Emergence of Meaning 9781139551632, 1139551639

Table of contents :
Cover
THE EMERGENCE OF MEANING
Series
Title
Copyright
Contents
Figures
Preface
Acknowledgements
1 Logic and human languages
1.1 Introduction
1.2 The disconnect between logic and language
1.3 Principles of logic and language
1.4 Downward entailment
1.5 Negative polarity items
1.6 Domain widening
1.7 Wh-words
1.8 Reversals of entailment
1.8.1 Universals with disjunction in the subject phrase
1.8.2 Negated universals with disjunction in the subject phrase
1.8.3 Negated universals with disjunction in the predicate phrase
1.9 Compositionality. 1.10 Information strength: weakening and strengthening1.11 Logical principles of Weakening
1.12 Logical truths
1.13 Contingent truths
1.14 Problems of scope
1.15 Pragmatic influences on logical inferences
1.16 The meaning of disjunction is contingent
1.17 The meaning of the universal quantifier is contingent
1.18 Conclusion
2 Competing approaches to language and logic
2.1 The experience-based approach
2.1.1 The constructivist theory
2.1.2 Conservative learning
2.1.3 Arguments against Universal Grammar
2.1.4 A hybrid model
2.2 The nativist approach
2.2.1 Core versus periphery. 2.3 Complex syntax2.3.1 Acquisition of passives
2.3.2 Acquisition of relative clauses
2.4 The Continuity Hypothesis
2.5 Evidence for continuity in child language
2.5.1 Medial wh-questions in child English
2.5.2 Why-questions in child English
2.6 Arguments against the experience-based approach
2.7 Linguistic universals
2.8 Empirical differences between the approaches
3 The case for logical nativism
PART I INNATE LINGUISTIC PRINCIPLES
3.1 Principle C
3.1.1 Wh-questions
3.1.2 Quantificational expressions
3.2 Extending core principles
3.3 Connectivity and Principle C. 3.4 Connectivity in pseudoclefts3.5 Connectionism in child language
3.6 A pragmatic alternative to Principle C
3.7 Syntax versus pragmatics
3.7.1 Crain and McKee (1985)
3.7.2 Kiguchi and Thornton (2004)
3.7.3 Crain and Thornton (1998)
3.7.4 Guasti and Chierchia (1999/2000)
3.8 Children's failures to make pragmatic inferences
3.9 Children's lack of sensitivity to stress
3.10 A theoretical problem with the pragmatic account
PART II INNATE PRINCIPLES AND PARAMETERS OF LOGIC
3.11 Downward entailment: a core logical principle
3.12 Cross-linguistic findings
3.13 Scope parameters. 3.14 The Semantic Subset Principle3.15 Negative evidence
3.16 Where child and adult languages cannot differ
3.17 Hidden units: focus operators
3.18 Canceling polarity: negated disjunctions
3.19 Canceling polarity: negated conjunctions
3.20 Where we are headed
4 Scope parameters
4.1 Negated disjunctions
4.1.1 A longitudinal study of 2-year-olds
4.1.2 Children's knowledge of scope in negated disjunctions
4.1.3 Children's knowledge of proximity in negated disjunctions
4.2 Negation and disjunction/conjunction
4.3 A parametric account of scope
4.3.1 The Conjunction Parameter.

Citation preview

Th e Em er ge nce of Me aning

Over the past forty years, scientists have developed models of human reasoning based on the principle that human languages and classical logic involve fundamentally different concepts and different methods of interpretation. In The Emergence of Meaning Stephen Crain challenges this view, arguing that a common logical nativism underpins human language and logical reasoning. The approach which Crain takes is twofold. First, he uncovers the underlying meanings of logical expressions and logical principles that appear in typologically different languages – English and Mandarin Chinese – and he demonstrates that these meanings and principles directly correspond to the expressions and structures of classical logic. Second, he reports the findings of new experimental studies which investigate how children acquire the logical concepts of these languages. A step-by-step introduction to logic and a comprehensive review of the literature on child language acquisition make this work accessible to those unfamiliar with either field. st e p h e n c r a in is a Distinguished Professor at Macquarie University and a fellow of the Academy of Social Sciences in Australia. He is also Director of the Australian Research Council Centre of Excellence in Cognition and its Disorders.

In this series 105. holger di e s s e l : The acquisition of complex sentences 106. s haron i nke l as and c he r yl zoll: Reduplication: doubling in morphology 107. s us an e dwar ds : Fluent aphasia 108. barba r a dancygi e r and e ve s w e e t s e r : Mental spaces in grammar: conditional constructions 109. matthew b ae r man, duns tan b r ow n and g r e v i l l e g . c o r b e t t : The syntax–morphology interface: a study of syncretism 110. ma rcus t omal i n: Linguistics and the formal sciences: the origins of generative grammar 111. s a muel d. e p s t e i n and t. dani e l s e e ly: Derivations in minimalism 112. paul de l acy: Markedness: reduction and preservation in phonology 113. yehuda n. fal k: Subjects and their properties 114. p. h. mat t he w s : Syntactic relations: a critical survey 115. ma rk c. b ake r : The syntax of agreement and concord 116. g illian c at r i ona r amc hand: Verb meaning and the lexicon: a first phase syntax 117. pieter muys ke n: Functional categories 118. juan ur i age r e ka: Syntactic anchors: on semantic structuring 119. d. ro ber t l add: Intonational phonology second edition 120. leonard h. b ab b y: The syntax of argument structure 121. b. ela n dr e s he r : The contrastive hierarchy in phonology 122. dav id adge r , dani e l har b our and l au r e l j. wat k i n s: Mirrors and microparameters: phrase structure beyond free word order 123. niina ni ng zhang: Coordination in syntax 124. neil s mi t h: Acquiring phonology 125. nina to p i nt zi : Onsets: suprasegmental and prosodic behaviour 126. cedric b oe c kx, nor b e r t hor ns t e i n and ja i r o n u n e s: Control as movement 127. michae l i s r ae l : The grammar of polarity: pragmatics, sensitivity, and the logic of scales 128. m. rita manzi ni and l e onar do m. s avo i a : Grammatical categories: variation in Romance languages 129. ba rbar a c i t ko: Symmetry in syntax: merge, move and labels 130. rachel wal ke r : Vowel patterns in language 131. mary dal r ymp l e and i r i na ni kol ae va: Objects and information structure 132. jerro l d m. s adoc k: The modular architecture of grammar 133. duns tan b r ow n and andr e w hi p p i s l e y: Network morphology: a defaults-based theory of word structure 134. bettel o u l o s , c o r r i e n b l o m , g e e r t b o o i j, m a r i o n e l e n b a a s and a ns van ke me nade : Morphosyntactic change: a comparative study of particles and prefixes 135. s tephen c r ai n: The emergence of meaning Earlier issues not listed are also available

CAMBRIDGE STUDIES IN LINGUISTICS General Editors: p. au s t i n, j. b r e s na n, b. comrie, s . c r a i n, w. d r e s s l e r , c . j. e w e n, r. lass, d. l i gh t f o o t, k . r ic e , i. r o b e r t s , s. rom aine, n. v. sm it h

The Emergence of Meaning

T HE EMERGENCE OF MEANING S t ep h en C r a in Macquarie University, Sydney

CA MBRIDG E UNI VE R S I T Y P R E S S Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Mexico City Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521674881 © Stephen Crain 2012 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2012 Printed and Bound in the United Kingdom by the MPG Books Group A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Crain, Stephen, 1947– author. The emergence of meaning / Stephen Crain, Macquarie University, Sydney. pages cm. – (Cambridge studies in linguistics ; 135) Includes bibliographical references and index. ISBN 978-0-521-85809-0 (hardback) – ISBN 978-0-521-67488-1 (paperback) 1.  Language and logic. I.  Title. P39.C73  2012 401′.43–dc23    2012016901 ISBN 978-0-521-85809-0 Hardback ISBN 978-0-521-67488-1 Paperback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

Contents

List of figures Preface Acknowledgements 1

Logic and human languages

page xi xiii xvii 1

1.1 Introduction 1.2 The disconnect between logic and language 1.3 Principles of logic and language 1.4 Downward entailment 1.5 Negative polarity items Domain widening 1.6 1.7 Wh-words 1.8 Reversals of entailment 1.8.1 Universals with disjunction in the subject phrase 1.8.2 Negated universals with disjunction in the subject phrase 1.8.3 Negated universals with disjunction in the predicate phrase 1.9 Compositionality 1.10 Information strength: weakening and strengthening 1.11 Logical principles of Weakening 1.12 Logical truths 1.13 Contingent truths 1.14 Problems of scope 1.15 Pragmatic influences on logical inferences 1.16 The meaning of disjunction is contingent 1.17 The meaning of the universal quantifier is contingent 1.18 Conclusion

1 2 6 10 18 25 28 34 36 38 40 42 43 45 48 50 53 55 57 59 62

2

Competing approaches to language and logic

64

2.1

The experience-based approach 2.1.1 The constructivist theory 2.1.2 Conservative learning 2.1.3 Arguments against Universal Grammar

64 66 70 72 vii

viii  Contents 2.1.4 A hybrid model The nativist approach 2.2.1 Core versus periphery 2.3 Complex syntax 2.3.1 Acquisition of passives 2.3.2 Acquisition of relative clauses 2.4 The Continuity Hypothesis 2.5 Evidence for continuity in child language 2.5.1 Medial wh-questions in child English 2.5.2 Why-questions in child English 2.6 Arguments against the experience-based approach 2.7 Linguistic universals 2.8 Empirical differences between the approaches

74 75 77 78 78 79 80 83 85 90 96 99 100

3

102

2.2

The case for logical nativism

Part I In nat e l in g u istic p r i n c iples Principle C 3.1.1 Wh-questions 3.1.2 Quantificational expressions 3.2 Extending core principles 3.3 Connectivity and Principle C 3.4 Connectivity in pseudoclefts 3.5 Connectionism in child language 3.6 A pragmatic alternative to Principle C 3.7 Syntax versus pragmatics 3.7.1 Crain and McKee (1985) 3.7.2 Kiguchi and Thornton (2004) 3.7.3 Crain and Thornton (1998) 3.7.4 Guasti and Chierchia (1999/2000) 3.8 Children’s failures to make pragmatic inferences 3.9 Children’s lack of sensitivity to stress 3.10 A theoretical problem with the pragmatic account

103 103 107 108 110 113 115 119 121 127 128 130 131 133 137 139 142

Part II Innate principles and parameters of logic 3.11 Downward entailment: a core logical principle 3.12 Cross-linguistic findings 3.13 Scope parameters 3.14 The Semantic Subset Principle 3.15 Negative evidence 3.16 Where child and adult languages cannot differ 3.17 Hidden units: focus operators

144 144 146 149 152 155 156 157

3.1

Contents  ix 3.18 Canceling polarity: negated disjunctions 3.19 Canceling polarity: negated conjunctions 3.20 Where we are headed

160 161 163

4

164

Scope parameters

4.1 Negated disjunctions 4.1.1 A longitudinal study of 2-year-olds 4.1.2 Children’s knowledge of scope in negated disjunctions 4.1.3 Children’s knowledge of proximity in negated disjunctions 4.2 Negation and disjunction/conjunction 4.3 A parametric account of scope 4.3.1 The Conjunction Parameter 4.3.2 The Disjunction Parameter 4.4 The Semantic Subset Principle 4.5 Child language 4.5.1 Negated disjunctions in child Japanese 4.5.2 Negated disjunctions in child Mandarin 4.6 Negated conjunctions 4.7 Disjunction and the preposition before 4.7.1 Scope ambiguity 4.7.2 Before and the Semantic Subset Principle 4.8 Before and child language

167 168 170 174 178 179 180 180 182 184 184 186 188 190 191 194 196

5

199

How something can be both positive and negative

5.1 Polarity-sensitive items 5.2 Existential indefinites as negative polarity items 5.3 Children’s comprehension of negative polarity items 5.4 Wh-indefinites in Mandarin 5.5 Existential indefinites as positive polarity items 5.6 Children’s production of existential indefinites 5.7 Children’s comprehension of existential indefinites

200 204 207 209 215 217 219

6

224

Two logical operators for the price of one

6.1 Focus operators 6.2 The two meaning components of focus operators 6.3 Covert negation is downward entailing 6.4 Polarity-sensitive expressions 6.5 How to cancel polarity sensitivity 6.6 Focus operators across languages: the case of Mandarin 6.7 Conjunction and disjunction are PPIs in some languages 6.8 Covert negation cancels polarity sensitivity 6.9 Conjunction and focus

227 227 228 231 232 236 237 239 240

x  Contents 6.10 Disjunction and focus 6.11 Focus operators in child language 6.12 Disjunction and focus in child language 6.13 Conjunction and focus in child language 6.14 Quantification without qualification 6.15 Asymmetric quantification in child language 6.16 Conclusions

Notes References Index

242 243 247 252 256 258 264

266 274 285

Figures

1.1 The extra-object context 3.1 C-command 3.2 C-command 3.3 No c-command 3.4 No c-command 3.5 Discourse blocks c-command 3.6 Connecting discourse 3.7 No c-command in pseudoclefts 3.8 Question-in-disguise analysis of pseudoclefts 4.1 A 2-year-old being interviewed 4.2 The tooth fairy story 4.3 Negation c-commands disjunction = the conjunctive entailment 4.4 Negation does not c-command disjunction 4.5 The Conjunction Parameter 4.6 The Disjunction Parameter 4.7 Experimental design 4.8 The blue ribbon test of negated disjunctions 4.9 The blue ribbon test was used again for negated conjunctions 4.10 Truth conditions: before takes scope over disjunction 4.11 Truth conditions: disjunction takes scope over before 5.1 Context for questions (23) and (24) 5.2 Pandas at breakfast 5.3 The villagers and the unwanted intruder 5.4 Mr. Owl requests help from one of his super friends 6.1 Condition 1 6.2 Every dog versus No dogs 6.3 Disjunction in the subject phrase 6.4 Disjunction in the predicate phrase

page 60 103 104 105 105 111 112 116 118 169 172 173 173 181 182 185 187 189 194 195 208 211 213 214 249 259 261 263

xi

Preface

This book is an introduction to logic and language. It reports the findings of experimental investigations of how logical expressions are acquired by English-speaking children and by Mandarin-speaking children. By comparing different languages, and by examining how logical expressions enter children’s language, we hope to shed some light on one of the key questions in linguistics, philosophy, and in cognitive science: are human languages logical? For at least forty years, it has been widely accepted that human beings are not logical, and that the culprit is the languages we speak. Researchers in the psychology of reasoning have concluded that the meanings of logical expressions in human languages are not the same as the meanings of the corresponding expressions in classical logic. Evidence cited in support of this conclusion includes assessments of people’s understanding of basic logical concepts, such as the expressions in human languages which correspond to disjunction in classical logic. In English the word for disjunction is or. In one series of experiments, English speakers were asked to respond to instructions such as Give me the red balloon or the blue balloon. In responding, subjects never gave the experimenter both the red balloon and the blue one. From a logical point of view, it would have been correct for the English-speaking subjects to have given the experimenter both balloons. Because in classical logic, a formula with disjunction, A or B, is true if both A and B are true, as well as in circumstances in which A alone, or B alone, is true. Based on the responses by subjects, reasoning experts inferred that the meaning of or in English is exclusive disjunction: A or B, but not both, rather than inclusive disjunction, A or B, and possibly both, as in classical logic. Of course this is just one finding, among many, that has led to the view that human languages and classical logic have little in common. I was not convinced. For one thing, the experiments that evoked the exclusive meaning of disjunction probably encouraged this interpretation, and discouraged the subjects from giving both the red and the blue balloon to the experimenter. After all, if the experimenter had wanted both balloons, he xiii

xiv  Preface would have said so. But more importantly, even if the subjects responded in a way that was consistent with an exclusive interpretation of disjunction this does not justify the conclusion that they lacked the inclusive-or meaning of disjunction. In classical logic, disjunctive statements such as A or B are true in three circumstances – when just A is true, or just B, or when both A and B are true. The finding that people judge sentences of the form A or B to be true if just A or just B is true does not entail that they would not also have judged A or B to be true in circumstances where both A and B were. No one seemed to have conducted an experiment in which the statement A or B was presented in a situation in which both A and B are true. Worse still, no one had tested people’s understanding of negative statements like Max doesn’t have a red balloon or a blue balloon. We have seen that, if English or is exclusive disjunction, then statements of the form A or B are false if both A and B are true. It follows that negative statements, Not A or B, should be true if both A and B are true. So, if English or is exclusive-or, then English speakers should accept Max doesn’t have a red balloon or a blue balloon in circumstances where Max has both a red balloon and a blue balloon. It seemed highly unlikely that human languages could be as illogical as this. About ten years ago, I was playing in the front yard with my (then) 4-yearold daughter Aurora. I tested her understanding of or by asking her whether or not the sentence Max has a red balloon or a blue balloon was a correct description of a situation in which a character named Max had both a red and a blue balloon. To cut a long story short, she said that my statement was correct. Before long, colleagues and I were testing English-speaking children’s interpretation of negative statements like Max doesn’t have a red balloon or a blue balloon, to further confirm that English or has the same meaning as the expression for disjunction in classical logic. Not long after that we were investigating children’s interpretation of disjunction in Mandarin Chinese, a language that is typologically distinct from English. This book reports the findings of much of that research also. As noted earlier, lots of other evidence has been offered in support of the conclusion that humans are not logical. Both children and adults have been found to make incorrect logical inferences in many reasoning tasks. But when the experimental subjects are informed about the mistakes they have made, they often readily understand the nature of their incorrect inferences, and how they should have responded. The fact that people recognize the correct patterns of inference when these are pointed out to them suggests that they are cognizant of the underlying logical principles, despite having failed to access these principles during the experiment.

Preface  xv Further evidence that humans are not logical has been derived from the observation that both children and adults struggle, and often fail to correctly judge whether or not one sentence logically entails another. But the errors that arise in this kind of situation, too, could be the consequence of the computational demands of the task, rather than a lack of knowledge. Moreover, people succeed far more often than they fail in making valid logical inferences, both in experimental settings and in ordinary life. In addition, certain observations about human languages invite the conclusion that human languages equip their speakers to make valid logical inferences. For example, regardless of the language children acquire, children from different linguistic communities grow up to be scientists. It is hard to see how this could be possible unless human languages somehow contain the essential ingredients for logical reasoning. Finally, reasoning tasks are not the only means at our disposal for assessing whether or not humans are logical. Another way to assess whether human languages are logical is to investigate these languages directly. We can assess the relationship between logic and language by seeing the extent to which the truth conditions children and adults assign to sentences with logical words are consistent with the truth conditions that are assigned to the logical formulas that correspond to these sentences. Of course this presupposes that we can translate sentences from human languages into logical formulas. Assuming this can be done, and if the truth conditions assigned to these sentences are the same as those assigned to the corresponding formulas, then this invites the conclusion that human languages are logical after all. As an undergraduate, I took classes in logic at UCLA. One of these classes was taught by Richard Montague, who showed us how English sentences could be recast using the symbolic expressions of logic. The present book adopts a similar approach, especially in Chapters 1 and 3. The remaining chapters are concerned with adjudicating between two different approaches to language acquisition. In broadest strokes, the alternative approaches can be characterized as the ‘nature’ approach and the ‘nurture’ approach. As will become clear, my own thinking about the nature versus nurture debate, and hence this book, have been strongly influenced by Noam Chomsky. At the same time I was taking classes from Montague and others at UCLA, I was reading Chomsky, whose proposals about a Universal Grammar have resonated with me ever since. Early in my career, I designed experiments with young children to evaluate the syntactic principles of Chomsky’s theory of Universal Grammar. More recently, I have turned my attention back to logic. With several colleagues, I have been investigating the possibility that the basic concepts of logic are

xvi  Preface innately embedded in the minds of children, and awakened by experience as children acquire human languages. So one way of looking at this book is as an attempt to build a bridge that spans a linguistic enterprise established by the work of Noam Chomsky  – exploring the emergence of innate linguistic knowledge in children – and the analysis of human languages using the tools of logic, an enterprise established by Richard Montague.

Acknowledgements

This research was conducted as part of the Australian Research Council Centre of Excellence in Cognition and its Disorders (CE110001021). It was funded in part by an ARC Federation Fellowship (FF0456432), ARC Discovery grants (DP1096160; DP0879842), a grant from the National Philosophy and Social Science Foundation of China (09BYY022) and by the HEARing CRC, established and supported under the Australian Government’s Cooperative Research Centres Program. This book is a culmination of work undertaken since our relocation to Australia. Special thanks to those who made this work a pleasure – Peng Zhou, Drew Khlentzos, Takuya Goro, Paul Pietroski, Terje Londahl, Anna Notley, Blake Johnson, Graciela Tesan, Qiong-peng Luo, Likan Zhan, Fran Ursini, Nobu Akagi, Esther Su, Min Lao, and especially Rozz Thornton and Aurora Crain. For help in preparing the manuscript, I want to thank Robin Blumfield, Peng Zhou, Aijun Huang, and Likan Zhan. I have benefited from discussions over the years with terrific colleagues  – Noam Chomsky, Gennaro Chierchia, Teresa Guasti, Tetsuya Sano, Laura Conway, Carrie O’Leary, Utako Minai, Yi-ching Su, Thomas Lee, Luisa Meroni, Andrea Gualmini, Carole Boster, Bill Crain, Janet Fodor, Diane Lillo-Martin, Henry Hamburger, Weijia Ni, Jim Huang, Ivano Caponigro, and Martin Hackl. I also wish to acknowledge some colleagues who will probably not recognize the role they played, but who have had a significant influence – Paul Hagstrom, K. A. Jayaseelan, Brian Byrne, Austin Crain, Howard Lasnik, Yukio Otsu, Ovid Tzeng, Liqun Gao, Max Coltheart, and Kermit the Frog. This book is dedicated to the memories of close friends  – Hisashi Kado, Fang Li, Tanya Reinhart, and Roger Wales.

xvii

1 Logic and human languages

1.1

Introduction

For thousands of years, everyone believed that the human mind was logical. This was so obvious that no one thought to question it, or to verify it. Forty years ago some scientists decided to investigate, and they found that people failed some simple tests of logical reasoning. Scientists concluded that our minds use rules that conflict with logic. New models of human reasoning have flourished, with a common theme – that human languages and classical logic involve different basic concepts, and different principles of interpretation. We think these conclusions were unwarranted, and that the new models of logical reasoning are misguided. In our view, the erroneous conclusions were reached by using experimental techniques that people find difficult, such as making abstract judgments about the entailments of sentences. We have chosen to take a different approach. We have advocated the research strategy of finding out how logical people are simply by looking at the languages they speak. In particular, we have chosen to investigate whether certain expressions and structures of typologically different languages, English and Mandarin Chinese, mean the same as the corresponding expressions and structures in classical logic. When we reason in English, there are particular words that we regularly use, words like if, and, not, or, all, and some. Mandarin Chinese has words that correspond to these English words, and it turns out that the words in Mandarin have pretty much the same meaning as the English words. In Mandarin Chinese, the word ruguo corresponds to English if, the word he corresponds to English and, mei means not, huozhe means or, and so on. In this book we will investigate the relationship between the logical words of English and Mandarin and the corresponding logical expressions of classical logic. In logic the symbols →, ∧, ¬, ∨, ∀, and ∃ are represented by the English words if, and, not, or, all, and some. Logic has strict rules for combining these and other symbols to form sentences, and it also has strict rules that transform older sentences that have been formed using these symbols into new 1

2  Logic and human languages sentences that contain them. Logic also has rules that state logical equivalences between sentences that have been formed and transformed using the basic rules for combining symbols. These rules are known as de Morgan’s laws of propositional logic. One of the logical equivalences in de Morgan’s laws states that a negated disjunction, ¬(A ∨ B), is equivalent to a conjunction of the negated disjuncts, ¬A ∧ ¬B. Let the letter A represent the English sentence Amy ate sushi and let B represent the sentence Bob ate sushi. Then ¬(A ∨ B) can be paraphrased as Neither Amy nor Bob ate sushi. The translation of ¬A ∧ ¬B can be paraphrased as Amy didn’t eat sushi and Bob didn’t eat sushi. So, if English adheres to this one of de Morgan’s laws, then Neither Amy nor Bob ate sushi should be logically equivalent to Amy didn’t eat sushi and Bob didn’t eat sushi. Intuitively, these two sentences are true in exactly the same circumstances, which means that they are logically equivalent. So English appears to conform to this one of de Morgan’s laws. One question we will attempt to answer is whether all of the world’s languages obey the basic laws of logic, such as this one of de Morgan’s laws. We obviously cannot study all the world’s languages, so our approach will be to examine two historically unrelated languages in detail, English and Mandarin Chinese. If these typologically distinct languages share a common logical foundation, then this is at least circumstantial evidence that all human languages adhere to these basic laws of logic. And if this is so, a second question arises. How do children acquiring different human languages discover that these laws hold? This leads to other questions. If children do manage to discover these laws, at what age do they know them, and do they make any mistakes in the course of acquiring them? Again, we will only investigate English-speaking children and Mandarin-speaking children, but the methodological techniques we apply, and the conclusions we reach about these children, can be applied to studies of children acquiring any other human language. 1.2

The disconnect between logic and language

The current literature on language and logic is rife with controversy about the nature of human reasoning. Some researchers maintain that humans reason using a mental logic (e.g., Rips 1994). The majority of researchers have reached the opposite conclusion, however, and have abandoned a logicbased approach to human reasoning in favor of non-logical approaches (e.g., Cosmides and Tooby 1992; Johnson-Laird and Byrne 2002). These researchers have offered several reasons for supposing that there is a disconnect between logic and human reasoning. First, it is well documented that humans

1.2 The disconnect between logic and language

3

perform poorly in applying inference rules in formal proofs. For example, the inference rule for introducing the disjunction operator ™ (corresponding to English or) holds that if a statement of the form P is true, then a statement of the form P ™ Q is also true. But few English speakers judge it to be valid to infer from the truth of the English statement snow is white to the truth of the statement that snow is white or Julia Gillard is the current Prime Minister of Australia. P

snow is white

P ™ Q snow is white or Julia Gillard is PM

The force of this argument against there being a mental logic is not compelling, in our view. Inference rules are governed not only by logic, but also by conversational principles, such as Be Cooperative, i.e., make the strongest statement that you are in a position to make. This conversational principle is relevant even in making basic inferences. To take the example under consideration, P ™ Q makes a weaker statement than P alone, in information-theoretic terms, so people are fully justified in rejecting the direct inference from P to P ™ Q, though there are also circumstances in which this inference is judged to be valid (cf. Crain 2008; McCawley 1981). A second reason has been given for supposing that there is a disconnect between formal logic and logical reasoning in human languages. This is the observation that valid arguments hold in virtue of their form, not their content; yet children younger than 12 (Inhelder and Piaget 1964) and even adults are often swayed by the content of an argument in making judgments of validity, leading to errors in many cases. Unless the premises of an argument are about familiar topics, most people experience difficulty, for example, in interpreting conditional statements (English If … then …), as attested by their poor performance on the Wason card selection task (e.g., Wason 1968). The force of this argument is blunted by noting that, as soon as people are told the solution to the Wason card selection task, they immediately accept the solution as correct. This is a clear demonstration of logic guiding human reasoning (van Benthem 2008). A third reason for supposing that there is a disconnect between logic and human reasoning is the observation that both children and adults perform poorly in judging entailment relations between sentences. For example, people often stumble over the following questions: Question 1: If every cow is a brown cow, then is every cow brown? (Answer: yes) Question 2: If only cows are brown cows then are only cows brown? (Answer: no)

4  Logic and human languages Question 3: If someone brought wine and beer, then did someone bring wine and did someone bring beer? (Answer: yes)

Although we acknowledge that such judgments cannot be made easily, there is more to logic than proof theory, and judgments of validity and entailment relations do not exhaust the logical apparatus that people utilize in reasoning. There is an entire area of research that has remained virtually unexplored in evaluating the role of logic in human reasoning, namely the interpretation of logical expressions in human languages, including child language. For the past decade, several colleagues and I have been investigating how logical expressions are interpreted across typologically different human languages, and how the meanings of these expressions are acquired by children. For the most part, we have focused on the meanings that language users assign to individual sentences, rather than asking them to judge entailment relations between sentences. Based on cross-linguistic research, and based on the findings of experimental research with children, we have come up with a series of principles of interpretation in human language that adhere to the precepts of classical logic (Crain 2008; Crain, Thornton, and Khlentzos 2008). The fact that different languages adhere to the same logical principles is circumstantial evidence that human languages draw upon an innate set of logical primitives that are used in speaking and in reasoning. As Aboriginal poet Neidjie (2002) put it, Language is different, like skin. Skin can be different, but blood same. This book presents a series of arguments for logical nativism, which is the proposal that humans are biologically equipped with the tools for logical reasoning. The purpose of the book is to show that human languages are logical, in the sense that the meanings of linguistic expressions corresponding to quantificational expressions (e.g., the universal quantifier) and logical connectives (e.g., negation, the disjunction and conjunction operators) are the same as the meanings of the corresponding expressions in classical logic. A number of putatively universal linguistic principles will be advanced, all conforming to first-order logic.1 Although these principles are manifested in typologically different languages, of which English and Mandarin represent our sample, they are only operative in complex structures in which disjunction combines with negation, or with the universal quantifier. It is highly unlikely that children have sufficient evidence from experience to learn the meanings of the logical expressions of human languages by observing how adult speakers use these expressions, contrary to usage-based accounts of learning. This invites us to consider the alternative possibility, that the

1.2 The disconnect between logic and language  5 meanings of logical expressions are innately specified, as part of the language faculty. We should make it clear what we take to be the relationship between logic and language. Our topic is the sentence-level language abilities of children and adults, as they comprehend sentences that contain expressions that correspond to those of first-order logic.2 We will not be discussing the broader range of abilities that are required to calculate entailment relations between sentences. Accessing the meanings of logical expressions is a necessary prerequisite for making such inferences, but it is not the whole story. In addition to knowledge of the meanings of the logical expressions, making inferences requires the resources provided by the recursive computational system (syntax). In Chomsky (2000a, p. 94), the following “evolutionary fable” was formulated to clarify the need for a computational system that interfaces with the cognitive and perceptual systems in order to use linguistic expressions to convey thoughts: Imagine some primate with the human mental architecture and sensorimotor apparatus in place, but no language organ. It has our modes of perceptual organization, our propositional attitudes (beliefs, desires, hopes, fears, etc.) insofar as these are not mentioned by language, perhaps a “language of thought” in Jerry Fodor’s sense, but no way to express its thoughts by means of linguistic expressions, so that they remain largely inaccessible to it, and to others.

The thought experiment by Chomsky (2000a) was further fleshed out by Reinhart (2006, p. 2), who endows the primate with an innate system of logical concepts that is the equivalent to that of humans. The primate would still lack the means to express its thoughts, including logical inferences, to other primates: Let us assume, further, that he has an innate system of logic, an abstract formal system, which contains an inventory of abstract symbols, connective functions, and definitions necessary for inference. What would he be able to do with these systems? Not much. Based on the rich concept system of humans, his inference system should in principle allow him to construct sophisticated theories and communicate them to his fellow primates. However, the inference system operates on propositions, not on concepts, so it is unusable for the primate in our thought experiment. Possibly he could code concepts in sounds, but not the propositions needed for inference. Pursuing this thought experiment, the goal of linguistic theory can be described as reconstructing the system the primate lacks, which consists of

6  Logic and human languages whatever is needed to facilitate the interface of his various cognitive systems. In other words, the goal is to construct the computational system (CS) (syntax in a broad sense) that defines language…

As Reinhart argues, a primate armed only with knowledge of the concepts of first-order logic would be unable to apply this knowledge in the production and comprehension of propositions, or in discerning the entailment relations between sentences that express these propositions. To put the logical vocabulary to use, a computational system is required. Following Chomsky and Reinhart, we will assume that a single computational system underpins all of the ways in which language is put to use by humans, including assigning truth conditions to sentences with logical expressions, and making logical inferences based on these assignments. In Chapter 3, we substantiate the claim that the same structural principles used to determine the reference of pronouns in human languages are also used (a) for the interpretation of logical expressions in sentences involving ­quantifier–variable binding, (b) to decide on the interpretations of sentences with disjunction, conjunction, and focus expressions, and (c) to compute the meanings of sentences with multiple logical expressions. As a final note, recent brain imaging research indicates that, in processing sentences with logical expressions, 4-year-old English-speaking and Mandarin-speaking ­children have been found to recruit the same brain regions that support language in adults (Heschl’s Gyrus, BA40 and BA44). Interestingly, the brain regions active in children are only a subset of those regions that have been found to distinguish adult Mandarin speakers and adult English speakers. The brain asymmetries that have been uncovered for adults, across languages, appear to develop only gradually in children. In the early stages of language acquisition, children acquiring different languages appear to engage a specialized language processing system (i.e., Language Acquisition Device) for processing sentences, both with and without logical expressions.

1.3

Principles of logic and language

We begin with an example of a statement that can be expressed in many human languages. This kind of statement invokes two of the logical operators of firstorder logic. The statement we have in mind contains disjunction in the scope of negation. Consider, as an example, the English sentence John didn’t see Ted order pasta or sushi. For English speakers, this sentence is true if (a) John didn’t see Ted order pasta and (b) John didn’t see Ted order sushi. We call

1.3 Principles of logic and language

7

this the conjunctive interpretation of disjunction under negation. In first-order logic, the conjunctive entailment of disjunction in the scope of negation is stated as one of de Morgan’s laws: —( A ™ B)  —A ˜ —B

where ™ is inclusive-or, ˜ is conjunction, ¬ is negation, and  indicates entailment. Examples (2–5) are translations of (1) John didn’t see Ted order pasta or sushi into Mandarin in (2), Japanese in (3), Dutch in (4), Russian in (5), Norwegian in (6), and Hungarian in (7). The interpretation of the corresponding sentence in each language is the same. Negation and disjunction are boldfaced in the examples. (1) (2) (3) (4) (5) (6) (7)

John didn’t see Ted order pasta or sushi. Yuehan mei kanjian Ted dian yidalimianshi huozhe shousi. John-wa Ted-ga sushi ka pasuta-o tanomu-no-o mi-nakat-ta. John zag Ted niet pasta of sushi bestellen. Dzhon ne videl/uvidel chto/kak Borja zakazal/zakazyval pastu ili sushi. Jon så ikke Ted bestille pasta eller sushi. János nem látta Edvardot tésztát vagy szusit rendelni.

The conjunctive entailment of disjunction in the scope of negation holds only if disjunction is interpreted as inclusive disjunction (inclusive-or), as in firstorder logic. To see this, consider the truth conditions of inclusive-or. A statement of the form (A ™ B) is true in three cases: (i) if A is true but not B, (ii) if B is true but not A, and (iii) if both A and B are true. A statement of the form (A ™ B) is false, therefore, only if both A and B are false. This means that the negated disjunction ¬(A ™ B) is true in cases where both A and B are false. It follows that ¬(A ™ B) logically entails (¬A ˜ ¬B).3 Despite examples like (1–7), many linguists and philosophers have concluded that the expressions corresponding to disjunction in human languages do not have the meaning of disjunction in first-order logic. Many researchers have reached the conclusion that the expressions for disjunction in human languages have the meaning associated with exclusive-or. Others are convinced that or is ambiguous between inclusive disjunction and exclusive disjunction. For example, Braine and Rumain (1983, p. 291) acknowledge the view that “equates or with standard logic,” yet reject this view on the grounds that “coherent judgments of the truth of or-statements emerge relatively late and are not universal in adults.” They conclude that disjunction is exclusive-or more often than not, even for adults (e.g., Kegley and Kegley 1978; Richards 1978).

8  Logic and human languages This conclusion is unwarranted, as Grice and others have argued. Consider the following situation – John watches Ted order sushi and then go back to order pasta. Now consider the following alternative descriptions of the situation. (8) (9)

John saw Ted order sushi or pasta. John saw Ted order sushi and pasta.

From a logical point of view, both statements are true, at least if the English word for disjunction, or, is assigned an inclusive-or interpretation in (8). But the statement with or in (8) is pragmatically odd as a description of the situation. Here is why. In judging the truth or falsity of sentences, people are influenced not only by the semantic properties of these expressions but also by pragmatic principles. One of the most basic principles of pragmatics is Grice’s Principle of Cooperation. This principle of conversation entreats speakers to be as informative as possible, and it can be invoked to explain why the use of or typically implies exclusivity (not both), at least for adults. Returning to (8) John saw Ted order sushi or pasta, this statement is judged by most adult English speakers to imply that John saw Ted order sushi, or John saw Ted order pasta, but not both. This implicature of exclusivity (not both) derives from the availability of another statement that is more informative, namely (9) John saw Ted order sushi and pasta. If John had seen Ted order both sushi and pasta, then (9) directly conveys what John saw. Example (8) also conveys this, but less directly – in the sense that (8) would also be true if John saw Ted order sushi but not pasta, or if John saw Ted order pasta but not sushi. Because (9) is true in only the one circumstance (in which John saw Ted order both), it is said to be more informative. More generally, a statement of the form A and B is more informative than one of the form A or B (where both statements are true descriptions of the events that took place). The statement A and B is more informative because a statement of this form is true only if both A and B are true, whereas a statement of the form A or B is true in the same circumstances, but it is also true in other circumstances as well, where only A is true, or where only B is true. So, the truth conditions that verify A and B constitute a subset of the circumstances that verify A or B. Consequently, the expressions or and and form a scale, based on information strength, with and being more informative than or. This is where the Principle of Cooperation comes in. Upon hearing someone use the less informative term or, listeners assume that the speaker was being cooperative, so they infer that the speaker was not in a position to use the more informative term and. Therefore, the speaker’s use of or is taken to imply the negation of the stronger statement, so the use of or is taken to imply not both A and B.

1.3 Principles of logic and language  9 The basic meaning of disjunction is inclusive-or. In positive statements, however, there is an implicature of exclusivity. Disjunction is still inclusive-or in statements of the form A or B, but hearers are invited to make a pragmatic inference that excludes the possibility of both A and B being true. So statements of the form A or B are interpreted as generating a “derived” meaning in human languages: A or B, but not both A and B. This derived meaning of disjunction is not generated in negated statements, so negated disjunctions retain the basic inclusive-or interpretation. This was illustrated in (1), repeated here as (10): John didn’t see Ted order pasta or sushi. This example entails that John didn’t see Ted order pasta and it entails that John didn’t see Ted order sushi. This conjunctive entailment of negated disjunctions follows only if disjunction is assigned the inclusive-or interpretation, as in first-order logic. Why is there no implicature of exclusivity in interpreting sentences of this form? To answer this, compare (10) and (11), where or has been replaced by and. (10) (11)

John didn’t see Ted order pasta or sushi. John didn’t see Ted order pasta and sushi. a. He just saw Ted order sushi. b. He just saw Ted order pasta. c. In fact, he didn’t see Ted order either.

Adults judge (11) to be true in various different circumstances, as indicated by the possible follow-up comments in (11a–c). By contrast, (10) is judged to be true in only one set of circumstances, where Ted ordered neither sushi nor pasta. This means that (10) is true in a subset of the circumstances that verify (11). The upshot is that negation reverses the subset/superset relations of truth conditions that hold for positive statements with or and and. In the scope of negation, the use of or makes a stronger statement than the corresponding statement with and. Under negation, therefore, the implicature of exclusivity for or is not generated.4 The moral is that the implicature of exclusivity (not both) must be removed to unveil the meaning that human languages assign to statements with disjunction. One way to remove the implicature is to reverse the scale of information strength, by introducing specific linguistic expressions, such as negation. By reversing the entailments that give rise to such implicatures, we clear the decks for a clearer look at the meaning of disjunction in human languages. Once this is done, we immediately see that the expressions for disjunction in many human languages conform to first-order logic. In previous work, we have adopted this research strategy to investigate whether or not typologically different languages assign the conjunctive entailment to negated disjunctions,

10  Logic and human languages as in one of de Morgan’s laws. Some of the findings are illustrated in the languages surveyed using examples (1–7). They reveal that human languages typically assign the conjunctive entailment to disjunction in negative sentences. We will use the same strategy, beginning in the next section, to demonstrate that the parallels between logic and language run much deeper than just adherence to one of de Morgan’s laws. In order to accomplish our goal, we will extend the range of linguistic expressions that reverse entailment relations. In fact, negation is just the tip of a very large iceberg. Other linguistic expressions that reverse entailments include (the subject phrase of) the universal quantifier and (the antecedent of) conditionals, among many others. The class of linguistic expressions that reverse entailments is called downward-entailing expressions. The definition and some of the diagnostic properties of downward entailment is the topic of the next section. Using examples from English and Mandarin, we will invoke downward-entailing linguistic expressions to argue that human languages draw extensively on the resources of first-order logic. Although we will limit the examples to just these two languages for the most part, we want it understood that the same case could have been made using many other languages. In addition to English and Mandarin Chinese, we have verified the logical principles that we describe in the present book across a broad spectrum of human languages, including Russian, Japanese, European Portuguese, Italian, and Dutch. 1.4

Downward entailment

To continue the discussion of the overlap between logic and language, this section will describe several principles that involve the semantic property of downward entailment. At the broadest cut, a linguistic expression is downward entailing if and only if it licenses inferences from general to specific reference. More precisely, a linguistic expression is downward entailing if it licenses inferences from expressions referring to sets (e.g., car) to expressions referring to their subsets (e.g., Prius). Formally, downward-entailing linguistic contexts reverse entailment relations, so a linguistic context C is downward entailing if it follows from the fact that A entails B that C(B) entails C(A) (e.g., Ladusaw 1980; Landman 1991). A context with the English negative determiner nobody (Mandarin meiyouren) is downward entailing, according to this definition, since it is logically valid to infer from the statement Nobody at this table ate fruit (Zhe zhuo meiyouren chi shuiguo) to the statement Nobody at this table ate apples (Zhe zhuo meiyouren chi pingguo). Where ⇒ indicates logical entailment, the following entailments hold in both English and Mandarin.

1.4 Downward entailment  11 C = nobody at this table ate… (Zhe zhuo meiyouren chi …) A = fruit/shuiguo B = apples/pingguo (i) A ⇒ B (If x is an apple/pingguo, then x is fruit/shuiguo) (ii) C(B) ⇒ C(A) Nobody at this table ate fruit Zhe zhuo meiyouren chi shuiguo ⇒ Nobody at this table ate apples Zhe zhuo meiyouren chi pingguo

Many other expressions in human languages are downward entailing according to this definition. For example, a sentence with a pre-subject universal quantifier every in English is downward entailing on its subject phrase. To see this, notice that if the following statement is true – Every linguist who bought a car got a rebate – then another statement must also be true – Every linguist who bought a Prius got a rebate. The same inference in (12) is valid in all of the languages mentioned above. We illustrate with the Mandarin (13) (where mei is a universal quantifier). (12)

Every SUBJ[linguist who bought a car] got a rebate. ⇒ Every SUBJ[linguist who bought a Prius] got a rebate.

