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VOLUME 27 NUMBER 2 MAY 2010

CONTENTS

139

Károly Varasdi A Higher Order Extensional Framework for the Progressive

177

Bernhard Nickel Generic Comparisons

207

Christopher Gauker Global Domains versus Hidden Indexicals

243

FORTHCOMING ARTICLES Terje Lohndal: More on Scope Illusions Jungmee Lee and Judith Tonhauser: Temporal Interpretation without Tense: Korean and Japanese Coordination Constructions Chris Cummins and Napoleon Katsos: Comparative and Superlative Quantifiers: Pragmatic Effects of Comparison Type


Cornelia Ebert and Stefan Hinterwimmer Quantificational Variability Effects with Plural Definites: Quantification over Individuals or Situations?

JOURNAL OF SEMANTICS

JOURNAL OF SEMANTICS


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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

OF

MANAGING EDITOR:

Philippe Schlenker (Institut Jean-Nicod, Paris; New York University) ASSOCIATE EDITORS: Danny Fox (Massachusetts Institute of Technology) Manfred Krifka (Humboldt University Berlin; ZAS, Berlin) Rick Nouwen (Utrecht University) Robert van Rooij (University of Amsterdam) Yael Sharvit (University of Connecticut) Jesse Snedeker (Harvard University) Zoltán Gendler Szabó (Yale University) Anna Szabolcsi (New York University) ADVISORY BOARD: Gennaro Chierchia (Harvard University) Bart Geurts (University of Nijmegen) Lila Gleitman (University of Pennsylvania) Irene Heim (Massachusetts Institute of Technology) Laurence R. Horn (Yale University) Hans Kamp (Stuttgart University and University of Texas, Austin) Beth Levin (Stanford University)

Barbara Partee (University of Massachusetts, Amherst) François Recanati (Institut Jean-Nicod, Paris) Maribel Romero (University of Konstanz) Roger Schwarzschild (Rutgers University) Bernhard Schwarz (McGill University) Arnim von Stechow (University of Tübingen) Thomas Ede Zimmermann (University of Frankfurt)

EDITORIAL BOARD: Maria Aloni (University of Amsterdam) Pranav Anand (University of California, Santa Cruz) 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) Mats Rooth (Cornell University) 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

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MANAGING EDITOR:

Philippe Schlenker (Institut Jean-Nicod, Paris; New York University) ASSOCIATE EDITORS: Danny Fox (Massachusetts Institute of Technology) Manfred Krifka (Humboldt University Berlin; ZAS, Berlin) Rick Nouwen (Utrecht University) Robert van Rooij (University of Amsterdam) Yael Sharvit (University of Connecticut) Jesse Snedeker (Harvard University) Zoltán Gendler Szabó (Yale University) Anna Szabolcsi (New York University) ADVISORY BOARD: Gennaro Chierchia (Harvard University) Bart Geurts (University of Nijmegen) Lila Gleitman (University of Pennsylvania) Irene Heim (Massachusetts Institute of Technology) Laurence R. Horn (Yale University) Hans Kamp (Stuttgart University and University of Texas, Austin) Beth Levin (Stanford University)

Barbara Partee (University of Massachusetts, Amherst) François Recanati (Institut Jean-Nicod, Paris) Maribel Romero (University of Konstanz) Roger Schwarzschild (Rutgers University) Bernhard Schwarz (McGill University) Arnim von Stechow (University of Tübingen) Thomas Ede Zimmermann (University of Frankfurt)

EDITORIAL BOARD: Maria Aloni (University of Amsterdam) Pranav Anand (University of California, Santa Cruz) 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) Mats Rooth (Cornell University) 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 2

CONTENTS CORNELIA EBERT AND STEFAN HINTERWIMMER Quantificational Variability Effects with Plural Definites: Quantification over Individuals or Situations?

139

KA´ROLY VARASDI A Higher Order Extensional Framework for the Progressive

177

BERNHARD NICKEL Generic Comparisons

207

CHRISTOPHER GAUKER Global Domains versus Hidden Indexicals

243

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

Journal of Semantics 27: 139–176 doi:10.1093/jos/ffq003 Advance Access publication March 1, 2010

Quantificational Variability Effects with Plural Definites: Quantification over Individuals or Situations? CORNELIA EBERT University of Stuttgart

Abstract In this paper, we discuss the fact that not only adverbially quantified sentences with singular indefinites or bare plurals but also ones containing plural definites show Quantificational Variability Effects (QVEs), that is, they receive readings according to which the quantificational force of the respective DP seems to depend on the quantificational force of the Q-adverb. We show that if the Q-adverb is a frequency adverb like usually, there is strong evidence that QVEs come about as indirect effects of a quantification over situations. This conclusion is based on the fact that in such cases the availability of QVEs is constrained in ways that have no parallel in sentences containing adverbs of quantity like for the most part or quantificational DPs instead of frequency adverbs. We show that these constraints can be derived from plausible assumptions about how the situations to be quantified over are constrained: they have to be located in time on the basis of the most specific locally available information, and their running times are not allowed to overlap.

1 INTRODUCTION Consider the sentences in (1a, c) below, which have prominent readings that can be paraphrased as in (1b, d), respectively1: (1) a. The people who lectured at the conference last summer were usually Japanese. b. Most (of the) people who lectured at the conference last summer were Japanese. 1 Note that the availability of these reading depends on the hearer’s willingness to make certain default assumptions, namely [e.g. in the case of (1a)] that the lectures (at least in their majority) are given by single persons and that no person is giving more than one lecture. If the context makes it clear that these conditions are not fulfilled, a QV reading is no longer possible (more on this below).

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STEFAN HINTERWIMMER Humboldt University Berlin

140 Quantificational Variability Effects with Plural Definites

c. The lions that Peter saw during the safari usually had a mane. d. Most (of the) lions that Peter saw during the safari had a mane. Also the sentence in (2) has a prominent reading that can be paraphrased as in (1d). (2) For the most part, the lions that Peter saw during the safari had a mane.

(3) a. A lion is usually brave. b. Most lions are brave. c. Lions are often brave. d. Many lions are brave. Notice, though, that in contrast to frequency adverbs like the ones in (3a) and (3c), the Q-adverb for the most part needs to be combined with a bare plural (or a plural definite) in order to give rise to QVEs. This is evidenced by the contrast between (4a) and (4c): while the most prominent reading of (4a) is the QV reading given in (4b), (4c) lacks such a reading. The sentence is deviant if be smart receives its standard interpretation as an individual-level predicate (henceforth: i-level predicate) and is not reinterpreted as a stage-level predicate (henceforth: s-level predicate) meaning to behave in a smart way [see Kratzer (1995) and Chierchia (1995a) on the difference between the two types of predicates as well as on the possibility of reinterpreting i-level predicates as s-level predicates]. (4) a. For the most part, lions are smart. b. Most lions are smart. c. *For the most part, a lion is smart. Concerning the QV readings of sentences like the ones in (3) above, two different types of explanation have been offered in the literature. The first one treats QVEs as the direct result of a quantification over individuals that comes about in the following way: Q-adverbs are unselective binders, capable of binding free variables of any type in


This phenomenon, that is, that adverbially quantified sentences have readings that can be paraphrased by sentences where the respective Qadverb has been replaced by a quantificational DP of corresponding quantificational force is generally referred to as the Quantificational Variability Effect (QVE) (since Berman 1991). It is usually discussed in connection with sentences containing singular indefinites or bare plurals such as those in (3a) and (3c), whose QV readings are given in (3b, d), respectively.

Cornelia Ebert and Stefan Hinterwimmer 141

(5) a. The parents of a toddler usually have little time for relaxation. [Graff (2006): example (44a)] b. Most parents of a toddler have little time for relaxation. c. For the most part, the students admire Mary. [Nakanishi & Romero (2004): example (31a)] d. Most (of the) students admire Mary. Graff (2001, 2006) explains the fact that a sentence like (5a) has a prominent reading that can be paraphrased as in (5b) as follows: the definite article introduces a maximality condition. It turns the (characteristic function of the) set denoted by the respective NP predicate into the (characteristic function of the) singleton that contains ‘the highest-ranked member of the extension of the common noun’ (Graff 2001: 20). In line with Sharvy (1980) and Link (1983), she takes singular nouns to denote sets of atoms and plural nouns to denote sets of sums of atoms. So in case the definite article combines with a plural noun, it returns the singleton set consisting of the maximal sum in the original set. Concerning singular nouns, in contrast, the definite article can only be


their scope. Furthermore, singular indefinites as well as bare plurals are analyzed as open expressions introducing free variables whose values have to satisfy the respective NP predicate [see Kamp (1981), Heim (1982), Diesing (1992) and Kratzer (1995) for details]. The second type of explanation treats QVEs as the indirect result of a quantification over (minimal) situations/events that each contain exactly one individual satisfying the NP predicate. This is a consequence of the respective DPs—which are interpreted as generalized quantifiers with existential force—being interpreted in the restrictor of the Qadverb. Furthermore, since the (minimal) situations/events quantified over are exclusively individuated via the (denotation of the) respective DP, the value assigned to the individual variable bound by the existential quantifier has to vary with the value assigned to the situation/event variable bound by the Q-adverb. This explains the ‘illusion’ that the respective Q-adverb quantifies over individuals directly [see Berman (1987), de Swart (1993), von Fintel (1994), (2004) and Herburger (2000) for details]. Concerning sentences with plural definites, in contrast, the only discussions of QVEs we are aware of can be found in Graff (2001, 2006) and Nakanishi & Romero (2004). But neither of them discusses sentences like (1a): Graff is primarily concerned with sentences like (5a), where the definite DP is modified by a possessive PP that contains an indefinite DP. Nakanishi and Romero, in contrast, exclusively discuss sentences like (5c), which contain the Q-adverb for the most part.


(6) Most x [dy[y is a toddler ^ x are the parents of y]] [x have little time for relaxation] Note that the QV reading in this case is a mere consequence of the fact that the maximality condition associated with the definite article is relativized with respect to the individuals introduced by the indefinite a toddler: for each such individual y, there is a different sum individual that uniquely satisfies the predicate parents of y. Since no element which may induce such a relativization is present in the case of (1a), this account is not general enough to cover the cases discussed in this paper. The account of Nakanishi & Romero (2004) will be discussed below. For the moment, suffice it to say that according to these authors, the QV reading of a sentence like (5c) does not come about via direct quantification over the atomic parts of the plural individual denoted by the definite DP, but rather indirectly, via quantification over the parts of a sum eventuality. Crucially, those parts stand in 1:1 correspondence to the atoms that the sum individual consists of. Somewhat ironically, we will argue below that while there are indeed good reasons to adopt a similar approach in the case of sentences like (1a), which combine plural definites with frequency adverbs like usually, there is evidence that the QV readings of sentences such as (5c) do not come about in the indirect way assumed by Nakanishi & Romero (2004). Rather, the Q-adverb for the most part directly quantifies over the atomic parts of the sum individual denoted by the students. Our argument is based on contrasts like the ones in (7)–(9): (7) a. The people who lectured at the conference last summer were usually Japanese. b. Most (of the) people who lectured at the conference last summer were Japanese.


combined with such a noun if it denotes a singleton set in the first place as there is no natural ordering available for the members of a set of atoms. The only difference between the approach of Sharvy (1980) and Link (1983), on the one hand, and the approach of Graff (2001, 2006), on the other, is that the former assume that the definite article turns a set into an individual, while the latter assumes that the definite article turns a set into a singleton set. Furthermore, Graff (2001, 2006) assumes that definites (as well as singular indefinites and bare plurals) in argument position function as the first argument (i.e. the restrictor) of either an overt Qadverb (if present) or of a covert existential quantifier or generic operator. Accordingly, a sentence like (5a) can be interpreted as shown in (6) if the definite DP functions as the first argument of the Q-adverb usually.


Consider the contrast between (7a) and (8a) first: (7a), where the tense of the matrix verb and the tense of the relative clause verb agree, is grammatical and receives a QV reading. (8a) on the other hand, where the relative clause verb is marked for past tense, while the matrix verb is marked for present tense, does not have such a reading. It only has a reading according to which the sentence is true if everyone among a certain plurality of people that have the property of having lectured at the conference last summer is Japanese in most salient situations. As be Japanese is an i-level predicate that is very hard or almost impossible to reinterpret as an s-level predicate, the sentence is very odd. The crucial point to note is that the same lack of agreement between the respective tense markings does not seem to matter if the Q-adverb usually is replaced by the determiner quantifier most or the Q-adverb for the most part: (8b, c) are both just as acceptable as (7b, c). A plausible explanation for this difference relies on the assumption that the domains of quantification differ in the respective cases: while this domain consists of eventualities/situations in the case of (7a) and (8a), it consists of individuals in the case of (7b, c) and (8b, c). Based on this assumption, we will argue below that quantification over eventualities/ situations must obey a constraint called the tense agreement constraint, which does not hold for quantification over individuals. This constraint is violated in the case of (8a). Next, consider (9a): the sentence is odd in spite of the fact that the tenses of the matrix verb and the relative clause verb agree. The only difference between (7a) and (9a) concerns the internal constitution of the eventualities introduced by the respective relative clauses: in the case of (7a), it is plausible to assume that this eventuality consists of parts


c. For the most part, the people who lectured at the conference last summer were Japanese. (8) a. *The people who lectured at the conference last summer are usually Japanese. b. Most (of the) people who lectured at the conference last summer are Japanese. c. For the most part, the people who lectured at the conference last summer are Japanese. (9) a. *The people who listened to Peter’s talk at the conference last summer were usually Japanese. b. Most (of the) people who listened to Peter’s talk at the conference last summer were Japanese. c. For the most part, the people who listened to Peter’s talk at the conference last summer were Japanese.



that are temporally distributed since there is no reason to assume that all lectures given at a conference take place at the same time. In the case of (9a), in contrast, it is almost inevitable to assume that the relative clause eventuality consists of parts that coincide temporally (or at least overlap to a very high degree) as one normally listens to a talk from start to finish. It seems that this difference in the internal constitution of the respective eventualities is responsible for the fact that (9a) in contrast to (7a) does not get a QV reading. We refer to this constraint on the internal constitution of the eventualities introduced by the respective relative clauses as the coincidence constraint. Again, we take the fact that both (9b) and (9c) are acceptable to constitute evidence in favour of our assumption that the respective quantificational domains differ. Furthermore, we will show below that the oddity of (9a) is not an isolated fact, but fits into a general pattern that can be explained by assuming that quantification over situations/ events is constrained in a way that does not hold for quantification over individuals. The facts discussed in this paper thus give us important clues as to how situations are to be individuated for the purposes of quantification, and they show that the local context in which a bound situation variable occurs plays an important role in this process, thus providing additional evidence for the context sensitivity of adverbial quantification. Last, but not least, they show that explaining QVEs in terms of quantification over situations/eventualities is not only a viable alternative to unselective binding approaches, but rather the only available option in the case of sentences with frequency adverbs. The paper is structured as follows. In section 2.1, we give some background on how QVEs in sentences with singular indefinites can be accounted for under the assumption that Q-adverbs exclusively quantify over situations/eventualities. In section 2.2, we discuss a prima facie plausible way of accounting for QVEs in sentences with plural definites under the assumption that these come about as indirect effects of quantification over situations. While this account works well in many cases, we show that it does not yield the correct results for sentences such as (8a). In section 3.1, we discuss the analysis of Nakanishi & Romero (2004) in sentences with the Q-adverb for the most part, and in sections 3.2 and 3.3, we show that an analysis using the same basic mechanism in combination with plausible assumptions concerning the temporal location of situations can explain the tense agreement constraint exemplified by (8a). In section 3.4, we discuss these results in light of the coincidence constraint in order to account for the oddity of sentences like (9a). Section 4 summarizes the main results of the paper.


2 COVARYING INDIVIDUALS

2.1 Background: QVEs in sentences with singular indefinites


In this section, we discuss how QVEs in sentences with singular indefinites can be explained as indirect effects of quantification over situations. Note that we assume the respective indefinite DPs to be deaccented in the examples discussed below, while the main accent of the clause (which is indicated by capital letters) is on the most deeply embedded VP-internal element. This has the consequence that the indefinite DP is interpreted as non-focal, while the rest of the clause is interpreted as focal [see Selkirk (1995) for details regarding the relation of accent placement and focus interpretation]. This is important because it is well known that information structure plays an important role when it comes to determining the arguments of Q-adverbs—in contrast to the arguments of determiner quantifiers, which are provided by the syntax. Glossing over some differences, most approaches to adverbial quantification agree on a mapping algorithm that can be informally described as follows (and that we will also assume for the time being; but more on this in section 4 below): the first argument (the restrictor) of a Q-adverb is the denotation of the non-focal part of the clause containing it, while the second argument (the nucleus) is the denotation of the whole clause minus the Q-adverb [see Rooth (1985), (1995), Chierchia (1995a), Krifka (1995), (2001), Partee (1995) and Herburger (2000) for details]. Note, however, that Beaver & Clark (2003, 2007) have recently shown convincingly that association with focus is presumably not conventionalized in the case of Q-adverbs—in contrast to operators like only—but rather comes about in a way that can roughly be described as follows: the first argument, that is, the restrictor, of a Q-adverb initially consists of a free variable ranging over event/situation predicates that needs to be resolved on the basis of contextual information. Since the non-focal part of a sentence corresponds (at least weakly) to given information, the situation/event predicate that is obtained via the algorithm sketched above is thus in most cases identical to the one that can be inferred on the basis of contextual information [see also von Fintel (1994) and (2004)]. Furthermore, in the case of sentences that are presented in isolation, focus marking gives an important clue as to how the variable in the restrictor of the Q-adverb is to be resolved. Thus, in order to be mapped onto the restrictor of a Q-adverb, a DP (at least in the default case) needs to be non-focal. As already mentioned in the introduction, the fact that a sentence like (10a) below receives the interpretation paraphrased in (10b) can be


explained as an indirect effect of quantification over situations: under the assumption that Q-adverbs like usually quantify over minimal situations exclusively [i.e. situations that contain nothing beyond what is strictly speaking required to satisfy the respective predicate; see von Fintel (1994) for detailed discussion], the truth conditions of sentences where an indefinite DP is interpreted in the restrictor of a Q-adverb come out equivalent to the truth conditions of sentences where the combination of Q-adverb and indefinite DP has been replaced by a quantificational DP of corresponding quantificational force.

Let us assume, following Kratzer (1989) and von Fintel (1994), that verbal as well as nominal and adjectival predicates and quantificational determiners take an additional situation argument. Furthermore, we follow the spirit of account sketched above by Beaver & Clark (2003, 2007) and assume for concreteness that frequency adverbs such as usually adjoin to TP at LF, taking the denotation of the TP segment they c-command as their nuclear scope, while the restrictor initially consists of a free variable that (in cases where a sentence is presented in isolation) is resolved on the basis of focus marking by default.2 Since in the cases under consideration, the indefinite corresponds to the nonfocal part of the TP, the free variable is resolved to a predicate which characterizes situations containing an individual that satisfies the respective NP predicate. Consider the LF of example (10a):

2 See Hinterwimmer (2008) for a different account, which is mainly based on facts concerning the interaction of Q-adverbs and strong quantificational DPs and on empirical evidence from German, where DPs can be reordered via scrambling and where the mapping from overt syntax to interpretation is thus more straightforward: non-focal/topical object indefinites have to be moved to a position where they c-command the Q-adverb overtly, while focal subjects tend to remain within their vP-internal base position, where they are c-commanded by the respective Q-adverb [see also Diesing (1992), Kratzer (1995) and Chierchia (1995b) for relevant discussion within an unselective binding approach].


(10) a. A dog is usually SMART. b. Most dogs are SMART.


The denotation of usually is given in (11a), the denotation of the lower TP segment in (11b) and (11c) shows the situation predicate that the free variable in the restrictor of usually is resolved to. Example (11d) gives a simplified version of the result of combining the three objects.

Note that the denotation of usually given in (11a) has to be so complicated because of the special nature of situations. First, due to the part-whole structure of situations, minimality is required in order to arrive at intuitively correct truth conditions [see von Fintel (1994) and (2004)]. Otherwise, the existence of one smart dog in the world of evaluation would be sufficient to make (10a) true since the world of evaluation also counts as a (maximal) situation. Therefore, every (maximal) situation containing a dog is also a (maximal) situation containing a smart dog. Second, existential quantification over situations extending the restrictor situations is required in the nuclear scope because otherwise the two sets would necessarily be disjoint: a situation that is minimal with respect to a predicate C cannot at the 3 Note that variables of type s range over situations as well as over worlds, where worlds are just maximal situations (Kratzer 1989). The reason for keeping the situation variable in the first argument of determiner quantifiers distinct from the one in the second argument is empirical: there are cases like (i) where the individuals quantified over satisfy the respective nominal predicate at a different time than the verbal predicate [see Musan (1997) and Percus (2000) for discussion].

(i) Most fugitives are in jail again. Furthermore, there is evidence from sentences with universally quantified DPs that the situation variable in the restrictor of quantificational determiners can only be bound by Q-adverbs under ccommand. This can be accounted for under the assumption that a (situation) variable-binding operator (in the sense of Bu¨ring 2004) is inserted directly beneath the Q-adverb, which has the effect of turning any (co-indexed) free variables in its scope into bound variables [see sections 2.2 and 4; see also Hinterwimmer (2006) and (2008) for detailed discussion].


(11) a. [[usuallyC]]g ¼ kP<s, t>. j{s: min(s, ks1.g(C)(s1))} \ {s2: ds3 [s2 < s3 ^ min(s3, ks4. g(C)(s4) ^ P(s4))} j > ½ j{s: min(s, ks1. g(C)(s1))} j where C is a domain-restricting variable of type <s,t> and min(s, P) iff P(s) ^ :ds#[s#< s ^ P(s#)] b. [[A dogs* is smart]]g ¼ ks. dx [dog(x)(g(s*)) ^ smart(x)(s)] where s* is a situation variable to which g assigns the world of evaluation w0 by default.3 c. ks. dx [dog(x)(g(s*)) ^ in(x)(s)] d. Most s [min(s, ks1.dx [dog(x)(w0) ^ in(x)(s1)])] [ds2 [s < s2 ^ min(s2, ks3. dx [dog(x)(w0) ^ smart(x)(s3)])]] ‘Most minimal situations that contain a dog can be extended to a minimal situation where a dog is smart’.


2.2 QVEs in sentences with definites Let us return to sentences like (1c) and (7a), which are repeated here as (12a, b). (12) a. The lions that Peter saw during the safari usually had a MANE. b. The people who lectured at the conference last summer were usually JapaNESE. Now, what options are there to explain the fact that such sentences receive QV readings if one wants to stick to the assumption that Qadverbs are only able to quantify over situations? It is clear that QVEs in sentences with definites do not come about in the same way as QVEs in sentences with indefinites: in contrast to the indefinite determiner, the definite determiner is not allowed to pick out different individuals from one and the same set in different situations. Rather, it has to pick out the maximal sum individual contained within the set it is applied to [see Sharvy (1980) and Link (1983)]. Consequently, covariation with the situations quantified over by a Q-adverb is excluded if the set denoted by the NP complement of the definite determiner does not vary with the situations. To put it the other way around, covariation is only possible if the NP complement of the definite determiner includes a situation variable that allows the set denoted by this NP to vary with the situations quantified over. There are indeed cases like (13b), where it is plausible to assume that QVEs arise precisely in this way.


same time be a situation that is minimal with respect to a predicate P (assuming P is not a subset of C). On the other hand, a minimal situation that satisfies the restrictor predicate C and the nuclear scope predicate P can be an extension of a situation that minimally satisfies C. Note furthermore that the minimality conditions ensure that the dogs introduced by the respective situation predicates are the same: a minimal situation that contains a dog and that is a situation of a dog being smart contains just one dog (namely a smart one), not two, as being smart in a situation entails being contained in that situation [cf. the simplification in (11d) above]. Since we do not want to predict that a sentence like ‘When a man is rich, a man is happy’ can be interpreted as ‘Most rich men are happy’, we follow von Fintel (1994, 2004) in assuming that the novelty condition (Heim 1982) still applies, but only at the syntactic level. With all these assumptions in place, the truth conditions of our example (10a) are thus identical to those that would result from direct quantification over dogs.


(13) a. ??The piano-player is usually SMART. b. I love going to jazz-concerts: The piano-player is usually SMART (and it’s nice to talk to him after the show).

(14) a. ??The violin-players are usually TALL. b. There’s a funny generalization concerning classical concerts: The violin-players are usually TALL. In the absence of a context that makes available a suitable situation predicate, the definite DPs cannot be interpreted as covarying with the situations quantified over, and the sentences containing them are very odd since the matrix predicates are i-level predicates. If such a context is provided, in contrast, the same definites can be interpreted as covarying: in (13b), the piano-players vary with the jazz concerts, and in (14b), the violin-players vary with the classical concerts. There are also cases where no context is required in order to accommodate a suitable situation predicate, but where this is possible on the basis of clause-internal information alone, namely if the NP predicate is stereotypically associated with a set of situations such that each of those situations contains either exactly one or a plurality of individuals that satisfy the predicate. Such examples are given in (15):


As argued for in detail in Hinterwimmer (2006, 2008), though, and as has been shown by the unacceptability of (13a) in contrast to (13b), the definite DP is solely interpreted in the nuclear scope of the Q-adverb. The restrictor, in contrast, contains a situation predicate that can be accommodated on the basis of contextual or clause-internal information and that fulfils the following condition: it characterizes a set of situations such that each of those situations can plausibly be assumed to contain either exactly one (in the case of singular definites) or a plurality of individuals (in the case of plural definites) that satisfy the respective NP predicate. In other words, it is not the case that the situations quantified over are defined on the basis of the denotation of the DP (as with indefinites). Rather, it has to be independently ensured that each of those situations contains individuals/exactly one individual of the required kind. Hinterwimmer (2006, 2008) argues that this is due to the fact that the definite determiner presupposes that the set it applies to contains a unique maximal element. Therefore, in order for this presupposition to be fulfilled at the point where the meaning of the respective definite DP is computed, it has to be guaranteed that each of the situations quantified over makes available such a set. To see this, consider the contrast between (13a) and (13b) and (14a) and (14b).


(15) a. Peter’s students are usually SMART. b. The pope is often ITAlian.

(16) [[thes*]]g ¼ kP<e,<s,t>>. r{x: P(x)(g(s*))}, where x ranges over sums as well as over atomic individuals and where r{x: P(x)(s)}¼def ix [P(x)(s) / "y [P(y)(s) / y < x]]. [see Link (1983)] The free variables can either be resolved to w0 (i.e. to the actual world) by default (as in the case of the indefinites discussed in section 2.1), or to a contextually salient situation, or they can be bound by a Q-adverb that c-commands the respective DP at LF via the insertion of a (situation) variable-binding operator directly beneath the ccommanding Q-adverb.4 The insertion of this operator has the consequence of turning any free variable in its scope that bears the same index into a lambda-bound variable, as shown in (17). The situation variables thus become bound by the respective Q-adverb when the Qadverb is combined with its sister via functional application5: (17) [[cn XP]]g ¼ ks. [ [[XP]]g[n/s] (s) ] where cn is the situation variable-binding operator and g[n/s] is the assignment function that (possibly) differs from the assignment function g insofar as it assigns the value s to all situation variables bearing the numerical index n. In cases like (13b), (14b) and (15a, b), the option of turning the situation variables into bound variables is chosen. The relevant reading of a sentence 4

Compare Bu¨ring (2004), who argues that pronouns are turned into variables bound by a ccommanding quantificational DP via the insertion of an individual variable-binding operator directly beneath the quantificational DP. 5 Note that XP is of type <s,t>, that is, it is a situation predicate. It therefore has to be applied to the variable s first before lambda-abstraction over this variable takes place, as otherwise we would get an object of type <s,<s,t>>, not one of type <s,t>, which we want.


In the case of (15a), the noun students is naturally associated with a set of suitable situations, namely a set of courses taking place at different times. In the case of (15b), too, the noun is stereotypically associated with a set of situations, albeit ‘world-size’ ones, namely the terms of office of the respective popes. Technically, we follow Hinterwimmer’s (2006, 2008) account of how covariation arises in the cases under consideration. We assume that not only quantificational determiners (see section 2.1) but also the definite determiner comes with a free variable (s*) [cf. Bu¨ring (2004) and Elbourne (2005)], as shown in (16):


like (15a), repeated here as (18a), whose LF is given in simplified form in (18b), can thus schematically6 be represented as shown in (18c). (18) a. Peter’s students are usually SMART. b.

6

For a full specification of the meaning of usually, see (11a) above.


Returning to examples like the ones in (12a, b), we have to decide whether in those cases QVEs come about in the way just described. Obviously, there is no contextual information on the basis of which a suitable situation predicate could be accommodated—that is, a predicate that characterizes a set of situations such that each of those situations contains a (different) plurality of individuals satisfying the NP predicate. This only leaves open the possibility that such a predicate is accommodated on the basis of the NP predicates themselves. But is it plausible to assume that these NPs provide the necessary information? Of course, they both contain relative clauses that introduce situations. But those situations already contain the whole sum of individuals that satisfy the respective predicate—that is, the whole sum of lions seen by Peter during his safari [cf. example (12a)] and the whole sum of individuals who lectured at the conference [cf. example (12b)]. This implies, however, that on the basis of these situations, no suitable predicate can be accommodated, that is, no situation predicate such that each of the situations characterized by this predicate contains a different set of lions or a different set of people giving lectures. In addition to that, it is not plausible that the NP predicates are stereotypically associated with a set of situations of the required kind in some other way as they are


(19) a. ??The lions that Peter saw during the safari usually have a MANE. b. Most of the lions that Peter saw during the safari have a mane. c. ??The people who lectured at the conference last summer are usually JapaNESE. d. Most of the people who lectured at the conference last summer are Japanese. We therefore have to look for a solution that allows us to stick to the assumption that Q-adverbs only quantify over situations. This is what we will do in the next section, where we discuss the analysis of for the most part by Nakanishi & Romero (2004) and show that a similar mechanism gives the right results for the cases under consideration, which involve frequency adverbs like usually. 3 QUANTIFICATION OVER THE PARTS OF COMPLEX SITUATIONS

3.1 Nakanishi & Romero (2004) on the Q-adverb for the most part As already mentioned in section 1, a sentence like (20a) has a QV reading that can be paraphrased as in (20b): (20) a. For the most part, the students admire [Mary]F. [Nakanishi & Romero (2004): example (31a)] b. Most of the students admire Mary. Based on differences regarding focus sensitivity and the availability of collective readings in sentences with accomplishment verbs, Nakanishi & Romero (2004) argue that while the quantificational determiner most operates on plural individuals, the Q-adverb for the most part operates on plural eventualities. For reasons of space, we simply discuss


far too specific. We therefore conclude that the QV readings of sentences like (12a, b) do not come about via covariation of the individuals denoted by the plural definites with the situations quantified over. One could further speculate that the Q-adverb quantifies over the atomic parts of the sum individuals denoted by the respective DPs. But if this really were the case, it would be completely unexpected that sentences such as (12a, b) have to obey the tense agreement constraint mentioned in the introduction, as evidenced by the unacceptability of (19a, c) below, while those in (19b, d) do not. If the Q-adverbs in (19a, c) had the same quantificational domains as the quantificational determiners in (19b, d)—namely individuals—why should the first ones be sensitive to non-agreeing tense markings, while the second ones are not?


(21) de[p(e) ^ de#[e# < e ^ je#j> ½ jej ^ "e$[e$ < e# / q(e$)]]]. (Nakanishi & Romero 2004: 8) ‘There is a general (possibly plural) event e for which p(e) holds and there is a (possibly plural) event e# that is a major part of e such that, for all subevents e$ of e#, q(e$) holds’. (Nakanishi & Romero 2004: 8) Note that e# < e means ‘e# is a part of e’, while je#j > ½ jej means ‘the cardinality of (the atomic parts of) e# is greater than or equal to half the cardinality of (the atomic parts of) e’. Nakanishi & Romero (2004: 9) assume that a QV reading ‘with respect to a given NP arises as a side effect of the following choices’: (22) (i) The semantic content and thematic predicate of the NP are within the restrictor p. (ii) The general event e is ‘measured’ by counting its atomic event units in [[V0]]. (iii) The NP is interpreted distributively in a one-to-one mapping. According to Nakanishi & Romero (2004), example (20a) above is thus interpreted as given in (23): (23) a. de [*admire(e) ^ Agent(e, the students) ^ de#[e# < e ^ je#j > ½ jej ^ "e$[e$ < e# / Theme(e#, Mary)]]]. [Nakanishi & Romero 2004: (31b)] b. ‘There is a general (possibly plural) event e such that *admire(e) ^ Agent(e, the students) and there is a (possibly plural) event e# that is a major part of e such that, for all subevents e$ of e#, Theme(e$, Mary)’. [Nakanishi & Romero 2004: (31c)]


the mechanism they propose in this section without going into the arguments they offer for adopting their event-based analysis of for the most part. This mechanism contains the basic ingredients that are necessary to account for the data discussed above. Nakanishi & Romero (2004) assume that a sentence of the form For the most part NP VP has the truth conditions in (21) below, where p corresponds to the denotation of the non-focussed material, while q corresponds to the denotation of the focussed material. Note furthermore that they assume a neo-Davidsonian event semantics [see Parsons (1990), Schein (1993), Herburger (2000) and Landman (2000) for discussion], according to which verbs only introduce an event argument directly, while the individual arguments of verbs are introduced via thematic role predicates like Agent, Theme, etc., and are combined with the predicate denoted by the verb via conjunction.


This analysis only works under the following two assumptions: (a) The individual arguments of verbs are separated from the respective verbal predicate at the level of semantic interpretation. (b) The denotation of the whole clause minus the Q-adverb is ‘cut’ into two parts: one part that contains non-focal material and one part that contains focal material.


