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VOLUME 27 NUMBER 1 FEBRUARY 2010 CONTENTS Kristen Syrett, Christopher Kennedy and Jeffrey Lidz Meaning and Context in C...

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VOLUME 27 NUMBER 1 FEBRUARY 2010

CONTENTS Kristen Syrett, Christopher Kennedy and Jeffrey Lidz Meaning and Context in Children’s Understanding of Gradable Adjectives

1

37

Donka F. Farkas and Kim B. Bruce On Reacting to Assertions and Polar Questions

81

Short Contributions J. P. Smit and Asbjørn Steglich-Petersen Anaphora and Semantic Innocence

119

Jon Gajewski Superlatives, NPIs and Most

125

FORTHCOMING ARTICLES Bernhard Nickel: Generic Comparisons Cornelia Ebert and Stefan Hinterwimmer: Quantificational Variability Effects with Plural Definites: Quantification over Individuals or Situations? Károly Varasdi: A Higher Order Extensional Framework for the Progressive Christopher Gauker: Global Domains versus Hidden Indexicals


Dorit Abusch Presupposition Triggering from Alternatives

JOURNAL OF SEMANTICS

JOURNAL OF SEMANTICS


Journal of

SEMANTICS www.jos.oxfordjournals.org

oxford

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

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

OF

MANAGING EDITOR:

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

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

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

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

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

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

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

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

OF

MANAGING EDITOR:

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

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

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

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

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

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

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

SUBSCRIPTIONS

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JOURNAL OF SEMANTICS Volume 27 Number 1

CONTENTS KRISTEN SYRETT, CHRISTOPHER KENNEDY AND JEFFREY LIDZ Meaning and Context in Children’s Understanding of Gradable Adjectives

1

DORIT ABUSCH Presupposition Triggering from Alternatives

37

DONKA F. FARKAS AND KIM B. BRUCE On Reacting to Assertions and Polar Questions

81

Short Contributions J. P. SMIT AND ASBJØRN STEGLICH-PETERSEN Anaphora and Semantic Innocence

119

JON GAJEWSKI Superlatives, NPIs and Most

125

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

Journal of Semantics 27: 1–35 doi:10.1093/jos/ffp011 Advance Access publication December 3, 2009

Meaning and Context in Children’s Understanding of Gradable Adjectives KRISTEN SYRETT Rutgers University

JEFFREY LIDZ University of Maryland

Abstract This paper explores what children and adults know about three specific ways that meaning and context interact: the interpretation of expressions whose extensions vary in different contexts (semantic context dependence); conditions on the felicitous use of expressions in a discourse context (presupposition accommodation) and informative uses of expressions in contexts in which they strictly speaking do not apply (imprecision). The empirical focus is the use of unmodified (positive form) gradable adjectives (GAs) in definite descriptions to distinguish between two objects that differ in the degree to which they possess the property named by the adjective. We show that by 3 years of age, children are sensitive to all three varieties of context– meaning interaction and that their knowledge of this relation with the definite description is appropriately guided by the semantic representations of the GA appearing in it. These findings suggest that children’s semantic representations of the GAs we investigated and the definite determiner the are adult-like and that they are aware of the consequences of these representations when relating meaning and context. Bolstered by adult participant responses, this work provides important experimental support for theoretical claims regarding the semantics of gradable predicates and the nature of different types of ‘interpretive variability’, specifically semantic context dependence v. pragmatic tolerance of imprecision.

1 INTRODUCTION

1.1 The goals of this study This study investigates children’s behaviour in evaluating a particular type of expression—definite descriptions based on gradable adjectives (GAs)—to investigate the nature of children’s understanding of contextual aspects of meaning, and as a means of distinguishing The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected].

Downloaded from jos.oxfordjournals.org by guest on January 1, 2011

CHRISTOPHER KENNEDY University of Chicago

2 Meaning and Context in Gradable Adjectives

between different varieties of context sensitivity. As part of this investigation, we also provide experimental support for a distinction between two classes of gradable predicates that differ in whether they express relations to context-dependent (relative) or fixed (absolute) standards of comparison in the positive form. In the remainder of this section, we present the theoretical and empirical background for the study. The experiments are presented in sections 2–4. Section 5 details the theoretical implications of the experimental results.

1.2 Relative GAs and standards of comparison Downloaded from jos.oxfordjournals.org by guest on January 1, 2011

GAs are adjectives whose core meanings involve a relation to a scalar concept on the basis of which objects can be ordered (e.g. height, weight, cost). Distributionally, GAs are identified by the fact that they can appear felicitously in comparative constructions (e.g. taller than, as heavy as, less expensive than) and with various types of degree morphemes (measure phrases, intensifiers, etc.) whose function is to specify where the argument of a GA is located on the corresponding scale. Our focus in this paper is the meaning and use of GAs in the positive form, which lack any overt degree morphology: examples such as (is) tall, (seems) heavy and (an) expensive (book), and so forth. From a semantic perspective, the positive form is interesting because its meaning is (typically) tied to the context: what counts as tall can vary, so the extension of tall is correspondingly context dependent. Contextual factors relevant to the calculation of the extension of the positive form include (but are not limited to): the denotation of a modified noun (tall snowman/building/mountain/etc.), an explicit or implicit comparison class (tall for a gymnast), extra-linguistic knowledge (e.g. that a snowman described as ‘tall’ was built by third graders v. fraternity brothers; see Kamp & Partee 1995), and the interests and expectations of the participants in the discourse (Graff 2000). In what follows, we will refer to GAs that have context-dependent positive forms as relative GAs (to be distinguished later in section 1.4 from a second class of GAs that do not). A common analysis of the positive form of relative GAs is that they denote properties that are true of an object just in case it can be related to a degree of the scalar concept encoded by the GA that exceeds a contextually determined standard of comparison (see, e.g. Bartsch & Vennemann 1972; Wheeler 1972; Cresswell 1976; Klein 1980 1991; von Stechow 1984; Ludlow 1989; Kennedy 1999 2007; inter alia). The standard of comparison is a degree that corresponds to something like an ‘average’ or ‘norm’ for the scalar concept relative to some salient set (a comparison class),

Kristen Syrett, Christopher Kennedy and Jeffrey Lidz 3

(1)

½½ posc ¼ kgÆe;dæ kxe gðxÞ > sðgÞðcÞ

Here s is a context-sensitive function that returns a degree on the scale used by g (its range) in context c that represents an appropriate standard of comparison for the kind of measurement that g expresses. Thus, if the adjective tall denotes the measure function tall (a function from objects to positive degrees of height), the denotation of the positive form of the adjective is the context-dependent property in (2), which is true of an object in context c iff its height exceeds the standard of comparison for height in c. (2)

½½ pos tallc ¼ kx:tallðxÞ > sðtallÞðcÞ

To see how this analysis allows variation in the extension of the positive form, let us consider the evaluation of a sentence like ‘Anna is tall’ in two different contexts: c(gymnasts), in which we are talking about female gymnasts, and c(women), in which we are talking about women in general. If the standards of comparison in these two contexts are distinct—and in particular if the standard in c(gymnasts) is lower than the standard in c(women), as will normally be the case—then given the semantics of pos, the set of things that the predicate is true of in the former context is a subset of the set of things it applies to in the latter context. If Anna’s height falls in between the standard of comparison in c(gymnasts) and c(women), as represented graphically in (3), then given (1), Anna is in the extension of ½½pos tallc(gymnasts) but is not in the extension of ½½pos tallc(women), and the truth of Anna is tall varies accordingly. 1 Degrees are elements of scales, which are triples In what follows, we will generally omit pos when referring to the positive form for perspicuity (i.e. we will say tall rather than pos tall), unless it is important to distinguish the compositional details of the positive form from some other form.

1.3 Shifting standards in definite descriptions

2 See Kyburg & Morreau (2000) for additional discussion of the semantics of such constructions and their implications for dynamic semantics.


The context dependence of relative GAs means that there is a great deal of flexibility in their use: the same GA can have different extensions in different contexts, while expressing the same property. A particularly striking example of this flexibility comes from the use of relative GAs in definite descriptions, which is the construction we will focus on in this paper.2 Definite descriptions have been the focus of a great deal of work in semantics, pragmatics and the philosophy of language, most of which converges in some form or another on two central semantic/pragmatic claims: use of a singular definite determiner phrase (DP) of the form the / introduces two presuppositions. First, it presupposes that there is an object that satisfies the property encoded by / (the existence presupposition). Second, it presupposes that the object uniquely satisfies / (the uniqueness presupposition). (See Russell 1905; Strawson 1950; Heim 1990; Kadmon 1990; Neale 1990; Birner & Ward 1994; Abbott 1999; Roberts 2003; and many others for representative discussion.) There are important differences of opinion on the relation between these conditions, the extent to which they can be overridden and the way that apparent violations should be handled, but for our purposes we can take them as reasonable approximations of what a speaker is committed to in order to felicitously use a definite description and what a hearer takes to be the case when accepting its use. The effect of these presuppositions on judgments of felicity can be illustrated by the following example. Consider a situation in which two individuals A and B are sitting across from each other at a table, there are two blue rods of unequal lengths on the table in front of B, and A’s goal is to get B to pass over one of the rods. In such a context, A cannot felicitously use (4a) to make this request, because the existence presupposition is not met: there is no object that satisfies the property red rod in the context. (We use the ‘#’ symbol to indicate infelicity.) By the same token, A’s utterance of (4b) would also be infelicitous, in this case because the uniqueness presupposition of the definite description


the blue rod is not met: there are two objects in the context that satisfy the property blue rod. Speaker A can, however, felicitously use (4c) to request the longer of the two rods. (4)

a. #Please give me the red rod. b. #Please give me the blue rod. c. Please give me the long rod.

(5)

kx:longðxÞ > sðlongÞðcÞ

In the situation described above, the presuppositions introduced by A’s use of the definite description the long rod require there to be a unique long rod in the context. Given that there are two salient rods in the context, the only way to satisfy these presuppositions is to make long true of one of them and false of the other one. Because the rods have unequal lengths, this result can be achieved by positing a standard that differentiates between the rods, as represented in (6). (6)

LENGTH: 0 - long(rod1) - s(long)(c) - long(rod2) -> Crucially, such a standard is posited automatically, as part of the discourse interpretation of the definite, regardless of whether the rods are independently judged to be long or not—that is, independently of the prevailing standard of length (for rods). This is thus an instance of 3 This is a bit of an oversimplification. As pointed out in Kennedy (2007: 19), the difference in length must be greater than a certain threshold: the long rod is infelicitous as a description of the longer of two rods that differ by only a small (but noticeable) degree, in contrast to an explicit comparative like the longer rod. This fact is presumably due to a second feature of relative GAs in the positive form, which we are setting to the side here: vagueness. Vagueness manifests itself both as an inability or unwillingness on the part of speakers to judge some objects in the domain of the predicate as (not) having the property (socalled ‘borderline cases’), and as an inability or unwillingness to distinguish between objects that are very similar to each other relative to the scalar property that the predicate encodes. The latter difficulty is what underlies the ‘threshold effect’ in definite descriptions, as well as the more commonly discussed judgments about the inductive premise of the Sorites Paradox (e.g. ‘any rod that is just a tiny bit shorter than a long rod is also long’). A full account of the semantics of the positive form needs to take both vagueness and context dependence into account (and indeed many accounts of the former make crucial use of the latter; see, e.g. Kamp 1980; Bosch 1983; Raffman 1994, 1996; Kamp & Partee 1995; Soames 1999; Graff 2000), but since our focus here is on relatively clear cases of context-dependent shifts in extension, we will set aside questions about vagueness.


Importantly, (4c) is felicitous regardless of whether the two rods are independently judged to be both long, both not long or one long and the other not: all that matters is that there is a difference in length between them.3 The crucial difference between (4c) and (4a–b) is that long is a positive form relative GA and so denotes the context-dependent property in (5), which is true of an object just in case its length exceeds the contextual standard for length in the context of utterance.


presupposition accommodation (Lewis 1968, 1970), whereby a new standard is accommodated in order to make the discourse model consistent with the presuppositions of the definite description.4

1.4 Absolute GAs

4 While accommodation of a standard in definite descriptions is in general quite flexible, some adjectives do impose additional constraints. For example, evaluative adjectives such as fat or pretty and polar-negative adjectives like short tend to impose a general requirement that their arguments have the property they measure above a certain threshold. Such markedness effects hold across constructions, however, showing up in morphological comparatives and other degree constructions, as well as the kinds of constructions we are focusing on here (see Bierwisch 1989; Rett 2008). 5 Rotstein & Winter (2004) refer to the two classes of absolute GAs we discuss (maximum and minimum standard) as total and partial gradable predicates, respectively.


It has often been assumed that all GAs have context-dependent positive forms, and some influential analyses of gradability and comparison have been built on this premise (Lewis 1970; Kamp 1975; Klein 1980; van Rooij forthcoming). However, in addition to the large set of relative GAs, there is a class of adjectives that are demonstrably gradable but which have been argued to have fixed, context-independent standards. Following Kennedy & McNally (2005) and Unger (1975), we refer to this class as absolute GAs (see also Rusiecki 1985; Rotstein & Winter 2004; Kennedy 2007).5 Previous researchers (see Rusiecki 1985; Cruse 1986; Rotstein & Winter 2004; Kennedy & McNally 2005; Kennedy 2007; Syrett 2007) have argued for a distinction between absolute and relative GAs on the basis of modifier selection and entailment patterns and have identified two distinct classes. Maximum standard absolute GAs such as full, straight, flat, dry, and pure require their arguments to possess a maximal degree of the relevant property. (Full is true of a container just in case it is completely full; straight is true of an object just in case it has no bend.) In contrast, minimum standard absolute GAs such as spotted, bumpy, wet, bent and impure merely require their arguments to merely possess some non-zero degree of a gradable property. (Spotted is true of an object as long as it has some spots; bent is true of an object if it has some degree of bend.) Evidence that absolute GAs are gradable comes from the fact that they combine with comparative and other degree morphology: we can talk about a container that is fuller than another, a line that is not straight enough, a tie that is less spotted than a shirt or a pole that is too bent for a tent. Such facts indicate that absolute GAs have the same core semantic type as relative GAs; on our analysis, this means that they denote measure functions. We can further account for the fixed standards of the positive form by positing denotations like (7a–b) for maximum and minimum


standard GAs, respectively (here exemplified by the denotations for positive form full and spotted), where max and min are functions that return the maximum and minimum degrees of the ranges of the measure functions denoted by the adjectives (the scales). (7)

a. kx.full(x) ¼ max(full) (maximum standard GA) b. kx.spotted(x) > min(spotted) (minimum standard GA)

6

Note, however, that we maintain the core assumption that all GAs denote functions of type Æe,dæ (or alternatively, relations of type Æd,etæ). As such, they may combine with the full range of degree morphology, modulo any constraints based on scalar properties (see Rotstein & Winter 2004; Kennedy & McNally 2005). For example, composition of full with a comparative [er than this cup] results in a property that is true of an object just in case its fullness (a measure of the amount of stuff it contains) is greater than that of the cup, which may be true even if it is not full in the absolute sense.


Note that these denotations are not what we would expect if the positive form of an absolute GA is derived in the same way as that of a relative GA, through combination with pos. Instead, we should expect a context-dependent denotation of the sort we posited for tall and long in (2) and (5). Kennedy (2007) has argued that truth conditions equivalent to (7a–b) can be derived for absolute adjectives using the denotation of pos given above in (1), by fleshing out the details of the standard-identifying function s in a way that takes into account the scalar properties of the adjective. However, since our focus here is not on how truth conditions equivalent to (7a–b) are actually derived, but rather on the predictions about the meaning and acceptability of uses of absolute GAs given such truth conditions, we will make the simplifying assumption that the positive forms of relative GAs and maximum/minimum standard GAs are distinct in the way presented here (e.g. because of an ambiguity in pos).6 Specifically, we are interested in two ways that absolute GAs can help us understand how much children know about context-dependent aspects of meaning. The first involves their use as controls for an investigation of the patterns of definite descriptions discussed in the previous section, which involved presupposition accommodation via contextual shifting of a standard of comparison (cf. (4)). Suppose we discover that children correctly associate, for example, the long rod with the longer of two rods across a range of contexts and rod lengths. We cannot actually conclude from this fact alone that they have acquired a context-dependent, relative meaning for long, because it is possible, especially for very young children, that they are misanalysing the morphologically positive long as the implicit semantically comparative longer (cf. work by Nelson & Benedict 1974). If this were the case, we


7

This is the predicted pattern of behaviour for adults. Since our study uses adult controls, a secondary result is to provide experimental support for the claim that absolute GAs do in fact have the denotations in (7a–b).


would not be able to conclude anything about their knowledge of the positive form. Absolute GAs provide a means of testing for this possibility. If children analyse the adjective in a definite description of the form the A NP as semantically positive, then relative and absolute GAs should pattern differently in contexts in which the A NP is used to distinguish between two objects that manifest different degrees of A. Children should always accept a description with a relative GA as applied to the higher ranked object, as outlined above. However, children should reject a description with a maximum standard absolute GA in contexts in which both objects fall below the maximum standard (e.g. the full jar used to describe the fuller of two observably non-full jars), as this violates the existence presupposition, given (7a). Similarly, children should reject a description with a minimum standard absolute GA in contexts in which both objects fall above the minimum standard (e.g. the spotted disk used to describe the more spotted of two observably spotted disks), as this violates the uniqueness presupposition, given (7b).7 In contrast, if children analyse the adjective as semantically comparative, relative and absolute GAs should pattern the same in these contexts, since the Aer NP can always be used to identify the higher ranked object, regardless of its relation to the standard associated with the corresponding positive form. The second reason that we are interested in absolute GAs is because they can provide insights into subtly different ways that context interacts with meaning and use. Our starting point is intuitions about the meanings of maximum standard absolute GAs such as full. Even though the literature cited above has provided a number of arguments in favour of the maximum standard denotation in (7a), there is nevertheless an initial intuition that this meaning is too strong, and that full instead merely requires that an object be ‘close to full’, allowing for different approximations to suffice in different contexts. For example, while it is clear that a jar that is only half full cannot be truthfully described as a full jar, and maybe not one that is 3/4 full either, judgments become murkier when we consider a jar that is 7/8 or 15/ 16 full, or any amount that is extremely close to being full. At some point we would typically be willing to start saying that the jar is full and would consequently be willing to refer to it as the full jar, and this point


2 EXPERIMENT 1

2.1 Introduction The experiments reported in this paper use definite descriptions to probe children’s sensitivity to the kinds of context–meaning interactions discussed in sections 1.2–1.4. Specifically, we were interested in determining whether children correctly shift the standard of comparison for relative GAs to accommodate the existence and uniqueness presuppositions of the definite description, and correctly avoid doing so for absolute GAs.9

2.2 Method 2.2.1 Participants Thirty children representing three age groups participated in this task: 10 three-year-olds (five boys and five girls, 8 A question that we will not address in this paper concerns the factors that determine whether a GA is relative or absolute. These are discussed in detail in other work (see Rusiecki 1985; Rotstein & Winter 2004; Kennedy & McNally 2005; Kennedy 2007; Syrett 2007). 9 Throughout the experiments reported in this paper, we make use of the increasing/polarpositive member of an antonym pair (e.g. big, not small, full, not empty), since our focus was on context sensitivity and not on the asymmetry between poles. Certainly, a sizable literature has been devoted to investigating this phenomenon in child language (cf. Clark 1972, 1973; Klatzky et al. 1973; Eilers et al. 1974; Brewer & Stone 1975; Bartlett 1976; Townsend 1976; Marschark 1977; Carey 1978; Keil & Carroll 1980; Barner & Snedeker 2008).


might be different in different contexts (based on our goals, the types of jars, the contents of the jars, etc.). One interpretation of these intuitions is that the denotation in (7a) is incorrect, and instead full should be assigned a context-dependent meaning just like long or tall (cf. Lewis 1979). However, another possibility is that (7a) is correct, and this fact indicates that speakers are willing to tolerate imprecision: use of a sentence or description that is false but ‘close enough to true’ for the purposes of the conversational exchange (Lasersohn 1999). The experiments we report in this paper provide new data relevant to these issues, because they indicate that (for children, at least) uses of relative GAs in which a standard of comparison is shifted to accommodate the presuppositions of a definite DP are processed differently from apparently similar, ‘imprecise’ uses of absolute GAs. This suggests that apparent context sensitivity manifested by the two classes of GAs involves different kinds of context/meaning relations: relative GAs are context sensitive relative to an aspect of their meaning (variability in the standard of comparison), while absolute GAs are context sensitive relative to their use (tolerance of imprecision).8


range: 3;5–3;11, M: 3;8); 10 four-year-olds (four boys and six girls, range: 4;1–4;11, M: 4;5) and 10 five-year-olds (three boys and seven girls, range: 5;1–5;8, M: 5;5). Twenty-four adults served as controls. All adults in our experiments were Northwestern undergraduates fulfilling an experimental requirement for a linguistics course and were native speakers of English. 2.2.2 Materials The materials consisted of a series of pairs of objects, each sharing a salient dimension (e.g. colour, shape, length). The experiment was divided into a training session and test session. The complete set of materials is presented in the following section. Downloaded from jos.oxfordjournals.org by guest on January 1, 2011

2.2.3 Procedure Participants were invited to play a game. Children were introduced to a puppet (played by a second experimenter) and were told that the purpose of the game was to help the puppet learn how to ask for things. They were then told that they would be shown two objects at a time and that every time they saw two objects, the puppet would ask for something. Their job was to determine if they could give the puppet what he asked for based on his request, and if they could not, to tell him why not. Even the youngest participants followed these directions easily and were eager to participate. Adult participants interacted with an adult experimenter instead of the puppet. There was an important twist in this task that distinguished it from previous forced-choice studies in which a child was asked to act on a request with an adjective such as big (e.g. Eilers et al. 1974; Bartlett 1976; Ravn & Gelman 1984; Gelman & Markman 1985; Ebeling & Gelman 1988; Gelman & Ebeling 1989; Harris et al. 1986; Sena & Smith 1990). In our task, the request was not always felicitous. This pragmatic manipulation was accomplished in the following way. Each request included a singular definite DP of the form the A one, where A was an adjective (e.g. ‘Please give me the red one’). As noted in section 1.3, this type of description presupposes both existence (e.g. there must be a red one) and uniqueness (e.g. there must be exactly one red one). We deliberately varied the felicity conditions of the request, presenting participants with pairs of objects that either satisfied or violated one or both of the presuppositions of the definite description. Therefore, for some pairs, the request (e.g. ‘Give me the red one’) was felicitous, because exactly one object fit the description (e.g. there was one red and one white object). For other pairs, the request was infelicitous, either because both members of the pair fit the description (e.g. there were two red objects) or neither did (e.g. there was a yellow object and



a blue object). In determining whether or not they could give the puppet what he asked for, children were in essence assessing the context with respect to the presuppositions of the definite description, and in some cases accommodating them. For this reason, we refer to this task as the Presupposition Assessment Task (PAT). Based on the semantics of the GAs discussed in the previous sections, we predict the following. Because relative GAs such as big and long depend on the context for the standard of comparison, participants should posit a new standard of comparison each time a new pair is introduced in order to ensure that the adjective is true of just one object (i.e. the bigger or longer one). Thus, participants should always be able to accommodate the presuppositions of the definite description and accept the request as felicitous. As we mentioned in the previous section, pairs involving absolute GAs provide important controls. Because absolute GAs in the positive form have fixed (maximum or minimum) standards of comparison and are not context dependent, they should not allow the same flexibility of use as relative GAs. For example, if spotted simply means ‘has some number of spots’, participants should reject requests for the spotted one when confronted with two spotted objects, even when they have significantly different numbers of spots, because this would incur a uniqueness violation. Likewise, if full means ‘is maximally full’, participants should reject requests for the full one when confronted with two partially filled containers, even when they contain significantly different amounts of stuff, because the request incurs an existence violation. Thus, rejection of presupposition-violating requests with the absolute GA pairs, coupled with acceptance of requests with the relative GA pairs, should constitute evidence for a semantic distinction between relative and absolute GAs. At the same time, this pattern of results should also provide evidence that participants are not just treating the positive form of the adjective in the definite description as semantically equivalent to the comparative form, that is treating ‘Please give me the A one’ as ‘Please give me the more A one’. If participants were reinterpreting the request in this way, they should always accept it, regardless of adjective type, since the comparative form of any GA can be used to uniquely pick out that member of a pair that has the greater degree of the relevant property: the more spotted one can be felicitously used to pick out the more spotted of two spotted disks, even though the spotted one cannot. Although it is unlikely that adults would reinterpret the A one in this way, it is a possibility that must be seriously considered for children, as their interpretation and use of comparative morphology at this young age is not fully adult-like (cf. Donaldson & Wales 1970;



Ehri 1976; Layton & Stick 1978; Gathercole 1979; Finch-Williams 1981; Gitterman & Johnston 1983; Graziano-King 1999; Moore 1999; Graziano-King & Cairns 2005). Acceptance of presupposition-violating requests could be interpreted in different ways, depending on the results. If such requests are accepted across the board, we must conclude that positive form absolute adjectives—and presumably relative ones as well—can be reanalysed as comparatives, for the reasons outlined above. If, however, such requests are accepted only in certain contexts—which is in fact what we will see below—we will need to consider the possibility that absolute adjectives also have standards that can be shifted in different contexts to accommodate the presuppositions of the definite determiner. To ensure that participants understood the rules of the game and to help them feel comfortable rejecting the request, we had them participate in a brief training session before the test session began. This training session was composed of two felicitous and two infelicitous requests with the adjectives happy, round, red, and blue, similar in design to the control items in the test session. If children were still hesitant to correct the puppet after the four training items, we introduced a fifth impromptu pair accompanied by an infelicitous request. Once it was evident that participants felt comfortable with the task, we proceeded to the test session. Items in the test session included target items whose salient property corresponded to one of the target GAs, as well as control items. Descriptions of the stimuli are presented in Tables 1 and 2. Table 1 presents the control stimuli used in the test session, while Table 2 presents the target stimuli used in the test session. Target GA stimuli were selected from four sets of adjectives used in previous experiments (Syrett et al. 2006) designed to identify default ‘cut-off points’ for relative and absolute GAs. The presentation of the pair members was counter-balanced so that the object fitting the description appeared on different sides of the pairs throughout the test session. The order of the pairs was also pseudorandomized with respect to three factors: the felicity of the request, the nature of the presupposition violation and the adjective. Participants were randomly assigned to one of two orders of presentation, a point that becomes important in the interpretation of the results. Experimental sessions with child participants were videotaped using a Sony Digital8 Handycam. Videotapes were imported from the camera onto a Macintosh computer as .mov files, which were then coded offline by research assistants in our laboratory using SuperCoder

Kristen Syrett, Christopher Kennedy and Jeffrey Lidz 13 Adjective

Pragmatic status of request

Pictures of a yellow bird and a black bird Red poker chip and a white poker chip Purple yo-yo and yellow yo-yo Pictures of a red square and a red circle

Felicitous Felicitous Infelicitous (existence) Infelicitous (uniqueness)

Pictures of a blue square and a yellow circle Pictures of a red triangle and a red square

Felicitous Infelicitous (existence)

Pictures of a sad face and a happy face Pictures of a sad face and an angry face (a) Pictures of a sad face and an angry face (b)

Felicitous Infelicitous (existence) Infelicitous (existence)

Table 1 Control stimuli for Experiment 1

Adjective Relative Big Big Long Long Absolute Spotted Spotted Full Full

Stimuli

Pragmatic status of request

Two Two Two Two

big blocks, one bigger than the other small blocks, one bigger than the other long rods, one longer than the other short rods, one longer than the other

Felicitous Felicitous Felicitous Felicitous

Two Two Two Two

disks, one with some spots, one with none disks, one with some spots, one with more jars, one full, one about 2/3 full jars, neither full, one fuller than the other

Felicitous Infelicitous (uniqueness) Felicitous Infelicitous (existence)

Table 2 Target stimuli for Experiment 1

software (Hollich 2003). The videos were coded frame by frame, where one frame is equal to 1/30 of a second.10 We present an analysis of children’s reaction times (RTs) for Experiments 1 and 2 in the Results section of Experiment 2.

2.3 Results The distribution of responses is presented in Table 3. Recall that for each pair, we predicted one of three possible responses to the 10 At least two coders were assigned to each experimental session, with one coder arbitrarily chosen as the default. The inter-coder rate of agreement across all trials averaged above 95%. In case of disagreements of more than five frames for any of the three measurements, a third coder was brought in as a tie-breaker for that item.