(13) Mei-ge SUBJ[mai-le qiche de yuyanxuejia] dou na-le huikou. every-cl buy-asp car de linguist all get-asp rebate 每个买了汽车的 语言学家都 拿了回扣。 ⇒ Mei-ge SUBJ[mai-le Puruisi qiche de yuyanxuejia] dou na-le every-cl buy-asp Prius car de linguist all get-asp huikou. rebate 每个买了普锐斯汽车的语言学家都拿了回扣。

In contrast to the subject phrase of sentences with a pre-subject universal quantifier, the predicate phrase of such sentences does not license the same inference – i.e., from the general term car to the specific term Prius. So, the English sentence Every linguist who got a rebate bought a car does not entail Every linguist who got a rebate bought a Prius, as (14) indicates. The same failure of entailment holds across all of the languages mentioned above. We illustrate with the Mandarin in (15). (14) (15)

Every linguist who got a rebate PRED[bought a car] *⇒ Every linguist who got a rebate PRED[bought a Prius] Mei-ge na-le huikou de yuyanxuejia PRED[dou mai-le every-cl get-asp rebate de linguist all buy-asp qiche]. car 每个拿了回扣的语言学家都买了汽车。

12  Logic and human languages *⇒ Mei-ge na-le huikou de yuyanxuejia PRED[dou mai-le every-cl get-asp rebate de linguist all buy-asp Puruisi qiche]. Prius car 每个拿了回扣的语言学家都买了普锐斯汽车。

To summarize, the subject phrase of the universal quantifier (English every, Mandarin mei) validates inferences from expressions referring to sets of things to expressions referring to subsets of those things. By contrast, the predicate phrase of the same sentences does not validate such inferences. We have made several observations now. First, disjunction generates a conjunctive entailment in the scope of negation. Second, negation is downward entailing. Finally, the universal quantifier is downward entailing on its subject phrase, but not on its predicate phrase. This invites us to ask whether disjunction generates a conjunctive entailment when it appears in the subject phrase of a universal quantifier, but not in the predicate phrase. The answer is affirmative. Consider the sentence Every person who ordered pasta or sushi became ill. This sentence entails the following: (a) every person who ordered pasta became ill, and (b) every person who ordered sushi became ill. So disjunction generates a conjunctive entailment when it appears in the subject phrase of a sentence with a pre-subject universal quantifier. The point is made graphically in (16). Example (17) shows that the same entailment holds in Mandarin. (16)

Every SUBJ[person who ordered pasta or sushi] PRED[became ill].

(17) Mei-ge SUBJ[dian-le yidalimianshi huozhe shousi de ren] every-cl order-asp pasta or sushi de person PRED[dou bing-le]. all ill-asp 每个点了意大利面食或者寿司的人都病了。 ‘Everyone who ordered pasta or sushi became ill.’ Meaning: everyone who ordered pasta became ill and everyone who ordered sushi became ill

Both negation and the subject phrase of the universal quantifier are downward entailing, and both license the conjunctive entailment of disjunction. So, we are led to ask if downward entailment and the conjunctive entailment of disjunction are in a one-to-one relation. Let us take a step towards answering this question by looking at the predicate phrase of the universal quantifier. The examples in (14) and (15) revealed that the predicate phrase is not downward entailing, either in English or in Mandarin. So, if downward entailment and the conjunctive entailment of disjunction are in a one-to-one relation, then disjunction should not generate a conjunctive entailment in the predicate phrase of the

1.4 Downward entailment  13 universal quantifier. To verify this, we can simply reverse the subject phrase and predicate phrase from the earlier examples, yielding example (18), where or appears in the predicate phrase. Compare this with (16), repeated here. (18) (16)

Every subj[person who became ill ] pred[ordered pasta or sushi] = Disjunctive Every subj[person who ordered pasta or sushi] pred[became ill] = Conjunctive

These examples reveal an asymmetry in the interpretation of disjunction in English sentences with the universal quantifier every. When English or appears in the predicate phrase, as in (18), it fails to generate a conjunctive entailment; (18) does not entail either that (a) every person who became ill ate pasta or that (b) every person who became ill ate sushi, so, (18) clearly cannot entail both (a) and (b). Instead, the truth conditions associated with or in the predicate phrase of every are quite broad in (18); the sentence is true if each person who became ill ate pasta or ate sushi, or both sushi and pasta. We will call this range of truth conditions associated with disjunction when it appears in nondownward-entailing linguistic contexts, disjunctive truth conditions. These disjunctive truth conditions are consistent with the proposal that disjunction is always interpreted as inclusive-or, as in the more restricted conjunctive truth conditions that are assigned when disjunction appears in a downward-entailing environment. The asymmetry in the interpretation of disjunction in the subject phrase versus the predicate phrase of the universal quantifier is schematically represented in (19). (19)

Every SUBJ[ … or … ] PRED[………….….]  Every SUBJ[ ….…….……] PRED[…. or …….]

= Conjunctive = Disjunctive

This is not just a fact about English. The same disjunctive truth conditions are assigned to the Mandarin translation of (18), as illustrated in (20). Similarly, for the other languages mentioned above, disjunction yields a conjunctive entailment in the subject phrase of the universal quantifier, but disjunction yields a wider range of disjunctive truth conditions when it appears in the predicate phrase of the universal quantifier. (20)

Mei-ge SUBJ[bing-le de ren] PRED[dou dian-le yidalimianshi every-cl ill-asp de person all order-asp pasta huozhe shousi]. or sushi 每个病了的人都点 了意大利面食或者寿司。 ‘Everyone who became ill ordered pasta or sushi.’

Across languages, then, the universal quantifier gives rise to an asymmetry in the interpretation of disjunction.

14  Logic and human languages Escalating further, let us look at another asymmetry involving downward entailment. The next linguistic structure under consideration is conditional statements. The first observation is that the antecedent clause of a conditional statement is downward entailing, as shown in (21). By contrast, the consequent clause of a conditional statement is not downward entailing, as shown in (22). (21)

If a linguist ordered a car, he got a rebate. ⇒ If a linguist ordered a Prius, he got a rebate.

(22)

If a linguist got a rebate, he ordered a car. *⇒ If a linguist got a rebate, he ordered a Prius.

Once again, this is not just a fact about the interpretation of conditional statements in English. If we translate the English examples into Mandarin, the same asymmetry is manifested. That is, the antecedent clause of a conditional statement is downward entailing, as shown in (23), but the consequent clause of a conditional statement is not downward entailing, as shown in (24). (23) Ruguo yi-ge yuyanxuejia mai-le qiche, ta jiu na-le huikou. if one-cl linguist buy-asp car he then get-asp rebate 如果一个语言学家买了汽车, 他就拿了回扣。 ‘If a linguist bought a car, he got a rebate.’ ⇒ Ruguo yi-ge yuyanxuejia mai-le Puruisi qiche, ta jiu na-le if one-cl linguist buy-asp Prius car he then get-asp huikou. rebate 如果一个语言学家买了普鲁士汽车, 他就拿了回扣。 ‘If a linguist bought a Prius, he got a rebate.’ (24) Ruguo yi-ge yuyanxuejia na-le huikou, ta jiu mai-le qiche. if one-cl linguist get-asp rebate he then buy-asp car 如果一个语言学家拿了回扣, 他就买了汽车。 ‘If a linguist got a rebate, he bought a car.’ *⇒ Ruguo yi-ge yuyanxuejia na-le huikou, ta jiu mai-le if one-cl linguist get-asp rebate he then buy-asp Puruisi qiche. Prius car 如果一个语言学家拿了回扣, 他就买了普鲁士汽车。 ‘If a linguist got a rebate, he bought a Prius.’

Having uncovered another asymmetry in downward entailment, we can check again to see how the words for disjunction (English or, Mandarin huozhe) are interpreted when they appear in the antecedent clause of a conditional statement, and when they appear in the consequent clause. Once again, the examples live up to expectations. In the antecedent clause of a conditional statement, disjunction generates a conjunctive entailment. This is illustrated in

1.4 Downward entailment  15 (25). By contrast, when disjunction appears in the consequent clause, it does not generate a conjunctive entailment; instead, the interpretation of disjunction is disjunctive, as illustrated in (26). (25) (26)

If Ted ordered pasta or sushi, then Max ordered pizza.  If Max ordered pizza, then Ted ordered pasta or sushi.

= Conjunctive = Disjunctive

Mandarin works the same way. In the antecedent clause of a conditional statement, disjunction generates a conjunctive entailment, as illustrated in (27). When disjunction appears in the consequent clause in Mandarin, the interpretation is disjunctive, as shown in (28). (27)

Ruguo Taide dian-le yidalimianshi huozhe shousi, name Makesi if Ted order-asp pasta or sushi, then Max dian-le pisa. order-asp pizza 如果泰德点了意大利面食或者寿司，那么马克思点了披萨。 ‘If Ted ordered pasta or sushi, then Max ordered pizza.’

(28)

Ruguo Makesi dian-le pisa, name Taide dian-le yidalimianshi if Max order-asp pizza, then Ted order-asp pasta huozhe shousi or sushi 如果马克思点了披萨，那么泰德点了意大利面食或者寿司。 ‘If Max ordered pizza, then Ted ordered pasta or sushi.’

The asymmetry in the interpretation of disjunction in the antecedent versus the consequent of a conditional statement is schematically depicted in (29). (29)

If ANT[ … or … ] then CONS[………….…..]  If ANT[ ….…….…… ] then CONS[…. or …….]

= Conjunctive  = Disjunctive

Here is where things now stand. Downward-entailing linguistic environments license the conjunctive entailment of disjunction, and non-downward-entailing linguistic environments do not license the conjunctive entailment of disjunction. Rather, non-downward-entailing linguistic environments license a disjunctive interpretation of disjunction. Let’s confirm this descriptive generalization with one more example. This example is the negative quantificational expression nobody. First, observe that nobody is downward entailing on its predicate phrase. As shown in (30), a setreferring expression, fruit, can be replaced by a subset-referring expression, apples, salva veritate. (30)

Nobody at this table pred[ate fruit] ⇒ Nobody at this table pred[ate apples]

16  Logic and human languages Now, as we have been led to expect, disjunction generates a conjunctive entailment in the predicate phrase of nobody. This is shown in (31). So, nobody contrasts with everybody. We saw earlier that everybody is not downward entailing on its predicate phrase, and does not license a conjunctive entailment of disjunction in that position, as (18), repeated here, illustrates. (31) (18)

Nobody who became ill pred[ordered pasta or sushi] Everybody who became ill pred[ordered pasta or sushi]

= Conjunctive = Disjunctive

What about Mandarin? In Mandarin, the quantificational phrase corresponding to English nobody is meiyouren. Example (32) corresponds to the English (30). The Mandarin example also indicates that it is valid to replace the set-referring term shuiguo ‘fruit’ by the subset-referring expression pingguo ‘apples’ in the predicate phrase of meiyouren. So, the negative quantificational expression meiyouren is downward entailing on its predicate phrase. (32) Zhe zhuo meiyouren chi shuiguo. this table nobody eat fruit 这桌没有人吃水果。 ‘Nobody at this table ate fruit.’ ⇒ Zhe zhuo meiyouren chi pingguo. this table nobody eat apple 这桌没有人吃苹果。 ‘Nobody at this table ate apples.’

Since meiyouren is downward entailing on its predicate phrase, it is anticipated that the word expressing disjunction in Mandarin, huozhe, will generate a conjunctive entailment when it appears in the predicate phrase of meiyouren, just as English or did in the predicate phrase of nobody. This is verified in (33). By contrast, it is anticipated that huozhe will not be interpreted conjunctively in the predicate phrase of the quantificational expression meigeren, just as we saw with English everybody. This is verified in (34). (33)

Zai jiuhui shang meiyouren chi-guo shousi huozhe yidalimianshi. at party prep nobody eat-asp sushi or pasta 在酒会上没有人吃过寿司或者意大利面。 ‘Nobody at the party ate sushi or pasta.’ = Conjunctive

(34)

Zai jiuhui shang meigeren chi-le shousi huozhe yidalimianshi. at party prep every-cl person eat-asp sushi or pasta 在酒会上每个人吃了寿司或者意大利面。 ‘Everybody at the party ate sushi or pasta.’ = Disjunctive

We have all the ingredients we need to make a generalization. We began by observing that disjunction generates a conjunctive entailment in the scope

1.4 Downward entailment  17 of negation, across languages. This is the human language equivalent of one of de Morgan’s laws: ¬(A ∨ B) ⇒ ¬A ∧ ¬B. We see now that disjunction also generates a conjunctive entailment when it appears with another negative expression, nobody. We observed that both expressions are downward entailing. We saw, in addition, that disjunction generates a conjunctive entailment when it appears in the subject phrase of the universal quantifier, but not in the predicate phrase; moreover, we saw that the subject phrase of the universal quantifier, but not the predicate phrase, is downward entailing. Finally, we saw that disjunction generates a conjunctive entailment when it appears in the antecedent clause of a conditional statement, but not in the consequent clause; and, again, the antecedent clause, but not the consequent clause, proved to be downward entailing. Let us propose, then, that disjunction generates a conjunctive entailment when it appears in the scope of any downward-entailing expression, Δ. If so, then de Morgan’s law is just the tip of a logical iceberg, which is represented in (35). We discuss further instances of this generalization in Chapter 3. (35)

Δ(A ∨ B) ⇒ Δ(A) ∧ Δ(B)

The class of downward-entailing expressions in human languages is a motley collection, including negation, negative adverbs, certain prepositional phrases, the antecedent of conditionals (but not the consequent), certain determiners (but not others), verbs expressing minimum conditions, comparatives, and many others. Apparently, however, these expressions form a natural class in human languages, in the sense that all of the downwardentailing expressions adhere to the generalization in (35). This suggests that there may be an underlying set of core semantic properties that crop up over and over again in human languages. One member of this set of core properties is disjunction. And, as we have seen, disjunction in human languages is inclusive-or, just as it is in first-order logic. Other core properties include negative quantificational phrases like nobody, the universal quantifier and its like, e.g., everybody, as well as conditional statements. The parallels between human languages and classical first-order logic run deep, although these parallels have not been previously spelled out in detail. Neither have they been thoroughly investigated in child language, which is another research area that is ripe for investigation. If it turns out that young children, across languages, adopt a semantics for logical expressions in human languages which parallels the semantics of the corresponding expressions in first-order logic, then this would be a further argument that humans are biologically fitted with a logic faculty.

18  Logic and human languages Before we discuss child language, it will be useful to discuss a few more examples of expressions in human languages that are associated with expressions in first-order logic. The next topic is a class of such expressions, called negative polarity items, such as English any and Mandarin renhe. Interestingly, negative polarity items have positive counterparts, and both kinds of expressions correspond in meaning, in one way or another, to the existential quantifier of classical logic. Even more interesting is the fact that negative polarity items are licensed in precisely those linguistic contexts where disjunction generates a conjunctive entailment – i.e., in downward-entailing linguistic environments, such as in the subject phrase of the universal quantifier, and in the antecedent of conditionals. This suggests that negative polarity items and disjunction are related in meaning. 1.5

Negative polarity items

This section extends the argument that human languages draw upon the resources of first-order logic. We describe another linguistic phenomenon that distinguishes downward-entailing expressions from expressions that are not downward entailing. This phenomenon concerns the acceptability of so-called negative polarity items (NPIs), such as English any and Mandarin renhe. In English, the negative polarity item any is the semantic twin of the indefinite article some. Both are indefinite existential expressions, with a meaning that corresponds at least in part to that of the existential quantifier in first-order logic (i.e., ∃). Roughly, the difference between any and some is in the linguistic contexts in which they can appear. Negative polarity items like any (and its ilk – ever, at all) are restricted to negative linguistic contexts. By contrast, some thrives in positive contexts, and does not enjoy the company of negative expressions (in a sense we will discuss momentarily), so it is commonly referred to as a positive polarity item (PPI). To see that some and any are related in meaning, it will be useful to point out some similarities in distribution and interpretation, as well as some differences. First, let’s look at a couple of the differences. We begin with a difference in distribution. As (36a) shows, the negative polarity item any is not tolerated in ordinary positive linguistic contexts, but the indefinite some is well received in such contexts, as (36b) shows. (36)

a. b.

John ate *any of the kangaroo. John ate some of the kangaroo. 

∃x(Kangaroo[x] ∧ John ate x)

A more subtle difference is in interpretation. Both any and some are acceptable in the scope of negation, as shown in (37). However, these expressions are

1.5 Negative polarity items  19 assigned different interpretations in such sentences. Notice first the possible and impossible continuations to (37a) and (37b). (37)

a. John didn’t eat any of the kangaroo. b. John didn’t eat some of the kangaroo. c. There’s some kangaroo that John didn’t eat.

(*But he did eat a little) (But he did eat a little) (But he did eat a little)

The fact that one cannot continue in the same way following some and any underscores a basic difference in interpretation. The negative polarity item any in (37a) is interpreted as making the strong statement that John avoided eating any of the kangaroo. Substituting some for any, as in (37b), yields a weaker statement. The reading of (37b) can be paraphrased as in (37c), where there is some kangaroo that John avoided eating, but there is an implicature that he did eat some of the kangaroo. The sentences in (37) can be rendered using first-order logic. Actually, (37a) can be rendered in first-order logic in two ways. First, John didn’t eat any of the kangaroo can be semantically represented using a logical form in which negation takes scope over the existential quantifier, as indicated below in (39). Second, the same statement can also be represented using the universal quantifier, ∀. This is also indicated below the example. If the universal quantifier is used, then the meaning of any is roughly the same as every, except that every takes scope over negation, and not the other way around.5 (38)

John didn’t eat any of the kangaroo.

(39) ¬∃x (Kangaroo[x] ∧ John ate x) ⇒ ∀x (Kangaroo[x] → ¬John ate x)

It is worth pointing out that neither of the logical forms in (39) presupposes the existence of some kangaroo for John to consume. Although the partitive structure any of the kangaroo implants the idea that there was some kangaroo in the conversational context, the logical form in (39) does away with this presupposition. It pays to recall that, in classical logic, the conditional logical form ∀x (Kangaroo [x] → ¬John ate x), is true if the antecedent is false, which will be the case if there is no kangaroo. It has been argued, however, that this kind of existential presupposition is one way in which human languages differ from classical logic (Strawson 1950; Diesing 1992; Higginbotham 1998). The use of quantification expressions like partitive expressions all of the…, some of the… and so on, all carry an existential presupposition, as indicated in (40). (40)

John didn’t eat any of the kangaroo. ∃x (Kangaroo[x]), ∀x (Kangaroo[x] → ¬John ate x)

20  Logic and human languages There is no need to worry about an existential presupposition when some appears in the scope of negation, as in (41). As the logical form indicates, this sentence asserts that there is some kangaroo that John didn’t eat. (41)

John didn’t eat some of the kangaroo. ∃x (Kangaroo[x] ∧ ¬John ate x)

As (41) indicates, some is interpreted as having scope over negation, even if disjunction appears in the scope of negation in the surface syntax: John didn’t eat some of the kangaroo. Accordingly, some is labeled a positive polarity item. Positive polarity items like English some stand in contrast to negative polarity items like any, which, as we have seen, are only licensed in negative contexts. The positive polarity item some is accepted in both negative and positive contexts: John ate some of the kangaroo, John didn’t eat some of the kangaroo. However, when the positive polarity item some appears in sentences with negation, it is interpreted as having scope over negation. So, John didn’t eat some of the kangaroo has just one logical form, as indicated in (41). The same logical form would be given to a sentence in which some preceded negation, as in There is some kangaroo that John didn’t eat. Although (41) John didn’t eat some of the kangaroo implies that John did, in fact, eat some of the kangaroo, this is not strictly speaking part of the meaning of the sentence. Rather, this feature of the meaning is contributed by an implicature. Assuming that the logical form in (41) adequately spells out the truth conditions for the statement John didn’t eat some of the kangaroo, then from a logical point of view, the statement is true if John didn’t eat any of the kangaroo (as long as the presupposition of existence is met). However, it does not follow that if it is true that there’s some kangaroo John didn’t eat, then it’s also true that John didn’t eat any of the kangaroo. That is, (38) asymmetrically entails (41). When logical form A entails logical form B (but not vice versa), then A is verified in a narrower set of circumstances than those that verify B. This means that A makes a stronger statement than B, since information strength is defined by asymmetric entailment. So, (38) John didn’t eat any of the kangaroo makes a stronger statement than (41) John didn’t eat some of the kangaroo. As we have seen, adherence to the Principle of Cooperation entreats speakers to use expressions that make the strongest statement they are in a position to make. So, if both (38) and (41) are known by the speaker to be true, then the speaker will choose to convey what they know using (38), with any rather than with some. If the speaker chooses to utter (41), then, this invites the pragmatic inferences that the speaker is not in a position to use (38), and chooses to use the

1.5 Negative polarity items  21 weaker statement in (41). By implication, the speaker intends to convey the message that John did indeed eat some of the kangaroo, but not all of it. Having pointed out some differences in the interpretation of some versus any, let us turn to some linguistic contexts where both some and any can appear, and where they receive the same interpretation. One such context is one in which negation appears in a higher clause than the clause that contains negation and the indefinite expression (some or any). This is illustrated in (42). Notice that (42) contains the statement in (38) as a constituent. In this constituent, either some or any may appear, salva veritate. (42)

You’ll never convince me that John didn’t eat some/any of the kangaroo.

Another linguistic context in which both some and any may appear, with the same interpretation, is in the antecedent of conditionals. This is illustrated in (43). (43)

If John eats some/any of the kangaroo, Max will order crocodile.

From the perspective of first-order logic, it is no accident that some/any should be interpreted in the same way in the antecedent of a conditional, such as (43), and in the scope of a higher negation operator, as in (42). This is because any occurrence of some/any within the antecedent of a conditional is already within the scope of a negation operator, from the standpoint of first-order logic, since A → B is logically equivalent to ¬A ∨ B. Based on the examples we have discussed so far, we can reach some general conclusions. First, the expressions some and any seem to be two sides of the same coin. Both are indefinite expressions, related to the existential quantifier in first-order logic. But the environments in which they are licensed are not the same. Some is licensed in both positive and negative sentences, whereas any is licensed only in negative sentences. However, when some appears in negative sentences, it is interpreted as having scope over negation. There are contexts, however, in which these expressions receive (almost) the same interpretation. These contexts include ones with an additional negative expression in a higher clause than the clause that contains some/any, and in the antecedent of conditionals. The next task is to establish the nature of the linguistic contexts that do and do not license any. Example (44) demonstrates that English any is tolerated in the predicate phrase of nobody, and (45) shows that any is blocked from appearing in the predicate phrase of everybody. Examples (46) and (47) reveal, similarly, that Mandarin renhe is accepted in the predicate phrase of mei­youren, but not in the predicate phrase of meigeren.

22  Logic and human languages (44)

Nobody on the bus PRED[drank any beverage]

(45)

Everybody on the bus PRED[drank *any beverage]

(46)

renhe yinliao] Gongche shang meiyouren PRED[he bus on nobody drink any beverage 公车上没有人PRED[喝任何饮料]。 ‘On the bus, nobody drinks any beverage.’

(47)

Gongche shang meigeren PRED[he *renhe yinliao] bus on everybody drink any beverage 公车上每个人PRED[喝*任何饮料]。 ‘On the bus, everybody drinks *any beverage.’

We saw that the negative polarity item any, as well as the indefinite some, is licensed in the antecedent of a conditional. This was expected because of the logical equivalence in first-order logic between A → B and ¬A ∨ B. This invites the inference that the negative polarity item any will not be tolerated in the consequent of a conditional, since there is no downward-entailing operator to license it in that position. Example (48) shows that, whereas any is licensed in the antecedent of a conditional statement, as shown in (48a), it is not licensed in the consequent clause, as shown in (48b). The same is true in ruguo conditionals in Mandarin.6 The adult speakers we have interviewed were found to judge (49a) as acceptable, where the negative polarity item renhe appears in the antecedent of a conditional statement, but they did not accept renhe in the consequent, as in (49b). (48)

a. If John ate any ice cream, he became ill. ANT[If John ate any ice cream] CONS[he became ill] b. If John became ill, he ate *any ice cream. ANT[If John became ill] CONS[he ate *any ice cream]

(49) a. ANT[Ruguo Yuehan chi-le renhe bingjiling] CONS[ ta jiu shengbing]. if John eat-asp any ice-cream he then become-ill ANT[如果约翰吃了任何冰激凌], CONS[他就生病]。 ‘If John ate any ice cream, he became ill.’ b. ANT[Ruguo Yuehan shengbing-le] CONS[ ta jiu chi *renhe bingjiling]  if John become-ill-asp he then eat any ice-cream ANT[如果约翰生病了]， CONS[他就吃*任何冰激凌] ‘If John became ill, he ate *any ice cream.’

It has come time to seek unification. We have been describing several linguistic phenomena: downward entailment, the interpretation of disjunction, and the licensing of negative polarity items. Although these phenomena look quite different at first glance, we have witnessed some striking parallels between them. We observed, first, that both the antecedent clause of conditionals and

1.5 Negative polarity items  23 the subject phrase of sentences with the universal quantifier every are downward entailing. By definition, a linguistic expression is downward entailing if it validates inferences from expressions referring to a set of entities (e.g., car) to expressions referring to a subset of those entities (e.g., Prius). This feature of both linguistic contexts is graphically represented in (50). (50) a. b.

If ANT[ set ⇒ subset ] then CONS[…….……….….] If ANT[ ….…….….…] then CONS[ set #⇒ subset ] Every SUBJ[ set ⇒ subset ] PRED[…..……..….….] Every SUBJ[ ….…….…….] PRED[ set #⇒ subset ]

We proceeded to consider how disjunction was interpreted in the same linguistic contexts. Although the basic meaning of disjunction is the same everywhere, namely inclusive-or, we saw that disjunction generates a conjunctive entailment in downward-entailing linguistic contexts, but not elsewhere. We attributed this to the fact that downward-entailing contexts reverse entailments and cancel scalar implicatures that arise in ordinary (non-downward-entailing) linguistic environments. This generalization across constructions is graphically represented in (51). (51) a. b.

If ANT[ … or … ] then CONS[………….…..] If ANT[ ….…….…… ] then CONS[….or …….] Every SUBJ[ … or … ] PRED[………….…..] Every SUBJ[ ….…….……] PRED[….or …….]

= Conjunctive = Disjunctive = Conjunctive = Disjunctive

The third linguistic phenomenon we discussed was the licensing of negative polarity expressions, such as English any and Mandarin renhe. So far, we have seen that these negative polarity expressions are accepted in the antecedent of conditionals, but not in the consequent, as indicated in (52a). And we have seen that any and renhe are not accepted in the predicate phrase of the universal quantifier. (52) a. b.

If ANT[ … any/renhe… ] then CONS[……..……..….…] If ANT[ ….……. ….…] then CONS[… *any/*renhe…] Every SUBJ[ … any/renhe … ] PRED[………….….…..] Every SUBJ[ ….……. ……] PRED[…*any/*renhe…]

There is just one cell to fill in before we can state an over-arching generalization. We must make sure that any and renhe are accepted in the subject phrase of the universal quantifier. For example, witness the unacceptability of the following sentence, with any in the predicate phrase: Every passenger who became ill ate *any ice cream. As anticipated, (53) shows that any is acceptable in the subject phrase of the universal quantifier every in English.

24  Logic and human languages (53)

Every book that is recommended by any professor is worth reading Every SUBJ[book that is recommended by any professor] PRED[is worth reading]

(54)

Every book that is worth reading is recommended by *any professor Every SUBJ[book that is worth reading] PRED[is recommended by *any professor]

It turns out to be difficult to construct Mandarin examples in which the universal quantifier mei can be used in combination with the negative polarity expression renhe. Interestingly, however, renhe can itself be used as a universal quantifier in certain linguistic environments. And as a universal quantifier, renhe licenses the negative polarity renhe in the subject phrase, as in (55), but it does not license renhe in the predicate phrase, as (56) illustrates. (55)

Renhe jiaoshou tuijian de renhe shu dou zhide kan. Renhe SUBJ[ jiaoshou tuijian de renhe shu] PRED[ dou zhide kan] every professor recommend de any book all worth reading 任何教授推荐的任何书都值得看。 ‘Every book that is recommended by any professor is worth reading.’

(56)

Renhe zhide kan de shu *renhe jiaoshou dou tuijianle. Renhe SUBJ[ zhide kan de shu] PRED[*renhe jiaoshou dou every worth reading de book any professor all tuijianle] recommend 任何值得看的书任何教授都推荐了。 ‘Every book that is worth reading is recommended by any professor.’

We have described three different phenomena: downward entailment, the interpretation of disjunction and the licensing of negative polarity expressions. In the next section, we will attempt to explain why disjunction generates a conjunctive entailment in downward-entailing linguistic environments and why negative polarity expressions are licensed in downward-entailing environments, but not otherwise. If our account is on the right track, these linguistic phenomena are just two sides of the same coin. As in any other science, progress is made in linguistics when apparently unrelated facts can be amalgamated. As the physicist Richard Feynman (1963, pp. 23–24) remarks: The things with which we concern ourselves in science appear in myriad forms, and with a multitude of attributes … Curiosity demands that we ask questions, that we try to put things together and try to understand this multitude of aspects as perhaps resulting from the action of a relatively small number of elemental things and forces acting in an infinite variety of combinations … In this way we try gradually to analyze all things, to put together things which at first sight look different, with the hope that we

1.6 Domain widening  25 may be able to reduce the number of different things and thereby understand them better.

Another reason to seek amalgamation is that this makes the task of language learning considerably easier. If several linguistic phenomena are related, then they will not have to be learned independently. As we have seen, two differentlooking linguistic phenomena (the interpretation of disjunction and the licensing of negative polarity expressions) crop up in the same linguistic contexts (downward-entailing contexts). This fact would be unexplained in accounts of language learning that treated these phenomena in isolation. In the next section we try to state what these two superficially unrelated phenomena have in common. This requires a discussion of what is called domain widening. 1.6

Domain widening

Assuming that the generalization we have reached is on the right track, we should ask why so-called negative polarity items such as English any and Mandarin renhe can only reside in downward-entailing linguistic contexts. Since disjunction words such as English or and Mandarin huozhe receive a unique interpretation (the conjunctive entailment) in the same contexts, we are invited to ask what negative polarity items have in common with disjunction words in human languages. The account we offer is tied to the fact that negative polarity items are used to extend a domain, so as to include entities beyond those that would ordinarily be assumed to be under consideration. This domain-widening flavor of English any is captured in the dialogue in (57). (57)

C u st om e r : W ai t e r : C u st om e r : W ai t e r :

Do you serve Mexican food? No. What about desserts? Do you have flan? We don’t serve any Mexican dishes.

Accounts that use domain widening to explain the licensing conditions for negative polarity items like any and renhe appeal to the fact that, from a logical point of view, widening a domain increases information strength. In other words, introducing any in a downward-entailing linguistic environment leads to a stronger statement than would have been made without any (i.e., with a bare NP). As we have seen, one of the central goals of conversational exchanges is for speakers to make the strongest statements they are entitled to make. So, the use of any is felicitous in downward-entailing environments because it makes the statement stronger than would be made otherwise. In

26  Logic and human languages non-downward-entailing contexts, by contrast, the use of any would result in weakening. For this reason, any is not tolerated in non-downward-entailing linguistic contexts. The formulas associated with domain widening are given in (58). (58)

Where D ⊆ D′, for any P, Q a. (∃x ∈ D)(P[x] ∧ Q[x]) b. ¬(∃x ∈ D′)(P[x] ∧ Q[x])

⇒ (∃x ∈ D′) (P[x] ∧ Q[x]) ⇒ ¬(∃x ∈ D) (P[x] ∧ Q[x])

We are advancing towards another generalization. It appears that downwardentailing linguistic contexts license the conjunctive entailment of disjunction, and it appears that these same linguistic contexts license negative polarity items such as any and renhe. This suggests that disjunction shares something in common with negative polarity licensing. An entryway into the relationship is to cite an observation made by Jayaseelan (2001, p. 79): think of the meaning of disjunction as an assertion that at least one of a given set of entities, if substituted for a variable in an open sentence, yields a true proposition.

Jayaseelan is pointing out a logical equivalence between disjunction and the indefinite noun phrase at least one, which is the human language counterpart to the existential quantifier in first-order logic, i.e., ∃. From a logical point of view, an expression using disjunction, such as L(a1) ∨ L(a2), is equivalent to one with an existential quantifier, ∃x: x ∈ { a1, a2 } [Lx]. Here is a ­simple example: suppose there are two people in the next room, Max and Jon. Suppose that one of them laughs, or they both laugh. In either case, the disjunctive statement Jon laughed or Max laughed is true. It also follows, by existential generalization, that the statement someone laughed is true. This is just one instance of the human language counterpart to the relationship between quantificational operators and logical connectives in classical logic: the existential quantifier is disjunctive, and the universal quantifier is conjunctive. In classical logic, in a domain with two objects, a and b, ∃xPx expands to Pa ∨ Pb; and ∀xPx expands to Pa ∧ Pb. The same relationship holds in human languages. The reason someone laughed can be expanded to Jon laughed or Max laughed is because the underlying logical form of someone laughed just is ∃xLx and the underlying logical form of Jon laughed or Max laughed just is Lj ∨ Lm. If there are only two objects j and m in the universe of discourse, the existential formula ∃xLx can be replaced at the level of logical form by its disjunctive expansion Lj ∨ Lm. Another parallel between existential quantification and disjunction concerns negation. As we know from one of de Morgan’s laws, the negation of

1.6 Domain widening  27 a disjunction is logically equivalent to a conjunction of the negations of each disjunct: ¬(A ∨ B) ⇒ ¬A ∧ ¬B. In the scope of negation, negative polarity items can also be viewed as a conjunction of negations, this time the negations extend to every element in the domain of discourse. (59)

Just as So

¬(A ∨ B) ⇒ ¬A ∧ ¬B ¬(∃x Fx) ⇒ ¬Fa ∧ ¬Fb ∧ ¬Fc….

As we have seen, negative polarity items are existential expressions. In addition, negative polarity items are domain widening. It may be helpful to look at domain widening in the following way. The extension of a negated existential formula, ¬(∃x Fx), is ordinarily taken to exclude the typical entities that are F (say a, b, c). However, when the existential NPI any is introduced, then the negated existential formula, ¬(any (x) Fx), extends the entities that are not F to include everything in the domain. So, under negation, the typical things that are F are excluded, ¬Fa and ¬Fb and ¬Fc, but less typical things that are F are also excluded, so ¬Fh and ¬Fi and ¬Fj and so on. Since any exhausts the entire domain, we might say that the existential any expresses an infinite disjunction which, under negation, is logically equivalent to an infinite conjunction of negations. The conclusion that the meaning of any is disjunctive can be traced back at least to Jackendoff (1972). The semantic relationship between the interpretation of disjunction and the interpretation of negative polarity items underscores the value of the nativist approach to the analysis of logical expressions in human languages. Although first-order logic does not encompass notions like information strength, it does provide the mechanisms for explaining such notions, and it also provides the mechanisms for unifying superficially unrelated linguistic phenomena, including disjunction and existential quantification. It turns out that another superficially unrelated class of expressions also has much in common with disjunction and negative polarity licensing in many human languages. These are expressions that are otherwise used to form whquestions. As we discuss in the following section, wh-expressions and negative polarity items are interpreted in the same way in many of the world’s languages. And, remarkably, in some languages wh-words are combined with disjunctive words to form indefinites (corresponding to English someone or something), and when such combinations appear in downward-entailing contexts, they are negative polarity items (corresponding to English anyone or anything). This is further evidence that an attempt to unify disjunction and negative polarity licensing is on the right track. Again, the glue that holds these superficially unrelated phenomena together is the semantic property of downward entailment.

28  Logic and human languages 1.7

Wh-words

In the previous section, we concluded that indefinites such as the existential expression some and the negative polarity item any are related in meaning to disjunctive words, such as English or. This section introduces another linguistic expression that is semantically related to both indefinites and disjunctive expressions, namely wh-words such as who, what, when, where, which, etc. First, consider the existential statement in (60). (60)

Someone took Max’s iPhone.

Existential statements with the indefinite some, such as (60), are true if there is a corresponding true statement in which some is replaced by a referring expression (i.e., a name, definite description, or demonstrative expression). The referring expression must pick out something in the domain of discourse which satisfies the predicate in the original expression with some. Thus, for Someone took Max’s iPhone to be true, some such statement as in (61) must be true, where the guy over there or Ted or he satisfies the predicate … took Max’s iPhone. (61)

a. The guy over there took Max’s iPhone. b. Ted took Max’s iPhone. c. He took Max’s iPhone.

Such statements in logic are said to be witnesses for the existentially quantified statement. Existential Generalization (a.k.a. Existential Introduction) is the rule in logic that allows one to infer from a witness Fa to the existential statement it grounds ∃xFx, where a is a definite referring expression. Disjunctions are exactly the same. If the disjunctive statement Ted or Jon took Max’s iPhone is true then either Ted took Max’s iPhone is true or else Jon took Max’s iPhone is true. More generally, A ∨ B is true in virtue of one or the other disjunct A, B being true. Thus, A (or B) is a witness for A ∨ B in the same way Fa is a witness for ∃xFx. This insight is encapsulated in the introduction rule for disjunction, called Weakening. This rule allows us to infer A or B from either A alone, or from B alone. From this perspective, existentially quantified statements such as ∃xFx are just generalized disjunctions: Someone took Max’s iPhone is true if either (i) Ted took Max’s iPhone, or (ii) the guy over there took Max’s iPhone, or (iii) he took Max’s iPhone, or … And the rule of Existential Generalization is Weakening, suitably generalized. When we assert a disjunction, A ∨ B, we are signaling we do not know which one of {A, B} holds. Similarly, when we assert an existential statement, ∃xFx, we are asserting that some object(s) satisfies the predicate F, but we are

1.7 Wh-words  29 also signaling that we do not know which one(s). If we did know which of the disjuncts made the disjunction true or if we did know that the instance Fa made ∃xFx true we would be held to have violated the Gricean maxim governing the use of a disjunction or an existential statement, because we would not be asserting the strongest statement that is compatible with the information we commanded. Recall, however, that downward-entailing environments reverse entailments, so negated disjunctions and negated existentials make stronger statements than bare negations and existentials. So, ¬[A ∨ B] entails ¬A and ¬B, and ¬∃xFx entails ¬Fa and ¬Fb and ¬Fc, and so on. Let us now consider the semantics of wh-questions. The function of whwords in questions is to signal our intention to reduce uncertainty about the identity of persons or objects, the locations of objects, dates/times of events, and so forth. When we ask a wh-question such as (62) Who took Max’s iPhone?, we are seeking to eliminate our current ignorance about the identity of the relevant individual that satisfies the predicate …took Max’s iPhone. In other words, (62) indicates that we are after a witness for the corresponding existential statement Someone took Max’s iPhone. The assertoric force of (62) is roughly that indicated in (63). (62) (63)

Who took Max’s iPhone? Find the x such that x took Max’s iPhone.

Karttunen (1977, p. 4) suggests that a better term for wh-questions would be search questions. Karttunen (1977, p. 19) remarks that “for semantic reasons, we make wh-phrases equivalent to existentially quantified noun phrases. For example, who and what … will have the same meaning as someone and something…” In fact, in some languages indefinites and wh-words are identical. For example, in the Australian language Jaminjung, the same word nanggayin means who/somebody (Schultze-Berndt 2000, p. 45). It is even suggested that indefinites and wh-questions are “really identical and have the general meaning ‘lack of information’” (Haspelmath 1997). It is felicitous to pose a wh-question like the one in (62), however, only if our background information already includes the corresponding existential statement. That is, it is felicitous to ask Who took Max’s iPhone? only if the existential statement, Someone took Max’s iPhone, has already been established in the conversational context. In other words, the meaning of (some) wh-questions presupposes the corresponding existential statements. By transitivity, wh-questions can be analyzed as disjunctions. So, in a conversational context in which there are only three individuals, Jon, Ted, and Bill, the meaning of the wh-question Who took Max’s iPhone? would be the set consisting

30  Logic and human languages of all the disjuncts = {Jon took Max’s iPhone ∨ Ted took Max’s iPhone ∨ Bill took Max’s iPhone, … }. In short, the meaning of a wh-question is the set of its possible answers.7 Other wh-questions are more open, in the sense that they do not presuppose that the corresponding existential statement is true. We have in mind questions like Who wants ice cream?, where the speaker is asking for a show of hands. A paraphrase would be All those who want ice cream raise your hands. Such wh-questions are designed to find out whether or not the corresponding existential statement is true: someone wants ice cream. The question Who wants ice cream? is not felicitous if the speaker knows that no one wants ice cream, but it could turn out that no one raises their hands in response to the query. So, it is possible, it seems, for someone to pose the wh-question Who wants ice cream? without presupposing the associated existential statement, just as in the Yes/No question Does anyone want ice cream? Regardless, wh-questions seek to secure a referring expression (i.e., a name or definite description or demonstrative expression) that identifies a particular person who satisfies the predicate (if there is any such person). So, the whquestion Who took Max’s iPhone? is asking for the addressee to identify the person who satisfies the predicate ... took Max’s iPhone and, thereby, to identify someone who grounds the corresponding existential statement (in the sense of Existential Generalization). Wh-questions are thus witness-identification questions. They are requests to search the domain of discourse for some witness that makes the corresponding existential statement true. The witness is provided in the associated answers to the wh-question, as in (64). (64)

a. The guy over there. b. Ted took it. c. He did.

The semantic relationship between wh-questions and existential quantification was first made explicit by Hamblin (1973) and Karttunen (1977). Essentially, these researchers defined the meaning of the wh-question Who took Max’s iPhone? to be the set of (for Karttunen, true) answers to the question, i.e., the set of propositions that identify a suitable value for the variable x in the existential formula (see note 7): ∃x.ιy (iPhone[y] ∧ Owns[Max,y] ∧ Took[x,y] ∧ x≠Max’).8 The semantic associations among the three kinds of expressions under ­discussion are manifested overtly in many human languages (but not in English). Cross-linguistic research verifies the semantic relations among (a) existential expressions like some and any, (b) disjunctive words like or,

1.7 Wh-words  31 and (c) wh-words like what and who. In Japanese, for example, the word for disjunction ka combines with the wh-word dare (English who) to form an indefinite. So, the Japanese expression corresponding to English someone is dare-ka. As illustrated in (65), the Japanese counterpart to Someone laughed is Dare-ka-ga warat-ta. Japanese also uses the disjunction word ka as a question marker, so the Japanese counterpart to the English wh-question Who laughed? is (66) Dare-ga warat-ta ka? Notice that the only difference between (65) and (66) is in word order. In (66), ka has been separated from dare, leaving dare to assume the function of a wh-word, and ka to serve as a question marker.9 Finally, a Yes/No question is formed by combining both dare-ka and the question marker ka, as in (67). (65)

Dare-ka-ga warat-ta who-or-nom laugh-past ‘Someone laughed.’

(66)

Dare-ga warat-ta ka? who-nom laugh-past q ‘Who laughed?’

(67)

Dare-ka-ga warat-ta ka? who-or-nom laugh-past q ‘Did someone laugh?’

