns are the canonical form for denoting objects while mass nouns are the canonical form for denoting substances. Nonetheless, it is well known that despite the association of count terms with individuable objects and mass terms with substances, there are many mismatches between the grammatical form and the properties of the denotation. Nouns like furniture and jewellery denote individuable entities, and there is cross-linguistic variation in mass/count categorization (e.g. jewellery is mass in English but Hebrew taxsˇit/taxsˇitim is count). This indicates that the grammatical distinction is not a direct reflection of the conceptual distinction. Furthermore, as well as direct counting, grammatical operations like partitive construction and reciprocal resolution are sensitive to the distinction between mass and count nouns. Example (1) shows that numerical partitives distinguish between definite DPs with mass noun heads and definite DPs with count noun heads. The examples in (2) from Gillon (1992) show that reciprocal resolution is also sensitive to the mass/count distinction:

Susan Rothstein 345

1 There is also a syntactic approach that argues that there is no lexical or semantic difference between mass and count terms, and that all differences follow from the syntactic structure in which they are inserted. Borer (2005) is the most recent representative of this approach, which I discuss in section 10.


have their denotations in the same domain but that count nouns make a set of atoms lexically accessible.1 In this article, I take the second approach and argue, like Krifka (1989), that count noun meanings are derived from mass noun meanings and are typally different from them but not in the way that Krifka suggests. I show that the assumption that (singular) count predicates make a set of atoms accessible is, by itself, insufficient to explain the behaviour of count nouns and that we need a theory of what atomicity is and how count nouns access the atoms grammatically. I start from the observation that the mismatch between form and denotation is two-way: as well as mass terms such as furniture and jewellery that denote sets of inherently individuable objects, there are also count terms that denote sets of entities that do not have spatial properties constant across time. Examples are fence, wall and bouquet. In order to treat these predicates as atomic, we need to know how the atomic elements in their denotation are determined. I shall propose that atomicity is context dependent and that part of specifying a context is specifying what counts as one entity in that context. Count nouns denote sets of entities indexed for the context in which they count as one. This results in a typal distinction between mass and count nouns that (unlike the typal distinction in Krifka’s account) is projected up to the DP, which is the extended projection of the nominal head. This allows us to explain the variety of grammatical differences between mass and count nouns, including the examples in (1) and (2). More generally, I will argue that to explain the grammatical behaviour of mass and count nouns we need to distinguish between three kinds of atomicity: formal atomicity, that is, being an atom in a Boolean structure; natural atomicity, or being inherently individuable; and semantic atomicity, which I shall define in the course of the article, and which is the atomicity characterizing singular count predicates. I argue that this allows a theory of the mass/count distinction that is both cognitively and semantically plausible and that explains linguistic behaviour. The article is structured as follows. In the next section, I review evidence that the mass/count distinction is a grammatical distinction independent of the structure of matter. In sections 3 and 4, I review previous accounts of the mass/count distinction and look briefly at the psycholinguistic evidence from Barner and Snedeker (2005). Sections 5–7 set up a semantics for count nouns based on the three-way


distinction between formal, natural and semantic atomicity. Section 8 compares this theory with Krifka (1989), and section 9 makes some preliminary extensions of the theory to classifier languages. In section 10, I argue against an approach that tries to derive the mass/count distinction from syntactic structure. 2 WHAT IS THE MASS/COUNT DISTINCTION?

(3) a. three girls, b. * three muds, c. three kilos of mud, d. three buckets of mud. Girl is a count noun since it can be directly modified by the numeral modifier three, while mud, a mass noun, can only be counted via a classifier expression like kilo or bucket. Classifiers may be individuating or they may be non-individuating measure phrases. On the measure reading of bucket, three buckets of mud denotes a quantity of mud and is synonymous with three bucketfuls of mud. In the individuating use of (3d), it refers to three actual buckets filled with mud as in three buckets of mud were standing in a row. Doetjes (1997), Landman (2004) and Rothstein (2009a) discuss some of the different syntactic and semantic properties of these two uses of classifier expressions. The distinction illustrated in (3) is a genuine grammatical distinction with linguistic implications. Count nouns are associated with a number of different syntactic and morphological properties, though not all grammatical differences appear in each language. The major differences that characterize the mass/count distinction are listed in (i) and (ii). (i) properties of the noun (a) count nouns occur with numeral determiners, mass nouns do not: three chairs, *three furniture (b) count nouns take plural morphology, mass nouns do not: chair/chairs, furniture/*furnitures (c) count nouns do not normally occur in the singular with classifiers, mass nouns do: *three pieces of chair/three pieces of furniture. (ii) sensitivity of determiners to the mass/count distinction (a) some determiners select only count nouns:


The mass/count distinction, illustrated in (3), is the distinction between nouns that can and nouns that cannot be explicitly counted by using numeral modifiers:

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each/every/a book, several/few/many books, *every/*several furniture(s) (b) some determiners select only mass nouns: little/much water, *little/*much book(s) (c) some determiners select mass and plural nouns: a lot of/plenty of wine, a lot of/plenty of books, *a lot of/*plenty of book, (d) some determiners are unrestricted: the/some book(s), the/some water.

(i) Entities that come in natural units of equal perceptual salience may differ in a single language as to whether they are mass or count, for example, rice is mass, while lentil/lentils is count. (ii) Within a single language, there are pairs of synonyms, or nearsynonyms, where one member of the pair is count and the other is mass. English: footwear/shoes, change/coins, carpeting/carpets, hair/hairs, rope/ropes, stone/stones. Dutch: het meubilair (the furniture)/het meubel (the piece of furniture). Hebrew: rihut (furniture)/rehit (piece of furniture). Note that these synonyms are of three kinds: (a) hair/hairs, a single lexical item can be realized as mass or count; (b) carpeting/carpets, two lexical items based on the same root are related by a morphological operation. One has a mass use and the other has a count use; and (c) footwear/shoes, there is no lexical relation between nearsynonyms where one is mass and the other count. (iii) Mass expressions in one language have count near-synonyms in another; for example, advice is mass in English but the Hebrew


Not all of these properties show up in all languages that distinguish between mass and count nouns. In Turkish, numerals modify only count nouns, but these nouns are not marked for the singular/plural distinction. Similarly, the selectional properties of determiners show up differently in different languages. For example, Hebrew does not have the distinction between (how) much and (how) many, although there are other ways to determine which nouns are mass and which are count. In general, while identical diagnostics may not be available cross-linguistically, variations on the diagnostics show that the mass/count distinction is one that occurs in many languages. The mass/count distinction is independent of the ‘structure of matter’. Chierchia (1998a) sums up many years of discussion by bringing four arguments in support of this claim:


These cross-linguistic differences show that while the mass/count distinction is clearly influenced by the structure of matter, it is not taken over from it. So, the question is: what is at the root of the mass/count distinction? 3 PREVIOUS ACCOUNTS OF THE MASS/COUNT DISTINCTION

3.1 Homogeneity and/or cumulativity is not at the root of the mass/ count distinction Much discussion of the mass/count distinction has focused on the downward and upward closure properties of the two kinds of nominals. Mass predicates are cumulative since their denotations are upwardly closed and homogeneous (divisive) since their denotations are downwardly closed: water + water forms a (possibly discontinuous) entity also in the denotation of water, while a quantity of water split into two gives two quantities of stuff both in the denotation of water. (Divisibility is usually said to work down to minimal parts, an issue which I will not discuss here.) This contrasts with singular count nouns that are characterized as neither cumulative nor homogeneous. The sum


equivalent etza has only a count use, as the contrast between (4a) and the ungrammatical (4b) shows. (4) a. hi natna li ˇsalosˇ etzot she gave me three-f advice-f-pl ‘She gave me three pieces of advice/(*three advices)’ b.* hi natna li harbe etza she gave me much advice-f-sg intended reading: ‘She gave me much advice’ (iv) Some languages, such as Chinese, have only nouns that behave as mass expressions. Count usages require classifiers; for example, Chinese xiońg, ‘bear’, is a mass expression, and counting requires a classifier (from Krifka 1995): (5) a. san zhıxiońg three classifier bear ‘three bears’ (objects) b. san quń xiońg three herd bear ‘three herds of bears’ c. san zh ong xiońg three classifier bear ‘three bears’(species)

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(6)

This ring is new, but the gold it is made out of is old.

Since the ring and the gold out of which the ring is made occupy the same spatiotemporal position and look like the same object, it seems as if (6) is predicating contradictory properties of a single object: the object that is the denotation of both this ring and the gold is simultaneously old and not-old. But if this ring denotes an entity a in the atomic domain, while the gold denotes an entity b in the non-atomic domain, related by the material part relation, then (4) is then no longer contradictory, but asserts that the old and the new


of two entities in the denotation of cup cannot itself be in the denotation of cup (but only in the denotation of the plural cups), while splitting a cup into two more or less equal parts gives you two pieces, neither of which is in the denotation of cup. It is possible to split a cup unequally into, say, a chip and the rest of the cup, and the larger part will probably still count as a cup, but this contrasts with water, where splitting a quantity of water into two unequal divisions gives you two quantities, both of which count as water. As Link (1983) and Landman (1991) point out, the predicate that parallels the mass noun in upward and downward closure properties is not the singular count noun but the bare plural count noun, which is also divisible down to minimal parts, these minimal parts being of course the atomic individuals in the denotation of the singular count noun. Link (1983) proposed a formal model to capture the difference between the mass and count domains. While explicitly not attempting to capture downward closure properties, he proposed a model that allowed linguists to represent the contrast between cumulative and non-cumulative predicates. Link proposed that both mass and count domains form lattices, with the essential difference that the count domain is atomic and the mass domain is non-atomic (Link leaves open whether it is or is not atomless or even Boolean). Nouns denote sets of entities that form Boolean sub-lattices of the respective domains. A singular mass noun denotes a sub-lattice of the non-atomic domain. A singular count noun denotes a set of atomic elements in the count domain. The corresponding plural count predicate denotes the closure of that atomic set under sum, and this plural set forms a Boolean sublattice of the count domain. These two domains, the mass and the count, are separate but related by a ‘material part’ relation. For example, gold is a mass term denoting quantities of stuff, and ring is a count term denoting a set of atomic individuals. If a specific ring, a, is made of gold, there is some quantity y in the denotation of gold, such that y is a material part of a. Support for positing two domains comes from a consideration of examples such as (6):


properties hold of two different objects a and b. Link represents the meaning of (6) as in (7), where MatPart is the material part relation: (7) dy [GOLD(y) ^ RING(a) ^ MatPart(a,y) ^ OLD(y) ^ :OLD(a)]. However, positing two different domains cannot be the solution to the paradox posed by (6) since the problem can be replicated with two nominals from the mass domain:2 (8) a. This jewellery is new but the gold it is made of is old. b. The curtaining is new, but the fabric it is made of is old.3

(9) Cumulativity: P is cumulative iff: "x"y[x 2 P ^ y 2 P / xky 2 P] ‘P is a cumulative predicate if when x and y are in P, then the sum of x and y is also in P.’

2 A reviewer has noted that the paradox can be replicated in the count domain, as in The mosaic is new, but the stones it is built out of are old. Note that in order for the paradox to be replicated, the mosaic must consist of nothing other than the stones, that is, no cement, glue and so on. 3 The solution to this paradox has to be in a theory of intensional properties. The issue is discussed in Landman (1989b), Chierchia (1984) and in a different context in Heim (1998). Ascription of properties is not directly to entities but to entities presented under particular guises or perspectives. Thus, Landman (1989b) argues that even if the judges and the hangmen are the same individuals, they may have properties as judges, such as ‘being professional’, ‘being efficient’, or ‘being on strike’, which they do not have as hangmen, as in (i):

(i) John is efficient as a judge but inefficient as a hangman. This seems to be what is going on with the examples in (8): the same entity may be old as gold but new when presented as a ring or as jewellery, without invoking a ‘constitutes’ or ‘material part’ relation.


Much of the force of Link’s proposal has come from the naturalness with which it models the distinction between homogeneous and nonhomogeneous predicates. Although Link explicitly refuses to discuss downward closure properties (because of the issues raised by the question ‘what are the minimal parts of water?’), his representation of the mass and count domains in terms of non-atomic and atomic lattice structures has often been made into the stronger distinction between atomless and atomic lattice structures, which directly expresses the distinction between mass and count predicates in terms of cumulativity and homogeneity. Upward homogeneity, or cumulativity, is defined as in (9) where k is the standard join or sum relation (the definition is based on Krifka 1998). Mass predicates are straightforwardly cumulative, while singular count predicates are not.

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Homogeneity or divisiveness is defined as in (10), where ‘8’ is the part-of relation, O is the overlap relation, and y and z are required to be non-empty (i.e. divisiveness cannot be satisfied trivially). (10) Homogeneity (divisiveness): P is homogeneous iff "x 2 P:dy dz [y 8 x ^ z 8 x ^ :O(y,z) ^ y 2 P ^ z 2 P] ‘P is a divisive (homogeneous) predicate if for every x in P, there is a way of splitting x into two non-overlapping parts, both of which are also in P.’ Downloaded from jos.oxfordjournals.org by guest on January 1, 2011

As discussed above, mass predicates are divisive or homogeneous since quantities of water or mud can be split into two portions of water or mud, but a count predicate like cat is not homogeneous or divisive since a cat cannot be split into two entities that both count as an instance of cat. A different property of predicates discussed in Krifka (1992, 1998) is quantization. A predicate P is quantized if for all entities x in P, no proper part of x is also in P. Intuitively, this property is supposed to pick out predicates that have only minimal instantiations of the predicate in their denotation. Homogeneity or divisiveness as defined in (10) is stronger than the property of being non-quantized. Suppose a jacket has detachable sleeve parts, then jacket is nonquantized (since the jacket has a subpart—the part without the sleeves—which is also a jacket), but it is not homogeneous. It is easy to see that an atomless Boolean algebra represents the denotation of a predicate that is both cumulative and non-trivially homogeneous. For any two elements in an atomless Boolean lattice L, the join of those elements is also in L (cumulativity). Since the lattice is non-atomic, that is, it is not constructed from minimal elements, any element is non-trivially the join of its parts. In the count domain, a singular count noun C denotes a set of atoms, that is, a subset of the minimal elements in the domain. Thus, the sum of two elements in the denotation of C cannot, by definition, also be in the denotation of C. Since atoms are minimal elements, a predicate of atoms cannot denote a non-trivially homogeneous property. While the claim that homogeneity and cumulativity characterize mass nouns and not count nouns makes sense intuitively, it runs into problems as soon as we try to use these as criteria for classifying predicates as mass or count. First, predicates like salt or rice are not, when it comes down to it, homogeneous. These predicates have in their denotations entities that count as instances of rice or salt but that are too small to divide into two subparts that are both rice or salt, and at the most extreme end, both salt and rice are constructed out of salt and rice atoms that can be divided into parts that are not salt and rice, so salt and rice are not fully


homogeneous predicates. This is the problem with downward closure that led Link to remain agnostic as to whether the structures representing the mass domain were atomless or merely non-atomic. The issue has been discussed extensively in Gillon (1992), Chierchia (1998a) and Landman (2007). Second, not all mass nouns are even intuitively homogeneous. In particular, the group of mass nouns that are sometimes called ‘superordinates’ or quasi-kind terms, such are jewellery or furniture, are not homogeneous. But this is not a general property of quasi-kind terms, and there seems to be no predictable pattern: fruit is mass in British English, but has a count use in American English, while vegetable(s) is always count; furniture is mass but toy(s) is count and so on.

One way to maintain the idea that homogeneity is involved in the mass/count distinction is to suggest that while mass nouns are indifferent as to the homogeneity/non-homogeneity of their denotations, count nouns are necessarily atomic. A theory that proposes this is Chierchia’s (1998a), who like Gillon (1992) argues that mass nouns as well as count nouns have their denotations in an atomic domain. Chierchia argues that mass predicates denote atomic Boolean semilattices, with the atomic entities in the denotation of a mass predicate being under-specified and vague. [Landman (2007) also argues that mass nouns have denotations in an atomic domain: he proposes that mass denotations are not Boolean but are composed out of substructures that are.4] Assume a Boolean domain with three individuals in it. It has the structure in (11): (11)

The individuals on the bottom line are the singularities, the atoms of the model, and the entities on the higher lines are the plural entities. The Boolean semi-lattice models the domain partially ordered by 8, the part-of relation, and closed under k, the sum or join operation. Thus, (12) holds: (12) a. a 8b 4 akb ¼ b. b. Overlap: "a"b[a s b 4 dc[c 8 a ^ c 8 b]] c. "a"b[a 8 b ^ :(a ¼ b) / dc[akc ¼ b]]. 4 Problems with the assumption that the mass domain is a Boolean algebra and that mass nouns denote sub-algebras of this domain are discussed in Landman (2007).


