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Acquiring quantificationSmits, Erik-Jan

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AcquiringQuantification

How children use semantics andpragmatics to constrain meaning

Erik-Jan Smits

Groningen Dissertations in Linguistics 84ISSN 0928-0030 | ISBN 978-90-367-4508-6

c©2010, E.J. SmitsPrinted by Scanlaser B.V., Zaandam.

The research presented in this thesis was carried out under the auspices of the NetherlandsNational Graduate School of Linguistics (Landelijke Onderzoeksschool Taalwetenschap,LOT) and the Center for Language and Cognition Groningen of the Faculty of Arts of theUniversity of Groningen. The research reported on in chapter 5 was supported by aFulbright 2005/2006 promovendus grant to Erik-Jan Smits to carry out research at theUniversity of Massachusetts, Amherst and by a collaboration grant (#235-70-006) of theDutch scientific research organization NWO to Angeliek van Hout (University ofGroningen) to initiate joint research between the University of Massachusetts, Amherst andthe University of Groningen.

This document is prepared with LATEX 2ε and typeset with pdfTEX in Adobe Garamond, atypeface modified for LATEX 2ε by Walter Schmitt and made available for free under theAladdin Free Public License at http://www.artifex.com/downloads/.

RIJKSUNIVERSITEIT GRONINGEN

Acquiring QuantificationHow children use semantics and pragmatics to constrain meaning

Proefschrift

ter verkrijging van het doctoraat in deLetteren

aan de Rijksuniversiteit Groningenop gezag van de

Rector Magnificus, dr. F. Zwarts,in het openbaar te verdedigen op

donderdag 16 september 2010om 13:15 uur

door

Erik-Jan Smitsgeboren op 19 Mei 1981

te Delft

Promotor: Prof. dr. J. Hoeksema

Copromotores: Dr. A. van HoutDr. B. Hollebrandse

Beoordelingscommissie: Prof. dr. P. HendriksProf. dr. H. de HoopProf. dr. T. Roeper

Preface

In the past six years, I carried out research in Groningen, Amherst and Sunderland(Massachusetts, United States of America) and Barneveld. Thanks to all the children,their parents and teachers that helped me with my experiments at De Pendinghe(Groningen), De Boomhut (Groningen), De Vrije school (Groningen), JohannesCalvijn School (Groningen), Prins Willem Alexander school (Barneveld), Mark’sMeadow Elementary School (Amherst, Massachusetts), Sunderland ElementarySchool (Sunderland, MA) and Sandhill School (Amherst, MA). And thank youAnke for drawing the pictures of some of the experiments and the ones in this thesis.

I would like to thank Jack Hoeksema, Angeliek van Hout and Bart Hollebrandsefor being my (co-)promotores. Thank you Angeliek, for going through variousdrafts of this thesis. Thank you for being a coach, raising over and over again thosequestions that needed to be answered first, and all the effort you put into readingmy drafts and giving comments. This same applies to Bart, but moreover thank youBart for introducing me into the fascinating world of first language acquisition inearly spring 2003, setting up experiments and working with children. Thank youalso for all the beers and the conversations about jazz and all that.

As a visiting PhD-candidate, I worked together with Tom Roeper in the fall/winterof 2005/6 at the University of Massachusetts, Amherst. Tom, I will never forget ourdiscussions, designing my experiment and everything I learned from you and thepeople I met at Umass. Thank you Tom and thank you Lisa Selkirk for invitingme. Thank you Jill DeVilliers, Chris Potts, Barbara Partee, Helen Stickney, TanjaHeizmann, Leontine Kremers, Arjen Zondervan (I will never forget biking aroundin the Happy Valley). A great thanks also to the Fulbright organization, the Dutchscientific research organization NWO and the Center for Language and CognitionGroningen that enabled me to stay at Umass.

At the university of Groningen, there are many people to thank. Just to thank afew (with the danger of forgetting a lot of people), thank you roommates MarjoleinDeunk and Holger Hopp, colleagues (Petra Hendriks, Jennifer Spenader, DickyGilbers, Roel Jonkers) and fellow PhD-candidates (Leonoor van der Beek, GerlofBouma, Jantien Donkers, Tanja Gaustad, Dieuwke de Goede, Julia Klitsch, MarliesKluck, Lonneke van der Plas, Jori Mur, Robbert Prins, Eleonora Rossi, LiefkeReitsma, Maartje Schreuder, Rasmus Steinkraus). In addition, a great thanks to mypresent colleagues at Infozorg and Ilona for enabling me to finish this thesis.

i

ii

Finally, family and friends need to be thanked. My parents and parents-in-lawnever stopped pushing me to finish the thesis and in the meanwhile never stoppedbeing as proud as they could be. Thank you mam and pap for everything. Andthank you oma for calling me every single week and keeping track of the thesis andits topic. Thank you Cora, Barry and my brothers-in-law, Maarten and Jan-Willemand of course Vanya and Judy for all kinds of distraction. And thank you Jackelien,Jacco, Annemarie, Lisette, Theo, Inge, Erik-Jan and of course Herman for all thosestimulating discussions at the faculty or somewhere else about related or non-relatedissues. Thank you Marjolein en Herman for being my paranimfen.

For you Hanne, I saved the last lines. Only you know how much you helpedme, how much you know about the topic of this thesis and only you know thatyour name should be on the cover as well (given that you made sure it was printed).Thank you for supporting me, helping me finishing it and following me everywhere,even to Massachusetts. I will never forget it.

voor Hanne

Contents

Contents iv

1 Introduction 1

2 The meaning and acquisition of quantifying expressions 72.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 The meaning of quantifying expressions . . . . . . . . . . . . . . . 82.3 The acquisition of quantification . . . . . . . . . . . . . . . . . . . 12

2.3.1 Logical reasoning in child language . . . . . . . . . . . . . 122.3.2 Children’s structures of quantified sentences . . . . . . . . 16

2.3.2.1 Roeper and De Villiers (1991) - a syntactic account 162.3.2.2 Philip (1995) - a semantic account . . . . . . . . . 172.3.2.3 Crain et al. (1996) - a methodological explanation 212.3.2.4 Drozd (2001) and Geurts (2003) - two pragmatic

accounts . . . . . . . . . . . . . . . . . . . . . . 222.4 Summary and concluding remarks . . . . . . . . . . . . . . . . . . 24

3 Quantification at the interfaces 273.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Quantification at the interfaces . . . . . . . . . . . . . . . . . . . . 27

3.2.1 Discourse context . . . . . . . . . . . . . . . . . . . . . . 283.2.2 Visual context . . . . . . . . . . . . . . . . . . . . . . . . 29

3.3 The Equilibrium Hypothesis . . . . . . . . . . . . . . . . . . . . . 343.3.1 Acquisition at the interfaces . . . . . . . . . . . . . . . . . 353.3.2 The Equilibirum Hypothesis in relation to previous studies 36

3.4 Optimal acquisition of optimal meaning . . . . . . . . . . . . . . . 373.4.1 A short introduction to Optimality Theoretic Semantics . 373.4.2 Optimal quantification . . . . . . . . . . . . . . . . . . . . 39

3.5 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . 43

4 Acquisition at the syntax-semantics interface 454.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.2 (Floating) Quantification in child language . . . . . . . . . . . . . 46

iv

Contents v

4.3 Quantifier flotation and the Dutch quantifier allemaal . . . . . . . 494.4 Hypothesis and predictions . . . . . . . . . . . . . . . . . . . . . . 514.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.5.1 Experiment I: Quantifier scope . . . . . . . . . . . . . . . 524.5.1.1 Method . . . . . . . . . . . . . . . . . . . . . . . 524.5.1.2 Results . . . . . . . . . . . . . . . . . . . . . . . 544.5.1.3 Discussion . . . . . . . . . . . . . . . . . . . . . 55

4.5.2 Experiment II: Quantifier scope and extra agents and objects 554.5.2.1 Method . . . . . . . . . . . . . . . . . . . . . . . 574.5.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . 594.5.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . 59

4.5.3 Experiment III: Quantifier position and interpretation . . . 604.5.3.1 Method . . . . . . . . . . . . . . . . . . . . . . . 614.5.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . 614.5.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . 63

4.6 General discussion and conclusions . . . . . . . . . . . . . . . . . 64

5 The many meanings of many 675.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.2 The many meanings of many and domain restriction . . . . . . . . 685.3 Semantic holes, incomplete quantifier domains and pragmatic rea-

soning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735.4 Accounting for the many meanings of many . . . . . . . . . . . . 77

5.4.1 Semantic or pragmatic context? . . . . . . . . . . . . . . . 775.4.2 Many in bi-directional Optimality Theory . . . . . . . . . 78

5.5 The relevance of many from an acquisition viewpoint . . . . . . . 885.5.1 Children’s understanding of weak versus strong quantifiers 89

5.5.1.1 Drozd and Van Loosbroek (1999) and Drozd (2001) 895.5.1.2 Krämer (2000;2005a,b) . . . . . . . . . . . . . . . 905.5.1.3 Geurts (2003) . . . . . . . . . . . . . . . . . . . 91

5.5.2 Pragmatic constraints . . . . . . . . . . . . . . . . . . . . 935.5.3 Intermediate conclusions . . . . . . . . . . . . . . . . . . . 95

5.6 Hypothesis and predictions . . . . . . . . . . . . . . . . . . . . . . 965.7 Experiment: the acquisition of many and many of . . . . . . . . . 98

5.7.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 985.7.1.1 Subjects . . . . . . . . . . . . . . . . . . . . . . 985.7.1.2 Materials . . . . . . . . . . . . . . . . . . . . . . 995.7.1.3 Procedure . . . . . . . . . . . . . . . . . . . . . 1015.7.1.4 Coding . . . . . . . . . . . . . . . . . . . . . . . 102

5.7.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1035.8 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . 103

6 Quantifying in context 107

vi Contents

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1076.2 The acquisition of quantification in relation to discourse . . . . . . 108

6.2.1 Satisfying the Condition of Plausible Dissent . . . . . . . . 1096.2.2 Presupposed sets . . . . . . . . . . . . . . . . . . . . . . . 1106.2.3 Providing a discourse topic . . . . . . . . . . . . . . . . . . 1136.2.4 Putting discourse into context . . . . . . . . . . . . . . . . 113

6.3 Context dependent domain restriction . . . . . . . . . . . . . . . . 1156.3.1 Optimality Theoretic Semantics; Hendriks and De Hoop,

2001 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1156.3.2 Centering Optimality Theory; Beaver, 2004 . . . . . . . . 118

6.4 Optimal acquisition; hypotheses and predictions . . . . . . . . . . 1246.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

6.5.1 Experiment 1: Align-Q and the Discourse Context . . . . . 1266.5.1.1 Method . . . . . . . . . . . . . . . . . . . . . . . 1286.5.1.2 Results . . . . . . . . . . . . . . . . . . . . . . . 1306.5.1.3 Discussion . . . . . . . . . . . . . . . . . . . . . 132

6.5.2 Experiment II: Forward Directionality and the DiscourseContext . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1336.5.2.1 Method . . . . . . . . . . . . . . . . . . . . . . . 1346.5.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . 1376.5.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . 138

6.6 General discussion and conclusions . . . . . . . . . . . . . . . . . 140

7 Summary, Discussion and Conclusions 1437.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1437.2 Main findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

7.2.1 Allemaal and the syntax-semantics interface . . . . . . . . . 1447.2.2 Many and the syntax-pragmatics interface . . . . . . . . . . 1477.2.3 The universal quantifier and the pragmatics-semantics interface148

7.3 Discussion and implications . . . . . . . . . . . . . . . . . . . . . 1507.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

Bibliography 153

Nederlandse samenvatting 165

Groningen Dissertations in Linguistics 173

1Introduction

Quantifiers enable us to talk beyond the realm of single entities; by means of wordslike many, all and every, we are able to generalize and to refer to a set of entities.Moreover, we are able to attribute characteristics to a set by means of these particularwords. Consider the sentence in (1).

(1) All children are playing outside

In (1), the quantifier all relates the set of children to the set of entities playingoutside, by stating that the former set is a subset of the latter.

All languages share the property of enabling the speaker to make such general-izations. However, the interpretation of quantified sentences has also been arguedto require “some more cognitive capacity above the normal apprehension of entitiesin the world” (Bloom, 2000:216). Acquiring quantification poses a difficult task forthe language learner. How and at which age does a child combine the concept of aset, the possibilities to refer to it and to reason about the relation between sets (i.e.to determine whether the children in (1) are indeed all playing outside or whetherthere is a subset of children that is not)? This thesis aims to answer this questionand connects cognitive development to the acquisition of one’s first language.1

The complex nature of quantification explains why its acquisition has been ad-dressed in various disciplines in the past decades. Starting with the groundbreakingwork of the psychologists Inhelder and Piaget (1958), the acquisition of quantifi-cation continued to be an often studied subject in subsequent years. In addition,given the indisputable effect of the linguistic structure of a quantified sentence onits meaning, the acquisition of quantification received much attention in linguisticwork on the growth of syntax, semantics and, in recent years, pragmatics in earlychildhood. Unfortunately, in neither discipline all characteristics of quantifiedexpressions were taken into account simultaneously. This resulted in a deadlock in

1Cf. the viewpoint of, among many others, Roeper and DeVilliers (1991) on the study of quantifi-cation that it “might reveal how cognition connects to grammar and how they are intertwined in theprocess of quantification” (1991:225).

1

2 Introduction

recent years. On the one hand, children were argued to apply adult like interpre-tations to quantifiers and, hence, there would not be any need to study children’sunderstanding of quantifiers. On the other hand, various people continued to findexperimental evidence for Inhelder and Piaget’s original observation that childreninterpret quantified sentences differently than adults. This underlined the need toexplore the exact conditions in which children show non-adult-like behavior inmore detail than had been done in the past two decades.

In addition, recent theoretical work on the meaning of quantifiers points ina similar way at the need to zoom in on the conditions in which children havebeen argued to show non-target-like or target-like behavior. Whereas, traditionally,quantifiers have been described in terms of their semantic characteristics and theway syntax provided their quantificational domain and nuclear scope (respectivelythe noun phrase children and the verb phrase are playing outside in (1)), recenttheories analyzed the possible effects of (visual or discourse) context on the meaningof quantified sentences and propose an account for these effects (e.g. Hendriksand De Hoop, 2001). Consider the example in (2) (from Hendriks and De Hoop,2001:17):

(2) The buildings are all two and three stories running half a block deep withbrick and glass fronts. Most were built together, a few have narrow alleysbetween them. Many are still boarded up, a couple were burned out years ago.

( John Grisham, The Rainmaker, cited in Hendriks and De Hoop, 2001)

This example illustrates that quantifiers take a noun phrase from the discourse(buildings) as their domain. This suggests that quantification is not a matter ofjust keeping track of the syntactic structure of a sentence and the meaning of aparticular word (cf. the difference in meaning between all and many), but ratherthat quantification is a matter of combining information from various sources (thesentence itself and the context).

Contextually inferred or pragmatic aspects of meaning have often been disre-garded in first language acquisition research (see also e.g. Papafragou 2006). Inthe past, researchers have chosen to focus on semantics in order to demonstratethat child language is constrained by specified universal knowledge (see Crain andThornton, 1998)). Given recent work that shows that pragmatics enriches the un-derspecified linguistic meaning of language (cf. also the radical pragmatics school,Cole (1981)) first language acquisition research crucially needs to take into accountthis interplay between syntax, semantics and pragmatics.2

In this thesis, I study this interplay in addressing the question to what extentchildren master the meaning of quantifiers. How does the child acquire somethinglike a ‘quantity sense’, i.e. the ability to generalize across entities, to refer to setsof entities by means of a quantified expression and to reason about the relations

2For recent initiatives, cf. for example the work of Van Hout (2008) and Spenader, Smits, andHendriks (2009).

Introduction 3

between these sets (i.e. to combine syntax, semantics and pragmatics)?3 Further-more, since quantifiers are typically related to their meaning by abstract (syntactic,semantic and pragmatic) rules, how does a child know how these rules work andhow does she know when to apply each of these different rules?

In sum, in this thesis I explore the hypothesis that acquiring quantification is amatter of establishing a target-like equilibrium between syntax, semantics and prag-matics. This thesis aims to contribute to a better understanding of the interactionbetween syntax, semantics and pragmatics and its role in first language acquisition.Moreover, the answer to this question will raise challenging predictions for futurefirst language acquisition research. If it is indeed the case that the acquisition ofquantification is a matter of fine-tuning the interaction between syntax, semanticsand pragmatics, it follows that studying the course of language development is amatter of unraveling which factors are at play at certain stages in developmentinstead of determining whether a child shows target-like behavior or not.

After presenting a summary of the main findings in the field in the past decadesregarding children’s understanding of quantified sentences in chapter 2 and dis-cussing my Equilibrium Hypothesis in detail in chapter 3, I present the data ofsix experiments addressing children’s understanding of quantified sentences in dif-ferent contexts. Chapter 4 presents three experiments, addressing the questionhow children use the syntactic structure of a quantified sentence when the visualcontext preceding these sentences is manipulated. Following up the work by Roeper,Strauss, and Pearson (2006) that the existence of floating quantifiers in the input tothe child might explain why children ignore the syntactic structure, I investigateDutch children’s understanding of the floating quantifier allemaal (‘all’). Floatingquantifiers are not followed by the noun phrase they quantify over, rather oneneeds to find the appropriate noun phrase in the sentence to determine its domain.Consider (3).

(3) DeThe

kinderenchildren

spelenplay

allemaalall

buitenoutside

‘The children are all playing outside’

In (3), the quantifier binds the variable introduced by de kinderen (‘the children’),but unlike (1), the quantifier does not precede the variable it binds. Roeper et al.(2006) argue that it is this characteristic of floating quantifiers that causes the child tolet a quantifier bind non-target variables, also for non-floated quantifiers. Childrenwould ignore the syntactic information provided by a quantified sentence and takethe entire sentence to supply a variable for the quantifier. In Dutch, the quantifierallemaal ‘all’ can be used either as a floating or non-floating quantifier, with different

3The development of this ‘quantity sense’ contrasts with the well-studied development of numbersense in infants. A clue that there exists something like a ‘quantity sense’, as opposed to the well-studiednumber sense in psychology, follows for example from the work Hurewitz, Papafragou, Gleitman,and Gelman (2006). They found that children of four years of age show different acquisition paths forcounting and quantification.

4 Introduction

meanings. The two uses are easily distinguishable (cf. the universal allemaal in(3) and the existential allemaal in (4)), and, hence, an ideal case to test children’sunderstanding of floating quantifiers versus non-floating quantifiers.

(4) ErThere

spelenplay

allemaal[allemaal]

kinderenchildren

buitenoutside

‘There are playing a lot of/many children outside’

The results of three experiments addressing children’s interpretation of this quantifiershow that children do not only include sets denoted by the object and/or the subjectin the domain of floating allemaal, but additionally include visually represented sets.This suggests that children differ from adults in their mapping of meaning to formand over-rely on visual clues to restrict the quantifier domain.

In chapter 5, I study the many meanings of the quantifier many in Englishchildren. Recently, it has been suggested that the acquisition of universal quan-tification can be characterized in terms of domain restriction that is characteristicfor existential quantifiers (see Geurts, 2003), in particular in terms of the contextdependent domain of many (Drozd and Van Loosbroek, 1999). However, there areonly few results to date of children’s understanding of quantifiers like many andtheir context dependence (with the exception of Krämer, 2005a,b on Dutch veel,‘many / a lot of’). Many allows different kinds of cardinal and proportional readings.Context plays an important role in establishing the actual interpretation of many.The possible interpretations of many point at the necessity to characterize (implicit)domain restriction in terms of the interplay between syntax, semantics and pragmat-ics (see Hendriks and De Hoop, 2001). This chapter presents experimental data onchildren’s understanding of many. The results suggest that children’s non-adult-likeunderstanding of many is due to the different order they apply syntactic, semanticand pragmatic constraints to determine its meaning.

Chapter 6 discusses children’s understanding of quantified expressions in dis-course. Various accounts argue that children are able to understand quantifiedsentences adult-like if the quantified sentence is embedded in a proper discourse(cf. among others Crain, Thornton, Boster, Conway, Lillo-Martin, and Woodams,1996). Given children’s non-adult like interpretation of quantified sentences whenthese are not embedded in a discourse, the question arises why and under whichconditions children show adult-like behavior if a discourse is provided. What are thecharacteristics of a discourse that enables a child to understand quantified expressionsadult-like? In chapter 6, I test children’s understanding of quantified expressions inseveral discourse manipulations.

In chapter 7, I summarize the experimental findings presented in this thesiswhich provide experimental evidence for the hypothesis that pragmatic principlesdetermine, next to linguistic structure, the meaning and acquisition of language.Formulating them in Optimality Theoretic Semantics (Hendriks and De Hoop,2001), I conclude that the results show that the acquisition of quantification isindeed a matter of establishing a target-like equilibrium between the usage of syn-

Introduction 5

tactic, semantic and pragmatic constraints. I argue that this provides the key forunderstanding the actual nature of the child’s quantificational system. Finding thebalance in using syntactic, semantic and pragmatic constraints is the necessary steptoward an adult understanding and use of quantification. This raises challengingquestions for future first language acquisition research and underlines the need ofjoined research of psychologists, theoretical syntacticians, semanticists, pragmaticistsand first language acquisition researchers.

2The meaning and acquisition of quantifyingexpressions

2.1 Introduction

In the past four decades, the acquisition of quantification received attention invarious academic disciplines. Originating from a psychological interest in the devel-opment and growth of logical thinking in the child (cf. the groundbreaking workof Inhelder and Piaget (1958, 1959, 1964)), the study of children’s surprisingly non-adult-like interpretations of quantified sentences during the seventies and eightieswas in the hands of the psychologists Donaldson and Lloyd (1974), Bucci (1978)and Freeman, Sinha, and Stedmon (1982). Since then, the study of the acquisitionof quantification shifted more and more to the field of linguistics and has beenused to illustrate universal syntactic, semantic and pragmatic constraints in variouslanguages.

Although Freeman et al. (1982) already pointed at the potential of the subject ofquantification to acquire insights into the course of language development due toits relatively circumscribed domain and the cross-disciplinary approach it allows,the study of the acquisition of quantification resulted in a deadlock in subsequentyears. Opposite claims were made concerning the nature of the child’s quantifiersystem, depending on the particular discipline the subject was studied from. Crain,Thornton, Boster, Conway, Lillo-Martin, and Woodams (1996) claim that, if theright methodology is used, children do not show any non-target-like behavior atall. And despite the possibility of joint research into the psychological foundationsof logical operators in language, the acquisition of quantification continues to bestudied in each discipline separately.

In this chapter, I aim to show that only by taking both linguistic and psychologi-cal work into account, we are able to break the deadlock and to gain more insightinto the child’s actual understanding of quantifying expressions. Before turning toan overview of previous studies and drawing this conclusion, I will first addresstwo characteristics of quantifying expressions that play a key role in this debate and

7

8 The meaning and acquisition of quantifying expressions

introduce some terminology that will be used throughout this thesis to refer to thesemantics of quantifying expressions.

2.2 The meaning of quantifying expressions

As a first characteristic, quantification allows one to state generalizations. In English,for example, it is possible to apply a predicate not just to a particular individual asin (1) but, by means of words like all, every and many, to a set of individuals. Toexpress, for example, that not only John is riding a horse, but all cowboys are, onecould say (2).

(1) John is riding a horse

(2) All cowboys are riding a horse

In (2), the quantifier all ranges over the set of cowboys. The verb phrase containsthe generalization itself, i.e. the predicate to ride a horse. The quantifier and itsrange (i.e. the determiner phrase all cowboys) express for which individuals thispredicate holds. If (2) is true, it holds for all cowboys that they are riding a horse.Moving towards a more fine-grained definition of quantification that will functionas a starting point for the remainder of this thesis, I will now discuss the natureof quantification from various perspectives. First, I will introduce the functionalperspective taken on quantification in Generalized Quantifier Theory (Barwise andCooper, 1981) and illustrate the close parellel between the meaning of a quantifiedstatement and its syntactic structure. Although different at first sight, this mirrorsthe approach taken by Heim (1982) and Diesing (1992) I will introduce subsequently.Second, I will discuss how a quanifier like all differs from a quantifier like some.

In Generalized Quantifier Theory (henceforth GQT, Barwise and Cooper, 1981),the quantified expression (i.e. the quantifier together with its range) is argued totake the predicate and this results in a sentence. Moreover, in GQT, it is assumedthat, before the quantified expression (called a generalized quantifier1) takes thepredicate, the quantifier first combines with a common noun. Whether the sentenceis true or false, depends on whether the property of riding a horse applies to everysingle cowboy or not, or, to put it differently, whether or not the denotation of thepredicate is part of the denotation of the generalized quantifier. In this sense, thequantifier is taken to be a function that takes the predicate as an argument, resultingin a quantified statement.

This functional perspective taken in GQT on quantification, (but cf. also earlierwork by Mostowski (1957) and Montague (1973)) mirrors the syntactic structure of

1In GQT the quantifier together with its range c.q. common noun is called a generalized quantifier.However, in much work on quantification and likewise in this thesis, the term ‘quantifier’ is used torefer to both the quantified expression (quantifier and common noun) as in ‘generalized quantifier’ inGQT and to the quantifier itself. To avoid confusion, I will refer to the quantifier itself with the term‘quantificational determiner’ whenever the distinction matters.

2.2. The meaning of quantifying expressions 9

quantified statements as represented in (3). In (3), the DP combines with the VP.This crucially differs from a standard logical representation of (2) as in (4) in whichall cowboys is not treated as one syntactic constituent and so this representation doesnot mirror the syntactic structure of the quantified sentence.

(3) S

DP

D

All

NP

cowboys

VP

are riding a horse

(4) ∀x(cowboys (x)→ riding a horse (x))

In this thesis, I follow the approach taken in GQT and take the syntactic structurerepresented in (3) to account for the meaning of quantified sentences. For (2), thismeans that the generalized quantifier all cowboys is taken to denote a set of predicates(sets of individuals that share the characteristic of being a cowboy).

The question rises how this approach works if the object is being quantified overas in (5) or if the quantifier does not directly follow the common noun, as with theso-called floating quantifier all in (6).

(5) The cowboy sold all horsesa. #“All cowboys sold the horse”b. “The cowboy sold all horses”

(6) The cowboys are all feeding the horses

Floating quantifiers do not directly precede their range, but rather are ‘floated’.Crucially, however, only the noun phrase c-commanding the quantificational deter-miner can form the quantifier’s restriction. For example, the range of the floatingquantifier all in (6) is the set of cowboys; the noun phrase the cowboys c-commandsthe quantificational determiner. The noun phrase the horses does not c-command alland cannot be the quantifier’s range here. Clearly, more is needed than the syntacticstructure in (3) to cover the nature of quantified expressions. How does the syntacticstructure relate to the meaning of a quantified expression?

Diesing’s (1992) Mapping Hypothesis provides a solution to this problem. Start-ing out from a different perspective on quantified sentences, but one that is compati-ble with the functional perspective taken in GQT (Heim and Kratzer, 1998), shetakes quantifiers (in line with Heim’s (1982) tripartite structures) to denote relationsbetween two sets (cf. Barwise and Cooper, 1981; Zwarts, 1983; Van Benthem, 1986).In such a relational perspective, which goes back to Aristotle, quantified sentencesare represented as tripartite structures in which the quantifier (the operator) estab-lishes a relation between its first argument (called its “restrictive clause” in Heim,


1982) and second argument (called its “nuclear scope” in Heim, 1982) (Heim, 1982;Kamp, 1981).2 For example, (2) can be represented as in (7) in which the nounphrase cowboys is the restriction of all (also called its first argument or A set) andthe predicate to ride a horse its nuclear scope (or the quantifier’s second argument orB set).

(7) S

Operator∀x

Restrictionx is a cowboy

Nuclear Scopex rides a horse

Diesing’s Mapping Hypothesis states that material from the VP is mapped ontothe nuclear scope and material from the NP outside the VP is mapped onto thequantifier’s restriction. In the case of quantification over the object as in (5), Quanti-fier Raising along the lines of May (1985) applies at LF and the object raises to thebeginning of the sentence as in (8-a). According to Diesing’s mapping hypothesis,this is then mapped onto a tripartite structure as in (8-b). In the case of subjectquantification, the subject raises in a similar way to the beginning of the sentence.

(8) a. [all horsesNP ]i [the cowboys are feeding ei]V P

b. S

Operator∀x

Restrictionx is a horse

Nuclear Scopethe cowboys are feeding x

A second characteristic of quantifiers is that they differ in relating their restric-tion and nuclear scope. Consider the quantifier all in (9) and some in (10).

(9) All boys are playing outside

(10) Some boys are playing outside

To determine the truth value of (9), we have to check whether or not the set of boysthat are not playing outside is empty; if there are boys that are playing inside insteadof outside, this sentence turns out to be false. Using a Venn-diagram in figure 2.1

2As will turn out to be important in the next section, along the same lines and by assuming an eventvariable, temporal quantification as in (i.) can be represented with a tripartite structure. For (i.), theadverb always is the operator quantifying over event variables, x are cowboys as the operators’s restrictionand x is riding a horse at event e as its nuclear scope (see Lewis, 1975).

(i.) The cowboys are always riding a horse

2.2. The meaning of quantifying expressions 11

below where A is the set of boys and B the set of individuals playing outside, thismeans that the sentence is false if the highlighted part is not empty (i.e. if there areboys who are not playing outside). Conversely, if the grey area (i.e. the set of boysthat are not playing outside) is empty, the sentence is true; all boys indeed turn outto be playing outside. The denotation of the quantifier’s restriction (A) minus theintersection of this set with the quantifiers nuclear scope (B), is important in theinterpretation of this universal quantifier.

A B

A−B

Figure 2.1: Set-theoretic representation of the denotation of all for which holds thatA - B (i.e. the grey area) should be empty

On the other hand, to evaluate the truth of (10), one has to consider whetherthe set of boys that are playing outside (i.e. the intersection of the set of boys andthe set of players outside) is empty or not. In terms of the Venn-diagram in figure2.2 where A is the set of boys again and B the set of individuals playing outside, thismeans that the sentence is true if the highlighted part in 2.2 is not empty. For thisexistential quantifier, it is the intersection that matters.

In sum, the relation that all and some establish between their restriction andnuclear scope is expressed in (11) and (12). Whereas all requires its restriction to bea subset of its nuclear scope, some only requires that the intersection of restrictionand nuclear scope is not empty.

(11) All(A,B) = 1 iff A ⊆ B(12) Some(A,B) = 1 iff A ∩ B 6= ∅

Milsark (1979) showed that the difference between some and all in the way theyrelate their arguments to each other also manifests itself syntactically. He observedthat some quantifiers are allowed in existential there-sentences, e.g. some, several,many, whereas others are not, e.g. all, every, most. This is illustrated in (13).

(13) a. There are some/many/several men that are crazy about green old-timers.


A B

A ∩B

Figure 2.2: Set-theoretic representation of the denotation of some for which holdsthat A ∩ B (i.e. the grey area) should not be empty

b. *There are all/every/most men that are crazy about green old-timers.

Milsark (1979) called this the ‘weak-strong distinction’ and labeled quantifiers thatcan occur in an existential there-sentence ‘weak’ and those that can not ‘strong’. Inthe terminology of Keenan (2002) (cf. Barwise and Cooper, 1981), the differencebetween these two kinds of quantifiers is seen as that between, respectively, co-intersective and intersective determiners: “Co-intersective (generalized universal)Dets depend on A - B, the A’s that are not Bs, just as intersective Dets depend on A∩ B" (Keenan 2002: 633). Since an existential sentence introduces an intersectionof two sets with there are ... and only weak quantifiers present such an intersection,strong quantifiers are blocked from this construction.

In conclusion, quantifiers relate two sets to each other, respectively called theirdomain restriction and nuclear scope. The relation quantifiers establish betweenthese sets differs per quantifier type. Different labels have been proposed to distin-guish quantifiers (weak versus strong, intersective versus co-intersective). Through-out this thesis and following Milsark, I will label a quantifier that establishes anintersective relation “weak quantifiers” and quantifiers that establish a subset relationbetween domain restriction and nuclear scope “strong quantifiers”.3

2.3 The acquisition of quantification

2.3.1 Logical reasoning in child language

Inhelder and Piaget (1958, 1959) present the first data on children’s interpretation ofquantified sentences. They asked children whether, for example, all circles are black

3As will become clear in subsequent chapters, it is important to distinguish the form and the meaningof a quantifier. The quantifier many for example is traditionally called a weak quantifier, but allows bothan intersective and a subset relation between its arguments. I will return to this issue in chapter 5.

2.3. The acquisition of quantification 13

in cases like the one depicted in figure 2.3. Children between four and seven years ofage answered “no, there are two black squares”. Similar non-adult-like answers weregiven when they asked the children whether all squares are white (child answer: “no,because there is a black one”) or whether all circles are black in a situation in whichthere are five black circles and three white squares (child answer: “no, because thereare white ones”).

Figure 2.3: Are all circles black?

Inhelder and Piaget explained the children’s answers in terms of class inclusion.They argued that, until the age of seven, children are unable to grasp the idea that setscan be a subset of other sets and, as a result, are unable to get an adult interpretationof a sentence containing all. They suggested that children apply all to both thesubject (circles) and the predicate set (black entities). This would lead the child tointerpret “Are all the circles black” as (14-a) instead of the adult interpretation (14-b).Inhelder and Piaget called the child’s interpretation (14-a) false quantification overthe predicate.

(14) Are all the circles black?a. “Are all of the circles all of the black (things)?”b. “Are all of the circles some of the black things?”

Whereas Inhelder and Piaget pointed at children’s lack of the notion of classinclusion, Donaldson and Lloyd (1974) take a different perspective on the matterand approach children’s understanding of quantified sentences in the context ofmapping linguistic form to the world. Does a child understand a quantified sentenceas a description of a particular situation? Being one of the first to use the by nowwell-established truth value judgment task, they asked children to judge quantified


sentences as true or false given a particular situation. In particular, they askedchildren to press a bell if a doll said something right and to press a buzzer if thedoll said something wrong. They asked children whether a sentence such as (15-a)correctly describes situations like the one in (15-b).

(15) a. All the cars are in the garagesb. 3 cars in garages, 1 garage empty

Their findings show that children, when they encounter a situation with two sets,they have difficulties determining which set is quantified over. The most commonresponse pattern they find is that, in the case of (15), children reject the sentence. If,conversely, they are shown a situation in which all garages are filled with cars andthere are no extra garages, they accept the sentence target-like. Note that also in thislatter case, the child has to quantify over two sets (cars and garages).

Donaldson and Lloyd propose a three-step account of what occurs when a childis faced with a situation like (15-b) and is asked to make a true/false judgment. First,they argue, the child looks a the physical array of objects and determines whatit is all about. Second, the child hears the question and interprets this question.Crucially, Donaldson and Lloyd take this interpretation to be deviant from theadult one; instead of being constrained by the syntactic structure, they take thechild to only derive a general theme from the sentence. As they put it: “linguisticconsiderations leave open to them certain options which the adult analysis woulddisallow” (1974:82). For (15), this means that the child takes the sentence to be aboutcars, garages, one being in the other and all. As a third step, they argue, the childtries to reconcile the physical array with the sentence. But then “the physical arraydisposes him, by virtue of its own form, to certain modes of structuring it” (1974:82).For (15), they take this to mean that the emptiness of one of the garages attracts thechild’s attention. Due to the lack of a decisive linguistic structure, the structuringof the physical array would then determine the child’s answer. As Donaldson andLLoyd put it, a quantified statement is difficult to judge for a child because:

“(a) if the linguistic constraints are not fully observed, the statementadmits of more than one interpretation as regards the relations involvedand (b) the physical array disposes the subject to favor the wrong inter-pretation.” (1974:83)

Bucci (1978) arrives at a similar conclusion. Taking the findings of Inhelder andPiaget to indicate children’s preference for a structurally neutral interpretation ofquantified sentences, she claims that children lack a subject-predicate distinction insentences of the form exemplified in (16-a). This results in a default, structurallyneutral interpretation of universally quantified sentences of the form exemplified in(16-b).

(16) a. All circles are blackb. All, circles, black


The child’s preference for this structurally neutral interpretation illustrates, accord-ing to Bucci, the existence of a pragmatic processing mode. In this mode, she claims,children do not determine the meaning of a quantified sentence by means of itsgrammatical structure but by means of “previously known factual relations betweenthe things which the words represent” (1978:55).4 This pragmatic mode would leadthe child to prefer a structurally neutral interpretation of a quantified sentence ofthe form ‘All the objects are F and G’. This explains Inhelder and Piaget’s findingsthat children answer “no, not that one” for Are all the circles black? with respect tofigure 2.3; children would interpret this sentence as ‘Are all the objects a circle andblack?’.

However, as Braine and Rumain (1983) point out in their detailed overviewof the development of logical reasoning, such an analysis raises the question whychildren would prefer a structurally neutral interpretation like (16-b). In theory,a structurally neutral interpretation would result in four possible interpretations(adapted from Braine and Rumain, 1983):

(17) a. All the objects are circles and blackb. All the circles are black objectsc. All the black objects are circlesd. All the circles are black objects and all the black objects are circles

Bucci’s account, Braine and Rumain point out, crucially needs experimental supportshowing that children prefer interpretion (17-d) above the other interpretations. Ifchildren indeed pay less attention to the syntactic structure than adults, they pointout, does this mean that they randomly pick one of the four interpretations in (17)?

Freeman, Sinha, and Stedmon (1982) (and Freeman and Stedmon, 1986) showedthat, by manipulating various variables in the experimental setting (such as showingmore than just one empty garage to the child or making one garage odd-colored),the child answers become more often target-like because a target-like answer be-comes more plausible in these two manipulations. They take this to mean that thechild’s language system does not differ much from the adult system in its formalcharacteristics, but rather that it is less flexible and that children have problemsdetermining what the sentence is actually about, or in their terms, “coordinatingquantification with reference” (1986:47). Taking the sentence to be about a violationof a one-to-one relation, children answer as reported by e.g. Inhelder and Piaget.Unfortunately, their data does not allow them, as they point out themselves, tomake any further predictions regarding the exact interaction between reference andchildren’s interpretations of quantified sentences. This then, they take to be thechallenge for further research. As they put it:

For the next round of research, it will be necessary to take a widerview of reference, and to use psychologically more expensive concepts,

4In fact, Bucci’s account is a theory wich states that, for children, syntax is ruled over by pragmatics.This idea returns in a more fine-grained version in my hypothesis in chapter 3.


such as topic-setting cues available in discourse. (Freeman and Stedmon,1986:47)

Summing up, various psychological accounts argue that children pay less at-tention to the syntactic structure than adults to determine the quantifier domain.The psychological field moved away from Inhelder and Piaget’s conclusion thatchildren have non-target-like understanding of class inclusion. New experimentalwork emerged on the interaction between syntactic structure and the mapping fromworld to language, investigating the question how children interpret a quantifiedsentence if they do not do it with the syntax. This received much attention in thefield of linguistics and gave rise to a body of research on children’s understandingof quantification from, first, a mainly syntactic and semantic point of view andlater a pragmatic point of view. Taking the conclusion that children do not usesyntax as a starting point, children’s non-adult-like understanding of quantifiedsentences was subsequently used to illustrate either that children lack certain aspectsof syntax or that linguistic principles are innate (and adult-like) and the experimentalmethodology used causes non-target-like behavior. In recent years, Freeman et al.’s(1986) conclusions regarding the discourse characteristics of quantified sentencesreceived attention again. In the next section, I present an overview of these differentlinguistic accounts.

2.3.2 Children’s structures of quantified sentences

2.3.2.1 Roeper and De Villiers (1991) - a syntactic account

Roeper and DeVilliers (1991) explore the hypothesis that children detach a quantifierfrom the noun it appears with (a process they call ‘Q-spreading’).5 Raising thequestion what the linguistic boundaries are for children to apply the quantifier to allnoun phrases in a clause, Roeper and DeVilliers (1991) report that children also givenon-adult-like answers when the sentence involves quantification over the object asin (18), a barrier like a relative clause as in (19) or an implicit object in an intransitivesentences as in (20) (cf. Takahashi (1991), examples from Roeper and DeVilliers,1991:247).

(18) A cat is on every chair

(19) Every whale that is lifting a boat smiled

(20) Every dog boy was driving. A truck was broken.

5The label ‘Q-spreading’ goes back to the work of Roeper and Matthei (1974) who found thatchildren interpret (i.a) as (i.b) and concluded in a similar way that children detach the quantifier from thenoun it syntactically combines with.

(i.) a. Some of the circles are blackb. Some of the circles are some black


If there were any linguistic boundaries on Q-spreading, children would give adult-like answers in these cases, Roeper and De Villiers point out. For example, in (18)there is no c-commanding relation between every and a cat in contrast to Everycowboy is riding a horse, and if it is this c-commanding relation that causes childrento give non-adult like answers, children are predicted to give adult-like-answers for(18). However, this is not the case, Roeper and De Villiers report. If the presence ofan object is a trigger for the child to give non-adult-like answers, no such answersare predicted for (19) and (20) which have no object. However, also for (19) and(20), Roeper and DeVilliers report Q-spreading. Neither a c-commanding relationor the mere presence of an object causes children to give non-adult-like answers.Roeper and DeVilliers point out that this might suggest that the phenomenon islinguistically unconstrained. However, referring to Takahashi (1991), they arguethat this is not the case. Takahashi (1991) found that children interpret intransitivesentences adult-like. The linguistic difference between intransitive sentences andtransitive sentences and the finding that children interpret the two constructionsdifferently, suggests that Q-spreading is linguistically constrained.