As Nakanishi & Romero (2004) acknowledge themselves, these two assumptions are crucial for the following reason: if q in the formula above was replaced by an eventuality predicate that contains the NP relative to which the QV reading arises—that is, if it was Agent(e$, the students) ^ Theme(e$, Mary) instead of only Theme(e$, Mary) in (23a)—one would not get the desired reading since the entire sum individual denoted by this NP would stand in the respective thematic relation to each atomic part of the smaller event e$. These assumptions are problematic for the following reason: Nakanishi & Romero (2004) do not offer a mapping algorithm that would give us the desired result, and it is not quite clear what such a mechanism would look like. One possibility would be the following: the whole clause minus the Q-adverb is adjoined to the XP dominating the Q-adverb, leaving behind a copy (see Chomsky 1995). In the higher copy, the focus-marked constituents are deleted, while in the lower copy the non-focus-marked constituents are deleted. This is similar to the algorithm proposed by Herburger (2000), the only difference being that according to Herburger nothing is deleted in the lower copy, that is, also non-focal material is repeated there. What is problematic about this algorithm is the fact that it is hard to imagine how the parts of the original clause should be interpreted in a compositional manner. How, for example, should an object like the students admire (with Mary deleted) be interpreted correctly (i.e. with the students as the Agent, not the Theme), and why should the focus-marked DP Mary be interpreted as Theme(e, Mary)? This problem could only be avoided if deletion did not apply to syntactic objects at LF, but to the denotations of these objects at the level of semantic interpretation, that is, if the two copies were both interpreted semantically before the objects corresponding to the focus-/non-focus-marked parts of the original sentence get deleted. This, however, is a dubious assumption as deletion is normally conceived of as a syntactic operation. Despite these problems, which are specific to this particular implementation, the underlying ideas of the mechanism just outlined can be applied to our problem concerning the interpretation of sentences with plural definites. We propose that QVEs in sentences with plural definites come about as indirect effects of a quantification over the


salient parts of complex situations. In the next section, we develop an approach that avoids the problems mentioned above and can be applied in the context of sentences that contain frequency adverbs like usually.

3.2 An extension of Nakanishi & Romero (2004)

Q-adverbs adjoin to TP at LF, taking the denotation of the TP segment they c-command as their nuclear scope. The restrictor initially consists of a free variable ranging over situation predicates that is either resolved on the basis of contextual information or (in the absence of such information) on the basis of focus marking. Non-focal DPs are accordingly interpreted in the restrictor of the Q-adverb by default.

Consider our familiar example (12b) again, repeated below as (24a), a simplified LF representation of which is given in (24b).


Let us assume that frequency adverbs like usually can also quantify over the parts of complex situations, if there is a natural way to identify these parts. This means that such Q-adverbs have to come in two (albeit systematically related) varieties: in order to account for the QV readings of sentences with singular indefinites and singular definites (and also covarying plural definites; see section 2.2), one still has to assume that there is a version of the respective Q-adverb that establishes a relation between two sets that have (minimal) situations as elements. But in light of the fact that sentences containing non-covarying plural definites get QV readings, too, a second, closely related meaning of the respective Q-adverb has to be available. This second meaning is modelled after the denotation Nakanishi & Romero (2004) assume for the Q-adverb for the most part. It introduces two existential quantifiers over (complex) situations and establishes a relation between the parts those situations can naturally be decomposed into: the cardinalities of the sets containing these parts have to stand in the respective relation. But now the crucial question is how to determine the two complex situations that are related this way, that is, which part of the (denotation of the) original clause is predicated of the first one and which part is predicated of the second one? In order to avoid the problems of the analysis by Nakanishi & Romero (2004) mentioned above, we stick to the basic mechanism introduced in sections 2.1 and 2.2, where adverbially quantified sentences with singular indefinites and definites were discussed. Its main features are repeated below:


(24) a. The people who lectured at the conference last summer were usually JapaNESE. b.

(25) a. [[usually-1C]]g ¼ kP<s,t>. j {s: min(s, ks1.g(C)(s1))} \ {s2: ds3[s2 < s3 ^ min(s3, ks4. g(C)(s4) ^ P(s4)]} j > ½ j {s: min(s, ks1. g(C)(s1))} j b. [[usually-2C]]g ¼ kP<s,t>. ds[g(C)(s) ^ ds1 < s[js1j > ½ jsj ^ P(s1)]] where js1j and jsj are abbreviations for jSalpart(s1)j and jSalpart(s)j and Salpart is a (partial) function that maps a complex situation s onto the set whose members are the parts that s can naturally be decomposed into, that is, the set consisting of its salient parts. The conditions under which a situation can be decomposed into a set of salient parts will turn out to be crucial for our explanation of contrasts like the ones in (19) above, so we will come back to this point below. Note that the difference between the two versions of usually basically boils down to the question of whether the elements of the two sets that the Q-adverb operates on are defined directly via the situation predicates it operates on or indirectly. In the first case, each element of the respective set satisfies the respective situation predicate. In the second case, in contrast, there are two complex situations that satisfy the respective situation predicates, and the sets whose cardinalities the Q-adverb relates are identified on the basis of the fact that their elements are parts of these complex situations. This means that the second version of a given Q-adverb can only be employed if the


Let us first turn to the interpretation of the Q-adverb usually: it comes in two closely related versions [given in (25a, b)], of which the second is relevant in the present context.


(26) ks. in(r{x: human(x)(g(s*)) ^ ds1[lecture(x)(s) ^ at(the c. last summer)(s1) ^ s(s1) < t0]})(s) where s is a function mapping situations onto their temporal location, < stands for temporal precedence and t0 is the utterance time. Let us turn to the denotation of the TP segment c-commanded by usually. Since the definite DP occurring there is c-commanded by usually, the free situation variable s* contained within it can be turned into a variable bound by this Q-adverb by inserting the situation variable-binding operator [whose definition is given in (17), section 2.2] directly beneath the Q-adverb. The TP segment is accordingly interpreted as given in (27): (27) [[The people who lectured at the conference last summer were Japanese]]g ¼ ks. Japanese(r{x: human(x)(s) ^ ds1[lecture(x)(s1) ^ at(the c. last summer)(s1)^ s(s1) < t0]})(s) As already mentioned, the matrix predicate be Japanese has to be interpreted distributively if it is applied to a sum individual, and in the case of the relative clause predicate lecture, this is at least the preferred option as lectures are normally given by single persons. Concerning the last point, the availability of a QV reading crucially depends on the hearer’s willingness to make the default assumption that the relative clause predicate is interpreted distributively (as already mentioned in footnote 1), that is, that each of the persons mentioned gives exactly one lecture. Why this is so will become clear in the next two sections, where we argue that the sets of situations whose cardinalities the Q-adverb relates are determined via the parts into which the relative clause situation can naturally be decomposed.


respective situation predicates characterize situations that can naturally be decomposed into parts. As we will see below, in the case under discussion, this is possible because the relative clause predicate as well as the matrix predicate most naturally receive a distributive interpretation. This makes it possible that the sets of situations whose cardinalities are related stand in a 1:1-relation to the atomic parts of the respective sum individuals, thus enabling the sentence to receive a QV reading. Consider next the situation predicate that the free variable in the restrictor of the Q-adverb is resolved to. As already said, we assume the plural definites in the examples under discussion to correspond to the non-focal part of the respective sentence. Consequently, the situation predicate given in (26) functions as the restrictor of the Q-adverb in (24a).


Let us assume for concreteness that both the relative clause and the matrix predicates are shifted via a distributivity operator7 that applies to them, as shown in (28a, b) [cf. Lasersohn (1998), who builds on Link (1983) and (1987)]: (28) a. DIST(kxks. lecture(x)(s) ^ s(s) < t0) ¼ kxks. "y 2 Atom(x): ds1 < s. lecture(y)(s1) ^ s(s1) < t0 b. DIST(kxks. Japanese(x)(s) ^ s(s) < t0) ¼ kxks. "y 2 Atom(x): ds1 < s. Japanese(y)(s1) ^ s(s1) < t0

(29) a. ks. in(r{x: human(x)(w0) ^ ds1["y 2 Atom(x): ds2 <s1. lecture(y)(s2) ^ s(s2) < t0 ^ at(the c. last summer)(s1) ]})(s) b. ks. "y 2 Atom(r{x: human(x)(s) ^ ds1["y 2 Atom(x): ds2 < s1. lecture(y)(s2) ^s(s2) < t0 ^ at(the c. last summer)(s1) ]}): ds3 < s. Japanese(y)(s3) ^ s(s3) < t0 The final step now consists in combining the denotation of usually-2 given in (25b) above with the two situation predicates in (29). This gives us (30a), which can be simplified to (30b): (30) a. ds [in(r{x: human(x)(w0) ^ ds1["y 2 Atom(x): ds2 < s1. lecture(y)(s2) ^ s(s2) < t0 ^ at(the c. last summer)(s1) ]})(s) ^ ds3 < s [js3j > ½ jsj ^ "y 2 Atom(r{x: human(x)(s3) ^ ds4["y 2 Atom(x): ds5 < s4. lecture(y)(s5) ^ s(s5) < t0 ^ at(the c. last summer)(s4) ]}): ds6 < s3. Japanese(y)(s6) ^ s(s6)< t0]] b. ds [in(r{x: human(x)(w0) ^ ds1[DIST(lecture(x)(s1) ^ s(s1) < t0) ^ at(the c. last summer)(s1) ]})(s) ^ ds2 < s [js2j > ½ jsj ^ DIST(Japanese(r{x: human(x)(s2) ^ . . . })(s2) ^ s(s2) < t0)]]

7 For concreteness, let us assume that the distributivity operator is adjoined to the constituents (i.e. the VPs) that denote the respective objects.


This has the consequence that the situation predicate in the restrictor of the Q-adverb is actually spelled out as given in (29a) below, while the one in the nuclear scope is spelled out as given in (29b):


Simplifying somewhat, this can be paraphrased as: ‘There is a situation s that contains the (maximal) sum of people who lectured at the conference last summer, and there is a situation s2 that is a part of s such that (a) the cardinality of the salient parts of s2 is more than half the cardinality of the salient parts of s and (b) s2 is a situation where the sum of people lecturing at the conference last summer that is maximal with respect to s2 is Japanese’.


Note that the problem with the analysis by Nakanishi & Romero (2004) discussed in the last section is circumvented in our formalization. Recall that Nakanishi and Romero had to assume that the original event predicate (i.e. the denotation of the whole clause minus the Q-adverb) is split up in the following way: the focal part is predicated of the ‘smaller’ event e#, while the non-focal part is predicated of the larger eventuality e. This was necessary in order to keep the (non-focal) definite DP from being repeated in the event predicate that is applied to e# since this would prevent the respective sentence from getting a QV reading. The problem with this assumption, however, is that it is unclear how the required split can be achieved in a compositional manner. In our formalization, this problem does not arise: The situation variable contained within the definite DP that is interpreted in the nuclear scope of the Q-adverb is turned into a variable that is bound by the existential quantifier introducing the smaller nucleus situation s2. Consequently, only the larger restrictor situation s contains the maximal sum of individuals that satisfy the NP predicate in the actual world, while the nucleus situation s2 only contains the maximal sum of individuals that satisfy this predicate in s2. Furthermore, the cardinality of the set of salient parts into which s2 can be decomposed is required to be more than half the cardinality of the set of salient parts into which s can be decomposed. Now, let us assume for the moment that the cardinality of the respective situations is determined in the way assumed by Nakanishi & Romero (2004), namely by establishing a 1:1 correspondence with the atomic parts of the respective sum individuals (we will see below that things cannot be quite this simple). It is thus clear that the cardinality of the maximal sum individual contained in s2 is at least more than half the cardinality of the maximal sum individual contained in s. And this yields the QV reading the sentence actually has. Returning to the question of how the sets of salient parts into which the respective situations can be decomposed are determined, the assumption made above seems rather obvious: both situations contain sum individuals with atomic parts. They can thus easily be divided into


parts that stand in 1:1 correspondence to the atomic parts of the respective sum individuals, as in the analysis of sentences by Nakanishi & Romero (2004) with for the most part. This, however, cannot account for the fact that sentences like (8a) and (9a), which are repeated below as (31a, b), are infelicitous. We explain this via the tense agreement constraint and the coincidence constraint, respectively, which were mentioned in section 1: according to the first one, the tense of the relative clause verb has to agree with the tense of the matrix verb, and according to the second one, it has to be plausible that the parts of the relative clause situation are temporally distributed. Example (31a) violates the first constraint, (31b) the second:

We will see in the next two subsections that both constraints can naturally be derived from the following assumptions: (a) The sets of situations whose cardinalities the Q-adverb relates are defined via the parts into which the relative clause situation can naturally be decomposed on its distributive interpretation. (b) The situations quantified over by a Q-adverb need to be located in non-overlapping time intervals. Concerning (b), Lasersohn (1995) and Zimmermann (2003) have argued that a similar constraint is operative in the interpretation of pluractional elements such as occasionally, again and again, etc., where it is also required that the respective atomic events/situations do not overlap.8 We take these constraints to follow from the fact that situations need to be individuated, and since they—in contrast to concrete individuals— often do not come with fixed boundaries, location in distinct, non-overlapping time intervals is a good way to set up boundaries. Note that as soon as we turn our attention from the quasi-generic cases discussed in section 2 to cases where the situations to be quantified over are located in a specific interval, it becomes obvious that such a constraint is also operative in cases where the first version of the respective frequency adverb has to be employed: (32a) below is only acceptable if the time span during which John lay on the beach can be split into distinct, 8

In fact, the constraint operative in these cases seems to be even stronger: it is not only required that the atomic events/situations do not overlap, but that they are separated by rather long stretches of time (cf. Lasersohn 1995 and Zimmermann 2003).


(31) a *The people who lectured at the conference last summer are usually JapaNESE. b *The people who listened to Peter’s talk at the conference last summer were usually JapaNESE.


non-overlapping units. This can be done in two ways: either one assumes that the time spans during which John lay on the beach are separated by time stretches where he did not lie on the beach or one assumes that the speaker went to the beach on several occasions and saw John lie there each time. In order for the sentence to be true, Mary has to be with John on most of these occasions. This is in clear contrast to (32b), which may well be true if John lay on the beach the whole day long, as long as Mary was with him for a time span that covers more than half of the day. (32) a. Yesterday, John usually lay on the beach with MAry. b. Yesterday, John for the most part lay on the beach with MAry.

(33) a. Yesterday, Mary kissed a lot of boys at Peter’s party. They were usually well DRESSED. b. Yesterday, Mary kissed a lot of boys at Peter’s party. For the most part, they were well DRESSED. c. Yesterday, a lot of people attended Mary’s concert. #They were usually well DRESSED. d. Yesterday, a lot of people attended Mary’s concert. For the most part, they were well DRESSED. The second sentence in (33a) is fine and receives an interpretation that can be paraphrased as ‘Most of them (¼of the boys kissed by Mary) were well dressed’, that is, a QV reading. The second sentence in (33c), in contrast, is rather odd in the context of the first one and, certainly, does not receive an interpretation that can be paraphrased as ‘Most of them (¼the people attending Mary’s concert) were well dressed’.9 9 Note that the sentence becomes much more acceptable if the matrix verb is marked for present tense, as in (i).

(i) Yesterday, a lot of people attended Mary’s concert. They are usually well DRESSED. But in this case, the sentence receives an entirely different interpretation, where the Q-adverb is interpreted in the scope of the distributivity operator. This reading can be paraphrased as ‘Each of them (¼the people who attended Mary’s concert) is well dressed on most relevant occasions’. Because this is a quasi-habitual interpretation, we assume that its availability depends on the present tense marking of the matrix verb (at least as long as the context does not make salient a past interval during which the respective habit can be assumed to hold), which explains why it is blocked in the case of (33b).


Let us return to sentences where the second version of the respective frequency adverb has to be employed (because what is given is a predicate that characterizes a complex situation that can be decomposed into parts, not a set of situations). There is also evidence that in cases where there is no relative clause modifying a definite DP, the coincidence constraint has to be in effect (while no such effect can be observed in sentences with adverbs of quantity):


(34) ds[at(the party yesterday)(s) ^ ^ dx[boys(x)(w0) ^ jxj > n ^ "y 2 Atom(x): ds1 < s. kiss(y)(Mary)(s1) ^ s(s1) < t0] ^ ^ ds2 [in(r{z: boys(z)(s)})(s2) ^ ^ ds3 < s2 [js3j> ½ js2j ^ "k 2 Atom(r{z: boys(z)(s)}): ds4 < s3. well-dressed(k)(s4) ^ s(s4) < t0]]] where n is a number counting as large in the relevant context. Returning to the difference between (33a) and (33c), intuitively, it is clear what is at issue: in the case of (33a), the first sentence introduces a complex situation consisting of smaller situations whose running times do not overlap—namely the single kissing situations (as one normally kisses one person a time). In the case of (33c), in contrast, the first sentence introduces a complex situation consisting of smaller situations whose running times have to be assumed to overlap, as attending a concert means being present from start to finish. This shows that the internal constitution of the situation introduced by the first sentence has a direct influence on the acceptability of the second sentence—similar to cases like (31b), where the internal constitution of the situation introduced by the relative clause modifying the definite DP in subject position determines the acceptability of the 10

See Staudacher (1987), Groenendijk and Stokhof (1990) and Chierchia (1995b) for a detailed discussion of the principles of dynamic binding. 11 Note that according to the principles of dynamic binding, two consecutive sentences are conjoined via dynamic conjunction by default, as a consequence of which variables contained within the second sentence can be bound dynamically by existential quantifiers that are contained within the first sentence.


Before turning to the difference between (33a) and (33c), let us first say a few words about how the QV reading of the second sentence in (33a), which contains a pronoun instead of a plural definite, comes about. Following Elbourne (2001, 2005), we take pronouns to be the surface forms of definite DPs that have undergone NP-ellipsis, which is licensed under identity with some immediately preceding NP. Now, in the case of (33a), the elided NP is presumably boys. Furthermore, we assume that the situation variable contained within the elided NP is dynamically bound by the existential quantifier that binds the situation variable introduced by the matrix verb of the first sentence.10 The pronoun in (33a) thus denotes the maximal sum individual consisting of the boys kissed by Mary at the party yesterday, and the QV reading of the second sentence can be accounted for in the way by now familiar from the preceding discussion, as shown in (38)11:


matrix clause. We will show that, in both cases, this is due to the fact that the running times of the respective situations constitute the most specific locally available temporal information.

3.3 Locating situations in time

(35) a. Peter’s girlfriends are usually CaNAdian. b. *Peter’s cousins are usually CaNAdian. c. For the most part, Peter’s cousins are CaNAdian. d. Most of Peter’s cousins are CaNAdian. Note that the oddity of (35b) is not simply due to the set of Peter’s cousins being too small a domain to quantify over as (35c, d) are both perfectly acceptable. Rather, what seems to make the difference is that in the case of (35a), there is a natural way to distribute the atoms of the


In the last section, we have seen how the fact that sentences with plural definites receive QV readings can be explained in principle: The free variable in the restrictor of the Q-adverb is resolved to a situation predicate that is determined on the basis of a (non-focal) definite DP’s denotation, while the situation predicate denoted by the TP segment that the Q-adverb c-commands at LF functions as the nuclear scope. The Q-adverb then relates the cardinalities of the sets of situations into which the two complex situations can naturally be decomposed. A QV reading is thus only available if there is a natural way to decompose the respective situations into countable units. Now, in the case of the nucleus situation, a distributive interpretation of the matrix predicate makes available such units in an obvious way. In the case of the restrictor situation, in contrast, which is determined solely on the basis of its containing the maximal sum individual denoted by the respective definite DP, the internal constitution of the sum individual is the only clue for constructing the required set. Nevertheless, we have seen that it does not seem to be enough to construct a set of situations such that each of these situations contains exactly one atomic part of the respective sum individual. Rather, what seems to be required is that the running times of the respective situations do not overlap. That no such overlap occurs, in turn, has to be determined on the basis of locally available information, which may either come from the relative clause modifying the respective definite DP or from an immediately preceding clause. If no such information is available, world knowledge is the decisive factor, as evidenced by the contrast between (35a) and (35b):


(36) [[usually-2c]]g ¼ kP<s,t>.ds [g(C)(s) ^ s(s) 4 s(r{s#:Q(s#)}) ^ ds1 < s [js1j > ½ jsj^ P(s1)]] Now recall that at the end of section 3.2, we have discussed cases like (33a, c), where the internal temporal constitution of a complex situation introduced by the immediately preceding sentence seems to determine the internal temporal constitution of the situation functioning as the restrictor of a Q-adverb. For this to be possible, the running time of the restrictor situation has to be located within the running time of the situation introduced by the immediately preceding sentence. Concerning the latter point, we can now see this as a consequence of the fact that the running time of the situation introduced by the immediately preceding sentence counts as the most 12 Of course, we assume that the denotation of the respective first variant has to be altered analogously. As argued for in detail in Endriss and Hinterwimmer (2007), the assumption that situations quantified over by a Q-adverb need to be located within contextually salient intervals makes it possible to account for tense agreement effects in adverbially quantified sentences containing indefinites modified by relative clauses.


sum individual denoted by the subject DP over a set of temporally nonoverlapping situations, while in the case of (35b) this is not the case: It is plausible to assume that Peter has one girlfriend a time, but it would be quite unnatural to assume that he has only one cousin at a time. After all, this would only be possible if (with the exception of his first cousin) no cousin of Peter is born before another cousin has died since having a cousin—in contrast to having a girlfriend—is a property one only ceases to have if the respective individual has died. Before turning to a formal implementation of the constraint against situations with overlapping running times, let us first turn to the mechanism by which locally available linguistic information is made use of. We follow Lenci and Bertinetto (1999) in assuming that the situations quantified over by a Q-adverb always have to be located in time. More concretely, we assume that they have to be located within the most salient interval that is made available by the (linguistic or extralinguistic) context—namely the running time of another situation that is uniquely characterized by some predicate, where this predicate is provided by the (linguistic or extralinguistic) context. Technically, this is achieved by intersecting the situation predicate characterizing the restrictor situation of the respective Q-adverb with the predicate ks. s(s) 4 s(r{s#:Q(s#)}), where Q is a free variable ranging over situation predicates. The denotation of a Q-adverb like usually (in its second variant12) thus has to be altered slightly, as shown in (36):


salient interval made available by the context: Q therefore has to be resolved to a predicate characterizing this situation in such a way that applying the r-operator to it yields the intended result. A predicate such as ks. dx[boy(x)(w0) ^ kiss(x)(Mary)(s) ^ at(the party yesterday)(s)] would do the job and the sequence in (33a) [repeated here as (37a)] is interpreted as given in (37b) (the relevant parts are given in bold). (37) a. Yesterday, Mary kissed a lot of boys at Peter’s party. They were usually well DRESSED.

Locating the restrictor situation s2 within the running time of the situation introduced by the preceding sentence is unproblematic since the parts of s are temporally distributed. As we will see in detail in section 3.4, this has the consequence that the parts of s2 are temporally distributed as well. We are now equipped to account for the oddity of our initial examples. Consider (7a) first, which is repeated here as (38): (38) The people who lectured at the conference last summer were usually JapaNESE. In this case, an even more salient interval (because of greater local proximity) is available where the running time of the restrictor situation can be located, namely the running time of the (maximal) lecturing situation whose existence is entailed by the relative clause modifying the definite DP in the restrictor. The free variable Q is therefore resolved to a suitable predicate such as ks. dx[human(x)(w0) ^ lecture(x)(s) ^ at(the conference last summer)(s)]. The sentence is interpreted as given (in simplified form) in (39) accordingly: (39) ds [in(r{x: human(x)(w0) ^ ds1[DIST(lecture(x)(s1) ^ s(s1) < t0) ^ at(the c. last summer)(s1)]})(s) ^


b. ds[at(Peter’s party yesterday)(s) ^ dx[boy(x)(w0) ^ jxj > n ^ "y 2 Atom(x): ds1<s. kiss(y)(Mary)(s1) ^ s(s1) < t0 ^ ds2 [in(r{z: boy(z)(s)})(s2) ^ t(s2) 4 t(s{s#: dx[boy(x)(w0) ^ kiss(x)(Mary)(s#) ^ at(Ppy)(s#)]}) ^ ds3 < s2 [js3j> ½ js2j ^ "k 2 Atom(r{z: boy(z)(s3)}): ds4 < s3. well dressed(k)(s4) ^ s(s4) < t0]]]]


t(s) 4 t(s{s#: dx[human(x)(w0) ^ lecture(x)(s#) ^ at(cls)(s#)] }) ^ ds2 < s [js2j > ½ jsj^ DIST(Japanese(r{x: human(x)(s2) ^ . . . }) (s2) ^ t(s2) < t0)]]

(40) *The people who lectured at the conference last summer are usually JapaNESE. In this case, too, the running time of the relative clause situation counts as the most salient interval, and the sentence is interpreted as given in (41): (41) ds [in(r{x: human(x)(w0) ^ ^ ds1[DIST(lecture(x)(s1) ^ s(s1) < t0) ^ at(the c. last summer)(s1)]})(s) ^ ^ t(s) 4 t(s{s#: dx[human(x)(w0) ^ lecture(x)(s#) ^ at(c.l.s)(s#)]}) ^ ^ ds2 < s [js2j > ½ jsj^ DIST(Japanese(r{x: human(x)(s2) ^ . . . })(s2) ^ ^ t0 4 t(s2))]] Since the two sentences (38) and (40) only differ with respect to the tense marking of the respective matrix verb, the only difference between the corresponding semantic representations (39) and (41) are the conditions imposed on the temporal location of the salient parts of the respective nucleus situations: in the case of (39), their running times have to precede the time of utterance, while in the case of (41) the time of utterance has to be included within their running times. While the first condition is unproblematic, the second one leads to a necessary contradiction: On the one hand, the restrictor situation s has to be located within the temporal trace of a situation s1 that took place before the utterance time. On the other hand, there has to be a part s2 of s such that s2 consists of smaller situations whose temporal traces include the speech time. Consequently, the temporal trace of s2 would include the speech time as well. Example (41) can never be true as it is impossible that there is a situation that took place before the speech time as a whole, but has a part that includes the speech time.


(39) is fine, too, as the parts of s1, within whose running time the restrictor situation s is located, are temporally distributed. Furthermore, there is no contradiction between the temporal specification of the restrictor situation and the temporal specification of the nucleus situation, which comes from the tense marking of the matrix verb. Let us turn to the infelicitous example (8a) next, which is repeated here as (40):


3.4 The coincidence constraint Let us return to our familiar example (9a), which is repeated here as (42): (42) *The people who listened to Peter’s talk at the conference last summer were usually JapaNESE. Recall that we have already arrived at an informal characterization of what goes wrong in this example in sections 3.2 and 3.3: the complex restrictor situation, which contains the sum individual denoted by the definite DP, needs to be decomposed into countable units on the basis of locally available information or (in the absence of such information) world knowledge. In the case at hand, information of the required kind is provided by the relative clause situation: Due to its distributive interpretation, it makes available a set of situations, each of which contains exactly one atomic part of the sum individual denoted by the definite DP. Because of its salience, this information cannot be ignored, which leads to the following problem: Q-adverbs are only allowed to operate on sets of situations whose running times do not overlap. It is, however, clear that the salient parts of the relative clause situation in (42) violate this constraint due to the following facts: First, the definiteness of the DP Peter’s talk requires that everyone listened to the same talk. Second, if one listens to a talk, one normally listens to it from start to finish. Therefore, the salient parts of the relative clause situation all coincide temporally. Since the parts of the restrictor situation are determined on the basis of the internal constitution of this situation, they all coincide temporally, too. In the case of the minimally contrasting example (38) discussed above, this is different. There, the temporal traces of the smaller situations that the relative clause


We thus have an account for the oddity of examples like (40), where the tense marking of the relative clause verb differs from the tense marking of the matrix verb: the fact that the restrictor situation has to be located in an interval that is determined on the basis of the most salient information available necessarily leads to a contradiction. We take this as evidence that frequency adverbs exclusively quantify over situations in sentences with plural definites—especially in light of the fact that comparable effects are entirely absent in the case of similar examples with quantificational DPs and adverbs of quantity like for the most part, which we assume to have other quantificational domains accordingly. In the next section, we turn to a formal implementation of the coincidence constraint, which also sets sentences containing frequency adverbs apart from sentences with quantificational DPs as well as from ones containing adverbs of quantity.


(43) s(s):¼ it. "s1[s1 2 Salpart(s) / s(s1) 4 t] ^ "t1["s2[s2 2 Salpart(s) / s(s2) 4 t1] / t 4 t1] where s is a complex situation. Note that s(s) in the formula above is understood to be discontinuous if the salient parts that make up s are temporally distributed, that is, s(s) does not contain the stretches of time that lie in between the temporal traces of those salient parts. We now assume that the temporal trace of a complex situation s is included in the temporal trace of another complex situation s1 if the smallest (discontinuous) interval that includes the temporal traces of the salient parts of s is included in the smallest (discontinuous) interval that includes the temporal traces of all salient parts of s1. At this point, it becomes relevant that the interval denoting the temporal trace of a complex situation is understood to be discontinuous if the temporal traces of the salient parts this complex situation consists of are temporally distributed: this has the consequence that for each salient part s2 of a complex situation s such that the temporal trace of s is included within the temporal trace of a complex situation s1, there has to be a corresponding salient part s3 of s1 such that the temporal trace of s2 is included in the temporal trace of s3. This is given more formally in (44): (44) s(s) 4 s(s1) :¼ "s2[s2 2 Salpart(s) / ds3 [s3 2 Salpart(s1) ^ s(s2) 4 s(s3)]] where s and s1 are both complex situations. Recall that in the sentences under discussion the restrictor situation is specified as being a situation that contains the sum individual denoted by the definite DP. By hypothesis, each salient part of the restrictor


situation consists of do not have to coincide: the talks given at a conference are normally distributed over the whole duration of the conference. The analysis developed in section 3.3 enables us to formally implement these assumptions: As the restrictor situation is temporally located within the running time of the relative clause situation, and as both situations are complex situations consisting of salient parts, it is natural to assume that the salient parts of the restrictor situation are located within the salient parts of the relative clause situation. That is, for each salient part s1 of the former, there has to be a salient part s2 of the latter such that the running time of s1 is contained within the running time of s2. This is based on the following consideration: The easiest way to define the temporal trace of a complex situation s is to define it as the smallest (possibly discontinuous) interval that includes the temporal traces of all salient parts of s. This is given more formally in (43):


situation has to be a situation that contains an atomic part of this sum individual.13 Moreover, since—also by hypothesis—the running times of all salient parts of the relative clause situation coincide temporally, all salient parts of the restrictor situation coincide temporally, too. We now need to make the constraint against situations with overlapping running times part of the denotation of the respective Q-adverbs, in order to derive the oddity of examples like (42). This is done in (45), where the condition that the salient parts of the restrictor situation may not have overlapping running times is added to the denotation of usually-2.14 Example (45) is thus the final denotation we assume for usually-2.

Consider now the interpretation we derive for (42) [which is repeated here as (46a)] according to our assumptions: (46) a. *The people who listened to Peter’s lecture at the conference last summer were usually JapaNESE. b. ds [in(r{x: human(x)(w0) ^ ds1[DIST(listen(Psl)(x)(s1) ^ s(s1) < t0) ^ at(c. l. s.) (s1)]})(s) ^ s(s) 4 s(r{s#: dx[human(x)(w0) ^ listen(P.s l.)(x)(s#) ^ at(c.l.s)(s#)] }) ^ "s3, s4 2 Salpart(s)[s3 6¼ s4 / :[s(s3) o s(s4)]] ^ ^ ds2 < s [js2j > ½ jsj^ DIST(Japanese(r{x: human(x)(s2) ^ . . . })(s2) ^ s(s2) < t0)]] The unacceptability of (46a) is an automatic consequence of (45) above: because it is highly salient, the temporal trace of the restrictor situation s, which is a situation that includes all the people who listened to Peter’s talk at the conference last summer, has to be included in the temporal trace of 13 Now note that there is no way to define a proper part of a situation that is just characterized by its containing a certain individual. Such a situation would always comprise the entire interval within which it is located. Therefore, if no other interval is made available by the context, the most natural assumption is that the respective situation comprises the whole lifetime of the respective individual. 14 This is probably too strong, as a sentence like (38) intuitively does not seem to require that there is no temporal overlap at all between the lectures mentioned there in order to be acceptable. Rather, what seems to be required is the condition that for a substantial proportion of the respective situations, it is the case that their temporal traces do not overlap. We have, however, employed the condition in (45) in order to keep things simpler as this is sufficient for our present purposes.


(45) [[usually-2C]]g ¼ kP<s,t>. ds [g(C)(s) ^ s(s) 4 s(r{s#: Q(s#)}) ^ "s2, s3 2 Salpart(s) [s2 6¼ s3 / :[s(s2) o s(s3)]] ^ ds1< s [js1j > ½ jsj^ P(s1)]] where o means overlaps.


(47) a. Yesterday, a lot of people attended Mary’s concert. #They were usually well DRESSED. b. *Peter’s cousins are usually CaNAdian. Let us end this section by citing two additional examples that support our analysis. Example (48) is only acceptable if it is interpreted in a specific way, namely if one is willing to assume that Peter did not meet all of his colleagues at the same time, but during the course of the afternoon: 15 Alternatively, it would also be possible to make the ban against overlapping situations a presupposition of frequency adverbs like usually. The oddity of examples like (46a) would then be due to a presupposition violation. The problem with such an account is, however, that the information that would lead to the presupposition violation is derived on the basis of a pragmatic process that determines a value for the free interval variable, which is also part of the meaning of the Q-adverb. The standard view on presuppositions is, however, that their satisfaction is a precondition for the computation of the truth conditions of the respective expression, that is, they would have to be checked before the computation of the truth conditional content starts, not afterwards, as the account under discussion would entail. We therefore stick to the alternative pursued in the main text for our present purposes.


the relative clause situation s1, which is the situation of these people listening to Peter’s talk. This has the consequence that for each salient part of s that includes one of these people there has to be a corresponding listening situation which is a salient part of s1, such that the temporal trace of the first is located within the temporal trace of the second (see the discussion above). Therefore, if the temporal traces of all salient parts of s1 overlap considerably—as it is the case with people listening to a talk from start to finish—it will also necessarily be the case that all salient parts of s overlap considerably. This, however, makes the sentence necessarily contradictory as it is explicitly stated that the running times of the salient parts of s do not overlap.15 In the case of examples like (38), in contrast, the fact that the salient parts of the restrictor situation are located within the running times of the salient parts of the relative clause situation does not necessarily lead to a contradiction: it is quite natural to assume that the single lectures given during the conference mentioned do not temporally coincide (recall that the sentence only receives a QV reading under the condition that this is taken for granted). We now have an account that not only explains the oddity of examples like (46a), where the internal constitution of the relative clause situation directly determines the acceptability of the matrix sentence but also of examples like (33c) [repeated here as (47a)] and (35b) [repeated here as (47b)]: in each case, the sentences are necessarily contradictory because it is clear that the salient parts of the restrictor situation have overlapping running times—either because of salient linguistic information or because of world knowledge.