3.2 The mass domain is an atomic domain

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(13) a. piece of furniture / {chair1, chair2, table1} b. pieces of furniture / {chair1, chair2, table1, chair1kchair2, chair1ktable1, chair2ktable1, chair1kchair2ktable1, } c. furniture /{chair1, chair2, table1, chair1kchair2, chair1ktable1, chair2ktable1, chair1kchair2ktable1, } This means that Chierchia can explain why that is furniture and those are pieces of furniture apparently have the same truth conditions: the sum of entities in the denotation of furniture and pieces of furniture just are the same objects. The same holds for pairs such as carpeting and carpets, curtaining and curtains and so on. The crucial difference between count nouns and mass nouns is that count nouns make a set of atoms grammatically accessible, while mass nouns do not. Count nouns do this since they ‘presuppose’ a set of atoms, and this presupposition makes the set of atoms salient in the 5 In (13), the plural of the count noun and the mass noun denote the same set. This is not the case in Chiercha’s account since for him the plural count noun denotes the set of plural elements without the atoms. This is problematic since in normal discourse a bare plural includes atoms in its denotation. ‘Do you have children?’ allows the answer ‘Yes, one’, while ‘No, only one’ is infelicitous. Chierchia (1998a) proposes a mechanism for circumventing this, but it complicates the theory considerably. I shall adopt the more conventional account of plural predicates in (13) since in any case, I propose later in the article a structural distinction between the mass and the count domains that solves the problem of the apparent synonymy between (13b) and (13c).


In a standard account of the singular/plural distinction (Link 1983; Landman 1989a), semi-lattices like (11) are used to model denotations of count expressions, with the singular count noun denoting the set of atoms, or bottom elements of the semi-lattice, here {a,b,c}, and the plural denoting the set of atoms closed under sum, that is, the set of elements in the structure in (11) {a,b,c, akb, akc, bkc, akbkc}. Chierchia (1998a) proposes that mass nouns too denote Boolean algebras, such as the one in (11). He argues that the crucial difference between mass and count nouns is that count nouns distinguish lexically between the set of atoms in the Boolean algebra and the set of plural elements, while mass terms are grammatically singular but lexically plural: ‘mass nouns come out of the lexicon with plurality already built in, and . . . that is the only way they differ from count nouns’ (Chierchia 1998a: 53). So, a grammatically singular count noun denotes a set of atoms, and the plural of the count noun denotes that set closed under the sum operation, but a grammatically singular mass noun denotes the closure under sum of a set of atoms. If the predicate piece of furniture denotes the set in (13a), the plural of that predicate denotes the plural set in (13b). The mass term furniture as a lexical plural will have the denotation in (13c), although it is morphologically singular:5


3.3 Homogeneous count nouns require an explicit theory of atomicity Chierchia’s theory relies on a presupposition of atomicity to explain why and how count nouns access their set of atoms. This is problematic for two reasons. In the first place, some mass nouns like furniture and footwear denote sets of inherently individuable entities, and since shoes is a near-synonym of footwear but a count noun, there must be a great deal of lexical idiosyncrasy underlying whether a predicate of atomic individuals is or is not marked count. However, a much more serious problem is that there are count nouns that denote entities that our realworld knowledge tells us are not inherently atomic but homogeneous. Homogeneous count nouns include nouns such as fence, line, plane, sequence, twig and rope. These have been noticed in the literature at various times over the past 20 years. Mittwoch (1988) shows that line and plane denote sets of entities that have proper parts that themselves are lines and planes; Krifka (1992) points out that entities in the denotation of sequence and twig have proper parts that count as a sequence or a twig; Gillon (1992)


discourse and available for the semantics to make use of. This replaces Link’s account of the contrasts in the examples in (3) and (4) above. Instead of count and mass nominals having their denotations in different domains, the fact that count nouns lexically access a set of atoms means that this atomic set is accessible to grammatical operations. Different grammatical operations exploit the mass/count distinction in different ways. Determiners that are sensitive to the mass/count distinction make use of functions that distinguish between mass and count predicates. For example, the function ‘SG’ applies to N and checks whether the denotation of N is either atomic or generated by pluralization from a lexically accessible atomic set. SG is the identity function when applied to singular or plural count nouns but is undefined for mass nouns. Since number modifiers like three are defined to apply to SG(N), three SG(N) will also only have a value when applied to count nouns. Other mechanisms account for the constraints on reciprocals and partitive constructions with mass nouns. Reciprocals require morphological plurals as antecedents and thus cannot take mass nouns such as furniture as an antecedent. Numerical partitives apply to definite plurals and not to definite mass nouns because the is sensitive to the distinction between plural and singular morphology and necessarily returns a singleton object when applying to a mass noun. Thus, the furniture denotes the singular group or collective entity formed out of the maximal plural object in the denotation of furniture. Since three of requires a plural complement, it cannot apply to the singularity denoted by the furniture.

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Figure 1

6

Zucchi and White (2001) discuss why non-quantized nominals in direct object position induce telic readings of accomplishment-headed VPs, but they do not discuss why homogeneous head nouns are count.


makes the same point for ‘flexible’ nouns that have both a mass and a count form, such as rope or stone: one rope can be cut into many ropes, one stone can be broken into stones and so on. Rothstein (1999, 2004) shows that the phenomenon is even more general and includes a wide variety of nouns such as fence, wall, hedge and bouquet. Other nouns with the same property denote organisms: a bacterium reproduces by dividing and a flatworm can be divided into two flatworms. These nouns are divisive in the sense of (10): there is way of dividing a fence or a bouquet or a bacterium into two parts, both of which count as fences or bouquets or bacteria. There have been only a few attempts to explain why these nouns are in fact count.6 Furthermore, these facts show that homogeneity is a real-world property and not a semantic property, and so a characterization in terms of homogeneity does not capture the independence of the mass/count distinction from the structure of matter. The reason why a flatworm can be divided into two flatworms, while a cat cannot, is because of differences in the systemic make up of flatworms and cats. Similarly, the reason why furniture is not homogeneous and linoleum is has to do with the different real-world properties of the two types of stuff, even though they are both mass predicates. Other predicates are ‘sometimes homogeneous’, depending on what entities are in their denotation in a particular model. For example, a part of a notepad may or may not be a notepad. If the original is one of those blocks with 500 pages joined by glue where you can tear off clumps of pages to make smaller notepads, then there is a bipartition of the notepad into two smaller notepads. If the notepad is bound and has a cover, then this cannot be done. Crucially, it depends on whether the original item has a structure that makes such a bipartition available. But in a model in which only the first kind of notepad exists, then notepad is a homogeneous predicate. Fence is more strongly homogeneous since the same piece of fencing may be analysable as one or several non-overlapping fences in the same situation under different criteria of individuation. The example given in Rothstein (1999, 2004) is as follows. Suppose four farmers, A, B, C and D build a fence each, as in Figure 1:


4 EVIDENCE FROM BARNER AND SNEDEKER (2005) In this section, we look briefly at the results of Barner and Snedeker (2005), which support the claim that natural atomicity and semantic or count atomicity are distinct phenomena. Barner and Snedeker investigate experimentally the basis of quantity judgments by asking adults and children the question, ‘Who has more X?’ in three different situations:


Then, either each farmer built a fence, and there are four fences, one on each side of the field, or the field is enclosed by a fence, in which case there is only one fence around the field. Here is a different example: suppose that I have a bouquet of flowers that I split, giving half to my daughter and half to her friend. Then, either there is a single bouquet that has been split so that each girl has half a bouquet, or each girl has a bouquet of flowers (albeit smaller than the original one). Similar examples can be constructed for count nouns such as wall, twig, quantity of milk and so on. Cumulativity does not fare any better as a defining property of the mass/count distinction. Mass nouns are indeed cumulative since water + water gives an entity in the denotation of water. But while cat + cat is not in the denotation of cat, there may well be situations in which the sum of two non-overlapping fences could be in the denotation of fence, given a context in which this sum of fence parts can be treated as a singularity, or two bouquets can be put together to make a single bouquet. What this shows is that inherent, or natural, atomicity is neither a necessary nor a sufficient criterion for count noun predicates, and homogeneity v. non-homogeneity cannot be at the root of the mass/ count distinction. Furniture is mass but naturally atomic and nonhomogeneous since it denotes sets of individual units and fence is count but homogeneous and not naturally atomic. This means that a theory of count nouns cannot rely on presuppositions of atomicity. Instead, we need a theory of what atomicity is and in what way count nouns like fence are atomic, while mass nouns like furniture are not. In what follows, I shall propose that Chierchia’s ‘association with a salient set of atoms’ is the result of a semantic operation deriving count nouns that is at the heart of grammatical countability. This operation, which derives semantically atomic predicates, as opposed to naturally atomic predicates, results in a typal difference between mass and count nouns that allows us to give a unified explanation of the grammatical differences between them.

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(a) where X is a mass substance term, such as mud (b) where X is a mass superordinate term, such as furniture (c) where X is a flexible noun, such as stone/stones, brick/bricks etc. We are interested only in the adult data. Adults were presented with pictures of quantities of the relevant entity and asked, ‘Who has more X’, and the results were as follows: (details of the experiments and the statistical analysis are given in Barner & Snedeker 2005).

Result II: In situation (b), when the question was asked using mass superordinate terms, for example, ‘Who has more furniture/ silverware?’, quantity judgments rely on number. Several small pieces of silverware were judged to be more ‘silverware’ than one big piece, whose overall volume was bigger than the smaller pieces. Several small chairs were judged to be more ‘furniture’ than one big chair, even when the volume/mass of the single big chair was greater than the combined mass of the small chairs. No context was given for the quantity judgment: the stimulus presented two sets of entities in a context-independent way.7 Result III: In situation (c), which tested nouns having both mass and count forms such as stone/stones, quantity judgments depended on the syntax of the noun. The stimulus was a picture of several small stones and one big stone, where the volume of the big stone was greater than the combined volumes of the small stones. When the question was asked using a count noun, three small stones were judged to be more than one big stone, and when the question was asked using a mass noun, one big stone was judged to be more than three small stones.

7 It is plausible that varying the situational context would affect what is understood as the individual entities relevant for quantity judgments. For example, suppose the relevant issue is who can seat more people in her office. I have three chairs and a colleague has two sofas. I might then say, ‘You have more furniture: we should have the meeting in your office’.


Result I: In situation (a), where the question was asked using mass substance nouns, for example, ‘Who has more mud?’, quantity judgments depended on overall quantity of stuff. One big heap of mud was consistently judged to be ‘more mud’ than three small heaps of mud.



Barner and Snedeker conclude from results I and II that some mass nouns denote sets of individuals, while others do not. A more precise formulation is that some mass nouns allow individuals to be salient for quantity judgments, and in these cases, the quantity judgments are based on comparing numbers of individuals and not overall mass. Result III shows that mass/count syntax influences the basis of quantity judgments where both options are available. Given a flexible noun with both mass and count forms, then when the noun is mass, even where individual lumps of stone are salient, quantity judgments are by comparison of total mass and not by comparison of number. So, although some mass nouns denoting sets of individuals make the individuals salient as a basis for quantity judgments, other mass nouns do not. Furthermore, result III indicates that count nouns individuate and that count stones required a comparison in terms of numbers of individuals and not in terms of overall volume. Barner and Snedeker suggest that there are two kinds of mass terms, ‘substance mass’ terms such as mud, salt and stone (on its mass reading), and those that pattern like furniture in result II, which they call ‘object mass’ and which tend to denote heterogeneous classes of objects. These object mass terms are those that rely on the salience of inherently individuable entities for quantity judgments. They therefore suggest that these terms appear in the lexicon marked [+individual], although they are not count, and that this feature marking represents that fact that ‘the conceptual apparatus associated with individuation is distinct from the linguistic feature which licenses its direct expression in the language’ (Barner & Snedeker 2005: 59). Without accepting the necessity for using a lexical feature [+individual], we see from their results that even when the salience of the individuals in the denotation of a mass term allows quantity judgments in terms of implicit counting, you still cannot count grammatically. If A has one big sofa and B has two small chairs and a small table, and you think that B has more furniture based on a comparison of numbers of pieces of furniture, you still cannot say ‘B has three furnitures’. Similarly, you can say ‘B has more furniture than A’ but not ‘B has two more furnitures than A’. This means that what is relevant for quantity judgments is not relevant for linguistic expressions of counting. In other words, the conceptual apparatus of individuation and the grammatical mechanisms that allow direct counting of individuals are distinct. This means that the grammar of count nouns is not directly dependent on or derived from the cognitive or perceptual salience of individuals.

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5 TOWARDS AN ACCOUNT OF THE SEMANTICS OF COUNT NOUNS

5.1 Two observations

(14) a. #John has three furnitures. b. #John has three furnitures more than Bill. A second piece of data showing that individual units may be salient even when nominals cannot be directly counted comes from adjectival modification. In Mandarin Chinese, bare nouns can never be directly counted but always require a classifier, as demonstrated in (15). (15) a. lia˘ng ge pıńgguoˇ two Cl apple(s) ‘two apples’ b. *lia˘ng pıńgguoˇ two apple(s) Nonetheless, the individual unit is salient and can be directly modified. So while the modifier ‘big’ cannot modify nouns such as shuı˘ ‘water’, as in (16a), the same modifier can directly modify the noun when the noun is of the ‘count type’ as in (16b). (16) a. *lia˘ng bei da` shuı˘ two Cl-cup big water b. lia˘ng ge da` pıńgguoˇ ‘two big apples’ c. woˇ ma˘i le da` pıńgguoˇ I buy perfective big apple(s) ‘I bought big apples.’


We now summarize the two observations made in the previous sections: (i) Observation 1: Even when you can count the objects in the denotation of mass nouns implicitly because the units are salient, you cannot count grammatically. While Barner and Snedeker (2005) show that the answer to ‘Who has more furniture?’ is determined by comparing the cardinality of two sets of individuals, English still does not allow (14):


So even though pıńgguoˇ, ‘apple(s)’, cannot be directly counted in Mandarin, the nominal denotes entities whose unit structure can be modified.8 The same is true of mass nouns like furniture in English, as (17) shows. This is noted independently in Schwarzschild (forthcoming), who calls predicates like big ‘stubbornly distributive predicates’. [Note that the verbal predicates distribute over the individual pieces of big furniture, particularly in the contexts relevant for (17c/d), although it might be argued that big furniture is a kind term in (17b)].

Doetjes (1997: 37) brings another example of linguistic sensitivity to perceptual salience. In Dutch, the classifier stuk ‘piece’ is used anaphorically in answering a question. It has two forms: stuks and stukken. In answering questions involving a count noun, stuks is used, and if the count noun is replaced by a mass noun, stukken must be used. (18) a. Hoeveel boeken neem je mee? Twee stuks/*stukken. How-many/much books take you with?Two pieces. ‘How many books do you take? Two.’ b. Hoeveel kaas heb je gegeten? Twee stukken/* stuks. How-many/much cheese have you eaten? Two pieces. ‘How much cheese did you eat? Two pieces.’ Doetjes notes that when the question involves a mass noun denoting a set of perceptually salient individuals, there is a strong tendency to use stuks and not stukken. (19) Hoeveel meubilair neem je me? How many/much furnituremass take you with? ‘How much furniture did you take with? Two pieces.’ Twee stuks/?stukken. Two pieces. (ii) Observation 2: Things that you can count grammatically do not necessarily come in individuated units and are not inherently atomic (Mittwoch 1988; Krifka 1992; Rothstein 1999, 2004; Zucchi & White 2001). As we saw, twig, sequence, line, fence, wall and quantity of milk 8 Even if da` pıńgguoˇ is understood as a complex kind, that is, the kind ‘big apples’, the kind exists as a generalization over the set of individual apples with the ‘big’ property.


(17) a. The furniture in our house is big. b. In a department store: ‘The big furniture is on the third floor.’ c. To movers who are emptying the house: ‘Please take the big furniture down first.’ d. ‘Don’t buy big furniture, the stairs are too narrow to carry it up.’