Pointing at the characteristics of adverbs, they take this all to mean that childreninterpret quantificational determiners as adverbs; adverbs quantify in a similar wayover the whole sentence.6 As they formulate their hypothesis (Roeper and DeVilliers, 1991:248):

(21) a. Quantifiers are analyzed as adverbsb. Adverbs can be given sentential scopec. Therefore all NPs within a clause are modified by the adverb

Roeper and De Villiers’ (1991) account should be understood in a broader acquisi-tion theory that (some) syntactic categories are delayed in the course of languagedevelopment, specifically the Determiner Phrase. Lacking the internal structure ofa DP means that the quantificational determiner remains unattached and thereforehas all the variables in the entire sentence in its scope.

2.3.2.2 Philip (1995) - a semantic account

Philip (1995), presenting the first full-range set of linguistic data on children’sunderstanding of quantified sentence, takes up Roeper and De Villiers’ idea andreformulates it in terms of event quantification. In line with Inhelder and Piaget(1959, 1964), Philip (1995) presents experimental data of children quantifying overthe horse not being ridden (the so-called extra object) in figure 2.4 and the walkingman in figure 2.5 (the so-called extra-subject) for (22). For both pictures, this resultedin a “no, not that one” answer which is correct for figure 2.5, but not for figure 2.4.

6This conclusion would furthermore be supported by the fact that all languages have some way toquantify over events. Quantification over entities, however, does not seem to be a universal characteristicof language. This suggests, Roeper and De Villiers argue, that adverb quantification is the basic case,therefore easier and hence the null stadium in acquiring a language (cf. Roeper et al., 2006).


Following Philip (1995), here and in the remainder of this thesis, I label the “no, notthat one” answer with respect to figure 2.4 the symmetrical answer.7

(22) Every cowboy is riding a horse

Figure 2.4: Extra-object situation for test sentence Is every cowboy riding a horse?

Philip’s Event Quantificational Account (EQA) claims that children interpretuniversal quantifiers as quantifying over event variables. As Philip puts it, childrenrestrict the quantifier domain to “the set of minimal events e’ ” if such a minimalevent meets one of two criteria. The first criterion is that the minimal event is “asubevent of e that has a participant object of the same type as the distinguishedparticipants of e” (from Philip, 1995:68). The second criterion is that “the minimalevent is a subevent of e that has a participant object of the type denoted by somereferring expression in S” (from Philip, 1995:68). Representing this by means of atripartite structure (Heim, 1982, see also section 2.2 above), the child’s symmetricalanswer for (22) is represented by Philip as follows:

7Additionally, Philip (1995) reports the exhaustive answer; so-called perfectionist children also answer“no, not that one” for a picture in which the extra man is replaced with, for example, a donkey. Childrenthen point at this donkey and explain that the donkey is not being ridden. This answer, however, liesoutside the scope of this thesis. This also applies to another child-answer which Freeman and Stedmon(1986) argue to be due to an “underexhaustive search” applied by the child; some children answer “yes” tothe question whether all cowboys are riding a horse and picture 2.5. However, following Hollebrandseand Visser (2006) and taking this last answer to indicate some kind of prequantificational stage, I will notaddress this fourth answer in more detail either.


Figure 2.5: Extra-subject situation for test sentence Is every cowboy riding a horse?

(23) S

Operator

∀e1

Restriction

∃e2[ e1 ≤ e2 &ride(cowboy,horse,e2) &

PART(cowboy,e1)]

or

∃e2[ e1 ≤ e2 &riding(cowboy,horse,e2) &

PART(horse,e1)]

Nuclear Scope

a cowboy is riding(e1)a horse

In this representation, events are indicated by the variable e1, e2. The quantifierevery is argued to quantify simultaneously over all those events that are a subeventof a cowboy-riding-a-horse event and those in which both a cowboy and a horse area participant. This explains why children answer “no, not that one”; there is onesubevent (i.e. the horse not being ridden) in which only the horse is a participantand not both a cowboy and a horse.8

In sum, Philip proposes that children differ from adults in the type of variablethey quantify over (i.e. an event variable instead of an individual variable) and,

8The exhaustive answer (see footnote 7) is explained in a similar way. In addition to the cowboysand horses, the child would also take a perceived object to be part of the quantifier’s restriction. SeePhilip (1995) for a more detailed account of the exhaustive answer (cf. Roeper et al., 2006).


moreover, they take the quantifier to quantify over the event variable which in-cludes event participants and therefore quantifies over ‘everything’ in the sentence.Addressing the question why children would prefer such an interpretation overan adult one, he points at two possibilities. On the one hand, quantification overevent variables would be easier than quantification over individual variables. On theother hand, children would have problems with deriving the correct logical form.In this acquisition stage, Philip claims, the child “often does not apply the linguisticprinciples that govern an adult-like reading of a determiner universal quantifierbut rather assigns a meaning to a universally quantified sentence that is similarbut semantically and truth-conditionally distinct from that which an adult assigns”(1995:3). It is especially this latter claim, i.e. that children do not apply, or are evenunable to apply, linguistic principles, that encountered fierce criticism from Crainet al. (1996).

Crain et al. (1996) ask why a child would prefer such an event quantificationalanalysis. Quantification over the event requires a more difficult mapping fromsyntax to semantics than quantification over objects, Crain et al. argue. And even ifPhilip’s event quantificational account is right, they continue, three questions arise.First, why is the child’s analysis of quantifiers more difficult than an adult analysisof events? The logical form of the symmetrical child is more complex, Crain et al.argue, than the representation of event quantification in the adult grammar (withonly one restriction). According to Philip’s EQA, either the subject or the objectis within the restrictor of every, cf. (23) above. Since this is not the way adverbquantification takes place in the adult grammar, it is unlikely, Crain et al. argue,that children analyze every in this way. Moreover, mapping a real adult analysis ofadverbs onto every would result in a reading of (22) for which the restrictor is theset of events in which there is a cowboy riding something, or in which there is acowboy and a horse or there is someone riding a horse (Crain et al., 1996). Thismeans that children will judge (22) with respect to figure 2.4 as true, contrary toPhilip’s own findings. Second, Crain et al. take Philip’s EQA to imply that thechildren’s grammar has to change enormously in order to reach an adult state. Buthow can that be, they point out, if children, next to the symmetrical answer, alsogive adult-like answers? Third, if children restrict a quantifier domain in a differentway than the syntax prescribes, they differ from adults and have to unlearn thisoption. This means, Crain et al., claim, that the child’s grammar is not compatiblewith the principles of UG, something that they take to be impossible.

Crain et al. (1996) argue that the child’s grammar does not have to do changeat all, simply because the child’s grammar does not deviate from the adult gram-mar. They explore an alternative hypothesis to account for children’s non-targetinterpretation of quantified sentences.


2.3.2.3 Crain et al. (1996) - a methodological explanation

Crain et al. (1996) argue that the experimental setup used by Philip (1995) andothers (cf. the psychological literature discussed above) might have caused the childto restrict the quantifier domain in a non-adult way . Alternatively, they claim, theyshould have used the Truth Value Judgment (TVJ) Task.

The TVJ task is a task in which puppets perform actions and talk ‘through’ anexperimenter. The child is asked whether the puppet describes a picture the rightway or the wrong way. By using the puppet, the task minimizes the possibility thatchildren answer yes or no by means of other mechanisms than linguistic competence;it is more likely that the puppet says something the right way or the wrong way,than an adult (according to the possible reasoning of the child that an adult knowswhen something is said the right or wrong way, so there is no reason for an adult toask such a question if the sentence is indeed correctly describing a picture).

In this respect, an experimenter should first of all consider whether the testsentence is true or false on the interpretation under investigation or under any otherinterpretation (by means of world knowledge etc.). Second, one should be able toanalyze a test sentence into the components background, assertion, possible outcomeand actual outcome. Crain et al. explain the terms background and assertion in termsof respectively a function and its argument. For a test sentence Every farmer is feedinga donkey, the background is that every farmer is feeding something, the assertionis ’a donkey’. The possible outcome is a possible alternative to the assertion, e.g.that the farmer is feeding a horse, whereas the actual outcome is that the farmeris feeding a donkey. Third, the Condition of Plausible Dissent and the Conditionof Plausible Assent should be met in each experiment. The Condition of PlausibleAssent makes sure that the test sentence is actually a possible outcome during theexperiment. This condition mirrors the Condition of Plausible Dissent, stating thatsome outcome other than the one corresponding to the target-like meaning of thetest sentence should be possible. Crain et al. argue that both conditions are metwhen the TVJ task is used.9

For (22), this means that it should be felicitous in the experimental setup toeither answer with Yes, every cowboy is riding a horse or No, not every cowboy isriding a horse. Crain et al. (1996) argue that the children in Philip (1995) were askedsuch a question in a context in which only the “yes” answer was felicitous (therewas no reason provided during the experiment why the sentence would not be trueand hence a ‘no” answer was not felicitous). At that point, the children did notknow why such a yes/no question was asked; only one answer is possible. Childrenwould then infer a context in which a yes/no question is felicitous, resulting in aninterpretation of the question as Is there a one-to-one relation between cowboys and

9In subsequent years, the Truth Value Judgment (TVJ) has become a standard methodology inthe field of first language acquisition to elicit children’s interpretations of sentences (cf. also Gordon(1996)) with respect to pictures. However, see Drozd (2004a, 2004b) and others for criticism against themethodology and starting points of Crain et al., 1996.


horses?.10

Crain et al. carried out seven experiments, using the methodology as describedabove, and aimed to replicate the findings of Inhelder and Piaget (1964) to Philip(1995) and to address their hypothesis that children do not miss any linguisticprinciples but that the experimental setup used in Philip (1995) and earlier researchcaused non-target-like behavior. Their results show that children give relatively few(i.e. 12%) symmetrical answers if the felicity conditions discussed above are met.They take this to show that Philip’s experiments indeed were not designed properly;his experiments would not satisfy the Plausible Assent condition and, hence, childrentook the test sentence to be about a one-to-one relation between farmers and donkeys.Children’s symmetrical answers would all be “errors due to flaws in experimentaldesign”(Crain et. al.; 1996:109). Crain et al. conclude that children have fulllinguistic competence and apply the same linguistic constraints as adults do. Untilproven otherwise, they argue, this hypothesis is on the right track; reasons toassume that childern’s adult-like answers are due to the introductions used in theirexperiments as a result of which the quantified sentences are easier to understand forthem, are not reasonable to accept without further arguments. However, recently,various people underline exactly the pragmatic effects of context on children’s non-adult-like interpretations (cf. Drozd, 2001; Drozd and Van Loosbroek, 2006; Geurts,2003). These pragmatic approaches are the subject of the next section.

2.3.2.4 Drozd (2001) and Geurts (2003) - two pragmatic accounts

Both Drozd (2001) (also Drozd and Van Loosbroek, 2006) and Geurts (2003) analyzechildren’s symmetrical answers in terms of a mapping problem between the differentmodules of the language faculty (i.e. pragmatics (discourse), semantics and syntax).Drozd (2001) and Drozd and Van Loosbroek (2006) propose an account in whichthe influence of pragmatic factors like context explains their non-adult behavior.Drozd and Van Loosbroek (2006) labeled Drozd’s proposal the Weak QuantifierStrategy (WQH). In a similar way, Geurts’ (2003) Weak Processing Strategy (WPS)underlines the effect of pragmatic factors on children’s interpretations of quantifiedsentences. I will now discuss these two accounts in more detail.

Drozd (2001) argues that children have difficulties constructing the restrictionand nuclear scope which are presupposed for interpreting universally quantifiedsentences. The so-called Westerståhl-sentences (Westerståhl, 1985) are central in hisaccount. Consider (24).

(24) Many Scandinavians have won the Nobel price in literaturea. There are many Scandinavians that have won the Nobel price in litera-

ture

10Of course, the question remains why they infer this interpretation. As will become clear, this willbe a central question throughout the remainder of this thesis.


b. There are many winners of the Nobel price in literature that areScandinavians

Sentence (24) can either be interpreted as (24-a) or (24-b). The difference betweenthose two readings is the presupposed set of Nobel price winners: either a pre-supposed set of Scandinavians is the restriction (in the case of (24-a)) or a certainexpected frequency of Nobel price winners (in (24-b)) (see chapter 5 for a moreextensive discussion of this example). Drozd claims that children interpret sentencescontaining a universal quantifier such as every, as if they contain a weak quantifier(in the sense of Milsark, 1979). A sentence as Is every cowboy riding a horse is theninterpreted similarly to (24-b) and an expected or ‘normal’ number of horse-riders ispresupposed. When such a question is asked with respect to an extra-object situation(cf. figure 2.4 displaying four horses of which only three are being ridden by acowboy), the answer will then be “no, not that one” because they miss a horse-rideron top of the horse not being ridden. In this way, children treat strong quantifiersas weak ones, since adults only use domain presuppositions to restrict the domainof a weak quantifier as in (24).11

Crain et al. (1996) presented the child with a situation in which an extra horse-rider (next to the ones displayed in the figure) is already presupposed. Drozd arguesthat this explains why they found fewer symmetrical answers. Rather than thesatisfaction of the condition of Plausible Dissent, Drozd concludes that offering acontext which makes it easier to resolve domain presuppositions (and not satisfyingthe Condition of Plausible Dissent) will improve the child’s interpretation in anadult way.

Geurts (2003) also points at the weak-strong distinction. Referring to the pro-cessing work of Just (1974) and Meyer (1970), he takes the null hypothesis to be thatweak quantifiers are easier to process because they impose an intersection relationbetween their arguments (see section 2.2):

“I assume that the distinction between weak and strong quantifiersis not just a linguistic curiosity, but is directly relevant to the waysquantified expressions are processed. This assumption is at the heartof the analysis [. . . ], according to which strong quantifiers must berepresented by relational structures, while weak quantifiers give rise tonon-relational representations by default; a weak quantifier calls for arelational representation only if it triggers a domain presupposition.”(Geurts, 2003:12)

Geurt’s account bears crucially on the formulation of the weak-strong distinction asa distinction between quantifiers that are inherently relational (i.e. strong quantifiers)and those that are not (i.e. weak quantifiers). Compare the following sentences witha strong quantifier (25) and a weak quantifier (26).

11For Drozd’s WQA, see also chapter 5.


(25) Most academics are absent-minded(26) At least five academics are absent-minded

In (25), it is expressed that most of all academics are absent-minded; the strongquantifier relates the set of absent-minded academics to the set of non-abent-mindedacademis with respect to all the academics, let us assume in this case, in the world.However, (26) means that either five academics are absent-minded or even morethan five; the weak quantifier is not relational with respect to some other set ofof academics (cf. the discussion of weak and strong quantifiers in section 2.2).Because interpreting a strong quantified expression would be harder, children mapthe grammatical form of a weak quantifying expression onto the structure of astrong quantifying expression.

For Every cowboy is riding a horse, this Weak Processing Strategy results ina representation in which every’s domain restriction is not filled with the set ofcowboys, but rather is left empty (mirroring adults’ interpretation of weak quanti-fiers). This mismapping between syntactic form and semantic representation wouldexplain why children resort to non-adult-like answers; because the domain of everyis undetermined. ‘Pragmatic inferencing’ in terms of determining the most salientdiscourse entity given the sentence focus and background assertions, would force areading in which either the horses or the cowboys are backgrounded. Dependingon the set that ends up in the restrictor by means of this pragmatic inferencing, thechild gives a symmetrical or an exhaustive answer.12

2.4 Summary and concluding remarks

In this chapter, I discussed two characteristics of quantifiers: they relate two sets toeach other and do this in different ways (cf. the difference between weak and strongquantifiers). Both have played an important role in the literature on children’sunderstanding of quantified expressions. Inhelder and Piaget explain children’snon-target-like answers in terms of their inability to recognize the subset relationa quantifier like all establishes between its nuclear scope and domain restriction.Donaldson and Lloyd (1974) (and also Bucci, 1978) argue that children are unable todetermine which sets constitute the quantifier’s domain restriction and nuclear scopeand, hence, children choose for a structurally neutral interpretation. Linguisticaccounts hypothesize that children are unable to quantify over the target-like (typeof) variable (Roeper and De Villiers, 1991; Philip, 1995). Recent pragmatic accountstake yet another perspective and point at the difference between weak and strongquantifiers and their differences (Geurts, 2003) or the role that context plays in theirinterpretation (Drozd, 2001 and Drozd and Van Loosbroek, 2006). Finally, Crain etal. (1996) argue that the methodology used in previous experiments on children’s

12Geurts (2003) accounts for the perfectionist answer in terms of quantification over all animateindividuals in the scene, resulting in a representation in which the set of all animals functions as thedomain of the quantifier (Geurts, 2003:16).

2.4. Summary and concluding remarks 25

understanding of quantified sentences caused them to interpret quantified sentencesin a non-adult-like way and showed that children are target-like with an improvedsetup (cf. also Freeman et al, 1982).

The overview presented in this chapter shows that there is no consensus regard-ing children’s understanding of quantified sentences. Various psychological andlinguistic accounts compete with each other and explain children’s non-adult-likeinterpretations of quantified sentences in different ways. An account is neededthat can explain the findings reported in literature and reconcile these differentperspectives on the acquisition of quantification. Crain et al.’s criticism (cf. alsorecent work by Meroni, Gualmini, and Crain, 2006) against all other accountsthat claim that children restrict a quantifier domain by other means than syntax(because this would run counter to the principles of universal grammar), providesa challenge to explore alternative hypotheses. The alternative hypothesis that Iwill explore in this thesis is that children use other means than syntax to restrict aquantifier domain (even if an experiment is set up along the principles they advocate).Crucially, I will argue that children attribute different weight than adults to thevarious factors that determine the meaning of quantifiers. It is a particular interplaybetween syntactic, semantic and pragmatics constraints that children have to masterin order to interpret quantified sentences target-like. In contrast to previous studies,I will take all these constraints into account. Moreover, recent work on adults’interpretations of quantified sentences legitimates such an approach (cf. Hendriksand De Hoop, 2001; De Hoop, Hendriks, and Blutner, 2007). Without disregardingany of the principles discussed in section 2.2 concerning the meaning and syntacticstructure of quantified sentences, these theories crucially explain adults’ interpreta-tions of quantified sentences in terms of an interaction between syntax, semanticsand pragmatics. Moreover, and crucial for current purposes, these theories allow usto model children’s understanding of quantified expressions, to incorporate bothpsychological and linguistic research and to formulate precise predictions regardingthe acquisition process of quantification. Therefore, in the next chapter, I willuse these theories to formulate my alternative hypothesis in more detail and toformulate precise predictions.

3Quantification at the interfaces

3.1 Introduction

In this chapter, I will argue that the essential task the child acquiring a language isfaced with is to establish a target-like equilibrium between syntax, semantics andpragmatics. The requisites for an adult understanding of quantified sentences involveuntangling exactly how and when each of the different kinds of constraints apply inthe target language (see chapter 3.2). This main hypothesis (which I will introduce insection 3.3) will function as the starting point for exploring children’s understandingof quantified sentences in subsequent chapters. After distilling precise predictionsfrom this hypothesis and discussing these predictions in the light of previous research,I will show in section 3.4 that Optimality Theoretic semantics (Hendriks and DeHoop, 2001) enables us to test this hypothesis with new experiments on children’sunderstanding of quantified expressions.

3.2 Quantification at the interfaces

In chapter 2, I showed that the syntactic structure of a quantified sentence determinesits meaning. In this respect, quantified sentences do not differ from other sentencesand obey the well-known principle of compositionality, stating that the meaningof every linguistic utterance is determined by its parts and the way these parts are(syntactically) combined. However, touching on a subject that has been around inthe literature for centuries, it is one thing to determine the meaning of a sentence ansich, but it is another to determine the meaning of a sentence in its discourse context.Moreover, given that the truth value of a quantified statement depends on theactual world or a picture that functions as the domain of interpretation, the visualcontext also plays a role (cf. for example Coventry, Cangelosi, Newstead, Bacon, andRajapakse, 2005). In the next two subsections, I will explore pragmatic constraints onthe meaning of quantifying expressions. I will conclude that, without disregardingany of the syntactic and semantic constraints on quantification identified in chapter

27

28 Quantification at the interfaces

2, these pragmatic constraints also have to be taken into account in the acquisitionof quantifying expressions.

3.2.1 Discourse context

The quantifier many is known for its context-dependent meanings. Consider thefollowing example:

(1) Many European soldiers are fighting in Iraqa. U.S. Secretary of Defense: “Many European soldiers relative to the

number of American soldiers, are fighting in Iraq” (FALSE)b. ECFR: “Many of the total number of soldiers in each European country,

are fighting in Iraq” (TRUE)

Given the criticism of the U.S. Secretary of Defense Robert Gates that the Europeancountries did not contribute sufficiently to the war on terrorism (Spits, February14th, 2008), he apparently took (1) to be false. A survey by the European Councilon Foreign Affairs (ECFR) showed that Europe contributed to a larger extent to thewar in Iraq than America did; Europe spent more money compared to the USA tosend soldiers to Iraq. Therefore, (1) was actually true. However, this was clearly notthe meaning Gates intended and the rumor continued that Europe should contributemore to the war in Iraq.

Example (1) clearly illustrates how one’s world knowledge or the discoursecontext in which the sentence is uttered determines its truth conditions.1 This isnot limited to sentences with the quantifier many. Various examples can be found inthe literature illustrating in a similar way that one has to take the discourse contextinto account to interpret quantifying expressions. Consider the following examplesand their intended meanings (see for other examples and a discussion of the relationbetween the intended meaning and the syntactic structure of such sentences, chapter5).

(2) Have you put all the knives on the table? (from Donaldson and Lloyd,1974,66)“Have you put all the knives that are needed, on the table?”

(3) The burglar took everything (from Recanati, 1986)“The burglar took all the valuable/important objects, when he broke into thehouse”

(4) Every German is proud of his car (from Geurts, 1999:281)“Every German who owns a car is proud of it”

1The issue returns in different forms in the literature as tacit quantifier domain restriction or contextdependent quantifier domain restriction. In psychology, ‘schemata’ often refer to the need to recoverbackground information to determine the meaning intended by the speaker. For references, see theremainder of this chapter and chapter 5 and 6.

3.2. Quantification at the interfaces 29

In addition to the syntactic and semantic properties of quantified sentences discussedin chapter 2, pragmatics plays a role in determining the meaning of these sentences.2As De Hoop, Hendriks, and Blutner (2007) point out, the interaction betweencontext and linguistic properties of quantifiers poses a major problem for linguistictheories that take a traditional perspective on meaning (i.e. theories that take theprinciple of compositionality as defined above as a starting point). As Hendriks andDe Hoop (2001) put it:

... building interpretation on syntactic structure alone has seriousshortcomings. Context as well as intonation play a major part and thequestion arises when, how and to what extent people use different prin-ciples to arrive at the proper interpretation of a quantified expressionin a given context. (2001:6)

Such a view on interpretation differs from the classical view of compositionalityin linguistics and led people working in the so-called ‘radical pragmatics school’(see for instance Cole, 1981) to conclude that the actual meaning expressed bya proposition is more than the meaning of only the sentence. Postponing thisdiscussion to chapter 5, at present, I take it to be the null-hypothesis that themeaning of quantified sentences crucially involves the interaction between syntax,semantics and the discourse context.

3.2.2 Visual context

A growing body of literature uncovers the effect of the visual context on adults’interpretations of quantified sentences. Freeman, Sinha, and Stedmon (1982) reportthat adults answer “no, that one”, in a similar way as children (see chapter 2) for asentence like (5) with respect to figure 3.1 (cf. also Brooks and Sekerina, 2006).

(5) Are all the cups on the saucers?

Freeman et al. take this to mean that adults mirror children’s behavior. Adultsseem to restrict all the cups to “all the cups which ought to be present” (Freemanet al., 1982:64), illustrating that adults restrict a quantifier domain by means of theperceived purposes and intention of the speaker.

As pointed out by Braine and Rumain (1983) (cf. Geurts, 2003), researchaddressing adults’ abilities to reason logically illustrates in a similar way that adultssometimes give answers similar to children’s symmetrical answers (see, among others,Newstead and Griggs (1983) and references therein). Newstead and Griggs (1983)

2The term ‘pragmatics’ should be understood here, and throughout this thesis, in terms of Sperberand Noveck’s (2004) ‘pragmatics in the narrow sense’. This contrasts with ‘pragmatic in the broadsense’ which involves the study of language use (ranging from, for example, the relation of language togesture and social ethnic customs). Pragmatics in the narrow sense, however, involves the study “howlinguistic properties and contextual factors interact in the interpretation of sentences” (Noveck andSperber, 2004:1).


Figure 3.1: Extra-object situation for the test sentence Are all the cups on the saucers?

asked adults whether “All Y are X” follows from “All X are Y”. 34% of the 96 adultsbelieved that “All Y are X” indeed implied that all X were also Y. Whatever causesadults to make these errors, I take these so-called illicit conversions to illustrate thatadults sometimes use different clues than syntax to interpret a quantified sentence.3

Newstead and Coventry (2000) and Coventry et al. (2005) provide further sup-port for the hypothesis that visual information plays a role in adults’ interpretationof quantifiers. Their work shows that both the spacing and grouping of the setsdenoted by the quantifier restriction and nuclear scope affect adults’ judgments ofquantified sentences. For example, whether (6) is judged as true or false depends onthe relative size of the balls in the bowl - i.e. true when the balls fill the entire bowland false if the balls are small and just fill a small part of the bowl (Newstead andCoventry, 2000).4

(6) There are many balls in the bowl

Trueswell, Sekerina, Hill, and Logrip (1999) points at the interaction betweenlanguage comprehension and visual context. They found that adults use the visualcontext to interpret temporarily ambiguous phrases like (7). This sentence is,

3In line with these findings, recent studies using brain-imaging techniques like fMRI and addressingadults’ understanding of quantified sentences in the context of a logical reasoning task, show that thevisual cortex is activated when adults are asked to interpret quantified statements, even when the stimuliare presented only verbally (see Knauff (2007) and references therein).

4More generally stated, Coventry et al. (2005) conclude that language comprehension “maps ontoperceptual processing” (Coventry et al., 2005:511). This is consistent, as they point out, with recentfindings on the relation between language comprehension and perception (see Coventry et al. andreferences therein).


without any visual context, temporarily ambiguous between the so-called ‘modifier’interpretation (7-a) and the so-called ‘destination’ interpretation (7-b); the DP on thenapkin can either indicate where the frog is or where the frog has to be put.

(7) Put the frog on the napkin on the boxa. Put the frog [on the napkin]modifier in the boxb. Put the frog [on the napkin]destination in the box

Trueswell et al. (1999) asked adults to carry out the instruction in (7) in two differentvisual contexts. In the so-called ‘2-referent’ context, there were two identical animals(e.g. two frogs), providing two possible referents for the noun phrase the frog. Oneanimal was sitting on the table, and the other animal was sitting on an object (e.g.a napkin). Two other objects were displayed, an empty napkin and an empty box.This visual context was designed to elicit the modifier interpretation; it is unclearwhich frog the frog in the 2-referent context refers to, and so adults are hypothesizedto chose a modification interpretation of on the napkin (understanding this PP tospecify the intended referent). The ‘1-referent’ context was designed to elicit thedestination interpretation. This context was identical to the other context, exceptthat now there were two different animals (e.g. a frog and a horse). Because thefrog now unambiguously refers to the frog, on the napkin is hypothesized to get adestination interpretation (which then leads to a garden path error). The resultsshow that when adults were asked to interpret (7), they indeed choose the modifierinterpretation when the visual context supported it (i.e. in the 2-referent context)and the destination interpretation when the visual context indicated that a modifierinterpretation was unnecessary, i.e. in the 1-referent context. This, Trueswell etal. (1999) claim, is consistent with the hypothesis put forward by, among manyothers, Tanenhaus, Spivey-Knowlton, Eberhard, and Sedivy (1995) that the languageprocessing system is highly interactive and leads them to conclude that adults’interpretations can be manipulated by visual context.

So exactly what in the visual context guides adults’ interpretation of linguisticstructures? Donaldson and Lloyd (1974) suggested that the Gestalt principles ofperception might be relevant. Gestalt psychologists took perception to be a matterof responding to large, whole patterns. They identified six principles of perception,of which the Principle of Pregnanz captures the process behind these six principles.This principle states that the perceptual system strives to perceive whole, organizedpatterns (i.e. with a symmetrical, regular and predictable shape). In some cases,this principle is so powerful that it is responsible for visual illusions. This explainswhy adults perceive a white triangle in figure 3.2; the tendency to perceive whole,organized patterns and objects is so compelling that an adult makes up the borderof a white triangle that is not actually there.

The distinction the Gestaltist Edgar Rubin makes between figure (the object thatattracts attention) and ground (the backgroud) in his analysis of visual scenes appealsto this same ‘aboutness of the picture’. Depending on what adults take the figure orthe ground to be, he argues, adults see the famous figure 3.3 alternately as a white


Figure 3.2: Adapted from Gray,1991:282

Figure 3.3: Adapted from Gray,1991:282

vase against a black background or two black profiles against a white background.Obviously, however, there is no similar kind of visual illusion going on in figure

3.4.

(8) All cowboys are riding a horse

Figure 3.4: Extra-object situation for the test sentence Is every cowboy riding a horse?

However, given the Principle of Pregnanz as a universal principle of “figural good-ness” (Coren, Ward, and Enns, 1999:301; cf. also the meaning of the German wordPregnanz ‘conveying the essence of something’) which only gives rise to visualillusions in particular cases, adults are likely to perceive figure 3.4 as symmetricalas possible. Their visual “interpretation” of this picture is about the exception to arule (i.e. one horse is not being ridden). However, in the context of a Truth-ValueJudgment task and a sentence about ‘cowboys’, I take adults to reanalyze the pictureand check whether or not each cowboy is riding a horse. Meroni, Gualmini, andCrain (2001) provide experimental support for such an analysis of figure 3.4. Usingan eye-tracker to study the on-line processing of quantified sentences like (8) inextra-object situations, they found that adults’ eye fixation patterns reveal looks atthe extra object. Crucially however, adults do not use this information in restricting


the domain in sentences like (8). In the cases in which adults mirror children’sbehavior and give answers in terms of the extra object (e.g. cups), such a reanalysisdoes not take place. I take the “no, not that one”-answers in the latter case to resultfrom the fact that the sentence subject is conceptually associated with another set(such as cups and saucers). This leads adults to take the picture as a leading clueand to interpret the sentence to be about the one-to-one relation between cupsand saucers and the exception to this rule. This effect might be enforced by thesaucer without a cup which ‘pops out’ immediately. Such pop-out effects are wellestablished in the literature on adults’ perception of scenes as in figure 3.5 (adaptedfrom Coren et al., 1999); the slanted line immediately pops out due its differentprimitive feature (i.e. being slanted instead of straight). In a similar way, I take theadults’ symmetrical answers reported by Freeman et al. (1982) to be triggered bythe fact that one cup differs in one salient aspect (i.e. not having a saucer) from theother saucers.

Figure 3.5: Pop-out effect; adapted from Gray, 1991:278

Donaldson and Lloyd (1974) suggest that it might be these same Gestaltist prin-ciples of perception that also affect children’s understanding of quantified sentences.The child, they argue, attaches more importance to the physical array than adults.The necessary step for a child to take toward an adult understanding of quantifiedsentences, they argue, is to determine the ultimate force of linguistic principles (cf.Bucci, 1978). For children, the syntax does not play a decisive role to restrict thequantifiers. Children allow the sentence figure and ground to be determined by thefigure or the ground of the scene. Depending on which set they take as the figureof the visual scene, children interpret a sentence like All cowboys are riding a horseto be either about the set of horses, the set of cowboys or the one-to-one relationbetween horses and cowboys. Following Donaldson and Lloyd, I hypothesize thatchildren primarily use the visual information to determine what the sentence isabout. Given the apparent violation of the one-to-one relation between cowboysand horses in the extra-object situation, the child focuses on the mismatch in thescene and assumes the sentence to address this (cf. in this respect also the pop-outeffect discussed above). As Donaldon and Lloyd put it:


“... young children do not encode the sentence with enough regard tothe structural properties of the language for this encoding to serve as aprecise determinant of the object (or picture) encoding. What happensis that the sentence initially serves to delimit a set of options. (Thisof course is not to imply that the child explicitly considers these asseparate possible interpretations.) Thereafter the direction of control isreversed and it is rather the encoding of the sentence that is contingenton the encoding of the physical array” (Donaldson and Lloyd, 1974:85)

In the next section, I will take up this suggestion and identify the hypothesisthat will drive the experiments presented in subsequent chapters.

3.3 The Equilibrium Hypothesis

In the previous section, I showed that the interpretation of quantified sentences isconstrained by the discourse and the visual context, in addition to the syntacticand semantics principles identified earlier. A growing body of research shows thatnext to syntactic information, adults use discourse context and visual context tointerpret a (quantified) sentence. In line with this body of research, I hypothesizethat pragmatics (discourse and visual contexts) interacts with syntax and semantics.The child is faced with the task to find out when and how each of these factorsconstrain the meaning of quantified sentences.

Crucially for current purposes, this interaction between syntax, semantics andpragmatics in the adult language implies that a different perspective needs to be takenon children’s acquisition of quantified sentences. Instead of focusing on the questionwhether or not children master the relevant syntactic, semantic and pragmaticconstraints, the question needs to be asked to what extent children master theinteraction between these constraints. This then leads to the following hypothesis:

(9) Equilibrium Hypothesis:The acquisition of quantification is a matter of establishing a target-likeequilibrium between syntax, semantics and pragmatics and their contributionto meaning

How do children restrict a quantifier domain? Or, to put it differently, howdoes the child’s equilibrium differ from adults’? To what extent do children attachdifferent importance to each of the factors that play a role in interpreting quantifiedexpressions than adults do? In the next section, I will identify three researchquestions that follow from (9).

3.3. The Equilibrium Hypothesis 35

3.3.1 Acquisition at the interfaces

Assuming an interaction between syntax, semantics and pragmatics as outlinedabove, it is at the interfaces of syntax-semantics, syntax-pragmatics and semantics-pragmatics that children are predicted to give non-adult-like interpretations. Zoom-ing in on each of these interactions, consider, first of all, the interaction betweensyntactic structure and semantics, illustrated with the Dutch quantifier allemaalin (10). The meaning of this quantifier as either an exhaustive or a non-exhaustivequantifier depends on the syntactic construction: allemaal as a floated quantifierin (10-a) gets an exhaustive reading whereas allemaal in an existential er (‘there’)-sentence as in (10-b) gets a non-exhaustive reading. So syntax determines the domainover which will be quantified.

(10) a. DeThe

papegaaienparrots

vliegenfly

allemaalallemaal

‘The parrots are all flying’b. Er

Therevliegenfly

allemaalallemaal

papegaaienparrots

‘There are many flying parrots’

The question arises how children interpret allemaal. Do they use the syntacticinformation or rather the information in the visual context (i.e. the picture to bejugded in a Truth-Value Judgment Task) to determine what this sentence is about?In chapter 4, I take up this question.

In a similar way, the question arises whether children differ from adults intheir interpretation of many when pragmatics interacts with the syntax to restrict aquantifier domain. Consider (11) which is true or false depending on the contextprovided (as illustrated in (11-a) and (11-b) respectively).

(11) Many parrots are flyinga. Situation: 20 out of 25 parrots are flyingb. Situation: 5 out of 25 parrots are flying, 20 out of 25 sparrows, 20 out

of 25 peacocks

Children’s interpretation of many is the subject of chapter 5.Finally, the question arises how children differ from adults when the syntax

does not provide sufficient information to restrict the quantifier domain. Considerthe second sentence in (12) for which the discourse is clearly needed to restrict thequantifier domain and hence determines the truth value of the sentence.

(12) The farmer owns several horses and a donkey. All horses are great jumpers.

The domain of all in the second clause in (12) is restricted to the set of horses thatthe farmer owns. A reading according to which all horses in the world are said tobe great jumpers is incorrect. This shows that domain restriction interacts with


the discourse even when the syntax provides the quantifier domain. In chapter 6, Iaddress the question how children integrate the discourse context into the meaningof a quantifying expression.

The hypothesis investigated is that children weigh various clues differently fromadults to determine the meaning of a quantified sentence.

3.3.2 The Equilibirum Hypothesis in relation to previous studies

Krämer (2000) shows that children’s non-adult-like interpretation of so-called highindefinites is due to their inability to integrate the discourse. Consider example(13) (from Krämer, 2000:175): (13-a) contains a low indefinite (note its positionbetween the adverbial and main verb) and allows both a wide-scope reading and anarrow-scope reading (i.e. een potje (a jar) might be either inside or outside the scopeof twee keer (twice); (13-b) contains a high indefinite (with the NP to the left of theadverbial) and only allows a narrow-scope reading (een potje is outside the scope oftwee keer).

(13) a. JeYou

magmay

tweetwo

keertimes

eena

potjejar

omdraaienturn

‘You may turn over a jar twice’ (may involve two jars)b. Je

Youmagmay

eentwo

potjetimes

tweea

keerjar

omdraaienturn

‘You may turn over a jar twice’ (should involve only one specific jar)

Children, however, also assign a wide-scope reading to (13-b) and turn over twodifferent jars. Given an analysis of the indefinite in (13-b) as a free variable whichneeds a bridge with the preceding discourse to identify its accommodation site (cf.Van Geenhoven, 1998), Krämer argues that this interpretation shows that childrendo not integrate the discourse to interpret the indefinite in (13-b). The EquilibriumHypothesis is compatible with these findings and, even more generally, hypothesizesthat it is not only the discourse that children use differently than adults, but that theentire interplay between syntax, semantics and pragmatics characterizes children’sinterpretation of quantified sentences. High and low indefinites present such cases,similarly as quantificational determiners such as every and all do.

The effect of visual context is known since Piaget who tested number conserva-tion in children (repeated by Dehaene, 1999). He showed that children between fourand six years of age, when they are asked which row out of two rows contains moreelements, use the visual information to answer this question. If both rows containthe same number of elements but there is more space between the elements in thesecond row which is therefore longer (as in figure 3.6), children use this misleadingclue and answer that this second row contains more elements. Dehaene (1997) arguesthat this is due to the fact that children actually understand the question to be aboutthe length of the lines and therefore answer non-adult like. Apparantly, children usevisual information in a particular situation whereas adults do not.

3.4. Optimal acquisition of optimal meaning 37

Figure 3.6: Are there more circles on the bottom row?

Children’s usage of visual information in language comprehension is furtherillustrated by Kelly (2001). He shows that the role of non-verbal pointing and eyegaze in language comprehension extends beyond the first years of life. Childrenbetween three and five years of age show significantly more target-like behaviorin complex pragmatic communication if the verbal message is accompanied withnonverbal pointing and gaze.

In sum, various kinds of data support the hypothesis that children’s non-target-like understanding of (pragmatically) complex sentences like quantified sentencesmight be due to an off-balance equilibrium between syntax, semantics and pragmat-ics. The extra-object condition used in previous experiments on quantification (seefigure 3.4) probes children’s understanding of quantified sentences precisely in asituation in which these constraints compete with each other; by asking childrento interpret a quantified sentence given this visual context, the child needs to applyboth syntactic and visual constraints. The Equilibrium Hypothesis explains whychildren answer differently than adults in these situations to quantified sentences;since children attach different importance to each of the relevant constraints thanadults, children judge quantified sentences differently than adults. The question tobe answered is how this non-adult-like equilibrium exactly looks like. Moreover,is there a way to model the equilibrium between syntax, semantics and pragmaticsand, hence, formulate precise predictions?

In the next section, I will introduce Optimality Theoretic semantics. Optimal-ity Theory semantics (Hendriks and De Hoop, 2001) provides us with a formalframework to do so. Moreover, and crucial for current purposes, this frameworkallows to translate the predictions regarding children’s versus adults’ interpretationsof quantified sentences to experimental settings.

3.4 Optimal acquisition of optimal meaning

3.4.1 A short introduction to Optimality Theoretic Semantics

Optimality Theoretic semantics has its roots in Optimality Theory (henceforth OT;Prince and Smolensky, 2004). In OT, a grammar consists of a set of constraints.What is grammatical in a language, depends on how these constraints are ordered inthis particular language. Acquisition is considered to be a reranking of constraints


in the target order (Smolensky, to appear).5 This means that a child does notunderstand or use language target-like until the child has ranked the constraints inthe target-like order.

Crucially, constraints in OT are soft and violable. In addition, Hendriks and DeHoop’s Free Interpretation Hypothesis states that the possible interpretations of asyntactic structure are in principle infinite. However, the most harmonic or optimalinterpretation is the preferred interpretation of a sentence. The interpretationwhose evaluation violates the least number of constraints and/or the least importantones, ends up as the actual interpretation of a sentence. Interpretation is consideredto be an optimization process with respect to a certain syntactic input. Cruciallyfor current purposes, the constraints against which all possible interpretations areevaluated can be syntactic or pragmatic in nature. This means that it is possibleto model how lexical material, syntactic structure and context play a role in theoptimization process from form to meaning. Note that such an approach takesa completely different view on compositionality; it crucially allows interactionbetween constraints of various nature. This differs from the classical view oncompositionality, i.e. the view that the meaning of an expression is a function ofthe meaning of its parts and of the syntactic rules by which they are combined.