Other languages are essentially the same. For example, Sinhala is historically unrelated to Japanese, but Sinhala and Japanese look like close relatives syntactically. As in Japanese, existential expressions in Sinhala are formed by combining wh-words with disjunction. So, the expression corresponding to English someone in Sinhala is kau-də, which combines the wh-word kauru ‘who’ and the disjunction word də. Example (68) illustrates the use of də to mark disjunction in Sinhala, and example (69) shows that də also serves as a question marker, just as ka is both a disjunction word and a question marker in Japanese, as we saw in examples (65) and (66). (68)

Mahatteatə tee dә koopi dә oonə? ‘Do you (the gentleman) want tea or coffee?’

(69)

Chitra ee potə kieuwa dә? ‘Did Chitra read that book?’

It is worth asking what the individual contributions of the two parts are to the formation of existential expressions, (a) the wh-word and (b) the disjunction word. Two analyses have been proposed which capitalize on the semantic kinship between disjunction and existential quantification. On one analysis, the

32  Logic and human languages wh-word is a variable. The disjunction operator applies to the variable to form an existential expression (Cheng 1991; Jayaseelan 2001). This analysis takes seriously the idea, discussed in the last section, that existential quantification is infinite disjunction. An alternative approach by Paul Hagstrom (class notes, 2000) postulates that the wh-word represents the set of entities under consideration, so the wh-word who represents a set of people {Ted, Max, Sally,…}. The disjunction word represents an existential quantifier ∃ which chooses an element from the set.10 Let us bring our attention back to negative polarity items, which are another brand of indefinite expressions, albeit with the added pragmatic feature of domain widening. Negative polarity items are also formed by combining disjunctive words and wh-words in many human languages. This underscores the point that both indefinites (e.g., some) and negative polarity items (e.g., any) are existential quantifiers, as discussed in the previous section. For example, a reduplicated combination of wh-word plus disjunction constitutes a negative polarity item in Malagasy, as illustrated in (70). (70) a. b. c.

Tsy hitako na aiza na neg find.1sg or where or ‘I can’t find my sheep anywhere.’ Tsy matahotra na inona na neg fear or what or ‘He doesn’t fear anything.’ Tsy mahatakatra izany na iza neg cause.reach that or who ‘No one can afford that.’ (lit.) ‘Anyone can’t afford that.’

aiza ny where det

ondriko. sheep.1sg

inona izy. what 3(nom) na iza. or who

Although conventional wisdom has it that Japanese lacks negative polarity items, there are a few semantic structures that have the flavor of negative polarity expressions, namely when a question word like nani ‘what’ is combined with the word for disjunction, ka. (71) a. John-wa [Ted-ga nani-ka-o tanomu no]-o mi-nakat-ta. John-top [Ted-nom what-ka-acc order-prt-nmlzr]-acc see-neg-past b. (moshi) Ted-ga chuusyoku-ni nani-ka-o tanon-da-ra, (if) Ted-nom lunch-dat what-ka-acc order-past-cond, John-wa odoroku-darou. John-top surprised-will. ‘If Ted orders anything for lunch, John will be surprised.’

In other languages, the disjunction word is suppressed in the formation of negative polarity items, such that wh-words alone are negative polarity items. These

1.7 Wh-words  33 wh-words are not ambiguous, however. Recall that in the Australian language Jaminjung, the same word, nanggayin, means who and somebody (SchultzeBerndt 2000, p. 45). In some languages wh-words serve dual semantic functions, as negative polarity items and as wh-question markers. This is hardly surprising because, as we have seen, the meanings of wh-words and indefinites are semantically related. For our purposes, what is important is that the core semantic property, downward entailment, dictates when a wh-word is used to ask a question, and when it is interpreted as a negative polarity item, i.e., part of an assertion.11 In Mandarin Chinese, question words sometimes function as negative polarity expressions in downward-entailing contexts. In non-downward-entailing contexts, however, wh-words make their ordinary semantic contribution, marking the string of words as a question. For example, when the Mandarin question word shenme ‘what’ appears in the predicate phrase of the universal quantifier meigeren ‘everybody,’ the speaker is asking a question. This is because the predicate phrase of meigeren is not downward entailing. (72)

Zai jiuhui shang meigeren chi-le shenme shuiguo? at party prep every-cl person eat-asp what fruit 在酒会上每个人吃了什么水果? ‘What kind of fruit did everybody eat at the party?’

By contrast, when the question word shenme is combined with the logical expression meiyouren ‘nobody,’ the speaker is making an assertion, as in (73). This is because meiyouren ‘nobody’ is downward entailing on its predicate phrase, in contrast to meigeren ‘everybody.’ In the scope of meiyouren, shenme is interpreted as a negative polarity expression, like English any and Mandarin renhe. (73)

Zai jiuhui shang meiyouren chi-guo shenme shuiguo. at party prep nobody eat-asp what fruit 在酒会上没有人吃过什么水果。 ‘Nobody at the party ate any fruit.’

It will be useful to consider another example showing that the difference between posing a question and making an existential assertion turns on the semantic property of downward entailment. We observed earlier that the antecedent of conditionals is downward entailing, but not the consequent. Example (74) shows that the question word shei functions as a negative polarity item in the antecedent of conditionals, a downward-entailing context. By contrast, the same word shei marks (75) as a question, because shei appears in the consequent clause, which is not downward entailing.

34  Logic and human languages (74)

Eyu qu yao shei, maotouying dou zhao-le zhizhuxia bangmang. croc go bite who owl all find-asp Spiderman help 鳄鱼去咬谁猫头鹰都找了蜘蛛侠帮忙。 ‘If the croc went to bite anyone, the owl found Spiderman for help.’

(75)

Eyu qu yao xiaozhu, maotouying dou zhao-le shei bangmang? croc go bite pig owl all find-asp who help 鳄鱼去咬小猪猫头鹰都找了谁帮忙? ‘If the crocodile went to bite the pig, who did the owl go to for help?’

In Mandarin, therefore, the difference between asking a question and making an assertion can be conveyed using the same words, in different semantic structures. 1.8

Reversals of entailment

The pre-subject universal quantifier (English every, Mandarin mei) assigns a conjunctive interpretation to disjunction in the subject phrase, and it assigns a disjunctive interpretation to disjunction in the predicate phrase. Both sets of truth conditions are based on the inclusive-or interpretation of disjunction. But the interpretation of disjunction in the subject phrase of the universal quantifier is more restricted, because the subject phrase is downward entailing. In the predicate phrase, disjunction makes sentences true in a broader range of circumstances, which we refer to as disjunctive circumstances. A similar asymmetry was uncovered in the interpretation of disjunction in conditional statements. The antecedent of conditionals was seen to yield a conjunctive entailment of disjunction, whereas the consequent clause yields a disjunctive interpretation. These asymmetries are illustrated in (76) and (77). It should be understood that the same asymmetries arise in Mandarin, and in many, if not all, other human languages. (76)

Every SUBJ[ … or … ] PRED[………….….] Every SUBJ[ ….…….……] PRED[…. or …….]

= Conjunctive = Disjunctive

(77)

If ANT[ … or … ] then CONS[………….…..] If ANT[ ….…….…… ] then CONS[…. or …….]

= Conjunctive = Disjunctive

Asymmetries such as these pose a potential problem for children in the throes of language acquisition. The child would be mistaken to assume that linguistic expressions, such as disjunction, have a fixed interpretation, always generating the same truth conditions regardless of their structural position in a sentence. The question is how the learner knows to keep on the lookout for the different interpretations of disjunction in different structural positions, such as in

1.8 Reversals of entailment  35 sentences with the universal quantifier, English every, Mandarin mei. We have seen that disjunction generates different interpretations even in sentences that contain the same lexical material. Unless language learners partition strings of words into the right structural components, the potential problems associated with learning the different interpretations of a single lexical item are quite profound. It is one thing to identify the linguistic contexts in which some particular lexical item (e.g., any) can and cannot appear, but another thing to identify the different interpretations that can be assigned to a lexical item depending on the linguistic environment. Without sufficient linguistic knowledge of the structure of sentences of human language, this problem is indeed formidable. In the next two sections we further amplify the problems of language learnability faced by language learners. Let us elaborate briefly on three potential pitfalls of language learnability. In dealing with logical expression, one problem the child learner confronts is to grasp the meaning of the expression. If the meaning of disjunction is acquired by attending to the circumstances in which people use disjunctive statements, rather than its basic meaning in first-order logic, then the disjunctive word is likely to be assigned the meaning of exclusive-or. It is a matter of record that the vast majority of young children’s experience is consistent with the exclusive-or interpretation of disjunction (e.g., Is it red or blue?, Do you want ice cream or cake?). The learner faces a second potential pitfall in deciding on the meaning of quantificational expressions, such as the universal quantifier every. Not only could the meaning of every be mistaken for other expressions, e.g., several, many, and always, but the learner must also figure out the scopal properties of every. Beginning with Inhelder and Piaget (1964), it has been claimed that children misanalyze the domain of quantification of universal quantifiers, such that, for children, Every boy is riding a donkey means that the boys and donkeys are in a one-to-one correspondence, as if every means equinumerous. The third potential peril arises when logical expressions appear in combination. Suppose that some young children adopt the exclusive-or interpretation of disjunction. If so, it is difficult to see how they will be able to learn that disjunction generates a conjunctive entailment when it appears in the scope of downward-entailing linguistic expressions, such as in the subject phrase of the universal quantifier every. To appreciate the problem, note first that the conjunctive entailment of disjunction asymmetrically entails the disjunctive interpretation. Consider the sentence Every passenger who ate pasta or sushi became ill. If the sentence is true, then every passenger who ate pasta became

36  Logic and human languages ill and every passenger who ate sushi became ill. That is, disjunction generates a conjunctive entailment because it resides in the downward-entailing subject phrase every passenger who ate pasta or sushi. But, if the conjunctive truth conditions are met, then so are the disjunctive truth conditions, since the truth conditions corresponding to the conjunctive reading are a subset of those corresponding to the disjunctive reading. On the disjunctive reading, Every passenger who ate pasta or sushi became ill is true if every passenger who ate pasta became ill or if every passenger who ate sushi became ill. Clearly, this will be the case if every passenger who ate either one became ill. So, the disjunctive reading makes the sentence true in a broader range of circumstances than the conjunctive reading does. But this means that children who assign disjunctive truth conditions will have their interpretation confirmed by the input provided by language users who are interpreting the sentence more stringently, as demanding conjunctive truth conditions. This makes it difficult to see how children could abandon an erroneous disjunctive interpretation, if this is children’s initial hypothesis. To summarize, children face three potential learnability problems: (a) acquiring the basic meanings of logical expressions, (b) figuring out the scopal properties of quantificational expressions, and (c) recognizing how the meanings of logical expressions act upon the truth conditions of other logical expressions. In the next section we will delve deeper into the third problem, by showing that the asymmetries we have observed in previous sections are reversed when another logical expression enters into the equation. The example we will look at is the introduction of negation in sentences with the universal quantifier and disjunction. 1.8.1 Universals with disjunction in the subject phrase Recall the asymmetry in the interpretation of disjunction in combination with the universal quantifier, in (76) repeated here as (78). Under negation, disjunction yields a disjunctive interpretation in the subject phrase of a pre-subject universal, but it yields a conjunctive entailment in the predicate phrase, as sketched in (79). (78)

Every SUBJ[ … or … ] PRED[………….….] Every SUBJ[ ….…….……] PRED[…. or …….]

= Conjunctive = Disjunctive

(79)

Not every SUBJ[ … or … ] PRED[………….….] Not every SUBJ[ ….…….……] PRED[…. or …….]

= Disjunctive = Conjunctive

This makes the learnability problem in deciding on the interpretation of the universal quantifier and disjunction even more problematic. However, a child

1.8 Reversals of entailment

37

armed with knowledge of first-order logic should sail effortlessly through these potential pitfalls of interpretation, since the reversals are the product of firstorder logic. Let us expand on the saving graces of first-order logic. Section 1.8.2 examines the interpretation of disjunction in the subject phrase of a negated universal quantifier. We’ll examine the predicate phrase in Section 1.8.3. At logical form (LF), a pre-subject universal quantifier takes two arguments. We’ll refer to these arguments using the metavariables Φ and Ψ, which correspond to the content of the subject phrase and the predicate phrase in sentences of human languages. One way of representing the relationship between the subject phrase and the predicate phrase is by using material implication, as in the following conditional statement. In words, this can be read as follows: everything that is Φ is Ψ. In short, the set Φ is a subset of the set Ψ: x ;&x m 9x =

Adopting this first-order semantic representation of the meaning of the universal quantifier, we can account straightforwardly for the meanings of many sentences of natural languages. Consider, for example, the sentence in (80). Its meaning is represented in pseudo-logic below the example. (80)

Everyone who ate pasta or sushi became ill. Every (x) [(x ate pasta or sushi) m (x became ill)]

If the variable P stands for ate pasta, S stands for ate sushi, and I stands for became ill, then the logical formula associated with (80) in first-order logic is as given in (81). (81)

x [(Px ™ Sx) m Ix]

In (81), disjunction appears in the antecedent of the conditional. This makes sense since disjunction is in the subject phrase of the corresponding English sentence: everyone SUBJ[who ate pasta or sushi]… The disjunctive antecedent clause in (81) can be partitioned into two conjoined clauses, using de Morgan’s laws and the laws of logical equivalence. This yields the formula in (82), with conjunctive truth conditions as stated in example (83). This is how the generalization in (84) is derived. (82) (83)

(84)

x (Px m Ix) ˜ x (Sx m Ix) Everyone who ate pasta or sushi became ill.  everyone who ate pasta became ill and everyone who ate sushi became ill Every SUBJ[ … or … ] PRED[………….….]

= Conjunctive

= Conjunctive

38  Logic and human languages This example illustrates the transparent semantic relationship between firstorder logic and English sentences with every and or, and Mandarin sentences with mei and huozhe. The relationship is further cemented in more complex linguistic structures. For example, if the structure in (81) is negated, then the interpretation of disjunction in the subject phrase should reverse. That is, the subject phrase of a negated universal should no longer generate a conjunctive entailment; the full range of truth conditions associated with inclusive-or should be available (subject to pragmatic implicatures). By contrast, disjunction should generate a conjunctive entailment in the predicate phrase of a negated universal. We will take these predictions one at a time. 1.8.2 Negated universals with disjunction in the subject phrase The first objective is to show that disjunction does not carry a conjunctive entailment in the subject phrase of a negated universal statement: (85)

To show: Not every SUBJ[ … or … ] PRED[………….….] 

= Disjunctive

For expository purposes, we will form a negated universal out of the English sentence we just discussed: Everyone who ate pasta or sushi became ill. The negative universal is given in (86), along with a pseudo-logical representation. (86)

Not everyone who ate pasta or sushi became ill. Not every (x) [(x ate pasta or sushi) → x became ill]

The first-order logical formula (LF) associated with (86) simply negates the logical form for the original universal statement in example (80). So, the LF of (86) is (87). (87)

¬∀x [(Px ∨ Sx) → Ix]

This is where things become interesting. To interpret a negated conditional, we affirm the antecedent and deny the consequent, since this represents the sole circumstance under which conditionals are false. The general schema is depicted in (88). (88)

¬∀x (Φx → Ψx)  ⇔  ∃x(Φx ∧ ¬ Ψx)

Adopting this logical equivalence, we can convert the LF of the negative ­universal statement in (86) (i.e., the LF in example (87)) into a logically equivalent existential statement ∃x [(Px ∨ Sx) ∧ ¬Ix]. The step from (87) to the existential statement is shown in (89). Notice that negation has moved from the antecedent to the consequent. (89)

¬∀x [(Px ∨ Sx) → Ix] (i.e., 87) ⇒ ∃x [(Px ∨ Sx) ∧ ¬Ix]

1.8 Reversals of entailment  39 According to this logical approach to the interpretation of human languages, to make a negative universal statement that Not everyone who ate pasta or sushi became ill is logically equivalent to making the existential claim that someone who ate pasta or sushi did not become ill, as in (90). (90)

Someone who ate pasta or sushi did not become ill. Some (x) [(x ate pasta or sushi) ∧ x did not become ill] ∃x [(Px ∨ Sx) ∧ ¬Ix]

The logical formula given in (90) can be expanded, again using de Morgan’s laws, as in (91). Notice that negation does not have scope over disjunction in (91). (91)

∃x [(Px ∧ ¬Ix) ∨ (Sx ∧ ¬Ix)]

So, to say Not everyone who ate pasta or sushi became ill amounts to the corresponding existential claim that (i) someone who ate pasta did not become ill or (ii) someone who ate sushi did not become ill, as in (92). (92) Someone who ate pasta or sushi did not become ill. ⇒ someone who ate pasta did not become ill or someone who ate sushi did not become ill

= Disjunctive

Again, neither disjunct in (92) is in the scope of negation. Hence, disjunction does not license a conjunctive entailment: (93) Someone who ate pasta or sushi did not become ill. * ⇒ Someone who ate pasta did not become ill and Someone who ate sushi did not become ill

*= Conjunctive

The conclusion is that disjunction in the subject phrase of the universal quantifier does not license a conjunctive entailment if the universal is in the scope of negation. (94) Not everyone who ate pasta or sushi became ill. * ⇒ Someone who ate pasta did not become ill and Someone who ate sushi did not become ill

This is in direct opposition to the interpretation of disjunction if the universal is not negated, as in (80): Everyone who ate pasta or sushi became ill. Without negation, disjunction generates a conjunctive entailment in the subject phrase of the universal quantifier. What about other languages? Taking Mandarin as our example, (95) shows that Mandarin works in exactly the same way as English, yielding the generalization in (96).

40  Logic and human languages (95)

Bushi mei-ge chi-le yidalimianshi huozhe shousi de ren not-be every-cl eat-asp pasta or sushi comp person dou shengbing-le. all become-ill-asp 不是每个吃了意大利面食或者寿司的人都生病了。 ‘Not everyone who ate pasta or sushi became ill.’ Meaning: at least one person who ate pasta or sushi remained unaffected.

(96)

Every SUBJ[ … or … ] PRED[………….….] Not every SUBJ[ … or … ] PRED[………….….]

= Conjunctive = Disjunctive

1.8.3 Negated universals with disjunction in the predicate phrase We have seen that disjunction generates a conjunctive entailment in the subject phrase of pre-subject every, but it receives a disjunctive interpretation if pre-subject every appears under negation. We have also seen that unadorned pre-subject every assigns a disjunctive interpretation to disjunction in the predicate phrase, as depicted in (97). It remains to show the second reversal of entailments, namely that, under negation, disjunction generates a conjunctive entailment in the predicate phrase of pre-subject every. (97) (98)

Every SUBJ[ ….…….……] PRED[…. or …….] To show: Not every SUBJ[ ….…….……] PRED[…. or …….]

= Disjunctive = Conjunctive

We will use (99) to show that disjunction generates a conjunctive entailment in the predicate phrase of negated every-sentences. (99)

Not everyone who became ill ate pasta or sushi. Not every (x) [x became ill] → [x ate pasta or sushi]

In (99), disjunction appears in the consequent clause of the conditional. This seems right since disjunction is in the predicate phrase of the corresponding English sentence: everyone SUBJ [who became ill] PRED [ate pasta or sushi]. To interpret a negated conditional, we affirm the antecedent and deny the consequent, since this represents the sole circumstance under which conditionals are false. The general schema is depicted in (88). Following this schema, the universal statement in (99) turns out to be logically equivalent to the existential statement in (100). The LFs for (99) and (100) are given in (101). (100) (101)

Someone who became ill did not eat pasta or sushi. ¬∀x [(Ix) → (Px ∨ Sx)]  ⇒  ∃x [Ix ∧ ¬(Px ∨ Sx)]

1.8 Reversals of entailment  41 In the existential statement, on the right-hand side of (101), we see that negation now has scope of disjunction. It follows, by one of de Morgan’s laws: ¬ [Φx v Ψx] → [¬ Φx & ¬ Ψx], that disjunction yields a conjunctive entailment in the sentence under consideration: (102) ∃x [Ix ∧ ¬(Px ∨ Sx)] ⇒ ∃x [(Ix ∧ ¬Px ∧ ¬Sx)]  (de Morgan’s laws)

Now we can translate the logical formula we derived, based on (100), back into English. The English result is given in (103), and the Mandarin translation is given in (104). (103) Not everyone who became ill ate pasta or sushi. ⇒ Someone who became ill did not eat pasta and Someone who became ill did not eat sushi (104) Bushi mei-ge shengbing de ren dou chi-le yidalimianshi not-be every-cl become-ill comp person all eat-asp pasta huozhe shousi. or sushi 不是每个生病的人都吃了意大利面食或者寿司。 ‘Not everyone who became ill ate pasta or sushi.’ Meaning: at least one person who became ill didn’t eat pasta and didn’t eat sushi.

So, to say Not every passenger who became ill ate pasta or sushi is to say that at least one passenger who became ill didn’t eat pasta and didn’t eat sushi (and, by inference, ate something else). And, as we saw earlier, to say Not every passenger who ate sushi or pasta became ill is to say that at least one of the passengers who ate sushi or pasta remained unaffected. Whereas disjunction licenses a conjunctive entailment in the subject phrase, but not in the predicate phrase, of the universal quantifier, the entailments are reversed in negated universally quantified statements, where disjunction licenses a conjunctive entailment in the predicate phrase, but not in the subject phrase. And such reversals of entailments show that the semantic contribution of the universal quantifier depends on its linguistic environment; it has no stable discourse or communicative function. As these phenomena attest, human language users draw detailed conclusions about the interpretation of combinations of logical expressions. These conclusions include intricate reversals of interpretation, as anticipated if the logical expressions in human languages have a transparent semantic relationship to the corresponding devices of first-order logic.

42  Logic and human languages 1.9

Compositionality

We have been looking in some detail at the semantics of human languages. We have tried to establish a strong connection between the interpretation of logical expressions in human languages, and the interpretations of the corresponding expressions in classical logic. We want to briefly introduce another relevant factor, sentence structure. As we will show, sentence structure is an essential ingredient to the correct interpretation of expressions of human languages. In fact, this observation is contained in the Principle of Compositionality, as proposed by Frege (1963). The Principle of Compositionality: the meaning of the whole is a function of the meaning of its parts, and their mode of combination.

The phrase mode of combination in the principle refers to sentence structure. This can be made clear with an example. Consider (105) and (106). (105) (106)

Plato was bald. The most famous teacher of Plato was bald.

In example (105), the predicate phrase was bald is being attributed to Plato. But when the sequence of words Plato was bald is repositioned into another sentence structure, as in example (106), the same predicate phrase was bald is now being attributed to a different individual, the most famous teacher of Plato, i.e., Socrates. This illustrates that Plato was bald is not a meaningful information unit in (106). We can call this an accidental occurrence of what would, in another context, be a meaningful unit of information. Another context in which the same sequence of words is a meaningful information unit is (107). (107)

He told the famous teacher that Plato was bald.

These examples illustrate a profound point about the interpretation of expressions in human languages, which can be summarized in the simple adage: semantic interpretation piggybacks on sentence structure. More simply: semantics piggybacks on syntax. There are implications for the dependence of semantics on sentence structure. We saw that the (pre-subject) universal quantifier every is downward entailing on its subject phrase, and that downward entailment validates inferences from set-denoting expressions to expressions that denote subsets of those expressions. Therefore, sentence (108) with a general term (dog) entails (109), with a more specific term (collie). (108) (109)

Every dog in town was vaccinated. Every collie in town was vaccinated.

1.10 Information strength: weakening and strengthening

43

If we cut and paste the string in (108), every dog in town was vaccinated, into certain strings of words, there will be no change in the direction of entailment, despite other changes in form and meaning. So, for instance, (110) entails (111), where (again) the set-denoting expression dog in (110) has been replaced by the subset-denoting expression collie in (111). (110) (111)

At least one vet who treated every dog in town was vaccinated. At least one vet who treated every collie in town was vaccinated.

But notice what happens if the string in (108), every dog in town was vaccinated, is pasted into (112), which begins with the negative determiner no. In this case, it is not valid to replace the set-denoting expression dog by a subset-denoting expression collie. That is, example (112) does not entail (113). To see this, suppose that only one vet was vaccinated, and this vet has treated every collie in town but no other breeds; suppose, further, that none of the vets who treated every dog in town was vaccinated. On this scenario, (112) is true but (113) is false. (112) (113)

No vet who treated every dog in town was vaccinated. No vet who treated every collie in town was vaccinated.

In fact, the entailment direction of the phrase with the universal quantifier every is reversed in (112) and (113). Now, the sentence (113) with the subset-denoting expression (collie) entails the sentence in (112) with the setdenoting expression (dog). This shows that when one downward-entailing expression (no) locally c-commands another (every), the lower expression becomes upward entailing, rather than downward entailing, as it would have been without the addition of the outermost downward-entailing expression. With these observations in mind, we proceed with our demonstration of the role played by first-order logic in determining the scope interpretations among logical expressions.12

1.10

Information strength: weakening and strengthening

As noted in section 1.7, the introduction rule for or is appropriately called Weakening: A

B

A™B

A™B

Most language users are not persuaded that it is valid to infer a statement of the form A or B from a statement of the form A, as licensed by Weakening. There are two possible sources of the unacceptability of Weakening. One possibility

44  Logic and human languages is that the meaning of or is exclusive-or, which we will label ⊕-disjunction. If so, the introduction rule of Weakening is not valid. According to ⊕-­disjunction, exactly one disjunct can be true, so A ⊕ B cannot be inferred from evidence that A is true, when B is also true. This contrasts with ∨-disjunction (inclusive or), where A ∨ B is true if both A and B are true. Another way to account for the unacceptability of the introduction rule for disjunctive statements supposes that disjunction in human languages is ∨-­disjunction. The alternative account places the responsibility for the unacceptability of Weakening on pragmatic principles and not on the meaning of disjunction. The story goes as follows. In using disjunctive statements, speakers and hearers are not just influenced by the meanings of individual terms but also by the pragmatic norms that people follow in conversational contexts. The pragmatic principle Be Cooperative (see Grice 1975) entreats speakers to be as informative as possible. Listeners assume that speakers are being cooperative and are therefore using the most informative statements they are in a position to make. It would be odd for a language user to produce a statement A and then follow it with the statement A or B, because the first statement is more informative than the second. According to the Principle of Cooperation, someone who produces A or B implies that s/he was not in a position to produce either A, or B. It is therefore, pragmatically infelicitous to use A followed by A or B. So disjunction is inclusive-or, but the introduction rule of Weakening is judged to be odd, due to pragmatic principles that govern the use of disjunction. To appreciate the weakening effect of disjunction in ordinary statements, consider (114), with one, two, or three occurrences of disjunction. As the example illustrates, as the number of disjuncts increases, the circumstances that verify the statements remain constant – in the sense that the truth of a single disjunct suffices to guarantee the truth of the entire statement, regardless of the number of disjuncts it contains. So if there are two disjuncts, then the truth of a single disjunct will suffice to make the statement true. Even if there are four (or more) disjuncts, the truth of a single disjunct will suffice to make the statement true. Consequently, disjunctive statements have weaker and weaker truth conditions. Suppose one makes a (disjunctive) claim with sixteen parts. Then, since just one of sixteen disjuncts will suffice to verify the claim, this is indeed a weak claim. (114)

Weakening A ∨ B A ∨ B ∨ C A ∨ B ∨ C ∨ D …

⇒ at least 1 of 2 arguments must be true ⇒ at least 1 of 3 must be true ⇒ at least 1 of 4 must be true

1.11 Logical principles of Weakening  45 We have seen, by contrast, that disjunction generates a conjunctive entailment under negation, a fact that was attributed to the reversal of entailment relations. We are led, therefore, to expect that as the number of disjuncts increases in negative statements, these statements should become stronger, in information-theoretic terms. This expectation is met, as the schematic (115) illustrates. (115)

Strengthening ¬ (A ∨ B) ⇒ ¬A ∧ ¬B ¬ (A ∨ B ∨ C) ⇒ ¬A ∧ ¬B ∧ ¬C ¬ (A ∨ B ∨ C ∨ D) ⇒ ¬A ∧ ¬B ∧ ¬C ∧¬D …

(2 arguments must be false) (3 arguments must be false) (4 arguments must be false)

We have made much of the semantic correspondence between the interpretation of disjunction and the licensing of negative polarity items. It is worth pointing out, therefore, that the weakening that is achieved by adding disjuncts in (114) has a natural counterpart with English any, as illustrated in (116). We have seen that the pragmatic import of words like any is to widen the domain, such that statements with any are stronger than their counterparts without any. (116) illustrates that as modification to any is increased, there is a decrease in information strength. Clearly, Ted will not argue with anyone is a much stronger claim than Ted will not argue with Max. The logical entailment in (117) shows the validity of inferences substituting expressions that result in weaker claims (e.g., Max) for ones that make stronger claims expressions (e.g., anyone). (116)

Weakening a. Ted will not argue with anyone. b. Ted will not argue with any man at the party. c. Ted will not argue with any man at the party wearing a bow tie. d. Ted will not argue with Max.

(117)

If Ted will argue with anyone, then Ted will argue with Max.

1.11

Logical principles of Weakening

There are several semantic structures, across languages, which reveal the validity of Weakening. First, we wish to point out the kind of context in which Weakening is not valid. For reasons that should be clear, Weakening is not valid in downward-entailing contexts. For example, suppose someone says: Ted did not order pasta. The following statement does not follow: Ted didn’t order pasta or sushi. The statement that Ted did not order either dish is clearly stronger than the statement that Ted did not order one of the dishes. So, a

46  Logic and human languages disjunctive clause under negation is stronger than one without disjunction, not weaker. Let us take another example. We have seen that the subject phrase of the universal quantifier is downward entailing. As (118) illustrates, Weakening is not endorsed in this context. Example (119) illustrates that the same holds in Mandarin. (118)

Everyone who ordered pasta became ill. *⇒ Everyone [who ordered pasta or sushi] [became ill]

(119) Mei-ge dian-guo yidalimianshi de ren dou shengbing-le. every-cl order-asp pasta de person all become-ill-asp 每个点过意大利面食的人都生病了。 ‘Everyone who ordered pasta became ill.’ *⇒ Mei-ge dian-guo yidalimianshi huozhe shousi de ren dou every-cl order-asp pasta or sushi de person all shengbing-le. become-ill-asp 每个点过意大利面食或者寿司的人都生病了。 ‘Everyone who ordered pasta or sushi became ill.’

We are led to expect, then, that Weakening is only operative in non-downwardentailing environments. We have considered a number of such environments, including ordinary declarative statements, the consequent clause of conditional statements, and the predicate phrase of statements with a pre-subject universal quantifier. Let us consider the last case. Suppose your friend says: Everyone who became ill ordered pasta. Although the judgment may be clouded by pragmatics, we think it follows that Everyone who became ill ordered pasta or sushi, as in (120). Mandarin speakers give the same judgments, as in (121). It is safe to conclude that Weakening is endorsed in the predicate phrase of the universal quantifier. (120)

Everyone who became ill ordered pasta. ⇒ Everyone who became ill ordered pasta or sushi.

(121) Mei-ge shengbing de ren dou dian-guo yidalimianshi. every-cl become-ill de person all order-asp pasta 每个生病的人都点过意大利面食。 ‘Everyone who became ill ordered pasta.’ ⇒ Mei-ge shengbing de ren dou dian-guo yidalimianshi every-cl become-ill de person all order-asp pasta huozhe shousi. or sushi 每个生病的人都点过意大利面食或者寿司。 ‘Everyone who became ill ordered pasta or sushi.’

1.11 Logical principles of Weakening  47 Here is where we are heading. If we introduce negation, the logical uses of Weakening should reverse. So, negated universals should have the opposite patterns of entailment, with Weakening being valid in the subject phrase of a negated universal, but not in the predicate phrase. Examples (122) and (123) illustrate the validity of Weakening in the subject phrase of negated universals, both in English and in Mandarin. (122)

Not everyone who ordered pasta became ill. ⇒ Not everyone who ordered pasta or sushi became ill.

(123) Bushi mei-ge dian-guo yidalimianshi de ren dou shengbing-le. not every-cl order-asp pasta de person all become-ill-asp 不是每个点过意大利面食的人都生病了。 ‘Not everyone who ordered pasta became ill.’ ⇒ Bushi mei-ge dian-guo yidalimianshi huozhe shousi de ren not every-cl order-asp pasta or sushi de person dou shengbing-le. all become-ill-asp 不是每个点过意大利面食或者寿司的人都生病了。 ‘Not everyone who ordered pasta or sushi became ill.’

Examples (124) and (125) illustrate that Weakening is not valid in the predicate phrase of negated universals, both in English and in Mandarin. (124)

Not everyone who became ill ordered pasta. * ⇒ Not everyone who became ill ordered pasta or sushi.

(125) Bushi mei-ge shengbing de ren dou dian-guo yidalimianshi. not every-cl become-ill de person all order-asp pasta 不是每个生病的人都点过意大利面食。 ‘Not everyone who became ill ordered pasta.’ *⇒ Bushi mei-ge shengbing de ren dou dian-guo yidalimianshi not every-cl become-ill de person all order-asp pasta huozhe shousi. or sushi 不是每个生病的人都点过意大利面食或者寿司。 ‘Not everyone who became ill ordered pasta or sushi.’

This concludes the effort to establish correspondences between first-order logic and the interpretation of logical expressions in human languages. In the past sections we have shown that Weakening (i.e., the inference from P to (P ∨ Q)) is not permitted in the subject phrase of sentences with a pre-subject universal quantifier, but is licensed in the predicate phrase. Under negation, the pattern of inferences reverses, just as expected in first-order logic. Negated universal statements permit Weakening in the subject phrase, but not in the predicate

48  Logic and human languages phrase. These patterns of inference are graphically represented in (126), and can be added to the other inference patterns associated with universal statements, and their reversal under negation, as repeated in (127). (126)

Every SUBJ[ P *⇒ P ∨ Q ] PRED[ P ⇒ P ∨ Q ] Not every SUBJ[ P ⇒ P ∨ Q ] PRED[ P *⇒ P ∨ Q ]

(127)

If ANT[ … or … ] then CONS[………….…..] If ANT[ ….…….…… ] then CONS[…. or …….]

= Conjunctive = Disjunctive



Every SUBJ[ … or … ] PRED[………….….] Every SUBJ[ ….…….……] PRED[…. or …….]

= Conjunctive = Disjunctive



Not every SUBJ[ … or … ] PRED[………….….] Not every SUBJ[ ….…….……] PRED[…. or …….]

= Disjunctive = Conjunctive

We have demonstrated that all of these patterns of inference occur in historically unrelated languages. We have used the examples of English and Mandarin, but we have verified all of these patterns in several other languages. In one sense, it is perhaps not surprising that human languages draw upon the resources of first-order logic. After all, logic is essential for all rational inquiry. Human languages lack such resources on pain of making their users irrational. Upon further inspection, however, the fact that the same patterns of inference arise over and over again across languages suggests either that these patterns are easy to learn, or that they are not learned, but are part of our innate knowledge of logic. We think that the latter is far more likely. It is difficult to see how even many of the basic meanings of logical expressions used in human languages could be learned, in view of the experience children have about them. Moreover, the reversals in the patterns of inferences, which involve multiple logical operators, indicate that the input data that would be needed for learning would need to be quite complex, and therefore these data are probably not available in abundance for every child. Therefore, if it is discovered that all children figure out these patterns of inference, at an early age, then this would add to the argument for logical nativism, and render an argument for learning less credible. 1.12

Logical truths

We have extolled the virtues of first-order logic as a means for explaining people’s subtle and detailed intuitions about the interpretation of exceedingly complex sentences. We have used an asymmetry, and its reversal under negation, as evidence of the complexity of these intuitions. First, recall the asymmetry:

1.12 Logical truths  49 (128) (129)

Everyone who ate pasta or sushi became ill. Everyone who became ill ate pasta or sushi.

Example (128) shows that disjunction licenses a conjunctive entailment in the subject phrase of the universal quantifier. Example (129) shows that disjunction does not license a conjunctive entailment in the predicate phrase. Next, recall the reversal of the asymmetry. In first-order logic, negation reverses entailments. For present purposes, the point is that negation reverses the asymmetry observed in (128) and (129). In negated universally quantified statements, disjunction licenses a conjunctive entailment in the predicate phrase, but not in the subject phrase. The negative statements in (130) and (131) illustrate the reversal of the asymmetry in (128) and (129). (130)

Not everyone who ate pasta or sushi became ill. ‘at least one of the passengers who ate pasta or sushi remained unaffected’

(131)

Not everyone who became ill ate pasta or sushi. ‘at least one passenger who became ill didn’t eat pasta and didn’t eat sushi’

 hese asymmetries and their reversals are graphically depicted in (132) T and (133). (132)

Every SUBJ[ … or … ] PRED[………….….] Every SUBJ[ ….…….……] PRED[…. or …….]

= Conjunctive = Disjunctive

(133)

Not every SUBJ[ … or … ] PRED[………….….] Not every SUBJ[ ….…….…….] PRED[…. or …….]

= Disjunctive = Conjunctive

Logical nativists contend that asymmetries such as these pose potential problems for the experience-based approach to language acquisition. In a recent article, Goldberg (2009) has responded to the challenge posed by logical nativism. Goldberg contends that facts such as the one expressed in (133) can easily be handled by the experience-based approach. Goldberg states (2009, p. 213) “it is possible to untangle the generalization [in (133)] and see that only very basic entailments that any rational system would make are required.” Goldberg then proceeds to spell out the assumptions that are deemed necessary to arrive at the generalization in (133) “by appealing to simple principles of general rationality.” The simple principles of general rationality that Goldberg cites are listed in (134). (134)

a. the basic fact that universally quantified statements can generally be captured by conditionals b. the basic meaning of conjunction is Boolean and c. the basic meaning of disjunction is inclusive or d. de Morgan’s law: ¬(A ∨ B) ⇒ ¬A ∧ ¬B

50  Logic and human languages Goldberg rejects logical nativism because she thinks it is unnecessary for children to have an innate grasp of first-order logic in order to learn facts such as those represented in (132) and (133). According to Goldberg, such generalizations follow from the meanings of the logical expressions: not, every, or, and. All that children need in order to figure out these facts, Goldberg contends, is the ability to reason from the basic meanings of these expressions – and this is something that any rational creature can do, using nothing more than their wholly general rational acumen. According to logical nativism, by contrast, it is a contingent fact that the generalizations in (132) and (133) are recognized and accepted by young children. The issue is why these entailments, rather than others, are sanctioned in the first place by young children acquiring historically unrelated human languages. 1.13

Contingent truths

There are two premises leading to the conclusion that (132) and (133) are contingent generalizations, and not generalizations that any rational system would derive. The first premise is that the meanings of logical expressions are contingent truths, and not properties of any rational system. This premise holds if it can be established that children could infer, without threat of incoherence, that statements of the form A or B mean exactly one of the alternatives A, B holds, rather than at least one of the alternatives A, B holds. The inference that or could mean exactly one without posing any threat to first-order logic is justified, for the following reason. A child who possesses the concepts of inclusive disjunction (∨), Boolean conjunction (∧), and negation (¬) could define the notion of exclusive disjunction in terms of them. To see this, let us use the symbol ⊕ to denote exclusive disjunction, and we use the symbol := to mean is defined as. The following definitions show that statements of the form A ⊕ B and A ∨ B are inter-definable in first-order logic: (i) (ii)

A ⊕ B := (A ∨ B) ∧ ¬(A ∧ B) A ∨ B := (A ⊕ B) ⊕ (A ∧ B)

This brings us to the second premise. If children were to adopt the exclusive meaning of disjunction, ⊕-disjunction, then the generalizations in (132) and (133) would not hold. The inter-definability of ⊕ and ∨ means that there is no basis logically for thinking that either of these is the basic meaning of disjunction. The two definitions (i) and (ii) are logically on a par. It follows that the facts in (132) and

1.13 Contingent truths  51 (133) do not hold of necessity in first-order logic, but the fact that these generalizations are logically valid helps to settle the question of which of the two logical expressions, ⊕ or ∨, is the standard meaning of disjunction in firstorder logic, namely ∨. To recap, we have established, first, that children could learn that disjunction is exclusive-or in human languages, without threat of incoherence in first-order logic. We know, second, that if disjunction is exclusive-or, then the generalizations expressed in (132) and (133) are not founded. These two premises lead to the conclusion that the facts described in (132) and (133) do not hold of logical necessity. Whether or not these generalizations are valid depends on which meaning of disjunction is assumed, ⊕ or ∨. They are not the natural byproducts of any rational system. Goldberg takes for granted that there are basic meanings of logical expressions in first-order logic, and that children assign these meanings to the corresponding expressions in human languages. One of the meanings Goldberg takes as basic is inclusive disjunction. It follows, according to Goldberg, that any system that is rational at all will validate the basic logical entailments of first-order logic that involve disjunction. The question Goldberg addresses, then, is the following: Why do the entailments involving disjunction, such as (132) and (133), hold in first-order logic? The answer is straightforward. As long as the logical expressions carry their basic meanings, as defined in first-order logic, the entailments in (132) and (133) can be trivially derived. We have just shown that this is not a valid conclusion, however, since the standard meanings of expressions in first-order logic can be used to define exclusive disjunction, and if that meaning is used, then the entailments in (132) and (133) are not valid. The claim that all rational systems adhere to the principles of first-order logic is not widely accepted, as the following interview with Jean-Yves Béziau (2006) makes clear: Some people in some countries have always tried to elaborate a universal system that would account for any sort of reasoning, or reasoning as a whole. Aristotelian logic was depicted itself as a universal one. More recently, firstorder classical logic appeared to some as a universal system accounting for mathematical reasoning as well as current one, that is, the one used to buy your bread at the bakery. But first-order classical logic was also criticized at length, whether ­concerning its claim to describe mathematical reasoning or physical, computational, current, philosophical ones, and the like. Many new logics were further developed, namely: intuitionistic logic, combinatory logic, linear logic, quantum logic, erotetic logic, modal logic, paraconsistent logic,

52  Logic and human languages polar logic, relevant logic and so many others, all the more that each of these is often to be divided into a disparate multiplicity, as in the case of modal logics.

Logical nativists agree with Goldberg that the basic meaning of disjunction in human languages is inclusive-or, as in first-order logic. According to advocates of logical nativism, however, this is a contingent fact. The question then boils down to: Why do children all assign the inclusive meaning to words for disjunction, and never the exclusive meaning? More generally, logical nativism is concerned with the question of how children, across languages, come to know the lexical meanings of logical expressions. The entailments that are accepted by English-speaking and Mandarin-speaking children provide evidence that children acquiring typologically different languages arrive at the same lexical meanings for certain logical expressions. Logical nativism asks Why is this so? Why do English-speaking children interpret the English word or inclusively despite the fact that so much of the linguistic input governing that word is consistent with an exclusive interpretation? The same question extends to children acquiring all languages: why do Japanese-speaking children reach the same conclusion about the meaning of the word ka, and why do Mandarin-speaking children reach the same conclusion about huozhe? The fact that children acquiring historically unrelated languages acquire the inclusiveor meaning of disjunction is compelling evidence that children interpret the expressions or, ka, and huozhe as in first-order logic  – when they need not have done so and, indeed, when children have little evidential support for this interpretation. We have seen that the basic meanings of the logical expressions of firstorder logic do not necessarily correspond one-to-one to the lexical meanings of the corresponding expressions in human languages, since alternatives such as exclusive disjunction, ⊕, can be defined in terms of the basic meanings. And since the exclusive disjunction has robust support from the linguistic input, the puzzle for experience-based accounts such as Goldberg’s is why no child qua inductive learner appears to ever access it. The conclusion of the logical nativist is that the meanings of logical concepts are innately specified. To the extent that these meanings are combined to form generalizations like those in (132) and (133), these logical generalizations are known a priori. Once the meanings of logical expressions become fixed, by evolution, then certain generalizations assume the status of logical truths for language users. In short, the generalizations in (132) and (133) are contingent a priori truths.

