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VOLUME 26 NUMBER 1 FEBRUARY 2009

CONTENTS ARIEL COHEN No Alternative to Alternatives

1

49

EUNHEE LEE AND JEONGMI CHOI Two nows in Korean

87

FORTHCOMING ARTICLES ALEX LASCARIDES AND NICHOLAS ASHER: Agreement, Disputes and Commitments in Dialogue


YAEL GREENBERG Presupposition Accommodation and Informativity Considerations with Aspectual Still

JOURNAL OF SEMANTICS

JOURNAL OF SEMANTICS

issn 0167-5133


Journal of

SEMANTICS www.jos.oxfordjournals.org

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JOURNAL OF SEMANTICS A N I NTERNATIONAL J OURNAL FOR THE I NTERDISCIPLINARY S TUDY THE S EMANTICS OF N ATURAL L ANGUAGE

MANAGING EDITOR: ASSOCIATE EDITORS:

OF

BART G EURTS (University of Nijmegen) DAVID B EAVER (Stanford University) R EGINE E CKARDT (Universität Göttingen) I RA N OVECK (Institut des Sciences Cognitives, Lyon) PAUL P ORTNER (Georgetown University,Washington) P HILIPPE S CHLENKER (Institut Jean-Nicod, Paris) YAEL S HARVIT (University of Connecticut, Storrs) A NNA S ZABOLCSI (New York University) EDITORIAL BOARD:

N ICHOLAS A SHER (University of Texas, Austin) C HRIS B ARKER (University of California at San Diego) J OHAN B OS (University of Edinburgh) P ETER B OSCH (University of Osnabrück) R ICHARD B REHENY (University College London) M IRIAM B UTT (University of Konstanz) G REG C ARLSON (University of Rochester) A NN C OPESTAKE (Stanford University) H ENRIËTTE DE S WART (Utrecht University) PAUL D EKKER (University of Amsterdam) K URT E BERLE (Lingenio Heidelberg) M ARKUS E GG (Universität des Saarlandes) U LRIKE H AAS -S POHN (University of Konstanz) L AURENCE R. H ORN (Yale University) H ANS K AMP (University of Stuttgart) G RAHAM K ATZ (University of Osnabrück) T IBOR K ISS (Ruhr University, Bochum) J ONAS K UHN (University of Texas, Austin)

CLAUDIA MAIENBORN (Humboldt University, Berlin) JULIEN MUSOLINO (Rutgers University) FRANCIS JEFFRY PELLETIER (University of Alberta) CHRISTOPHER POTTS (University of Massachusetts, Amherst) MARK STEEDMAN (University of Edinburgh) ZOLTAN GENDLER SZABO (Cornell University) KEES VAN DEEMTER (University of Aberdeen) ROB VAN DER SANDT (University of Nijmegen) ROBERT VAN ROOIJ (University of Amsterdam) KAI VON FINTEL (Massachusetts Institute of Technology) ARNIM VON STECHOW (University of Tübingen) BONNIE WEBBER (University of Edinburgh) HENK ZEEVAT (University of Amsterdam) THOMAS EDE ZIMMERMANN (University of Frankfurt)

EDITORIAL CONTACT: [email protected] © Oxford University Press 2009 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 For subscription information please see back of journal.

Scope of this Journal The Journal of Semantics publishes articles, notes, discussions, and book reviews in the area of academic research into the semantics of natural language. It is explicitly interdisciplinary, in that it aims at an integration of philosophical, psychological, and linguistic semantics as well as semantic work done in logic, artificial intelligence, and anthropology. Contributions must be of good quality (to be judged by at least two referees) and must report original research relating to questions of comprehension and interpretation of sentences, texts, or discourse in natural language. The editors welcome not only papers that cross traditional discipline boundaries, but also more specialized contributions, provided they are accessible to and interesting for a general readership in the field of natural language semantics. Empirical relevance, sound theoretic foundation, and formal as well as methodological correctness by currently accepted academic standards are the central criteria of acceptance for publication. It is also required of contributions published in the Journal that they link up with currently relevant discussions in the field of natural language semantics. Information for Authors Papers for publication should be submitted to the Managing Editor by email as a PDF file or PS file attachment. If this is not feasible please contact the Managing Editor.The receipt of submissions is confirmed by email (when there is more than one author to the first author, whom we assume to deal with all correspondence, unless we are instructed differently), and the paper is reviewed by two members of the editorial board or external experts chosen by the editors. The reviewers remain anonymous. An editorial decision is normally reached within 2-3 months after submission. 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 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. The style requirements of the Journal of Semantics can be found at www.jos.oxfordjournals. org, under “Instructions to Authors”, and are binding for the final version to be prepared by the author when the paper is accepted for publication. LATEX submission Please use the Journal class file (http://www3.oup.co.uk/semant/instauth/semant.cls). A tex file (http://www3.oup.co.uk/semant/instauth/guide.tex) is available on how to use the .cls file. Authors who are planning to send source files by email should also include a postscript or PDF version of their paper. Please follow all the instructions to authors that are detailed above and note the text width should be set to 28pc and the text height to 41\baselineskip. Electronic figures can only be used in ps or eps format.

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JOURNAL OF SEMANTICS A N I NTERNATIONAL J OURNAL FOR THE I NTERDISCIPLINARY S TUDY THE S EMANTICS OF N ATURAL L ANGUAGE

MANAGING EDITOR: ASSOCIATE EDITORS:

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BART G EURTS (University of Nijmegen) DAVID B EAVER (Stanford University) R EGINE E CKARDT (Universität Göttingen) I RA N OVECK (Institut des Sciences Cognitives, Lyon) PAUL P ORTNER (Georgetown University,Washington) P HILIPPE S CHLENKER (Institut Jean-Nicod, Paris) YAEL S HARVIT (University of Connecticut, Storrs) A NNA S ZABOLCSI (New York University) EDITORIAL BOARD:

N ICHOLAS A SHER (University of Texas, Austin) C HRIS B ARKER (University of California at San Diego) J OHAN B OS (University of Edinburgh) P ETER B OSCH (University of Osnabrück) R ICHARD B REHENY (University College London) M IRIAM B UTT (University of Konstanz) G REG C ARLSON (University of Rochester) A NN C OPESTAKE (Stanford University) H ENRIËTTE DE S WART (Utrecht University) PAUL D EKKER (University of Amsterdam) K URT E BERLE (Lingenio Heidelberg) M ARKUS E GG (Universität des Saarlandes) U LRIKE H AAS -S POHN (University of Konstanz) L AURENCE R. H ORN (Yale University) H ANS K AMP (University of Stuttgart) G RAHAM K ATZ (University of Osnabrück) T IBOR K ISS (Ruhr University, Bochum) J ONAS K UHN (University of Texas, Austin)

CLAUDIA MAIENBORN (Humboldt University, Berlin) JULIEN MUSOLINO (Rutgers University) FRANCIS JEFFRY PELLETIER (University of Alberta) CHRISTOPHER POTTS (University of Massachusetts, Amherst) MARK STEEDMAN (University of Edinburgh) ZOLTAN GENDLER SZABO (Cornell University) KEES VAN DEEMTER (University of Aberdeen) ROB VAN DER SANDT (University of Nijmegen) ROBERT VAN ROOIJ (University of Amsterdam) KAI VON FINTEL (Massachusetts Institute of Technology) ARNIM VON STECHOW (University of Tübingen) BONNIE WEBBER (University of Edinburgh) HENK ZEEVAT (University of Amsterdam) THOMAS EDE ZIMMERMANN (University of Frankfurt)

EDITORIAL CONTACT: [email protected] © Oxford University Press 2009 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 For subscription information please see back of journal.

Scope of this Journal The Journal of Semantics publishes articles, notes, discussions, and book reviews in the area of academic research into the semantics of natural language. It is explicitly interdisciplinary, in that it aims at an integration of philosophical, psychological, and linguistic semantics as well as semantic work done in logic, artificial intelligence, and anthropology. Contributions must be of good quality (to be judged by at least two referees) and must report original research relating to questions of comprehension and interpretation of sentences, texts, or discourse in natural language. The editors welcome not only papers that cross traditional discipline boundaries, but also more specialized contributions, provided they are accessible to and interesting for a general readership in the field of natural language semantics. Empirical relevance, sound theoretic foundation, and formal as well as methodological correctness by currently accepted academic standards are the central criteria of acceptance for publication. It is also required of contributions published in the Journal that they link up with currently relevant discussions in the field of natural language semantics. Information for Authors Papers for publication should be submitted to the Managing Editor by email as a PDF file or PS file attachment. If this is not feasible please contact the Managing Editor.The receipt of submissions is confirmed by email (when there is more than one author to the first author, whom we assume to deal with all correspondence, unless we are instructed differently), and the paper is reviewed by two members of the editorial board or external experts chosen by the editors. The reviewers remain anonymous. An editorial decision is normally reached within 2-3 months after submission. 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 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. The style requirements of the Journal of Semantics can be found at www.jos.oxfordjournals. org, under “Instructions to Authors”, and are binding for the final version to be prepared by the author when the paper is accepted for publication. LATEX submission Please use the Journal class file (http://www3.oup.co.uk/semant/instauth/semant.cls). A tex file (http://www3.oup.co.uk/semant/instauth/guide.tex) is available on how to use the .cls file. Authors who are planning to send source files by email should also include a postscript or PDF version of their paper. Please follow all the instructions to authors that are detailed above and note the text width should be set to 28pc and the text height to 41\baselineskip. Electronic figures can only be used in ps or eps format.

JOURNAL OF SEMANTICS Volume 26 Number 1

CONTENTS ARIEL COHEN No Alternative to Alternatives

1

YAEL GREENBERG Presupposition Accommodation and Informativity Considerations with Aspectual Still

49

EUNHEE LEE AND JEONGMI CHOI Two nows in Korean

87

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

Journal of Semantics 26: 1–48 doi:10.1093/jos/ffn005 Advance Access publication August 28, 2008

No Alternative to Alternatives ARIEL COHEN Ben-Gurion University

Abstract

‘Only if there are alternatives can one hope to get insight into what is truly at stake.’ Peter F. Drucker, The Effective Executive (p. 147) 1 INTRODUCTION How does focus restrict the domain of quantification? Rooth (1985, 1992) proposes a two-dimensional account. He claims that every expression u has two semantic values: in addition to the ordinary semantic value, ½½uO, u also has a focus semantic value, ½½uF, which is a set of alternatives to the focused elements of u. Rooth proposes a compositional way to compute the focus semantic value: the focus semantic value of u is a function of the focus semantic values of the parts of u. Moreover, the combinatory rules used to compute the focus semantic value are the same rules used in the computation of the ordinary semantic value. For example, if the ordinary semantic value ½½:uO is the negation of ½½uO, then the focus semantic The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected].

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Rooth’s (1985, 1992) theory of focus requires, in addition to the ordinary semantic value of an expression, the focus semantic value, which is a set of alternatives generated by focus. Rooth claims that the union (disjunction) of the focus semantic value is accommodated into the restrictor of an adverbial quantifier. More recently, however, some researchers (Krifka 2001; Geurts & van der Sandt 2004) have argued convincingly that what is accommodated is, in fact, the existential presupposition induced by focus. It would appear, then, that there is no need for assuming the focus semantic value. However, in this paper, I argue that, although the primary effect of focus is, indeed, presuppositional, the focus semantic value cannot be dispensed with. Not only is the focus semantic value necessary but, in fact, additional semantic values are required too. Unlike focus, the analyses of these other semantic values cannot be reduced simply to existential presupposition. I will concentrate on a special reading of some quantificational sentences, the relative reading, whose adequate account, I propose, requires the use of semantic values triggered by alternatives to various elements: the focus, background marking and the world of evaluation.

2 No Alternative to Alternatives value ½½:[u]FF is a set containing the negations of the elements in ½½[u]FF. According to Rooth, the union (or disjunction) of the focus semantic value is accommodated into the restrictor of a quantificational adverb (henceforth Q-adverb). Geilfuß (1993) and de Hoop & Sola` (1995) make a similar proposal regarding determiners. For example, the preferred interpretation of (1) is that the majority of linguists who arrived did so by bus; it does not mean that the majority of all linguists in the world came by bus. (1) Most linguists came by [bus]F.

(2) People usually manage to survive a week without [food]F. If the role of focus were to provide a set of alternatives that restrict the domain of usually, we would expect (2) to mean that people who manage to survive a week without something usually survive a week without food. However, (2) has no such reading; rather, it means that people who have to survive a week without food usually make it. This is accounted for by the proposal that it is the presupposition of manage, rather than the alternatives introduced by focus, that is accommodated into the restrictor.3 Such examples abound,4 and I believe they 1

More accurately, Krifka claims that it is not focus as such that gives rise to the accommodated presupposition, but that presuppositional indefinites are characterized by de-stressing. 2 For dissenting opinions, see, among others, Rooth (1999), who argues that assuming that focus contributes an existential presupposition leads to incorrect predictions; Beaver (2001), who denies that presuppositions are accommodated into the restrictor, and von Fintel (1994), who claims that focus affects the context, rather than the restrictor. 3 An anonymous reviewer wonders why it is the presupposition of manage, rather than the existential presupposition of focus, that is accommodated. The reason might be due to the distinction between the two types of presupposition trigger (Zeevat 1992; Geurts forthcoming): lexical triggers, like manage, must be accommodated, while focus, which is anaphoric, does not have to be. 4 See also Schubert & Pelletier (1987) and Beaver & Clark (2003) for similar observations.


Krifka (2001) and, more recently, Geurts & van der Sandt (2004) have objected to this two-dimensional account. They suggest, instead, that it is the existential presupposition produced by focus that is accommodated, and there is no need for a set of alternatives.1 These proposals have attracted considerable interest. There appears to be fairly convincing evidence that what is accommodated into the restrictor really is presupposition, and not the union of the set of focus alternatives as compositionally defined by Rooth.2 Perhaps the strongest piece of evidence comes from cases where there is a clash between presupposition and focus; in such cases, it is presupposition that is accommodated into the restrictor. The following example is from Cohen (1999b):

Ariel Cohen 3

5

The article by Geurts and van der Sandt is published together with comments by several linguists. For more discussion on this issue, see these comments and the response from Geurts and van der Sandt.


provide strong support for the positions of Krifka and Geurts and van der Sandt, in so far as they demonstrate that what is accommodated into the restrictor is a presupposition, and not Rooth’s alternatives.5 Does this mean that the device of alternatives can be done away with? Not necessarily. First, note that we do not have to eliminate alternatives from the theory. We could still maintain the use of alternatives, if we change Rooth’s compositional definition, and replace it with a set of rules for generating presuppositions, i.e. rules that reflect the projection behaviour of presuppositions (Cohen 1999b). For example, since presupposition is normally unaffected by negation, ½½[u]FF and ½½:[u]FF will be the same. Note that giving a role to alternatives need not contradict the theories of either Krifka or Geurts and van der Sandt; it would simply add another dimension to their accounts. But why would we want to go that way? Why do we need a two-dimensional account, with more than one semantic value, when we could simply use existential presupposition directly? I believe there is a reason. In this paper, I argue that if the full range of readings of quantificational structures is to be accounted for, one needs additional semantic values, indicating alternatives to other elements besides focus. The analyses of these other elements cannot be reduced simply to existential presupposition; hence, whatever one wishes to propose regarding focus, there is no alternative to a multidimensional theory. The rest of the paper is organized as follows. In section 2, I consider some semantic values that have already been proposed in the literature, and propose another one: the B semantic value. In section 3, I discuss a specific reading of some quantificational sentences: the relative reading. In section 4, I argue that a proper account of relative readings requires the semantic values from section 2. In section 5, I propose an answer to two questions: why only some quantifiers exhibit relative readings and what is the relation between the relative and non-relative reading of a quantifier. I argue that answering these questions requires two additional semantic values, which consider alternative possible worlds. Section 6 provides some speculative thoughts about the implications of the theory and concludes the paper.

4 No Alternative to Alternatives 2 ALTERNATIVES TO FOCUS AND NON-FOCUS

2.1 Focus semantic value

(3) A: Eva only gave xerox copies to the GRADUATE STUDENTS. B: No, PETR only gave xerox copies to the graduate students. In A’s utterance, there is pitch accent on graduate students, and the phrase is interpreted as focus: only associates with it, and the interpretation is that Eva gave xerox copies to nobody besides graduate students. B’s utterance contains a second occurrence of graduate students. This utterance is also interpreted as if there is focus on graduate students, and only associates with this focus: B is saying that Petr gave xerox copies to 6 Keeping in mind that, as discussed above, the focus semantic value must be calculated according to the rules of presupposition projection, rather than according to Rooth’s proposed rule.