(48) The people Peter met yesterday afternoon were usually colleagues of his. Finally, as noted by Nakanishi & Romero (2004), sentence (49a) below [their example (52a)] is unacceptable, while the minimally varying (49b), where usually has been replaced by for the most part is fine. In this case, too, it is natural to assume that the unacceptability of the variant with usually is due to the fact that all salient parts of the relative clause situation necessarily coincide temporally—due to the progressive aspect on the verb.16

4 CONCLUSION AND OUTLOOK In this paper, we have discussed QVEs in sentences containing plural definites. We have argued that frequency adverbs like usually unambiguously quantify over situations—either over the elements of a set of situations (in the case of sentences with singular indefinites) or over the salient parts of a complex situation (in the case of sentences with plural definites). This conclusion was based on the fact that sentences containing frequency adverbs behave differently from sentences containing quantificational DPs and adverbs of quantity with respect to two newly observed constraints: the tense agreement constraint and the coincidence constraint. While sentences of the former type have to obey these constraints in order to be fully acceptable, this is not the case for sentences of the latter type. We have argued that both constraints concern the temporal location of situations and that the contrast between sentences containing frequency adverbs, on the one hand, and sentences containing quantificational DPs and adverbs of quantity, on the other, shows that while in the former quantification over situations is always involved, quantification over individuals is an option in the latter. 16 In their brief discussion, Nakanishi & Romero (2004) speculate that the unacceptability of (49a) is due to the fact that Q-adverbs like usually may only quantify over generic situations that satisfy the respective predicate. This is based on the observation that (i) below, where the relative clause verb is marked for generic tense, is fine.

(i) The students who sit over there are usually smart [Nakanishi & Romero (2004): example (51a)]. This explanation, however, does not cover the acceptable cases discussed above, where surely no generic tense is involved. Note furthermore that example (i) is presumably best analyzed in the way discussed in section 2.2, that is, as a case where the denotation of the definite DP varies with the situations quantified over.


(49) a. *The students sitting over there now are usually smart. b. For the most part, the students sitting over there now are smart.


(50) a. Most of the boys lifted the piano together. b. Most of the boys built a raft together. c. #For the most part, the boys lifted the piano together. d. #For the most part, the boys built a raft together. From this, Nakanishi and Romero conclude that the quantificational domains differ in the two cases and that quantification over (the atomic parts of sum) eventualities is directly associated with distributivity, while in the case of quantification over individuals there is more flexibility. There is thus a tension between the empirical facts supporting our assumption that adverbs of quantity and quantificational DPs can both quantify over individuals and the empirical facts supporting the assumption by Nakanishi and Romero that they have different quantificational domains. In principle, this tension can be resolved by taking the tense agreement constraint and the coincidence constraint to be operative only with frequency adverbs and not assuming that these constraints follow from the need to individuate the situations quantified over on the basis of their temporal location. Both analyses could then coexist peacefully as the fact that sentences with adverbs of quantity neither obey the coincidence constraint nor the tense agreement constraint would no longer show that no quantification over situations/eventualities is involved. The fact that sentences combining adverbs of quantity and plural definites behave differently from sentences with corresponding quantificational DPs with


As already mentioned, the assumption that adverbs of quantity do not have to quantify over (the salient parts of complex) situations is at odds with the assumptions by Nakanishi & Romero (2004), on whose analysis of sentences containing plural definites and adverbs of quantity like for the most part our own analysis of sentences containing plural definites and frequency adverbs like usually is based. The assumption by Nakanishi and Romero that QV readings of sentences with plural definites come about as indirect effects of quantification over (the salient parts of sum) eventualities rather than as direct effects of quantification over (the atomic parts of sum) individuals is based on the following observation: sentences combining plural definites and the adverb of quantity for the most part behave differently from sentences containing quantificational DPs headed by most with respect to the availability of distributive readings. More concretely, while the latter allow collective readings with accomplishment and activity verbs (but not with states and achievements), as shown in (50a, b) below, the former never allow collective readings, as shown in (50c, d).


Acknowledgements The authors’ names appear in alphabetical order. Parts of this paper have been presented at Sinn und Bedeutung 9 in Nijmegen and at the Semantics Circle at ZAS (Berlin, Germany). We would like to thank the audiences of both events as well as Sigrid Beck, Andreas Haida, Christian Krause, Manfred Krifka, Peter Staudacher and Malte Zimmermann for discussion, comments and technical help. Furthermore, we would like to thank two anonymous reviewers for their valuable comments and helpful suggestions. This research was partly funded by the Deutsche Forschungsgemeinschaft as part of the Sonderforschungsbereich 632 (Information Structure).

STEFAN HINTERWIMMER Humboldt-Universita¨t zu Berlin SFB 632 ‘‘Information Structure’’ Unter den Linden 6 10099 Berlin Germany e-mail: [email protected]


respect to the availability of distributive readings would thus not show that the quantificational domains differ, but rather that the precise lexical semantics is different in the two cases. However, since it is very plausible that the tense agreement constraint as well as the coincidence constraint follow from the need to individuate the situations quantified over on the basis of their temporal location, we consider this strategy at least worth pursuing. This would mean, however, that the analysis of for the most part by Nakanishi and Romero cannot be maintained, and the facts discussed by them as support for their analysis have to be explained in some other way. In Endriss and Hinterwimmer (in preparation), we therefore argue (based on additional data) that adverbs of quantity like for the most part are topic-sensitive quantifiers that can take objects of any kind as their arguments, as long as these objects can naturally be decomposed into parts (cf. Lahiri 2002). Furthermore, we show that by building distributivity directly into the meaning of these quantifiers, the facts discussed by Nakanishi and Romero can be explained without having to assume that adverbs of quantity necessarily quantify over situations/events, thus allowing these quantifiers to operate directly over the atomic parts of plural individuals in sentences with plural definites.


REFERENCES Endriss, C & S. Hinterwimmer. (2007). ‘Tense and adverbial quantification’. In J. Doelling and T. Heyde-Zybatow (eds.), Event Structures in Linguistic Form and Interpretation. Mouton de Gruyter. Berlin, Germany. 389–412. Graff, D. (2001). ‘Descriptions as predicates’. Philosophical Studies 102:1–42. Graff, D. (2006). Descriptions with Adverbs of Quantification. Draft, Princeton University. Princeton, NJ. Groenendijk, J & M. Stokhof. (1990). ‘Dynamic predicate logic’. Linguistics and Philosophy 14:39–100. Heim, I. (1982). The Semantics of Definite and Indefinite Noun Phrases. Ph.D. thesis, University of Massachusettes. Amherst, MA. Herburger, E. (2000). What Counts. Focus and Quantification. MIT Press. Cambridge, MA. Hinterwimmer, S. (2008). Q-Adverbs as Selective Binders: The Quantificational Variability of Free Relatives and Definite DPs (revised version of the homonymous Ph.D. thesis). Mouton de Gruyter (Interface Explorations). Berlin, Germany. Hinterwimmer, S. (2006). ‘The interpretaion of universally quantified DPs and singular definites in adverbially quantified sentences’. In Proceedings of the 25th West Coast Conference on Formal Linguistics (WCCFL 25) 195–203. Kamp, H. (1981). ‘A theory of truth and semantic representation’. In J. Groenendijk, T. Janssen, and M. Stokhof (eds.), Formal Methods in the Study of Language. Mathematisch Centrum, University of Amsterdam. Amsterdam, The Netherlands. 277–322. Kratzer, A. (1989). ‘An investigation of the lumps of thought’. Linguistics and Philosophy 12:607–653.


Beaver, D & B. Clark. (2003). ‘ Always and Only: why not all focus-sensitive operators are alike’. Natural Language Semantics 11:323–362. Berman, S. (1987). ‘Situation-based semantics for adverbs of quantification’. In J. Blevins and A. Vainikka (eds.), University of Massachusetts Occasional Papers 12. GLSA, University of Massachusetts. Amherst, MA. 45–68. Berman, S. (1991). The Semantics of Open Sentences. Ph.D. thesis, University of Massachusetts. Amherst, MA. Bu¨ring, D. (2004). ‘Crossover situations’. Natural Language Semantics 12:23–62. Chierchia, G. (1995a). ‘Individual level predicates as inherent generics’. In G. Carlson and F. J. Pelletier (eds.), The Generic Book. University of Chicago Press. Chicago, IL. Chierchia, G. (1995b). Dynamics of Meaning. University of Chicago Press. Chicago, IL. 176–223. Chomsky, N. (1995). The Minimalist Program. MIT Press. Cambridge, MA. de Swart, H. (1993). Adverbs of Quantification: A Generalized Quantifier Approach.. Garland. New York. Diesing, M. (1992). Indefinites. MIT Press. Cambridge, MA. Elbourne, P. (2001). ‘E-type anaphora as NP-deletion’. Natural Language Semantics 9:241–288. Elbourne, P. (2005). Situations and Individuals. MIT Press. Cambridge, MA. Endriss, C & S. Hinterwimmer. (2006). ‘Topic interpretation in determiner and adverbial quantification’. In C. Davis, A.R. Deal, and Y. Zabbal (eds.), The Proceedings of the 36th Conference of the North Eastern Linguistic Society (NELS 36). GLSA, University of Massachusetts. Amherst, MA. 241–252.

Cornelia Ebert and Stefan Hinterwimmer 175 Musan, R. (1997). ‘Tense, predicates and life-time effects’. Natural Language Semantics 5:271–301. Nakanishi, K & M. Romero. (2004). ‘Two constructions with Most and their semantic properties. In K. Moulton and M. Wolf (eds.), Proceedings of NELS 34.GLSA. University of Massachusetts. Amherst, MA. 453–468. Parsons, T. (1990). Events in the Semantics of English. MIT Press. Cambridge, MA. Partee, B. (1995). ‘Quantificational structures and compositionality’. In A. Kratzer, E. Bach, E. Jelinek, and B. Partee (eds.), Quantification in Natural Languages. Kluwer. Dordrecht, The Netherlands. 541–602. Percus, O. (2000). ‘Constraints on some other variables in syntax’. Natural Language Semantics 8:173–229. Rooth, M. (1985). ‘Association with focus’. Ph.D. thesis, University of Massachusetts. Amherst, MA. Rooth, M. (1995). ‘Indefinites, adverbs of quantification and focus semantics’. In G. Carlson and F.J. Pelletier (eds.), The Generic Book. University of Chicago Press. Chicago, IL. 265–299. Schein, B. (1993). Plurals and Events. MIT Press. Cambridge, MA. Selkirk, E. (1995). ‘Sentence prosody: Intonation, stress, and phrasing’. In J.A. Goldsmith (ed.), The Handbook of Phonological Theory. Blackwell. London. 550–569. Sharvy, R. (1980). ‘A more general theory of definite descriptions’. The Philosophical Review 89:607–624. Staudacher, P. (1987). ‘Zur Semantik indefiniter Nominalphrasen’. In B. Asbach-Schnitker and J. Roggenhofer (eds.), Neuere Forschungen zur Wortbildung und Historiographie in der Linguistik. Narr Verlag. Tu¨bingen, Germany. 239–258.


Kratzer, A. (1995). ‘Stage-level predicates and individual-level predicates’. In G. Carlson and F. J. Pelletier (eds.), The Generic Book. University of Chicago Press. Chicago, IL. 125–175. Krifka, M. (1995). ‘Focus and the interpretation of generic sentences’. In G. Carlson and F. J. Pelletier (eds.), The Generic Book. University of Chicago Press. Chicago, IL. 238–264. Krifka, M. (2001). ‘Non-novel indefinites in adverbial quantification’. In C. Condoravdi and G. Renardel de Lavelette (eds.), Logical Perspectives on Language and Information. CSLI Publications. Stanford, CA. 1–40. Lahiri, U. (2002). Questions and Answers in Embedded Contexts. Oxford University Press. Oxford. Landman, F. (2000). Events and Plurality. Kluwer. Dordrecht, The Netherlands. Lasersohn, P. (1995). Plurality, Conjunction and Events. Kluwer. Dordrecht, The Netherlands. Lasersohn, P. (1998). ‘Generalized distributivity Operators’. Linguistics and Philosophy 21:83–93. Lenci, A & P. M. Bertinetto. (1999). ‘Aspect, adverbs, and events: habituality vs. perfectivity’. In F. Pianesi, J. Higginbotham, and A.C. Varzi (eds.), Speaking of Events. Oxford University Press. Oxford. 245–287. Link, G. (1983). ‘The logical analysis of plurals and mass terms: A latticetheoretical approach’. In R. Baüerle, C. Schwarze, and A. von Stechow (eds.), Meaning, Use and Interpretation of Language. de Gruyter. Berlin. Germany. 302–323. Link, G. (1987). ‘Generalized quantifiers and plurals’. In P. Ga¨rdenfors (ed.), Generalized Quantifiers. Linguistic and Logical Approaches. Reidel. Dordrecht, The Netherlands. 151–180.

176 Quantificational Variability Effects with Plural Definites von Fintel, K. (1994). Restrictions on Quantifier Domains. Ph.D. thesis, University of Massachusetts. Amherst, MA. von Fintel, K. (2004). ‘A minimal theory of adverbial quantification’. In H. Kamp and B. Partee (eds.), Context-Dependence in the Analysis of Linguistic Meaning. Elsevier. Oxford. 137–175.

Zimmermann, M. (2003). ‘Pluractionality and complex quantifier formation’. Natural Language Semantics 11:249–287. First version received: 25.05.2006 Second version received: 02.2008 Accepted: 10.12.2009


Journal of Semantics 27: 177–206 doi:10.1093/jos/ffq002 Advance Access publication March 3, 2010

A Higher Order Extensional Framework for the Progressive KA´ROLY VARASDI Applied Logic Laboratory, Budapest

This paper proposes an extensional event-based framework for the progressive aspect. The proposal differs from that of Parsons (1990) in that it does not have incomplete events in its base ontology but constructs ‘proxies’ for such events through certain sets of properties of complete events.

1 INTRODUCTION One of the puzzling features of natural language is its capacity to refer to unfinished events through the use of the progressive aspect. Although the introduction of event variables into the semantic representation of verbal elements, initiated by Davidson (1967), has proved fruitful in several areas of formal semantic research [see, e.g. Pianesi and Varzi (2000) for an overview], the semantics of the progressive construction has turned out to be difficult to analyze within the extensional framework suggested by Davidson and his followers, primarily because of the phenomenon known as the ‘imperfective paradox’ in the literature. According to a widely accepted view, the imperfective paradox and, consequently, the progressive aspect require a modal treatment. The goal of the present paper is to challenge this view by outlining an extensional framework for the progressive in which the relevant issues can be tackled with at least as much explanatory power as in the various modal approaches proposed in the literature. The paper consists of two main parts. In the first, largely historical, part in section 2, we discuss two ‘paradoxes’ that motivate the theory explained in the second part: the imperfective paradox, which we have already mentioned, and the multiple-choice paradox, which has been brought into the foreground recently by Bonomi (1999). In the second part of the paper, beginning in section 3, we outline an extensional event-based framework in which both of the ‘paradoxes’ The Author 2010. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected].


Abstract

178 An Extensional Framework for the Progressive

2 TWO ‘PARADOXES’ ABOUT THE PROGRESSIVE

2.1 The imperfective paradox Put briefly, the imperfective paradox is the observation that whereas the truth of the progressive of activities implies that their perfective is also true, the progressive of accomplishments neither implies the simultaneous truth of the perfective nor does it imply that the perfective will ever be true. The classic presentation of the imperfective paradox is due to David Dowty [although the observation goes back to at least Kenny (1963)]. Dowty (1977) writes that ‘the inference from (1) to (2) fails’, while ‘the inference from (3) to (4) is intuitively valid’: (1) (2) (3) (4)

John John John John

was drawing a circle. drew a circle. was pushing a cart. pushed a cart.

He then continues: The meaning of an accomplishment verb phrase invariably involves the coming about of a particular state of affairs. [. . .] I maintain that it is impossible to give an adequate semantic analysis of accomplishment verb phrases without providing for the entailment that such a result-state comes about. Yet it is just this entailment that such a result-state comes


discussed in the first part are resolved. From an ontological point of view, the framework is more parsimonious than those of Parsons (1989, 1990) because it does not contain ‘incomplete events’; instead, such events are treated as hypostatized entities characterizable by certain second-order properties of (complete) events. In section 4, we present a detailed illustration of the general approach developed in section 3. In section 5, we briefly touch upon three related issues: section 5.1 discusses some predictions of the theory concerning Vendlerian classes other than accomplishments; section 5.2 explains why verbs of creation pose no particular problem to the theory; and finally, in section 5.3, we will see how the theory gets unexpected further support from an observation concerning events that are impossible to accomplish. For the most part of the paper, we concentrate on accomplishments because accomplishments present the greatest challenge to any theory of the progressive. Also, our target language is English, simply because it is this language that has been most extensively researched in formal aspectology.

Ka´roly Varasdi 179

about which fails when the accomplishment verb phrase appears in the progressive tense. In other words, the problem is to give an account of how (1) entails that John was engaged in bringing-a-circle-intoexistence activity but does not entail that he brought a circle into existence. This is the ‘‘imperfective paradox’’. (Dowty 1977: 261)

As I pointed out earlier, however, one should be able to conclude from (1) no more than that the existence of a circle was (or will be) a possible outcome of John’s activity. This observation suggests that the progressive is not simply a temporal operator, but a kind of mixed modal-temporal operator. (Dowty 1977: 270)

2.2 Dowty’s modal solutions The fact that the truth of a progressive sentence does not entail the actual occurrence of the culmination is reminiscent of the pattern that characterizes some modal operators, such as possibility: eu does not entail u (although they are compatible). Indeed, Dowty (1977)’s definition of the progressive, in which the diamond quantifies over the historical alternatives accessible from the actual world at the end point of the evaluation interval, exploits precisely this analogy. However, Dowty soon became dissatisfied with the definition in Dowty (1977) and changed it radically in Dowty (1979). The reason plays a key role in the discussion later, so let us quote him at some length again: As it stands, [the definition of the progressive given in Dowty (1977)] has an undesirable consequence called to my attention by Richmond Thomason. Suppose a coin is flipped but not yet landed. (To make the illustration clear, let us add that the coin has not been tampered with and nothing else about the situation predetermines how it will land.) Clearly, we would want to say in this situation that there is a possible world just like the actual world up to the present in which the coin comes up heads, as well as one in which it comes up tails. Hence [the definition of the progressive given in Dowty (1977)] requires that the sentences The coin is coming up heads and the coin is coming up tails should both be true, but this is a counterintuitive result. (Dowty 1979: 147)


Dowty also points out that the inference fails irrespective of the particular tense chosen because ‘to say that John was, is, or will be drawing a circle is not to commit oneself to the coming into existence of (a representation of) a circle at any time’. The imperfective paradox therefore suggests, according to Dowty, that the semantics of the progressive operator involves modality:


2.3 The multiple-choice paradox In a highly influential article, Landman (1992) suggested an alternative to Dowty’s inertia world approach. Landman’s proposal is an event-based modal theory that draws upon the concept of the counterfactual


Although Thomason’s puzzle might seem a minor problem at first sight, it touches upon a central issue. The correct use of the progressive requires the identification of events that are only partially realized, and the coin-flipping case is a particularly revelatory illustration of the problems posed by the classification of such events. These problems are related to the openness of the future, which usually offers a multitude of possible ways to complete an unfinished event. In Thomason’s example, this multitude is reduced to the bare minimum of two possibilities but, as we will see later, discussing Bonomi’s multiple-choice paradox, it highlights the critical issues even in this simplified form. In order to cope with Thomason’s puzzle, Dowty changed the definition of the progressive operator so that it require the truth of the completed accomplishment not just in some historical alternative of the actual world but, rather, in all the inertia worlds assigned to the evaluation index, where inertia worlds are ‘to be thought of as worlds which are exactly like the given world up to the time in question and in which the future course of events after this time develops in ways most compatible with the past course of events’ (Dowty 1979: 148). The theory modified in this way can solve the coin-flipping problem, claims Dowty, because neither will the coin come up heads nor will it come up tails in all the inertia worlds associated to the evaluation index. Since its publication in 1979, Dowty’s theory has met with several criticisms (see, e.g. Vlach 1981; Lascarides 1988, 1992; Parsons 1990; Kearns 1991; Asher 1992; Landman 1992; Glasbey 1996; Gendler Szabo´ 2004; Higginbotham 2004), most of which have expressed dissatisfaction with the suggested concept of inertia worlds. In response to the criticisms, Portner (1998) has proposed an explication of the notion within the modal framework of Kratzer (1977, 1981, 1991), while recently Lambalgen & Hamm (2005) and Fernando (2008) have suggested that inertia worlds should be defined in terms of fluents borrowed from situation calculus (McCarthy & Hayes 1969) and its variants. We will not discuss the criticisms or the various definitions of inertia worlds that can be found in the literature. The goal of this paper is to suggest an extensional alternative and show that the issues raised by Thomason’s challenge and the imperfective paradox can be addressed without reference to the controversial notion of inertia worlds.


[t]he idea is that you follow [the event] e in our world: if its continuation stops, you follow it in the closest world where it does not stop, if that world is a reasonable option for e in w; if the continuation stops in that world, you go to the closest world again, if it’s reasonable, and you continue until either in some world it doesn’t stop (and then you stay in that world) or, the more normal case, you reach a point where going to the closest world is no longer reasonable and you stop there. (Landman 1992: 27) The progressive is true according to Landman if there is a continuation branch constructed by the above procedure that starts at the actual world


continuations of events that break off without culminating in the actual world. The basic idea of the theory is this: if a telic event breaks off without culminating, then there must be something which caused the interruption; if this cause had not interfered with the event, the event would have continued, which is equivalent to saying that it does continue in the closest counterfactual alternative in which this particular cause of interruption is absent. If the event gets interrupted there as well, we move to the next counterfactual alternative where the cause of interruption is absent. In this way, by always moving to counterfactual alternatives, we can keep the event going on until it stops because it finally culminates. This is, however, obviously too weak: since the culmination can always be reached by repeating the counterfactual step described above, the strategy, if not constrained in some substantial way, may predict all progressives to be true. Landman avoids this unwanted consequence by introducing the notions of event stages and the reasonability of an event stage growing into a more developed stage. According to Landman’s explanation, the stage-of relation is a partial ordering on the set of events like the part-of relation, but they are different relations (although the stages of an event are also parts of that event). An event is a stage of another event if the latter can be seen as a more developed version of the former, which is not required of parts in general. The counterfactual continuation of an interrupted event can be identified in terms of the stage-of relation: the continuation has the interrupted event as a stage, not simply as a part. As for reasonability, what is relevant here, according to Landman, is whether the process is the kind which is normally ‘reasonably’ within the agent’s capacity to complete, that is, the crucial factor is the agent’s inherent capacity to bring the process to culmination, possibly in counterfactual circumstances. We can test this capacity by performing iterated thought experiments to see if it is reasonable to assume that the agent could indeed bring the process to culmination. In Landman’s words:


(5) The avalanche was descending to a valley populated by chamois when it was destroyed by a special cannon, none of the sentences (6), (7) or (8) is true. (6) The avalanche was descending to valley A when it was destroyed by a special cannon. (7) The avalanche was descending to valley B when it was destroyed by a special cannon. (8) There is a valley x populated by chamois such that the avalanche was descending to x when it was destroyed by a special cannon. To see why this scenario presents a problem for Landman, let us consider sentence (5). On Landman’s account, for sentence (5) to be true, the continuation branch must end at a world where the avalanche falls into valley A or valley B. Let us assume that the continuation branch ends at a world in which the avalanche falls into valley A. But in this case, there is a continuation branch that starts at the present world and ends at a world in


and ends at a world of culmination. Since Landman treats the progressive as a sophisticated possibility operator, in spite of all the other important differences between the two frameworks, his theory is akin to the theory proposed in Dowty (1977). While Dowty (1977) applies a simple ‘future possibility’ operator, Landman (1992) interprets the relevant type of possibility ‘constructively’, drawing on the truth conditions of the counterfactual conditional proposed in Stalnaker (1968). But if Landman’s theory belongs together with Dowty’s early attempt with respect to its logical structure, we expect that it faces similar problems as Dowty’s proposal. And this is, indeed, the case. Bonomi (1999) presents a problem for Landman that he calls ‘the multiple-choice paradox’, which is similar to Thomason’s coin-flipping challenge to Dowty (1977). Bonomi describes two scenarios, that of a traveling music lover who has not yet made up his mind as to which of three particular cities he should go to and that of a falling avalanche threatening two valleys. We are going to focus on the case of the avalanche because that example does not involve any reference to the intentions of an agent. Consider an avalanche which normally descends to a gorge and can run only in two distinct directions with equal probabilities afterwards: either it falls into valley A or it falls into valley B. On a particular occasion, because both valleys were temporally populated by chamois, the avalanche was destroyed with a special cannon right at the point where it would otherwise have turned into one of the valleys (Bonomi 1999: 183). In this case, although sentence (5) is true,


3 AN EXTENSIONAL FRAMEWORK

3.1 Ontology We use the generic term eventuality, introduced by Bach (1986), as a cover term to refer to event-like entities in a general sense. Sentence radicals (i.e. sentences devoid of aspectual and tense markers) express


which the avalanche falls into valley A, which makes sentence (6) true as well. However, this is a false prediction since sentence (6) is not true. Bonomi’s argument only exploits the logical structure of Landman’s theory without making an appeal to any of the informal notions of the theory. The theory in Landman (1992) is unable to handle Bonomi’s counterexample for the same reason Dowty (1977) was in trouble with Thomason’s—both theories define the progressive as a possibility operator; but the progressive does not interact with disjunctions in the same way as possibility does: most importantly, the progressive does not ‘distribute over’ disjunctions. Incidentally, the multiple-choice paradox demonstrates nicely that the problem of the opacity of the progressive construction is not confined to verbs of creation in the progressive (although verbs of creation provide a particularly conspicuous illustration of the phenomenon). As shown by the falsity of sentence (8), the lack of existential exportation is intimately related to the semantics of the progressive itself, not to that of verbs of creation per se: in spite of the fact that in Bonomi’s example, the existential quantifier quantifies over existing physical entities, the exportation of the quantifier is definitely blocked. Dowty (1979) proposed to meet the challenge by exchanging the possibility operator for a necessity operator. Necessity interacts with disjunctions in the desired way because it does not license the inference to the disjuncts. Basically, this is Bonomi’s strategy, too, couched within an event-based modal framework: he posits that the progressive universally quantifies over a contextually constrained ‘stereotypical’ subset of possible event development branches, and a progressive sentence is true if all these branches can develop into a culminated event of the required type. Bonomi’s notion of stereotypical frames and contexts of concomitant facts can be seen as an attempt to flesh out Dowty’s notion of inertia worlds by incorporating Landman’s observations into the picture. Again, as in the case of inertia worlds, we do not discuss the possible problems that Bonomi’s theory, especially the notion of stereotypical frames, raises, but argue in the rest of the paper that the progressive can be analyzed without appealing to such auxiliary notions.


1 Although the distinctions discussed here and below, strictly speaking, apply to properties of eventualities, for the sake of brevity, we will often refer to them as if it were eventualities themselves that had these characteristics, and talk about, for example, ‘telic eventualities’ instead of the correct ‘eventualities falling under a telic eventuality property’. 2 Sometimes this claim is qualified in the case of activities by the phrase ‘down to minimal parts’, see, for example, Rothstein (2004: 18). This hypothesis, already present in Taylor (1977) and defended at length in Dowty (1979: 166–8), is strongly criticized, along with Dowty’s argument for it, in Kearns (1991: 118–21). Since it is beyond the scope of the paper to settle this complex issue, we remain neutral on the existence of smallest parts in the case of atelics in this paper, but formulate our theory so that it is compatible with the ‘minimal parts’ hypothesis.


properties of eventualities, and these properties can, in turn, be further categorized by various metaproperties such as those introduced by Vendler (1967) into accomplishments, achievements, activities and states.1 In the bulk of the paper, we will concentrate on accomplishments. Accomplishments, together with achievements, are telic, but accomplishments, as opposed to achievements, are protracted (noninstantaneous). The remaining Vendlerian categories, activities and states, are atelic. Telic eventualities, which we will often refer to simply as events, have a set of associated conditions (a telos) that must be fulfilled or attained for the eventuality to qualify as finished. The moment of attaining the telos is a moment beyond which the eventuality cannot continue to develop because at that moment it becomes a temporally fully actualized token. As opposed to telic eventualities, atelic eventualities do not have such conditions. As a consequence, any protracted telic eventuality (a Vendlerian accomplishment) may cease to continue in either of two ways: becoming finished by attaining its telos or breaking off unfinished. In contrast, atelic eventualities, that is, states and activities, break off simpliciter, because the question whether they have attained their telos or not does not apply in their case for lack of a telos. The existence or lack of a telos is also relevant to a couple of related metaproperties, such as quantization and (weak or strong) homogeneity (Rothstein 2004: 10). An eventuality property is quantized if, whenever it is true of an eventuality, it is not true of any of the proper subeventualities thereof. As regards homogeneity, an eventuality property is weakly homogeneous if, whenever it is true of an eventuality token, it is true of some of its proper parts, and it is strongly homogeneous if, whenever it is true of a token, it is true of all the proper parts thereof. Telic eventualities are usually quantized and never (strongly) homogeneous, while atelic eventualities are strongly—and, therefore, also weakly—homogeneous.2


3

A property P is said to be exemplified by an eventuality e if e 2 P.


Turning now to the formal model, the universe of discourse of our model M is partitioned into three non-empty domains: the set of objects O, the set of eventualities E and the set of moments of time T with the usual linear ordering on it. We refer to the elements of O and E as tokens and to the sets of tokens as properties or types. In the majority of the paper, we will be concerned with eventuality tokens and eventuality types. Intuitively, eventuality tokens are concrete, non-repeatable, spatiotemporally located happenings or states, which can be described by various sentence radicals. For example, suppose that Mary crossed Regent Street twice yesterday, first at 10 o’clock in the morning in one direction and then at half past 4 in the afternoon in the other direction. The particular event e1 of Mary’s crossing Regent Street that occurred at about 10 falls under the same eventuality type expressed by the sentence radical Mary cross Regent Street as the particular event e2 of Mary’s crossing Regent Street that occurred at about half past 4, although they are two non-identical individual events differing in countless minor details not specified by the sentence radical above. Sentence radicals are assumed to be translatable into lambda-terms of the formal representation language, and the resulting expressions are taken to denote a set of eventuality tokens. Thus, for example, the sentence radical Mary cross Regent Street receives as its translation the term ke cross#(Mary#, Regent-street#, e) or simply ke cross#(m, r, e), and its extension contains all and only the eventuality tokens of Mary’s (complete) crossing of Regent Street at some time or other. Not only can there be several tokens falling under the same type, one and the same token itself may fall under different types. One and the same token of Mary’s crossing Regent Street may be described, in appropriate contexts, as Mary’s crossing a street or, at an even more general level, as Mary’s moving. Since describing an eventuality token is a matter of highlighting certain features of the token while ignoring others, a particular eventuality token may exemplify3 infinitely many properties which are not equally interesting to language users, the choice of the relevant properties depending on various contextual and pragmatic factors. We will not discuss these factors here but, by treating tokens as ‘classified entities’ (or ‘entities under some description’), we simply incorporate into the theory elaborated in section 3.3 the observation that language users have a bias toward certain properties of a token, and we will represent tokens together with the types deemed interesting in a particular context.


4

Hence, the U relation is different from Landman’s stage-of relation we discussed in section 2.3: a crossing may encompass a step as a subevent, but it cannot be seen as a ‘more developed version’ thereof. 5 As one of the anonymous reviewers pointed out, this simple picture gets more complicated when we include activities and states as well. Indeed, Parsons sees activities as ‘a series or amalgam of events’ (Parsons 1990: 184), and therefore, they can also be said to culminate or hold. In contrast, states can only be said to hold and never to culminate (Parsons 1990: 21).


The set I of temporal intervals can be constructed out of the set of moments T in the usual way as the convex subsets of T. Furthermore, the model M specifies a binary relation U 4 E 3 E, the mereological part-of (or subeventuality-of) relation between eventuality tokens, and a function s : E [ O / I, the temporal trace function, which assigns every eventuality or object the time interval at which the eventuality occurs or the object exists. We put the fairly weak constraint on U that it be reflexive, transitive and antisymmetric, making ÆE,Uæ a partially ordered set (possibly, but not necessarily, a lattice). In other words, all we assume here is that the eventuality tokens in the universe are partially ordered by parthood; for example, given the set of all crossings of Regent Street by Mary and the set of all steps taken by Mary, we assume that speakers can determine if a particular step is a subevent of a particular crossing.4 Also, as is usual, we require of s that it respect U, that is, that for any e, e#2 E, eUe# imply s(e) 4 s(e#). In the ontology assumed in Parsons (1989, 1990), an accomplishment sentence radical denotes a subset of the universe of events containing both complete and incomplete tokens. Taking the example of Mary’s crossing Regent Street again, the extension of ke cross#(m, r, e) contains, beside finished crossings, those unfinished crossings of Regent Street by Mary that never reached completion for whatever reason. Parsons’s theory of the progressive aspect is directly based on the assumption that types are partitioned in this way, defining the progressive of an accomplishment to be true at a certain moment in time just in case there is an unfinished event at that particular moment that belongs to the denotation of (the translation of) the accomplishment sentence radical. To represent the difference between progressive and non-progressive accomplishment sentences in the logical form, Parsons introduces two non-logical constants, Hold and Cul, relating moments of time and eventualities. The intended meaning of the formula Hold(e, t) is that the event token e is unfinished at t, while that of Cul(e, t) is that the event token e culminates, that is, turns into a finished (completed) event at t.5 The logical form of progressive sentences contains a conjunct with the Hold operator, whereas those of non-progressive sentences contain a conjunct with the Cul operator [see Parsons (1989) and Parsons (1990) for further details].


3.2 Partiality and existence 3.2.1 Parts and wholes: a simple mereological proposal If we forget about the complications caused by the imperfective paradox for a moment, the progressive can be defined drawing on simple mereological considerations. The simple mereology-based definition below is insufficient, of course, but it will be our starting point for a subsequent generalization in section 3.3.3 which can cope with the imperfective paradox as well. Thus, let ,e (nabla e) denote the set of the 7 proper mereological parts of an eventuality e 2 E, that is, def let ,e ¼ e# 2 E e#9e ; we extend the , operator to a set of tokens 6 For instance, as Zucchi (1999) points out, since Hold is a primitive and Parsons does not say much about the conditions under which an eventuality can be said to hold at a time, the theory, as it stands, does not have much predictive power. Note, however, that trying to specify these conditions immediately brings back all the issues, now simply relegated to the ontological level, that make the semantic analysis of the progressive hard. Zucchi himself suggests making amendments along the lines of Landman (1992) but we will not discuss the details of his proposal here. [See also Verkuyl (2000) on this point.] 7 For e, e#2 E, e# is a proper part of e, denoted as e#9 e, if e#U e ^ e#6¼ e.