Colour Yellow Red Green Red Shape Square Round Mood Sad Happy Happy

Stimuli

14 Meaning and Context in Gradable Adjectives Age group 3 years

Control Control Big Big Long Long Spotted Spotted Full Full

(felicitous) (infelicitous) (big) (small) (long) (short) (felicitous) (infelicitous) (felicitous) (infelicitous)

5 years

Adults

1

0/2

1

0/2

1

0/2

1

0/2

98 4 100 90 80 100 100 20 100 60

2 90 0 10 20 0 0 80 0 40

100 0 100 90 90 100 100 30 100 70

0 98 0 10 10 0 0 70 0 30

100 0 100 100 100 100 100 10 100 70

0 100 0 0 0 0 0 90 0 30

100 0 100 96 100 96 100 4 96 12

0 100 0 4 0 4 0 96 4 88

Table 3 Distribution of responses in Experiment 1 The types of control and test items, corresponding to the target adjectives, are listing in the column to the right of the row numbers. Responses for each of the item types from the four participant age groups are presented in each of the columns. Cells contain the percentage of participants responding in the manner indicated for the item in question (i.e. accepting or rejecting the request).

accompanying request, based on the above felicity patterns: participants would accept the request and give one object, give neither object, or give both objects. Both the second and third responses—either giving neither object or giving both—count as rejecting the request, since both indicate a presupposition failure for the singular definite description. For this reason, these responses were collapsed and are designated as ‘0/2’ in Table 3. Whenever one object is given, such a response can only be considered appropriate when the member of the pair with the greater degree of the relevant property is targeted, since no matter how the request is interpreted, the adjective can never be interpreted as highlighting a degree below the cut-off. During the experimental sessions, we recorded which of the two objects the participant gave in response to the request. There were only four instances of children giving the lesser degree object across all items, and only with control items. Thus, in the following table we present only those instances where participants gave the object with the greater degree of the property, designated as ‘1’ in Table 3. Three clear trends stand out in these data. First, all participants regardless of age group gave the ‘greater degree’ member of the pair in response to felicitous requests in which only one of the two objects satisfied the request (the control items in row 1 and the full and spotted test items in rows 7 and 9). Second, participants consistently rejected


1 2 3 4 5 6 7 8 9 10

4 years



infelicitous requests for the control items (row 2) and the infelicitous spotted test items (row 8). Indeed, there is no statistical difference between the target spotted pair and the control shape pair, both of which participants saw once (Fisher’s exact test, children: P > 0.22, adults: P ¼ 1.00). In rejecting the puppet’s request, children often offered responses such as ‘Oh, but I have TWO red ones!’; ‘What red one? He should say what shape!’; ‘He thinks there must be two different colours!’; or ‘They’re ALL spotted!’ Third, despite the size of the blocks or rods, when asked for the big or long one, participants nearly always gave the object that had the greater degree of the relevant property (cf. rows 3– 6). We found no significant difference in responses to the trials containing relative adjectives and the control trials (Pearson’s v2 ¼ 0.036, df ¼ 2, P > 0.98). Thus, participants were willing and able to shift the standard of comparison for the two relative GAs, a pattern that reflects the context-dependent denotations participants assigned to these adjectives. Children’s responses only diverged from adults’ in one instance (row 10). Instead of rejecting the puppet’s request when shown the infelicitous full pair, as adults categorically did, children gave the puppet the fuller of the two containers when asked for the full one [Pearson’s v2 ¼ 13.14 (with Yates’ continuity correction), df ¼ 1, P < 0.001]. However, we have reason to believe children do not actually differ from adults in their semantic treatment of full. First, many of these children knew that the fuller member of the pair was, in fact, not full. 18 children who participated in this experiment also participated in the experiments described in Syrett et al. (2006), designed to identify default standards, within approximately 3 weeks time. The fuller member of the infelicitous full pair from the current set of experiments appeared as the fourth item in a seven-item series of containers which children were asked to characterize as ‘full’ or ‘not full’. In that research, not one of these 18 children judged a container beyond the third one to be full, but in the current experiment, 11 of them returned this container in response to a request from the puppet for the full one. Second, this pattern cannot be because the children treated all of the adjectives as semantically comparative (understanding the full one as the fuller one), since they did not give the puppet the more spotted of the two disks when shown the infelicitous spotted pair. Note that rows 8 and 10 of Table 3 differ significantly (Pearson’s v2 ¼ 11.47, df ¼ 1, P < 0.001). We therefore sought to determine whether there was another explanation for this behaviour. Indeed, the order to which participants was assigned appears to have had an effect. Every single one of the 15


children assigned to the order in which the infelicitous full pair appeared earlier in the sequence than the felicitous full pair accepted the puppet’s request for the full one and gave him the fuller of the two containers. Only five of the 15 children in the condition in which this pair appeared after the felicitous full pair responded this way. We address the implications of this finding in the following section.

2.4 Discussion

3 EXPERIMENT 2

3.1 Introduction The goal of Experiment 2 was to identify the source of the order effect observed in Experiment 1. Specifically, we sought to determine whether the prior presentation of a relative GA pair in the sequence influenced children to treat full as context dependent, causing them to give the puppet the fuller of the two infelicitous full containers in response to his request for the full one.


Experiment 1 provides initial evidence that both adults and children distinguish between relative and absolute GAs in assigning the former context-dependent denotations and the latter context-independent denotations, where context (in)dependence is manifested in the standard of comparison: variable v. maximum/minimum. The only difference between children and adults involved the maximum standard GA full: a significant number of children gave the puppet the fuller container in the infelicitous condition, despite the fact that many of these same children separately judged this container not to be full. One potential explanation for this behaviour is that children are uncertain as to whether full is absolute, but settle on such an interpretation (in the context of the experimental task) when they receive early exposure to an object that exemplifies the maximal standard (the full container). A second possibility is that children were influenced by their judgments about the examples involving the relative adjectives. In this experiment, whenever the infelicitous full pair appeared first, it was also immediately preceded by one of the pairs involving the relative adjective long. It is therefore possible that the relative adjective induced a kind of priming effect, causing the children to treat full as relative on analogy to their previous decisions about long. Experiment 2 was designed to adjudicate between these two possibilities.


3.2 Method 3.2.1 Participants Seventeen children representing three age groups participated in this task: six 3-year-olds (three boys and three girls, range: 3;1–3;11, M: 3;5); six 4-year-olds (two boys and four girls, range: 4;2–4;11, M: 4;6); and five 5-year-olds (one boy and four girls, range: 5;2–5;10, M: 5;4). Ten adults served as controls.

3.3 Results The results are presented in Table 4. Because our purpose in conducting Experiment 2 was solely to investigate the order effect described at the end of Experiment 1, here we only present responses to the two pairs whose position in the sequence was swapped (the long pair and infelicitous full pair), as well as the felicitous full pair for comparison. All of the other responses were a replication of Experiment 1 and will not be discussed here. The pattern of responses is highly similar to the one observed in Experiment 1, with children across age groups—but not adults—targeting the fuller member of the infelicitous full pair as the full one in response to the speaker’s request [Pearson’s v 2 ¼ 5.33 (with Yates’ continuity correction), df ¼ 2, P < 0.02].11 (Compare the bottom row of Table 4 to Age group 3 years 1 Long Full Full

(long) (felicitous) (infelicitous)

100 100 100

4 years

0/2 0 0 0

5 years

Adults

1

0/2

1

0/2

1

0/2

100 100 83

0 0 17

100 100 60

0 0 40

100 100 30

0 0 70

Table 4 Distribution of key responses in Experiment 2 11

Adults who gave the fuller of these two containers noted at the end of the experimental session without any prompting that they realized their mistake later in the experiment and wished to make clear to the experimenter that they knew what full means.


3.2.2 Materials and Procedure The same materials and procedure were used as in Experiment 1. The only difference was in the sequence of items. In Experiment 1, the infelicitous full pair was almost immediately preceded by a long pair, with only one control pair intervening. To evaluate the influence of the relative GA pair, we simply switched the order of the long and infelicitous full pair so that the latter preceded the former.


Children Adults

1

2

3

Experiment 1: long < #full < full 0 75

Experiment 2: #full < long < full 18 70

Experiment 1: full < long < #full 67 100

Table 5 Percent of time participants rejected the request when shown the infelicitous full pair The ordering of the target pairs is indicated by ‘ q’ for ‘q is an implication of p’.


questions and focus) contribute sets of alternative propositions, without contributing anything which amounts to a semantic presupposition. Instead, there is a process which generates a presupposition from the alternative set. This provides for a parameterization of the semantics, where the presupposition may be present or not. Attention will be focused on about half a dozen soft triggers: achievements with preparatory phases, inchoatives, contrastive statives, affirmation–negation, verbs of reciprocal and accompanied action, questions and focus. These include a core of constructions where the case for the analysis which will be proposed here is relatively strong, plus additional ones to which that analysis can be extended. The paper is organized as follows. The remainder of this introduction reviews the soft-triggering constructions I will be talking about. In section 2, I present an approach to soft triggering that I call the basic conjunctive strategy and argue that it cannot work without the addition of some kind of semantic structuring. Section 3 introduces the analysis using presupposition triggering from alternative sets. The approach is first developed for four core constructions: focus, questions, affirmation– negation and contrastive statives. Then, it is extended to other softtriggering constructions. Section 4 considers the issue of compositional filtering and transformation of presupposition. Although these phenomena superficially favour a standard approach where presupposition triggering is encoded semantically, I will show that triggering from alternatives can be formulated in a way which accounts for compositional filtering. Section 5 corrects a gap in the earlier reasoning about focus related to the ‘anaphoric’status of focus. Section 6 discusses two alternatives to the theory of sections 3 and 4, and section 7 sums up the paper. To show that a lexical item or construction is a soft trigger in my sense, one needs to show that it is a presupposition trigger in the first place, using tests of survival and transformation of presuppositions in contexts such as negation and conditionals, plus intuitions involving the common ground interpretation of presupposition. Second, one needs to demonstrate ‘softness’ by showing that the presupposition can be cancelled fairly easily. In (3), I go through these steps for win, which is an achievement with a preparatory phase.1 In (3a,b), there is an intuition that the implication that John participated in the Road Race projects through negation and from the if-clause of a conditional.2

Dorit Abusch 39

Example (3c) illustrates compositional transformation of a presupposition. It can easily be understood as implying not that John participated in the Road Race but that if he woke up on time, he participated in the Road Race. (3)

Example (3d) illustrates that the implication in (3b) that John participated can be cancelled by a discourse context which explicitly expresses ignorance. Thus, (3a–c) are being used to show that the implication that John participated is projected and transformed in the way characteristic of presuppositions, while (3d) shows that the projected presupposition is cancellable, or in other terms, contextually defeasible. Finally, there is an intuition that (3a, b) would typically only be used in a conversational context where it is taken for granted that John participated and that (3c) would only be used in a context where it is taken for granted that if John woke up on time, he participated. Here, we are checking against our intuitions the pragmatic interpretation of presupposition as entailment by the common ground (Stalnaker 1974).3 Since it is my purpose to distinguish a class of soft triggers from other presupposition triggers, it is crucial to contrast the degree of cancelability found with the different classes of triggers. Example (4) checks the acceptability of a cleft in a discourse context which explicitly expresses ignorance about the presupposed existential implication. The combination is odd, if not completely unacceptable. Example (5a) does the same for the presupposition trigger too. Again, the combination is very odd, though I find the variant (5b) a bit better.

3 The pragmatic test is used here not as a definition of presupposition, but as one of a group of linguistic tests which tend to correlate. Arguably, most of the linguistic theory of presupposition would be the same if presupposition was not interpreted as entailment by the common ground. Matthewson (2006) argues that in the St’a´t’imcets language, linguistic presuppositions do not have the common ground pragmatics.


Achievement with preparatory phase a. John didn’t win the Road Race. b. If John won the Road Race, he’s got more victories than anyone else in history. c. If John woke up on time today, he won the Road Race. d. I have no idea whether John ended up participating in the Road Race yesterday. But if he won it, then he has more victories than anyone else in history.

40 Presupposition Triggering from Alternatives (4) Cleft ??I have no idea whether anyone read that letter. But if it is John who read it, let’s ask him to be discreet about the content. (5) Too a. ??I have no idea whether John read that proposal. But if Bill read it too, let’s ask them to confer and simply give us a yesno response. b. ?John may or may not have read the proposal. If Bill read it too, let’s ask them to confer and simply give us a yes-no response.

(6) Contrastive stative a. Does she have a green card? b. She doesn’t have a green card. c. If she has a green card, we can pay her from the DOD grant. d. If she’s not a native, she has a green card. Otherwise she wouldn’t be working on the DOD grant. Imagine a bar where Thursday is Green Card night, and green card holders are greeted in an especially enthusiastic way and given a free drink. The experienced bartender (perhaps knowing the customer) could use (7a) while instructing the novice bartender about the policy, without presupposing that the customer satisfies the genus predicate.


Throughout the paper, clefts will be used as a core case of a ‘hard’ presupposition trigger, where it is impossible or at least relatively hard to cancel the presupposition. Contrastive statives are predicates such as newcomer, have a green card and bachelor which seem to carry with them contrasting predicates which are not merely their complements. In our insular town, being a newcomer contrasts with being an old-timer. In many situations, having a green card contrasts with being a non-citizen resident without a green card. Bachelors are contrasted with married adult men. A different but compatible viewpoint is that these predicates describe species (the ‘species’ of bachelors or of newcomers to our town) and implicitly refer to a specific genus or superclass (the ‘genus’ of adult men or residents of our town). These predicates defeasibly presuppose their genus predicates. Example (6) illustrates this for have a green card. It is perhaps vague what the genus predicate is in this case. I will take it to be ‘human being who is not a native of the USA’. In most contexts, (6a, b, c) would be understood to imply that she satisfies the genus predicate, that is she is not a native of the USA. Example (6d) illustrates compositional satisfaction of the presupposition by virtue of the if-clause in the conditional entailing the genus presupposition of the main clause.

Dorit Abusch 41

The same goes for (7b). This illustrates the context-based defeasibility of the genus presupposition. (7)

a. She doesn’t have a green card. She doesn’t get a free drink. b. If she has a green card, give her a free drink.

(8) Affirmation/negation John is in Boston and not in New York. (9) John is in Boston. Example (10) illustrates presupposition projection and transformation for affirmation–negation. While (10a) is simply too awkward to evaluate (presumably because of the double negation), the implication that John is in Boston or New York projects through the negative predicate in (10b), and from the if-clause of the conditional in (10c). In (10d), there is a conditionalized implication that if John is out of town, he is in Boston or New York. (10) a. ??John isn’t in Boston and not in New York. b. It is doubtful that John is in Boston and not in New York. c. If John is in Boston and not in New York, his mother will be furious. d. If John is out of town for the weekend, he is in Boston and not New York. An interesting feature of affirmation–negation is that the presence of the presuppositional reading is sensitive to the affirmed predicate and the negated one being incompatible. Consider (11a). The area of Manhattan south of 23rd St does not overlap the area north of 42nd St, so the affirmed predicate and the negated predicate are incompatible. And (11a) seems to presuppose that the office is not between the two streets. On the other hand, (11b) has affirmed and negated predicates


Affirmation–negation is the construction with and not that is illustrated in (8). To start with the pragmatic interpretation, there is an intuition that the sentence would normally be used only in a context where it is taken for granted that John is in one of the cities of Boston and New York. From one point of view, this is surprising. Assuming that and and not in (8) have their standard Boolean interpretations, and taking as given that Boston and New York are non-overlapping regions of space, (8) is informationally equivalent to (9), which does not have the presupposition of (8). So, either and not in (8) does not have its standard compositional semantics or there is some indirect route to the presupposition.

42 Presupposition Triggering from Alternatives which are compatible, and it has no presupposition comparable to the presupposition of (11a). This is one kind of ‘cancellation’ of the presupposition of affirmation–negation. In (12a), cancellation is achieved with a discourse structure which justifies a contrast between John (who is permitted to miss the meeting) missing it, and Bill (who is not permitted to miss the meeting) missing it, without supporting a presupposition that one of them missed it. Example (12b) gives contrasting data with a cleft.4

A variety of multi-agent verbs such as symmetric transfer verbs and verbs of accompanied motion have soft presuppositions. In (13a) and (13b), there is an intuition that the implication that Mary crossed the footbridge projects through the negation and the conditional. But this implication can easily be cancelled, as shown by the sequence in (13c). (13) Accompanied motion a. John didn’t accompany Mary across the footbridge. b. If John accompanied Mary across the footbridge, they are friends again. c. John didn’t accompany Mary across the footbridge, I know that, because he was with me. Perhaps she didn’t cross it either. The transfer implications of (14a) are (i) that John gave up possession of his bike and (ii) that in return, he got possession of some money. In (14b) and (14c), there is an intuition that implication (i) projects through the negation and the conditional. Example (14d) is an extension of (14c) where implication (i) is cancelled, presumably because the sentence suggests that John would not have given up possession of the bike in a transaction other than a sale. 4

I would like to hedge the claim of a contrast between (12a) and (12b) in two ways. First, I have the impression that the second sentence in (12a) is licensed by the fact that the first sentence presents it as possible for John to miss the meeting. If one makes this sort of context more explicit, even the cleft version becomes fully good: (i)

Bill was ordered to be at the meeting, and John was permitted to attend or to miss it. As it turned out, it was Bill who missed it.

Second, the discourse in (12b) with the cleft in fact seems fine to some speakers. Perhaps these speakers are readily able to imagine a discourse structure like the one in (i).


(11) a. The office is south of 23rd St, and not north of 42nd St. b. The office is north of 23rd St, and not west of 5th Ave. (12) a. Bill was ordered to be at the meeting, and for John attendance was optional. As it turned out, Bill and not John missed it. b. ?Bill was ordered to be at the meeting, and for John attendance was optional. As it turned out, it was Bill who missed it.

Dorit Abusch 43

(14) Symmetric transfer a. John got money for his bike. b. John didn’t get money for his bike. c. If John got money for his bike, he should pay the electricity bill. d. If John got money for the bike he was trying to sell, he should pay the electricity bill.

(15) Question a. Who took Mary’s bike? b. It isn’t clear who took Mary’s bike. c. It isn’t clear that it is Jennie who took Mary’s bike. d. Mary wonders who took her bike. The tendency for a presuppositional reading of constituent questions is not absolute, however. In (16a) and (16b), the second sentence is understood as leaving open the possibility that nobody will vote for the speaker. This is made explicit in the third sentence. Similarly, the second sentence in (16c) is understood as leaving open the possibility that nobody is available to teach field methods. Again, this is made explicit in the third sentence. (16) a. I’ve alienated my colleagues completely. I wonder who will vote for me. Probably nobody will. b. I’ve alienated my colleagues completely. Who will vote for me? Probably nobody. c. There’s a severe problem with this schedule. It’s not clear who is available to teach field methods. Unless I am mistaken, nobody is. These data suggest that matrix and embedded questions have a systematic but defeasible existential presupposition. This picture falls


Turning to the next construction, there is a strong tendency for questions to be understood presuppositionally, with (15a) presupposing that someone took Mary’s bike. It is not possible to apply projection tests such as negation and conditional contexts due to the limited distribution of questions in embedded positions. But (15b) seems to imply that someone took Mary’s bike. This could be taken to indicate that the implication that someone took Mary’s bike is projecting through the predicate clear and the negation. Example (15c) indicates that at least clear with a that-complement is a presupposition hole, with the cleft presupposition that someone took Mary’s bike projecting. Then, (15b) is accounted for by the assumptions that the embedded question triggers an existential presupposition and that also the question-embedding clear (together with the negation) is a presupposition hole.

44 Presupposition Triggering from Alternatives between the position that constituent questions are presupposition triggers (e.g. Horn 1972; Gawron 2001) and the position that they have no systematic existential presuppositions (e.g. Groenendijk & Stokhof 1984; Fitzpatrick 2005).5 In Groenendijk and Stokhof ’s logical analysis of the question-answer relation, (17b) comes out as a complete answer to the question (17a), not a rejection of a presupposition.6 (17) a. Who on earth will vote for me? b. Nobody will.

(18) Focus a. the x such that Bill likes x—is John b. Bill likes JohnF. Geurts & van der Sandt (2004) is an extended defence of a presuppositional semantics for focus. They describe a presuppositional semantics as a null assumption and point out that projection data like (19) favour a presuppositional semantics because the projection behaviour is the same as what one sees with semantic presuppositions. Just as the presupposition that Fred has a wife is filtered in (19a), they observe the presupposition that someone stole the tarts is filtered in (19b).7 5 One point raised by Horn is that the presupposition can be obviated by an if-phrase as in (i), which seems to indicate satisfaction of a genuine presupposition, rather than some kind of cancellation. These data turn out to be consistent with the analysis proposed in section 4.

(i) John wonders who if anyone will vote for him. 6 An interesting point about (16) and (17) is that an analysis using semantic presupposition plus accommodation will not work. In (17), there is no space for local accommodation because the question is a top-level one, and a global accommodation of the existential presupposition is inconsistent with the second sentence. In (16a), there might be space for local accommodation within the attitude predicate, but it seems this would give the wrong result, a presupposition that the speaker believes that someone will vote for her. 7 Section 5 argues that (19b) is actually irrelevant but that (20a) is genuine evidence for an existential presupposition of focus.


My approach to the question data is to claim that direct and embedded questions have no strict semantic existential presupposition. However, there is a default process which generates a presupposition from the semantic representation of the question. The final soft-triggering construction that I would like to consider is intonational focus. In studies of focus, there is an argument about whether the semantics of focus involves an existential presupposition. Chomsky (1972) used the informal logical form (18a) for the focus sentence (18b). This suggests an existential presupposition since definite descriptions have existential presuppositions.

Dorit Abusch 45

(19) a. If Fred has a wife, then Fred’s wife stole the tarts. b. If someone stole the tarts, then [Fred’s wife]F stole the tarts. The point can be strengthened by constructing an example where the existential presupposition is conditionalized, rather than completely filtered. In (20a), the presupposition that someone opened the vault is weakened to (20b). This weakened presupposition might be satisfied because it is taken for granted that the Trust Company keeps all its money and valuables in the vault, so that it could not be robbed without the vault being opened.

Notice that the same conditional weakening is seen with the cleft in (20c). I am assuming that clefts are genuine semantic presupposition triggers. If we hypothesized that also focus is a semantic presupposition trigger, then we would have an explanation for the fact that the implication that someone opened the vault gets compositionally transformed in the same way in the focus example (20b) and the cleft example (20c). The presupposition filtering and transformation data look like a strong argument that focus triggers a semantic presupposition. But other arguments indicate that the semantics of focus cannot be anything as strong as an existential presupposition because sometimes the context does not satisfy the constraint on context which would follow from an existential presupposition.8 Here, is an example and argument from Rooth (1999). A betting contest called a football pool is held in the department, where people bet on the outcome of football games. Consider the exchange below. (21) A: Did anyone win the football pool this week? B: Probably not, because it’s unlikely that MaryF won it, and she’s the only person who ever wins. The observation is that focus on Mary does not give an existential presupposition ‘someone won the football pool’ which projects to the top level. This is clear because A’s question indicates that A does not know whether someone won, and so it is not common ground that 8

See Ja¨ger (2004) and Kratzer (2004) for related discussion.


(20) a. If Abner and Lana robbed the Trust Company, then sheF opened the vault. b. If Abner and Lana robbed the Trust Company, then someone opened the vault. c. If Abner and Lana robbed the Trust Company, then it was she who opened the vault.

46 Presupposition Triggering from Alternatives someone won. In (22), we change the example by substituting an itcleft for intonational focus. The result is quite bad, and this can be attributed to the it-cleft producing a semantic presupposition that projects to the top level. This presupposition is in conflict with the first thing that B says, namely probably not, meaning that probably nobody won the football pool. (22) A: Did anyone win the football pool this week? B: #Probably not, because it’s unlikely that it’s MaryF who won it, and she’s the only person who ever wins.

(23) [probably not, because it’s unlikely that [[MaryF won it];Q]] Rooth uses these data as an argument against analyses where intonational focus introduces a semantic existential presupposition. Instead, he says, focus just introduces a set of alternative propositions, which has to find an antecedent in the discourse representation. But why then is there such a strong tendency for focus to be understood as conveying an existential presupposition? Here, I will take the same line as for questions: although the semantics for focus does not involve an existential presupposition, the semantics for focus does create the potential for a default process to generate a presupposition. Summing up, in each of the constructions, I am calling softtriggering constructions, there is an implication which has presuppositional character because it shows the compositional behaviour of presuppositions (i.e. certain patterns of presupposition projection, filtering and transformation) and the characteristic pragmatic interpretation of presupposition (i.e. a requirement of entailment by the common ground). My strategy in this paper will be to claim that the soft-triggering constructions do not primitively encode presuppositions. Instead, they have a certain semantic property, the property of contributing alternatives sets, and this creates the potential for generating a presupposition by a default process.


Example (23) is a representation for (22) which includes focus interpretation in the framework of Rooth (1992). By virtue of the semantics of focus and of focus interpretation, Q is constrained to be a set of propositions of the form ‘x won the football pool’. This set is introduced by focus interpretation. On the analysis that Rooth advocates, the operator ‘;’ in (23) does not express an existential presupposition, and so there is no semantic presupposition that someone won the football pool at any level. Notice by the way that the scope of the focus is the embedded sentence, but focus is justified non-locally, by A’s question.

Dorit Abusch 47

(24) a. I’m worried that John might have gone to the climbing wall. b. Of course if Mary is there too, there’s no reason for concern. She is experienced and safety-conscious. c. If John is at the climbing wall and Mary is there too, there’s no reason for concern. d. Of course if Mary were there too, there would be no reason for concern. So, we need a theory where local accommodation can apply in certain circumstances even for hard triggers or where there are mechanisms that mimic accommodation, such ones involving free variables or discourse structure [along the lines of von Fintel (1994) and Beaver (2004a)]. Given this, there is the possibility of analysing the apparent cancellation of presuppositions with soft triggers using local accommodation. In developing an analysis where also soft triggers are primitive presupposition triggers, one has to find an account for the differential behaviour of hard and soft triggers that was discussed in this section. van der Sandt & Geurts (2001) investigated this problem in the context of a Discourse Representation Theory account of presupposition (van der Sandt 1992). Although in that theory all presuppositions are in a sense anaphoric, hard triggers are distinguished by a stricter anaphoricity requirement which is also found with pronouns, van der Sandt and Geurts hypothesize. This harder requirement is resistant to accommodation. So, the analysis of the data repeated below is that won triggers a presupposition, which in (25a) is locally accommodated at the level of the if-clause. The corresponding analysis is not possible for (25b) because the pronominal presupposition in (25b) is resistant to local accommodation.


A different approach is that soft triggers do encode presuppositions lexically or constructionally and that these presuppositions can be turned into assertions by local accommodation. This possibility is not to be excluded on my assumptions. I am assuming that there are primitive semantic presupposition triggers (e.g. it-clefts and too). And there are constructions and discourse structures, such as the one in (24), where there appears to be the equivalent of local accommodation. The presupposition of too in the if-clause of (24b) is that someone other than Mary is at the climbing wall. In the context (24b), the presupposition can be understood as conjoined within the if-clause to the left of the assertion, so that the sentence is equivalent to (24c). So, (24b) has the structure of (maximally) local accommodation, with the presupposition added in as embedded a position as possible. The situation is similar in example (24d) with conditional morphology.

48 Presupposition Triggering from Alternatives (25) a. I have no idea whether John ended up participating in the Road Race yesterday. But if he won it, then he has more victories than anyone else in history. b. ??I have no idea whether anyone read that letter. But if it is John who read it, let’s ask him to be discreet about the content. Going deeply into van der Sandt and Geurts’ proposal would carry me far afield, partly because of the significant differences in framework. However, I believe that it is a viable alternative to the proposal being articulated here.