Rooth (1985) proposes that every expression u has, in addition to its ordinary semantic value ½½uO, also a focus semantic value ½½uF. The intuition underlying the focus semantic value can be put roughly as follows: the focus semantic value is generated by replacing the focusmarked element (or elements) with its alternatives. Focus-sensitive operators interact with this focus semantic value. For example, in adverbial quantification, the union of the focus semantic value is used to restrict the domain of quantification.6 What exactly is focus? It is very hard to answer this question, especially since different sources may mean different things by this word: the word may refer to a psychological, intonational, syntactic, semantic, or pragmatic notion (cf. Beaver et al. 2004). Focus has a distinct informational role: intuitively, the focused element is ‘new’, ‘informative’, or ‘unexpected’, whereas the unfocused part of the sentence is ‘background’, ‘old’, or ‘given’. It is notoriously hard to provide a precise definition of these notions (see Schwarzschild 1999 for discussion), but the intuitive meaning, I believe, is fairly clear. For the purposes of the current paper, a precise theory of the informational role of focus is not necessary. In addition to its informational role, focus is often associated with a specific intonation pattern: what Jackendoff (1972) called the A-accent, characterized by a fall. This pattern, however, is not a necessary condition for a phrase to be interpreted as focus. Of particular relevance here is the phenomenon of second occurrence focus, exemplified by the following exchange, from Partee (1991, 179):

Ariel Cohen 5

2.2 An additional semantic value Jackendoff (1972) distinguishes between A-accent, which as we have seen is usually used to indicate focus, and B-accent. The latter is characterized by a fall–rise contour (L+H* in the notation of Pierrehumbert 1980).8 Bu¨ring (1997, 1999) discusses the interpretation of elements pronounced with this intonation contour. He claims that, like focus, they too introduce alternatives, and proposes that their adequate account requires an additional semantic value, which he calls the topic semantic value. According to Bu¨ring, this semantic value takes into account alternatives to both the B-marked and the focusmarked elements. The notation I will use for it is, therefore, ½½uB+F. This is a set of sets of elements of the type of u. In each such set, all elements share a B-marked constituent, but vary with respect to the focus. Following the standard assumption that the meaning of a question is the set of its possible answers, Bu¨ring’s semantic value can be interpreted as a set of questions. Bu¨ring argues that a question– answer pair is felicitous only if the question is a member of the topic semantic value of the answer. For example, Bu¨ring notes that (4b) is a felicitous answer to (4a). (4) a. Which book would Fritz buy? 7

Cf. Rooth (1995) who ‘would like to leave aside the question whether this expected focus marking is really phonologically defensible’ (p. 270). 8 A more accurate representation, which includes the boundary tone, is probably L+H* LH% (Pierrehumbert & Hirschberg 1990; Steedman 1991; Vallduvı´ & Zacharski 1994; Vallduvı´ & Engdahl 1996); a precise characterization of the intonation of B-accent, however, is not necessary for our purposes here.


nobody besides graduate students. Yet, the phrase graduate students is pronounced very differently this time and does not appear to carry a pitch accent. Does this mean that focus has no obligatory phonetic realization? This question cannot be said to have been satisfactorily settled. Rooth (1996), Bartels (2004) and Beaver et al. (2004) have conducted experiments to investigate whether second occurrence focus is realized phonetically and have found no pitch accent. However, they do report finding other phonetic correlates, like a small increase in duration and a very slight (possibly insignificant) increase in intensity. Doing justice to this question lies outside the scope of this paper. Instead, I will simply treat focus as a feature, saying little about its phonological manifestation: some parts of a sentence may be marked with this feature, others would not.7

6 No Alternative to Alternatives b. Well, [I]B would buy [‘The Hotel New Hampshire’]F. The topic semantic value of (4b), according to Bu¨ring, is:

This corresponds to the following set of questions: (6) fWhich Which Which Which

book book book book

would would would would

you/I buy?, Paul Simon buy?, Fritz buy?, Fritz’s brother buy?, . . .g

Since the question (4a) is a member of this set, the exchange in (4) is felicitous. An important question to consider is whether B-accent, like A-accent (when it is associated with focus), gives rise to an existential presupposition. It is hard, however, to answer this question based on exchanges like (4). The reason is that, in addition to whatever presuppositions are induced by the B-accent itself, Bu¨ring’s constraint on felicity is also operative. In this case, this constraint requires that the context contain a question of the form (7) Which book did x buy? Since (7) presupposes that x bought some book, the felicity of (4b) requires the truth of (8). (8) Somebody bought some book. This is precisely what we would get if we assumed that B-accent induces an existential presupposition.


(5) f fI would buy ‘War and Peace’, I would buy ‘The Hotel New Hampshire’, I would buy ‘The World According to Garp’, . . .g, fPaul Simon would buy ‘War and Peace’, Paul Simon would buy ‘The Hotel New Hampshire’, Paul Simon would buy ‘The World According to Garp’, . . .g, fFritz would buy ‘War and Peace’, Fritz would buy ‘The Hotel New Hampshire’, Fritz would buy ‘The World According to Garp’, . . .g, fFritz’s brother would buy ‘War and Peace’, Fritz’s brother would buy ‘The Hotel New Hampshire’, Fritz’s brother would buy ‘The World According to Garp’, . . .g, . . .g

Ariel Cohen 7

(9) a. A: B: b. A: B:

I thought they all took one. [Ann]B did (p. 170). Can Jack and Bill come to tea? [Bill]B can (p. 173).

B’s response in (9a) does not presuppose that somebody took one. This fact can be confirmed by standard presupposition tests. For example, if B’s answer is inside the scope of a possibility modal, it no longer follows that anyone did: (10) It is possible that [Ann]B did. Now consider what happens when Ann is focused: (11) a. [Ann]F took one. b. It is possible that [Ann]F took one. In this case, (11a) does presuppose that somebody took one, a presupposition that projects from within the scope of a possibility modal, as can be seen in (11b).9 Similarly, B’s response in (9b) does not presuppose that somebody can come to tea; indeed, it does not follow from (12) that anyone can: (12) It is possible that [Bill]B can. In contrast, (13a), where Bill is focused, does presuppose that someone can come for tea, and this presupposition can survive a possibility modal: 9

Of course, (11a) would no longer be a felicitous response to A’s statement.


Does this mean that we can do away with Bu¨ring’s topic semantic value and rely on existential presupposition alone, as has been proposed for focus by Krifka (2001) and Geurts & van der Sandt (2004)? The answer is no, for two reasons. One reason why an additional semantic value is necessary is that even if B-accent does give rise to an existential presupposition, we would be able to explain why (4b) presupposes (8), but not why it presupposes a question of the form (7); the finer distinctions made possible by the topic semantic value appear necessary. The second reason is that there are good reasons to deny that B-accent, on its own, induces an existential presupposition. This can be seen more clearly when we consider examples with B-accent, but without A-accent. Consider the following examples, from O’Connor & Arnold (1973):

8 No Alternative to Alternatives (13) a. [Bill]F can come to tea. b. It is possible that [Bill]F can come to tea. Hence, if Bu¨ring’s theory is correct, it provides evidence that a multidimensional analysis of semantic value is necessary anyway, regardless of the way focus is dealt with. Hence, the motivation for doing away with the focus semantic value is substantially lessened.

2.3 Contrast semantic value

(14) a. A: What did the pop stars wear? B: The [female]B pop stars wore [caftans]F (Bu¨ring 1997, ex. 12, p. 56). b. Eight boys had read ‘City of Glass’. [Two]B boys had even read [the entire trilogy]F (Bu¨ring 1997, ex. 21, p. 100). Whether or not B-accented elements are appropriately called topics, it is clear that they belong to the background. I will therefore henceforth refer to such elements as Background-marked, or B-marked. What distinguishes these elements from other elements in the background? Here, there appears to consensus that B-marked elements are contrastive in some sense. This notion can be made more concrete in terms of what Vallduvı´ & Vilkuna (1998) call thematic contrast.10 Suppose we have a contrast set of comparable elements M ¼ fa, b, c, . . .g. In a contrastive context, if it is said, of some property P, that P(a), then it is implied that some comparable property holds for some other element of M.11 Hence, if an element requires a contrastive context, and is not a focus, then it is B-marked. 10 Actually, Vallduvı´ and Vilkuna refer to it as kontrast, to distinguish it from other notions of contrast. 11 Vallduvı´ and Vilkuna believe that only topics, or, in their terms, links can exhibit this kind of contrast, whereas, as discussed above, I think it can also apply to tails, i.e. non-topical ground.


Bu¨ring applies his theory to elements that are pronounced with a Baccent, which he claims are topics. Whether B-accented elements are really topics is controversial, however. Jackendoff (1972) agrees that they have the information status of topics, but Portner & Yabushita (1998) and Kadmon (2001) believe they are foci, and Krifka (1998) claims they have both topical and focal features. Indeed, if one takes the view (as I do) that topics are what the sentence is about (Reinhart 1981), then topics must be referential. But non-referential elements may be expressed with a B-accent, as can be seen in Bu¨ring’s own examples:

Ariel Cohen 9

(15) a. The boys were eating ice cream. They were happy. b. The boys met the girls at the ice cream parlor. They were happy. However, there are cases when the antecedent does not denote a subset of the reference of the anaphor; Hendriks and Dekker call this type of anaphora non-monotonic anaphora, and argue that this is what is expressed by the fall–rise contour. For example: (16) John fed the animals. The cats were hungry. Normally, we would interpret the sentence as an expression of monotonic anaphora: the cats and the animals refer to the same set of individuals (in context), which means that all the animals fed by John were cats. However, Hendriks and Dekker point out that if cats is uttered with a fall–rise intonation, we get a different interpretation: the set of cats does not contain the set of animals (in context), so that John fed some animals that were not cats. In many cases, non-monotonic anaphora expresses contrast; hence, one might get the impression that B-marked elements are associated with the L+H* contour. However, non-monotonic anaphora do not always express contrast, hence not all L+H* accents are cases of contrast; and, I would like to add, not all cases of contrast are nonmonotonic anaphora. Indeed, in section 3 we will see examples of elements that require contrastive contexts, and are not foci, so they are


Since it is not clear that B-marked elements are topics, but it is clear that they are contrastive, I will refer to Bu¨ring’s semantic value as the contrast semantic value, rather than the topic semantic value. As with the case of focus, an important question is the relation between B-marking and intonation. Are B-marked elements always associated with a fall–rise contour? Here, again, opinion is divided. Some would say there is a tight connection, while others would deny this, or would claim such a connection only for some cases of B-marked elements. In this context, it is interesting to consider the proposal made by Hendriks & Dekker (1996). Usually, when a discourse referent Y is anaphoric to an antecedent X, they have the same reference, as in (15a): both antecedent and anaphor refer to the set of boys. Sometimes, the reference of an antecedent is a subset of the reference of the anaphor, as in (15b), where the plural pronoun they has two antecedents, the boys and the girls, each of which denotes a subset of the reference of the pronoun.

10 No Alternative to Alternatives B-marked. Yet, they do not indicate non-monotonic anaphora; hence, they are not required to exhibit the fall–rise contour. Since B-marking is not always associated with a specific contour, I will treat B-marking, just like focus marking, as a feature; its meaning is an indication of contrast, but I will leave aside its phonological realization.

2.4 B semantic value

(17)

Semantic Value

Alternatives to F?

Alternatives to B?

½½uO ½½uF ½½uB+F ?

No Yes Yes No

No No Yes Yes

The question mark in the table begs to be replaced with yet a fourth type of semantic value: the B semantic value—½½uB. This semantic value is obtained by replacing B-marked elements with alternatives.12 Some evidence that the B semantic value is necessary comes from Artstein (2002). He works on echo questions, as in: (18) Amy: I gave flowers to George. Bill: You gave FLOWERS to George? According to Artstein, the word in capitals (FLOWERS) is expressed with a B-accent. The normal interpretation of such an echo question is that Bill misheard or misunderstood what Amy was saying, and is seeking clarification. Artstein notes that Bill’s question means roughly the same as: (19) You gave WHAT to George? He therefore concludes that the meaning of both is a set of propositions of the form ‘Amy gave x to George’: It should be emphasized that ½½uB+F is not derived compositionally from ½½uB and ½½uF. The notation merely indicates that the contrast semantic value is sensitive to both the focus and the background. 12


Let us take stock. We have three types of semantic value: the ordinary semantic value, which takes no alternatives into consideration; the focus semantic value, which considers alternatives to the focus, and the contrast semantic value, which considers alternatives to both the focus and the B-marked element. The types of semantic value can be described in a table:

Ariel Cohen 11

(20) fAmy gave flowers to George, Amy gave chocolate to George, Amy gave wine to George, . . .g

3 RELATIVE READINGS In this section, I briefly discuss the theory of relative readings I have proposed in Cohen (2001b).

3.1 Many It is widely accepted that many and few are ambiguous between cardinal and proportional readings (Partee 1988).14 For example, (21) is ambiguous. (21) Many kids attended the faculty picnic. Under the cardinal reading, (21) simply means that the number of kids at the picnic was high (relative to some standard). But (21) also has a proportional reading, according to which it says that a large proportion of all kids attended the picnic. Thus, if n kids were at the picnic, and n is considered high, then (21) would be true under the cardinal reading. But if n kids constitute only a small percentage of the total number of contextually relevant kids, (21) would be false under the proportional reading. Besides the cardinal and proportional readings, Westersta˚hl (1985) claims there is an additional reading of many and few, his ½½many4,k (p. 404; the ‘4’ indicates his fourth formalization of many, and the ‘k’ is 13 I will return to Artstein’s theory in section 5.4 below, where it will be further argued why the accented expressions are not focused. 14 It has, in fact, been suggested that they have additional readings—see Lappin (2000) for an overview. Lappin proposes dealing with all these readings using a parameterized representation. I will return to this issue in section 5 below.


Artstein derives this interpretation by treating B-accent as a case of focus. Thus, (20) would be the focus semantic value of Bill’s utterance. But, as we have seen above, there are reasons to doubt that B-accent indicates focus.13 Hence, it would seem more plausible to treat Baccent as a case of B-marking; in this case, (20) would be the B semantic value of Bill’s utterance, and we would get the same result. But is there additional evidence that the B and contrast semantic values are necessary? Specifically, do they affect truth conditions? In the rest of the paper, I will argue that the answer is yes. I will discuss a class of interpretations of some quantified sentences that, I claim, provide just this kind of evidence.

12 No Alternative to Alternatives a parameter indicating what proportion counts as many). He produces the following example: (22) Many Scandinavians have won the Nobel Prize in literature.

(23) Many Scandinavians who have distinguished themselves in some fashion, have won the Nobel Prize in literature. What it means to distinguish oneself is of course quite vague, but it is unlikely that the number of Scandinavians who have done so is so small as to make 14 out of them a high proportion. Consequently, I concur with Westersta˚hl that the sentence is true under neither the cardinal nor the proportional reading; its apparent truth, then, is in need of explanation. The reading Westersta˚hl proposes may be paraphrased as follows: (24) Many of the winners of the Nobel Prize in literature were Scandinavians. This interpretation is the proportional reading, but with the order of arguments reversed; I will call this view, namely that the normal order of arguments dictated by the syntax may be reversed, the Reverse Interpretation view. Alternatively, de Hoop & Sola` (1995) propose that the reading exemplified by (22) is just the usual cardinal reading. It is the context which determines what number of Scandinavians who have won the Nobel Prize in literature would be considered ‘many’. Both these approaches suffer from serious problems—I will briefly go over a few of them.15 For either view, the number of Scandinavians who have won the Nobel Prize in literature affects the truth of (22). It 15

See Cohen (2001b) for an extensive discussion.


As of 1984, out of a total of 81 winners of the Nobel Prize in literature, 14 came from Scandinavia. Given this fact, Westersta˚hl judges (22) to be true, though, he claims, it would be false under either the proportional or the cardinal reading. Note that this interpretation cannot be explained away as a case of domain restriction. As mentioned above, the domain of a determiner is restricted by the disjunction (union) of the focus semantic value of its scope (Geilfuß 1993; de Hoop & Sola` 1995). One may suppose that, if we take this fact into account, (22) will turn out to be true under the proportional reading after all. But this does not seem to be the case. If we assume that the VP in (22) is focused and that it induces alternative forms of distinguishing oneself, (22) would mean something like:

Ariel Cohen 13

does so either directly (de Hoop and Sola`) or after being divided by the number of Nobel Prize winners in literature (Westersta˚hl). In contrast, according to both approaches, the total number of Scandinavians does not affect the truth of the sentences in any way. However, this does not seem to be correct, as can be seen in (25). (25) Many Andorrans have won the Nobel Prize in literature.