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may rely on context to determine what one counts as one entity in the denotation of the singular predicate. So, when N is a count noun, the entities in its denotation can be counted even when what counts as a single unit is not uniquely determined. These two observations lead to the following conclusions: Conclusion I: We cannot define the mass/count distinction in terms of properties of the denotations of the nouns themselves, or via a presupposition of atomicity (or lack of it).

Conclusion III: the mass/count distinction can only be explained in terms of how the expressions refer, and not in terms of the things they refer to. This means it is a grammatical and not an ontological distinction. We will argue that count nouns are a mechanism for grammatical counting. They allow grammatical counting because they keep track of their atomic members via a semantic operation, and not presuppositionally or because of any ‘real-world’ properties such as inherent individuability/atomicity. So, while agreeing with Chierchia that count nouns make accessible a set of atoms, we need to now show what the semantic mechanism is which does this.

5.2 Modelling the Mass/Count distinction We assume that nominals are interpreted with respect to a complete atomic Boolean algebra M. kM, the sum operation on M is the complete Boolean join operation (i.e. for every X 4 M: kMX 2 M). With Chierchia, I assume that the set of atoms A of M is not fully specified, vague. The denotation Nroot of a root noun is the Boolean algebra generated under kM from a set of atoms AN 4 A [so root noun denotation Nroot has the same 0 as M, its atoms are AN and its 1 is kM(AN)]. I assume that mass nouns have the denotations of root nouns, so Nmass ¼ Nroot.9 (Note that we assume this particular theory of mass nouns for simplicity but the choice is not essential to 9

Arguably, mass nouns should denote kinds, as proposed in Chierchia (1998a,b). For a version of this theory in which the meaning of the mass noun is the kind associated with Nroot, see Rothstein (2009b).


Conclusion II: Although there is a clear tendency for naturally atomic objects to be denoted by count nouns and ‘stuff ’ to be denoted by mass nouns, being a naturally atomic predicate is neither a necessary nor a sufficient condition for being a count noun. Therefore,



what follows. In particular, the mass domain may be only partially atomic.) For a noun like furniture that naturally denotes a set of inherently individuable units that are pieces of furniture, the atoms in the denotation of the nominal will usually be these single pieces of furniture. These are the individuals that Barner and Snedeker have shown are relevant for quantity judgments. But the choice of the atoms in the denotation of a mass predicate is vague and underdetermined, and in different contexts, the set may be constructed on the basis of different salient minimal elements, for example, the set of parts of modular, build-it-yourself furniture or the set of sitting places made available by the furniture (see footnote 7). Whatever the atomic elements are, they are not lexically accessible, and there is no lexical item that denotes the set of atomic elements. For mass substance nouns like mud, we assume, like Chierchia, that the atoms of the set are the minimal relevant quantities of mud. Chierchia argues that the minimal elements here are specified by context or may be left vague and unspecified, and thus, the information as to what counts as a minimal element is usually neither explicitly nor implicitly specified, nor recoverable from context nor identifiable via perceptual salience. This explains why, in these cases, quantity evaluation judgments in Barner and Snedeker’s experiment are evaluated in terms of overall quantity and not in terms of number of minimal elements. As with furniture, the set of minimal elements is not lexically accessible and is not countable. Count nouns differ from mass nouns because they allow direct grammatical counting. Counting is putting entities in one-to-one correspondence with the natural numbers and requires a contextually determined choice to what counts as one entity. Grammatical counting is direct modification of a nominal by a number word, expressing the results of this one-to-one matching operation. As our discussion of nouns like fence and wall showed, count nouns do not necessarily presuppose a specific set of salient atomic entities; instead, the model needs to specify a context-dependent choice of atomic elements relative to which the count noun is derived, and count noun denotations must specify the context in relation to which they are to be interpreted. In general, along with specifying contextual parameters such as those that provide values for indexicals, time and location, part of specifying a context is specifying what are the set of ‘things which count as one for the purposes of counting’. The choice of this counting parameter is determined by discourse considerations and is updated ceteris paribus in the standard way (see,

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e.g. discussion in Partee et al. 1990/1993: chapter 15). Since in this article the only relevant contextual parameter is the counting parameter under discussion, I will for ease of notation identify contextual counting parameters and contexts. If you think this is too short you may read counting context or counting perspective wherever it says context. (20) A context k is a set of objects from M, k 4 M, K is the set of all contexts. (21) The set of count atoms determined by context k is the set Ak ¼ {: d 2 k}

(22) Bk is the unique complete atomic Boolean algebra (up to isomorphism) with set of atoms Ak. We let kk stand for the corresponding complete join operation on Bk. However, we would like to lift this order from the mass domain as much as we can. The idea is: if k# 4 k and k# is a set of mutually nonoverlapping objects in M, there is no problem in lifting part-of relations of the sums of k#-objects from the mass domain. (k’ is a set of mutually non-overlapping objects in M iff for all d, d# 2 k#: d lM d# ¼ 0). Thus, we impose the following constraint: (23) For any set k# 4 k such that the elements of k# are mutually Mdisjoint, the Boolean substructure Bk# of Bk is given by: Bk# ¼ {: X 4 k#} with the order lifted from kM. The plurality order is not lifted from the mass domain for objects that overlap, that is, the sum of my hands and my fingers is a sum of 12


Ak is going to be the set of atoms of the count structure Bk to be determined below. The objects in k are not mutually disjoint with respect to the order in M since we may want, in a single context, say, my hands and each of my fingers to count as atoms, that is, to be members of the same contextual set of atoms. Thus, it may be the case that for two entities lt and lh (my left thumb and my left hand), lt 8M lh, but nevertheless lt, lh 2 k. In that case , 2 Ak. So both my left thumb and my left hand are atoms to be counted in context k. Given this, we cannot lift the order on the count Boolean domain from the mass domain. We want the count domain Bk to be a complete atomic Boolean algebra generated by the set of atoms Ak. Up to isomorphism, there is only one such structure:


(24) (i) For any X 4 M: COUNTk(X) ¼ {: d 2X \ k} (ii) The interpretation of a count noun Ncount in context k is: ½½Ncount ¼ COUNTk(Nroot). We will use Nk for the interpretation of Ncount in k. The denotation of a singular count noun in context k is thus Nk, an ordered pair whose first projection is a set of entities Nroot \ k and whose second projection is context k. We call such sets semantically atomic sets since the criterion for what counts as an atom is semantically encoded by the specification of the context. The set Nroot \ k, or Nroot,k is the set of atomic N-entities used to evaluate the truth of an assertion involving Ncount in a particular context k. The atoms in k are not constrained by a non-overlap condition since we want to allow examples like (25), which make reference to atomic elements and their atomic parts: (25) a. I can move my hand and my five fingers. b. It took 2500 bricks and a lot of cement to build this wall.


atoms, hence not lifted from the mass domain (atom here is a metalanguage predicate). (Singular) count predicates, in particular count nouns, denote subsets of Ak. We propose that they are derived as follows. All lexical nouns N are associated with a root noun meaning Nroot. As I stated above, the root noun meaning is a Boolean algebra generated under kM from a set of M-atoms. The mass noun denotation, Nmass, is identical to the associated Nroot, that is, Nmass¼ Nroot 4 M. Count noun meanings are derived from root noun meanings by an operation COUNTk, which applies to the root noun meaning Nroot and gives the set of ordered pairs {: d 2 N \ k}. These are the entities that in the given context k count as atoms and thus can be counted. The parameter k is a parameter manipulated in context. Thus, in the course of discourse we have as many relevant k’s around as is contextually plausible. We can think of these contexts as contextually defined perspectives on a situation or model, and the set of contextually relevant contexts is rich enough so that there may be different numbers of N entities in a situation depending on the choice of k, that is, the choice of counting perspective that is chosen. In sum:

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But since the entities in k are strictly atomic, the relation between the wall and the bricks that it is made of will not be expressed visibly in Bk.10

10

(i) For any plural entity y in Bk, [p(y) is the group entity whose members are the atomic parts of p1(y), that is, the members of the group are those parts of p1(y) that are in k. (ii) Y[p1(y) ¼ p1(y), that is, Y applied to a group gives the original plurality back again.We now define the set GROUPk of group entities, and the set k*, a superset of k, which includes members of k and the singular groups constructed from them via [. We also define the set of atomic groups AGROUPk. (iii) GROUPk ¼ {x: dy 2 Bk: x ¼ [p1(y)} (iv) k* ¼ k [ GROUPk (v) AGROUPk is the set of ordered pairs {<x,k*>: x 2 GROUPk} GROUPk is the unique atomic Boolean algebra generated by GROUPk with the corresponding join operation kGROUPk and GRPk is the unique atomic Boolean algebra generated by AGROUPk and the corresponding join operation kGRPk with the order lifted from GROUPk. Nouns such as deck denote functions from Bk into Ak*, that is, functions from plural entities into the atomic collections formed from them via the [ operation. Plural group predicates such as decks denote subalgebras of GRPk. This means that deck does not have a denotation in k, and, thus CARDroot \ k is just the set of atomic individual cards in k and does not include any sums or decks. I discuss these group classifiers further as part of study of the semantics of classifiers in work in progress. A more difficult version of the problem arises with pairs of singular count nouns such as brick and wall, not in the general case illustrated in (25b) but in the specific case where [unlike the case in (25b)] a wall entity consists only of a sum of bricks and has no other parts, such as cement. This would occur if the wall was a dry-stone wall (see footnote 2). If such a wall entity is in k, but is represented merely as a sum of bricks, then the wall entities will be in BRICKroot \ k and thus in the denotation of the singular count noun brick. One possible solution is to treat wall analogously to deck, justifying this by the plausible assumption that walls are greater than the sums of bricks that compose them. However, against this is the intuition that while deck is defined as a set of cards, wall denotes a set of entities that are objects in their own right, rather than being an expression that classifies bricks, and thus, wall should have a denotation in k. However, this problem is a version of the problem that occurs in the mass domain too, as we saw in the examples in (8) above. This jewellery is new, but the gold it is made of is old. The mass entity in jewellery cannot be equated with the mass entity in gold since they have different properties, even though they are apparently identical. This implies that generally ‘artefact’ predicates like jewellery involve a packaging or perspective function as part of their lexical meaning, so that d 2 GOLDroot and d# 2 JEWELLERYroot can be identified as the same spatiotemporal entity but presented under different perspectives or guises and with different properties. But if this kind of lexical packaging is needed anyway in the mass domain, then the problem of the wall and the sum of bricks that makes it up can be solved at the level of WALLroot and BRICKroot, in which case BRICKroot \ k will not include the sum of bricks presented as a wall.


As two reviewers have pointed out, a difficulty still remains when we want to be able to count singular entities in k, which themselves consist of a sum of a set of atoms in Nroot \ k, for some Nroot. One example of this is the predicate deck of cards. A deck of cards consists of 52 cards. If we treat the count noun deck as an ordinary count predicate, then it will denote a set of entities in M 3 {k}, each of which is a sum of 52 cards. This means that when in context k we construct the count noun meaning of the singular count noun card, CARDk, CARDroot \ k will include not only the individual atomic cards but also the sums of 52 cards in the denotation of deck. This is obviously not desirable. Landman (1989a,b) analyses nouns like group (of boys), class (of children) and deck (of cards) as ‘group nouns’, singular count nouns that refer to atomic collections of count entities. These group nouns do not have ordinary count noun denotations. I shall analyse them as a form of count noun classifier, as follows: We assume that alongside Bk, there is a set GROUPk, the set of (abstract) singular entities that are derived from sums of count entities via ‘group-formation’ or parcelling, which uses the group function [ defined as follows (see also Chierchia 1998a, who defines essentially the same function):


Non-overlap is not irrelevant though. I assume it comes in as a constraint on default contextual interpretations: (26) Constraint on count predicates: In a default context k, the interpretation of singular count predicate P is a set of mutually non-overlapping atoms in k (where and do not overlap iff a lM a# ¼ 0).

(27) *A ¼ {d: dY 4 A: d ¼ kY} For a two-place relation Nk, the n-th projection of Nk (where n ¼ 1, 2) is given by: (28) p1(Nk) ¼ {d: 2 Nk} p2(Nk) ¼ k For convenience, we also define pn directly for pairs: (29) p1() ¼ d p2() ¼ k Note that for any 2 Nk, p2() ¼ p2(Nk) ¼ k. With this, we lift the *-operation to the present count structures: (30) In default context k: PL(½½Ncount) ¼ *Nk ¼ {: d 2 *p1(Nk)} (In non-default contexts, we do not lift plurality from the mass domain: In non-default context k: *p1(Nk) ¼ {d: dY 4 Ak: d ¼ kkY}) Some crucial points: first, the non-overlap condition in (26) guarantees that in default contexts, the order of the plural count noun denotation is lifted directly from M. The denotation of the plural count noun depends on the contextually determined denotation of the singular Nk. It denotes a set of ordered pairs where the first element is in the closure of Nroot,k under sum and the second element is the context k. Nroot,k may vary depending on choice of k, and the denotation of the plural set will similarly vary. Crucially, the information about the context determining the set of atoms is preserved in the plural denotation. Note


This guarantees that when we count entities in the denotation of Nk, we will be counting contextually discrete non-overlapping entities. Plural count nouns are derived from singular count noun meanings, using the standard plural operation, defined for these count structures. The plural operation gives the closure of Nroot,k under the sum operation, while keeping track of the context. Link’s (1983) plural operation is given in (27):

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11 There seems to be a constraint even at the N-level that N conjunctions of predicates can be modified by numerals only if the conjunction can be reinterpreted as a quasi-lexical item or natural predicate. (i) and (ii) are felicitous but note that the conjunction is interpreted differently in each case: (i) Ten boys and girls came to the party. (ii) There are six cups and saucers in the cupboard. In (i), boys and girls is naturally interpreted as a synonym for the ‘superset’ children and then sentence (i) asserts that ten children came. In (ii), we count cup + saucer pairs and (ii) is not equivalent to There are six pieces of crockery in the cupboard, that is, it cannot be used to describe a situation where the cupboard contains three cups and three saucers (or four cups and two saucers). However, these strategies are highly constrained in ways that are not generally understood. Thus, (iii) and (iv) are not felicitous [although (iv) is minimally different from the felicitous a cat has four paws]: (iii) #?John has twenty fingers and toes. (iv) #?A human has four hands and feet. (A cursory search on Google produced about 60 000 references to ‘walking on hands and feet’ and no references at all to ‘walking on four hands and feet’.) Similarly, he received 10 letters and parcels is more felicitous than he received 10 letters and magazines presumably because in the first, and not the second, the conjoined N predicate can be reinterpreted as pieces of mail.


that, even with a flexible predicate like hair, there is no guarantee that HAIRroot,k and the set of atoms in HAIRroot are the same set. So though the hairmass and the hairs may well refer to the same real-world entity, this is not necessarily the case. The second point is that since k is not constrained by a non-overlap condition, the plural domain may contain elements not lifted from M. These plural entities will not be in the denotations of lexical predicates, but they will be in the denotations of other expressions built up in the grammar like the conjunctive definite my hand and its five fingers in (25a). In a normal context, my hand will count as an atom, and its five fingers as a sum of five fingers, and consequently, in Bk my hand and its five fingers will denote a sum of six atoms. Nevertheless, when I say in a context I moved my hand and its five fingers, it is not necessarily the case that it would be felicitous in that context to conclude, Hence I moved six body parts. The reason is that counting is a grammatical operation introduced by numerical modifiers that applies at the N-level to lexical predicates. The predicate body part in a default context will be interpreted as denoting a set of non-overlapping objects, and thus, though there are six atoms in my hand and its five fingers, we are unlikely in a normal context to allow the overlapping entities, hands and fingers, into the denotation of body parts. There are specific contexts in which this default assumption may be overruled, for example, a medical examination of a paralytic, but then the predicates will usually be reinterpreted so the entities in its denotation are not overlapping. He can move five limbs: one hand and four fingers is naturally interpreted as a statement about movement at the hand joint and the finger joints rather than movement of overlapping entities.11 Similarly, How many


Root nouns: Nroot 4 M: Root nouns denote a Boolean algebra of mass entities, the closure of a set of atoms in M under the sum operation kM. Mass nouns: Nmass ¼ Nroot: Mass nouns just are root nouns. Singular count nouns: Nk 4 M 3 {k}: A singular count noun denotes a set of ordered pairs of which the first projection is Nroot \ k, a subset of Nroot whose members do not (generally) overlap, and the second projection is the context k. Plural count nouns: In a default context k, PL(Nk) 4 M 3 {k}, where the first projection is the closure of Nroot \ k under sum, and the second projection is k. The definition of context that I gave in (20) is purely formal. While I have not given any constraints on the construction of contexts other than formal ones, we can assume that the set of contexts, although rich enough to give us what we need, is not unconstrained. Intuitively, Nroot \ k, the set of N-entities that count as one in a particular context, are N-entities that count as one by a single criterion of measurement.


things are there on the table? in the default case usually assumes a contextual decision as to what non-overlapping entities count as THINGk. There are a few cases where we do count genuinely overlapping entities without reinterpreting the predicate or making contextual decisions about what the non-overlapping atomic entities are. These are of two kinds. First, there are a few lexical predicates that are defined as having overlapping entities in their denotations. The most obvious example (pointed out by a reviewer) is subset, as in I wrote down the 16 subsets of the four member set. Here, the meaning of the predicate (which, as a technical term, has a formal definition of what counts as a countable entity) overrules the default assumption in (26). The second case in which we count overlapping entities is in contexts that are explicitly or implicitly intensional, where we are instructed to count in alternative k-contexts and sum the results. An example is a situation where you are given a picture of embedded cubes and asked How may cubes do you see in this picture? Here, we are asked to consider alternative choices of sets of non-overlapping atoms, where the union of these sets is a set of overlapping entities. How many cubes do you see in this picture is as an instruction to count the number of atoms in each relevant context k1. . .. kn and take the sum of the results. The variety of nominal denotations is thus summed up as follows:

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(31) Tables and other furniture were standing around the room. Conjunctions of this kind must be at the type of mass noun, as shown by the contrast in partitive constructions in (32a/b).12 12

A referee suggested that if tables and other furniture are conjoined at the mass type, the conjunction should induce singular agreement, as mass nouns usually do, rather than plural agreement as in (31). But conjunctions of mass nouns above the N-level generally allow and usually indeed prefer plural agreement as in (i) and (ii), and when definite mass terms are conjoined as in (iii), plural agreement is obligatory. (i) Furniture and curtaining were/???was on sale at much reduced prices last weekend. (ii) Bread and milk are/???is being delivered between 2 and 4 this afternoon. (iii) The bread and the milk are/#is being delivered between 2 and 4 this afternoon. Given these facts it is expected that tables and other furniture can induce plural agreement too. Note that some mass/count conjunctions may also induce singular agreement as in (iv), and plural count phrases may induce singular agreement when understood as denoting quantities as in (v): (iv) Carpets and curtaining is on the 5th floor of the store. (v) Ten tables and twenty chairs is not enough.