Stalnaker (1974) suggested a pragmatic approach to the presuppositiontriggering behaviour of know. This analysis is only sketched, it was perhaps offered just as an example of the general kind of analysis one should consider, and know is not one of the triggers being analysed in my paper. But for my purposes, it is useful to consider a version of the proposal as an introduction to the idea of triggering from structured lexical entries. The starting point is the assumption that the content of a clause ‘x know p’ can be divided into two conjuncts. One conjunct is the factive component, and the other is a predication attributing a propositional attitude to x. Using the relation symbol K for the attitude, the content can be written as p ^ K(x, p). The formula K(x, p) is assumed to entail that x believes p and to have additional entailments related to the source of the belief. Because the factive component is written as a conjunct, K(x, p) is assumed not to entail p. Assuming this much, we can reason as follows (Stalnaker 1974: 206). ‘Suppose a speaker were to assert that x knows that P in a context where the truth of P is in doubt or dispute’. Then, he would be ‘saying in one breath something that could be challenged in two different ways. He would be leaving unclear whether his main point was to make a claim about the truth of P’ (i.e. to assert the factive conjunct), ‘or to make a claim about the epistemic situation of x’ [i.e. to assert the attitude conjunct K(x, p)]. If the speaker did that, he would be violating the presumption of being orderly, not confusing the listener, and not violating the reasonable expectations of the listener. Both the speaker and the hearer can be expected to recognize that it would violate maxims of conversation to use ‘x knows p’ in a context where both entailments are at issue. The hearer can be expected to infer that the speaker assumes the contrary, that is that one of the entailments is taken for granted. This gives a pragmatic presupposition


2 A BASIC CONJUNCTIVE ANALYSIS

Dorit Abusch 49

(26) a. John knows that he is a jerk. b. John knows [fact [that he is a jerk]] Or it might be plausible to theorize that the verb know is a compound of a null predicate FACT with a root OKNOW which has the attitude meaning. In either case, a division between the factive predicate and the attitude predicate is given in syntax. Alternatively, one could claim that there is a cognitive capacity which makes the factive and attitude entailments of know salient. On this account, it is somehow a property of human cognition that when someone entertains the proposition ‘x know p’, the two entailments p and K(x,p) pop into consciousness, so that they can be used in the pragmatic argument BC. Or finally, one can hypothesize that the semantic value of ‘x knows p’ is given by compositional semantics as a set fp, K(x,p)g. It should be stipulated that this set has a conjunctive interpretation, but because it is a set, it makes the factive and attitude entailments available. These are different ways of executing the requirement that BC must have access to the factive and attitude entailments of ‘x knows p’. Assuming the set of two entailments fp, K(x, p)g is given somehow, there is a further problem. In BC, we hypothesize that it would somehow be confusing and uncooperative to communicate the entire formula p ^ K(x, p) as novel information. If this problem is resolved if p


that the factive entailment is true, leaving the attitude entailment as the speaker’s main point. Let us call this strategy for deriving presupposition triggering the basic conjunctive strategy (BC). There are a couple of gaps in the strategy which indicate a need for a degree of structuring in the semantic input. First, we must assume that there is some process which pulls the entailments p and K(x, p) out of the proposition denoted by ‘x knows p’. For a given proposition q, except in trivial cases, there are many number of ways of picking q1 and q2 such that q ¼ q1 ^ q2. If we are given the proposition q which is denoted by ‘x knows p’, we cannot uniquely factor q into two propositions q1 and q2 such that q ¼ q1 ^ q2, in the way that the number 14 uniquely factors into two prime numbers 2 and 7. We have to assume that the factive and attitude entailments are given in some way. One possibility is that the two entailments are represented syntactically or morphologically. Kiparsky & Kiparsky (1968) suggested a syntactic structure for sentences with know (and generally for factive predicates) which includes the noun fact in the complement. Sentence (26) is an example of the syntactic deep structure.

50 Presupposition Triggering from Alternatives

(27) a. b. (28) a. b. c.

John knows that Mary and Bill are having an affair. John is right that Mary and Bill are having an affair. John is right that Mary and Bill are having an affair. Is John right that Mary and Bill are having an affair? If John is right that Mary and Bill are having an affair, that would explain their odd behavior yesterday. (29) p ^ H(x,p) Here is a pair involving one of the soft triggers from section 1. The sense of ‘x got money for y’ which is illustrated in (30) is close to being a synonym of ‘x sold y’. Both have (i) a transfer entailment that there was an event of x transferring ownership of y to some z, (ii) a countertransfer entailment that there was an event of z transferring money to x and (iii) an intensional entailment capturing that x and z intend for the two transfers to be in exchange for each other. It is plausible to claim 9

Important progress on factive and semifactive verbs is made in Simons (2007). She shows that in evidential contexts like (i) where the factive implication is at issue, the factive implication is systematically not presupposed. (i)

Why isn’t Louise coming to our meetings these days? Henry discovered that she’s left town.

This is evidence for ‘‘softness’’ of triggering by factives (or semifactives). The theory being criticized in the text leads us to expect that there would be discourse contexts where the attitude entailment comes out presupposed for discover or know. 10 Fillmore discusses pairs like accuse/blame for. Know/be right and sell/get money for are my own additions.


is in the common ground of information, it seems that it could also be resolved if K(x,p) is in the common ground. So, it is not clear why p rather than K(x,p) comes out presupposed.9 Near-minimal pairs I call Fillmore pairs make this problem worse. Fillmore (1971) pointed out pairs of verbs or constructions which have the same group of conceptually distinct entailments, but with different distributions of presupposition. Here is a case involving factivity.10 Examples (27a) and (27b) have a factive implication (Mary and Bill are having an affair) and an attitude implication (John believes or has claimed that they are having an affair). For know, we want the factive implication to come out presupposed, and for be right, we want the belief implication to come out presupposed since the data in (28) indicate presuppositional status for this implication. It is difficult to see how one can make (27a) and (27b) come out differently if they have the simple conjunctive representation (29), where H is the attitude predicate, or if they just make available the pair of entailments fp, H(x, p)g.

Dorit Abusch 51

that the conjunction of these entailments capture the content of both ‘x got money for y’ and ‘x sold y’.11 But the two forms show different presuppositional behaviour. The data in (30), repeated from section 1, indicate a presuppositional status for the transfer entailment T of (30a), which is stated in (30e). The conditional (30b), the question (30c) and the negated version (30d), each have the implication T. John got money for his bike. If John got money for his bike, he paid the phone bill. Did John get money for his bike? John didn’t get money for his bike. Transfer entailment T. There was transfer of possession of John’s bike from John to someone else.

Here are the versions with sold. Example (31a) has the entailment T, but this implication is not preserved under conditionalization, questioning and negation in (31b–d). Instead, what is preserved is a weaker implication that John owned the bike. (31) a. b. c. d.

John sold his bike. If John sold his bike, he paid the phone bill. Did John sell his bike? John didn’t sell his bike.

So, we have a near-minimal pair consisting of constructions u1 and u2, the meaning of which can be expressed as the conjunction of a set of entailments fp1, p2, . . .g. For u1, a certain conjunction of pi’s has presuppositional status, while for u2, a different conjunction of pi’s has presuppositional status. It is impossible to capture these data if the semantic values of both are simply the conjunction p1 ^ p2, . . . and the process which accounts for presuppositional status can see only the semantics of the sentence because then there is no way of getting different results for u1 and u2. For the same reason, it is impossible to capture the data if the compositional-semantic component delivers the same conjunctively interpreted set fp1, p2, . . .g for u1 and u2.12 I interpret these data as showing, to develop an indirect triggering account similar to BC, the triggering process has to have access to some degree of structuring of the semantic value either because the 11

This kind of structured lexical representation for sell is articulated in Jackendoff (1990). In section 6, working backwards from my alternative semantics theory, I show that by making the right choice for p and r in a structured denotation fp, rg, one can solve this problem. The general point is that u1 and u2 could be represented by different sets fp1, p2, . . .g and fq1, q2, . . .g, with p1 ^ p2 ^ . . .[ q1 ^ q2 ^ . . . . 12


(30) a. b. c. d. e.


3 TRIGGERING FROM ALTERNATIVE SETS This section introduces a mechanism for presupposition triggering from alternative sets. The mechanism is first motivated by and applied to focus and question data and then extended to other soft-triggering constructions. Section 1 reviewed an argument against the hypothesis that focus triggers a semantic existential presupposition. This leaves us with the question of why there is such a strong tendency for focus to be understood as associated with an existential presupposition. I suggest that this is a secondary effect related to a role for focus alternative sets as topical questions. A representation like (32) with focus interpretation contributes a variable Q with the type of a set of propositions according to the analysis of Rooth (1992).14 The semantics of focus does not contribute a presuppositional constraint that the disjunction of Q is true. However, pragmatic literature on focus has suggested that the alternative sets signalled by focus and topic features can take on the role of question topics, so-called questions under discussion or QUDs (Carlson 1983; Roberts 1996; Bu¨ring 1997, 2003). And very often, when a question like ‘who read it’ is under discussion, it is taken for granted that one of the alternatives is true, that is it is taken for granted that someone read it. 13 But see section 6. There I sketch a theory which tries to attribute triggering to an aspectual distinction which is reflected in patterns of truth with respect to intervals in interval semantics. Arguably, this is not a matter of structuring, but of a theory of triggering which refers to aspectual distinctions. I do not think that approach would be able to distinguish sell from get money for. 14 See section 5 for some discussion of how things come out if we assume the givenness theory of Schwarzschild (1999) or consider representations licensed by the theory of Rooth (1992) where the antecedent for focus has a propositional type, rather than a question type.


structuring is expressed syntactically or just semantically.13 Developing an account along these lines is the topic of sections 3 and 4. It is worth mentioning that using a semantic presupposition operator, it is easy to express the presuppositional difference between get money for and sell. Given any set of entailments fp1, p2, . . .g, we can stipulate that any one of them is a presupposition by hypothesizing a representation like @p1 ^ p2 ^ . . ., where @ is the presupposition operator (Beaver 1995). This is in one way good but also shows that it is too easy to stipulate the results one wants using a semantic presupposition operator. As explained in section 6, the theory being developed here does better only for the subset of the soft triggers where there is independent motivation for a representation involving alternatives.

Dorit Abusch 53

(32) a. [. . . [[MaryF read it];Q] . . .] b. Q is a set of propositions of the form ‘x read it’, where x ranges over a set of relevant individuals.

(33) a. Who took Mary’s bike? b. It isn’t clear who took Mary’s bike. According to Hamblin’s (1973) semantics, questions, just like the semantic objects contributed by focus, have the semantic type ÆÆs,tæ,tæ. We can apply exactly the same logic as for focus—a direct or indirect question contributes a semantic object with type ÆÆs,tæ,tæ.15 This triggers a default presuppositional constraint that the proposition formed as the disjunction of the set is true. Because this amounts to a presupposition that some alternative in the set is true, I will call a presupposition derived in this way the some-alternative presupposition. For direct questions, the story seems very plausible—it is probably typical that when a speaker uses a direct wh-question, she intends to assume that the question has a positive answer and intends for the listener to recognize this assumption. So, it is natural to claim that for 15 The difference at most is in how the proposition set in the two cases is located in the system of semantic values. See Rooth (1985) and Beck (2006).


Thus, the idea is to derive the existential presupposition of focus in two steps. Focus interpretation contributes a semantic object of type ÆÆs,tæ,tæ, which is the semantic type of questions. This object is annotated here as Q. Secondarily, there is a process which interprets an object like this as a topical question which as a default satisfies the presuppositional constraint that the disjunction of Q is true. As well as deriving the presupposition from a motivated representation for the semantics of focus, this gives us an account of why the presupposition of focus can be cancelled. We just have to assume that the secondary process which generates the presupposition has a default nature, which is not operative when the context of utterance, or other considerations of plausibility, is inconsistent with the existential presupposition. Let us consider now presupposition triggering from direct and indirect questions. As reviewed in section 1, there is a strong tendency for both direct questions like (33a) and embedded questions like (33b) to be understood as presupposing that someone took Mary’s bike. This was supported both by pragmatic interpretation and by projection tests. But in the right contexts, the existential presupposition of questions can be cancelled. For this reason, both direct and indirect questions have the status of soft presupposition triggers.

54 Presupposition Triggering from Alternatives direct wh-questions, the some-alternative presupposition is imposed as a discourse-structural default. Formally, then, we can treat focus and questions as being subject to the same process of generating a presupposition from an alternative set. There is a construction (either a wh-question or focus) which introduces an alternative set Q. This is a set of propositions whose specific identity is in part given by compositional semantics and in part constrained pragmatically. The representation triggers a default presupposition that the disjunction _Q is true. Example (34) summarizes the steps for a direct question.

As already discussed, existential presuppositions are also observed for wh-questions in embedded positions. In a default context, (35a) seems to presuppose the same thing as (35b), that somebody took Mary’s bike. But one can also tease out a different presupposition that Mary believes someone took her bike. Switching the examples, it is clear that a speaker for (36) does not want to imply that someone voted against Mary. But because of the first sentence, a presupposition that Mary believes someone voted against her is supported. (35) a. Mary wonders who took her bike. b. Who took Mary’s bike? (36) Mary incorrectly believes somebody voted against her. She wonders who voted against her/She wonders who. This pattern is typical for presupposition triggers in attitude contexts (Heim 1991). There is an intuition that in a default context, (37a) presupposes that someone voted against Mary. But with the context (37b), this is weakened to Mary believing that someone voted against her. (37) a. Mary believes it is Chris who voted against her. b. Mary incorrectly believes somebody voted against her. Mary believes it is Chris who voted against her. c. It is Chris who voted against Mary. In Heim’s (1991) study of presupposition projection in attitude contexts, a compositional rule is stated which predicts that (37a) presupposes that Mary believes someone voted against her by virtue of (37c) semantically presupposing that someone voted against Mary. This


(34) a. [Who took Mary’s bike] (¼ Q) b. Q is a set of propositions of the form ‘x took Mary’s bike’, where x ranges over a set of relevant people. c. There is a default presupposition _Q, i.e. a default presupposition that somebody took Mary’s bike.

Dorit Abusch 55

suggests the following strategy for deriving a presupposition from the complement of wonder. (i) By virtue of the embedded question denoting an alternative set Q, a default presupposition _Q is generated. (ii) Some additional process produces the transformed presupposition that Mary believes someone voted against her.

(38) a. John is in Boston and not New York. b. John is in Boston. There is a similarity between the focus data and the affirmation– negation. Example (39a) repeats an example which demonstrates compositional transformation of a focus presupposition. It seems that one can understand the presupposition to be either (39b) or the weaker (39c). Presumably, we get the stronger presupposition if we take the salient alternatives to Lena to be just Abner and Lena, and the weaker


Part (i) is triggered by the presence of a construction which contributes a semantic object of type ÆÆs,tæ,tæ, in this case the complement question. This part of the account should be developed in a way which covers the embedded question in (35a), the direct question (34a) and the focus structure (32a) in exactly the same way. Part (ii) has no counterpart in the examples discussed so far because it is clear that it involves some kind of interaction between the indirect triggering mechanism and the compositional semantics. Working out an account which satisfies the requirement (ii) is the topic of section 4. There is another point about (37b). So far, I said that the somealternative presupposition was associated with a proposition set taking on the role of a question under discussion. It seems doubtful, though, whether the question ‘who voted against Mary’ is under discussion at the global level in this example because the first sentence already indicates that nobody did. Perhaps one could appeal to a notion of a question being ‘under discussion’ in a hypothetical context. While I do not think that direction of analysis is absurd, in section 4, I will drop reference to the QUD construct and refer simply to the logical type of the semantic object which triggers the default presupposition. The next construction to be considered is affirmation–negation. Section 1 presented evidence that the and not construction in (38a) contributes a defeasible presupposition that John is in Boston or New York. It was pointed out that this is in a way puzzling because assuming a Boolean semantics for and and not and taking for granted that Boston and New York are disjoint areas of space, (38a) carries the same information as (38b).

56 Presupposition Triggering from Alternatives presupposition if also other individuals are alternatives to Lena. Notice now that the presupposition of the affirmation–negation sentence (39d) is precisely the stronger of the two options for the focus sentence, namely the presupposition (39b). This suggests that the presupposition of (39c) comes from the affirmation–negation construction (39d) somehow contributing the alternative set (40).

The most direct route to the alternative set would be to assume the denotation (41a) for and not. I use an operator written with three dots and a double bar that in this case introduces a two-element alternative . set. In general, the notation ‘u .. w1 k . . . k wn’ is understood as ‘u, with the alternative set fw1,. . ., wng introduced’. The. term u names the ordinary denotation, while after the vertical dots ‘..’ there are terms wi naming the alternatives, separated by ‘k’. So, in (41a), the body of the lambda expression is understood as ‘P(x), with the alternative set fP(x), P(y)g introduced’. With this denotation for and not in example (39d), the propositional alternative set (40) gets introduced. Using triggering from alternative sets, this triggers a default presupposition which is the disjunction of the alternative set, that is (41b). This is not quite right because we want the transformed presupposition (39b). But as shown in the next section, it is the right start.16 .

(41) a. kykxkP[P(x) .. P(x) k P(y)] b. Abner opened the vault or Lena opened the vault. The denotation (41a) is too weak, however, because it does not explain why (42a) is contradictory. Here, there is a contrast with the 16 Getting from (41a) to (40) in a derivation for (39d) requires a logic where lambda conversion and intensionality interact with alternatives in the right way. Solutions have been developed in literature on alternative semantics for focus and questions (Rooth 1985: Ch. 2; Shan 2004). The appendix to this paper outlines an adaptation of Rooth’s solution to my notation.


(39) a. If Abner and Lena robbed the trust company, then sheF opened the vault. b. If Abner and Lena robbed the trust company, then Lena or Abner opened the vault. c. If Abner and Lena robbed the trust company, then someone opened the vault. d. If Abner and Lena robbed the trust company, then Lena and not Abner opened the vault. (40) fkw.openw(Abner, v), kw.openw(Lena, v)g (The set containing two propositions ‘Abner opened the vault’ and ‘Lena opened the vault’.)

Dorit Abusch 57

focus example (42b). Clearly, what is wrong with (41a) is that the standard content (ignoring the alternative set) does not entail :P(y). In (42c), this is fixed by adding :P(y) as a conjunct. Example (42d) gives the semantics of and not combined with its three arguments. (42) a. Abner and not Lena read the letter. And perhaps Lena read it too. b. AbnerF read the letter. And perhaps .Lena read it too. c. ½½and not ¼ kykxkP[P(x) ^ :P(y) .. P(x) k P(y)] d. ½½and not(y) (x)(P) ¼ P(x) ^ :P(y), with the alternative set fP(x), P(y)g introduced.

.

(43) ½½newcomer ¼ kx[newcomer(x,y) .. newcomer(x,y) k middletimer(x,y) k oldtimer(x,y)] (44) a. Paul is no newcomer. . b. :[newcomer(p,o) .. newcomer(p,o) k middletimer(p,o) k oldtimer(p,o)] One point about contrastive statives may be of significance to the theory of presupposition triggering. Arguably, the opposition between


The denotation (42c), which introduces an alternative set, interacts in the required way with presupposition triggering from alternatives. It also has the advantage of being close to a standard Boolean interpretation for and and not. Here is a twist on the analysis. We assume the straightforward Boolean meaning for and not, that is (42c) minus the introduction of the alternative set. Instead of stipulating the alternative set, we treat it as being derived discourse structurally. The idea is that affirmation–negation instantiates a rhetorical pattern of affirming one alternative and negating the others. When a sentence with and not is interpreted as an instance of the rhetorical pattern, the alternative set is indirectly identified. The next construction I would like to look at is contrastive statives. By now the plot is clear. I would like to claim that contrastive statives inherently ‘carry along’ their contrasting terms, for example for newcomer, the contrasting term old-timer and, since a resident may be neither a newcomer nor an old-timer, middletimer. Example (43) puts this into a lexical entry. A free parameter y is included, whose value might be our town (the town of Ovid in upstate New York). This inclusion of a free parameter follows the analysis of phrases like a local bar in Mitchell (1986). Example (44) shows how an example should work out. In (44b), the part after the dots introduces an alternative set fnewcomer(p,o), middletimer(p,o), oldtimer(p,o)g. The presupposition is generated as the disjunction of this alternative set, which we can assume to be resident(p,o).

58 Presupposition Triggering from Alternatives newcomers and old-timers is primitively a sociological and cognitive opposition, not a linguistic one. The lexicon of English alludes to this distinction, but it does not seem quite right to claim that the distinction is stipulated in the lexicon of English as a semantic presupposition. From this point of view, the representation (43) is perhaps preferable to one like (45) with a semantic presupposition.17 (45) ½½newcomer ¼ kx[@resident(x,y) ^ newcomer(x,y)]

17

Expressions like (45) are given a meaning in typed logics for presupposition such as Beaver & Krahmer (2001). @ is the presupposition operator. 18 Beaver (2004b) pointed out that an alternatives analysis would be motivated by cases where the alternatives vary with context. There is a technical issue of how to fit contextually determined alternatives into the architecture where alternatives are introduced with operators as in (42b) and (43). Applying a standard architecture with context variables (Stanley 2000), one needs some kind of context variable and an operator which can optionally add expressions that introduce alternative sets. . If following the pattern of (43), the target is kx[dy[greencard(y) ^ have(x, y)] .. dy[greencard(y) ^ have(x, y)] k Aifxg], where Ai is a. context variable of property type, then the operator that introduces alternatives is kQkx[Qfxg .. Qfxg k Aifxg]. It combines with the denotation of have a green card. The variable Ai has a property type because the contextual alternative is a property, not an extensional set. In this formal shell of an analysis, the alternative is introduced at a compositional level, rather than a lexical one. If one is willing to think informally, it seems clear that it is have a green card rather than have or green card that has a salient alternative.


Also, the Green Card Night scenario from section 1 suggests that the contrasting terms evoked by contrastive statives can be context dependent. This has a natural place in the alternatives theory, but it is harder to see where to locate it in a theory using lexical semantic presuppositions.18 At this point, triggering from alternative sets has been applied to focus, direct and indirect questions, the affirmation–negation construction and contrastive statives. For each of them, there is some kind of case that the independently motivated semantics or pragmatics of the construction involves alternative sets, though certainly analyses without alternative sets are possible, such as the partition semantics in the case of questions. While an analysis of these constructions using semantic presuppositions plus some mechanism (such as local accommodation) for eliminating the presupposition has not been refuted, I have made a case that the alternatives analysis is a better match for what is known or believed about the grammar and semantics of these constructions. Assuming this much, there is the possibility of analysing other soft presupposition triggers using triggering from alternative sets, rather than with a direct lexical encoding of a semantic presupposition. I will work this out for inchoatives. Let us return for a moment to affirmation–negation. Consider example (46a), as used by a nurse with reference to her work shift. Intuitively, the sentence presupposes that the patient was asleep at the start of the shift. This is supported by projection data in (46b), where

Dorit Abusch 59

the presupposition is either preserved or transformed into a presupposition that the nurse believes the patient was asleep. (46) a. The patient was asleep and then awake, and not asleep the whole time. b. The nurse doubts that the patient was asleep then awake and not asleep the whole time.

(47) a. b. c. d.

asleep(z1) asleep(z1) T awake(z1) fasleep(z1) T awake(z1), asleep(z1)g asleep(z1) T z1 ¼ z1

The point of going through this is that the examples (46a,b) are close to being paraphrases of the inchoative sentences (48a,b). The two versions are nearly equivalent in their assertions.20 And as reviewed in section 1, change-of-state sentences have their pre-states as soft 19

Dowty (1979) stated this semantics for T using an interval semantics framework where denotations are relative to time intervals. [uTw] is true at an interval I iff (1) there is an interval J containing the lower bound of I such that u is true at J and w is false at J, (2) there is an interval K containing the upper bound of I such that w is true at K and w is false at K, and (3) there is no non-empty interval I’I such that (1) and (2) hold for I’ as well as for I. He defines an inchoative operator as [BECOME u] ¼ [:uTu]. This agrees with my discussion. Explaining notation like that in (49) and (50) requires integrating interval semantics with a typed intensional logic of alternatives. I haven’t thought about this, except to guess that time intervals should be treated as worlds are treated in Rooth (1985) or Shan (2004). On this, see the appendix. 20 It needs to be established whether there are aspectual differences. Initially I thought that the and then . . . not complex was bad with punctual adverbs, unlike with inchoatives like (i). But (ii) is perhaps relatively OK.

(i) At 2:13, the patient woke up. (ii) At 2:13, the patient was asleep and then awake and not simply asleep.


In the analysis I proposed, presupposition triggering is attributed to the and not phrase contributing an alternative set. The individual alternatives can be described using a logic of change interpreted in an interval semantics. Following Dowty (1979), sentences and formulas of the logic of change have truth values relative to intervals, and stative sentences are true relative to an interval iff they are true at every point in the interval. This makes the atomic formula (47a) an adequate representation of ‘the patient was asleep the whole time’, where z1 designates the patient. In (47b), change of state is represented using the operator T ‘and then’ from von Wright (1968).19 The alternative set then is (47c). As we want, the disjunction of the alternatives entails that the patient was asleep at the start of the reference interval, something that can be expressed with (47d).

60 Presupposition Triggering from Alternatives presuppositions. Sentence (48b) is a projection example comparable to (46b), where the implication that the patient was awake at the start of the shift survives embedding under the negative verb doubt.21 (48) a. The patient woke up. b. The nurse doubts that the patient woke up.

(49) a. b. c. d. (50) a. b. c.

inc ¼ kPkx .:P(x) T P(x) ½½black–en ¼ ½½–en(½½black) ¼ inc(black) The sky blackened. :black(s) T black(s) .. . :P(x) T P(x) k :P(x) inc ¼ kPkx .:P(x) T P(x) .. [:black(s) T black(s) . :black(s) T black(s) k :black(s)] :black(s) T s ¼ s

There is an advantage in putting the introduction of alternatives into the inchoative because this predicts that any verb formed from this operator is a soft trigger. A language learner does not have to learn independently that each inchoative is a soft trigger, she just has to learn its morphology. Admittedly this kind of advantage can be obtained with other analyses of the triggering properties of inchoatives, for example we could try to write a semantic presupposition into the inchoative operator, perhaps using the definition (51).22 21 The predicted projected presupposition is that the nurse believes the patient was asleep. As in (46b), one can also perceive the strengthened presupposition that the patient was asleep. 22 Since I have not described an integration of interval semantics as in Dowty (1979) with a typed logic of presupposition, (51) is no more than a guess at the appropriate definition of a presuppositional inchoative.


So, the particular assertion–negation complex in (46) is effectively a compositionally constructed inchoative, which not only has the right assertion but also exhibits the soft-triggering behaviour of inchoatives. Assuming that the alternatives analysis of assertion–negation is right, this suggests the possibility of a lexical analysis of inchoatives as introducing alternatives. All that is required is a lexical entry for the inchoative which contributes the alternatives which are contributed by assertion–negation in (46). Example (49a) is the definition of an inchoative operator describing a transition from the subject not being in the state described by the predicate to the subject being in that state. If we assume that the inchoative suffix –en denotes inc, as indicated in (49b), then we get (49d) as the semantics for (49c). Example (50a) modifies the inchoative operator to include an alternative set, resulting in the semantics (50b) for (49c). The disjunction of the alternatives is equivalent to (50c). So, to presuppose the disjunction is to presuppose that the sky was black at the start of the interval of evaluation.

Dorit Abusch 61

(51) inc ¼ kPkx . (@:P(x)) T P(x)

(52) a. b. c. d.

John got money for his bike. T( j) ^ C( j) fT( j) ^ C( j), T( j) ^ :C( j)g [T( j) ^ C( j)] _ [T( j) ^ :C( j)] [ T( j)

This analysis has revealed a problem: it turns out to be too trivial to identify an alternative set which produces the right presupposition. Suppose, we have a construction or lexical item with an observed presupposition p and assertion q. If we stipulate a binary alternative set fp ^ q, p ^ :qg, then by propositional logic the disjunction of the alternatives is equivalent to p. On this basis, it is possible to stipulate any desired presupposition, and the fact that the presupposition is to be generated from an alternative set provides no constraint at all. So, for constructions where there is no independent motivation for the representation with alternatives, generating the presupposition from alternatives is just a way of representing the softness of the triggering. I discuss this problem further in section 6.


Summing up, this paper has claimed that an analysis using triggering from alternatives is motivated for focus, direct and indirect questions, affirmation–negation and contrastive statives. If we observe soft-triggering behaviour for another construction, lexical item or class of lexical items (call it X), and can identify an alternative set whose disjunction is the desired presupposition, then hypothesizing a representation with an alternative set is a way of producing a defeasible presupposition for X. The case for analysing the construction using triggering from alternatives will be stronger if there is independent motivation for the alternative set. But even if there is not such independent motivation, the analysis using triggering from alternatives has the advantage of predicting softtriggering behaviour. Consider how this works out for the transfer construction in the example repeated in (52a). Assume the content of (52) is expressed with the conjunctive formula (52b), where T(j) is the transfer entailment and C(j) is the counter-transfer entailment. Then, we can get the transfer entailment to come out as a soft presupposition by stipulating the alternative set (52c) because of the Boolean logic (52d). The appropriate alternative is simply John giving up his bike without getting money.