(26) a. Most/all/no/some alligators like to sunbathe. b. Most/all/no/some alligators are alligators that like to sunbathe. To say that Q is conservative is to say that when evaluating Q(w, /) we only count ws, never non-ws. For example, to determine the truth of (26a), it only matters how many alligators like to sunbathe, and no fact about non-alligators is relevant. The cardinality interpretation of de Hoop and Sola` implies that many, under the reading exemplified by (22), ought to be conservative with respect to its complement; under the Reverse Interpretation view, it ought to be conservative too, but with respect to the VP. It turns out, however, that the reading of many under discussion is not conservative with respect to either the complement or the VP. If many were conservative with respect to the first argument, (22) would be equivalent to (27), but this is clearly not the case. (27) Many Scandinavians are Scandinavians who have won the Nobel Prize in literature. For Westersta˚hl, many ought to be conservative with respect to the VP. So, (22) ought to be equivalent to (28), but, in fact, it is not.


It may be sufficient for as few as two or three Andorrans to have won the Nobel Prize in literature for (25) to be true, but such a small number would not be enough for the truth of (22). Intuitively, the reason for this judgment is that there are many more Scandinavians than Andorrans. Note that this judgment cannot be explained by either the cardinal or the proportional reading of many. According to the cardinal reading, if two or three Scandinavians are few, so should two or three Andorrans be. Turning to the proportional view, if we divide 2 or 3 by the total number of Andorrans (about 60,000) we get an extremely small number, which can hardly be considered ‘many’. Perhaps the reason for the problematic nature of examples like (22) is that they fail to exhibit conservativity. A generalized determiner Q is conservative iff, for all properties w and /, Q(w, /) is equivalent to Q(w, w \ /). For example, (26a) is equivalent to (26b).

14 No Alternative to Alternatives (28) Many Scandinavians who have won the Nobel Prize in literature, have won the Nobel Prize in literature.

16

In fact, this is very similar to yet another reading of many proposed by Westersta˚hl (1985), his ½½manyM 2 (the ‘2’ indicates his second formalization of many and ‘M’ is the universe of discourse). According to this interpretation, Many As are Bs means that ‘the frequency of Bs on A is greater than a certain normal frequency of Bs . . . we let the normal frequency of Bs simply be the frequency of Bs in the universe M’ (p. 402, original emphasis). Thus, according to this reading, given a universe M, j/j many(w, u) is true iff jw\/j jwj > jMj .


We have seen that, when evaluating many(w, /) in sentences such as (22), the number of ws affects the truth value of the sentence. Of course, the number of ws that are /s also matters. It appears, therefore, that we are dealing with some sort of proportional reading. We have also seen that this interpretation of many, unlike the standard proportional reading, is not conservative. This means that it is not sufficient to look only at ws, we need to consider non-ws too. I have therefore suggested that (22) expresses a comparison between various countries with respect to the proportion of the population who have won the Nobel Prize in literature. The sentence is true just in case this proportion is greater in Scandinavia than it is in general in the world. This does not require that the proportion of Nobel Prize winners be greater in Scandinavia than in every other country, but it does require that it be greater than the proportion among the world population in general.16 I refer to this interpretation of many as its relative proportional reading, since according to it, the meaning of many(w, /) is defined relative to the properties of non-ws; I refer to the standard proportional reading as the absolute proportional reading. Crucial to this interpretation of many is the idea that alternatives to Scandinavians are considered. Does this mean that Scandinavians is focused? Herburger (1997) believes that it does. She follows the Reverse Interpretation view for sentences like (22), but claims that this reading is only possible when Scandinavians is focused (see also Eckardt 1994). Herburger does not, however, explain how focus is expressed in her examples. How does she know that Scandinavians is focused in (22)? Presumably, Herburger feels that the noun carries some pitch accent, but it is not clear that this pitch accent is even necessary for this interpretation (Westersta˚hl does not mention any particular intonation pattern), and even if it is, what is its exact nature. Since pitch accent is, as mentioned above, neither necessary nor sufficient to determine whether an element is focused, in order to be clear about the information status of Scandinavians, we need to turn to pragmatics, rather than phonology. Note that, under the interpretation in question, (22) seems to be licensed only in a contrastive context; out of the blue, this sentence,

Ariel Cohen 15

with the reading under discussion, is actually rather odd. But in the context of the exchange in (29), it is perfectly acceptable. (29) Amy: Have many Israelis won the Nobel Prize in literature? Bill: No, many Scandinavians have won the Nobel Prize in literature.

(30) a. #The King of France is bald. b. The exhibition was visited by the King of France. His explanation is that the King of France is the topic of (30a), but not (30b). Now examine the following exchange: (31) Amy: The President of France is bald. Bill: #No, the King of France is bald. Bill’s utterance in (31) is odd, indicating that the King of France is the topic of this sentence, even when there is pitch accent on the subject. Now consider: (32) #Many Martians have won the Nobel Prize in literature. Assuming there are no Martians, (32) is odd, indicating that it carries a presupposition that Martians exist. Note that this would be the case even when we stress Martians. The descriptive content of the complement of many, then, is presupposed, even when stressed. Hence, we can conclude that the complement of many is a topic, rather than a focus.17 17 Of course, there are cases, such as (i), suggested to me by an anonymous referee, where the whole DP may be focused.

(i)

The exhibition was visited by many Scandinavians.

It is hard to judge whether (i) has a relative reading, nor is it clear what the information status of Scandinavians is (focus? subordinate topic? cf. Erteschik-Shir 1997). But the point is that for Herburger’s theory to work, the complement of many must be a focus in non-controversial cases like (22), which, if I am correct, it is not.


The complement of many, then, is interpreted contrastively. Foci may, indeed, be contrastive, but topics may be contrastive too. Is Scandinavians a focus or a topic? In order to answer this question, additional tests are needed. The clearest way, perhaps, to test for whether a phrase is a topic is to check whether its descriptive content is presupposed (Strawson 1964; Reinhart 1981). Strawson notes that while the classic (30a) presupposes the existence of a king of France, and is therefore odd, (30b) is straightforwardly false.

16 No Alternative to Alternatives In contrast, Herburger would predict that the descriptive content of the VP, rather than the subject, is presupposed, since proportional quantifiers presuppose the non-emptiness of their restrictor, and the VP is claimed to be mapped onto the restrictor. However, (33) is perfectly fine (though false), even though there is no Nobel Prize in silly walks: (33) Many Scandinavians have won the Nobel Prize in silly walks.

(34) a. Russia has the greatest number of scientists in the world, but . . . b. . . . few of the people in Russia are scientists. c. . . . #few SCIENTISTS are in Russia. We can conclude, then, that the complement of the determiner in (22), regardless of accent, is not a focus, as Herburger claims, but rather a (contrastive) topic. I will leave a discussion of the nature of contrastive topics for another occasion; it suffices for current purposes to note that a contrastive topic is contrastive, but is not a focus; hence, it must be B-marked. Scandinavians, then, is a B-marked element in (22). Note that intonation alone would not have been sufficient to determine this, since it need not be expressed with a fall–rise contour, because it does not involve non-monotonic anaphora (cf. section 2.3 above).

3.2 Often The phenomenon of relative readings is not only restricted to many and few but also extended to their adverbial counterparts: often and seldom, and their synonyms. The following example is due to de Swart (1991): (35) Paul often has a headache. De Swart observes that (35) has a reading under which in many of the contextually relevant situations, Paul has a headache. This


Additional evidence that the complement of many in sentences such as (22) is actually a topic comes from discourses such as (34) (from de Hoop & Sola` 1995; my explanation, however, differs from theirs). Sentence (34a) establishes Russia as a topic; since (34b) is about the people in Russia, it follows felicitously. According to the Reverse Interpretation view, (34b) ought to mean the same as (34c), which consequently ought to be fine too, but the fact is that (34c) is distinctly odd in this context. The reason is that the topic of (34c) is actually scientists, which is not the topic established by (34a).

Ariel Cohen 17

interpretation of often corresponds to the absolute proportional reading of many. But de Swart notes an additional reading: ‘The sentence can also be taken to mean that the situations of Paul having a headache occur with a frequency superior to the average’ (p. 21). This sounds very much like the relative proportional reading of many: Paul has a headache more frequently than the average just in case he is more likely to have a headache than an arbitrary person is. Relative readings obtain also with the atemporal use of Q-adverbs: (36) A politician is often crooked.

(37) Amy: The main suspects are a politician, a physician, and a linguist. Who do you think did it? Bill: Well, a politician is often crooked. As the context of (37) indicates, a politician is contrastive and belongs to the background; hence, it is B-marked. Note that if the background is clearly delimited and does not include the subject, the relative reading disappears. For example, fronting the Q-adverb has precisely this effect (Cohen 2004b): (38) a. Often, Paul has a headache. b. Often, a politician is crooked. Sentence (38a) can only mean that there are many situations where Paul has a headache, not that Paul has headaches more frequently than the average; (38b) can only mean that many politicians are crooked, not that they are more likely to be crooked than other people are. Note that in (37) focus is on crooked, not politician. In fact, if we force politician to be focused, by stressing it and uttering the sentence in a context in which politicians are not part of the background, the result is quite bad: (39) Amy: We live in bad times—there is corruption everywhere. Bill: ??A [politician]F is often crooked.


Sentence (36) is ambiguous: on one reading, the absolute reading, it would be true just in case many politicians are crooked; under this reading, (36) is false. However, we may feel uncomfortable declaring unequivocally that the sentence is false. This, I suggest, is because (36) has another reading, namely that a politician is more likely to be crooked than an arbitrary person is. Under this reading, (36) may, to our misfortune, be true. The right context is important, perhaps crucial, for obtaining the relative reading:

18 No Alternative to Alternatives To the extent that Bill’s utterance in (39) is interpretable at all, it means something very different from the relative reading: namely, that many crooked individuals are politicians. This fact indicates that accounting for relative readings in terms of the Reverse Interpretation view is incorrect in the case of Q-adverbs, just as it is incorrect in the case of many and few. Similar points can be made about applying the cardinality view of de Hoop & Sola` (1995) to often.18

3.3 Generics Consider the following examples:

It is not the case that Frenchmen, in general, eat horsemeat, and yet (40a) is true. Very few Bulgarians are good weightlifters, and yet (40b) is true. How can the truth of (40a) and (40b) be accounted for? This type of sentence poses a challenge to any theory of generics. Take, for example, the commonly held view that generics express modalized universal quantification, restricted by context (Chierchia 1995; Krifka 1995; Pelletier & Asher 1997, among many others). According to this view, the generic (41a) means roughly (41b). (41) a. As are Bs b. All relevant normal As are Bs. Thus, (40a) would be true just in case all relevant normal Frenchmen eat horsemeat. But it is hard to see any plausible restriction of the domain of Frenchmen that would include only the horsemeat eaters and would filter out all others as irrelevant or abnormal. Similarly, (40b) would mean that all relevant normal Bulgarians are good weightlifters, and its truth would require that Bulgarians who are not good weightlifters be considered irrelevant or abnormal. Thus, examples like (40) pose a significant problem to the view of generics as contextually restricted modalized universals. Some researchers, most notably Carlson (1977), have used such sentences to argue that generics are not quantificational at all. Yet, a non-quantificational account of generics would leave their truth conditions stipulated, rather than explained. Moreover, it would be difficult to account for phenomena such as scope ambiguity and quantificational variability, as Carlson himself admits in a later article (Carlson 1989). 18

In fact, this is the way in which de Swart attempts to explain the relative reading of (35).


(40) a. The Frenchman eats horsemeat. b. Bulgarians are good weightlifters.

Ariel Cohen 19

Others, most notably Krifka et al. (1995), have sought to maintain the advantages of a quantificational account of generics in general, but deny such an account to examples like the sentences in (40). According to their view, such sentences express direct kind predication and are not quantificational. This is rather a disappointing move, in that it treats the truth conditions of such generics as primitive and leaves no room for explaining them in terms of properties of arbitrary individuals. Moreover, the same arguments favoring a quantificational account of generics can apply to such examples too. For example, (42) expresses a scope ambiguity: An alternative approach, proposed, most explicitly, by Wilkinson (1991), is to keep the quantificational view of generics, but apply the Reverse Interpretation view to this particular type of example. According to this approach, the meanings of the sentences in (40) can be paraphrased as follows: (43) a. Horsemeat eaters are Frenchmen. b. Good weightlifters are Bulgarian. In other words, (40a) is a generic statement about horsemeat eaters, rather than Frenchmen, and (40b) is about good weightlifters, rather than Bulgarians. However, just as with many and often, the Reverse Interpretation view is problematic, and for similar reasons. One problem is that the paraphrases in (43) fail to capture the truth conditions of the sentences in (40). Suppose that most horsemeat eaters were actually, say, Belgian, and that most good weightlifters were Russian. The sentences in (40) might still be true, but those in (43) would definitely be false. An additional difficulty for the Reverse Interpretation view comes when conservativity is taken into account. Examples like those in (40) fail to exhibit conservativity: (44) a. The Frenchman is a Frenchman who eats horsemeat. b. Bulgarians are Bulgarians who are good weightlifters. The sentences in (44) are not paraphrases of their counterparts in (40); the former are false, whereas the latter are true. The Reverse Interpretation view implies that the generic quantifier is conservative with respect to the VP, i.e. with respect to eat horsemeat for (40a) and be a good weightlifter for (40b). However, this does not seem to be correct, as (45a) and (45b) are not equivalent to (40a) and (40b), respectively, and are, in fact, necessarily true.


(42) Bulgarians are good at some sport.

20 No Alternative to Alternatives (45) a. Frenchmen who eat horsemeat eat horsemeat. b. Good Bulgarian weightlifters are good weightlifters. An additional problem is that the sentences in (40) definitely seem to be about Frenchmen and Bulgarians, respectively. Standard tests for topicality confirm this intuition: (46) a. As for the Frenchman, he eats horsemeat. b. As for Bulgarians, they are good weightlifters. The same test shows that, in contrast, the topics of the sentences in (43) are horsemeat eaters and good weightlifters, respectively:

If topics are mapped onto the restrictor, it follows that the Frenchman and Bulgarians are mapped onto the restrictor of the generic, rather than the nuclear scope, contradicting the Reverse Interpretation view. Based on the arguments above, I conclude that the Reverse Interpretation view is wrong. And yet, it cannot be denied that this view has a certain initial appeal. Why is this? I submit that the reason is that although the Frenchman is the topic of (40a), this sentence would not really be felicitous in the context of a discussion of French people. Instead, it would be more appropriate in the context of a discussion of various nationalities and their eating habits. Similarly, although Bulgarians is the topic of (40b), the sentence would not normally be said in the context of a description of Bulgarians. Rather, such a sentence might be said as part of a conversation about weightlifting, or perhaps sports in general, comparing the accomplishments of people from various nationalities. In other words, the subjects of the sentences in (40) are contrastive. Since they are topics, hence part of the background, they are B-marked. The sentences in (40), I propose, are evaluated with respect to alternative nationalities, and receive a relative reading. Sentence (40a) would be true just in case a Frenchman is more likely to eat horsemeat than a person of arbitrary alternative nationality is. Note that this might still hold if few Frenchmen eat horsemeat, or if the majority of horsemeat eaters are, say, Belgian. Similarly, (40b) is true since a Bulgarian weightlifter is more likely to be a good one than a weightlifter of some arbitrary nationality is. Again, this would be true even if a good weightlifter were more likely to be, say, Russian, rather than Bulgarian. Relative readings of generics are more common than may seem at first sight. Indeed, many naturally occurring generics are only true if given a relative interpretation. Consider (48), for example:


(47) a. As for horsemeat eaters, they are Frenchmen. b. As for good weightlifters, they are Bulgarian.

Ariel Cohen 21

(48) Tigers eat people. This sentence is false under the absolute reading: it is not the case that, in general, tigers eat people—very few do, in fact. Nor is it true that, in general, people who are eaten by some animal are eaten by tigers. However, (48) is true under the relative interpretation, since a tiger is more likely to eat people than an arbitrary animal is. In section 4.3, I will demonstrate that if we replace the view of generics as contextually restricted modalized universals with a theory that takes them to express probability judgments, the relative readings receive a straightforward interpretation.

Relative readings require an explanation; preferably, the explanation should be the same for all three constructions, and independently motivated. In this section, I intend to demonstrate that the relative readings of all three constructions can be accounted for in a general way using the four semantic values proposed in section 2. The basic idea is this:19 in both the absolute and relative reading, we look at a certain proportion (or probability), call it P. The absolute reading simply requires that P be high, whereas according to the relative reading, we compare P with a similar proportion (or probability) that is obtained after taking into account alternatives to the B-marked element.