The constraints used in OT are either markedness or faithfulness constraints.Whereas markedness constraints are only related to the output, faithfulness con-straints are related to both the input and the (possible) output. Consider a situationin which somebody utters (14). A faithfulness constraints states that the subject ofthe sentence expresses the agent of the action denoted by the verb. This means thatone gets the interpretation that the cowboy loves his horse and one does not getthat the horse loves the cowboy.

(14) The cowboy loves his horse

An often used example of a markedness constraint is that every sentence needs tohave a subject (Grimshaw, 1997).

The constraints form one component of the OT framework. Next to the set ofconstraints (CON), there is a mechanism that generates a set of candidates givena certain input (GEN) and a mechanism that evaluates these candidates againstthe set of constraints (EVAL). In OT semantics, taking a comprehension point ofview c.q. hearer perspective, this means that GEN takes a form and generates aset of possible interpretations of this form. This set of possible interpretationsis in principle infinite. EVAL assigns to each interpretation a constraint profile.This constraint profile codes how harmonically the interpretation satisfies the setof ranked constraints. The candidate with the highest harmony is selected as the

5Note that the constraints themselves are by some authors considered to be innate and universal(Prince and Smolensky, 2004) and to be learned by others (Boersma, 1998; Boersma and Hayes, 2001).For current purposes, it does not matter which position is taken.


output.6 For comprehension, this means that optimality can be defined as in (15)(from Blutner 2000:199-200).7

(15) A form-meaning pair 〈f,m〉 is a comprehension optimal iffa. 〈f,m〉 ∈ Genb. and there is no 〈f,m′〉 ∈ Gen such that 〈f,m〉 � 〈f,m′〉

In sum, in an Optimality Theoretic framework, attributing a meaning to a linguisticstructure involves an optimization procedure from form to meaning. This procedureis constrained by principles of various nature (syntactic, semantic and pragmatic).How can we account for quantification, and, additionally, how can we modelchildren’s non-target-like interpretations of quantified sentences? In the next twosections, I will address these two issues.

3.4.2 Optimal quantification

For quantification, several constraints of different nature are at play. First, thereis a syntactic constraint that states that a quantifier takes its N’ as its restriction(Hendriks and De Hoop, 2001). Hendriks and De Hoop (2001) label this constraintSyntactic Structure.

(16) Syntactic Structure:Use the N’ to restrict a quantifier domain (Hendriks and De Hoop, 2001:22)

Second, quantified sentences with a weak quantifier like many illustrate that therelation the quantifier establishes between its first and second argument can becontextually restricted. What counts as many flying birds, for example, is clearlycontext-dependent, since it depends on one’s measure of comparison (see for asimilar approach Krämer, 2000). This only applies to weak quantifiers like manyand few. Strong quantifiers like every and each might be contextually restricted (inthe case of All boys are laughing, all boys is contextually restricted to the set of boysin the domain of interpretation), but note that the truth conditions do not changein this respect; whether all boys are laughing still depends on whether there are

6‘Harmonic ordering’ is the key concept here. This is defined in Tesar and Smolensky(1998:233) asfollows (their italics):

(i.) Harmonic ordering:A grammar’s constraint ranking induces a harmonic ordering � a of all structural descriptions.Two structures a and b are compared by identifying the highest-ranked constraint C with respectto which a and b are not equally marked: the candidate that is less marked with respect to C isthe more harmonic, or the one with higher Harmony (with respect to the given ranking).

7Alternatively, optimality can be defined in terms of optimal production (Blutner, 2000) and, evenmore generally, optimality can be defined without committing oneself to a speaker (production) or hearer(comprehension) perspective to language (cf. Prince and Smolensky’s original definition of optimality).However, to keep things clear and given the focus of this thesis on the interpretation of quantifiedsentences, I will discuss here and in the remainder of this thesis only the comprehension view.


boys that are not laughing. By making use of the distinction between weak andstrong quantifiers (in the sense of Milsark, 1979), I propose the constraint SemanticRelation which captures the context-dependence of quantifiers like many:8

(17) Semantic relation:For weak quantifiers, use the discourse topic to select the set against thebackground of which the interpretation of the quantified expression needsto be determined.

Not only the measure of comparison is context dependent; the context can alsorestrict the quantifier’s domain. Hendriks and De Hoop argue for the constraintDOAP (Don’t Overlook Anaphoric Possibilities, Williams (1997)).9

(18) Don’t Overlook Anaphoric Possibilities (DOAP) (Williams, 1997)Make sure that anaphoric elements are related to the previous discourse.

This constraint makes sure that one interpret all for example in (19) as ‘all therabbits that were everywhere’.10

(19) Rabbits were everywhere. All suddenly jumped out of the magician’s hat.

A fourth constraint arises from the observations discussed above that visual contextcan also affect the quantifier domain. For adults, this is only the case when thesyntax does not provide sufficient information (i.e. Syntactic Structure is rankedhigher than Faith-Vis).

(20) Faith-Vis: Make sure that anaphoric elements are related to the theme of apicture (i.e. visually prominent items).

In (20), ‘visually prominent’ has to be understood as, for example, exceptions to arule or generalization which stand out more than non-exceptions (cf. the Principleof Pregnanz as discussed in section 3.2.2). In the case of the classical extra objectpicture with one horse without a cowboy sitting on it, this horse clearly stands outas an exception and therefore is a visually prominent item. By means of Faith-Vis weare now able to account for adults’ disambiguation of sentences by means of visualinformation as reported by Trueswell et al. (1999); if the visual context supports an

8See chapter 5 for a refinement on this constraint.9Actually, DOAP is a family of constraints. I return to this issue in chapter 5 and 6 where I discuss

the relevant constraints of DOAP. In chapter 6, I crucially also argue for an approach that incorporatesboth the family of constraints called DOAP and the constraints (with some modification) from CenteringOptimality Theory (Beaver, 2004). In a similar way, I redefine Semantic Relation as a family of constraintsin chapter 5.

10Note that ‘anaphoric elements’ in the definition of DOAP should be understood rather broadly. Ina similar way as in (19), the sets the quantifier all relates to each other in All men love baseball is taken tobe solved by means of anaphora resolution. Or, in the words of Geurts (2003:205): “a strongly quantifiedNP “Q X” is like an anaphoric pronoun in that it prompts a search for a contextually salient collectionof Xs, which are to serve as Q’s domain”.


interpretation that does not violate any syntactic constraints, this interpretationbecomes the optimal one. Moreover, it explains the findings of Meroni et al. (2001)that adults’ eye fixation patterns reveal that adults notice the horse without a cowboyon top of it in figure 3.4 when they are asked to interpret (21); adults check whetherthere is a visually prominent item, and seem to check whether Faith-Vis is violatedor not.

Consider example (21). In OT, the meaning of a sentence is typically representedin a tableau. In an OT tableau, the top row contains the input (i.e. a sentence,represented by the example number) and then the relevant constraints in rank order.The strongest constraint is on the left, the weakest constraint on the right. Thefollowing rows display candidates, here possible interpretations, each star marking aviolation of this candidate with respect to a certain constraint. The optimal candidate(indicated by ‘+ ’) is the candidate that violates the least number of constraintsor the candidate that only violates those constraints that are ranked lower thanthe constraints violated by other candidates. Constraints that are irrelevant (forexample, because they only apply when the sentence is embedded in a discourse) aremarked gray. See (22) for an example.


Using these four constraints we can now account for adults’ interpretation of (21) asin (22) (in which A is the set of cowboys and B the set of horses).11

(22)

Example (14) SYN

TA

CT

ICST

RU

CT

UR

E

DO

AP

SEM

AN

TIC

REL

AT

ION

Faith

-Vis

+ Every(A,B) *Every(A,B) ∧ Every(B,A) *!

In (22) Syntactic Structure is violated by the second candidate since the quantifierdomain contains the set of horses instead of the set denoted by the N’ (cowboys). Theconstraint DOAP does not apply (there is no discourse context) and is thereforemarked gray. Semantic Relation does not apply either since this constraint is onlycalled into action when the quantifier is a weak quantifier (i.e. passes Milsark’s (1979)existential there-sententence test). Faith-Vis is violated by the first interpretation

11For easiness sake, the interpretations of Every cowboy is riding a horse in this and the followingtableaus are represented with Every(A,B) and Every(A,B) ∧ Every(B,A). Crucially, in the latter case, thedomain of every is both A (the set of cowboys) and B (the set of horses).


since the visually prominent item (i.e. the horse) is not related to the quantifier’s firstargument set. The first candidate ‘wins’ because it is the most optimal interpretationfor (21).

Following Donaldson and Lloyd (1974) and Bucci (1978) and hypothesizing inline with the Equilibrium Hypothesis that children rank Faith-Vis above SyntacticStructure, the child’s non-target-like answer of (21) in the extra-object pictures cannow be accounted for as in (23) (in which the constraints that do not apply are leftout of the tableau).

(23)Example (21) FA

ITH

-VIS

SYN

T.S

TR.

Every(A,B) *!+ Every(A,B) ∧ Every(B,A) *

Taking the work of Donaldson and Lloyd (1974) and Bucci (1978) as a starting pointthat children use visual information to interpret a quantified sentence before theyrely on syntactic information, Syntactic Structure is ranked below Faith-Vis in (23).The violations for Syntactic Structure and Faith-Vis are the same as in (22); it is onlythe child ranking that returns the interpretation of (21) as ‘All cowboys are riding ahorse and all horses are being ridden by a cowboy’ as the most optimal one. Usingthis same ranking, it also follows that such a non-target-like answer disappears ifmore horses are depicted than in the classical case (i.e. 20) (see Crain et al, 1996and Sugisaki and Isobe, 2001). In these cases the horses without a cowboy on topof it are not an exception to a generalization anymore, hence there is no visuallyprominent item and Faith-Vis is irrelevant. Since Syntactic Structure is violated bythe non-target-like interpretation, the target-like answer is now the optimal one asillustrated in (24).12

(24)Example (21) with 20 horses FA

ITH

-VIS

SYN

T.S

TR.

+ Every(A,B)Every(A,B) ∧ Every(B,A) *!

12One might even argue that in pictures with lots of horses, the cowboys are visually prominentand force a target-like interpretation. Note that in this case, Faith-Vis is only satisfied by the target-likeinterpretation since the quantifier’s domain is in line with the visually prominent set. Since SyntacticStructure is violated by the non-target-like interpretation, the target-like answer also turns out to be themost optimal one in this line of thinking.

3.5. Summary and conclusions 43

In other cases the constraints Semantic Relation and DOAP are crucially neededto determine the most optimal meaning of a given form. Consider again example(11) and (12), repeated as (25) and (26).

(25) Many parrots are flyinga. Situation: 20 out of 25 parrots are flying; Trueb. Situation: 5 out of 25 parrots are flying, 20 out of 25 sparrows, 20 out

of 25 peacocks; False

Given the status of many as a weak quantifier, Semantic Relation applies in (25).Semantic Relation is violated by an interpretation according to which the discoursetopic is not used to restrict a quantifier domain. This means that many gets a cardinalinterpretation in a situation as described in (25-a) and the set of parrots is taken asdiscourse topic. If the set of flying entities is taken as the discourse topic in (25-b),this results in the opposite truth value since not many parrots are flying comparedto the other flying animals. The constraint DOAP does not play a role here, sincethere is an N’ to restrict the quantifier and no (discourse or visual) context to narrowdown this set of parrots to a particular set introduced before this sentence (seechapter 5 for more details).

For (26), DOAP applies in addition to Syntactic Structure (and Semantic Relationdoes not, since the all is a strong quantifier).

(26) The farmer owns several horses and a donkey. All horses are great jumpers.

This means that the domain of all is restricted to the set of horses the farmer owns.An interpretation according to which all horses in the world are great jumpers istherefore ruled out. Syntactic Structure still makes sure that all quantifies over horsesand not over jumpers.

In sum, by using these three constraints, we can model the aspects of interpreta-tion of quantification discussed above (the effect of discourse and visual context). Inthe next three chapters, I will zoom into the effects of discourse and visual contexton children’s interpretations of quantified sentences and redefine Semantic Relationand DOAP into an ordered family of constraints. Moreover, in each chapter I willexplore how children use (i.e. rank) these competing constraints.

3.5 Summary and conclusions

In this chapter, I have argued that an adult understanding of quantified sentencesinvolves attaching the right importance to syntactic, semantic and pragmatic con-straints. I formulated the hypothesis that children’s non-adult-like understandingof quantified sentences as reported in the literature is due to a non-adult-like equi-librium between these constraints of various nature. This hypothesis led to severalresearch questions concerning children’s interpretations of quantified sentences. I


identified three research questions that underly the research presented in the nextthree chapters:

1. How do children use syntactic information when the visual context competeswith syntactic information?

2. How do children use pragmatics to restrict a context-dependent quantifierdomain?

3. How do children integrate the discourse context when establishing the mean-ing of a quantifying expression?

4Acquisition at the syntax-semanticsinterfaceChildren’s understanding of the Dutch floating quantifier allemaal∗

4.1 Introduction

In the literature on children’s non-adult-like interpretation of quantified sentencesdiscussed in chapter 2, it has been suggested that children differ from adults intheir use of syntactic information to restrict the domain of a quantifier (Roeperand De Villiers, 1991; cf. Crain, Thornton, Boster, Conway, Lillo-Martin, andWoodams, 1996). Whereas adults restrict the domain to the noun phrase followingthe quantifier, children between four and six years of age impose an ‘over-exhaustive’interpretation when they answer ‘no, not that one’ for a sentence like Are all cowboysriding a horse? for a picture displaying four horses of which three are ridden by acowboy (the so-called extra object situation, see chapter 2). This has been called an‘exhaustive pairing answer’ because the child seems to prefer a one-to-one relationbetween cowboys and horses, instead of only quantifying over the set of cowboys.Why do children ignore the syntax, which prescribes that the subject noun phrase isthe domain of the quantifier, and also include the set denoted by the object? Or, toput it more precisely, why do children consider other sets as part of the quantifierdomain than the set denoted by the noun phrase directly following the quantifier?In this chapter, I take up these questions. Following up on the work by Roeper et al.(2006) that the existence of floating quantifiers in the input to the child might play akey role, I investigate children’s understanding of a floating quantifier.

Floating quantifiers are not followed by the noun phrase they quantify over,rather one needs to find the appropriate noun phrase in the sentence to determine itsdomain. Roeper et al. (2006) argue that it is this characteristic of floating quantifiers

∗Part of the results presented in this chapter has been published in B. Hollebrandse & Smits, E.J.(2006) The acquisition of the weak-strong distinction; the case of the Dutch quantifier “allemaal”. In: S.Vogeleer (Ed.) “Bare Plurals, Indefinites, and Weak-Strong Distinction”. Special issue of the BelgiumJournal of Linguistics 19. 247-264. John Benjamins.

45

46 Acquisition at the syntax-semantics interface

that causes the child to include non-target noun phrases in the domain, also fornon-floated quantifiers. Children would ignore the syntactic information providedby a quantified sentence and take the entire sentence to supply a possible quantifierdomain. Roeper et al. predict that children restrict the domain of a floatingquantifier in a similar way as for non-floating quantifiers.

In Dutch, the quantifier allemaal ‘all’ is such a floating quantifier. In fact, it canbe used either as a floating or non-floating quantifier, with different meanings. Thetwo uses are easily distinguishable (one is directly followed by a noun phrase, theother is not), and, hence, an ideal case to test children’s understanding of floatingquantifiers versus non-floating quantifiers.

This chapter presents three experiments investigating children’s interpretationof the Dutch (floating) quantifier allemaal. The results show that not only dochildren include sets denoted by the object and/or the subject in the domain offloating allemaal, but additionally include visually represented sets. This mirrorschildren’s understanding of non-floating allemaal. This suggests that children dif-fer from adults in their mapping of meaning to form and perform a shortcut tointerpretation by over-relying on visual clues to restrict a quantifier domain. Thissupports the hypothesis identified in chapter 2 that acquiring quantification involvesfine-tuning the interplay between syntax, semantics and pragmatics.This chapterproceeds as follows. In section 4.2, I discuss the acquisition literature on children’sinterpretations of floating versus non-floating quantifiers. Section 4.3 continueswith a discussion of the Dutch quantifier allemaal. After having formulated themain predictions in section 4.4, the three experiments testing these predictions arepresented in section 4.5. I end this chapter with several conclusions about children’sunderstanding of floating quantifiers and the role of syntax in section 4.6.

4.2 (Floating) Quantification in child language

Floating quantifiers can occur at multiple positions in a clause, ‘away’ from theirNP. Consider (1) in which all can occur both before and after have.

(1) a. The boys should all have been playing outside with their toysb. The boys should have been all playing outside with their toys

Floating quantifiers require an (appropriate) antecedent within the same clause, in asimilar way as bound anaphora such as reflexives. Consider (2) and (3):

(2) The boysi I met yesterday when I was talking with the girlsj from next doorwere ashamed of themselvesi,∗j

(3) The boysi I met yesterday when I was talking with the girlsi from next doorwere are alli,∗j very nice

In (2) and (3), only the boys is a possible antecedent for the floating quantifier all, andnot the girls. Just like reflexives must be c-commanded by their antecedent, floating

4.2. (Floating) Quantification in child language 47

quantifiers must be c-commanded by their antecedent.Floating quantifiers crucially differ from their non-floating counterparts in that

they do not require their restriction to directly follow them (cf. (1)) and instead allowa noun phrase in the preceding part of the sentence to supply its domain. Roeperet al. (2006) argue that children carry this over to non-floating quantifiers: instead ofrestricting the quantifier domain to the noun phrase following the quantifier, theyargue that the child also takes other noun phrases in the sentence to supply (partof) the quantifier domain. The child’s exhaustive pairing answer for All cowboysare riding a horse comes about as an effect of including another noun phrase inthe quantifier domain than the one following the quantifier. As a result, childrenquantify over both the subject and the object.

Note however, as pointed out above, that floating quantifiers do not randomlyrestrict their domains by means of the noun phrase available in the sentence. Float-ing quantifiers must be c-commanded by their antecedent. This, Roeper et al. (2006)argue, marks the difference between children’s and adults’ understanding of quanti-fied sentences. Adults recognize the nature of a floating quantifier (it is not followedby ‘its’ noun phrase), and, first, look for a suitable domain and, second, restrictthis search to the noun phrase c-commanding the floating quantifier. Childrenovergeneralize the first characteristic of floating quantifiers to their non-floatedcounterparts and ignore this second requirement.1

The question arises what this means for children’s understanding of floatingquantifiers. Roeper et al. suggest that, once children are able to distinguish floatingquantifiers from non-floated ones, they will interpret quantified sentences adult-like.2 Before they make this distinction, they do not use syntax as a clue to restrict

1This is supported by Roeper et al’s finding of three developmental stages in the acquisition ofquantification. In the first, so-called ‘adverb stage’, children neither restrict the quantifier domain to theconstituent following the quantifier nor even to other noun phrases in the sentence. Roeper et al. takethis to mean that children treat quantifiers as adverbs in this stage. This explains why some children evenanswer ‘no, not that one’ for sentences like (i.) and a picture in which three horses are eating hay andone bunny is eating a carrot (i.e. the so-called perfecionist answers in Philip (1995), see chapter 2).

(i.) Every horse is eating hay

In the second so-called ‘each stage’ or floating quantification stage, Roeper et al. argue, children inparticular disobey the syntactic conditions for restricting a quantifier domain and take the entire sentenceto provide a suitable quantifier domain. This results in the exhaustive pairing answer. The floatingquantification stage is followed by a final, adult stage, in which the child correctly makes a distinctionbetween floating quantifiers like all and each and non-floated quantifiers like every (cf. *The boys shouldevery have been playing outside). In this sense, the existence of every would trigger children to distinguishdomains available in the clause from domains that the syntax allows as appropriate (i.e. those nounphrases c-commanding the floating quantifier).

2Philip’s (1995) Event Quantification Account (EQA) makes a different claim. As he pointed out inPhilip (2004), the EQA explicitly rejects the idea that children’s exhaustive pairing answers are relatedto their understanding of floating quantifiers. Moreover, Philip (2004) argues that the EQA ratherclaims that the exhaustive pairing answer is due to the “intrinsic semantic complexity of distributiveuniversal quantification, which can consume too much of the allocated processing resources for thechild to maintain an adult LF containing a determiner universal quantifier.” (Philip, 2004:8). Note


their domain.Labelle and Valois (2002, 2003) provide support that children’s understanding

of floating-quantified sentences indeed mirrors their understanding of non-floatingquantifiers. Labelle and Valois examined children’s understanding of French quan-tifiers. In French, the domain of the quantifier beaucoup (a so-called quantifier ata distance, Obenauer, 1983, 1984) must be restricted by the object. This contrastswith floating quantifiers in French, like chacun, which only allow quantificationover the subject. Consider (4) and (5) (examples from Labelle and Valois,2003:1).

(4) a. [LesThe

enfants]ichildren

onthave

chacuni

eachreçureceived

una

ballonballoon

‘The children each received a balloon’b. *[Les

Theenfants]children

onthave

chacuni

eachreçureceived

lesthe

ballonsi

balloons‘The children each received the balloons ’

(5) a. *[LesThe

enfants]ichildren

onthave

beaucoupi

a-lotreçureceived

una

ballonballoon

‘A lot of the children received a balloon’b. [L’enfant]

The childrenahave

beaucoupi

a-lotreçureceived

deof

ballonsi

balloons‘The children received a lot of balloons’

The data of Labelle and Valois (2003) show that whereas children correctly restrictthe quantifier domain to the object in the case of the quantifier at a distance beaucoup,they allow the floating quantifier chacun to quantify over both subject and object.This mirrors their understanding of non-floated quantifiers and shows that childrendo not restrict the domain of floating quantifiers adult-like.

A similar conclusion can be drawn from the work of Brooks and Braine (1996)on children’s understanding of English each as in Each flower is in a vase. They showthat children have trouble restricting the domain of each in extra-object situations.Brooks and Braine conclude that children ignore syntax:

We suspect that children initially learn to associate each with a “pairing”or one-to-one semantic feature without attending to the quantifier’ssyntactic position (i.e., if the objects described by a sentence are in per-fect one-to-one correspondence, children may grasp the pairing featureassociated with each without attending to which NP is modified by each).Given the circumstance that a partial one-to-one correspondence occurs,

however that children also give exhaustive pairing answer with all, which is not distributive. Moreover,if it is indeed the case that the distributivity features of universal quantifiers cause the child to interpretquantified statements differently than adults, this provides an additional reason to the one provided byRoeper et al. (2006) to look into children’s understanding of floating quantifiers; floating quantifiers areknown for their distributive characteristics and even have been argued to carry a distributivity operator(Hoeksema, 1996).

4.3. Quantifier flotation and the Dutch quantifier allemaal 49

children will initially make comprehension errors because they fail toattend to the syntactic position of each. (Brooks and Braine, 1996:247)

In sum, explaining why children take the domain of the quantifier too liberally,Roeper et al. (2006) argue that the child restricts the quantifier domain like adults doin the case of floating quantifiers by looking for a suitable noun phrase to restrict thedomain all over the sentence. Children, however, do not limit the quantifier domainto the noun phrase following the quantifier, but rather ‘overuse’ the other nounphrases in the sentence. Children thus ignore the syntactic information to determinethe quantifier domain. To leave this developmental stage, the child must realizethat there is a difference in restricting the domain of a floating versus a non-floatingquantifier. When do children realize the difference between floating quantifiers andnon-floated quantifiers? From Roeper et al., it follows that this is not before the ageof six (the age the over-exhaustive answers with non-floating quantifiers disappear).But is this indeed the case? The Dutch quantifier allemaal allows us to answer thisquestion experimentally.

4.3 Quantifier flotation and the Dutch quantifier allemaal

In the case of the Dutch quantifier allemaal, the syntax does not only determinethe quantifier domain, but also affects the kind of relation the quantifier establishesbetween its domain and the nuclear scope. This provides an ideal case to testchildren’s use of syntax to interpret a quantified sentence (see also Hollebrandse andSmits, 2006). Before turning to three experiments on children’s understanding ofthe Dutch floating quantifier allemaal, I first take a close look at the nature of theDutch quantifier allemaal. Essentially, allemaal has two meanings: an exhaustivemeaning and a existential meaning.

The quantifier allemaal in (6-b) is the floated counterpart of prenominal alle ‘all’(cf. (6-a) and (6-b)).

(6) a. AlleAll

jongensboys

lachenlaugh

‘All boys are laughing’b. De

Thejongensboys

lachenlaugh

allemaalallemaal

‘The boys are all laughing’

Allemaal allows both quantification over the subject (exemplified in (6-b) and (7-a))and quantification over the object (exemplified in (8-a)). It alternates with the moreformal and archaic floated alle (Ax, 1977; Doetjes, 1997) which in a similar wayallows the subject to be its domain (cf. (7-b)) as well as the object (cf. (8-b)).3

3The formal alle becomes allen if it is not followed by an overt noun phrase.


(7) a. DeThe

jongensboys

dragencarry

allemaalallemaal

eena

koffersuitcase

‘The boys are all carrying a suitcase’b. De

Thejongensboys

dragencarry

allenall

eena

koffersuitcase

‘All boys are all carrying a suitcase’

(8) a. DeThe

jongenboy

draagtcarries

dethe

kofferssuitcase

allemaalallemaal

‘The boy is carrying all the suitcase’b. De

Thejongenboy

draagtcarries

dethe

kofferssuitcases

allenall

‘The boy is carrying all the suitcases’

In addition, allemaal can be used prenominally in an existential sentence, in which itonly allows a weak, existential reading (in the sense of Milsark, 1979) (cf. In ’t Veld,1990; Hollebrandse, 2002).4

(9) ErThere

vliegenfly

allemaalallemaal

papegaaienparrots

‘There are flying many parrots’

The differences between floated and prenominal allemaal suggest that there aretwo distinct usages of allemaal in Dutch (cf. Hoeksema, 1996). Whereas theprenominally used allemaal has an intersective, non-exhaustive interpretation, itsfloated counterpart has an universal, exhaustive (i.e. non-intersective) interpretation(in the sense of Barwise and Cooper, 1981).5 So (9) is true if say four out of fiveparrots are flying, whereas (10) is crucially false in the same situation. Hollebrandse(2002) argues that the syntactic position of allemaal determines its interpretation aseither exhaustive or non-exhaustive.

(10) DeThe

papegaaienparrots

vliegenfly

allemaalallemaal

‘The parrots are all flying’

The Dutch quantifier allemaal is remarkable because it has two contrasting readings.According to Milsark (1979), quantifiers allow either an intersective reading (andare labeled weak) or a non-intersective reading (and are labeled strong) (cf. chapter2). Quantifiers that allow both readings like some and many are called ambiguous.However, these latter quantifiers are ambiguous depending on the discourse context(they are non-floating quantifiers on both readings, cf. chapter 5) For allemaal, the

4The Mandarin Chinese dou ‘all’ as cited from Dowty and Brodie (1984) by Bobaljik (2003) issimilarly allowed in a floated position and not as a strong universal quantifier in a prenominal position.

5As Hoeksema points out, allemaal differs in this respect from its Afrikaans cognate almal whichdoes allow an exhaustive reading when used prenominally. See Hoeksema (1996) and references therein.

4.4. Hypothesis and predictions 51

syntactic position determines its interpretation. No matter what kind of discourseis added, (10) turns out to be false if one parrot is not flying. This presents evidencethat the two usages of allemaal are not related to each other.6 Most important forcurrent purposes, it is the syntax that enables one to determine which interpretationis at issue. The case of the Dutch quantifier allemaal therefore provides the ideal casefor testing whether or not children take syntax into account in their interpretationof quantifiers, or more generally how they understand the interplay between syntaxand semantics.

4.4 Hypothesis and predictions

In this chapter, I hypothesize that children do not use syntactic information torestrict the quantifier domain (cf. Roeper et al., 2006, Brooks and Braine, 1996) ofthe Dutch floating quantifier allemaal.

(11) Hypothesis:Children do not use the syntactic information to interpret a quantifiedsentence

Starting out from the literature reporting children giving exhaustive pairing answersfor non-floating quantifiers, (11) makes two predictions. First, (11) predicts thatchildren will show similar behavior for sentences with floating and non-floatingquantifiers because they, by hypothesis, do not use the syntax to restrict theirdomain. Second, (11) predicts that children do not distinguish between allemaalquantifying over the subject or the object; in both cases, children allow the entiresentence to supply a quantifier domain since, again by hypothesis, they do not usesyntax to determine the domain.

The question is what kind of information children use to restrict the quantifierdomain instead. Is it the visual presence of the extra object (as already argued byDonaldson and Lloyd, 1974 and Bucci (1978); see chapter 3) or rather the experi-mental setup (as argued by Crain et al.) that causes children to give a non-adult-likeanswer? Moreover if children do not use syntax for interpreting a quantified sen-tence, does this mean that they do not distinguish between the two interpretationsof allemaal, i.e. its exhaustive and non-exhaustive reading? Brooks and Braine (1996)show that children master the exhaustive reading of the universal quantifiers eachand all and therefore argue that children have an adult quantifier system. Extendingthis to Dutch allemaal and given the hypothesis in (11), the third prediction followsthat children only to allow exhaustive readings for allemaal. Three experimentsaddress these predictions. After presenting these three experiments, I will returnto the main hypothesis of this thesis outlined in chapter 3 that the acquisition of

6Although they might historically be. Compare English all sorts of, all manner of, which hasdeveloped into some kind of elaborate indefinite, as evidence by their occurence in existential sentences:There were all sorts of problems with the new software (Hoeksema, p.c.).


quantification is a matter of establishing a target-like equilibrium between syntax,semantics and pragmatics and account for the results in terms of the OT frameworkintroduced there.

The first experiment examines children’s understanding of floating quantifiers;do they restrict the domain of allemaal depending on the syntactic position of thequantifier? The second experiment addresses the question what kind of informationchildren use to restrict a quantifier domain. By presenting children items containingboth an extra object and an extra agent, this second experiment zooms in on thequestion what the role of the visual presence of the extra object and agent plays inchildren’s understanding of quantified sentences. The third experiment examineschildren’s usage of syntax to distinguish prenominal allemaal from floated allemaal.

4.5 Experiments

4.5.1 Experiment I: Quantifier scope

The first experiment aims to answer the question whether children use syntacticinformation to restrict the domain of allemaal.

4.5.1.1 Method

Participants Fifteen children of elementary school De Vensterschool, Paddepoel(Groningen, The Netherlands) were tested. The children varied in age from 4 to 6 (9boys, 6 girls). Ten adults served as a control group.

Design All test items (twelve in total) contained the floating quantifier allemaal.The variables were Sentence Type and Picture Type, each containing two levels.The test sentences either contained quantification over the object (six items) or thesubject (six items). Consider the pair in (12), illustrating quantification over theobject and quantification over the subject respectively.

(12) a. DeThe

jongensboys

hebbenhave

dethe

kofferssuitcases

allemaalall

vastfixed

‘The boys are holding all the suitcases’b. De

Thejongensboys

hebbenhave

allemaalall

dethe

kofferssuitcases

vastfixed

‘The boys are all holding the suitcases’

The pictures accompanying these sentences contained either an extra object (3 itemsper sentence type) or an extra subject (3 items per sentence type). For example, (12-a)is false for figure 4.1 containing an extra object and true for figure 4.2 containing anextra agent. Conversely, (12-b) is true for 4.1 and false for 4.2.

In addition to these test items, there were three control items with subjectquantification and three items with object quantification, accompanied by a picture

4.5. Experiments 53

Figure 4.1: Extra Object situation targeting a yes-answer for sentences with subjectquantification and a no-answer for sentences with object quantification

Figure 4.2: Extra Subject situation targeting a no-answer for sentences with subjectquantification and a yes-answer for sentences with object quantification

like figure 4.3. These control items targeted a yes-answer for both quantification overthe object and subject and were added to the experiment to see if participants havean exhaustive reading for allemaal. Additionally, there were two control yes-fillersto check whether children were paying attention.

Figure 4.3: Control item eliciting a yes-answer for both sentences with subject andobject quantification

Procedure The children were tested using a Truth Value Judgment Task (Crainand Thornton, 1998). We presented children with pictures analogous to figure 4.1and figure 4.2. They had to judge prerecorded test sentences and say whether or notthese sentences matched the pictures that were shown to the child on a laptop screen.


Furthermore, every child was asked to explain each of her answers. We asked forexplanations for both yes and no answers. This enabled us to determine the domainthe child was quantifying over. The children’s answers were noted down during theexperiment. When the child pointed at the denotation of the object to explain heranswer, this was coded as object quantification. In a similar way, when the childpointed at the subject-denotation, the child was taken to quantify over the subject.This was done to investigate why children answered ‘yes’ or ‘no’.

4.5.1.2 Results

The data were analyzed with a (2) x (2) x (2) repeated measures analysis of variance.The within-subject factors were Picture Type (Extra Agent Picture or Extra ObjectPicture) and Sentence Type (quantification over the subject or the object) and Agewas the between-subject factor (child or adult). This revealed an interaction effectbetween Age, Picture Type and Sentence Type (F (1,23) = 33.62, p < 0.001), andan interaction effect between Sentence Type and Picture Type (F (1,23) = 14.03, p =0.001). No main effects were found.

The adults answered as predicted (cf. figure 4.4); they answer significantly moreoften yes in the Extra Object condition than in the Extra Agent condition in thecase of subject quantification (t(9) = -2.714, p = 0.024) and, conversely, they answersignificantly more often yes in the Extra Agent condition than in the Extra Objectcondition in the case of object quantification (t(9) = 3.934, p = 0.003).

The children showed guessing behavior for all test items, as revealed by a two-tailed binomial test; the mean percentages yes-answers (displayed in figure 4.5)are not significantly different from what would be expected were they randomlyguessing (see table 4.1). This means that children did not consistently either pointat the extra object or the extra agent depending on the syntactic structure of thesentence, but rather applied a guessing strategy to restrict the quantifier domain.

Picture Type Sentence Type Mean percentage Std. Deviation

Extra Agent Subject Quantification 48.89∗ 39.57Object Quantification 53.33∗∗ 39.44

Extra Object Subject Quantification 60.00∗∗∗ 33.81Object Quantification 42.22∗∗∗∗ 42.66

∗t(14) = -0.109, p = 0.915; ∗∗t(14) = 0.327, p = 0.748; ∗∗∗t(14) = 1.146, p = 0.271;∗∗∗∗t(14) = -0.706, p = 0.492

Table 4.1: Mean percentages ‘yes’ answers children for both sentence types andboth picture types and their difference from at chance behavior (all t-tests reveal nosignificant difference from 50%)

4.5. Experiments 55

Figure 4.4: Mean percentages yes-answers adults for the Extra Object condition andthe Extra Subject Condition for sentences with subject quantification (black) andobject quantification (white)

4.5.1.3 Discussion

The results show that children restrict the domain of a floating quantifier differentlythan adults. This supports the hypothesis in (11) that children do not use syntacticinformation to restrict the quantifier domain; children do not differentiate betweensentences with subject and object quantification. Moreover, children point at theextra object and extra agent for sentences with floating quantifiers as they arereported in the literature to do for sentences with non-floating quantifiers. Finally,children seem to guess as to what restricts the domain of a floating quantifier.

4.5.2 Experiment II: Quantifier scope and extra agents and objects

The question arises whether children are not able to restrict the appropriate quanti-fier domain (i.e. they do not use the syntax) or whether they are rather intriguedby the extra object or agent in the picture. Donaldson and Lloyd (1974) and Bucci(1978) already argued that children’s interpretations of quantified sentences areaffected by visual information. In addition, Crain et al. (1996) and also Sugisaki andIsobe (2001) found that the exhaustive pairing answer disappears if more than oneextra object is added. In line with these results, the results of experiment I confirmsthe idea that children allow the visual information to play a more important role


Figure 4.5: Mean percentages yes-answers children for the Extra Object conditionand the Extra Subject Condition for sentences with subject quantification (black)and object quantification (white)

than the syntactic information to restrict a quantifier domain. But if it is indeed themere visual presence of an extra object (or agent) that causes the child to includethe object (or agent) in the quantifier domain, one predicts that children do notrestrict the domain of a floating quantifier at chance if both an extra object andextra subject are displayed. In that case, there are two extra entities and, hence, adultdomain restriction is predicted. The next experiment tests children’s understandingof quantification in such a situation.

If children apply a floating quantifier interpretation strategy to both floatingand non-floating quantifiers (cf. Roeper et al. (2006) and the previous experiment)and restrict the domain of the quantifier by looking for a suitable domain in theentire sentence instead of the noun phrase that c-commands it, the question arisesas to how children will interpret quantified sentences if the accompanying picturedisplays both an extra object and an extra agent. Having an extra agent and an extraobject in the picture offers a way of testing how children determine the domain ofa quantifier: do they restrict the quantifier by anything extra in the visual contextor do they use syntactic information in such a case? The child’s explanation to thequestion whether the quantified sentences matches the picture or not will bring outthis difference.

The previous experiment showed that children do not make a distinction be-tween subject and object quantification with floated quantifiers in the Extra Object

4.5. Experiments 57

and Extra Agent situations. Children pointed at the extra object or the extra subjectto explain why they found the sentence with a floated quantifier false. However,when an extra object and extra subject are displayed simultaneously children mustchoose which extra element they point to, thus revealing which domain they arequantifying over. If they point at the extra object in the case of object quantificationand at the extra subject in the case of subject quantification, this would show thatchildren do make a distinction between sentences with subject and object quantifica-tion. Alternatively, children could point at both the extra object and extra agent(due to quantifying over both object and subject), point at the extra agent in bothconditions (due to a preference for subject quantification) or point at the extra objectin both conditions (due to a preference for object quantification).

4.5.2.1 Method

Participants Thirty-nine subjects (age range 4;1 to 6;7, 19 girls, 20 boys) from theafter-school program of De Boomhut and elementary school De Vrije School (bothlocated in Groningen, The Netherlands) were tested. In addition, seven adults weretested as a control group.

Materials The children were tested on their understanding of the difference be-tween subject quantification (cf. (13), three items) and object quantification (cf. (14),three items), both targeting a no-answer for pictures presenting an extra object andan extra agent as in figures 4.6 and 4.7. Crucially, the reason why (13) and (14) arefalse differs; in the case of (13) and figure 4.6, it is because one girl does not ride ahorse and in the case of (14) and figure 4.7, it is because one donkey is not beingcarried.7

(13) DeThe

meisjesgirls

rijdenride

allemaalallemaal

opon

eena

paardhorse

‘The girls are all riding a horse’

(14) EenA

manman

draagtcarries

dethe

ezelsdonkeys

allemaalallemaal

‘A man is carrying all the donkeys’

Additionally, children were tested on control conditions for sentences withquantification over the subject (three items) and quantification over the object (threeitems). For these control conditions, pictures were shown displaying an exhaustivesituation as in figure 4.8, without any extra objects or extra agents. The total numberof items was twelve and the items were presented mixed with the test items and the

7Some native speakers of Dutch might disagree and reject (14) due to a collective reading accordingto which there should be one man carrying all donkeys. Despite this different reason, the adult answerwill still be ‘no’ which is most important for the current experiment.


Figure 4.6: The girls are all riding a horse

Figure 4.7: A man is carrying all the donkeys

three control no-items and three control yes-items items of the experiment presentedin section 4.5.3.

Figure 4.8: A man is carrying all balloons

Procedure The children were tested using a Truth Value Judgment Task (Crainand Thornton, 1998). We presented children with pictures analogous to figure 4.6and 4.7 on a laptop. They had to judge prerecorded test sentences and say whetheror not these sentences matched the pictures. Furthermore, every child was asked to

4.5. Experiments 59

explain each of her answers. As before, we asked for explanations for both yes- andno-answers.

4.5.2.2 Results

There were two subgroups of children. Ten of the total of thirty-nine childrenanswered yes on the experimental condition on four or more than four out of thetotal of six test items. These children (who answered adult-like on the controlconditions and control items) did not master the exhaustive property of allemaal.8

The remaining twenty-nine children all gave no-answers on the test conditionswhich allowed me to look at their explanations in detail. Figure 4.9 shows thedistribution of answer qualifications per sentence type. Adults answer as expectedand explain their answers in terms of the target domain (subject or object dependingon the condition). A chi-square analysis of the explanations of these twenty-ninechildren shows that the distribution of the children’s answers (either in terms of thesubject, object, both object and subject, the world (e.g. Robots do not hold balloons)or non-interpretable c.q. ‘unknown’ terms) does not vary per sentence type (χ2(4)= 3,608, p = 4.33).

4.5.2.3 Discussion

This experiment aimed to answer the question whether children treat sentenceswith quantification over the subject differently from quantification over the objectif they are faced with pictures displaying both an extra object and an extra subject.The results show that children do not make a distinction between sentences withallemaal quantifying over the subject and sentences with allemaal quantifying overthe object. This suggests that children do not use syntactic information to restrictthe quantifier domain (i.e. they do not take into account the c-commanding relation(or even subjacency) between the quantifier and its domain).

Do children also ignore the syntactic information provided by the sentence todistinguish between allemaal with a non-exhaustive reading (i.e. when it is usedprenominally) and allemaal with an exhaustive reading (i.e. when it is used as afloating quantifier). The experiment presented in the next section addresses thisquestion.