As we saw in the discussion about fences above, how we count fences depends on what we choose to consider one fence, how we pick out the atomic fence units. So a context k can be thought of as pragmatically constrained by a set of ‘atomicity conditions’, which (partly) specify what the criteria are for an N-entity to count as an atomic N in context k. This is what allows contexts to be distinguished pragmatically and governs the appropriate choice of context in a particular interpretation. It is also what underlies the constraint on the derivation of lexical count nouns in (26). Grammatical counting and related grammatical operations apply to Nk and PL(Nk) since what counts as one is semantically encoded in these noun denotations. The two kinds of nominal expressions, mass nouns and count nouns, are of different types: mass nouns are of type , while count expressions are of type , and this explains why some semantic operations will distinguish between them, as we will see below. Some operations do not distinguish between them: many adjectives apply equally well to mass or count expressions, as in expensive chairs, expensive furniture. For these cases, we use the pn function defined above in (28)–(29). We use P as a variable of predicates of type , P for count predicates of type and x and x for variables of type d and type d3k, respectively. Expensive, when it applies to mass nominal expressions of type , denotes the function kPkx.P(x) ^ EXPENSIVE(x). When it applies to count expressions of type , it denotes the derived function kPkx.P(x) ^ EXPENSIVE(p1(x)). The pn function is also used in deriving conjunctions of mass and count DPs, as in (31):


(32) a. *Three/*Many of [the tables and the furniture] arrived damaged. b. Some/Much of the tables and the furniture arrived damaged. (As we will see in section 8, conjunction at the mass type also gives the right results for reciprocal resolution.) Furthermore, as example (33) shows, a numeral cannot have scope over a conjunction of a mass and a count term. Example (33) refers to a sum consisting of furniture that includes at least 10 tables, as well as other furniture. (33) The movers delivered ten tables and furniture.

(34) ½½tables and (other) furniture ¼ AND(p1(½½tables), ½½furniture) ¼ AND(*TABLEroot,k, FURNITURE) Turning to coordinations of definite expressions, I assume, following Link (1983) and references cited there, that the is defined using the join operation: ½½the (X) ¼ r(X) ¼ kX if kX 2 X, otherwise undefined. In our case, this gives the following interpretations, with kM and kk being the complete join operations on M and on Bk, respectively. For mass nouns: rN ¼ kMN, the (unique) maximal entity in N, if defined. For count nouns: rNk ¼ kk(Nk) ¼ , if defined. For mass nouns, kMN is a plural individual, while for plural count nouns kkN is the ordered pair consisting of the maximal entity in the pluralization of Nroot,k and its context k. (For singular count nouns, it gives the relevant ordered pair if and only if N denotes a singleton set, otherwise it is undefined.) The interpretation of coordination of definite count and mass nouns follows naturally: (35) ½½the tables and the other furniture ¼ AND(p1(½½the tablesk), ½½the furniture) ¼ AND(p1(<rp1(TABLESk), k>), rFURNITURE) ¼ AND(rp1(TABLESk), rFURNITURE) ¼ AND(r*TABLEroot,k, rFURNITURE) Despite the difference in types between mass nouns and count nouns, there is no ontological distinction between the entities with respect to which they are interpreted, and these entities are thus


Given that and conjoins arguments at the same type, in cases of type mismatch, the count nouns lower to a mass reading via the pn function, which, as we have just seen, is available for adjectival modification anyway:

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6 MASS NOUNS V. COUNT NOUNS Mass nouns are root nouns. Like plural nouns, they denote Boolean algebras, which is why Chierchia (1998a) calls them lexically plural. A mass noun has the same denotation as a root noun, that is, a mass noun denotes Nmass the closure under sum of a vague set of minimal parts in Nmass. These minimal parts may be perceptually salient in a particular context but need not be so. Predicates that consistently denote sets of salient individuals such as furniture or jewellery are naturally atomic, and the minimal entities in their denotations are available as the basis of quantity judgments (Barner & Snedeker 2005). Crucially, even when the contextually relevant minimal elements of N are perceptually salient, this is not encoded semantically, and they are not grammatically accessible for counting and related operations. This is because they are not of the right type: mass nouns are of type , that is, functions from individuals to truth values, while counting operations apply to count nouns of type , that is, functions from ordered pairs to truth values. In order for the minimal elements of Nmass to be counted, a classifier must be used. The most neutral classifiers are unit of and piece of and can be thought of as an explicit expression of the COUNTk operation as in (36): (36) I bought a unit of furniture/one piece of furniture. Without going seriously into the semantics of classifiers here, we can hypothesize that unit of is analysed as a function from M into


recoverable from the count noun meaning. This captures both Chierchia’s intuition that the carpeting and the carpets can be used to refer to the same pile of entities and also fact that they need not do so (see discussion in section 6). To sum up so far, we have argued against Chierchia’s (1998a) proposal that the grammatical accessibility of atomic sets in the denotation of singular count nouns is determined by the notion of salience, derived presuppositionally. Instead, we have proposed a grammatical definition of countability, namely that we count semantic atoms, entities that count as one relative to a particular context k and that are indexed for that context. Count nouns are of a different type from mass nouns and are derived from mass nouns via the operation COUNTk. We can now look more closely at the lexical derivation of mass and count nouns (in section 6) and the differences in their grammatical behaviour (in section 7).


M 3 K, which applies to a mass noun and which individuates entities relative to a particular context. This is illustrated for unit in (37a,b). Some classifiers add more lexical information than unit, for example, strands of hair, cups of coffee and so on. We assume that these add properties conjunctively to the semantic atoms as in (37c,d), though we will not discuss this further here.

Singular count noun meanings are derived from root noun meanings via the COUNTk function. Intuitively, there are two sorts of count nouns, those that denote things that are inherently individuable and those that do not. The first kind are naturally atomic predicates. Case 1: naturally atomic count nouns: boy, pencil, cat, etc. These are the predicates that first come to mind when we think of count predicates. They are naturally atomic because what counts as one entity is not determined by context but by the naturally atomic structure of the stuff. What counts as one P is part of our knowledge of what a P is, whether P is cat, boy, pencil and so on. So the atomic entities in Nk are not determined by the choice of k but by our knowledge of the world. It would be nice to say that naturally atomic predicates are never context dependent and that COUNTk(Nroot) always yielded the same set on a particular domain for these predicates, no matter what the choice of context, but this is an oversimplification. Child is a naturally atomic predicate since children come in inherently individuated units. What counts as the denotation of child, though, may vary depending on aspects of the situation that are independent of the choice of atomic entities. What child means with respect to paying bus fares (under 12 in the Netherlands and under 14 in the UK) is different from what it means when filling out tax declarations. But this kind of context dependence is different from the context dependence shown by fence: child is a vague predicate because of borderline cases, but there is never any doubt as to what counts as ‘one’. The kind of context dependence shown by child is not


(37) a. ½½unitk of ¼ kPkx.p1(x) 2 (P \ k) ^ p2(x) ¼ k b. ½½unitk of furniture ¼ ½½unitk of (½½furniture) ¼ kx.p1(x) 2 (FURNITURE \ k) ^ p2(x) ¼ k c. ½½strandk of ¼ kPkx.p1(x) 2 (P \ k) ^ LONG-AND-THIN(p1(x)) ^ p2(x) ¼ k d. ½½strandk of hair ¼ ½½strandk of (½½hair) ¼ kx.p1(x) 2 (HAIR \ k) ^ LONG-AND-THIN(p1(x)) ^ p2(x) ¼ k

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(38) Natural atomicity: If N is a naturally atomic predicate then: "x"k"k’[x e p1(Nk) ^ x e p1(*Nk#) /p1(Nk#) ‘If N is naturally atomic, then for any two contexts k and k#, if x is an atom of Nk, and x is in the denotation of Nk#, x is also an atom in Nk#.’ Note that what counts as a natural atom here is usually not dependent on size but on some systemic property that defines what counts as one N. For example, what counts as one boy is dependent on ‘boy-ness’. A giant preteenager and a small premature male baby each count as one instance of boy and together they make a plurality of boys with the cardinality two. [Note also that (38) can be used to define naturally atomic mass as well as count predicates.] Case 2: homogeneous nouns: fence, wall, sequence, quantity, bouquet. These predicates are not naturally atomic since the entities do not come in inherently individuated units. The predicate itself does not uniquely determine an individuating function, and thus, the set of atomic entities will vary from context to context. Assume a root noun denotation {a, b, c, akb, akc, bkc, akbkc}. COUNTk(N) applied to this set could choose as a set of atoms {a,b,c} or {a, bkc} or {akb, c} or {akc,b} or {akbkc} depending on the choice of k. The set of atomic entities in fencek need not be identical to the set of


dependent on the choice of contextual counting parameter k since a 13-year-old girl will count as ‘one entity’ and thus be a member of k for any choice of k, whether or not she counts as a child in k. Vagueness shows up in the mass domain too; childhood is vague in the same way that child is, as can be seen from the vagueness of expressions like during childhood. Vagueness of this kind may be treated by the theory of supervaluations proposed by Kamp (1975) or by other treatments in which precisifications of vague predicates are dependent on contextual factors. Given the existence of borderline vague naturally atomic predicates, we cannot say that if N is naturally atomic, COUNTk(N) is a constant function independent of choice of k. Rather, when N is naturally atomic, COUNTk(N) is constrained so that for any two contexts k and k#, if d is a semantic atom in context k, then it will be a semantic atom in k# as well. So a thirteen-year old may count as a child in some contexts and not in others, but if she does count as a child in context k, then she will necessarily count as a semantic atom in context k# too. This means we can give a definition of natural atomicity as follows:


(i) If I and my neighbour build adjoining walls, we may say either ‘Together we built a wall in front of both our houses’ or ‘We each built a wall in front of our respective houses’. (ii) If I have a bunch of flowers and I divide it in two and give a part of each to my daughter and her friend, then either each has a bunch of flowers or each has half a bunch of flowers. (iii) If a restaurant owner puts together tables a and b to make a bigger table akb and tables c and d to make another bigger table ckd, then a, b, c and d no longer count as semantic atoms in that context. There are either two tables or four tables in the restaurant,


contextually salient minimal elements in fenceroot and need not even cover it. For example, suppose the contextually salient minimal elements in the denotation of the root noun are the pieces of fencing which different individuals possess, but that not all of these fence pieces are big enough to count as actual fences in a given context k. Some of these small fence pieces in FENCEroot may be construed as parts of other atomic fences, while other pieces may be so small as to be irrelevant and may not be included at all. Which set we get in FENCEk depends on what the context k chooses to count as ‘one’ fence. As mentioned above, the denotation of the plural of a count noun depends directly on the choice of k. So while Chierchia is correct in arguing that the same pile of objects may be the denotation of the furniture and the pieces of furniture or the carpeting and the carpets, this need not be the case. Suppose that the denotation of carpeting is generated in M from a set of atoms that includes all pieces of carpeting, for example, {a,b,c,d}, but that CARPETk ¼ COUNTk(CARPETING) is the intersection of that set with k and includes only those atoms in carpeting that are in the context ‘big enough’ to count in k, for example, {a,b}. Then, the maximal entity in p1(*CARPETk) will not be the same entity as the maximal entity in carpeting. This seems right. If I say to the movers, ‘Please take all the carpets out of the attic’, they can say they have complied if they leave a few odds and end lying there. But if I say, ‘Please take all the carpeting out of the attic’, that requires them to take all the small pieces away too. [Landman (2007) suggests other cases where substituting apparently synonymous mass and count predicates for each other leads to different truth-values.] Once we start thinking about it, we can find more cases in which the atomic individuals in the denotation of a count noun are context dependent:

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but no other possibility (i.e. not six and not three). This makes clear the contrast with the mass domain, where if I put sand together with sand, the original sand parts and the sum of the parts fall under the denotation of sand simultaneously.


However, even with non-naturally atomic predicates, there is frequently a default measure unit, usually something like ‘perceptually salient, spatially distinct unit’, although it can be overridden by an appropriate context. Context and convention determine how far the denotation can vary with choice of context. In the UK, final school examinations (A-level exams) are taken in three or four subjects, and for each subject, the exam may consist of a number of sessions. One can refer to ‘the geography exam I took this morning’ or say that ‘There are four different geography exams’, using exam to mean ‘examination session’. Or one can say, ‘The geography exam has four parts’ or ‘This year’s geography exam was very difficult and the grades for the exam will be low’, using the singular term to denote the subject examination as a whole. Still, it would be infelicitous to refer to the whole set of school finals across subjects as ‘the A-level exam’ in the singular rather than the plural. It seems then that natural atomicity is a property that comes in degrees, and the range of contextual variation that is possible with different choices of k depends on the meaning of the predicate. Tables seem to come in inherently distinguishable units, and for most contexts k, COUNTk(TABLE) will yield a set of inherently individuable tables with little variation, but nonetheless, as we just saw above, COUNTk(TABLE) may still vary for some choices of k. While we can define a formal notion of natural atomicity as in (38), there is a sense in which natural atomicity is a gradable property. Example (38) defines ‘highly naturally atomic predicates’, and the degree of natural atomicity can perhaps be defined in terms of the proportion of relevant contexts for which (38) is violated. Note though that when a predicate P is highly naturally atomic, COUNTk, the function deriving count nouns, cannot choose a context that overrides natural atomicity and pick entities other than the natural atoms as the atoms of the context. Overriding natural atomicity in count nouns is done through group-forming classifier, as in a class of boys, a deck of cards and so on (see footnote 10).