62 Presupposition Triggering from Alternatives 4 COMPOSITIONAL INTERACTIONS

(53) Mary does not like John’s twins. > John has twins. (presupposition q#) (54) If John has children, then Mary will not like his twins. > If John has children then he has twins. (presupposition p / q#) This transformation of presuppositions is captured in a dynamic compositional account using semantic presuppositions (Heim 1983), accounts using three-valued valuations (Beaver & Krahmer 2001) and in Schlenker’s (2006) account using incremental evaluations in a static two-valued system. The potential problem for my analysis is that, as we already saw in section 1, when we check similar examples with soft triggers, the data come out in the same way, with conditional weakening of the presupposition. Here is an example with and not. The clause in (55) presupposes that John is in Syracuse or Binghamton. In (56), this clause is embedded as a main clause in a conditional. (55) John is in Syracuse and not Binghamton. > John is in Syracuse or in Binghamton. (56) If John is in a city, he is in Syracuse and not Binghamton. > If John is in a city, he is in Syracuse or in Binghamton. 23 The twins examples are from Heim (1983), who credits them to personal communication from Peters. Although (or perhaps because) the conditional presupposition is so bizarre, I find these data clear. The pragmatic prediction is that (54) should be usable only in a context where the common ground entails the conditionalized presupposition, and this seems right. For instance, it could be common ground that John is a member of a species (a kind of armadillo) whose firstborns are always twins. Then, if John has any children at all, he has some twins. In this paper, clefts rather than definite descriptions are the paradigm example of hard triggers. The cleft version (i) of the bank robbery example illustrates conditional transformation with clefts.

(i)

If John and Mary robbed the Trust Company, then it is she who opened the vault. If John and Mary robbed the Trust Company, then someone opened the vault.


There is a group of observations about presupposition projection which are considered characteristic of semantic presupposition, first because these effects show up with clear cases of semantic presupposition and second because systematic accounts of them have been given in compositional-semantic accounts (Karttunen 1973, 1974; Karttunen & Peters 1979; Heim 1983; Beaver & Krahmer 2001; Schlenker 2006). One case is the transformation of presuppositions in conditionals which served as a test for presupposition in section 1. In isolation, (53) presupposes that John has twins; this presupposition q# comes from the definite description. In a conditional context (54), the presupposition q# is transformed to p / q#, where p is the assertion of the if-clause (in this case, that John has children).23

Dorit Abusch 63

(57) fJohn is in Syracuse, John is in Binghamtong

(58) Every one of them is in Worcester, and not his home town. [every one of them].2 [x2 is in Worcester .. x2 is in Worcester k x2 is in x2’s home town]] 24 The point being made here does not have to do with the restricting domains of quantification to satisfy presuppositions. According to some intuitions, in (i) the domain gets restricted to Germans who have Mercedes automobiles. This matter is independent of the point I am bringing up about (58). No matter how the domain is restricted, one alternative in (58) contains a bound variable his.

(i)

Every German likes his Mercedes.


It seems clear that the presupposition that John is in Syracuse or in Binghamton, which is obtained as the disjunction of the alternative set (57), is conditionally weakened to the implication showed in (56). Furthermore, there is an intuition that to contextualize (56), one has to imagine a common ground which supports the conditionalized implication. For instance, it could be common ground that John is in an electronically monitored parole programme which makes it impossible for him to visit cities other that Syracuse and Binghamton. So, with and not, we see the compositional transformation of content that is characteristic of semantic presupposition, and the characteristic pragmatic interpretation of entailment by the common ground. If and not was analysed with a semantic presupposition, then this behaviour would fall out. In a theory using triggering from alternative sets, it has to be explained how the same effects follow. Putting the point in terms of the alternatives theory, the problem is that in an normal utterance context for (56), the some-alternative constraint is not met at the global level. That is, the common ground does not entail that John is in Syracuse or in Binghamton. Indeed, with a common ground like that, (56) is odd because it casts doubt on something that is taken for granted. So, it is not clear how the analysis from section 3 is to be applied. Another compositional effect related to presupposition is interaction with bound variables in quantified contexts. This is discussed in van der Sandt (1992); see also Beaver (1997). In (58), the and not-phrase includes a bound pronoun. As a consequence, each of the alternatives generated by and not has a bound variable, as shown in the description of the alternative set in the last part of the labelled bracketing. The problem for my analysis is that since each alternative contains a variable x2 which is free in the alternative, but bound in the sentence context, it is unclear what interpretation the alternative set could get at the discourse level.24



These two problems (presupposition projection and interaction with variable binding) are similar because they involve interactions with compositional semantics. Accounts which assume lexical semantic presuppositions have the resources to deal with them because they manipulate denotations which encode presuppositions. Furthermore, since the problems have to do with what is happening at embedded levels in the sentence, they seem to involve compositional semantics, rather than discourse-level reasoning. And finally, these phenomena have been analysed in the literature on the compositional semantics of semantic presuppositions. How could the account using triggering from alternative sets do as well? Some literature on presupposition triggering expresses optimism that presuppositions which are triggered in some indirect way (such as by conversational implicature) would be filtered and transformed in the same way as semantically triggered presuppositions (Chierchia & McConnell-Ginet 1990: 113; Kadmon 2001: 216). The question is how to achieve this in detail in the analysis using alternatives for triggering. This cannot follow from any very general considerations because presupposition filtering in semantic accounts is the result of certain specific mechanisms and interactions, and there can be no general expectation that these mechanisms and interactions would work the same way with presuppositions which are the result of an indirect mechanism. In fact, the analysis from section 3, stated in a way that refers to global QUDs, is an example of an indirect triggering mechanism which does not interact with compositional semantics to predict filtering and transformation of presuppositions. I will approach this problem by re-formulating the theory in dynamic semantic terms, taking advantage of the same dynamic compositional interactions which are used in semantic accounts of presupposition projection. In the standard picture adopted here, the pragmatic interpretation of presuppositions relates to the global common ground (Stalnaker 1974). On the other hand, in the compositional phenomena above, it seems that one has to consider what information is available in a local compositional context. This is what dynamic semantic theories do when they check semantic presuppositions against a local information state. This creates a tension between the global and the local information levels in the analysis which was suggested in section 3. To resolve it, I will state the analysis in a way which refers to local compositionally determined information states and drop the assumption that the alternative sets which are used in the derivation are necessarily questions under discussion at the discourse level.

Dorit Abusch 65

The notion of local compositionally determined information states is illustrated in (59), which is the compositional rule for conditionals from Heim (1983), stated in her file-change notation. c is an input information state for a conditional [if u then w]. The formula describes the result of incrementing c with a conditional sentence in terms of a binary increment operator ‘+’ and Boolean operators. The formula predicts presupposition transformation because the local context for the main clause w is the state term c + u rather than c, and u can contribute to satisfying the presuppositions of w. The notation d will be used for local compositional contexts such as c + u, reserving c for the global information state. Suppose that the clause w in (59) contributes an alternative set Q. The discussion of (56) showed that it will not work (or will not always work) to impose a default constraint that the global context c entails the disjunction of Q. Referring instead to the local context in the constraint on alternatives results in a weaker presuppositional constraint since the local context has the information contributed by u, which in (56) is the information that John is in a city. This will result in the same filtering and transformation of presuppositions which is obtained with semantic triggering. This approach is expressed in a default constraint L stated in (60).25 The constraint is ultimately a constraint on the global information c, and so it has a presuppositional character. But it also refers to the correspondence between c and the local context d which is established by compositional semantics. Example (61) shows how L applies to (56). c is the entire sentence, and w is the main clause of the conditional, which contains and not and contributes the alternative set. As a result of the compositional rule (59), the local context for w is the one described in (61b). In the constraint, d is required to entail the disjunction of the alternative set (61c). Since d is defined in terms of c, this provides a constraint on the global common ground c which is equivalent to the conditional presupposition shown in (56). 25

This analysis has a certain connection with the analysis of soft triggering in Simons (2001), which refers to this Question raising principle. If A says S, and S embeds q, then A raises the question whether q. Both theories use the idea that embedded clauses can raise (or in my case, refer to) questions. A problem from the point of view of the theory being developed here is that a whether question Q derived from a non-presuppositional proposition q will derive a trivial some-alternative presupposition. See a prepublication version of this paper (doi: 1813/12212) for some discussion of Simons’ pragmatic derivation.


(59) c + if u then w ¼ c ((c + u) (c + u + w))

66 Presupposition Triggering from Alternatives (60) Default Constraint L If a sentence c is uttered in a context with common ground c, and c embeds a clause w which contributes an alternative set Q, then c is such that the corresponding local context d for w entails the disjunction of Q. (61) a. [c [if John is in a city], [w he is in Syracuse and not Binghamton]] fQ John is in Syracuse, John is in Binghamton Qg w] c] b. d ¼ c + John is in a city c. fin(j,s), in(j,b)g

(62) a. Mary didn’t tell JOHNF about it. b. c + not u ¼ c c + u So, if one wanted to motivate L as a true statistical generalization, cases like these where the alternative set is a QUD provide a bunch of positive cases for the generalization. It is also important that L can also be triggered in cases like (56) where the alternative set is not or does


Notice that in constraint L, Q is described as an alternative set, not as a question under discussion. An ‘alternative set’ is just a semantic object with the type of a set of propositions. These alternative sets can have a variety of origins: an origin in focus semantics, a social institution in the case of contrastive statives, a rhetorical pattern in affirmation–negation, the ordinary denotation in the case of questions or the inchoative operator for inchoative verbs. Alternative sets with these origins can have the role of QUDs, but they do not need to have that role in order for L to be triggered. The constraint is stated in this way because it must apply in cases where the alternative set in question is not a global question under discussion, for instance (56). Although there is no reference to QUDs in L, cases where the alternative set is a QUD contribute to the motivation for the constraint. Questions under discussion often obey the some-alternative constraint, and the alternative sets which figure in L are often questions under discussion (as in the case of focus in matrix answers and direct questions). This extends to cases where the trigger for the alternatives is in an embedded position. In (62a), the focus is embedded under negation, but it can be motivated by a discourse context where the question ‘who did Mary tell about it?’ is topical, and where that question obeys the some-alternative constraint relative to the global context c. In a context like that, (62a) is consistent with L because by virtue of the update rule (62b) for negation, the local context d for the embedded clause with the focus is c itself.

Dorit Abusch 67

(63) Max fell. John helped him up. It is an important feature of this theory that constraints interact and compete with each other and can be in effect ‘cancelled’ by contextual information. This is my model for what happens in the cancellation cases from section 1. Simply stated, speakers and hearers will assume that the some-alternative constraint is not in force for a particular question variable, if the some-alternative presupposition is either inconsistent with context or made implausible by context. 5 ANAPHORICITY OF FOCUS This section identifies and fixes a weakness in the argument about focus from section 3. That discussion used the focus interpretation theory of Rooth (1992), but it ignored the important ‘anaphoric’ component of that theory: focus interpretation does not just contribute an alternative set, it also requires that the alternative set be available as an antecedent in the discourse representation. The requirement for antecedents for focus interpretation is the core of the givenness theory of Schwarzschild (1999). In a focus-triggering question-answer dialogue like (64a), the set of propositions introduced by focus interpretation is coindexed with the question in the way shown in (64b) in Rooth’s indexing representation. 26 Other possible theoretical settings for L are I-implicature (Levinson 2000), and enrichment reasoning (Carston 2002).


not have to be a QUD. Arguably, when an alternative set is contributed in an embedded position by a focus, indirect question, affirmation– negation construction or contrastive stative and is not a QUD, it still has a certain discourse-structural role which is shared with matrix questions. I would like to claim that there is a linguistic and cognitive phenomenon of alternative sets which by default obey the somealternative constraint relative to a local information state. This phenomenon is instantiated by alternative sets which are QUDs, but not limited to them. What is the theoretical status of constraint L? I suggest that it should be located in a theory such as the one articulated by Asher & Lascarides (2003), where discourse structure is governed by a variety of constraints with a default character.26 An example of this is the default assumption about the temporal order of events in (63), which Asher and Lascarides propose is governed by a constraint Narration(p1, p2), which requires that the post-state for the event ep1 described by the clause p1 overlap the pre-state of the event ep2 described by the second sentence p2.

68 Presupposition Triggering from Alternatives (64) a. Who went to the reception? BillF went there. b. [who went to the reception]1 [BillF went there];1

(65) a. If John didn’t go there, I doubt that BillF went there. b. If not [John go there]3, I doubt that [BillF went there];3. In the anaphoric focus theories, (65a) gets an analysis like (65b), where the antecedent for the focus is the part of the if-clause under the negation. This representation is licensed by the theory of Rooth (1992) because ‘John go there’ can be obtained from ‘Bill go there’ by making a substitution in the position of the focused subject, and in the theory of Schwarzschild (1999) because John going there entails someone going there.27 27 The theories of Rooth (1992) and Schwarzschild (1999) license representations with propositional antecedents, in addition to representations with proposition-set antecedents. Formally, Schwarzschild’s givenness theory does not refer to indices. Instead, it requires that salient antecedents be present.


There are a couple of ways in which the anaphoric dimension of focus theories complicates the picture for the argument of this paper. First, in a representation like (64b), one might wonder whether it is the focus alternative set or the antecedent (in this case the question) which is responsible for the existential presupposition. Since matrix questions generate default some-alternative presuppositions, and (64) has a matrix question as well as a focus, this example does not constitute evidence that focus generates a default some-alternative presupposition. We could say that the presupposition comes from the question and that there is no default constraint which generates a some-alternative presupposition from a focus. I think this worry is not a very serious one. In the representation (64b), the question is identified with the proposition-set constrained by focus by indexing. It does not matter whether the some-alternative constraint applies to the question, the focus variable or both. To ask which alternative set the some-alternative constraint applies to is to create a false distinction because there is only one alternative set. A second point is that it is easy to construct examples with anaphoric uses of focus which do not satisfy a some-alternative constraint. Consider example (65). If one works through the predictions of L, one finds that the conditionalization of the presupposition is trivial, so that a default presupposition that someone went there is derived. But it is easy to think of contexts for the sentence where this presupposition is not satisfied—imagine a scenario where John and Bill are exploring a cave that nobody has ever visited before, and ‘there’ refers to a certain narrow underwater tunnel.

Dorit Abusch 69

Here, it can be pointed out that in both theories, the index 3 has the propositional type Æs,tæ rather than the question type ÆÆs,tæ,tæ. As a result, constraint L is not triggered at all, and the theory does not predict a default existential presupposition for structure (65b). A third issue is that the anaphoric part of Schwarzschild’s and Rooth’s focus theories represents a lack of analogy between focus and the other soft-triggering constructions. For instance, with inchoatives like (66a, b), or a contrastive stative like (66c), there is no feeling that the relevant alternative set has to be present in the preceding discourse or antecedent discourse representation.

A lack of analogy between focus and other soft triggers does not count against the analysis using L though because the theory does not claim that soft triggers are similar in every respect, just that soft triggers (or a significant subgroup of them) are analogous in the one respect of contributing alternative sets. The constraint L does not require the alternative set Q is either anaphoric or novel, so it applies both to anaphoric Q’s (such as certain focus variables) and non-anaphoric ones (such as the hypothesized alternative set in the representation of inchoatives).28 So far, none of these points has undermined in a decisive way the analysis using L or the motivation for it which comes from focus data. However, I think a substantial issue can be synthesized from the first two points. Suppose, we adopt an anaphoric theory of focus interpretation, say the givenness theory of Schwarzschild (1999). That theory requires a focus to have (in a certain sense) an antecedent in the discourse, call it A. Suppose, we say that the antecedency constraint exhausts the semantic/pragmatic impact of focus and that focus does not interact with a constraint like L. If one takes that position, then it is no surprise that a focus existential presupposition is sometimes satisfied, and sometimes not. The possible discourse representations divide into three types: (i) A has type ÆÆs,tæ,tæ and satisfies the some-alternative constraint. 28

Still, it must be recalled that this paper has stated no independent evidence that inchoatives contribute alternative sets. If they contributed anaphoric alternative sets, that would be detectable, providing evidence for the representation.


(66) a. In the cold snap, the lake froze over. b. Despite the cold snap, the lake didn’t freeze over. c. He doesn’t have a green card.

70 Presupposition Triggering from Alternatives (ii) A has type ÆÆs,tæ,tæ and does not satisfy a some-alternative constraint. (iii) A has another type such as Æs,tæ and the issue of satisfying a some-alternative constraint does not arise.


If representations of type (i) are very prevalent compared to representations of type (ii), one could claim that this provides motivation for subjecting focus alternative sets to a default constraint like L. But one could also claim that the prevalence of representations of type (i) is a fact about the salient antecedents of type ÆÆs,tæ,tæ which happen to be available in discourses: for instance, many of these salient antecedents are matrix questions, and matrix questions usually meet the some-alternative constraint. The objection, then, is that if focus is anaphoric, the antecedents for focus alternative sets in particular utterance contexts already decide the question whether the some-alternative constraint is satisfied in the particular utterance situation or not. There appears to be little room for a default constraint to favour interpretations where the constraint is satisfied over ones where it is not. This objection might be strong enough to undo the motivation for constraint L coming from focus, if focus is always anaphoric in the sense of there being an overt antecedent. However, it is a commonplace in discussions of anaphoric theories of focus that antecedents need not be overt in the discourse (e.g. Rooth 1992). Consider the example repeated in (67a). Certainly, this sentence, with a focus on the subject she, can be used in a discourse where there is no overt antecedent for the focus, such as the question (67b) or the existential clause (67c). Rather, the focus can be licensed by the implicit assumption or common knowledge that the Trust Company keeps all money and valuables in the vault, so that if Lena and Albert robbed it, somebody opened the vault. When (67a) is used in this kind of context, there is no overt discourse antecedent along the lines of the question ‘who opened the vault’. So it is not possible to attribute the presuppositional effect to properties that an antecedent happens to have, independent of the focus. There is literally nothing in the overt discourse or in the sentence grammar which could be held responsible for the presupposition, except for the contrastive accent on the subject she. Note also that a matrix question like (67b) could not be responsible for the conditionalized presupposition which is observed in (67a). My conclusion is that discourses like this where there is no overt antecedent for focus do provide motivation for constraint L.

Dorit Abusch 71

(67) a. If Lena and Albert robbed the Trust Company, then sheF opened the vault. b. Who opened the vault? c. Someone opened the vault.

(68) If LEna and ALbert robbed the TRUST Company, then SHE opened the VAULT. 6 OTHER VERSIONS OF THE CONSTRAINT In section 2, I argued that any indirect account of triggering would have to assume some degree of structuring of lexical entries. I first considered a theory where a denotation was structured into a set of entailments, and then in sections 3 and 4 developed the theory of triggering from alternative sets. It was proposed that lexical entries can specify alternative sets Q and that these interact in a certain way with the default constraint L. The constraint always uses an alternative set in 29 There are other representational and analytic possibilities, however. One alternative, pointed out to me by David Beaver, is that grammatical focus on she has a narrower scope, expressing simply a contrast between Lena and Abner. In the indexing theory, this might be represented as [[sheF ;1] opened the vault], where 1 is an index with value fLena, Albertg. This would presumably not predict a conditionalized presupposition along the lines of the one I am discussing, or entail that the subject she is more prominent than the predicate opened the vault. Another possibility is that the accent on vault, rather than being the kind of accent characteristic of discourse-new material in Selkirk’s analysis, is a topic accent in the sense of Bu¨ring (1997). The Focus–Topic combination would contribute an implicit discourse structure along the lines of ‘what about opening the vault? Who did that?’ or ‘who performed what action involved in robbing the Trust Company?’.


An interesting additional dimension in focus data like this has to do with the phonological realization of the scope of the focus on she, that is the adjunction site of the ; operator that interprets the F feature. In (67a), I assumed that the focus scope was the clause ‘she opened the vault’. Some literature has claimed when phrases in the scope of the focus are not discourse given, rather than having a flat intonation, they are realized with pitch accents (Selkirk 2002; Fery & Samek-Lodovici 2006). When (67a) is used in the context described above, pitch accents naturally fall in the positions indicated with capitals in (68), and it is not possible to de-accent the VP starting with opened. Selkirk explicitly argues that the scope of the focus feature in examples like this is phonologically detectable because the pitch accent corresponding to the F feature has greater prominence than pitch accents in discoursenew material that is not focused. Thus, there might be phonological evidence bearing on my claim that the scope of the focus in (67a) is the then-clause.29


(69) a. John is in Syracuse rather than Binghamton. b. fJohn is in Syracuse, John is in Syracuse or Binghamtong The set denotation fp, qg can serve a couple of purposes at once because the standard denotation can be recovered as the conjunction ^fp, qg ¼ p, while the potential presupposition can be recovered as the disjunction _fp, qg ¼ q. Because of the latter fact, the appropriate version of constraint L, which is stated in (70), looks almost the same as before. (70) Default Constraint L# If a sentence w is uttered in a context with common ground c and w embeds a clause u which contributes a denotation set S, then c is such that the corresponding local context d for u entails that the disjunction of S is true. This version of the alternative-set approach perhaps looks like a formal tweaking of the old one, so that there might not be much to decide between them. If one wanted to adopt the second approach, one would have to show how to extend it to cases like constituent questions, where there can be more than two alternatives in Q, and where there is independent evidence about what the denotation should be. Next I would like to discuss whether, assuming that the analysis using L is motivated for certain soft triggers such as focus and affirmation–negation, it is attractive to extend it to others soft triggers such as inchoatives, where there is no independent evidence for a representation with an alternative set. If we do hypothesize a representation with an alternative set, soft-triggering behaviour is predicted. This can be seen as an extension of an available mechanism


a specific way—it checks the disjunction of Q against a local information state. Suppose that instead of encoding an alternative set Q, soft triggers directly encoded a proposition q which is the disjunction of the alternative set Q which is assumed in the formulation from sections 3 and 4. If we put q and the standard semantic value p together into a set fp, qg which is contributed by the compositional semantics for a clause, this almost brings us back to the set-ofentailments proposal from section 2. The difference is that since p asymmetrically entails q, there is an inherent ordering on the set, so that it is possible for a process which manipulates fp, qg to select q as the presupposed entailment. Sentence (69a) is an example. In the structured semantic value, ‘John is in Syracuse’ is the stronger proposition p, and ‘John is in Syracuse or Binghamton’ is the weaker proposition q.

Dorit Abusch 73

(71) a. b. c. d. (72) a. b. c.

He finished the six-mile race at 12:27. He lost his wallet at 12:27. He shut down the system at 12:27. He entered Canada for the first time at 12:27. #He ran the race at 12:27. #He built a house at 12:27. #He spent two weeks in Canada at 12:27.

The sentences in (71) do have entailments about the time period prior to 12:27—it is not that all the information entailed by the sentence is about the time point 12:27. For instance, (71d) entails that he was not in Canada at any time before 12:27, and (71c) entails that the system was up shortly before 12:27. As a baseline theory, say that verbs in the achievement class have an entailment s describing an event which is located within the time parameter which interacts with temporal frame adverbs, and an entailment r describing a preparatory process or precondition that is located prior to the time frame described by a temporal frame adverb, rather than within it. Syntactically, suppose we use a formula constructor T which in the formula rTs constructs a proposition in the achievement class from a formula r describing the precondition, and a formula s describing the change. T is like von Wright’s operator T, except for the possible difference that the logic 30 The commentary Abusch & Rooth (2006) criticized Thomason et al.’s paper for not explaining what the concepts of presupposition and precondition have to do with each other, almost as if there was a terminological confusion. Now, it seems to me that reducing triggering of linguistic presuppositions to features with independent character and motivation is exactly right.


to cover additional data. But it is also unsatisfactory because it is a way of recording status as a soft trigger, in the absence of insight into what lexical feature is responsible for soft-triggering behaviour. Arguably, instead of mechanically applying the alternatives analysis to all soft triggers, we should look for other features (presumably, other kinds of structuring) which might be responsible for triggering behaviour in other classes of soft triggers. I will briefly sketch one possibility inspired by Thomason et al. (forthcoming).30 In a class of triggers including inchoatives, achievements with preparatory phases and agentive verbs such as sell with preconditions, one can independently establish a kind of temporal structuring of the entailments of the predicate. As shown in (71), predicates in these classes are compatible with punctual time adverbs. In this respect, they contrast with predicates in the aspectual class of accomplishments: the sentences in (72) are odd because of implausible entailments, contradictory, and/or difficult to contextualize.


(73) Presuppositions from preconditions If a sentence w is uttered in a context with common ground c and w embeds a clause u with precondition r, then c is such that the corresponding local context d for u entails r. To apply the constraint, one needs a semantic model where it is possible to recover the preconditions of the embedded clause u. If that can be worked out, I do not see a reason to prefer an analysis using alternatives to the one referring directly to preconditions. 7 CONCLUSIONS The argument of this paper can be summarized like this. (i) There are various ‘soft’ presupposition triggers, where triggering behaviour is defeasible. (ii) For some of these triggers, a representation involving alternatives is motivated, and for these, it is attractive to derive presupposition triggering from the alternatives. (iii) An account of presupposition filtering and transformation can be adapted from Heim (1983), and the whole analysis can be expressed as a default constraint L which refers to logical forms that contribute alternative sets. (iv) For 31

See footnote 19.


and compositional semantics should be set up so that when rTs is modified by a temporal frame adverb, s rather than the sequence r, s gets located within the temporal frame.31 With these assumptions, a particular representation rTs for predications such as achievements and changes of state is motivated by frame adverb modification and other criteria developed on literature on aspectual classification (Kenny 1963; Dowty 1979; Krifka 1992). These criteria are independent of presupposition phenomena. Consider now how the defeasible presuppositions of predications in the achievement class should be derived. In the approaches considered so far, one would state a semantics for rTs which introduced an alternative set frTs, rg or a set denotation frTs, rTs _ rg. Then application of constraint L (the alternatives constraint) or constraint L# (the setdenotation constraint) results in checking that the local information state entails the precondition. That is, one obtains a default presuppositional status for the precondition. One could also proceed more directly, and state a default constraint like (73) referring to preconditions, and try to motivate that constraint. Example (73) handles the facts of presupposition projection in exactly the same way as L.

Dorit Abusch 75

APPENDIX The definition in (42c) is intended to generate the propositional alternative set fAbner read the letter, Lena read the letterg at the level of the first sentence in (42a). This appendix sketches a logic for such expressions. (42) a. Abner and not Lena read the letter. And perhaps Lena read it too. b. AbnerF read the letter. And perhaps .Lena read it too. c. ½½and not ¼ kykxkP[P(x) ^ :P(y) .. P(x) k P(y)] d. ½½and not(y)(x)(P) ¼ P(x) ^ :P(y), with the alternative set fP(x), P(y)g introduced. My approach is to simplify alternative semantics for focus so that alternatives propagate less. In alternative semantics for focus, alternatives can propagate past functions because there is the need to


triggers where we have not found any independent motivation for a representation with alternatives, once we have L, we can derive soft triggering anyway, by stipulating a lexical representation with a set of alternatives whose disjunction is the observed presupposition. (v) But perhaps, where a representation using alternatives is not independently motivated, it is better to look for a different constraint referring to some lexical feature which is motivated. An example is a constraint referring to preconditions. Part (iii) is in one way a modest success: the basic mechanism for presupposition filtering is identical to what is found in dynamic semantics, and from this point of view, there is little independent interest to it. But this can also be seen the other way around: in the alternatives analysis, it is easy to deal with presupposition filtering by using the mechanisms of dynamic semantics. So, the facts of presupposition filtering are not a barrier to the alternatives analysis, or more generally, to indirect analyses of presupposition triggering. The overall programme being advocated here is one of tying presupposition-triggering behaviour to motivated features of lexical semantics, constructional semantics or pragmatic status which are not inherently presuppositional. This paper has made a case for a derivation from alternatives, focusing on a handful of constructions. If this kind of approach is correct, it is plausible that the full story would involve a number of distinct features which can be responsible for softtriggering behaviour.

76 Presupposition Triggering from Alternatives generate wide-scope alternatives for focused phrases in embedded positions. (i) is an example. To propagate alternatives, recursive rules for alternative sets are used that define a ‘focus semantic value’ ½½. . .f, together with the ordinary semantic value ½½. . .o. (ii) is the simplest version of the recursive semantic rule for focus semantic values for function/argument terms. This definition of the focus semantic value ½½a(b)f of a function term a(b) propagates alternatives from both the function subterm a and the argument subterm b.