8These children mirror the behavior of children giving so-called underexhaustive answers on taskswith non-floating quantifiers and do not take allemaal as an exhaustive quantifier. Hollebrandse (p.c.) sug-gests that children giving under-exhaustive answers might point at the existence of a pre-quantificationalstage, marking a developmental stage between target-like understanding of cardinal items and non-target-like understanding of quantifiers. In this stage, children do not yet quantify, but rather just check whetherthe denotation of the quantifier domain is present in the test item. This explains their yes-answer onexperimental conditions like the extra-object situation and a sentence containing quantification over thesubject. The answers of the ten children found in this experiment, present additional evidence for such apre-quantificational stage.


Figure 4.9: Distribution of children’s kind of answers for both sentences withquantification over the subject and quantification over the object

4.5.3 Experiment III: Quantifier position and interpretation

The results of the previous experiment lead to the next question. Recall from section4.3 that allemaal has an intersective or non-intersective reading depending on itssyntactic position. Consider again (9), repeated here as (15), in which allemaal isa floating quantifier and receives an exhaustive reading and (10), repeated here as(16), in which allemaal is used in an existential there-sentence and only allows anon-exhaustive interpretation.

(15) Dethe

ezelsdonkeys

huilencry

allemaalallemaal

‘The donkeys are all crying’

(16) Erthere

huilencry

allemaalallemaal

ezelsdonkeys

‘There are many donkeys crying’

If children do not take into account the syntax to restrict a quantifier domain as theresults of experiment 1 and 2 suggest, they are predicted not to differentiate thesetwo meanings of allemaal.

4.5. Experiments 61

4.5.3.1 Method

Participants The same participants were tested as in experiment 2. See section4.5.2.1.

Materials Both children and adults were tested on sentences with exhaustiveallemaal like (15) (3 items) and sentences with non-exhaustive allemaal like (16) (6items). To control for exhaustive interpretations, non-floated alle as in (17) was usedin three extra-agent situations. All testitems were accompanied by a picture with anExtra Agent like the one in figure 4.10. Intransitive sentences were used to rule outa possible effect of the object at the children’s interpretation.

(17) Alleall

ezelsdonkeys

huilencry

‘All donkeys are crying’

Figure 4.10: The donkeys are all crying?

In addition to the test items, three control no-items and three control yes-itemswere included. The control no-items were plural sentences accompanied by picturesin which only one object was performing an action (e.g. one donkey was crying).The control yes-items were sentences containing alle ‘all’ accompanied by picturesin which all the objects were performing an action (e.g. all donkeys were crying).The total of sentences was eighteen. The items were mixed with the items of theexperiment discussed in section 4.5.2.1.

Procedure The same procedure was used as in experiment 2. See section 4.5.2.1.

4.5.3.2 Results

The mean percentages of yes-answers are displayed in figure 4.11 for items containingthe exhaustive allemaal, prenominal alle and the items containing non-exhaustiveallemaal for both children and adults. Overall, children overwhelmingly answer‘no, not that one’ for all three sentence types and e.g. point at the donkey that isnot crying. They do this even for sentences with non-exhaustive allemaal as in (16)with respect to figure 4.10. In contrast, the adults answered as expected; they accept


a sentence with non-exhaustive allemaal in such cases (with the exception of oneadult) and answer as expected in 0% of the cases ‘yes’ with exhaustive allemaal ornon-exhaustive alle). Both children and adults answered adult-like on the controlitems.

Figure 4.11: Mean given yes-answer children and adults for exhaustive allemaal(white bar), prenominal alle (dashed bar) and non-exhaustive allemaal (gray bar) forboth children and adults

Since the three items with alle were only added to the experiment to control forexhaustive interpretations (and children show adult behavior on these items, 15.38%versus 0.00%, t(44) = 1.325, p = 0.192) and the focus of the experiment is children’sunderstanding of the two interpretations of allemaal, prenominal alle was left outfrom further analysis of the data.

The data were analyzed with a (2) x (2) repeated measures analysis of variance.Sentence type (floated allemaal versus prenominal allemaal) was chosen as within-subjects variable, Age (adults and children) was chosen as between-subject variable.This revealed an interaction effect between Sentence Type and Age (F (1,44) = 113.49,p < 0.001) and a main effect of Sentence Type (F (1,44) = 113.49, p < 0.001). Inaddition, a main effect was found for Age (F (1,44) = 7.392, p = 0.009). T-testsrevealed that children differ significantly from adults in their interpretation of non-exhaustive allemaal (t(44) = -6.03, p < .001). For exhaustive allemaal, no significantdifference between children and adults was found (p > 0.05).

Figure 4.12 illustrates the individual results in a subject analaysis. Dots repre-sent children’s individual interpretations of floated allemaal (on the x-axis) versus

4.5. Experiments 63

prenominal allemaal (on the y-axis).

Figure 4.12: Mean given yes-answer for exhaustive allemaal ‘all’ versus non-exhaustive allemaal ‘a lot of’ per child

To answer the question whether children interpreted the items with alle differ-ently than the items with floated allemaal, an item analysis was performed. Thisrevealed no difference between the items with prenominal alle and floated allemaal(Cronbach’s alpha = 0.843). This means that floated allemaal and the prenominalalle are interpreted the same; both exhaustively. An analysis using Pearson’s cor-relation coefficient then showed that there was a significant positive correlationbetween children’s interpretations of floated allemaal/prenonimal alle and theirinterpretations of non-exhaustive allemaal (r(37) = 0.843, p < 0.001; r2 = 0.711).Children who more often answered yes for floated allemaal/prenominal alle alsosignificantly more often answered yes for prenominal allemaal. Such an effect is notfound for adults.

4.5.3.3 Discussion

The results of the third experiment show that children’s interpretations of non-exhaustive allemaal differ from adults’ interpretations; children, but not adults,only allow an exhaustive reading of allemaal. The children are adult-like for floatedallemaal. This means that children allow an exhaustive reading for allemaal, in-dependent of its position. Children ignore the syntactic position of allemaal insentences with the floated allemaal and the sentences with non-exhaustive allemaal.


For children, both positions of allemaal have an exclusively exhaustive reading.Adults only give this reading for floated allemaal.

4.6 General discussion and conclusions

The three experiments presented in this chapter aimed to test the prediction thatfollowed from the work by Roeper et al. (2006) who argued that, at a stage at whichchildren do not yet recognize the difference between floating quantifiers and non-floating quantifiers, they resort to a floating quantification strategy for determiningthe domain of the quantifier. Floating quantifiers allow the entire clause to providetheir suitable domain (within the boundaries of c-command), in contrast to non-floating quantifiers for which the noun phrase following the quantifier provides thedomain. Roeper et al. hypothesize that children do not use the syntax to interpret aquantified sentence. Instead, they would take any NP in the clause to provide thedomain, which results in exhaustive-pairing interpretations. This led to the mainhypothesis in (11), repeated here as (18).

(18) Hypothesis:Children initially do not use the syntactic information to interpret a quanti-fied sentence

Three predictions followed from this hypothesis which were tested in three ex-periments. First, children were predicted to give exhaustive pairing answers forsentences with floating quantifiers; since children’s exhaustive pairing answers forsentences with non-floating quantifiers are hypothesized to be due to not usingsyntax to restrict a quantifier domain (cf. Roeper et al., 2006), children are predictedto ignore the syntax in a similar way if sentences with floating quantifiers are atissue. The results of experiment 1 support this prediction. They show that childrengive similar non-adult like answers for sentences with floating quantifiers as withnon-floated ones. This suggests that children’s search for a suitable domain of afloating quantifier is not limited to those noun phrases that are in a c-commandingrelation with the quantifier.

Second, children were predicted to use a different clue than syntax to restricta quantifier domain. Because children’s interpretations of quantified sentences areknown to be affected by visual information (i.e. the extra object in the extra objectcondition), children are predicted to restrict the domain of a floating quantifier atchance if both an extra object and extra subject are displayed. In that case, there isno ‘extra’ entity that is visually more prominent than the other displayed entitiesand, hence, adult domain restricted is predicted. The second experiment testedchildren’s understanding of quantification in such situations. The results revealedthat children do not make a distinction between sentences with quantification overthe subject and sentences with quantification over the object in such a situation. Inboth cases, children answered similarly and either point at the subject, object, both

4.6. General discussion and conclusions 65

subject or object or gave an answer in terms of their world-knowledge.This led to a third prediction regarding children’s understanding of the pe-

culiarities of the Dutch quantifier allemaal. This quantifier gets an intersective,non-exhaustive reading when it used prenominally or a non-intersective, exhaustivereading if it used as a floating quantifier. To keep these two interpretations apart,it is crucial to take into account the syntactic environment the quantifier occursin. The third experiment presented above addressed children’s understanding ofthe two usages of the Dutch quantifier allemaal. The results showed that they onlyallow an exhaustive reading for allemaal, regardless of the syntactic environment thequantifier occurs in. This means that children do not use the syntactic position ofthe quantifier to determine what kind of relation the quantifier establishes betweenits domain and nuclear scope (i.e. an exhaustive and non-exhaustive reading).

In sum, the results presented in this chapter show that children do not use syntaxto restrict a quantifier domain. The results support the hypothesis identified inchapter 3 that the acquisition of an adult-like understanding of quantified sentencesinvolves the fine-tuning of the interaction between syntax, semantics and pragmatics.Children differ from adults in their mapping of meaning to form by giving differentweight than adults to the clues to restrict a quantifier domain; whereas adults usesyntax in all experiments reported in this chapter, children clearly do not.

If children use other clues than syntax to restrict a quantifier domain, what arethese other clues? Crucially, in all experiments in this chapter the visual informationcompeted with the syntactic information; in experiment 1, an extra agent or objectwas displayed an hence, a visually prominent item was present, in experiment 2,an extra agent or extra object might have distracted the child and in experiment3, an extra agent again was a visually prominent item. In this respect, the resultspresent experimental evidence that children do not use syntactic information whenthe visual contexts competes with this syntactic information. This confirms thehypothesis outlined in 3 that children rank visual information higher than syntacticinformation. Clearly, more experimental data is needed to address the effect ofvisually prominent items in more detail.

Crucially, the question needs to be answered whether children are also able toanswer target-like if such a visually prominent item is not present (anymore) inthe stimulus. Drozd and Van Loosbroek (2006) present experimental evidence thatsuggests this might indeed be the case. When the child is first pointed at certain setsin the picture, children gave adult-like answer for quantified sentences. In relation tothis question, the question arises how children interpret quantifiers whose domainis context dependent. And do children also become adult-like if the test items areembedded in a particular discourse context (cf. also Drozd, 2001, cf. Hollebrandse,2004)? If it is indeed the discourse context that children use to restrict a quantifierdomain, what kind of information do children use from this context to restrict aquantifier domain? These two questions will be respectively addressed in the nexttwo chapters.

5The many meanings of manyHow children use pragmatics to constrain meaning∗

5.1 Introduction

This chapter addresses children’s understanding of the weak quantifier many and,in particular, their understanding of the context dependent meanings of many.Recently, it has been proposed that the way in which children interpret universalquantifiers may initially be rather similar to the way they interpret many (cf. Drozdand Van Loosbroek, 1999), c.q. in a strongly context dependent way (Geurts, 2003).However, there are only few results to date of children’s understanding of quantifierslike many and their context dependence (with the exception of Krämer, 2005a and2005b). Many allows different kinds of cardinal and proportional readings. Contextplays an important role for all these readings of many. The possible interpretationsof many point at the necessity to characterize (implicit) domain restriction in termsof the interplay between syntactic, semantic and pragmatic constraints (cf. Hendriksand De Hoop, 2001). This chapter aims to characterize the acquisition of many interms of the interplay between these constraints and to establish how this differsfrom the way these consraints interact in adult language.

By investigating the hypothesis that the acquisition of quantification is a matterof fine-tuning the interplay between constraints of various nature (cf. chapter 3) formany, I test the prediction that arises from the work by Drozd and Van Loosbroek(1999) that children use pragmatics to restrict a quantifier domain. I will take intoaccount the semantic and pragmatic characteristics of many and investigate Englishlearners’ understanding of this quantifier. I compare their understanding of many totheir understanding of the universal quantifiers all and many of.

This chapter proceeds as follows. I start with discussing the many interpretationsof many in adult language in section 5.2. After presenting various solutions that

∗Part of the results from this chapter has been published as Smits, Roeper, and Hollebrandse(2007). Children’s ambiguous understanding of weak and strong quantifiers. In: M. Anderssen and M.R.Westergaard (Eds.) Papers from the Language Acquisition Workshop, SCL 2006. Nordlyd 34(3). 187-208.CASTL, Tromsø. http://www.ub.uit.no/munin/nordlyd

67

68 The many meanings of many

have been proposed in the literature to account for the context dependence ofquantification in general and all and every in particular in section 5.3, section 5.4applies these different solutions to the case of many and presents a new, pragmaticaccount of this quantifier in terms of bidirectional optimality theory (Blutner, 2000).Section 5.5 discusses the relevance of many from an acquisition viewpoint. In section5.6, I derive a hypothesis from this account about children’s understanding of manyand discuss the predictions, focusing on the context dependence of many. Section5.7 presents the experiment testing these predictions. Section 5.8 discusses the mainresults and conclusions.

5.2 The many meanings of many and domain restriction

In Generalized Quantifier Theory (Barwise and Cooper, 1981, Zwarts, 1983, VanBenthem, 1986), quantifier domain restriction is described in terms of the notionof conservativity. The notion of conservativity enables us to characterize the manymeanings of many.

In Generalized Quantifier Theory (GQT), a determiner relates two sets: A andB, which are both subsets of the universe U. The notion of conservativity holds thatevery quantified expression relates two sets to each other in such a way that onlythe quantifier’s first argument set (set A) and the intersection of this set with B (thequantifier’s second argument set) need to be inspected to determine the truth valueof the quantified expression. Conservativity is defined in (1).

(1) CONSERVATIVITY:If A,B ⊆ U, then QU (A,B)⇔ QU (A, A ∩ B)

For a conservative determiner, one must determine whether the members of the setdenoted by the common noun phrase (the quantifier’s first argument set A) have theproperty that is denoted by the verb phrase (the quantifier’s second argument set B).Hence, it suffices to evaluate just the members of A in relation to the members ofset B; individuals that have properties denoted by the verb phrase B but are not inthe denotation of the common noun A, are irrelevant.

For example, take a look at figure 5.1. In this figure, five parrots, one dog andone monkey are wearing a hat. Twenty parrots are not wearing a hat, nor are fivedogs and five monkeys. The notion of conservativity says that, to judge sentence (2)as false, one only has to look at the set of all parrots (those that are wearing a hatplus the ones that are not). The set of hat-wearers that are not parrots (i.e. the dogand monkey that are wearing a hat) is irrelevant.

(2) All parrots are wearing hats

The quantifier many is different, because the notion of conservativity as definedin (1) does not hold for all its readings (a proportional reading, a cardinal readingand Westerståhl’s reading). To start with the proportional reading of many and why

5.2. The many meanings of many and domain restriction 69

Figure 5.1: All parrots are wearing hats

conservativity does not hold for this reading, consider the following sentence (theexample and the discussion below is based on Westerståhl, 1984):

(3) Many farmers attended the workshop on language acquisition

In (3), what counts as many (i.e. whether the sentence is true or false) is context-dependent. If next to 20 undergraduates, 10 farmers attended a workshop onlanguage acquisition, 10 would count as many, because farmers typically do notattend such workshops, and, as a result, (3) turns out to be true. Compare this to(4).

(4) Many people in the class are right-handed.

Example (4) will be judged false in a situation of ten right-handed undergraduates andtwenty left-handed undergraduates. In this latter case, our expectation is contradictedthat, usually, more people are right-handed than left-handed and so ten is not many.The proportional interpretation of many in (3) and (4) involves comparing thenumbers of two sets (and hence violates conservativity). Crucially, what counts asmany depends on the context.

A second reading of many is the cardinal one, exemplified in (5). (5) is consideredto be true if more than an arbitrary number of bikes are parked in front of the trainstation (e.g. if more than six hundred bikes are parked in front of the train stationin Groningen, this sentence is true). However, note that for this cardinal reading,context also can affect the truth value of a sentence. Using the very same criterionfor what counts as many, is (5) true or false, given two hundred bikes parked infront of the train station in Barneveld (note that Barneveld is a significantly smallertown than Groningen, having no university, and hence, two hundred bikes does


count for the station in Barneveld)?

(5) Many bikes are parked in front of the train station

Westerståhl (1984) describes a third reading of many. This reading is exemplifiedin (6) (example from Westerståhl, 1985:403)

(6) Many Scandinavians have won the Nobel prize in literaturea. “Many of the inhabitants of Scandinavia have won the Novel price in

literature”b. “Many winners of the Nobel prize in literature are Scandinavians”

In order to determine the truth value of (6), we have to inspect the set of Scan-dinavians and the set of Nobel Prize winners. Taken literally, as in the readingparaphrased in (6-a), (6) is obviously false; it is not the case that many of the Scandi-navians have won the Nobel prize in literature. Westerståhl points out a different,and in this case preferred reading, he argues, paraphrased in (6-b). On this reading,(6) might be true. The reading exemplified in (6-b) involves ratios: the numberof Scandinavians that have won the Nobel Prize in literature as compared to thenumber of Nobel Prize winners from other countries (in view of the number ofinhabitants in those countries). Given that there were 14 Scandinavians out of 81winners in the years up to 1984 (the year Westerståhl came up with this example),14 might be viewed as many and, as a result, (6) is true under the (b)-paraphrase.In the remainder of this chapter, I will refer to this reading as the ‘Westerståhlreading’.1 The Westerståhl reading is yet another example of the context dependenceof quantifier domain restriction (cf. Westerståhl, 1984).

So for all three readings of many, context plays an important role. In theliterature, this context dependence has been represented by way of different truthconditions of the different readings (cf. Westerståhl, 1984; Partee, 1989; Partee,Ter Meulen, and Wall, 1993). As for the proportional reading of many, contextdependence can be represented by adding a contextually provided restriction thatspecifies what counts as many. In this way, one can account for the fact that (3) istrue if 10/30 people are farmers and (4) is false if 10/30 people are right-handedbecause per context, one needs to determine what counts as many. This has beenformalized in the following way (from Partee, 1993:394 ; but cf. among othersWesterståhl, 1984):

(7) PROPORTIONAL READING OF many - PRELIMINARY VERSIONmany1

E (A)(B) = many1A(A ∩ B) where |(A ∩ B)| > c · |A|

Many in (7) obeys conservativity and relates its first argument set to the intersectionof the first argument set with the second argument set. The restriction is added that

1Recently, Cohen (2001) labeled this reading the ‘relative proportional reading’ whereas Herburger(1997, 2000) calls it the ’switched reading’. In the current chapter, it does not concern us how to label thisreading but rather why adults allow such a reading in the first place.

5.2. The many meanings of many and domain restriction 71

a sentence containing many can only be true if the cardinality of the intersection ofthe first and second argument is bigger than the cardinality of the first argument setin a particular context (c in (7)).

Such an approach violates compositionality and runs counter to the idea that aspeaker is able to determine the meaning of a sentence based on the interpretationof its elements. In the case of many, one obviously has to do something more, andthis varies per context. Per context, the hearer has to determine what the standardof comparison is that the speaker presupposes. As Westerståhl (1984) and Partee(1989,1993) point out, this problem can be solved by replacing the formula in (7)with the one in (8). In (8) (from Partee et al., 1993:394), the frequency of A isnot dependent on the context, but rather depends on the frequency of the firstargument set relative to the frequency of the second argument set in the universe ofinterpretation (U).

(8) PROPORTIONAL READING OF many - FINAL VERSION

many1U (A)(B) = many1A(A ∩ B) where |(A ∩ B)| > |B|

|U | · |A|

In (8), the meaning of many is not expressed in terms of a context variable cbut in comparison to the universe of interpretation. This means, however, thatconservativity is violated. Instead of restricting the domain of quantification tothe first argument set and its intersection with the second argument set, one nowhas to take the entire second argument set into account. For example, in order todetermine the truth value of sentence (2) given figure 5.1, one has to take the entireset of hat-wearers into account.

As for the cardinal reading, a sentence containing many is true if the cardinalityof the intersection of A and B is more than a certain value. This cardinal reading isdefined in (9):

(9) CARDINAL READING OF many - PRELIMINARY VERSIONmany2

U (A)(B) = many2A(A ∩ B) where |(A ∩ B)| ≥ n

As Partee et al.(1993) points out (cf. Westerståhl, 1984), this reading obeys conserva-tivity but again raises the question what determines the value of n. Is the value ofthis variable context dependent like the value of c in (7)? As example (10) shows, acardinal reading can indeed be contextually dependent.

(10) a. I saw many women in traditional costumes in Groningen last weekb. I saw many women in traditional costumes at an open-air folk museum

last week.

For a cardinal reading of (10), world knowledge determines what counts as manyfor each location: the chance you meet a woman in a traditional Dutch costume atan open-air folk museum is bigger than that you meet one in Groningen. So (10-a)might be judged as true and and (10-b) as false if there were, say, three women intraditional costumes.


Hence, it is also necessary to account for the context dependence of the cardinalreading of many. Westerståhl (1984) and Partee et al.(1993) replace the definition ofthe cardinal reading in (9) with (11), mirroring the definition of many’s proportionalreading in (8) (adapted from Partee et al., 1993: 393):

(11) CARDINAL READING OF many - FINAL VERSIONmany2

U (A)(B) = many2A(A ∩ B) where |(A ∩ B)| ≥ f (|U|)

In (11), the standard of comparison is not a given, context-independent number (e.g.many is ‘equal to more than three’), but some minimum number fixed by the size ofthe universe of interpretation U. Again, this reading of many violates conservativity.

The Westerståhl reading points at a third way to represent the context depen-dence of many. This can be characterized as follows (from Partee et al., 1993:395,their many4):

(12) Westerståhl reading of manymany3

U (A)(B)= many3A(A ∩ B) where |(A ∩ B)| > c · |B|

In (12), many quantifies over two sets (e.g. for (6), the set of Scandinavians and theintersection of A and B, i.e. Scandinavian Nobel prize winners). For (12) to be true,the cardinality of the intersection of set A and B has to be bigger than the cardinalityof the B set times a certain contextually given value (c in (12)). This interpretationof many also violates conservativity since inspection of the entire B set is necessary.

In conclusion, for all three readings of many, context plays a role. As to howto represent this in the truth conditions of many, this differs from reading toreading. And so the question remains how to exactly define the relation betweenquantifier domains and context. These questions have been answered differentlyin the literature. In the next two sections, I will discuss some answers. Thestarting point for this discussion is that many is ambiguous between three readings (aproportional reading, a cardinal reading and a Westerståhl reading); what counts asmany differs from context to context. Partee points out (cf. the quote below) that itis this context dependence that blurs the picture whether many is really ambiguous:

‘It is a familiar fact that many is a vague, context-dependent quantifier.How many counts as many is context-dependent. ... In this respect,many shares properties with relative adjectives like big and small. Thepuzzling question is whether many is also ambiguous. In particular,is many ambigiuous between a cardinal and a proportional reading?What makes the question challenging is that if they are ambiguous,each reading is still undoubtedly vague, and that vagueness obscuresthe kinds of evidence that normally would be used to help settle thequestion whether many is ambiguous.’ (Partee, 1989:383)

5.3. Semantic holes, incomplete quantifier domains and pragmatic reasoning 73

5.3 Semantic holes, incomplete quantifier domains andpragmatic reasoning

Westerståhl (1984) (cf. Westerståhl, 1985) introduces the notion of ‘restriction’ intoGQT to account for the context dependence of many.2 Positing that the contextassigns a value to a so-called ‘context variable’ attached to a determiner (C in (13)),he accounts for the observation that the domain of many is restricted by the context.The contextually given set intersects with the quantifier’s first argument set A,forming the quantifier’s domain. According to the definition of restriction in(13) (from Westerståhl, 1984:56), this means that in (6), repeated here as (14), thequantifier’s first argument set A intersects with a context set C. For (14), A is the setof Scandinavians and B is the set of Nobel Prize winners. The context set C is theset of contextually relevant Scandinvians. This leads to interpretation (14-a).3

(13) Restriction:DC

U A,B⇔ DU ((C ∩ A),B)(14) Many Scandinavians have won the Nobel prize in literature

a. “Many Scandinavians have won the Nobel prize in literature, comparedto Nobel prize winners from other countries ”

Similar approaches to represent the context dependence of quantifier domainsin terms of a context-variable can be found in Von Fintel (1994) and more recentlyin a series of articles by Stanley (2000, 2005) and Stanley and Szabó (2000). Allthese accounts postulate a context variable that needs to be filled in by the context.4Since what counts as many differs from context to context, this context variableis filled in differently per context. Defining context variables in this way shouldbe understood, as Von Fintel points out, as “a typical tool in isolating the points

2The context dependence of quantifier domains is not taken into account in GQT (Barwise andCooper, 1981). Barwise and Cooper presuppose a fixed context assumption.

3Note that Westerståhl (1985) does not apply his notion of restriction to this special case of many.4They differ in where and how to represent this context variable. For example, Von Fintel (1994)

follows Westerståhl (1984) and proposes a similar account of the context-dependence of many in termsof, what he calls, resource domains (Westerståhl’s context sets): in a similar way as in (13), Von Fintelassumes an extra index on the determiner which is a free variable whose type needs to be supplied bythe pragmatics. This context variable (C) also intersects with the common noun argument. WhereasWesterståhl and Von Fintel take the context variable to be attached to the quantificational determiner,Stanley and Szabó (2000) (cf. Stanley, 2005) argue that the contextual variable is attached to the nounphrase following the quantificational element. They assume that two indexes are connected to the nounphrase: a function index f and a variable index i. The function index should be understood as taking,relative to a context, objects from the context to properties, and the argument index as an object (Stanley,2005:28). To get the preferred reading of many Scandinavians in (14) as Many winners of the Nobel prizein literature are Scandinavians, Scandinavians gets intersected with the set denoted by f(i), i.e. thefunction that takes Scandinavians to the property of being a Scandinavian candidate for the Nobel Prizein literature. For current purposes, it only concerns us that context dependent quantifier domains clearlypoint at the need for a theory that underlines the interaction between semantics and pragmatics. Moredetails on the issue where this interaction needs to be represented in the semantic structure can be foundin the work of e.g. Giannakidou (2004) and Neale (1990).


of contact between semantics and pragmatics. These free variables are holes in thesemantic structures which will be filled by the pragmatics.” (1996:35). Restrictingthe quantifier domain by means of a context variable, is one possible way to accountfor the context-dependence of many. Von Fintel (1994) ultimately aims to modelthe interaction between semantics and pragmatics.

However, postulating such covert variables raises several problems. For example,how many context variables do we have to assume in order to get the meaningintended by the speaker if we take all possible factors on the quantifier’s domaininto account, e.g. the effect of focus, and introduce for each factor a new contextvariable (Hendriks and de Hoop, 2001, Roberts, 2004)? Moreover, the questionremains unanswered how values are assigned to these context variables and whatkind of role context plays in this respect (Roberts, 2002). Maintaining the viewpointthat such implicit domain restriction operates at the intersection of semantics andpragmatics, an alternative solution comes to mind: the context-dependence of manyis a pragmatic matter, rather than a semantic one. Bach (1994, 2000, 2001, 2005)proposes this alternative account.

Bach (2000) argues that incomplete quantifier domains are pragmatically re-stricted by the audience in the context5, which has nothing to do with the syntacticor semantic structure of a sentence, he argues (contra the approaches that usecontext-variables discussed above). According to Bach, a distinction should be madebetween two kinds of contextual information. One kind is semantically motivated.This so-called semantic context provides, together with linguistic information, theinformation that is needed to determine what is said. For example, for indexicalslike the pronoun I in (15) and for tense with before in (16), the semantic context iscrucial to determine the truth value.

(15) I am the Queen of The Netherlands

(16) John did not finish his thesis before he went to the USA

If (15) is uttered by Beatrix, the sentence is true. Similarly, if John did not finish histhesis before September 2007 (i.e., the moment he went to the USA), (16) is true.Semantic context provides information about the speaker’s identity and speech time,without which the truth value of (16) nor the truth value of (15) can be determined.

Another kind of contextual information, Bach argues, is pragmatic in nature.Pragmatic context is the “mutually and readily accessible information that speak-ers can count on each other to count on in figuring out what they mean whenthey say what they say” (2000:272). Bach argues that context dependent domainrestriction operates at the pragmatic level of what is being communicated, not atthe syntactic/semantic level what is being said or interpreted.6

5As Neale (2000) points out, the label ‘incomplete’ is probably due to Sellars (1954:199), addressing“utterances . . . [that] are not complete and are only made complete by the context in which they areuttered” (cited in Neale, 2000:284).

6In fact, Bach argues that Stanley and Szabó’s claim that meaning is determined by context is too

5.3. Semantic holes, incomplete quantifier domains and pragmatic reasoning 75

For a quantified sentence like (17), this means that, at a pragmatic level, thedomain is restricted to the set of bottles that the speaker, for example, just bought.Bach represents the proposition that is expressed and interpreted in (17) as in (17-a).However, the proposition that is communicated is the one expressed in (17-b) (italicsmarks it as the proposition communicated). Moreover, Bach argues that sentences(17) and (18) involve distinct propositions. What the speakers are communicating,however, is the same.

(17) Every bottle is emptya. [∀x: bottle x] (x is empty)b. Every bottle I just bought is empty

(18) Every bottle I just bought is empty

Bach calls (17) a case of a conversational implic-i-ture (as opposed to Grice’sconversational implic-a-ture) (see Bach, 1994, but also Bach, 1994, 2000, 2001, 2005).In the case of a conversational implic-a-ture, the speaker means something differentthan he actually says (i.e. in everyday speech, (19) is understood to mean (19-b)), butin the case of an implic-i-ture, Bach argues “one says something but does not meanthat; rather, what one means includes an implicit qualification on what one says,something that one could have made explicit but didn’t.” (Bach, 2001:257).7

(19) a. If it rains, a linguist goes for a beerb. ‘Only if it rains, a linguist goes for a beer (if it does not rain, he is at

work)’

The controversy about the role of context in determining a quantifier’s domainthus boils down to the question whether the matter concerns a semantic or a prag-matic problem. Westerståhl (and Von Fintel, Stanley and Stanley and Szabo) arguesthat it is a matter of, using Bach’s (2000) terms, semantic context and solves theproblem by adding a context variable to the semantic representation of a quantifiedsentence. Bach on the other hand argues that pragmatic context is involved and,making a distinction between the proposition expressed and the proposition com-municated, claims that the pragmatic context is only related to the latter kind ofproposition. Put differently, the question how to represent the role of context fordetermining the domain of a quantifier boils down to the question whether filling inan incomplete quantifier domain concerns the proposition being expressed as in thesemantic approach with a context variabele or the proposition being communicatedas in Bach’s pragmatic approach. How can we test these opposite claims?

Bach relies on Grice’s (1975) cancellability test to check whether something ispart of the proposition being expressed or communicated. When a speakers utters a

strong and that there is not such a thing as contextually determined quantifier domains (since it happensat a pragmatic level.)

7This is reminiscent, as Bach (2006) points out, of what in Relevance Theory (Noveck and Sperber,2004) is called an explicature. See Bach (2006) for minor differences between the two notions.


sentence S and the hearer concludes that the speaker implied P, the cancellabilitytest checks whether the hearer’s conclusion P can be explicitly ‘cancelled’ by addingbut not P to the uttered sentence S. If this results in a contradiction, P is partof the proposition expressed; if this does not result in a contradiction, P is onlyimplicated and therefore part of the proposition communicated. Consider (19-a)again. Strictly speaking, the speaker did not say that only if it rains, a linguist goesfor a beer. However, a hearer infers that the speaker means (19-a); had the speakernot meant (19-a), she should/could have been more explicit. Applying Grice’s (1975)cancellability test, explicitly negating the hearer’s conclusion that a linguist goesfor a beer only if it rains does not result in a contradiction and shows that theimplicature that a linguist only goes for a beer if it rains is part of the propositioncommunicated and not part of the proposition expressed.

(20) If it rains a linguist goes for a beer, but not only if it rains, a linguist goesfor a beer

Contrast this to the cases that Bach takes to illustrate the effect of semantic contexton interpretation, like (21-a): if uttered by Beatrix, adding but Beatrix does not resultsin a contradiction. This shows that the reference of I is part of the propositionexpressed.

(21) a. Beatrix: I like huntingb. Beatrix: I like hunting but Beatrix does not

At this point, the question arises when exactly pragmatic context comes into play.Bach claims that sentences for which the quantifier domain needs to be determinedby the context involve a non-literal sense, and it is crucially the hearer who needs tospot these implicit quantifier domains. Consider the following lengthy quote fromBach (2001) (italics added):

“As with any nonliteral utterance, with sentence nonliterality the audi-ence is to recognize that the speaker couldn’t plausibly be taken to meanexactly what he said. Assuming that the speaker is trying to communi-cate something and is therefore trying to make what he means evident,the audience has to find some salient connection between what is saidand what is meant. Generally speaking, that involves finding some wayof taking the utterance that is pertinent to the current purposes of theconversation . . . Of course, this is not to say precisely how, in any givencase, the hearer figures out just what that is. That is a difficult andunanswered question for the psychology of communication.” (Bach,2001:256)

Bach thus redirects the question as to when context affects the domain of quantifica-tion to the field of, what he calls, “psychology of communication”. I will now takeup this question in order to model the implicit domain restriction of many. Are the

5.4. Accounting for the many meanings of many 77

different readings of many discussed in section 5.2 all illustrations of Bach’s notionsof implic-i-ture? In the next section, I analyze the role of context on the domainrestriction of many: does it involve semantic or pragmatic context? I will then arguethat the framework of bidirectional Optimality Theory Semantics provides a way todefine the interplay between syntax, semantics and pragmatics in the case of implicitquantifier domains.

5.4 Accounting for the many meanings of many

5.4.1 Semantic or pragmatic context?

When exactly does contextual information play a role in determining the domain ofmany? Or rather, what kind of contextual information plays a role in setting thetruth value of a sentence containing the quantifier many? Following Bach, I will useGrice’s cancellabily test to answer this question. Consider the different readings ofmany discussed in section 5.2 again, respectively illustrating the proportional andcardinal reading of many, in the (c) sentences now conjoined with a clause in whicha (potentially) implied domain of many (cf. the (b) sentences) is canceled:

(22) a. Many students passed the examb. Many students that attended my class passed the examc. Many students passed the exam but many students who attended my

class did not pass the exam

(23) a. I saw many women in traditional costumes in Groningen last weekb. I saw many of the women that you normally see in traditional costumes in

Groningen last weekc. Last week, I saw many women in traditional costumes in Gronin-

gen but I did not see many of the women that you normally see intraditional costumes in Groningen

Adding the extra clause to (22-a) and (23-a) does not result in a contradiction (cf.(22-c) and (23-c)). This shows that the implicit domain of many for a proportionaland a cardinal reading is part of the proposition communicated rather than the oneexpressed. So pragmatic context rules in these cases. Does this also holds for theWesterståhl reading of many?

The intended domain of many Scandinavians in (24) (i.e. the Scandinaviansthat are relevant to the Nobel price in literature as compared to the number ofpeople per country that have won the price in the past years) is negated in theconjoined sentence (to make things clear, Scandinavians is replaced with inhabitantsof Scandinavia). Similarly as in (22-c) and (23-c), this does not result in a contradic-tion (however, the sentence does turn out to be obviously false). Again, Grice’scancellability test is passed. This shows that the implicit domain of many in (24) (i.e.


the set of winners of the Nobel prize in literature) is part of the proposition beingcommunicated.

(24) a. Many Scandinavians have won the Nobel price in literatureb. Many Nobel price winners are Scandinaviansc. Many inhabitants of Scandinavia have won the Nobel price in literature

but not many Scandinavians that are relevant to the Nobel price inliterature compared to the number of people per country that havewon the price in the past years, have won the Nobel price in literature

All sentences with many pass Grice’s cancellability test; the context-dependentdomain of many is clearly restricted by means of the pragmatics, instead of on thebasis of the semantics alone (as would be the case if the sentences would not passthe cancellability test). The implicit domain of many is thus not determined at asemantic level but rather by the speaker at a pragmatic level. Taking such a pragmaticapproach to the many meanings of many, there is no need to postulate the existenceof a covert context-variable which is then filled with contextual information.

In sum, and answering the question I started this section with, many allowsseveral context dependent readings when there is a mutual understanding betweenspeaker and hearer that the hearer has to fill in the domain of the quantifier onthe basis of the shared knowledge between them. Or, to put it in terms of a bi-directional view on language (Blutner, 2000), the speaker’s optimal expression ofa meaning depends on the hearer’s optimal interpretation (and vice versa) in aparticular context. Taking such an optimization view on interpretation, I will arguein the next section, is the key to account for the role pragmatics plays in the case ofquantified expressions.

5.4.2 Many in bi-directional Optimality Theory

De Hoop, Hendriks, and Blutner (2007) present an optimization approach tolanguage in order to deal with the competition between a syntactically optimalinterpretation and a pragmatically optimal interpretation as in (26).

(25) Most people sleep at night

(26) Most people drink at night

The interpretation of (25) is that most of the people in the world indeed sleep atnight (and not during the day); most relates two sets to each other and, in this case, ifthe set of people that sleep at night is bigger than the set of people that do somethingdifferent than sleeping at night, this sentence is indeed true. However, for (26),world knowledge c.q. context comes into play and, Blutner et al. argue, outrankslexical meaning. Since it is implausible that most of the people in the world drinkat night (and not during the day), a different interpretation comes into play and atnight in (26) is generally understood as modifying the A set of the quantifier (most


people). This results in the reading of (26) that most of the people at night drink(alcohol).8 For this interpretation, (26) is true if most of the people who drinkalcohol, drink at night; the interpretation is such that the set of people intersectswith the generalized union over the set of alternatives for the set of drinkers atnight (De Hoop and Solà, 1995).9 World knowledge outranks the lexical meaning ofthe sentence. This ‘suboptimal’ interpretation (suboptimal if syntax prescribes theoptimal interpretation) provides the solution for the conflict that arises between theinformation provided by the syntactic structure and the information provided byour world knowledge. This explains why (25) and (26) get a different interpretationdespite of their parallel syntactic structure.

In the bi-directional OT framework of De Hoop et al. (2007), it is assumedthat the context of the hearer is the same as the context of speaker: “If a formis associated with a certain interpretation within a certain context by a hearer,then with that same context, the same meaning would have been expressed by thesame form if the hearer would have been the speaker” (2007) Moreover, a leadingprinciple for the speaker to state his message is the principle of recoverability; thespeaker is only allowed to leave those elements unpronounced that are recoverablefrom the local context. In the case of example (26) and its pragmatically optimalinterpretation that most people who drink alcohol, drink at night, this means thatthe domain of most people is tacitly assumed by the speaker to be recoverable fromthe context (world-knowledge) to people who drink. This allows the speaker to leavethe domain of the quantifier implicit, despite of the fact that the hearer cannotderive the meaning intended by the speaker by just combining the constituentsas the syntax prescribes (see also Blutner, De Hoop, and Hendriks (2006) and thediscussion of (26) in chapter 3 and Geurts’ (2003) examples (53) and (54) in section5.5).

The view on interpretation of De Hoop et al. (2007) is the starting point foraccounting for the many meanings of many. As discussed in section 5.4, the contextdependence of many is a pragmatic matter and crucially involves the assumptionsof the hearer the speaker is talking about on the one hand and on the other handthe assumptions of the speaker as to what he takes to be shared knowledge (e.g. thecontext) between him and the speaker. In addition to this, Blutner (2000) argues that

8Bach (2000), not working within a OT framework, claims that it is not the implausibility of theliteral meaning, but rather the lack of relevant specificity, that causes the hearer to take a pragmaticallypreferable interpretation. However, for current purposes, what gives rise to a pragmatic interpretation, isirrelevant.

9Note that this reading gets even more plausible if the NP is focused, as Blutner et al. point out, “ifintonational information is available, then the constituent that gives rise to this set of alternatives is thesyntactic argument containing the focus (where focus is marked by sentential accent)”. De Hoop andSolà (1995) argue that this relevant set of alternatives, called the C-set in Rooth’s alternative semantics, isthe generalized union over the set of alternatives of a focused constituent. It is this generalized unionthen that can be used to determine the context variable which is always associated to the quantifier’s firstargument set (cf. Westerståhl’s (1985) notion of restriction). I will address the mechanism how to restrictan implicit quantifier domain later in this section, but the effect of focus, however, falls outside the topicof this chapter.


speaker’s and hearer’s optimizations are computed simultaneously. This means thatinterpretation and production both involve mapping form to meaning and mappingmeaning to form. Using language to convey a message does not only mean that youutter a sentence in a way you think is the correct way of stating your message, butcrucially also that you consider the possible ways the hearer can understand yourmessage (and vice versa). This mechanism, I will show in this section, enables meto account for the many meanings of many; the different interpretations of manyare the result of different assumptions the speaker makes about the recoverableinformation from the context and the possible ways the hearer can interpret this.Now, how does this all work?