7 GRAMMATICAL OPERATIONS ON MASS AND COUNT NOUNS

(i) Modification by numerals: what stops three from modifying furniture in (39)? (39) *three furnitures/three chairs/three pieces of furniture Krifka (2008b) suggests that the difference is presuppositional, that is, that number words presuppose the atomicity, or discreteness, of the set that they modify, and thus can modify count nouns and not mass nouns. But as we have seen, some mass nouns such as furniture do denote sets of discrete entities, while some count nouns such as fence do not, and a presuppositional account is not able to make the necessary distinctions. In the analysis of the mass/count distinction presented here, numerals cannot modify mass nouns because there is a type mismatch: mass and count nouns denote different entities and numerals are sensitive to this distinction. Determiners may be sensitive to the distinction, although some determiners such as some and the apply to both types. We treat numerals as adjectival modifiers and assume that a numeral such as three in its modifier meaning denotes a function from M 3 {k} into M 3{k}, that is, from count predicate denotations into count predicate denotations. It applies to a plural count expression and gives a set of ordered pairs where the first element has three atomic parts and the second element preserves the information about the context in which these parts count as atoms. The typal sensitivity of the numeral is justified theoretically by the fact that while the cardinality function j j is a function mapping entities onto the number of its atomic parts, numeral modifiers can only count relative to


With these distinctions in place, we can explain the grammatical differences between count and mass nouns. We have already seen why grammatical pluralization is restricted to count nouns: it is an operation on semantic atoms and thus restricted to expressions of type . It is irrelevant in the mass domain because the mass domain is already Boolean. As we saw in section 2, there are three other central issues: (i) modification of N by numerals and sensitivity of determiners in general to the mass/count distinction, (ii) sensitivity of the numeral phrase in partitive constructions to the mass/count status of the head of the complement DP, and (iii) sensitivity of each other to the mass/count status of the head noun of its antecedent. I shall show that in each of these cases, the relevant grammatical operation is sensitive to the typal distinction between mass and count nouns.

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(40) ½½Three ¼ kPkx.P(x) ^ jp1(x)jp2(P) ¼ 3 ‘Three denotes a function which applies to a count predicate of type and gives the subset of the count predicate i.e. a set of ordered pairs where the first projection of each ordered pair has three parts which count as atoms in k.’ Since three must apply to a count predicate with a denotation in M 3{k}, the infelicity of three furniture(s) is due to a type mismatch. If three is treated as a determiner denoting a function from predicates into generalized quantifiers, then a similar explanation can be given in terms of the selectional properties of the determiners. This can be extended to other determiners: every, which does not occur with mass nouns, denotes a function from singular count predicates into sets of count predicates or generalized quantifier denotations; many denotes a function from plural count predicates into generalized quantifier denotations; and much from type into generalized quantifier denotations. (ii) Numerical partitives take only count DPs as complements. Numerical partitives take only count DPs as complements while expressions such as some of the take either mass or count DPs as complements as in (41): (41) a. three of the pieces of furniture/*three of the furniture b. much of the furniture/*much of the pieces of furniture c. some of the pieces of furniture/some of the furniture These examples are crucial support for this theory of count nouns, as they show that the distinction between mass and count


a fixed context k. So three, and other numeral modifiers, make use of the parameterized cardinality function j jk that assigns a value to a plural entity depending on the number of its atomic parts in k. Numerical modifiers thus apply to noun denotations in which a context k is grammatically encoded. The numeral expression three thus denotes a function from count noun denotations into count noun denotations and is of type . It applies to a set of ordered pairs Nk and gives the subset of Nk, such that all members of p1(Nk) are plural entities with three parts each of which is an (atomic) entity in k. [As above, P is a variable over count predicates of type and x a variable of type d3k. p2(P) is the context parameter on the parameterized cardinality function, which is dependent on the context relative to which the count predicate has been derived.]


r(X) ¼ kX if kX 2 X, otherwise undefined. For mass nouns: rN¼ kMN, the(unique) maximalentity inN, if defined. For count nouns:rNk ¼ , if defined. We need to recover the denotation of the predicate head from the DP. We define an operation PARTITIVE on definite DPs that gives the set of parts of kN, N the lexical head of the DP. We lift the part-of relation on ordered pairs in M 3 {k} from M: <x1, k> 8k <x2, k> iff x1 8M x2 The partitive operation follows the following definition schema, operating on a definite complement and giving the set of its parts (we use x as a generalization over x and x): PARTITIVE(rN) ¼ {x: x 8 (rN)} For a mass predicate, PARTITIVE(r(Nmass)) ¼ {x: x 8M r(Nmass)}, which is Nmass itself. For a count predicate, in a default context k, PARTITIVE(r(Nk)) is again lifted from M: PARTITIVE(rNk) ¼ {<x,k>: <x,k> 8k } Crucially, since we kept track of the context k during all the operations involving the composition of the embedded DP, the operation giving the set of parts of rNk will still have access to the original context k. The partitive determiners three and some can now have exactly the same semantics as they have as N modifiers. Since three(of) makes use of the parameterized cardinality function that makes reference to k, it can apply to PARTITIVE(½½the chairs) or PARTITIVE(½½the pieces of furniture) that are sets of type , but not to PARTITIVE(½½the


nominals must be accessible outside the DP itself, and that the structural difference between mass and count nouns must be preserved at all levels of compositional structure that they project. Three modifies plural count nouns, and thus, three of applies to DPs lexically headed by plural count nouns; much (of) applies to mass nouns and definite DPs headed by mass nouns, while some (of) applies both to count and mass nouns, at the N and the DP level. (I assume that D is the functional head of DP and N its lexical head.) The embedded DP in partitive constructions is always definite. In section 6, we gave the interpretation of the following Link (1983) and references cited there in terms of the r operation:

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furniture), which is a set of type . Much(of) can take only PARTITIVE(Nmass) and some(of) can take any definite complement.13,14 (iii) A reciprocal cannot take a mass noun as antecedent although it is ‘lexically plural’. This is illustrated in (42) and in Gillon’s examples, in (43) repeated from (4).

The interpretation of reciprocals is too complicated to discuss in detail here, involving as it does a variety of interpretations including the so-called intermediate interpretations. I offer only a suggestion of how aspects of the mass/count distinction may be involved in the process.

13 I assume that the PARTITIVE operation also applies to group predicates as in three of the decks of cards. For group nouns: rNGROUP ¼ kGRPk, if defined. PARTITIVE(rNGROUP) ¼ {<x,k*>: <x,k*> 8GRPk rNGROUP} PARTITIVE(½½the decks of cards) is the set of group parts of the maximal entity in decks of card (since the join relation is not lifted from Bk but from GROUPk), that is, the set of deck entities. Thus, three of the decks of cards denotes pluralities of decks (of cards) and not pluralities of cards. 14 A reviewer suggests that a syntactic copy account of partitives makes the problem of how to project the typal distinction between mass and count nouns beyond the DP level irrelevant. In such an account (e.g. Sauerland & Yatsushiro 2004 and references cited there), three of the boys contains a copy of the sortal boys outside the definite. At LF, the expression to be interpreted is three boys of the boys. The typal distinction between mass nouns and count nouns is thus directly available outside the definite DP. But the semantic interpretation of the syntactic copy theory has only been worked out for the simple cases and not for more complicated cases where the embedded nominal is a relational noun. Three of the mothers of children in this class is not equivalent to three mothers of the mothers of children in this class just as three of the successors of 10 is not equivalent to three successors of the successors of 10. If of is constrained to be interpreted as a partitive relation, as in Sauerland and Yatsushiro (2004; see also Barker 1998), then the higher sortal cannot be a copy of the denotation of the embedded noun but needs to shift into the appropriate non-relational meaning. Doing this is non-trivial (see, e.g. the discussion in Partee and Borschev 2003 about shifts of this kind in genitive constructions), especially since non-relational uses of nouns like mother are highly restricted. The attractiveness of the copy theory as an alternative to the theory that I propose here is thus considerably reduced. Sauerland and Yatsushiro (2004) do not discuss how the copy theory would handle these cases. In a different version of the copy theory, Barker (1998) assumes a null nominal head without suggesting that the content is copied from the lower noun, thus avoiding the problem of relational nouns. However, he does not discuss the mass noun/count noun contrast in partitives and gives a theory of partitivity that does not explain the ungrammaticality of *three of the furniture. In fact, his theory cannot explain it without adopting a typal difference between mass and count nouns.


(42) a. (The) pieces of furniture are piled on top of each other. b. #The furniture is piled on top of each other. c. #Furniture was piled on top of each other. (43) a. The curtains and the carpets resemble each other. b. The curtaining and the carpeting resemble each other.


As has long been known, whatever interpretations (intermediate, non-intermediate) are acceptable, the antecedent of a reciprocal must be a plural noun phrase, as illustrated in (44): (44) a. The boys helped each other. b. The chairs stood on top of each other. c. The boy and the girl helped each other. d. John and Mary helped each other. e. *The boy helped each other. f. *The furniture stood on top of each other.

(45) The curtaining and the carpets resemble each other. Chierchia suggests that the impossibility of (44e/f) should be put down to a requirement that antecedents of reciprocals must be morphologically plural, but this is too weak for two reasons: first, this makes appeal to morphological agreement when other argumentation (both in this and in his article) has been at the level of semantic structure, and second, there are examples with singular antecedents that are much better than (44e/f), namely examples where the singular is an inherently group term. While the examples in (46) are not perfect, they are better than (44e/f). (46) a. The family stood next to each other and consoled each other at the funeral. b. The committee argued with each other for some time before coming to a unanimous conclusion. We assume that the semantic effect of a reciprocal is twofold: it identifies two thematic arguments as satisfied by the same plural DP, and it constrains semantically how the atomic parts of the plural DP participate in the event denoted by V. We show how this works explicitly, using the account of plural arguments from Landman (1997, 2001). Landman (1997, 2000) argues that verbs can be either semantically singular, denoting sets of singular events or semantically plural, denoting sets of pluralities of events. He assumes that singular verbs assign singular thematic roles to singular DPs, while plural verbs assign plural roles to plural DPs. As plural events are sums of singular events, so plural roles are


Plural noun phrases can be definite plurals on a distributive reading as in (44a/b), conjunctions of singular definites or proper names as in (44c/d), but not singular definites or mass nouns as in (44e/f). As (43) shows, conjunctions of definites and conjunctions of mass nouns are also possible. Conjunctions of mass and count nouns are also possible, as in (45):

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(47) The boys helped each other carry the piano upstairs (#together). This account applies straightforwardly to reciprocal resolution with mass and count antecedents. Reciprocal antecedents must be plural count nouns such as the boys or conjunctions of singularities like John and Mary or the boy and the girl but not mass nouns or collectives. Assume that proper names always denote semantic atoms, that is, are inherently of type d3k. This is plausible since, as constants, they are contextually rigid and denote the same individual cross-contextually relative to a model. (If proper names are rigid designators, this follows automatically.) Then, antecedents for reciprocals are constrained to be pluralities of semantic atoms, as in (48): (48) Constraint on reciprocal interpretation: An antecedent for a reciprocal must be a plural entity in M 3 {k}.15 In (44a), The boys helped each other, the reciprocal associates the value of the theme relation with the value of the agent. Helped denotes the set of plural events *HELP, and *Ag and *Th are the plural roles 15 The antecedent can be also be a plural of a group predicate. So more correctly, the antecedent of a reciprocal must be a plural entity in Boolean algebra generated by Ak* (see footnote 10).


sums of thematic roles. The intuition behind this is that only singular entities participate directly in events. John helped Mary is true if the individuals denoted by John and Mary participated directly in the helping event. Plural individuals do not directly participate in events: rather, event participation distributes down to the atomic parts of the entities denoted by the plural noun phrase. In The boys helped the farmer, the boys satisfies the plural agent role of helped syntactically, and the sentence is true iff the atomic parts of the plural individual, that is, the individual boys denoted by the boys, each participated in helping the farmer. Intuitively, if the boys is the antecedent of a reciprocal, as in (42a), the thematic participation in the event must distribute down to the atomic parts of the plural DP in such a way that for any two atomic parts of DP, the relevant relation between them is reciprocal. Collective readings of DPs such as the boys are derived as follows. The plural entity denoted by the boys is rBOYS, the maximal sum of individual boys. This is lifted to the group reading [(rBOYS) and is treated as a higher order singular entity that can be assigned a thematic singular role. On the collective reading, The boys helped the farmer is true if the group collectivity denoted by the boys directly participated as a singularity in the event of helping the farmer. The individual parts of the group entity are not accessible to the interpretation and so the collective cannot be an antecedent for a reciprocal, as (47) shows:


assigned by *HELP to its arguments. x remains a variable of either type or since help does not restrict its arguments to either mass or count DPs. Help each other is interpreted as in (49a). The reciprocal requires that the variable must be of type and introduces the constraint on interpretation in (49b):

Plural DPs with count noun heads can be antecedents of reciprocals since they are of type d3k. Conjunctions of singular definites and proper names can be antecedents of reciprocals, under the assumption (Link 1983) that conjunction of entities is a summing operation that results in pluralities. We add to Link’s summing operation the constraint that both conjuncts within a conjoined DP must be interpreted relative to the same context. Conjunctions of proper names then denote pluralities in M 3{k}. Singular definites and proper names cannot be antecedents for reciprocals since they do not denote pluralities. We can either stipulate that x in (49b) ranges over plural objects or assume that (49b) cannot be satisfied trivially. Mass nouns cannot be antecedents for reciprocals since they are of the wrong type. With respect to examples like (46), we assume that some (but very few) of the count nouns in English that denote groups of individuals (i.e. group nouns) are marked as inherently plural and under certain circumstances allow access to the atomic entities that they group together. This is why they can marginally be antecedents for reciprocals, and also why they allow plural agreement as in The family are arriving this evening or The committee are arguing about it right now.16 We now go back to Gillon’s examples in (43), repeated here: (43) a. The curtains and the carpets resemble each other. b. The curtaining and the carpeting resemble each other.

16

This appears to be possible only if the noun denotes a group of animate individuals, that is, family, class of boys and herd of cattle appear to take plural agreement but not deck of cards and set of silverware.


(49) a. ½½Help each other ¼ kx.*HELP(e) ^ *Ag(e) ¼ x ^ *Th(e) ¼ x b. Interpretation of the reciprocal: kx.*HELP(e) ^ *Ag(e) ¼ x ^ *Th(e) ¼ x / "y,z [y 8ATOM x ^ z 8ATOM x ^ :(y ¼ z) / de# [e# 8e ^ Ag(e#) ¼ y ^ Th(e#) ¼ z]]

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(45) The curtaining and the carpets resemble each other. This is predicted since, as we saw above in section 5.2, coordination of the mass and count nominals is at the mass type, and thus, within the coordination the carpets will denote the same type of entity as the carpeting. To conclude this section, we have shown that the characteristic grammatical distinctions between mass and count nouns are due to the sensitivity of some grammatical operations to the typal distinction between them. This sensitivity reflects the fact that the grammatical operations that are essentially counting operations (numerical modification and partitives), as well as reciprocals, are constrained to apply to semantic or counting atoms, atoms that count as one relative to a particular context. This is quite a natural restriction for counting operations, but perhaps less natural for reciprocals. However, we do not want the connection between reciprocals and semantic atomicity to be too direct because in fact there are languages where it does not hold and where reciprocal resolution is sensitive to natural as well as semantic atomicity. As Pires de Oliveira and Rothstein (in preparation) show, reciprocal resolution in Brazilian Portuguese is one such case. Although (50a) is ungrammatical in English, (50b) is perfectly acceptable


Example (43a) is ambiguous. The first reading, the distributive reading, is that all the curtains and carpets resemble each other. On this reading, the conjoined DP denotes the sum of the maximal plurality of curtains and the maximal plurality of carpets, and the interpretation of the reciprocal requires every two atomic entities (i.e. atomic parts of rCURTAINS ^ rCARPETS) to resemble each other. On the second reading, the curtains as a group, or singular collection, resemble the carpets as a group, or singular collection, and vice versa. On this reading, rCURTAINS and rCARPETS are treated as collections and are raised to the group atoms [(rCURTAINS) and [(rCARPETS) (see Landman 1989a,b). In (43b), where the antecedent of the reciprocal is the curtaining and the carpeting, the distributive reading is not available. Curtaining and carpeting are nouns of type and the definites denote maximal sums of entities in M, so condition (48) is not satisfied. The group reading is available since rCURTAINING and rCARPETING can be raised to atomic collections [(rCURTAINING) and [(rCARPETING), respectively. They then satisfy (48) in exactly the same way that the collections based on count nouns do. Finally, note that in (45), repeated here, we get only the group reading. Example (45) means the same as (43b).


in Brazilian Portuguese, and also in European Portuguese, although, predictably, (50c) is not. (50) a.*Furniture (of this brand) fits into each other b. Mobı´lia (dessa marca) encaixa uma na outra. Furniture (of+this brand) fits one in+the other ‘Furniture (of this brand) fits into each other.’ c.*Ouro cai um atra´s do outro. Gold falls one behind of-the other.