4.1 Many Let us repeat (22), annotated for focus marking and B-marking: (49) Many [Scandinavians]B have [won the Nobel Prize in literature]F. I am assuming that many is a relation between two sets. While there are reasons to believe that many is intensional (Keenan & Stavi 1986; Kamp & Reyle 1993), the intensions of the related properties only affect the threshold for being many, not the arguments of many themselves (Fernando & Kamp 1996). We will return to the intensionality of many in section 5.1 below. The logical form of (49), then, is something like the following (where scand is the property of being a Scandinavian, and wnpil is the property of winning a Nobel Prize in literature): (50) many(scand, wnpil) 19

I thank Sigrid Beck (personal communication) for her help in formulating the idea.


4 A MULTIDIMENSIONAL ACCOUNT OF RELATIVE READINGS

22 No Alternative to Alternatives Under the absolute (proportional) reading, (49) is true iff the proportion of literature Nobel Prize winners among Scandinavians is high. This can be formalized as follows:

j½½scandO \ ½½wnpilO j j [ ½½scandB \ ½½wnpilO j > (52) j [ ½½scandB j j½½scandO j If the alternatives to scand consist of all nationalities, its union will simply be PEOPLE, the set of all people. The truth conditions then become: j½½scandO \ ½½wnpilO j jPEOPLE \ ½½wnpilO j > jPEOPLEj j½½scandO j In words, the proportion of literature Nobel Prize winners among Scandinavians is higher than the proportion of literature Nobel Prize winners among people in general. This is the desired interpretation. We can now make a first attempt at a definition of relative readings:

(53)

Definition 1 (many, relative reading, first version) many(w, u) is true iff

j½½wO \ ½½/O j j [ ½½wB \ ½½/O j . > j [ ½½wB j j½½wO j

One potential problem with this definition is that there are some reasons to believe that the first argument of the quantifier leaves, at LF, a copy at the second argument position.20 This means that w appears 20

This is argued for by Fox (1999: p. 183): A sentence such as [(i)] has [(ii)] as the output of QR, which can in turn be converted to one of the structures in [(iii)]. Economy principles determine that the interpreted structure is [(iii.b)]. (i) John1 [VP t1 likes every boy]. (ii) John1 [every boy [VP t1 likes every boy (iii) a. *John1 [every boyx [VP t1 likes x (ruled out by economy) b. John1 [every boyx [VP t1 likes boy x

Thus, in [(iii.b)], the logical form of [(i)], the predicate boy appears in both restrictor and nuclear scope. Presumably, the same considerations apply to other quantifiers, and to many in particular.


j½½scandO \ ½½wnpilO j > q; where q is ‘large’. (51) j½½scandO j What about the relative reading? Again we are talking about the proportion of literature Nobel Prize winners among Scandinavians. But this time, instead of simply saying that it is high, we will compare it to the proportion of literature Nobel Prize winners among all people who belong to a nationality that is an alternative to scand. This set of people is the union of the B semantic value of the subject. We get the following truth conditions:

Ariel Cohen 23

not only as the first argument of many but also as part of the second argument. If this is the case, definition 1 would yield the wrong result: we would be comparing the proportion of Scandinavian winners among Scandinavians to the proportion of Scandinavian winners (rather than winners in general) among people in general. The sentence would therefore be erroneously predicted trivially true. In order to avoid this problem, let us take the union of the B semantic value of u as well.21 Here is the revised definition: Definition 2 (many, relative reading, second version) j½½wO \ ½½/O j j [ ½½wB \ [ ½½/B j > . j [ ½½wB j j½½wO j

Definition 2 is an improvement, but it is still not quite right. The reason is that it does not take focus into account; yet, as we have seen above, the union of the focus semantic value restricts the domain of quantification of a determiner. For example, in order to get the reading paraphrased by (23) above, we need to consider not simply the proportion of winners among Scandinavians, but among Scandinavians who have distinguished themselves. In general, when we evaluate many(w, u) (either absolutely or relatively), we need to consider not only j½½wO \ ½½/O j , j½½wO j but also

(54)

j½½wO \ [ ½½/F \ ½½/O j (55) . j½½wO \ [ ½½/F j For simplicity, let us assume that, in general, an expression is always a member of the set of its own focus semantic value.22 Then, [ ½½uF \ ½½uO is equivalent to ½½uO, and we consider (56)

j½½wO \ ½½/O j . j½½wO \ [ ½½/F j

For the absolute reading, (56) ought to be ‘large’. What about the relative reading? As before, we would like to take the unions of the B semantic values of the elements in (56) and place the result in the righthand side. However, since the denominator of (56) contains not only 21 22

Of course, if Fox’s theory is wrong, no harm will be done by this move. Though this is not always the case (Cohen 1999b).


many(w, u) is true iff

24 No Alternative to Alternatives the ordinary semantic value of u but also the union of its focus semantic value, we need to take, so to speak, the B semantic values of this union: which means the union of the union of the contrast semantic value of u. The result is this: j [ ½½wB \ [ ½½/B j . (57) j [ ½½wB \ [ [ ½½/B+F j The general definition of the relative reading of many, then, is: Definition 3 (many, relative reading, third version) j½½wO \ ½½/O j j [ ½½wB \ [ ½½/B j . > j½½wO \ [ ½½/F j j [ ½½wB \ [ [ ½½/B+F j

Applying this definition, (49) would be true iff j½½scandO \ ½½wnpilO j j [ ½½scandB \ [ ½½wnpilB j (58) > j½½scandO \ [ ½½wnpilF j j [ ½½scandB \ [ [ ½½wnpilB+F j In order to evaluate this inequality, let us write ½½scandO ¼ SCAND and ½½wnpilO ¼ WNPIL. Let us assume that the alternatives to winning the Nobel Prize in literature are the properties of winning various distinguished prizes. Thus, (59) [ ½½wnpilF ¼ PRIZE-WINNERS, where PRIZE-WINNERS is the set of people who won some distinguished prize. Let us assume that, as before, (60) [ ½½scandB ¼ PEOPLE. Since the property wnpil is not B-marked, (61) [ ½½wnpilB ¼ WNPIL, and (62) [ [ ½½wnpilB+F ¼ [ ½½wnpilF ¼ PRIZE-WINNERS. Now, (49) is true iff jSCAND \ WNPILj

jPEOPLE \ WNPILj

(63) jSCAND \ PRIZEWINNERSj > jPEOPLE \ PRIZEWINNERSj In words, the proportion of distinguished Scandinavians who have won the Nobel Prize in literature is greater than the corresponding proportion in the world at large. This appears to be the correct interpretation.


many(w, u) is true iff

Ariel Cohen 25

4.2 Often

(64) a. Mary always takes [John]F to the movies. b. [Mary]F always takes John to the movies. c. always(ks.take(Mary, John, s)) 23

Herburger (1997) disagrees; see Cohen (2001b) for arguments against her view. Emphasizing, once again, that the focus semantic value is calculated by the rules of presupposition projection. 25 Krifka develops such a system, and then discards it in favor of a system that uses existential presupposition instead of sets of alternatives. 26 To be more precise, Q-adverbs apply to sets of minimal situations (Heim 1990; von Fintel 1994), but I will not endeavour to represent minimality in my logical forms. 24


For the semantics of often and other Q-adverbs, I will use probabilities rather than proportions, so as to reflect their lawlike nature (Cohen 1999a). Readers who are uncomfortable with probabilities may wish to continue to think in terms of proportions; the analysis presented here will work just as well with proportions. Unlike the case of many, where syntax determines which elements go into the restrictor,23 in the case of often, syntax is not sufficient. I will therefore assume that the Q-adverb has sentential scope, and that the restriction is determined by focus. More precisely, I will follow Rooth (1985) by assuming that the union of the focus semantic value restricts the domain of a Q-adverb.24 In a probabilistic semantics, this means that the union of the focus semantic value forms the reference class of the conditional probability. Before we can discuss the logical forms of sentence involving often, we first need to determine what the Q-adverb quantifies over. One possibility is to take often (and other Q-adverbs) to quantify over cases (in the sense of Lewis 1975). It turns out, however, that it would be rather complex to provide a formal specification of focus semantic values of the resulting logical forms (though quite possible; see Rooth 1995 and Krifka 200125 for examples of such systems). Specifying the other types of semantic value would presumably be even more complex. Therefore, so as not to be distracted from the main point of the paper by overly complex formulations, I will assume that Q-adverbs quantify over situations. That is to say, propositions denote sets of situations, and therefore Q-adverbs, whose scope is a proposition, apply to sets of situations.26 Thus, for example, the logical form of both (64a) and (64b) is (64c); the difference in their truth conditions will result from different values assigned to the restrictor, as a consequence of the difference in their respective focus structures.

26 No Alternative to Alternatives Note that (64c) contains only a nuclear scope, not a restrictor; the value of the restrictor is provided by the union of the set of alternatives.27 How do we get the different interpretations of (64a) and (64b)? In a probabilistic semantics, always(/) is true iff the probability of /, given the restrictor, is 1: (65) P(½½/Oj [ ½½/F) ¼ 1 In the case of (64a), ½½/F is a set of propositions, namely a set of sets of situations. In each set of situations, Mary takes a different individual (e.g. John, Bill or Fred) to the movies:

The union of the focus semantic value is then: (67) fs j dx take(Mary, x, s)g Thus, (64a) is true iff (68) P(fs j take(Mary, John, s)gjfs j dx take(Mary, x, s)g) ¼ 1 This means that (64a) is true iff the probability that Mary is taking John to the movies, given that she is taking someone to the movies, is 1. This appears to be the correct interpretation. In (64b), ½½/F is different. Consequently, we compute different truth conditions: (69) P(fs j take(Mary, John, s)gjfs j dy take(y, John, s)g) ¼ 1 Thus, (64b) is true iff the probability that Mary is taking John to the movies, given that someone is taking him to the movies, is 1—the desired interpretation. Let us now turn to often. Under its absolute reading, we take some expression, /, and consider the probability of / given the union of the alternatives to the focused elements of /. This can be defined formally as follows: Definition 4 (often, absolute reading, first version) often(/) is true iff P(½½/Oj [ ½½/F) > q, where q is ‘large’. The account of relative readings is the same, except that the value of q is given a definite value: the same as the left-hand side, but with alternatives to the B-marked element considered. As with the absolute 27 Equivalently, we could maintain the appearance of a tripartite structure, by following authors such as Rooth (1992) and von Fintel (1994, 2004) and adding an empty restrictor, indicated by a free variable.


(66) ffs j take(Mary, John, s)g, fs j take(Mary, Bill, s)g, fs j take(Mary, Fred, s)g, . . .g

Ariel Cohen 27

reading, we take some expression /#, and consider its probability given the union of the alternatives to the focused elements of /#. In the case of the absolute reading, /# was simply / itself, but for the relative reading it is the union of the B semantic value of /. This means that we consider the probability of [ ½½/B given [ [ ½½/B+F. Hence, the definition of the relative reading is as follows: Definition 5 (often, relative reading) often(/) is true iff P(½½/Oj [ ½½/F) > P([ ½½/Bj [ [ ½½/B+F). We can now see how these definitions work. Consider again Bill’s answer in (37), repeated below, with B-marking and focus marking: Its logical form would be (where pl is the property of being a politician, and crkd is the property of being crooked): (71) often(ks.dx(in(x, s) ^ pl(x) ^ crkd(x))) Let us indicate the nuclear scope by u. Then the ordinary semantic value is: (72) ½½/O ¼ fs j dx(in(x, s) ^ pl(x) ^ crkd(x))g With regard to the focus semantic value, it is important to identify where the focus is. The adverb may be stressed, but since Q-adverbs require focus (Cohen 2004a), there must be (possibly second occurrence) focus inside the nuclear scope; since pl is B-marked, the only possibility is focus on crkd. Assuming the only alternative to crkd is honest, the focus semantic value is: (73) ½½/F ¼ ffs j dx(in(x, s) ^ pl(x) ^ crkd(x))g, fs j dx(in(x, s) ^ pl(x) ^ honest(x))gg The union of the focus semantic value is then simply (74) [ ½½/F ¼ fs j dx(in(x, s) ^ pl(x))g Assuming that the alternatives to pl are physician and linguist, the B semantic value is: (75) ½½/B ¼ ffs j dx(in(x, s) ^ pl(x) ^ crkd(x))g, fs j dx(in(x, s) ^ physician(x) ^ crkd(x))g, fs j dx(in(x, s) ^ linguist(x) ^ crkd(x))gg Its union is simply (76) [ ½½/B ¼ fs j dx(in(x, s) ^ crkd(x))g


(70) A [politician]B is often [crooked]F.

28 No Alternative to Alternatives The contrast semantic value is: (77) ½½/B+F ¼ fffs j dx(in(x, s) ^ pl(x) ^ crkd(x))g, fs j dx(in(x, s) ^ pl(x) ^ honest(x))gg, ffs j dx(in(x, s) ^ physician(x) ^ crkd(x))g, fs j dx(in(x, s) ^ physician(x) ^ honest(x))gg, ffs j dx(in(x, s) ^ linguist(x) ^ crkd(x))g, fs j dx(in(x, s) ^ linguist(x) ^ honest(x))ggg This corresponds to the following set of questions:

These questions are implied by the context of (37), hence the felicity of the exchange. The union of the union of the contrast semantic value is just (79) [ [ ½½/B+F ¼ fs j dx(in(x, s) ^ person(x))g We can now account for the two readings of (71). According to the absolute reading, often(/) is true iff P(½½/Oj [ ½½/F) is ‘large’. In this case, this means that (80) P(fs j dx(in(x, s) ^ pl(x) ^ crkd(x))gjfs j dx(in(x, s) ^ pl(x))g) > q, where q is ‘large’. In words, the sentence is true just in case a situation involving a politician is likely to be situation involving a crooked politician, as desired. Under the relative reading, often(/) is true iff (81) P(½½/Oj [ ½½/F) > P([ ½½/Bj [ [ ½½/B+F). In this case, this is the requirement that (82) P(fs j dx(in(x, s) ^ pl(x) ^ crkd(x))gjfs j dx(in(x, s) ^ pl(x))g)> P(fs j dx(in(x, s) ^ crkd(x))gjfs j dx(in(x, s) ^ person(x))g). In words, the sentence is true just in case a situation involving a politician is more likely to be a situation involving a crooked politician than a situation involving an arbitrary person is likely to be a situation involving a crook. This is the desired relative reading.

4.3 Generics I will assume that characterizing generics, like Q-adverbs, are quantificational. Following Krifka et al. (1995), I draw a distinction


(78) fHow honest is a politician?, How honest is a physician?, How honest is a linguist?g

Ariel Cohen 29

between direct kind predication, as in (83a), and characterizing generics, exemplified by (83b). (83) a. Lions are an endangered species. b. Lions have a bushy tail.

Definition 6 (generics, absolute reading, first version) gen(w, u) is true iff P(½½uOj½½wO \ [ ½½uF) > 0.5. To obtain the relative reading, we will employ the same principle as with the other constructions above: the right-hand side of the inequality is the same as the left-hand side, except that we consider alternatives to the B-marked element. Definition 7 (generics, relative reading) gen(w, u) is true iff P(½½uOj½½wO \ [ ½½uF) > P([ ½½uBj [ ½½wB \ [ [ ½½uB+F). For example, consider (40b), repeated below, with focus and B marking: (84) [Bulgarians]B are [good]F weightlifters. Its logical form is (where bl is the property of being a Bulgarian and gwl indicates the property of being a good weightlifter): (85) gen(ks.dx(in(x, s) ^ bl(x)), ks.dx(in(x, s) ^ gwl(x)))

28 The idea that topics are mapped onto the restrictor of a quantifier is not at all new—see, among many others, Reinhart (1981) and Chierchia (1992). For a specific discussion of topicality and the generic quantifier, see Cohen (1996, 2001a) and Cohen & Erteschik-Shir (2002). 29 See section 5.3 below for the origins of this number. Some might say that 0.5 is too low, and does not capture the intuition that generics are true of ‘almost all’ instances. In Cohen (1996, 1999a), I suggest that generics are subject to additional constraints, whose effect is to create the appearance of a much higher threshold.