If a form is associated with a certain interpretation within a certain contextby a hearer, then within that same context, the hearer would have used the sameform to express that meaning if he/she were the speaker. Both meaning and formare subject to soft, i.e. violable constraints. In a bi-directional OT framework (incontrast to a uni-directional OT framework like the one presented in chapter 4,form-meaning pairs are evaluated against these constraints. Form-meaning pairsare ordered depending on whether there exists a more optimal (a so-called ‘super-optimal’) form-meaning pair (i.e. the form-meaning pair which violates the leastnumber of constraints). A form-meaning 〈f,m〉 is called super-optimal “if and onlyif there is no other super-optimal pair 〈f ′,m〉 such that 〈f ′,m〉 is more harmonicthan 〈f,m〉 and there is no other super-optimal pair 〈f,m′〉 such that 〈f,m′〉 ismore harmonic than 〈f,m〉” (Blutner, 2000).

Crucially, there can be more than one super-optimal pair. In (27), there are twosuper-optimal pairs; f2 is not an optimal form andm2 is not an optimal meaning and⟨f1,m1⟩ and

⟨f2,m2⟩ are the two super-optimal pairs. The arrows in (27) represent

how to determine these two form-meaning pairs;⟨f1,m1⟩ is more harmonic than⟨

f1,m2⟩ etcetera.

(27)

⟨f1,m1⟩ ←−−−− ⟨

f2,m1⟩x x⟨f1,m2⟩ ←−−−− ⟨

f2,m2⟩The two candidates

⟨f1,m2⟩ and

⟨f2,m1⟩ are not super-optimal, because they are

both blocked by the other super-optimal pair⟨f1,m1⟩. The pair

⟨f2,m2⟩ is also

super-optimal.Regarding the many meanings of many, I identified three possible meanings (the

cardinal reading, the proportional reading and the Westerståhl reading). This leadsto six possible form-meaning pairs. In order to determine the super-optimal pair(s),these six pairs then need to be considered against several constraints.

In chapter 3, I introduced the very general constraint Semantic Relation, repeatedbelow.


(28) Semantic relation:For weak quantifiers, use the discourse topic to select the set against thebackground of which the interpretation of the quantified expression needsto be determined.

Defining this constraint more precisely, Semantic Relation divides into two con-straints, *Intersective (29) and Context Dependence (30).

(29) *IntersectiveStrong quantifiers do not satisfy the intersective condition

(30) Context DependenceFor each quantified expression D(A,B) where |(A ∩B)| > c · |C|, C is thediscourse topic

I will now discuss these two constraints in more detail.Barwise and Cooper already concluded that only weak quantifiers satisfy the

intersective condition as defined in (31) (from Barwise and Cooper, 1981:189/190):

(31) INTERSECTIVE CONDITIOND satisfies the intersection condition if for all modelsM = 〈E, ‖ ‖〉 and all X,A ⊆ E,X ∈ ‖D‖ (A) iff X ∈ ‖D‖ (A ∩X)

Strong quantifiers violate this condition, Barwise and Cooper (1981) argue, butthe weak quantifiers many and few give rise to a difference in opinion between thetwo authors (the labels ‘weak’ and ‘strong’ are used here in the sense of Milsark(1979), see also chapter 2). Whereas Cooper takes many and few always to satisfythe intersection condition, Barwise takes them to violate the intersective conditiongiven their context dependent domains as discussed in section 5.2. Compare thefollowing examples.

(32) a. Few entities that love Mary are men that love Maryb. Few men love Mary

(33) a. All entities that love Mary are men that love Maryb. All men love Mary

Whereas (32-a) and (32-b) are logically equivalent (i.e. they express the same meaningand hence violate the intersective condition), (33-a) and (33-b) are not (i.e. theyexpress a different meaning). For (34-a) and (34-b) containing the quantifier many, itis not clear whether they are logically equivalent or not:

(34) a. Many entities that love Mary, are men that love Maryb. Many men love Mary


Barwise takes many therefore to violate the intersective condition. Here and in theremainder of this thesis, I will therefore only argue that strong quantifiers do notsatisfy the intersective condition. The case of many shows that weak quantifiers allowreadings that are both non-intersective (i.e. the proportional and the Westerståhlreading, cf. section 5.2) and intersective (i.e. the cardinal reading). Since strongquantifiers never allow an intersective interpretation, strong quantifiers clearly neversatisfy the intersective condition.

With respect to the second refinement of Semantic Relation, recall from section5.2 that strong quantifiers presuppose their first argument set to be established inthe discourse before uttering the quantified sentence, whereas weak quantifiers donot convey such a presupposition. Uttered out of the blue, (35) is odd and raises thequestion which students the speaker is talking about.

(35) All students passed the exam

Most of the time, it is this oddity that forces the hearer to recover a relevant set ofstudents the speaker is talking about from the local context and interpret studentsas e.g. students in class . . . . (36) however, uttered again out of the blue, is felicitousand does not presuppose a set of students to be mentioned earlier in the discourse.This shows that weak quantifiers do not presuppose their first argument set to be adiscourse familiar set in contrast to strong quantifiers (cf. Heim’s (1982) familiaritycondition).

(36) Many students attended my class

However, in section 5.2, I pointed out that weak quantifiers can get a propor-tional reading in which they do presuppose the existence of their first argument set.Consider also the use of the weak quantifier two in (37) (from Geurts, 2007:269):

(37) Fred owns three sheep. He had two sheep vaccinated in the spring.

In (37), the weak quantifier two is restricted to two of the three sheep Fred owns. In asimilar way, many in (38) is restricted to many of the one hundred sheep Fred owns.

(38) Fred owns one hundred sheep. He had many vaccinated in the spring.

This shows that weak quantifiers allow readings that do establish a discourse linkwith a discourse entity in the previous discourse (in this case, the set of sheep Fredowns). The constraint Context Dependence captures the observation that it does nothold that all weak quantifiers presuppose the existence of the first argument set bystating that only non-intersective quantifiers presuppose the existence of their firstargument set in the previous discourse.10

10Examples with so-called specific and non-specific readings of indefinites illustrate the existence ofsimilar interpretations of the same forms next to each other. Example (39) can either mean that Johntalked with a professor, unknown which one, or that he talked with a specific professor, e.g. Chomsky.


Two other constraints apply; on the one hand, there is the constraint SyntacticStructure (Hendriks and De Hoop, 2001) that makes sure that the N’ is chosenas the quantifier’s first argument and, on the other hand, there is the constraintForward Directionality (Hendriks and De Hoop, 2001).11 The constraint ForwardDirectionality (FD) takes directionality as a “topic structural property of discourse”(Hendriks and De Hoop, 2001:19) and makes sure that the quantifier domain isrestricted to the discourse topic.12

(39) Syntactic Structure:If there is an N’ that constitutes an NP together with a determiner, use thisN’ to restrict the domain of quantification of that determiner. (Hendriksand De Hoop, 2001:22)

(40) Forward Directionality:The topic range induced by the domain of quantification of a determiner(set A) is reduced to the topic range induced by the intersection of the twoargument sets of this determiner (A ∩ B). (Hendriks and De Hoop, 2001:19)

This results in the reading of (37) that Fred vaccinated three of the sheep he owns.Syntactic Structure is satisfied since sheep is the domain of the quantifier three for bothinterpretations and so the N’ is used to restrict the domain. Forward Directionalityis violated by the interpretation of three arbitrary sheep since the domain of manyis in this case not restricted to the intersection of the set of sheep in the world andthe set of sheep that Fred owns.

(i.) John talked with a professor.

I take these cases to illustrate the same role pragmatic is able to play as it is in the case of restricting thedomain of many. In a similar way as pointed out in the previous section that quantified sentences withmany pass Grice’s cancellability test, (38) does:

(ii.) a. John talked with a professorb. John talked with Chomskyc. John talked with a professor but be did not talk with Chomsky

The OT analysis of many can be easily translated to account for the specific and non-specific readings ofindefinites. This, however, lies outside the scope of this thesis

11The constraint Forward Directionality is part of the family of constraints labled DOAP (Don’tOverlook Anaphoric Possibilities). Whenever Forward Directioality is satisfied DOAP is satisfied. Ireturn to the other constraints of DOAP in chapter 6.

12In chapter 6 I return to the issue of topic setting in a discourse and define this by means of CenteringOptimality Theory (Beaver, 2004).


(41)Example (37) SY

NT

.ST

R.

FD

+ three of the sheep Fred ownsthree arbitrary sheep *!

We can now use these constraints to answer the question when each reading of manyoccurs (i.e. the cardinal reading, the proportional reading and the Westerståhl’sreading), taking as additional factors the strength and the context dependence of thequantifier, the syntactic structure and the topic of the discourse. Consider example(42).

(42) Many birds fly

This sentence can occur in a context in which either the quantifier’s first or secondargument set has already been mentioned (e.g. in a context about birds, or a contextabout flying entities). In the OT tableaus in (43)- (44), the set mentioned in thediscourse preceding the quantified statement is marked by underlining. In (42),two possible contexts in which to express Many(A,B) and the possible ways how tointerpret Many(A,B) (using the definitions of these meanings discussed in 5.3) leadto six possible form-meaning pairs. For each pair 〈f,m〉, the form comes beforeand the meaning after the semicolon. For each form, the type of the quantifiers isindicated (weak or strong, many is always weak given that it passes Milsark’s test, seechapter 2, and many of is strong) plus its two arguments and their syntactic status (N’or VP). The meaning following each form after the semicolon follows the definitionused in section 5.3 to characterize the cardinal, proportional or Westerståhl reading(i.e. a contextually determined value (c) considered against the universe (U) for thecardinal reading, the quantifier’s first argument set (A) for the proportional readingand the quantifier’s second argument set (B) for the Westerståhl reading).

I now discuss the role played by each of the constraints in (43) for each form-meaning pair and show how which pairs turn out to be the super-optimal ones.*Intersective is satisfied in all cases, since it states that only strong quantifiers vio-late the intersective condition. A weak quantifier like many is allowed to get anintersective reading (i.e. a cardinal reading) and a non-intersective reading (i.e. aproportional or Westerståhl reading). Context Dependence is violated by pairs 3 and5; the C set is not mentioned in the discourse preceding the quantified statement(i.e. the underlined noun, representing the set mentioned in the discourse precedingthe quantified statement, differs from the C set that needs to be taken into accountaccording to the interpretation in pair 3 and 5). Syntactic Structure is never violatedsince the N’ is always taken as the quantifier’s first argument set. Forward Direc-tionality is violated by pairs 4, 5 and 6 because the quantifier’s first argument set(birds) is not in accordance with the discourse topic of the set of flying entities (cf.


(43)

Man

y(A

,B)

*INTERSECTIVE

CONTEXTDEP.

SYNTACTICSTRUCTURE

FD

,1.〈[M

any] w

ea

k[birds]

n′fly

vp;|

(A∩B

)|>c·|U|〉

,2.〈[M

any] w

ea

k[birds]

n′fly

vp;|

(A∩B

)|>c·|A|〉

3.〈[M

any] w

ea

k[birds]

n′fly

vp;|

(A∩B

)|>c·|B|〉

*

4.⟨ [M

any] w

ea

k[birds]

n′fly

vp;|

(A∩B

)|>c·|U|⟩

*

5.⟨ [M

any] w

ea

k[birds]

n′fly

vp;|

(A∩B

)|>c·|A|⟩

**

,6.⟨ [M

any] w

ea

k[birds]

n′fly

vp;|

(A∩B

)|>c·|B|⟩

*


the underlining in the tableau).To determine the set of super-optimal interpretations, two rounds of optimiza-

tion take place. After the first round, it turns out that both the cardinal andproportional reading are super-optimal interpretations if the quantifier’s first argu-ment set is mentioned in the preceding discourse; both pairs violate no constraints.A second round then takes place in which the remaining possible candidates areevaluated. All form-meaning pairs that contain a form or a meaning that is alsopart of the super-optimal form-meaning pairs are blocked (i.e. pair 3, 4 and 5).The Westerståhl reading in a context in which the quantifier’s second argument setis mentioned (form-meaning pair six) then turns out to be another super-optimalpair.13

In sum, evaluating all form-meaning pairs against the four constraints resultsin three super-optimal pairs; a cardinal reading or a proportional reading if thediscourse contains the quantifier’s first argument set and a Westerståhl reading if thediscourse marks the quantifier’s second argument set as a discourse topic.

The ambiguity of many does not hold for strong quantifiers; strong quantifierscan only get a proportional reading. For a strong quantifier all or the partitive manyof, this indeed follows from the OT model when we apply the same constraints inthe same contexts as in tableau (43).

The only difference between the tableau in (43) and the tableau in (44) with thestrong quantifier many of is that pair 1 and 4 in this case violate *Intersective; sincethese form-meaning pairs both contain an intersective reading (i.e. cardinal reading)and *Intersective constraints the meaning of a strong quantifier like many of to anon-intersective reading, *Intersective is violated. Surprisingly, table (44) shows thatalso strong quantifiers are predicted to allow Westerståhl readings if the quantifier’ssecond argument set is already mentioned in the discourse. Herburger (1997, 2000)argues that strong quantifiers do not allow a Westerståhl reading. However, it israther her paraphrase of the Westerståhl reading in terms of switching around thequantifier’s arguments that leads her to this conclusion, than the sentence itself.

13Note that there are other restrictions on the different readings of many. Whereas in (i) the quantifiermany only allows both a cardinal interpretation and a proportional reading as respectively exemplifiedin (ia) and (ib.), (ii.) only allows a proportional reading (cf. (ii.a) and (ii.b); example originally due toDiesing, 1992).

(i.) Many firemen are availablea. “There are many firemen available”b. “Many of the firemen are available”

(ii.) Many firemen are altruistica. #“There are many firemen altruistic”b. “Many of the firemen are altruisitc”

The different possible interpretations of many, can be attributed to the different kind of predicates in(i.) and (ii.) (Milsark, 1979); whereas (i.) contains a stage being predicated over, (ii.) contains a propertybeing predicted over. These cases, however, are outside the scope of this chapter.


(44)

Man

yof

(A,B

)

*INTERSECTIVE

CONTEXTDEP.

SYNTACTICSTRUCTURE

FD

1.〈[M

anyof

the]

str

on

g[birds]

n′

[fly

] vp

;|(A∩B

)|>c·|U|〉

*

,2.〈[M

anyof

the]

str

on

g[birds]

n′ [fly

] vp

;|(A∩B

)|>c·|A|〉

3.〈[M

anyof

the]

str

on

g[birds]

n′

[fly

] vp

;|(A∩B

)|>c·|B|〉

*

4.⟨ [M

anyof

the]

str

on

g[birds]

n′

[fly

] vp

;|(A∩B

)|>c·|U|⟩

**

5.⟨ [M

anyof

the]

str

on

g[birds]

n′

[fly

] vp

;|(A∩B

)|>c·|A|⟩

**

,6.⟨ [M

anyof

the]

str

on

g[birds]

n′

[fly

] vp

;|(A∩B

)|>c·|B|⟩

*


At first sight, Herburger’s paraphrase of the Westerståhl reading in (45-b) seemssimilar to the alternative, more precise paraphrase of the reading in (45-c).

(45) a. Many Scandinavians have won the Nobel price in literatureb. “Many winners of the Nobel price in literature are Scandinavians”c. “Many of the Scandinavians that are relevant to winning a Nobel price

in literature, have won a Nobel price in literature”

However, whereas (46-a) rules out the reading in (46-b), it does not rule out (46-c).In a similar way, (47-a) rules out reading (47-b) but it allows reading (47-c).

(46) a. All Scandinavians have won the Nobel price in literatureb. *“All winners of the Nobel price in literature are Scandinavians”c. “All Scandinavians that are relevant to winning a Nobel price in litera-

ture, have won a Nobel price in literature”(47) a. Many of the Scandinavians have won the Nobel price in literature

b. *“Many of the winners of the Nobel price in literature are Scandina-vians”

c. “Many of the Scandinavians that are relevant to winning a Nobel pricein literature, have won a Nobel price in literature”

This shows that Westerståhl readings also exist for strong quantifiers like all andmany of. Herburger’s observation that sentences containing all and many of do notallow their arguments being ‘switched’, does not prove that these sentences does notallow a Westerståhl reading, but rather that a description of this reading in terms ofswitching around the arguments does not cover its meaning. My account of manyin OT as discussed above shows that one does not have to assume that argumentsare syntactically ‘switched’ or even that the Westerståhl reading violates syntacticprinciples. The more refined properties of the discourse rather allow such a readingto arise or not.

In sum, the framework of (bi-directional) OT accounts for two observations.One, in the case of implicit quantifier domains, syntax, semantics and pragmaticscompete for the quantifier’s final meaning. Two, it incorporates the idea thatshared knowledge between speaker and hearer is the basis for selecting the rightinterpretations. Bi-directional OT thus allows us to account for the many readingsof many. In addition, by taking an optimization approach to interpretation, it isnot necessary anymore to posit the existence of any kind of covert domain variablesor syntactic anomalies.

5.5 The relevance of many from an acquisition viewpoint

Recently various authors have argued that the weak quantifier many and the rolepragmatics c.q. context plays in determining its domain provides the key for under-standing children’s non-adult like interpretation of sentences containing a universal

5.5. The relevance of many from an acquisition viewpoint 89

(strong) quantifier. I discuss two such approaches; Drozd and Van Loosbroek (1999)and Geurts (2003). Neither paper however presents experimental evidence as towhat kind of pragmatic information children exactly use to constrain meaning. Iwill argue for an account that can explain why the interplay between syntactic,semantic and pragmatic constraints in child language differs from the interactionbetween these constraints in the target language.

5.5.1 Children’s understanding of weak versus strong quantifiers

As discussed above, for adults, expectations c.q. world knowledge determine thedomain of weak quantifiers, in particular for the quantifier many. Drozd andVan Loosbroek (1999) argue that, in a similar way as adults allow contextual ex-pectations to restrict the domain of many, children let their expectations (aboutthe quantifier’s first argument set) take precedence over the syntactic structure todetermine the meaning of strong quantifiers. In the next sections, I will discussthe account in which this peculiar interpretation (and the characteristics of weakquantifiers more generally) plays an important role for accounting for children’snon-target-like interpretation of universally quantified sentences (see chapter 2 foran introduction to this subject).

5.5.1.1 Drozd and Van Loosbroek (1999) and Drozd (2001)

Drozd and Van Loosbroek (1999) and Drozd (2001) argue that children also allow aWesterståhl reading for sentences with a universal quantifier and propose the WeakQuantification Hypothesis (WQH). This hypothesis states that children allow contextto determine the domain of the quantifier. This, they argue, will especially be thecase if the quantifier’s first argument set is not discourse active or salient enough:

“According to the WQH, children interpret universal quantifiers asweak cardinal quantifiers . . . because they find it difficult to distinguishthe two sets they need to represent in order to proceed with a presuppo-sitional interpretation of the universal quantifier. Children faced withsuch contexts will analyze the quantifier as a weak cardinal quantifier,whose interpretation is both supported by such contexts and requiresno presuppositional commitments” Drozd (2001:367)

Their experimental results show that children are indeed sensitive to the salienceof the first argument set.14 Drozd and Van Loosbroek (1999) and Drozd (2001)conclude that the difference between universal and existential quantifiers plays a cen-tral role in acquiring quantification. Universal quantifiers, in contrast to existentialquantifiers (‘strong’ and ‘weak’ in Milsark’s (1979) terminology), presuppose the

14See also chapter 6 and the results of Drozd and Van Loosbroek (2006) that children’s interpretationof quantified sentences improves when the quantifier domain is introduced previously in the discourse.


existence of the NP they are quantifying over. For example, (48) implies that thespeaker assumes that there exist certain men in the universe of interpretation. Inorder to inerpret the sentence, one needs to check whether there is no man that isnot carrying a donkey. Conversely, for (49), with the weak quantifier some whichdoes not presuppose the existence of one or more men, one rather has to checkwhether there are any men that are carrying donkeys (cf. Strawson, 1952).15

(48) Every men is carrying a donkey

(49) Some men are carrying a donkey

Whereas a sentence with a weak quantifier is felicitous if the speaker and hearer donot share the assumption that the quantifier first argument set exists, a sentence witha strong quantifier is only felicitous if the existence of the quantifier’s first argumentset is background information, i.e. part of the information shared by the speakerand the hearer.16

In sum, Drozd and van Loosbroek argue that children accept an interpretationfor strong quantifiers similar to what adults accept for (6), repeated below as (50)(i.e. reading (50-a)). Children differ from adults in that they allow their expectationsor ratios of the quantifier’s first argument set to overrule the syntactic structure ofthe sentence in cases in which adults do not allow this.

(50) Many Scandinavians have won the Nobel prize in literaturea. ‘Many winners of the Nobel prize in literature are Scandinavians’

5.5.1.2 Krämer (2000;2005a,b)

Krämer (2005a,b) presents data on children’s understanding of veel, ‘many’ inDutch. Krämer shows that children between four and eight years of age mainly havecardinal interpretations of “many” followed by an noun phrase, regardless of thesyntactic structure (existential sentence or canonical sentence). Compare (51) and(52) (examples from Krämer, 2005b:355)

15Hence, Drozd and Van Loosbroek (2006) relabel the WQH and call it the ‘PresuppositionalAccount’.

16This is confirmed by using classic tests (Strawson, 1952) for presuppositions which show thatsentences with strong quantifiers keep their presupposition in different contexts and, hence, show thatthe presupposition arises due to the type of the quantifier and not due some special meaning expressed inthe sentence. For example, (i.) keeps its presupposition of existence of the set of men in a yes-no questionor when embedded in a clause with a verb like wonder. In (ii.) however, no presupposition shows up, nomatter what kind of context the sentence is embedded in, because it may be that the are no such men.

i. a. Is every men carrying a donkey?b. I wonder whether every men is carrying a donkey?

ii. a. Are some men carrying a donkey?b. I wonder whether some men are carrying a donkey?


(51) Veelmany

eiereneggs

zittensit

inin

dethe

mandbasket

‘A lof of eggs are in the basket’

(52) Erthere

zittensit

veelmany

eiereneggs

inin

dethe

mandbasket

‘There are a lot of eggs in the basket’

Children do not make a difference between (51) and (52) as adults do (i.e. a propor-tional reading for (51) and a cardinal reading for (52)) and allow a cardinal reading inboth cases

Krämer explains her findings by arguing that children do not aim for a mutualunderstanding of the conveyed information between speaker and hearer. Krämer(2005b), following Clark and Marshall (1981), takes as a null-hypothesis that, inorder to interpret a sentence with many, a standard of comparison must be derivedfrom information that is available for both the speaker and the hearer (i.e. the hearerwill make an effort to retrieve the speaker’s Standard of Comparison and the speakerwill provide the hearer with sufficent information in this respect, cf. Clark andHaviland (1977)’s speaker-hearer contract, cited in Krämer, 2005b). Adults, Krämerargues, put different weight to the different kinds of information that indicate whatcounts as many. This can be e.g. visual information (cf. in this respect also the workof Newstead and Coventry (2000) who show that the size of a container effectsthe interpretation of many), encyclopedic knowledge or syntactic information.Crucially, the syntactic information does not ‘force an interpretation’, but ratheris one of the hints to the Standard of Comparison. Children, according to Krämer(2005), only employ a context-independent Standard of Comparison, circumventingto take the speaker’s perspective into account. This would explain why childrendo not pay attention to syntactic clues to determine the different interpretations ofmany and allow a cardinal reading of many in both a canonical and an existentialsentence; for a proportional reading, there needs to be a mutual understandingbetween speaker and hearer which set the speaker is talking about. And it is exactlythis mutual understanding, Krämer argues, that children do not aim for.

From this perspective, children’s interpretations of many are in line with theargument put forward in Krämer (2000) that children’s non-target-like interpretationof universally quantified sentences, does not illustrate syntactic or semantic devel-opment but rather pragmatic development. It is children’s difficulty in handlingshared knowledge between the speaker and the hearer that is causing their non-adultlike behavior.

5.5.1.3 Geurts (2003)

Geurts (2003) also points at the difference between universal and existential quanti-fiers and the role of context c.q. pragmatics. He explains children’s interpretationof quantified sentences as a mapping problem between syntax and semantics and


introduces the Weak Processing Account (WPA). Due to a “malfunctioning mappingfrom syntactic structure to semantic representation” (2003:203), the domain ofquantification remains undetermined. This allows more room for pragmatics todetermine the domain of quantification. Geurts argues that there is no incompletesyntactic, semantic or pragmatic system in child language. The only differencebetween adults and children is a different mapping from syntax to semantics.

Discussing the pragmatic constraints that play a role in the target language torestrict a quantifier domain, Geurts singles out two that he argues to play a rolein children’s interpretations of universal quantifiers. Geurts treats the presupposi-tionality of strong versus weak quantifiers in a similar way as anaphoric pronouns.Just like one needs to retrieve the identity of a pronoun in the preceding context,one must retrieve in the context preceding a universally quantified sentence “acontextually salient collection of Xs, which are to serve as Q’s domain. Or, to put itthe other way, the context constrains the domain of the quantifier by making salientthis or that set of individuals” (2003:205).

A second constraint on quantifier domains is focus (cf. Hendriks and De Hoop,2001). Consider the following set of examples (based on Geurts, 2003:205):

(53) Most people visit Berlin [in the spring]Fa. Most people who visit Berlin (at some point in time), do so in the

spring

(54) Most people visit Berlin in the springa. Most of the people visit Berlin in the spring

In (53), part of the VP is focused (i.e. in the spring) and, as a result, the remainder ofthe VP visit Berlin is backgrounded. Only the backgrounded material enters in thequantifier’s first argument set (as illustrated in (53-a)). In the default case in (54), inwhich focus does not play a role at all and the quantifier’s first argument set is the setof people and the quantifier’s second argument set the people that visit Berlin in thespring, the entire VP set is the quantifier’s second argument set. Accordingly, (54)gets interpretation (54-a) which says that most of the (contextually relevant) peoplevisit Berlin in the spring (and not that most of the contextually relevant people thatvisit Berlin, do so in the spring).

Geurts claims that children use these two pragmatic constraints to restrict aquantifier domain for strong quantifiers instead of restricting it by means of syntacticand semantic constraints. As for why children should resort to these pragmaticconstraints to determine the quantifier domain, Geurts claims that children preferto process quantified statements as easily as possible and, therefore, interpret allquantifiers as if they were weak; weak quantifiers pose a symmetrical, intersectiverelation between their arguments and are therefore easier to process (see chapter2).17

17Geurts points out that this is supported by processing research by Just (1974) and Meyer (1970).


Geurts’ ‘Weak Processing Account’ (WPA) states that children interpret quanti-fied sentences in a two-step fashion; first, the child analyzes a quantified sentence as ifit contained a weak, existential quantifier since these quantifiers are easier to process.This leaves the domain of the quantifier undetermined. Second, because childrenhave adult knowledge of the meaning of universal quantifiers and make a distinctionbetween the first and second argument set, they use pragmatic constraints like focus-background and contextual saliency to restrict the quantifier domain. This wouldexplain why a child answers ‘no, not that one’ when asked Is every cowboy riding ahorse in an extra object situation. The child represents the sentence as saying thatthere are cowboys riding a horse and then continues by restricting the quantifier’sfirst argument set by means of the salience of the horses in the picture (due to thefact that one horse is not being ridden). As a result, for the child, the quantifierdomain consists of the set of horses and the set of cowboys instead of only the set ofcowboys as in the target language. For a child, the sentence Every cowboy is riding ahorse is only true if there is no cowboy that is not riding a horse and there are nohorses that are not being ridden by a cowboy. The pragmatic constraints the childuses (i.e. the ones discussed above) are universal and play a role in both the childand the target language. As Geurts puts it:

“Pragmatic reasoning can play a larger role in children than in adultswhenever an incorrect mapping from surface form to semantic repre-sentation leaves the quantifier’s domain undetermined, but the prag-matic mechanisms that take over at this point are the same for all ages”(2003:208/9)

5.5.2 Pragmatic constraints

Crain, Thornton, Boster, Conway, Lillo-Martin, and Woodams (1996) also pointout that children allow pragmatics to play a role in determining a quantifier domainin situations in which adults do not. Crain et al. do not take this strategy to be alinguistic one but rather to result from the setup of the experiments used to testchildren’s understanding of quantified sentences. They take the explanation of chil-dren’s non-adult like understanding of quantified sentences to lie outside linguistics(see also chapter 2). They differ from Geurts and Drozd and Van Loosbroek in notrelating children’s difficulties with quantified sentences to a difference between weakand strong quantifiers.

In more recent papers, Crain and colleagues argue why the weak-strong distinc-tion is not at issue. First, Meroni, Gualmini, and Crain (2006) claim that Drozd andVan Loosbroek’s WQH poses a learnability problem (and see Meroni et al. (2006)for similar arguments against Geurts (2003)). According to Meroni et al., Drozd’sand Van Loosbroek’s accounts presupposes that the child, at a certain moment inher language development, has to accept the target-like interpretation and disregardthe non-target-like interpretation. Becoming an adult means that a child disregardsone interpretation and only allows the target one to be the correct interpretation of


a quantified sentence. Meroni et al. doubt whether the child is ever able to do so,given the input the child receives.

Second, Meroni et al. take the WQH to imply that children assign a meaningto the VP set that the syntax does not allow. They take the WQH to imply thatthe quantifier’s first argument set is reversed with the quantifier’s second argumentset. This implies according to Meroni et al. that the child restructures the VPis riding a horse as e.g. is being ridden by a cowboy. Only then can the child’sanswer “no, not that one” be explained in the case of Is every cowboy riding a horseand the extra-object situation. This would also raise a learnability issue; how willthe child unlearn this option given that, as Meroni and colleagues take to be thenull-hypothesis, an adult does not add material to the VP set to restrict a quantifierdomain or uses other than syntactic information to determine the quantifier’s firstor second argument?18

Third, Meroni et al. take the WQH to predict that extra agents pose a problemfor children; adding an extra cowboy instead of an extra horse, the WQH alsopredicts non-adult-like behavior. Meroni et al. present experimental data that thisprediction is, however, not born out. Children give adult-like answers when theyare asked whether (55) is true in a situation in which there are three balloons andfour tigers and only three tigers are holding a balloon (in 90% of the cases, theycorrectly answer“no” to (55)). Given Meroni et al.’s interpretation of the WQH,this situation is however predicted to give rise to a yes-answer, according to theanalysis that (55) gets a similar interpretation as (54), cf. (55-a).19

18Note however that this is not the case in adult language at all; focus and background and contextcan affect the quantifier domain (cf. the examples from Geurts discussed above, and among many otherHendriks and De Hoop, 2001).

19In addition, Meroni, Gualmini, and Crain (2007) present evidence against the prediction of both theWQH and the WPA that children treat universal quantifiers as existential ones by looking at children’sunderstanding of have. Have is ambiguous between a possession reading and a custodial reading only if itis not followed by a universally quantified sentence as exemplified in respectively (55) and (56). Theyset up an experiment in which children were to judge similar sentences as (54). The reasoning behindthis experiment is that, if a child knows that every is a strong quantifier, the child should only assign acustodial interpretation to the verb have. Their experimental results show that this is indeed the case;children only assign a possession reading to the verb to have in 12% of the cases when both of the readingsare made equally plausible in a discourse preceding the test item.

(i.) Tiger has some roosters that the farmer feda. Tiger owns the roosters that were fed by the farmerb. Tiger has custody of the roosters that were fed by the farmer

(ii.) Tiger has every rooster that the farmer feda. Tiger owns the roosters that were fed by the farmerb. *Tiger has custody of the roosters that were fed by the farmer

Despite these experimental results against any account that argues that the difference between weakand strong quantifiers is the key to children’s understanding of quantifiers, note that this experimentonly presents indirect evidence against such an hypothesis. For example, if children are able to access acustodial reading of to have solely on the basis of the (experimental) context, bypassing the information


(55) Every tiger is holding a balloona. (balloon ∩ λx [x is held by a tiger]) ∈ EVERY(balloon)

5.5.3 Intermediate conclusions

Summing up, in the literature on the acquisition of quantification, the differencebetween weak and strong quantifiers and the pragmatic factors that constrain quan-tifier domains have played a central role. In the adult language, many and most allowpragmatics (discourse context) to constrain their meaning and, as such, illustrate thekind of pragmatic constraints that are argued to be used by children above syntacticand semantic constraints to constrain meaning (Drozd and Van Loosbroek, 1999;Geurts, 2003). Crain et al. (1996) and Meroni et al. (2006, 2007) come to a related,yet different conclusion about the role children allow pragmatics to play. Theycrucially maintain the view that children resort to a non-adult-like interpretationbecause the experimental setup forces them to. This differs from Drozd and VanLoosbroek and Geurts who argue that children restrict a quantifier domain bymeans of the pragmatics in the first place. Crain et al. argue that this cannot be rightsince it raises a learnability issue: both Drozd and Van Loosbroek’s WQA accountand Geurt’s WPA presuppose that children have to unlearn their interpretation of aquantified sentence, and crucially have to learn to restrict a quantifier domain solelyon the basis of the syntactic structure of the sentence. According to Crain et al. andMeroni et al., this is impossible given the input the child receives.20

However, the null-hypothesis of Crain and colleagues that quantifiers typicallyrestrict their domain in the target language on the basis of their syntactic structureis unsubstantiated. As a result, their learnability argument against both Drozdand Van Loosbroek (1999) and Geurts (2003) turns out be irrelevant. Rather, thequestion needs to be answered how children use pragmatic reasoning to restrict aquantifier domain. The work of Brooks and Braine (1996) points into the samedirection. Presenting an experiment on children’s ability to restrict all to the subjectnoun phrase (e.g., All of the men are carrying a box) or the object noun phrase(e.g., There is a man carrying all of the boxes), Brooks and Braine argue that childrenhave no difficulty with restricting the domain of all. Note however that the testsentences contain the overt partitive all of the. This construction is known forthe presupposition of existence the noun phrase it modifies conveys. For example,All of the men are carrying a box presupposes that there exists a set of men. Thepresupposition might provide an additional clue to the child how to restrict a

the strength of the quantifier provides about this matter does not result in any different readings thanthe experimental results show. To put it differently, experimental data is needed about children’sunderstanding of the different constraints that play a role in quantifier domain restriction before we canjump to any conclusions about how they use these constraints to solve other ambiguity issues as with theverb have. See Partee (1999) for the different readings of have.

20Moreover, as Jack Hoeksema (p.c.) pointed out to me, note that the WQH implies that the lexicalsemantics of determiners changes in the course of acquisition, not just the role of pragmatics. This raisesanother learnability question: what can trigger this lexical shift?


quantifier domain. If this is indeed the case, the results of Brooks and Braine with alldo not necessarily mean that children use the syntax to restrict a quantifier domain.Rather, it is possible that children apply a similar strategy as they found for each andignore the syntactic information available to them. It is the presuppositional natureof all of the that enables them to localize the target-like domain. In this respect, thework of Brooks and Braine (1996) underlines yet again that the question needs to beanswered which clues children use to restrict a quantifier domain.

The quantifier many provides a tool to address this question in detail (cf. Drozdand Van Loosbroek (1999) who already pointed at many). In order to use thisquantifier to examine children’s usage of the discourse context to restrict a quantifierdomain, its many meanings should first be taken into account. Before turning toan experiment addressing children’s understanding of many, and taking its manyreadings into account, I will distill an hypothesis on the basis of the accounts ofmany presented in this chapter and the findings reported in this section.

5.6 Hypothesis and predictions

Do children use the same principles to restrict a quantifier domain as adults? Insection 5.4, I showed that interpreting many crucially concerns taking into accountconstraints that appeal to the discourse context and the type of quantifier (weak orstrong). The possible readings of many were explained in terms of a bi-directionalOT framework, a framework that takes successful communication as a startingpoint and, moreover, allows to account for the different readings of many in variousdiscourse contexts.

De Hoop and Krämer (2005/2006) argue that children acquire the ability toreason bi-directionally relatively late; until the age of 6-7, children are unable to takeinto account the speaker’s alternatives to formulate his message. This hypothesishas been applied to children’s interpretation of pronouns, indefinite objects andimperfectives (cf. Hendriks and Spenader (2006) for pronouns, De Hoop andKrämer (2005/2006) for indefinites and Van Hout (2008) for imperfectives).

For a child, interpreting many would therefore not be a matter of consideringall the form-meaning pairs identified in the previous section, but simply of checkingwhich meaning is the optimal meaning for one particular form. The ultimate taskthe child is faced with, according to De Hoop and Krämer (2005/2006), is to learn toapply bi-directional reasoning and to recognize when each reading is allowed. Thismeans that a child is only predicted to check which of the first three form-meaningpairs violates the least number of constraints in the tableau in (43). As illustratedin the uni-directional tableau in (56), the child is predicted to randomly interpretmany as a cardinal or proportional quantifier if the set of birds is mentioned inthe discourse. Alternatively, the child is predicted to randomly interpret many as acardinal or a Westerståhl quantifier if the set of flying entities is mentioned in thedicourse (see the uni-directional tableau in (57)).

5.6. Hypothesis and predictions 97

(56)

Many(A,B) *IN

TER

SEC

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SYN

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ICST

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+ 〈Many [birds] fly; cardinal〉

+ 〈[Many [birds] fly; proportional〉

〈Many [birds] fly;Westerståhl〉 *

(57)

Many(A,B) *IN

TER

SEC

TIV

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SYN

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ICST

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+⟨[Many] [birds] fly; cardinal

⟩*⟨

[Many] [birds] fly; proportional⟩

* *

+⟨[Many] [birds] fly;Westerståhl

⟩*

Taking De Hoop and Krämer’s (2005/2006) viewpoint that children do notreason bi-directionally until the age of 6-7, children are thus predicted to randomlyaccept a cardinal or proportional reading for many. Both readings are the most-optimal readings for a discourse context containing the quantifier’s first argumentset as a discourse topic (given that these first two form-meaning pairs in the tableauviolate no constraints). I label this discourse context the ‘Discourse A context’. Ifthe discourse introduces the quantifier’s second argument set as discourse topic (the‘Discourse B context’), children are predicted to also interpret many as an ambiguousquantifier, but now between a cardinal and a Westerståhl reading.

In a similar way, children are predicted to assign a proportional reading to manyof in a Discourse A context (given that the first and third form-meaning pairs violateconstraints), and a Westerståhl reading to the Discourse B context (given that this


Discourse A context Discourse B contextmany cardinal/proportional cardinal/Westerståhlmany of proportional Westerståhl

Table 5.1: Children’s predicted interpretations for many and many of in a DiscourseA context and a Discourse B context

form-meaning pair only violates Forward Directionality which is ranked lower thanthe constraints form-meaning pair 4 and 5 violate). The predictions are summarizedin table 5.1.

Assuming that children are not yet able to reason bi-directionally between fourand six years of age, children are thus predicted to differ in their interpretation ofmany and many of in that they do not take many of to be ambiguous betweenvarious readings, whereas they do for many. Moreover, children are predicted todistinguish a Discourse A from a Discourse B context and to know how thesedifferent discourses affect the interpretations of many.

The Equilibrium Hypothesis identified in chapter 3 is the alternative hypothesis.According to the Equilibrium Hypothesis (which does not say anything about bi-directional reasoning), children have a non-target-like equilibrium between syntax,semantics and pragmatics. In this line of thinking, if the present experiment showsthat children use the discourse information to restrict a quantifier domain regardlessof the type of the quantifier (weak or strong), this shows that children use thediscourse and neglect to take the syntax into account (supporting the EquilibriumHypothesis and not the bi-directional hypothesis as formulated above21).

5.7 Experiment: the acquisition of many and many of

How do children interpret many in different discourse contexts and is this differentfrom adults? The present experiment uses a setup in which the discourse contextgives a clue which interpretation of many the speaker intended.

5.7.1 Method

5.7.1.1 Subjects

Twenty-eight children were tested. Seven children were excluded from furtheranalysis because they did not answer the control items correctly, suggesting that theydid not pay attention or did not understand the task. The remaining twenty-one

21As Petra Hendriks (p.c.) pointed out to me, this would not show that the Equilibrium Hypothesisis not compatible with a bidirectional OT account an sich, but only that the data does not supportthe hypothesis I formulated above. Moreover, Hendriks (2008) shows how an explanation of languageacquisition in terms of constraint reranking (cf. the Equilibrium Hypothesis) is comptabile with abi-directional OT explanation (cf. also Fikkert and De Hoop,2009).

5.7. Experiment: the acquisition of many and many of 99

children varied in age from 4;1 and 7;3 (mean age 5;10). All children were recruitedat preschools in the area of Amherst, Massachusetts (USA).

5.7.1.2 Materials

The pictures used in the experiment differed from the pictures used in other experi-ments on quantification. Next to the set of individuals denoted by the noun phraseand the verb phrase, an alternative set of the first argument set and an alternative setof the second argument set was depicted. These alternative sets were depicted to en-able the child to select a standard of comparison, either in terms of the denotation ofthe quantifier’s first or second argument set. For Many parrots are wearing hats, thismeant that, next to the set of parrots, also other animals (the alternative set of thequantifier’s first argument) were depicted and, next to the set of hat-wearing parrots,also other hat-wearers (the alternative set of the quantifier’s second argument set).The scenarios were used to test children’s comprehension of sentences containingthe different types of quantifiers: many (6 items) versus many of (6 items).

(58) Many/Many of the parrots are wearing hats

Figure 5.2: Many/Many of the parrots are wearing hats

As a control condition, children were asked to interpret sentences containing all withrespect to a picture like in figure 5.3 (6 items). The picture for the control conditioncontained alternative sets of hat-wearers (similar to the Extra Agent condition usedin classic tests on children’s understanding of quantifiers, see chapter 2).