What is peculiar to Parsons’s system is the admittance of ‘parts’ that might not have corresponding ‘wholes’ in the ontology of the model. Parthood, then, is not a relation anymore: an element may qualify as ‘partial’ simpliciter, without there being anything it is a part of. Or, to put it more precisely, there may be an element in the ‘unfinished’ subset of an event type without there being any element in the ‘finished’ subset of the same type such that the former is a part of the latter. We will return to this important point later in section 3.3.2. It is useful to consider a reason that may have convinced Parsons to introduce this non-standard concept of parthood. Parsons could have defined the progressive of an event to be true whenever a partial realization of that event actually occurs. While such a definition would indeed assign the correct truth value to the progressive description of the event tokens that do culminate, it could not cope with those cases, witnessed by the imperfective paradox, when the progressive is true despite the fact that there is no culminated event in the universe which it is the progressive description of. This problem apparently disappears if the universe is enhanced with partial events that are not required to have a complete counterpart because they can then serve as the truth makers of such progressives. But, as is sometimes pointed out by critics of Parsons, the disappearance of the problem is illusory because the theoretical status of such eventualities raises as difficult questions as the progressive itself.6

188 An Extensional Framework for the Progressive def

Q 4 E in the expected way as ,Q ¼ [ ,e. A simple, mereologye2Q

8 Let us define ks[Q], the convex envelope of the union of the temporal traces of the elements of Q 4 E after Landman (1991: 172) as follows: for any set of moments of time X, the convex envelope C(X) of X is the set {t 2 Tjdt#, t$ 2 X : t#< t < t$}. The convex envelope of the union of a set of def intervals X is then defined as kX ¼ Cð [ XÞ. Then u is in progress relative to a moment of time t if u is in progress relative to a set of tokens Q such that sup(ks[Q]), the supremum of ks[Q], is t. 9 Howard B. Garey characterizes atelicity in the classic paper of Garey (1957) as follows: ‘Atelic verbs are those which do not have to wait for a goal for their realization, but are realized as soon as they begin’. The sense which Garey means by ‘realized’ is the sense which we mean by ‘completed’ here. 10 See footnote 2.


based attempt to define the progressive is then as follows. Definition 1 (Progressivity: a mereology-based attempt) Given an eventuality type u, u is in progress relative to a set of tokens Q 4 E, if there is an eventuality e 2 E such that ,Q @ ,e and u(e), that is, if Q is a proper partial realization of an eventuality token e of type u. Definition 1 is relativized to tokens, not times, but the link between tokens and times is easy to establish with the help of the temporal traces of the tokens in question,8 so we will adhere to the more abstract tokenoriented view exemplified in Definition 1 in the rest of the paper. A useful aspect of Definition 1 is that it suggests a way to define a related notion, that of the completeness of an eventuality type with respect to a set of tokens. As can be seen from the definition above, an eventuality type u fails to be in progress relative to Q if either there is no eventuality e 2 E of type u or it is not true of any e of type u that ,Q @ ,e, the latter condition being fulfilled in two cases: if neither ,e nor ,Q is a subset of the other, or if ,e 4 ,Q. Of these cases, we define the last one to be the case when the eventuality type is completed: Definition 2 (Completeness) An eventuality type u is completed relative to a set of tokens Q 4 E, if there is an eventuality token e 2 E such that ,e 4 ,Q and u(e). Progressivity and completeness, as defined in Definition 1 and Definition 2, exclude each other in the case of events (telic eventualities), but are (almost) equivalent in the case of atelics such as activities and states. This is due to the Janus-faced nature of atelic eventualities, namely that they are complete as soon as they begin, that is, as soon as they are in progress.9 The formal reason why this is so is that atelic eventualities, as opposed to telic ones, are homogeneous. To see this, let a be a token of the atelic type A. Then, whenever a is non-minimal in A,10 A is completed relative to fag because, owing to homogeneity, we can always choose an eventuality a# such that


3.2.2 Atemporal existence versus being present Before suggesting an answer to this question, let us introduce an important distinction between atemporal and temporal points of view. The single atemporal point of view, sometimes called ‘God’s eye view’, looks at the universe ‘from the outside’, ignoring the flow of time. Seen from the atemporal stance, particular events or objects either exist or do not exist, and there are no ‘incompletely realized’ objects or events ‘in development’ in the universe. As opposed to the atemporal point of view, temporal points of view are always relative to a given moment in time’s flow. This is the inescapable stance of temporally situated cognitive agents, like human beings, whose perception of an event is restricted by the particular position they occupy in time. For such a time-bound agent, events seem to ‘begin’, ‘unfold in time’ and then ‘get finished’ or ‘break off unfinished’; objects ‘come into being’, ‘are present’ and then ‘perish’, as the agent’s temporal points of view occupy consecutive positions in time. Seen from a temporal point of view, the question of which objects ‘exist’ amounts to the question of which objects are present at that point of view (i.e. have an overlapping temporal trace with that


a#9 a—which implies that ,a# 4 ,fag—and A(a#). On the other hand, whenever a is non-maximal in A, that is, whenever there is a token a$ 2 A such that a9 a$, A is in progress relative to fag because ,fag @ ,a$ and A(a$). This peculiarity of atelic eventualities will be taken into account in our final definition of the progressive in section 3.3.3. (Although the main topic of this paper is telic eventualities, especially accomplishments, we will briefly return to the question of atelic eventualities in section 5.1.) As we have noted above, the simple mereology-based proposal for the progressive in Definition 1 is inadequate in the case of ‘abandoned’ events because then there is no u–token in E which the elements of Q constitute a part of. The failure of the proposal can be traced back to the condition that parthood is a binary relation on the universe of eventualities. As we have seen, Parsons’s extensional theory gives up this requirement to be able to account for the progressive of events that fail to culminate in the actual world. Modal theories, however, can comply with it because the domain of eventualities assumed by such theories may contain ‘counterfactual wholes’ for events that contingently fail to get accomplished in our world. The question that we need to address now is the following: is there a way to define the progressive in an extensional framework without sacrificing the relational nature of parthood?


(9) Mary’s crossing of Regent Street failed to get completed. Also, sentence (9) can be continued felicitously with (10) In fact, it came to a sad end when she was hit by a bus. In at least one of its possible interpretations, the anaphoric pronoun it in sentence (10) refers back to the unrealized complete event of Mary’s crossing of Regent Street. In this paper, we call such postulated, though not necessarily actualized, complete events eventoids, and we refer to the elements in our base ontology of events as genuine events. An eventoid may be identical with some genuine event, and if there is a moment in time at which a particular eventoid could be perceived by an appropriately situated subject as actualized, then the eventoid in question is in fact one of the elements of the universe. However, it may be the case that there is no such point in time; in this case, we say that the eventoid is a purely nominal event (event ‘in name only’).12 The structure of our extended ontology is depicted in Figure 1. Nominal events play a crucial role in interpreting progressive sentences that refer to events that fail to culminate for some reason or other, so nominal events have a function similar to those of Parsons’s essentially incomplete events, with the important difference that nominal events do not belong to the universe. Our task now is to show

11

Consequently, being constrained by a temporal stance is different from being constrained by lack of knowledge. Consider a perfectly well-informed agent in a deterministic world: even if the agent knows that a particular event will happen in the future, she is not in the position to perceive it until her temporal position actually overlaps with the temporal trace of the event foreseen. 12 Since atelic eventualities are actualized as soon as they begin (see footnote 9), there are no ‘nominal activities’ or ‘nominal states’.


particular point of view). Similarly, the question of which events have already been actualized (will be actualized) amounts to the question of which events have their temporal trace located in the past (respectively, in the future) of the temporal vantage point assumed by the agent.11 Although they are constrained by their particular location in space and time, agents have a propensity to postulate complete entities which ‘stand behind’ and ‘keep together’ the fragments of information gathered. Regarding events, for example, whenever subjects perceive an unfinished event, they conceive of it as a partial actualization of a complete event. Even if Mary does not accomplish her crossing of Regent Street, we can, nevertheless, refer to a postulated complete event which happened to be ‘abandoned’; thus, the following is not contradictory:


Figure 1

3.3 Characterizing eventoids 3.3.1 General characterization In the next two sections, we propose a way to reconcile the lack of modal means in our extensional framework and the need for events that fail to get accomplished by looking at the latter, that is, nominal events and eventoids in general, not as events constituted by their parts, but as events characterized by certain properties concerning their parts. On this view, eventoids are characterized by certain sets of properties, and they are the hypostatized entities assumed to ‘stand behind’ the collection of those properties: eventoids are what the properties in the set are properties of. Such hypostatized entities have been suggested in other contexts in various places in the literature [see, e.g. the Meinongian objects of Parsons (1974, 1979, 1980) and the pegs and partial objects of Landman (1986)], and although they may raise certain philosophical issues, we take speakers’ willingness to postulate them at face value. In accordance with what we have said above, we are going to represent eventoids indirectly, as special entities characterized by proper filters on the set of events. We list four general conditions that a secondorder property F over E must satisfy in order to qualify as a characterization of an eventoid: 1. 2. 3. 4.

F 6¼ Ø: F cannot be empty. This is the obvious requirement that the characterization of an eventoid has some property. Ø;F . The property that is true of no genuine event whatsoever is not true of any eventoid, either. If u 2 F and u4u# , then u# 2 F . If an eventoid has a particular property, then it has all the more general properties as well. If u 2 F and w 2 F , then u \ w 2 F . If two properties are true of an eventoid, so is their conjunction.


how eventoids can be characterized without appealing to modal concepts or admitting them into the basic ontology.


13 F is a principal ultrafilter on E if there is an element e in E, the generating element of F , such that F ¼ fX4 E j feg4Xg. If F is an ultrafilter on E, then for each H 4 E, either H 2 F or E\H 2 F . Principal ultrafilters are in one-to-one correspondence with the elements of the universe. (Non-principal ultrafilters also exist on infinite sets, but we do not use them in this paper.) 14 The reader familiar with the Montagovian tradition will have noted that the present approach is closely related to Montague (1973)’s type raising, where—the intensional features of Montague’s system put aside—the proper name John is taken to denote the set of John’s properties, that is, the principal ultrafilter that the individual called John generates. There are important differences, though: first, the individuals we are concerned with are eventuality tokens and, second, we aim at getting additional individuals (namely nominal events) by not restricting ourselves to principal ultrafilters only. 15 This is the description of the story from the temporal stance. Seen from the atemporal stance, there never was a genuine event in the first place, and the destruction of the avalanche simply revealed this fact to time-bound agents.


The proper filters on E are perfectly fitted for the purpose of characterizing eventoids, for at least the following reasons. First, there are much more proper filters than elements in E, so there is ample room for eventoids that fail to get accomplished (nominal events). Second, not being part of the basic ontology, such proper filters and the eventoids characterized by them do not multiply the entities of the universe. Third, proper filters can represent partial and complete events alike—the former by non-maximal proper filters, the latter by maximal proper filters (principal ultrafilters13)—‘bracketing’, as it were, their existential status, which permits a uniform treatment of eventoids, whether genuine or purely nominal.14 Indeed, it is perfectly possible that a proper filter F does not contain of u: this simply makes F either property u or the complement u a partial characterization of a genuine or a nominal event. But there is a fundamental difference between genuine events and nominal events: the former, but not the latter, can be exhaustively characterized by an ultrafilter, the maximality of which implies that it must contain either . In other words, ultrafilters settle all property u or its complement u the issues that non-maximal proper filters may ‘keep open’. Let us illustrate this with the help of Bonomi’s multiple-choice paradox discussed in section 2.3. The avalanche was destroyed when the event of its falling had already developed to the extent that it had the property of falling into a valley populated by chamois but, at that time, it had not yet developed enough to qualify either as falling into valley A or as falling into valley B. In other words, when the avalanche was destroyed, the eventoid in progress was indeterminate between the two types: The avalanche fall into valley A and The avalanche fall into valley B, and there was nothing, at that time, that could have decided the issue. The destruction of the avalanche at the gorge ensured that the eventoid would never get actualized but remains a nominal event.15


On the other hand, had the avalanche not been destroyed by the cannon at the gorge, the event in progress could have developed further into the avalanche falling into, say, valley A and settle this particular issue in this way. And even in that case, it would have remained an event in progress leaving some further issues open until the avalanche had indeed fallen into valley A completely to settle all those issues as well.


3.3.2 Involvement If what we have said so far is to be transformed into a workable theory, we have to find a systematic way to generate the proper filters that characterize eventoids, and to do so, we need to find appropriate properties out of which we can build them. This section is probably the hardest part of the paper, but the reader will be presented a worked-out example in the next section, so we suggest coming back to this section again after reading the example. Let us start with the second issue mentioned above. The gist of the imperfective paradox is the puzzling observation that certain happenings can be readily classified as partially actualized complete events in spite of the fact that the complete event which seems to be required by the act of classification is never actualized, that is, it does not exist. As we have seen at the end of section 3.1 discussing Parsons’s theory, this leaves little room for a simple mereology-based approach. As we also pointed out, the reason for this is that the simple mereology-based approach draws on the part-of relation between tokens, and there are not enough tokens in the universe; in particular, there are no tokens corresponding to the ‘abandoned’ events. A possible way around this problem is to ascend to the level of types and define the central relation on which to base the definition of the progressive there. Our basic idea will be that events can be characterized by what kind of eventualities they involve as a proper part, so instead of tokens, certain properties will be used as the basis for characterizing eventoids. Thus, let P 4 E be a property of eventuality tokens and e 2 E an arbidef trary eventuality. The binary relation involves ¼ kPkede# ðe# 9 e ^ Pðe# ÞÞ is introduced to express the fact that at least one eventuality token exemplifying the eventuality property P occurs as a proper part of the eventuality token e. We say that an event e involves a P-eventuality if involves(P)(e) holds (i.e. if e has a proper part that satisfies P). For instance, any eventuality token of walking involves a taking-a-step eventuality because every token of walking has at least one step taking as a proper part.


From a formal point of view, it is possible to look at involves as that unary function from }(E) to }(E) which maps any property P to that subset16 involves(P) of E that contains precisely those elements which have the common property of involving a P-eventuality, and in the rest of the paper, we will adhere to this functional view of involves. A trivial but useful consequence of the definition of involves is that for any P, Q 4 E, the fact that Q 4 involves(P) is equivalent with the truth of the conditional (11) "eðQðeÞ/involvesðPÞðeÞÞ:

16 As is usual, here and in what follows, we freely exploit the correspondence between sets and their characteristic functions. 17 That is, if e#9e, then "PðPðe# Þ/involvesðPÞðeÞÞ. 18 The restriction on finiteness can be dropped by requiring the set BC below only to be a filter subbase, that is, a non-empty family of non-empty subsets of E, the set of finite intersections of which forms a filter base and generating the filter F BC from this filter base in the usual way. We ignore this technicality below.


The conditional in (11) says that every Q-eventuality involves a Peventuality, and as we will see in section 4, such conditionals are often convenient to use because they allow us to express the relationship between types induced by involves in a simple way. Let us now turn to the first issue, that of generating the appropriate filters for eventoids. It is easy to check that if e#9 e, then for any property P of e#, involves(P) is a property of e.17 This suggests that we characterize eventoids with non-empty sets of properties of the kind ‘involves P’, where P’s are properties exemplified by the eventuality tokens assumed to constitute the eventoid. Thus, basically, an eventoid is a hypostatized entity that is characterized by what kinds of actual eventualities it is assumed to involve, together with all the properties that follow from those. We are therefore going to construct the appropriate filters for eventoids with the help of the involves function using principal filters: a principal filter [X generated by a non-empty subset X of E is simply the set of all the supersets of X, that is, def [X ¼ Y4E X4Y . Also, in accordance with what we have said in section 3.1 about the importance of token classification, we are not building on tokens per se, but on a classification relation C between tokens and types (i.e. on ‘classified tokens’ or ‘tokens under a particular description’). Thus, let C 4 E 3 (}(E)\{Ø}) be a finite18 set of ordered pairs of the tokens and the type (or types) considered relevant in a particular context. We call the classifying properties P1 ; P2 ; . . . ; Pn occurring in C the features,


3.3.3 The progressive Having settled both issues that we raised at the beginning of the previous section, we can finally turn to the question of progressivity. First note that the tokens in the generator set \BC of F BC are special: they and only they have the common property of involving tokens exemplifying all the features P1 ; . . . ; Pn . Consequently, if the eventoid e* characterized by F BC happens to be a genuine event then, and only then, is e* actually an element of the generator set of F BC . We can now define the progressive of an eventuality property in full generality as follows (the definition is somewhat complicated because it must incorporate what we have said about atelic eventualities as well): Definition 3 (Progressivity: final version) Let Q be a set of eventuality tokens, and C a particular classification of the elements of Q. An eventuality property u is in progress relative to C if u is true of the eventoid based on C—that is, if u 2 F BC —and either for no e 2 \ BC is it true that ,e 4 ,Q, or there is an e 2 \ BC such that ,Q @ ,e. The definition comprises two parts. The first part establishes the categorial identity of the eventoid through an appropriate principal filter based on the highlighted types P1 ; P2 ; . . . ; Pn of the tokens in Q, while the second part expresses a disjunctive incompleteness condition. The first disjunct targets telic eventuality properties, in the case of which, as we have seen in section 3.2.1, completeness and being in 19 This might suggest an identity condition for eventoids: two eventoids are the same if, and only if, they have the same anchors, and these anchors are taken to exemplify the same features (in which

def

case the same principal filters are generated): e ¼ e # 5 ÆQ; F BC æ ¼ ÆQ# ; F #BC# æ.


while the tokens classified the anchors, of the eventoid to be constructed on the basis of C. We are now in a position to formalize the notion of (the characterization of) an eventoid on the basis of what kind of events are involved in it. We say that the family of sets BC ¼ finvolvesðP1 Þ; involvesðP2 Þ; . . . ; involvesðPn Þg is a basis for the characterization of an eventoid e* based on these features if it satisfies the minimal requirement of consistency, that is, if \BC 6¼ Ø. In other words, what we require here is that there be at least one genuine eventuality in the universe involving all the features present in C. If the basis for the characterization is consistent, then there is def a proper filter F BC ¼ [ð\BC Þ ¼ fX 4 Ej \BC 4Xg, the principal filter generated by \BC (the generator set of F BC ), that characterizes the eventoid e* based on the features P1 ; P2 ; . . . ; Pn .19


4 ILLUSTRATION: DRAWING PLANE FIGURES In this section, we look at a concrete scenario, inspired by a concern voiced by Dowty with respect to the imperfective paradox: [T]o say that John was drawing a circle is not the same as saying that John was drawing a triangle, the difference between the two activities obviously having to do with the difference between a circle and a triangle. Yet if neither activity necessarily involves the existence of such a figure, just how are the two distinguished? (Dowty 1977: 261) Imagine the following scenario in which the goal is to teach children to recognize some elementary types of simple polygon; in particular, triangles and two types of quadrilateral: trapezoids and rectangles. The child is asked to watch a computer screen where a dot d is moving about drawing various polygons, and she is to decide, as quickly as she can, which one of the following accomplishment sentences is true: (12) (13) (14) (15)

The The The The

computer computer computer computer

is is is is

drawing drawing drawing drawing

a a a a

triangle. trapezoid. rectangle. quadrilateral.

For the sake of simplicity, let us assume that the dot always starts at point A in Figure 2, moves along the vectors r1, . . . , r9, and the drawing of a particular figure is completed when it arrives back at point A (of course, the vectors and the vertices are hidden from the child). Whenever the dot arrives at a vertex where it may continue to move in more than one direction, the computer makes a completely random choice.


progress relative to a set of tokens exclude each other, so we must rule out the case in which the property embodied in the generator set is complete relative to the set of tokens Q. In the case of atelic eventuality properties, however, as we have also seen, completeness and being in progress do not exclude each other (quite to the contrary), and this necessitates the second disjunct (with which, incidentally, genuine telic eventualities also comply). Fortunately, much of the complexity present in Definition 3 can be ignored as long as we are only interested in telic eventualities. The detailed example in the next section will be of help to show how the concepts introduced so far can be put to work in the case of accomplishments; other Vendlerian classes will be considered briefly after the example.


Figure 2

Acc ¼ eABC [ eABD [ eABE [ eABCD [ eABDE [ eABCE ; and Act ¼ er1 [ er2 [ er3 [ er4 [ er5 [ er6 [ er7 [ er8 [ er9 : Turning to the conditionals true in this scenario (which, as we have mentioned in section 3.3.2, are a handy means to capture involvement relations), it is easy to check that (16) below- states one of them: (16) "eðdxðABC#ðxÞ^draw#ðeÞðxÞðcÞÞ /involves½ke#movealong#ðe#Þðr1 ÞðdÞðeÞÞ: 20

By ‘trapezoid’, we mean a simple quadrilateral having exactly one pair of parallel sides.


As can be seen from Figure 2, the computer may draw three different types of triangles (ABC, ABD, ABE), two trapezoids20 (ABCD, ABDE) and one rectangle (ABCE). Any particular accomplishment token completed by the computer creates a particular instance of one of the figures mentioned, so, for example, the sentence radical The computer draw a triangle ABC will be translated into the term kedx(ABC#(x) ^ draw#(e)(x)(c)); its denotation in the model, that is, the set of the genuine drawing events that have the computer as agent and some particular ABC-type triangle as patient, will be represented by eABC. We assume that the child can decide correctly if the dot is actually moving along a particular vector and, also, that she can recall the set of vectors that the dot has moved along since it last occupied vertex A. We represent the type of activity The dot move along vector r1 formally as ke move-along#ðeÞðr1 ÞðdÞ, and its denotation as er1 . The set E of eventuality tokens in the model of this particular scenario contains two sorts, accomplishments (Acc) and activities (Act), where


(17) The computer is drawing a trapezoid ABDE or a triangle ABD. At this moment of time, there do not exist any further facts that could single out either disjunct in sentence (17) as opposed to the other. Such a fact might come into being only later, at vertex D, when the computer makes its random decision whether to move the dot along r7 or r8. And if the computer breaks down before reaching that point, then there will never be anything that would decide in favour of either of the disjuncts. Next, assume that the dot finally arrived at vertex D, the computer has made its random choice and now the dot is moving along r7 (see

Figure 3 21

We will discuss an important issue related to this assumption in section 5.3 below.


The conditional in (16) says that for any accomplishment e 2 E of drawing an ABC triangle, there exists an activity e# 2 E of the dot moving along vector r1 which is a proper subevent of e. The reader can check that there are altogether 22 such conditional constraints pertaining to the scenario described above. Now let us consider a couple of particular cases to see how the concepts introduced can be applied. Throughout the example, we will omit reference to the anchors of the relevant features because they can be easily reconstructed. Assume that the child is watching the computer at work and that the dot has gone from vertex A to B, and right now it is moving along vector r3 (see Figure 3). Since involvesðer1 Þ ¼ Acc [ er1 and 21 involvesðer3 Þ ¼ eABDE [ eABD [ er3 , assuming that neither is empty, their intersection, eABDE [ eABD, is not empty either. Therefore, the family B0 ¼ finvolvesðer1 Þ; involvesðer3 Þg is a consistent basis for the characterization of an eventoid. The eventoid characterized on the basis of B0 is given by the filter F B0 ¼ [ eABDE [ eABD , and it makes sentence (17) true:


Figure 4). This situation gives rise to the family of sets B1 ¼ finvolvesðer1 Þ; involvesðer3 Þ; involvesðer7 Þg ¼ fAcc [ er1 ; eABDE [eABD [ er3 ; eABCE [ eABDE [ er7 g, the intersection of which, \ B1 , is eABDE. Therefore, we obtain the relevant filter F B1 as [(eABDE). Since eABCD [ eABDE 2 F B1 , the set of properties of the eventoid now contains the property The computer draw a trapezoid, so the child can recognize at this point that sentence (13), (13) The computer is drawing a trapezoid,

(18) The computer was drawing a quadrilateral (when it broke down).

Figure 4

Figure 5


is true; moreover, she can name trapezoid ABDE as the trapezoid that the computer is drawing. Finally, consider the case in Figure 5 when the dot has moved along r1 and r2, and now is moving along r5. The filter F B2 generated by the current filter base is [(eABCD [ eABCE) and, since both ABCD and ABCE are quadrilaterals, F B2 contains the event property of The computer draw a quadrilateral. Accordingly, even if the computer breaks down at this point, sentence (18) is true:


But in this case, unlike in the previous one, there was no particular quadrilateral that the computer was drawing when it broke down, which is exactly parallel to what we saw earlier discussing the multiplechoice paradox. 5 SOME RELATED ISSUES

5.1 Other Vendlerian classes In this section, we briefly discuss how Vendlerian categories other than accomplishments might be integrated into the framework developed above; we have discussed accomplishments proper in the extended example in section 4. Let us start with achievements. Rothstein (2004) develops a theory of why certain achievements are felicitous in the progressive, in spite of the fact that most theories of aspect would predict that such achievements do not exist because achievements lack the part structure required by the progressive. In developing the explanation, she distinguishes between lexical accomplishments, on the one hand, and derived (abstract) accomplishments, on the other, the latter being the results of a certain aspectual shift operation that associates an activity with the instantaneous event described by a lexical achievement predicate.22 By postulating such an aspectual shift mechanism, Rothstein is able to explain the existence of progressive achievements, which presents a problem for other theories. Discussing Rothstein’s theory of abstract accomplishments is beyond the confines of this paper. For now, we must content ourselves with showing that lexical achievements—having no proper parts—cannot be in progress according to our definition of the progressive. To see this, suppose that H denotes a property that only contains eventuality tokens that have no proper parts whatsoever and that H is in progress relative to some set of tokens (i.e. that H 2 F BC , where F BC is an appropriate 22 Rothstein also discusses another shifting operation, triggered by the resultative construction, deriving accomplishments from lexical activities, but that operation does not concern us here.


It would be impossible in a single paper even to try to touch upon all the various issues that have been raised in the vast literature concerning the progressive. What we can do here is to choose three major themes and indicate, in broad outlines, how the framework proposed can handle them in its present form or after extending it in an appropriate way.


The real difference between state and activity seems to lie in the perspective taken. If we view an eventuality as an activity, the input of effort or energy is profiled; if we view an eventuality as a state, the result of that input is profiled. (Lambalgen & Hamm 2005: 91) If Lambalgen and Hamm are right, then we might speculate that, in English, the otherwise conflicting cases of being in progress and being completed are utilized to signal something different in the case of atelic eventualities than in the case of telic eventualities, highlighting the cognitively presumably important difference between states and activities mentioned in the quotation.

23

See footnote 2.


principal filter on E). The (non-empty) generator set \ BC of F BC is, by definition, a subset of any element of F BC ; in particular, \ BC 4H, which means each and every element of BC has a non-empty intersection with H. Let, for some property P, involves(P) 2 BC be an arbitrary element of the basis. Since involves(P) \ H 6¼ Ø, there is at least one element e 2 H such that e contains an element of P as a proper part. But we have assumed that the elements of H have no proper parts at all, which is a contradiction; therefore, our assumption that H 2 F BC , that is, that H is in progress is false. Let us turn now to atelic eventualities, that is, states and activities. As we have seen in section 3.1, atelic eventuality types have a double nature due to their homogeneity: we have shown that in the present theory, they qualify both as completed and as in progress. Since these categories flatly exclude each other in the case of telic eventualities, we might expect the application of the progressive to atelic eventualities to have idiosyncratic features. And, indeed, it is an old observation that the two subclasses of atelics, states and activities, form a more or less complementary pair of categories with respect to the progressive in English: while states normally do not allow the progressive, activities normally do. Yet, it is notoriously difficult to account for this difference between states and activities in purely formal terms related to their structural properties.23 It may turn out that the relevant difference between states and activities cannot be pinned down in terms of purely structural terms but requires such external concepts as that of effort or energy invested in keeping the activity alive, which is not required with states. As Lambalgen and Hamm put it:


5.2 Verbs of creation

5.3 Impossible events Recall from the discussion in section 3.3.1 that for any proper filter F, Ø;F . The fact that we characterize eventoids with proper filters on E therefore has the consequence that properties that happen to have the null extension in E cannot occur as properties of eventoids, so we


As may be suspected from our discussion so far, verbs of creation have traditionally been thought to present a particularly hard case for extensional theories of the progressive. A famous and at the same time oft-criticized solution is that of Parsons (1989, 1990). Parsons argues that beside incomplete events, we must acknowledge the existence of incomplete objects that may serve as the denotation of the object noun phrase of a verb of creation in the progressive. In the present framework, there is no need to postulate incomplete objects in the ontology to explain the behavior of verbs of creation in the progressive. In fact, as we have argued in section 2.3, verbs of creation pose no more serious a problem than Bonomi’s multiple-choice paradox; and in fact, both problems disappear once we take the difference between the atemporal and the temporal stance seriously and distinguish the existence of the object from its being present at a certain moment of time. The fact that a property expressed by an existentially quantified term (i.e. one whose object-sort variables are existentially closed) belongs to a filter characterizing an eventoid does entail the existence of an object of the appropriate kind, but it does not entail anything about the location of the temporal projection of this object. The existential quantifiers in our terms are atemporal quantifiers, quantifying over the (atemporal) domain O (this is also the case in Parsons’s model but he allows incomplete objects in the domain beside complete ones). In the event-semantic framework, a creation verb denotes a threeplace relation between the creator, the created object and the event of creation. In order for this relation to hold, all the three participants must exist. And if they exist then, and only then, do they have temporal traces satisfying the ordering constraint such that the temporal trace of the created object begins precisely when the temporal trace of the creation event ends. Exchanging this ordering constraint for one requiring that the temporal trace of a certain participant always include the temporal trace of the event, we may characterize ‘extensional’ verb phrases such as that of cross (the street), although the exact implementation of this idea would require extending the present framework with a mechanism to treat temporal constraints in a principled way.


predict that sentence radicals that translate into a contingently empty property are odd in the progressive. This prediction is not borne out by the linguistic data, however: even if the computer of section 4 happens to crash each and every time when it is drawing vector r6, never finishing one single instance of drawing a triangle ABC, we would not hesitate to tell the programmer, perfectly truthfully, that (19) The computer crashes every time when it is drawing a triangle ABC.

(20) Mary was crossing the Atlantic (by swimming), the completion of which is impossible for an ordinary human without a divine intervention. This aspect of the progressive can be explained easily if we assume that eventoids are characterized by proper filters on the set of events. Since impossible events have a necessarily null extension, enlarging the universe of events with possible ones does not help here: not even in the enhanced domain Ee can proper filters be constructed that


The problem can be overcome by requiring that the universe of the model contain, beside actual events and objects, possible events and objects as well. Then the fact that the computer contingently fails to draw a triangle ABC is irrelevant because the possible drawing events of such a triangle are available together with the information as to what they involve (e.g. all possible drawings e of a triangle ABC involve a drawing of vector r6, whether e is actual in our world or not). Note that the inclusion of possible events into the universe serves the single goal of providing the missing building blocks for generating the required filters for eventoids and is not related to the way how the imperfective paradox and the multiple-choice paradox are resolved in the present framework. In fact, both ‘paradoxes’ arise and get resolved in the purely extensional setting that we have assumed so far. Enhancing the universe with possible events, however, gives unexpected support for the theory under discussion because in the enhanced set Ee, there are again properties that have a null extension. These are the properties that no event can possibly satisfy, events that are ‘impossible events’. We argue that impossible events offer further evidence for our central claim that eventoids are characterized by proper filters on the set of (actual or possible) events. It has been noted by several researchers that sentences that describe an impossible event are markedly odd in the progressive (Landman 1992; Glasbey 1996; Naumann & Pinõń 1997; Bonomi 1999; Higginbotham 2004; and others]. A by-now classic example is Landman’s sentence


would be able to characterize them, which explains the semantic deviancy of sentence (20). 6 CONCLUSION

Acknowledgements This paper would not have been possible without the invaluable help and unflagging support of Zso´fia Gyarmathy. Beside her, I owe sincere gratitude to Andra´s Simonyi, whose constructive comments helped me to form a clearer idea of many of the issues discussed in the article. I also thank Zoltań Gendler Szabo´ and Zso´fia Zvolenszky for giving me substantive feedback on earlier versions of this paper. I am also grateful to Philippe Schlenker, Emmanuel Chemla and Simon Charlow for suggesting changes that have greatly enhanced the readability of the paper and, last but not least, my special thanks are due to the two anonymous reviewers of Journal of Semantics for their comments which made me rethink and generalize my earlier approach. Needless to say, none of the people mentioned are responsible for any mistakes that may have remained in the paper.


In this paper, we have outlined a higher order extensional framework for the progressive. The central claim of the theory is that progressive sentences make reference to hypostatized complete events (eventoids) and that these hypostatized events can be characterized through a set of properties exemplified by certain genuine eventualities (the anchors of these events). Since eventoids are accessed through the set of properties attributed to them, it may turn out that an eventoid is not identifiable with any of the genuine events in the universe. Although this might lend eventoids a slightly exotic air, treating them on a par with genuine events would directly lead to the multiple-choice paradox. To see this, consider again the strategy in Landman (1992) (or in Dowty 1977): in order to preserve the relational nature of mereological parthood, Landman makes sure that a particular possible event exists such that the partial event in the actual world is a stage of it. But then there is nothing that could prevent Bonomi’s argument from going through. The only way to block the argument is to recognize the category of eventoids as different from that of (actual or possible) genuine events. Dowty (1979) and Bonomi (1999) can cope with the multiple-choice paradox, but at the price of incurring an unnecessary explanatory debt by the use of modalities that seem to defy an unequivocal definition. In fact, their ability to cope with the multiple-choice paradox hinges on the universal quantifier, hidden in the necessity operator of these theories, which can be uncovered in the concept of eventoids as well since, as is known from the theory of generalized quantifiers, principal filters are just the denotations of universal quantifiers.