8 KRIFKA (1989) The relevance of natural atomicity to the semantics of count nouns has been pointed out in the literature before, notably in Krifka (1989, 1995). He also pursues the idea that count nouns involve an implicit measure function and are derived from abstract nominal predicates and that they thus differ in type from mass nouns. However, the theory proposed here differs from Krifka’s work in a number of important respects. Most crucial is the fact that Krifka’s typal distinction between mass and count nouns is a lexical distinction that is neutralized as soon as a noun is inserted into a nominal phrase. The typal difference is not projected higher up into the NP nor into the DP and is not accessible to operations such as partitivity and reciprocal resolution. Krifka (1989) analyses count nouns as two-place relations between numbers and entities, taking as a model expressions in English such as five head of cattle. He analyses the classifier head of as a measure function. In five head of cattle, the noun mass predicate cattle is interpreted as kx.CATTLE(x), a function applying to plural entities. The function is associated with a lattice structure L representing the set of individual cattle closed under sum. Head of introduces a measure function represented by NU (for natural unit), and five head thus denotes the measure function kPkx.P(x) ^ NU(P)(x) ¼ 5. This measure function, when applied to the denotation of cattle, yields the function compatible with the lattice L, namely kx.CATTLE(x) ^ NU(CATTLE)(x) ¼ 5, equivalently, the set of plural entities in the denotation of cattle that are sums of five individuals. Krifka proposes that in count nouns, the reference to a natural unit is built into the meaning of the head noun. The count noun cow


This indicates that there is a cross-linguistic parametric difference as to whether reciprocal resolution is constrained to have plural semantic atoms as antecedents and further supports the claim that the distinction between semantic and natural atomicity is a grammatical one.

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(as opposed to cattle) denotes the two-place relation COW’ between numbers and entities given in (51a), where the relation between COW’ and an abstract predicate COW is given in (51b): (51) a. knkx.COW’(x,n) b. COW’(x,n) 4 COW(x) ^ NATURAL UNIT(COW)(x) ¼ n.

17

Krifka (2008a) has accepted that the problems raised by nouns like fence and sequence require the NU function to be at least partially context dependent, though he has not been explicit about how this should be implemented.


COW is in effect what we have called Nroot, and COW’ the denotation of the count noun. This noun either combines directly with a numeral, for example, five, to give the predicate kx.COW’(x,5), or there is existential quantification over the expression in (51a) to give the expression kxdn.COW’(x,n). Thus, the count noun as used in the syntax is of the same type as the mass noun. Count nouns differ structurally from mass nouns since they are born at type , while mass nouns are born as predicates at type , but the typal difference is not accessible above the N-level. Singular count nouns do not have a special status; they are simply functions from the number 1 to sets of singleton cows and are just one instance of the relation denoted by COW’. One cow or a cow denotes the predicate kx.COW’(x,1), while five cows denotes kx.COW’(x,5) and the bare plural cows denotes kx.dn[COW’(x,n)]. Plural marking, that is, the contrast between cow and cows, is a matter of agreement: one or a induces singular morphology on the head noun, while five induces plural morphology on the head noun. Krifka’s account makes countability the result of an individuation operation and treats count nouns as measure operations from a number n to sets of plural individuals with cardinality n. But the content of the NU function is presupposed and is as general as possible: ‘. . . we can assume that NU yields the same measure function for entities of a similar kind . . . NU(CATTLE) and NU(GAME) should denote the same measure function’ (Krifka 1989: 84).17 The theory proposed here differs crucially, both grammatically and conceptually. In both theories, the grammatical distinction is expressed in the typal difference between mass and count nouns, but for Krifka, the difference is in basic nominal meanings, and the typal resolution is designed so as to be neutralized as low as possible in the syntactic projection of the N. When count nouns combine with a number, they get back immediately to type , and if they do not combine with a number, existential quantification over the n argument at the N-level gets the noun



back to type . Thus, operations that apply at the NP or DP level cannot distinguish between count and mass nouns. In the account presented in this article, the typal distinction between mass and count nouns is not neutralized but persists up to the level of the DP and is used to explain a series of syntactic and semantic combinatorial differences (number modification, partitive construction, plurality and reciprocal resolution). The difference in meaning between mass and count nouns thus determines the combinatorial possibilities all the way up the tree. Since Krifka (1989) is concerned with aspectual issues rather than with explaining the grammatical differences between mass and count nouns, he does not discuss how to account for partitives and reciprocals, but there is no natural way in which a typal difference between count and mass nouns neutralized at the N-level could explain them. The different ways in which the two theories exploit typal distinctions corresponds with the conceptual difference between the two theories. For Krifka, count nouns are extensive measure functions that measure in terms of (presupposed) natural units. Count nouns are analogous to expressions such as kilo and litre, which measure in terms of kilo and litre units. Units that have measure value 1 have no special status beyond entities whose value is 5 or 2500. In this article, however, we do not treat singular count nouns as measure functions but as expressions that denote sets of countable units, where a countable unit is a pair consisting of an entity and a context. These are what we have called semantically atomic sets. The idea underlying this is that counting and measuring are two very different operations. Counting puts entities (which already count as ‘one’) in correspondence with the natural numbers, while measuring assigns an (plural) individual a value on a dimensional scale. So while Krifka treats count nouns as extensive measure functions assigning pluralities of entities a value n, we treat them as expressions grammatically encoding countability, indexing individuals for the contexts in which they count as ‘one’. And this is essential since, as we saw in sections 3 and 4, countability is not necessarily a property of inherently individuable entities, and natural atomicity (being a natural unit) is neither a necessary nor a sufficient condition of countability. Furthermore, counting pluralities is a modification operation on the plural of the count noun, indicating how many atomic (countable) parts the plurality has and not a measure function on the denotation of the root nominal. This distinction between counting and measuring is an important one that shows up in other places in language, in particular in the interpretation of classifier constructions (see discussion in Rothstein 2009a).

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9 EXTENSIONS TO CLASSIFIER LANGUAGES: MANDARIN CHINESE An obvious question for any theory of the mass/count distinction is how it extends to classifier languages. A detailed discussion is impossible in the framework of this article, but we look briefly in this section at how this theory extends naturally to Mandarin Chinese. Classifier languages are those that do not grammaticalize the mass count distinction as a distinction between nominal heads and require classifiers to intervene between all numerals (and demonstratives) and the nominals they modify. Classifier languages exhibit variation in the use they make of classifiers (Sybesma 2008), but nonetheless some preliminary generalizations are possible (some of which apply also to English classifier + mass noun/plural count noun constructions). Note


To sum up, we have distinguished between three different kinds of atomicity: formal atomicity, semantic atomicity and natural atomicity, all of which are relevant in different ways. Formal atomicity is a property of Boolean algebras generated by a set of atoms. By hypothesis (Chierchia 1998a, b), mass nouns have denotations in the formally atomic domain. A count predicate makes accessible a set of semantic atoms, derived via the COUNTk operation, and mechanisms such as grammatical counting and reciprocals are sensitive to semantic atomicity. Naturally atomic predicates denote a set of entities that are inherently individuable and that are cognitively salient as individuals. Natural atomicity is not the basis of grammatical countability but is a phenomenon that grammatical systems are sensitive to. Grammatical counting operations and semantic atomicity may hitch a ride on the back of natural atomicity but do not always do so. As Barner and Snedeker have shown, quantity judgments are sensitive to natural atomicity. Other grammatical phenomena that are sensitive to natural atomicity include modification by predicates such as big/small, as well as the alternation between stuks and stukken in Dutch. Furthermore, there appears to be cross-linguistic variation as to whether reciprocal resolution is sensitive only to semantic atomicity (e.g. English) or may also be sensitive to natural atomicity (e.g. Brazilian and European Portuguese). By hypothesis, the dependence of grammatical counting on semantic atomicity is presumed to be universal, although semantic atomicity may not be expressed via count nouns. In section 9, we look briefly at how the distinction between semantic and natural atomicity shows up in classifier languages, where semantic atomicity is expressed only through classifier phrases.


that in English (Chierchia 1998a; Landman 2004; Rothstein 2009a), classifiers may denote either individuating/counting functions or measure functions. We assume, following Li (in progress), that classifiers in Mandarin show the same variation and restrict our discussion here to counting or individuating classifiers. Since classifiers are needed to make all nouns countable, there is no grammatical difference between bare ‘count’ or bare ‘mass’ nouns. Thus, pıńgguoˇ, ‘apple(s)’, in Mandarin Chinese cannot be explicitly counted without a classifier, as we saw above.

We assume (as does Krikfa 1995) that the count operation that derives count nouns in the lexicon in languages with a lexical mass/ count distinction is expressed by the classifier in languages such as Mandarin Chinese. In our theory, this means that Mandarin Chinese does not allow the COUNTk operation as a lexical operation, but requires it to be introduced explicitly by a syntactic element, the classifier. As well as being explicit expressions of the COUNTk operation, classifiers may add information about the criterion used for individuation in a particular context k. Thus cloud can be the complement of at least four different classifiers (Li, in progress) (53) a. yı duoˇ yuń one Cl-blossom cloud c. yı tuań yuń one Cl-ball cloud

b. yıpıàn yuń one Cl-piece cloud d. yı lu˘ yuń one Cl-stream cloud

This is parallel to the way that, in English, we can say pieces of cotton or strands of cotton, but strands gives additional information, namely that the pieces are long and thin. In general, for individuating classifiers (or classifiers on their individuating uses), ½½Classifier (N) ¼ COUNTk(Nroot \ Q) where Q is a (possibly empty) expression , with the classifier performing the individuation function and Q possibly adding more information about the properties of the individual unit. Frequently, these properties are topological, as in piece of v. strand of or the examples in (53) but they need not be; zhı, from example (5) applies to naturally atomic predicates and includes the information that the individual d is a unit of animal, while ke used in lia˘ng ke shu` ‘two units of tree’ applies to naturally atomic predicates and includes the information that d is a plant. In (52), ge` is the neutral classifier, also used as a default classifier


(52) lia˘ng *(ge) pıńgguoˇ two Cl apple(s)

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(Erbaugh 2002), which applies to naturally atomic predicates adding no additional information (i.e. Q is empty). 10 GRINDING, NATURAL ATOMICITY AND THE LEXICAL DERIVATION OF COUNT NOUNS


In this article, I have argued that count nouns and mass nouns are of different types and denote different kinds of entities. I have argued further that while mass nouns are root nouns, count noun meanings are derived from root noun meanings by a lexical operation. In principle, there is a second way to think about count nouns: we might assume that all nouns come out of the lexicon as root nouns and that count nouns are derived in the syntax, with the COUNTk operation triggered by count syntax. On this approach, hair is a unique unambiguous lexical item, whose default interpretation is mass. When it occurs in the context of count syntax, it shifts to a count interpretation, COUNTk(hair). So the syntactic context forces count semantics on the nominal, and learning English requires learning that in the presence of indicators of count syntax, the COUNTk operation must apply. A general discussion of the pros and cons of these two approaches is given in Pelletier and Schubert (1989). Sharvy (1978) suggests a slightly different version of this approach, that is, that count nouns in English are in fact mass nouns that appear as the complement of null classifiers in contexts in which count interpretation is obligatory. Borer (2005) has proposed a syntactic account that is very similar to Sharvy’s: she suggests that classifiers and number fill the same syntactic node and have the semantic function of introducing a ‘dividing’ operation, DIV, on the denotation of the nominal predicate. This dividing operation is obligatory if counting is to take place. When number is present, DIV(N) derives a count noun that can then be counted. When a classifier is present, a classifier + mass noun concatenation is derived, which can also be counted. If neither a classifier nor a number fills the node, then the noun is interpreted as mass. The complementary distribution between classifiers and plurality in a DP is thus explained. There is one very strong argument against these approaches, which is based on the semantic distinction between natural and semantic atomicity, and the fact that furniture and boy are naturally atomic, although only the latter is semantically atomic. If count nominals are derived in the syntax, there should be no reason why a noun like boy should not be usable without count syntactic indicators, in which case it would receive a mass interpretation. Earlier discussions of the data


(e.g. Borer 2005) have implicitly assumed that a mass interpretation of a noun like boy should have only the universal grinder interpretation discussed in Pelletier and Schubert (1989), where, following suggestions by David Lewis, it is suggested that the mass interpretation of boy/ bicycle is derived by grinding atomic entities into stuff: (54) a. After he had finished the job, there was bicycle all over the floor. b. After the accident, there was boy all over the ground.

(55) a. There is now furniture in my house. b. *There is now boy in my class. c. There is a lot of furniture in my house now that the four chairs and two tables have been delivered. d. *There is a lot of boy in my class now that John, Bill and Peter have enrolled. Furthermore, one might expect nouns like boy to be usable with classifier expressions if there is no expression of number. (Note that to say that with some nouns, expression of number is obligatory is just to say that some nouns are marked as explicitly count, which is exactly what the syntactic account of count nouns is trying to avoid.) (56) *There are four units/pieces of boy in my class. But (56) is ungrammatical just like (55b) and (55d), indicating that boy really is lexically a count expression, independent of the syntactic context. It is no good arguing that real-world knowledge leads us to prefer the count form for some nominals: exactly what we have seen is


But, as predicates like furniture show, mass interpretation does not require a non-atomic interpretation of the predicate. On a mass interpretation, boy would denote BOYroot and display the same kind of behaviour as furniture: it would be syntactically a mass noun but would denote a set of naturally individuable entities. These expressions could not be directly counted, but when counting is not relevant, this should not be a problem for interpretation. This is of course the situation in Mandarin Chinese, where a bare naturally atomic noun like pıńgguoˇ, ‘apple’, has mass syntax and a classifier is inserted only if individuation is grammatically necessary, for example, in counting contexts. So, if count semantics is induced by count syntax, English should allow a bare ‘count’ noun such as boy to have the same kind of interpretation as a naturally atomic nominal without a classifier in Mandarin Chinese. This means that (55b/d) should be allowed on a par with (55a/c). However, as these examples show, this is not the case.

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(57) They ordered two orange juices, two beers and a single malt scotch. I suggest (54) illustrates a genuine operation of syntactic type shifting. In examples like there was bicycle/boy all over the floor, the noun is not being used in its root/mass form since a naturally atomic mass predicate is not a predicate of ground stuff. Instead, the lexically count noun is being shifted into a mass interpretation in the syntax, triggered by the syntactic context that allows only mass nouns. The semantic effect of type shifting cannot be to shift the noun back to its original interpretation: since boy and bicycle are naturally atomic predicates, the original root/mass meaning is not significantly different from the count meaning, and a plausible extension of the blocking principle of Chierchia (1998a), allows us to assume that type shifting will be blocked unless the resulting interpretation is sufficiently different from interpretations that are otherwise available. Type shifting from count to mass is thus associated with a new interpretation, the ‘ground’ interpretation. [Blutner (2000) gives a very similar account of grinding in terms of optimality theory.] In the ground interpretation, the atomic elements in the denotation of the predicate are not the naturally atomic entities but parts of the 18 Although the division between mass and count nouns differs from language to language, there may be both cross-linguistic generalizations as to what is count and what is mass, and patterns that are specific to a particular language. Wierzbicka (1988) discusses English v. Slavic patterns in mass/count classification, and Smith-Stark (1974) argues that animacy is a linguistic feature associated with count nouns cross-linguistically.


that knowledge of natural atomicity is neither a necessary nor a sufficient condition for imposing count syntax (though other linguistic mechanisms might be sensitive to it). Notice also that the assumption that count nouns are marked as such in the lexicon explains why different languages can mark different nouns as count since lexical derivational process are known to be idiosyncratic,18 while type-shifting operations are not. If count nouns are derived via a syntactic type-shifting operation, we would need an explanation for why different languages allow the operation to apply to different nouns in parallel syntactic contexts. Examples such as (54), derived via the ‘universal grinder’, are genuine mass nouns, although some people feel that the examples are odd and have only an ironic interpretation. There are related examples using what Lewis called the ‘universal packager’ function, illustrated in (57), which shifts noun meanings from mass to count interpretations. Note that many people consider these much more natural than the examples in (54).


naturally atomic entities: SHIFTmass applied to a count noun is the operation given in (58), which applies to a singular count predicate P of type and gives an expression of type , denoting the set of proper parts of some semantic atoms of P. (58) kPkx.dy[y 2 p1(P) ^ x 8 y ^ :x ¼ y]

So if a mass denotation is imposed via type shifting because of a syntactic mismatch, the minimal parts are not the individual boys and the individual bicycles but the set generated by a set of smaller-thanatomic boy-parts and bicycle-parts, hence the interpretation of (54). This explains several points. First, grinding, or using count nouns in mass contexts, is odder than packaging, or using mass nouns in count contexts. This is because grinding involves reanalysing a naturally atomic predicate so as to override its naturally atomic structure, while packaging involves imposing an individuating structure on a mass domain. But then packaging is an operation that the grammar uses naturally to interpret classifiers. So (57) can be straightforwardly analysed as involving an implicit classifier and it fits naturally into the range of syntactic structures and semantic operations available. Second, we have an explanation for the observation in Cheng et al. (2008) for why Mandarin Chinese does not allow ground interpretations of bare nouns. Cheng et al. point out that (60a) only has a plural reading, and the ground interpretation requires (60b). ‘Substance’ nouns such as shuı˘ behave as they do in English. (60) a. qiańg-shang d ou shı` goˇu wall- top all COP dog ‘There are dogs all over the wall’ (NOT ‘There is dog all over the wall.’) b. qiańg-shang d ou shı` goˇu-roù wall- top all COP dog-flesh/meat ‘There is dog all over the wall.’ c. dı`-shang d ou shı` shuı˘ floor-top all COP water ‘There is water all over the floor.’