In addition to the effect of Quantifier Type, the effect of Discourse Type wastested by varying the introduction to each picture. The description either introducedthe quantifier’s first or second second argument set (i.e. the discourse was eithera Discourse A context or a Discourse B context). Additionally, the experimenter


Figure 5.3: All parrots are wearing hats

pointed at the set of individuals denoted by the noun or verb phrase. This isrespectively illustrated in figure 5.4 and figure 5.5.22

Figure 5.4: Many/Many of the parrots are wearing hats in a Discourse A context

In a Discourse A context, adults are hypothesized to answer ‘no’. Both aproportional reading and a cardinal reading results in a ‘no’ answer; with a cardinal

22Gesture was used to achieve joint attention, cf. psychological work that shows that “pointinggestures circumscribe a referential domain by directing gaze to an approximate spatial region”; seeBangerter (2004:415) and references therein. Children by the age of four are known to understand themechanism of pointing to establish joint attention of speaker and hearer.

5.7. Experiment: the acquisition of many and many of 101

Figure 5.5: Many/Many of the parrots are wearing hats in a Discourse B context

reading five does not count as many23 and with a proportional reading, only five outof the total of twenty-five parrots are wearing hats does not count as many either.Conversely, in a Discourse B context, adults are hypothesized to answer ‘yes’ (dueto a Westerståhl reading). For figure 5.3 and the quantifier all, the experimenterpointed in a similar way at the quantifier’s first or second argument set. In bothcases, adults are hypothesized to answer ‘yes’.

Finally, two control items using many and two with all were tested. The controlitems were used in combination with a picture in which respectively only e.g. oneparrot was wearing a hat (triggering a ‘no’ answer for many and all) or e.g. fourparrots were all wearing a hat (triggering a ‘yes’ answer). The total number of itemswas 22.

5.7.1.3 Procedure

The children were tested using a Truth Value Judgment Task. Instead of introducinga blindfolded puppet to the child, the experimenter told the child the followingstory:

At the university, I built this computer and as you will see, there are a lotof pictures on it and it is also able to play sentences via those speakers!But the problem is, I don’t know whether I built this computer entirelythe right way. So, I need your help to check whether the computer hasbeen built the right way or the wrong way. Do you want to help me?OK, well, I show you the pictures I have on this computer and when I

23Of course, a cardinal reading might also lead to a ‘yes’ answer if an adult considers e.g. five parrotswearing a hat to be many given the fact that parrots normally do not wear a hat.


will show you a picture, you will also hear something. Now, if you justwant to tell me if this matches the picture or not. All right?

A laptop was used to present the pictures and two separate speakers were used toplay prerecorded test items. The experimenter said “Let’s hear what the computersays” and subsequently asked the child to press a button on the keyboard to playthe prerecorded test sentence. As illustrated in the introduction story above, thechild was instructed to check whether the pictures matched the sentences or not.This instruction was given to prevent children from answering in terms of world-knowledge (e.g. “parrots do not wear hats in the real world, so the picture is notright”). In addition to this question, I asked the child to explain her answer, bothfor ‘yes’ and ‘no’ answers.

5.7.1.4 Coding

The number of yes- and no-answers were scored. Moreover, the qualifications of theanswers revealed which interpretation participants assigned to the quantifier. Thechild’s answer was labeled a ‘proportional answer’ in a case like (59) about balloonsinstead of parrots:

(59) Child A (age: 5;8.15)Computer: Many girls are holding balloonsChild: No! Many girls are NOT holding balloons

In (59), the child refers to the first argument set (i.e. the set of girls) to explain heranswer. Moreover, the child points out that many girls are not holding balloons;she quantifies over the first argument set of the quantifier and checks whether thiscounts as many. She concludes that this is not the case; many girls are not holdingballoons (i.e. 20 girls) which is more than the girls that are holding balloons (i.e. 5girls).

The child’s answer was called a cardinal reading if the child explained her answerby referring to a certain number (e.g. more than one of the dogs have red tails) or asthe answer in (60):

(60) Child B. (age: 7;2.20)Computer: Many of the dogs have red tailsChild: YesExperimenter: That’s true? OK. Why is that?Child: Because there is more than one.

Example (61) illustrates a case of a Westerståhl reading of a child:

(61) Child C. (age: 6;4.23)Computer: All parrots have yellow wingsChild: No.

5.8. Discussion and conclusions 103

Experimenter: Why not?Child: That’s why: all of the characters have yellow wings

In (61), the child explains her answer in terms of the second argument set of thequantifier (all entities that have yellow wings). Put differently, the child quantifiesover the intersection of the set of characters with yellow wings and the set of parrotsand then checks whether there are no characters that have yellow wings outside thisintersection. However, this is not the case; the picture also contains other charactersthat have yellow wings (cf. the child’s description of the picture in the last line of(61). This ‘no’-answer was taken to reveal a Westerståhl reading.

Finally, children’s answer were labeled ‘other’ if it was unclear what the childmeant or could not explain her answer.

5.7.2 Results

For both many and many of, children gave more cardinal interpretations than propor-tional, Westerståhl and ‘other’ interpretations (t-tests with Bonferroni adjustmentof alpha divided by 4, for all comparisons p < 0.001); 41% (SD = 1.08) of all an-swers were cardinal intepretations, 35% were non-intersective readings (SD = 1.82)and Westerståhl readings 10% (SD = 1.16). 15% (SD = 2.40) of the answers wereirrelevant (‘other’). Each child gave all four readings (per child, no preferences werefound for one particular reading).

Figure 5.6 shows how these different types of readings were distributed over thetwo quantifiers many and many of. The two bars represent the different quantifiertypes many and many of and the mean given answer types (in percentages) aremapped on the y-axis.

Children do not make a difference between many and many of. Chi-squareanalysis revealed no statistically significant associations between the answer the childgave (cardinal, proportional, Westerståhl or other) and the type of the quantifier(many or many of (χ2(3) = 0.739, p = 0.864).

Do children differentiate their responses on the kind of discourse information?A chi-square analysis revealed no statistically significant difference between thedistribution of answers in the discourse A context (χ2(3) = 0.868, p = 0.833) nor inthe discourse B context (χ2(3) = 2.152, p = 0.542).

5.8 Discussion and conclusions

Despite suggestions in the literature that context-dependent domain restriction ofweak quantifiers is the key for understanding children’s non-adult-like interpreta-tions of quantified sentences, there are few studies on the semantics and acquisitionof context-dependent domains of such quantifiers (e.g. many). In this chapter, Idefined the various interpretations of many and accounted for these readings in abi-directional OT framework. I showed that constraints of various nature restrict the


Figure 5.6: Children’s cardinal (in white), proportional (in grey), Westerståhl(dashed) and other (in black) interpretations of many and many of

possible interpretations of this quantifier and, depending on the discourse the quanti-fied sentences occurs in, adults accept cardinal, proportional or Westerståhl readingsof many. The ability of the hearer to consider the alternative forms the speakercould have used to formulate his message, play a central role in this bi-directionalframework and, hence, in the account of many presented in this chapter.

Following De Hoop and Krämer (2005/2006), I formulated the null-hypothesisthat children are unable to reason bi-directionally before the age of six/seven. Giventhe account of many presented above, this predicts that children interpret many andmany of differently, depending on the discourse the quantifiers are used in.

The results show that children allow cardinal readings, proportional readingsand Westerståhl readings for many across the board. Children’s answers are notaffected by quantifier type (many vs. many of ) or discourse context (a discourse Aor Discourse B context). The children thus interpreted many differently as predictedand the hypothesis that children’s interpretation of many and many of can beaccounted for in terms of bi-directionally reasoning is not supported.

The Equilibrium Hypothesis identified in chapter 3 provides an explanationfor the findings. According to the Equilibrium Hypothesis (which does not sayanything about bi-directional reasoning), children have a non-target-like equilibrium

5.8. Discussion and conclusions 105

between syntax, semantics and pragmatics. Since the results show that children usethe discourse information to restrict a quantifier domain regardless of the type of thequantifier (weak or strong), this indicates that children, in line with the EquilibriumHypothesis, use the discourse differently than aduls to restrict a quantifier domain.Whereas adults take the difference between weak and strong quantifiers into account(regardless of the discourse), children do not and start out with the informationprovided by the discourse to restrict a quantifier domain.

In conclusion, the hypothesis formulated in this chapter that children are unableto reason bi-directionally is unable to explain children’s interpretations of many andmany of ; the data do not confirm the predictions that follow from the hypothesisthat children lack bidirectional reasoning as a result of which they interpret manydifferently than adults. This means that this hypothesis as formulated in this chapteris not supported. In line with the Equilibrium Hypothesis, I therefore concludethat it is the more refined property of projecting the (syntactic and pragmatic)characteristics of quantified sentences onto their semantic representations that arethe locus of the problem.

6Quantifying in Context

6.1 Introduction

In this chapter, I discuss children’s understanding of quantified expressions in adiscourse. Various studies have shown that children interpret quantifiers adult-likeif the quantified sentence is appropriately embedded in a discourse (Freeman, Sinha,and Stedmon, 1982; Crain, Thornton, Boster, Conway, Lillo-Martin, and Woodams,1996; Drozd and Van Loosbroek, 2006; Hollebrandse, 2004). Given children’s non-adult like interpretations of quantified sentences when these are not embedded in adiscourse, the question arises why and under which discourse conditions children showadult-like behavior if such a discourse is provided. What are the characteristics of adiscourse that enable a child to understand quantified expressions adult-like? In thischapter, I test children’s understanding of quantified expressions in two discoursemanipulations.

Section two summarizes the acquisition literature on the acquisition of quan-tification and discourse. Section three is devoted to context-dependent domainrestriction in adult language. Taking an optimization approach to interpretation anddiscourse coherence along the lines of (Centering) Optimality Theoretic Semantics(Hendriks and De Hoop (2001) and Beaver (2004)), I analyze context-dependentquantifier domain restriction in terms of the constraints ALIGN-Q and FORWARDDIRECTIONALITY. I rephrase the results from the acquisition literature on quantifica-tion using these two characteristics. I present two experiments in section five whichboth address the question how children use the discourse to determine the quantifierdomain. Can we decipher to what extent children are able to determine the rolethat syntax and semantics allow pragmatics to play in different, well-controlled andmanipulated discourse conditions? This chapter thus aims to contribute to a betterunderstanding of the interaction between syntax, semantics and pragmatics andits role in first language acquisition. I conclude that establishing an equilibriumbetween pragmatics, semantics and syntax is the necessary step for the child towardan adult understanding of quantifiers. An approach along these lines to first languageacquisition in general and to the acquisition of quantification in particular allows us

107

108 Quantifying in context

to formulate new, precise predictions for further research and reveals a new horizonin both child language acquisition research and theoretical syntax, semantics andpragmatics.

6.2 The acquisition of quantification in relation to discourse

Since the work of Inhelder and Piaget (1958), it is well-known that children betweenfour and six years of age assign non-adult interpretations to universally quantifiedexpressions (see chapter 2). When children are asked to judge a sentence like Isevery cowboy riding a horse, some children will answer (one more often than theother) “no, not that one” in a situation in which three cowboys are each riding ahorse and one fourth horse is not being ridden (the so-called extra-object situation).Conversely, if an extra-subject item is displayed (e.g. three horses are displayed andthree cowboys are each riding a horse, leaving one cowboy doing nothing), somechildren answer yes to the question Is every cowboy riding a horse?. In the literature,both answers, which are not given simultaneously by the same child, are known assymmetrical responses (see Philip (1995) and chapter 2). Starting with the work ofFreeman, Sinha, and Stedmon (1982), various people have pointed at the notion ofdiscourse to explain these two kinds of responses.

Freeman et al. argue that children in previous research were confronted withtest situations (i.e. the extra object pictures) in which they had to choose between agrammatical analysis or a pragmatic (discourse-based) analysis to determine whetherthe test item correctly described the displayed picture or not. Since the test itemsin the experiments were presented without any kind of discourse, the child mightconclude that the speaker could not be talking about the actual topic of the sentence(i.e. cowboys for the sentence Is every cowboys riding a horse?), and so she inferred adiscourse topic she assumed the speaker intended. In this sense, the child had theoption to choose between a grammatical analysis and a pragmatic analysis. Freemanet al. argue that children go for the pragmatic analysis and understood test itemsas being about the violation of a one-to-one relation between horses and cowboysin the extra-object situation. The child guesses what the speakers means (insteadof figuring out what the words mean). As Freeman et al. put it, the child triesto understand “the speaker’s purpose and intended frame of reference” (1982:54).Children resort to such a strategy because the actual topic of the sentence is notin line with the child’s assumption about the topic of the sentence. The child’sexhaustive pairing answer is thus explained as a context-driven interpretation; thechild guesses a topic instead of relying on the topic of the sentence itself.

Subsequent work on the acquisition of quantification also points at the relationbetween the (lack of a) discourse context and children’s non-adult like interpretationsof quantified sentences. Drozd and Van Loosbroek (2006) suggest that children “lackor do not invoke the pragmatic principles adults use to constrain the interpretationof universal quantifiers at the discourse level” (2006:135). This is reminiscent ofMeroni, Gualmini, and Crain’s (2006:101) conclusions that “young children are

6.2. The acquisition of quantification in relation to discourse 109

subject to the same discourse constraints as adults and older children; youngerchildren are just less successful in making the necessary accommodations whendiscourse principles are flouted”. Hollebrandse (2004) also concluded that childrenuse pragmatic information to restrict a quantifier domain. The question arisesexactly what kind of pragmatic principles or discourse constraints affect children’sunderstanding of quantifiers. I will review these three theories (Crain et al., 1996;Drozd and Van Loosbroek, 2006; Hollebrandse, 2004)) to discuss in more detail theeffect of discourse on children’s understanding of quantified sentences.

6.2.1 Satisfying the Condition of Plausible Dissent

Crain et al. (1996) show that children are able to interpret a quantified sentenceadult-like if the test item is embedded in a discourse context that provides both ayes and a no-answer as a possible answer to the test item (cf. later work by the sameauthors, e.g. Meroni et al. (2006)). Compare the following discourse context forthe quantified sentence Every skier drank a cup of hot apple cider (from Crain et al.,1996:126).

(1) Characters and crucial props:Three skiers (a mom and her two girls)Five bottles of soda and five cups of apple ciderA styrofoam mountain, with an arch to ski throughProtocol:Exper.: In this story, this mom and her two girls go skiing. They’re going to

ski down this mountain here and try to ski through this arch. Overhere are the drinks at the ski lodge for when they’ve finished skiing.First, they all go on the ski lift to the top of the mountain. Then,this girl skis down the mountain.

Girl 1: This looks a bit scary. Here I go! Whee! Oops, here comes the arch. . . Yeah I made it! <first girl skis down the mountain, and safelythrough the arch>.

Girl 2: Now it’s my turn. Whee! Oops, I nearly fell. But I made it. Yeah!<second girl skis down the mountain and safely through the arch>.

Mom: OK girls, watch me. Whee! Oh wow, I didn’t realize this arch wasso low, I’ll have to really bend down to make it through <mom skisdown mountain, but barely makes it through the arch>, Oh girls,that gave me a real fight. I almost banged into the arch. Let’s go innow and get a drink <mom and girls go over to drinks set out on atable>. I’ll have a cup of this nice hot apple cider. This will helpcalm me down <mom takes a cup of cider>.

Girl 1: Oh, look at these sodas. I want this bottle of orange soda.Girl 2: I want this bottle of cola.


Mom: Girls, don’t take a bottle of soda. You should have a cup of hot applecider so you get nice and warm. You can have soda another time.

Girl 1: OK. I’ll take this cup, it’s full to the top.Girl 2: I want a full cup too. Are any of these other cups of cider full?Kermit: That was a hard story, but I think I know something that happened.

Every skier drank a cup of hot apple cider.Child: Yes.

orNo, not these cups of apple cider. (symmetrical interpretation).

In this discourse, the so-called Condition of Plausible Dissent is satisfied whichstates that “it is felicitous to ask whether a sentence S is false on a reading only if thediscourse context is such that S has been under consideration on that reading” (Crainand Thornton, 1998:237). This is the case in (1): because the children considereddrinking a soda instead of the apple cider, it is felicitous to ask whether Every skierdrank a cup of hot apple cider. This would explain why 88 % of the answers is inline with the target reading of Every skier drank a cup of hot apple cider. In thisrespect, Crain et al. differ from Freeman et al. since they do not attribute children’sadult-like interpretations to a spelled-out discourse topic in the discourse precedingthe quantified statement.

These are two missing elements in their explanation. Crain et al. do not answerthe question why children cannot derive a target-like semantic representation whenthe test item is not embedded in a proper discourse. Specifically, why do they resortto an exhaustive pairing answer when the Condition of Plausible Dissent is notsatisfied? Adults do not need a discourse to restrict the quantifier domain and sothe question arises how Crain et al. can explain how a child will become an adultlanguage user (for similar and other criticism against Crain et al.’s explanation, seeamong others Drozd (2004a,b); Philip (2004); Geurts (2000, 2003).

6.2.2 Presupposed sets

Drozd and Van Loosbroek (2006) (cf. Drozd and Van Loosbroek, 1999; Drozd,2001) argue for an alternative approach and claim there is a similarity between thechild’s exhaustive answer and, what they call the adult non-conservative reading(2-a) of (2).1,2

(2) Many French have won the Tour de France

1The notion of conservativity states that one only has to inspect the quantifier’s first argument setand the intersection of the first and the second argument set to interpret a quantified sentence. As aresult, only the part of the second argument set that intersect with the first argument set plays a role ifone is asked to interpret a quantified sentence. However, since the entire second argument set of many in(2) needs to be considered for an interpretation in (2-a), conservativity seems to be violated here (but foran alternative explanation, see chapter 5 and references therein.)

2In chapter 5, I have labeled this the Westerståhl reading.


a. “Many Tour de France winners are French”

For reading (2-a) of (2), the hearer interprets the sentence in terms of the set ofFrench Tour de France winners (and finds that their number exceeds some expectednumber). When children are faced with a sentence like Every cowboy is riding a horse,Drozd & Van Loosbroek argue, they apply just such a non-conservative reading,for which they compare the number of horse-riding cowboys against an expectednumber of horse-riding cowboys (i.e. a one-to-one relation between cowboys andhorses).

Drozd and Van Loosbroek raise the hypothesis that children need the domainof quantification to be properly introduced in the preceding discourse. Referringto Szabolcsi (1997), they point at adults’ use of a so-called witness set. The witnessset is the set in the real world to which the quantifier’s domain needs to be linkedin order to determine the truth value of the quantified expression.3 Consider (3),describing a situation in which a man loves all the jaguars in his garage (and thejaguars in his garage is the witness set that the linguistic expression refers to).

(3) The man loves all the jaguars in his garage

Children interpret a quantified sentence adult-like when such a witness set is intro-duced (“presupposed” in Drozd and Van Loosbroek’s terms) and its members areproperly identified in the previous discourse, which is the case in the Crain et al.(1996) paradigm, Drozd and Van Loosbroek argue:

“children’s performance improves on conditions like Crain et al.’s SkiersCondition because the set the children need to represent as the domainof quantification for the quantifier every is presented as presupposedbefore Kermit presents the test sentence for judgment. This makesit possible for children to establish the restriction and nuclear scopearguments for the quantifier as independent sets and to proceed withthe presuppositional interpretation of the quantifier.” (Drozd and VanLoosbroek, 2006:119)

Drozd and Van Loosbroek (2006) set out to confirm this hypothesis by asking Dutchchildren, before asking the test item with a quantifier, to point out a set (the witnessset) in a pictured context (the Show Me Condition, exemplified in (4)) or to answera question irrelevant to the quantified sentence (the Irrelevant Property Condition,exemplified in (5) below). After the child answered this question, the child was askedto judge the test item.4

3Formally, a witness set for a quantifier D(A) living on A is any subset w of A such that w ∈ D(A)(Barwise and Cooper, 1981) and, as Barwise and Cooper point out, the mechanism behind this is “... nottotally unlike some computational models for the verification of quantified sentences which have beensuggested in the psychological literature...” (Barwise and Cooper, 1981:104).

4There was a third condition in Drozd & Van Loosbroek’s (2006) experiment, which was argued tosatisfy the Condition of Plausible Dissent and in which children did not answer significantly different


(4) The Show Me ConditionExperimenter:

Dit lijkt wel een woestijn.(‘This looks like a desert.’)Allemaal zand en bergen. (‘All sand and mountains’)En dit zijn jongens? (‘And these are boys?’)Hier zie je?(olifanten) (‘Here you see?’ (elephants))

Cookie Monster:Wijs de jongens eens aan. (‘Point to the boys.’)

Experimenter:Rijden alle jongens op een olifant (“Are all boys riding an elephant”)

(5) The Irrelevant Property ConditionExperimenter:

Dit lijkt wel een woestijn. (‘This looks like a desert.’)Allemaal zand en bergen. (‘All sand and mountains’)En dit zijn jongens? (‘And these are boys?’)Hier zie je?(olifanten) (‘Here you see?’ (elephants))

Cookie Monster:Heeft iedere jongen schoenen? (‘Does every boy have shoes?’)

Experimenter:Rijden alle jongens op een olifant (“Are all boys riding an elephant”)

Since the child’s attention is drawn to the intended domain of quantification inboth conditions (the set of boys), Drozd and Van Loosbroek argue that “eachcondition provided contextual support for the presuppositional interpretation ofthe universal quantifier” (2006:127). Their results show that this is indeed thecase; children’s interpretation of quantified sentences improves in both conditions,which Drozd and Van Loosbroek argue to be due to the introduction of the set inthe discourse before the quantified question was asked. On the basis of children’simproved behavior on (4) and (5) in contrast with a classical extra-object task withno discourse, Drozd and Van Loosbroek then suggest that children do not updatetheir discourse model in contexts which are incompatible with the “presuppositionalrequirements” (2006:138) of a universal quantifier. Providing a context which iscompatible with the “presuppositional requirements” (like in (4) and (5) above, theyargue), would result in adult-like interpretations.

The question arises whether children are able to use such pragmatic informationto restrict the quantifier domain also in other discourse manipulations. A clue thatchildren are indeed able to comes from the work by Hollebrandse (2004).

than in the other conditions. However, Crain, Meroni, and Gualmini (2000) (commenting on an earlierpresentation of Drozd and Van Loosbroek’s (2006) results) argues that this third condition in Drozd &Van Loosbroek (2006) does not satisfy the Condition of Plausible Dissent at all. For this reason, Crain etal. rejects Drozd & Van Loosbroek’s conclusion that satisfying the Condition of Plausible Dissent doesnot result in significantly different improved performance.


6.2.3 Providing a discourse topic

Hollebrandse (2004) shows that topicality plays a role in children’s interpretations ofquantified sentences. Hollebrandse compared the behavior of Dutch children whoconsistently gave exhaustive pairing answers in a classical paradigm, i.e. withouta discourse, to their behavior in conditions with a discourse. In the discoursepreceding the quantified sentence, either the subject or the object was the discorusetopic. An example of a translated test item can be found in (6) in which the set ofknights is the topic.

(6) And after a while the Indians run into two knights, who are kings. TheIndians give the chickens to the knights <photograph: Indians give chickento the knights>. The knights invite the Indians for dinner at their new home.The knights have just moved <photograph: two knights, one is lifting twochairs>Puppet interrupts:Wow, look there! A knight is lifting all chairs

In this situation, the set of knights is the topic and the quantifier domain is restrictedto the set of chairs. The results show that children who initially gave a symmetricalanswer, interpret a sentence containing a quantified subject adult-like if the subjectwas the discourse topic (cf. Philip and Lynch (2000) for similar results). Conversely,if the subject was not topicalized or the object was quantified over, significantly feweradult-like answers were found. Hollebrandse concludes that children use pragmaticinformation to restrict a quantifier domain: “These spreaders behaved more adult-like (less spreading) in the cases in which pragmatic information (topichood) wasadded” (2004:213).5

Hollebrandse (2004) does not discuss why children now suddenly choose adiscourse-based interpretation of the quantified sentence. Why would it be easier tointerpret a quantified subject topic than an object topic? Is it the status as discoursetopic that helps the child to quantify over a particular set, and if so how exactly, oris it because of some other effect?

6.2.4 Putting discourse into context

In sum, various people explained the child’s exhaustive-pairing answer in terms ofa lack of a proper discourse context. ‘Discourse context’ can either be understoodas an ‘intended frame of reference’ (Freeman et al., 1982) or satisfaction of certainpragmatic felicity conditions (Crain et al., 1996). Drozd and Van Loosbroek (2006)argue that children give an adult-like interpretation of a quantifier when the domainof the quantifier is presupposed in the preceding discourse. Hollebrandse (2004)argues that it is a discourse topic that enables the child to interpret a quantifiedsentence adult-like when a discourse is provided.

5Hollebrandse follows Roeper and DeVilliers (1991) and calls children who give an exhaustive pairinganswer spreaders.


The controversy about the correct explanation of children’s improved perfor-mance in a discourse, is a first reason to take up the question what the actualcharacteristics of a discourse are that turn the child into an adult language user. Is itsatisfying the Condition of Plausible Dissent, help with presupposing the quantifierdomain or providing a discourse topic that leads the child to an adult interpretationof a quantified sentence?

A second reason to look in more detail at children’s understanding of quanti-fied sentences in a discourse is that all accounts discussed above fail to address thequestion why children differ from adults in the classical condition and apparentlycannot interpret a quantified expression adult-like without a discourse. Why andunder which conditions do children differ from adults?

A third reason to take up this matter is formulated by Meroni et al. (2006), whoargue that the current debate in the acquisition of quantification is in fact a debateabout the learnability of linguistic principles. The view that linguistic principlesneed to be acquired implies, according to Meroni et al., that children’s grammarshave to change over time. In the case of the acquisition of quantification, childrenhave to acquire how to obey compositionality and apply universal properties ofdeterminer meanings like conservativity. Meroni et al. point out that Drozd andVan Loosbroek’s approach implies that children’s grammar violates conservativity.Children have to unlearn this non-conservative reading for every. This leads to aserious learnability problem, they argue, since it implies that the child’s grammarhas to change enormously in order to reach an adult state. But how can that be, theypoint out, if children, next to the symmetrical answer, also give adult-like answersat least in certain conditions? For this reason, Meroni et al. argue that Drozd andVan Loosbroek’s analysis should be rejected (and for the same reason, Crain et al.reject the work of Philip and Lynch (2000) and Geurts (2003) which they take raisessimilar learnability problems) and conclude that children have adult knowledge ofquantified expressions.

On the one hand, children are argued to apply non-adult like interpretations toquantifiers. On the other hand, children are argued to have adult-like readings ofquantified expressions but the experiments testing this knowledge blurs this picture;the test situation is infelicitous and confuses the children. A key argument for Crainand colleagues is that other, linguistic accounts all pose a learnability problem andso they to maintain the latter view and argue for a non-linguistic account. However,Meroni et al.’s account also raises a learnabality question: given that adults do notneed a discourse to interpret quantified sentences, how do children learn to interpreta quantified expression adult-like without a discourse? A solution to the learnabilityproblem is to take an alternative view on quantification and discourse along thelines of Hendriks and De Hoop (2001) and Beaver (2004).

6.3. Context dependent domain restriction 115

6.3 Context dependent domain restriction

In this section, I present an optimization approach to interpretation along the linesof Hendriks and De Hoop (2001) and Beaver (2004). I will argue that this enablesus to avoid both the “pitfalls” of a linguistic account and a non-linguistic account.Hendriks and De Hoop’s Optimality Theoretic semantics is specifically developed toaccount for the role of context on e.g. quantifier domains. Moreover, it takes a totallydifferent perspective on compositionality and constraints on determiner meanings.My explanation of children’s understanding of quantified sentences in terms ofOptimality Theoretic semantics circumvents all problems Meroni et al. argue alinguistic account runs into by taking a new perspective on the learnability issueand, even more importantly, enables us to formulate a new hypothesis reconcilingearlier psychological, syntactic and pragmatics work on children’s understanding ofquantified sentences. Beaver’s (2004) reformulation of Centering Theory (Grosz,Joshi, and Weinstein, 1983, 1995) in OT enables us to narrow down the constraintDOAP introduced in chapter 3 and to formulate precise predictions how discoursecoherence and topicality interact with quantifier domain restriction in child language.I will now discuss how (context dependent) domain restriction works in OptimalityTheoretic semantics and how quantifier domain restriction is related to discoursecoherence and topicality in adult language.

In adult language, the context can restrict a quantifier domain. Compare thefollowing example (a modified example from Recanati (1986)):

(7) Back from my holidays, I found that my house had been broken into. Andyes, the burglar took everything.

Without any further kind of information, one will take the burglar took everythingin (7) to mean that the burglar took all objects from the house he broke into (andworld-knowledge might even lead you to conclude that the burglar took everythingof value or everything he could reasonably take, e.g. everything that he couldcarry). The discourse context leads you to this interpretation and rules out a readingaccording to which the burglar took all objects in the world. By taking a newperspective on interpretation, Hendriks and De Hoop (2001) account for the role ofdiscourse context in interpretation by using Optimality Theory semantics (for anintroduction to OT semantics, see chapter 3.).

6.3.1 Optimality Theoretic Semantics; Hendriks and De Hoop, 2001

Hendriks and De Hoop formalize the effect of context and syntax on the possiblemeanings of a quantified expression with the following two soft constraints (fromHendriks and De Hoop, 2001:22,15; cf. chapter 3): Syntactic Structure and Don’tOverlook Anaphoric Possibilities.


(8) Syntactic StructureIf there is an N’ that constitutes an NP together with a determiner, use thisN’ to restrict the domain of quantification of that determiner.

(9) Don’t Overlook Anaphoric Possibilities (DOAP) (Williams, 1997)Make sure that anaphoric elements are related to the previous discourse.

The constraint Syntactic Structure makes sure that each quantifier domain is re-stricted to the N’ the quantifier accompanies. This constraint is argued to be neverviolated.6 This approach to quantifier domain restriction is not different from eitherthe functional or relation perspective on quantified sentences (see chapter 2). Toillustrate the role of DOAP, consider (10).

(10) Some like to fly, others do not.

In (10), the determiner is not followed by an N’. To interpret this sentence in whichthe domain of quantification is not spelled out by the speaker, one has to fill it inoneself by means of the discourse context. The hearer has to select a set availablein the (discourse) context which appears to be the most relevant one. For (10), thismight be e.g. a set of particular birds. Starting out from the assumption that e.g.pronominally used determiners as in (10) establish an anaphoric relation with anantecedent in the preceding discourse, the constraint DOAP makes sure this set isactually selected in the preceding discourse.7

Now consider example (11) (cited in Hendriks and De Hoop, 2001:6).

(11) The buildings are all two and three stories running half a block deep withbrick and glass fronts. Most were built together, a few have narrow alleysbetween them. Many are still boarded up, a couple were burned out yearsago.

In (11), we take the discourse topic to be buildings. The constraint Topicality in(12) states that the antecedent is the topic of an anaphoric expression, if no otherconstraints apply. ‘Topic’ should be understood, as Hendriks & De Hoop point out,in terms of e.g. Vallduví (1990).8

6But cf. for an alternative account e.g. Herburger (1997, 2000).7Note that such an approach on context dependent quantifier domain restriction differs from the

one taken by Westerståhl (1985) and Von Fintel (1994)). Crucially, these accounts differ from Hendriks& De Hoop (2001) in assuming that each quantificational determiner is accompanied by a covert contextvariable. Although Hendriks and De Hoop point in a similar way at the anaphoric relation between thequantifier’s arguments and certain sets in the discourse, they do not assume that this anaphoric relationis a lexical characteristic of quantificational determiners. Hendriks and De Hoop rather assume that it isa general pragmatic preference to interpret anaphora as related to the previous discourse.

8Topics (grounds in Vallduví, 1990) are also known as backgrounds or presuppositions, as Vallduvípoints out (cf. Vallduvi and Engdahl (1996) and references therein). Vallduví identifies topicalisation asone of the clues that enables the hearer to understand the speaker’s sentence as optimal as possible. Assuch, topicalisation is a pragmatic factor that affects the sentential form. Moreover, Vallduví argues thattopicalisation is a particular form of information packaging (or information structure). The idea behind


(12) TopicalityAs the antecedent of an anaphoric expression, choose a topic.

However, it is not always the topic that restricts the quantifier domain. Considerexample (13).

(13) Ten students attended the meeting. Three spoke.

In (13), the domain of the second quantifier, three, is not restricted to just the topicof the first sentence (students), but to the set of students who attended the meeting.This is, as Hendriks & De Hoop point out, in line with the notion of conservativity.Conservativity states that, for the interpetation of a quantified sentence, one onlyhas to inspect the denotation of the first argument set and the denotation of theintersection of the first and the second argument set. It is the intersection of thefirst and second argument set that is the first argument of the quantifier three in (13).This is captured by the constraint Forward Directionality (Kuppevelt, 1996).

(14) Forward Directionality: The topic range induced by the domain of quantifi-cation of a determiner (set A) is reduced to the topic range induced by theintersection of the two argument sets of this determiner (A ∩ B).

DOAP is satisfied whenever Forward Directionality or Topicality is obeyed.

In sum, Hendrik’s & De Hoop optimization approach to interpretation statesthat a quantifier domain is restricted by the syntactic structure of the quantifiedexpression and by the discourse context. They account for this by assuming thatsoft, i.e. violable constraints on the possible meanings of a quantified sentence(i.e. Topicality and Forward Directionality) interact with the constraint SyntacticStructure.9 The advantage of Hendriks’s & De Hoop’s optimization approach isthat they incorporate syntactic, semantic and discourse constraints in one model,thereby modeling the interaction between these different modules.

While Hendriks and De Hoop (2001) explain how topichood plays a role inquantifier domain restriction, they do not incorporate how sets introduced inthe discourse context are marked as topic/non-topic and function with respectto restricting the quantifier domain. Beaver’s (2004) reformulation of CenteringTheory (Grosz et al., 1983, 1995) in Optimality Theoretic semantics (COT) allowsus to do so and to refine DOAP in even more detail.

information packaging is that a speaker structures information in a precise and well-defined way and bydoing so, offers the hearer all kind of clues how to integrate this information to understand the speaker’smessage as optimal as possible. Topicalisation is one of such clues.

9But see for example Herburger (1997, 2000) who argues that focus can overrule the syntacticstructure of a sentence.


6.3.2 Centering Optimality Theory; Beaver, 2004

Beaver (2004) reformulates the Centering theoretic model of anaphora resolutionand discourse coherence (Grosz et al., 1983, 1995) in Optimality Theory. In aCentering Theory (CT) analysis all the referents referred to in a sentence are orderedin a so-called “forward-looking center list” according to their argument role orgrammatical obliqueness, with subjects being less oblique than direct objects, directobjects less oblique than indirect objects, etcetera. The least oblique element (theentity ranked highest in the forward-looking center list, i.e. the subject) is termedthe “preferred center”(Cp). Further, the discourse entity referred to in the currentsentence that was also the least oblique or the most prominent discourse entityunder discussion in the previous sentence (i.e. the entity ranked highest on theprevious sentence’s forward-looking center list) is identified as the topic of thecurrent sentence, or “backward looking center” (Cb). A continuing discourse isa discourse in which the backward-looking center is unchanged and is also thepreferred center of the new sentence. Consider example (15):

(15) a. Janei likes Maryj

b. Shek often gives herl flowers

In (15-a), the forward-looking center list contains Jane and Mary with Jane being thepreferred center (Cp). According to the definition of ‘topic’ or ‘backward lookingcenter’ as the entity most prominent under discussion in both the current and theprevious sentence, Jane in (15-b) is identified as the topic or backward looking center(Cb). Additionally, Rule-I in CT says that “If there are pronouns in the currentsentence, then one of them refers to the backward looking center of the currentsentence” (cited in Beaver, 2004:8). This means that she in (15-b) can only referto Jane. Since continuations from (15-a) to (15-b) (the backward-looking center isunchanged and is also the preferred center of the new sentence) are preferred overretentions (the backward-looking center is unchanged but is no longer in preferredposition), she should be identified with Jane and her with Mary in (15-b). Note thatthe backward-looking center of (15-a) is empty; there is no previous sentence and, asa result, no backward-looking center can be mapped onto the entity in the currentsentence which is also the most significant entity under discussion in the previoussentence.

Centering Theory provides an elegant way of accounting for discourse coherence.However, as Beaver (2004) points out, despite the fact that Centering Theory hasbeen central in natural language processing and psycholinguistic studies, far lessattention has been attributed to the framework in formal semantics and pragmaticswhich “have tended to concentrate on absolute semantic constraints on what canbe anaphoric to what, rather than to build up detailed pictures of which discourseentities are salient, and hence likely to be referred to, at which times.” (Beaver,2004:3). Beaver (2004) tries to bridge the gap between these different disciplines by


reformulating CT in Optimality Theory.10

First, Beaver replaces the term backward-looking center with topic to link thenotion to a large body of linguistic research on the very same matter. I will adoptBeaver’s terminological change and define topic as in (16) (from Beaver, 2004:14).

(16) The topic of a sentence is the entity referred to in both the current andthe previous sentence, such that the relevant referring expression in theprevious sentence was minimally oblique. If there is no such entity, thetopic is undefined.

Second, Beaver introduces six violable, soft constraints. Two of them are relevantfor our current purposes (since his other constraints are only relevant for resolvingpronouns): COHERE (motived, as Beaver points out, by among others Givón, 1983)and ALIGN. These constraints are defined as follows (from Beaver, 2004:15):

(17) COHERE: The topic of the current sentence is the topic of the previous one.ALIGN: The topic is in subject position.

When we apply these constraints to the sentences (15-a) and (15-b), we can constructan OT tableau. Note that for (15-a), the topic is by definition undefined since thereis no preceding sentence (in a similar way as there was no backward-looking centerin CT for discourse-initial sentences). This means that, next to COHERE, ALIGNis also not relevant (indicated by the gray cells in (18)). This means that (15-a) isinterpreted by means of other constraints, e.g. stating that for a transitive verb,the subject is the actor and the object is the patients (represented by the constraintSubject in (18)). This results in the reading according to which Jane likes Mary(indicated by the little hand in the tableau in (18)) and not the other way around.

(18) Example (15-a) SUBJ

ECT

CO

HER

E

ALI

GN

+ Like( j,m)Like(m,j) *!

When we now consider (15-b), notice that COHERE and ALIGN make a differencebetween two possible interpretations (‘Jane often gives Mary flowers’ and ‘Maryoften gives Jane flowers’). First, COHERE is violated in both cases since the topic ofthe first sentence is undefined. Second, the interpretation that Mary gives flowersto Jane is ruled out since this interpretation violates ALIGN. The topic of (15-b)must be the subject of (15-a) since that is the entity referred to in both sentences andmoreover occupies the minimally oblique position in (15-a). Since ALIGN states thatthe topic should be a subject, she needs to be identified with Jane. This means that,

10It is not my purpose to motivate Centering Optimality Theory here. I refer to Beaver (2004) formore motivation for a reformulation of Centering Theory in Optimality Theory.


for the reading in which Mary gives flowers to Jane, ALIGN is violated. Since this isnot the case for the reading in which Jane gives flowers, this interpretation turnsout to be the most optimal interpretation of She often gives her flowers.

(19) Example (15-b) CO

HER

E

ALI

GN

+ k = i, l = j *k = j, l = i * *!

I will now use Beaver’s Centering Optimality Theory to account for the effect ofdiscourse on quantifier domain restriction. However, only using Beaver’s contraintsto model (context dependent) domain restriction is not sufficient. It is not alwaysthe case that the discourse topic needs to be related to the sentence’s subject. Asexample (11) illustrated, repeated here as (20), in the case of a quantified sentence ina discourse, the topic (buildings in this case) relates to the quantifier’s first argumentset rather than to the sentence’s subject. This results e.g. in the interpretation ofmost as most of the buildings.

(20) The buildings are all two and three stories running half a block deep withbrick and glass fronts. Most were built together, a few have narrow alleysbetween them. Many are still boarded up, a couple were burned out yearsago.

Partee (1991) also pointed in a similar way at the relation between the (discourse)topic and the quantifier’s first argument set. Moreover, as she points out, topic-hood might affect the quantified structure, but not to the extent that the syntaxis overruled (Partee, 1991). This is in line with Hendriks and De Hoop’s (2001)approach discussed above that next to Syntactic Structure (paraphrased as ‘use theN’ to restrict the quantifier domain’) other factors play a role in domain restriction(see the previous section). If we now combine these approaches and take ALIGN-Qto be a more fine-grained version of Beaver’s ALIGN stating that one has to use thetopic to determine the quantfier’s first argument set, the following constraints arerelevant to our current endeavor to account for the effect of discourse on quantifierdomain restriction (in rank order, with the top constraint the highest ranked):

(21) SYNTACTIC STRUCTURE: Use the N’ bar to restrict a quantifier’s domainCOHERE:The topic of the current sentence is the topic of the previous oneALIGN-Q: Use the topic to restrict a quantifier’s domainFORWARD DIRECTIONALITY: The topic range induced by the domain of

quantification of a determiner (set A) is reduced to the topic rangeinduced by the intersection of the two argument sets of this determiner(A ∩ B).


By means of these constraints, we can explain why the set of cows is understoodas the restriction of many in (22-c) (Forward Directionality is not relevant here forthis case and is left out from the tableau).