Sentence (83a) is predicational, expressing the statement that the kind Leo has a certain property. In contrast, (83b) is quantificational, expressing a statement about individual lions. Unlike Q-adverbs, the generic quantifier does not have sentential scope: the topic of the sentence is mapped onto the restrictor, and the rest of the sentence is mapped onto the scope.28 However, just like the case of Q-adverbs, the focus semantic value (as well as presuppositions) can further restrict the domain of the generic quantifier. I will assume that generics, again like Q-adverbs, express probability judgments (Cohen 1999a). Under the absolute reading, a true generic requires this probability to be greater than 0.5:29

30 No Alternative to Alternatives Let w be the restrictor and u the nuclear scope. Their respective ordinary semantic values are: (86) a. ½½wO ¼ fs j dx(in(x, s) ^ bl(x))g b. ½½uO ¼ fs j dx(in(x, s) ^ gwl(x))g Assuming, for simplicity, that the only alternative to gwl is bwl (the property of being a bad weightlifter), the focus semantic value of the nuclear scope is: (87) ½½uF ¼ ffs j dx(in(x, s) ^ gwl(x))g, fs j dx(in(x, s) ^ bwl(x))gg

(88) [ ½½uF ¼ fs j dx(in(x, s) ^ wl(x))g Since u does not contain B-marking, its B semantic value is just a singleton set of its ordinary semantic value, so that its union is just the ordinary semantic value: (89) a. ½½uB ¼ ffs j dx(in(x, s) ^ gwl(x))gg b. [ ½½uB ¼ fs j dx(in(x, s) ^ gwl(x))g The contrast semantic value is: (90) ½½uB+F ¼ fffs j dx(in(x, s) ^ gwl(x))g, fs j dx(in(x, s) ^ bwl(x))ggg The union of its union is: (91) [ [ ½½uB+F ¼ fs j dx(in(x, s) ^ wl(x))g The B semantic value of the restrictor is: (92) ½½wB ¼ ffs j dx(in(x, s) ^ bl(x))g, fs j dx(in(x, s) ^ Russian(x))g, . . .g Its union is simply: (93) [ ½½wB ¼ fs j dx(in(x, s) ^ person(x))g We can now account for the two readings of (84). The absolute reading will be true just in case (94) P(½½uOj½½wO \ [ ½½uF) > 0.5 Inserting the values for (84) into this inequality, we get: (95) P(fs j dx(in(x, s) ^ gwl(x))gjfs j dx(in(x, s) ^ bl(x) ^ wl(x))g) > 0.5.


Its union, then, will be (where wl is the property of being a weightlifter):

Ariel Cohen 31

This says that a situation involving a Bulgarian weightlifter is likely to be a situation involving a good weightlifter. Keeping in mind that the situations are minimal (see note 26 above), this is the desired interpretation. The relative reading will be true iff (96) P(½½uOj½½wO \ [ ½½uF) > P([ ½½uBj [ ½½wB \ [ [ ½½uB+F) In this case, it is the requirement that

In words, a (minimal) situation involving a Bulgarian weightlifter is more likely to be a (minimal) situation involving a good weightlifter than a (minimal) situation involving an arbitrary weightlifter is likely to be a (minimal) situation involving a good weightlifter. 5 THE ORIGINS OF RELATIVE READINGS We have seen that many (and few), often (and seldom) and generics have relative readings, and traced the differences in these readings to the value of the parameter q. The idea of accounting for different readings of many by different values of parameters is not new. Lappin (2000) proposes a parameterized representation and applies it with impressive success to a variety of interpretations of many. Lappin proposes some general, plausible constraints on the possible values of the parameters; however, he cannot specify why they have the particular values they do. Moreover, Lappin offers no explanation for why other quantifiers do not receive such parameterized representations. More to the point of the present paper, other quantifiers besides many, few, their adverbial counterparts and generics do not seem to have relative readings. Consider: (98) a. Most Scandinavians have won the Nobel Prize in literature. b. Paul usually has a headache. c. A politician is almost always crooked. Regardless of context and intonation, (98a) can only mean that the majority of (relevant) Scandinavians have won the Nobel Prize in literature, not that the proportion of Scandinavians who have done so is higher than that among people in general; (98b) means that a relevant situation containing Paul is likely to be a situation where he has a headache, not that Paul has a headache more frequently than the


(97) P(fs j dx(in(x, s) ^ gwl(x))gjfs j dx(in(x, s) ^ bl(x) ^ wl(x))g) > P(fs j dx(in(x, s) ^ gwl(x))gjfs j dx(in(x, s) ^ person(x) ^ wl(x))g)

32 No Alternative to Alternatives average and (98c) only means that if someone is a politician, he or she is almost certainly crooked, not that he or she is more likely to be crooked than an arbitrary person is. Why is it that only some quantifiers, but not others, give rise to relative readings? And how are their relative readings related to their absolute readings?

5.1 Many

(99) a. There were few faculty children at the 1980 picnic. b. Few egg-laying mammals turned up in our survey, perhaps because there are few. Sentence (99a) can be true even if all faculty children came to the picnic, provided that there were few faculty children in 1980. And (99b) will be true even if the survey included all egg-laying mammals. So, how many is many? Since the quantifier itself does not give us any clue, we need to find some strategy to determine if a given proportion, in a given context, qualifies. The absolute and relative readings turn out to be two strategies to accomplish this.30 Fernando and Kamp (1996) consider this problem and suggest that, under the absolute proportional reading,31 many(w, u) is true iff it could well have been the case that fewer ws are us. In other words, there are more ws that are us than expected. For example, (100) means that more academics watched the 2006 World Cup than one would expect of academics (who watch TV). (100) Many academics watched the 2006 World Cup on TV. Note than when we change the arguments of many, the expectations might change, and the threshold will change with them: (101) Many sports fans watched the 2006 World Cup on TV. 30 31

I thank Hans Kamp for suggesting this direction to me. They do not consider relative readings.


The key to the answer is, I believe, the fact that many and few (and, correspondingly, often and seldom) are vague. They are not the only vague quantifiers: there are others, e.g. almost all, hardly any, several. But these other quantifiers differ from many and few in that, while vague, they do provide some information about the required proportion: it is reasonably clear that 99% qualifies as almost all, whereas 1% does not. In contrast, the requirements for many and few seem completely open ended. In fact, Huettner (1984) (as cited by Partee 1988) presents cases where few(w, u) can be true even if all ws are us:

Ariel Cohen 33

(102) Many people admired by David Beckham watched the 2006 World Cup on TV. Let us follow the spirit, if not the letter, of the proposal by Fernando and Kamp. The truth conditions of many depend on our expectations, in the sense that many(w, u) is true iff there are more ws that are us than expected. I propose a formalization of this notion in which the notion of alternatives is central, and which, as I will demonstrate, can be extended to handle relative readings.32 Let us propose a new type of semantic value: world semantic value, ½½uW, which takes into account alternatives to the world of evaluation. ½½uW is a set of extensions of u, one for each world. Formally, this is the range of the intension of u. If u is a property, ½½uW is a set of sets of individuals. I will assume Lewis’ (1968, 1971, 1986) counterpart theory, so that the individuals in different worlds are different.33 If we then apply union to the world semantic value, [½½uW, we get the set of all individuals that are in the extension of u in some world. For example, take (100), whose logical form is something like (103) (where wc is the 2006 World Cup, and acad is the property of being an academic). (103) many(acad, kx.watch(x, wc)) The union of the world semantic value of the restrictor, [½½acadW, is the set of possible academics, i.e. the set of individuals who are 32

The formalization of Fernando and Kamp, while appropriate for absolute readings, is not easily extended to the case of relative readings. 33 See Kratzer (1989) for using counterpart theory in situation semantics, and specifically von Fintel (2004: note 2) for an argument for using it in accounts of adverbial quantification. Alternatively, we could say that properties denote sets of pairs of worlds and individuals (cf. Schubert & Pelletier 1989), but I will not explore this possibility here.


Sentence (101) is exactly like (100), except that the predicate academic has been replaced with sports fan. But since more sports fans are expected to watch soccer matches than academics, (101) will require a higher proportion to be true. In this way, Fernando & Kamp (1996) are able to solve the following puzzle, first noted by Keenan & Stavi (1986): if we replace one of the arguments of many with an argument that is co-extensional with it, the truth conditions of the sentence may change. For example, suppose that David Beckham, the soccer star, admires all and only academics. Thus, the predicates academic and person admired by David Beckham have the same extension. And yet, since we may expect people admired by David Beckham to watch soccer on TV, we may assign to (102) truth conditions that are different from those of (100).

34 No Alternative to Alternatives academics in some world. The union of the world semantic value of the scope, (104), is the set of individuals who watched the 2006 World Cup on TV in some world. (104) [½½kx.watch(x, [wc]F)W

(105) many(acad, kx.watch(x, [wc]F)) The union of the union of the W+F semantic value of the scope, [ [ ½½kx.watch(x, [wc]F)W+F, is the set of individuals who watched something on TV in some world. Now consider the probability that something is a u in some world, given that it is a w in some world and an alternative to u in some world: (106) P([ ½½uW j [ ½½wW \ [ [ ½½uW+F) Since individuals in different worlds are different, (106) is the probability that if an individual in some world is a w and an alternative to u, then it is a u. This is precisely the expectation that a relevant w is a u, required by the theory of Fernando and Kamp. For (100), we are considering the probability (107) P([ ½½kx.watch(x, [wc]F)W j [ ½½acadW \ [ [ ½½kx.watch (x, [wc]F)W+F). This is the probability that someone who is an academic and watched something on TV in some world watched the 2006 World Cup in that world. So, the absolute reading of many is defined as follows: Definition 8 (many, absolute reading) many(w, u) is true iff j½½wO \ ½½/O j W W W+F Þ. O F >Pð[½½/ j [ ½½w \ [ [ ½½/ j½½w \ [½½/ j 34 Just like in the case of contrast semantic value, this notation is not meant to indicate that ½½uW+F somehow ought to be derived compositionally from ½½uW and ½½uF.


We can also combine the world semantic value and the focus semantic value, in a way analogous to the way the contrast semantic value combines the B semantic value and the focus semantic value. ½½uW+F is a set of sets; each set is the focus semantic value of u in some world. If, again, u is a property, [ [ ½½uW+F is a set of individuals; each one is a member of the extension of some focus alternative to u in some world.34 For example, consider (100) again. Let us assume that there is focus on the 2006 World Cup on TV, so that its logical form, annotated for focus, is:

Ariel Cohen 35

Applying this definition to (100), the sentence is true iff the proportion of academics who watched the 2006 World Cup on TV among academics who watched something on TV is higher than the expectation that an academic who watched something on TV watched the 2006 World Cup. These appear to be the correct truth conditions. Now, note what happens if we change W to B: we get precisely the relative reading of many, except that on the right-hand side we have a probability rather than a proportion. I suggest that this is, in fact, the relative reading of many:

j½½wO \ ½½/O j B B B+F . Þ O F >Pð[½½/ j [ ½½w \ [ [ ½½/ j½½w \ [½½/ j By having probabilities, rather than proportions, on the right-hand side of the inequality, we extend the idea of Fernando & Kamp (1996) to the case of relative readings: many is intensional, yet it expresses a relation between sets, and its intensionality only affects the threshold of the inequality. Thus, for example, sentence (49), repeated below, means (under the relative reading) that the proportion of Scandinavians who have won the Nobel Prize in literature is greater than the probability (rather than proportion) that just anybody will win this prize. (108) Many [Scandinavians]B have [won the Nobel Prize in literature]F. We can conclude, then, that there are two strategies to decide how many is many: one involves looking at alternative worlds and the other involves looking at alternative values for the B-marked element. If we pick the first strategy, we get the absolute reading, whereas if we pick the second strategy, we get the relative reading. B-marking facilitates the relative reading; if no element is B-marked, we get absolute readings instead.

5.2 Often The relation between the absolute and relative readings of often is similar. Often is a vague quantifier, which gives no clue as to the required threshold probability. Hence, one of two strategies is employed: either the one that utilizes the world semantic value or, if an element is B-marked, the one that utilizes the B semantic value. We can now rephrase definition 4 using the new semantic values, so that the definition of the absolute reading of often is:


Definition 9 (many, relative reading, final version) many(w, u) is true iff

36 No Alternative to Alternatives Definition 10 (often, absolute reading, final version) often(u) is true iff P(½½uOj [ ½½uF) > P([ ½½uWj [ [ ½½uW+F). And, as in the case of many, if we change W to B, we get the relative reading, whose definition I repeat below for completeness: Definition 11 (often, relative reading) often(u) is true iff P(½½uOj [ ½½uF) > P([ ½½uBj [ [ ½½uB+F). To see how the revised definition works, consider again (70) and its logical form (71), repeated below:

We have seen that this sentence is true, according to the absolute reading, iff (110) P(fs j dx(in(x, s) ^ pl(x) ^ crkd(x))gjfs j dx(in(x, s) ^ pl(x))g) > q, where q is ‘large’. We can now give a value to q. Note that (111) [ ½½uW ¼ fs j s is a situation in some world containing a crooked politiciang, and (112) [ [ ½½uW+F ¼ fs j s is a situation in some world containing a politiciang. According to definition 10, u is equal to the conditional probability of (111) given (112). In words, u is the probability that in some world, a situation containing a politician contains a crooked politician, hence the expectation that a politician will be crooked. Thus, (109) is true just in case the probability in the actual world for a politician to be crooked is greater than expected. Since the definition of the relative readings has not changed, its calculation proceeds as before.

5.3 Generics Generics are not usually considered vague.35 Indeed, in the above, I have proposed that their absolute reading is an inequality with a precise threshold 0.5. But where did this value come from? And why do generics have relative readings, like vague quantifiers? 35 Though they are by some researchers: for example, according to Farkas & Sugioka (1983) generics express the vague quantifier significantly many.


(109) a. A [politician]B is often [crooked]F. b. often(ks.dx(in(x, s) ^ pl(x) ^ crkd(x)))

Ariel Cohen 37

Let us assume for a moment that generics really are vague. If so, how are they interpreted? The absolute reading of generics should be defined just like the absolute reading of often (except that topic of the generic is mapped onto the restrictor): Definition 12 (generics, absolute reading, second version) gen(w, u) is true iff P(½½uOj½½wO \ [ ½½uF) > P([ ½½uWj [ ½½wW \ [ [ ½½uW+F).

(113) a. Academics like to watch sports on TV. b. People admired by David Beckham like to watch sports on TV. It appears, therefore, that the threshold for both (113a) and (113b) is the same, hence the expectations are the same. What does it mean to have the same expectations about academics as about people admired by David Beckham? If we know something about either academics or David Beckham’s object of admiration, surely we will have some expectations about them, and these expectations will differ. If our expectations about them are the same, this means that we have no prior beliefs about what academics or people admired by David Beckham are likely to do. Thus, when we calculate the threshold for the absolute reading of generics, we do so as if we have no relevant prior knowledge. What is the reason for this? Elsewhere (Cohen 1996, 1997) I have proposed that the use of a generic is to state a default rule. A default rule is a rule that one has to resort to in the absence of relevant information. For example, someone who utters (114) suggests a rule of reasoning, 36 In fact, they are co-extensional throughout a long period of time; this is necessary when we apply this test to generics, since they are parametric on time (Cohen 1999a).


How can we put a value on the right-hand side of the inequality, namely the threshold? In the case of many(w, u) (and its adverbial counterpart), the threshold represented the expectation that a w is a u, following Fernando & Kamp (1996). As we have seen, one of the arguments for this proposal is that when we replace one of the arguments of many with another that is co-extensional with it, the truth conditions of the sentence may change. However, this is not the case with generics. Let us assume, once again, that David Beckham admires all and only academics. Then the predicates academic and person admired by David Beckham are coextensional.36 Nonetheless, (113a) and (113b) appear to have the same truth conditions:

38 No Alternative to Alternatives according to which, if we know that Nevermore is a raven, and we do not know anything else about Nevermore, we may conclude that it is black. (114) Ravens are black.37

Definition 13 (generics, absolute reading, final version) gen(w, u) is true iff P(½½uOj½½wO \ [ ½½uF) > P([ ½½uWj [ ½½wW \ [ [ ½½uW+F) ¼ 0.5. As before, if we change W to B, we get the relative reading as defined in 7, repeated below: Definition 14 (generics, relative reading) gen(w, u) is true iff P(½½uOj½½wO \ [ ½½uF) > P([ ½½uBj [ ½½wB \ [ [ ½½uB+F).

5.4 Independent evidence for the world semantic value? The world semantic value appears to provide us with a uniform account of both absolute and relative readings. But is there independent evidence 37 The meaning and use of a generic are not unrelated: the default rule is sound (or ‘useful’) iff the generic sentence is acceptable and true. 38 Of course, prior knowledge is necessary in order to evaluate the truth value of the generic, e.g. whether ravens are, in fact, black.