1.14 Problems of scope  53 1.14

Problems of scope

Goldberg (2009) also takes for granted that all humans adhere to “very basic entailments that any rational system would make.” Two of the very basic entailments are stated in de Morgan’s laws:13 (iii) (iv)

¬(A ∨ B) ⇒ ¬A ∧ ¬B ¬(A ∧ B) ⇒ ¬A ∨ ¬B

So, Goldberg contends, for example, that the law governing negated disjunctions, stated in (iii), is an entailment that any rational system would make. We have already seen that this entailment is not readily evident in all human languages, due to scope ambiguities. As a consequence of different scope relations, human languages differ in the interpretation of statements corresponding to the surface form of both of de Morgan’s laws. In English, negation takes scope over disjunction in negative statements that mirror the form of the law expressed in (iii). To repeat several earlier examples, disjunction yields a conjunctive entailment in example (135). So, example (135) entails that John didn’t bring beer and didn’t bring wine. So negated disjunctions in English conform to (iii). (135)

John didn’t bring beer or wine to the party.

By contrast, negated disjunctions in Mandarin Chinese assign the opposite scope relations in sentences that are similar in surface form, as illustrated in (136); the Mandarin disjunction word, huozhe, has the same surface structural relation to negation, meiyou, as in English. In contrast to English, adult speakers of Mandarin judge (136) to mean that John didn’t bring beer or John didn’t bring wine. (136)

(Wo cai) Yuehan meiyou dai pijiu huozhe hongjiu qu jiuhui. (I guess) John not bring beer or wine go party. (我猜)约翰没有带啤酒或者红酒去酒会。 ‘It’s either beer or wine that John did not bring to the party.’

The cross-linguistic difference between English and Mandarin can be credited to different scope relations, not to the fact that disjunction is interpreted differently in English versus Mandarin. Disjunction means inclusive-or in both languages. Attesting to this is the fact that if negation appears in a higher clause than the clause with disjunction, negation takes scope over disjunction in both languages. In such sentences, disjunction generates a conjunctive entailment, as in one of de Morgan’s laws. But in simple negative sentences, disjunction takes scope over negation in Mandarin, whereas negation takes scope over disjunction in English.

54  Logic and human languages As we have also reported, it turns out that children acquiring both English and Mandarin initially assign the same scope relations to negated disjunctions, with negation taking scope over disjunction, as in English. So, children acquiring Mandarin assign different scope relations than adults do. This is an apparent problem for the experience-based account. It also calls into question Goldberg’s conjecture that any rational system will accept generalizations such as (132) and (133), repeated here. (132)

Every SUBJ[ … or … ] PRED[………….….] Every SUBJ[ ….…….……] PRED[…. or …….]

= Conjunctive = Disjunctive

(133)

Not every SUBJ[ … or … ] PRED[………….….] Not every SUBJ[ ….…….…….] PRED[…. or …….]

= Disjunctive = Conjunctive

Findings like these should not be taken for granted. Even if all human languages agree on the meanings of logical expressions, and even if these meanings correspond to those of classical logic, when these expressions are used in combination, scope ambiguities may arise. Because scope ambiguities complicate performance in many instances, they make it exceedingly difficult to establish correspondences between the meanings of expressions in first-order logic and the meanings of the corresponding expressions in human languages. Another difference between children and adults can be credited to scope ­relations. This is the application of de Morgan’s law governing negated conjunctions: ¬(A ∧ B) ⇒ ¬A ∨ ¬B. This law is obeyed by adult English speakers in interpreting sentences like (137). (137)

John didn’t bring both beer and wine to the party.

Adult English speakers judge (137) to be true in three circumstances: if John brought just beer to the party, if John brought just wine to the party, and if John brought neither beer nor wine to the party. Mandarin assigns a different semantic interpretation to negated conjunctions. The most transparent way of translating (137) into Mandarin is given in (138), where meiyou corresponds to English not, and he corresponds to and. (138)

Yuehan meiyou dai pijui he hongjiu qu jiuhui. John not bring beer and wine go party 约翰没有带啤酒和红酒去酒会。 ‘As for both beer and wine, John did not bring them to the party.’

In contrast to English, the Mandarin sentence in (138) is judged to be true in only one circumstance, where John failed to bring either beer or wine. Although the conjoined clause pijui he hongjiu appears in the scope of negation in the

1.15 Pragmatic influences on logical inferences

55

surface syntactic structure of (138), this phrase is interpreted as having scope over negation at the level of semantic interpretation (logical form). As we will show in Chapter 4, children acquiring both English and Mandarin initially assign the same scope relations to negated conjunctions. In this case, English-speaking children and English-speaking adults differ in how they assign scope to negated conjunctions such as (137) John didn’t bring both beer and wine to the party. Children assign the same scope relations as Mandarinspeaking children and adults assign to (138), with conjunction taking scope over negation. So, English-speaking children interpret (137) to mean that John did not bring beer and did not bring wine, whereas English-speaking adults interpret it to mean that John did not bring both drinks. This difference between child and adult English does not conform to the expectations of the experiencebased account. Moreover, it reveals another apparent disconnect between the meaning of expressions in first-order logic and the meanings of the corresponding expressions in human languages. 1.15

Pragmatic influences on logical inferences

In addition to the appearance (but not the fact) that de Morgan’s laws are not accepted in all human languages, it turns out that other inferences sanctioned by classical logic are not accepted by language users. As we discussed in section 1.10, the introduction rule for or is Weakening: A

B

A™B

A™B

Most language users are not persuaded that it is valid to infer from a statement A to A or B, although this inference is sanctioned by Weakening. One possible source of the unacceptability of Weakening is that the meaning of or is not inclusive-or, but exclusive-or, . If disjunction in human languages is -disjunction, then the introduction rule of Weakening is not valid. By contrast, Weakening is valid if the meaning assigned to disjunction is inclusive-or. Of course, we have already argued that the unacceptability of Weakening can be laid at the feet of pragmatic principles and not on the meaning of disjunction, and Goldberg could appeal to this observation to explain why people do not accept Weakening. In brief, it is pragmatically odd for a speaker to produce a statement A and then follow it with the statement A or B, because the first statement is more informative than the second. Someone who produces A or B implies that s/he was not in a position to produce either A, or B. It is therefore pragmatically infelicitous to use A followed by A or B. This explains why the

56  Logic and human languages introduction rule of Weakening is judged to be odd. It is not because disjunction is exclusive-or, but rather because our use of logical expressions, including disjunction, is governed by pragmatic principles. Another example is the inference from statements of the form A and B to ones of the form A or B. Because disjunction in human languages is inclusiveor, statements of the form A or B are true if both disjuncts are true. Children readily assent to this inference, but adults do not. According to Goldberg, this inference should be valid in any rational system. It is valid in first-order logic, of course, but it does not follow from this that humans accept the inference. Because the use of disjunction in adult language is governed by the implicature of exclusivity, most adults reject statements of the form A or B in circumstances where both disjuncts are true. Children are less sensitive to the scalar implicature, so they appear to be more logical than adults. It is not a trivial discovery that human languages accept the patterns of entailments depicted in (132) and (133). A rational creature could know the basic meanings of logical expressions and still not accept entailments generated by these meanings. We have seen two possible factors that could contribute to an apparent disconnect between logic and language. One is the influence of pragmatic principles that govern conversation, and the other is ambiguity of scope. Apparently, neither of these factors sways our judgments concerning the patterns of entailments in (132) and (133), but even if they did, this would not lead us to abandon the view that human languages adopt the same meanings of certain logical expressions as in classical logic. There is a third reason for thinking that a creature could be rational and yet not accept generalizations such as those in (132) and (133). Entailments such as these hold in virtue of their form, not in virtue of their content. But, it has been found that children younger than 12 (Piaget 1964), and sometimes even adult language users, are often influenced by the content of a sentence in making judgments about its validity, rather than its form. This leads to errors in many cases. For example, unless the premises of an argument are on familiar topics, most people experience difficulty, for example, in interpreting conditional statements (English if…, then…), as attested by their poor performance on the Wason card selection task (e.g., Wason 1966). However, the fact that people make errors is not compelling evidence that human languages do not adhere to the same meanings of logical expressions as in classical logic. For one thing, as soon as people are told the solution to the Wason card selection task, they immediately accept the solution as correct. This demonstrates how logic guides human reasoning (van Benthem 2007).

1.16 The meaning of disjunction is contingent  57 The idea that humans have an innate logical faculty is a cornerstone of Rationalism. According to Rationalist doctrine, humans possess an innate logical competence that structures human thought and assists humans in the acquisition of language. This doctrine has nothing to say about the nature of logic itself, and it is quite compatible with poor performance in deductive reasoning tasks, for example, because only the simplest inference rules may be accessible to consciousness. In view of people’s poor performance on many logic tasks, we might wonder why we should believe in the existence of an innate logic faculty at all. We think that logical nativism is an empirical claim, to be settled by empirical research. The main reasons for believing in an innate logic faculty come from cross-linguistic research and from studies of language acquisition. If all rational systems adhere to the meanings of logical expressions in firstorder logic, as Goldberg contends, then logical nativism would be true a priori. According to Goldberg, apparently, since all human languages are rational systems, they must adopt the meanings of logical expressions and the combinatory laws of classical logic. But in the case of logical expressions and logical inferences, then, there is no appeal to experience or to the learning mechanisms associated with the experience-based approach. The approach simply adopts logical nativism when it comes to basic logical concepts, as well as complex interactions of logical expressions. This seems to be Goldberg’s argument, as far as we can see. This conclusion is at odds with many advocates of the experience-based approach to language acquisition, as we will see. In contrast to Goldberg, other researchers who embrace the experience-based approach contend that the meanings of logical expressions are learned through experience, namely by observing how other members of the linguistic community use such expressions. Even logical nativists would disagree with Goldberg’s conclusion that any rational system must adopt the basic principles of first-order logic. There could be rational systems that violate these principles. To further defend the assertion that the meanings of logical expressions are specific contingent facts about human languages, we will recount proposals about the meanings of two logical expressions. One is disjunction, which many researchers have concluded is not inclusive-or. The other is the universal quantifier. Many researchers have concluded that the meaning of the universal quantifier cannot be “generally captured by conditionals,” as Goldberg contends. 1.16

The meaning of disjunction is contingent

The experience-based approach to the acquisition of logical expressions is committed to the claim that whatever meaning or carries in English, it is

58  Logic and human languages learned through observing how other members of the linguistic community use or. Many researchers in linguistics, psychology, and philosophy are convinced that disjunction in human languages is not the operator of classical logic, inclusive-or. Rather, they think human language disjunction is exclusive-or. Just as many, perhaps, are convinced that or is ambiguous between inclusive disjunction and exclusive disjunction. One way to determine which disjunction is used in human languages is to conduct empirical studies. For example, Braine and Rumain (1983, p. 291) acknowledge the view that “equates or with standard logic,” yet reject this view on the grounds that “coherent judgments of the truth of or-statements emerge relatively late and are not universal in adults.” Braine and Rumain (1983) conclude that disjunction is exclusive-or more often than not, even for adults. We would argue that the interpretation of ­disjunction in human languages is inclusive-or, as in classical logic. But our view is that this is a specific contingent fact about human languages, and not a property of any rational system, as Goldberg claimed. Humans have evolved such that all possible human languages adopt inclusive-or as the meaning assigned to disjunction words, but it could have been otherwise. Of course, once the meaning of disjunction and other logical connectives becomes fixed, through evolution, then logical truths that conform to these laws will be accepted without question, ceteris paribus.14 But if evolution had pursued a different path, such that disjunction was exclusive-or, then speakers of human languages would accept different logical laws as a priori truths. But, human languages would still be considered rational systems, presumably. Logical nativism is committed to the claim that whatever meaning or and every carry, these are fixed innately. Specifically, logical nativism contends that the meaning of or in human languages is innately specified as inclusive-or, as in classical logic. Logical nativists concede that the truth conditions associated with exclusive-or are the only ones that are relevant in many circumstances, e.g., when the alternatives are mutually exclusive. So children hear things like: Is his name Bill or Bob?, Was it red or blue? But these circumstances do not suffice to show that English or is exclusive-or. What must be shown is that a disjunction word in some human language is never true when both disjuncts are true, even when the disjunction is formed from non-mutually exclusive disjuncts, both of which are true. It is sometimes argued that Latin had two words for disjunction, vel and aut, and that the meanings of these words in Latin proves that human languages allow both exclusive-or (vel), and inclusive-or (aut). However, as Jennings (2001) points out, one of the oddities of exclusive-disjunction is that statements of the form ¬(A ⊕ B) are true if both A and B are true (as

1.17 The meaning of the universal quantifier is contingent  59 well as when both A and B are false). Therefore, Jennings argues, if aut meant exclusive-or, then the negative statement Nemo timebat tribunos aut plebes ‘no one feared the magistrates or the mob’ should be judged to be true if everyone feared both the magistrates and the mob. But there is no evidence that this meaning can be assigned to negated disjunctions in Latin or in any other human language. In making judgments about the truth or falsity of sentences, moreover, language users are not only influenced by the semantic properties of these expressions, but also by pragmatic principles that govern how words are interpreted in conversation. The use of or implies exclusivity but does not entail it (e.g., Chierchia and McConnell-Ginet 1990). So, learning the lexicon is only one component of what is required for children to use logical expressions in the same way as adult speakers. To manifest adult-like behavior in using or, a child must also have achieved the relevant pragmatic knowledge. Interestingly, pragmatic principles often implicate the negation of some of the truth conditions of logical expressions. In fact, it turns out that young children are less sensitive than adults to certain of these pragmatic principles that govern the linguistic inferences made by adults. As a consequence, children have been found to behave more logically than adults, accessing the entire range of truth conditions specified at logical form. As a consequence of children’s lack of sensitivity to pragmatic principles, they readily accept the use of disjunction in circumstances in which adults reject it. More specifically, children younger than 5- or 6-years-old accept Ted ordered pasta or sushi as a description of a situation in which Ted ordered both pasta and sushi. Since adults reject the same disjunctive statement in this situation, adults are not likely to be the source of children’s acceptances. This is another way in which children differ from adults that is not expected on the experience-based approach. But, for our purposes, the inference we wish to make is that both children and adults know that English or (and Mandarin huozhe, and so forth) are inclusive-or, just as Goldberg states in her list of concepts that any rational system would draw upon, but this is just a specific contingent fact about human languages. There could be rational systems that draw upon exclusive-or. 1.17

The meaning of the universal quantifier is contingent

Another of Goldberg’s principles that is putatively shared by all rational systems is “the basic fact that universally quantified statements can generally be captured by conditionals.” There is considerable disagreement about whether

60  Logic and human languages

Figure 1.1. The extra-object context

or not classical first-order logic accurately provides the meanings that humans assign to conditionals. This makes conditionals suspect as the underlying meaning of universally quantified statements. It would seem that few linguists or logicians agree that the conditional of first-order logic has any correspondence to human languages. A particularly succinct statement to this effect is made by Kratzer (1986), who remarks “The history of the conditional is the story of a syntactic mistake. There is no two-place ‘if … then’ connective in the logical form for natural languages.” The meaning that is assigned to universally quantified statements is a contingent fact about human languages. The meaning is not one that must be assigned by any rational system. Supporting this conclusion is the fact that Inhelder and Piaget (1964) proposed that children and adults assign different meanings to sentences containing the universal quantifier. Much subsequent research has reached the same conclusion. There are empirical findings that support this conclusion. For example, when shown a picture such as Figure 1.1, young children sometimes respond with a negative answer to the question in (139). If asked to justify this answer, children often point to the extra elephant, i.e., the elephant that is not being ridden by a boy. Since children who respond in this fashion appear to demand symmetry (i.e., a one-to-one relation) between boys and elephants, this response by children is called the symmetrical response in the literature.

1.17 The meaning of the universal quantifier is contingent  61 (139)

Is every boy riding an elephant?

According to Inhelder and Piaget, children initially require a symmetrical (one-to-one) mapping between the object denoted by the subject phrase and the ones denoted by the object phrase, as if every meant equinumerous. For adults, by contrast, the answer to the question is positive, so adults do not require a symmetrical mapping. The point is that the meaning assigned to the universal quantifier in human languages may not be the one that is required by any rational system. This particular meaning has been fixed, through evolution, but it could have been otherwise. Inhelder and Piaget (1964) thought it was otherwise, at least for children. According to logical nativism, children’s semantic competence is innately specified. In the case of the universal quantifier, logical nativism contends that children cannot interpret the universal quantifier to mean equinumerous, since this would violate a putatively innate constraint on the meaning of determiners (called conservativity or the lives on relation). In support of this conclusion, we have demonstrated that children’s symmetrical responses to questions like (139) fail to emerge in certain experimental conditions. Children’s performance dramatically improves when they are tested using a variant of the truth-value judgment task (see e.g., Crain, Thornton, Boster, Conway, Lillo-Martin, and Woodams 1996). The improvement in children’s performance is attributed to the satisfaction of the felicity conditions associated with questions like (139). More specifically, Crain et al. attribute children’s consistent adult-like performance to the satisfaction of the condition of plausible dissent. Essentially, the point of plausible dissent was made by Bertrand Russell (1948, p. 138), who stated: Perception only gives rise to a negative judgment when the correlative positive judgment has already been made or considered.

According to Russell, a positive answer to the question Is every boy riding an elephant? would be felicitous if, for example, every boy considered riding an elephant, but some boy(s) decided to ride something else, say a dinosaur. This is exactly what was found. In experimental situations that satisfied the felicity conditions of the universal quantifier, children performed about as well as adults in responding to questions like this. Based on this, it was argued that children’s non-adult behavior in previous research was due to the failure to provide a possible outcome, that is, a reason for asking the question in the first place. For present purposes, we are using the example of children’s non-adult behavior in response to questions with the universal quantifier as evidence that the meaning it carries in human languages is a contingent fact, and is not a

62  Logic and human languages meaning that is required in any rational system. As we saw in the case of disjunction, both children and adults know that English every (and Mandarin mei, and so forth) can generally be rendered using conditionals, as Goldberg states in her list of logical assumptions that any rational system would make, but this is just a contingent fact about human languages. There could be rational systems that draw upon other meanings that cannot be rendered by a conditional, such as equinumerous, which would require two conditional statements in order to derive the one-to-one mapping relation between the entities denoted by the subject phrase, and the entities denoted by the object of the predicate phrase. 1.18

Conclusion

We will report the findings of experimental studies designed to investigate the emergence of logic in child language, including studies of children’s mastery of basic logical concepts and studies of the combinatory laws of logic (Chapters 3–6). In Chapter 2, we describe in general terms the two main approaches to language acquisition. The findings of the studies reported in the later chapters are intended to serve to adjudicate between these alternative accounts. We look in detail at children acquiring two typologically distinct languages, English and Mandarin Chinese. We will show, for example, that both children acquiring English and ones acquiring Mandarin know that disjunction is assigned a conjunctive entailment when it appears in the scope of negation, and in the restrictor of the universal quantifier. Moreover, children know these logical facts as early as they can be tested, by about 3- or 4-years-old. The aim is to demonstrate the similarities in children’s acquisition in both languages, their adherence to universal logical principles, and also to demonstrate that, where children differ from adults in the use of logical expressions, it is due to the fact that children initially adopt different values for parameters that are associated with logical expressions. One of our main aims is to demonstrate that human languages draw upon the logical concepts and combinatory laws of classical (first-order) logic. Our research strategy is to support the logical nativist approach by making several demonstrations of children’s knowledge of the semantic concept of downward entailment. Using this property of human languages, we will demonstrate adherence by children and adults, in two typologically unrelated languages, to the laws of classical logic, e.g., de Morgan’s laws governing negated disjunctions and negated conjunctions. Crucially, these laws are valid only if disjunction, conjunction, and negation are analyzed as Boolean operators.

1.18 Conclusion  63 To establish children’s knowledge that certain expressions of human languages are downward entailing, we will be employing a series of diagnostic tests. One diagnostic test of downward entailment concerns the interpretation of disjunction words in downward-entailing linguistic contexts; disjunction generates a conjunctive entailment when it appears in a downward-entailing context. Applying this test, we will demonstrate children’s knowledge of downward entailment using five linguistic structures: negation, the antecedent of conditionals, the subject phrase of sentences with a pre-subject universal quantifier, the preposition before, and the predicate phrase of sentences with a pre-subject focus operator (English only, Mandarin zhiyou). Investigating children’s knowledge across a range of linguistic structures permits us to make a firm generalization about children’s linguistic competence. In both languages, young children know that the semantic property of downward entailment governs the interpretation of disjunction in a range of linguistic structures. Of course, logical nativism cannot be proven by a demonstration that children acquiring two languages have early mastery of logical concepts such as downward entailment. The findings prove neither that downward entailment is innately specified, nor that the patterns of linguistic phenomena that it governs are universal. What this does show, however, is that logical nativism is not only plausible, but it also has considerable empirical backing. The complex patterns of young children’s linguistic behavior across languages cast doubt on the experience-based approach to language development, which we introduce in the next chapter. It may seem to be a modest goal, but it is worth underscoring the plausibility of the nativist account of language acquisition, as it is all too often dismissed as a radical departure from common assumptions.

2 Competing approaches to language and logic

Without special training or carefully sequenced input, every normal child acquires a language in just a few years. By 3- or 4-years-old, children around the world have converged on a grammar that is equivalent to that of adult speakers in the same linguistic community. By the time most children begin primary school, they have effectively become adults in their linguistic competence. Children are able to understand an unlimited number of novel sentences, to discern relations of paraphrase and entailment, and to judge the truth or falsity of indefinitely many statements that they may encounter in conversations. There are two main approaches to the emergence of children’s linguistic abilities. The alternative approaches can be traced back to the nature versus nurture debate about how knowledge is acquired in any domain. The debate dates back to Plato’s dialogue The Meno. In this dialogue, the Greek philosopher and protagonist, Socrates, attempts to demonstrate to an aristocrat, Meno, that a young slave knows more about geometry than he could possibly have learned from experience. By extension, the term Plato’s Problem refers to any gap between one’s experience and the knowledge that one has attained. If experience is not required to attain knowledge, then it is arguably innately specified. Logical nativists follow in the footsteps of Socrates. Logical nativists contend that young children know more about the meanings of logical expressions and the combinatory laws of logic than they could possibly have learned from experience. According to logical nativism, children’s mastery of the language of logic is innately specified, as part of a Universal Grammar. Before we describe the logical nativist approach, let us outline the alternative, experience-based (nurture) approach. 2.1

The experience-based approach

The experience-based approach to the acquisition of knowledge, including language, contends that experience provides the essential ingredients children 64

2.1 The experience-based approach  65 need in order to develop the grammars of human languages. On this approach, the processes by which children acquire language are the same processes that children use to acquire knowledge in any cognitive domain, including social skills, learning to count, learning to read, and so forth. So this is a domaingeneral approach to cognitive development. The experience-based approach maintains that language development consists in adding construction after construction, each one based on sequences of expressions encountered in the environment. This approach highlights children’s use of information that is readily available to them through experience. In a recent review of the current nature versus nurture debate, Pullum and Scholz (2002) argue that the evidence does not suffice to conclude that children are innately endowed with specific contingent facts about natural languages. They contend that positive evidence alone may suffice for language learning. In line with the experience-based approach, Pullum and Scholz argue that the grammars children formulate are likely to consist of shallow linguistic representations that are hypothesized and tested using the same kind of domain-general cognitive mechanisms that children use to learn about other (non-linguistic) things. The experience-based approach has many advocates in the philosophical literature. For example, the famous philosopher Quine (1992, pp. 37–38) writes: In psychology one may or may not be a behaviorist, but in linguistics one has no choice. Each of us learns his language by observing other people’s verbal behavior and having his own faltering verbal behavior observed and reinforced or corrected by others. We depend strictly on overt behavior in observable situations. As long as our command of our language fits all external checkpoints, where our utterance or our reaction to someone’s utterance can be appraised in the light of some shared situations, so long all is well. Our mental life between checkpoints is indifferent to our rating as a master of the language. There is nothing in linguistic meaning beyond what is to be gleaned from overt behavior in observable circumstances.

Dummett (1978, pp. 216–217) also explicitly adopts this view regarding the acquisition of logical concepts and logical laws: The meaning of a mathematical statement determines and is exhaustively determined by its use. The meaning of a mathematical statement cannot be, or contain as an ingredient, anything which is not manifest in the use made of it, lying solely in the mind of the individual who apprehends that meaning: if two individuals agree completely about the use to be made of the statement, then they agree about its meaning. The reason is that the meaning of a statement consists solely in its role as an instrument of communication between individuals, just as the powers of a chess-piece consist solely in its role in the game according to the rules.

66  Competing approaches to language and logic Another advocate of the experience-based approach to the acquisition of logical concepts is Brandom (2000, p. 27), who adheres to “Sellar’s principle that grasping a concept is mastering the use of a word.” Brandom (2007, p. 635) states how logical connectives are acquired on this principle: Here the idea is to generalize the Gentzen-style specifications of the meanings of the logical connectives by pairs of introduction and ­elimination rules to notions of circumstances and consequences of application of an expression.

According to advocates of the experience-based approach, such as Quine, Sellars, and Brandom, children learn the meanings of logical concepts from experience, and gradually develop the competence to generate logical inferences by observing the patterns of use (inferences) by adults. 2.1.1 The constructivist theory The main contingent of researchers who advocate the experience-based approach to language acquisition adopt what is called the constructivist ­theory.1 Advocates of the constructivist theory propose that human children learn constructions, not a generative grammar.2 Constructions are the basic building blocks of languages (Croft 2001; Goldberg 1995; Langacker 1991). According to this theory, learning constructions involves two processes. The first process enables children to build up loosely organized inventories of lexical frames. These lexical frames are item-based construction islands that children formulate in response to the kinds of linguistic input that are encountered with considerable frequency (Cameron-Faulkner, Lieven, and Tomasello 2003, p. 866). There are two basic tenets to the theory. First, constructions are learned solely from the evidence children encounter in the course of language development (see, e.g., Pullum and Scholz 2002). Second, frequency plays a large part in determining the pattern of acquisition. For example, the following quote from Rowland and Pine (2000, p. 165) indicates their adherence to these basic tenets of the experience-based approach. Such an approach relies on there being a strong relationship between the nature of the lexically-specific patterns in the child’s speech and the frequency with which such patterns occur in the child’s input.

The products of learning, according to constructivists, are shallow grammars. Children’s grammars are essentially compilations of constructions that encode the linguistic patterns represented in the input. Construction types are sometimes conceived as concatenated sequences of category labels, such as NP, V, neg, INF, P, etc., which are drawn from an intuitively simple typology.

2.1 The experience-based approach  67 The information gathered from experience not only aids children in creating constructions, it also serves them as the basis for forming generalizations based on these constructions. This is the second process involved in language learning, on the experience-based approach. In forming generalizations, children utilize basic learning mechanisms such as statistical learning algorithms (including distributional analysis), cut-and-paste operations, analogical processes, and schematization. Using these mechanisms, children abstract over previously learnt lexical frames that share semantic, pragmatic, and/or distributional content. According to Goldberg (2006), children base their linguistic generalizations on information-structure, including topic (matters of current interest), focus domain (what is newly asserted), and background elements (e.g., presuppositions). In much of the literature, information-structure is referred to as communicative function. The communicative function of a construction type is essential in accounting for its distribution in a language. For example, subject noun phrases are taken to be default devices for marking the topic of a clause. On the experience-based approach, linguistic generalizations are based on a ­combination of linguistic form and communicative function. The function of a construction type is essential in accounting for its distribution in a language. These functions are directly related to meaning. For example, Cameron-Faulkner, Lieven, and Theakston (2007, pp. 252–266) propose that negators (e.g., no, not) express three functions in child language: non-existence (e.g., There’s no juice left), rejection (e.g., I don’t want anymore), and prohibition (e.g., No swimming). When the specific negator, no, was followed by a verb in the productions by one child, this no V construction was associated with four subfunctions, ­failure (No move), prohibition (No touch), rejection (No apple), and inability (No reach). According to Goldberg (2006), information-theoretic notions also play a role in formulating the meanings of constructions, both for children and adults. These information-theoretic notions include topic (matters of current interest), focus domain (what is newly asserted), and backgrounded elements, such as presuppositions. The experience-based approach purports that, in tandem, form and function also explain how children build up relations among constructions at the final stages of language development. The process is outlined by Lieven and Tomasello as follows (2008, p. 171): Finally, the child has to abstract the relations between constructions. Evidence that this has occurred is that the child is able to transform an utterance in one construction into another construction, for instance a declarative into a whquestion or an active into a passive. This could be done by forming a semantic

68  Competing approaches to language and logic representation of what the speaker wishes to say, thereby allowing the production of the other construction. Whether and when the learner actually maps the form–function mappings of one construction to those of the other is an empirically open question at the moment. It depends on the metalinguistic expertise and/or educational level of different speakers.

In addition to generalizations within a language, any viable account of language development owes an explanation of cross-linguistic generalizations. On the experience-based approach, cross-linguistic generalizations (recurrent patterns) are the by-product of general cognitive constraints, such as analogical processes, processing factors, and discourse-pragmatic factors (Goldberg 2006). On the constructivist theory, when children’s generalizations extend beyond their experience, this is just one instance of a completely general induction problem that arises for all learning that involves projecting beyond one’s experience (see, e.g., Cowie 1999). Another important prediction of the experience-based approach, in contrast to the nativist approach, is that there should be substantial variability among the constructions that appear in different human languages. According to Tomasello (2003, p. 238), cultural imitative learning plays the leading role in language acquisition. In contrast to mimicking, which is “repeating verbatim something the adult has just said, with little or no understanding,” cultural imitative learning requires learners to recognize “the purpose or function of the behavior she is reproducing.” As Tomasello (2003, p. 238) remarks: With regard to language in particular, the child has to understand a special class of intentions known as communicative intentions. Thus, a child might hear her father exclaim, “Look! A clown!” To fully understand his linguistic behavior (with an eye to reproducing it) she must understand that her father intends that she share attention to a particular object; that is to say, understanding a communicative intention means understanding precisely how another person intends to manipulate your attention.

On the experience-based approach, child language is expected to match that of adults, more or less, with more frequently attested construction types being learned earlier than less frequently attested ones (Tomasello 2000). This approach attempts to avoid the conclusions of nativists about the innate specification of linguistic principles. When children make errors, these can be purged from children’s grammars by (direct or indirect) negative evidence (parental lack of understanding, corrective feedback), entrenchment (one expression being drowned out by the frequency of a different expression), and pre-emption (adult recasts of a child’s expression using an alternative expression). These mechanisms assume the role played by the innate principles and

2.1 The experience-based approach  69 parameters that are postulated by nativists (Cowie 1999; Crain and Pietroski 2001, 2002). Imitative cultural learning is also invoked to explain children’s errors in language development. For example, at about 24 months children learning English progress through a stage at which they produce non-finite verbs in root clauses. Examples of children’s non-adult productions might include He open it and She eat grapes. According to Tomasello (2000), imitative cultural learning can explain this stage of language development. Children’s productions with non-finite verb forms arise simply because children omit the initial verbal element from the corresponding adult expressions they encounter. So, for example, the adult question Should he open it? becomes the child’s truncated expression He open it, and the adult question Did she eat grapes? becomes the child’s She eat grapes. During the same period, children also produce sentences with non-nominative subject pronouns, i.e., with a pronoun in subject position marked with accusative or genitive case. These utterances (e.g., Her open it, My open it) are also deviant for adults. According to the truncation account of children’s productions advanced by Tomasello (2000), children’s non-nominative subjects can also be explained by imitative cultural learning. In this case, children encounter adult utterances like Let her open it, and then children reproduce a truncated version that lacks the initial verbal element, let. As these examples illustrate, the experience-based approach views the patterns of children’s non-adult linguistic behavior as simply less filled-out linguistic expressions than those produced by adults in the same linguistic community. Lacking full linguistic competence, children’s productions are adult-like, except that they are missing certain words or word-endings, for example. The experience-based account is also equipped to explain the absence of certain non-adult productions by children. Children never make non-adult productions by using a direct object pronoun with nominative case, such as Mary hit I. According to Tomasello (2000, p. 240), “[t]he reason they do not make this error is that they never hear adults say anything like this in any linguistic construction.” Where experience provides abundant evidence of statistical regularities, however, children quickly become faithful to the patterns they encounter and, in that sense, children begin to match the input they encounter. In essence, children are expected to reproduce either exactly what they experience or some partial variant of it. In a word, children are conservative learners.3 According to the experience-based approach, children would not be expected to produce utterances that do not reflect the target language, but are well-

70  Competing approaches to language and logic formed utterances in some other human languages. As Lieven and Tomasello (2008, p. 171) remark: The difference between young children’s inventories and those of adults is one of degree: many more, initially all, of children’s constructions are either lexically-specific or contain relatively low-scope slots. As well as being less schematic than many adult constructions they are also simpler with fewer parts. And, finally, children’s constructions exist in a less dense network  – they are more “island-like.”

According to the nativist perspective, as we will see in Section 2.2, children are expected to sometimes follow developmental paths to the adult grammar that would be surprising on the experience-based approach. From the nativist perspective, children are free to try out various linguistic options (compatible with Universal Grammar) before they set these parameters in the same way as the particular human language that is spoken to them, e.g., Mandarin Chinese or English. This line of thought is called the Continuity Hypothesis (section 2.4) (Crain 1991, 2002; Crain and Pietroski 2001; Pinker 1984). 2.1.2 Conservative learning Almost all of the research supporting the experience-based approach has come from studies of children’s spontaneous productions, rather than from experimental studies of children’s language comprehension. By parity of reasoning, however, children would be expected to have an imperfect grasp of the local language in comprehension just as they do in production. In addition, children’s comprehension difficulties would be expected to gradually diminish as children modify their deviant constructions to become more adult-like, in response to environmental input. Some researchers who advocate the experience-based approach have discussed children’s developing grasp of the meanings associated with linguistic constructions. Most notably, these researchers have proposed that children restrict the meanings they assign to constructions to ones that they have witnessed in the linguistic input (van Hoek 1995; Rosen and Rosen 1994). We might call this the conservative learning of form/meaning correspondences. Because children are conservative learners, in this sense, these researchers have concluded that it is unnecessary to postulate innate linguistic constraints to explain the meanings children do and do not assign to linguistic constructions. An example of this line of argument was offered by van Hoek (1995). The example involves constructions in which a name, e.g., Papa Bear, and a pronoun, him, appear in the same simple sentence, as in (1).

2.1 The experience-based approach  71 (1)

Papa Bear is covering him.

On the generative approach, the name Papa Bear and the pronoun him must be disjoint in reference due to an innate linguistic constraint known as Principle B. Principle B is the second of three constraints on anaphoric relations between different kinds of noun phrases. Principle B pertains to pronouns. According to Principle B, a pronoun in object position, such as the accusative pronoun him in (1), cannot be anaphorically linked to a referring expression, such as the name Papa Bear, in subject position. Because Principle B rules out coreference between these expressions, the only possible interpretation of (1) assigns different referents to Papa Bear and him. The expectation is that, since children are conservative learners, they will reject coreference between the pronoun and the name in constructions like (1). But the reason children reject coreference is not because they know Principle B. It is simply because children have never experienced circumstances where a pronoun in object position, and the noun phrase in subject position, are used to pick out the same referent. Using (1), van Hoek (1995, p. 337) proposes the following: Grammaticality judgments constitute judgments that a particular expression is congruent with – or in conflict with – conventionally established patterns in the language established through schemas. As noted …, speakers acquire schemas or templates through exposure to actually-occurring expressions, and use those schemas to sanction new expressions … A sentence such as (1) is acceptable if it is judged as an example of a pronominal construction without coreference, but it is unacceptable if it is understood to involve coreference.

Because children are conservative learners, according to van Hoek, there is no need to postulate that they have access to innate prohibitions on sentence forms and meanings. In addition, there is also no need for negative evidence for children to learn to avoid forming constructions in which names and pronouns are coreferential. The absence of the coreferential interpretation merely reflects the fact that children do not witness sentences like (1) in circumstances in which the name Papa Bear and the pronoun him are coreferential. In the absence of such (positive) experience, children do not assign a coreferential interpretation to (1). Rosen and Rosen (1994, p. 73) remark: Perhaps the mental grammar actually consists of positive constructs that license sentences, perhaps ample positive evidence is available, and perhaps positive evidence can support learning. If so, then the negative evidence hallmark is irrelevant to questions about innateness …

To unpack the argument advanced by Rosen and Rosen, a distinction must be drawn between positive evidence and negative evidence. Positive evidence

72  Competing approaches to language and logic reveals to children that certain expressions are generated by the grammar of the local language. By contrast, negative evidence reveals that certain expressions are not generated by the grammar of the local language. One kind of negative evidence is corrective feedback. Not only is corrective feedback rare, for both children’s syntactic and semantic errors, but children are notoriously insensitive to it when it does occur (e.g., Bowerman 1988; Brown and Hanlon 1970; Marcus 1993; Morgan and Travis 1989). Based on a number of studies, it is widely acknowledged that the linguistic input to children consists primarily of positive evidence.4 But only negative evidence or some substitute for it can falsify a grammar that overgenerates, i.e., permits form/meaning pairs that are not in local language. The attribution of conservative learning to children obviates the need for negative evidence, and also makes it unnecessary to postulate innate constraints, according to the experience-based approach. 2.1.3 Arguments against Universal Grammar Perhaps the most basic argument of the experience-based approach to language acquisition is that learning is sufficient for the acquisition of core linguistic principles. A distinction between core and periphery is at the heart of the argument. One premise of the argument is that all human languages contain a wide range of semi-idiosyncratic, peripheral constructions. The second premise is that the periphery of human languages cannot be accounted for by core linguistic principles. On any account of language acquisition, including nativist accounts, peripheral constructions of human languages must be learned. The conclusion, according to the experience-dependent account, is that the same mechanisms that children use to learn these constructions are also used to learn the core phenomena of human languages. The reason, the account contends, is that the main difference between core phenomena of human languages, on the one hand, and the idiosyncratic patterns of human languages, on the other, is that core phenomena are more regular, and occur more frequently. If so, then the core phenomena should be even easier to learn than the peripheral phenomena (Goldberg 2006), with more frequently attested constructions being mastered earlier than less frequently attested constructions (Tomasello 2003). Here is a representative quote from Goldberg (2006, p. 14): Crucially, all linguists recognize that a wide range of semi-idiosyncratic constructions exist in every language, constructions that cannot be accounted for by general, universal, or innate principles or constraints. Generative linguists argue that these constructions exist only on the “periphery” or “residue” of language – that they need not be the focus of linguistic or learning theorists.

2.1 The experience-based approach  73 Constructionists on the other hand have zeroed in on these constructions, arguing that whatever means we use to learn these patterns can easily be extended to account for so-called “core” phenomena. In fact, by definition the core phenomena are more regular, and tend to occur more frequently within a given language as well. Therefore, if anything, they are likely to be easier to learn.

On the same wavelength, Tomasello (2003, pp. 104–105) remarks that “not only must there be a mechanism for learning the idiosyncratic, but this mechanism produces an output that has all of the properties of core grammar, except for maximal generality.” In short, advocates of the experience-based approach take the position that core properties of human languages are ones that have maximal generality and, hence, properties whose effects appear with greater regularity in a language, as compared to peripheral phenomena. It follows that language learners will have an even easier time learning core properties. Once children have mastered the basic construction types that are well attested in the ambient language, these are merged into more and more complex patterns, until the language of the child approximates that of an adult. On this approach, then, child language is just a less articulated version of the adult language, and becomes more articulated as children gradually converge on the target. A final point of contention between the experience-based approach and the nativist approach is the existence of linguistic universals. By its very name, Universal Grammar, it is clear that the nativist account contends that there are linguistic properties in common to all human languages. Advocates of the experience-based approach deny this. Here are some representative quotes: Talk of linguistic universals has given cognitive scientists the impression that languages are all built to a common pattern. In fact, there are vanishingly few universals of language in the direct sense that all languages exhibit them. Instead, diversity can be found at almost every level of linguistic organization. This fundamentally changes the object of enquiry from a cognitive science perspective. (Evans and Levinson 2009, p. 429) … there is very little evidence in the typological literature for the existence of contentful language universals of the type one would normally associate with an innate universal grammar. (Tomasello 2003, p. 19) In one sense, there is no Universal Grammar. That is, there is no universal syntactic template to which the grammars of all particular languages conform. Nor is there an inventory of universal syntactic categories, relations or even constructions which the grammar of all particular languages draw from. … Constructions are language-specific … If so, then virtually all of the formal syntactic properties of grammar are language-specific and therefore

74  Competing approaches to language and logic must be learnt inductively … In the process of categorizing utterances into constructions, the child has effectively induced the categories of the elements of those utterances, since those categories are defined by the constructions … It makes no sense to ask if children have the same categories as adults do …, because such a question assumes the existence of global syntactic categories. Categories are defined by constructions, and children do not have the same constructions as adults do. Eventually, as the child becomes able to process all aspects of the input and is exposed to more and more varied instances of constructions, s/he gradually builds up a taxonomic network of constructions and their categories that comes to equal that possessed by adult speakers of the language. (Croft 2001, p. 58)

In Section 2.6, we present counterarguments to these claims. In a nutshell, logical nativism contends that, because universal linguistic principles are designed to tie together a variety of linguistic phenomena, it is highly unlikely that there will be human languages that lack all of the relevant phenomena. We will discuss examples of ‘core’ principles both from syntax (Chapter 3) and from semantics (Chapters 3–6). 2.1.4 A hybrid model One model of language acquisition has been advanced that combines innate knowledge with the proposal that experience largely drives children’s grammar formation. This is the Coalition model of Hirsh-Pasek and Golinkoff (1996). On the Coalition model, grammar formation is viewed as the learner’s response to a coalition of language-related input sources. The model admits of certain innate knowledge, which selectively guides the child to place various weights on different sources of input. There are three different phases of language acquisition, at which children have biases to attend to different external cues: prosody is the predominant cue for the child in phase I, semantic cues dominate in phase II, and syntax dominates in phase III. At each phase, the primary source of linguistic knowledge is the environment (Hirsh-Pasek and Golinkoff 1996, p. 189): … we have suggested that the mechanism for progress within each phase is guided by distributional analysis. That is, first the child is primed to selectively attend to certain information within each domain that forms the coalition (e.g., prosody, syntax). Second, the child mines these selected inputs across domains to construct an interpretation of the linguistic stream and to build mental models.