Ka´roly Varasdi 205 KA´ROLY VARASDI Applied Logic Laboratory, Budapest Hankoćzy u. 7. 1022 Budapest Hungary e-mail: [email protected]

REFERENCES Glasbey, Sheila. (1996). ‘The progressive: A channel-theoretic analysis’. Journal of Semantics 13:331–61. Higginbotham, James. (2004). ‘The English progressive’. In Jacqueline Gueron and Jacqueline Lecarme (eds.), The Syntax of Time. The MIT Press. Cambridge, MA, 329–58. Kearns, Katherine Susan. (1991). The Semantics of the English Progressive. Ph.D. thesis. MIT. Cambridge, MA. Kenny, Anthony. (1963). Action, Emotion and Will. Routledge & Kegan Paul. New York. Kratzer, Angelika. (1977). ‘What ‘must’ and ‘can’ must and can mean’. Linguistics and Philosophy 1:337–56. Kratzer, Angelika. (1981). ‘The notional category of modality’. In HansJuumlrgen Eikmeyer and Hannes Rieser (eds.), Words, Worlds, and Contexts. Walter de Gruyter, Berlin, Germany, 38–74. Kratzer, Angelika. (1991). ‘Modality’. In Arnim von Stechow and Dieter Wunderlicht (eds.), Semantics: An International Handbook of Contemporary Research. Walter de Gruyter, Berlin, Germany, 639–50. Lambalgen, Michiel van & Fritz Hamm. (2005). The Proper Treatment of Events. Wiley–Blackwell. Oxford, UK. Landman, Fred. (1986). ‘Pegs and alecs’. In Proceedings of the 1986 Conference on Theoretical Aspects of Reasoning about Knowledge. Morgan Kaufmann Publishers, Inc, San Francisco, CA, 45–61.


Asher, Nicholas. (1992). ‘A default, truth conditional semantics for the progressive’. Linguistics and Philosophy 15: 469–508. Bach, Emmon. (1986). ‘The algebra of events’. Linguistics and Philosophy 9: 5–16. Bonomi, Andrea. (1999). ‘The progressive and the structure of events’. Journal of Semantics 14:173–205. Davidson, Donald. (1967). ‘The logical form of action sentences’. In Nicholas Rescher (ed.), The Logic of Decision and Action. University of Pittsburgh. Pittsburgh, PA, 81–95. Dowty, David. (1977). ‘Towards a semantic analysis of verb aspect and the English ‘‘imperfective’’ progressive’. Linguistics and Philosophy 1: 45–77 Also reprinted in 2002. In Paul Portner and Barbara H. Partee (eds.), Formal Semantics: The Essential Readings, Blackwell Publishing, Inc., 261– 88. (Page numbers refer to the reprint). Dowty, David. (1979). Word Meaning and Montague Grammar: The Semantics of Verbs and Times in Generative Grammar and in Montague’s PTQ. D. Reidel Publishing Company. Dordrecht, The Netherlands. Fernando, Tim. (2008). ‘Branching from inertia worlds’. Journal of Semantics 25:321–44. Garey, Howard B. (1957). ‘Verbal aspect in French’. Language 33:91–110. Gendler Szabo´, Zoltań. (2004). ‘On the progressive and the perfective’. Nouˆs 38:29–59.

206 An Extensional Framework for the Progressive Parsons, Terence. (1990). Events in the Semantics of English: A Study in Subatomic Semantics. MIT Press. Cambridge, MA. Pianesi, Fabio & Achille C. Varzi. (2000). ‘Events and event talk: An introduction’. In James Higginbotham, Fabio Pianesi, and Achille C. Varzi (eds.), Speaking of Events. Oxford University Press. New York. 3–47. Portner, Paul. (1998). ‘The progressive in modal semantics’. Language 74: 760–87. Rothstein, Susan. (2004). Structuring Events: A Study in the Semantics of Aspect. Explorations in Semantics. Blackwell Publishers Oxford, UK. Stalnaker, Robert. (1968). ‘A theory of conditionals’. In Nicholas Rescher (ed.), Studies in Logical Theory. Blackwell, Oxford. 98–112. Taylor, Barry. (1977). ‘Tense and continuity’. Linguistics and Philosophy 1:199–220. Vendler, Zeno. (1967). Linguistics in Philosophy. Cornell University Press, Ithaca, NY. Verkuyl, Henk J. (2000). ‘Aspectual composition and event semantics’. In James Higginbotham, Fabio Pianesi, and Achille C. Varzi (eds.), Speaking of Events. Oxford University Press, 169–205. Vlach, Frank. (1981). ‘The semantics of the progressive’. In Philip Tedeschi and Annie Zaenen (eds.), Syntax and Semantics, Volume 14: Tense and Aspect. Academic Press, Inc, New York. 271–92. Zucchi, Sandro. (1999). ‘Incomplete events, intensionality and imperfective aspect’. Natural Language Semantics 7:179–215. First version received: 20.10.2009 Second version received: 03.11.2009 Accepted: 17.11.2009


Landman, Fred. (1991). Structures for Semantics. Kluwer Academic Publishers. Dordrecht, The Netherlands. Landman, Fred. (1992). ‘The progressive’. Natural Language Semantics 1:1–32. Lascarides, Alex. (1988). A Formal Semantic Analysis of the Progressive. Ph.D. thesis, Center for Cognitive Science, University of Edinburgh. Edinburgh. Lascarides, Alex. (1992). ‘The progressive and the imperfective paradox’. Synthese 87:401–47. McCarthy, John & Patrick J. Hayes. (1969). ‘Some philosophical problems from the standpoint of artificial intelligence’. In Bernard Meltzer and Donald Michie (eds.), Machine Intelligence 4. Edinburgh University Press. Edinburgh. 463–502. Montague, Richard. (1973). ‘The proper treatment of quantification in ordinary English’. In Jaakko Hintikka, Julius Moravcsik, and Patrick Suppes (eds.), Approaches to Natural Language: Proceedings of the 1970 Stanford Workshop on Grammar and Semantics. Reidel. Dordrecht, The Netherlands. 221–42. Naumann, Ralf & Christopher Pinõń. (1997). ‘Decomposing the progressive’. In Paul Dekker, Martin Stokhof, and Yde Venema (eds.), Proceedings of the 11th Amsterdam Colloquium. University of Amsterdam. Amsterdam. 241–47. Parsons, Terence. (1974). ‘A prolegomenon to Meinongian semantics’. The Journal of Philosophy 71:561–80. Parsons, Terence. (1979). ‘Referring to nonexistent objects’. Theory and Decision 11:95–110. Parsons, Terence. (1980). Nonexistent Objects. Yale University Press. New Haven, CT. Parsons, Terence. (1989). ‘The progressive in English: events, states, and processes’. Linguistics and Philosophy 12:213–41.

Journal of Semantics 27: 207–242 doi:10.1093/jos/ffq004 Advance Access publication February 23, 2010

Generic Comparisons BERNHARD NICKEL Harvard University

Abstract

1 INTRODUCTION Many paradigmatic generic sentences seem to express quite strong generalizations, ones that might not hold universally but whose exceptions are plausibly considered deviations from the norm, such as (1) and (2). (1) (2)

Ravens are black. Tigers have stripes.

A semantic theory for generics starting out from these examples may well analyse them as true just in case most or all of the normal members of the kind satisfy the property predicated. Let us call such a theory a strong quantificational theory—I will give a more precise statement below. There are, however, many examples that cast doubt on the basic workability of this approach. These are all true generics that an analysis in terms of all normal or most seems to predict to be false. This article discusses a subclass of these problem cases, illustrated by (3) and (4). (3) (4)

Girls do better than boys in grade school. Horses are taller than cows.

Example (3) is not appropriately paraphrased as saying that all normal girls do better in grade school than all normal boys nor as saying that most girls do better than most boys. The former is clearly too strong, the latter can be true even when (3) is false. The same holds, The Author 2010. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected].


This article discusses comparative generic sentences As are F-er than Bs—girls do better than boys in grade school, for example—which pose severe problems for extant accounts. In their stead, the article proposes reconceiving the logical form (LF) of generic sentences as more closely akin to that of sentences containing non-generic plurals, paradigmatically plural definite descriptions. Given this one crucial change, several otherwise puzzling features of comparative generics are immediately explicable, including their relatively weak truth conditions and some of the logical relations they enter into.

208 Generic Comparisons

[SANDWICH] Scholastic achievement among boys is quite heavily polarized: a third of all boys are excellent, so good in fact that the boys in that third are all better than any girl. The other two thirds of

Figure 1

SHIFT.


mutatis mutandis, of (4). Sentences like (3) and (4) are what I will call generic comparisons: sentences of the form As are F-er than Bs. Generic comparisons are particularly interesting for at least two reasons. First, they resist a treatment that is plausible for many other potential counterexamples to strong quantificational theories. Lions have manes or chickens lay eggs are true, even though neither all normal nor most lions have manes, and even though neither all normal nor most chickens lay eggs. These cases can nonetheless be analysed as involving a suitable restriction of the domain of quantification so that, in the restricted domain, the paraphrase in terms of most or all normal is appropriate. Proponents of this strategy have to answer many questions, such as what exactly the relevant restriction is and what factors determine it. But at least it does not seem completely ad hoc that such a restriction is available. Unfortunately, appeals to such a restriction will not help with generic comparisons. Very basic features of strong quantificational theories conspire to predict truth conditions for generic comparatives that are far too strong. Second, these examples are completely systematic. Other sentences that are often cited as problematic for strong quantificational theories, such as mosquitoes carry plasmodia or sharks attack bathers are isolated, and the intuitions of well-informed native speakers vary on their acceptability. By contrast, generic comparisons form a systematic class of troublesome cases, and intuitions concerning their truth values are very firm. In particular, I want to highlight two relevant cases that will guide much of the discussion to follow. First, here is a case that intuitively verifies (3), described in terms of a distribution of scholastic achievement represented in Figure 1. I will call it the SHIFT scenario. Though some boys outperform many of the girls, the distribution of scholastic achievement among girls is systematically shifted to the right of that among boys. By contrast, here is a situation that intuitively falsifies (3). I will call it the SANDWICH scenario.

Bernhard Nickel 209

boys are terrible, so bad in fact that the boys in these two thirds are all worse than even the weakest girl.

(5)

Dutchmen are good sailors.

I will argue that both of these approaches are empirically inadequate, as are some natural extensions of their motivating ideas not discussed in the literature. In their stead, I will propose a compositional semantics for generic comparisons that derives their relatively weak truth conditions as an interaction effect between a strong generic quantificational element and independently motivated aspects of the interpretation of comparatives in plural constructions. Doing so forces us to reconceive the nature of the representations of (1) and (2) relevant for determining meaning—i.e. their logical form (LF). After some preliminaries in section 2, I formulate the problem the interpretation of generic comparisons pose more precisely in section 3. There, I also explain why I reject alternative approaches. Section 4 contains the positive proposal, beginning with a discussion of comparatives in non-generic plurals and extending the treatment to generic comparisons. 2 PRELIMINARIES I have so far spoken of generics simpliciter, but I need to narrow my focus since generics form a semantically and syntactically heterogeneous class. Some seem to explicitly predicate a property of a kind, such as ravens are widespread or dodos are extinct. I want to set these aside.2 I also want to set aside merely existential sentences containing bare plurals, such as ravens are on my lawn. Finally, I will only discuss 1

Note, for example, that a paraphrase of (3) in terms of most is true in the SANDWICH scenario. That is not to say that a semantics for generics can simply treat the fact that bare plurals appear in both kind-predications and in generalizations like (3) and (4) as an orthographic accident. But we face enough problems without trying to solve that one too. 2


The challenge for semantic theories of generics is to predict that (3) is true in the SHIFT but false in the SANDWICH scenario.1 One of my major claims in this article is that no extant theory can meet it. Several options are available to attempt a solution to the problem, drawing on one or another proposal offered to deal with other problem cases. Below, I will consider the prospects of analysing generic comparisons as kind predications, following some remarks of Krifka et al. (1995: 83) who recommend this strategy for many otherwise troublesome examples. I will also consider the possibility of using the alternative generic quantifier that Cohen (1999b: 54ff ) introduces to deal with the (in)famous (5).


sentences with bare plural subjects, not ones with singular definite or indefinite descriptions. I will call the sentences under investigation characterizing sentences.3 I impose these restrictions because the phenomenon of interest seems to be confined to bare plural generics, as the examples in (6) illustrate. (6) a. A girl does better than a boy in grade school. b. The girl does better than the boy in grade school.

3

Save for my restriction to bare plurals, my terminology coincides with that of Krifka et al. (1995). See Krifka et al. (1995: §1.2.6) for an overview of some of the options, as well as Pelletier and Asher (1997). 4


While (3) can be true in a situation in which there is significant overlap in performance, such as the SHIFT, (6a) and (6b) cannot—if they are even interpretable as generics. A quantificational account of characterizing sentences adopts two hypotheses, one about the proposition these sentences express and the other about their LF and compositional semantics. The first holds that there is a systematic, albeit complex, relationship between facts about the distribution of properties among individuals (perhaps across possible worlds and times) and the truth of a distinctively generic proposition conveyed by a characterizing sentence. It holds, for example, that there are certain distributions of blackness among ravens (across space, time and possible worlds) such that, if and only if any one of them obtains, the generic proposition that ravens are black is true. Likewise, there are certain distributions of stripiness among tigers (across space, time and possible worlds) such that, if and only if any one of them obtains, the generic proposition that tigers have stripes is true. We can mark this correlation between facts about individuals and the truth of generic propositions by introducing a generic quantifier GEN into our metalanguage and saying that the generic proposition expressed by, for example, ravens are black is a quantified proposition, the proposition [GEN x: Raven(x)](Black(x)). At this point, we face the theoretically important question of how to further describe this proposition, which is to say, what the systematic relationship between facts about individuals and the truth of generic propositions is. Much of the debate concerning the semantics of characterizing sentences is about just this question, although strictly speaking, this is not directly a semantic issue.4 It is not a semantic issue because so long as we agree that generics express propositions, all of the prevailing semantic approaches are compatible with the view that generic facts that make generic propositions true are not metaphysically basic, including kind-predicating views such as Carlson’s (1977).

Bernhard Nickel 211

(7)

a. Books are paperbacks. b. Prime numbers are odd.

Since (7a) and (7b) are both false, even though the majority of books are paperbacks, and the vast majority of prime numbers are odd, (7a) and (7b) must express very strong generalizations.6 3 INAPPROPRIATE TRUTH CONDITIONS Consider again (3), repeated here. (3)

Girls do better than boys in grade school.

We need make only very few and weak assumptions in order to predict inappropriate truth conditions for (3). Being explicit about them allows us to categorize responses to the problem posed. 5 Thus, gen is the element in the object language that appears in the LF of characterizing sentences, GEN the quantifier in the metalanguage used to interpret the object language gen. 6 Quantifiers in the generalized quantifier description are usually identified as second-order properties that satisfy permutation invariance, conservativity and extension. However, for the purposes of this discussion, I will not assume that the generic operator GEN satisfies these constraints—this practice seems to be in line with how quantificational accounts of generics are usually discussed. The reason to call the accounts I discuss in the main text quantificational is that there is an element that encodes the relationship between the instantiation of a property among the individuals making up a kind and the corresponding generic, a relationship that is broadly speaking about how many.


The second hypothesis characteristic of quantificational accounts specifically concerns semantics. Not only is the proposition expressed by a characterizing sentence quantificational but so is its logical form. A quantificational element in their LF, call it gen, encodes the relationship between facts about individuals and the truth of the generic proposition expressed by the sentence.5 Saying only this much about quantificational theories leaves open various semantic and syntactic options. They leave open where in the LF the generic quantifier originates, whether it is a determiner of the bare plural, an adverb of quantification or something else. They also leave open the meaning of gen. A strong quantificational account takes a stand on that meaning. Since generics tolerate exceptions, gen can obviously not be analysed as a universal quantifier. A strong quantificational account analyses it as something that falls just short, such as quantification over most of the members of the kind or all of the normal ones. I already mentioned the intuitive sense that the initial examples (1) and (2) are appropriately paraphrased as strong generalizations. Perhaps more important is the more directly empirical observation that some generics are false, even though most members of the kind at issue conform to the generalization, as in (7).


(8) John is taller than Bill. In order to evaluate this sentence, John and Bill are both mapped to a degree of height (the scale associated with tallness), and (8) is true iff there is some threshold that John’s degree of height meets or exceeds and that Bill’s height neither meets nor exceeds. In formal terms: (9) dh (height( j, h) ^ :height(b, h)) Schwarzschild’s proposal is especially well suited to my purposes since it posits that the predicate appears twice in the semantic interpretation of the comparative, and the occurrence that corresponds to the object in the initial sentence is within the scope of negation. That means that once we introduce other scope-taking operators, such as quantifiers, we have further options to consider. But if extant treatments of generics still cannot give a proper interpretation of (3), that gives us good reason to look elsewhere.9 7 For the determiner option, see, for example, Asher and Morreau (1995); for the adverb of quantification option, see Cohen (1999a, 1999b), Schubert and Pelletier (1989) and Wilkinson (1991). 8 See, also Kennedy (1999, 2007). 9 This proposal is useful for another reason. It essentially assumes that all comparatives are ‘clausal’, that is, that the LF of a sentence like (8), John is taller than Bill is John is taller than Bill is tall. This is a very plausible hypothesis insofar as bare plurals in object position are not usually interpreted generically—see Diesing (1992). That suggests in turn that when bare plurals are interpreted generically, they are not really in object-position but are instead in a clause.


First, we need to assume that (3) has a quantificational LF. Second, both bare plurals are interpreted generically, so that both are associated with a generic quantifier. Third, the generic quantifier that appears in the LF of (3) is the same strong quantifier as appears in the LF of the initial examples (1) and (2). Fourth, and finally, the generic quantifier occupies one of two standard positions for quantifiers: a nominal determiner or an unselective binder modelled on Lewis (1973).7 At this point, it will be useful to say something about how I will assume we interpret comparatives, and especially how quantifiers are interpreted when they occur in the scope of comparatives. Since I want to argue that we cannot get a proper treatment of generic comparisons given the assumptions I have just set out, I want to assume the most flexible theory of comparatives and their interactions with quantification. I will essentially employ the theory offered by Schwarzschild (2008), what he calls the A-notA approach. On this view, a comparative a is F-er than b is interpreted in two steps. First, a and b are mapped to a degree on a scale associated with F-ness. The comparative then says that a meets or exceeds some threshold that b fails to meet or exceed (i.e. one that b falls below).8 Consider example (8).

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With this in mind, let me turn to the interpretation of (3). By the first assumption, (3) has quantificational truth conditions. By the second, both bare plurals introduce variables bound by a generic quantifier. Suppose that this generic quantifier is a nominal determiner (the first option for the fourth assumption). In that case, (3) can be paraphrased as saying that GEN-many girls do better in grade school than GEN-many boys. Put in formal terms, we have two possible interpretations here, depending on how the scope of generic quantifier that binds the variable associated with boys is related to the negation in the comparative construction. The possibilities are given in (10a) and (10b).

By the third assumption, these formulae have roughly the following truth conditions. We interpret (10a) as saying that all normal or most girls meet or exceed a threshold that all normal or most boys fail to meet. These are the truth conditions most naturally understood for (11a) or (11b). (11) a. Every normal girl does better in grade school than every normal boy. b. Most girls do better in grade school than most boys. Example (11a) is far too strong since it is false in the SHIFT scenario. Example (11b) is too weak since it predicts that (3) is true in the SANDWICH scenario as all of the girls do better than two thirds of the boys. Turning now to (10b), we find excessively weak truth conditions. In line with the third assumption, it is interpreted roughly as saying that all normal or most girls meet or exceed a threshold that not all normal or most boys meet or exceed, that is, that all normal or most girls exceed a threshold that at least one normal boy fails to meet. In other words, it says that all normal girls do better than the weakest normal boy (and mutatis mutandis for a most-interpretation). That is far too weak. The situation is no different if gen is an unselective quantifier that occupies the position of an adverb of quantification. In that case, we would paraphrase (3) as saying that generically (generally, typically), a girl does better in grade school than a boy, that is, as saying that GEN-many pairs Æx, yæ satisfy the condition. Given, again, that we are


(10) a. [GEN x: Girl(x)][d h](Does.Well(x, h) ^ [GEN y: Boy(y)](:Does.Well(y, h))) b. [GEN x: Girl(x)][d h](Does.Well(x, h) ^ :[GEN y: Boy(y)](Does.Well(y, h)))


interpreting the generic quantifier as a relatively strong quantifier, we predict that (3) has roughly the truth conditions of the examples in (12). (12) a. In all normal cases, a girl does better than a boy in grade school. b. Mostly, a girl does better than a boy in grade school.

3.1 Kind-reference and other aggregative proposals Generic comparisons are at least superficially similar to paradigmatic characterizing sentences. Nonetheless, one could try to assimilate them to such kind-predicating sentences as ravens are widespread, which predicate a property of a kind directly. This is the proposal of Krifka et al. for many sentences that would otherwise spell trouble for a strong quantificational theory. In essence, the strategy is to transfer the semantics for comparatives involving individuals, such as (8), John is taller than Bill, without the detour through quantification. We simply move from comparing particular objects to comparing kinds. In this case, each of the kinds mentioned is mapped to a degree on an appropriate scale, and the generic comparison As are F-er than Bs is true just in case there is a threshold on the scale of F-ness that the As—considered as a kind—meet or exceed and that the Bs fail to meet or exceed. Since it is surely a context-sensitive matter how the relevant


As before, these truth conditions are far too strong. Regardless of whether we pursue the nominal determiner or the adverb of quantification options, the asserted relation—doing better in grade school—has to hold between any pair we can form by taking one of GEN-many girls and one of GEN-many boys, and that in turn entails that the weakest of the GEN-many girls still does better than the strongest of the GEN-many boys. One of the four assumptions has to go. My own account will reject the fourth, that the generic quantifier occupies one of the standard positions. By way of motivation, I will consider rejecting one of the other three. I will begin with the first, that generic comparisons like (3) should be analysed quantificationally (section 3.1). I will then consider a proposal on which we reject the third, that the generic quantifier is analysed as a strong quantifier (section 3.2). Finally, I will consider rejecting the second assumption, that both of the noun phrases (NPs) are interpreted generically. The core idea is that the object NP—boys in girls do better than boys in grade school—is a dependent plural (section 3.3).

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(13) a. a is F-er than b. b. b is F-er than a. c. a is (exactly) as F as b.

10

In example (13c), and all of the corresponding examples below, I insert the parenthetical exactly to ensure that we do not read it as a is at least as tall as b. I do not mean to imply that anything turns on a particular standard of precision. I am also taking for granted that the interpretation of the predicate F is the same in all of the examples in (13). Some predicates can be associated with different scales in different contexts, such as big or good. The reason to require that these predicates are interpreted uniformly can be brought out with an example. Suppose that John is taller and lighter than Bill. In that case, all of the following are false if we consider the dimension of comparison indicated in parentheses. (i)

a. John is bigger (by weight) than Bill. b. Bill is bigger (by height) than John. c. John is (exactly) as big (by weight) as Bill.

But so long as we hold the dimension fixed, the schemas in (13) jointly exhaust logical space and one of them must be true.


degrees are determined, the account makes no general prediction about the relationship between the degrees to which individual As and Bs are F and the degrees the corresponding kinds are assigned. The account therefore is not saddled with predicting inappropriate truth conditions, largely because it makes no general predictions on this point at all. But that need not be ad hoc. The kind-referring strategy should liken the determination of the relevant mapping to the determination of the reference of demonstratives: saying how either determination is made is no part of the semantics of these expressions, and in neither case should we think that this division of labour is at all problematic. Prima facie, this proposal is theoretically unattractive because it denies the apparent similarities between generic comparisons and paradigmatic characterizing sentences since the latter are given a broadly quantificational treatment, while the former are not. However, I here only want to focus on a more straightforwardly empirical problem, to wit, that this proposal draws the analogy between comparisons of individual objects and generic comparisons too closely. The two kinds of comparisons exhibit different patterns of logical compatibility and entailment, and the kind-predicating strategy cannot account for this difference. When comparing two individual objects where both can be associated with degrees on the relevant scale, it will always be true that one stands in the comparative relation to the other, the other to the one or that they are equal. That is to say, one of the schemas in (13) must be true.10


In the case of John, Bill and comparisons of tallness, if there is a degree to which John is tall, and there is a degree to which Bill is tall, then one of the following three sentences must be true. (14) a. John is taller than Bill. b. Bill is taller than John. c. John is (exactly) as tall as Bill. However, the corresponding pattern does not hold for generic comparisons, as the examples in (15) show—assume as before that we measure the height of a quadruped at the shoulder.

All of these are false in the actual world—the tallest horses are taller than the tallest cows, and the shortest horses are shorter than the shortest cows. Moreover, the problem is not that cows and horses somehow resist comparison with respect to height, as the truth of the examples in (16) shows. (16) a. Cows are taller than cats. b. Elephants are taller than horses. More generally, then, in the case of generic comparisons, the schemas in (17), corresponding to (13), do not jointly exhaust logical space. (17) a. As are F-er than Bs. b. Bs are F-er than As. c. As are (exactly) as F as Bs. A proponent of the kind-predicating strategy thus needs to identify some difference between comparisons of individuals and generic comparisons. One initially plausible attempt points to vagueness: kinds cannot be assigned to precise degrees on an associated scale but only a vague range on such a scale. And we know that, when vagueness is involved, sets of sentences that one might think jointly cover all of logical space (so that at least one of them must be true) can nonetheless all be false. If John is a borderline case of baldness, then it might be false both that he is bald and that he is not.11 11

Giving up on classical logic in this way is one way of dealing with the initial phenomenon, which is just that we find neither John is bald nor John is not bald to be unproblematically acceptable. For an overview of this and other options, see Williamson (1994).


(15) a. Cows are taller than horses. b. Horses are taller than cows. c. Cows are (exactly) as tall as horses.

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But the approach I am considering on behalf of the kind-predicating strategy is unpromising if we take the appeal to vagueness seriously. It is a commonplace that predicates that exhibit vagueness in their positive form do not exhibit vagueness once they are in an explicitly comparative construction. Two paint chips might both be on the borderline between orange and red, so that neither (18a) nor (18b) is definitely true or definitely false. (18) a. Chip1 is red. b. Chip2 is red.

(19) a. Chip1 is redder than chip2. b. Chip2 is redder than chip1. c. Chip1 is (exactly) as red as chip2. The proponent of the kind-predicating strategy should therefore not appeal to vagueness as the model by which to explain the possibility that all of the examples in (17) can be false at the same time. Instead, she might point to imprecision as a feature of a situation that is preserved even once we move to explicit comparisons and that might account for the observation about (17). However, imprecision generally does not interfere with the usual logical relations. Suppose it is hard to tell exactly how tall John and Bill are. We might model this by mapping them not to a precise degree of height but to a range of the scale. Even in that case, we are usually happy to accept that one of the sentences in (14)—the height comparisons between John and Bill—is true, even if we do not know which it is because our measuring situation is unfavourable. Which sentence is true may well also depend on subtle features of the context, but given standards of precision in a context, one of them will be true. The kind-predicating strategy is therefore unpromising. An appeal to vagueness is untenable because vagueness disappears in comparatives. An appeal to imprecision may be theoretically acceptable, but it does not allow us to predict that all of the sentences are false. Thus, the logical relations that generic comparisons enter into differ from those that comparisons involving individual objects enter into, and the kindpredicating strategy cannot account for this fact. The problem I have raised for the kind-predicating strategy is a problem for any strategy that seeks to aggregate all of the members of the kind that the generic is about, assign that aggregate a single degree and then compare the degree assigned to one aggregate with that


Even in this situation, the relevant instances of (13), given here in (19), exhaust logical space and one of them is definitely true.


assigned to another aggregate. For example, one might interpret a generic comparison by paraphrasing it in terms of averages. On this approach, (3) is paraphrased as the average girl does better than the average boy in grade school.12 This approach makes precisely the same predictions as the kind-predicating strategy in that comparisons involving averages pattern with comparisons between individual objects, not generic comparisons. In general, one of the schemas in (20) must be true if the average A and the average B can be assigned any degree of F-ness at all.

Hence, any aggregative proposal that seeks to assign a single degree to all of the members of the kind relevant to determining the truth of generic comparisons is inadequate.

3.2 An alternative generic quantifier I now turn to a way of rejecting the assumption that the quantifier that appears in generic comparisons is the usual strong one. This section focuses on Cohen’s introduction of a so-called relative generic quantifier. The discussion is largely exploratory since he is primarily concerned with sentences like (5), Dutchmen are good sailors, and does not discuss generic comparisons.13 Nonetheless, I want to investigate whether we can extend his treatment to comparative constructions because of the close semantic connection between gradable predicates in their positive form, such as are good sailors, and comparatives. To introduce Cohen’s system, let me begin with the core examples (1) and (2), which he calls absolute generics. He interprets the generic quantifier in such a way that its restrictor is determined, at least in part, by the predicate via its association with a set of alternatives. To interpret As are F, we have to compute the set of alternatives ALT(F). In most cases, F is included in ALT(F), and in most cases, the alternatives are mutually exclusive. For example, to interpret (1), ravens are black, we associate the property of being black with alternative colours. With that set in hand, Cohen gives the following truth conditions.14 12 Moreover, there are already detailed semantic proposals for average, so that a proponent of the aggregative approach can simply help herself to them. See, for example, Carlson and Pelletier (2002) and Kennedy and Stanley (2009). 13 Except for a passing remark at Cohen (2004: 549). 14 See Cohen (1999b: 37).


(20) a. The average A is F-er than the average B. b. The average B is F-er than the average A. c. The average A is (exactly) as F as the average B.

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(21) As are F is true iff the probability that a randomly chosen A that also satisfies at least one of the properties in ALT(F) is F is greater than .5.

(22) As are F is true iff the probability that a randomly chosen A that satisfies one of the alternatives in ALT(A) is F is higher than the probability that an arbitrarily chosen object that satisfies one of the members of ALT(A) and one of the members of ALT(F) is F. As applied to (5), this theory predicts the truth conditions that an arbitrarily chosen Dutch sailor is more likely to be a good sailor than an arbitrarily chosen sailor from one of the alternative nations. We can see why this interpretation is aptly called relative. A relative generic requires for its truth that the relevant members of the kind be more likely to satisfy the predicate than members of some other kind(s), that is, we are relating different kinds, such as Dutchmen and Swiss. So that we may evaluate this proposal, let me say how claims about probabilities are related to facts ‘closer to the ground’. For our purposes, we can simply translate talk of probabilities into talk of ratios. To say that the probability that a randomly picked Dutch sailor is good 15 See Cohen (1999b: 55f ). One benefit of Cohen’s strategy is that it makes the difference between relative and absolute generics not completely ad hoc. As he argues in Cohen (2001), the difference between the two readings can be reduced to a difference in the setting of one parameter, one we also see in some non-generic cases involving many and often.


The reason to introduce alternatives is to solve the problem posed by sentences such as lions have manes. If we interpreted this simply as saying that the probability that a randomly chosen lion has a mane is greater than .5, we would be committed to more than half of all lions having manes, which would mean that we predict the sentence to be false. The set of alternatives ALT(F) effectively restricts the domain to lions with some form of ornamentation. However, Cohen accepts that his theory as applied (5) yields the truth conditions that the probability that a randomly picked Dutch sailor is a good one is greater than .5, and that is too strong. In response, Cohen introduces relative generics, generic sentences that are analysed in terms of an alternative generic operator. Characterizing sentences are therefore systematically ambiguous, depending on whether they are analysed as absolute or relative. When As are F is analysed as a relative generic, we do not just consider the alternatives to F but also the alternatives to A, ALT(A). In the case of (5), ALT(A) might include other nationalities. Relative generics have the truth conditions in (22).15


(23) A randomly picked girl is more likely to do well in grade school than a randomly picked boy. As a side note, it is somewhat opaque how we could arrive at these truth conditions compositionally. The question really turns on the interpretation of the predicate does better than boys in grade school, and specifically boys. I have already suggested that we cannot interpret it as an ordinary generic bare plural, which in Cohen’s system is interpreted as an absolute generic. That would make the reading too strong. And it is not immediately obvious what a relative reading of that NP would amount to. The best strategy I can imagine interprets the comparative morphology and the comparative phrase as arguments of the relative generic operator directly. On this approach, the explicitly comparative generic (3) just supplies the arguments explicitly that the positive (relative) generic has to take implicitly. For the particular case of (3), -er than boys simply specifies that ALT(½½girls) contains the property of being a boy. But I do not want to focus on the compositional semantics. Even taking for granted that we can predict (23) as stating the truth conditions of (3), there are problems with the proposal. It predicts that a comparative generic has the same truth conditions as a positive relative generic, so long as the same set of alternatives are salient in the context. This prediction fails, as the examples in (24) illustrate. 16 Within the context of Cohen’s theory, the initial interpretation of generics in terms of probabilities plays other roles than simply introducing ratios. It also allows him to motivate various constraints on the classes within which the relevant ratios are assessed, what he calls homogeneity constraints. For more discussion, see Cohen (1999a, 2004).


is higher than the probability that a randomly picked sailor from some other country is amounts to the claim that the ratio of good Dutch sailors to Dutch sailors of any skill is higher than the ratio of good sailors from other countries to sailors from these countries of any skill.16 Let me now consider whether we can make use of a relative generic quantifier to yield adequate semantics for generic comparisons. The most direct application of the theory analyses (3) as saying that a randomly picked girl is more likely than a randomly picked member of ALT(½½girls) to satisfy the predicate does well in grade school. Given the context, especially the linguistic context, it is clear that ALT(½½girls) just consists of the set of boys. Example (3) is thus predicted to have the truth conditions (23).

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(24) a. Feathers are heavier than appleseeds, though of course no feathers nor any appleseeds are heavy. b. Molecules are larger than atoms, though of course no molecules nor any atoms are large. c. Dwarves are taller than hobbits, though of course no dwarves nor any hobbits are tall.

(25) a. Mary is taller than Sue, even though neither Mary nor Sue are tall. b. John is richer than Bill, even though neither John nor Bill are rich.


Each of these examples is predicted to be contradictory on the relative generic strategy. Consider (24a). The first clause says that the incidence of heavy feathers among feathers is higher than the incidence of heavy appleseeds among appleseeds. The second clause asserts that the incidence of heavy feathers among feathers is the same as the incidence of heavy appleseeds among appleseeds—to wit, nil. But that is a straightforward contradiction. And this prediction of a contradiction is unacceptable since all of the examples in (24) can be true. One might object that what counts as heavy depends on the context, and we can surely imagine contexts in which feathers count as heavy, while appleseeds do not. So there is nothing wrong with saying that a randomly picked feather is more likely to be heavy than a randomly picked appleseed. This is true enough, but it is not enough to rescue the relative generic strategy. In order for this rebuttal to defuse my objection, it must accept that the contextually determined standard of heaviness changes between the interpretation of the two clauses. That is because the point of the objection is not that either of the clauses feathers are heavier than appleseeds or neither feathers nor appleseeds are heavy is unacceptable on its own. The point is that the relative generic proposal I am considering is committed to saying that they are contradictory when they clearly are not. And the only way to avoid this prediction of contradictoriness is to accept that the interpretation of heavy in the two clauses changes. But in general, the context does not change in the course of interpreting the kind of sentence I am considering: I am tall, though of course I am not tall is simply contradictory. That the present proposal founders on such cases should be unsurprising since, in general, a comparative can be true even though the corresponding positive is false.