(22) a. In The Netherlands, there are cowsh everywhere.b. Cowsi are great animalsj .c. Manyk are black and white, and somel are brown.d. But I love them all.

In (22-c), COHERE is satisfied since the entity of cows is referred to in both thecurrent and the previous sentence and moreover occupies the first position on theforward-looking center list in (22-b) (i.e. cows are the subject). ALIGN-Q is onlyviolated if something else than cows is the domain of quantification. As a result, themost optimal candidate is the one that does not violate either COHERE or ALIGN-Q.This leads one to interpret the speaker of (22-c) as being talking about many cowsinstead of many animals. This is represented in the tableau in (23).

(23)Example (22-c) C

OH

ERE

ALI

GN

-Q

+ k = ik = j *!

Syntactic Structure only applies if there is an N’. If not, Align-Q takes overand supplies a set (i.e. the discourse topic) to restrict the domain of the quantifier.Take for example sentence (24) with the discourse topic pigeons and (25) with thediscourse topic parrots.

(24) a. There are pigeons everywhere in Amsterdam.b. Pigeons are great.c. Many are gray.

(25) a. Parrots live in the rainforest.b. Parrots are great.c. Many pigeons are gray.

Syntactic Structure does not apply in (24) since there is no N’ and Align-Q suppliesthe quantifier domain (i.e. the set of pigeons). In (25) Syntactic Structure applies(since there is an overt quantifier argument) and provides the set of pigeons as thedomain of many. Due to the ranking of Syntactic Structure and Align-Q, this is alsothe most optimal interpretation, despite of the fact that this violates Align-Q andCohere because of the discourse topic of the set of parrots. This is illustrated in (26)and (27).


(26)

Example (24-c) SYN

TA

CT

ICST

RU

CT

UR

E

CO

HER

E

ALI

GN

-Q

‘Many parrots are gray’ *!+ ‘Many pigeons are gray’

(27)

Example (25-c) SYN

TA

CT

ICST

RU

CT

UR

E

CO

HER

E

ALI

GN

-Q

‘Many parrots are gray’ *! *+ ‘Many pigeons are gray’ *

Turning to quantified sentences with an overt argument like (28), SYNTACTICSTRUCTURE ensures that, for adults, an exhaustive pairing answer is impossible. Ifsuch an answer is possible in the target-language, this would mean that somethingelse than the N’ is used to restrict the quantifier domain and that such a constraintoverrules Syntactic Structure or, to put it differently, is ranked higher than SyntacticStructure. This is clearly not the case in the adult language; if there is an overtargument, one has to use the N’ to restrict the domain. (Cohere and Align-Q areviolated since the topic is undefined.)


(29)Example (29) SY

NT

.ST

R.

CO

HER

E

ALI

GN

-Q

+ Every(A,B) * *Every(A,B) ∧ Every(B,A) *! * *


So discourse does not make a difference for adults in the interpretation of (28);a reading for which something else than the N’ is used to restrict the quantifierdomain is ruled out by Syntactic Structure. This is illustrated in (30) in which thequantified sentence is embedded in a discourse, but the exhaustive pairing answer isstill not possible (as shown in (31)).

(30) a. Horses are great. Wow, a lot of horses are out there!b. Every cowboy is riding a horse.

(31)Example (30-b) SY

NT

.ST

R.

CO

HER

E

ALI

GN

-Q

+ Every(A,B)Every(A,B) ∧ Every(B,A) *! *

Recall that there is also the constraint Forward Directionality (FD). This con-straint, ranked below ALIGN-Q, makes sure that the quantifier’s first argument setintersects with the discourse topic (cf. the definition of FD in (21)). This resultsin the reading of (32-b) that three of the students who attended the seminar passedthe exam. Cohere is violated because the topic of (32-a) is undefined (since there isno previous sentence, see (16)), ALIGN-Q and SYNTACTIC STRUCTURE are bothsatisfied since respectively the topic students is the domain of the quantifier three forboth interpretations and the N’ is used to restrict the domain.

(32) a. Ten students attended the seminarb. Three students passed the exam

(33)Example (32-b) SY

NT

.ST

R.

CO

HER

E

ALI

GN

-Q

FD

+ three students who attended the seminar *three arbitrary students * *!

In sum, combining the work of Hendriks and De Hoop (2001) and Beaver (2004),the effect of discourse on quantifier domain restriction can be accounted for bytaking an optimization approach to interpretation, i.e. all possible interpretationsof a sentence need to be evaluated against the constraint SYNTACTIC STRUCTUREon the one hand and the constraints that I take all to be related to DOAP on theother hand (COHERE, ALIGN-Q and FORWARD DIRECTIONALITY). In the nextsection, I will use the constraints to account for children’s non-adult interpretationsof quantified sentences and formulate the predictions about the role of context inchildren’s interpretations that follow from this.


6.4 Optimal acquisition; hypotheses and predictions

As outlined in section 6.2, different approaches point at the importance to takeinto account the notion of discourse to account for children’s understanding ofquantified sentences. This is the starting point for the two experiments that willbe discussed in the next section. The null-hypothesis is that acquisition is a matterof re(ranking) constraints (Smolensky, to appear) and, more particular, that acquir-ing quantification is a matter of reranking the syntactic, semantic and pragmaticconstraints identified in the previous section.11 I hypothesize that, in line with theEquilibrium Hypothesis and the literature discussed in chapter 3 and the conclusionsdrawn in chapter 4 and 5 that, for children between four and six years of age, theconstraint SYNTACTIC STRUCTURE is ranked lower than ALIGN-Q and FORWARDDIRECTIONALITY.

Recall from chapter 4 that the child’s non-target-like interpretation of (34) can beillustrated as in (35) (in which the child’s non-target-like interpretation is representedas Every(A,B) ∧ Every(B,A)). Cohere and Align-Q are violated since there is nodiscourse topic. For the same reason, Forward Directionality is violated. Since theseconstraints do not make a distinction between the first or second interpretation,they are left out from the tableau in (35).


(35)Example (34) FA

ITH

-VIS

SYN

T.S

TR.

Every(A,B) *!+ Every(A,B) ∧ Every(B,A) *

Crucially, the ranking of the constraints in (35) differs from the adult ranking.Whereas adults rank Syntactic Structure above Cohere, children are hypothesizedto rank Syntactic Structure below Cohere and even below Faith-Vis, the constraintintroduced in chapter 3 that makes sure visually prominent items are incorporatedinto the interpretation of a quantified sentence.

(36) FAITH-VIS:Make sure that anaphoric elements are related to the theme of a picture (i.e.visually prominent items)

In (36), ‘visually prominent’ has to be understood as, for example, exceptions toa rule/generalization which stand out more than non-exceptions (see chapter 3).In the case of the classical extra object picture with one horse without a cowboy

11Different views can be found in the literature what triggers such a reranking of constraints. Thisquestion, however, lies outside the scope of this thesis.

6.4. Optimal acquisition; hypotheses and predictions 125

sitting on it, this horse clearly stands out as an exception and therefore is a visuallyprominent item. It explains the findings of Meroni et al. (2001) that adults’ eyefixation patterns reveal that adults also look at the horse without a cowboy on topof it in an extra-object figure; adults check whether there is a visually prominentitem, possibly to check whether Faith-Vis is violated or not.

Turning back to the role of discourse in the interpretation of quantifiers, wecan now formulate precise prediction regarding children’s understanding of theidentified discourse constraints. When the child is asked to interpret a quantifiedsentence preceded by a discourse as in (37), the current (C)OT framework andthe proposed child ranking predicts that children will interpret the sentence likeadults. Forward Directionality applies and is satisfied for both the target and non-target-like interpretation; the quantifier domain cowboys is restricted to the set ofcowboys that are identified in (37-a). COHERE and ALIGN-Q also apply. The latteris violated by the non-target-like interpretation because the quantifier domain forthis interpretation (cowboys and horses) is not in line with the topic cowboys in thepreceding discourse. Syntactic Structure is violated by the second interpretationbecause its domain contains more than the N’. The adult interpretation (Every(A,B)in the tableau in (38)) thus turns out to be the optimal one despite its violation ofFAITH-VIS. This is in line with the results of Hollebrandse (2004) (and Drozd andVan Loosbroek, 2006).

(37) a. Cowboys are great. Wow, a lot of cowboys are out there!b. Every cowboy is riding a horse.

(38)Example (37) C

OH

ERE

ALI

GN

-Q

FD FAIT

H-V

IS

SYN

T.S

TR.

+ Every(A,B) *Every(A,B) ∧ Every(B,A) *! *

In contrast, when the discourse is about the set denoted by the object, e.g. horses,the child is predicted to give an exhaustive pairing answer; the first interpretationin (40) violates ALIGN-Q, while the other violations remain the same. Becausethis constraint is higher ranked than SYNTATIC STRUCTURE, the second readingbecomes the optimal one. The experimental data of Hollebrandse (2004) confirmthat, for (39), children indeed give more exhaustive pairing answers than for (37).12

(39) a. Horses are great. Wow, a lot of horses are out there!b. Every cowboy is riding a horse

12Note that also Krämer (2000) predicts that children’s interpretation of quantified sentences improvesif discourse clues are provided.


(40)Example (39) C

OH

ERE

ALI

GN

-Q

FD FAIT

H-V

IS

SYN

T.S

TR.

Every(A,B) *! *+ Every(A,B) ∧ Every(B,A) *

In sum, children’s understanding of quantified sentences and the helpful orconfusing role of context can be explained in terms of (C)OT semantics. Moreover,with the framework and the proposed child ranking discussed in the previous section,we can account for children’s improved performance in a discourse and answer thequestion why they differ from adults. The hypothesized child ranking in (41) is thesubject of the experiments discussed in the next section.

(41) HYPOTHESIZED CHILD RANKING:Cohere » Align-Q » Forward Directionality » Faith-Vis » Syntactic Structure

6.5 Experiments

Two experiments test children’s use of discourse to restrict the quantifier domain.Both experiments aim to answer the question whether children ’s interpretationsare affected by discourse prominent items versus visually prominent items (as in theclassic paradigm). To put it differently, these experiments explore the possibility torephrase children’s non-adult understanding of quantified sentences in terms of rank-ing the pragmatic constraints ALIGN-Q and FORWARD DIRECTIONALITY higherthan SYNTACTIC STRUCTURE. Do children differ from adults in their understandingof quantified sentences due to a non-adult ranking of these constraints?

6.5.1 Experiment 1: Align-Q and the Discourse Context

Experiment 1 addresses the hypothesis in (42).

(42) Hypothesis:Children rank ALIGN-Q higher than SYNTACTIC STRUCTURE

The underlying assumption of (42) is that children use the constraint ALIGN-Qto restrict the quantifier domain (cf. Hollebrandse, 2004). Starting out fromHollebrandse’s (2004) (cf. Philip and Lynch, 2000) findings that children prefer touse topichood to restrict the quantifier domain instead of the syntactic structure, theresearch question is what happens if both the quantifier’s first and second argumentset are topicalized in the discourse preceding the quantified sentence. With such anambiguous context (which Hollebrandse and Philip crucially did not have in theirexperiments), children can interpret either the subject or the object as the discoursetopic. In the first case target-like behavior is predicted, in the latter non-target-like

6.5. Experiments 127

behavior. This is examplified for (43) in tableau (44-a) when the subject is selectedas the discourse topic (DT in (43)) and in (44-b) when the object is selected as thediscourse topic (DT in (43)). With a picture accompanying (43) displaying an extraobject, the constraint Faith-Vis is violated by the first interpretation since the picturedisplays an exception to a rule (i.e. one fry is not being eaten is not being eaten).Syntactic Structure is violated for the second interpretation since the non-target-likeanswer takes another set than the one denoted by the N’ as the quantifier’s firstargument. Crucially, children are predicted to randomly interpret (43) as (43-a) or(43-b).

(43) All elephantsDT are eating friesDT

a. ‘All elephantsDT are eating fries’b. ‘All elephants are eating friesDT ’

(44) a.Interpretation (43-a), topic: elephants C

OH

ERE

ALI

GN

-Q

FD FAIT

H-V

IS

SYN

T.S

TR.


b.Interpretation (43-b), topic: fries C

OH

ERE

ALI

GN

-Q

FD FAIT

H-V

IS

SYN

T.S

TR.

Every(A,B) *! *+ Every(A,B) ∧ Every(B,A) *

Note that for adults (with a ranking according to which Syntactic Structure isranked above Cohere and the other discourse constraints), having introduced twodiscourse topics does not result in chance behavior; for both options (either choosingthe subject or the object as the discourse topic), the exhaustive interpretation(Every(A,B) ∧ Every(B,A)) is ruled out:

(45) a.Interpretation (43-a) SY

NT

.ST

R.

CO

HER

E

ALI

GN

-Q

FD FAIT

H-V

IS



b.Interpretation (43-b) SY

NT

.ST

R.

CO

HER

E

ALI

GN

-Q

FD FAIT

H-V

IS

+ Every(A,B) * *Every(A,B) ∧ Every(B,A) *!

Experiment I thus looks for further support, although from a different per-spective, for the findings of Hollebrandse that children prefer pragmatic cues likediscourse context to syntactic structure. In addition, it would also present furtherevidence for the hypothesis that the acquisition of quantification is a matter ofestablishing a target-like equilibrium between syntax, semantics and pragmatics.

6.5.1.1 Method

Participants Twenty-six Dutch speaking children were tested at a local elementaryschool in Groningen, The Netherlands. From this group three children wereexcluded from further analysis because they incorrectly answered more than four ofsix control items, strongly suggesting they were not paying attention during the task.The twenty-three children remaining (12 boys and 11 girls) ranged in age from 4;2 to6;7 (mean age 5;9). As a control group, twenty-five adult native speakers of Dutchwere tested. They were all undergraduate students at the University of Groningen,The Netherlands.

Materials The test had a 2x2 design plus six control items (three control yes-itemsand three control no-items). The Discourse Condition consisted of six extra-objectstories with a discourse and the Single Sentence Condition consisted of six extra-object items without a discourse (and only one picture). The Single Sentencecondition was used to identify children that give exhaustive pairing answers. Theitems with a discourse were accompanied by five pictures. Each story was abouttwo sets of entities, rather than one as in Drozd and Van Loosbroek (2006) andHollebrandse (2004). The introduction did not mention one set more often thananother. It also did not consider an alternative outcome to the test item as in Crainet al.’s (1996) experiment (i.e. the Condition of Plausible Dissent was not satisfied).

1. Picture 1 shows one set. The experimenter introduces this set with a bareplural and introduces a second set in a similar way, e.g. Here you see some friesthat John made himself. He is going to give the fries to his friends the elephants.

2. Picture 2 displays the second set. The experimenter introduces this set with“the N” and the first set is mentioned again, e.g. Here you see the elephants. Theyreally like fries!

3. Picture 3 displays an event, marking one of the members of the first set as anoutlier, e.g. Oeps! One bag of fries slips out of John’s hands.


4. Picture 4 shows an extra-object situation, similar to the extra-object itemswithout a discourse. The experimenter tells what happens, e.g. John gives thefries to the elephants!

5. Picture 5 shows a neutral picture; the experimenter points out that this is theend of the story and without mentioning one of the two sets or using thepredicate of the test item, e.g. And now, there is no food left.

All test sentences were similar in syntactic structure and contained a transitivesentence and quantification over the subject as in (46). An example of a set ofpictures that accompanied the test items (in this case (46)) is displayed in figure 6.1.

(46) AlleAll

olifantenelephants

eteneat

eena

patatjefry

‘All elephants are eating french fries’

Figure 6.1: Example test item for Alle olifanten eten een patatje ’All elephants areeating chips’

Procedure In the Discourse Condition, the pictures appeared one after anotheron a row in the middle of the screen. After the fifth picture, the puppet commentedon what he thought had happened (the test sentence) while all pictures remainedvisible. In a similar way, the puppet described the extra-object picture while thepicture remained visible in the Single Sentence Condition. The experimenter thenasked the child whether the puppet was right or not and to explain her answer. Allpictures were displayed on a laptop screen by means of Microsoft Powerpoint 2003.

Children were brought individually from their class to a room by the mainexperimenter and the child sat in front of the test screen next to the main experi-menter. The child was told by a puppet that the computer had been built by theexperimenter, but that the puppet believed that the computer was built the wrongway. The puppet then commented on each picture displayed on the screen. Foreach item, the experimenter asked the child whether the puppet was right or notand to explain her answer. The experimenter noted down the child’s answer and,additionally, the child’s response was audio recorded.


6.5.1.2 Results

Children A t-test comparing the distribution of yes-answers for the Single Sentenceand the Discourse Condition reveals a significant difference between the SingleSentence Condition (mean 47.83%, S.D. = 40.30%) and the Discourse Condition(mean 73.91%, S.D. = 28.35%) (t(22) = 3.896, p < .001). However, the large standarddeviations indiciate that there is a lot of variance in the mean given yes-answersbetween children. In figure 1, a boxplot shows the variance of the yes-answers inpercentages for both the Single Sentence Condition and the Discourse Condition.Taking a closer look at individual answer patterns, the results show that, in theSingle Sentence Condition, ten out of the twenty-three children answered in morethan four out of six cases “no, not that one” or gave an answer similar to that. I labelthese children as spreaders and distinguish them from the remaining 13 non-spreaders;children who gave in three or less than three out of six cases an exhaustive answer.But do these spreaders restrict the quantifier domain at chance in the DiscourseCondition?

Figure 6.2: Boxplot mean given yes-answers for the Single Sentence Condition andthe Discourse Condition

A comparison between the spreader mean given yes-answers in the Single Sen-tence Condition and the mean given yes-answers in the Discourse Condition turnsout to be significant (see table 6.1 and figure 6.3; 8.33% in the Single SentenceCondition versus 55% in the Discourse Condition; t(9) = -5.056, p = .001). Toput it differently, the spreaders have a guessing strategy in the Discourse Condition(analysis by means of a t-test shows a non-significant difference with at chance per-


formance; t(9) = 0.502, p = 0.627).13 The non-spreaders do not answer differentlyin the Single Sentence Condition than in the Discourse Condition (78.33% versus88.46%; t(12) = -1.477, p = 0.165). No significant differences were found betweenthe mean ages of spreaders and non-spreaders.

Figure 6.3: Mean yes-answers for spreaders, non-spreaders and adults on the SingleSentence and the Discourse Condition.

Adults As predicted, the adults do not answer differently in the Single SentenceCondition (mean yes-percentage 93,33%, S.D. = 14.43) than in the DiscourseCondition (mean yes-percentage 84,67%; t(24) = 1.915, p = 0.067). The table belowshow the mean yes percentage and standard deviations for children and adults.

Adults versus Children Two one-way ANOVAs were used to determine, percondition, whether children differ from adults. The one-way ANOVAs with groupas independent variable (spreaders, non-spreaders and adults), for the Single SentenceCondition and the Discourse Condition an effect of group was found in both theSingle Sentence Condition (F (2,47) = 89.80, p < .001) and the Discourse Condition

13The large standard deviations in the Discourse Condition for the spreaders, however, indicate againthat that there is a lot of variance in the answers of the children. This is partly due to two children,who continue giving exhaustive pairing answers in the Discourse Condition. However, leaving these tochildren out of the analysis, a t-test still shows a non-significant difference from chance performance forthe remaining children in the Discourse Condition (mean yes percentage 66.67%, S.D. 21,82%; t(7) =2.160, p = 0.068).


group Condition Mean S.D.non-spreaders (n=13) Single Sentence 78.21 24.89

Discourse 88.46 14.25spreaders (n = 10) Single Sentence 8.33 8.78

Discourse 55.00 31.48adults (n = 25) Single Sentence 93.33 14.43

Discourse 84.67 18.58

Table 6.1: Mean yes-answer for spreaders, non-spreaders and adults in the SingleSentence Condition and the Discourse Condition

(F (2,47) = 8,84 p = .001). Posthoc analyses (t-tests with Bonferroni adjustments)shows that the difference lies between adults and spreaders and adults and non-adultsin the Single Sentence Condition (p < 0.001 and p = 0.039), but only betweenadults and spreaders in the Discourse Condition (p = 0.001).

In sum, the children who gave a non-target-like answer in the Single SentenceCondition showed a guessing strategy to determine the quantifier’s domain in theDiscourse Condition. This contrasts with children who gave a target-like answer inthe Single Condition, since these children also answer target-like in the DiscourseCondition.

6.5.1.3 Discussion

Experiment 1 tested the hypothesis that for children, SYNTACTIC STRUCTUREis ranked below ALIGN-Q. This hypothesis was tested by providing a discoursewhich preceded the quantified sentence, which contained two discourse topics. Forchildren who behave non-target-like at the classical Single Sentence Condition, atchance behavior was predicted in such a Discourse condition with two topics.

The results from the Single Sentence Condition confirm earlier findings thatchildren violate SYNTACTIC STRUCTURE. Second, the results show that thesechildren answered at chance in a Discourse Condition in which the quantifier’sfirst and second argument set were discourse topics. This confirms the hypothesisthat children indeed consider two interpretations of a quantified sentence; an adultreading and a non-adult-like, exhaustive pairing reading. Since they take satisfactionof ALIGN-Q to be more important than SYNTACTIC STRUCTURE, this then results ineither the adult answer yes or no, not that one, depending on the discourse topic theytake to be the one intended by the speaker. In the experiment, I take this to meanthat, for the child, this specific discourse turns the quantifier into an ambiguous one;the child assigns either an adult interpretation to it or a non-adult-like, exhaustiveinterpretation. This is exactly what follows from the hypothesis that children rankSYNTACTIC STRUCTURE below ALIGN-Q, disambiguate the test item by means of


Align-Q and randomly select the quantifier’s first or second argument set as thediscourse topic.

6.5.2 Experiment II: Forward Directionality and the DiscourseContext

The second experiment tests whether children use FORWARD DIRECTIONALITY.Are children able to restrict a quantifier domain by means of this constraint whenthe syntax does not provide sufficient information? Drozd and Van Loosbroek (2006)account for children’s adult-like interpretations of quantified sentences in a discourseby pointing at the explicit activation of the quantifier’s domain in the precedingdiscourse. This presupposes that children are able to distill this information fromthe discourse. This second experiment continues along these lines and addresses thequestion whether children are also able to restrict the quantifier domain to a certainsubset introduced previously in the discourse, given the hypothesized child ranking:

(47) Hypothesis 2:Children rank FORWARD DIRECTIONALITY higher than SYNTACTIC STRUC-TURE

What does the ranking in (47) predict for children’s interpretation of (48)? Considerits possible interpretations in (48-a) and (48-b).

(48) Mary bought ten fish and went home. All the fish are now swimming in afishbowla. ‘All fish that Mary has at home are swimming in a fishbowl’b. ‘All fish that Mary bought are swimming in a fishbowl’

In (48-b), the set of fish is restricted to the fish Mary bought. Syntactic Structure isviolated since the quantifier domain is more than the N’. Forward Directionality ishowever satisfied, since the quantifier domain intersects with the discourse topic.Note that the first interpretation (48-a) violates Forward Directionality. This con-straint thus turns out to be a crucial one to interpret (48) correctly and despite ofthe non-adult ranking of Forward Directionality above Syntactic Structure childrenare predicted to interpret (48) target-like as (48-b). This is illustrated in (49) (childranking) and (50) (adult ranking):

(49) Child ranking:

Example (48) CO

HER

E

ALI

GN

-Q

FD FAIT

H-V

IS

SYN

T.S

TR.

(48-a) *! *+ (48-b) *


(50) Adult ranking:

Example (48) SYN

T.S

TR.

CO

HER

E

ALI

GN

-Q

FD FAIT

H-V

IS

(48-a) * *!+ (48-b) *

To test whether this prediction is born out, the present experiment is set up in sucha way that, for example in the case of (48), the different interpretations result indifferent truth values. By doing so, we will be able to know whether children indeedare able to restrict a quantifier by means of context despite their non-adult rankingof the relevant constraints (Forward Directionality versus Syntactic Structure).

Note that children’s target-like use of Forward Directionality becomes especiallyrelevant when the so-called over-exhaustive answers are taken into account. In theliterature (among others Philip, 1995), it has been reported that children answeraffirmative to the question Are all cowboys riding a horse. From the perspective ofthe OT account proposed above, these children do not seem to grasp the notion ofForward Directionality and restrict the quantifier domain to a set the speaker hasnot in mind (i.e the set that makes the sentence true). To control for these answersin the next experiment, children are also tested on such Extra Subjects items tocheck whether they not only violate Forward Directionality in these particular casesbut also for discourse context as (48).

6.5.2.1 Method

Participants Twenty Dutch speaking children from a local elementary school inGroningen, The Netherlands, were tested. From this group four children answeredtwo or more control items incorrectly. Taking this again (similarly as in ExperimentI) to suggest that these children were not paying attention or did not understandthe task, I excluded these four children from further analysis. The sixteen childrenremaining (10 boys and 6 girls) ranged in age from 4;1 to 5;11 (mean age 5;2). Asa control group, the same 25 adults that were tested in the first experiment weretested.

Materials The participants were asked to interpret 12 stories, plus 6 Extra Subjectitems and 6 control items (3 control yes-items and 3 control no-items). An exampleof an Extra Subject item and a control item can be found in respectively (51-a) and(51-b). All test sentences in the stories were intransitive and had a quantified subjectas in (52).


(51) a. AlleAll

cowboyscowboys

rijdenare

opriding

eenat

paarda horse

‘All cowboys are riding a horse’b. Alle

Allapenmonkeys

slapensleep

‘All monkeys are sleeping’

The Extra Subject items displayed a situation in which three cowboys are riding ahorse and a fourth cowboy is not. The stories were accompanied by five pictures.At the third picture, the experimenter always wondered whether the same thingwould happen to the set he just introduced than had happened to the first set (i.e.the Condition of Plausible Dissent was satisfied). The experimenter then continuedthat something else happened to this second set and explained why. The storiespresent two subsets of similar entities (e.g. fish) and an action that happens to one ofthe subsets. We varied when in the story the targeted subset is mentioned as the firstor last subset. In the Subset-First condition, the experimenter referred to the firstmentioned subset which happens with the second picture in a series of five picturesthat accompanied the story. An example of such a (translated) story and the picturesshown to the child can be found in (52) and figure 6.4.

(52) 1.The introduction of a set; Mary went to the pet shop. She bought a bagwith new fish.

2.Something happens to the set just introduced; On her way home, shethinks sitting in bag is not nice for the fish. She throws them in a canal, sonow they are free and can swim.

3.The introduction of another set; At home, Mary has a fish bowl with fishin it. An orange and a blue one. Mary considers setting them free.

4.Something that happened to the second set just introduced; But itmight be too cold for the fish in a canal. The fish are hungry, look, Mary isfeeding them.

5.A neutral picture; And now, Mary is going to play outside.6.Experimenter: All fish are swimming in a canal

-

Figure 6.4: Example subset-first Condition; Alle vissen zwemmen in een sloot ‘Allfish are swimming in a canal’ - targeting a no-answer for adults according to theinterpretation All fish that Maria has at home are swimming in a canal


In the Subset-Last condition (six items), the experimenter referred to the actionmentioned with the fourth picture in the series of five pictures:

(53) 1.The introduction of a set; John went to the flower shop. He holds ayellow and a red flower.

2.Something happens to the set just introduced; On his way home, he seeshis girlfriend. He gives Mary the flowers.

3.The introduction of another set; At home, John has a bunch of redflowers. Will he give these to Mary as well?

4.Something that happened to the second set just introduced; No, Johnputs these flowers into a vase. That looks beautiful.

5.A neutral picture; John loves flowers.6.Experimenter: All flowers are in a vase

Figure 6.5: Example subset-last condition; Alle bloemen staan in een vaas ‘All flowersare in a vase’ - targeting a yes-answer for adults according to the interpretation Allflowers that John has in a vase at home are in a vase

For adults, satisfying Forward Directionality in the Subset-First condition resultsin a no-answer and satisfying Forward Directionality in the Subset-Last conditionresults in a yes-answer. For example, for (52) and 6.4 (a subset-first item in whichthe experimenter referred to the action mentioned in the second picture in figure6.4), the interpretation arises that all fish that Mary has at home are swimming in afish bowl and not in a canal. This is not true in the story, hence a no-answer. In theSubset-Last condition, satisfying Forward Directionality results in a yes-answer. For(52) and figure 6.5, for example, the Dutch testitem Alle bloemen staan in een vaas‘All flowers are in a vase’ targets a yes-answer for adults since indeed All flowers thatJohn has in a vase at home are in a vase.

Procedure In a similar way as in experiment I, all pictures were displayed on alaptop screen by means of Powerpoint. Children were brought individually fromtheir class to a room and sat in front of the screen next to the main experimenter. Thechild was told by a puppet that the computer had been built by the experimenter, butthat the puppet believed that the computer was built wrong. The pictures appearedone after another on a row in the middle of the screen. After the fifth picture, thepuppet commented on what he thought had happened (the test sentence) while allpictures remained visible. For each item, the experimenter asked the child whether


the puppet was right or not and to explain her answer. The experimenter noteddown the child’s answer and, additionally, the child’s response was audio recorded.

For the Extra Subject items and the control items, only one picture was shownto the child. In the same manner as with the Subset-First items and the Subset-Lastitems, the puppet commented on what he thought happened at the picture and theexperimenter asked the child whether the puppet was right or not and to explainher answer.

To control for an effect of the order in which the items were displayed, half of thechildren were first presented all six Subset-First stories and then all six Subset-Laststories and the other half of the children were first presented 6 Subset-Last storiesand then 6 Subset-First stories. In both lists, the Extra Subject items and controlitems were mixed in with the Subset-First and the Subset-Last items.

6.5.2.2 Results

Children The children give a yes-answer for the Extra Subject trials in 15.62%of the cases. This percentage is mainly due to two children who accepted 6 out of6 times and two children who accepted one out of six possible times a quantifiedsentence like All cowboys are riding a horse. Maintaining a similar criterion as inExperiment I, I label the two children who gave such an answer in more than 5 outof 6 times under-exhaustive children. However, these two children did not answersignificantly different from the other children in the Subset-First and Subset-Lastcondition (a chi-square analysis shows that there is no significant difference betweenthe answers of these two children and the other children; χ2(1) = 2.636, p = 0.104).Therefore, in the analysis, the results of the children giving non-exhaustive answersand the other children are collapsed. This results in a mean yes answer of 30.21% inthe Subset-First condition and 58.33% in the Subset-Last condition. This differenceturns out to be significant (t(15) = -3.878, p = .001).

An additional effect was found of the order in which the items were presented.If the child is first asked to look at the Subset-First items and then to the Subset-Lastitems, the child accepts the quantified sentence in respectively 70.83% versus 25% ofthe cases (t(7) = -5.60, p = .001). The difference disappears if the child is asked tofirst look at the Subset-Last items and then to the Subset-First items (t(7) = -1.26, p= .25).

Adults The adults answer significantly more often yes on the Subset-Last condition(25.33%) compared to the Subset-First task (2%; t(24) = -3.055, p = 0.005). Table 6.2summarizes the main findings for adults and children.

Adults versus Children Comparing adults with children, a one-way ANOVAshows that there is a significant effect of group for both the Subset-First condition(F (1,40) = 16.249, p < 0.001) and the Subset-Last Condition (F (1,40) = 8.185, p =0.007).


group Condition Mean S.D.children (n=16) Subset-First 30.21 34.54

Subset-Last 58.33 33.33adults (n = 25) Subset-First 2.00 5.53

Subset-Last 25.33 37.61

Table 6.2: Mean percentages yes-answers for children and adults for the Subset-FirstCondition and the Subset-Last condition.

6.5.2.3 Discussion

The current experiment aimed to answer the question whether children rank For-ward Directionality above Syntactic Structure and whether they, despite of thisranking, show target-like behavior. Children were predicted to answer adult-likedespite of this different ranking since no other constraints interfered. To answerthis question, a subtle experiment was set up targeting children’s domain restrictionby means of Forward Directionality. Crucially, the sets Forward Directionalityapplied to were either introduced at the beginning of the story or towards the end,eliciting respectively a quantifier domain that was restricted by the first introducedset (the Subset-First Condition) and a quantifier domain that was restricted by thelast introduced set (the Subset-Last Condition).

The results show that children make a distinction between the Subset-First andthe Subset-Last condition, like adults do. This means that they are sensitive tothe order in which the sets are presented, and that they use this information torestrict the quantifier domain. When the targeted subset is mentioned first, it isnot taken to restrict the quantifier domain whereas when the subset is mentionedlast, this latter set is taken to restrict the quantifier domain. This confirms theprediction that children, despite of their ranking of Syntactic Structure belowForward Directionality, restrict their domain adult-like to the topic range of thedeterminer. In a typical OT tableau, this is shown in (54) and (55) for the Subset-First condition (respectively adult and child ranking) and in (56) and (57) for theSubset-Last condition (respectively adult and child ranking). In both cases, eitherthe first or last subset restricts the quantifier domain. This explains why children,similarly as adults, distinguish the Subset-First from the Subset-Last items.

(54) All fish are swimming in a canala. ‘All fish that Mary has at home are swimming in a canal’: NOb. ‘All fish that Mary bought are swimming in a canal’: YES


(55) a.Example (54) FD SY

NT

.ST

R.

+ (48-a)(48-b) *!

b.Example (54) SY

NT

.ST

R.

FD

+ (48-a)(48-b) *!

(56) All roses are in a vasea. ‘All roses that John has at home are in a vase’: YESb. ‘All roses that John bought are in a vase’: NO

(57) a. Example (56) FD SYN

T.S

TR.

+ (56-a)(56-b) *!

b. Example (56) SYN

T.S

TR.

FD

+ (56-a)(56-b) *!

There is also a difference between children and adults; in general, adults answermore often no. This might be due to the fact that adults consider, next to (58-a) and(58-b), a third reading of a test item like (58), i.e. the interpretation represented in(58-c).

(58) All fish are swimming in a canala. “All fish that Mary has at home are swimming in a canal”b. “All fish that Mary bought are swimming in a canal”c. “All fish in the story are swimming in a canal”

Whereas (58-a) and (58-b) resulted in respectively a no and yes-answer in the experi-


ment (cf. figure 6.4), (58-c) results in a no-answer too. Apparently children do notconsider a no-answer as often as adults. 14

6.6 General discussion and conclusions

The experiments presented in this chapter aimed to answer the question of whenand under which conditions children resort to a discourse-based interpretation ofquantified sentences. I discussed how various acquisition accounts make use ofdifferent discourse characteristics to explain children’s improved performance in adiscourse. Subsequently, I addressed the relation between a quantifier domain anddiscourse from the perspective of (Centering) Optimality Theory and identifiedAlign-Q and Forward Directionality as the crucial constraints in addition to Syntac-tic Structure to interpret a quantified sentence in a discourse. I hypothesized thatchildren allow discourse constraints to play a more important role in interpreting aquantified sentence than the syntactic constraint (i.e. children rank Align-Q andForward Directionality higher than Syntactic Structure). From this perspective,I then investigated the effect of discourse context on children’s interpretation ofquantified sentences in two experiments.

Experiment I zoomed in on children’s understanding of the constraint Align-Qand children were asked to interpret a quantified sentence preceded by a discoursecontaining two discourse topics (DT in (59) below) as represented in (59).

(59) All elephantsDT are eating a fryDT

For children who behave non-target-like for the classical extra-object items (i.e.condition labelled the Single Sentence Condition in Experiment I to distinguishthese items from the discourse items), chance behavior was predicted (these childrenwere labeled as ’spreaders’); children randomly pick the quantifier’s first or secondargument set as the quantifier’s domain. This prediction was born out.

Experiment II zoomed in on children’s understanding of Forward Directionalityas in (60) (preceded by a story which either yielded interpretation (60-a) or (60-b)):

(60) All fish are swimming in a canala. ‘All fish that Mary has at home are swimming in a canal’b. ‘All fish that Mary bought are swimming in a canal’

Despite of the hypothesized non-adult-like ranking of this constraint above SyntacticStructure, target-like behavior was predicted in this experiment because SyntacticStructure was satisfied for all interpretations. This meant that children were pre-dicted to distinguish (60-b) from (60-b) and restrict the quantifier domain respectively

14I leave it for further research whether adults’ interpretations are rather like (58-c) than like (58-a).Crucially, the domain of quantification in (58-a) is a result of applying Forward Directionality, whereas(58-c) clearly is not (since it does not concern the last mentioned set, but rather the superset that functionsas the domain of interpretation in general).

6.6. General discussion and conclusions 141

to the set mentioned in the discourse. The results of the second experiment showedthat children, similarly as adults, distinguish these two discourse contexts and restrictthe quantifier domain target-like.

The results of the two experiments present further evidence for the idea pro-posed in the literature that children use discourse information to restrict a quantifierdomain (Drozd and Van Loosbroek, 2006; Hollebrandse, 2004). Crucially, thepresent findings present experimental evidence for the proposed relation betweenquantifier domain restriction and discourse context. I conclude that, in line withthe Equilibrium Hypothesis introduced in chapter 3 that the acquisition of quan-tification crucially concerns fine-tuning the interaction between syntax, semanticsand syntax. It is this process of fine-tuning which explains children’s non-target-likeanswers, rather than the hypothesis that children have not acquired yet certainlinguistic rules. Moreover, the results in this chapter show that the acquisition stepto an adult way of understanding language lies in restricting the role of pragmatics tosuch an extent that the syntactic structure overrules any discourse based constraintson quantifier domains.

7Summary, Discussion and Conclusions

7.1 Introduction

In the past four decades, children’s non-adult-like understanding of quantified sen-tences has been explained in syntactic, semantic or pragmatic terms (see chapter 2).Recently, it has been suggested that quantification is a matter of taking into accountsyntax, semantics and pragmatics simultaneously rather than applying purely syn-tactic, semantic or pragmatic constraints on meaning. Explanations until now didnot take such an integrated approach. Given the interaction of syntax, semanticsand pragmatics, I explored children’s non-adult-like interpretations of quantifyingexpressions in terms of a developing balance of all these constraints on the meaningof quantified sentences. The starting point for this new approach to the acquisitionof quantification is my Equilibrium Hypothesis presented in chapter 3 that theacquisition of quantification is a matter of establishing a target-like equilibrium be-tween syntax, semantics and pragmatics and each of their contributions to meaning(repeated below as (1)).

(1) Equilibrium Hypothesis:The acquisition of quantification is a matter of establishing a target-likeequilibrium between syntax, semantics and pragmatics and their contributionto meaning

The Equilibrium Hypothesis was tested in chapters 4, 5 and 6, providing the basisfor an empirical investigation of the interplay between these constraints of variousnature in child language.

The experiments discussed in previous chapters aimed on the one hand to gainmore insight into children’s understanding of quantified expressions and, on theother hand, to present experimental data on the interaction between syntax, seman-tics and pragmatics. The starting point for this investigation is the distinction madein chapter 3 between syntactic constraints concerning the scope of quantificationaldeterminers, semantic constraints concerning the relation between the quantifier’sargument sets and pragmatic constraints concerning the effect of discourse context

143

144 Summary, Discussion and Conclusions

and visual context on the scope of the quantificational determiner and the relationbetween the quantifier’s first and second argument set. The experiments presentedin chapter 4, 5 and 6 each differ in their focus on the hypothesized interactionbetween syntax, semantics and pragmatics.

In this final chapter, I discuss the main experimental results and their implicationsfor children’s understanding of quantified expressions. I argue that children usedifferent clues than adults to interpret quantifying expressions. Whereas adults onlyrestrict the quantifier domain by means of discourse or visual context in cases inwhich the syntax does not provide sufficient information to do so, children alwaysuse the (visual) context to restrict a quantifier domain. I conclude that these resultsare compatible with the Equilibrium Hypothesis.

This chapter is structured as follows. In section 7.2, I summarize the mainfindings of this thesis and discuss the results for each grammatical interface (syntax-semantics, semantic-pragmatics and syntax-pragmatics). After discussing the mainimplications of these findings in section 7.3 for the discussion concerning children’sunderstanding of quantifying expressions, I end this chapter with a short summaryof the main conclusions.

7.2 Main findings

Each of the three sets of experiments addressed a different interface between syntax,semantics and pragmatics. Whereas the experiments presented in chapter 4 focusedon children’s understanding of the interaction between syntax and semantics, theexperiments in chapter 5 addressed the interaction between syntax and pragmaticsand chapter 6 focused on the interaction between semantics and pragmatics. Inchapter 4 (experiment 1 - 3), I focused on the interaction between the syntacticstructure of a quantifying expression and the semantic difference between strong andweak quantifiers, in chapter 5 (experiment 4) I focused on the interaction between thesyntactic difference between weak and strong quantifiers and pragmatics (discourse)and in chapter 6 (experiment 5 and 6) I focused on the interaction between thepragmatic discourse and the semantic notion of domain restriction. I will nowsummarize the results of these three sets of experiments.

7.2.1 Allemaal and the syntax-semantics interface

Testing the hypothesis of Roeper et al. (2006) that children do not restrict thequantifier domain to the noun phrase c-commanding the quantificational determiner,chapter 4 set out to explore children’s understanding of the interaction betweensyntax and semantics. I tested children’s interpretation of the Dutch quantifierallemaal which can be used as a floating quantifier or prenominally. The syntaxplays a crucial role to determine which reading is at issue. Therefore, the Dutchquantifier allemaal provided an excellent tool to test children’s understanding of

7.2. Main findings 145

the interaction between syntax and semantics. The central research question wasformulated as follows:

(2) How do children use syntax to determine the meaning of allemaal?