Knowledge of syntax develops mainly in phase III on the Coalition model. In any event, learning complex syntax is a discovery process, in which the child is predisposed to notice co-occurring patterns in the input:

2.2 The nativist approach  75 Finally in phase III, children learn to comprehend and produce language to represent more complex events that they may not have even witnessed, as well as multi propositional cross-clause constructions. Here, … children are biased to rely on syntactic cues (although other aspects of the coalition still influence their interpretation of what they hear). With increased capacity to hold more than one event in mind, they are motivated to learn about specific linguistic properties in their language …

The Coalition model is unique in proposing that children’s disposition to attend to particular environmental cues changes over time. On the Competition model, the weights that the child assigns to different cues are strictly determined by the input. By contrast, Hirsh-Pasek and Golinkoff (1996, p. 189) state “These cues are available to the child at all times; however, they are not equally accessible to the child at different points in development.” 2.2

The nativist approach

As we noted earlier, the experience-based approach anticipates that children’s use of logical statements will mirror the use by adult speakers. Of course, children must refine their usage of logical expressions as they accrue relevant experience, so as to comport fully with adult usage. But the experience-based approach is essentially an input-matching account of language development, as compared to logical nativism. According to logical nativism, the competence language users attain in using logical expressions depends on a confluence of factors. Semantic knowledge is one factor, but pragmatic knowledge, parsing principles, and real-world knowledge also come into play. In addition, logical expressions are governed by parameters. As we will discuss, children sometimes initially favor parameter values that are not attested in the local language. In such cases, children exhibit patterns of usage of logical expressions quite different from those of adults. The expected differences between child and adult logic should be highly circumscribed, however, so their existence can be confirmed or disconfirmed by experimental investigation. The experience-based approach expects cross-linguistic variation, rather than cross-linguistic generalizations. The logical nativist approach expects cross-linguistic generalizations, and only highly circumscribed cross-linguistic variation. According to logical nativism, children do not have sufficient evidence from experience to learn the meaning of logical expressions by observing how adult speakers use them. There are two possible sources of input: (a) adult’s behavioral application of inference rules for logical expressions and (b) simple sentences that contain these expressions in human languages. It is

76  Competing approaches to language and logic highly implausible, on the nativist account, that either of these sources of input is the basis for children’s acquisition of the meaning of logical expressions in human languages. The nativist approach proposes that children are biologically fitted, as part of the human genome, with a theory of Universal Grammar (e.g., Chomsky 1965, 1975, 1986). Pointing to the contrast between the nativist and other approaches to language acquisition, Chomsky (2000b, pp. 64–65) observes: There is, it seems rather clear, a rich conceptual structure determined by the initial state of the language faculty (perhaps drawing from the resources of other genetically-determined faculties of mind), waiting to be awakened by experience … Many have found such conclusions completely unacceptable, even absurd; the idea that there is something like an array of innate concepts and that these are to a large degree merely “labeled” in language acquisition – as the empirical evidence suggests – certainly departs radically from many common assumptions.

By hypothesis, the human genetic blueprint for language, Universal Grammar, is essentially uniform for the species. Universal Grammar contains the core principles of language. These principles enable children to almost reflexively execute many of the non-trivial tasks that allow them to successfully navigate through the considerable latitude of experience, that is they as children converge on a grammar. Convergence is accomplished rapidly and effortlessly. Before long, children have attained a grammar that is equivalent to that of adult speakers of the local language. An important factor in the development of language is experience. Not even the staunchest nativist denies that experience matters. After all, children raised in Beijing learn Mandarin, and children raised in Sydney learn English. However, the nativist is quick to point out that there is almost no residual trace of experience left on the linguistic systems that children develop. Individual children exposed to vastly different sets of data rapidly settle on grammatical systems that are remarkably similar. Advocates of the theory of Universal Grammar contend that this follows from the fact that all human languages share a set of core principles and that children know these principles by virtue of their genetic endowment. On the nativist approach, language learning is the by-product of a domainspecific computational mechanism that enables children to acquire any human language without formal instruction and despite the considerable latitude in experience that different children encounter. Universal linguistic principles are not learned by the computational mechanism, but are implicit in the structure of the mechanism itself. Logical nativism supposes that, in addition to properties that are specific to language, the human genome also contains a set of innate logical structures. Chomsky (1988, p. 99) remarks:

2.2 The nativist approach  77 The logical notions are embedded in our deepest nature, in the very form of our language and thought, which is presumably why we can understand some kinds of logical systems quite readily whereas others are inaccessible to us without considerable effort … if at all.

Luria (1973, p. 141) makes a similar point, from a biologist’s perspective: To the biologist it makes eminent sense to think that, as for language structure, so also for logical structures, there exist in the brain network some patterns of connections that are genetically determined and have been selected by evolution as effective instruments for dealing with the events of life.

We will be supposing that the innate logical structures are part of Universal Grammar, but nothing hinges on this, as far as this book is concerned. So, we will speak interchangeably of the nativist account of logic and of language. 2.2.1 Core versus periphery The nativist approach disagrees with several of the basic tenets of the experience-based approach. One of the main bones of contention concerns the distinction between core and peripheral linguistic structures. Although both approaches probably agree on the linguistic phenomena that are seen to be peripheral, the two approaches have different conceptions of the meaning of the term core. Where advocates of the experience-based approach speak of core phenomena, researchers who advocate the nativist approach speak of core properties. Core properties do indeed explain regularities in human languages, as the experiencebased approach maintains. However, the regularities that are discussed by nativists are not the same as those discussed by advocates of the experience-based approach. The following quote by Chomsky (1965, p. 6) mentions the kinds of regularities that are the subject matter of Universal Grammar. [t]he grammar of a particular language … is to be supplemented by a universal grammar that … expresses the deep-seated regularities which, being universal, are omitted from the grammar itself. Therefore it is quite proper for a grammar to discuss only exceptions and irregularities in detail. It is only when supplemented by a universal grammar that the grammar of a language provides a full account of the speaker-hearer’s competence.

The deep-seated regularities envisioned by nativists have two main features. First, they are universal. The phenomena governed by core linguistic principles are regular in the sense that they are manifested in all human languages. Core linguistic principles express regularities in a second sense. Core principles express deep-seated regularities in the sense that they govern a range of phenomena. Crucially, these regularities often appear to be unrelated on the surface. If linguistic theory postulates abstract core principles that tie together

78  Competing approaches to language and logic clusters of facts that appear to be unrelated, then these principles provide a unique testing ground to distinguish the nativist approach from the experiencebased approach. This is the topic of Chapter 3. 2.3

Complex syntax

The empirical differences between the experience-based approach and the nativist approach are probably most pronounced in their accounts of complex syntactic structures. All things being equal, the nativist approach anticipates the early emergence of complex syntax in child language, both in comprehension and in production. The experience-based approach anticipates the gradual accrual of linguistic knowledge by children, with more abstract and less frequent constructions being acquired later. Before turning to a detailed examination of the acquisition of wh-questions on the two accounts, we briefly consider two other complex syntactic structures: passives and relative clauses. 2.3.1 Acquisition of passives On the nativist approach, passives (e.g., The rock star is being chased by a fan) are formed by A(rgument)-movement. A-movement is one of the basic building blocks of generative syntax, according to the theory of Universal Grammar. On the experience-based approach, according to advocates Ambridge and Lieven (2011, p. 276), “passive utterances are not formed by transformations or movement. Rather, the passive construction is initially acquired on an itemby-item basis, beginning with simple ‘adjectival’ passives (e.g., It’s broken), then gradually accruing lexically specific formulas (e.g., The X was broken by the Y), and finally incorporating more abstract constructions (X be/get verb by Y).” Based on a review of the literature, Ambridge and Lieven (2011, p. 276) reach the following conclusion: the two sides … are essentially in agreement with regard to the data. Englishspeaking children first acquire adjectival stative passives (e.g., It’s broken), then full actional passives (e.g., It got broken by the hammer) and finally non-actional passives (e.g., The boy was seen by the girl). Furthermore, both sides agree that, given the right experimental circumstances, children aged as young as 3 demonstrate at least some abstract knowledge of the full passive.

From the nativist perspective, probably the most successful study of the passive to date was an elicited production study reported in Crain, Thornton, and Murasugi (2009). We interviewed thirty-two English-speaking children (ages 3;4 to 4;9), and we were successful in eliciting full actional passives, with byphrases, from twenty-nine of these children, including the youngest child, who

2.3 Complex syntax  79 was 3;4. Twenty-four children produced at least three full passives. The majority of children’s productions were get-passives, as illustrated in (2). (2) She got knocked down by the Smurfie. (Phoebe 3;4) The car got flied over by that helicopter right there. (Kyle 3;9) It got pushed over by the bus, and the bus is bringing him to the hostibul. (Michael 3;11) Point to the car that being crashed by the helicopter. (Joey 3;11)

In previous research, children younger than 5-years-old have been found to experience difficulty comprehending other kinds of passives, however. For example, children have difficulty comprehending non-actional passives with the copula be and a by-phrase (e.g., The horse is seen/heard by Donald Duck), although 3- and 4-year-olds were more successful in comprehending truncated versions of this structure (e.g., The horse is seen/heard). Nevertheless, some children appear to have difficulty with these specific verb forms (seen/heard), as the experience-based account would anticipate. 2.3.2 Acquisition of relative clauses Research has investigated children’s acquisition of several two-clause structures, including sentences with relative clauses. A relative clause is a modifier that expresses a proposition about the noun phrase it modifies. Relative clauses have a missing argument (Subject Phrase or Object Phrase), and they can attach to lexical noun phrases in the main clause. Consider sentence (3). (3)

The boy fed the elephant that _ squirted the giraffe.

In this sentence, the Object of the main clause, the elephant, is being modified by the relative clause, … that _ squirted the giraffe, and the relative clause has a missing NP in Subject position (as indicated by the ‘_’). Consider the slightly different sentence in (5). (4)

The boy that the elephant squirted _ fed the giraffe.

In example (4), the Subject of the main clause, the boy, bears the relative clause, …that the elephant squirted _ …, and the relative clause has a missing NP in Object position. There are several other kinds of relative clause structures, in addition to those in (3) and (4). According to the nativist approach, all varieties of relative clauses involve basic syntactic operations. All things being equal, therefore, the nativist approach anticipates early emergence of relative clause structures, both in comprehension and in production. By contrast, the experience-based approach anticipates only gradual development of different kinds of relative clause constructions, based on properties of the input.

80  Competing approaches to language and logic There is some empirical support for both approaches. The nativist approach takes heart from some findings, such as the finding that children produce sentences with relative clauses before age 3. Based on an elicited production technique devised by Hamburger and Crain (1982), Crain, McKee, and Emiliani (1990) elicited relative clauses from twenty Italian-speaking children, ranging in age from 2;8 to 3;11. Nine of the twenty children produced relative clauses on all twelve of the experimental trials. This included two of the youngest children, aged 2;8 and 2;10. Every child, moreover, produced at least six relative clause structures. The experience-based approach takes heart from the findings from other comprehension studies, where children have been found to perform with different degrees of success on different varieties of relative clause structures. Ambridge and Lieven (2011, p. 293) observe that, on the nativist approach, “children should be equally adept at understanding or producing all types. In fact, early comprehension studies revealed that children have considerably more difficulty with some types of relative clause than others.” Nativists would counter that, in subsequent studies, attention to minimizing task demands has resulted in improved performance (Correa 1995; Hamburger and Crain 1982). Children younger than 5-years-old, however, do not achieve adult-like levels of performance on all varieties of relative clause structures. On the nativist approach, delays in children’s comprehension may be attributed to the processing limitations experienced by younger children. On the experience-based approach, delays in acquisition are taken as evidence that children are progressing from simpler to more complex grammars, based on properties of the input. In fact, these alternatives cannot easily be teased apart, since the inherent processing difficulty of some kinds of relative clauses could prevent adults from producing these structures, thereby limiting their frequency in the input to children. 2.4

The Continuity Hypothesis

Any model of language acquisition is based on three factors: (a) the linguistic competence children achieve, (b) the linguistic input children receive, and (c) the non-linguistic capacities of children to form and evaluate generalizations based on their experience. The nativist approach contends that experience dramatically underdetermines the competence children achieve, even given optimistic assumptions about children’s non-linguistic capacities to extract information and form generalizations on the basis of statistical regularities in the input. Nativists propose that the residual gap between children’s emerging

2.4 The Continuity Hypothesis  81 linguistic knowledge and their experience is filled by innate principles and parameters of language. Children are not expected to violate any core principles of Universal Grammar, even in cases where they might be tempted to violate these principles if they adopted general-purpose learning algorithms. Moreover, even when child and adult language diverges, children are expected to follow the natural seams of human languages. In addition to core principles, Universal Grammar spells out particular ways in which human languages can vary. For example, direct objects precede verbs in some languages, but follow verbs in others. Children raised in Korea fix on the first option; children raised in English-speaking countries fix on the second. It is possible, however, that children learning English could initially select the Korean option, or vice versa. Presumably, if children initially select the incorrect option, they would be able to make the required adjustment to their grammars on the basis of input provided by parents and other caregivers. On this scenario, children may pass through stages that make it look as if they are speaking a fragment of a foreign language for a while. Taken together, the core principles and parameters of Universal Grammar establish the boundary conditions on what counts as a possible human language and, thereby, diminish the role of experience in language acquisition. But children are free to navigate within these boundaries in the course of language development. The parameters of Universal Grammar permit children to sometimes try out parameter values that generate constructions that are unattested in the local language. Because parameters are innately specified options, when children adopt a different value of a parameter from the value assigned by adult speakers of the local language, they are nonetheless adopting a value that is assigned by adult speakers of some human language. So, the differences in the linguistic behavior of children and adults are highly constrained. In essence, children’s language can differ from the language spoken by adults only in ways in which adult languages can differ from each other. So, children’s non-adult linguistic behavior will consist of constructions that are attested in other human languages (Crain and Pietroski 2001, 2002; Crain and Thornton, 1998). This is the Continuity Hypothesis proposed in Crain (1991). A more general statement of the Continuity Hypothesis was advanced by Pinker (1984, p. 6), who asserted that “the null hypothesis in developmental psychology is that the cognitive mechanisms of children and adults are identical …” In the field of developmental psycholinguistics, the Continuity Hypothesis is generally extended to the internal modules of the grammar (i.e., the phonology, the syntax, and the semantics). For some researchers, moreover,

82  Competing approaches to language and logic the Continuity Hypothesis applies to the performance systems of language understanding and production. As Pinker states: “one should assume that the child’s grammar is realized in his or her linguistic performance in the same qualitative way as for adults” (see Crain and Thornton 1998; Crain and Wexler 1999). In broadest terms, the Continuity Hypothesis is a research strategy – to circumscribe the possible explanations of children’s rapid and universal mastery of language, by reducing the degrees of freedom in accounts of language acquisition. The Continuity Hypothesis tolerates only highly circumscribed differences between child language and adult language. As Pinker remarks: “the fewer the mechanisms, the more parsimonious the theory and the more explanatory its accounts.” In his more recent work, Chomsky (1995) has emphasized that certain design specifications of the human faculty for language must be satisfied in order for languages to be learned and used. In developing the Minimalist Program, the goal has been to determine the extent to which the language faculty provides optimal solutions to these design specifications, producing linguistic entities that are legible to cognitive systems outside the language faculty, i.e., the interface systems. In response to empirical research that provides compelling evidence of imperfections of language acquisition or use, a strong minimalist thesis prompts linguists to look for alternative sources of these imperfections, other than inherent defects in the language faculty. Pinker (1984, pp. 6–7) offers a list of ways in which the cognitive mechanisms of children and adults might differ without posing a threat to the Continuity Hypothesis: The most explanatory theory will posit the fewest developmental changes in the mechanism of the virtual (cognitive) machine, attributing developmental changes, where necessary, to increases in the child’s knowledge base, increasing access of computational procedures to the knowledge base, and quantitative changes in parameters like the size of working memory.

To maintain the Continuity Hypothesis, it must be demonstrated that children’s grammatical options are limited to ones made available by Universal Grammar. What children cannot do, according to the Continuity Hypothesis, is entertain linguistic hypotheses that lie outside the boundary conditions imposed by Universal Grammar. To the extent that children’s non-adult linguistic behavior conforms to the natural seams of natural language, children’s non-adult productions and non-adult interpretations provide compelling evidence for the theory of Universal Grammar. In the absence of plausible alternative accounts of non-attested but UG-compatible forms and meanings in child language, the stages of child language development at which children speak a foreign language constitute counterexamples to the experience-based approach.

2.5 Evidence for continuity in child language  83 If the Continuity Hypothesis is correct, we should not be surprised if young English-speaking children exhibit some properties of Germanic, Romance, or East Asian languages, even in the absence of any evidence for these properties in children’s experience. Indeed, theory-driven mismatches between child and adult language may be the strongest argument for Universal Grammar, and against models according to which children construct hypotheses based on linguistic experience. According to the Continuity Hypothesis, children are expected to project beyond their experience in ways that are attested in natural languages, although not necessarily in ways that are attested in the local language. So, children’s non-adult linguistic behavior need not match the input, as experience-based approaches suppose. Rather, the input guides children through an innately specified parametric search space, made available by Universal Grammar. Within this space, children are free to adopt hypotheses that differ from those of adults, as long as children’s choices can later be retracted using positive evidence, if need be, such that children converge on a grammar that is sufficiently like that of other speakers of the local language to foster communication (see Crain 2008; Crain and Pietroski 2001, 2002; Thornton 1990). It bears repeating, however, that children are not expected to entertain linguistic hypotheses that exceed the boundary conditions imposed by Universal Grammar. And children’s projections  – that are unattested by experience  – constitute dramatic support for a nativist approach. From a nativist perspective, language acquisition is viewed as a process of language change, where at any given time children are speaking a possible human language, just not the language that is being spoken around them (Crain, Goro, and Thornton 2006). 2.5

Evidence for continuity in child language

In the next section, we present support for the Continuity Hypothesis using an example from the domain of syntax. Further evidence for the Continuity Hypothesis is reported in Chapters 3 and 4, as it pertains to logical expressions. The experimental research reported in those chapters investigates children’s interpretations of the human language expressions corresponding to the logical connectives (negation, disjunction, and conjunction). Across languages, words for disjunction and words for conjunction are able to assume different scope relations in negative statements. This variation across languages is encoded in two parameters, one parameter for the interpretation of conjunction and one for disjunction. For reasons of learnability, children are expected to initially favor the parameter value that makes sentences true in the narrowest range of

84  Competing approaches to language and logic circumstances (the subset value). This ensures that children will have access to positive evidence if the local language favors the alternative (superset) value, which makes the same sentences true in a broader range of circumstances. The subset value for conjunction is the value observed in Japanese and Mandarin, but not in adult English. Therefore, children acquiring English are predicted to interpret negated conjunctions as they are interpreted in Japanese and in Mandarin. Just the opposite pattern is expected for negated disjunctions. The subset value is the value observed in English, but not in adult Japanese or in adult Mandarin. So children acquiring Japanese and ones acquiring Mandarin are predicted to interpret negated disjunctions as they are interpreted by English speakers, rather than in the way they are interpreted by adult speakers of Japanese or Mandarin. Chapters 3 and 4 report the findings of experimental studies of children’s initial settings of these parameters. As predicted, children are found to ­initially favor the subset parameter values that are associated with these logical connectives, even when these values conflict with those assigned by adult speakers of the local language. For conjunction, English-speaking children initially favor the value attested in Japanese and Mandarin, but not in English. For disjunction, Japanese- and Mandarin-speaking children initially favor the value attested in English and Korean, but not in Japanese or in Mandarin. The nature of children’s non-adult linguistic behavior is an important area of experimental research, especially if the goal is to adjudicate between the competing accounts of language acquisition. As noted, the experience-based approach anticipates that children’s non-adult language will be adult-like, except that it will have missing words or word-endings, or the words that are produced will appear in a non-adult order. By contrast, the Continuity Hypothesis anticipates that children’s non-adult behavior will have a completely different character. Essentially, children are expected to speak fragments of foreign languages, due to differences in the initial parameter settings that children assign, as compared to the settings assigned by adults. The findings reported in Chapters 3 and 4 support the Continuity Hypothesis and pose a challenge for usage-based account of language development, since child language differs from that of adults in systematic ways, rather than simply being less articulated than the corresponding adult constructions, as the experience-based approach would have it. On a parameter-setting model, moreover, children could just as easily produce structures that involve commissions, as ones that involve omissions. An example is described in the next section.

2.5 Evidence for continuity in child language  85 2.5.1 Medial wh-questions in child English A well-known example of children’s non-adult, but UG-compatible, commissions in syntax is the medial-wh phenomenon reported in Thornton (1990). Using an elicited production task, Thornton (1990) discovered that about onethird of the 3- to 4-year-old English-speaking children that she interviewed consistently inserted an extra wh-word between clauses in their long-distance (two-clause) questions, as illustrated in (5) and (6) (see also Crain and Thornton 1998, Thornton 1996). (5) (6)

What do you think what pigs eat? Who did he say who is in the box?

The appearance of the medial-wh in the language of young English-speaking children cannot be explained as children’s response to the input, because these constructions are not grammatically well-formed in English. However, structures like (5) and (6) are attested in other languages, such as dialects of German, and Romani. A German example is (7) (from McDaniel 1989). (7)

Werj glaubst du werj nach Hause geht? who think you who to home goes ‘Who do you think (who) goes home?’

On the Continuity Hypothesis, such similarities between child English and adult German are as unsurprising as similarities between cousins who have never met. Thornton (1990) argues that such cross-language variation is due to a parameter, based on the finding that English-speaking children produced several other ­linguistic structures that are permitted in German. First, “full” wh-phrases (with lexical content) cannot be repeated in German, as illustrated in (8). (8)

*Wessen Buchj glaubst du wessen Buchj Hans liest?  whose book think you whose book Hans reads ‘Whose book do you think whose book Hans is reading?’

And English-speaking children did not repeat lexical wh-phrases in medial position, so (9) provides an unattested case, as indicated by the “#.” Instead, children produced a “bare” wh-phrase or omitted the wh-phrase altogether, as indicated in (10). (9) (10)

#Which Smurf do you think which Smurf is wearing roller skates? Which Smurf do you think (who) is wearing roller skates?

Second, children never used a medial-wh in extracting from an infinitival clause. This too is not a grammatical option in languages that permit a medialwh. Insertion of medial-wh in infinitival complements is universally outlawed.

86  Competing approaches to language and logic So, in German, sentences like (11) are unacceptable. Instead, a long-distance structure such as (12) would be used. (11)

#Who do you want who to win?

(12)

Wen versucht Hans anzurufen? Whom tries Hans to-call ‘Whom is Hans trying to call?’

The similarities between child English and German provide the kind of data that is anticipated on the Continuity Hypothesis. Experience-based accounts of language development are hard pressed to explain why English-speaking children should produce constructions exhibited in German, say, but not in English. On the other hand, the nativist account can make sense of the finding that English children try out structures that are not attested in the local language, but are attested in other languages. Of course, children are not expected to ever try out structures that violate principles of Universal Grammar. This complex pattern of children’s linguistic commissions and omissions suggests that many English-speaking children go through a stage at which they speak a language that is like adult English in many respects, but one that is also like German (or Mandarin) in other respects, such as allowing for the medialwh. Such a child language is entirely consistent with the theory of Universal Grammar. It just so happens that the parents of these English-speaking children, whether they live in New York or in Sydney, do not speak exactly the same language as their children. Following Thornton’s seminal work, medialwh structures have been documented in a number of studies of children acquiring languages that do not permit this structure, including Dutch (van Kampen 1997), French (Oiry and Demirdache 2006), Basque (Gutierrez 2004), and Spanish (Gutierrez 2006). In recent work, advocates of the experience-based approach have taken up the challenge. Here is a quote from Dąbrowska, Rowland, and Theakston (2009, p. 571): A number of researchers have claimed that questions and other constructions with long distance dependencies (LDDs) are acquired relatively early, by age 4 or even earlier, in spite of their complexity … Analysis of LDD questions in the input available to children suggests that they are extremely stereotypical, raising the possibility that children learn lexically specific templates … rather than general rules of the kind postulated in traditional linguistic accounts of this construction.

Citing the findings of an experiment from Thornton and Crain (1994, Experiment 1), Dąbrowska et al. (2009) introduce some children’s non-adult productions, and they advance an experience-based account of these productions:

2.5 Evidence for continuity in child language  87 Interestingly, in their productions of LDD children sometimes produced questions like [13] and [14], with a WH word at the beginning of both the main clause and the subordinate clause. [13] [14]

What do you think what is in the box? What way do you think how he put out the fire? Thornton and Crain regard such ‘medial WH’ questions as evidence for the … application of movement… Note, however, that such utterances could also be produced by simply juxtaposing two independent questions (what do you think? + what is in the box?) or an independent question and an indirect question (what way do you think? + how he put out the fire?). (p. 273; the examples are renumbered here)

As examples (13) and (14) indicate, the Thornton and Crain (1994) study was designed to enable us to make a specific comparison of children’s long-distance adjunct wh-questions (with how, why), and their argument wh-questions (with what, who). The evidential base, however, is considerably more substantial than the findings of this one experiment. A fuller array of findings has been articulated and discussed in numerous places (e.g., Crain, Gualmini, and Pietroski 2005; Crain and Pietroski 2001, 2002; Crain and Thornton 1998; Pietroski and Crain 2011; Thornton 1990, 1995, 1996). The arguments advanced in support of the theory of Universal Grammar are primarily based on the extensive experimental findings reported in Thornton (1990). Using an elicited production technique, Thornton (1990) was able to elicit a variety of wh-questions from 2- to 5-year-old children (including long-distance wh-questions from one child at 2;6). Among the structures Thornton elicited were both subject and object extraction long-distance wh-questions. These included both bare wh-words like who and what and ones with full wh-phrases like what Smurf and which one of the babies. Children as young as 3, and even younger, had no apparent difficulty producing a range of long-distance wh-questions, as well as other complex wh-questions. In one study, Thornton elicited 121 long-distance questions with subject extraction, as in (13), as well as 94 long-distance questions with object extraction, as in (14). These whquestions were elicited from twenty English-speaking children (aged from 2;10 to 5;5); half the children were under 4-years-old. Another experiment was designed to elicit wh-questions with bound pronouns, as shown in (15) and (16). (15) (16)

Which two said they have ants in their pants? Which one of these babies said they like the pants?

(P.B. 4;3) (K.B. 4;4)

Questions like (15) and (16) are not long-distance wh-questions. The complement clauses of these questions express a complete proposition (with

88  Competing approaches to language and logic no gap), and the main clause does not have do-support. Nonetheless, these wh-questions involve sentential embedding, so children’s successful productions of these wh-questions provide evidence of their early linguistic competence with complex syntactic structures. Seventeen children (aged from 3;5 to 5;9) participated in the experiment, and every child produced at least five of the targeted wh-questions. In another experiment, Thornton elicited wh-questions with the verb want, as in (17) and (18). The purpose of the experiment was twofold. First, Thornton sought to determine if children would contract want+to to form wanna in object extraction wh-questions like (17), but not in subject extraction wh-questions like (18). By hypothesis, contraction of want+to is blocked in subject extraction questions, due to a residual “trace” of the moved constituent at the site of extraction. The experimental hypothesis was that children would adhere to this putatively innate constraint on contraction, and that is exactly what Thornton found. (17)

a. Who do you want to help _? b. What do you wanna help _?

(18)

a. Who do you want _ to help us? b. #Who do you wanna help us? (# indicates unacceptability)

The wh-questions in (17) and (18) served another purpose. Because they contain a non-finite form of the verb (to help) in the complement clause, children’s wh-questions of this form could be compared to ones like (15) and (16), in which a finite verb appears in the complement clause. Against this backdrop we can return to the debate about the source of Englishspeaking children’s long-distance wh-questions, including ones with an extra wh-word in medial position. These so-called medial-wh questions include questions with extraction of the subject of the complement clause, as in (19), and ones with extraction of the object of the complement clause, as in (20). (19) (20)

What do you think what’s in here? What do you think what babies drink to grow big?

(Pieter 2;10) (Matthew 3;3)

It is conceivable, as Ambridge and Lieven (2011, p. 306) remark, that medialwh questions like (19) could have been formed simply by juxtaposing two independent questions (What do you think? + What’s in here?). Example (20) is trickier, since the underlying question fragment …what babies drink to grow big? is not acceptable as an independent question; it lacks do-support. Note that the corresponding question with do-support is well-formed, What do babies drink to grow big? Nonetheless, the question fragment …what babies drink to

2.5 Evidence for continuity in child language  89 grow big is acceptable as the complement of an indirect question (Do you know what babies drink to grow big?). This observation led Dąbrowska et al. (2009) to propose that children’s medial-wh questions like (20) may be created by the juxtaposition of an independent question and an indirect question. Thornton (1990, p. 242) considered the juxtaposition analysis of children’s medial-wh questions, but rejected it on the grounds that no child ever produced medial-wh questions with two occurrences of do-support, as in (21). According to the juxtaposition analysis, questions like (21) could be formed by juxtaposing two independent questions, as in (22), so the fact that questions like (21) were never produced argues against the analysis. (21) (22)

#What do you think what does Cookie Monster like? What do you think? What does Cookie Monster like?

This leaves open the possibility, of course, that children’s medial-wh questions with object extraction, such as (20), could have been composed using an independent question and an indirect question, as in (23). (23)

What do you think? (Do you know) what Cookie Monster likes?

So, the juxtaposition analysis could be maintained, but only if children were to adopt one strategy for composing long-distance subject extraction wh-questions, and a different strategy for composing long-distance object extraction wh-questions. This seems highly unlikely. Moreover, the absence of medial-wh questions like (21) is just one argument against the juxtaposition analysis of children’s medial-wh questions. Two further arguments have been offered (e.g., Crain and Pietroski 2002; Crain et al. 2005). One argument against the juxtaposition analysis is based on the finding that children (also) never produced medial-wh questions that contain two full wh-phrases (e.g., which Smurf), as in (24). As example (25) indicates, two independent questions could be juxtaposed to form (24), but this never happened. Instead, the extra ingredient in children’s questions with full wh-phrases (e.g., which Smurf) was a bare wh-word (e.g., who), or there was no extra ingredient, so children produced adult-like long-distance wh-questions. These options are indicated in (26), where the parentheses mark optionality. (24) (25) (26)

#Which Smurf do you think which Smurf is wearing roller skates? Which Smurf do you think? Which Smurf is wearing roller skates? Which Smurf do you think (who) is wearing roller skates?

A third argument against the juxtaposition analysis is based on the finding that children (also) never produced medial-wh questions with a non-finite form of the verb (e.g., to play) in the complement clause, as in (27). The juxtaposition

90  Competing approaches to language and logic analysis anticipates that wh-questions like (27) should be produced by children, since these can be derived by juxtaposing an independent question and an indirect question, as in (28). But, again, this never happened. (27) (28)

#Who do you want who to play with? Who do you want? (I know) who to play with?

To summarize, three kinds of medial-wh questions that are expected on the juxtaposition analysis never occurred. 2.5.2 Why-questions in child English With few exceptions, the wh-word or wh-phrase in English wh-questions must be immediately followed by an inflected auxiliary verb (i.e., a tensed form of be, do, can, have, etc.).5 Therefore, simple one-clause why-questions are acceptable only with subject/auxiliary inversion, as in (29a–d), whereas whyquestions without inversion are deviant, as illustrated in (29e–h). We will refer to these as matrix questions, because they do not involve embedding. (29)

a. b. c. d. e. f. g. h.

  Why are you here?   What do you want to do?   Where is he going?   Who don’t you want to win the game? *Why you are here? *What you want to do? *Where he is going? *Who you don’t want to win the game?

In studies of child English, it has repeatedly been observed that children produce non-adult matrix why-questions such as in (29e–h), instead of ones with subject/auxiliary inversion, as in (29a–d). This finding has been reported in the literature for well over twenty years (e.g., Labov and Labov 1978; Stromswold 1990). Why-questions in child English lack inversion to a greater extent than other wh-questions do (e.g., ones with what or who), from the earliest stages of language development. Moreover, the absence of inversion for why-questions persists in children’s speech well after inversion is consistently present in other wh-questions (e.g., de Villiers 1991). Both the experience-based account of language development and the nativist account have recently advanced proposals about the source of children’s non-adult why-questions. We will first consider the experience-based account proposed by Rowland and Pine (2000). To explain the non-inversion errors in children’s why-questions, Rowland and Pine (2000) adopt a variant of the distributional analysis developed by Tomasello (1992). The main claim, according

2.5 Evidence for continuity in child language  91 to Rowland and Pine (2000, pp. 165–166), is that children produce adult-like wh-questions with inversion only after they are exposed to such constructions in sufficient quantity, as the following quotes indicate: such an approach relies on there being a strong relationship between the nature of the lexically-specific patterns in the child’s speech and the frequency with which such patterns occur in the child’s input. … A distributional learning mechanism that acquires and reproduces lexicallyspecific wh-word+auxiliary combinations which have been heard in the input could provide an answer to the question of how children learn to produce correctly inverted wh-questions without access to a subject–auxiliary inversion rule.

As Rowland and Pine acknowledge, it remains an open question what actually counts as a sufficient quantity of input. They contend, nonetheless, that there is a significant correlation between parental wh-word+auxiliary (hereafter wh+aux) combinations and the emergence of the corresponding wh+aux combinations in the language of one child, Adam (see Brown 1973). This claim is based on a study that was conducted to see if Adam’s adult-like wh+aux combinations corresponded to those that appeared most frequently in his input. At the same time, the study examined the extent to which Adam’s incorrect wh+aux combinations, lacking inversion, corresponded to adult wh+aux combinations that occurred with less frequency. The results of both analyses were interpreted by Rowland and Pine (2000, p. 176) as support for their analysis: In line with the predictions of the hypothesis, the wh+aux combination that the child uses are more frequent in the mother’s input than those the child fails to use.

This interpretation of the data is unwarranted, however. In fact, the data actually pose a challenge for the experience-based approach. For example, during the period investigated by Rowland and Pine, Adam produced adult-like whquestions on 26 occasions. However, there was corresponding input for only 15 of the 26 correct wh+aux combinations that Adam produced. So, Adam produced 11 adult-like wh+aux combinations for which there was no corresponding input. In sum, only 57 percent of Adam’s correct combinations were attested in the transcripts analyzed by Rowland and Pine (2000). In addition, the pattern of Adam’s non-adult why- and how-questions represents a challenge to the experience-based analysis. For Adam, how-questions exhibited inversion to a far greater extent (85 percent) than did why-questions (8 percent). On the experience-based approach, this difference should have been expected to correlate with a difference in input, with how-questions being

92  Competing approaches to language and logic more frequent in the input than why-questions. But the findings are exactly the opposite. There were over twice as many why-questions (there were 44) as how-questions (there were 21) in the input to Adam. The finding that why-questions follow a more protracted course of development, as compared to other wh-questions, despite their high frequency in the input, conforms to the descriptive generalization that has emerged from previous studies of child English. Rowland and Pine (2000) acknowledge the difficulty posed by this generalization. To deal with the problem, Rowland and Pine point out that the majority of why-questions in Adam’s input were of the particular form: why don’t you… They propose that Adam could not take full advantage of these particular why questions, because the structure why don’t you… is unsuitable for the kinds of why-questions that Adam was attempting to form at the stage of development under consideration. This proposal, however, does not get off the ground until Rowland and Pine abandon their initial analysis, which was limited to frequency count of wh+aux combinations. The subsequent proposal advanced by Rowland and Pine was that Adam filtered out wh+aux combinations that were followed by the subject pronoun you. They remark “there is no reason why only wh+aux combinations should function as wh-question markers for the child” (2000, p. 178). True, but introducing an ad hoc filtering mechanism to eliminate certain input is clearly a step backwards for the experience-based account. Let’s see if the nativist account fares any better. Adopting the Continuity Hypothesis, Thornton (2004, 2008) suggests that children of English-speaking adults initially treat the question word why in the same way as Italian adults treat perché (cf. de Villiers et al. 1990). In Italian, the wh-word corresponding to English why is perché. Italian perché differs from other Italian wh-words in matrix questions.6 As the example in (30) illustrates, the adverb già as well as an entire subject phrase (I tuoi amici) can intervene between perché and the inflected verb (hanno) (Rizzi 2001). Why-questions are the exception in Italian. In who-questions and in what-questions, no linguistic material can intervene between the wh-words and the inflected verb. (30)

Perché (i tuoi amici) già hanno finito il lavoro? Why (the-Pl your friends) already have-3pl finished the-sg work ‘Why have they (your friends) already finished the work?’

In complex wh-questions with perché, the intervention of short adverbs or a subject phrase is not tolerated. The inflected verb immediately follows the question word in Italian, just as it does in English. Consider the questions in (31). As long as (31) is asking a why-question about the content of the embedded clause,

2.5 Evidence for continuity in child language  93 i.e., the reason he had for resigning, no intervening material is tolerated between perché and the inflected verb ha.7 (31)

Perché ha detto che si dimetterà? Why have-3sg said that self resign-3sg/future ‘Why did he say that he would resign?’

Complex why-questions like (31) pattern the same way in Italian and in English, whereas matrix why-questions are subject to cross-linguistic variation. To explain the variation, it has been argued that in languages like Italian, Spanish, and Basque, matrix why-questions are (base) generated in a different position than the corresponding wh-words in who-questions and what-questions (Rizzi 1990; Uriagereka 1999). These so-called argument wh-words (used in forming who-questions and what-questions) “move” to a higher projection than the base-generated why-questions. Now we can appreciate Thornton’s analysis of English-speaking children’s why-questions. Thornton proposes that children learning English initially distinguish between why-questions and argument wh-questions, just as adult speakers of Italian, Spanish, and Basque do. This distinction is not overt in adult English, so it is not attested in children’s input. Nevertheless, children acquiring English make the distinction in their grammars, on this account. In time, experience informs English-speaking children that why-questions are not distinguished from argument questions; both kinds of wh-questions require subject/auxiliary inversion in English, for both matrix and complex wh-questions. According to Thornton’s analysis, English-speaking children should differ from adult English speakers in exactly the ways in which Italian differs from English. First consider matrix why-questions. Not only are English-speaking children expected to fail to invert the subject and the auxiliary verb in matrix why-questions, but in addition they are expected to permit linguistic material to intervene between the why-word and the subject. When it comes to complex wh-questions, including why-questions, English-speaking children are expected to parallel English-speaking adults, in producing well-formed longdistance why-questions with inversion, since Italian and English do not differ in how they form complex wh-questions. From an experience-based perspective, this pattern is surely not anticipated. Since matrix questions are far more frequent in the input, matrix why-questions should become adult-like far in advance of complex why-questions. To test her proposal, Thornton conducted a longitudinal study of over 900 why-questions produced by one child, A.L., from 2- to 6-years-old. For present purposes, we will limit our attention to a three-week period, when A.L. was

94  Competing approaches to language and logic 3;5. At this stage, A.L. was asking many questions, including many matrix wh-questions, including who-questions, what-questions, and why-questions. Like the majority of children, A.L. produced adult-like wh-questions for all wh-words except for why. That is, when A.L. produced matrix who-questions and what-questions involving object extraction, these questions positioned an auxiliary verb, or the “dummy” verb do, immediately following the sentenceinitial wh-word. However, the majority of A.L.’s why-questions lacked subject/auxiliary inversion; the subject NP immediately followed why. Non-adult why/questions persisted in (over 80 percent of) A.L.’s matrix questions until she reached the age of 5;6. Some examples are given in (32). (32)

Why you have your vest on? Why she doesn’t have any hanger? Why he’s woofing? Why that guy has tookened Walker? Why he’s following the guy? Why that kind of thing could break? Why she doesn’t go to sleep? Why one guy that is 3 is in the yellow room? Why you’re going to take it back? Why we can’t skip the run? Why we can’t skip it today? Why you are going in that one? Why you don’t want to clean it up? Why Emily can’t go? Why they’ve already gone outside? Why just our family is here? Why you need to sharpen this? Why those are gonna be brown? Why she’s the one who can hold it? Why it’s still breakfast time? Why you’re a scaredy cat? Why he can’t go in Noah’s Ark? Why it’s his favorite time of day? Why does he know which way we go? Why he ate him? Why that table’s moved over there? Why they don’t work? Why it’s your favorite? Why he wasn’t afraid of Boomer? Why I can’t have cheese puffs?

The resemblance to Italian runs much deeper than this, however. As we saw, Italian why-questions permit linguistic material to intervene between perché and the subject noun phrase. A.L.’s why-questions also frequently had various phrases intervening between why and the subject NP. Examples are given in (33). (33)

a. b. c. d.

Why some of your make up I can’t use [and some I can]? (5;2) Why this time you’re opening them like that? (4;2) Why when I was a baby I loved Boomer’s dog food? (3;6) Why always when he rings I’m asleep? (5;3)

In (33a), the object NP has been fronted in a speech act involving contrastive focus. In (33b), an adverbial phrase intervenes between why and the subject NP. In (33c), the intervener is a subordinate clause, and (33d) has both an intervening adverb and a subordinate clause. A.L. also permitted topics to intervene between why and the subject NP. In particular, time adverbials were

2.5 Evidence for continuity in child language  95 abundant. The first example was witnessed at age 4;2, and there were ten further examples before A.L. was 5;6. A sample is in (34). (34)

a. Why this time you’re opening them like that? (4;2) b. Why every winter there’s a snowstorm? (4;3) c. Why every day when I wake up the hall light isn’t on? (5;1) d. Why last time in XX you didn’t give me a bath (but a shower instead)? (5;2) e. Why every day we’re still in the black car? (5;3) f. Why this morning you weren’t as pleased as you usually are when I read a book? (5;3)

Interestingly, during the period in which A.L. was consistently producing nonadult matrix why-questions, she produced adult-like why-questions for one class of matrix why-questions, namely ones that had the illocutionary force of suggestions.8 Some examples are given in (35). As these questions clearly indicate, A.L. was fully able to produce adult-like why-questions, but reserved this operation for suggestions. (35)

a. Why don’t I try it on? (playing Cinderella, and suggesting she try on the shoe) b. Why don’t we get the TV ready to scare them? (to rid the garden of deer) c. Why don’t you make it and cook it first? (before going to work) d. Why don’t we work together on what we want to do? e. Why don’t we make something with glue? f. So why don’t you come on the train and we’ll go to my house? g. Why don’t you use this as a magic wand? h. Why don’t you don’t go?