This discussion at least strongly suggests that we will not be able to extend the relative generic strategy to deal with generic comparisons.17

3.3 Dependent plurals I now turn to a way of rejecting the second assumption, that both bare plurals are interpreted generically. The most reasonable way of implementing such a rejection is to take the object NP as a dependent plural of the kind illustrated in (26), due to Chomsky (1975). (26) Unicycles have wheels.

(27) a. [GEN x: Girl(x)][dh](Does.Well(x, h) ^ [GEN y: Boy(y)](:Does.Well (y, h))) b. [GEN x: Girl(x)][dh](Does.Well(x, h) ^ :[ GEN y: Boy(y)](Does.Well(y, h))) The present proposal simply replaces the second generic quantifier with an existential one, as in (28a) and (28b).

17 It seems to me that this result also casts doubt on the viability of the relative generic strategy as it applies to its intended range of cases, such as (5). Given that the semantics of gradable predicates in their positive and comparative forms are very closely related, we should expect a proper treatment of their contribution to generic sentences to be uniform. Hence, any semantic theory for the positive case that does not extend to the comparative case is therefore undermined. 18 For more detailed discussion, see, for example, Spector (2007) and Zweig (2008) and references therein.


Any one unicycle only has one wheel, so the plural morphology of the object NP wheels does not indicate that any one of the objects picked out by the subject has more than one wheel. Rather, it conveys roughly that between them, the unicycles have more than one wheel.18 So to a good approximation, a sentence with a dependent plural conveys that for each thing x denoted by the subject, there is at least one thing y denoted by the object such that x stands in the relation denoted by the predicate to y, and further, that the xs together stand in that relation to more than one y. In other words, we can essentially treat the bare plural in the object position as existentially quantified. The point of the present proposal is perhaps best appreciated by contrasting it with the interpretations of (3) that resulted from interpreting both bare plurals in terms of a generic quantifier, repeated here as (27).

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(28) a. [GEN x: Girl(x)][dh](Does.Well(x, h) ^ [dy: Boy(y)](:Does.Well(y, h))) b. [GEN x: Girl(x)][dh](Does.Well(x, h) ^ :[dy: Boy(y)](Does.Well(y, h)))


These truth conditions are more extreme versions of the doubly generic ones (27a) and (27b) and hence face the same problems, only more so. In this case, (28a) is the weak member of the pair, saying that all normal (most) girls meet or exceed a threshold of scholastic achievement that at least one boy fails to meet or exceed—that is, they all do better than the weakest boy. Again, this is far too weak. (28b), by contrast, is far too strong, since it says that all normal girls do better than any boy, that is, better than even the strongest boy. Consider now what happens when we weaken the dependent plural analysis by combining it not with a strong generic quantifier but with Cohen’s weaker relative generic operator. Since this weakens the predicted truth conditions, we need not consider (28a) with the relative generic operator. Focus instead on (28b). The relative interpretations of generics, recall, compares the likelihood that a randomly picked member of one set has a property of interest with the likelihood that a randomly picked member of some other set or sets (the alternatives) has that property. As before, I will assume that the initial set is the set of girls and that the alternative set is the set of boys. The property is somewhat complex: it is the property of meeting or exceeding a threshold that no boy meets or exceeds. Reflecting on this property shows us immediately that the incidence of this property among the set of boys is, by necessity, nil. Hence, the relative generic version of (28b) is true so long as the probability that a randomly picked girl does better than any boy is greater than 0, that is, so long as the best student is a girl. In other words, on the relative generic version of (28b), the sentence is simply equivalent to the claim that the best student is a girl. These truth conditions are also clearly wrong since they can be satisfied when a single girl is the best student, while all of the worst students are made up by the remainder of the girls. Thus, even if we reject one or more of the three assumptions I have discussed so far, we still will not have an empirically and theoretically viable treatment of generic comparisons.


4 GENERICS, COVERS AND COMPARATIVES

(17) a. As are F-er than Bs. b. Bs are F-er than As. c. As are (exactly) as F as Bs. The SANDWICH scenario I offered in the first section is an instance of this pattern. All of the examples in (29) are false when evaluated as descriptions of this scenario. (29) a. Girls do better than boys in grade school. b. Boys do better than girls in grade school. c. Girls do as well as boys in grade school. This also immediately shows that the whole distribution of girls and boys is relevant to determining the truth or falsity of these examples. It will not do to simply interpret As are F-er than Bs as requiring that the most F As are F-er than the most F Bs. In this case, it would amount to interpreting boys do better than girls in grade school as saying that the best boys do better than the best girls, and clearly, that condition is satisfied in the SANDWICH scenario, even though the original generic comparison is false. I will now argue that we see precisely corresponding phenomena when we consider the interpretation of comparatives in non-generic plurals. I will use that observation to motivate a treatment of generic comparisons that is modelled very closely on the non-generic case.

19 For a thorough introduction to covers, see especially Gillon (1987, 1992) and Schwarzschild (1994, 1996).


I now turn to my proposal. It rejects the assumption that the generic quantificational element is either a nominal determiner or an adverb of quantification. To introduce an alternative, I will discuss some phenomena in non-generic plurals that are very similar to those observed for generic comparatives, along with a theoretical treatment in terms of covers.19 As I emphasized in the beginning, generic comparisons can be true even if it is not the case that GEN-many elements picked out by the subject term stand in the relation to GEN-many elements picked out by the object term. In my critical discussion of other proposals, I also drew attention to two other facts. First, it is possible for every sentence in the schema (17) to be false.

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4.1 Comparatives in non-generic plurals Just as in the case of generic comparisons, comparisons involving two plural definite descriptions can be true even when not all of the things denoted by the one description stand in the relevant relation to all of the things denoted by the other. Examples (30)–(32) illustrate the structure. (30) The Hatfields are taller than the McCoys. (31) The frigates are faster than the destroyers. (32) The buses that ran today were emptier than the subways that ran today.

20

See, for example, Fodor (1970) and Sharvy (1980) for reasons for adopting this view.


Each of these has an appropriately weak reading. Example (30) has a reading that requires only that the Hatfield men are taller than the McCoy men, the Hatfield women taller than the McCoy women, and so on. Example (31) is discussed by Schwarzschild, who observes that it is true in the following situation. The fleet has seen two model years, so that there are new and old frigates along with new and old destroyers. The fleet is deployed to two different areas, one in which a speedy response is important, one in which it is not, so that the newer frigates and destroyers are deployed to the former area and the older frigates and destroyers to the latter. Example (31) is true even if the advances in naval technology are such that the newer destroyers are faster than the older frigates, so long as within each area, the frigates are faster than the destroyers. Finally, (32) has a reading on which it is true if the buses were emptier than the subways running at the same time, even if the rush-hour buses were not emptier than the late-night subways. Note crucially that the interpretation of the data I am giving is consistent with an exhaustive interpretation of the plural NPs, that is, that a predicate is truly predicated of a plural description only if it truly applies to all of the things denoted by it.20 Brisson (2003) has suggested that in some cases, exhaustivity is suspended. She focuses on examples such as the girls jumped in the lake, which does not entail that every single one of the (contextually salient) girls jumped. However, trying to account for the data on comparatives by suggesting that exhaustivity is suspended is unpromising here. If the reason for the acceptability of (say) (31) was that the fast destroyers were irrelevant to the truth in the way that some girls are irrelevant to the truth of the girls jumped in the lake, then no matter what was the case with the irrelevant ships, the truth value of (31) should not change. But that is not what we find. If


the fast destroyers were faster than the fast frigates, (31) would be clearly false. So just as in the case of the generic comparisons, members of both kinds across the whole distribution matter to the interpretation of the comparison. The approach to these data that I will discuss makes use of the technical apparatus of covers, which we can introduce as a generalization of simple distributivity. When a plural NP is used distributively, it is used to summarize what a number of things did individually. This contrasts with collective uses, where the predicate that applies to the collection does not apply to each of its members. Example (33) illustrates both.

Example (33a) entails that each of the children woke up at 8:00, while (33b) does not entail that each of the children gathered in the yard. We could assume that distributivity is simply a brute feature of certain verbs, so that distributivity or collectivity is part of their lexical meaning. As several theorists have argued, a better account posits a distributive operator D.21 As a rough first approximation, we assume that a plural NP picks out a plurality and that the distributive operator applies to a verb phrase (VP). Assuming that the children picks out some contextually determined children, the LF of (33a) is given in (34a). Example (34b) gives the truth conditions we would like for (34a), and (34c) is the semantic value of the distributive operator. (I use capital variables to indicate that the variable ranges over pluralities and the expression Xx to indicate that x is among the Xs.) (34) a. [S[NThe children][VD woke up at eight]] b. ["x: Among.The.Children(x)](Woke.Up.At.Eight(x)) c. ½½D ¼ kf. kX.["x: Xx ¼ 1](f (x) ¼ 1) However, positing a simple distributive operator does not allow us to capture all of the semantic possibilities for interpreting sentences containing plural NPs because there are sentences that are not collective, but in which the predicate cannot be distributed all the way down to the individuals making up the plurality, either. Suppose we are buying apples. Each apple costs 50 cents, and we buy 12. We can describe that situation accurately both by (35a) and (35b).22 21 See, for example, Beck and Sauerland (2000), Landmann (2000), Lasersohn (1995), McKay (2006), Pietroski (2005), Schein (1993), Schwarzschild (1996) and Winter (2000). 22 Examples like these are due to the work of Roger Schwarzschild, as is the introduction of covers to account for them. See Schwarzschild (1994, 1996).


(33) a. The children woke up at 8:00. b. The children gathered in the yard.

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(35) a. The apples cost fifty cents. b. The apples cost six dollars. We can predict both of these readings. In (35a), the VP contains the D operator, while it is absent in (35b). But if the apples come prewrapped in six-packs, we can also truly describe the situation with (36). (36) The apples cost three dollars.

(37) The apples are such that six among them cost three dollars. The predicate is not distributed to each of the objects picked out by the subject term but rather to collections that in turn make up the collection picked out by the subject term, in this case, the pre-wrapped six-packs. That suggests that we should allow the distributive operator to distribute the predicate not just to the atoms but to subclasses of the plurality denoted by the subject. Moreover, it seems as if the possibility of such intermediate readings depends heavily on the context. Without the information that the apples come in six-packs, (36) is extremely hard to hear as true. Once we have made the six-packs salient, the relevant reading becomes available. That suggests that the distributive operator should be sensitive to the context. The key formal tool to accomplish all of these goals is that of a cover, which for our purposes we can simply treat as a partition. [COVER] Where A is a set, C covers A iff (i) C is a set of subsets of A, (ii) ("x 2 A)(d!B)(B 4 A ^ B 2 C ^ x 2 B) and (iii) ;;C.23 That is, a set of sets C covers a set A just in case for every member of A, there is exactly one subset of A that contains that member and that subset is in C. In the case of the apples, for example, A consists of the 23 This is usually called a cover, rather than simply a partition because covers are supposed to allow that for some members of A, there is more than one subset in C, each of which contains that member. This is impossible for partitions. But that is a complication we can ignore, so that I will remain with partitions.


We have already exhausted the possibilities with respect to the D operator in the LF of these sentences. When it is present, (35a) is true, while (35b) and (36) are false. When it is absent, (35b) is true and the other two are false. Either way, we cannot predict the true reading of (36). What we would like is a formal way of capturing roughly the paraphrase (37) of (36).


(38) a. [S[NPThe apples][VP[D COV] cost three dollars]]. b. Presupposition: ½½COV covers ½½The apples Assertion: ["y: y 2 ½½COV](Cost.Three.Dollars(y)) More generally, the LF of a simple subject–predicate sentence with a non-generic plural is given in (39a), the corresponding truth conditions in (39b) and the semantic value of the revised D operator in (39c).25 (39) a. [S[NPThe AsPL][VP[D COV]F]] b. Presupposition: ½½COV covers ½½A Assertion: ["y: y 2 ½½COV](½½F(y) ¼ 1) c. ½½D ¼ kc. kf. kX: c covers X.[["x: x 2 c](f (x) ¼ 1)] Distribution to the atoms is then simply the special case in which the cover consists of singleton sets, each of which contains just one of the members of the set picked out by the subject term.26 We are very close to having an account of the example of the frigates and the destroyers. All we need to do is generalize the semantics presented thus far to sentences that contain a transitive verb and a plural noun phrase as a direct object. Following Schwarzschild, I assume that 24 Though the interpretation of the cover argument depends on the context, I will suppress explicit reference to the context throughout for ease of exposition. Thus, in (38b), we are really evaluating ½½COVig, that is, an indexed cover variable that is assigned a value by the contextually salient assignment function (see Heim & Kratzer 1998). But nothing I say will depend on being explicit about this. 25 I use the notation ka :b.c to express that the k-abstract carries the presupposition that b is satisfied. 26 A formal note: the proposal I am discussing in the text has the result that a distributive reading of a sentence with a plural subject predicates the property denoted by the VP of a singleton set containing an atom making up the plurality. This analysis thus implicitly relies on the convention that we may conflate a singleton set with its member for the purposes of the semantics. This idea is due to Quine (2004).


12 apples, and the contextually salient cover C consists of two subsets, each of which contains the members of one six-pack. We now need to incorporate covers into the semantics of the distributive operator. According to (34c), D takes a predicate as argument and returns another one. We now let D take two arguments, a predicate as before and a contextually determined cover COV. Thus, the LF of (36) is given by (38a) and the truth conditions are (38b). On the assumption that the denotation of COV indeed is the set of two sets containing six apples each, these truth conditions are the ones we wanted to predict. Here and in what follows, I will treat it as a presupposition that the contextually supplied cover covers the collection picked out by the subject.24

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covers need not just be sets of sets. They can also be sets of pairs of sets. Formally, we introduce paired covers. [PAIRED COVER] T is a paired cover of ÆA, Bæ iff there is a cover of A, call it CA, and there is a cover of B, call it CB, such that (i) T 4 CA 3 CB, (ii) ("x 2 CA)(dy 2 CB)(Æx, yæ 2 T) and (iii) ("y 2 CB)(dx 2 CA)(Æx, yæ 2 T).

(31) The frigates are faster than the destroyers. a. [S[NPThe frigates][VP[[DT COVT] are faster than] the destroyers] b. Presupposition: ½½COVT covers Æ½½the frigates, ½½the destroyersæ] Assertion: ["Æp1, p2æ: Æp1, p2æ 2 ½½COVT](Faster( Æp1, p2æ )) The next issue concerns interpreting the nuclear scope in (31b), especially when the paired cover does not distribute all the way to the atoms of the pluralities denoted by the subject and object. Assume for concreteness that the old frigates are F1, F2 and F3; the new frigates F4 and F5; the old destroyers are D1 and D2; and the new destroyers D3 and D4. Assume also that the contextually salient cover COVT contains the pairs in (40). (40) ½½COVT ¼ {Æ{F1, F2, F3}, {D1, D2}æ, Æ{F4, F5}, {D3, D4}æ} So in order to evaluate (31b), we have to evaluate (41). (41) Faster(Æ{F1, F2, F3}, {D1, D2}æ) Here, two sets are compared. I propose that we introduce the following meaning postulate. When we compare two sets, the asserted relation holds between the two sets iff it holds between any pair of atoms from the two sets. (42) ½½comp(ÆS1, S2æ) ¼ 1 iff ["x: x 2 S1]["y: y 2 S2](½½comp(Æx, yæ) ¼ 1) This postulate requires that each of F1, F2 and F3 is faster than any of D1 or D2. The motivation for adopting this assumption comes from


In order to accommodate paired covers in the semantics, I will introduce a distributive operator DT (the subscript T indicates that it is suitable for interpreting transitive verbs), which takes as one of its arguments such a paired cover. We can then give the truth conditions of our initial target sentence (31), by assigning it the LF (31a) and the truth conditions (31b).


reflecting on the following example from Schwarzschild (1996: 86). Consider Table 1, which can be truly described by (43). (43) The fiction books complement the non-fiction books.

(44)

a.

b. Presupposition: ½½COVT covers Æ½½Subj, ½½Objæ Assertion: ["Æp1, p2æ : Æp1, p2æ 2 ½½COVT] (½½TransVerb(Æp1, p2æ) ¼ 1) c. ½½DT ¼ kc. kf. kX. kY : c covers ÆX, Yæ. [["Æp1, p2æ : Æp1, p2æ 2 c]( f(Æp1, p2æ))] In this presentation I am skirting over several large issues, in particular, over how distributivity interacts with comparative

Fiction Alice in Wonderland

Non-fiction Aspects Language (Bloomfield) Gray’s Anatomy Das Kapital The Wealth of Nations Freud’s Introduction to Psychology

Fantastic Voyage David Copperfield Hard Times Oedipus Rex Agamemnon Richard III

Machiavelli’s The Prince Table 1

Books


The true reading comes about when we assume that a pair-cover is contextually salient, which pairs books from the same line. Crucially, (43) becomes false if we add a non-corresponding book to any of the lines. That is why I suggest we impose the demanding condition that the relation holds between every pair that can be formed from the two sets. We can now state the general view, where the schematic LF (44a) is assigned the truth conditions (44b) and the semantic value of the transitive distributive quantifier is given in (44c).

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morphology to compositionally determine the interpretation I am giving here.27 What is crucial for my purposes is that the distributive operator applies to the predicate before it applies to the subject and object.28 Since the relevant readings are clearly attested, and this assumption seems to be quite clearly required in order to derive them, I will remain at this level of generality. But even at this level of description, we can already see that the semantics for non-generic comparisons predicts the following fact about logical relations. Consider the schemata in (45).

The semantics I have just presented immediately predicts that all of these can be false. The basic point is just that the three schemata in (45) do not jointly exhaust the space of possibilities. Suppose that we have a paired cover over the As and the Bs. It may be true that for some pairs in that cover, the As in that pair are F-er than the Bs, while for other pairs, the Bs are F-er than the As. In that situation, all of the schemata in (45) are false. And crucially, the semantics makes that prediction precisely because the As and the Bs throughout the distribution of F-ness are relevant to determining the truth of (45a)–(45c), not just the As and the Bs that are F-est, or the average A and the average B.

4.2 Covers in generic comparisons The fact that we see such a close parallel in the logical relations among non-generic comparatives involving plurals and generic comparisons suggests that we can make progress on the latter by adapting the semantics of the former. That is what I will do right now. In the case of the non-generic plurals, the basic quantificational force derives from a distributive operator, so the most direct way of transferring this mechanism is to treat the generic operator not as a nominal determiner nor as an adverb of quantification but as a distributive operator. Moreover, the analogy with the universal distributive operator in the non-generic case suggests that we treat the generic operator as a universal quantifier of some stripe. Clearly, characterizing sentences are not well paraphrased as universally quantified claims since they are compatible with what would be 27

For relevant discussion, see Fitzgibbons et al. (2009) and references therein. I assume that this occurs via movement of the subject and object, but I will suppress the interpretation of the movement. For discussion, see Beck and Sauerland (2000), Sauerland (1998) and Sternefeld (1998). 28


(45) a. The As are F-er than the Bs. b. The Bs are F-er than the As. c. The As are (exactly) as F as the Bs.


(46) a. Chickens lay eggs. b. Chickens are hens. If the restriction of the quantifier were the same in both (46a) and (46b), then (46a) would entail (46b). After all, since a chicken lays eggs only if it is a hen, (46a) requires that all of the chickens in the scope of the quantifier are hens, and if the scope of the quantifier in (46b) were the same, it would follow that chickens are hens. Informally, we might say that what is at issue is not being a normal chicken, but being a chicken that is normal in a respect, and that the respect is determined by the predicate of the characterizing sentence. Thus, (46a) might be about all of the chickens that are normal with respect to how chickens extrude offspring (and no male qualifies for being normal in this respect), while (46b) might be about all of the chickens that are normal with respect to having a gender (which includes both female and male chickens).29 It is also true that generics can be non-vacuously true, even when there are no normal members of the kind at issue in the world of evaluation at the time of evaluation. To take a simple example, lions have four legs can be non-vacuously true even when there are not any normal lions perhaps because all of the lions have lost a leg in accidents or fights. That means that when we evaluate a generic, we always need to ensure that we evaluate the restricted universal quantifier with respect to a suitably representative domain. One way to accomplish this is to introduce a counterfactual element into the semantics. Simple generic sentences of the form (47a) are thus interpreted as (47b). 29 Cohen implements the same strategy by using a set of alternatives to the predicate in order to restrict the domain of his generic operator.


counterexamples to the corresponding universal claim. Hence, we should interpret the generic operator as a restricted universal quantifier. For the purposes of this article, I will say that the restriction is to the normal members of a kind. It is obviously extremely difficult to say what makes a member of a kind normal in any kind of general way, but when we are confronted with a particular generic, we have a clear enough sense of which members of the kind are intuitively relevant to its truth and which ones are not. For example, when we are evaluating (3), we are not interested in academic outliers. We have a notion of a normal student, girl or boy, and the generic is evaluated with respect to those girls and boys, not the ones that are exceptionally good or exceptionally bad. Quantificational accounts generally need to make the restriction of the quantifier sensitive to the predicate of the generic. The need for this is most easily brought out by considering the pair of sentences in (46).

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(47) a. As are B. b. If there was a relevantly normal A, then all relevantly normal As would be B.

(48) Ravens are black. a. [S[NP ravens][VP[gen black]]] Thus, I want to interpret the LF (48a) as having the truth condition (48b), which we can achieve compositionally if gen has the lexical semantics in (48c).


Here, relevantly normal just abbreviates normal in the respect determined by the predicate. If there are relevantly normal As in the world of evaluation at the time of evaluation, then (47b) just collapses into a simple quantificational claim. Moreover, we see a useful interplay between the fact that we need to consider not normal As but relevantly normal As since that helps make the counterfactual strategy work. Suppose, for example, that we were interested in evaluating lions have manes and analysed it as if there were any normal lions, then all normal lions would have manes. We would not have any grounds for denying that female lions are normal lions. Hence, we would predict that lions have manes is false. But by restricting the generic quantifier to those lions that are normal with respect to their ornamentation, we may exclude the female lions. The rest of this section is devoted to combining this basic semantic theory for non-comparative generics with the semantics for nongeneric comparatives. Return to (3), girls do better than boys in grade school, for illustration. Suppose that we have decided on the relevantly normal boys and girls, excluding the outliers, and suppose that the SHIFT scenario obtains. Here is a way of assigning truth conditions to (3) that makes the correct prediction. We match up subsets of the girls with subsets of the boys, where each of the subsets comprises a certain part of the distribution, for example, pairing deciles of girls with corresponding deciles of boys. The sentence is true iff within each such pairing, each of the girls does better than any of the boys. Graphically, we can represent this strategy as in Figure 2, where areas that are shaded the same way are compared to each other. That is the informal idea I now give a formally more rigorous implementation of. I will go stepwise, beginning with simple sentences and adding complexity as I go along. If gen occupies the position of a distributive operator, and ignoring covers for now, the LF of the simple characterizing sentence (1), repeated here as (48), is (48a).


Figure 2 Correspondences for

SHIFT.

(48) b. ["x: Relevantly.Normal(x) ^ Raven(x)](Black(x)) c. ½½gen ¼ kf. kg.[["x : Relevantly.Normal(x) ^ g(x)]( f(x) ¼ 1)]

(49) a. [S[NP subj ][VP[gen COV] pred]] b. ½½gen ¼ kc. kf. kX: c covers X. [["x: Relevantly.Normal(x) ^ x 2 c]( f(x) ¼ 1)] As before, quantification over the atoms in the set picked out by the subject term falls out as a special case. To account for the interpretation of generic comparisons, I make use of paired covers. Thus, I want to offer roughly the LF (50a) as the interpretation of (3) and the semantics for the nodes in the tree in (50b). (50) a.


We can immediately introduce covers. Just as the distributive operator takes an extra cover argument, the generic quantifier gen does too. The only important change we have to make is to alter the interpretation of the subject term to be more in line with the denotation of non-generic plurals. Rather than have the subject term pick out a property, it should pick out the plurality of members of the kind. The relevant LFs, truth conditions and lexical semantics are given in (49).

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b. ½½Girls ¼ {x: x is a girl} ½½Boys ¼ {y: y is a boy} ½½do better than ¼ kY. kX.[X does better in grade school than Y] ½½genT ¼ kc.kfkY. kX: c covers ÆX, Yæ.["Æp1, p2æ : Æp1, p2æ 2 c ^ Relevantly.Normal( p1) ^ Relevantly.Normal( p2)] ( f(p2)(p1) ¼ 1) The derivation of (3), given this information, is the following.

That is to say, for every pairing in the contextually salient cover, every girl in the pairing does better in grade school than every boy in that pairing. Given that the contextually salient cover pairs up girls and boys in the same decile in the distribution, we have the following interpretation of (3): it is true just in case every girl in the top decile of girls does better than every boy in the top decile of boys and so on down the distribution of scholastic achievement. This proposal requires some further comments before I discuss its benefits. First, one might worry that these truth conditions are too demanding. For concreteness, consider a situation in which all but one girl is better than all of the boys, but in which the weakest student is a girl. One might think that my semantics predicts that (3) is false—after all, this is just an extreme SANDWICH-style scenario—but that intuitively, (3) is true. This objection is too quick, and to see why, it will help to spell out the situation further. Different ways of spelling it out will yield different intuitive truth-value judgments, and my proposal is in accord with these judgments. The crucial question is whether the very weak girl is


[DERIVATION OF ½½3] ½½a ¼ kfkY.kX: ½½COVT covers ÆX, Yæ. [" Æp1, p2æ : Æp1, p2æ 2 ½½COVT ^ Relevantly.Normal(p1) ^ Relevantly.Normal(p2)]( f(p2)(p1) ¼ 1) ½½b ¼ kY.kX: ½½COVT covers ÆX, Yæ.["Æp1, p2æ: Æp1, p2æ 2 ½½COVT ^ Relevantly.Normal( p1) ^ Relevantly.Normal(p2)] ( p1 does better in grade school than p2) ½½c ¼ kX: ½½COVT covers ÆX, {y: y is a boy}æ. [["Æp1, p2æ: Æp1, p2æ 2 ½½COVT ^ Relevantly.Normal( p1) ^ Relevantly.Normal(p2)] ( p1 does better in grade school than p2)] ½½d ¼ Presupposition: ½½COVT coversÆ{x: x is a girl}, {y: y is a boy}æ Assertion: ["Æp1, p2æ: Æp1, p2æ 2 ½½COVT ^ Relevantly.Normal(p1) ^ Relevantly.Normal(p2)] ( p1 does better in grade school than p2)


30 An anonymous referee has emphasized a conflicting intuition regarding this example. Even if the weakest student is a girl and she is completely normal, it can be true that girls do better than boys in grade school. I can see at least two possible responses to this observation. The first is that comparative generics are simply ambiguous between the reading I have been focusing on and a reading in terms of averages. The second is that, once we have relatively large groups, we allow for a bit of imprecision in our speaking. Regarding the second point, notice that how good (3) is in a situation in which the weakest student is a girl seems to vary with how large the population of students is: the more students, the easier it is to disregard the weakest girl as somehow not standing in the way of (3)’s truth. I leave as an open problem how this kind of situation can be handled.


normal for the purposes of evaluating (3). Perhaps we are thinking about (3) in the context of designing social policy, or wondering why women are not more heavily represented in many academic disciplines. So now suppose that the weakest girl is doing poorly in school because of a learning deficit. In that case, she is not normal for the purposes of evaluating (3), so that she is not in the scope of the generic operator and my semantics makes the intuitively correct prediction that (3) is true. Suppose, however, that this girl is in no relevant way different from the girls at the top, aside from her level of achievement—there is nothing we could point to that certifies her as an outlier. In that case, my semantics predicts that (3) is indeed false. A potentially confounding factor may be the fact that whenever we see a single girl or a single boy in a chunk of the distribution, we naturally assume that this child is an outlier. After all, there are so many kids that generally shared factors should produce the same outcome in multiple cases. That is why in the extreme situation I just described, the easiest judgment is that (3) is true. And the prediction of my semantics conforms to that judgment.30 One may, of course, also worry about my appeal to an unanalysed notion of normality in the semantics. And it is certainly true that it can be hard to determine what exactly counts as normal for the purposes of evaluating (3): what factors determine whether a distribution is normal for our purposes? But I take it to be an advantage of my account that it leaves these questions open. After all, it happens quite frequently, especially when we are considering topics like gender differences, which speakers agree on the statistical facts but disagree on the generic facts. I diagnose this as a disagreement over what counts as relevantly normal. Finally, let me briefly address what happens when we do not have a representative domain. Because of some random fluke, a part of the distribution that is normally occupied by some girls is completely vacant. Perhaps it just so happened that all of the high-performing girls moved away. It is in order to deal with this problem that I suggest that the cover itself be intensional. That allows me to say the following: it

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(17) a. As are F-er than Bs. b. Bs are F-er than As. c. As are (exactly) as F as Bs. My semantics predicts that this is possible without further assumptions. I will give the argument for the particular example of (3). That is, I will show that the three claims in (29), repeated from earlier, can all be false in the SANDWICH scenario. (29) a. Girls do better than boys in grade school. [¼(3)] b. Boys do better than girls in grade school. c. Girls do as well as boys in grade school. Given the semantics I worked out for (29a), it is true iff within each decile, every girl does better than every boy. Since there are some deciles in which each of the boys does better than the girls—the ones at the top—it is false that girls do better than boys. By parallel reasoning, (29b) is true iff within each decile, every boy does better than every girl. Since there are some deciles in which each of the girls does better than any of the boys—the ones at the bottom—it is false that boys do better than girls. Finally, (29c) is true iff within each decile, the girls do as well as the boys. It does not matter how exactly we make precise the notion of one group’s doing as well as another. For concreteness, assume that two groups do equally well when the top girl does as well as the top boy in that group, and the bottom girl does as well as the bottom boy in that group. However, we choose to settle the matter, it will always turn out that some of the deciles fail that condition, for example, the top deciles in which the boys do far better than the girls.


has to be the case for each pair ÆAi, Biæ in the paired cover over the normal As and the normal Bs that, if there were As and Bs in the cells Ai and Bi, then each of the As in Ai would be F-er than any of the B in Bi. For the special case of (3): for each pair ÆGirlsi, Boysiæ in the contextually selected paired cover over the normal girls and normal boys, if there were any girls in Girlsi and any boys in Boysi, then each of the girls in Girlsi would do better in grade school than any of the boys in Boysi. In other words, the counterfactual strategy for dealing with non-representative domains I introduced above for non-comparative generics can be directly extended here. In section 3.1, I observed that the logical relations among generic comparisons do not mirror those of comparatives involving individual objects. Schematically, all of the sentences in (17) can be false.


4.3 Dimensions of contextual variation

(51) a. Men are taller than women. b. Fathers are taller than mothers. On its most salient reading, (51a) is true. We simply compare the distribution of men and women with respect to height and pair up occupants of corresponding parts. By contrast, (51b) has two natural readings, one on which it is true, another on which it is false. The true reading is the one that is parallel to the reading of (51a) I just described: we compare the tallest men who happen to be fathers with the tallest women who happen to be mothers, the less tall such men with the less tall such women and so on down the distribution. However, (51b) also has a very natural reading on which we do not pair the tallest men who happen to be fathers with the tallest women who happen to be mothers, but instead pair each father with the mother of their common child or children. In that case, (51b) is false because there are plenty of pairings consisting of fathers and mothers, both of whom fall in the respective normal height ranges where the father is shorter than the corresponding mother. We can make this latter reading salient by mentioning this kind of pairing, as in (52). (52) Couples with kids can be very varied—fathers (certainly) aren’t taller than mothers. The very same phenomenon is present in non-generic plurals, as (53) shows. (53) Even though the couples in our study were not married, the men did display aggressive behavior towards the women. (Schwarzschild 1996: 87, #209)


My semantics combines two distinct semantic features to yield interpretations for generic comparisons, a univocal generic operator that I am glossing as a restricted universal quantifier and a contextually selected paired cover. Since both of these features are present in sentences besides generic comparisons, we should be able to find commonalities between generic comparisons and those sentences in which one, but not the other, of the features is present. I want to argue that this is exactly what we do find, focusing on kinds of contextual variability, beginning with variability in the contextually determined cover and then turning to contextual variability in what counts as normal. Consider the two sentences in (51).

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The concessive in the first part of the sentence makes salient a pairing of men and women according to the couples that were formed, and the main clause is interpreted with respect to this pairing. If we remove the concessive, this reading becomes harder to hear. (54) In our study, the men displayed aggressive behavior towards the women.

(55) Dogs are heavier than cats. It is clear that, at the top of the distribution, dogs are far heavier than cats. Indeed, this is true for most parts of the size distribution. The interesting aspect of the case is located at the bottom of the distribution, specifically when we consider so-called teacup dogs, breeds of dogs that are lighter than even the lightest cats. These teacup dogs exist only because of very targeted selection by breeders, and individuals of these species usually suffer from health problems and various genetic disorders. Given this information, the sentence (55) has at least a true and a false reading, depending on whether we take teacup breeds into account. Put in terms of the proposal I am putting forth, the difference between the context in which (55) expresses a truth and one in which it expresses a falsehood is simply a matter of whether such intervention by breeders disqualifies a dog from being normal. The point I want to draw attention to is that the very same kind of contextual variability can be seen in non-comparative generics, as the texts in (56a) and (56b) show. Some background: at birth, Dobermanns have floppy ears and long tails. In many countries, including the United States, breeders then surgically insert posts into the ears that remain there for about 6 weeks until the cartilage in the ears hardens, at which point the posts are removed. They also dock the dogs’ tails. (56) a. Different breeds of dogs focus on different senses. Some dogs have very acute hearing, while others have a specialized sense of smell. The latter have floppy ears that agitate the air when they’re following a trail. This is true of dobermans: they don’t have pointy ears, they have floppy ears.


It is clear that there is some matching of men with women, though for all that the context provides, it could be that every man in the study displayed the behaviour towards every woman in the study. Turn now to contextual variation in what counts as normal. Consider (55).


b. Welcome to the Westminster Kennel Club show. We have a wide range of dogs, some homely, some truly regal. The dobermans are beautiful, dynamic creatures. Dobermans have pointy ears. They don’t have floppy ears.