If lexically triggered alternatives also propagated from the argument part of application terms, one would get the alternative set (iv) for (iii), where the alternatives coming from freeze have propagated past the function impossible. This is undesirable because the disjunction of (iv) is not a presupposition of (iii). (iii) It’s impossible that the pool water froze. This is Tel Aviv! (iv) fit’s impossible that the pool water was liquid and became frozen, it’s impossible that the pool water was liquid and remained liquidg So, lexically triggered alternatives should not propagate from the argument part of an application term. They should propagate from the function part because for instance in (42), the alternatives fAbner read the letter, Lena read the letterg should be generated from the denotation (42c) for and not, which has a functional type and contributes the alternatives. In fact, all the examples in the paper follow this pattern: a lexical item denoting a function and contributing an alternative set should be ‘filled out’ to set of alternative propositions, by adding arguments. This suggests the definition (v), where ½½. . .a is a semantic value function for lexically triggered alternatives, and ½½. . .o is the ordinary semantic value. (v) ½½a(b)a ¼ fx(y) j x 2 ½½aa ^ y ¼ ½½bog Since lambda is used in (42c) and other definitions of triggers in the paper, a semantics for abstraction is also needed. There are proposals for this in literature on alternative semantics for focus (Rooth 1985; Shan 2004). (vi) is Rooth’s solution applied to the alternatives value ½½. . .a. All semantic values have additional argument positions for assignment functions and for worlds. (vii) is (v) adjusted to the raised types. (viii) defines the alternative value for the intension operator. Other clauses


(i) Sue wants JOHNF to marry her. [She doesn’t want Bill to marry her.] (ii) ½½a(b)f ¼ fx(y) j x 2 ½½af ^ y 2 ½½bfg

Dorit Abusch 77

should not propagate alternatives, for example (ix). (x) defines the alternative semantic value of an atomic symbol as the unit set of the ordinary semantic value. (vi) (vii) (viii) (ix) (x)

½½kx.aa ¼ fkgkwky.f(g[y/x])(w) j f 2 ½½aag ½½a(b)a ¼ fkgkw.x(g)(w)(y(g)(w)) j x 2 ½½aa ^ y ¼ ½½bog ½½âa ¼ fkgkwkv.f(g)(v) j f 2 ½½aag ½½u ^ wa ¼ f½½u ^ wog ½½aa ¼ f½½aog, where a is atomic.

Finally, here is the clause for the operator that initiates the alternative set. This operator does not affect ordinary denotations: . (xii) ½½u .. w1 k . . . k wn o ¼ ½½uo

In this system, where u is a formula, ½½ua has type [[Assignments / Worlds / Bool] / Bool], while the ordinary semantic value ½½uo has type [Assignments / Worlds / Bool]. A set of propositions (characteristic functions of worlds) is recovered from ½½ua using a contextual assignment g as ff(g) j f 2 ½½uag. Acknowledgements An earlier paper, with part of the material presented here, was presented at SALT XII and appeared as Abusch (2002). The current paper was presented in different versions at the Workshop on Information Structure in Bad Teinach, July 2004, at colloquia at MIT in November 2004, at Tel Aviv University in January 2005, at the University of Rochester in April 2005, at the University of Potsdam in June 2006 and at the University of Frankfurt at June 2006. Thanks to the audiences on these occasions. I would like to thank Mats Rooth for accompanying various stages of this paper and providing me with extensive and valuable criticisms and observations. I would also like to thank David Beaver, Cleo Condoravdi, Tim Fernando, Caroline Fery, Hans Kamp, Pauline Jacobson, Manfred Krifka, Paul Portner, Sally McConnell-Ginet, Magda Schwager, Cecile Meier, Ken Shan, Peter Staudacher, Arnim von Stechow, and Ede Zimmermann for their comments and references. Two thoughtful reviewers for the Journal of Semantics made important contributions to my paper. I am solely responsible for any errors or misconceptions.

DORIT ABUSCH Department of Linguistics Morrill Hall Cornell University Ithaca, NY 14853 e-mail: [email protected]


. (xi) ½½u .. w1 k . . . k wn a ¼ f½½w1o, . . ., ½½wnog

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Geurts, Bart & Rob van der Sandt (2004), ‘Interpreting focus’. Theoretical Linguistics 30: 1–44. Groenendijk, Jeroen & Martin Stokhof (1984), Studies on the Semantics of Questions and the Pragmatics of Answers. Doctoral dissertation, Universiteit van Amsterdam, Amsterdam. Hamblin, Charles (1973), ‘Questions in Montague English’. Foundations of Language 10: 41–53. Heim, Irene (1983), ‘On the projection problem for presuppositions’. In Michael Barlow, Daniel Flickinger, and Michael Wescoat (eds.), Proceedings of WCCFL II. CSLI, Stanford University. 397–405. Heim, Irene (1991), ‘Presupposition projection and the semantics of attitude verbs’. Journal of Semantics 9:183–221. Horn, Larry (1972), On the Semantic Properties of Logical Operators in English. Indiana University Linguistics Club. Bloomington, IN. Jackendoff, Ray (1990), Semantic Structures. Current Studies in Linguistics 18, MIT Press. Cambridge, MA. Ja¨ger, Gerhard (2004), ‘Alternatives or presuppositions? A comparison of the background-presupposition rule with alternative Semantics’. Theoretical Linguistics 30: 111–122. Kadmon, Nirit (2001), Formal Pragmatics. Blackwell. Oxford. Karttunen, Lauri (1969), ‘Some observations on factivity’. Papers in Linguistics 5: 55–69. Karttunen, Lauri (1973), ‘Presuppositions of compound sentences’. Linguistic Inquiry 4:169–193. Karttunen, Lauri (1974), ‘Presuppositions and linguistic context’. Theoretical Linguistics 1:181–194. Karttunen, Lauri & Stanley Peters (1979), ‘Conventional implicature’. In Choon-Kyu Oh and David Dinneen (eds.), Syntax and Semantics

80 Presupposition Triggering from Alternatives In Rachel Hastings, Brendan Jackson, and Zsofia Zvolenzky (eds.), Proceedings of Semantics and Linguistic Theory XI. CLC Publications. Ithaca, NY. 431–448. Simons, Mandy (2007), ‘Observations on embedding verbs, evidentiality, and presupposition’. Lingua 117: 1034–1056. Stalnaker, Robert (1974), ‘Pragmatic presuppositions’. In Milton Munitz and Peter Unger (eds.), Semantics and Philosophy. New York University Press. New York, NY. 197–214. Stanley, Jason (2000), ‘Context and logical form’. Linguistics and Philosophy 23: 391–434. Thomason, Richmond, Matthew Stone, & David DeVault, ‘Enlightened update: a computational architecture for presupposition and other pragmatic phenomena’. In Donna Byron, Craige Roberts, and Scott Schwenter (eds.), Presupposition Accommodation. Prepublication version distributed by Ohio State Pragmatics Initiative, forthcoming (http://ling.osu.edu/pragwiki/ index.php). von Wright, Georg Henrik (1968), An Essay on Deontic Logic and the General Theory of Action. Acta Philosophica Fennica Fasc. XXI. North-Holland, Amsterdam. First version received: 18.01.2007 Second version received: 01.03.2008 Accepted: 25.03.2008


Cognitive, and Computational Perspectives. Cambridge University Press. Cambridge. 232–236. van der Sandt, Rob (1992), ‘Presupposition projection as anaphora resolution’. Journal of Semantics 9:333–377. van der Sandt, Rob & Bart Geurts (2001), ‘Too’. In Robert van Rooy and Martin Stokhof (eds.), Proceedings of the 13th Amsterdam Colloquium. University of Amsterdam. Amsterdam. 180–185. Schlenker, Philippe (2006), ‘Antidynamics: presupposition projection without dynamic semantics’. Journal of Logic, Language, and Information 16: 325–356. Schwarzschild, Roger (1999), ‘Givenness, avoidF and other constraints on the placement of accent’. Natural Language Semantics 7:141–177. Selkirk, Elisabeth (2002), ‘Contrastive FOCUS vs. presentational focus: prosodic evidence from right node raising in English’. In Bernard Bel and Isabel Marlein (eds.), Speech Prosody-2002. Laboratoire Parole et Langage. Aix-en-Provence. 643–646. Shan, Chung-chieh (2004), ‘Binding alongside Hamblin alternatives calls for variable-free semantics’. In Kazuha Watanabe and Robert Young (eds.), Proceedings of Semantics and Linguistic Theory XIV. CLC Publications. Ithaca, NY. 289–304. Simons, Mandy (2001), ‘On the conversational basis of some presuppositions’.

Journal of Semantics 27: 81–118 doi:10.1093/jos/ffp010 Advance Access publication September 15, 2009

On Reacting to Assertions and Polar Questions DONKA F. FARKAS University of California Santa Cruz KIM B. BRUCE Pomona College

The aim of this paper is to capture the similarities and differences between assertions and polar questions so as to be able to account for the systematic partial overlap that exists in reactions to these speech acts in English and beyond. We first discuss the discourse components we assume and then define default assertions and default polar questions in a way that allows us to characterize two types of responses to these speech acts, confirming and reversing reactions. The common characteristics of assertions and polar questions are responsible for the fact that both allow these reactions; the differences between the two speech acts explain the different contextual effects confirming and reversing moves have depending on whether they react to an assertion or a polar question. We then examine the distribution of a set of ‘polarity’ particles in Romanian in terms of the notions defined in the rest of the paper and end with a series of predictions concerning polarity particles across languages.

1 INTRODUCTION Our aim here is to explain the systematic similarities and contrasts between a particular class of reactions to assertions and polar questions. We start, in section 2, by laying out the context structure we use in the rest of the paper and then turn in section 3 to a characterization of assertions and polar questions against this background. In section 4, we explore a special type of reactions to assertions and polar questions that exhibits the partial overlap we are interested in capturing. In section 5, we study the distribution of a set of particles occurring in a subtype of such reactions and then conclude. In the rest of this section, we provide an introduction to the issues the paper engages with. One of the cornerstones of work on discourse structure is Stalnaker (1978), where it is suggested that discourse unfolds against an everchanging background made up of a set of propositions already confirmed by the discourse participants, the common ground (cg), whose The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected].


Abstract

82 Assertions and Polar Questions

(1) Anne: Sam’s home. Ben: Yeah, he is./No, he isn’t./Why do you think so? Earlier, as well as very recent, work (see, for instance, Hamblin 1971; Gunlogson 2001) has stressed the role of public individual commitments in discourse. According to Gunlogson (2001), the main effect of uttering a declarative sentence with falling intonation is to add its propositional content to the speaker’s list of public commitments. This view, we claim, goes too far in neglecting the fact that such speech acts also steer the conversation towards turning the content of the declarative sentence into a shared or joint commitment. The context components we adopt here allow us to capture both the commitment publicizing and the proposal nature of default assertions. As we will see below, in contrast with assertions, default polar questions do not register author commitment. They propose to add to the cg either the denotation of their sentence radical or its complement. The fact that assertions project the addition of a proposition to the cg is crucial to the empirical focus of our work, namely capturing the similarities and differences between reactions to assertions and reactions to polar questions. This is an issue that has not received the attention it

1

Note that Stalnaker’s cg corresponds to grounding at level 4 in Clark & Schaefer (1989) and Clark (1992). For recent discussion of matters pertaining to grounding at lower levels, see Ginzburg (forthcoming). 2 A large amount of work since Stalnaker (1978) has been devoted to the need to refine the notion of context so as to get to the level of discourse referents. The issues we are dealing with here are not relevant to these concerns and therefore they will be ignored below.


intersection is the context set (cs). In what follows, we adopt this view of the cg.1 The essential effect of assertions on the context in which they are made, according to Stalnaker, is to add the content of the assertion to the cg, ‘provided’, Stalnaker adds, ‘that there are no objections from the other participants in the conversation’. Assertion, in this view, is a proposal to change the context by adding the propositional content of the asserted sentence to the cg.2 We follow Clark & Schaefer (1989), Clark (1992) and Ginzburg (1996, forthcoming), among many others, in emphasizing the proposal nature of assertion, an aspect that Stalnaker himself does not stress. Characterizing ordinary assertion as proposing additions to the cg, rather than actually changing it, is necessary in order to make room for the large variety of conversational moves that react to assertions signalling, for instance, confirmation, rejection or the need for further discussion, as exemplified in (1):

Donka F. Farkas and Kim B. Bruce 83

deserves. The overlap between the two types of reactions is illustrated in (2): (2) Anne: Sam is home. Ben: Yes/Yeah, he’s home./No, he isn’t home. (3) Anne: Is Sam home? Ben: Yes/Yeah, he’s home./No, he isn’t home.

(4) Ana: Horea e acasa˘? ‘Is Horea home?’ Petru: Nu, nu e./*Ba nu, nu e. ‘No, he isn’t.’ (5) Ana: Horea e acasa˘. ‘Horea is home.’ Petru: Nu, nu e./Ba nu, nu e. ‘No, he isn’t.’ We return to these particles in section 5.3 3 As noted by an anonymous reviewer, a further difference between default assertions and default polar questions is that reactions such as ‘You are right/You are wrong’ and their equivalents in other languages are possible after the former but not the latter. Such reactions can only follow moves that add a commitment to their author’s list, which assertions do but default polar questions do not.


On the differences side, we argue that Ben’s negative reaction in (2) creates a ‘conversational crisis’, while his negative reaction in (3) does not. Anne’s contributions in (2) and (3) raise the issue of Sam’s whereabouts; in (2), but not (3), she also adds the proposition denoted by ‘Sam is home’ to her public commitments. At the root of the conversational crisis brought about by Ben’s second reaction in (2) are the following two assumptions: (i) conversational changes that result in addition to commitments are less marked than those that result in the retraction of such commitments and (ii) raising an issue steers the conversation towards a state where the issue is resolved. Now in (3), Anne can go on to accept either one of Ben’s responses without further ado, thus reaching a conversational state in which the issue is resolved by the addition of a proposition to the cg. In (2), on the other hand, after Ben’s negative reaction the issue of Sam’s whereabouts can be settled only after either Ben or Anne retracts a commitment. Ben’s negative reaction in (3) then is more dramatic than in (2) because it takes the conversation to a state from which reaching the canonical future of settling the issue raised by Anne can be reached only via a non-canonical move of commitment retraction. The difference between the contextual effect of contradicting an assertion and giving the ‘opposite’ answer to a polar question affects their formal properties as well. We illustrate the difference with Romanian, where the particle ba is possible when contradicting a positive assertion but not in a negative answer to a positive question:


We have briefly illustrated here that there are significant parallelisms between reactions to assertions and reactions to polar questions but that the two diverge as well. Our main goal in this paper is to capture this partial overlap. While reaching it we also have to differentiate between initiating assertions (exemplified by Anne’s conversational contributions above) and ‘reactive’ assertions (exemplified by Ben’s contributions) in a way that allows us to account for the distribution of particles such as yes and no and their relatives in other languages. But first we turn in section 2 to the context components we work with.

In this section, we present a model of context structure that combines features of earlier proposals, especially those in Ginzburg (1996, forthcoming), Gunlogson (2001) and Asher & Lascarides (2003), within the tradition of foundational work by Hamblin (1971), Stalnaker (1978) and Carlson (1983). Since our focus is to capture the similarities and differences between assertions and polar questions, we do not go beyond those elements of context structure that are necessary for our task. An essential component of models of context, acknowledged since the earliest works on the topic, is the representation of the discourse commitments of participants. We assume here that discourse commitments are propositions (i.e. sets of worlds) publicly taken by the participants in a conversation as being true of the world of the conversation, from the perspective of the conversation. (See, for instance, Sacks 1992.)4 A much debated issue is how to relate discourse commitments to participants. Stalnaker (1978) assumes a single set of shared public commitments, the cg. In Hamblin (1971) and Gunlogson (2001), on the other hand, each participant is associated with a set of discourse commitments. Gunlogson (2001) defines the common ground as an ancillary notion made up of the union of the participants’ commitment sets. Stalnaker’s cg can be defined as the intersection of these sets. In Ginzburg’s work, there is a common ground, called FACTS, as well as a dialogue game board containing both public and private aspects associated with each participant in the conversation. In Asher & Lascarides (2003), each participant is associated with a segmented discourse representation structure that represents their cognitive state. The common ground in Asher & Lascarides (2003) is reconstructed via 4 Note also that in the sense in which we use the term discourse commitment, participants can only be committed to propositions and not to ‘issues’ or ‘questions’.


2 CONTEXT COMPONENTS


5 This relation is more general than the Stalnakerian cg because ‘settled’ contents include not only agreed upon propositions but also questions participants are committed to supplying an answer to as well as requests they are publicly committed to carrying out. For recent refinements of the view of Asher and Lascarides, see Asher & Lascarides (2008) and Lascarides & Asher (2008).


a relation, called ‘settled’, defined between a content and a discourse structure.5 We present here a model that separates a Stalnakerian cg from the discourse commitment set of each participant. The discourse commitment set of a participant A at a time t in a conversation c contains those propositions A has publicly committed to in the course of c up to t and which have not (yet) become mutual commitments. The cg, on the other hand, is that set of propositions that have been agreed upon by all participants in c at t together with the propositions that represent the shared background knowledge of the discourse participants. Having the cg as a separate component allows us to capture what Stalnaker takes the crucial effect of assertions to be, namely, that of proposing to add the propositional content of the asserted sentence to the cg. This aspect of ordinary assertive speech acts allows us to explain the fact that assertion acceptance is a default move, while assertion contradiction or denial is not. It also allows us to explain the existence of conversational pressure in the direction of increasing the cg by turning publicized commitments into joint commitments. Without such pressure, the collaborative principle of Walker (1996) would remain mysterious. This principle requires participants to provide evidence of detected ‘discrepancy in belief ’ as soon as possible in a conversation. Were it not for the drive to build a cg, discrepancy in publicized belief would not be problematic, and thus in no special need of being signalled. Commitment sets (whether the cg or individual commitment sets) can be upgraded or downgraded. The former change, we take it, is more canonical than the latter. See again Walker (1996), who assumes the existence of a default rule that makes beliefs persistent. In our terms, this means that addition is a canonical change to a commitment set, while retraction is not. More concretely, we assume that a discourse structure K contains a (possibly empty) set of propositions DCX for each participant X in the conversation, made up of those propositions that X has publicly committed to during the conversation up to the relevant time, and which are not shared by all the other participants. In addition, K contains a set of propositions, the cg, whose elements are those propositions that have been confirmed by all participants in the conversation as well as



a set of background propositions. The total discourse commitment of a discourse participant X is DCX [ cg. By default, the set of total discourse commitments of a participant is taken to be a subset of her doxastic base (cf. Grice’s quality maxim). Discourse commitments are not required to be correct, and therefore they need not be in fact true of the world in which the conversation takes place, but from the perspective of the conversation, they are assumed to be correct. Because of this assumption, a discourse participant is coherent iff her total discourse commitments are consistent and a discourse whose cg is inconsistent is in crisis. Separating participants’ discourse commitments from the cg is essential in accounting for disagreements in ordinary discourses. One way a discourse may survive denial, for instance, is when participants agree to disagree. Leaving the details for section 4, assume now that A has committed to p during a conversation with B, while B has committed to :p and that A and B have agreed to disagree on p. The state of the discourse in this case should record A’s commitment to p and B’s commitment to :p but neither p nor :p should be in the cg. In our model, in such a case p will be an element of DCA, :p will be an element of DCB and neither p nor :p will be an element of the cg. Thus, it is possible to have a conversation state with a consistent cg and coherent participants even though DCA [ DCB is not consistent. This, we take it, is a welcome result. Note also that the level that counts for purposes of presupposition satisfaction in such cases is the cg rather than either of the participants’ commitment set. Thus, after having agreed to disagree on whether Sam is home, it would be infelicitous for A to say ‘Since Sam is home, the children are not alone’ even if A has previously committed to Sam being home. We follow the literature, and especially Ginzburg (1996), Roberts (1996) and Bu¨ring (2003) in having a discourse component that records the Questions Under Discussion (Ginzburg’s QUD). We rechristen it ‘the Table’ and assume that the items on it are syntactic objects paired with their denotations. Having syntactic objects on the Table is needed because a grammar of cross-turn conversation and ellipsis has to have access to the grammatical form (and not just the content) of immediately previous utterances. For instance, in many languages polar questions can be answered by repeating the main verb of the question with the same or the reverse polarity. Access to the morphosyntax of the question is needed to account for the form of these ‘fragment answers’ independently of the finer details of their treatment. Given what was just said, asserting a sentence such as ‘Sam is home’ makes a different contribution to the Table from asking the question ‘Is Sam


6 Ginzburg (1995, forthcoming) prefers a partial order, but we have no need for the extra flexibility in the simple examples handled here. 7 In order to render these definitions precise, one needs to give an underlying logic and semantics that defines when a proposition follows from a set of propositions. Simply assuming that a proposition follows from a set of propositions if the intersection of the latter is a subset of the former is too course-grained for our purposes since in that case all logically necessary propositions would count as decided in all conversations. In this paper, we focus on the context structures needed to represent discourse states and simply assume that such an underlying logic and semantics exists. What we propose here is consistent with the logic in Asher & Lascarides (2003) and Asher & Lascarides (2008).


home?’ since the former adds a declarative sentence, while the latter adds an interrogative one. For simplicity, we assume that the items on the Table form a stack.6 The Table records what is ‘at issue’ in the conversation. When the Table is not empty, the immediate goal of the conversation is to empty it, that is, to settle the issue at hand. The stack discipline allows us to capture the tight connection between initiating conversational moves, such as an initiating assertion or question, and responding moves that address the issue an immediately preceding utterance has placed on the Table, a matter we come back to in section 4. Finally, having the Table as a separate component allows us to differentiate between context states that can serve as natural end points of a discourse and states that cannot. As long as there are items on the Table, there are issues that need to be dealt with. A conversation is in a stable state when its Table is empty; a conversation is at a natural end point only when it is stable. We assume that two fundamental engines that drive conversations are the need to increase the cg and the need to reach a stable state. The former drives participants to place items on the Table; the latter drives them to take the necessary steps to remove these items in such a way as to increase the cg. A novelty of our approach is that we attempt to capture these twin goals by assuming that every conversational move that places an item on the Table is associated with a canonical way of removing that item from the Table. The canonical way of removing an issue from the Table is to reach a discourse state in which the issue is decided. A proposition p is decided relative to a common ground cg if and only if p follows from the cg or if :p follows from the cg. If a proposition p is decided relative to the common ground cgK of a conversational state K, p is decided in K.7 More specifically, we assume that a conversational move that places an item on the Table simultaneously projects a set of future common grounds relative to which the issue on the Table is decided. These projected sets are supersets of the current cg. We call these privileged


8 Our ps is different from the projection set of Gunlogson (2001), which contains all non-empty subsets of the current context set. 9 Our canonical Table-emptying operations correspond to Ginzburg’s operations that downgrade QUD and upgrade the FACTS once a resolution of the issue on the Table has been agreed upon.


future common grounds the ‘projected set’ (ps) and represent them in a separate component. As we see in detail in section 3, an assertion projects confirmation in that it projects a future common ground that includes the asserted proposition. A question projects resolution in the sense that it projects a set of future common grounds arrived at by adding to each common ground in the input ps each (contextually) possible answer to the question. Assertions and questions are similar in that their effect on the ps is to add their denotations to the elements of the input ps. They differ in that for assertions, only one proposition is added and therefore only one resolution is projected, while in the case of questions one adds a non-singleton set of propositions, thus projecting a non-singleton set of resolutions. When the Table is empty, the ps contains the current cg as its only element. When the Table is not empty, the elements of the ps are computed based on what is on the Table.8 The ps assumes a central role in our view because it is at this level that the anticipatory nature of certain conversational moves is captured. In this respect, we differ from most previous work where the fact that moves may steer conversations towards particular privileged futures is not directly represented in the conversational state. Thus, in the work of Asher and Lascarides, for instance, a move affects the future of the conversation only insofar as future moves must find a possible rhetorical relation that attaches them to it. This is different from but compatible with our proposal. We distinguish privileged future states that particular conversational moves direct the conversation towards. An assertion may be contradicted, confirmed, called into question, elaborated on or corrected. Out of all possible reactions, we capture the special nature of confirmation by assuming that this is what is projected at the ps level. Similarly, resolution is only one of the many possible ways in which one can react to a question. We treat resolution as the privileged future projected by raising the question. Thus, in our view, moves that place items on the Table intrinsically define a conversational goal state (or set of such states) reached when the item in question is removed from the Table in a way that maximally increases the cg.9 We use the ps in characterizing what A’s proposal is when she makes her assertion, as well as what the questioner directs the conversation towards when he asks his question. Furthermore, the ps allows us to import the insights of earlier work on the context change


(6)

Sample context structure A

Table

DCA

S

Common Ground cg

B DCB

Projected Set ps

Here DCA and DCB are the propositions A and B have individually publicly committed to and which are not joint commitments. The cg is the set of propositions that are joint commitments of the participants. The contents of the Table, S, are items that are still under discussion, while the ps is a set of common grounds that reflects canonical ways of settling the issues on the Table. Before turning to assertions and polar questions, we define here the notation we use throughout the rest of the paper. The Table T in


of assertions and questions, but, instead of performing these changes at the level of the cg (or its intersection, the context set), we perform them at the level of the ps. We take it that a conversation is in crisis if its cg is inconsistent or if all the sets in its ps are inconsistent. Requiring consistency of the cg is a consequence of the assumption that the propositions in the cg are assumed, for the purposes of the conversation, to be true of the world in which the conversation takes place. Having at least one consistent set in the ps means that there are canonical moves that lead to emptying the Table while at the same time reaching a consistent cg. For the matters we discuss here, further additions to context structure such as the agendas of participants or representations of their private doxastic states are not necessary. The model we provide is consistent with expansion in these directions, as well as with additions of finer-grained structures for dealing with anaphoric relations. Finally, we note that the information we do represent is redundant for the examples we discuss. In particular, the contents of the ps can always be calculated from the current cg and the items on the Table. We nevertheless include it in our representation for the sake of clarity and for emphasizing similarities between what we propose and previous approaches. We represent the context K of a conversation between two participants A and B in diagrams of the form below:


a context structure is represented as a stack. The following notation is used to represent traditional stack operations on T: 1. 2. 3. 4.

push(e, T) represents the new stack obtained by adding item e to the top of the stack T. pop(T) represents the stack obtained by popping off the top item of T. top(T) represents the top item of the stack T. remove(e, T) represents the stack obtained by removing the topmost occurrence of e from stack T. If e does not occur in T, then T is returned.

3 DEFAULT ASSERTIONS AND DEFAULT POLAR QUESTIONS In this section, we characterize default assertions and default polar questions in order to be able to capture the details of their similarities and differences. We take it that any approach that cannot capture these similarities and differences cannot explain why there is overlap in the range of reactions to them and why this overlap is only partial.

3.1 Default assertions We assume, following a large body of literature, that it is useful to include assertions in the repertory of speech acts one defines. Obviously, there are many subtypes of assertions, and the complex issue of drawing their typology is not within our aims. We take it that a default assertion is performed when a participant X utters a declarative sentence S with falling intonation. Some assertions are non-default


Lastly, let ps ¼ fcg1, . . ., cgng be a collection of sets of propositions (e.g. possible common grounds) and let P ¼ fp1, . . ., pmg be a set of P ¼ fcgi [ fpj g j1 < i < n; 1 < j propositions. Then define ps [ < mg fcg#jcg# is inconsistentg. Thus, the result of the operation P is to create a new collection of sets of propositions, where ps [ each new set is formed by adding one of the elements of P to an existing cgi. At the end, any new set that is inconsistent is discarded. Finally, we also assume an operator that rebuilds the projected set ps from the current cg and the contents of the Table T by iteratively performing the ps changes associated with each item on the Table. This operation is needed after a non-canonical conversational move is made, such as retracting an assertion, agreeing to disagree or withdrawing a question. The definition of the move is straightforward and omitted here.


(7)

K1: Initial context state A

Table

B

Projected Set ps1 ¼ fs1g

Common Ground s1

Suppose now that A asserts the sentence ‘Sam is home’, with propositional content p against input context K1. The main effects of A’s assertive move are the following: (i) p is added to DCA; (ii) the syntactic structure representing this sentence and its denotation, fpg, are entered on the top of the Table stack; (iii) confirmation is projected at the level of ps by adding p to each element of the input ps. The output context state K2 after A’s move is given in (8): (8)

K2: A asserted ‘Sam is home’ relative to K1 A p

Table

B

Æ‘Sam is home’[D];fpgæ

Common Ground s2 ¼ s1

Projected Set ps2 ¼ fs1 [ fpgg


even if they conform to this characterization if they place specific demands on the input context. We discuss one such non-default assertion type in section 5. Other non-default assertions, which are not addressed here, are ‘rising declaratives’ as well as assertions followed by interrogative tags. We assume that declarative and interrogative sentences are distinguished by the sentential features [D] and [I], respectively. We treat these features as sentential markers because it is crucial to what follows for the sentence radical to which they attach to be accessible in subsequent discourse. Furthermore, we assume, in line with Hamblin (1971), that the denotation of a declarative sentence S[D] is the singleton set containing the proposition denoted by its sentence radical. Let us begin with the simple context state K1 given in (7) in which the discourse commitment lists of the two participants, A and B, are empty, and so is the Table. The ps of K1 includes only s1, the initial common ground at the start of the conversation.