Therefore, a generic, unlike many, does not assume any prior knowledge from the hearer in order to determine its threshold.38 The value of the threshold is that which indicates no knowledge. In order to calculate this value, we can use The Principle of Indifference. Keynes (1921) describes the principle this way: ‘The Principle of Indifference asserts that if there is no known reason for predicating of our subject one rather than another of several alternatives, then relatively to such knowledge the assertions of each of these alternatives have an equal probability’ (p. 42, original emphases). In the case of the generic gen(w, u) we have two alternatives: either ws are us or they are not. Since we calculate the probabilities as if we had no prior knowledge about w and u, both options will receive equal probability, namely 0.5. The difference, then, between the absolute readings of often and generics is that, with the latter, the threshold is fixed at 0.5. The final version of the truth conditions of generics expresses this fact:

Ariel Cohen 39

that it is a real phenomenon? And is it, like focus and the contrast semantic values, typically, though perhaps not obligatorily, associated with a specific intonation contour? In this admittedly speculative section, I would like to argue that the answer to both questions is, in fact, yes. Specifically, I propose that the world semantic value plays a role in the interpretation of incredulity questions. Suppose Bill hears Ann uttering (115a); in response, Bill utters (115b).39 (115) a. Ann: John is going to get the job. b. Bill: JOHN is going to get the job?!

(116) fJohn is going to get the job, Mary is going to get the job, Julie is going to get the job, . . .g This set of alternatives corresponds to a question inquiring which of these alternatives was asserted. Artstein can therefore account for the question aspect of an echo question: it is used when one interlocutor failed to 39 Capitals indicate pitch accent. The interpretation of this pitch accent will be discussed momentarily.


How are we to interpret Bill’s utterance? On the one hand, it looks like a question—specifically, an echo question. Bill’s utterance ends with a rising intonation, and it can get the same sort of answer that a genuine question would elicit. Thus, ‘yes’ is a perfectly reasonable response to (115b). On the other hand, however, Bill’s utterance is not really a question. Bill is not seeking information; we can safely assume that Bill understood what Ann was saying. The point of Bill’s utterance is to express incredulity. Bill does not question the fact that John will, indeed, get the job, but expresses surprise—this is not at all what Bill expected, so much so that it is hard for Bill to believe it. For instance, Bill may believe that John is an extremely unsuitable choice, so that his appointment is incredible. Alternatively, Bill can express indignation: Bill may be interpreted as saying that John’s appointment is bad, unethical, unjust or the like. For example, Bill may have received a promise to get the job himself, and John’s appointment breaks this promise. Incredulity questions are often treated as a kind of echo questions, because they share many syntactic properties (Authier 1993). Looking at the semantics of echo question may therefore help us figure out the meaning of incredulity questions. We have already seen in section 2.4 above the theory of echo questions proposed by Artstein (2002). According to him, the meaning of (115b) is a set of alternatives of the form:

40 No Alternative to Alternatives

(117) fJohnw1 , Johnw2 , Johnw3 , . . .g. We combine the world semantic value of John with the other elements of the sentence, using the standard semantic combinatory rule. The resulting world semantic value of (115b) is a set of propositions of the form: (118) fJohnw1 is going to get the job, Johnw2 is going to get the job, Johnw3 is going to get the job, . . .g40 40 We need to be careful about what propositions are. In this case, it makes little sense to equate them with sets of possible worlds, and we probably want what Lewis (1986) calls a singular proposition: (ia) is identified with the ordered pair (ib), and is true iff the first element is a member of the second (see Dorr 2005 for arguments for using singular propositions in counterpart theory in general).

(i)

a. Johnwi is going to get the job. b. Æ Johnwi , the set of individuals who are going to get the job in some worldæ


understand or hear clearly what the other one is saying. Thus, if we interpret (115b) as an echo question, the implication is that he did not hear clearly and is seeking confirmation about the identity of the person who will get the job. Artstein acknowledges that in addition to clarification seeking echo questions, there are also cases where an echo question is used to express incredulity or indignation about some proposition, usually the previous utterance or an entailment of it. However, he does not explain how these particular aspects of the meaning follow from his system: how does it follow that if Bill is inquiring about the identity of the person who got the job, that Bill knows it is John, but expresses incredulity or indignation about the fact? Moreover, incredulity questions differ in their intonation from pure echo questions. In fact, they have a tune similar to that of ordinary declaratives, except that, being questions, they have a final rise rather than a final fall (Moulton 1987). As Gunlogson (2003) points out, this, in itself, is not sufficient for the interpretation of incredulity: rising declaratives can express a wide range of speaker attitudes, and incredulity is only one of them. The meaning of incredulity is expressed not through the tune but via expanded pitch range (Hirschberg & Ward 1992; Herman 1996; Jun & Oh 1996; Ladd & Morton 1997; Gunlogson 2003; Lee 2005). Nonetheless, I believe that Artstein’s insight, namely that incredulity questions, just like echo questions, involve reference to a set of alternatives, is correct. However, the relevant semantic value here is not the focus semantic value, but the world semantic value. Expanded pitch range is used to indicate that the world semantic value of John ought to be considered. This is the set of counterparts to John in each one of Bill’s belief (or normative) worlds:

Ariel Cohen 41

What Bill is actually asking, then, is this: in which world is John going to get the job? The domain of worlds that Bill is asking about depends on the modal base (which, in turn, is dependent on the context). The modal base can be epistemic, i.e. the alternative worlds are Bill’s belief worlds: in each one of these worlds, some candidate is getting the job. Bill is then asking us to find a world among them in which John gets the job. This is a rhetorical question, because Bill already knows the answer—he hardly needs us to tell him what is in his belief worlds! Normally, a rhetorical wh-question is interpreted as implying that the answer is the empty set.41

Thus, (119a) implies that nobody believes such nonsense, (119b) implies that he has never spoken against his mother, (119c) implies that it makes no difference. Therefore, when Bill is asking about his belief worlds, he is implying that the answer is the empty set: i.e. in none of his belief worlds does John get the job. Hence, he getting the job is incredible.42 Alternatively, the modal base may be deontic. In this case, Bill refers to worlds that are permissible, according to his norms. Once again, this is interpreted as a rhetorical question, since Bill’s norms are obviously known to himself. Therefore, Bill is implying that in none of these worlds does John get the job. This is how the indignation interpretation is generated: the appointment of John to the job constitutes a violation of Bill’s norms of conduct. Thus, an incredulity question has a dual aspect. On the one hand, it really is a question: Bill is asking in which world John is going to get the job. If Ann answers yes, she is indicating such a world—the actual world (though this world may not be among Bill’s belief or normative worlds). On the other hand, it is a statement of incredulity or indignation: by being rhetorical, the question implies that none of the possible answers are true, i.e. that the echoed statement is incredible or outrageous. If this account is on the right track, it provides an additional case where the world semantic value plays a role in interpretation and is associated with a distinct form of intonation: expanded pitch range. 41 I am using the neutral term ‘implying’, since it is not relevant to our discussion here whether this is an entailment, a presupposition or an implicature. 42 Of course, we are referring to Bill’s belief worlds before Ann spoke; after he heard Ann and accepted what she said, Bill’s belief worlds will obviously contain the fact that John will get the job.


(119) a. Who believes such nonsense? (Bolinger 1957, 158) b. When has he ever said a word against his mother? (Horn 1978: 151) c. What difference does it make? (Quirk et al. 1985: 826)

42 No Alternative to Alternatives 6 CONCLUSIONS

(120) [I]B would buy [‘The Hotel New Hampshire’]F. Then ½½uF+B would be (121).


In this paper, I have proposed that there are two strategies to interpret vague quantifiers: both strategies use the same principle of utilizing alternatives, but one involves taking alternative worlds into account, while the other considers alternatives to B-marked elements. Neither of these strategies involves use of existential presuppositions; hence, I conclude that the device of alternatives is necessary in order to explain the range of interpretations of quantificational structures. The conclusion is, then, that the focus semantic value, far from being a spurious addition to the semantics, is only one of an arsenal of semantic values: in fact, six such values have been proposed in this paper. If the analysis presented here in on the right track, the phenomenon of various semantic values, generated by considering alternatives to various elements (focus marked elements, B-marked elements, worlds) is quite ubiquitous. In hindsight, this is perhaps not so surprising. Multidimensional theories are constantly being proposed, to account for a variety of phenomena at the interface of semantics and pragmatics. Indeed, Potts (2007) identifies so many such accounts, that he sees the need to classify them. And as we go even more deeply into the interaction between semantics and pragmatics, it is to be expected that such multidimensional theories will require more and more semantic values. There were times, not too long ago, when it was thought that focus merely expressed some pragmatic notion (‘newness’ or some such), and had no influence on truth conditions. In those days, there was indeed no need for additional semantic values. But when the effect of focus on truth conditions began to be recognized, the time was ripe for Rooth’s additional semantic value. Later, when Bu¨ring attempted to incorporate an additional pragmatic phenomenon into semantics, he saw the need for yet another semantic value. It is important to note that the semantic values are not arbitrarily chosen: there seems to be some internal structure to the set of semantic values. ½½uB+F is, in a sense, a combination of ½½uB and ½½uF; similarly, ½½uW+F combines ½½uW and ½½uF. But are there alternatives to other elements? And are there other combinations of semantic values? Is there, for example, ½½uF+B? This would be a set of B semantic values for each alternative to the focus. For example, suppose u is (4b), repeated below as (120).

Ariel Cohen 43

Is there such a semantic value? The answer ought to be empirical—is there a phenomenon whose explanation requires it? As far as I have been able to determine, the answer is no. There also does not appear to be any evidence for a ½½uF+W semantic value. It seems, then, that there is a certain order in the combination of the background or the world semantic value with focus, so that the focus semantic values is, in a sense, ‘more basic’ than the other two. Why is this? A complete answer would have to await future research, which will chart the domain of semantic values and identify the principles dictating the kind of things to which alternatives can be considered, and the sanctioned combinations of semantic values to create new ones. For now, I will offer a tentative speculation. The beginnings of an explanation might be in the realization that focus really is very basic, in that it is used to indicate new information, or the ‘point’ of the sentence, or some such. It might even be the case that, as argued in Erteschik-Shir & Lappin (1987), focusing is an integral part of the computational systems of all modes of perception, and is a single task-specific mechanism that identifies the foregrounded constituent in representations of all modular systems. If that is correct, then focus, in a sense, comes for free. Seen in this light, the ½½uB+F or ½½uW+F semantic values are natural: they denote a set of sets. Each such set corresponds to the focus semantic value of a sentence that contains focus marking. In contrast, the ½½uF+W or ½½uF+B semantic values, had they existed, would be rather unnatural. They, too, would denote a set of sets. But now, each set would correspond to the background/world semantic value of a sentence without any focus. In other words, the background or world


(121) f fI would buy ‘War and Peace’, Paul Simon would buy ‘War and Peace’, Fritz would buy ‘War and Peace’, Fritz’s brother would buy ‘War and Peace’, . . .g, fI would buy ‘The Hotel New Hampshire’, Paul Simon would buy ‘The Hotel New Hampshire’, Fritz would buy ‘The Hotel New Hampshire’, Fritz’s brother would buy ‘The Hotel New Hampshire’, . . .g, fI would buy ‘The World According to Garp’, Paul Simon would buy ‘The World According to Garp’, Fritz would buy ‘The World According to Garp’, Fritz’s brother would buy ‘The World According to Garp’, . . .g, . . .g

44 No Alternative to Alternatives semantic values would be treated as more basic than the focus semantic value. Acknowledgements I thank David Beaver, Sigrid Beck, Hans Kamp and two anonymous referees for many helpful comments and suggestions. This work has been made possible in part by a grant from the Alexander von Humboldt Foundation.

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ARIEL COHEN Department of Foreign Literatures and Linguistics Ben-Gurion University of the Negev Beer Sheva 84105 Israel e-mail: [email protected]

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Lewis, D. (1971), ‘Counterparts of persons and their bodies’. Journal of Philosophy 68:203–11. Lewis, D. (1975), ‘Adverbs of quantification’. In E. L. Keenan (ed.), Formal Semantics of Natural Language. Cambridge University Press. Cambridge, MA. 3–15. Lewis, D. (1986), On the Plurality of Worlds. Blackwell. Oxford. Moulton, W. G. (1987), ‘On the prosody of statements, questions, and echo questions’. American Speech 62:249–61. O’Connor, J. D. & G. F. Arnold (1973), The Intonation of Colloquial English: A Practical Handbook. Longman. London. Partee, B. H. (1988), ‘Many quantifiers’. In J. Powers and K. de Jon (eds.), ESCOL’88: Proceedings of the Fifth Eastern States Conference on Linguistics. Ohio State University. Columbus, OH. 383–402. Partee, B. H. (1991), ‘Topic, focus and quantification’. In S. Moore and A. Z. Wyner (eds.), Proceedings of the First Conference on Semantics and Linguistic Theory. Cornell University. Ithaca, NY. 159–87. Pelletier, F. J. & N. Asher (1997), ‘Generics and defaults’. In J. van Benthem and A. ter Meulen (eds.), Handbook of Logic and Language. Elsevier. Amsterdam, The Netherlands. 1125–77. Pierrehumbert, J. (1980), The Phonology and Phonetics of English Intonation. Ph.D. thesis, MIT, Cambridge, MA. Pierrehumbert, J. & J. Hirschberg (1990), ‘The meaning of intonational contours in discourse’. In P. Cohen, J. Morgan and M. Pollack (eds.), Intentions in Communication. MIT Press. Cambridge, MA. 271–311. Portner, P. & K. Yabushita (1998), ‘The semantics and pragmatics of topic phrases’. Linguistics and Philosophy 21:117–57.

48 No Alternative to Alternatives von Fintel, K. (1994), Restrictions on Quantifier Domains. Ph.D. thesis, University of Massachusetts, Amherst. von Fintel, K. (2004), ‘A minimal theory of adverbial quantification’. In Kamp and Partee (eds.). 137–75. Westersta˚hl, D. (1985), ‘Logical constants in quantifier languages’. Linguistics and Philosophy 8:387–413. Wilkinson, K. (1991), Studies in the Semantics of Generic Noun Phrases. Ph.D. thesis, University of Massachusetts, Amherst. Zeevat, H. (1992), ‘Presupposition and accommodation in update semantics’. Journal of Semantics 9: 379–412. First version received: 04.08.2006 Second version received: 10.12.2007 Accepted: 12.04.2008


Psychology. Cambridge University Press. Cambridge. Strawson, P. F. (1964), ‘Identifying reference and truth values’. Theoria 30. Reprinted in Steinberg and Jakobovits (1971). Vallduvı´, E. & E. Engdahl (1996), ‘The linguistic realization of information packaging’. Linguistics 34:459–519. Vallduvı´, E. & M. Vilkuna (1998), ‘On rheme and kontrast’. In P. W. Culicover and L. McNally (eds.), The Limits of Syntax. Academic Press. New York. 79–108. Vallduvı´, E. & R. Zacharski (1994), ‘Accenting phenomena, association with focus, and the recursiveness of focus-ground’. In P. Dekker and M. Stokhof (eds.), Proceedings of the 9th Amsterdam Colloquium. ILLC. Amsterdam. 638–702.

Journal of Semantics 26: 49–86 doi:10.1093/jos/ffn009 Advance Access publication December 1, 2008

Presupposition Accommodation and Informativity Considerations with Aspectual Still YAEL GREENBERG Bar Ilan University

This paper deals with a newly observed phenomenon which lies at the interface of the semantics and pragmatics of aspectual still (as in John is still asleep), namely the fact that still is infelicitous when it appears in past tense sentences whose reference time is not specified by some temporal adverbial or the utterance context. The main claim of the paper is that in such sentences, the truth of the assertion and that of the ‘prior time’ presupposition this particle triggers can be both inferred from the truth of the minimally contrasting still-less counterpart. Moreover, in such cases the presuppositional status of the ‘prior time’ claim is lost. Hence, the use of still in such sentences is uninformative and thus infelicitous. The analysis has several more general theoretical implications. Concerning the semantics of still, it shows that the novel data cannot be accounted for by using current definitions of the presupposition triggered by still. Instead, a modified definition of still is developed, which, following Ippolito (2007), uses one eventuality variable in both the assertion and the presupposition of sentences with still but, unlike this theory, does not require the denotation of this variable to be contextually salient. As for the analysis of tense and temporal structure of clauses, the interaction of still with frame adverbials supports the view that such adverbials denote intervals identical to the reference time of the sentence, rather than including it. In addition, the paper argues that the contrast between felicitous and infelicitous cases of still can only be explained if, contrary to many current analyses, we assume that past tense is not necessarily anaphoric but can be represented in some cases as a new variable bound by existential closure. Given the proposed analysis, the felicity or infelicity of still in past tense sentences can be seen as a diagnostic for determining whether or not the reference time in such sentences is anaphoric or not.

1 INTRODUCTION This paper deals with a newly observed phenomenon which lies at the interface of the semantics and pragmatics of aspectual still (as in John is still asleep), namely the fact that still is systematically infelicitous when the time described by the sentence (or more technically, the reference time) is not given a specific characterization by a temporal adverbial or the utterance context. The main claim I make is that this kind of infelicity results from the fact that in such constructions the use of still is uninformative. Ó The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected].