Truth-value judgment tasks examined whether or not children use the syntacticstructure of the sentence to determine the quantifier’s scope (i.e. the subject versusthe object being in the quantifier’s scope, cf. the difference between (3-a) and and(3-b) and (4-a) and (4-b), tested in experiment 1 and experiment 2 respectively)and the relation the quantifier establishes between its first and second argumentset (whereas allemaal gets an exhaustive reading in (5-a), it only allows a weak,existential reading (in the sense of Milsark, 1979) in (5-b), see experiment 3).

(3) a. DeThe

jongensboys

hebbenhave

allemaalallemaal

dethe

kofferssuitcases

vastfixed

‘The boys are all holding the suitcases’b. De

Thejongensboys

hebbenhave

dethe

kofferssuitcases

allemaalallemaal

vastfixed

‘The boys are holding all the suitcases’(4) a. De

Themeisjesgirls

rijdenride

allemaalallemaal

opon

eena

paardhorse

‘The girls are all riding a horse’b. Een

Amanman

draagtcarries

dethe

ezelsdonkeys

allemaalallemaal

‘A man is carrying all the donkeys’(5) a. De

Theezelsdonkeys

huilencry

allemaalallemaal

‘The donkeys are all crying’b. Er

Therehuilencry

allemaalallemaal

ezelsdonkeys

‘There are many donkeys crying’

Children were asked to judge sentences like in (3) - (5) for situations as depicted inrespectively figure 7.1, 7.2 and 7.3.

The experimental data confirm the hypothesis that children do not restrict thequantifier domain by means of the syntactic notion of c-command. Children donot differentiate between sentences with subject and object quantification and showguessing behavior when the visual context contains both an extra object and anextra object as in figure 7.2. Moreover, the children overwhelmingy choose for anexhaustive interpretation of allemaal in an existential there-sentence in the case ofa situation as depicted in figure 7.3, in contrast to adults’ interpretations of suchsentences.

In sum, the research question whether children rely entirely on syntax to deter-mine the meaning of a quantifying expression can be answered negatively; children


Figure 7.1: EXPERIMENT 1 - SUBJECT VERSUS OBJECT SCOPE WITH EXTRA OBJECT;De jongens hebben allemaal de koffers vast ‘The boys are all holding the suitcases’

Figure 7.2: EXPERIMENT 2 - SUBJECT VERSUS OBJECT SCOPE WITH EXTRA SUBJECTAND EXTRA OBJECT; De meisjes rijden allemaal op een paard ‘The girls are all ridinga horse’

Figure 7.3: EXPERIMENT 3 - EXHAUSTIVE VERSUS INTERSECTIVE allemaal; Er huilenallemaal ezels ‘There are crying many donkeys’

use syntax neither to restrict the quantifier domain, nor to determine the relationthe quantifier establishes between its arguments. This presents the first evidencefor the Equilibrium hypothesis that children rank syntactic information differentlythan adults to constrain the meaning of quantifying expressions.


7.2.2 Many and the syntax-pragmatics interface

In chapter 5, I showed that, in the case of many, domain restriction is a pragmaticmatter instead of a syntactic or semantic one; the surrounding discourse contextof a quantified sentence plays an important role in determining the meaning. Theinterpretion of many depends on this discourse context. This becomes especiallyclear in the case of many versus many of ; whether one considers something asmany, depends on the discourse context of this sentence. In some cases, it suffices tounderstand many in terms of a certain cardinality; if there are five parrots, wearing ahat, this might be judged as many (given that they never wear a hat). In other cases,many should be understood as the partitive ‘many of’ as in Many students got anA (meaning ‘many of the students in my class got a A’). The interaction betweenpragmatics and the syntactic structure of a sentence containing many determinesthe domain of these quantifiers. To what extent do children master this interactionbetween pragmatics and the syntactic structure of a quantified sentence?

(6) Research question: How do children use pragmatics to restrict a context-dependent quantifier domain?

The interaction between syntax and pragmatics was examined by investigatingEnglish learners’ usage of discourse context (introduction of a certain set as discoursetopic) and visual context (a pointing gesture to that set) for the interpretation ofmany versus many of. The syntactic difference between many and the partitive manyof was used to control for children’s usage of syntactic information to restrict aquantifier domain. In addition to a truth value judgment, I asked children to explainwhy they judged sentences like (7) true or false. The pictures shown to the childrenallowed both a cardinal reading (7-a), a proportional reading (7-b) and the so-calledWesterståhl reading (7-c). The pragmatic context needed to be used to determinewhich reading was intended; the attention was pointed toward the denotation ofthe quantifier’s first or its second argument. For adults, this resulted in respectivelya proportional or cardinal interpretation and a Westerståhl reading. For many of,no such effects were found for adults with the quantifier’s first argument set asdiscourse topic, but an effect was found with the quantifier’s second argument set asthe discourse topic (i.e. a Westerståhl reading).

(7) Many parrots are wearing hatsa. ‘5 parrots are wearing hats’ (cardinal reading)b. ‘many of the parrots are wearing hats’ (proportional reading)c. ‘Many parrots that are relevant to wearing a hat are parrots’ (Westerståhl

reading)

(8) Many of the parrots are wearing hatsa. *‘5 parrots are wearing hats’ (cardinal reading)b. ‘many of the parrots are wearing hats’ (proportional reading)


c. ‘Many parrots that are relevant to wearing a hat are parrots’ (Westerståhlreading)

Figure 7.4: EXPERIMENT 4 - THE MANY EXPERIMENT; Many/Many of the parrotsare wearing hats

The results of experiment 4 show that children are capable of carrying out allthree kinds of set comparisons, i.e. they give cardinal readings, proportional readingsand Westerståhl readings. Children sometimes allowed cardinal reading when such areading is not allowed (e.g. in the case of many of and when the quantified sentencewas preceded by a discourse in which the quantifier’s second argument set wasalready mentioned). Children’s answers were not affected by quantifier type (manyvs. many of ) or pragmatic context (a discourse about the quantifier’s first or secondargument set).

The findings of experiment 4 add a new perspective to the discussion of the exactnature of children’s understanding of quantified sentences. The results show thatit is not a more restricted set of readings that children allow - on the contrary, thechildren had the same three kinds of readings as adults - but rather how pragmaticslimits (in a different way than for adults) when to accept these readings. This explainsthe finding that children allow the same readings for many and many of.

7.2.3 The universal quantifier and the pragmatics-semantics interface

Traditionally (see chapter 2), syntax is taken to prescribe the quantifier’s first ar-gument set. However, in the case of (9-a), in addition to the syntax, the discoursecontext of (9-b) is needed to restrict the quantifier domain of all in (9-a) to the fishMary has at home (whereas the syntax only restricts the domain of all to the set offish).


(9) a. Mary went to the pet shop. She bought a bag with new fish. On herway home, she thinks it is not nice for the fish to be in the bag. Shethrows them in a canal, so now they are free and can swim. At home,Mary has a fish bowl with fish in it. An orange and a blue one. Maryconsiders letting them free. But it might be too cold for the fish in acanal. The fish are hungry, look, Mary feeds them. And now, Mary isgoing to play outside.

b. All fish are swimming in a canal

This raises the following research question, subject of the experiments presented inchapter 6:

(10) Research question: How do children integrate the discourse context intothe interpretation of a quantifying expression?

The experiments presented in chapter 6 aimed to answer the question when and un-der which conditions children allow a ‘discourse-based interpretation’ of quantifiedsentences. I discussed how various accounts in the literature point at a different char-acteristics of discourse to explain children’s improved performance with quantifiersin a discourse. Subsequently, I rephrased the discussion in the literature in terms ofthe interaction between pragmatic and syntactic constraints. From this perspective,I investigated the effect of discourse context on quantifier domains in adult and childlanguage. Children were tested on their reistriction of the domain of all in the extraobject situation preceded by a discourse and the series of pictures depicted in figure7.5 and for sentences like (9) accompanied by the series of pictures in figure 7.6.

(11) a. Here you see a bag of fries that John made himself. He is going to givethe fries to his friends the elephants. Here you see the elephants. Theyreally like fries! Oops! A bag of fries slips out of John’s hands. Johngives the fries to the elephants! And now, there is no food left.

b. All elephants are eating chips

Figure 7.5: EXPERIMENT 5 - THE FRY CONTEXT EXPERIMENT; Alle olifanten eteneen patatje ‘All elephants are eating chips’

The results of these two experiments showed that children’s understanding ofquantified sentences interacts with the introduction of two discourse topics in thecontext preceding the quantified sentence. When children are asked to judge an


Figure 7.6: EXPERIMENT 6 - THE FISH CONTEXT EXPERIMENT; Alle vissen zwem-men in een sloot ‘All fish are swimming in a canal’

extra-object situation as true or false (see figure 7.5 and the test-sentence) whenthis situation is preceded by the introduction of two discourse topics, this resultsin chance behavior; when both argument sets are made salient in the previousdiscourse, children randomly use one of the two sets introduced in the discourse asthe quantifier domain (whereas the discourse does not affect adults’ interpetations).Crucially, the results of experiment 6 show that, when no extra object is depicted (i.e.the picture is visually faithful to the syntactic structure), children show adult-likebehavior and integrate the discourse in a target-like way. I account for these resultsby using Beaver’s (2004) Centering Optimality Theory, integrating the possibleeffects of the visual context into this framework (see chapter 6). These resultspresent further evidence that children’s non-adult-like interpretations of quantifiedsentences do not stem from an incomplete grammatical system (i.e. not havingacquired certain linguistics or pragmatic rules), but rather from ranking the relevantconstraints on the meaning of quantified sentences in a non-adult way. This explainsthe findings of experiment 5 and 6.

7.3 Discussion and implications

Each of the experiments presented in this thesis focused on a different interplaybetween syntax, semantics and pragmatics. Whereas adults use information fromthe discourse context if there is not sufficient syntactic information to determinethe meaning of a quantified sentence, the results show that children between fourand six years of age rank the relevant syntactic, semantic and pragmatic constraintsin a different way. How can we define this developmental stage in more detail?In chapter 3, I identified Optimality Theoretic (OT) semantics (Hendriks and DeHoop, 2001) as an ideal framework to do.

In OT semantics, interpretation is considered to be an optimization processwith respect to a certain syntactic input. The constraints against which all possibleinterpretations are evaluated can be syntactic, semantic or pragmatic in nature. Thismeans that it is possible to model how lexical material, syntactic structure andcontext play a role in the optimization process from form to meaning. Note thatsuch an approach takes a completely different view on compositionality; it crucially

7.4. Conclusions 151

allows interaction between constraints of various nature. This differs from theclassical view on compositionality, i.e. the view that the meaning of an expressionis a function of the meaning of its parts and of the syntactic rule by which theyare combined. In chapter 3, I concluded that the complex nature of quantifiers canonly be accounted for if a constraint-based approach is taken. Moreover, my studyof the acquisition of quantification points into a similar direction to account forthe various effects of (visual and discourse) context on children’s interpretations ofquantified sentences (cf. chapter 2).1

In sum, the results showed that adults rank these constraints differently thanchildren. Whereas adults only use visual information when there are no other cluesto restrict a quantifier domain or when this visual clue is very prominent, childrenbetween four and six always use this visual information to interpret a quantifiedsentence. This explains the results in chapter 4 that children’s understanding ofquantified sentences interacts with the presence of an extra object or extra subjectitem in the picture and also the results in chapter 6 that a child’s interpretationinteracts with the introduction of two discourse topics in the context precedingthe quantified sentence. Moreover, these latter results show that children use thediscourse context, and not syntax, to restrict a quantifier domain (and even startguessing when the discourse provides two possible quantifier domains). This leadsto the following conclusions (‘»’ should be understood as ‘is preferred above’):

(12) Adult ranking:Syntax » Discourse Context » Visual Context

(13) Child ranking:Visual Context » Discourse Context » Syntax

The present thesis adds a new perspective to the current body of literature on theacquisition of quantification. In particular, whereas previous work always focusedon one particular aspect of quantification (the syntactic structure of the quantifiedsentences, the discourse or visual context), this thesis aimed to take all these aspectsinto account simultaneously. In this respect, the main conclusions of this thesis arenot opposite to those that were drawn earlier by various other people. Rather, thisthesis tries to reconcile the various conclusions made in the literature and encouragesto explore the Equilibrium Hypothesis in more detail.

7.4 Conclusions

The results presented in this thesis underline that more insight can be gained into thecourse of language development when multiple factors that are relevant to assigningmeaning to linguistic structures are taken into account. For quantified sentences,

1With respect to the effect of visual context on children’s interpretations of quantified sentences,Rahklin (2004) points into a similar direction and argues that children indeed use the visual contextdifferently than adults do.


this means that both syntax, semantics and pragmatics have to be taken into account.Instead of focusing on either the syntactic, semantic or pragmatic constraints thatare at play when one (adult or child) is asked to interpret a sentence, a more dynamicapproach is needed that incorporates all factors that determine interpretation. In thisthesis, I took such an approach by using the framework of (Centering) OptimalityTheory, following recent work by Hendriks and De Hoop (2001) and Beaver (2004).Moreover, by taking the alternative view on compositionality of De Hoop et al.(2007) as a starting point, the present thesis explored an alternative approach to theacquisition of quantification. I showed that acquiring quantification is neither a caseof ‘lacking’ certain grammatical rules nor a case of just the ‘wrong’ experimentalsetup that elicits a non-target-like answer. Instead, I presented experimental datashowing that the acquisition of quantification is a matter of establishing a target-likeequilibrium between syntax, semantics and pragmatics.

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Nederlandse samenvatting

Kwantoren als alle, veel en allemaal stellen de taalgebruiker in staat te generaliserenen naar verzamelingen van entiteiten te verwijzen. Zo wordt alle in (1) bijvoorbeeldgebruikt om uit te drukken dat alle cowboys op een paard rijden. Anders gezegd,met behulp van alle kunnen we de eigenschap dat cowboys op een paard rijden aande gehele verzameling van cowboys toewijzen.

(1) Alle cowboys rijden op een paard.

Alle talen delen de eigenschap dat ze de taalgebruiker in staat stellen te kwantificeren.Het verwerven van kwantificatie stelt de taalleerder echter voor een moeilijke opgave.Hoe en op welke leeftijd combineert een kind het principe van een verzameling,de mogelijkheid om daar naar te verwijzen en te redeneren over de relatie tussenverzamelingen (bijvoorbeeld of alle cowboys inderdaad allemaal op een paard rijdenof dat er één cowboy is die geen paard berijdt)?

De complexe aard van kwantificatie verklaart waarom het verwerven van kwan-tificatie in de afgelopen decennia in verschillende disciplines is bestudeerd. Meerdereonderzoeken tonen aan dat kinderen in de leeftijdscategorie van vier tot zes jaarzinnen met een kwantor anders interpreteren dan volwassenen. In de literatuuris dit fenomeen op verschillende manieren verklaard, waarbij wordt gewezen opof de syntactische of de semantische of de pragmatische eigenschappen van kwan-toren die moeilijkheden voor kinderen zouden opleveren. Dit onderzoek raaktein een impasse toen enerzijds werd aangetoond dat de experimentele setup van degebruikte experimenten een verklaring voor de niet-volwassen antwoorden zouzijn en kinderen helemaal geen problemen met kwantificatie hebben en anderzijdsander onderzoek opnieuw bewijs leverde voor de eerste bevindingen van Inhelderen Piaget (1959) dat kinderen wel degelijk gekwantificeerde zinnen anders inter-preteren dan volwassen. Dit onderstreept de noodzaak om meer gedetailleerd dande afgelopen decennia is gedaan te verkennen onder welke condities kinderen nuprecies wel en niet gekwantificeerde zinnen volwassen interpreteren. Daarnaastgeeft recent theoretisch onderzoek aanleiding tot gedetailleerder onderzoek naarde verwerving van kwantificatie te kijken. Hendriks en De Hoop (2001) conclu-deren dat een volwassen interpretatie van een gekwantificeerde zin een complexsamenspel is van syntactische, semantische en pragmatische regels (constraints). Waar

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166 Nederlandse samenvatting

traditioneel gekwantificeerde zinnen altijd werden beschreven in termen van hunkwantificationele domein en bereik (respectievelijk cowboys en rijden op een paard in(1)), laat ander onderzoek bovendien zien dat ook de visuele context en de discoursecontext van grote invloed kunnen zijn op het domein van de kwantor. Juist dezepragmatische informatie verrijkt de betekenis van een gekwantificeerde zin en on-derstreept daarmee de mogelijke rol die deze pragmatische informatie kan spelen inde verwerving van kwantificatie. In dit proefschrift neem ik deze interactie tussensyntaxis, semantiek en pragmatiek als uitgangspunt om een antwoord te vinden opde vraag hoe kinderen deze syntactische, semantische en pragmatische aspecten vankwantificatie nu precies verwerven en wanneer zij welke regel toepassen.

Dit proefschrift toont aan dat het verwerven van kwantificatie een kwestie isvan het vinden van een volwassen evenwicht tussen de rollen die syntaxis, semantieken pragmatiek spelen in de betekenisgeving aan een gekwantificeerde uitdrukking.Data van zes experimenten laten zien dat kinderen in specifieke contexten een andergewicht toekennen aan het gebruik van syntactische, semantische en pragmatischeprincipes dan volwassenen. Waar volwassenen alleen syntactische principes gebrui-ken om te bepalen waarover bijvoorbeeld in (1) precies gekwantificeerd wordt, latenkinderen pragmatische informatie een rol spelen in het toekennen van een betekenisaan (1). Het gebruik van dergelijke pragmatische informatie is volwassenen nietvreemd, betoog ik, maar voor volwassenen is deze informatie alleen bepalend voorde betekenis van een gekwantificeerde zin als de syntaxis onvoldoende informatielevert. Het is een noodzakelijke voorwaarde voor een volwassen begrip van ge-kwantificeerde zinnen dat kinderen leren welk gewicht in welke context zij aansyntactische, semantische en pragmatiche principes moeten toekennen.

In hoofdstuk 2 ga ik in op twee aspecten van kwantificatie en schets ik hoe beideaspecten in de literatuur over de verwerving van kwantificatie sinds het werk vanInhelder en Piaget (1959) een belangrijke rol hebben gespeeld. Enerzijds wordenkwantoren er door gekenmerkt dat zij twee verzamelingen aan elkaar relateren.Anderzijds verschillen kwantoren in de manier waarop zij verzamelingen aan elkaarrelateren. Waar in het eerste geval het verschil tussen het domein en het bereik(respectievelijk cowboys en individuen die op een paard rijden in (1)) een belangrijkerol speelt, speelt in het laatste geval het verschil tussen sterke of universele en zwakkeof existentiële kwantoren (Milsark, 1979) een belangrijke rol. Sterke kwantorenzoals alle dingen af dat de restrictor een deelverzameling is van het bereik (dat wilzeggen dat de verzameling cowboys een deelverzameling is van alle individuen dieop een paard rijden en er dus geen cowboys zijn die niet op een paard rijden), terwijlzwakke kwantoren zoals enkele slechts afdwingen dat de doorsnede van de restrictoren het bereik niet leeg is. Beide eigenschappen van kwantoren hebben een belang-rijke rol gespeeld in de literatuur over de verwerving van kwantoren. Ik concludeerin hoofdstuk 2 dat er echter geen concensus in de literatuur is over waarom dezeeigenschappen van kwantificatie nu precies aanleiding zijn voor kinderen om zinnenals (1) anders te interpreteren dan volwassenen.


In het eerste gedeelte van hoofdstuk 3 wijs ik op de belangrijke rol die de prag-matiek speelt in het bepalen van het domein van de kwantor, aanvullend op hetgeende syntaxis en semantiek van een gekwantificeerde zin hierover zeggen (zoals beschre-ven in hoofdstuk 2). Zo wordt het domein van allemaal in (2) niet alleen bepaalddoor de syntactische structuur, maar met name door de voorafgaande discourse.Dit verklaart waarom (2) niet de interpretatie toestaat dat Billy op dat moment allepaarden in de wereld te eten geeft.

(2) Cowboy Billy heeft vier paarden. Hij geeft de paarden vandaag allemaal watextra te eten.

Ik betoog in hoofdstuk 3 bovendien dat op vergelijkbare wijze als met behulp vande discourse context het domein van een kwantor in bepaalde situaties kan wordenbepaald aan de hand van de visuele context.

Dit is aanleiding voor het opstellen van mijn Equilibrium Hypothese: het ver-werven van kwantificatie is een kwestie van een volwassen evenwicht vinden tussensyntactische, semantische en pragmatische constraints en hun bijdrage aan de betekenisvan gekwantificeerde zinnen. Het verwerven van kwantificatie omvat het uiteenra-felen van welke contraints op welk moment een rol spelen bij het toekennen vaneen betekenis aan een gekwantificeerde zin. Ik formuleer deze hypothese vervol-gens in het framework van Optimality Theoretic semantics (Hendriks en De Hoop,2001). Aan het einde van hoofdstuk 3 beschrijf ik hoe dit leidt tot de volgende drieonderzoeksvragen.

1. Hoe gebruiken kinderen syntactische informatie op het moment dat de visueleinformatie tegenstrijdig is met de syntactische informatie over het domein vande kwantor?

2. Hoe gebruiken kinderen de pragmatiek om het domein van een context-afhankelijke kwantor te bepalen?

3. Hoe integreren kinderen de discourse context bij het bepalen van de betekenisvan een gekwantificeerde zin?

Deze drie onderzoeksvragen zijn onderliggend aan een zestal experimenten die inde rest van het proefschrift aan de orde komen.

In hoofdstuk 4 onderzoek ik met behulp van drie experimenten het begrip van kin-deren van de kwantor allemaal. Al naar gelang de syntactische positie van allemaal,heeft deze kwantor een andere betekenis; een prenominaal gebruik van allemaal ineen existentiële zin kan alleen de betekenis van veel krijgen, waar een zogenaamd‘zwevend’ allemaal alleen een uitputtende lezing (in de zin van ‘alle’) kan krijgen.Gegeven de conclusie van Roeper et al. (2006) dat kinderen het domein van deEngelse kwantor all (‘alle’) niet beperken tot de nominale phrase die de kwantor


c-commandeert, richt dit hoofdstuk zich op de vraag of kinderen dan ook geensyntactische informatie gebruiken om te bepalen wat het domein van allemaal is.Maken kinderen geen onderscheid tussen prenominaal en ‘zwevend’ allemaal, en ookniet tussen allemaal dat kwantificeert over het subject en allemaal dat kwantificeertover het object? De resultaten van drie experimenten met kinderen van 4;0 tot 6;7jaar laten zien dat dit inderdaad het geval is; de kinderen maken geen onderscheidtussen zinnen met kwantificatie over het object en subject, noch kiezen ze vooreen uitputtende lezing van allemaal in een existentiële zin. Deze resultaten zijn heteerste bewijs dat kinderen de syntaxis een andere rol toebedelen dan volwassenen eneen belangrijke rol toekennen aan de visuele informatie bij de betekenisgeving aankwantoren.

In hoofdstuk 5 toon ik aan dat de betekenis van het Engelse many (‘veel’) in hogemate wordt bepaald door de context waarin deze kwantor wordt gebruikt; hetdomein van de kwantor is context-afhankelijk. In sommige gevallen volstaat hetbijvoorbeeld om many in termen van cardinaliteit te begrijpen; wanneer er sprakeis van vijf papagaaien die een hoed op hebben, zal een volwassene eerder geneigdzijn om te zeggen dat er in dat geval veel (many) papegaaien een hoed op hebben,gegeven het feit dat papegaaien nooit een hoed op hebben. In andere gevallen heeftmany de proportionele betekenis ‘veel van de’. Denk bijvoorbeeld aan een situatiewaarin een docent zegt dat veel (many) van de studenten een 10 hadden voor hettentamen. In dat geval moet veel (many) als ‘veel van de studenten die de docent lesgeeft’ worden begrepen. In bepaalde contexten kan many nog een andere betekeniskrijgen, zoals Westerståhl (1989) voor het eerst beschrijft. Zo kan (3) betekenendat ‘veel van de winnaars die ooit de Nobelprijs in literatuur hebben gewonnen,Scandinavisch zijn’. Strikt genomen betekent deze zin echter iets anders, namelijkdat veel van de Scandinaviërs de Nobelprijs in literatuur hebben gewonnen. Tochbeoordelen veel mensen (3) als waar wat aangeeft dat men inderdaad ervan uit gaatdat degene die (3) uitspreekt kwantificeert over de Nobelprijswinnaars en niet overde Scandinaviërs.

(3) ManyVeel

ScandinaviansScandinaviërs

havehebben

wongewonnen

thede

NobelNobel

priceprijs

inin

literatureliteratuur

‘Veel van de winnaars die ooit de Nobelprijs in literatuur hebben gewonnenzijn Scandinaviër’

In het verlengde van deze drie lezingen van many, richt het experiment dat inhoofdstuk 5 wordt beschreven zich op de vraag hoe kinderen deze pragmatischeinformatie gebruiken om de context-afhankelijke betekenis van many te bepalen. Ditwordt afgezet tegen hun gebruik van syntactische informatie om te bepalen dat manyof (‘veel van de’) door diens partitieve constructie altijd alleen een proportionelelezing afdwingt.

Naast een truth-value judgment task, werd aan 28 kinderen ook de vraag voor-gelegd waarom ze een zin wel of niet een plaatje correct vonden beschrijven. De


plaatjes die aan de kinderen werden getoond lieten zowel een cardinale lezing alseen proportionele lezing en een Westerståhl lezing toe. Om te bepalen welke lezingde juiste was, was het noodzakelijk de pragmatische context mee te nemen; deonderzoeker vestigde de aandacht van de kinderen voordat zij het testitem kregen tehoren, op de denotatie van het eerste of tweede argument van de kwantor. Dezecontext resulteerde bij volwassenen in cardinale lezingen van many in het geval vanextra nadruk op de denotatie van het eerste argument van de kwantor. Wanneer dedenotatie van het tweede argument werd benadrukt, resulteerde dat bij volwassenenin of een proportionele lezing of een Westerståhl lezing. Voor many of resulteerdealleen nadruk op de denotatie van het tweede argument van de kwantor op eenWesterståhl lezing.

De resultaten laten zien dat kinderen many en many of niet anders interpreterenin beide contexten; nadruk op de denotatie van het eerste argument van de kwantorof nadruk op de denotatie van het tweede argument van de kwantor resulteerde nietin meer of minder cardinale, proportionele of Westertåhl lezingen bij many of manyof zoals dat bij volwassenen het geval was. Dit toont aan dat kinderen de discoursecontext noch de syntactische informatie (nl. het verschil tussen many en de partitiefmany of ) op een volwassen manier gebruiken om het domein van many en many ofte bepalen.

De resultaten tonen aan dat kinderen geen lezing van many en many of toestaandie volwassenen vreemd is - kinderen accepteren alle lezingen die volwassenen ooktoestaan. Bovendien tonen de resultaten aan dat pragmatische informatie voor kin-deren niet een zelfde lezing afdwingt zoals dat voor volwassenen het geval is en datkinderen geen verschil maken tussen many en many of.

Hoofstuk 6 gaat verder in op het effect van discourse context op het domein vande universele kwantor. Waar de betekenis van veel duidelijk context-afhankelijkis, is de betekenis van alle dat niet. Toch speelt ook bij alle de discourse contexteen belangrijke rol om te bepalen over welke verzameling wordt gekwantificeerd.Vergelijk de situatie in (4) waar alle in de tweede zin duidelijk verwijst naar deverzameling vissen die Marie net gekocht heeft.

(4) Marie heeft tien vissen gekocht en ging naar huis. Alle vissen zwemmen nuin een vissekom.

Hoe en onder welke condities gebruiken kinderen de discourse context om het do-mein van de kwantor te bepalen? Ik zet in hoofdstuk 6 uiteen hoe er in de literatuurop verschillende eigenschappen van discourse is gewezen om volwassen interpre-taties van kinderen van gekwantificeerde zinnen te verklaren. Ik formuleer dezediscussie opnieuw in termen van het gebruik van syntactische versus pragmatische(discourse) informatie door kinderen. Twee experimenten tonen aan dat kinderendoor een discourse die zowel over het object als het subject van de gekwantificeerdezin handelt, in de war gebracht worden; ze laten zich leiden door de discoursecontext en wanneer ze wordt gevraagd een gekwantificeerde zin te interpreteren


ten opzichte van een extra-object situatie, resulteert dit in gok-gedrag. Wanneerde kinderen wordt gevraagd een vergelijkbare zin te interpreteren wanneer er geensprake is van een extra-object situatie2, integreren ze de discourse context op eenvolwassen manier. Ik verklaar deze resultaten door gebruik te maken van Beaver’s(2004) Centering Optimality Theory, waarbij ik ook de visuele eigenschappen van deextra-object situatie meeneem. Op grond van de resultaten kunnen we concluderendat niet-volwassen interpretaties van gekwantificeerde zinnen in een discourse doorkinderen niet het resultaat zijn van een incompleet grammaticaal systeem (d.w.z.doordat kinderen bepaalde regels nog niet hebben geleerd), maar eerder doordatkinderen een ondergeschikte rol toekennen aan de discourse context in extra-objectsituaties. Volwassen gebruiken deze informatie juist als primaire bron in de getestesituaties om de betekenis van de gekwantificeerde zin te herleiden.

Samenvattend betoog ik in dit proefschrift dat, waar volwassenen de discoursecontext gebruiken op het moment dat er onvoldoende syntactische informatie is omhet domein van een kwantor te bepalen en alleen visuele informatie erbij betrekkenwanneer er geen andere aanwijzingen zijn om het domein van de kwantor te bepalenof de visuele aanwijzingen heel erg dominant zijn, kinderen in de leeftijd van vier totzes jaar altijd als eerste naar de discourse context en de visuele context grijpen. Ditverklaart de resultaten in hoofdstuk 4 waar de interpretatie van gekwantificeerdezinnen door kinderen interacteert met de aanwezigheid van een extra object of eenextra subject in de afbeelding. Op vergelijkbare wijze verklaart het de resultatenvan hoofdstuk 6 dat de interpretatie van kinderen interacteert met de aanwezigheidvan twee discourse topics in de context voorafgaand aan de gekwantificeerde zin.Bovendien laten deze resultaten zien dat kinderen de discourse context, en niet desyntaxis, gebruiken om het domein van de kwantor te bepalen (en zelfs het domeingokken als de discourse twee mogelijke domeinen aanrijkt).

Ik concludeer dat kinderen primair de visuele context gebruiken om het domeinvan een kwantor te bepalen. Indien deze visuele context ontbreekt of geen duidelijkeaanwijzingen geeft, gebruiken kinderen de discourse context. Pas wanneer zowelde discourse context als de visuele context geen informatie verschaffen over hetdomein van de kwantor, gebruiken kinderen de syntaxis. Dit in tegenstelling totvolwassenen. Volwassenen gebruiken de syntaxis als eerste om het domein vaneen kwantor te bepalen. Als de syntaxis geen of onvoldoende aanwijzingen geeft,gebruiken zij de discourse context. Volwassenen gaan pas op zoek naar visueleaanwijzingen voor het domein van de kwantor, als ook deze discourse contextonvoldoende aanwijzingen geeft. Hiermee biedt dit proefschrift een nieuw inzichtin de verwerving van kwantificatie.

In tegenstelling tot eerder werk over de verwerving van kwantificatie, focust ditproefschrift niet eenzijdig op de verwerving van of de syntactische of de semantische

2Een situatie waarin bijvoorbeeld drie van vier paarden worden bereden door cowboys, waarbij éénpaard niet wordt bereden.


of de pragmatische eigenschappen van kwantoren, maar neemt het al deze eigen-schappen in ogenschouw. De resultaten die in dit proefschrift worden gepresenteerdonderstrepen hiermee dat meer inzicht kan worden verkregen in het verloop vantaalverwerving, wanneer alle factoren die relevant zijn om betekenis aan taal toe tekennen tegelijkertijd in ogenschouw worden genomen. In het geval van kwantificatiebetekent dat dat de verwerving van de syntactische, semantische en pragmatischeeigenschappen van kwantificatie moet worden onderzocht. In plaats van op éénvan deze eigenschappen te focussen, is het cruciaal dat voor een meer dynamischebenadering wordt gekozen waarin alle eigenschappen van kwantificatie wordenmeegenomen. In dit proefscrift heb ik voor een dergelijke benadering gekozendoor gebruik te maken van Optimality Theoretic semantics. De resultaten van zesexperimenten laten zien dat de verwerving van kwantificatie geen kwestie is vanhet ontbreken of nog niet verworven hebben van bepaalde grammaticale regels ofeen ‘verkeerd’ experimenteel ontwerp. Sterker, de resultaten ondersteunen mijnEquilibrium Hypothese dat het verwerven van kwantificatie een kwestie is van hetvinden van een volwassen balans in het gebruik van syntactische, semantische enpragmatische regels bij het toekennen van betekenis aan een gekwantificeerde zin.

Groningen Dissertations in Linguistics(GRODIL)

1 Henriëtte de Swart (1991). Adverbs of Quantification: A Generalized QuantifierApproach.

2 Eric Hoekstra (1991). Licensing Conditions on Phrase Structure.

3 Dicky Gilbers (1992). Phonological Networks. A Theory of Segment Representa-tion.

4 Helen de Hoop (1992). Case Configuration and Noun Phrase Interpretation.

5 Gosse Bouma (1993). Nonmonotonicity and Categorial Unification Grammar.

6 Peter Blok (1993). The Interpretation of Focus: an epistemic approach to prag-matics.

7 Roelien Bastiaanse (1993). Studies in Aphasia.

8 Bert Bos (1993). Rapid User Interface Development with the Script LanguageGist.

9 Wim Kosmeijer (1993). Barriers and Licensing.

10 Jan-Wouter Zwart (1993). Dutch Syntax: A Minimalist Approach.

11 Mark Kas (1993). Essays on Boolean Functions and Negative Polarity.

12 Ton van der Wouden (1994). Negative Contexts.

13 Joop Houtman (1994). Coordination and Constituency: A Study in CategorialGrammar.

14 Petra Hendriks (1995). Comparatives and Categorial Grammar.

15 Maarten de Wind (1995). Inversion in French.

16 Jelly Julia de Jong (1996). The Case of Bound Pronouns in Peripheral Romance.

173

174 GRODIL

17 Sjoukje van der Wal (1996). Negative Polarity Items and Negation: TandemAcquisition.

18 Anastasia Giannakidou (1997). The Landscape of Polarity Items.

19 Karen Lattewitz (1997). Adjacency in Dutch and German.

20 Edith Kaan (1997). Processing Subject-Object Ambiguities in Dutch.

21 Henny Klein (1997). Adverbs of Degree in Dutch.

22 Leonie Bosveld-de Smet (1998). On Mass and Plural Quantification: The Caseof French ‘des’/‘du’-NPs.

23 Rita Landeweerd (1998). Discourse Semantics of Perspective and TemporalStructure.

24 Mettina Veenstra (1998). Formalizing the Minimalist Program.

25 Roel Jonkers (1998). Comprehension and Production of Verbs in Aphasic Speak-ers.

26 Erik F. Tjong Kim Sang (1998). Machine Learning of Phonotactics.

27 Paulien Rijkhoek (1998). On Degree Phrases and Result Clauses.

28 Jan de Jong (1999). Specific Language Impairment in Dutch: Inflectional Mor-phology and Argument Structure.

29 H. Wee (1999). Definite Focus.

30 Eun-Hee Lee (2000). Dynamic and Stative Information in Temporal Reasoning:Korean Tense and Aspect in Discourse.

31 Ivilin Stoianov (2001). Connectionist Lexical Processing.

32 Klarien van der Linde (2001). Sonority Substitutions.

33 Monique Lamers (2001). Sentence Processing: Using Syntactic, Semantic, andThematic Information.

34 Shalom Zuckerman (2001). The Acquisition of “Optional” Movement.

35 Rob Koeling (2001). Dialogue-Based Disambiguation: Using Dialogue Status toImprove Speech Understanding.

36 Esther Ruigendijk(2002). Case Assignment in Agrammatism: a Cross-linguisticStudy.

37 Tony Mullen (2002). An Investigation into Compositional Features and FeatureMerging for Maximum Entropy-Based Parse Selection.

GRODIL 175

38 Nanette Bienfait (2002). Grammatica-onderwijs aan allochtone jongeren.

39 Dirk-Bart den Ouden (2002). Phonology in Aphasia: Syllables and Segments inLevel-specific Deficits.

40 Rienk Withaar (2002). The Role of the Phonological Loop in Sentence Compre-hension.

41 Kim Sauter (2002). Transfer and Access to Universal Grammar in Adult SecondLanguage Acquisition.

42 Laura Sabourin (2003). Grammatical Gender and Second Language Processing:An ERP Study.

43 Hein van Schie (2003). Visual Semantics.

44 Lilia Schürcks-Grozeva (2003). Binding and Bulgarian.

45 Stasinos Konstantopoulos (2003). Using ILP to Learn Local Linguistic Struc-tures.

46 Wilbert Heeringa (2004). Measuring Dialect Pronunciation Differences usingLevenshtein Distance.

47 Wouter Jansen (2004). Laryngeal Contrast and Phonetic Voicing: A LaboratoryPhonology Approach to English, Hungarian and Dutch.

48 Judith Rispens (2004). Syntactic and Phonological Processing in DevelopmentalDyslexia.

49 Danielle Bougaïré (2004). L’approche communicative des campagnes de sensibili-sation en santé publique au Burkina Faso: les cas de la planification familiale, dusida et de l’excision.

50 Tanja Gaustad (2004). Linguistic Knowledge and Word Sense Disambiguation.

51 Susanne Schoof (2004). An HPSG Account of Nonfinite Verbal Complements inLatin.

52 M. Begoña Villada Moirón (2005). Data-driven identification of fixed expressionsand their modifiability.

53 Robbert Prins (2005). Finite-State Pre-Processing for Natural Language Analysis.

54 Leonoor van der Beek (2005). Topics in Corpus-Based Dutch Syntax.

55 Keiko Yoshioka (2005). Linguistic and gestural introduction and tracking ofreferents in L1 and L2 discourse.

176 GRODIL

56 Sible Andringa (2005). Form-focused instruction and the development of secondlanguage proficiency.

57 Joanneke Prenger (2005). Taal telt! Een onderzoek naar de rol van taal-vaardigheid en tekstbegrip in het realistisch wiskundeonderwijs.

58 Neslihan Kansu-Yetkiner (2006). Blood, Shame and Fear: Self-PresentationStrategies of Turkish Women’s Talk about their Health and Sexuality.

59 Mónika Z. Zempléni (2006). Functional imaging of the hemispheric contributionto language processing.

60 Maartje Schreuder (2006). Prosodic Processes in Language and Music.

61 Hidetoshi Shiraishi (2006). Topics in Nivkh Phonology.

62 Tamás Biró (2006). Finding the Right Words: Implementing Optimality Theorywith Simulated Annealing.

63 Dieuwke de Goede (2006). Verbs in Spoken Sentence Processing: Unraveling theActivation Pattern of the Matrix Verb.

64 Eleonora Rossi (2007). Clitic production in Italian agrammatism.

65 Holger Hopp (2007). Ultimate Attainment at the Interfaces in Second LanguageAcquisition: Grammar and Processing.

66 Gerlof Bouma (2008). Starting a Sentence in Dutch: A corpus study of subject-and object-fronting.

67 Julia Klitsch (2008). Open your eyes and listen carefully. Auditory and audiovi-sual speech perception and the McGurk effect in Dutch speakers with and withoutaphasia.

68 Janneke ter Beek (2008). Restructuring and Infinitival Complements in Dutch.

69 Jori Mur (2008). Off-line Answer Extraction for Question Answering.

70 Lonneke van der Plas (2008). Automatic Lexico-Semantic Acquisition for Ques-tion Answering.

71 Arjen Versloot (2008). Mechanisms of Language Change: Vowel reduction in15th century West Frisian.

72 Ismail Fahmi (2009). Automatic term and Relation Extraction for MedicalQuestion Answering System.

73 Tuba Yarbay Duman (2009). Turkish Agrammatic Aphasia: Word Order, TimeReference and Case.

GRODIL 177

74 Maria Trofimova (2009). Case Assignment by Prepositions in Russian Aphasia.

75 Rasmus Steinkrauss (2009). Frequency and Function in WH Question Acquisi-tion. A Usage-Based Case Study of German L1 Acquisition.

76 Marjolein Deunk (2009). Discourse Practices in Preschool. Young Children’sParticipation in Everyday Classroom Activities.

77 Sake Jager (2009). Towards ICT-Integrated Language Learning: Developing anImplementation Framework in terms of Pedagogy, Technology and Environment.

78 Francisco Dellatorre Borges (2010). Parse Selection with Support Vector Ma-chines.

79 Geoffrey Andogah (2010). Geographically Constrained Information Retrieval.

80 Jacqueline van Kruiningen (2010). Onderwijsontwerp als conversatie. Prob-leemoplossing in interprofessioneel overleg.

81 Robert G. Shackleton (2010). Quantitative Assessment of English-AmericanSpeech Relationships.

82 Tim Van de Cruys (2010). Mining for Meaning. The Extraction of Lexico-semantic Knowledge from Text.

83 Therese Leinonen (2010). An Acoustic Analysis of Vowel Pronunciation inSwedish Dialects.

84 Erik-Jan Smits (2010). Acquiring quantification. How children use semanticsand pragmatics to constrain meaning.

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