5 CONCLUSIONS I have argued that generic comparisons exhibit a range of interpretations that are problematic for extant semantic treatments. I have also argued that these problems can all be solved in a theoretically motivated way if we treat generics not as quantificational constructions or instances of direct reference to kinds but as plural constructions making use of a special generic distributive operator. Clearly, such a reconfiguration of the LF of generics will have many other implications, a fuller exploration of which I leave to further work. Acknowledgements The initial impetus for writing this article came from a challenge by Carrie Jenkins to account for generic comparisons within the framework of quantificational theories of generics. An ancestor of this article was given at the conference ‘Generics: Interpretation and Use’ in Paris in 2009. I thank the participants there for many helpful suggestions. I also thank three anonymous reviewers of this journal. BERNHARD NICKEL Department of Philosophy Harvard University Cambridge, MA 02138 USA e-mail: [email protected]


In each context set up by the discourses preceding the italicized sentences, we can deny a sentence that is asserted in the other. That shows that the difference between (56a) and (56b) really is a difference in the proposition expressed, and not just a pragmatic phenomenon that does not influence semantics. We can thus observe kinds of contextual variation in sentences other than generic comparisons. The discussion of these examples illustrates a general strategy for testing the proposal I have made. If we see contextual variability in the interpretation of generic comparisons, we should be able to trace it to an aspect of their interpretation that they share with either non-generic plural comparisons or non-comparative generics. These examples suggest that this strategy can, in fact, be carried out.

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REFERENCES Fodor, J. D. (1970). The Linguistic Description of Opaque Contexts. Ph.D. thesis. MIT. Gillon, B. (1987). ‘The readings of plural noun phrases’. Linguistics and Philosophy 10:199–220. Gillon, B. (1992). ‘Towards a common semantics for English count and mass nouns’. Linguistics and Philosophy 15: 597–640. Heim, I & A. Kratzer. (1998). Semantics in Generative Grammar. Blackwell. Malden, MA. Kennedy, C. (1999). Projecting the Adjective. Garland. New York. Kennedy, C. (2007). ‘Vagueness and grammar: the semantics of relative and absolute gradable adjectives’. Linguistics and Philosophy 30:1–45. Kennedy, C. & J. Stanley. (2009). ‘On ‘‘average’’’. Mind, 118:583–646. Krifka, M, F. J. Pelletier, G. N. Carlson, A. ter Meulen, G. Chierchia & G. Link. (1995). ‘Genericity: an introduction’. In G. N. Carlson & F. J. Pelletier (eds.), The Generic Book. University of Chicago Press. Chicago. 1–124. Landmann, F. (2000). Events and Plurality. Kluwer Academic. Dordrecht, The Netherlands. Lasersohn, P. (1995). Plurality, Conjunction, and Events. Kluwer Academic. Dordrecht, The Netherlands. Lewis, D. K. (1973). ‘Adverbs of quantification’. In E.L. Keenan (ed.), Formal Semantics of Natural Language. Cambridge University Press. Cambridge, UK. 3–15. McKay, T. J. (2006). Plural Predication. Oxford University Press. Oxford. Pelletier, J & N. Asher. (1997). ‘Generics and defaults’. In J. van Bentham & A. ter Meulen (eds.), Handbook of Logic and Language. Elsevier and MIT


Asher, N & M. Morreau. (1995). ‘What some generic sentences mean’. In G. N. Carlson & F. J. Pelletier (eds.), The Generic Book. University of Chicago Press. Chicago. 300–39. Beck, S & U. Sauerland. (2000). ‘Cumulation is needed: a reply to winter (2000)’. Natural Language Semantics 8:349–71. Brisson, C. (2003). ‘Plurals, all, and the nonuniformity of collective predication’. Linguistics and Philosophy 26: 129–84. Carlson, G. N. (1977). Reference to Kinds in English. Ph.D. thesis. University of Massachusetts. Amherst. Carlson, G. N. & F. J. Pelletier. (2002). ‘The average American has 2.3 children’. Journal of Semantics 19:73–104. Chomsky, N. (1975). ‘Questions of form and interpretation’. In R. Austerlitz (ed.), The Scope of American Linguistics. Peter de Ridder Press. Lisse, The Netherlands. 159–96. Cohen, A. (1999a). ‘Generics, frequency adverbs, and probability’. Linguistics and Philosophy 22:221–53. Cohen, A. (1999b). Think Generic! CSLI Publications. Stanford, CA. Cohen, A. (2001). ‘Relative readings of many, often, and generics’. Natural Language Semantics 9:41–67. Cohen, A. (2004). ‘Generics and mental representation’. Linguistics and Philosophy 27:529–56. Diesing, M. (1992). Indefinites. MIT Press. Cambridge, MA. Fitzgibbons, N., Y. Sharvit & J. Gajewski ‘Plural superlatives and distributivity’. Proceedings of SALT XVIII, (2009). URL: http//hdl.handle.net /1818/13041.

242 Generic Comparisons constructions’. Language and Linguistics Compass 2:308–31. Sharvy, R. (1980). ‘A more general theory of definite descriptions’. The Philosophical Review 89:607–24. Spector, B. (2007). ‘Aspects of the pragmatics of plural morphology: on higher-order implicatures’. In U. Sauerland & P. Stateva (eds.), Presupposition and Implicature in Compositional Semantics. Palgrave Macmillan. Houndmills, UK. 243–81. Sternefeld, W. (1998). ‘Reciprocity and cumulative predication’. Natural Language Semantics 6:303–37. Wilkinson, K. (1991). Studies in the Semantics of Generic Noun Phrases. Ph.D. thesis. University of Massachusetts. Amherst. Williamson, T. (1994). Vagueness. Routledge. London. Winter, Y. (2000). ‘Distributivity and dependency’. Natural Language Semantics 8:27–69. Zweig, E. (2008). Dependent Plurals and Plural Meaning. Ph.D. thesis. New York University.

First version received: 01.08.2009 Second version received: 02.11.2009 Third version received: 30.12.2009 Accepted: 31.12.2009


Press. Amsterdam, The Netherlands. 1125–77. Pietroski, P. M. (2005). Events and Semantic Architecture. Oxford University Press. Oxford. Quine, W. (2004). Set Theory and Its Logic (revised edition). Belknap Press. Cambridge, MA. Sauerland, U. (1998). ‘Plurals, derived predicates, and reciprocals’. In U. Sauerland & O. Percus (eds.), The Interpretive Tract. MITWPL. Cambridge, MA. 177–204. Schein, B. (1993). Plurals and Events. MIT Press. Cambridge, MA. Schubert, L. K. & F. J. Pelletier. (1989). ‘Generically speaking, or using discourse representation theory to interpret generics’. In G. Chierchia, B. H. Partee, and R. Turner (eds.), Properties, Types, and Meaning, Vol. II. Kluwer Academic. Dordrecht, The Netherlands. 193–268. Schwarzschild, R. (1994). ‘Plurals, presuppositions, and the sources of distributivity’. Natural Language Semantics 2:201–48. Schwarzschild, R. (1996). Pluralities. Kluwer Academic. Dordrecht, The Netherlands. Schwarzschild, R. (2008). ‘The semantics of comparatives and other degree

Journal of Semantics 27: 243–270 doi:10.1093/jos/ffq001 Advance Access publication February 12, 2010

Global Domains versus Hidden Indexicals CHRISTOPHER GAUKER University of Cincinnati

Abstract

1 INTRODUCTION Most linguists and philosophers of language will now acknowledge that a semantic theory for a natural language must posit domains of discourse that vary with context of utterance. Thus, a semantic theory for English will not say simply that the sentence ‘Everyone is happy’ is true if and only if absolutely everyone in the universe is happy. Rather, it will say that each context of utterance introduces at least one domain, and perhaps many, such that ‘Everyone is happy’ is true in a context if and only if everyone who belongs to a certain domain introduced by the context is happy. Stanley and his collaborators have brought to light some interesting features of the relation between the quantificational structure of a sentence and the context in which it is uttered (Stanley & Williamson 1995; Stanley 2000; Stanley & Szabo´ 2000). When one quantifier is syntactically subordinate to another, we may have to countenance a plurality of domains corresponding to the members of the domain relative to which we interpret the superordinate quantified phrase. For example, the sentence ‘Every girl answered every question’ might be true in a context if and only if for each girl in the domain that the The Author 2010. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected].


Jason Stanley has argued that in order to obtain the desired readings of certain sentences, such as ‘In most of John’s classes, he fails exactly three Frenchmen’, we must suppose that each common noun is associated with a hidden indexical that may be either bound by a higher quantifier phrase or interpreted by the context. This paper shows that the desired readings can be obtained as well by interpreting nouns as expressing relations and without supposing that nouns are associated with hidden indexicals. Stanley’s theory and the present alternative are not equivalent, however. They differ over the status of sentences such as ‘Every student is happy and some student is not happy’. On Stanley’s theory, this sentence will be true in some contexts, while on the present alternative it will be true in no context. Considerations in favour of the present theory’s verdict on such sentences are presented. The broader question at issue is the correct way to incorporate context-relativity into formal semantics.

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1 Since truth conditions of sentences are to be relativized to contexts, it may not be evident what it means to provide a ‘reading’ of a sentence. My assumption will be that we can speak of a sentence as expressing a proposition relative to a given context—its reading for that context—in light of the truth-in-a-context conditions of the sentence and the particulars of the given context. I should note also that I will acquiesce in the common practise of using the term ‘context’ equivocally to refer both to the concrete situation in which an utterance takes place and to the sort of set-theoretic specification of parameters that we might appeal to in a definition of truth-in-a-context. If precision demanded it, we could preserve the distinction but relate the two notions by saying that for each context-as-situation, there is a unique context-as-parameter that pertains to it.


context somehow associates with ‘every girl’ (perhaps the girls in a certain class in a certain school), that girl answered every question in a domain that the context somehow associates with that girl (perhaps the questions on her copy of a test). Call such sentences bound quantifier sentences (since in such sentences a subordinate quantifier phrase is in some sense bound by a superordinate quantifier phrase). Stanley has proposed a particular way of generating the desired interpretations of bound quantifier sentences compositionally. (From here on out I will refer to Stanley as the exponent of this idea, but Szabo´ presumably deserves much of the credit as well.) We are supposed to recognize that the syntax of quantifier phrases includes certain elements that do not appear in speech, which I will call hidden indexicals. Our semantics will assign meanings to each of the lexical items at the terminal nodes of the syntactic tree for the sentence, and then the meaning of the sentence as a whole will be generated compositionally so that the meaning of each node in the tree is a function of the meanings of the nodes immediately stemming from it. Stanley wants to allow that pragmatics may play a role in the assignment of meanings to the leaf nodes. But after that, pragmatics plays no role, and the meaning of the sentence as a whole is generated compositionally on the basis of the meanings of the terminal nodes and the composition rules of the language. My aim in this paper is to show that there is a very different way of generating the desired readings of bound quantifier sentences than Stanley’s. I will accept his assumption that the meanings of sentences ought to be assigned compositionally. But I will argue that there is no need to posit Stanley’s hidden indexicals in the syntax. On my account, the desired readings will be obtained by treating common nouns as expressing relations. For instance, we can interpret the noun ‘question’ in ‘Every girl answered every question’ as a relation between grounding objects (which might be girls) and questions (which might be questions on a test taken by the grounding object).1 Stanley’s theory and my theory will not be equivalent, however. They will generate the same interpretations of bound quantifier

Christopher Gauker 245

sentences. However, they will differ on the interpretation of sentences in which two quantifier phrases are at the same syntactic level. For instance, in the sentence (S) Every student is happy and some student is not happy

2 In the postscript to his 2007 (248–49) collection, Stanley notes that his own writings have displayed some ambivalence over the way in which the syntax associates the hidden indexicals with the nominal. In some of his earlier papers, he treated them as ‘cohabiting’ a node in syntax together with a noun, while in his 2005b, he treated them as occupying their own node, which allows them to combine with adjective–noun combinations. Nothing I will say will turn on this issue, but my presentation of Stanley’s theory may be read as reflecting the resolution that he has plumped for, which is that of his 2005b.


neither of the phrases ‘every student’ nor ‘some student’ is subordinate to the other. I will show that Stanley’s theory allows that in some contexts, (S) will be true; whereas on my theory, (S) is not true in any single context. Further, I will defend this consequence of my theory against Stanley’s rejection of it. The difference between our theories to which this difference can be traced is that on my theory each context is associated with what we might call a global domain (for that context), whereas on Stanley’s theory, there are no such global domains and all domains are associated with hidden indexicals. Hence the title of this paper. A different kind of debate that one might have with Stanley concerns where exactly in the syntactic representation of a sentence to place the hidden variables. For Stanley, they are to be associated with noun phrases. A noun phrase combines with a hidden indexical to form an entity that combines with a determiner to form a determiner phrase. In his seminal paper on domain restrictions, Westersta˚hl (1985) associated domain indices with the determiner (quantifier) itself (although Westersta˚hl did not offer an account of bound quantifier sentences). In his 2003, Pelletier argues by appeal to anaphora that one should introduce the hidden variable at the level of the determiner phrase (i.e. at a non-terminal node) rather than introducing it with the noun phrase. In this paper, I will not discuss the data that might decide between these alternatives. If either Westersta˚hl’s or Pelletier’s alternative is preferable, then a corresponding alteration of my alternative to Stanley’s theory might be called for. But the modified theory would still differ from these other views over (S).2 My aim in this paper will not be to establish that my account of bound quantifier sentences meets all reasonable tests. I do not even aim to refute Stanley’s theory. For first, I will note some questionable consequences that Stanley’s theory and my theory share. And second, I

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do not think my defence of the claim that (S) is true in no context is really a proof. My objective is only to cast new light on the subject of bound quantifier sentences and, more generally, the subject of domains of discourse, by showing that there is another way to account for the data that Stanley himself draws on and to show that Stanley has fallen far short of demonstrating that we need to posit hidden indexicals to account for bound quantifier sentences. 2 STANLEY’S THEORY INFORMALLY

3

Stanley (2002b: 374–76) argues that there are bindable function variables hidden in the syntax of natural language sentences. I do not find his example persuasive, but I will not take up the issue here. See also note 11 below.


Stanley does not present his theory of bound quantifier sentences in a precise way but uses only a variety of improvised formalisms. What he does not do is first tell us precisely how to define the meanings of the lexical atoms for a simple language (e.g. a fragment of English) and then tell us how those meanings go together to generate his intended readings of the bound quantifier sentences. Consequently, in initially setting forth his theory in an impartial way, I will have to employ the same kind of informal presentation. Subsequently, in section 4, I will try to spell the theory out more precisely, and at that point, a question will arise whether Stanley’s theory can live up to all of his own requirements. Settling, for the moment, for an informal presentation, Stanley’s view may be characterized as follows: For every sentence containing a quantified noun phrase, an explicit representation of the syntax of that sentence will associate with each common noun an index of the form ‘f(i)’. ‘f ’ denotes in context a function that, given an object that ‘i’ denotes in context, yields a set of objects—a domain for the noun. In the cases of interest here, ‘f ’ is treated as a constant, not a variable, since in each context the function it denotes is fixed and it is never bound by a quantifier.3 ‘i’ is sometimes treated as a constant as well, namely when our evaluation of a sentence depends on the object that a context assigns to it. However, ‘i’ is treated as a variable when it is in the scope of a quantifier that binds it. My term for all these things, ‘f(i)’, ‘f ’ and ‘i’, will be hidden indexicals. I will also call ‘i’ a variable. I believe that this terminology should be acceptable to Stanley, so long as we are clear that the ‘i’ in ‘f(i)’ may function as a variable and that these indexicals are not what Stanley calls ‘narrow indexicals’ (Stanley 2000: 411),


4 Stanley himself describes ‘f(i)’ as a complex variable (Stanley 2000: 417) and as a contextual variable (Stanley & Szabo´ 2000: 251) and labels it the quantifier domain variable or domain index (Stanley & Szabo´ 2000; Stanley 2002b, 2005b). He does not seem to have any special word for the letters, such as ‘f ’ and ‘i’, that occur in function and argument positions, although at one point he calls them function index and object index (Stanley 2005b, 245 note). 5 This is what I referred to above as an improvised formalism. This particular formalism is my own invention. It constitutes a slight improvement over notation employed by Stanley himself in his 2005b study. What I do not like about the notation in Stanley 2005b is that he sometimes appends a variable to a bracketed item and sometimes does not, and so writes: ‘[Every Æstudent, f(j)æ]-i answered every Æquestion, f(i)æ’ (234).


which are words such as ‘I’ and ‘now’ that cannot function as variables because they cannot be bound by quantifiers.4 Thus, the truth-in-a-context conditions of ‘Every bottle is empty’ can be represented as the truth-in-a-context conditions of: ‘For every j in Æbottle, f(i)æ, j is empty’.5 Here ‘bottle’ denotes (in all contexts) the set of bottles, ‘i’ denotes in context c some object assigned to ‘i’ by c, ‘f ’ denotes in c a function assigned to ‘f ’ by c, ‘f(i)’ denotes in c a set that the function assigned to ‘f ’ assigns to the object assigned to ‘i’, and ‘Æbottle, f(i)æ’ denotes in c the intersection of the set of bottles and the set that ‘f(i)’ denotes in c. So this sentence will be true in a context c if and only if c(‘i’) is some object r, c(‘f ’)(r) is some set, and every bottle in c(‘f ’)(r) is empty. The object that c assigns to ‘i’ might be a certain room in a certain house. I will call this a grounding object for the context. So c(‘f ’)(r) might be the set of objects in that room. (I put quotation marks around ‘f ’ and ‘i’ because we are thinking of them as actual vocabulary items of the object language, albeit not spoken.) The virtue of Stanley’s idea becomes apparent when we turn to bound quantifier sentences. Consider, ‘In some room, every bottle is empty’. In this sentence, the quantifier ‘in some room’ can be said to bind the subordinate quantifier ‘every bottle’ inasmuch as the sentence tells us that for some room the bottles we have to consider are just those that are in that room. This sentence may be represented as ‘In some i in Æroom, f(k)æ, for every j in Æbottle, g(i)æ, j is empty’. The grounding object that context c assigns to ‘k’ in this case might be a certain house. The set that the function c(‘f ’) assigns to that house might be the set of enclosed spaces in that house, so that ‘Æroom, f(k)æ’ denotes in c the set of rooms in the set of enclosed spaces in that house, that is, the set of rooms in that house. For each room i in that house, c(‘g’)(i) might be the set of perceptible objects in i, so that ‘Æbottle, g(i)æ’ denotes in c the set of bottles that are perceptible objects in room i, that is, the set of bottles in i. So this sentence will be true in such a context if and only if in each room r in that house, every bottle in r is empty. (There is some sleight-of-hand in this explanation,

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6

I owe this observation to Greenhall’s 2006 dissertation.


inasmuch as I have equivocated between thinking of ‘i’ as belonging to the object language and thinking of it as belonging to the metalanguage. How to avoid that will be an issue in section 4.) Or consider, ‘In most of John’s classes, he fails exactly three Frenchmen’ (cf. Stanley 2002b: 371). This can be spelled out as, ‘In most j in ÆJohn’s classes, f(i)æ, there are exactly three k in ÆFrenchmen, g(j)æ such that John fails k’. Supposing that the grounding object that context c assigns to ‘i’ is a certain university and c appropriately interprets ‘f ’ and ‘g’, this sentence will be true in c if and only if in most j of the classes that John teaches at that university, John fails exactly three Frenchmen who are among the students in j. Off hand, Stanley’s theory might seem to have a problem with sentences like ‘Every girl answered every question’. In the improvised formalism I have been using, this comes out as: ‘For every j in Ægirl, f(i)æ, for every k in Æquestion, g(j)æ, j answered k’ (cf. Stanley 2002a: 152, 2002b: 368). Stanley’s theory may not sufficiently constrain the allowable relations between girls and questions. Stanley’s theory even allows that in some contexts this sentence will be true under the same conditions as ‘Every girl answered every question that she answered’, which is trivial. (Thanks to Jeffrey Pelletier for pointing this out to me.) The answer to this doubt may be that if we resist the more liberal readings, that is only because the contexts that would generate them are unfamiliar or improbable. A perhaps more serious problem is that there might not be as many legitimate readings of a sentence such as ‘In every class, every girl answered every question on her exam’ as Stanley’s theory allows. What this presumably means is that in each class in a certain domain (e.g. in a certain school), every girl in that class answered every question on her exam. On Stanley’s theory, what it means is that for each class in a certain domain, for each girl in the set that the context associates with that class, the girl answered every question on her exam. This will generate our reading if the set that the context associates with each class is the set of students in that class. The trouble is that Stanley’s theory also allows very different sorts of contexts, for instance, contexts in which the set associated with each class is the set of children in some other country. The word ‘in’ seems to be doing work that Stanley’s theory does not acknowledge.6 But I will not make an issue of these extraneous readings because my theory will generate them just as well.


For later purposes, it will be important to have looked at one more example. According to Stanley and Szabo´ (2000: 249), the sentence Every sailor waved to every sailor

3 BOUND QUANTIFIERS WITHOUT HIDDEN INDEXICALS I next present an alternative account of bound quantifier sentences that entirely dispenses with Stanley’s hidden indexicals. Like Stanley, I will


can be read as true in a certain context if and only if every sailor on the ship waved to every sailor on the shore. One might even think (although Stanley and Szabo´ do not say this) that it can be read as true in a certain context if and only if every sailor on the ship waved to every sailor on the shore and every sailor on the shore waved to every sailor on the ship (whoever else they might have waved to). Call this the reciprocal reading of the sailor sentence. (Compare the treatment of a similar sentence by Stanley and Williamson (1995: 294). They seem to be thinking of a reciprocal reading.) In the formalism I have been using to represent Stanley’s theory, this sentence can be expressed as ‘For every j in Æsailor, f(i)æ, for every k in Æsailor, g(j)æ, j waved to k’. On this representation, obtaining either reading is a matter of supposing that a context can select suitable values for ‘i’, ‘f ’ and ‘g’. For example, we obtain the reciprocal reading in a context that assigns to ‘i’ the shipcum-shore, assigns to ‘f ’ a function that takes the ship-cum-shore into the union of the set of people on the ship and the set of people on the shore, so that ‘Æsailor, f(i)æ’ denotes the set of sailors who are either on the ship or on the shore, and assigns to ‘g’ a function that assigns to each sailor on the ship a set that includes the set of sailors on the shore and assigns to each sailor on the shore a set that includes the set of sailors on the ship. For later comparisons, it bears emphasis that on Stanley’s theory, the most superordinate quantifier phrase in a sentence will carry a variable that is not bound by any higher quantifier. For example, in ‘For every j in Ægirl, f(i)æ, for every k in Æquestion, g(j)æ, j answered k’ that variable is ‘i’. The context has to assign to that variable an object, which I have called a grounding object. (Though formally it remains a variable, it is treated by the context as a kind of deictic singular term.) So ultimately Stanley will owe us an account of what makes it the case in any given context that one grounding object rather than another is assigned to that variable.

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½½Nc ¼ {Æx, yæ j y 2 ½½N and y 2 fc(x)}.8 In other words, relative to each context c, a noun is interpreted not as a set but as a binary relation. For each pair in this relation, the first member is what I am calling a grounding object, and the second member is a member of both the traditional extension of the noun and the set that fc assigns to the first member. For instance, in some context c, where Æx, yæ 2 ½½girlc, x might be Mrs Kaplinger’s sixth-grade class, fc(x) might be the set of students in Mrs Kaplinger’s sixth-grade class, and then y will be a girl in Mrs Kaplinger’s sixth-grade class. Or where Æx, yæ 2 ½½questionc, x might be a student, Shelly Mason, and fc(x) might be the set of questions on Shelly Mason’s final history exam in

7 We must be sure to distinguish between contextually determined domains of discourse and the ‘universe’ of a model-theoretic interpretation. One difference is that every proper name of an existing thing must name an object in the universe of the interpretation, but there may be names of existing things that do not name anything in the contextually determined domain of discourse. To accommodate context-relativity in model-theoretic interpretations, interpretations have to be defined as containing sets of contexts, and different contexts in that set may be associated with different domains. Only in this way can we represent variation in context against the background of a fixed interpretation of names and predicates. 8 A note on terminology: Expressions of the form ½½Xc may be thought of as denoting either extensions or meanings (defined as functions from contexts to extensions) but not intensions (functions from worlds to extensions). It denotes an extension if we think of the subscript ‘c’ as denoting a particular context, and it denotes a meaning if we think of the ‘c’ as a variable over contexts.


be concerned with extensions only, not intensions. We will suppose that each context c is associated with a non-empty domain of discourse, Dc. Dc is the ‘global domain’ referred to in the title of this paper.7 Further, we will suppose that each context c is associated with a function fc, having domain Dc, that assigns a subset of Dc to every member of Dc. In addition, each context c identifies a particular member ac of Dc. Call ac the default grounding object for c. We will use ac to find a domain for a noun when no higher quantifier hands an object to fc. Initially, sentences will be interpreted as sets of potential grounding objects, but then a sentence will be interpreted as true relative to a context c if the default grounding object for c is a member of the set. The function fc will play a role similar to the role played by the function assigned to ‘f ’ on Stanley’s theory, but here ‘f ’ is exclusively a term of the semantic metalanguage and not a hidden indexical in the object language. To start, each noun N will be assigned a ‘traditional’ extension ½½N, which is just a set of objects. But then in addition, to each noun N, we will assign a context-relative interpretation; thus,


Mrs Kaplinger’s sixth-grade class, and then y will be a question on Shelly Mason’s exam. The rule for transitive verbs will be nearly trivial: ½½Vc ¼ {Æx, yæ j Æx, yæ 2 ½½V}. Here are some composition rules: ½½[V [every N]]c ¼ {x j "y(Æx, yæ 2 ½½Nc / Æx, yæ 2 ½½Vc)}. ½½[[every N] VP]c ¼ {x j "y(Æx, yæ 2 ½½Nc / y 2 ½½VPc)}. ½½[[In every N] S]c ¼ {x j "y(Æx, yæ 2 ½½Nc / y 2 ½½Sc)}. These rules do not assign a truth value to a sentence, but only a set of objects. For example,

This is the set of objects x in Dc such that for each girl y in fc(x) and for each question w in fc(y), y answered w. Further, ½½[[In every class] [[every girl] [answered [every question]]]]c ¼ {x j "y(Æx, yæ 2 ½½classc / y 2 {z j "w(Æz, wæ 2 ½½girlc / w 2 {u j "v(Æu, væ 2 ½½questionc / Æu, væ 2 ½½answeredc)})})}. This is the set of objects x in Dc such that for each class y in fc(x), for each girl w in fc(y) and for each question v in fc(w), w answered v. It is worth remarking that the three rules given here for phrases containing [every N] (or [In every N]) are evidently quite similar and can be viewed as species of a single genus differentiated only by the adicity of the phrase to which [every N] (or [In every N]) is attached. Finally, we say that a sentence is true in a context if and only if the default grounding object for c, ac, is a member of the extension of the sentence in the context: (Truth Rule) S is true in context c if and only if ac 2 ½½Sc. In other words, a sentence is true in a context if and only if the default grounding object for the context is in the extension of the sentence. As we have seen, the extension of ‘Every girl answered every question’ in c is the set of objects x in Dc such that for each girl y in fc(x), y answered every question in fc(y). So the sentence is true if and only if for each girl y in fc(ac), y answered every question in fc(y). So if ac is a certain class at a school and fc(ac) is the set of students in that class and for each girl y in the class, fc(y) is the set of questions on that girl’s exam, then the


½½[[Every girl] [answered [every question]]]c ¼ {x j "y(Æx, yæ 2 ½½girlc / y 2 {z j "w(Æz, wæ 2 ½½questionc / Æz, wæ 2 ½½answeredc)})}.

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sentence will be true if and only if every girl in the class answered every question on her exam, which is precisely the result we expect. Similarly, the sailor sentence can be analyzed thus: ½½[[Every sailor] [waved to [every sailor]]]c ¼ {x j "y(Æx, yæ 2 ½½sailorc / y 2 {z j "w(Æz, wæ 2 ½½sailorc / Æz, wæ 2 ½½waved toc)})}.


Obtaining the various readings of this sentence is a matter of choosing fc in such a way that ½½sailorc turns out to be a suitable relation. To obtain the reading according to which every sailor on the ship waved to every sailor on the shore, we can let the ship be the default grounding object for the context, and we can choose fc in such a way fc(ship) is the set of people on the ship, and for each sailor sship on the ship, fc(sship) is the set of people on the shore. Thus, ½½sailorc turns out to be a relation such that for every sailor sship on the ship, Æship, sshipæ is a member, and for every sailor sship on the ship and every sailor sshore on the shore, Æsship, sshoreæ is a member (and which may include other pairs as well). What the sentence means in that context is that for every sailor sship on the ship such that Æship, sshipæ 2 ½½sailorc and every sailor sshore on the shore such that Æsship, sshoreæ 2 ½½sailorc, sship waved to sshore. To obtain the reciprocal reading of the sailor sentence, we let the ship-cum-shore be the default grounding object for the context, and we choose fc in such a way that fc(ship-cum-shore) is the set of people who are either on the ship or on the shore, and for each sailor sship on the ship, fc(sship) is the set of people on the shore and for each sailor sshore on the shore, fc(sshore) is the set of people on the ship. Thus, ½½sailorc turns out to be a relation such that for every sailor s either on the ship or on the shore, Æship-cum-shore, sæ is a member, and for every sailor sship on the ship and every sailor sshore on the shore, both Æsship, sshoreæ and Æsshore, sshipæ are members (and which may include other pairs as well). By the present account, a context for an utterance or a conversation must specify a default grounding object. So the question may be raised: What in general determines which object is the default grounding object pertinent to an utterance or a conversation? I do not think it should be terribly difficult to answer that question. In general, a conversation will be about a larger or smaller situation. So the context that pertains to a conversation may, at the very least, have as its default grounding object the situation to which the conversation pertains. Moreover, Stanley’s theory is at no advantage in this regard. As I noted at the end of the previous section, he too owes an account of what makes it the case that a certain object is the referent of the hidden variable associated with the noun in a highest-level quantifier phrase. In


9 Moreover, the idea of treating nouns as relations is not new. Cresswell (1996) treats ‘enemy’ as a relation in order to obtain the reading of ‘Every soldier faced an enemy’ as meaning for every soldier x, x faced an enemy of x’s. As it stands, however, Cresswell’s framework will not yield the desired readings of bound quantifier sentences because he does not incorporate anything like the function f into his semantics.


fact, his theory incurs an obligation that mine does not, namely, to explain how that object becomes associated with a hidden variable. Against the present account, it may be objected that it is just too odd to interpret a sentence as a set of objects and to ‘postpone’ the evaluation of the sentence as true or false until it is decided whether a certain particular object is a member of that set. However, we will see in the next section that one way of giving a precise formulation to Stanley’s theory results in this feature as well, and moreover, it seems inevitable that our semantics will work in this way wherever there are variables that may either be bound, if the sentences containing them are embedded under other quantifier phrases, or remain free, in which case they must be interpreted ‘deictically’ or in light of the context (provided we do not adopt any kind of ‘dynamic’ semantics). Consider, for example, ‘There is a dog such that Johnny loves it’ (obviously, not a very natural sentence of English). We will want to say that this is true if and only if there is a dog in the set of things that satisfies ‘Johnny loves x’. So if ‘Johnny loves it’ is to have the same meaning when it stands alone as when it is embedded under the phrase ‘There is a dog such that’, we will want to say that ‘Johnny loves it’ denotes, not a truth value, but a set of assignment functions, and is true if and only if the assignment function selected by the context is in that set. Against the present account, it may also be objected that it is just too odd to interpret a noun as a relation. The answer to that is, first, that it is not exactly true that the account interprets nouns as relations. Rather, as I emphasized, it is nouns relative to contexts that are interpreted as relations, and that interpretation of nouns relative to contexts is given in terms of the traditional interpretation of nouns as sets. And second, if it is granted that the context might affect which subset of the traditional extension of a noun is the subset that the truth value of a sentence relative to the context depends on, and that, moreover, the context might pick out various different subsets of the traditional extension (so that they may be ‘quantified over’ in bound quantifier sentences), then it should not be surprising that the contextrelative extension of a noun should be a relation between grounding objects and members of the traditional extension.9

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4 STANLEY’S THEORY MORE PRECISELY

According to one formulation of this principle, a semantic theory is compositional just in case, for each complex expression, there is exactly one way, determined solely by its structure, in which the meanings of its constituents are combined by the semantic theory to yield its meaning.10 (2000: 395) This commitment to compositionality rules out the kind of semantic evaluation employing variable assignments familiar from first-order logic. In first-order logic, we typically say that the sentence ‘"x(Student(x) / Walks(x))’ is true relative to variable assignment s if and only for every x-variant of s, if ‘Student(x)’ is true on that x-variant of s, then so is ‘Walks(x)’. This way of formulating the semantics for the usual sort of language for logic (there might be others) does not qualify as compositional, according to Stanley’s standard, because it is not the case that we proceed by assigning a single meaning to ‘Student(x)’ and a single meaning to ‘Walks(x)’ and then combining them in a manner associated with the syntactic form ‘"x(F / G)’. Rather, we have to compare the value of ‘Student(x)’ and ‘Walks(x)’ for each of the xvariants of variable assignment s.

10 Stanley (2000: 395) immediately goes on to say: ‘It follows from this principle that, although the meaning of a non-complex word may vary with context, the way in which the interpretation of a complex expression is derived from the interpretations of its parts cannot vary with context’. On the legitimacy of this particular stricture, see the critical comments in Pelletier 2003.