Abstract

50 Presuppositions and Informativity with Aspectual still

2 THE NEWLY OBSERVED DATA: FELICITOUS V. INFELICITOUS OCCURRENCES OF STILL I will be concerned with felicity contrasts exemplified in (1): (1)

A: How’s John? B: Well, he is (still) unemployed (but we hope he will have a job soon) B#: Well, he was (#still) unemployed (but now he has a job)

As seen in (1), the still-less versions of both present and past tense sentences are felicitous.1 However, whereas when adding still to the 1 One may claim here that a past tense answer to a present tense question as in (1B#) is, or should be, infelicitous even without still, due to the tense mismatch which could lead to incoherent discourse. However, all my informants accepted such discourses with no problems. One potential explanation of this could be that A is not asking how John is at the moment of utterance, but more generally, how John is ‘these days’, to which an answer encompassing the near past is relevant. Another explanation might be that the discourse is coherent because B wants to emphasize John’s present situation (having a job) by contrasting it with the past (where he was unemployed). Thanks to an anonymous reviewer for pointing out this potential difficulty. Notice, though, that some past tense sentences may be perfectly felicitous without having clear relevance to the present. For example, a teacher can felicitously utter the out of the blue (ii). Notice that still is infelicitous here too:

(ii) Shakespeare (#still) lived in England.


The analysis, which is couched within a Discourse Representation Theory (DRT) framework (Kamp 1981), also argues for two more general theoretical points. First, I show that the data cannot be accounted for by using current definitions of the presupposition triggered by still. I propose a modified definition of still which, following Ippolito’s (2007) analysis, uses one eventuality variable in both the assertion and the presupposition of sentences with still, but, unlike this theory, does not require the denotation of this variable to be contextually salient. Second, as opposed to many current theories, I show that the data on still support a view where tense in past tense sentences is not necessarily anaphoric or pronominal, but rather potentially existentially closed and novel. The novel data are described in section 2. Section 3 gives background about the anaphoric vs. novel characterization of tense and reference times and about the semantics of still. After examining some potential explanations of the data in section 4 and pointing out their shortcomings, I turn to my own proposal for the semantics of still in section 5 and show how it can account for the novel data. Section 6 examines the compatibility of the analysis with current claims on presuppositions and informativity. Section 7 concludes the paper and examines some remaining questions and directions for further research.

Yael Greenberg 51

present tense (1B) this felicity is maintained, adding it to the past tense (1B#) renders it strikingly infelicitous. Similar felicity contrasts are found in other minimally contrasting present/past tense sentences, for example (2)–(4): (2)

(3)

What is the reason for this contrast? No direct answer to this question can be found in the literature on still, simply because these kinds of data have not yet been examined in any theory dealing with this particle. Of course, one might be tempted to stipulate that still is simply bad with the past tense and fine only with the present tense. However, not only is this generalization unmotivated, but as the felicity of still in (5B)–(8B) shows, it is simply wrong: (5) (6) (7) (8)

A: How’s John? B: Well, I saw him last month. He was (still) unemployed. A: Look at this poor building! It was so much nicer in the 1980s! B: Were you (still) living in it then? A: I heard lots of stories about Mr. Smith. B: Me too. During the war he was (still) very rich. A: There is an important meeting tonight. B: Yes. John came in and told me about it. But I was (still) ill, so I told him that I must rest and that I won’t be able to arrive.

The occurrence of still in these past tense sentences is a lot better than in (1B#)–(4B#) above. The difference between the two types of sentences seems to be related to the specification of the reference time. Intuitively, what all felicitous past tense sentences in (5B)–(8B) seem to share is that their reference time is specified by an adverbial in the previous sentence [as in (5)] and in the sentence itself [as in (6) and (7)] or by the eventuality time of the previous sentence [i.e. the time when John told me about the meeting, in (8)]. In contrast, no specification of the reference time seems to exist in the past tense (1B#4B#), and A’s


(4)

A: There is an important meeting tonight. B: I won’t be able to be there. I am (still) ill, and I must rest. B#: I won’t be able to be there. I was (#still) ill, and I must rest. A: Look at this poor building! B: Are you (still) living in it? B#: Were you (#still) living in it? A: I heard lots of stories about Mr. Smith. B: Me too. He is (still) very rich. B#: Me too. He was (#still) very rich.

52 Presuppositions and Informativity with Aspectual still utterances in these sentences do not supply any exact specification of that time either. It should become clear now what the felicitous past tense sentences in (5B)–(8B) share with the felicitous present tense sentences in (1B)– (4B) above: in the latter case too, the reference time can be said to be specified, namely, to refer to the speech time of the sentence. These intuitions can be informally summarized as in (9): (9) still can only be felicitous in a sentence whose reference time is specified by/refers to another time in the linguistic or discourse context.2

3 SOME BACKGROUND: CHARACTERIZING REFERENCE TIMES AND THE SEMANTICS OF STILL

3.1 Reference times, eventuality times and speech times 3.1.1 Basics. I follow here ideas developed and used in, for example, Partee (1973, 1984), Hinrichs (1986), Kamp & Reyle (1993), Ogihara (1994) and Kratzer (1998). Following the tradition of Reichenbach (1947), these theories analyse the temporal structure of sentences using three temporal parameters: the speech time, the reference time and the eventuality time. In simple sentences, the tense node denotes a time argument which stands for the reference time of the sentence and whose position is determined relative to the speech time.3 Specifically, in present tense 2

As pointed out to me by a reviewer, it is interesting to note that the situation with the perfect aspect seems to be the opposite, namely we get infelicity when the reference time is specific or anaphoric, as in (i). This ‘opposite’ correlation with the specificity/anaphoricity of the reference time may warrant further exploration. (i)

#John has been sick yesterday. 3

Notice that although the use of the term ‘reference time’ in these theories is inspired by Reichenbach’s notion, it is not necessarily identical to the Reichenbachian usage. In this paper, I use the term as it is used in Partee (1973, 1984), Hinrichs (1986), Kamp & Reyle (1993), Ogihara (1994), Kratzer (1998), and as defined above. Comparing this and the Reichenbachian uses of the term is beyond the scope of this paper, but see, for example, Partee (1984) and Nelken and Francez (1995) for some comparisons.


The immediate aim of this paper is to explain this novel generalization. In the next section, I examine some background assumptions concerning the two main components of the analysis, namely the characterization of reference times and the semantics of still. In section 5, I show that once these two components are defined appropriately, their interaction leads to a natural explanation of the generalization in (9).

Yael Greenberg 53

(10)

a. Yesterday afternoon John saw Mary/wrote a letter b. Yesterday afternoon John was very ill/was writing a letter

3.1.2 Are reference times necessarily anaphoric/pronominal? Unlike the reference times of present tense sentences, whose characterization is quite simple (equal to the speech time), the situation with past tense sentences is more complicated. Prior (1967) analysed past tense as existential quantification over times. However, as Partee (1973) shows in her famous example in (11a), taking such a sentence to talk about ‘some time in the past’ would come out wrong, no matter whether we have wide scope negation, as in (11b), which is too strong and seems false, or narrow scope negation, as in (11c), which is too weak and seems trivially true: (11)

a.

I didn’t turn off the stove

4 Given this view, the present tense is anaphoric and not merely ‘indexical’. This is part of a general tendency in the modern semantic literature, which assumes that the traditional distinction between anaphoric (or more precisely, co-referring) and indexical (or deictic) uses of pronouns need not be maintained and does not seem to have real linguistic significance (see, e.g. the discussion in Heim & Kratzer 1998, p. 239–42). A similar position regarding anaphoric and indexical uses of tense is held in, for example, Partee (1973, 1984) and reviewed in section 3.1.2. 5 Heim (1993) and others take this information to be a presuppositional component of tense. For simplicity reasons, I will not attempt to represent this presuppositional status in the DRT-based analysis I propose below (although this is perfectly compatible with what I will suggest).


sentences, the reference time equals the speech time,4 and in past tense sentences, it precedes it.5 Locating temporal adverbs update the reference time. For example, in ‘John woke up at 9.00’, the denotation of at 9.00 is processed in the beginning and updates the reference time to be a time prior to the speech time, equal to 9.00. The speech time (now) is a contextually salient time, and like other contextually salient arguments, its value is given by a contextually supplied assignment function gc (see, e.g. Heim 1994). As for the eventuality time, represented as s(e), aspectual factors determine its position relative to the reference time. In simple sentences, the time of eventive/perfective predicates is taken to be included in the reference time, whereas the time of stative or imperfective (progressivized) predicates is taken to include or overlap it. For example, in (10a), with eventive predicates, the eventuality times of seeing Mary and writing the letter are included in yesterday afternoon, whereas in (10b) the stative/imperfective eventualities of being very ill and writing the letter temporally overlap yesterday afternoon and may even include that time:

54 Presuppositions and Informativity with Aspectual still b. :dt#[t#< t ^ I turn off the stove at t#] c. dt#[t#< t ^ :I turn off the stove at t#]

(12)

a. At 3 p.m. June 21st, 1967, Mary had a brilliant idea b. Mary woke up sometime during the night. She turned on the light. c. When Mary telephoned, Sam was always asleep.

Following Partee, the view that tense can behave as pronominal/ anaphoric is by now standard. What is not agreed upon, however, is whether tense must be anaphoric/pronominal. Unlike the supporters of the ‘reference time as only pronominal’ approach (e.g. Hinrichs 1986; Kratzer 1998; Avrutin & Reuland 2002; Beck 2006, inter alia), there are theories which represent the reference time in some past tense sentences as existentially closed (such as Comrie 1985; Ogihara 1994; Bonomi 1995; Musan 1997; Kehler 2000; von Fintel & Iatridou 2002; Pancheva & von Stechow 2004).6 I tend to agree with the latter approach, since besides cases where reference times are indeed anaphoric to temporal antecedents, there also seem to be felicitous sentences where no such antecedent is found, that is where, using Heim’s (1982) terminology, the reference time is novel. One such construction is ‘out of the blue’ past tense questions, as in (13a) and (13b), discussed in Kratzer (1998) and Partee (1984), respectively: (13)

a. Who built this church? Borromini built this church. b. Who killed Julius Caesar?

Kratzer (1998) points out that ‘. . .the English question [in (13a)] is acceptable out of the blue. If past tense is pronominal, this is surprising. There is no contextually salient past time in this context’ (p. 16). To solve the problem, Kratzer suggests that what seems to be a simple past sentence in (13a) is, in fact, a sentence with present tense and perfect 6 Other theories are neutral with respect to this question. For example, Abusch (1997) assumes that tense can be pronominal but does not explicitly say whether it must be so.


Instead, Partee claims that the reference time of (11a) is anaphoric to a contextually supplied time, for example the time immediately before I left home. The sentence then asserts that I didn’t turn off the stove at that (contextually supplied) time. This parallels nominal anaphoricity of ‘free’ pronouns, as in ‘She left me’, where the pronoun she is anaphoric to a contextually salient antecedent, for example an individual pointed at. In addition, Partee shows that tense can have other kinds of antecedents that pronouns are known to have, namely definite, indefinite (i.e. existentially closed) and quantified antecedents, as in (12a–c), respectively:

Yael Greenberg 55

(14)

John didn’t build this church.7

Besides ‘out of the blue’ questions and negative sentences, there are also affirmative past tense sentences, uttered in context, whose reference time seems existentially closed. I believe that (15B), the still-less version of (1B#) above, is one such sentence: (15)

A: How’s John? B: Well, he was unemployed (but now he has a job).

Although (15B) is not uttered out of the blue, but rather against the context of (15A), this context does not give us any information about the location of the past reference time of (15B). Intuitively, this reference time is novel, meaning ‘some time in the past’, as in (16) 7

Thanks to a reviewer for pointing out this example to me.


aspect (not to be confused with the ‘perfect’ auxiliary have). Thus, the reference time of (13a) is indeed pronominal: it is anaphoric to the utterance time (due to the present tense) and, due to the perfect aspect, it asserts that the event time is over by the reference (utterance) time, that is the event is in the past. This suggestion, however, is problematic if we want to maintain the more intuitive view that sentences like (13a) express simple past and not present perfect. Partee (1984) admits that the reference time of (13b) seems to be ‘some time in the past’ but maintains that it is, in fact, anaphoric and suggests that it is ‘large, vague, and possibly even irrelevant . . . (and) . . . could potentially be ‘‘the whole of the past’’’ (p. 314). According to her, the reason we understand the killing of Julius Caesar to happen ‘some time before now’ is because of the well-known condition that the event time is included in the reference time. This explanation, however, would not work for questions with state verbs like ‘Who admired Julius Caesar?’, which are also understood as asking about a state which took place some time in the past. Unlike events, which are assumed to be included in the reference time (here ‘the whole of the past’), states are supposed to include or overlap it. It is not clear, then, why we necessarily get the existential reading in such cases too. In addition, the reference time of some negative sentences does not seem to be anaphoric, but rather existentially closed and novel. (14), for example, neither means that John didn’t build that church in a contextually salient past time nor means that there is a contextually salient past time where he didn’t build it, but rather that he never built this church, that is there is no past time which overlaps a Johnbuilding-this-church eventuality:

56 Presuppositions and Informativity with Aspectual still (where, here and henceforth, ‘O’ is the temporal overlap relation and ‘s(e)’ gives the running time of the event e): (16) de,t[John-unemployed (e) _ t < n ^ t O s(e)]

(17) de,t [John-unemployed (e) ^ t D ^ t < n ^ t O s(e)]

3.2 The semantics of still 3.2.1 The ‘prior time’ presupposition and a potential problem with it Turning now to the semantics of still, virtually all theories analysing this particle (e.g. Ko¨nig 1977; Lo¨bner 1989; Michaelis 1993; Mittwoch 1993; van der Auwera 1993; Krifka 2000; Ippolito 2007) take still U to implicate that U continues at the reference time of U. According to these theories, (18), for example, implicates that John continues to be asleep at the speech time: 8 In this sense, we may say that the use of past tense in (15B) is similar to the use of a specific indefinite Noun Phrase as in John spoke with some/a woman. As with the existential reading of the past tense, the semantic structure of such sentences contains existential quantification over an individual woman. Even if the speaker has a certain individual woman in mind when uttering it, this information is not part of the semantic structure, and crucially, unlike what happens with real pronouns, the felicity of the sentence does not depend on the listener’s ability to identify this individual. 9 Compare with claims in, for example, Bonomi (1995). 10 One may also claim that this restriction should not be part of the semantic structure of (15B) at all but is provided by the pragmatics (e.g. by the need to make a true and relevant assertion). I will not try to develop this approach here but continue to take (17) as a possible representation of (15B#).


There are two potential objections to this representation. First, one may say that although the context in (15A) does not seem to supply a unique past reference time, the speaker has a certain time in mind which he is referring to when uttering (15B). However, notice that even if the speaker knows that the listener has no way of knowing when exactly John was unemployed, his use of the past tense in (15B) is felicitous. In contrast, if a speaker knows that the listener has no way of identifying the denotation of the pronoun she in ‘She is nice’, he will not use the pronoun, or else, his use of the pronoun will be infelicitous.8 A second objection is that (16) is too weak as a representation of (15B): Clearly, the reference time in this sentence is not any time in the past. (It will not be, e.g. an interval in the prehistoric period.) Rather, it is restricted by the presuppositions and implications of the sentence, for example it is expected to be an interval which appears within John’s life time, and most probably when he is already grown up (where being unemployed is relevant). This can be represented in (17), where the reference time is restricted to occur within a relevant period D (the period where John is alive and grown up):9,10

Yael Greenberg 57

(18)

John is still asleep

(19)

a. John is writing a letter. b. John entered the room. Mary was in the living room c. John entered the room. Mary kissed him.

Given such observations, some theories (e.g. Moens 1987; Moens et al. 1987) have taken this temporal ‘surrounding’ intuition to be, in fact, a defining property of stative predicates (sometimes referred to as ‘the superinterval property’). The problem for the approach to still described above is that if these theories are right, then the ‘prior time’ presupposition triggered by still comes out trivial. For example, the presupposition that John was asleep before 6.13 [in (20a)] would be completely trivial if the still-less (20b) independently entails that the sleeping state holds both before and after 6.13: (20)

a. At 6.13 John was still asleep b. At 6.13 John was asleep

Since still does not seem trivial in (20a), then either the assumption that the ‘prior time’ presupposition is the only contribution of still11 or 11 That is, one can claim that still has an additional contribution to the semantics of the sentence. This kind of view is found in, for example, Michaelis (1993) and van der Auwera (1993), who suggest that still also adds the implication that the state is expected to cease at the reference time. I deal with this suggestion in section 4 below.