The critical parallel between child English and adult Italian is the form taken by complex (long-distance) wh-questions in child English. Recall that complex why-questions exhibit subject/auxiliary inversion in both English and Italian. According to the version of the Continuity Hypothesis advanced by Thornton, therefore, children such as A.L. should be expected to use subject/auxiliary inversion in their long-distance questions, at the same stage at which they lack inversion in their matrix why-questions. On the experience-based account, this pattern is not anticipated. In fact, the experience-based account would surely predict just the opposite, i.e., that matrix why-questions would become adultlike sooner than complex why-questions do, because matrix questions are far more frequent than long-distance questions in the input to children. Until recently, only data corresponding to children’s matrix wh-questions were available, so it was difficult to adjudicate between the experience-based account and an account based on the Continuity Hypothesis. In an experimental

96  Competing approaches to language and logic and longitudinal diary study, however, Thornton (2004, 2008) recorded both matrix and complex questions by one child, A.L., between the ages of 1;10 and 5;6. By age 3;0 A.L. produced adult-like long-distance why-questions, with subject/auxiliary inversion, during the same period in which she was producing non-adult matrix why-questions, without inversion. From the time A.L. was 3-years-old to the time she reached the age of 5;6, She produced 21 long-distance why-questions, and only four of these lacked inversion. During the same period, all 62 of A.L.’s complex questions with wh-words other than why exhibited subject/auxiliary inversion. Some representative examples are given in (36). (36)

a. b. c. d.

Why do you think you like Cat in the Hat books? Why do you think mummy would not wanna watch the show? What do you think is under your chair? How do you think he can save his wife and her at the same time?

To summarize, the production data reported by Thornton suggest that an English-speaking child analyzes why-questions in the same way as the corresponding questions are analyzed in Romance languages, such as perché in Italian. In producing matrix why-questions, moreover, A.L. was ignoring abundant evidence in the input indicating a mismatch between her grammar and that of adult speakers in the same linguistic community. However, A.L. adhered to grammatical principles that govern all human languages, producing adult-like complex why-questions, with inversion, despite producing non-adult matrix why-questions, without inversion. See Thornton (2004, 2008) for further parallels between A.L.’s why-questions and those of adult speakers of Italian. 2.6

Arguments against the experience-based approach

No nativist tries to prove that children could never acquire English given any possible data, supplemented by any learning theory. After all, if linguists can discover principles of human grammars by collecting data and deploying the scientific method, then it is at least conceivable that children could also do so. But even if children were able scientists, they would not have access to the kinds of adult judgments that drive linguistic analysis. Linguists have access to cross-linguistic data, negative evidence, judgments of acceptability versus unacceptability, and judgments of ambiguity versus non-ambiguity. The child’s primary linguistic data do not include evidence like this, as far as we know. Yet in just a few years children achieve a grammar that is governed by the principles that trained linguists have discerned in their investigations of adult grammars. According to nativists, therefore, it is unlikely that children could

2.6 Arguments against the experience-based approach  97 have learned the adult language given the data available to them. In this ­context, available means plausibly available to all normal children. Of course, there is room for dispute about what is available (see, e.g., Lightfoot 1991). And, if adults can judge certain strings of words to be unacceptable or ambiguous, then children must certainly acquire such abilities by the time they are adults. But that leaves a lot of time for exposure to a lot of data. According to logical nativism, learning is a highly implausible way to account for children’s emerging linguistic competence. There are several strands to the nativists’ argument. One is to demonstrate that all children know complex properties of human languages at an early age. If all young children, across languages, demonstrate knowledge of the principles that characterize adult grammars, then the acquisition problem is considerably compressed. As noted earlier, no one can prove that 3-year-olds have not already utilized a vast range of (positive and negative) data. But the case for nativism is strengthened in so far as children respect grammatical constraints before they are plausibly exposed to the experience that would be required by learning-theoretic accounts. The argument for nativism is even stronger if the experience children require includes complex and/or rare expressions. It is highly implausible that all normal children will come across (and attend to, and utilize) such data at a very young age. We saw that advocates of the experience-based approach contend that children do not require innate knowledge. Instead, either children are viewed as being conservative learners, or they are seen as having access to indirect negative evidence (e.g., Cowie 1999; but cf. Crain and Pietroski 2001, for arguments against the availability of indirect negative evidence). There are good reasons to think, however, that children are not conservative learners. In fact, there is evidence that children produce the very interpretations that proponents of conservative learning argue they do not produce. Children have been found to accept local coreference between a pronoun and a referring expression in sentences like Papa Bear is covering him. That is, they accept this sentence as a description of a situation in which Papa Bear is covering himself, but is not covering another male individual (for a review, see Thornton and Wexler 1999). This is a case of overgeneration of meaning. Such cases undermine the proposal that children are conservative learners, as proposed by van Hoek (1995) and by Rosen and Rosen (1994). There is a deeper problem with conservative learning. If language learners only adopt grammatical principles that generate expressions that have been encountered in the linguistic environment, then learners will undergenerate; i.e., their grammars will only generate a subset of the expressions of the adult

98  Competing approaches to language and logic language. Such learners would not achieve the stable state that allows for production and comprehension of sentences never before encountered. As Pinker (1989, p. 6) remarks, “children cannot simply stick with the exact sentences they hear, because they must generalize to the infinite language of their community.” By the time children reach the stable state, they are able to project beyond their data so as to produce and comprehend (an unbounded number of) novel sentences. The experience-based approach anticipates that children’s non-adult linguistic behavior will be less filled-out versions of the linguistic expressions produced by adults. Lacking full linguistic competence, children’s productions are expected to resemble those of adults, but lacking certain words or word-endings, for example. By contrast, the nativist approach predicts that children may appear to be speaking a foreign language for a while. This effect is achieved when children adopt a different value of a parameter from that exhibited by adult speakers of the local language. But, as long as the differences between child and adult language mirror differences that are attested among adult languages, then children’s behavior is circumscribed by Universal Grammar. According to the nativist approach, therefore, children may effectively ignore the input from adults, and produce sentences and assign meanings that are not attested in the target language. This finding is perhaps the strongest evidence in favor of the nativist approach, and against the experience-based approach. In addition to being too weak, the learning mechanisms associated with the experience-based approach are too “strong,” in the sense that they would predict that children should be able to learn construction/meaning pairs that, as a matter of fact, they cannot learn. For example, Read and Schreiber (1982) found that 7-year-old children cannot learn structure-independent rules, such as the rule “drop the first four words of a sentence.” To the extent that experience-based learning mechanisms can form such structure-independent generalizations, they are quite unlike human brains. As Smith (1996, p. 7) concludes from the evidence, “structure dependence is the prerequisite to, not the outcome of, language acquisition.” More generally, the learning mechanisms of the experience-based approach should have little trouble learning many construction/meaning pairs that violate putatively innate linguistic constraints. To take just one example, there is a constraint prohibiting extraction from coordinate structures. This constraint prevents languages from forming questions such as What did Ted order sushi and? According to the experience-based approach, presumably, this construction should be easy for children to acquire, on analogy with What did Ted order sushi with? To the extent that children have

2.7 Linguistic universals  99 difficulty acquiring constructions that violate the coordinate structure constraint, and many more like it, this would pose a challenge to the experiencebased approach.9 2.7

Linguistic universals

Another argument between advocates of logical nativism and advocates of the experience-based approach concerns linguistic universals. As we have seen, universal linguistic principles are designed to tie together a variety of linguistic phenomena, so it is unlikely that there will be large numbers of human languages lacking all members of the relevant classes. Consider the semantic property of downward entailment. Downward entailment governs the interpretation of disjunction, as we have seen. In addition, downward entailment dictates where NPIs (e.g., English any, Mandarin renhe) are ­tolerated. This is not an accident. Suppose your favorite restaurant serves three kinds of fish – trout, bass, and cod. When you arrive on Friday night, however, the waiter informs you – We don’t have any fish left. It follows from the waiter’s statement that there is no trout and no bass and no cod. As with disjunction, any entails a conjunction of negatives when it appears in the scope of negation. As long as a human language has at least one downwardentailing expression (e.g., negation), then if it has either disjunction or negative polarity items, the phenomena associated with downward entailment will be witnessed in that language. Suppose a language lacks both disjunction and negative polarity items. All is not lost for the logical nativist. Downward entailment might still be manifested as a substantive linguistic universal in all human languages. This is based on the defining property of downward entailment  – the licensing of inferences from general to particular expressions. So long as all human languages categorize objects into both superordinate and basic-level categories, and as long as all human languages contain at least one downward-entailing expression, then downward entailment will be operative in all languages. This is not merely idle speculation. According to the anthropologist Donald Brown (1991), there are certain features of language and logic “for which there are no known exceptions.” Included among these are the basic ingredients for downward entailment, including not and general/particular. In addition to the basic ingredients for downward entailment, Brown lists, as part of human nature, other concepts that are essential for logical reasoning: distinguishing true and false, choice making (choosing alternatives), as well as the logical concepts and, equivalent, opposite, part/whole, and same (also see Pinker 2002).

100  Competing approaches to language and logic To conclude, if some researchers are struck by the diversity of human languages, others are also struck by the common themes, including logical concepts. Nearly everyone admits that there are linguistic universals in some sense. At issue is whether the universals of human languages are specific to language and logic, or whether cross-linguistic generalizations simply owe to the fact that all humans are born with the “same basic conceptual apparatus” that any rational system requires (Goldberg 2003, p. 16). In Chapter 1, we presented reasons for thinking that the interpretations generated by logical expressions in human languages are contingent facts that are governed by language-specific constraints, and are not simply entailments that any rational system would make. 2.8

Empirical differences between the approaches

Logical nativism distinguishes meaning from use. According to logical nativism, knowledge of the meanings of logical expressions is specified as part of the innate endowment of the species. This view, therefore, predicts that all languages will access the same semantic representations of logical expressions. If so, then there should be abundant evidence that human languages all associate the same truth conditions with a logical expression such as disjunction. The experience-based account, by contrast, expects cross-linguistic variation, rather than cross-linguistic generalizations. On this account, there is no reason to suppose that the words corresponding to disjunction will follow the same patterns of usage in all languages. The expression for disjunction in Japanese (ka) could have inference rules corresponding to exclusive disjunction, whereas the expression for disjunction in Chinese (huozhe) could have inference rules corresponding to inclusive disjunction. Other languages, say Latin, could have two expressions for disjunction, one associated with inference rules corresponding to exclusive disjunction, and the other with inference rules corresponding to inclusive disjunction. Therefore, logical nativism and the experience-based account make divergent empirical predictions about the existence of language universals. The accounts also make divergent predictions about the nature of language learning. The experience-based account anticipates that children’s use of logical statements will mirror the use by adult speakers. Of course, children must refine their usage of logical expressions as they accrue relevant experience, so as to comport fully with adult usage. But the experience-based account is essentially an input-matching account of language development, as compared to logical nativism. According to logical nativism, as we saw, children’s competence in

2.8 Empirical differences between the approaches  101 using logical expressions depends on a confluence of factors, semantic knowledge being just one. Therefore, children may be expected to exhibit patterns of usage that differ from those of adults. The expected differences will be highly circumscribed, however, so their existence can be confirmed or disconfirmed by experimental investigation. There is another aspect to language learning that could make children use logical expressions differently than adult speakers do. Children must fix the parameters of the target language. If a parameter involves the logical expression and or or, then it is possible for children to initially adopt a parameter value that is incorrect for the target language. This would require the child to reset the parameter, presumably in response to the mismatch between the child’s use of and and or and that of adults. During the period in which the child has adopted the wrong parameter value, though, children’s use of the logical expression would not resemble that of adults. In summary: • The principles of Universal Grammar provide a unified account of linguistic phenomena which may appear unrelated, but which co-occur across languages. • The linguistic principles of Universal Grammar explain why language users do not produce certain linguistic forms, and why they do not assign certain meanings to forms they do produce. • Parameters circumscribe children’s non-adult linguistic behavior (the Continuity Hypothesis). • The principles of Universal Grammar are abstract, and not clearly demarcated in children’s experience.

3 The case for logical nativism

Logical nativists contend that human languages and their learners exhibit ­deep-seated regularities. Many of these regularities, or core linguistic principles, pertain to logical expressions, including both the basic meanings of logical expressions and the interpretations given to combinations of these expressions. Because core linguistic principles are candidates for innate specification, they are expected to meet the diagnostics of innateness. These diagnostics can, in turn, be used to distinguish the logical nativist approach from the experiencebased approach. Let us briefly review these features. First, linguistic phenomena governed by core linguistic principles are expected to be universal. Second, core linguistic principles are expected to range over several phenomena, including ones that may appear on the surface to be unrelated. If abstract principles pertain to clusters of facts that appear to be unrelated on the surface, then these principles provide a unique testing ground to distinguish the logical nativist approach from the experience-based approach, such as the constructivist model discussed in Chapter 2. Because the experience-based approach postulates shallow linguistic representations, it follows that the experience-based approach and logical nativism make radically different empirical predictions about the nature of language, and about the language acquisition process. For one thing, core linguistic principles are expected to be evident in children’s language as soon as they can be tested, even where children lack decisive evidence for them in the primary linguistic data. This chapter spells out some of the main theoretical and empirical foundations of logical nativism, by describing a series of linguistic phenomena that satisfy the hallmarks of an innate logic faculty. We begin by considering arguments for nativism that have been offered for a syntactic constraint, Principle C of the binding theory. This principle was chosen for several reasons. First, both syntactic and non-syntactic (e.g., pragmatic) accounts of the relevant linguistic phenomena have been proposed in the theoretical literature. Second, Principle C has been investigated in the literature on child language. Third, this principle invokes a structural property (c-command) that also governs the semantic 102

3.1 Principle C  103 representations of sentences with logical expressions, so the discussion of ­syntax takes us directly to the main topic of the book, logical nativism. Part I Innate linguistic principles We begin the exposition by introducing a core linguistic property from syntax. Although this text is about the logical principles of human languages, it will be useful to rehearse some of the basic points about core principles using a familiar example. Moreover, as it turns out, one of the structural relations that is basic to core syntax, namely c-command, also plays a critical role in the interpretation of logical expressions in human languages. And, as with the logical phenomena we have been considering, core syntactic principles play a unifying role in tying together a variety of phenomena using the same basic ingredients. 3.1

Principle C

We take as our example Principle C of the binding theory. The binding theory is a set of three principles that govern the anaphoric relations that obtain between different kinds of noun phrases and their antecedents. The third principle, Principle C, governs referring expressions such as names and definite descriptions. To a first approximation, the principle asserts that referring expressions must be free, where free means that a referring expression must be contra-indexed with and, hence, disjoint in reference from an antecedent that c-commands it. To a first approximation, a noun phrase NP1 c-commands another noun phrase NP2 if there is a path (in the constituent structure) that proceeds upward from NP1 to the first branching node above it, and then downwards to NP2, as depicted in Figure 3.1.

NP1

NP2

Figure 3.1. C-command

104  The case for logical nativism

he said Max ordered

sushi

Figure 3.2. C-command

The sentences in examples (1) and (2) illustrate how c-command is applied by Principle C to rule out coreference between pronouns and referring expressions, including names like Max.1 Principle C governs the English (1). Example (2) is the Mandarin translation of (1). In both languages, Principle C eliminates coreference between the pronoun and the name, leaving just the interpretation on which he (ta) and Max (Makesi) are disjoint in reference. (1)

He said Max ordered sushi.

(2)

Ta shuo Makesi dian le shousi he say Max order asp sushi 他说马克思点了寿司. ‘He said Max ordered sushi.’

In these examples, the name Max and its (potential) antecedent, the pronoun he (Mandarin ta), must have disjoint reference. The reason for this is shown in Figure 3.2. As Figure 3.2 indicates, the pronoun he (Mandarin ta) c-commands Max in the surface structure that is assigned to the English example (1), and to the Mandarin example (2), so coreference between these expressions is prohibited. As these examples illustrate, the search for core principles of human languages is based partly on what people actually say and what they mean by what they say, i.e., positive evidence. But just as important in forming linguistic generalizations are facts about what people do not say, and what they cannot mean by what they say. In contrast to the examples (1) and (2), he and Max are permitted to pick out the same referent in (3) and (4). Coreference between these expressions is permitted, because Principle C is not operative (i.e., he does not c-command Max). These examples also license an interpretation on which he and Max refer to different individuals. So, these examples are ambiguous, whereas (1) and (2) are unambiguous, because Principle C eliminates the coreferential interpretation, leaving just the interpretation on which the pronoun he and the referring expression Max are disjoint in reference.

3.1 Principle C  105

Max said he ordered

sushi

Figure 3.3. No c-command

While he

Max

was holding

ordered the pasta

sushi

Figure 3.4. No c-command

(3) (4)

Max said he ordered sushi. While he was holding the pasta, Max ordered sushi.

Figure 3.3 illustrates why coreference between the pronoun he and the referring expression Max is allowed in (3) Max said he ordered sushi. As the figure indicates, the c-command domain of the pronoun extends downward into the predicate phrase … ordered sushi, so the name Max is not c-commanded by the pronoun. Therefore coreference is tolerated. It should be noted that the pronoun may also bear direct (deictic) reference, i.e., it may refer to some male individual who is not mentioned in the sentence, so (3) is ambiguous. Figure 3.4 indicates why coreference is permitted between the pronoun he and the referring expression Max in (4) While he was holding the pasta, Max ordered sushi. As Figure 3.4 shows, the pronoun he c-commands the phrase …was holding the pasta, but the pronoun he does not c-command the phrase …Max ordered sushi. Therefore, Principle C does not apply, leaving open the possibility of coreference between the pronoun he and the name Max, as well as the possibility that the pronoun has direct reference, i.e., the pronoun could also be used deictically to refer to some unmentioned male individual in the domain of discourse.

106  The case for logical nativism As the examples also illustrate, one of the consequences of Principle C is the absence of an interpretation. It is not easy to see, though, how children can learn that sentences lack an interpretation (see section 3.15 for discussion).2 As far as we know, this kind of information is not attested in children’s primary linguistic data, much less a regular component of the input available to children. This invites the conclusion that Principle C is not learned by children; rather, it is innate. Two other observations bolster this conclusion. One is that Principle C is exhibited in typologically different languages. A second is that children have been found to adhere to the principle as early as they can be tested (see Crain and Thornton 1998, Chapter 27). The finding that young children adhere to Principle C will be used as evidence against an account of the linguistic phenomena that is stated in terms of pragmatic principles, rather than syntactic principles (e.g., Levinson 2000). The argument we make will be that, because young children demonstrate knowledge of the relevant linguistic phenomena before they are able to compute the relevant pragmatic inferences, this renders the pragmatic account of the phenomena untenable (see section 3.8). A core linguistic principle is a plausible candidate for innate specification if (a) the principle is universal, (b) it ties together apparently unrelated phenomena, (c) it emerges early in the course of language development in every (normal) child, and (d) it emerges without decisive evidence in the primary linguistic data. Principle C satisfies all four hallmarks of innateness. In addition to meeting these hallmarks, Principle C meets all of these criteria for being a core principle of Universal Grammar. We have been focusing mainly on the fact that core principles explain a range of linguistic phenomena. Both Principle C and the structural notion c-command are noteworthy in this regard. First we need to introduce a little bit of formal machinery, using declarative sentences. Consider the sentences (5) and (6). In declarative sentences like these, the pronoun he and the name Morris must be disjoint in reference. Disjoint reference (or non-coreference) is indicated by the different numerical subscripts on these NPs, as in example (5), where the pronoun is he1 and the name is Morris2. For simplicity, we will not put an index on the name Ted. When NPs are assigned the same index, as in (6), this is taken to indicate that the NPs pick out the same individual, but this is prohibited by Principle C, since the pronoun he1 in (6) c-commands the name Morris1. According to Principle C, a referring expression (i.e., a name or definite description) must be disjoint in reference from any NP that c-commands it. We use an asterisk ‘*’ to mark deviance, as in (6).

3.1 Principle C  107 (5) (6)

He1 said Ted criticized Morris2. *He1 said Ted criticized Morris1.

3.1.1 Wh-questions In addition to statements with pronouns, Principle C governs the interpretation of wh-questions, as in (7). This, and other examples in this section, have been adapted from Chomsky (1981). (7)

Who did he say Ted criticized? (for which person x, he said Ted criticized x)

To see why Principle C applies in wh-questions like (7), let us suppose that a friend, Anne, knows that some salient male said that Ted criticized someone, but she doesn’t know who he said Ted criticized (but we already know it was Morris). In this case Anne might pose the question in (7). There are two steps to the derivation of the logical form corresponding to question (7). These steps are depicted in (8). (8)

Step A. He said Ted criticized who1. Cf. He said Ted criticized Morris. Step B. [Who1 ][he2 said that Ted criticized t1]

First (Step A), the wh-word originates in the same position as the name Morris did in the statement, He said Ted criticized Morris, following the verb criticized. The wh-word who qualifies as an obligatory argument for the verb criticize, in just the way the name Morris qualifies for this in the declarative statement. In fact, as we have seen, wh-words remain in argument position in Mandarin Chinese, i.e., they are pronounced in situ, rather than being displaced, as in English. In English wh-words must be raised to a higher structural position in the surface syntax. This is Step B. Notice that when the wh-word raises in English, it crosses over a c-commanding pronoun. For this reason, questions like (7) Who did he say Ted criticized? are called crossover questions. When the wh-word raises, it leaves a trace behind at its site of origin (written t). Principle C applies at logical form. Because the pronoun he c-commands the trace at logical form, these constituents cannot be anaphorically linked; i.e., Principle C dictates that they must receive different indices. Consequently, the pronoun he must be interpreted as a deictic pronoun in crossover questions; it must refer to some salient male in the conversational context. Thus, when Anne poses the question Who did he say Ted criticized?, she is asking for the identity of a person (or persons) such that he (some salient male) said that Ted criticized that person.3 If the pronoun and the trace are coindexed, as in (9), then this would constitute a violation of Principle C.

108  The case for logical nativism (9)

*[Who1][ he1 say Ted criticized t1] (for which person x, x said Ted criticized x)

The interpretation in (9), which is ruled out by Principle C for crossover questions like (8), is permitted in other wh-questions, where the pronoun does not c-command the trace. An example is (10). The wh-word who originates in the subject position of sentence (10). This means that the trace precedes the pronoun and, hence, the pronoun does not c-command the trace. Therefore, Principle C does not apply. (10)

Who said he criticized Morris?

The wh-question (10) is ambiguous. Its interpretations are represented in (11) and (12). (11) (12)

[Who1 ][ t1 said he1 criticized Morris] (for which x, x said x criticized Morris) [Who1 ][ t1 said he2 criticized Morris] (for which x, x said he criticized Morris)

Because Principle C is not operative in the question in (10), nothing prevents the wh-word from binding the pronoun he. Pronominal binding (a.k.a. variable binding) by the wh-word is permitted (by transitivity) when the trace of the wh-word is coindexed with the pronoun. That is, all three NPs receive the same numerical index {who1, he1, t1}. The interpretation depicted in (11) is called the bound pronoun (or bound variable) interpretation. The same sequence of words also has a reading on which the pronoun he is used deictically, i.e., to refer to some salient male in the conversational context. This is sometimes called the extrasentential reading of the pronoun. This reading is represented in (12). We saw previously that, due to Principle C, only the deictic interpretation of the pronoun is permitted in the crossover question, Who did he say Ted criticized? So, crossover questions are unambiguous, whereas questions like (10) are ambiguous, because they also allow a bound pronoun reading. 3.1.2 Quantificational expressions In addition to statements with pronouns, and crossover questions, Principle C governs the interpretation of sentences with quantifiers. One example is (13). The derivation of the logical form corresponding to (13) is given in (14). In the second step of the derivation, the quantificational expression everyone is raised, in the same way as wh-words are raised in crossover questions. The difference is that wh-words are raised overtly, so the fact that they are displaced is manifested in the surface syntax, whereas quantifiers are raised covertly, at

3.1 Principle C  109 the level of logical form. The common feature, however, is that wh-words and quantifiers both leave a trace behind (Step B). The trace cannot be coindexed with a c-commanding pronoun, due to Principle C. The upshot is that the pronoun he must be used deictically in (13), just as it was in the crossover question Who did he say Ted criticized? (13)

He said Ted criticized everyone. (for every person x, he said Ted criticized x)

(14)

Step A. He said Ted criticized everyone.   Cf. He said Ted criticized Morris. Step B. [everyone1 ][ he2 said Ted criticized t1]

Not surprisingly, the interpretation that is ruled out by Principle C is permitted in other sentences with quantificational expressions, in cases where the pronoun does not c-command the trace. An example is (15). Again, the example is ambiguous. Because Principle C is not operative, nothing prevents the pronoun he (and the trace of the quantifier) from being bound by the universal quantifier. This yields the bound pronoun (bound variable) interpretation in (16). The example in (15) also has a reading on which the pronoun he is used deictically, i.e., to refer to some salient male in the conversational context. This reading is represented in (17). (15) (16) (17)

Everybody said he criticized Ted. [everyone1 ][ t1 said he1 criticized Ted] (for every x, x said x criticized Ted) [everyone1 ][ t1 said he2 criticized Ted] (for every x, x said he criticized Ted)

To rule in the desired interpretations of crossover questions and sentences with quantificational expressions, and to rule out the undesired one, it is postulated that a trace is a referring expression. So, referring expressions include names, definite descriptions, and they also include the traces left behind by wh-words and by quantificational expressions. The proposal that a trace functions as a referring expression may seem counterintuitive. Recall, however, that the meaning of a wh-question is the set of (possibly true) answers to the question. The meaning of the wh-question Who did he say Ted criticized? is the set of propositions {he said Ted criticized Morris, he said Ted criticized Noam, …}. And each of these propositions is governed by Principle C. To sum up the discussion so far, Principle C provides a unified account of a range of apparently disparate linguistic phenomena, including the interpretation of declaratives, wh-questions, and quantificational expressions. This makes Principle C a viable candidate for being a core property of human language.

110  The case for logical nativism 3.2 Extending core principles Principle C is a constraint that prevents the assignment of certain interpretations to well-formed sentences. For one thing, Principle C prevents interpretations on which there is coreference between pronouns and referring expressions in sentences where the pronoun c-commands the referring expression. Principle C is built upon the structural property of c-command. For example, the pronoun he c-commands the referring expression Max in (18), so Principle C dictates that these expressions must pick out different individuals in the domain of discourse. The same is true in Mandarin, as shown in (19). (18)

He said Max ordered sushi.

(19)

Ta shuo Makesi dian he say Max order 他说马克思点了寿司。 ‘He said Max ordered sushi.’

le asp

shousi sushi

Principle C is a core linguistic principle in the sense that it ties together a set of linguistic phenomena that at first glance look unrelated. We have seen that, in addition to declarative sentences like those in (18) and (19), Principle C governs crossover wh-questions, and it governs sentences with quantifiers. So, Principle C enforces prohibitions on two kinds of anaphoric relationships. One anaphoric relationship is coreference, which links pronouns and referring expressions. Principle C prevents coreference, and requires disjoint reference, between a referring expression and its c-commanding potential antecedents. The second anaphoric relationship is variable binding, which is a relationship between quantificational expressions and pronouns. Principle C prohibits whwords and quantifiers from binding pronouns in certain configurations. It has recently been proposed that Principle C governs discourse phenomena, such as the discourse exchanges illustrated in the English example (20) and in the corresponding Mandarin example (21). Just as disjoint reference is enforced in the English declarative sentence He said Max ordered sushi, the pronoun he in the assertion by Speaker A cannot be anaphorically linked to the name Max in the comeback by Speaker B, and the Mandarin pronoun ta cannot be linked to Makesi in (21). (20)

Speaker A: I know who he said ordered sushi. Speaker B: Me too. Max.

(21) Speaker A:

Wo zhidao ta shuo shei dian le shousi I know he say who order asp sushi 我知道他说谁点了寿司。 ‘I know who he said ordered sushi.’

3.2 Extending core principles  111 Speaker B:

Wo ye zhidao. Makesi. I also know Max 我也知道。马克思。 ‘I also know. Max.’

he Speaker A

Max Speaker B

Figure 3.5. Discourse blocks c-command

Principle C and its associated structural component, c-command, don’t appear to be operative in discourse sequences such as (20) and (21). As we have seen, c-command is a relationship between elements that can be connected by a path through a phrase structure diagram. Clearly, no path can be drawn between an expression in Speaker A’s utterance and one in Speaker B’s utterance. This could invite the conclusion that connected sentences and disconnected discourse sequences are unrelated. This is graphically depicted in Figure 3.5. The examples in (20) and (21) contain all the necessary ingredients for the application of Principle C. It’s just that some of the ingredients are in Speaker A’s contribution, and some are in Speaker B’s contribution. If the ingredients could be connected in some way, then Principle C could be applied. Principle C would then govern both sentence-level and discourselevel phenomena. Recently, linguists have tackled the problem, arguing that Principle C, as well as other linguistic principles, are operative in both individual sentences and in discourse sequences (e.g., Merchant 2004). The supposition is that the interpretation of discourse involves connecting disjoint elements at some level of representation, and applying the linguistic principles to the connected representations. These representations include linguistic material that is not always witnessed, but is there nonetheless. The relevant connected representation for the discourse in (20) and (21) is made by Speaker B. In formulating a

112  The case for logical nativism

he said Speaker A

he Speaker B

said Max

Figure 3.6. Connecting discourse

response to Speaker A, Speaker B computes a representation that includes relevant structure from Speaker A’s utterance. Speaker B does not need to overtly produce all of the relevant content from Speaker A’s utterance. All of it can be repeated or, instead, Speaker B may produce an elided response (a.k.a., a fragment answer). In the elided response, some of the content from Speaker A’s utterance, although computed, is not pronounced. Because the content of Speaker A’s utterance is counted in Speaker B’s representation, the fragment answer has the same semantic interpretation as a connected statement. This analysis of the dialogues in (20) and (21) is graphically depicted in (22), where the content of (a) and (b) are semantically equivalent. (22) Speaker A: I know who he said ordered sushi. Speaker B: a. Me too. He said Max ordered sushi. b. Me too. He said Max ordered sushi.

The same connectedness (a.k.a. connectivity) approach has been taken to explain many other linguistic phenomena, including discourse sequences with logical expressions. For example, suppose someone gives a negative answer to a Yes/No question that is posed in the form of a disjunction, as in (23). The negative answer licenses a conjunctive entailment for the disjunction word that appears in the question. So, the negative answer excludes both of the mentioned disjuncts, i.e., sushi and pasta. Again, the connectivity proposal supposes that the answer contains material that has been elided, as indicated by the strikethrough. (23)

Question: Did Max order sushi or pasta? Answer: No. Max didn’t order sushi or pasta.

The literature on child language includes various studies showing that English-speaking children have the ability to recover the connected linguistic

3.3 Connectivity and Principle C  113 structure that is needed to enforce linguistic principles, including Principle C. In these studies, children have been found to interpret even complex structures in the same way as adults do (e.g., Guasti and Chierchia 1999/2000; Kiguchi and Thornton 2004; Syrett and Lidz 2009). Since our interest is in the interpretation of logical expressions, we will discuss some relevant experiments in this domain. But it is important to keep in mind that the same linguistic properties that determine the interpretations of logical expressions in human languages are also operative in other linguistic phenomena. Unification of disparate-looking phenomena is one of the main hallmarks of core grammar, after all. We begin, then, with a discussion of research findings of studies of children’s knowledge of syntax, and then we turn our attention to how the same principles are used in deriving the meanings of sentences with logical expressions. 3.3 Connectivity and Principle C Principle C prohibits coreference in declarative sentences like (24). It is intuitively clear that in (24) the pronoun he cannot refer to Chuckie, but must refer to some other salient male in the conversational context. (24)

*He1 sent the letter to Chuckie1’s house.

As mentioned, it has recently been proposed that Principle C also governs coreference relations in some discourse contexts, as illustrated in (25) and (26). (25)

Speaker A: I know where he1 sent the letter. Speaker B: Me too. To Chuckie2’s house.

(26)

Speaker A: I know where he1 sent the letter. Speaker B: Me too. *To Chuckie’s1 house.

The judgments about coreference are strikingly similar to the judgments for the declarative sentence He sent the letter to Chuckie’s house. This raises the possibility that the same constraint governs both linguistic phenomena. The idea is that part of the structure of the statement by Speaker A is reconstructed by Speaker B, but subsequently deleted. This is illustrated in (27). (27)

Speaker A: I know where he1 sent the letter. Speaker B: Me too. He1 sent the letter to Chuckie2’s house.4

Even though only a fragment answer (to Chuckie’s house) is actually produced by Speaker B, it has the same propositional content as a full sentence. These discourse sequences can be translated into Mandarin, with the same results, as illustrated in (28).

114  The case for logical nativism (28) a. Speaker A: b. Speaker B:

Wo zhidao ta ba xin song qu nali le I know he ba letter send go where asp 我知道他把信送去哪里了。 ‘I know where he sent the letter.’ Wo ye zhidao. Taide de jiali I also know Ted de house 我也知道。泰迪的家里。 ‘I also know. To Ted’s house.’

Adopting the theory proposed by Merchant (2004), Conroy and Thornton (2005) investigated the hypothesis that Principle C is invoked by children to prohibit coreference in discourse contexts. In the Conroy and Thornton (2005) study, twenty English-speaking children (mean age 4;6) were presented both full sentences and discourse sequences to see whether they made similar judgments in response to both. On a typical trial of the relevant experimental condition, one of the characters, Tommy, was preparing to send a letter to Chuckie’s house, but then decided against it. In response, Chuckie sent a letter to his own house. Against this backdrop, half of the time, children heard a complete sentence (He sent the letter to Chuckie’s house), and half of the time, they heard a discourse like the one in (29). (29)

Speaker A: I know where he sent the letter. Speaker B: Me too. To Chuckie’s house.

The main finding was that children rejected both the full sentences and the discourse sequences an equal proportion of the time (86 percent rejections, as compared to 89 percent rejections, respectively). This finding is consistent with the hypothesis that the same negative constraint against coreference, Principle C, underlies children’s responses to both phenomena. The findings from the Conroy and Thornton study are important for several reasons. The lessons to be learned follow from the observation that discourse sequences like (29) lack c-command, at least on the surface. So, if children do not themselves impose c-command on such sequences, then one possibility is that they learn to prohibit coreference between pronouns and referring expressions in one way in connected sentences, and in some different way in discourse. Or, putting it the other way around, if children do not impose c-command on discourse sequences at some level of representation, then whatever mechanism children determine to be operative in discourse sequences could also be used in individual sentences, so the non-coreference facts in discourse sequences could be taken by children to be evidence that c-command is not operative in individual sentences, any more than it is operative in discourse

3.4 Connectivity in pseudoclefts  115 sequences. This poses a dilemma. The dilemma becomes exacerbated when we consider other linguistic structures in which the non-coreference constraint seems to apply, despite the absence of c-command. The structures in question are pseudoclefts. 3.4 Connectivity in pseudoclefts Pseudoclefts look simple. They consist of a wh-clause on one side or on the other side of the copula, with some kind of phrase (e.g., NP, PP) on the side opposite to the wh-clause. In other words, the copula (designated be) is the centerpiece, making two types of pseudoclefts, referred to as Type 1 and Type 2.5 (30)

Type 1: wh-clause BE NP Type 2: NP be wh-clause

E.g., What Max ordered is sushi. E.g., Sushi is what Max ordered.

An interesting observation is that coreference is prohibited between pronouns and referring expressions in pseudoclefts. This is illustrated in (31). (31)

What he is is fed up with Max.  he ≠ Max

What makes this interesting is that the pronoun in (31) does not appear to c-command the referring expression in the surface syntactic structure, so it is unclear why coreference between these expressions is prohibited. As shown graphically in Figure 3.7, the pronoun in the wh-clause in (31), is too low in the syntactic structure to c-command the NP following be. Despite the absence of surface c-command between he and Max in (31), some principle enforces disjoint reference. Even inverting the word order to yield a Type 2 pseudocleft, as in (32), does not diminish the non-coreference effect.6 (32)

Fed up with Max is what he is.

he ≠ Max

The absence of c-command in the surface structure of pseudoclefts raises a learnability dilemma. On the nativist account, children innately impose ­non-coreference, due to Principle C, whenever a referring expression is ­c-commanded by a potential antecedent NP. From a learnability perspective, the fact that disjoint reference is enforced in pseudoclefts could be taken by children as evidence that Principle C is not the operative principle determining nonconference in pseudoclefts. But if some alternative to Principle C is operative in pseudoclefts, then the same alternative could, presumably, also be operative in declarative sentences, and in wh-questions, and so on. So, why doesn’t the fact that pronouns and referring expressions are disjoint in reference in pseudoclefts simply prove that the non-coreference effects do not depend on Principle C?

116  The case for logical nativism

is

What is

fed up

he

Max with

Figure 3.7. No c-command in pseudoclefts

In fact, several alternative principles, invoking information-theoretic principles, have been offered (see, e.g., Levinson 2000). The nativist answer to this question appeals to two phenomena within the realm of logic which are manifested in pseudoclefts. First, negative polarity items like any are licensed in pseudoclefts. This is illustrated in (33). Second, the conjunctive entailment of disjunction is generated in pseudoclefts. This is illustrated in (34). (33) What Max didn’t order was any dessert. (34) What Max didn’t order was sushi or pasta. (Max didn’t order sushi and Max didn’t order pasta.)

In most circumstances, a downward-entailing expression must c-command the position occupied by a negative polarity item, such as English any. Otherwise the negative polarity item is not tolerated. For example, negation is downward entailing. Accordingly, when negation c-commands the structural position of any, as in (35), the sentence is acceptable. When negation is too low in the phrase marker to c-command any, as in (36), the result is unacceptable. (35) (36)

The girl who stayed up late will not get anything. The girl who didn’t go to sleep will get *anything.

The requirement for negative polarity items to be licensed by a c-commanding downward entailing expression is a cross-linguistic generalization. For example, the Mandarin counterpart to English any is renhe. The examples in (37) and (38) indicate that Mandarin renhe is licensed when it appears in the scope of (i.e., is c-commanded by) negation, bu, but not otherwise. (37)

Shui-de-wan de nühai bu hui dedao renhe dongxi. stay-up-late de girl neg will get any thing 睡得晚的女孩不会得到任何东西。 ‘The girl who stayed up late will not get anything.’

(38)

Mei neg

shuijiao de sleep de

nühai hui dedao *renhe girl will get any

dongxi. thing

3.4 Connectivity in pseudoclefts  117

没睡觉的女孩会得到*任何东西。 ‘The girl who didn’t go to sleep will get *anything.’

Another phenomenon governed by c-command is the conjunctive interpretation of disjunction. For this interpretation to arise, disjunction must be c-commanded by a downward-entailing expression. For example, when negation c-commands disjunction, as in (39), it generates a conjunctive entailment, but no such entailment is generated in (40), where negation fails to c-command disjunction. (39) (40)

The girl who stayed up late will not get a coin or a jewel. The girl who didn’t go to sleep will get a coin or a jewel.

The requirement for disjunction to generate a conjunctive entailment only when it is c-commanded by a downward-entailing expression is another crosslinguistic generalization. The same requirement is operative in Mandarin. This is illustrated in (41) and (42). In example (41), the Mandarin disjunction word huozhe generates a conjunctive entailment, because it is c-commanded by the negated modal, bu hui. By contrast, huozhe receives a disjunctive reading in (42), because negation mei does not c-command huozhe. (41)

Shui-de-wan de nühai bu hui dedao yingbi huozhe baoshi.7 stay-up-late De girl neg will get coin or jewel 睡得晚的女孩不会得到硬币或者宝石。 ‘The girl who stayed up late will not get a coin or a jewel.’

(42)

Mei shuijiao de nühai hui dedao yingbi huozhe baoshi. Neg sleep De girl will get coin or jewel 没睡觉的女孩会得到硬币或者珠宝。 ‘The girl who didn’t go to sleep will get a coin or a jewel.’

The critical observation is that c-command is a prerequisite for stating the licensing conditions on negative polarity items, and for stating when the conjunctive entailment of disjunction is generated. And, like the non-coreference facts, these phenomena are manifested in pseudoclefts in the apparent absence of c-command.8 These joint observations invite us to consider an alternative analysis of pseudoclefts, on which c-command is operative, not in the surface syntax, but at the level of logical form. Several such analyses of pseudoclefts have been proposed. For expository purposes, we will present what is called the question-in-disguise analysis of pseudoclefts (e.g., Den Dikken, Meinunger, and Wilder 2000; Schlenker 2003). On the question-in-disguise analysis, pseudoclefts are expected to behave in important respects like pairings of questions with their associated fragment

118  The case for logical nativism

What is he

is

he is fed up with

Max

Figure 3.8. Question-in-disguise analysis of pseudoclefts

answers. To understand how the question-in-disguise analysis works, it will suffice to consider some representative derivations. First, consider the derivation schematized in (43), and in the graphic in Figure 3.8. As the figure indicates, the pronoun he does indeed c-command the referring expression Max in the derivation. The connection between he and Max is broken at the level of phonological form, but the c-command connection is reinstated at logical form, so non-coreference is enforced, due to Principle C. (43)

What he is is fed up with Max. [What he is _] is [he is fed up with Max].

The following are schematic derivations for the licensing of negative polarity items (NPIs) and for the conjunctive entailment of disjunction, for both Type 1 and Type 2 pseudoclefts. These examples contain the downward-entailing expression refuse. In ordinary declarative sentences, the verb refuse must c-command the position of any, and it must c-command or to license a conjunctive entailment. As the following examples indicate, the c-command connection between refuse and these expressions is established at the level of logical form, and not in the surface syntax. As the representations underneath the examples indicate, some of the surface structure is copied at the level of logical form, where Principle C is applied. The structure that is copied is not pronounced, however. Type 1 (44)

What Max refused to order was any dessert. [What Max refused to order ] was [Max refused to order any dessert]

(45)

What Max refused to order was sushi or pasta. [What Max refused to order ] was [Max refused to order sushi or pasta]

Type 2 (46)

Any dessert was what Max refused to order.9 [Max refused to order any dessert] was [what Max refused to order].

3.5 Connectionism in child language  119 (47)

Sushi or pasta was what Max refused to order. [Max refused to order sushi or pasta] was [what Max refused to order].

3.5 Connectionism in child language If children know innately that c-command is operative in Principle C, in NPI licensing, and in generating the conjunctive entailment of disjunction, then children are expected to adhere to the c-command constraint on these same linguistic phenomena in pseudoclefts. This prediction was investigated in experiments with English-speaking children by Kiguchi and Thornton (2004), and more recently in a study of Mandarin-speaking children by Zhou and Crain (2011). In the Kiguchi and Thornton experiment, pseudoclefts like (48) and (49) were presented to 4-year-old children using a truth-value judgment task. The experimental hypothesis was that Principle C would be operative in children’s grammars, prohibiting coreference in (48), but not in (49). This is exactly what they found. Children demonstrated adult-like knowledge of connectedness effects, in the absence of surface c-command. (48) (49)

What he said was the blue magician’s trick was the best. What the blue magician said was his trick was the best.

In addition to Principle C sentences, Kiguchi and Thornton investigated children’s interpretation of disjunction in Type 2 pseudocleft structures, ones with the form NP be wh-clause, as in (50). In such sentences, negation does not c-command disjunction in the surface syntax, but disjunction licenses a conjunctive entailment nonetheless, so (50) entails that no child chose a teddy and no child chose a dice. (50)

A teddy or a dice is what no child chose.