I now want to consider how Stanley’s own theory might be formulated more precisely. This will serve two purposes. First, on the assumption that the formulation I come up with is correct, we will find that the overall ‘shapes’ of the two theories are quite close. Second, this formulation will reveal that Stanley’s theory is like mine in requiring a second appeal to the context in assigning truth values to sentences. However, the present precisification of Stanley’s theory will not play any role in the comparison of my theory to his in section 5. In presenting Stanley’s theory, we may hold him to a certain requirement of compositionality that he explicitly endorses. What his compositionality requirement means is, roughly, that we should be able to generate the meaning of each compound expression by taking the meanings of the expression’s subcomponents and applying to those meanings a function associated with the grammatical rule that combines those subcomponents to form the compound expression. Stanley’s way of formulating the requirement is this:


½½ÆN, f(i)æc ¼ ½½N \ c(‘f ’)(c(‘i’)). Where t is a term and o is an object, let c[t/o], called the t-o-variant of c, be the context just like c except that it assigns o to t instead of whatever c assigned to t. Then whole sentences may be interpreted on the pattern of the following: ½½[[Every Ægirl, f(i)æ] [answered [every Æquestion, g(j)æ]]]c ¼ True iff "x(x 2 ½½Ægirl, f(i)æc / x 2 ½½[answered [every Æquestion, g(j)æ]]c[‘j’/x]) iff "x(x 2 ½½Ægirl, f(i)æc / "y(y 2 ½½Æquestion, g(j)æc[‘j’/x] / Æx, yæ 2 ½½answered)). Assuming the context assigns appropriate functions to ‘f ’ and ‘g’, this gives us the desired reading of ‘Every girl answered every question’. The trouble with this approach is that, contrary to Stanley’s intentions, this account fails to be compositional in just the way in which the familiar account of ‘"x(Student(x) / Walks(x))’ fails to be compositional, as I explained above. The context-relative truth value of a sentence is not calculated solely on the basis of the context-relative extensions of its components. When calculating the semantic value of [[Every ÆN, f(v)æ] VP] at c, we need to know more than the value of VP at c; we need to know the value of VP at each of a number of variants of c (one for each member of the extension of ÆN, f(v)æ at c). A preferable alternative, therefore, might be to let the composition rule for expressions of the form ÆN, f(i)æ interpret such expressions as expressing relations, thus:


The main problem we face when we try to formulate Stanley’s theory in a precise way is how to interpret the expressions of the form ÆN, f(i)æ that occur in his syntactic representations. Whenever Stanley confronts this question himself, what he says about it is just not right. What he says (Stanley & Szabo´ 2000: 253; Stanley 2002b: 370) is that the extension of ‘Æman, f(i)æ’ relative to a context c is the intersection of the extension of ‘man’ and c(‘f ’)(c(‘i’)). But that is not right since it treats ‘i’ as a constant (relative to the context) and not a variable and so does not give us the extension of ‘Æman, f(i)æ’ in the case in which ‘i’ is supposed to be a variable bound by a higher quantifier. Off hand, it might seem that we could let Stanley retain the assumption that ‘i’ is a constant but then treat it also as a variable by letting contexts do duty as variable assignments and introducing, in the course of our interpretation, ‘variants’ on the context. Suppose the extensions of nouns (such as ‘girl’) are specified as Stanley and Szabo´ propose, thus:

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½½ÆN, f(v)æc ¼ {Æx, yæ j y 2 ½½N and y 2 c(‘f’)(x)}.11 So the extension of a noun-indexical pair in a context c is a set of pairs in which the first member is a grounding object, as I have been calling it, and the second member is an object in the intersection of the extension of the noun and the set of objects (the domain) generated from the grounding object by the function that the context assigns to ‘f ’. For example, the extension of ‘Ægirl, f(i)æ’ in context c might be a set of pairs such that the first object in each pair is a class in a school and the second object in the pair is a girl in the set of students in that class. The rule for transitive verbs such as ‘answers’ can be the following nearly trivial rule: Composition rules for verb phrases and sentences may include the following: ½½[V [every ÆN, f(v)æ]]c ¼ {x j "y (Æx, yæ 2 ½½ÆN, f(v)æc / Æx, yæ 2 ½½Vc)}. ½½[[every ÆN, f(v)æ] VP]c ¼ {x j "y (Æx, yæ 2 ½½ÆN, f(v)æc / y 2 ½½VPc)}. These rules generate an extension for ‘Every girl answered every question’, as follows: ½½[[Every Ægirl, f(i)æ] [answered [every Æquestion, g(j)æ]]]c ¼ {x j "y(Æx, yæ 2 ½½Ægirl, f(i)æc / y 2 {z j "w (Æz, wæ 2 ½½Æquestion, g(j)æc / Æz, wæ 2 ½½answeredc)})}. Thus, the extension of the sentence is the set of grounding objects such that for each girl in the domain associated with that grounding object, that girl answered every question in the set of questions associated with that girl. But our reconstruction of Stanley’s theory is not finished until we explain what it takes for a sentence to be true in a context. For this, Stanley’s theory, as I am presently developing it, will require the following additional rule: If i is the sole free variable in [S], and c(i) ¼ a, then [S] has a truth value in c and the truth value of [S] in c is True if and only if a 2 ½½Sc. (This rule can readily be generalized to cover the case in which a sentence contains more than one free variable.) Thus, while the extension of 11

job.

If, as Stanley (2002b: 374–76) argues, ‘f ’ too is truly a variable, then this account will not do the


½½Vc ¼ {Æx, yæ j Æx, yæ 2 ½½V}.


a sentence remains a set of grounding objects, a sentence may be treated as a closed formula and has a truth value if the context assigns an object to i. Thus, as I anticipated at the end of the previous section, we find that Stanley’s theory too interprets a sentence as a set of objects and ‘postpones’ the evaluation of the sentence as true or false until it is decided whether a certain particular object is a member of that set. At this point, it might seem as though my account of Stanley’s theory has violated Stanley’s own strictures on the form of a semantic theory. In a continuation of the passage that I quoted above, Stanley writes:

In light of what Stanley means by ‘element’, the second sentence in this passage seems clearly to say that context can play a role at most in assigning values to leaf nodes; context cannot play a second role, as it does in my reconstruction, in interpreting the remaining free variable in a sentence.12 For the following reason, it seems to me that there will be no trick by means of which Stanley will be able to avoid this second application of the context: Throughout the composition of the extension of a sentence, we must assume that the ‘i’ in an expression of the form ÆN, f(i)æ is a variable, not a constant. That is because we must always be prepared to find that an expression of which it is a part is a component of a larger expression in which the variable is bound. Only once we have reached the top node of the syntactic tree will we be in a position to determine finally that the ‘i’ can be treated as a referring pronoun (and may be not even then, if it is an anaphor with an antecedent in an earlier sentence in the text). At that point, we have to appeal to the context again to determine the semantic value of the pronoun. 12

Incidentally, what Stanley supposes in the first sentence in this passage clearly does not imply what he infers in the second sentence. An effect of context might be ‘traceable to logical form’ though the effect of context is not the assignment of any kind of value to any particular lexical item. For instance, we could have a theory of conditionals on which the value of a conditional relative to a context always depended on the content of a domain of possibilities provided by the context. That would not force us to think of that domain of possibilities as a value that the context assigned to the word ‘if ’. Perhaps Stanley would disagree. King and Stanley assume that if a similarity relation among worlds has a bearing on the content of a subjunctive conditional, then it must be ‘traceable to the syntax of the conditional construction, perhaps to the words ‘‘if ’’ and ‘‘then’’ themselves’ (King & Stanley 2005: 152), but they offer no argument for this assertion. This same mistaken inference is repeated in the final paragraph of Stanley 2000 (431).


Suppose my principal claim is true, that all effects of extra-linguistic context on the truth-conditions of an assertion are traceable to logical form. Then, the effects of context on the truth-conditional interpretation of an assertion are restricted to assigning values to elements of the expression uttered. (2000: 396)

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5 THE NEED FOR GLOBAL DOMAINS As I noted at the start, Stanley’s theory and mine are not equivalent. They yield different interpretations of some sentences. In particular, they differ in their interpretations of the following sentence: (S) Every student is happy and some student is not happy, On Stanley’s theory, there will be a single context in which (S) is true. On my theory, by contrast, there is no single context in which (S) is true. So we might still have a reason to posit Stanley’s hidden indexicals in syntax if we could be persuaded that (S) is really true in some contexts. Whereas, if (S) is not true in any context, then there might be no reason remaining not to prefer the present theory of bound quantifier sentences without hidden indexicals.


A direct comparison of Stanley’s theory, as I have formulated it, to my own theory shows that they are really very close. Stanley’s theory adds an expression of the form ‘f(v)’to each noun and uses the context to interpret ‘f ’ rather than, as on my theory, just letting the context supply a function f and then using that function to provide the context-relative interpretation of the noun. Moreover, if ‘v’ remains free, then the truth value of a sentence may depend on what context assigns to it rather than depending on a default grounding object that context supplies. Nonetheless, as we will see in the next section, these differences are enough to make a difference to the readings that Stanley’s theory and mine supply for certain sentences. I should acknowledge, incidentally, that I have not shown that either Stanley’s theory or mine conforms to every requirement that might be imposed under the aegis of compositionality. In particular, I have not shown that the composition rules of our theories can be formulated in such a way that the meaning of each expression can be calculated from the meaning of its daughter nodes alone. (In presenting both theories, I have used rules that invoke the granddaughters.) In a strictly ‘local’ semantics, a quantifier phrase of the form [every N] will have a single meaning that is the same whether it occurs in subject position or object position. As it turns out, it is not straightforward to obtain the result that a single meaning expressed by [every N] generates both the meaning of a verb phrase such as [V [every N]] and the meaning of a sentence such as [[every N] VP] (Heim & Kratzer 1998: chap. 7). The sentences that interest us here, such as [[Every girl] [answered [every question]]], have such phrases in both these positions.


In the following subsection, I will show that the two theories do indeed differ in this way. After that, I will argue that the preferable result is that of my own theory.

5.1 That the theories differ

½½VPintc ¼ {x j x 2 ½½VPint}. ½½neg(VPint)c ¼ {x j x ; ½½VPintc}. ½½[[some N] VP]c ¼ {x j dy(Æx, yæ 2 ½½Nc and y 2 ½½VPc)}. ½½[[S1] and [S2]]c ¼ {x j x 2 ½½S1c and x 2 ½½S2c}. (Let neg(VPint) be a syntactically correct negation of VPint.) By these rules, it follows that ½½[[[Every student] [is happy]] and [[some student] [is not happy]]]c ¼ {x j "y (Æx, yæ 2 ½½studentc / y 2 ½½is happyc) and dy (Æx, yæ 2 ½½studentc and y ; ½½is happyc)}. Since that set is inevitably empty, it cannot happen that ac is a member, and so, by the Truth Rule, the sentence will not be true in c. So (S) is not true in any context. On Stanley’s theory, the syntactic structure underlying (S) contains hidden indexicals and that underlying syntactic structure is certainly one that may be true in some context. So rather than formulating the question as whether (S) itself is true in some context, we should perhaps formulate it as the question whether (S) should be understood as having an underlying syntactic structure that is true in some context. But inasmuch as (S) itself will in any given context inherit a semantic


On Stanley’s theory, reverting to the improvised notation, sentence (S) is represented as, ‘For every j in Æstudent, f(i)æ, j is happy, and for some h in Æstudent, g(k)æ, h is not happy’. So represented, there are contexts in which (S) is true. It will be true in a context if the context assigns to ‘f(i)’ a group of students who are happy and assigns to ‘g(k)’ a different group of students that includes one who is not happy. (Even if we write ‘f ’ in place of ‘g’, there will be contexts in which the result is true since the function is applied to different objects, i and k, in the two conjuncts.) By contrast, on my theory, (S) is not true in any single context. To obtain the result that the sentence (S) is not true in any context, all we need to add to the apparatus of section 3 is a rule for the extension of intransitive verb phrases such as ‘is happy’ and a few more composition rules:

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13 The corresponding concept of validity at a world would be this: A sentence is valid at a world if and only if for each context in that world, it is true in that context at that world. A sentence is valid in this sense across all worlds if and only if for each world w, for each context c in w, the sentence is true in c at w. This generalized notion of validity corresponds to what Kaplan (1989: 547) calls ‘valid in LD’, although Kaplan’s notation reduces the double reference to worlds to one.


value from that of its underlying structure, we can just as well formulate it as the question whether (S) itself is true in any context. We might express the difference between Stanley’s theory and mine by saying that on his theory, (S) is not a contradiction, while on mine, it is a contradiction. But here we have to give some thought to what we mean by ‘contradiction’. Traditionally, for languages not permitting context-relativity, contradictions have been defined in either of two ways. We may say either (1) that a sentence is a contradiction if it is not true on any interpretation of the non-logical vocabulary or (2) that a sentence is a contradiction if it is not true in any possible world; it expresses the empty set of worlds. These are not equivalent of course since there may be sentences that are true on some interpretation but not true in any possible world given the meanings that the constituent terms actually have. But both notions have currency, and the second has been used with increasing frequency in recent decades. For definiteness, I will take (2) as our initial concept of contradiction. If now we want to extend that concept of contradiction to a language permitting context-relativity, we can go in any of three directions. We can say that a sentence is a contradiction in a context if and only if in that context it is true at no worlds; in that context, it expresses the null proposition. Or second, we can say that a sentence is a contradiction at a world if and only if for each context in that world, it is not true in that context at that world.13 Or third, we can say that a sentence is a contradiction (simpliciter) if and only if it is not true in any context at any world (letting context and world vary independently). All these notions might have their uses, but we need to be clear about which one we are using. If we speak in terms of the first, context-relative concept of contradiction, then we might say that even Stanley’s theory allows that (S) is a contradiction in some contexts (and not merely that it is false in some contexts). But if we speak in terms of either the world-relative or the absolute conception of contradiction, then we must say that on Stanley’s theory, (S) is simply not a contradiction. In this paper, I have not been concerned with intensions, only extensions; evaluations at possible worlds other than the actual have not been at issue. So for present purposes, we can collapse the distinction between contradictions-at-a-world and


14 If he did say this, then he would have to cancel some of his objections to contextualism about ‘knows’ in Stanley 2005a (60–8).


contradictions simpliciter. What we should say then is that Stanley’s theory and mine differ over whether (S) is a contradiction in the sense that it is not true in any context; Stanley says it is not, and I say it is. Similarly, when we define the validity of arguments for languages permitting context-relativity, we can go in various directions. We can say that an argument is valid at a context if and only if the intersection of the sets of worlds that the premises express at that context is included in the set of worlds that the conclusion expresses at that context; that an argument is valid at a world if and only if, for each context in that world, if the premises are all true in that context at that world, then so is the conclusion; or that an argument is valid (simpliciter) if and only it preserves truth across variation in both context and world. But, again, for present purposes, we can collapse the third definition into the second. Stanley’s theory and mine will differ on what they regard as valid in the sense that for every context in which the premises are true, the conclusion is true. For instance, on Stanley’s theory, the argument having ‘Everyone is happy’ as premise and ‘Every child is happy’ as conclusion will not be valid in that sense; but on my theory, that argument will be valid in that sense. The main features of Stanley’s theory could be preserved, while ensuring that (S) is true in no context, by stipulating that for any two occurrences of a single noun in a single sentence, if neither is subordinate to the other, then the same domain of objects has to be assigned to the indexicals associated with those two occurrences.14 We would have to exempt cases in which one occurrence is subordinate to another; otherwise, we will not get the readings that Stanley wants for bound quantifier sentences like ‘Every sailor waved to every sailor’. But no such simple proposal will solve the problem in any case. The sentence ‘Every mammal is healthy, every rodent is a mammal and some rodent is not healthy’ is equally a contradiction, but the modified theory would still allow us to interpret this sentence as not a contradiction, because even on the modified theory there will be a context in which the domain associated with ‘mammal’ in the first conjunct is the animals in the zoo and the domain associated with ‘rodent’ in both occurrences is the animals on earth and the domain associated with the second occurrence of ‘mammal’ is also animals on earth. The second occurrence of ‘mammal’ is subordinate to ‘rodent’, and therefore, the proposed modification does not restrict it to the animals in the zoo. In such a context, this sentence will be true if every

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mammal in the zoo is healthy but there is an unhealthy rodent in a waste dump somewhere.

5.2 Reasons to affirm that (S) is true in some contexts

(H) He is happy and he is not happy. This sentence, I think we should agree, may be true in a single context. In a single context, the two occurrences of ‘he’ may refer to different people, and in such a context, the sentence will be true if the first occurrence of ‘he’ refers to a happy person and the second occurrence refers to a person who is not happy. However we understand contexts and context-relativity, it is surely not the case that we can interpret (H) as true only by positing a shift between the context in which we


Stanley himself has not said in print that sentences such as (S) are not contradictions, not even when the issue arose in the context of his paper with Williamson (Stanley & Williamson 1995). On the first page, Stanley and Williamson acknowledge the contradictory aspect of such sentences, but they do not propose an account of it, and as far as I am aware, Stanley has not addressed the issue in any other publication. Here I cannot decisively prove that (S) is true in no context, but I think I can rebuff two reasons that might be given to think that (S) is true in some contexts, and in the next section, I will give one, not completely decisive reason to maintain that (S) is not true in any context. But first I have to forestall a confusion. On two occasions, I have been surprised to be told that if I interpret (S) as a contradiction (i.e. not true in any context), then I cannot obtain the desired readings of the sailor sentence. (It was precisely in order to address this objection that I brought up the sailor sentence in sections 2 and 3.) I suppose the thought has been that if a single context can interpret the two occurrences of ‘every sailor’ relative to different domains in order to obtain the desired readings of the sailor sentence, then a single context can interpret ‘every student’ and ‘some student’ in (S) relative to different domains, so that (S) will be true in some contexts. However, that’s a mistake. The crucial difference between the sailor sentence and (S) is that in the sailor sentence the second occurrence of ‘every sailor’ is syntactically subordinate to the first occurrence, while in (S) ‘every student’ and ‘some student’ are coordinate. We have seen that my own theory can yield either of the desired readings of the sailor sentence, given suitable contexts, while still treating (S) as not true in any context. A first thought that might give one reason to expect that (S) will be true in some contexts is the fact that it is comparable to:


15 I do not think there is any ‘received view’ about how context-relativity should be understood so as to accommodate different referents for distinct occurrences of a single word, but surely we must accept that that may occur. Kaplan’s 1989 would be the first place to look, but actually he discusses a couple ways of handling the matter. One way involves putting subscripts on the pronouns. The other way involves thinking of the pronoun as accompanied by a gesture or (in the postscript) an intention. On both these approaches to sentences like (H), Kaplan in effect denies that we are dealing with two occurrences of the same lexical item; rather, the first ‘he’ and the second ‘he’ are two different lexical items.


evaluate the first conjunct and the context in which we evaluate the second.15 So it might be said that, in precisely the same way, sentence (S) will be true in a context in which the hidden indexical associated with ‘student’ in ‘every student’ refers to a domain in which every student is happy and the hidden indexical associated with ‘student’ in ‘some student’ refers to a domain in which some student is not happy. But I think the comparison should not persuade us that (S) may be true in some context, because there are at least two relevant differences between (S) and (H). First, the demonstrative expressions in (H) are on the surface, whereas no such demonstrative expressions lie on the surface of (S). Consequently, one cannot reason by any direct analogy from the fact that (H) is true in some context to the conclusion that (S) is true in some context. Moreover, this difference may undercut any attempt to establish a hidden analogy between (H) and (S). It is often by means of the speaker’s creating some relation between an utterance of ‘he’ and the object that it refers to that the speaker brings it about that the hearer understands what an occurrence of ‘he’ does refer to. For example, the speaker may say ‘he’ while pointing at the referent or while staring at him, and the very simultaneity of the uttering with the pointing or staring indicates to the hearer that the referent of ‘he’ is the person pointed to or stared at. Whereas since Stanley’s hidden indexicals are inaudible, it cannot be any relation between an occurrence of one of them and the set of things that it picks out that serves as the basis for the hearer’s understanding. Another point of difference between (S) and (H) is that, while there are conventions that speakers can exploit to put hearers in a position to decide on an interpretation of demonstratives such as ‘he’, there do not seem to be comparable conventions that speakers can exploit to put hearers in a position to select a domain for a noun phrase such as ‘student’. This is not the same difference as that identified in the previous paragraph, because not all those conventions rely on gestures and simultaneity. For example, it is conventional to rely on syntactic parallels with prior texts. Consider:

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(H#) Alfred got the blue doll and Bruno got the pink one. He was happy and he was not happy. This is a bit odd considered as a written text, but if we think of it as a transcript of spoken words, we have no difficulty understanding that, barring indications to the contrary elsewhere, the first ‘he’ will refer to Alfred, because he was mentioned first, and the second ‘he’ will refer to Bruno because he was mentioned second. By contrast, in the following text, the domains that might be associated with nouns do not seem so readily recoverable:

If we had to guess, we might expect, on the basis of the connection between fun and happiness and between tests and unhappiness, that the domain for the first ‘student’ is Mrs Kaplinger’s class and that the domain for the second ‘student’ is Mr Tufigno’s class, but the fact that Mrs Kaplinger’s class is mentioned first and Mr Tufigno’s class is mentioned second plays no role. Even in the case of ‘he’, the correct interpretation will depend on a variety of considerations, such as pointing, syntactic parallelism, and which interpretation is most charitable in light of the meanings of the other words in the sentence, and none of these factors dominates the others. So the conventions, such as they are, do not strictly determine an interpretation (Gauker 2008). However, in the case of the domains for nouns, it does not seem that even to this extent the correct interpretation is governed by commonly recognized conventions. Normally, the only way to differentiate the domains associated with distinct occurrences of a single noun is to add differentiating phrases such as ‘in Mrs Kaplinger’s class’ and ‘in Mr Tufigno’s class’. A second thought that might give one reason to expect that (S) will be true in some contexts is the fact that a person could conceivably express a truth by uttering (S). We might imagine that a school principal, gesturing towards a classroom on the left side of the hall, begins by saying, ‘Every student is happy. . .’, and, then, gesturing towards a classroom on the right side of the hall, continues, ‘. . .and some student is not happy’. In that case, it might seem, (S) will be true if every student in the classroom on the left is happy but some student in the classroom on the right is not happy. My answer to this will be that we do not have to understand the principal as expressing something true by uttering a sentence that is true in the context of her


(S#) The students in Mrs Kaplinger’s class always had lots of fun, but in Mr Tufigno’s class there were always lots of tests. Every student was happy and some student was not happy.



utterance. But first I have to explain why I do not answer the observation in a different way. One thing to say in response to the example of the principal, on behalf of the thesis that (S) is not true in any single context, would be that her utterance involves a context shift. Between the utterance of the first conjunct and the utterance of the second, the context shifts, so that the domain for the utterance of the first conjunct is the set of people in the classroom on the left side of the hall and the domain for the utterance of the second conjunct is the set of people in the classroom on the right side of the hall. If that were true, then the story of the principal would not give us what Stanley’s theory needs, namely a case in which the whole of (S) is true relative to a single context. Even my own account of bound quantifier sentences without hidden indexicals could allow that both conjuncts were true relative to different contexts (with their different grounding objects and different domain assignment functions). If in all such cases Stanley conceded that (S) is true only across a pair of contexts, there might be no reason left to prefer his theory of hidden indexicals over the present theory of bound quantifier sentences without hidden indexicals. But in fact, it is probably not reasonable to posit a context shift in the example of the principal. Contrary to what is often said, we should not think of contexts as things that shift whenever a shift is necessary in order for the speaker’s sentence to qualify as true relative to the context that the speaker is in. If on a Wednesday I say, ‘Today is Tuesday’, I cannot make it the case that the context assigns a Tuesday to the word ‘Today’ so that what I say is true. If I utter the words ‘Today is Tuesday’ under normal circumstances (ignoring answering machine cases and the like), then what I say is true only if the time of my utterance is during a Tuesday, even if my hearer succeeds in recognizing that what I have in mind is some other day. Similarly, if I point to a garish green and pink necktie and say ‘That is a tasteful tie’, I do not make what I say true just by thinking of some other tasteful tie. If I point to the garish tie and say ‘That is a tasteful tie’, then what I am saying is, regarding the tie I am pointing at, that it is a tasteful tie even if I succeed in communicating to my interlocutor that the tie she had in her hand before that one came before my eyes is a tasteful tie. More generally, if we want to think of truth in a context as some kind of ideal that speakers should strive for, then we should not make achieving it too easy by supposing that the context always shifts to accommodate the truth of whatever we say relative to the context of our speaking.

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However, there is a different response that we can make to the example of the principal on behalf of the assumption that (S) is true in no context. Quite often, when a person says something untrue, though we cannot believe that he or she made the same mistake in thought, we conclude that the speaker did not say what he or she had in mind. In the case of the principal, we may say that while her sentence was strictly speaking untrue relative to her context, what she had in mind may have been perfectly true, where what she had in mind in this case was that every student in the classroom on the left side of the hall was happy and some student in the classroom on the right side of the hall was not happy. We expect the principal to recognize the sentence she uttered as a contradiction (true in no context) as well as we do. So we figure that what she had in mind must have been something different from what her sentence really means; her gestures to one side of the hall and then the other serve as clues to the meaning she had in mind (which is not to say that she intended them as such). Perhaps her uttering of a contradiction was just a slip due to her nervousness, trying to speak too fast and omitting words that she meant to speak. Or perhaps the principal and her interlocutor took logic together in college and the principal wishes to test her interlocutor’s memory of what she learned while at the same time communicating something about the students. Furthermore, if we allow that (S) is true when the principal utters it merely on the grounds that we can perfectly well understand what she meant in uttering it and what she meant was true, then by the same token, we will find ourselves making rather implausible claims about the validity of arguments. Suppose that Mick and Marty are two trouble-making friends whom the sheriff suspects of being accessories to a crime. Mick is indeed guilty but Marty is innocent. The sheriff says to the deputy, ‘Mick was an accessory to the crime’, and, then, gesturing to the room next door where Marty is locked up, continues, ‘So someone was an accessory to the crime’. Do we really want to say that the sheriff ’s premise is true in his context but his conclusion is not true in his context on the grounds that none of the people whom the sheriff has in mind in saying ‘someone’, namely people in the next room, is an accessory to the crime? If we say that and, as before, decline to posit a context shift, then there is a single context in which the sentence ‘Marty was an accessory to the crime’ is true and the sentence ‘Someone was an accessory to the crime’ is not true. So the argument from the first sentence to the second sentence is invalid. And if we say that, then the prospects of a logic for natural language begin to look dim. This is not to say that Stanley’s theory puts an end to logic; it does


not. But the example does indicate that we need a better reason to favour Stanley’s theory than the example of the principal can provide.

5.3 A reason to deny that (S) is true in any context

(a) Tipper is ready and Tipper is not ready. (b) Tiny is big, Dumbo is small, and Dumbo is bigger than Tiny. (c) France is hexagonal, and Italy is not boot-shaped. (d) The ham sandwich wants his check, and the ham sandwich is only half-eaten. (e) Sam knows that his car is in his driveway, but he doesn’t know that it hasn’t been stolen.16 In some of these cases, the oddness is clearly not metaphysical impossibility. For example, (c) is not impossible. France could be perfectly hexagonal while Italy was not at all boot-shaped. In each case, the oddness consists in the fact that one part of the sentence suggests that some phrase in the sentence is to be interpreted, in light of the context, in one way, but another part of the sentence suggests that that same phrase is to be interpreted, in light of the context, in a different, incompatible way. For example, given the actual shapes of France and Italy, the first conjunct of (c) tells us that ‘hexagonal’ is to be understood in context in such a way that anything that is as close to being truly hexagonal as France is will qualify as belonging to the extension of ‘hexagonal’. But then if we are interpreting shape terms as generously as that, it seems wrong to deny, as the second conjunct of (c) does, that Italy falls into the extension of ‘boot-shaped’. Two facts about (a)–(e) and (S) suggest that the oddness of these sentences should be the object of a semantic explanation. First, we do not have to think very hard about the scenarios in which such sentences might be uttered in order to see that there is something wrong with them. Their oddness is not due simply to the fact that we 16

This last example comes from MacFarlane 2009 (240). MacFarlane uses the example to argue, against Stanley, that it is not necessary to think of elements of the context as assigned to elements of syntax, which is the point I am pressing as well.


In the previous section, I have at most pointed to paths by which we can escape the conclusion that a sentence like (S) is true in some contexts. Next I want to indicate a positive, though certainly not decisive, reason to think that we should deny that (S) is true in any context. Here are some other sentences that are odd in the same way as (S):

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have a hard time imagining a scenario in which a speaker might use one of these sentences to communicate something reasonable. If that were the source of their oddness, then we would expect the oddness to dissipate if we managed to imagine a circumstance in which one of these sentences might be uttered (such as the example of the principal); but that is not the case. Compare the case of ‘I am not here now’. Under the influence of Kaplan (1989), the oddness of this was often considered semantic. The sentence was supposed to express a kind of contextual impossibility. But in light of answering machine cases (reviewed in Predelli 2003), it is now generally recognized that there is nothing wrong with this sentence other than the exceptionality of the circumstances under which it might be correctly used. Thus, the oddness of ‘I am not here now’ turned out to be pragmatic, not semantic. But the oddness of (a)–(e) and (S) is not merely of this kind. So the oddness of these sentences does not in this way turn out to be merely pragmatic. The second fact that indicates the need for a semantic account of the oddness of these sentences is that there is a similarity between these sentences with respect to the way in which they are odd that cries out for a uniform explanation, and it is hard to see how the needed generalization might pertain to the pragmatics of interpersonal communication rather than to the semantic properties of these sentences. In the case of a paradigmatically pragmatic phenomenon, such as conversational implicture, what the various cases have in common, if anything, is an inference scheme by which the hearer draws conclusions from what the speaker literally said and the circumstances of speaking. But in the case of (a)–(e) and (S), any attempt to explain why a speaker is unlikely to mean anything sensible in uttering them takes us back to their semantic properties. In each case, we can say that the several conjuncts lead the hearer to draw incompatible conclusions, but when we ask how they do this, the answer seems to be that the several conjuncts demand that the context set the values of certain parameters in incompatible ways. For each of the sentences (a)–(e) and (S), the oddness can be explained as follows: For each of these sentences, there is a parameter p of interpretation, the value of which is set by the context of utterance c, such that there is a conjunct S1 in the sentence and a kind K of values that p can take such that S1 is true relative to c only if the value of p in c is of kind K, and there is another conjunct S2 that can be true in c only if the value of p in c is not of kind K. Consequently, the sentence as whole is true in no context (assuming that other demonstrative elements are interpreted uniformly). In the case of sentence (S), the


pertinent parameter is the domain of objects that the context assigns to the contextually determined grounding object, via the function fc, as I have explained in section 5.1, above. The truth of ‘Every student is happy’ in context demands that that domain for the context include only happy students (kind K is domains that include only happy students), and the truth of ‘Some student is not happy’ in context demands that the domain include at least one student who is not happy (in which case the domain is not of kind K). 6 THE BROADER SIGNIFICANCE OF THIS ISSUE

Acknowledgements I thank Jason Stanley, Zoltań Gendler Szabo´, Francis Jeffry Pelletier, and Owen Greenhall for feedback on this project at various stages. Of the three anonymous referees for the Journal of Semantics, one in particular provided very extensive and useful comments. I also thank The Taft Research Center of the University of Cincinnati for research support during 2008–2009.

CHRISTOPHER GAUKER Department of Philosophy University of Cincinnati Cincinnati, OH 45221-0374 USA e-mail: [email protected]


In the past twenty years or so, philosophers of language have become increasingly aware that in many ways the semantic value of a sentence is relative to a context of utterance. Those of us who think that contextrelativity is not a reason to abandon hope for a precise, recursive semantics for natural languages have wished to impose some discipline on claims about context-relativity. The requirement that contextrelativity is exclusively the context-relative evaluation of indexical elements in the syntax of the sentence would be one way to impose some discipline, and Stanley appears to be partly motivated by this consideration (cf. 2002a, passim; Stanley 2002b: 365, 387; King & Stanley 2005: 142). But this requirement would assimilate all contextrelativity to the context-relative evaluation of demonstratives such as ‘this’ and ‘that’, and with good reason that may be deemed a mistake. Here we have seen that without abandoning the hope for a precise recursive semantics for natural language we can admit that semantic value is relative to context in other ways as well.

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REFERENCES phy 23:391–434. (Reprinted in Stanley 2007.). Stanley, Jason. (2002a), ‘Making it articulated’. Mind and Language 17:149–68. (Reprinted in Stanley 2007.). Stanley, Jason. (2002b), ‘Nominal restriction’. In Gerhard Preyer & Georg Peter (eds.), Logical Form and Language. Oxford University Press. Oxford. 365–88. (Reprinted in Stanley 2007.). Stanley, Jason. (2005a), Knowledge and Practical Interests. Oxford University Press. Oxford. Stanley, Jason. (2005b), ‘Semantics in context’. In Gerhard Preyer & Georg Peter (eds.), Contextualism in Philosophy. Oxford University Press. Oxford. 221–53. (Reprinted in Stanley 2007.). Stanley, Jason. (2007), Language in Context. Oxford University Press. Oxford. Stanley, Jason & Timothy Williamson. (1995), ‘Quantifiers and contextdependence’. Analysis 55:291–95. Stanley, Jason & Zoltań Gendler Szabo´. (2000), ‘On quantifier domain restriction’. Mind and Language 15:219–61. (Reprinted in Stanley 2007.). Westersta˚hl, Dag. (1985), ‘Determiners and context sets’. In Johann van Benthan & Alice ter Meulen (eds.), Generalized Quantifiers in Natural Language. Foris. Dordrecht. 45–71. First version received: 14.07.2009 Second version received: 19.10.2009 Accepted: 05.01.2010


Cresswell, M. J. (1996), Semantic Indexicality. Kluwer Academic Publishers. Dordrecht. Gauker, Christopher. (2008), ‘Zero tolerance for pragmatics’. Synthese 165: 359–71. Greenhall, Owen. (2006), The Semantics/ Pragmatics Distinction: A Defense of Grice. Unpublished D.Phil. thesis, New College. Oxford University. Oxford. Heim, Irene & Angelika Kratzer. (1998), Semantics in Generative Grammar. Blackwell. Oxford. Kaplan, David. (1989), ‘Demonstratives: an essay on the semantics, logic, metaphysics, and epistemology of demonstratives and other indexicals’. In Joseph Almog, John Perry, and Howard Wettstein (eds.), Themes from Kaplan. Oxford University Press. Oxford. 481–564. King, Jeffrey C. & Jason Stanley. (2005), ‘Semantics, pragmatics, semantic content’. In Zoltań Gendler Szabo´ (ed.), Semantics versus Pragmatics. Oxford University Press. Oxford. 111–64. (Reprinted in Stanley 2007.). MacFarlane, John. (2009), ‘Nonindexical contextualism’. Synthese 166:231–50. Pelletier, Francis Jeffry. (2003), ‘Context dependence and compositionality’. Mind and Language 18:148–61. Predelli, Stefano. (2003), Contexts: Meaning, Truth and the Use of Language. Oxford University Press. Oxford. Stanley, Jason. (2000), ‘Context and logical form’. Linguistics and Philoso-

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