‘Grinding’ the denotation of boy will give (59), the set of proper parts of some semantically atomic entities in BOYk. This is a set of contextually determined minimal boy-parts and their sums, but not whole atomic boys. (59) kx.dy[y 2 p1(BOYk) ^ x 8 y ^ :x ¼ y]

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On the account given here this is expected. The ground reading of dog/boy is obtained only as a result of type shifting to resolve a syntactic mismatch occurring when a count noun appears in a mass syntactic context. But in (60a), there is no such mismatch since a naturally atomic mass noun appears in a perfectly appropriate context. Since the denotation of a naturally atomic mass noun is the set of individual dogs closed under sum, the appropriate interpretation of (60a) is that a plurality of (individual) dogs is all over the wall. The ground reading requires an explicit operation deriving a set of dog parts from the naturally atomic set. I discuss this further in Rothstein (2009b). A third issue relating to type shifting is raised by Barner and Snedeker’s (2005) results. They show that with mass nouns like furniture, quantity judgments involve comparing individuals, whereas with flexible terms like stone, the basis for comparison depends on whether the noun is count or mass. Mass nouns such as stone never allow quantity judgments based on a comparison of number of individuals but only on the basis of overall volume. They suggest that this is because furniture but not stone is marked as [+individual], and thus, three small chairs can be judged as ‘more furniture’ than one big chair. However, we can now explain this without recourse to a [+individual] (or [+naturally atomic]) feature. Assume that in general, when a mass predicate is naturally atomic, quantity judgments compare quantities of perceptually salient natural atoms, even when the syntax does not allow grammatical counting. This explains the results that Barner and Snedeker got for predicates like furniture. We now need to explain why in expressions like stone, the basis of quantity judgments is determined by the syntax of the noun and not by whether in context the predicate denotes a set of perceptually salient individuals. Put differently, if in context, stone denotes a set of salient entities, why does who has more stone? require you to ignore the natural atoms and base quantity judgments on overall volume? There is an obvious pragmatic explanation. We have been assuming that when COUNTk applies to a nominal root predicate, the root nominal is no longer available in the active lexicon, and thus, for example, boy and fence do not have mass forms lexically available. Flexible nouns such as stone, rope and brick, which have mass and count forms, are an exception to this in English since the root nominal is still available in the active lexicon as a mass noun even after the count predicate has been derived. Assume, then, that it is part of our knowledge of English that stone has a mass form and a count form. Since we have the possibility of choosing which form to use, the question who has more stones? is an explicit request to form a quantity judgment on the basis of number. As a consequence, the question who has more stone? using the mass noun


(61) We have the same furniture. But the elements relevant for making the quantity judgments do need to stay constant through a single context. So, if you and I have the same modular parts, but I have three chairs and you have a couch, I can either say (61) or I can say ‘I have more furniture than you’, but I cannot say (62), although each conjunct separately may be true relative to a different analysis of minimal parts. (62) #We have the same furniture but I have more than you. The big question that we still have not answered is of course why some nouns have mass forms, some have count forms and some have both. Some generalizations can be made. For example, Smith-Starke (1974) pointed out that if a language has count nouns, then animate entities will naturally be denoted by count nouns, and Wierzbicka (1988) has shown that other cross-linguistic patterns can be observed. But the point of this article has not been to analyse patterns of mass/ count distribution cross-linguistically. It has been to show that natural atomicity in the denotation of a predicate is neither a necessary nor a sufficient condition for count syntax, that countability is grammatically encoded and that it is dependent on semantically atomic structure, which is grammatically derived and contextually dependent.

Acknowledgements The roots of this article lie in the discussion of homogeneity in the verbal and nominal domain in my 1999 NALS paper, and my 2004 book. Fred Landman has been thinking about counting and the semantics of mass nouns almost continuously over this same period, and the article owes an enormous amount to him and to the


will naturally be taken as a request to make an evaluation based on quantity and to ignore the number of the atomic stones. So, the availability of both mass and count nouns forces us to interpret the choice of one or another noun as a request for a particular kind of quantity judgment. Notice finally that even with predicates like furniture that are naturally atomic to a relatively high degree, we are not always forced to take the individual pieces of furniture as the entities relevant for making quantity judgments. Landman (2007) points out that in a context in which furniture is modular, the minimal parts are not the individual pieces of furniture but the modular parts. Thus, if I have three chairs and you have a couch made of the identical parts, I can naturally say:

Susan Rothstein 395

SUSAN ROTHSTEIN Gonda Multidisciplinary Brain Research Center Bar-Ilan University Ramat Gan 52900 Israel e-mail: [email protected]

REFERENCES Barker, C. (1998), ‘Partitives, Double Genitives and Anti-uniqueness’. Natural Language and Linguistic Theory 16:679–717. Barner, D., & J. Snedeker. (2005), ‘Quantity Judgements and Individuation: Evidence That Mass Nouns Count’. Cognition 97:41–66. Blutner, R. (2000), ‘Some Aspects of Optimality in Natural Language Interpretation’. Journal of Semantics 17:189–216. Borer, H. (2005), Structuring Sense, Part I: In Name Only. Oxford: Oxford University Press. Cheng, L. L., J. Doetjes., & R. Sybesma. (2008), ‘How Universal is the Universal Grinder’. Linguistics in the Netherlands 2008:50–62. Chierchia, G. (1984), Topics in the Syntax and Semantics of Infinitives and

Gerunds. Ph.D. thesis, University of Massachusetts at Amherst. Chierchia, G. (1998a), ‘Plurality of mass nouns and the notion of ‘‘semantic parameter’’’. In S. Rothstein (ed.), Events and Grammar. Kluwer. Dordrecht. 53–104. Chierchia, G. (1998b), ‘Reference to Kinds across Language’. Natural Language Semantics 6:339–405. Doetjes, J. (1997), Quantifiers and Selection. Ph.D. thesis, University of Leiden. Erbaugh, M. (2002), ‘Classifiers Are for Specification: Complementary Functions for Sortal and General Classifiers in Cantonese and Mandarin’. Cahiers de Linguistique—Asie orientale 31: 33–69. Gillon, B. (1992), ‘Toward a Common Semantics for English Count and Mass Nouns’. Linguistics and Philosophy 15:597–640.


many discussions we have had about the topic over these years (interspersed with some conversations about other matters too). Many thanks also to Fred for help with technical aspects of the theory. I presented an earlier version of the article at the ISF workshop at the Hebrew University of Jerusalem in honour of Anita Mittwoch, at seminars at the Phonetics Laboratory of the University of Belgrade, at ZAS in Berlin and at the Leiden-Utrecht Semantics Circle, and the paper benefited from the comments of participants at all these events. Two reviewers gave thorough and helpful comments on earlier versions, and Philippe Schlenker gave excellent editorial advice. I thank all of them. Part of the work on this article was done when I was a guest at the Linguistics Department during 2009–2010, and I thank the department for its hospitality. Discussions with my doctoral student Xuping Li and with Lisa Cheng and Rint Sybesma have opened my eyes to the subtleties of the classifier system in Mandarin Chinese and enriched my thinking about counting tremendously.

396 Counting and the Mass/Count Distinction Landman, F. (1989a), ‘Groups I’. Linguistics and Philosophy 12.6:559–605. Landman, F. (1989b), ‘Groups II’. Linguistics and Philosophy 12.6:723–45. Landman, F. (2004), Indefinites and the Type of Sets. Blackwell. Oxford. Landman, F. (2007), On the Mass/Count Distinction. Unpublished MS, Tel Aviv University. Li, X. P. The Semantics of Classifiers in Chinese. Ph.D. thesis, Bar-Ilan University, in progress. Link, G. (1983), ‘The logical analysis of plurals and mass terms: A latticetheoretical approach’. In R. Bauërle, C. Schwarze, and A. von Stechow (eds.), Meaning, Use and Interpretation. de Gruyter. Berlin/New York. 303–23. Reprinted in P. Portner and B. Partee (eds.), Formal Semantics: The Essential Readings. Blackwell. Oxford. 2002. Mittwoch, A. (1988), ‘Aspects of English Aspect: On the Interaction of Perfect, Progressive and Durational Phrases’. Linguistics and Philosophy 11:203–54. Partee, B. H., A. ter Meulen., & R. Wall (1990/1993). Mathematical Methods in Linguistics. Kluwer. Dordrecht. 1990. Second printing, corrected first edition, 1993. Partee, B. H., & V. Borschev. (2003), ‘Genitives, relational nouns, and argument-modifier ambiguity’. In E. Lang, C. Maienborn, and C. FabriciusHansen (eds.), Modifying Adjuncts. Mouton de Gruyter. Berlin. 67–112. Pelletier, F. J., & L. K. Schubert. (1989), ‘Mass expressions’. In D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, Reidel. Dordrecht. 327–408. Pires de Oliveira, R., & S. Rothstein, Bare Singular Is Really Mass in Brazilian Portuguese. MS Universidade


Heim, I. (1998), ‘Anaphora and semantic interpretation: A reinterpretation of Reinhart’s approach’. In U. Sauerlandand and O. Percus (eds.), The Interpretive Tract. MIT Working Papers in Linguistics No. 25. 205–46. Linguistics Department, MIT. Jespersen, O. (1924), The Philosophy of Grammar. Allen and Unwin. London. Kamp, H. (1975), ‘Two theories about adjectives’. In E. Keenan (ed.), Formal Semantics of Natural Languages. Cambridge University Press. Cambridge. 123–55. Krifka, M. (1989), ‘Nominal reference, temporal constitution and quantification in event semantics’. In R. Bartsch, J. van Bentham, and Peter van Emde Boas (eds.), Semantics and Contextual Expressions. Foris. Dordrecht. 75–155. Krifka, M. (1992), ‘Thematic relations as links between nominal reference and temporal constitution’. In I. Sag and A. Szabolsci (eds.), Lexical Matters. CSLI. Stanford, CA. 29–53. Krifka, M. (1995), ‘Common nouns: A contrastive analysis of English and Chinese’. In G. Carlson and F.J. Pelletier (eds.), The Generic Book. Chicago University Press. Chicago. 398–411. Krifka, M. (1998), ‘The origins of telicity’. In S. Rothstein (ed.), Events and Grammar. Kluwer. Dordrecht. Krifka, M. (2008a), ‘Masses and countables: Cognitive and linguistic factors’. Invited talk at The Syntax and Semantics of Measurement, September 17–18, 2007, CASTL, University of Tromsø. Krifka, M. (2008b), ‘Different kinds of count nouns and plurals’. Invited talk at the Syntax of the World’s Languages III, September 25–28, 2008, Freie Universita¨t Berlin. Landman, F. (1991), Structures for Semantics. Kluwer. Dordrecht.

Susan Rothstein 397 Federal de Santa Catarina and Bar-Ilan University, in preparation. Prasada, S, K. Ferenz., & T. Haskell. (2002), ‘Conceiving of Entities as Objects and as Stuff ’. Cognition 83: 141–65. Rothstein, S. (2004), Structuring Events: A Study in the Semantics of Lexical Aspect. Blackwell. Oxford.

Rothstein, S. (2009b), ‘Bare nouns and natural atomicity: A crosslinguistic perspective’. Workshop on Bare Nouns Handout, 2–28 November 2009, Universite´ Paris 7. Sauerland, U., & K. Yatsushiro. (2004), ‘A silent noun in partitives’. In K. Moulton and M. Wolf (eds.), Proceedings of NELS 34. GLSA, University of Massachusetts. Amherst. Schwarzschild, R. ‘Stubborn distributivity, multiparticipant nouns and the



Rothstein, S. (2009a), ‘Individuating and measure readings of classifier constructions: Evidence from Modern Hebrew’. In Brill Annual of Afroasiatic Languages and Linguistics, Brill leiden. vol. I.106–145.

count/mass distinction’. In Proceedings of NELS 39, forthcoming. Smith-Stark, C. (1974), ‘The Plurality Split’. Chicago Linguistics Society Papers 10:657–71. Soja, N, S. Carey., & E. Spelke. (1991), ‘Ontological Categories Guide Young Children’s Induction of Word Meaning: Object Terms and Substance Terms’. Cognition 38:197–211. Sharvy, R. (1978), ‘Maybe English Has No Count Nouns: Notes on Chinese Semantics’. Studies in Language 2: 345–65. Sybesma, R. (2008), Classifiers, Number and Countability. Unpublished MS, Leiden University. Wierzbicka, A. (1988), The Semantics of Grammar. John Benjamin. Amsterdam. Zucchi, A., & M. White. (2001), ‘Twigs, Sequences and the Temporal Constitution of Predicates’. Linguistics and Philosophy 24:223–70.

Journal of Semantics 27: 399–407 doi:10.1093/jos/ffq009 Advance Access publication April 8, 2010

More on Scope Illusions TERJE LOHNDAL University of Maryland

Abstract

1 INTRODUCTION The sentence in (1) can be understood to say that every swimming competition was won by an American, possibly a different American for every swimming competition. I will call this reading the ‘dependent reading’, which is similar to the ‘standard’ inverse reading in (2). All the sentences with the dependent reading will have present tense morphology, which in this case is an indication of genericity. Therefore, I will say that (1) is an instance of ‘generic quantification’. (1) At the Olympic games, it is an American that wins every swimming competition. (d>", ">d)1 (2) An American wins every swimming competition. (d>", ">d) This might be represented by letting every swimming competition take scope over an American. This would be an island violation for whmovement, and assuming that quantifier raising (QR) obeys the same island restrictions (e.g. Lakoff 1970; Farkas 1981; pace Rodman 1976), QR should in the present cases not be able to move beyond the finite clause. It is well known that certain indefinites do not behave as standard generalized quantifiers in terms of locality constraints (e.g. Cooper 1979; Fodor & Sag 1982; Ruys 1992; Abusch 1994; Reinhart 1997; Winter 1997; Kratzer 1998; Schwarzschild 2002; Matthewson 2005), but 1

There is variability among native speakers as to whether they get the dependent reading in cases like (1), but the majority of the speakers I have consulted get the readings. The judgments I will be reporting in the present paper are the ones the majority of the consulted speakers have. The Author 2010. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected].


This paper extends the analysis of Fox & Sauerland (1996) of scope illusions and argues that what look like inverse scope readings in clefts with indefinite noun phrase pivots are really illusory cases of scope inversion. Instead, inverse scope comes about due to generic quantification over situations. Furthermore, the present paper adds to Fox and Sauerland by observing differences between a and some indefinites, where only the former yields illusory scope.