As controls, children were presented with pseudocleft sentences with the universal quantifier every, as illustrated in (51). In the control sentences, disjunction does not license a conjunctive entailment, because every is not downward entailing on the predicate phrase, as we have seen. (51)

A teddy or a dice is what every child chose.

Zhou and Crain (2011) extended the original Kiguchi and Thornton (2004) study by using the same materials to investigate the judgments of Mandarinspeaking children and adults. The Zhou and Crain study used sentences with a similar structure to Type 2 pseudoclefts in English, and similar control sentences. Examples of the test and control sentences are given in (52) and (53).

120  The case for logical nativism (52)

Xiaoxiong huozhe shaizi tamen (dou) mei na. Teddy or dice they all not take 小熊或者色子他们都没拿。 ‘A teddy or a dice is what they all did not take.’

(53)

Xiaoxiong huozhe shaizi tamen (dou) na-le. Teddy or dice they all take-asp 小熊或者色子他们都拿了。 ‘A teddy or a dice is what they all took.’

The findings were exactly as expected on the logical nativist account. Both English-speaking children and Mandarin-speaking children generated the conjunctive entailment of disjunction in sentences with no and mei, and Mandarinspeaking children generated the conjunctive entailment in sentences with dou and in ones without dou. English-speaking children appeared to generate a conjunctive entailment for disjunction, although significantly less often, in response to the control sentences with every, as in (51), and to Mandarin sentences without negation (mei), as in (53).10 Adult controls were also interviewed. As expected, adults interpreted disjunction as taking scope over negation in sentences like (52), without dou. This is another instance where children could not have learned the interpretation they assign on the basis of adult input. The quantificational adverb dou turns adults back into children in assigning an interpretation to (52); child and adult Mandarin-speakers interpret disjunction combined with dou in the same way, as licensing a conjunctive entailment.11 It is reasonably safe to assume that pseudoclefts are rare in the input to children (Especially Type 2 pseudoclefts in English). Nevertheless, both children acquiring English and ones acquiring Mandarin displayed adult-like behavior in responding to these complex structures (with just the one exception, (52) without dou). We take the findings as evidence that children are not basing their interpretation of these structures on their surface syntax. It seems more plausible to suggest that children are drawing on UG principles in assigning these interpretations, and generating derivations in which there is c-command between negation and disjunction, as on the question-in-disguise account of pseudoclefts. We conclude the discussion of pseudoclefts by underscoring the key features of the experimental studies of children’s interpretation of disjunction. First, children’s (just like adults’) assignment of the conjunctive entailment to negated disjunctions in English pseudoclefts and to their counterparts in Mandarin shows that children know that disjunction has the truth conditions

3.6 A pragmatic alternative to Principle C  121 of inclusive-or, as in classical logic. This is another instance of children’s adherence to de Morgan’s laws. Second, we conclude that children know that negation, or other downward-entailing operators, must c-command disjunction in order to license the conjunctive interpretation of disjunction. Although negation does not c-command disjunction at the level of surface syntax, we have given reasons to suppose that c-command holds, nonetheless, at some level of representation. This highlights another prediction of the logical nativist account. The fact that children, across languages, impose abstract representations on complex sentences, in the absence of evidence, invites us to infer that such structures are innately specified, and not learned from experience. Finally, we want to emphasize the importance not only of cross-linguistic research on child language, but also of investigating children’s emerging competence in a variety of linguistic structures. We have approached children’s interpretation of disjunction, and other logical expressions, from a variety of angles. The findings all point to the same conclusion – that children know, innately, that disjunction is inclusive-or, and combines with other logical expressions in a manner that is consistent with first-order logic.

3.6 A pragmatic alternative to Principle C In view of the range of linguistic phenomena that is governed by Principle C, both within individual languages and across languages, it is worth asking whether there are plausible alternative explanations of the facts we have described. For concreteness, this section will discuss Levinson’s (2000) pragmatic account of some of the phenomena that are governed by Principle C, including sentences in which a pronoun precedes a referring expression, i.e., cases of backwards anaphora. Levinson (2000) contrasts Principle C (which he calls Condition C) with a set of pragmatic inferential procedures that determine, for example, why referring expressions are judged as having disjoint reference from pronouns that appear earlier in the same clause. In accounting for Principle B effects, Levinson’s pragmatic account relies on an opposition between reflexives and reciprocals (themselves, each other), on the one hand, and ordinary pronouns (he, him), on the other. To account for Principle C effects, he cites a further opposition between pronouns, on the one hand, and referring expressions (names and definite descriptions), on the other. As Levinson remarks (2000, p. 289):

122  The case for logical nativism Thus a case can be made for the elimination of both Condition B and Condition C from principles of (universal) grammar – their effects seem to be predicted by independently motivated pragmatic principles… It is certainly of interest that these anaphoric patterns should be predicted by a relatively structured, independently motivated pragmatic apparatus that is sufficiently constrained to make sharp predictions.

According to the syntactic account, Principle C is triggered by a structural relationship between the NPs, viz., c-command. According to Levinson, pragmatic constraints represent a viable alternative to the structural constraint involving c-command in explaining the phenomenon. Acknowledging that Principle C is much more robust cross-linguistically than other constraints on anaphoric relations (i.e., Principles A and B), Levinson (2000) presents a case against the syntactic account by listing fifteen putative counterexamples, where coreference between a referring expression and a c-commanding pronoun is acceptable for English speakers. Based on these counterexamples and several others, Levinson (2000, p. 303) reaches the following conclusion. It is thus quite easy to get the pronoun-c-commanding-NP coreferential reading under certain semantic/pragmatic conditions  – for example, where the NP expresses an identity relation that is not obvious either to the addressee or to the subject, or where the NP makes explicit a double identity, or where what is relevant is the identity of the same referent under a second description, and so on. Any attempt to hang on to a syntactic version of Condition C runs straight into the morass of these many kinds of exceptions. A pragmatic account on the other hand specifically allows for defeasibility under principled circumstances.

Since Levinson’s pragmatic alternative is motivated in part by the apparent counterexamples to Principle C, it is worth discussing them. Before that, however, it will be useful to review how Principle C works in more detail. Principle C asserts that referring expressions cannot be assigned the same index as a potential antecedent that c-commands them. The potential antecedents include pronouns, epithets like the idiot, the bastard, and other referring expressions. Principle C rules out anaphoric relations between NPs in oneclause sentences (e.g., She brushed Ann, The idiot brushed Ann), in two-clause sentences (e.g., She thinks Ann is clever, The idiot thinks Ann is clever), in three-clause sentences (e.g., She heard Nobu say that Ann is clever, The idiot heard Nobu say that Ann is clever), and so forth. The additional postulation that the traces of wh-movement and quantifier raising are referring expressions extends the range of Principle C effects, to exclude anaphoric binding between wh-words and pronouns that c-command their traces, and between

3.6 A pragmatic alternative to Principle C  123 quantificational NPs and pronouns that c-command their traces. We will concentrate here, as Levinson does, on ordinary referring expressions, such as names and definite descriptions, but we will return to consider how Principle C eliminates anaphoric binding in wh-movement structures and quantifier raising structures in section 3.7, where we discuss evidence of children’s knowledge of Principle C in these complex structures. At this point, we wish to point out a division of labor between the syntax and the semantics/pragmatics in the theory of Universal Grammar. Principle C is a syntactic constraint, preventing a referring expression from being coindexed with a c-commanding antecedent. Typically, when referring expressions and their antecedents bear different indices, they are interpreted as being disjoint in reference.12 This is typically how the semantics/pragmatics interprets the fact that two NPs have been assigned different indices. But sometimes contra-indexation of NPs does not suffice to guarantee that they are disjoint in reference, as Levinson and many others have noted. Linguists and philosophers have responded to this in several ways. One approach has been to treat Principle C as an elsewhere condition. This approach was taken by Chien and Wexler (1990), who advanced the following pragmatic principle: (54) Principle P: Contraindexed NPs are noncoreferential unless the context explicitly forces coreference.

Principle P assumes that the language apparatus has modular architecture, where syntactic derivations (including the assignment of indices) are computed before semantic interpretation and reference to the context (for further discussion, see Thornton and Wexler 1999, and references therein). In ordinary circumstances, two NPs that bear different indices have disjoint reference. In certain contexts, however, the fact that two NPs have different indices does not prevent them from having the same reference, according to pragmatic Principle P; coreference can be forced by contextual factors. As Lasnik (1976) points out, it would be difficult to prevent a pronoun from accidentally picking out the same individual as a referring expression because the referent of a pronoun can be assigned by virtue of someone’s salience in the conversational context (e.g., I wouldn’t want to be his-EMPH editor), or by pointing to someone. This explains apparent violations of Principle C, like someone saying He’s your Uncle Bob while pointing to a man in a photograph. In any event, Principle P establishes a division of labor between the syntax and the pragmatics. Syntax proposes, but pragmatics may override what has been proposed. Another modular approach to syntax and semantics is the theory of guises advanced by Heim (1998). The theory of guises distinguishes between the

124  The case for logical nativism cognitive value of a sentence and the proposition it expresses. The cognitive value provides an account of how the referents are presented in the world. One of the guises associated with a person could have been formed in the memories of the speaker and hearer, based on their impressions of the person from previous events. When a speaker employs a name, e.g., Joan Bresnan, the speaker presupposes that the hearer knows the intended referent under such a memory entry. The same person can be presented in a different guise at the time of the utterance in question, however. This alternative guise is based on the here-andnow visual impression of the person, so this is called a deictic guise (e.g., the woman on the podium, who is speaking about Joan Bresnan). A deictic guise of a person could arise in the conversational context based on salience, or in virtue of a pointing gesture by the speaker. On this guises approach, the syntax assigns different indices to referring expressions and their c-commanding antecedents, due to Principle C. But all that is required by the pragmatics is that the individual being denoted by these NPs be presented in different guises. We now return to consider Levinson’s proposed counterexamples to Principle C (2000, p. 302). The counterexamples fall into several subclasses. The three putative counterexamples in (55) are in one class ((55c) is a slightly modified version of the original). Presumably, these examples express an identity relation that is not obvious to the addressee. (55)

a. He became known as Napoleon. b. She’s called Madonna. c. He succeeded Elizabeth I as James I of England.

It is questionable, however, whether Principle C applies to these examples, because the expressions in object position (Napoleon, Madonna, James I of England) are not referring expressions and, hence, are not governed by Principle C. These expressions denote the names of individuals, not individuals. They have the semantics of quotations, as appropriate for the predicates is called, became known as, and succeeded Elizabeth I as. According to one influential view of the semantics of quotations, by Davidson (1979, p. 37) “it is the quotation marks that do all the referring, and they help to refer to a shape by pointing out something that has it.” In other words, the speaker of (55b) is pointing out that the individual referred to by the pronoun she has the name Madonna. To ascribe these statements to Principle C is to ignore the distinction between use and mention. A second class of putative counterexamples is represented in (56). These are presumably statements of identity of the same referent under a second description.

3.6 A pragmatic alternative to Principle C  125 (56)

a. He managed to become the President of the United States. b. She thinks it unfair that the Chair of the Department always has to be her. c. He thinks the only reliable teacher of linguistics is himself.

The sentences in (56) are not identity statements, however. Identity is a symmetric relation, such that the order in which terms are presented does not impact on truth. Consider these identity statements: Cicero is Tully, water is H2O, William Shakespeare was the author of Hamlet. If terms are swapped around in identity statements, there is no change in truth value: Tully is Cicero, H2O is water, The author of Hamlet was William Shakespeare. Yet if we swap around the NPs in the examples in (56), the meanings are clearly different, or the sentences become gibberish, as attested by (57). (57)

The President of the United States managed to become him.

The examples in (56) are not identity statements for the following reason. The denotations of definite descriptions like the Chair of the Department and the President of the United States pick out different individuals at different times. In this respect, definite descriptions contrast with names like Bill Clinton, Ronald Reagan, and Barack Obama. Names are called rigid designators because they pick out the same individual at different times.13 In contrast, definite descriptions like the President of the United States are used at different times to denote different individuals, e.g., Bill Clinton, Ronald Reagan, and Barack Obama. So the truth of the statement He managed to become the President of the United States depends not only on the referent of the pronoun, but also on the time at which the utterance is produced. A third class of putative counterexamples is in (58). (58)

a. He’s doing what John always does. b. Clark Kent hurried. He realized that Superman was urgently needed. c. She knows what Joan Bresnan currently believes, because she is Joan Bresnan.

The theory of guises was designed to handle a number of apparent counter­ examples to Principle C, including ones like those in (58). According to the theory of guises, the examples in (58) do not constitute violations of Principle C, because pronouns and names can refer to the same individual under different guises, and that is all that the contra-indexation of NPs requires. In (58b), for example, the same individual is referred to by the pronoun he, using a deictic guise, and by the two names Clark Kent and Superman, which have different memory entries. So, the cognitive value associated with these NPs picks out the same individual under three different guises.

126  The case for logical nativism The theory of guises has been invoked to handle another class of apparent counterexamples to Principle C. This class is referred to as structured meaning contexts. Two such cases are discussed by Levinson (2000, p. 290). These are given in (59) and (60), where the indices indicate that coreference between a pronoun and a name is permissible for adult speakers of English, and the non-coreference between the pronoun and the name is reinforced by the use of emphasis or marked stress (indicated by -EMPH). According to Levinson, emphasis is another mechanism that triggers an implicature to the complement of the normal (disjoint) interpretation (Levinson 2000, p. 332). (59) Everybody thinks John is a genius, why even he-EMPH thinks John is a genius. (60) Everybody loves Sue. Her husband thinks Sue is adorable, her parents think Sue is adorable, why even she-EMPH thinks Sue is adorable.

In Levinson’s discussion of example (59), he observes that “the context [in 59] sets up a special relevant property of, say, thinking-John-to-be-a-genius.” This property is attributed to everybody and, since everybody has the property of thinking-John-to-be-a-genius, John himself surely has this property. According to the theory of guises, the pronouns he in (59) and she in (60) are used in deictic guises. However, as Levinson observes, the names (John, Sue) are mentioned in structured propositions, John is a genius, Sue is adorable. These are clearly not cases in which a pronoun and a name have the same cognitive value, so Principle C does not apply to such cases. As noted earlier, Levinson contends that the advantage of a pragmatic account of non-coreference is it “specifically allows for defeasibility under principled circumstances.” In response to Levinson’s counterexamples, we have described how Principle C can withstand the force of such counterexamples. Essentially, the force of these counterexamples is blunted by adopting a modular conception of the language apparatus. According to this modular model, Principle C provides a structural description, with indices. In the structural description assigned to sentences with referring expressions, a different index is assigned to a pronoun and a referring expression if the pronoun c-commands the referring expression. This yields non-coreference at the level of semantic interpretation in ordinary circumstances. However, in certain circumstances, contra-indexed NPs pick out the same individual, either because the NPs are accidentally coreferential, or because they are presented in different guises. The pragmatic account of non-coreference advanced by Levinson (2000) has certain features in common with the syntactic account. On both accounts, the basic pattern for interpreting NPs is to assign them disjoint reference. As Levinson comments: “The starting point is a stabilized pattern of interpretation

3.7 Syntax versus pragmatics  127 where clause-mate NPs are preferentially interpreted as distinct in reference” (Levinson 2000, p. 328). The origin of the pragmatic constraint on interpretation could be functionally derived, according to Levinson, based on the prototypical interpretation of transitive sentences in which “agents normally act upon entities other than themselves” (Levinson 2000, p. 328). This putative functional explanation underpinning Levinson’s pragmatic account of non-coreference brings out two main differences as compared to the syntactic account. First, the pragmatic account has a plausible functional explanation, which is lacking on the syntactic account. Second, the pragmatic prohibition initially applies only to one-clause transitive sentences, whereas the syntactic account applies to referring expressions and their potential antecedents in the same clause or in different clauses. These are modest differences, as the following remark by Levinson (2000, p. 363) makes clear: There is of course no general challenge here to some concept of a rich, restrictive innate linguistic ability or Universal Grammar – only an argument that we need to look elsewhere. Equally, there is no suggestion here that the current patterns of anaphora in, say, English, are entirely pragmatic  – rather that the central facts can be seen to have functional motivation, that diachronic explanations might refer more to pragmatic principles than to principles of UG, and that defeasibilities of interpretation, at the margins as it were, are the stigmata of the functional origin of currently grammaticalized patterns.

On the other hand, advocates of the syntactic account of the coreference phenomena must be content with drawing a distinction between the operations of the syntax and the pragmatic uses to which the products of these syntactic operations are put. 3.7 Syntax versus pragmatics At this point, the syntactic account and the pragmatic account might both appear to be reasonable contenders. In fact, since the syntactic account invokes semantic/pragmatic principles, in addition to Principle C, the pragmatic account might appear to be favored. However, there is compelling evidence from child language in favor of the syntactic account, and against the pragmatic account. First, children know the non-coreference facts from the earliest stages of language acquisition, i.e., by age 3. Second, children younger than 5- or 6-years-old are notoriously insensitive to the kinds of pragmatic principles and markedness conventions that the pragmatic account of the non-coreference facts relies upon.

128  The case for logical nativism 3.7.1 Crain and McKee (1985) The question of children’s knowledge of Principle C was pursued in a comprehension experiment by Crain and McKee (1985). A new experimental technique was developed for this purpose, the truth-value judgment task (see Crain and Thornton 1998). As the name suggests, this task requires subjects to judge the truth or falsity of a sentence, according to its fit to the context. Two experimenters are needed to conduct the task. One experimenter uses toys and props to act out different vignettes, in front of the child. A second experimenter manipulates a puppet, often Kermit the Frog. Following each situation, Kermit the Frog says what he thought happened on that trial. When Kermit the Frog accurately describes something that happened in the story, the child is instructed to reward him with something he likes to eat, say with a strawberry. Sometimes Kermit doesn’t pay close attention, however, and he says the wrong thing. In that case, the child is instructed to give Kermit something to remind him to pay closer attention, say a food that he likes less than strawberries. These procedures make it fun for children to attend to Kermit’s statements. Notice that both (a) the events corresponding to the meaning of the target sentence, and (b) the target sentence itself are provided for the children. This allows unparalleled experimental control and at the same time reduces extraneous processing demands that are present in comprehension tasks in which children are required to act out events themselves. The truth-value judgment task was designed to assess whether or not children assigned more than one meaning to a target sentence. In the case of ambiguous sentences, contexts associated with both meanings can be presented, on different occasions. In the Crain and McKee (1985) study, children encountered sentences like (61). This sentence is ambiguous for adults, because the pronoun could be interpreted deictically, or as referring to the Ninja Turtle. Examples of this kind were presented to children in circumstances corresponding to both interpretations. (61)

While he1 ate pizza, the Ninja Turtle1/2 danced.

On one interpretation, the pronoun he and the referring expression the Ninja Turtle have the same index. This is called backwards anaphora. It is backwards in the sense that the pronoun comes first. More typically a pronoun follows the expression with which it is anaphorically linked. This is called forwards anaphora. On the alternative interpretation of (61), the referring expression the Ninja Turtle is not coindexed with the pronoun he1, so it is labeled the Ninja Turtle2. This is the deictic interpretation of the pronoun. Sometimes, it is said

3.7 Syntax versus pragmatics  129 that the pronoun has extrasentential reference, because it refers to an individual who is not mentioned in the sentence. For ambiguous sentences such as (61), the same sentence was presented on two separate occasions, in two contexts. In one context for (61), the Ninja Turtle was dancing and eating pizza; in the other, someone else ate pizza while the Ninja Turtle was dancing. Kermit uttered the same sentence following both situations. The results were that children accepted the backwards-anaphora reading about two-thirds of the time, in appropriate contexts. The deictic (extrasentential) reading of the pronoun was accepted only slightly more often. Only one of the sixty-two 2- to 5-year-old children (mean age 4;2) interviewed in the Crain and McKee study consistently rejected the backwards anaphora interpretation. In the Crain and McKee (1985) study, children were also exposed to sentences governed by Principle C, such as (62), in order to investigate children’s knowledge of the constraint against coreference. In one condition, sentence (62) was presented in a context that made the sentence true only if children assigned the meaning that is ruled out by Principle C. For example, a context that makes sentence (62) true on the interpretation that is ruled out by Principle C is one in which the Ninja Turtle danced and ate pizza at the same time. In addition to the Ninja Turtle, there was a salient male character in the context, say Robocop. In the context, Robocop considered dancing, but then thought better of it (because he has a metal suit on), and he declined to dance while the Ninja Turtle ate pizza. This made it reasonable for children to give a “No” response, provided that their grammars did not permit coreference between the pronoun and the referring expression, the Ninja Turtle. (This feature of the task is called plausible dissent by Crain and Thornton 1998.) (62)

He1 danced while the Ninja Turtle2 ate pizza.

If children adhered to Principle C, they were expected to consistently interpret the pronoun he as a deictic pronoun, referring to Robocop, in example (62). This is exactly what happened. The child subjects, including children just turning 3-years-old, judged sentences like (62) to be false almost 90 percent of the time. The findings show that children as young as 3-years-old prohibit backwards anaphora when structural conditions (involving c-command) dictate that they should. The findings of this experiment provide further evidence that children do not always rely on experience in making linguistic judgments. Since there is nothing in children’s experience to tell them which meanings are not allowed, there is no way to learn the structural constraint prohibiting coreference in sentences like (62).

130  The case for logical nativism A related series of experiments focusing on Principle C in declarative sentences was reported by Guasti and Chierchia (1999/2000). In experiments with 3- to 5-year-old Italian-speaking children, it was found that children produced robust rejections of Principle C violations in sentences like (63). Eighty percent of the time, children rejected the backwards-anaphora interpretation of (63), in which a musician rode a rocking horse while playing the trumpet. By contrast, children allowed a backwards-anaphora reading in sentences like (64) 92 percent of the time, in a context in which the clown was dancing at the same time as he was playing the guitar. (63)

Andava sul cavallo a dondolo, mentre un musicista suonava was-riding on-a rocking horse while a musician was-playing la tromba. the trumpet ‘(He) was riding a rocking horse, while a musician was playing the trumpet.’

(64)

Mentre ballava, un pagliaccio suonava la chitarra. while was-dancing a clown was-playing the guitar ‘While (he) was dancing, a clown was playing the guitar.’

3.7.2 Kiguchi and Thornton (2004) Another Principle C experiment was conducted by Kiguchi and Thornton (2004). The study included complex sentences such as (65). (65)

He jumped over every fence that Kermit tried to.

The research question in the Kiguchi and Thornton study was whether or not children know that the pronoun he and the name Kermit cannot be coreferential in sentences like (65) (as compared to control sentences in which the pronoun did not c-command the name). That is, do children know that (65) cannot be interpreted as meaning that Kermit jumped over every fence that he tried to jump over? The experiment used the truth-value judgment task. As in most studies using this technique, the experimental situations that were presented to children in the Kiguchi and Thornton study were ones in which the target sentences were true if Principle C did not apply to them, but false if Principle C did apply to them. The decision to make the target sentences false if children adhere to Principle C was motivated by the fact that children (like adults) tend to accept sentences that they do not understand. Therefore, if children don’t understand the test sentence, or are confused by the task demands, they will produce the kinds of responses that count against the experimental hypothesis, i.e., that children know Principle C. Following this strategy is one way to guard against Type 1 errors, i.e., mistakenly accepting the experimental hypothesis.

3.7 Syntax versus pragmatics  131 In the story associated with (65), Kermit and Cookie Monster participated in a jumping competition. The goal was to jump over three tall fences. Both Kermit and Cookie Monster succeeded in jumping over the first two fences. Kermit then tried to jump over the last and tallest fence and was successful. Cookie Monster, who had barely made it over the second one, failed to clear the highest fence. At the end of the story, the target sentence was produced by a puppet, following a lead-in that mentioned both characters: That was a story about Cookie Monster and Kermit the Frog. They had a jumping contest, and I know what happened. He jumped over every fence that Kermit tried to. Both Cookie Monster and Kermit are mentioned in the lead-in to the target sentence, but Kermit is mentioned last, so if children take pronouns to refer to the most-recently mentioned individual, this maneuver would encourage them to assign the non-adult reading, in violation of Principle C. This is another way to avoid Type 1 errors. Suppose that, for one reason or another, children interpret the pronoun he to be coreferential with the name Kermit, in violation of Principle C. Then the interpretation children assign matches the outcome of the story, so children would be expected to say “Yes” in response to the target sentence He jumped over every fence that Kermit tried to. By contrast, if the pronoun he and the name Kermit are assigned disjoint reference, due to Principle C, then the sentence fails to match the outcome of the story, and it should evoke “No” responses from children. The main finding was that thirteen children (4;2–5;1) rejected the target sentences as accurate descriptions of the contexts 94 percent of the time (but accepted control sentences equally often). The experimental findings indicated that the child subjects correctly ruled out illicit coreference between the pronoun in the matrix subject position and the name in the relative clause in the test sentences. 3.7.3 Crain and Thornton (1998) At the beginning of the chapter, we discussed another linguistic phenomenon governed by Principle C, crossover wh-questions. One of the examples was the question in (66). By Principle C, the pronoun he in (66) must be construed as a deictic pronoun, just as it is in the declarative in (67), where it must be disjoint in reference from Ted. So, just as (67) cannot be paraphrased as Ted said he criticized Morris, due to Principle C, the wh-word who cannot bind the pronoun he in (66). (66) (67)

Who did he say criticized Morris? (which person x, he said x criticized Morris) He said Ted criticized Morris.

132  The case for logical nativism Recall why Principle C is operative in the wh-question (66). The reason is that the wh-word crosses over the pronoun as it raises and, when it raises, it leaves a trace behind. The pronoun c-commands the trace. Since a trace is a referring expression, the pronoun and the trace cannot be assigned the same index, due to Principle C. By transitivity, the pronoun and the wh-word must be assigned different indices. This, then, explains why the pronoun he in (66) cannot be bound by the wh-word. This leaves only the deictic interpretation of the pronoun, so crossover questions like this are unambiguous. Both (66) and (67) can be contrasted with (68). The wh-question in (68) is ambiguous, in contrast to (66) and (67). In the wh-question (68), the pronoun he can either be interpreted deictically, or it can be bound by the wh-word. If the pronoun in (67) is bound by the wh-word, it functions as a variable, as indicated in the parenthetical paraphrase. On this reading, the answer can have multiple referents (e.g., He did and he did), since more than one individual can be the value of the variable. (68)

Who said he criticized Morris?   (which person(s) x, x said x criticized Morris)

Another structure governed by Principle C is indirect wh-questions. In indirect questions, the wh-word remains in an embedded clause, as illustrated in (69). Notice, however, that the pronoun he can only be interpreted deictically in (69). The reason is that the wh-word crosses over the pronoun as it raises to the front of the embedded clause. This yields the representation in (70). (69) (70)

I know who he said has the best food. I know who2 he1 said t2 has the best food? (I know which person(s) x, he said x has the best food)

Not surprisingly, there are other indirect wh-questions in which the wh-word does not cross over a pronoun, so Principle C is not operative. As you will have guessed, when an indirect wh-question is not within the purview of Principle C, it is ambiguous. An example is (71), which has the interpretive possibilities indicated in (72). (71) (72)

I know who said he has the best food. I know who1 t1 said he1/2 has the best food? (I know which person x, x said x/he has the best food)

On one reading of (71), the pronoun he is used deictically (as indicated by the subscript 2). But, in addition, the pronoun he can be bound by the whword who (as indicated by the subscript 1). This yields a bound pronoun interpretation (where the answer could provide just one, or possibly multiple referents).

3.7 Syntax versus pragmatics  133 Using a truth-value judgment task, Crain and Thornton (1998) compared children’s performance on crossover questions like (73), and bound pronoun questions like (74). The main finding was that the twelve English-speaking children between 3;7 and 4;8 (average age 4;2) rejected the multiple referent answer (Grover and Big Bird) 92 percent of the time, as expected by Principle C. Children accepted the deictic interpretation (the Ninja Turtle) 100 percent of the time. In response to the bound pronoun trial, children accepted indirect questions like (74) as asking about more than a single person 50 percent of the time. For these ambiguous questions, the pronoun was interpreted deictically 50 percent of the time. (73)

Crossover trial Kermit: I know who he said has the best food. Grover and Yogi Bear. Child: No. Experimenter: What really happened? Child: The Joker said that the Ninja Turtle has the best food. Or Kermit: I know who he said has the best food. The Ninja Turtle. Child: Yes.

(74)

Bound variable trial Kermit: I know who said he has the best food. Grover and Yogi Bear. Child: Yes.

Children’s adherence to Principle C has been investigated in several other linguistic phenomena. We will finish our review of children’s adherence to Principle C by reporting the findings of one further study by Guasti and Chierchia (1999/2000). This study is important, because it represents a counterexample to the pragmatic account of the non-coreference facts covered by Principle C. 3.7.4 Guasti and Chierchia (1999/2000) The Guasti and Chierchia (1999/2000) study investigated children’s comprehension of sentences where a prepositional phrase (PP) is moved to sentenceinitial position. Example (75) illustrates the phenomenon, which is called PP-preposing. At the level of logical form, the preposed-PP is reconstructed, i.e., put back into its original position, as depicted in (76). As a consequence of reconstruction, the pronoun he and the name John in (76) are expected to have disjoint reference at the level of logical form, due to Principle C. (75) (76) (77)

Near John’s bicycle, he saw a snake. [he1 saw a snake PP[near John2’s bicycle]]. He saw a snake near John’s bicycle.

134  The case for logical nativism According to the reconstruction account, the PP-preposing example (75) should be on a par with the declarative sentence in (77), where disjoint reference is clearly enforced. In fact, both the sentence with PP-preposing (75) and the one without it (77) have the logical form in (76). As Guasti and Chierchia remark (1999/2000, pp. 130–131): According to reconstruction approaches, the structures of [75] and [77] are virtually identical and, hence, the ruling out of the two cases has to be uniform. If Universal Grammar drives acquisition, this seems to predict that as soon as children get [77] right, they must also get [75] right. This is the opposite of what one would expect just by considering how forward and backward anaphora work in general. Thus, looking at reconstruction effects in child grammar might help us choose among these different hypotheses.

On the pragmatic account, the PP-preposing example in (75) (repeated below) is on a par with (78), rather than with the backwards-anaphora example (77). (75) (78)

Near John’s bicycle, he saw a snake. John saw a snake near his bicycle.

According to the account, disjoint reference is governed by pragmatic inferences in cases of backwards anaphora, where the pronoun precedes the referential NP. These pragmatic inferences are not operative in cases of forwards anaphora, so (75) is expected to be acceptable in the same circumstances that validate (78), where John saw a snake near his own bicycle. The syntactic account and the pragmatic account, therefore, make the opposite predictions about how sentences with PP-preposing will be interpreted, such as (75) Near John’s bicycle, he saw a snake. According to the syntactic account, Principle C applies to these sentences, prohibiting coreference between the pronoun he and the referring expression John. Although this is a case of forwards anaphora in the surface syntax, it is a case of backwards anaphora (with c-command) at the level of logical form. The pragmatic account predicts that coreference will be permitted in these sentences. The PP-preposing examples are cases of forwards anaphora, according to the pragmatic account. A number of studies have been conducted to investigate children’s comprehension of PP-preposing sentences. Unfortunately, the earliest studies produced mixed results. Using an act-out task, Lust and Clifford (1986) found that even the youngest children (3;5–3;11) produced responses indicating disjoint reference in sentences like (78) 87 percent of the time. In a review of the literature, Lust (2006, pp. 214–221) concludes “Children give significantly fewer

3.7 Syntax versus pragmatics  135 coreference judgments in structures where anaphora is blocked grammatically, whether backward … or forward.” Other researchers, however, interpret the results differently, pointing out that children did not consistently adhere to Principle C in other studies. These mixed findings led some to conclude that performance factors probably intrude on children’s judgments in certain experimental contexts. If the goal is to accurately assess children’s knowledge of Principle C, these factors must be (experimentally) dealt with, according to these researchers (see, e.g., Carden 1986). It is conceivable that both Lust and her critiques are correct. It is worth noting that Lust (2006, p. 216) reached another conclusion about children’s adherence to Principle C, namely that “the strongest indication of Principle C may be evidenced in younger children.” For example, Somashekar et al. (1997) found that younger Hindi-speaking children (mean age 3;07) showed greater adherence to Principle C than did older children. According to Somashekar et al., children’s developing pragmatic knowledge is more likely to interact with syntactic principles as children mature. We will expand on this point in the two sections that follow. As we will document, it has been found that younger children (before 5- or 6-years-old) are less sensitive to the kinds of pragmatic inferences (e.g., scalar implicatures) and phonological cues (e.g., emphatic stress) that influence the judgments of older children and adults, including judgments about the circumstances in which sentences are true or false. In short, judgments made by young children may be a better source of evidence about the development of linguistic knowledge, because young children’s judgments are free from the intrusions of extraneous factors. It is worth noting that the lack of sensitivity to pragmatic principles sometimes makes younger children appear to be more logical than older children and even more logical than adults. Conceding that extraneous factors may have influenced children’s responses in previous research, Guasti and Chierchia (1999/2000) attempted to overcome some of these difficulties. For one thing, they used the truth-value judgment task, rather than employing the kinds of tasks that had evoked the controversial findings in earlier studies (e.g., the imitation task, the act-out task). Another innovation by Guasti and Chierchia was in the construction of the test sentences. It has been found that children respond differently to sentences with quantified NPs (e.g., every pirate) as compared to referential NPs (e.g., Father Smurf) in studies of Principle B (e.g., Thornton and Wexler 1999). Many studies have found children to respect Principle B significantly more often when it is applied to binding relations (e.g., Every pirate washed him), rather than coreference relations (e.g., Father Smurf washed him). Based on this asymmetry in children’s responses to Principle B, Guasti and Chierchia investigated

136  The case for logical nativism children’s knowledge of Principle C in sentences with quantified NPs, as in (79), rather than in sentences with referential NPs, as in (80). (79)

a. He put a gun in every pirate’s barrel. b. In every pirate’s barrel, he put a gun.

(80)

a. He put a gun in Father Smurf’s barrel. b. In Father Smurf’s barrel, he put a gun.

The pair of sentences in (79) are ungrammatical on the reading in which the pronoun he is anaphorically dependent on (i.e., bound by) the quantified NP every pirate. In the pair of sentences in (80), the NP Father Smurf must be disjoint in reference from the c-commanding pronoun he. The Guasti and Chierchia study was designed to see if pronominal binding, rather than coreference, provided an effective way to assess children’s knowledge of Principle C. The experiment reported in Guasti and Chierchia (1999/2000) investigated eighteen Italian-speaking children’s comprehension of PP-preposing sentences like (81). The logical form is represented in (82). As (82) indicates, the preposed PP (nel barile di ciascun pirata con cure) is reconstructed, such that the pro (the null subject) c-commands the PP at the level of logical form (LF). In addition, the quantified NP (ciascun pirata) is raised at LF. As it raises, the quantificational NP crosses over the null subject, pro. Like an overt pronoun, the null subject pro and the trace must be contra-indexed. Therefore the quantified expression ciascun pirata cannot bind the pro. (81)

Nel barile di ciascun pirata con cura (pro) ha messo una pistola. In-the barrel of each pirate with care (he) has put a gun ‘He put a gun with care in the barrel of each pirate.’

(82)

*[[ciascun pirata]1 [con cura pro1 ha messo una pistola [PP nel barile di t1 ]]]

The main finding of the study was that by age 3;10 (mean age = 4;6) children rejected the illicit bound pronoun reading 90 percent of the time (according to which every pirate put a toy gun in his barrel). The same children accepted sentences like (83) on a bound pronoun interpretation of pro (the null subject) 89 percent of the time. As the logical form in (84) shows, the bound pronoun reading of (83) is permitted because the trace of the quantificational expression ciascun bambino c-commands pro, not vice versa. (83)



Il tesoro di ciascun bambino, le scimmie lo nascondono The treasure of each child the monkeys it hide mentre (pro) dorme. while (he) is-sleeping ‘The monkeys hide the treasure of each child while he is sleeping.’

3.8 Children’s failures to make pragmatic inferences  137 (84) [[ciascun bambino]1 [le scimmie lo nascondono [PP il tesoro di t1 ] mentre pro1 dorme]]

The results from Guasti and Chierchia’s experiments are important because they provide evidence that children are computing Principle C at the level of logical form. If children were to use the forwards-anaphora sequence (ciascun pirata … pro) as the basis for determining anaphoric binding, then there would be no reason for children to reject sentences like (81). In a subsequent summary of the findings of the Guasti and Chierchia study, Guasti (2002, p. 308) concludes: “We can reject the hypothesis that children are guided by a linear constraint in their comprehension of anaphoric dependencies. Children instead base their judgments on a structure-dependent constraint, Principle C.” 3.8 Children’s failures to make pragmatic inferences The previous section showed that 3- and 4-year-old children, across languages, know the facts governed by Principle C. These findings are unexpected on the pragmatic alternative account, because it has been found, in addition, that children younger than 5- or 6-years-old are not sensitive to the kinds of pragmatic inferences that form the basis of the account. For one thing, before they are about 6-years-old, children do not compute scalar implicatures anywhere near to the same extent as adults do (Chierchia, Crain, Guasti, Gualmini, and Meroni 2001; Gualmini, Crain, Meroni, Chierchia, and Guasti 2001; Guasti, Chierchia, Crain, Foppolo, Gualmini, and Meroni 2005). To cite a representative study, Chierchia et al. (2001) found that children accepted the use of disjunction in the predicate phrase of the universal quantifier every far more often than adults did, in one relevant experimental context. Because the predicate phrase of the universal quantifier every is a non-downward-entailing linguistic context, the use of disjunction generates a scalar implicature, at least for adults. As we discussed in Chapter 1, it is pragmatically odd for a speaker to produce a statement of the form A or B, if the speaker knows that a more informative statement, A and B, is also an accurate description of the situation. If someone produces a statement of the form A or B, this invites the listener to infer that the speaker was not in a position to assert A and B. The use of statements with disjunction, therefore, is interpreted (at least by adults) as generating a scalar implicature, i.e., that A or B, but not both A and B. Scalar implicatures are canceled in downward-entailing contexts, because these contexts reverse entailment relations, so disjunction makes a stronger statement in a downward-entailing context than the corresponding statement with conjunction. For example, Max didn’t eat rice or beans makes a stronger

138  The case for logical nativism statement than Max didn’t eat rice and beans, because negation is downward entailing. The Chierchia et al. study investigated children’s command of the implicature of exclusivity (not both) that is engaged by disjunctive statements, when the corresponding statements with conjunction are also true. On a typical trial, children were told a story about four boys at a summer camp who were about to choose some toys to play with. After considering their options, the four boys each decided to take both a skateboard and a bike. Following the conclusion of the story, the puppet (Kermit the Frog) produced the target sentence: (85)

Every boy chose a skateboard or a bike.

Since the disjunction operator occurs in a non-downward-entailing environment, the implicature of exclusivity should be (mentally) computed in (85). To compute the scalar implicature, the child must recognize that an alternative sentence is available as a description of the context under consideration, namely (86). (86)

Every boy chose a skateboard and a bike.

A further step in the child’s mental computation requires the observation that the puppet used (85), and not (86). As a consequence, the child should construct a derived interpretation of the target sentence (85). The derived interpretation results from conjoining the target sentence (85) and the negation of the alternative statement (86), yielding (87). (87) Every boy chose a skateboard or a bike, and it is not the case that every boy chose a skateboard and a bike.

Since (87) is more informative than the target sentence (85), the child should adopt (87) as its derived interpretation, and should therefore reject the sentence in the context, on the grounds that the corresponding statement with and would have been a more informative description of the story. This was only partly true. Fifteen children (3;5–6;2, with a mean age of 5;2) participated in the experiment. They accepted the target sentences 30 times out of 60 trials (50 percent). Eight English-speaking adults served as a control group, and these adult controls always rejected the target sentences. The responses of the adult controls are entirely consistent with the pragmatic account of the noncoreference facts we have been discussing, since they command the relevant pragmatic inferences. However, only a small number of child subjects younger than 5- or 6-years-old would appear to be equally adept at making the requisite pragmatic inferences.

3.9 Children’s lack of sensitivity to stress  139 Taken together, the findings of the last two sections lead to the following conclusions. First, that children as young as 3- and 4-years-old are the equals of adults in assigning disjoint reference and in rejecting pronominal binding in a variety of linguistic structures, as expected on the syntactic account of Principle C. These structures include declaratives, indirect crossover whquestions, pseudoclefts, discourse sequences, and sentences with quantified NPs. The second conclusion is that 3- and 4-year-old children are less able than older children and adults to compute scalar implicatures. These conclusions undermine the pragmatic account proposed by Levinson, because scalar implicatures are precisely the kinds of pragmatic inferences that are required to account for the relevant linguistic phenomena, according to Levinson. This invites the conclusion that children’s judgments about these phenomena are not based on pragmatic inferences but, rather, on the structural properties of sentences (c-command). 3.9 Children’s lack of sensitivity to stress On Levinson’s alternative to Principle C, non-coreference is enforced by pragmatic inferences that apply to the use of marked forms (a referential expression, rather than pronoun). An additional way of indicating a marked form is to use emphasis. For example, John hit him-EMPH indicates that the non-coreferential interpretation of the destressed pronoun (John hit him) is not intended, so the sentence John hit him-EMPH is judged to mean that John hit himself. There are both positive and negative findings concerning the development of the use of prosodic cues by children. On the one hand, it has emerged from production studies (which include knowledge of stress or word accent) that children generally produce relevant prosodic cues in their own speech. A second positive finding is that children are able to perceive stress-bearing lexical items. There are several important negative findings, however. First, children younger than 5- or 6-years-old have proven to be insensitive to the use of prosodic cues in deciding on the intended reference of pronouns in sentences spoken to them (e.g., Maratsos 1973; Solan 1983). And second, children younger than 5- or 6-years-old have proven to be insensitive to prosodic markedness (e.g., emphatic stress) in resolving ambiguities (Gualmini, Maciukaite, and Crain 2002; Halbert, Crain, Shankweiler, and Woodams 1995; Szendröi 2004). These findings need to be put in context. As we have seen, children as young as 3-years-old command the linguistic facts associated with Principle C. Therefore, children’s difficulties in using prosodic cues at this age pose a challenge to accounts of these facts that rely on children’s knowledge of prosody.

140  The case for logical nativism We will report the findings of two relevant studies. The first study, by Maratsos (1973), investigated children’s understanding of coordinate structures with and without stress on the pronoun. The pronoun appeared in either subject or object position, yielding four sentence types, as illustrated in (88). (88)

a. b. c. d.

Susie jumped over the old woman, and then Harry jumped over her. Susie jumped over the old woman, and then Harry jumped over her-EMPH. Susie bumped into the old woman, and then she bumped into Harry. Susie bumped into the old woman, and then she-EMPH bumped into Harry.