(9) A(S[D], a, Ki) ¼ Ko such that (i) DCa,o ¼ DCa,i [ fpg (ii) To ¼ push(ÆS[D];fpgæ, Ti) (iii) pso ¼ psi [ p (Those elements of Ko that are unaffected by the move have not been listed.) The change in (i) is common to all types of assertions, default or not. The other two are part of all assertion types we discuss here as well except for an assertion that simply confirms a previous assertion, in which case these two changes are fully redundant. A default assertion then commits its author to the propositional content of the asserted sentence, it raises an issue by placing an item on the Table and it directs the conversation towards a unique resolution of that issue, namely, confirmation of the assertion. The ‘issue’ is the denotation of the sentence radical added to the Table in the course of the assertion. Given the effect of default assertions on their author’s discourse commitment list and on the ps, an assertion yields an output context that is categorically biased in favour of confirmation of the asserted proposition. The changes A brings about echo those in Poesio & Traum (1998), where an assertion is defined as committing the speaker to the belief in its propositional content, while simultaneously attempting to get the addressee to believe that content as well. The main difference is that we are considering here changes triggered by particular linguistic forms that target particular conversational components, and thus, they are


The cg of the output context, K2, is the same as that of the input context, K1. The change involves the author’s discourse commitment list, the Table and, consequently, the ps. Further conversational moves must now attend to the item on the top of the Table stack and eventually remove it from there in order to reach a stable state. The privileged future state projected by the assertion act is one whose cg is updated with the asserted proposition. Projected confirmation, registered at the level of the ps, is the conversational goal an assertion steers the conversation towards. We follow Krifka (2001) (see also Ginzburg forthcoming) in assuming that there are speech act operators that take sentences as arguments and that are functions from input context states to output context states. We define the default assertion operator A as a function from an input context Ki to an output context Ko, as in (9), where a is the author of the assertion, DCa,o and DCa,i are a’s output and input context discourse commitments and To and Ti are the output and input Table, respectively:


10 Ginzburg (forthcoming), entertains both the possibility of assertions always raising an issue and the possibility of their doing so only in case the interlocutors do not immediately confirm it.


independent of participants’ actual beliefs and intentions. The author of a default assertion may in fact aim at provoking her interlocutor to contradict her, or she may simply wish to publicize a commitment or, more radically, she might be in cahoots with her interlocutor and aim at misleading an eavesdropper or have other complex agendas. Here, we are interested in those conversational effects that are constant across all these situations and which, in our view, are connected to sentence form, prosodical properties and the input conversation state. We thus define speech acts in terms of their Heimean context change potential rather than in terms of the actual intentions of speakers. We follow here Stalnaker’s suggestion that a side effect of any speech act is to register in the common ground the fact that the speech act in question has occurred. Consequently, as a side effect of an assertion the common ground is automatically updated with the proposition that the author of the assertion has made the assertion. We will ignore this secondary effect of speech acts in what follows. For Stalnaker, the essential context change associated with assertions is the addition of p to the common ground. The parallel change for us is the addition of p to the elements of the ps. Not changing the current common ground directly leaves room for moves that react to assertions, moves that have been long recognized and discussed in the literature on dialogue. Our view that assertions raise an issue by entering an item on the Table follows earlier proposals and is closest to Ginzburg’s. For us, just as for Ginzburg, asserting a sentence with propositional content p raises the issue of whether p.10 In our approach, however, it does so in a way that differs significantly from how the issue is raised when the corresponding polar question is asked, as we will see shortly. The addition of the asserted proposition to the author’s discourse commitment list is the essential feature of declarative updates in Gunlogson (2001), which we import here. Assertions project confirmation, and therefore the move of confirming an assertion is the least marked next discourse move. The ability of separating confirmation from all other possible moves that follow a default assertion is a feature we exploit below in capturing differences between reactions to assertions and reactions to polar questions. Note that what we call here default assertions may initiate a discourse but they may also connect to previous discourse by a variety


3.2 Default polar questions In this section, we consider how the context changes when a polar question speech act is performed, that is, when a speaker utters a polar interrogative sentence such as (10): (10) Is Sam home? Syntactically, we represent polar interrogatives as S[I] and assume that S and its denotation, p, are available for discourse manipulation. The denotation of S[I] is fp, :pg.11 When a participant A asks a polar question S[I], where S denotes p, A raises the issue whether p by placing on the conversational Table the interrogative sentence and its denotation, namely fp, :pg. Placing a question on the Table steers the conversation towards a state in which the question is resolved. For us, this means that the effect of asking a question on the input ps is to add to each of its elements each of the elements in the denotation of the question. Note that the effect of assertions and questions on the Table and on the ps is identical in the sense that in both cases a sentence and its denotation are added to the Table and each element of the denotation 11 Following Karttunen (1977) we assume that the denotation of an interrogative sentence is the set of its complete answers.


of rhetorical relations of the type that form the focus of Asher & Lascarides (2003), such as elaboration or counterevidence. The view of assertion given above is compatible with their participating in these rhetorical relations but the details of how that happens are not within the scope of this paper. Note that the veridicality of assertions, a property that is crucial in Asher & Reese (2007), follows from the first and third change in (9) above. Finally, let us note that assertions, as well as questions and other speech acts, are associated not only with literal content but with implicated content as well. We suggest that implicated content is added on the Table conjoined with but separated from the literal content making it possible for further moves to react to both implicated and literal content. One difference between the two types of content is that only literal content is associated with syntactic material on the Table, and therefore we predict differences between them when it comes to discourse ellipsis. In what follows, we are concerned with literal content only. Leaving our discourse in suspense for now with respect to whether Sam is home, we turn in section 3.2 to polar questions.


of the sentence is added to each element of the input ps. The differences follow from the fact that the denotation of the declarative sentence is a singleton set while that of an interrogative is not (cf. Hamblin 1971; Groenendijk 2003). Assuming that in the input context state both the Table and the participants’ discourse commitment lists are empty, as in (7), the context state after asking the polar interrogative sentence ‘Is Sam home’? is as illustrated in (11):12 (11) K4: ‘Is Sam home?’ was asked relative to the initial input context K1 Table

B

Æ‘Sam is home’[I]; fp, :pgæ Common Ground s1

Projected Set ps1 ¼ fs1 [ fpg, s1 [ f:pgg

We define the polar question operator PQ as in (12), where S[I] is a polar interrogative sentence and where p is the denotation of S: (12) Polar question operator (PQ) PQ(S[I], Ki) ¼ Ko such that (i) To ¼ push(ÆS[I];fp, :pgæ, Ti) p; :p (ii) pso ¼ psi [ The context state after a default polar question is inquisitive with respect to the denotation of the sentence radical the move has placed on the Table because the ps contains both future common grounds to which p was added and future common grounds to which :p was added. The most immediate way in which such an inquisitive context is returned to a stable state is by the addressee providing a complete direct answer to the question followed by a confirmation of this answer by the participants in the conversation, which in turn leads to the addition of the answer to the cg. If this happens, the common ground of the conversation becomes one of the common grounds projected by the question.

12 Our discourse structures do not keep track of who placed a particular item on the Table because nothing we discuss here is sensitive to this aspect. Adding such a mechanism would not cause any problems we are aware of. Similarly, adding information with respect to who acts as source for a commitment, as argued for in Gunlogson (2008), is perfectly compatible with our proposals.


A


(13) Isn’t Sam home? The issue of question bias is much debated in the literature (see, for instance, van Rooy & Safarova 2003; Romero & Han 2004, and references therein). We cannot add anything substantive to this debate and will not deal with external negation questions here.13 Note that the two speech acts we are concerned with in this paper contrast in both whether they affect author commitment and how they affect the ps. Default assertions add to author commitment and project a non-inquisitive ps. Default polar questions do not add to author commitment and project an inquisitive ps. Non-default assertions and non-default polar questions can depart from their default counterparts in either property. In order to characterize the many types of special assertions and questions and their hybrids, further finer distinctions are needed. The most often discussed non-default questions are those involving some type of bias. Here, we mention another non-default question, special in that it indicates that settling the issue is not necessarily a projected conversational future and therefore that answering the question is optional. In Romanian, such questions are signalled by the presence of the particle oare: (14) Oare Petru a sosit deja? oare Peter has arrived already Has Peter arrived already? 13 We assume that questions that introduce strong bias are non-default. We come back to weak bias involved in positive and in inner negation polar questions in section 4.2.


Conversational moves following a (polar) question then have to attend to getting the question removed from the Table. The goal of the conversation after the registering of the question is to resolve it by reaching a conversational state whose common ground is an element in the current ps. Default polar questions are non-biasing in the sense that they do not commit their author to either proposition in their denotation and project an inquisitive context with respect to their sentence radical. There are, however, non-default polar questions that are not impartial. In English, polar interrogatives involving external negation, as exemplified in (13), have been treated as involving some sort of preexisting bias on the part of the questioner in favour of the proposition in the scope of the negative operator, that is, in this case, in favour of Sam being, in fact, at home.


(15) Is Sam not home? has the same effect on the ps as its positive counterpart. It differs from it, however, in that it places a negative rather than a positive sentence on the Table. Pragmatic differences between positive and negative polar questions as well as differences in the way they can be answered are connected, in our view, to the difference in the contribution the two types of questions make to the Table without having to give up the uniform account of the denotation of affirmative and negative questions. To sum up, the major differences between default assertions and default (polar) questions under the view presented above are (i) default assertions upgrade their author’s commitment list while default (polar) questions do not; (ii) default assertions enter a declarative sentence on the Table, while polar questions enter an interrogative sentence; (iii) at the level of the ps, default assertions result in a non-inquisitive context, whereas default questions result in an inquisitive one. The major similarity between asserting a sentence S[D] and asking the corresponding polar question by uttering S[I] is that the same sentence radical, S, is placed on the Table. The major difference between S[D] and S[I] is that the denotation of a former is a singleton and that of the latter is not. In both cases, the sentence radical is decided relative to each element of the output ps. Reactions to these two speech acts, we predict, will be sensitive to this common denominator as well as to the differences involved. These predictions are explored in the rest of the paper.


We can accommodate oare questions in our system by assuming that the output ps includes not only projected common grounds in which the question is decided but also a copy of the elements of the input ps, thereby indicating that not answering the question is one of the projected discourse futures. Such questions are special in that for them removal from the Table without change in the current cg is a projected option. Our characterization correctly predicts that oare questions are not appropriate on forms, as exam questions or as questions asked in court or by a policeman. Before concluding, we mention a welcome consequence of our approach to polar questions. Having the uttered sentence entered on the Table allows us to differentiate between positive and negative polar questions while at the same time assigning them the same denotation. An (inner negation) negative polar question such as:


4 REACTING TO DEFAULT ASSERTIONS AND DEFAULT POLAR QUESTIONS A default assertion and a corresponding polar question (our ‘Sam is home’ and ‘Is Sam home?’ examples) raise the same issue: that of deciding the status of the proposition expressed by the sentence radical they place on the Table. In this section, we characterize two main conversational move types that deal head on with the issue raised, confirmation and reversal. This sets the stage for the discussion of responding assertions and polarity particles in section 5.

Let us turn back to the aftermath of an assertion and assume that the current context state is as in (8). The least marked reaction to an assertion is confirmation, a move that commits its author to the propositional content of the sentence on the Table. We define in (16) an explicit assertion confirmation operator, AC, as a function from an input context Ki to an output context Ko. S[D] is a declarative sentence with denotation fpg that has been asserted by some discourse participant a in a previous move and is currently at the top of the Table, as well as on a’s commitment list in Ki. Let b be the participant confirming the assertion and let DCb,o and DCb,i stand for b’s discourse commitments in the output and input context states, respectively. (16) Assertion Confirmation (AC) a. Input context conditions: (i) top(Ti) ¼ ÆS[D]; fpgæ (ii) p in DCa,i b. Change: AC(b, Ki) ¼ Ko where DCb,o ¼ DCb,i [ fpg The fact that p is an element of some discourse commitment list follows from S[D] being on the Table. If the author of the confirmation is the same participant as the author of the assertion he is confirming, the confirmation move is informationally redundant. Such a redundant move may be used for adding emphasis or for other rhetorical purposes. After all participants in a conversation confirm an assertion, p, the proposition denoted by the asserted sentence radical is present on the commitment list of each participant. We assume that in this case an auxiliary move M# applies, whose effects are given in (17).


4.1 Confirming and reversing an assertion


(17) Common ground increasing operation M# If an operator M contains a change of the form DCX,o ¼ DCX,i [ fpg, and, as a result, p is now present on the commitment list of each participant in the conversation in Ko, add the following changes to M: 1. cgo# ¼ cgi [ fpg, 2. DCX,o# ¼ DCX, o – fpg for all participants X. 3. Pop off of the top of the Table all items that have as an element of their denotation an item q that is entailed by cgo#.

(18) Anne: Sam’s home. Ben: Yes, he is. We call the type of assertion exemplified in Ben’s utterance above a responding assertion and we discuss it in detail in section 5. There are many other ways of indicating assertion confirmation, some of which involve implicature. (For discussion, see Walker 1996.) Note that assertion confirmation may be left unsignalled altogether. This is, we claim, unsurprising given the default nature of the move, under the natural assumption that the more canonical a move is the less overt marking it needs.14 In what follows, we only deal with overt assertion confirmation moves.

14 While silence can be taken as assertion confirmation, we do not suggest that its overall impact is identical to that of a responding assertion or some other overt confirmation marker. Confirmation by failure to object is the weakest possible way of signalling conversational commitment. Silence can be seen as implicating confirmation based on Walker’s collaborative principle.


M# adds the proposition that is present on each commitment list to the cg and removes it from individual commitment lists. We assume that if any of the propositions in the denotation of an item on the Table are decided relative to the cg of the conversation, that item is popped off from the Table, and therefore items from the Table that are decided as a result of the addition of p to the cg are popped off from the Table as part of M#. Confirmation is the default reaction to an assertion because the change it performs is a necessary step towards reaching the cg projected by the assertion and thus canonically settling the issue raised. Assertion confirmation can be signalled in a variety of linguistic and nonlinguistic ways. One can nod, say uh huh, sure, right, you bet, yup, etc. One can also express assertion confirmation by reasserting the asserted proposition, as in (18), using a more or less truncated form.


Finally, note that what was said so far distinguishes between the three assertions in the short conversation in (19), even though they are identical with respect to their propositional content: (19) Anne: Sam is home. Ben: Yes, he is. Anne: (Yes,) Sam is home.

(20) Anne: Mary ordered chicken yesterday. Ben: No, she didn’t./No, it was beef. We follow van der Sandt & Maier (2003) in taking denials to be special conversational moves that commit their author to the complement of the denotation of a declarative sentence placed on the Table by the preceding move. Denials are highly marked and therefore they must be explicit and must be signalled, Walker (1996) argues, as early as possible. As already mentioned in section 1, denials are marked moves in our terms because the proposition the author of a denial commits to cannot become a joint commitment in a coherent discourse without retraction on the part of another participant, and therefore the issue placed on the Table by the initial assertion cannot be removed in a canonical way. We restrict our attention here to denials expressed by an assertion, as in the examples above. Ben’s two moves are assertions, that is, they commit their author to the proposition denoted by the asserted sentence, call it p#, and they place that sentence and its denotation on the Table. The special nature of these assertive moves resides in the fact that they react to a previous assertion whose propositional content is


Assuming that Anne’s first assertion occurs in a context in which Sam’s whereabouts were not yet discussed, it raises the issue of whether Sam is home or not and commits Anne to the claim that he is. Ben’s assertion signals confirmation, a non-redundant move; the proposition expressed by ‘Sam is home’ is now on Ben’s commitment list as well. If this is a dialogue between Anne and Ben, the issue is resolved and M# applies. Anne’s second assertion, on the other hand, is redundant. It recommits Anne to a proposition she just committed herself to and, if not a reactive move, it raises an issue that has just been settled. Assertion confirmation decides the issue raised by an assertion as far as the author of the confirmation is concerned, in the direction of the proposal made by the original assertive move. Another way of deciding the issue for the author of the reactive move is to reverse the asserted proposition in toto or partially. We call assertion reversing moves total or partial denial. A total denial is exemplified by Ben’s first reaction; his second illustrates partial denial:


(21) K4: Denial on the Table A p

Table ÆS[D];fpgæ

B :p

Æ:S[D];f:pgæ Common Ground s4 ¼ s2

Projected Set ps4 ¼ ;

Denial moves may be performed by assertions, as was the case in our example, or by various reversing markers such as no way, definitely not, etc. Denying responding assertions, exemplified by Ben’s assertion above will be examined in detail in section 4.2. We define below a total denial assertive move as one that reacts to a previous move whereby p was asserted and which asserts a sentence S# whose propositional content is :p. (22) Total Denial (TD) a. Input context conditions: (i) top(Ti) ¼ ÆS[D]; fpgæ (ii) p in DCa,i b. Change: (i) TD(b, Ki) ¼ Ko where DCb ¼ DCa [ f:pg (ii) To ¼ push(ÆS#[D]; f:pgæ, Ti) When denial does not involve an overt assertion, the changes are the addition of :p to the author’s discourse commitment list and to the Table. 15

See also Asher & Lascarides (2003) for insightful discussion.


inconsistent with p#. The ps of the conversational state that results after they have been made is empty, and the conversation is in crisis. Total denials contradict the previously asserted proposition; partial denials contradict a subpart of what has just been asserted but commit their author to everything else that the previous assertion contributed. As noted by van der Sandt and Maier, partial denials must have access to the totality of the message conveyed by the assertion they react to, its entailments, presuppositions and conversational as well as conventional implicatures.15 We narrow our focus further to total denials. The starkest form of total denial is to assert the opposite of the previously asserted sentence. Such a situation is given in (21), where s2 is the common ground of the discourse state K2 from (8) that served as the output from A’s assertion:


(23) K5: A and B have agreed to disagree relative to K4 A p Common Ground s5 ¼ s4

Table

B :p

Projected Set ps5 ¼ fs5g

The common ground in K5 is identical to the common ground in K4, K3 and even K1, the context state that served as input to the move in which A asserted S[D]. Under the assumption that the common ground, s4, was consistent and that it was consistent with both p and :p, the context state K5 is consistent at every level and therefore the conversation is no longer in crisis, even though the commitment lists of the two participants in K5 are mutually inconsistent. Separating commitment lists from the cg is crucial in capturing the fact that, after a move of agreeing to disagree, the conversation is not in crisis. In future context states, however, in order for A to remain coherent, her public commitments have to be consistent with p, while in order for B to stay coherent, his public commitments have to be consistent with :p. The move of agreeing to disagree requires an input context that has a denial on the top of the Table. The operation it performs is to remove the contradictory items from the Table and reconstruct the ps based on what remains on the Table. Such a move is usually proposed by one of the participants by uttering an imperative such as ‘Let’s agree to disagree/Let’s not pursue this further.’ It is carried out after the other participants agree to comply with the imperative. The imperative in


In the aftermath of a denial, one can eventually reach a stable state in one of two ways: (i) one of the participants retracts their assertion or (ii) the participants ‘agree to disagree’. We deal here only with the latter because it underscores the need to separate participant commitments from the cg, a point we insisted on in section 2. Besides, the complexities raised by retractions go beyond the scope of this paper. Let us assume that A asserted S[D], where S denotes p, and B responded by asserting S#[D], where S# denotes :p. The move of ‘agreeing to disagree’ involves removing ÆS[D]; fpgæ and ÆS#[D]; f:pgæ from the Table without removing either p or :p from the relevant commitment lists. Each participant remains publicly committed to the propositional content of whatever they asserted, but neither p nor :p is added to the cg. The state of the conversation after the move of agreeing to disagree has been carried out in our example as in (23):


this case is special in that compliance with it involves a change in the context state of the conversation.

4.2 Confirming and reversing a polar question

(24) P-Question Confirmation (P-QC) a. Input context condition: top(Ti) ¼ ÆS[I]; fp, :pgæ b. Change: (i) P-QC(b, Ki) ¼ Ko where DCb,o ¼ DCb,i [ fpg, where p is the denotation of S. (ii) To ¼ push(ÆS[D]; fpgæ, Ti) Polar question confirmation is similar to assertion confirmation in that the author of such a move commits to the propositional content of the sentence radical on the Table. Once the other participants in the conversation also commit to this proposition, the issue is decided and M# applies, adding p to the cg, and removing the relevant items from the Table and from the commitment lists of the participants. Therefore, it comes as no surprise that the two types of acceptance moves share responses. In English, polar question confirmation, just as assertion confirmation, can be signalled by nodding, by saying uh huh as well as by assertions that repeat the previous assertion, as exemplified in (25): (25) A: Is Sam home? B: Yes, he is.


Recall that default polar questions, just like assertions, place a sentential issue on the Table. Unlike assertions, however, they do not commit their author to a particular resolution of that issue and they project acceptance of both the denotation of the sentence radical and its complement. After a polar question has been placed on the Table, the canonical way of removing it is by deciding the issue raised. In our example in (11), this means deciding whether Sam is home or not. The most direct way of achieving this is by adding either p or :p to the current cg, where p is the denotation of the sentence radical the polar question has placed on the Table. We address separately these two possible responses, as the distinctions will be useful to us later. We call polar question confirmation the move that reacts to a polar question by committing the author to the propositional content of the sentence radical on the Table. We define it in (24).


When a polar question confirmation move is made by an assertion, the asserted sentence as well as its propositional content is added to the Table. Note that the addition is not redundant in this case because it affects the input ps leading to the elimination of those elements that are inconsistent with the denotation of the sentence radical. Generalizing over assertion confirmation and polar question confirmation, we characterize a type of discourse move we call confirming in (26):

A move is confirming iff it reacts to an immediately previous move that has placed a proposition-denoting sentence radical on the Table, and the move commits its author to that proposition. Both assertion confirmation and polar question confirmation are confirming moves. Assertions that qualify as confirming move types will be called confirming assertions. Confirming a polar question is crucially different from confirming an assertion because in the case of polar questions, confirmation is not the only projected outcome in the input context: reversing is also projected. This, we claim, is responsible for the fact that assertion confirmation can be left completely implicit, while polar question confirmation cannot. Silence after a default polar question cannot be normally taken as confirmation. Note that a polar question confirmation move does not necessarily lead to agreement on the issue at hand between the author of the question and the author of the confirmation move since the former has not publicly committed to either outcome. Such agreement arises only after the author of the polar question confirms the resolution proposed by the author of the confirmation move. Assuming that Anne and Ben are the only participants in the conversation in (25) above, the issue of whether Sam is home will be decided in favour of him being in fact home only after Anne confirms Ben’s assertion. In the most common case, that of information-seeking questions, the questioner is assumed not to know the answer to her question and to assume that the addressee does, and therefore her confirmation of the addressee’s answer is even less marked than in the case of ordinary assertions. Reversing a polar question, just like in the case of reversing an assertion, involves committing to :p, the complement of the


(26) Confirming move type a. Input context condition contains: top(Ti) ¼ item whose sentence radical denotes a proposition p b. Change contains: DCa,o ¼ DCa,i [ fpg


proposition expressed by the sentence radical on the top of the input Table. In the case of polar questions, such a move is not a denial, however, and it does not result in a crisis because a default polar question does not categorically bias the context in favour of one resolution v. another, the way assertion does. Ben’s reactions in (27), therefore, do not result in crisis: (27) Anne: Is Sam home? Ben: No, he isn’t. The move of polar question reversing is defined below:

Generalizing over what is common in moves that reverse assertions and polar questions we define a move type we call reversing as in (29): (29) Reversing move type a. Input context condition contains: top(Ti) ¼ item whose sentence radical denotes a proposition p b. Change contains: DCa,o ¼ DCa,i [ f:pg Reversing moves are reactions to immediately previous moves that place a proposition-denoting sentence radical on the Table and commit their author to the complement of that proposition. Common to denials and polar question reversal is that they are reversing moves. The difference between them is due to the differences in the input context: in the case of denials, the input context is categorically biased in favour of the proposition denoted by the sentence radical on the top of the input Table, while in the case of polar question reversal, this is not so. Assertions that have the property of being reversing moves will be called reversing assertions.16 Confirming moves are formally simpler than reversing moves because the relation they involve is identity rather than 16 We have defined here only total reversal. For partial reversal, we require the author of the move to commit to a proposition that, together with the current cg, is inconsistent with the denotation of the sentence radical on the top of the input Table (or one of its implicatures). Partial reversal can be made directly or by implicature.


(28) P-Question Reversing (P-QR) a. Input context condition: top(Ti) ¼ ÆS[I]; fp, :pgæ b. Change: (i) P-QR(b, Ki) ¼ Ko where DCb,o ¼ DCb,i [ f:pg, where p is the denotation of S. (ii) To ¼ push(Æ:S[D]; f:pgæ, Ti)


(30) Responding move type a. Input context condition contains: top(Ti) ¼ item whose sentence radical denotes a proposition p b. Change contains: DCa,o ¼ DCa,i [ fpg or DCa,o ¼ DCa,i [ f:pg Responding moves commit their author to the denotation of a sentence radical on the Table or to its complement.

4.3 Responses to assertions v. responses to polar questions We conclude this section by looking back at the similarities and differences between responses to assertions and responses to polar questions. We call here responding assertions those assertions that perform a responding move, and initiating assertions those subtypes of assertions that are not responding. Since initiating assertions and polar questions place an issue on the Table in the form of a proposition-denoting sentence radical, moves that react to them can be responding and therefore confirming or reversing. Since constituent questions do not place a proposition-denoting sentence radical on the Table, reactions to such questions can be neither confirming nor reversing.


complementation. If we take this into account, the answers polar questions project are not identical even in non-biased questions, since confirming answers are less marked than reversing ones. This allows us to further distinguish positive and negative polar questions. If we assume that polar questions involve a weak bias towards the least marked answer, we capture the weak bias of positive polar questions towards a positive answer and the weak bias of negative polar questions towards the negative answer noticed in van Rooy & Safarova (2003). Just as agreeing to disagree is a non-canonical way of removing an assertion from the Table, one can agree not to pursue a question if there is no agreement on an answer, thereby removing it from the Table without having resolved it. Such a move is non-canonical because the question is popped off the stack without any concomitant enrichment of the common ground. Once the question is removed, the projected set must be recalculated. Such moves may be prompted by participants declaring their inability to provide information that would lead to answering the question. Generalizing now over confirming and reversing moves, we define in (30) a move type we call responding:


In order to capture the common denominator of responding moves, we propose to introduce two relative polarity features, [same] and [reverse], the former marking confirming moves and the latter marking reversing ones. They are defined in (31): (31) a. A responding move has the feature [same] if and only if it is a confirming move. b. A responding move has the feature [reverse] if and only if it is a reversing move.

5 RESPONDING ASSERTIONS AND POLARITY PARTICLES In this section, we narrow our attention to responding assertions of the type illustrated in Ben’s assertions below: (32) Anne: Sam’s home. Ben: Yes, he is./No, he isn’t. (33) Anne: Is Sam home? Ben: Yes, he is./No, he isn’t. These are the most direct responding assertions possible in that they assert the denotation of the sentence radical on the top of the input Table or its opposite.

5.1 Responding assertion typology The category of responding assertions extends the notion of answers to questions discussed briefly in Sadock & Zwicky (1985: 189–91), so as to cover reactions to assertions as well as reactions to questions. As


Recall that the crucial difference between assertions and (polar) questions is that the former, but not the latter, commit their author to the propositional content of the asserted sentence. It therefore follows that confirmation in the case of assertions but not in the case of polar questions amounts to agreement. By the same token, reversing in the case of assertions, but not in the case of polar questions, amounts to denial. Given these observations, we predict partial overlap when it comes to the form of responding moves reacting to assertions and polar questions. We expect overlap as far as the responding nature of the move is concerned. The expected differences should be ultimately connected to the differences in the state of the input context to the reactive move. We discuss these predictions in more detail in section 5, where we focus on responding assertions.