This intuition is usually captured using an assertion and a presupposition. (18) is taken to assert that John is asleep now and presuppose that he was also asleep for some time before and up to now. I will henceforth call this latter component the ‘prior time’ presupposition and a large part of the following discussion will be concerned with its formalization. Before doing that, however, let us examine a potential problem for this approach to still in general. As mentioned above, eventualities denoted by stative or progressivized predicates (with which still typically occurs) are standardly taken to include or overlap the reference time. However, when the reference time is denoted by point adverbials, like ‘at 6.13’, ‘when the bell rang’ or even ‘now’, the intuitions tend to be stricter: in such cases, the states seem not merely to overlap but to surround the point reference times, that is to obtain both before and after such points of time. For example, (19a) seems to imply that the writing of the letter started before now. Similarly, unlike the eventive predicate in (19c), the stative predicate in the second sentence of (19b) seems to temporally surround the entering event, so it does not ‘move the narrative forward’ (see, e.g. Partee 1984; Hinrichs 1986):

58 Presuppositions and Informativity with Aspectual still the assumption that states must surround point reference times should be rejected. I believe it is the second assumption which should be rejected, since, as has been convincingly shown by other theories (e.g. Partee 1984; Dowty 1986; Hinrichs 1986; Lascarides & Asher 1993; Ogihara 1994; de Swart & Verkuyl 1999), the ‘surrounding’ effect, though intuitively strong, is, in fact, not entailed and sometimes not even implicated by the use of stative predicates. Consider, for example, (21a,b), from Hinrichs (1986) and de Swart and Verkuyl (1999), respectively: (21)

Here the states get an ‘inceptive’ or an ‘inchoative’ reading, and they do ‘move the narrative forward’.12 Similar examples are found in Dowty (1986), who claims that the ‘superinterval property’ of statives is a cancellable implicature and not part of their Semantics. Even more relevant to us are cases in which the stative or progressive predicates are used with point adverbials or in present tense. Consider, for example, the sentences in (22) (with the stative or progressive predicates in italics): (22)

a. b. c. d. e. f.

We weren’t sure whether John will participate in the race or not, but at 2.00, when the gun went off, he was running.13 The bomb exploded exactly at 14.31 John was inside his room then. That was very lucky—half a second before he was still outside. We did as much as we could, but at 12.34 John was dead. The minute I saw her I was disappointed. When John left the room too I was all alone. John dialed 911 at 17.08. At 17.19 sharp the firefighters were there.

None of these sentences entails that the state denoted by the underlined predicate holds before the time denoted by the point adverbial (e.g. that John was running before the gun went off, that I was all alone before John left the room, etc.). In fact, given the contexts constructed in these examples, such readings would be quite odd. Assuming that states necessarily surround point reference times would wrongly predict such sentences to be infelicitous. 12

This seems to be related to the understood causal relation between the first and second eventualities in (21) (see Lascarides and Asher 1993). 13 Thanks to S. Rothstein (personal communication) for pointing out this example to me.


a. Sue switched off the light. It was pitch dark in the room. b. Hilary entered the room. Phil was happy to see her.

Yael Greenberg 59

Less extreme cases are illustrated in (23). Here the states can be understood as surrounding the reference time. But crucially, this is not necessary: (23)

When John heard that his father died he was miserable. (The pilot to the passengers): We are in the air! Oh no! The baby is awake! John entered the boss’s room at 2.00. At 2.01 he was unemployed. e. At 6.13 John was asleep.

a. b. c. d.

3.2.2 Two formulations of the assertion and presupposition of sentences with ‘still’ I will focus here on two formulations of the assertion and 14 Of course, this conclusion is dependent on the assumption that there is no subclass of stative predicates which necessarily entail (and not only strongly implicate) the truth of the eventualities at a time before the reference time. If such stative predicates are found, then we should expect still to be systematically infelicitous with them. Felicity of still with such hypothesized predicates will indeed pose a difficulty for the theories followed in this paper, which take the contribution of still to the sentence to be its ‘prior time’ presupposition. However, I am not aware of such a subclass. Notice, for example, that although Ogihara (1994) claims that progressive predicates cannot be inchoative (i.e. they must have the ‘super interval property’), this characterization does not seem right in light of the perfect felicity of (22a) above, with a progressive verb. But further research should look more closely at this question.


(23a), for example, is potentially ambiguous between a reading where John was already miserable when he heard the bad news and a more salient one where he wasn’t (he became miserable as a result of hearing the bad news). Similarly, (23b) can be uttered just as the plane takes off (so ‘being in the air’ is not necessarily true before now), (23c) can be true if the baby was asleep a second ago, (23d) can be true even if a second before 2.01 John was not unemployed yet and (23e) can, in fact, be true even if John was not asleep before 6.13. This is exactly why adding still to such sentences nontrivially entails that the states hold also before the reference time. For example, adding still to (23a) (‘When John heard that his father died he was still miserable’) clearly disambiguates it, excluding the reading where John became miserable when he heard the bad news. The same holds for the other sentences in (23). To summarize, still indeed triggers a ‘prior time’ presupposition, and this presupposition is not trivial, exactly because in reality states do not necessarily surround their reference time. Rather they only overlap or include it.14 We can now turn to a closer and more precise examination of this ‘prior time’ presupposition.

60 Presuppositions and Informativity with Aspectual still presupposition of sentences with still found in the literature. First, following Lo¨bner (1989), Krifka (2000) defines the assertion and presupposition of sentences like (18) as in (24), where U(t) is true iff U is true throughout an interval t, and t } t# iff t# began before t and abuts it (cf. Ko¨nig 1977; Mittwoch 1993): (24)

a. Assertion: John is asleep (t) b. Presupposition: dt# t# } t [John is asleep (t#)]

(25)

Assertion: de,t [t ¼ now ^ asleep (e, john) ^ t O s(e)] (¼ John is asleep) b. Presupposition: de,t#[asleep (e, john) ^ t# } now ^ t# O s(e)] a.

A somewhat different semantics for still is proposed in Ippolito (2007). (26) is a simplified version of Ippolito’s truth conditions for the sentence ‘John is still cooking’, where e1 is a free eventuality variable, whose value is supplied by the context: (26)

‘John is still cooking’ is defined if dt’ < now [t# 4 e1 and time(e1) is a time at which John is cooking] b. If defined, ‘John is still cooking’ is true iff now 4 e1 and time(e1) is a time where John is cooking a.

It is crucial for Ippolito that the eventuality variable in both the presupposition in (26a) and the assertion in (26b) denotes the same (contextually salient) eventuality. According to her, this guarantees the ‘continuity’ feeling found with aspectual still. The sentence ‘John is still cooking’ presupposes that there is a time earlier than the speech time such that the running time of a salient eventuality of John’s cooking includes this past time and asserts of that 15 It is important to notice that the overlap relation between the eventuality time and the reference time will hold for all sentences with still, since, as seen in (i) and (ii), still is compatible with lexical stative or progressivized verbs but not with eventive verbs (see, e.g. Michaelis 1993):

(i) John was (still) on the roof/running (ii) John (#still) spoke with Mary/ran.


Using the more detailed temporal framework reviewed above with speech times, reference times and eventuality times, the assertion of (18), which is identical to the assertion of the still-less sentence ‘John is asleep’, will be represented as in (25a), asserting that there is a sleeping eventuality of John whose time overlaps the speech time (now). Given this, the presupposition of (18) in (24b) can be rephrased as in (25b), saying that there is a sleeping eventuality of John whose time overlaps some time prior to and abutting now:15

Yael Greenberg 61

4 SOME POTENTIAL EXPLANATIONS OF THE DATA Before presenting my own account of the contrast between felicitous and infelicitous occurrences of still, repeated in (27), let us briefly look at some alternative explanations of it: (27)

A: B: B#: B$:

How’s John? He was (#still) unemployed He is still unemployed Last June, he was still unemployed

First, one might try to use the contextual saliency of the eventuality argument, required in Ippolito (2007). Ippolito explicitly claims that ‘out of the blue’ utterances with still, where no such contextually salient eventuality is present, are infelicitous: the sentence [‘John is still cooking’] will be felicitous only if the common ground entails that (a) there is a salient eventuality of cooking by John, and (b) the time of this eventuality includes a past time. Therefore, the sentence John is still cooking cannot be felicitously uttered out of the blue. [p. 10] One might want to claim, then, that the reason for the infelicity of still in (27B) is that although the sentence is not uttered out of the blue, but against the context of A’s question, this context does not supply any salient past eventuality of John being unemployed. However, given the felicity of (27B#) and (27B$) this cannot be right. The only difference between (27B) and (27B#) is tense. Crucially, both are uttered against the same context, and in neither of them is there any reference to a salient eventuality of John being unemployed.


eventuality that its running time includes the speech time. [. . .] because the assertion is about that very salient eventuality, the sequence [‘Two days ago John was cooking. He is still cooking’] is understood as talking about a single event stretching over 2 days, for the second clause requires that John’s current cooking be salient in the context and that it overlaps a past time (Ippolito 2007: 11). In contrast, in the reformulation of Krifka’s definition in (25) above, the assertion and the presupposition need not necessarily talk about the same eventuality of John’s sleeping (or cooking), and the continuity intuition is captured by explicitly using the abutting relation. In addition, unlike Ippolito, who insists that the eventuality argument in sentences with still is contextually salient, no such requirement is made in the definition in (25).


(28)

The baby is still asleep. Please be quiet!

In addition, we cannot attribute the infelicity of (27B) to a general difficulty in accommodating presuppositions, of the sort which has been claimed for the presuppositions of too and again (see, e.g. Zeevat 2003; Geurts & van der Sandt 2004). The felicity of (27B#) and (27B$) indicates that no such general problem is found with still. The felicity of (28) also shows that the ‘prior time’ presupposition triggered by still can be accommodated like other types of presuppositions, for example those triggered by definite (like the baby). Another promising idea is to try and attribute the contrast in (27) to the tendency of sentences with still to express surprise that the state (referred to by the VP) continues and has not stopped yet.16 For example, ‘John is still asleep’ seems to implicate or presuppose surprise at the fact that John is asleep now, although he was no longer supposed to be asleep. One might want to claim, then, that this kind of ‘surprise’ implication can only arise when the reference time is specified. For example, it is not surprising that there is a time at which John continued to be asleep, if he was asleep, but it may be surprising now, or at 5 p.m. or when Harry arrived. Perhaps, the lack of ‘surprise’ effect is what causes the infelicity of (27B). However, as has been already noted in, for example, Lo¨bner (1999) and Krifka (2000) inter alia, the ‘surprise’ effect seems to be cancellable implication of sentences with still. Consider (29a,b): (29) 16

a.

Unsurprisingly, John was still angry this morning. (This was expected given the way he was treated yesterday).

See, for example, van der Auwera (1993), who formulates this implication as falsity of the asserted state in the ’worlds of expectations’. Thanks to an anonymous reviewer for pointing out this potential explanation.


Similarly, (27B$) differs minimally from (27B) in that the reference time is said to be last June (instead of being unspecified). This sentence too does not make the eventuality of John being unemployed any more salient than (27B) does. The problem with (27B), then, has to do with the saliency of the reference time not that of the eventuality argument. In general, then, we see that the eventuality referred to by the Verb Phrase (VP) need not be salient in order for still to be felicitous. In fact, this can be seen even in completely ‘out of the blue’ utterances with still. (28) can be the first thing I say to a guest of mine as I open the door for her. Crucially, even if the guest doesn’t know in advance that the baby was asleep (or, for that matter, that I have a baby), she could easily accommodate this information:

Yael Greenberg 63

b. c.

Given the fact that you went to sleep so late yesterday night, it is not surprising that you are still very tired. Usually John is still asleep at 7.00 (Unexpectedly today, he is awake)

(30)

A: How’s John? B: Unsurprisingly, he was (#still) unemployed. B#: Unsurprisingly, he is (still) unemployed.

It seems, then, that a different direction is needed in order to explain the infelicitous occurrence of still. In the next section, I turn to develop such a direction. 5 THE ANALYSIS

5.1 A modified, DRT style, definition of still Since we will be dealing here with updating reference times in different contexts, it will be very useful to couch the semantics of still within a DRT framework, in which such pieces of information are easily represented. I assume familiarity with DRT and will make the following simplifications and notational decisions: I will use a bracket notation, as in Geurts (1999), in which the variable e is used for all 17 Both attribute it to the interaction between the semantics of still and the Gricean maxim of relevance. 18 One may argue that the ‘surprise’ effect with still should be always evaluated with respect to a certain perspective, so that even with explicit adverbials like ‘unsurprisingly’, it is possible to have in mind a perspective with respect to which it is in fact surprising that, for example, John continues to be angry this morning or continues to be asleep at 7.00 [in (29a) and (29c), respectively]. If this direction is taken, however, we should be able to say very precisely why it is that the existence of a perspective for a surprise effect is always possible with specific or anaphoric reference times, but systematically blocked with existentially closed ones. Such problems may be solved once a precise theory of the surprise effect with still is developed. At the present stage, however, this direction does not seem to provide a satisfying way of accounting for the newly observed data described in section 2.


The sentences in (29) are perfectly felicitous, despite the fact that the ‘surprise’ implication seems to be explicitly cancelled in them. Thus, as argued in Lo¨bner and Krifka, this kind of component does not seem to be an inherent part of the semantics of still but is a conversational implicature.17 It would be strange to claim, then, that the striking infelicity of (27B) is due to the fact that this cancellable implicature does not arise. Moreover, as seen in (30), the felicity contrast between past tense and present tense sentences with still remains the same even in cases in which the ‘surprise’ implication is cancelled. This is unexplained if the reason for this contrast is the existence or absence of the ‘surprise’ implication:18


(31)

a. John is asleep b. [n, t, e: john asleep(e), t ¼ now, t O s(e)]

In (31b), the reference time of the clause, namely t, is equated with the speech time (‘now’), since the sentence is in the present tense, and is taken to overlap the eventuality time, since the type of eventuality is stative. After existential closure, the sentence asserts that there is a sleeping eventuality of John whose time overlaps the speech time interval (i.e. now). Having these notational issues in mind, I propose the following modified definition of the assertion and presupposition of still (where tr and tps stand for the reference time of the sentence and the time variable introduced in the ‘prior time’ presupposition, respectively): (32) Assuming a clause U, with reference time tr and a predicate P with an eventuality e s.t. P(e), (a) still U is defined iff the universe of U has a time interval tps. which meets the following two conditions: tps. < tr, tps. O s(e) (b) If defined, then still U is true iff [tr,e: P(e), tr O s(e)] Notice that, as in the reformulation of Krifka’s definition in (25) above, here too the assertion of still , given in (32b), is equivalent to the assertion of the corresponding U without still. Thus, the only thing we have to add to the DRS of a sentence with still is the ‘prior time’ presupposition, given by the definedness condition in (32a). Following Geurts’ (1999) notation of underlying presupposed material, then, the DRS of the present tense (33a) will be (33b), which after existential closure will give us (33c):


eventualities and (ignoring tense for a moment) the Discourse Representation Structure (DRS) of John ran will be [e: john-run(e)] instead of the more precise [e,x: x ¼ john, run(e,x)] (or the even more precise [e,x: x ¼ john, run(e), agent(e) ¼ x]). This is because the focus of this paper is on the relationship between times, not individuals. For this reason, I will not try to systematically capture nominal anaphora. For example, I will represent the second sentence of John left the room. He was tired as [e: john-tired(e)] (again ignoring tense). I will take the relationship between the reference time and the imperfective eventuality time (e.g. running time of lexical statives and progressives) to be O(overlap) instead of inclusion (4) (though using inclusion will be just as compatible with my claims below). For illustration, let us look at the representation of the present tense (31a) in (31b):

Yael Greenberg 65

(33)

a. John is still asleep b. [ n, t, e, tps.: john-asleep(e), t ¼ now, t O s(e), tps.< t, tps.O s(e)] c. de[John-asleep(e) ^ n O s(e) ^ dt# t# < n ^ t# Os(e)]

5.2 Accounting for the data 5.2.1 ‘Still’ with existentially closed reference times We are now in a position to explain the infelicitous occurrences of still described above. In section 3.1.1 above, we suggested that the reference time of the past tense still-less (34a) is existentially closed. Starting from the ‘unrestricted’ version of the DRS in (16) above, repeated here as (34b), adding still [as in (34c)] will give us DRS (34d): (34)

a.

(How is John?)—He was unemployed (but now he has a job) b. [n, e, t: John-unemployed (e), t < n, t O s(e)] c. (How is John?)—#He was still unemployed (but now he has a job) d. [n, t, e, tps.: john-unemployed (e), t < n, t O s(e), tps.

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