400 More on Scope Illusions

a similar case has not been made for every. In fact, as Reinhart (1997) argues, hardly any such examples involving universal quantifiers are attested. Thus, it seems problematic and stipulative to argue that every actually undergoes QR out of the finite clause in a cleft construction as in (1). Interestingly, the sentence in (1) contrasts with the one in (3), which does not have a dependent reading. (3) At the Olympic games, it is some American that wins every swimming competition. (d>", *">d)

2 FOX & SAUERLAND (1996) F&S discuss a number of cases that they called ‘scope illusions’ [see also Alexopoulou (2009) and Sauerland (2009) for developments of these ideas in a different direction]. These are cases where it looks like a quantifier has undergone QR, but it actually turns out that there is no QR. F&S argue that this is because of universal quantification over situations, and they provide many examples of such scope illusions. Here I will focus on two cases. The sentences in (4) and (5) are scopally unambiguous (F&S: 72). (4) Yesterday, a guide ensured that every tour to the Louvre was fun. (d>", *">d) (5) When we entered the conference, a grad student was checking that everybody had a badge. (d>", *">d) The sentence in (4) is only true if there is one guide who ensured that all the tours were fun and not if the guides vary with the tours. Now, compare (4) to the following sentences in (6) and (7) (F&S: 72). (6) In general, a guide ensures that every tour to the Louvre is fun. (d>", ">d) (7) At linguistics conferences, a grad student checks that everybody has a badge. (d>", ">d) Aside from the adverbials and tense, the sentences in (6) and (7) are identical to the ones in (4) and (5). However, as we can see, the truth


The contrast between some and a is robust, and I will return to it in section 4. The paper is organized as follows. In section 2, I outline the data reported in Fox & Sauerland (1996) (henceforth F&S) and sketch their analysis. Section 3 shows how F&S’s analysis can be extended to the data in (1). In section 4, I elaborate on the difference between some and a. Section 5 concludes the paper.

Terje Lohndal 401

conditions are different in another dimension as well. (6) could mean that whenever there is a tour to the Louvre, there is a guide that ensures that the tour is fun. It is possible for the guides to vary with the tours. This could be interpreted as a case where the embedded universal quantifier scopes over the matrix existential, but F&S instead argue that this dependent reading is the result of generic quantification over minimal situations. Let us see how this argument is made. Consider the contrast in (8) from F&S. (8) a. Yesterday, I gave a tourist every leaflet. b. In general, I gave a tourist every leaflet.

(d>", *">d) (d>", ">d)

(9)

a. Planes disappear in the BERMUDA TRIANGLE. b. PLANES disappear in the Bermuda Triangle.

The assertions are different in these two cases. (9a) asserts that in every case in which planes disappear somewhere, this place is in the Bermuda Triangle. (9b), on the other hand, asserts that in every case in which


Consider the episodic (8a). In this case, the sentence is only true if there is a single tourist who gets all the leaflets. The sentence is not true in a situation where every leaflet is given to a different tourist. Based on this observation, Larson (1990) argues that the relative scope of the indirect object and the direct object is fixed. From this perspective, (8b) is a puzzle. The innovation that F&S suggest to get the dependent reading is that instead of viewing the relevant portion of the world as one situation, we divide the world into minor portions and say the following: In each situation in the world, there is a tourist who gets every leaflet, but the situation is small enough that it only contains one leaflet. Hence, there is a tourist who gets all the leaflets in each situation, and this world is still true as a general description of situations such as (8b). That is, in each situation that contains just one leaflet and one tourist, every leaflet (i.e. the one leaflet in that situation) goes to one individual. Here is how F&S relate this to generic quantification and scope illusions: ‘We get the illusion that a universal quantifier has wide scope relative to an existential quantifier because the generic operator allows the existential to pick out a different individual in each relevant portion of the world’ (F&S: 75; see also Krifka et al. 1995). I will assume that the generic operator [see Krifka et al. (1995) for much discussion] always has a restrictor and that this restrictor often is determined by pragmatic factors. In the present case, the choice of the restrictor is constrained by focus (see F&S for their account). We can see this in (9), which F&S take from Krifka (1995) [see also Rooth (1985) on focus].


something disappears in the Bermuda Triangle, it is a plane. We can give situation–semantic paraphrases of these sentences as in (10) (F&S: 76–7). (10) a. Every situation s such that [a plane disappears somewhere in s]RESTRICTOR is a situation in which [a plane disappears in the B-T]NUCLEUS b. Every situation s such that [something disappears in the B-T in s]RESTRICTOR is a situation in which [a plane disappears in the B-T]NUCLEUS

(11) In general, I give a tourist every leaflet. It is necessary to know what the focus value of the sentence in (11) is. Let us suppose that focus is placed on a tourist in (12a). This will restrict the operator to situations in which there is someone to whom I give every leaflet (12b), thus the situations satisfy the restrictor of (12b) (F&S: 78). (12) a. In general, I give A TOURIST every leaflet. b. Every situation s such that [I give someone every leaflet in s]RESTRICTOR is a situation in which [I give a tourist every leaflet]NUCLEUS In the next section, I will apply this analysis to the cleft cases. 3 CLEFTS AND SCOPE ILLUSIONS It is well known that generic quantification over situations gives rise to quantificational variability (Lewis 1975; Berman 1987; Kratzer 1989; Heim 1990; von Fintel 1994). (13) and (14) suggest that this might be

2

There are two open questions at this point. One question concerns many. F&S note that the trick of getting wide scope via domainshrinking trivialization of the quantifier does not work with a quantifier like many: (i) In general, a guide ensures that many tours are fun (d>MANY, *MANY>d) However, sentences with numerals point in another direction: (ii) In general, I give a tourist two leaflets. (d>2, 2>d) (iii) In general, it was a pig that ate two pizzas. (d>2, 2>d) Another issue that may be related is that the restrictor of a universal quantifier cannot be a singleton in plain cases, as seen in (iv) (thanks to an anonymous reviewer for raising this issue). (iv) a. John loves [his mother]/*[every mother of his] b. *Every nose of the victim was red.


Now we are ready to see how F&S get scope illusions. Consider (11).2

Terje Lohndal 403

what is going on in the present case as well (the lead-ins are drawn from Bhatt 1999). (13) Yesterday, at the apple-eating contest, it was a pig that ate every apple. (d>", *">d) (14) In those days, it was a pig that ate every apple. (d>", ">d)

(15) a. It is a DOG that eats every apple. b. Every situation s such that [it is someone that eats every apple in s]RESTRICTOR is a situation in which [it is a dog that eats every apple]NUCLEUS The reading says that in each situation a single dog eats every apple in that situation. It does not say that in that situation a different dog eats every apple. 4 QUANTIFICATIONAL VARIABILITY: A V. SOME In principle, the account developed so far in this paper should extend to all indefinites, yet that expectation turns out to be incorrect. We know that indefinites behave non-uniformly (e.g. Strawson 1974; Farkas 1994, 2002; Becker 1999),5 and this is also true in the present case. As seen in (3), repeated as (16), some does not prompt the illusion that a does. 3

I set aside how situation variables relate to event variables. See Kratzer (2009) for discussion. I set aside how clefts should be analysed. See, for example, Percus (1997) for both a syntactic and a semantic analysis that also accommodates the obligatory presupposition in clefts: if we say that it was John who did x, the sentence presupposes that someone did x. 5 Just to remind the reader of one such difference, which, as far as I can see, is independent of the data on clefts: (i) shows that there is a difference between some and a related to implications. (i) a. Most of the time, an officer danced with a ballerina. b. Most of the time, some officer danced with a ballerina. (ia) can imply that ‘most officers danced with ballerinas’, whereas (ib) cannot have this implication. 4


Overt adverbials favour the episodic reading (11) to the universal/generic reading (12). When we force an episodic interpretation with the adverbial yesterday, the dependent interpretation disappears. This suggests that the latter comes about because the existential depends on generic quantification over minimal situations [see Berman (1987) and Heim (1990) on the latter], a reading which we can paraphrase as ‘In every case of an apple-eating, a pig is the food-eater’. The account would say that for each minimal situation, a pig was the food-eater. That is, the reading varies by situations, not by the universally quantified DP.3 This parallel suggests that F&S’s analysis can be extended to clefts as well. Let us see how. The pivot carries focus and thus restricts the generic operator such that we get the scope illusion similar to (11). An example is shown in (15).4


(16) In general, it is some pig that eats every piece of food. (d>", *">d) Notice that there is a difference where the stress is put for a and some. In the former case, stress is put on the noun, whereas in the latter case it is put on the quantifier. Interestingly, the contrast between some and a also obtains for the cases that F&S discuss. This is shown in (17) and (18). (17) In general, I give some tourist every leaflet. (d>", *">d) (18) In this restaurant, the waiter serves some foreigner every meal. (d>", *">d)

(19) a. It is some pig that eats every piece of food. (d>", *">d) b. It is some pig or other that eats every piece of food. (d>", ">d) We see that if we replace some pig with some pig or other, the latter acts like a pig. A certain also makes (20) very similar to a sentence where we replace the indefinite with a proper name or a definite description (21). (20) It was a certain soccer player who scored every goal in the match. (d>", *">d) (21) It is John/the man that eats every piece of food. (d>", *">d) Given the data in (21), I argue that a focused some noun phrase (NP) phrase is interpreted as a specific NP. There is evidence that focus and stress may be what are forcing the surface scope reading for some (cf. Milsark 1974). It turns out that if one de-stresses some, the dependent reading appears.6(22) and (23) illustrate this.7 The judgments were obtained by explicitly asking speakers not to put stress on some, and always together with a sentence with stressed some, so that the contrast was as perspicuous as possible. (22) It is sm dessert that every dog wants. (23) It is sm books that every student reads. 6

(d>", ">d) (d>", ">d)

Carlson’s (1977: 55) argument that sm is the plural of a might be of relevance here, though I will not explore that possibility. 7 Simple count nouns are not possible: (i) *It was sm book that every student read. The generalization seems to be that plurals and mass nouns are the ones that allow de-stressed some.


In this section, I will present more data and sketch a couple of possible analyses. Consider the following contrast:

Terje Lohndal 405

This fact supports an analysis where focus and stress force a specific (wide scope) reading. There are various ways one can implement this formally, either through a singleton analysis (Portner 2002; Schwarzschild 2002) or through a (skolemized) choice function analysis [Reinhart (1997) and the following literature; though see Schwarz (2004) for problems]. I leave it to the reader to decide which of these is the better as the main point here is to present the data and make the point that some and a behave differently.

The main aim of this paper was to elaborate on F&S’s analysis of scope illusions. The paper has discussed clefts where the pivot is headed by an indefinite and where the embedded clause has a generic quantifier that seems to scope over the indefinite. If the indefinite is a, the surprising dependent reading appears, whereas if the indefinite is some, this dependent reading does not appear. I have argued that the dependent reading should not be accounted for by way of QR out of the finite embedded clause, but rather as a scope illusion due to generic quantification over situations, as in F&S’s analysis. I have also discussed why this illusion does not occur with stressed some and suggested a link between focus and stress and the emergence of dependent readings.

Acknowledgements Thanks to members of the Department of Linguistics at UMD for providing judgments, in particular to Brad Larson. Thanks also to two anonymous reviewers, Chris Barker, Atle Grønn, Jeremy Hartman, Paul Pietroski, Roger Schwarzschild, Kjell Johan Sæbø and especially Danny Fox and Alexander Williams for their helpful comments. Special thanks go to Valentine Hacquard for encouraging me to work on this topic and for providing many detailed comments on several drafts of this paper.

TERJE LOHNDAL Department of Linguistics University of Maryland 1401 Marie Mount Hall College Park, MD 20742, USA e-mail: [email protected]


5 CONCLUSIONS


REFERENCES Fox, Danny & Uli Sauerland. (1996), ‘Illusive scope of universal quantifiers’. Proceedings of North East Linguistic Society 26:71–85. Heim, Irene. (1990), ‘E-type pronouns and donkey anaphora’. Linguistics and Philosophy 13:137–77. Kratzer, Angelika. (1989), ‘An investigation of the lumps of thought’. Linguistics and Philosophy 12:607–53. Kratzer, Angelika. (1998), ‘Scope or pseudoscope? Are there wide-scope indefinites?’. In Susan Rothstein (ed.), Events and Grammar. Kluwer. Dordrecht. 163–96. Kratzer, Angelika. (2009), Situations in Natural Language Semantics. Stanford Encyclopedia of Philosophy (http: //plato.stanford.edu/entries/situationssemantics). Krifka, Manfred. (1995), ‘Focus and the interpretation of generic sentences’. In Greg N. Carlson and Francis Jeffry Pelletier (eds.), The Generic Book. The University of Chicago Press. Chicago, IL. 238–64. Krifka, Manfred, Francis Jeffry Pelletier, Greg N. Carlson, Alice ter Meulen, Gennaro Chierchia & Godehard Link. (1995), ‘Genericity: an introduction’. In Greg N. Carlson and Francis Jeffry Pelletier (eds.), The Generic Book. The University of Chicago Press. Chicago, IL. 1–124. Lakoff, George. (1970), ‘Repartee’. Foundations of Language 6:389–422. Larson, Richard K. (1990), ‘Double objects revisited: reply to Jackendoff ’. Linguistic Inquiry 21:589–632. Lewis, David. (1975), ‘Adverbs of quantification’. In Edward Keenan (ed.), Formal Semantics of Natural Languages. Cambridge University Press. Cambridge. 3–15.


Abusch, Dorit. (1994), ‘The scope of indefinites’. Natural Language Semantics 2:83–136. Alexopoulou, Theodora. (2009), ‘Binding illusions and resumption in Greek’. MIT Working Papers in Linguistics 57:34–48. Becker, Misha. (1999), ‘The some indefinites’. UCLA Working Papers in Linguistics 3:1–13. Berman, Stephen. (1987), ‘Situationbased semantics for adverbs of quantification’. Proceedings of West Coast Conference on Formal Semantics 6: 17–31. Bhatt, Rajesh. (1999), Covert Modality in Non-finite Contexts. Unpublished Ph.D. thesis, Department of Linguistics, University of Pennsylvania, Pennsylvania. Carlson, Greg N. (1977), Reference to Kinds in English. Unpublished Ph.D. thesis, Department of Linguistics, University of Massachusetts, Amherst, MA. Cooper, Robin. (1979), ‘Variable binding and relative clauses’. In Franz Guenthner and Sigfried J. Smith (eds.), Formal Semantics and Pragmatics for Natural Languages. Reidel. Dordrecht. 131–69. Farkas, Donka. (1981), ‘Quantifier scope and syntactic islands’. Proceedings of Chicago Linguistic Society 17:59–66. Farkas, Donka. (1994), ‘Specificity and scope’. In Lea Nash and George Tsoulas (eds.), Langue et Grammaire. vol. 8. Universite Paris. Paris. 119–37. Farkas, Donka. (2002), ‘Varieties of indefinites’. Proceedings of Semantics and Linguistic Theory 12:59–83. Fodor, Janet Dean & Ivan Sag. (1982), ‘Referential and quantificational indefinites’. Linguistics and Philosophy 5:355–98.

Terje Lohndal 407 sis, OTS, University of Utrecht, Utrecht. Sauerland, Uli. (2009), ‘On Greek illusions: a semantic account of Alexopoulou’s generalization’. MIT Working Papers in Linguistics 57:49–56. Schwarz, Bernhard. (2004), ‘Indefinites in verb phrase ellipsis’. Linguistic Inquiry 35:344–53. Schwarzschild, Roger. (2002), ‘Singleton indefinites’. Journal of Semantics 19:289–314. Strawson, P. F. (1974), Subject and Predicate in Logic and Grammar. Methuen. London. von Fintel, Kai. (1994), Restrictions on Quantifier Domains Unpublished Ph.D. thesis, Department of Linguistics, University of Massachusetts, Amherst, MA. Winter, Yoad. (1997), ‘Choice functions and the scopal semantics of indefinites’. Linguistics and Philosophy 20:399–467.



Matthewson, Lisa. (2005), ‘In the interpretation of wide-scope indefinites’. Natural Language Semantics 7:79–134. Milsark, Gary. (1974), Existential Sentences in English. Unpublished Ph.D. thesis, Department of Linguistics and Philosophy, Massachusetts Institute of Technology, Cambridge, MA. Percus, Orin. (1997), ‘Prying open the cleft?’. Proceedings of North East Linguistic Society 27:337–51. Portner, Paul. (2002), ‘Topicality and (non-)specificity in Mandarin’. Journal of Semantics 19:275–87. Reinhart, Tanya. (1997), ‘Quantifier scope: how labor is divided between QR and choice functions’. Linguistics and Philosophy 20:335–97. Rodman, Robert. (1976), ‘Scope phenomena, ‘‘movement transformations’’, and relative clauses’. In Barbara H. Partee (ed.), Montague Grammar. Academic Press. New York. 165–76. Rooth, Mats. (1985), Association with Focus Unpublished Ph.D. thesis, Department of Linguistics, University of Massachusetts, Amherst, MA. Ruys, Eddy. (1992), ‘The scope of indefinites’. Unpublished Ph.D. the-

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