17

If the context is already in crisis, there are no elements in the input ps. An exception is when the answer to the question already follows from the contents of the input cg, as is the case with rhetorical questions such as ‘Is the Pope Catholic?’. Other types of rhetorical questions are special only in that the author of the response is assumed to be the same participant as the author of the question, as in the case of rhetorical questions asked during lectures. 18


such, it cannot be seen as a subtype of the question–answer pair (QAP) rhetorical relation discussed in the work of Asher and Lascarides. That notion is not general enough to capture the fact that responding assertions span reactions to polar questions and assertions. On the other hand, QAP is meant to cover answers to all types of questions, not only polar ones, and therefore it is too wide for our purposes. The formal parallelism between responding assertions responding to assertions and those responding to questions, on the other hand, points to the need for the category we provide. Responding assertions can be differentiated based on three criteria: (a) whether they respond to an assertion or a polar question, (b) whether they are confirming or reversing and (c) whether the sentence they assert is positive or negative. The first criterion concerns the status of the input context. In the case of responses to assertions, the input context is already categorically biased in favour of the proposition denoted by the sentence radical. At least one of the participants is committed to that proposition and all elements of the input ps already have that proposition as an element.17 In the case of responses to polar questions, no such categorical bias has been brought about by the item on top of the Table in the input context. Normally, the input ps contains both elements that decide the issue in favour of the denotation of the sentence radical and elements that decide the issue in favour of the complement of that proposition.18 The second criterion concerns the relationship between the proposition the assertion commits its author to and the propositional content of the sentence radical on the top of the input Table. There are two possibilities: (i) the response is confirming, in which case it bears the relative polarity feature [same], or (ii) the response is reversing, in which case it bears the relative polarity feature [reverse]. Combining the two criteria, we get [same] and [reverse] responses to assertions and [same] and [reverse] responses to polar questions. As discussed above, [same] responses to assertions are predicted to be the least marked possible reactions. A [reverse] response to an assertion (a denial) is the most marked reaction. In the case of responses to polar questions, neither [same] nor [reverse] responses necessarily lead to crisis. We take it, however, that [same] assertions are simpler than [reverse] ones because the former assert the sentence radical already


(34) Anne: Sam is home./Is Sam home? Ben: Yes he is. ([same, +]) Connie: No, he isn’t. ([reverse, –]) (35) Anne: Sam is not home./Is Sam not home? Ben: Yes, he is. ([reverse, +]) Connie: No, he isn’t. ([same, –]) In what follows, we examine the role of these two polarity features in accounting for the particles that occur at the leftmost edge of sentences functioning as responding assertions.

5.2 Polarity particles In this section, we take a closer look at particle usage in responding assertions and examine the parameters they are sensitive to, basing our discussion on the typology and features given in section 4. Our aim is to provide a glimpse of the use of these features in accounting for the distribution of polarity particles concentrating on a three-polarity particle language, Romanian. The discussion illustrates how the approach we developed so far is able to capture the partial overlap between responding assertions that react to assertions and polar questions, respectively. So far we have established that in dialogues such as (36): (36) Anne: Sam is home. Ben: Yes, he is./No, he isn’t. (37) Anne: Is Sam home? Ben: Yes, he is./No, he isn’t.


present on the top of the input Table. Thus, we expect that [same] assertions will be less marked than [reverse] assertions even when reacting to a polar question. The third criterion is specific to responding assertions. In [same] assertions, the polarity of the asserted sentence matches the polarity of the sentence radical on the top of the Table of the input context; in [reverse] assertions, the polarity of the asserted sentence is the reverse of that of the sentence radical on the top of the Table of the input context. We assume that a responding assertion that asserts a positive sentence has the absolute polarity feature [+], while a responding assertion that asserts a negative sentence has the absolute polarity feature [–]. We also assume, following Horn (2001) and many others, that [+] assertions are less marked than [–] assertions. We illustrate our two polarity features in (34) and (35):


(38) Anne: Sam is not home. Ben: Yes. He is not./No. He is. Both intonation and context help separate these two functions of the English polarity particles.19 The particle overlap between [+] and [same] on the one hand, and [–] and [reverse] on the other, seen in English, is not surprising given the unmarked nature of the features [same] and [+] and the marked nature of the features [reverse] and [–]. See Pope (1976) for further discussion and examples. Recall now that a [reverse] assertion in reaction to a polar question, though intrinsically more marked than a [same] assertion, does not lead to conversational crisis. Such a move in reaction to an assertion, on the other hand, does lead to crisis. We call [reverse] assertions that react to an assertion denials and [reverse] assertions that react to a polar question reverse answers. Denials and reverse answers share the [reverse] feature but are distinguished with respect to both their input and their output context states. Denials are conversationally marked moves because they lead to conversational crisis. Recall also that confirming reactions to 19 Note also that the use of yes is correlated not only with [same] and [+] but also with the author being the source of the information the move commits her to, as discussed in Gunlogson (2008).


Ben’s utterances are responding assertions. The first answer is a [same] response, and the second is a [reverse] one. In the case in which these assertions respond to a previous assertion, the first amounts to confirmation and the second to total denial. In English, the particles yes and no placed at the left edge of a declarative sentence signal the responding nature of the assertion. We treat them both as presupposing that the assertion is responding, that is, confirming or reversing. These particles are therefore predicted to be inappropriate in assertions made relative to an input context state whose Table does not contain, on the top of its stack, a proposition the reactive assertion can be seen as confirming or reversing. We thus correctly predict that yes and no are inappropriate in initiating assertions as well as in answers to a wh-question. The choice between yes and no in responding assertions is influenced, we claim, by the two polarity features introduced in section 5.1. In (36) and (37), yes can be seen as marking both [same] and [+], and no can be seen as marking both [reverse] and [–]. In (35), yes marks [+] and no marks [–]. These two particles can also be used to encode relative polarity only, with yes signalling [same] and no signalling [reverse]:


20 In the terminology of Sadock & Zwicky (1985), the latter languages have a yes/no system, while the former have an agree/disagree system.


assertions and confirming reactions to polar questions share the feature [same] but differ in that the former are the least marked conversational moves discussed here. Given this partial similarity between reactions to assertions and polar questions, we expect partial overlap in their form, with denials being formally more marked than reverse answers and confirming reactions to assertions being less marked than confirming reactions to polar questions. Thus, the similarities in the form between Ben’s moves in (36) and (37) above are due to the fact that the yes and no responses have identical relative and absolute polarity features independently of whether they react to an assertion or a polar question. The differences in the conversational states that result after Ben made his response in the two dialogues above stem from the differences in the input context state in the two cases. The importance of the two types of polarity features of reactive assertions introduced here becomes evident once we consider the inventory of polarity particles across languages. We cannot go here into a detailed study of polarity particles within a language or crosslinguistically. We will, however, illustrate with polarity particles in Romanian and end with some general predictions our approach makes. For details on the Romanian particle system, see Farkas (forthcoming). We assume here that polarity particles, such as the use of yes and no illustrated above, are items that occur at the leftmost edge of a root sentence, in a node we christen PolP, that houses the absolute and relative polarity features of a responding assertion. The sister node of PolP is a complementizer phrase (CP) whose polarity agrees, by definition, with the absolute polarity feature in PolP. As discussed in Pope (1976), there are languages, such as Japanese, that use particles to signal only relative polarity, that is, [same] and [reverse], while other languages use polarity particles meant to primarily signal the absolute polarity of the asserted sentence in responding assertions.20 There are also languages that have a mixed system, with some particles primarily associated with absolute polarity and others primarily associated with relative polarity. As mentioned in section 1, Romanian is such a language. It has three polarity particles, the positive particle da, the negative particle nu and a third particle, ba, whose function is, we claim, to signal [reverse]. We call da and nu absolute polarity particles because their use is primarily sensitive to the polarity of the sentence they assert. We


assume here that sentence radicals are either positive or negative, a fact encoded in their form. Recall that a responding assertion has the polarity feature [+] iff its sister CP is positive and the polarity feature [–] iff its sister CP is negative. As seen below, the positive polarity particle da in Romanian occurs in [+] responding assertions, while nu occurs in [–] responding assertions:

In (40) we see nu in a [same, –] reaction; in (44) below we will see da in a [reverse, +] reaction. As exemplified above, absolute polarity particles may occur on their own in Romanian, as well as in English. Responses whose only overt item is a polarity particle can be treated as involving sentential ellipsis or some sort of pro-sentential form. We treat such utterances as responding assertions but stay neutral with respect to whether ellipsis or a sentence pronominalization is involved. For an ellipsis account, see Kramer & Rawlins (forthcoming), who follow Merchant (2004). Turning now to the third particle, ba, we illustrate its distribution below:21 (42) A: Ana a plecat. ‘Ana left.’ B: Ba nu, n-a plecat./*Nu, n-a plecat. ‘No, she didn’t.’ (43) A: Ana a plecat? ‘Has Ana left?’’ B: Nu./Nu, n-a plecat./*Ba nu./*Ba nu, n-a plecat. ‘No, she hasn’t.’ (44) A: Ana nu a plecat. ‘Ana didn’t leave.’ B: Ba da./Ba a plecat./Ba da, a plecat. ‘You are wrong, she did.’ (45) A: Ana nu a plecat? ‘Didn’t Ana leave?’ B: Ba da./Ba a plecat./Ba da, a plecat.’ ‘Yes, she did.’ We now turn to some generalizations drawn on the basis of the distribution of these particles. First, note that the above examples show 21 Romanian, unlike English, does not have a syntactic contrast between internal and external negative questions.


(39) A: Ana a plecat. ‘Ana left.’ B: Da./Da, a plecat. ‘Yes./Yes, she left.’ (40) A: Ana nu a plecat. ‘Ana didn’t leave.’ B: Nu, n-a plecat. ‘No, she hasn’t.’ (41) A: Ana a plecat? ‘Did Ana leave?’ B: Da./Da, a plecat./Nu./Nu, n-a plecat. ‘Yes./Yes, she left. No./ No, she hasn’t left.’


22 There are non-standard dialects where this is not so and where ba may occur on its own, in which case it is interpreted as an absolute negative polarity particle.


that ba functions as a signal of the feature [reverse]. It may occur only in moves marked with this feature, both as reactions to assertions and as reactions to polar questions. What follows ba expresses overtly the absolute polarity of the asserted sentence, under the assumption that this can be done both by absolute polarity particles and the polarity of the verb of the asserted sentence. Under the assumption that the absolute polarity of the asserted sentence must be overtly expressed in Romanian, we account for the fact that ba cannot occur on its own.22 As illustrated in (42), a responding assertion marked with ba can be used to return a negative assertion when the input context presented a positive sentence, in which case ba is followed by nu and/or the negative asserted sentence. It can also be used (as in (44) and (45)) to return a positive sentence when the input context presented a negative one, in which case the absolute polarity is expressed by da and/or a positive sentence. So far then, we have seen that the existence and distribution of the particle ba confirm the necessity of recognizing the class of [reverse] responses. The Romanian data discussed so far also points to the necessity of separating absolute and relative polarity. In characterizing relative polarity, it is crucial to be able to define confirming and reversing move types, which in turn relies on being able to make reference to the polarity of the proposition-denoting sentence radical on the top of the input Table. Recall now that our characterization of responding assertions makes a distinction between denials and reverse answers. We therefore predict the possibility of a differentiation in polarity particle distribution that is sensitive to this distinction. Furthermore, given that denials are the most marked conversational moves, we expect the reverse particle to be used in denials more readily than in reverse answers. The distribution of ba in Romanian confirms these expectations. The contrast between (42) and (43) above shows that the distribution of ba is sensitive to whether the move is a reaction to an assertion or a question: in assertions whose features are [reverse] and [], ba is required in denials but is not possible in reverse answers. We thus see a difference between denials and reverse answers with denials being more marked than reverse answers, as expected. The data in (44) and (45) above show that the contrast between denials and reverse answers just noted disappears in case the absolute polarity feature of the reverse assertion is [+], that is, when the


(46) A: Anne n’est pas partie. ‘Anne didn’t leave.’ B: Mais si. ‘You are wrong, she did.’ (47) A: Anne n’est pas partie? ‘Didn’t Anne leave? ’’ B: Mais si. ‘Yes, she did.’ (48) A: Anna kommt nicht mit ins Kino. ‘Anna isn’t coming along to the movies.’ B: Doch! Sie kommt schon. ‘You are wrong. She’s coming.’ (49) A: Wollen Sie den Job nicht? ‘Don’t you want this job? ’ B: Doch! Ich brauche das Geld. ‘But I do. I need the money.’ A parallel tension exists in responding assertions whose features are [same] and [–]. In their case, a negative particle may express the absolute but not the relative feature, while a positive particle could express the relative but not the absolute feature. This combination is less problematic, however, because the absolute feature is not contrastive and the relative feature is the unmarked one. In Romanian in such cases, the relative polarity remains unexpressed, a fact that is in keeping


responding move reverses a negative sentence radical on the top of the input Table. It appears therefore that, at least in Romanian, the overt marking of the feature [reverse] is sensitive not only to whether the move is a denial or not but also to its absolute polarity feature. The data suggest that the combination [reverse] and [+] calls for the use of a reverse marker more readily than the [reverse] and [] combination. In looking for a justification for this fact, we recall the observation in Pope (1976), who notes that absolute [+] particles may double to express [same], while [] particles may double to express [reverse], as exemplified in English with yes and no. Given this affinity between [reverse] and [] on the one hand, and [same] and [+] on the other, the combination of [reverse] and [+] appears special because its component features are not compatible. Using a single relative particle to express both features is problematic because of the impossibility of [reverse] particles to mark [+]; having recourse to a single absolute particle on the other hand is problematic because of the impossibility of [+] particles to mark [reverse]. Note also that in these responses [+] is contrastive and therefore we expect it to require special marking, unlike in [same, +] cases. In support of the special nature of the combination of [reverse] and [+], we note that in French and German the particles si and doch appear to be used in responding assertions precisely to mark the combination of these two features. Thus, the French and German ‘third’ particles do the job of the Romanian ba da sequence:


with [same] being the unmarked relative polarity feature. In English, the combination yeah no can be used for just such cases: (50) Anne: Sam is not home./Is Sam not home? Ben: Correct./Yup./Yeah no.23

23 We are grateful to undergraduates from University of California Santa Cruz who brought the ‘yeah.no’ answer to our attention.


Finally, note that the fact that in Romanian the third particle is used to mark [reverse] rather than [same] is unsurprising given the fact that reversing moves are more marked than confirming ones. The brief glimpse of polarity particles this subsection has provided has shown, we hope, the usefulness of the two types of polarity features we have identified as characterizing responding assertions. In defining relative polarity features, we have relied on the material in sections 3 and 4, which allows us to capture the similarities and differences between reactions to assertions and polar questions and in characterizing responding move types. These sections, in turn, exploit the context components discussed in section 2. The finer details of polarity particle distribution in Romanian have shown the relevance of the established differences between reactions to assertions and reactions to polar questions. These data appear to confirm the predictions made by our characterization of responding assertions. The question that arises now is whether further cross-linguistic data will do the same. In closing, we list the expectations our approach leads us to: (i) We expect partial overlap in the marking of responding assertions sharing relative and/or absolute features. (ii) We expect the possibility of relative polarity markers as well as that of absolute markers. (iii) Given the more marked nature of reversing moves, we do not expect a language with a [same] particle but without a [reverse] one, though the opposite situation is not surprising. (iv) We expect [reverse] to be more marked in denials than in reverse answers, and therefore we would find it surprising if a language were to use a [reverse] particle in reverse answers but not in denials. (v) We expect the [reverse, +] combination to be specially marked relative to [reverse, ]. We therefore do not expect to find languages that have a special particle used in [reverse, ] responses but no special marker for [reverse, +] ones. In the same vein, we expect the [same, ] combination to be specially marked relative to [same, +].


6 CONCLUSIONS

Acknowledgements We thank audiences at talks given at University of California Santa Cruz and Pomona College for useful questions and comments. We are also grateful to Bart Geurts and three anonymous referees for detailed, careful and useful suggestions. All remaining errors are, of course, our own.

DONKA F. FARKAS Stevenson College University of California Santa Cruz 1156 High Street Santa Cruz CA 95064 e-mail: [email protected]

KIM B. BRUCE Pomona College Computer Science Department 185 E. Sixth Street Claremont CA 91711 e-mail: [email protected]

REFERENCES Asher, Nicholas & Alex Lascarides. (2003). Logics of Conversation. Cambridge University Press. Cambridge.

Asher, Nicholas & Alex Lascarides. (2008). ‘Commitments, beliefs and intentions in dialogue’. Proceedings of


We have focused here on default assertions and default polar questions with the aim of capturing both the similarities and the differences found in a subset of reactions to these speech acts. The details of the context structures we have used, as well as the characterization of the main contextual effects of default assertions and default polar questions, allow us to capture both what is the same and what is different in these two speech acts, as well as in conversational moves that confirm/reverse an assertion or a polar question. We thereby have accounted for the partial overlap found in the form of these reactions. Our discussion, we hope, opens the door towards a systematic crosslinguistic study of responding assertions and the particles that are used in them, a topic that has not received the attention it deserves. On the other hand, there are many much discussed issues that we have been silent about, such as the various types of bias various types of nondefault questions and assertions come with. We hope to have nevertheless shown that focussing on the details of the reactions to default polar questions and default assertions turns out to be a useful step in understanding the nature of these two speech acts and the contexts in which they occur.

Donka F. Farkas and Kim B. Bruce 117 Gunlogson, Christine. (2001). True to Form: Rising and Falling Declaratives as Questions in English. Routledge. London. Gunlogson, Christine. (2008). ‘A question of commitment’. Belgian Journal of Linguistics 22:101–36. Hamblin, C. I. (1971). ‘Mathematical models of dialogue’. Theoria 37:130–55. Horn, Laurence. (2001). A Natural History of Negation. CSLI. Stanford, CA. Karttunen, Lauri. (1977). ‘Syntax and semantics of questions’. Linguistics and Philosophy 1:3–44. Kramer, Ruth & Kyle Rawlins. (2008). ‘Polarity particles: an ellipsis account’. In Proceedings of NELS 39, Ithaca, NY. Krifka, Manfred. (2001). ‘Quantifying into question acts’. Natural Language Semantics 9:1–40. Lascarides, Alex & Nicholas Asher. (2008). ‘Agreement and disputes in dialogue’. In Proceedings of the 9th SigDial Workshop on Discourse and Dialogue (SIGDIAL). Columbus, Ohio. 29–36. Merchant, Jason. (2004). ‘Fragments and ellipsis’. Linguistics and Philosophy 27:661–738. Poesio, Massimo & David Traum. (1998). ‘Towards an axiomatization of dialogue acts’. In Proceedings of the Twente Workshop on the Formal Semantics and Pragmatics of Dialogues (13th Twente Workshop on Language Technology). Enschede. 207–22. Pope, Emily. (1976). Questions and Answers in English. Mouton. The Hague, The Netherlands. Roberts, Craige. (1996). ‘Information structure in discourse’. In J.H. Yoon & A. Kathol (eds.), OSU Working Papers in Linguistics 49: Papers in Semantics. Ohio State University. Columbus, OH.


the 12th Workshop on the Semantics and Pragmatics of Dialogue (Londial). London 35–42. Asher, Nicholas & N. Reese. (2007). ‘Intonation and discourse: biased questions’. In S. Ishihara, S. Jannedy, & A. Schwarz (eds.), Working Papers of the SFB632, Interdisciplinary Studies on Information Structure (ISIS). vol. 8. Universitatsverlag Potsdam. Potsdam. 1–38. Bu¨ring, Daniel. (2003). ‘On D-trees, beans, and B-accents’. Linguistics and Philosophy 26:511–45. Carlson, L. (1983). Dialogue Games. Reidel. Dordrecht, The Netherlands. Clark, H. (1992). Arenas of Language Use. University of Chicago Press. Chicago, IL. Clark, H & E. F. Schaefer. (1989). ‘Contributing to discourse’. Cognitive Science 13:259–94. Farkas, Donka F. ‘Polarity particles in Romanian’. In Di Sciullo, Anna Maria, & Virginia Hill (eds.), Interface Properties: Edges, Heads and Projections. John Benjamins, forthcoming. Ginzburg, J. (1995). ‘Resolving questions, I & II’. Linguistics and Philosophy 18:459–527, 567–609. Ginzburg, Jonathan. (1996). ‘Dynamics and the semantics of dialogue’. In J. Seligman & Dag Westersta˚hl (eds.), Language, Logic, and Computation. vol. 1. CSLI Lecture Notes. CSLI. Stanford, CA. 221–37. Ginzburg, Jonathan. The Interactive Stance: Meaning for Conversation. CSLI Publications. Stanford, CA, forthcoming. Groenendijk, Jeroen. (2003). ‘Questions and answers: semantics and logic’. In Proceedings of the 2nd ColgNET-ElsET Symposium. Questions and Answers: Theoretical and Applied Perspectives 16–23.

118 Assertions and Polar Questions Romero, Maribel & Chung-hye Han. (2004). ‘On negative yes/no questions’. Linguistics and Philosophy 27:609–58. Sacks, H. (1992). Lectures on Conversation. Blackwell. Oxford. Sadock, J. M. & A. M. Zwicky. (1985). ‘Speech act distinctions in syntax’. In T. Shopen (ed.), Language Typology and Syntactic Description. Cambridge University Press. Cambridge. 155–96.

First version received: 28.02.2008 Second version received: 27.01.2009 Accepted: 09.06.2009


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van der Sandt, R & E. Maier. (2003). ‘Denials in discourse’. In Michigan Philosophy and Linguistics Workshop. van Rooy, Robert & Marie Safarova. (2003). ‘On polar questions’. In R. Young & Y. Zhou (eds.), Proceedings of SALT XIII. Cornell University. Ithaca, NY. Walker, Marilyn A. (1996). ‘Inferring acceptance and rejection in dialogue by default rules of inference’. Language and Speech 39:265–304.

Journal of Semantics 27: 119–124 doi:10.1093/jos/ffp012 Advance Access publication November 18, 2009

Anaphora and Semantic Innocence J. P. SMIT Stellenbosch University ASBJØRN STEGLICH-PETERSEN Aarhus University

Semantic theories that violate semantic innocence, that is require reference shifts when terms are embedded in ‘that’ clauses and the like, are often challenged by producing sentences where an anaphoric expression, while not itself embedded in a context in which reference shifts, is anaphoric on an antecedent expression that is embedded in such a context. This, in conjunction with a widely accepted principle concerning unproblematic anaphora (the ‘Principle of Anaphoric Reference’), is used to show that such reference shifting has absurd consequences. We show that it is the widely accepted principle concerning anaphora that is to be blamed for these consequences and not the supposed sin of reference shifting.

1 THE ARGUMENT FROM ANAPHORA Below we will sketch an argument for semantic innocence that we will call the ‘Argument from Anaphora’. Consider the following sentence: (1)

Lois Lane believes that Clark Kent can’t fly. He can.

Now consider the following widely accepted principle concerning anaphora that we shall call the Principle of Anaphoric Reference (PAR). PAR: An anaphoric term has the same referent as its antecedent. Needless to say, PAR does not amount to a theory of all anaphora, but it is commonly thought to govern simple cases like (1). If we take the pronoun ‘he’ in (1) to be anaphoric on the embedded name ‘Clark Kent’, then PAR entails that ‘he’ has the same referent as that embedded name. In order to avoid absurdity, we have to say that ‘he’ refers to Clark Kent, and hence, the intuitive interpretation of the sentence, coupled with the claim that ‘he’ in (1) is anaphoric, and PAR yield the result that the embedded name ‘Clark Kent’ refers to Clark Kent. Ó The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected].


Abstract

120 Anaphora and Semantic Innocence

The above argument1 is simple but, if sound, accomplishes a stunning result. Any semantic theory which proposes that the embedded name ‘Clark Kent’ in (1) does not refer to Clark Kent, but to its customary sense, or to a linguistic entity, and so on, will, if PAR is accepted, have the consequence that it is the customary sense of ‘Clark Kent’, or some linguistic entity, that can fly. This is absurd, and hence, all semantic theories that violate semantic innocence in such a way stand refuted. In other words, the Argument from Anaphora leads us to reject more than a century of Fregean semantics.2

The claim we wish to defend is that the Argument from Anaphora is, in fact, toothless since PAR has absurd consequences. The first point to note is that, while it may be open to debate whether terms shift reference when embedded in that-clauses, it is uncontroversial that when embedded in quotation marks, terms do shift reference. Exactly how quotations are to be understood is of course a matter of some controversy. The theories commonly offered include the identity theory, the demonstrative theory, the name theory, the description theory, and several variations of these.3 But all these theories, and, indeed, common sense, tell us that quotation does change the semantic content of the quoted expressions. Call this the Quotation Intuition (QI). Consider then the following sentence: (2) Lois Lane considered whether the sentence ‘Clark Kent can fly’ is true. It is; he can fly. If we take the ‘he’ in (2) to be anaphoric and accept the obvious reading of the sentence on which ‘he’ refers to Clark Kent, then PAR commits us to the conclusion that the name ‘Clark Kent’ embedded in the quotation refers to Clark Kent. The reasoning here is perfectly analogous to the reasoning used above in connection with 1 This argument has been endorsed by Bach (1997, 2000) and has gained enough currency to feature in McKay & Nelson (2008). Our version is a reconstruction of Bach’s version. 2 We do not mean to imply that Bach thinks that the argument, by itself, manages to refute a century of Fregean semantics. He does express reservations when he writes that ‘‘this difficulty might not be insuperable, but it illustrates why denying semantic innocence just doesn’t ring true’’ (1997: 217). We take this to imply that he does, at least, think that there is a case for the Fregean to answer and that such an answer will probably involve some theoretical costs. We try to show that the use of PAR in the above argument has such absurd consequences that there simply is no case to answer. 3 We take this typology from Saka (1998), where he develops his own Multiple Ostension theory.


2 THE ARGUMENT REFUTED

J. P. Smit and Asbjørn Steglich-Petersen 121

3 OBJECTIONS We will briefly look at some possible responses from those who wish to save the Argument from Anaphora. It might be objected that (2) is somehow suspect or not well formed. If this verdict is simply based on raw linguistic intuitions, it seems ill-founded. Example (2) looks perfectly fine to us, and some informal questioning of nonphilosophers has not yet turned up anyone who could even understand why we would ask if (2) is an acceptable English sentence. But let us pursue this line of reasoning a bit further. The most obvious way to develop it would be to admit that non-philosophers might well not find anything suspect, but to attribute this to an insufficient understanding of the relation between the semantics of (2), and the content it can be used to convey, that is pragmatics. The objector could insist that PAR is 4 A reviewer pointed out that since the quoted expression in (2) is a whole sentence, and not just the constituent term ‘Clark Kent’, it may be strictly compatible with QI that the semantic content of ‘Clark Kent’ is unaffected by the quotation marks. However, we take QI to concern all the constituents of quoted expressions and not just the expression in its entirety. We are not aware of any theories of quotation, which involve changing the semantic content of whole quoted contexts without also changing the semantic content of the elements of such contexts. In any case, example (6*) below makes our point without relying on the stronger reading of QI.


propositional attitude contexts. But that violates QI, which predicts that, whatever the quoted name ‘Clark Kent’ refers to, it is not Clark Kent.4 This now leaves us with a dilemma. If we accept that (2) is well formed, and that ‘he’ in (2) is anaphoric, then PAR and QI are jointly inconsistent in cases like the above. PAR, coupled with the above assumptions and the obvious reading of the sentence, leaves us with the obviously wrong conclusion that the quoted ‘Clark Kent’ refers to Clark Kent. But if we leave QI intact, perhaps by saying that the quoted ‘Clark Kent’ refers to itself, then we can only preserve PAR by providing a reading of (2) so that it says that the name ‘Clark Kent’ can fly. This is even more absurd. We see no way of surrendering QI in cases like (2) and are forced to conclude that PAR is at fault. This vindicates our main claim that pronominals that seem to refer to antecedents introduced in attitude contexts, as in (1), do not present any problem for the Fregean. For cases like (2) make it plain that anaphoric reference can occur, even where there is the clearest possible reference shift, namely quotation. Anaphoric reference is perfectly compatible with reference shifts. PAR, and hence the Argument from Anaphora, collapses.



correct and say that (2), literally, does say that the name ‘Clark Kent’ can fly. However, speakers confuse this with the content that (2) would typically be used to convey, and so do not find fault with (2). The problem with such an objection is that it seems to beg the question. What, we may ask, is the principled basis being used here to declare (2) improper? We fail to see how this can be based on anything more than an adherence to PAR since, if PAR were false, there would be no obstacle to regarding (2) as having the literal meaning suggested by intuition. As an argumentative strategy for someone wishing to defend PAR, the objection thus begs the question. Another difficulty, if this sort of reasoning is allowed, is that it opens the door for the Fregean to declare (1) improper on similar grounds. The Fregean could, based on his deep commitment to reference shifts in attitudinal contexts, claim his theory compatible with PAR by insisting that (1) literally says that the common sense of ‘Clark Kent’ can fly. But, the Fregean could continue, most speakers do not realize this as they confuse what (1) is typically used to convey with its literal meaning and mistakenly think that (1) coupled with PAR count against the Fregean. Hence, the Fregean could challenge (1) in the exact same way that the objector challenges (2), and the Argument from Anaphora loses its force. We have no principled basis to adjudicate this debate and reach stalemate. The second potential objection would be to deny that ‘he’ in (2) is anaphoric. There are different ways such an account could go, but we will only look at one version as we fail to see a version that does not run into similar difficulties. The objector could claim that ‘he’ in (2) is a demonstrative that just happens to be preceded by a term that has the same ordinary referent as ‘he’ in (2), and this misleads us into thinking that ‘he’ is anaphoric. Rather ‘he’ in (2) is a demonstrative referring to a contextually salient ‘he’, or something similar, and not a true anaphoric pronoun. We have no objections to such an account. Note, however, that if any such an account is to be useful in the present argumentative context, it must have one decidedly odd feature. It needs to show that ‘he’ in (2) is not anaphoric but also to avoid the consequence that ‘he’ in (1) is not anaphoric. If it fails to draw such distinction, then PAR is not applicable in (1) either, and the Argument from Anaphora fails to get off the ground. We fail to see any basis on which to drive such a wedge between (1) and (2). If the objector motivates the non-anaphoric nature of ‘he’ in (2) by saying that there cannot be anaphoric reference to a term in a quoted context, this again will boil down to an appeal to PAR. In the present context that is circular. Furthermore, we are not aware of any

J. P. Smit and Asbjørn Steglich-Petersen 123

(3) (4)

Lois Lane considered whether Clark Kent can fly. He can. Lois Lane considered the truth or falsity of the sentence ‘Clark Kent can fly’. He can.

Whereas (3) is well formed, example (4) seems odd. Consider also the following pair: (5) (6)

Lois Lane knows Clark Kent. She likes him. Lois Lane knows the name ‘Clark Kent’. She likes him.

Whereas (5) is well formed, example (6) seems odd. This presents a prima facie problem for our account, for does our use of sentence (2) not lead one to expect that (4) and (6) should be well formed? However, there are compelling reasons to think that the oddness of (4) and (6) comes down to pragmatics rather than anaphora failure. What makes (4) and (6) odd is that their first sentences lead us to expect a follow-up concerning the truth value of a sentence, and Lois Lane’s knowledge of a name, respectively, and not a follow-up concerning Clark Kent. But this does not rule out anaphora into the quoted contexts. To see this, consider how (4) and (6) can be fixed by adding a clause to their second sentences, speaking directly to the subject raised by their first sentences, while preserving the anaphoric clause: (4*) Lois Lane considered the truth or falsity of the sentence ‘Clark Kent can fly’. It is true; he can. (6*) Lois Lane knows the name ‘Clark Kent’. In fact, she not only knows the name; she likes him. In both (4*) and (6*), the expectation raised pragmatically by the first sentence is discharged in a way consistent with this expectation. This 5

We would like to thank an anonymous referee for urging us to consider these cases.


theory of anaphora that would give a principled distinction between the use of ‘he’ in (1) and (2), and we seriously doubt that such a theory is possible. All that the introduction of such a view, and others like it, would do in the present context is to open the door to the Fregean to argue that ‘he’ in (1) is actually a demonstrative referring to some contextually salient ‘he’. This would mean that ‘he’ in (1) is not a true anaphoric expression at all, in which case the Argument from Anaphora fails. The final objection we wish to discuss concerns cases where anaphoric reference to an antecedent term in a quoted context seems ‘odd’ or forced, thus providing some evidence against the possibility of this kind of anaphora.5 Consider, for example, the following pair:


renders both sentences immaculate, and hence, we have every reason to believe that the oddity of (4) and (6) is entirely pragmatic. To our minds, the Argument from Anaphora stands refuted. Acknowledgements We would like to thank the editors, three anonymous reviewers for Journal of Semantics, and Johan Oosthuizen for helpful comments and criticism. Asbjørn Steglich-Petersen would like to thank the Danish National Research Council for Culture and Communication for financial support.

ASBJØRN STEGLICH-PETERSEN Department of Philosophy Aarhus University Jens Chr. Skous Vej 7 8000 Aarhus C, Denmark fi[email protected]

REFERENCES Bach, K. (1997). ‘Do belief reports report beliefs?’. Pacific Philosophical Quarterly 78:215–41. Bach, K. (2000). ‘A puzzle about belief reports’. In K. Jaszczolt (ed.), The Pragmatics of Propositional Attitude Reports. Elsevier. Oxford. 99–109. McKay, T. & M. Nelson. (2008). ‘Propositional attitude reports’. In E. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Fall 2008 Edition). The Metaphysics Research Lab, Center for

the Study of Language and Information, Stanford University. Stanford, CA. http://plato.stanford.edu/archives/fall2008/entries/prop-attitude-reports/ Saka, P. (1998). ‘Quotation and the usemention distinction’. Mind 107: 113–35.

First version received: 08.07.2009 Second version received: 14.09.2009 Accepted: 29.09.2009


J. P. SMIT Department of Philosophy Stellenbosch University Private Bag X1 Matieland 7602 South Africa [email protected]

Journal of Semantics 27: 125–137 doi:10.1093/jos/ffp013 Advance Access publication January 15, 2010

Superlatives, NPIs and Most JON GAJEWSKI University of Connecticut

Abstract

1 INTRODUCTION Negative polarity items (NPIs) occur felicitously in the restrictor of the English determiner most, see any in (1). Most is not downward entailing (DE) in its restrictor, compare (2). This fact has been used as an argument against the influential hypothesis that NPIs must appear in DE environments (Ladusaw 1979) and as motivation for various alternative accounts (cf. Heim 1984, Ludlow 1995, Rothschild 2006 and many others). (1) (2)

Most people with any brains have already left town. Most students are diligent. 2 Most semantics students are diligent.

In this paper, I argue that, despite appearances, NPIs in the restrictor of most are in fact licensed by being in the scope of a DE operator. Hackl (2009) argues that most should be analyzed as the superlative of many. von Fintel (1999) argues that superlatives license NPIs because they are Strawson downward entailing (SDE). I show that the combination of Hackl’s and von Fintel’s theories predicts that NPIs should be licensed in the restrictor of most. In Section 2, I lay out the semantics of the The Author 2010. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected].


The ability of English determiner most to license negative polarity items (NPIs) has long stood as a puzzle for theories that follow Ladusaw (1979) in claiming that NPIs must appear in the scope of downward entailing (DE) operators. Most licenses NPIs such as any and ever in its restrictor but is not downward, or upward, entailing with respect to its restrictor. In this paper, I argue that despite appearances to the contrary, NPIs in the restrictor of most are in the scope of a DE operator. I make crucial use of a recent proposal by Hackl (2009) to compositionally analyze determiner most as a superlative expression. When the semantics of the superlative morpheme is spelled out correctly, this derives the result that most licenses NPIs in its restrictor. In addition, I show that this approach correctly predicts the NPI-licensing properties of relative most, as in English the most students. Finally, I discuss some consequences of this approach for the proper integration of contextual restriction into the semantics of the superlative morpheme.

126 Superlatives, NPIs and Most

2 THE SEMANTICS OF SUPERLATIVES The superlative form of a gradable adjective A is a predicate that is true of an individual x just in case x has A to a degree that no relevant alternative individual does. Heim (1999) proposes the Logical Form in (4)a for superlatives1 and the lexical entry in (4)b for gradable adjectives and encodes these truth conditions for superlatives in (5).2 (3) Fred is the oldest linguist. (4) a. LF of oldest linguist: [AP[DegP -est ] [AP old [NP linguist] ] ] b. ½½old ¼ kP<e,t>.kdd.kxe.AGE(x) > d & P(x) ¼ 1 (5) For any D of type > and x of type e, ½½-est(D)(x) ¼ 1 iff dd[D(d)(x) ¼ 1 & "y[ y 6¼ x / D(d)(y) ¼ 0] ] In (4)a, D ¼ [kd.kx.AGE(x) > d & x is a linguist] Superlative sentences like (2) have also been claimed to carry several presuppositions. Perhaps, the most obvious presupposition of (3) is that Fred is in fact a linguist (cf. von Fintel 1999 and others). The status of

1

I use the Abney-style LF, where A takes NP as a complement, compare Heim 1999, fn. 7. In many contexts, (3) will not be used to say that Fred is the oldest linguist in the world; but only that he is the oldest among a certain salient group of linguists. This can be accounted for by assuming that NPs are contextually restricted to their intersection with a salient set C, compare Stanley & Szabo (2000). We can represent the restriction as a subscript C on NP, where ½½NPCa ¼ ½½NP\a(C), and state the first presupposition of a superlative construction as in (i). 2

(i) Presupposition 1: X is the Adj-est NPC presupposes that X is a NPC

(P1)

For simplicity’s sake, I will leave such restrictions implicit in most of this paper. Heim (1999) defines ½½-est itself relative to a contextual restriction. I return to this below in Section 5.


superlative morpheme -est based on Heim (1999) and Hackl (2009), paying special attention to its presuppositions. In Section 3, we make use of these presuppositions in reviewing von Fintel’s evidence that the superlative morpheme is SDE. In Section 4, I show how Hackl’s analysis of most coupled with the approach to superlatives sketched in Sections 2 and 3 predicts NPI licensing in the restrictor of most. Furthermore, I explain in detail why most’s restrictor does not appear to be DE or even SDE. The solution lies in the covert structure of most and the principles of presupposition projection. Then, in Section 5, I show that this account also makes correct predictions about the NPIlicensing properties of relative most. Finally, in Section 6, I discuss how the account in Section 5 affects the implementation of contextual restriction in relative superlatives.

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this as a presupposition can be seen in its survival under negation: (6) still implies that Fred is a linguist. (6) (7)

Fred is not the oldest linguist. Presupposition 1: [X is the Adj-est NP] presupposes that X is a NP (P1)

In addition to (P1), superlatives carry presuppositions about the size of the classes to which their subjects are being compared. It is odd or ironic to say (8), given that we take it for granted that no one can have more than one (biological) mother. #You are the best mother I have. (Hackl 2009) Presupposition 2: [X is the Adj-est NP] presupposes that j½½NPj >2 (P2)3

We can incorporate these presuppositions into the lexical entry of -est in the style of Heim (1999, fn. 8) and Hackl (2009) as shown in (10) below. (10)

For all D of type > and x of type e, ½½-est(D)(x) is defined only if dd[D(d)(x) ¼ 1] & dy[y 6¼ x & de[D(e)(y) ¼ 1] ]

The presupposition says that the subject and another individual have the degree predicate D to some degree. Notice that satisfying the syntactically complex predicate D to some degree entails satisfying the NP, linguist in (4)a. Hence, (P1) and (P2) are accounted for. 3 SUPERLATIVES AND NPI LICENSING An important additional clue about the semantics of superlatives comes from the fact that they license NPIs like any and ever: (11) a. Erin is the quickest volleyball player I have ever seen. b. Art is the tallest biologist who has any publications in Crustacea. Ladusaw (1979) has influentially proposed that such NPIs are licensed in environments that are DE, that is, that license inferences from sets to subsets. For example, no licenses NPIs in its scope, (12)a. This mirrors the fact that the downward inference from publications to publications in Crustacea is valid in (12)b. 3 In fact, the superlative may require that ½½NP contain at least three members. This may be an effect of competition with comparatives and, anyway, will not affect our results.


(8) (9)


(12) a. No linguist has any publications in Crustacea. b. No linguist has publications. [ No linguist has publications in Crustacea. Though superlatives license any and ever in their NPs as shown in (11), they do not intuitively license inferences from sets to subsets. For example, the inference in (13) is not valid. Erin might indeed be the quickest athlete, but if she does not play volleyball, she cannot be the quickest volleyball player. (13) a. Erin is the quickest [NP athlete]. b. [ Erin is the quickest [NP volleyball player].

(14)

Erin is the quickest athlete. Erin is a volleyball player. There is another volleyball player. [ Erin is the quickest volleyball player.

This inference is indeed valid, which means that (13)a Strawson entails (13)b, and thus that -est is SDE. von Fintel argues that being SDE is a necessary condition for being a licenser of NPIs like any and ever. Our final lexical entry for -est is (15). It is similar to von Fintel’s (1999) in being SDE, compare (14); Heim’s (1999) in being compatible with -est movement, compare Section 5; and Hackl’s (2009) in including a presupposition about the size of the comparison class.4 (15)

4

For all D of type > and x of type e, ½½-est(D)(x) is defined only if dd[D(d)(x) ¼ 1] & dy[y 6¼ x & de[D(e)(y) ¼ 1] ] If defined, ½½-est(D)(x) ¼ 1 iff dd[D(d)(x) ¼ 1 & "y[ y 6¼ x / D(d)(y) ¼ 0] ]

However, (15) is not identical to Heim’s, von Fintel’s or Hackl’s lexical entry. Heim’s is not only SDE but also Strawson UE. von Fintel’s is not compatible with movement. Hackl’s does not require the members of the comparison class to meet D to some degree. See Section 6 for more discussion.


von Fintel (1999) proposes a solution to this problem. He suggests that when we assess entailment, we must take for granted the presuppositions of the conclusion. He calls this special kind of entailment ‘Strawson entailment’. As we have observed above, a superlative presupposes that its subject meets the descriptive content of its NP. So, (13)b presupposes that Erin is a volleyball player. Thus, to assess whether Strawson entailment obtains, we see if the inference in (14) is valid.

Jon Gajewski 129

In the next section, we apply this semantics for -est to a superlative analysis of most and demonstrate why most licenses NPIs in its restrictor. 4 MOST LICENSES NPIS BECAUSE IT IS A SUPERLATIVE

(16) ½½most(A)(B) ¼ 1 iff jA\Bj > .5jAj The apparent non-monotonicity of most in its first argument poses a significant puzzle. NPIs such as any and ever show up felicitously in the restrictor of most, compare (1), in conflict with our judgments about monotonicity. Fortunately, there is reason to believe the lexical entry in (16) is incorrect. That lexical entry ignores the structural complexity implied by the superlative form of most. See Hackl (2009) for additional arguments for treating most as a superlative. Though most’s superlative heritage is transparent, it has long been a puzzle how the proportional reading could be derived from the standard meaning for the superlative morpheme combined with many. Hackl (2009) provides a compelling solution to this puzzle. His important insight has to do with how we apply the semantics of superlatives to gradable predicates that apply to pluralities, like many. Hackl’s lexical entry for many is (17).5 (17)

For any A of type <e,t>, d of type d, and x type e: ½½many(A)(d)(x) ¼ 1 iff A(x) ¼ 1 & jxj > d

Hackl adopts an approach to superlatives the same, for our purposes, as that sketched in (15). Hence, the LF for the proportional reading of most students is as in (18). (18) 5

[AP [DegP-est] [AP many [NP student PL]6 ] ]

I have reordered the arguments to fit the syntax in (18). Hackl’s entry takes d first. If we included a contextual restriction—see footnote 2: ½½[NPC]PLa ¼ *(½½NP\a(C)), where ‘*’ is an operator that closes the extension under sum formation. 6


The English word most derives historically from the superlative form of a quantity expression related to many, compare Oxford English Dictionary. In many languages, the superlative form of MANY shares with English most the proportional (‘more than half ’) meaning illustrated in (16) in a Generalized Quantifier-type lexical entry [but not in all languages, cf. Zˇivanovic´ (2008) for discussion of crosslinguistic differences in the readings of MOST]. Notice that this lexical entry predicts that most is neither upward entailing (UE) nor DE with respect to its first argument, its restrictor. This accords with intuition, see (2) for example.


(19) a. [DP d [AP [DegP-est] [AP many [NP students] ] ] ] b. ½½d¼ kP<e,t>.kQ<e,t>.there is an x 2 De s.t. P(x) ¼ 1 and Q(x) ¼ 1 (cp. Partee 1987) Hence, [most students VP] is true if and only if there is a plural individual composed of more than half the students that also satisfies the predicate denoted by VP. In this way, Hackl shows us how to derive the proportional reading of most from the meaning of -est. As we saw above, -est is a SDE operator. Thus, NPI licensing is expected in the scope of -est. This solves the puzzle of (1); any is c-commanded by -est in the LF of (1): (20) [IP [DP d [AP [DegP-est] [AP many [NP people with any brains] ] ] ] have left town] Furthermore, the fact that the superlative morpheme is merely SDE, and not DE in the stricter sense, partially accounts for the fact that downward inferences do not appear valid in most’s restrictor. The presupposition of the superlative morpheme interferes with our perception of the validity of the inference, as in (13). In addition to being merely SDE, the superlative component of most has its monotonicity further masked by embedding. Recall that Hackl proposes that a covert existential quantifier closes off the meaning of the DP most students. The presupposition of the superlative morpheme must be projected through this existential quantifier. Beaver (1994: 25) proposes the following generalization about the projection of presuppositions from the restrictors of quantifiers.


Hackl derives the proportional reading of most from the superlative of many by clarifying how we interpret the clause ‘y 6¼ x’ in the lexical entry in (15) when x and y range over pluralities. Hackl suggests that we interpret this clause as saying that x and y do not overlap, i.e., they share no atomic parts. With this understanding, the denotation of (18) is a predicate that is true of an individual x just in case x is a plurality of students and every plurality of students that shares no atomic parts with x has fewer atomic parts than x. This means that the denotation of (18) is true just of those pluralities that are made up of more than half of the students. If x were composed of less than half the students, there would be a plurality of students with more atomic members, namely the complement of x in ½½students. To give us a meaning for most students that is equivalent to the Generalized Quantifier entry in (16), Hackl proposes that the predicate denoted by (18) is closed by a covert existential quantifier:

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(21) Existential projection from quantified contexts: If / presupposes w, then (for Q a quantifier and T any tautology): Q(x;/;v) presupposes some(x;T;w) In other words, if the restrictor of a quantifier carries a presupposition, the quantificational statement, as a whole, presupposes that some element in the domain satisfies that presupposition. This predicts that the presupposition of (22)a is (22)b.

Notice that, after projection, downward inferences in the NP position are no longer even Strawson-valid. For example, (22)a does not Strawson entail (23). We cannot conclude that there is a plurality made up of more than half the semantics students all of whom are diligent from the assumptions that (i) there are two non-overlapping pluralities of semantics students and (ii) there is a plurality made up of more than half the students all of whom are diligent. In sum, embedding and presupposition projection make it so that the restrictor of most does not appear to be DE or even SDE. Example (24) illustrates the idea that the constituent AP2 is SDE with respect to the position NP U, while the constituent DP is not SDE with respect to the position NP U. (24)


(22) a. Most students are diligent. b. dx[x are students & dy[y does not overlap x & y are students] ] (23) Most semantics students are diligent.


5 RELATIVE READINGS OF MOST AND NPI LICENSING In addition to the proportional (‘more than half ’) reading, most has a relative reading, illustrated in (25). For (25) to be true, Sue need not own more than half of the Beatles albums; she need only own more than any other relevant individual owns. A question arises as to what happens with NPI licensing in relative readings of most (and superlatives more generally). In English, the relative reading of most is signaled by the presence of the definite determiner (for reasons that are unknown): (25)

Sue owns the most Beatles albums. ‘Sue owns more Beatles albums than anyone else does.’

(26) LF for relative reading: Sue -est 1[ 2[ t2,e owns [d8 [ t1,d [many : j————————–—j albums] ] ] ] ] This raises an interesting question. If -est is SDE and can raise just below the subject, perhaps it should license any NPI c-commanded by the subject. Example (27)a shows that it does not. Notice, however, that relative most does license NPIs in the NP of its containing DP, compare (27)b. (27) a. Sue (*ever) owns the most books. LF: Sue -est 1[ever owns [t1,d many books] ] b. Sue owns the most [NP books that have ever been banned for profanity]. LF: Sue -est 1[ owns [ D [t1,d [ many [NP books that . . . ever . . .] ] ] ] ] (28) Sue (*ever) talked to no one. Possible LF: no one 1[Sue ever talked to t1] There are two possible approaches to explaining the data in (27). On the first approach, the reason licensing fails in (27)a is demonstrated in (28): NPIs in English must be c-commanded 7

To allow the class of individuals to which Sue is compared to be contextually restricted, the superlative itself must carry a covert restriction, C. I follow Hackl (2009: 79) and others in assuming that C is set equal to the denotation of the NP when -est remains in situ. The addition of C introduces some additional wrinkles that are addressed in Section 6. 8 I follow Szabolcsi (1986) and Heim (1999) in assuming that the definite determiner is converted to d at LF in the relative reading.


I follow Hackl (2009), who follows Heim’s (1999) and Szabolcsi’s (1986) accounts of relative (or ‘comparative’) superlatives, in assuming that the relative reading of most derives from covert movement of the superlative morpheme.7 The subscripts e and d in (26) indicate the semantic types of the traces.

Jon Gajewski 133

6 COMMENTS ON CONTEXTUAL RESTRICTION IN RELATIVE SUPERLATIVES As noted in footnote 7, to allow the individuals that Sue is compared to in (25) to be contextually restricted, the superlative morpheme itself must be relativized to a comparison class C. This raises the question of how C should be incorporated into our semantics for superlatives in (15). In particular, we must reassure ourselves that its inclusion does not interfere with the NPI-licensing properties of -est. A standard approach to including C is given in Heim (1999): (29)

For all D of type > and x of type e, ½½-est(C)(D)(x) is defined only if x 2 C & dy[ y 6¼ x & y 2 C] & "z 2 C dd[D(d)(z) ¼ 1] When defined, ½½-est(C)(D)(x) ¼ 1 iff dd[D(d)(x) ¼ 1 & "y[y 6¼ x & y 2 C / D(d)(y) ¼ 0]]

Note, in particular, that Heim assumes that every member of C has the degree predicate D to some degree.9 This assumption is problematic for NPI licensing, as I will now show. Let us begin by assessing the SDE-ness of superlatives with this presupposition, informally. For example, does being the tallest student Strawson entail being the tallest semantics student? Example (31) shows that satisfying (30)a Strawson entails satisfying (30)b. 9

Hackl (2009) follows Heim on this point, though he does not state the universal presupposition explicitly. Hackl’s truth conditions for -est do, however, reference the maximal degree to which each individual in C has D. Thus, he must assume that every member of C has D to some degree.


overtly by their licensers (see Ladusaw 1979: 111 ff., but see also Uribe-Etxebarria 1996). Even though negative quantifiers can in some circumstances scope over other quantifiers, they do not license NPIs under inverse scope. The NPI in (27)b, on the other hand, is licensed because it is c-commanded by the base position of -est, just like the NPI in (20). The second approach to (27) would be to adopt the idea that relative readings are not derived by movement but by contextual restriction (cf. Sharvit & Stateva 2002). Then the NPI in (27)a would never be c-commanded by -est and licensing would not be expected. The NPI in (27)b would still be licensed in the surface scope of -est.


(30)

a. tallest student b. tallest semantics student (31) -est is Strawson DE Proof: Suppose ½½-estC tall student(a) ¼ 1, then a and another individual are in C, C is a subset of the students and a is taller than all other members of C. Now we assume the conclusion is defined; so C is a subset of the semantics students. If a is taller than all members of C, then a is taller than all semantics students in C.

(32)

-est is Strawson UE Proof: Suppose ½½-estC tall semantics student(a) ¼ 1, then a and another individual are in C, C is a subset of the semantics students and a is taller than all other members of C. Now we assume the conclusion is defined; so C is a subset of the students. If a is taller than all members of C, then a is taller than all students in C.

This conclusion holds because the presupposition of the premise guarantees that the members of the contextual restriction are all semantics students. Thus, being taller than all semantics students in C means being taller than all students in C—since C contains only semantics students. Hence, (29) predicts that -est is both SDE and Strawson UE. Guerzoni and Sharvit (2007) argue, building on Lahiri (1998), that expressions that are both SDE and Strawson UE cannot license NPIs. The example to which they point as support for this conclusion is the case of singular definites. Singular definites are both SDE and Strawson UE—as (33) and (34) show, respectively—but do not license NPIs (35). (33)

(34)

(35)

thesg is SDE The student is tall (which implies there is exactly one student). There is exactly one semantics student. [The semantics student is tall. thesg is Strawson UE The semantics student is tall. There is exactly one student. [The student is tall. *The student I have ever seen is tall.


This is a positive result, but here is the problem. The addition of the presupposition about C means that -est is also Strawson UE:

Jon Gajewski 135

So, the boxed presupposition in (29)—the standard approach to including C in the semantics of -est—leads to the disqualification of -est as an NPI licenser. Fortunately, there is reason to believe that the universal presupposition of (29) is too strong. Consider what this universal presupposition predicts for the context in (36). It says that all members of C must satisfy the degree predicate to some extent. Assuming that the context below sets C to the group of Canadians I know, this presupposition seems too strong. (36) Of all the Canadians I know, Bill owns the longest yacht.

(37)

(38)

For all C of type <e,t>, D of type > and x of type e, ½½-est(C)(D)(x) is defined only if x 2 C & dd[D(d)(x) ¼ 1] & dy[ y 6¼ x & y 2 C & dd[D(d)(y) ¼ 1] ] When defined, ½½-est(C)(D)(x) ¼ 1 iff dd[D(d)(x) ¼ 1 & "y[y 6¼ x & y 2 C / D(d)(y) ¼ 0]] -est is Strawson DE Proof: Suppose ½½-est tall student(a) ¼ 1, then a is a student, there is another student in C, and a is taller than all other students in C. Now we assume the conclusion is defined; a is a semantics student. If a is taller than all students in C, then a is taller than all semantics students in C.

Unlike the lexical entry in (29), however, the lexical entry in (37) does not make -est Strawson UE. Let us show this by constructing a counterexample to the claim that -est is Strawson UE. We will show that (39)a does not Strawson entail (39)b. (39)

a. Bill is the tallestC semantics student. b. Bill is the tallestC student.


This sentence does not suggest that all the Canadians I know own yachts. Rather the context just winnows the individuals I am comparing Bill to down to my Canadian acquaintances. This suggests that a weaker presupposition is preferable. I propose that we amend (29) to include a weaker existential presupposition concerning C, see (37). In the context of (36), this implies that the superlative presupposes that there is at least one Canadian I know other than Bill who owns a yacht. This is unobjectionable. A further benefit to the weakening of the presupposition is the effect that this has on our predictions about the NPIlicensing capabilities of superlatives. The lexical entry in (37) makes -est SDE, compare (38).


7 CONCLUSION The NPI-licensing abilities of determiner most have long stood as a thorn in the side of theories that seek to explain the distribution of NPIs in terms of downward entailingness. I have argued that the appearance of NPIs in the restrictor of most is compatible with such DE theories. The keys to my analysis have been (i) the recognition of covert complexity in the structure of most, argued for by Hackl, and its effects on our judgments about monotonicity and (ii) fine-tuning the presuppositions of superlatives in a way that dovetails with von Fintel’s Strawsonian version of the DE theory. Acknowledgements Thanks to two anonymous Journal of Semantics reviewers and participants in the fall 2009 LING 6010 workshop at the University of Connecticut for invaluable comments on this paper. All errors are my own.

JON GAJEWSKI Department of Linguistics, U-1145 University of Connecticut 337 Mansfield Road Storrs Mansfield, CT 06269 USA e-mail: [email protected]


Suppose that C contains three individuals: Bill, Fred and Mary. Bill and Fred are both semantics students and Mary is a phonology student. Bill is 6# tall, Fred is 5#9$ tall and Mary is 6#2$ tall. The presuppositions of -est are met with respect to C in both (39)a and (39)b. However, (39)a is defined and true in this scenario; while (39)b is defined and false: Bill is a student in C, there is another student in C, but Bill is not taller than all other students in C. In sum, I have proposed that -est carries an existential presupposition about C, (37). This is weaker than the standard universal presupposition, (29). The benefits to this are twofold. First, it handles scenarios like (36) better than a universal presupposition. Second, unlike the universal presupposition, the existential presupposition makes -est SDE but not Strawson UE. In this way, we can incorporate contextual restriction into the semantics of relative superlatives, without losing our predictions concerning NPI licensing.

Jon Gajewski 137

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