As Maratsos observed, when the pronoun is unstressed, as in (88a), adults prefer to interpret both clauses using parallel structures. Since the NP old woman is the direct object of the verb jumped in the first clause, the unstressed pronoun her is taken to be the direct object of jumped in the second clause. However, when the pronoun is emphatic, as in (88b), this cancels the parallelism effect for adults. Therefore, adults prefer to interpret the pronoun her-EMPH in the second clause of (88b) as referring to the subject of the first clause, i.e., Susie. Because emphatic stress indicates a marked interpretation, i.e., a departure from the default assignment of parallel structures, Maratsos reasoned that children might take some time to acquire the marked interpretations that are associated with emphatic stress. To explore this hypothesis, Maratsos tested 106 children between 3- and 5-years-old. The children were divided into groups by age. All three groups responded in the same way as adults to the sentences with unstressed pronouns. The 3-year-olds responded like adults 87 percent of the time, 4-year-olds 83 percent of the time, and 5-year-olds 93 percent of the time. However, children’s sensitivity to the role of emphatic stress increased with age. The group of 3-year-olds responded in the same way as adults to the sentences with stressed pronouns only 47 percent of the time. The group of 4-year-olds produced adult-like responses 67 percent of the time, and 5-yearolds were adult-like 78 percent of the time. In addition to young children’s lack of sensitivity to the function of stressed and unstressed pronouns in comprehension, children younger than 5-yearsold have been found to differ from older children and adults in several related areas: (a) in establishing phrasal groupings (Choi and Mazuka 2003; Halbert et al. 1995), (b) in resolving ambiguities of phrasal attachment (Snedeker and Trueswell 2001; Snedeker and Yuan 2008), and (c) in associating focus particles with appropriate expressions (Gualmini et al. 2002; Halbert et al. 1995; Höhle, Berger, Müller, Schmitz, and Weissenborn 2009; Hüttner, Drenhaus, van de Vijver, and Weissenborn 2004; Szendröi 2004).

3.9 Children’s lack of sensitivity to stress  141 A second study, by Halbert et al. (1995), reached a similar conclusion. This study investigated the sensitivity of 4- and 5-year-old children to the use of contrastive stress in resolving structural ambiguities. The goal of the study was to document children’s understanding of dative constructions in sentences with the focus operator only. Two experiments were conducted, using a truth-value judgment task. Examples of the test sentence from one experiment appear in (89). (89)

a. b. c. d. e.

Bill only gave a banana to Sue. Bill only gave a banana-EMPH to Sue. Bill only gave a banana to Sue-EMPH. Bill only gave Sue a banana-EMPH. Bill only gave Sue-EMPH a banana.

In (89b), for example, the focus operator was used in conjunction with stress on a banana. For adults, this use of contrastive stress conveys the message that Bill give a banana, but nothing else, to Sue. On the other hand, (89c) conveys the message that Sue, and no one else, received a banana. Data from thirty-one children (ranging in age from 3;10 to 6;3) were reported. Thirteen children were extremely proficient at using stress to assign the intended interpretations of the target sentences. These children performed at the same high level of accuracy as a control group of adults. The other eighteen children, however, were completely insensitive to stress, but different children used different default strategies for interpreting the target sentences. Eleven children strongly favored associating the focus operator only with the theme (i.e., a banana), ignoring the fact that stress was placed on Sue in (89c) and (89e). Another five children associated only with the recipient (i.e., Sue). These children interpreted (89c) and (89e) in the same way as adults, but they interpreted (89b) and (89d) in a non-adult fashion. The remaining two children associated only with the rightmost constituent of the structure. In summary, the majority of the child subjects assigned one or another non-adult interpretation to the test sentences, disregarding the use of stress as a cue to the intended interpretation. The second experiment in the Halbert et al. study presented children with sentences that were ambiguous between a double object interpretation and a compound noun interpretation. A typical set of test sentences with the verb give is given in (90). The verb throw was also used, in another set of sentences. With stress on the word food, as in (90b) the message is that the cat was given food, rather than something else, say milk. This is double object structure. In example (90c), with stress on the word cat, the preferred structure for adults is that some female person was given cat food, not something else, such as fish food. This is the compound noun interpretation.

142  The case for logical nativism (90)

a. Bill gave her cat food. b. Bill gave her cat food. c. Bill gave her cat food.

Eighteen children (3;0–5;3) were interviewed. The finding was that children’s success with using stress as a cue to the intended interpretation depended on the particular verb that was used. Sixteen of the eighteen children tested were able to use stress to assign adult-like interpretations to sentences with the verb throw. However, only seven of the children were successful in responding to sentences with the verb give. Ten of the remaining eleven children reverted to a default interpretation, consistently assigning the double object interpretation, or the compound noun interpretation. The one remaining child invariably said the sentences were ambiguous. The empirical evidence underscores the observation by Cutler and Swinney (1987) that children appear adult-like in their abilities to use contrastive stress in production, but children younger than 5-years-old are unable to use such information effectively in deciding on the intended interpretation of sentences that are spoken to them. The observation that production appears to outstrip comprehension in certain aspects of language is striking, and paradoxical. On the surface, this would be like discovering that adults are better at recalling names than recognizing them. Nevertheless, an unexpected production/comprehension asymmetry has been observed in several areas of language development, including children’s sensitivity to scalar implicatures, to sentences governed by Principle B of the binding theory, and in the use of context in resolving structural ambiguities. 3.10 A theoretical problem with the pragmatic account Principle C is based on the structural property, c-command. The pragmatic account offered by Levinson (2000) denies that c-command is required in order to explain the facts; rather, pragmatic inferences suffice. We have established, however, that a considerable body of evidence indicates that children know the non-coreference facts well before they have access to the kinds of pragmatic knowledge that are envisioned, by the pragmatic account, to be the basis for people’s judgments about how NPs are interpreted in the relevant linguistic phenomena. There is another reason to question the adequacy of the pragmatic account. The same structural relation, c-command, that underpins the judgments of ­children and adults about coreference and variable binding in sentences with referential NPs also underpins the judgments of children and adults about other

3.10 A theoretical problem with the pragmatic account  143 linguistic phenomena. We have seen, for example, that c-command is a necessary ingredient for negative polarity licensing; when negation (or any other downward-entailing expression) c-commands the structural position of any, the sentence is acceptable. When negation is too low in the phrase marker to c-command any, the result is unacceptable. Similarly, c-command is an essential ingredient in assigning the conjunctive interpretation of disjunction. If c-command is not the correct structural property for determining anaphoric relations among referential expressions and their potential antecedents, then we must ask why NPI licensing, the interpretation of disjunction, and the noncoreference facts are observed in the same linguistic environments. To illustrate, all three of these linguistic phenomena have been compressed into the same sentences, in examples (91) and (92). In example (91) the plural pronoun they and the negation operator both c-command the embedded infinitival clause … for Fred or Manny to receive any of the prize money. Consequently, (a) the pronoun they must be disjoint in reference from the plural NP Fred or Manny, (b) this disjunctive NP generates a conjunctive entailment, and (c) the NPI any is licensed. (91)

a. They didn’t vote for Fred or Manny to receive any of the prize money. b. They1 didn’t vote for [Fred orconj Manny]2/*1 to receive √any of the prize money

Example (91) can be contrasted with (92), where the plural pronoun they and the negation operator both appear in a subordinate clause and, hence, neither of them c-commands the clause Fred or Manny will receive any of the prize money. In this case, (a) the pronoun they can be coreferential with Fred or Manny, (b) the disjunctive NP generates disjunctive truth conditions, and (c) the NPI any is not licensed. (92)

a. *Because they didn’t vote, Fred or Manny will receive any of the prize money. b. Because they1 didn’t vote, [Fred ordisj Manny]1 will receive *any of the prize money.

These examples underscore how these three apparently distinct linguistic phenomena crucially depend on c-command. The fact that these phenomena cooccur in English, and across human languages, would be lost on an account such as Levinson’s, which denies that anaphoric relations are determined by the same structural property that governs the interpretation of disjunction and the licensing of negative polarity items. We even witnessed one linguistic construction, specificational pseudoclefts, where all three of these linguistic phenomena co-occur, in the apparent absence

144  The case for logical nativism of c-command, as attested in examples (93)–(95). We saw, though, that if we modified the structural description of these sentences at the level of logical form, then we would be repositioned to provide a unified account of the cooccurrence of these linguistic phenomena. On the pragmatic account, one set of principles is needed for example (93), and another is needed for examples (94) and (95). This account, therefore, abandons the unification of these phenomena that is captured by c-command on the syntactic account. (93) (94) (95)

What he said was the blue magician’s trick was the best. What no child chose was a teddy or a dice. What no child chose was any fruit.

Part II Innate p ri ncip les and parameters of logic In the preceding sections, we have examined a core property of syntax, Principle C. This has long served as a parade case for an innate linguistic principle. In the remainder of the chapter, we shift gears, to concentrate on arguments for logical nativism. We begin with a discussion of a candidate for an innate semantic universal, downward entailment. 3.11 Downward entailment: a core logical principle We have seen that, in classical logic, whenever disjunction appears in the scope of negation (with no intervening logical expressions), it generates a conjunctive entailment, as in one of de Morgan’s laws: ¬(A ∨ B) ⇒ ¬A ∧ ¬B. In adult English, too, disjunction generates a conjunctive entailment when it appears in the scope of negation in simple negative statements of this form. This is illustrated in (96), which is only true in circumstances in which John didn’t bring beer to the party and John didn’t bring wine to the party. (96)

John didn’t bring beer or wine to the party.

We have found that, before 3-years-old, English-speaking children know that negated disjunctions carry a conjunctive entailment. Children’s adherence to this one of de Morgan’s laws provides circumstantial evidence that disjunction is assigned the truth conditions of inclusive-or, since this interpretation serves as the foundation for de Morgan’s laws pertaining to formulas that contain disjunction. Another linguistic structure is conditional statements (e.g., English if…, then …). In Chapter 1, we showed that the antecedent of a conditional is

3.11 Downward entailment: a core logical principle  145 downward entailing, and that disjunction licenses a conjunctive entailment in the antecedent of conditionals. The English sentence in (97) illustrates that disjunction licenses a conjunctive entailment when it appears in the antecedent of a conditional, so (97) is true only if both (97a) and (97b) are true. The same is true of Mandarin. (97)

If John brought beer or wine, then Max brought soft drinks. a. If John brought beer, then Max brought soft drinks. b. If John brought wine, then Max brought soft drinks.

The logical entailment made by example (97) is equivalent to one of the laws of propositional logic: (A ∨ B) → C ⇒ (A→ C) ∧ (B→ C). This leaves us with two logical laws, (98) and (99), that have counterparts both in English and in Mandarin. (98) (99)

¬(A ∨ B) ⇒ ¬A ∧ ¬B (A ∨ B) → C ⇒ (A → C) ∧ (B → C)

Despite their superficial differences, a generalization is lurking beneath these two logical laws. Notice that a disjunction appears on the left-hand side of each entailment (indicated by ‘⇒’). The disjunction is negated in (98), ¬(A ∨ B), and the disjunction implicates another proposition in (99), (A ∨ B) → C. On the right-hand side, both of these properties are attributed to both disjuncts. So, on the right-hand side of (98), the original disjuncts appear in a sequence of negative formulas combined by conjunction, ¬A ∧ ¬B. And on the right-hand side of (99), both of the original disjuncts appear in a conjunction of conditional statements with the proposition C at the consequent, i.e., (A → C) ∧ (B → C). Let the expression Δ represent both negation and the antecedent of conditionals (English if …). The common features in (98) and (99) can then be expressed in one general statement: Δ(A ∨ B) ⇒ Δ(A) ∧ Δ(B). This clearly includes the de Morgan law involving negated disjunctions, ¬(A ∨ B) ⇒ ¬A ∧ ¬B, but the generalization extends to all downward-entailing expressions. Let us perform a simple test to check whether the generalization Δ(A ∨ B) ⇒ Δ(A) ∧ Δ(B) extends to other downward-entailing expressions, by applying it to an expression that we have not discussed earlier, the preposition before. First, we should ascertain whether or not English before is downward entailing. To see, consider (100). This example indicates that before validates inferences from sets to subsets, and licenses the negative polarity item any. These are two of the basic diagnostics of downward entailment. (100)   Ted finished the puzzle before any linguist. ⇒ Ted finished the puzzle before Morris.

146  The case for logical nativism It is anticipated that the English before will comply with another diagnostic of downward entailment, namely licensing a conjunctive entailment for disjunction. This diagnostic is applied in (101). Since the embedded clause … before Morris or Noam entails both … before Morris and before Noam, the English expression before again qualifies as being a downward-entailing expression. So, before can be replaced by Δ in the generalization under consideration: Δ(A ∨ B) ⇒ Δ(A) ∧ Δ(B). (101)

Ted finished the puzzle before Morris or Noam. Cf. Ted finished … Δ(Morris ∨ Noam) ⇒ Δ(Morris) ∧ Δ(Noam)

We have now witnessed several downward-entailing expressions that can be substituted for Δ in the generalization. To add to the story, let us look at one more downward-entailing linguistic structure, the restrictor of the universal quantifier, every. We saw in Chapter 1 that the restrictor of the universal quantifier is downward entailing. Let us check then to see if it conforms to the generalization. It does, as illustrated in (102). So English every is another downward-entailing expression Δ that satisfies the generalization: Δ(A ∨ B) ⇒ Δ(A) ∧ Δ(B). (102)

Every person who ordered pasta or sushi became ill. a. Every person who ordered pasta became ill. and b. Every person who ordered sushi became ill.

3.12 Cross-linguistic findings We have made much of the fact that core principles, such as downward entailment, unify a range of linguistic phenomena. Once a core principle has been postulated, it is instructive to see how the phenomena that are associated with it are manifested in different languages. It is reasonable to suppose that downward-entailing linguistic structures will exhibit much the same array of properties across languages. For example, it is expected that all human languages satisfy the generalization about disjunction that we have extracted: Δ(A ∨ B) ⇒ Δ(A) ∧ Δ(B). Chapter 1 noted that, in addition to licensing the conjunctive entailment of disjunction, downward-entailing linguistic contexts license negative polarity items such as English any and Mandarin renhe. There are interesting crosslinguistic differences in the kinds of linguistic expressions that function as negative polarity items. We suggested that wh-words are the semantic relatives of existential indefinites, corresponding in meaning to English some (and

3.12 Cross-linguistic findings  147 any) in certain linguistic environments. In Mandarin, for example, the wh-word shenme ‘what’ is similar in meaning to the negative polarity item any when it appears in certain downward-entailing linguistic contexts, such as in the predicate phrase of sentences with the negative subject noun phrase meiyouren ‘nobody’ as in (103).14 (103)

Zai jiuhui shang meiyouren chi-guo shenme shuiguo. at party prep nobody eat-asp what fruit 在酒会上没有人吃过什么水果。 ‘Nobody at the party ate any fruit.’

In non-downward-entailing contexts, by contrast, the appearance of the whword shenme ‘what’ leads to its ordinary semantic contribution, i.e., marking the sequence of words as a question. For example, when the Mandarin question word shenme ‘what’ appears in the predicate phrase of the universal quantifier meigeren ‘everybody,’ as in (104), the speaker is asking a question. As we noted earlier, the predicate phrase of meigeren ‘everybody’ is not downward entailing. (104)

Zai jiuhui shang meigeren chi-le shenme shuiguo? at party prep every-cl person eat-asp what fruit 在酒会上每个人吃了什么水果? ‘What kind of fruit did everybody eat at the party?’

In short, the interpretation that is assigned to Mandarin wh-words like shei ‘who’ and shenme ‘what’ depends on whether or not these words appear in downward-entailing linguistic environments. In downward-entailing contexts, wh-words are sometimes interpreted like negative polarity items, such as Mandarin renhe or English any.15 Chapter 5 reports the findings of studies showing that English-speaking children know the licensing conditions of English any, and that Mandarin-speaking children know the semantics of shei ‘who’ and shenme ‘what,’ by 4 years old. It is time we returned to unifying principles. In Chapter 1 we showed that the relationship between disjunction and existential expressions runs deep. In classical logic, for example, in a domain with two individuals, a and b, ∃xFx expands to Fa ∨ Fb. As Rooth and Partee (1982, p. 360) remark, “The logical parallelism between disjunction and existential quantification is well known; disjunction is tantamount to quantification over an explicitly given finite domain.” The same holds true in human languages. For example, in a context where there are just two individuals, Jon and Max, the statement Someone laughs entails Jon laughs or Max laughs. So, as long as the domain is finite and each individual can be named, an expression using disjunction

148  The case for logical nativism is equivalent to one with an existential quantifier, both in logic and in human languages. We have seen that wh-words also involve existential quantification. As Jayaseelan (2001) points out, the semantic relationship between wh-words and existential quantification has been recognized since the earliest days of generative grammar. For example, Jayaseelan notes that Katz and Postal (1964) transformationally derived who from wh + someone and derived what from wh + something. Jayaseelan (2001, p. 87) observes that “the second part expresses the intuition that there is an existential quantifier here.” We have also seen that negative polarity items, such as English any and Mandarin renhe, can be analyzed as existential expressions. In the scope of negation, negative polarity items can also be viewed as a conjunction of negations, extending to every element in the domain of discourse. Just as this one of de Morgan’s laws is valid, ¬(A ∨ B) ⇒ ¬A ∧ ¬B, so is the following law: ¬(∃x Fx) ⇒ ¬Fa ∧ ¬Fb ∧ ¬Fc…. Perhaps the best way to think about this is to say that, under negation, the existential any expresses an infinite disjunction, ¬(Fa ∨ Fb ∨ Fc….). The infinite disjunction is logically equivalent to an infinite conjunction of negations, ¬Fa ∧ ¬Fb ∧ ¬Fc…. Recall also that wh-expressions and negative polarity items have a similar semantics in many of the world’s languages. Based on these observations, we might postulate that there is a deeper generalization that covers both disjunction and existential expression in human languages. Let us use α as a variable ranging over both disjunction and existential expressions (wh-expressions, and negative polarity items). If a, b, c… are individuals in the domain of discourse, and where Δ designates downward-entailing linguistic structures: Δ(… α …) ⇒ Δa ∧ Δb ∧ Δc… Cross-linguistic research verifies the semantic relations among (a) existential expressions like some and any, (b) disjunctive words like or, and (c) whwords like what and who. In Malayalam, for example, when the question word aar ‘who’ is suffixed with the disjunction marker -o, the resulting expression can form an existential quantifier, as (105) illustrates (the example is from Jayaseelan 2001, p. 66). (105)

ñaan iruTT-il aar-e-(y)oo toTTu. I darkness-in who-acc-disj touched ‘I touched somebody in the dark.’

Moreover, across languages, negative polarity items are formed by combining disjunctive words and wh-words. A major difference between the experience-based approach to language acquisition and the nativist approach is beginning to emerge. According to

3.13 Scope parameters  149 logical nativism, languages such as English are expected to exhibit patterns that can be described at various levels of abstraction. In addition to the constructions that languages exhibit, there are generalizations across linguistic structures, such as the generalization about disjunction that we first extracted: Δ(A ∨ B) ⇒ Δ(A) ∧ Δ(B). It appears that this generalization can be extended to existential expressions, more generally, yielding the broader generalization: Δ(… α …) ⇒ Δa ∧ Δb ∧ Δc… These kinds of generalizations are expected on the logical nativist approach, which contends that human languages are built from an innately specified conceptual structure that is, in Chomsky’s words (2000b, pp. 64–65) “waiting to be awakened by experience,” including concepts that are “to a large degree, merely ‘labeled’ in language acquisition.” The prediction of logical nativism is that as soon as children identify the expressions in the local language that correspond to disjunction, negation, the universal quantifier, before, existential indefinites, and so on, they are expected to know the meanings of these expressions, and they are expected to know how their meanings can be combined to form the meanings of larger expressions. 3.13 Scope parameters Most of the studies we will discuss in subsequent chapters involve scope ambiguities. And many of the studies reveal differences between children and adults. Scope ambiguities arise when two logical operators appear in the same clause. One example is sentences with negation and disjunction. In negated disjunctions in English, negation takes scope over disjunction, so disjunction yields a conjunctive entailment. For example, (106) entails that John didn’t bring beer to the party, and John didn’t bring wine to the party. This shows that English negative statements with disjunction correspond to one of de Morgan’s laws of propositional logic: ¬(A ∨ B) ⇒ ¬A ∧ ¬B. (106)

John didn’t bring beer or wine to the party.

Other languages, including Japanese and Mandarin Chinese, assign the opposite scope relations. In (107), the Mandarin word huozhe appears with negation, meiyou. Although the surface order of negation and disjunction are the same in Mandarin as in English, adult speakers of Mandarin judge (107) to mean that John didn’t bring beer or John didn’t bring wine. (107)

(Wo cai) Yuehan meiyou dai pijiu huozhe hongjiu qu jiuhui. (I guess) John not bring beer or wine go party. (我猜)约翰没有带啤酒或者红酒去酒会。 ‘It’s either beer or wine that John did not bring to the party.’

150  The case for logical nativism Adult speakers of Mandarin accept (107) in three circumstances, where (i) John brought beer, but not wine, (ii) John brought wine, but not beer, and (iii) John brought neither beer nor wine. In logic, the corresponding formula for the interpretation of (107) in Mandarin is (¬A ∨ ¬B), which does not entail (¬A ∧ ¬B). At first glance, it may appear that the Mandarin disjunctive word huozhe has the truth conditions of exclusive-or, in contrast to the disjunctive word or in English, which (as we saw) has the truth conditions associated with inclusiveor, as in classical logic. However, if Mandarin disjunction is exclusive-or, then adult Mandarin speakers should reject (107) in circumstances in which John brought neither beer nor wine, since exclusive disjunctions are false when both disjuncts are true. But adult speakers accept (107) in this circumstance, so an alternative explanation is called for. The alternative is to attribute the difference to a parameter, which we call the Disjunction Parameter. According to the parameter account, disjunction words always mean inclusive-or, but languages fall into one of two classes. In one class of languages, disjunction takes scope over negation in simple negative sentences. Let us call this the (or > neg) value of the parameter. Although the phrase with disjunction pijui houzhe hongjiu is c-commanded by negation in the surface syntactic structure of (108), this phrase is interpreted as having scope over negation at the level of logical form. So, this is an example of inverse scope, where the surface position of the logical expressions is the inverse of the scope relations between these expressions at the level of logical form. In the second class of languages, including English, negation takes scope over disjunction both in surface syntax and at logical form. These languages adopt the (neg > or) value. The two values of the Disjunction Parameter are depicted in (108). (108)

English: Surface Scope (neg > or) John didn’t bring beer or wine to the party.



Mandarin: Inverse Scope (or > neg) pijiu huozhe hongjiu Yuehan meiyou dai pijiu huozhe hongjiu qu jiuhui

Another example of scope ambiguities includes sentences with negation and conjunction. In a recent investigation of children’s interpretation of negated conjunctions, another difference between children and adults was uncovered in a study of English-speaking children.16 This study demonstrated that Englishspeaking children differ from adults in the interpretation they assign to negative statements like (109). (109)

John didn’t bring both beer and wine to the party.

3.13 Scope parameters  151 First, let us discuss the interpretation that is assigned to negative statements like (109) by adults, in both English and Mandarin. Adult English speakers take (109) to be true in three circumstances, where (a) John just brought beer, where (b) John just brought wine, or where (c) John brought neither beer nor wine. Mandarin differs in the semantic interpretation assigned to negated conjunctions. There are two ways to translate the English example (109) into Mandarin. One way mirrors the word order of English. The translation is given in (110), where meiyou is the Mandarin equivalent to English not, and he is equivalent to and. (110)

Yuehan meiyou dai pijui he hongjiu qu jiuhui. John not bring beer and wine go party 约翰没有带啤酒和红酒去酒会。 ‘As for both beer and wine, John did not bring them to the party.’

Although the conjoined clause pijui he hongjiu is c-commanded by negation in the surface syntactic structure of (110), this phrase is interpreted as having scope over negation at the level of logical form. So, this is another example of inverse scope. Another way to translate the English sentence John didn’t bring both beer and wine to the party into Mandarin is (111). Here, the quantificational adverb dou (meaning ‘both’ or ‘all’) appears. The Q-adverb dou takes scope over expressions to its left, so the conjunctive phrase in (111) must precede dou and, as a consequence, the conjunctive phrase precedes the word for negation meiyou. In contrast to (110), example (111) generates the surface scope interpretation, on which there is an isomorphism between surface structure and logical form. (111)

Yuehan pijiu he hongjiu dou meiyou dai qu jiuhui. John beer and wine both not bring go party 约翰啤酒和红酒都没有带去酒会。 ‘As for both beer and wine, John did not bring them to the party.’

Examples (110) and (111) are assigned the same interpretation in Mandarin. This rules out the possibility that Mandarin speakers use precedence (linear order) to determine scope relations. So, both (110) and (111) are interpreted in the same way in Mandarin, but differently than the English sentence John didn’t bring both beer and wine to the party. Mandarin generates a stronger interpretation, according to which John brought neither beer nor wine to the party. If we want to convey this meaning in English, we must adopt the movement strategy illustrated in the Mandarin example (111). This is shown in the

152  The case for logical nativism glosses beneath the Mandarin examples, or English speakers can adopt other structures to yield the same interpretation. As (110) attests, however, Mandarin derives the inverse scope reading without moving the disjunction phrase in surface syntax. The disjunction phrase moves at the level of logical form. The variation illustrated by English versus Mandarin can be attributed to a second scope parameter. The parameter determines how negated conjunctions will be interpreted across languages. The meaning of conjunction is the same across languages (i.e., Boolean conjunction). Nevertheless, human languages fall into one of two classes, according to which parameter value they adopt. In one class of languages, conjunction takes scope over negation in simple negative sentences. Let us call this the (and > neg) value of the parameter. This class of languages includes Mandarin. At first look, languages like Mandarin appear to violate this law. However, appearances are deceiving. Since conjunction takes scope over negation in Mandarin, the law does not apply. For languages in the second class, negation takes scope over conjunction, so this is the (neg > and) value. This second class of languages includes English. Languages with the neg > and value of the parameter conform to one of de Morgan’s laws in simple negative sentences with conjunction: ¬(A ∧ B) ⇒ ¬A ∨ ¬B. The different values of the Conjunction Parameter are depicted in (112). (112)

English: Surface Scope (neg > and) John didn’t bring both beer and wine to the party



Mandarin: Inverse Scope (and > neg) pijiu he hongjiu Yuehan meiyou dai pijiu he hongjiu qu jiuhui

3.14 The Semantic Subset Principle We have proposed that children are free to select parametric options that differ from those of adult language users, but only if positive evidence is available to inform children of their wayward linguistic behavior. To ensure that children can be set straight when necessary, it has been proposed that children’s hypotheses are constrained by a learning principle called the Semantic Subset Principle (Crain, Ni, and Conway 1994; see Chapter 4). To see how the Semantic Subset Principle works, let us consider the Disjunction Parameter. It is easily verified that the circumstances in which sentences are true on the (or > neg) value comprise a superset of those circumstances that make sentences true on the (neg > or) value. In other words, the binary values are in a subset/superset relation. To see this, note that the

3.14 The Semantic Subset Principle  153 neg > or value yields a neither reading, whereas the or > neg value yields a not both reading. Clearly, the statement neither A nor B is true in a subset of the circumstances corresponding to the statement not both A and B. When parameter values are in a subset/superset relation, a principle of learning dictates that children acquiring all languages must initially select the subset value. Adopting the Semantic Subset Principle, Goro predicted that children learning languages like Mandarin and Japanese (the language that Goro studied) would initially interpret negated disjunction in the same way as Englishspeaking children and adults interpret them, as generating a conjunctive entailment (e.g., John didn’t bring beer or wine to the party entails that John did not bring beer and John did not bring wine). That is, children acquiring Mandarin were predicted to initially set the parameter to (neg > or), whereas adults assign the alternative value. If so, then children should generate a conjunctive entailment for sentences like (113), whereas adult speakers do not. In short, the commonality that is predicted is between Mandarin child language and English rather than between Mandarin child language and Mandarin adult language. (113)

(Wo cai) Yuehan meiyou dai pijiu huozhe hongjiu qu jiuhui. (I guess) John not bring beer or wine go party. (我猜)约翰没有带啤酒或者红酒去酒会。 ‘It’s either beer or wine that John did not bring to the party.’

The prediction, then, is that children learning Mandarin would speak a fragment of a foreign language, one from a class that includes English. This prediction was first confirmed in an experimental study of Japanese-speaking children, reported by Goro and Akiba (2004a, b). We have replicated the Goro and Akiba findings with Mandarin-speaking children. Children acquiring both languages generate a conjunctive entailment for disjunction when it appears in the scope of negation, whereas adult speakers of both languages do not. The experience-based approach owes us an account of such findings. (114)

Mandarin: (or > neg) for adults, (neg > or) for children Adults: pijiu huozhe hongjiu Yuehan meiyou dai pijiu huozhe hongjiu qu jiuhui



Children: Yuehan meiyou dai pijiu huozhe hongjiu qu jiuhui

The Conjunction Parameter should have the opposite effects. It can easily be verified that the circumstances in which sentences are true on the (and > neg) value comprise a subset of those circumstances that make sentences true on the (neg > and) value. Simply note that the and > neg value yields a neither reading, whereas the neg > and value yields a not both reading. Clearly, the

154  The case for logical nativism statement neither A nor B is true in a subset of the circumstances corresponding to the statement not both A and B. According to the Semantic Subset Principle, children acquiring all languages must initially select the subset value, i.e., the neither reading of the parameter and > neg, which corresponds to Mandarin. Logical nativism is therefore compelled to predict that children learning English, a superset language, should initially behave like child and adult speakers of Mandarin, a subset language. In short, the commonality that is predicted is between English child language and Mandarin, rather than between English child language and English adult language. This finding was also confirmed in a series of recent experiments at our laboratory. We found that English-speaking children rejected negated conjunctions, such as (115) as a description of circumstances where John just brought beer, or just brought wine, or brought neither beer nor wine. (115)

John didn’t bring both beer and wine to the party.

English-speaking adults interpret (115) as meaning that John brought only beer or only wine to the party. By contrast, the only circumstance that makes (115) true for English-speaking children is one in which John failed to bring either beer or wine to the party. This is the same interpretation of negated conjunctions that is assigned to the corresponding Mandarin sentences by Mandarin-speaking children and adults, but it is not the interpretation favored by English-speaking adults. This finding is, once again, in keeping with the Continuity Hypothesis. (116)

English: (and > neg) for adults, (neg > and) for children Adults: John didn’t bring both beer and wine to the party



Children: both beer and wine John didn’t bring both beer and wine to the party

There is another relevant observation for logical nativism. Child language differs from the language of adults, such that child and adult Mandarin differ, and child and adult English differ. That is, children acquiring Mandarin interpret negated disjunction like English speakers do, and children acquiring English interpret negated conjunctions like Mandarin speakers do. However, the initial assignments of meanings by children do not differ across languages. In interpreting negated disjunctions, both children acquiring Mandarin and ones acquiring English initially favor the neg > or value of the parameter. And, in interpreting negated conjunctions, children acquiring both languages initially favor the and > neg value. The interpretations assigned by children are evidence that children acquiring both English and Mandarin favor the subset value of the relevant parameters.

3.15 Negative evidence  155 These findings illustrate how cross-linguistic differences provide a unique testing ground for the alternative theories of language acquisition. The fact that children don’t emulate their parents is evidence that children do not attempt to match the input, as the experience-based approach contends. Instead, children use the linguistic input to assist them in navigating through the space of parametric options made available by Universal Grammar. In the course of language development, children are free to try out unattested options, so long as ones that prove to be incorrect can later be retracted on the basis of positive evidence. That is where experience matters – not because children base their grammatical hypotheses on experience, but because experience brings the child back on track when s/he has taken a wrong path. This guarantees that children will converge on a grammar that is equivalent to those of adults in the same linguistic community. 3.15 Negative evidence There is an alternative to the Semantic Subset Principle. Suppose that children overgenerate, and produce sentences or meanings beyond those that are accepted by adult speakers of the local language. It is conceivable that children could jettison the illicit forms and meanings from their grammars by another means, such as negative feedback from adults. Negative evidence, or some substitute for it, can inform children that they have overshot the target language. It is worth asking, then, if negative evidence is available to children. Over the past thirty years, many researchers have examined the input to children to see whether or not children receive various forms of negative reinforcement for ill-formed sentences. The earliest study was by Brown and Hanlon (1970), who analyzed tape recordings of children interacting with their parents. In their analysis, Brown and Hanlon investigated whether parents comprehended children’s well-formed questions better than their ungrammatical questions. Each reply by a parent was analyzed to see if the parent understood or misunderstood the child’s question. The main finding of the analysis was that the parental replies indicated a lack of comprehension to as many grammatical questions (42 percent) as to ungrammatical ones (47 percent). Brown and Hanlon concluded that “In general, the results provide no support for the notion that there is a communication pressure favoring mature constructions” (p. 45). Parental approval and disapproval were tied to one important aspect of child language, viz., truth. Brown and Hanlon found that children received approval from their parents when what they said was true, and disapproval when what

156  The case for logical nativism they said was false. For example, the parent might have responded to a 2-yearold child who said, “Doggie sit chair” by saying “Yes, that’s right,” as long as the child was correctly conveying the information that the dog was sitting on the chair. There were few instances of negative feedback, such as “No, don’t say it that way, say: ‘The doggie is sitting on the chair’.” But if the child said something that wasn’t true, the parent showed disapproval. In short, adults reward children selectively for what they say, but the pattern of rewards does not explain how children might learn about syntactic or semantic errors. Other researchers have reached the same conclusions (e.g., Bowerman 1988; Marcus 1993; Morgan and Travis 1989). Bowerman (1988) argues that what little negative evidence has been uncovered to date is irrelevant for the specific cases of overgeneration that are attested in the literature on child language. Slobin (1972) concludes that children are not corrected for ungrammatical utterances in many of the societies studied by his research group. Even if negative evidence were available, children may not avail themselves of it. There is no evidence showing that children exposed to negative evidence use it to purge their grammars of incorrect hypotheses (see Newport, Gleitman, and Gleitman 1977). Pinker (1990, p. 217) reaches the following conclusion: When parents are sensitive to the grammaticality of children’s speech at all, the contingencies between their behavior and that of their children are noisy, indiscriminate, and inconsistent from child to child and age to age.

Along with Pinker, we assume that if children do indeed overgenerate, then their eventual retreat to the adult grammar is not driven by learning. It is still conceivable that children overgenerate, but retreat to grammars that are equivalent to those of adults, due to maturation or due to other changes in children’s grammars (see Gualmini and Schwarz 2009). Another possibility, of course, is that children do not overshoot in the first place. This is an empirical matter, to be decided in the language acquisition laboratory. It is noteworthy, however, that (with few exceptions, such as apparent Principle B violations) there is only anecdotal evidence of children committing errors of overgeneration in the literature on child syntax or semantics. By contrast, there is abundant evidence that children overgenerate in the acquisition of morphological processes such as forming the past tense and past participial forms of verbs, and the plural forms of nouns. 3.16

Where child and adult languages cannot differ

To sum up, the meanings of logical words could have been different than they are. Also note that language allows apparent violations of logical laws, scope

3.17 Hidden units: focus operators  157 relations. So, de Morgan’s laws are based on the meanings that are assigned to logical expressions in classical logic. As we have seen, it is a contingent fact if human languages assign the same meanings to the corresponding expressions.17 For example, it turns out that human languages assign the meaning to disjunction words, such as English or and Mandarin huozhe, that comports with classical logic, namely inclusive-or. Once the meanings of logical expressions have been fixed, then humans will assent to certain entailment relations and deny others. One of the truths humans are expected to assent to is the following one of de Morgan’s laws: ¬(A ∨ B) ⇒ ¬A ∧ ¬B. Both English-speaking children and adults readily assent to statements that conform to this surface pattern, but adult speakers of other languages, including Mandarin, do not. There are at least two ways to bring adult speakers of Mandarin in line, such that they interpret disjunction in the same way as Mandarin-speaking children, as well as Englishspeaking children and adults. As noted earlier, polarity sensitivity is a strictly local affair. When disjunction is in a lower clause than the clause that contains negation, disjunction loses its proclivity to take scope over negation. With negation taking scope over disjunction in such structures, moreover, the interpretation that is assigned in such sentences adheres to de Morgan’s law: ¬(A ∨ B) ⇒ ¬A ∧ ¬B. In adult Mandarin, for example, disjunction licenses a conjunctive entailment in (117), just as it does in its English counterpart in (119). (117)

Taide mei kanjian Yuehan dai pijui huozhe hongjiu qu jiuhui. Ted not see John bring beer or wine go party 泰德没看见约翰带啤酒或者红酒去酒会。 ‘Ted didn’t see John bring beer or wine to the party.’

(118)

(Taide mei kanjian [Yuehan dai pijui huozhe hongjiu qu jiuhui])

(119)

Ted didn’t see John order pasta or sushi.

(120)

(Ted didn’t see [John order pasta or sushi])

Polarity sensitivity is a local affair. It holds of negation and polarity expressions that appear in the same clause. Once negation is positioned in a higher clause than the one that contains the polarity expression, the polarity effect is canceled.18 3.17

Hidden units: focus operators

Another linguistic structure cancels polarity sensitivity, in most cases, and reveals the logic underlying human languages. The structure involves focus

158  The case for logical nativism operators such as English only and Mandarin zhiyou. It turns out that disjunction licenses a conjunctive entailment, across languages, when it appears in the predicate phrase of sentences with focus operators. Before we discuss this property of focus operators, it will be instructive to describe the semantics of focus operators in more detail. Sentences with focus operators can be partitioned into (a) a focus element and (b) a contrast set. Consider example (121). (121)

Only Julia ordered kangaroo. Presupposition: Julia ordered kangaroo. Assertion: Everybody else did not order kangaroo.

The focus element is Julia. The use of the focus operator only in (121) presupposes that there are individuals in the conversational context that are being contrasted with Julia. This is the contrast set. Sentences with focus operators have two meaning components. These are called the presupposition and the assertion. The presupposition is about the focus element. The presupposition is roughly the meaning of the sentence, minus the focus operator. The presupposition of (121) is Julia ordered kangaroo. The second meaning component is the assertion. The assertion expresses a proposition about the contrast set. The assertion entails that everyone in the contrast set lacks the property being attributed to the focus element, i.e., … ordered kangaroo. So, the assertion of (121) is the proposition Everyone else (being contrasted with Julia) did not order kangaroo. Now it can be appreciated why the predicate phrase of sentences like (121) is downward entailing. The assertion introduces negation as part of the meaning of the sentence, and negation is downward entailing. This is why (121) entails that everyone else did not order kangaroo. Further tests of the downward-entailing properties of the predicate phrase yield similar positive results. The predicate phrase following the focus operator only licenses the negative polarity item any. This is shown in (122). (122)

Only Julia ordered any vegetables.

And disjunction generates a conjunctive entailment in the predicate phrase of sentences with focus operators, in the assertion. The sentence is true only if both (123a) and (123b) are true. (123) Only Julia brought beer or wine to the party. Assertion: Everybody else did not bring beer or wine to the party. a. Everyone else did not bring beer to the party. and b. Everyone else did not bring wine to the party.

3.17 Hidden units: focus operators  159 However, focus operators contribute two meaning components, and only one of them is downward entailing. Consequently, disjunction is interpreted in one way in the assertion, but in another way in the presupposition. This dual functioning is shown in (124), where disjunction generates disjunctive truth conditions in the presupposition, but generates a conjunctive entailment in the assertion. (124) Only Julia brought beer or wine to the party. Presupposition: Julia brought beer or wine to the party. a. Julia brought beer to the party. or b. Julia brought wine to the party. Assertion: Everybody else didn’t bring beer or wine to the party. c. Everybody else didn’t bring beer to the party. or d. Everybody else didn’t bring wine to the party.

As a consequence of the disjunctive truth conditions in the presupposition, disjunction generates a scalar implicature in the presupposition, so Julia is not expected to have brought both beer and wine to the party. So focus operators cancel the polarity sensitivity of indefinite expressions in the predicate phrase. This leads to another interesting prediction, based on our conjecture that the indefinite some and the negative polarity item any are allomorphs. If this is true, then both expressions should be licensed in sentences with only, without a change of meaning, since the focus operator cancels polarity sensitivity. This is confirmed in example (125). (125)

Only Julia ordered some/any dessert.

There is more here than meets the eye. Notice what happens if a speaker asserts the presupposition and the assertion out loud. Neither the assertion nor the ­presupposition contains the focus operator, so its effects are canceled. In the presupposition, therefore, the indefinite expression some is obligatory, as shown in (126). The NPI any is not tolerated in the presupposition, because it does not contain a downward-entailing expression. And the negative polarity item any is obligatory in the assertion, because the use of some would generate the wrong truth conditions. (126)

Only Julia ordered some/any dessert. Presupposition: Julia ordered some/*any dessert. Assertion:   Everybody else did not order ?some/any dessert.

Suppose we use some in the assertion, yielding Everybody else did not order some dessert. In this case, the assertion would entail that, for each individual

160  The case for logical nativism in the contrast set, there is some dessert which that person did not order. The entailment of the assertion is stronger than this, namely that no person ate any dessert. In short, the assertion requires a negative polarity item, and cannot make do with a positive polarity item. This becomes relevant when we consider languages in which the word for disjunction and the word for conjunction are positive polarity items (PPIs), as in Mandarin. The expectation is that neither disjunction nor conjunction will be analyzed as positive polarity items in the assertion of focus operators. Rather, these expressions are expected to receive the meanings corresponding to classical logic. Such findings would constitute further support for logical nativism. These predictions are followed up in the next two sections. 3.18 Canceling polarity: negated disjunctions On the logical nativist account, Mandarin sentences with the focus operator zhiyou are expected to have exactly the same semantic properties as their English counterparts. The Mandarin translation of Only John brought beer or wine to the party is given in (127). (127)

Zhiyou Yuehan dai le pijiu huozhe hongjiu qu jiuhui. Only John brought Asp beer or wine go party 只有约翰带了啤酒或者红酒去酒会。 ‘Only John brought beer or wine to the party.’ Presupposition: John brought beer or wine to the party. a. John brought beer to the party. or b. John brought wine to the party. Assertion: Everyone else didn’t bring beer or wine to the party. a. Everyone else did not bring beer to the party. and b. Everyone else did not bring wine to the party.

Again, this is due to the fact that focus operators introduce covert negation. This shows that the polarity sensitivity of disjunction is a surface phenomenon. At the level of logical form, logical expressions are interpreted in their structural position, and are not permitted to scope out. This conclusion is reinforced by considering statements with focus expressions containing conjunction. (128)

Polarity is canceled pijiu huozhe hongjiu [qita-ren meiyou dai pijiu huozhe hongjiu qu jiuhui]

X

3.19 Canceling polarity: negated conjunctions  161 3.19 Canceling polarity: negated conjunctions There is one last group to bring in line, English-speaking children. We observed that English-speaking children differed from adults in interpreting negated conjunctions like (129). (129)

John didn’t bring both beer and wine to the party.

Adult English speakers interpret (129) in conformity with classical logic, assigning it the not > and reading. So, (129) is true for adults if John just brought beer, or just wine, or neither beer nor wine. As we saw earlier, Mandarin has two ways to translate the English example (129), as given in (130) and (131). In both cases, the interpretation differs from English. Both child and adult speakers of Mandarin have been found to assign the neither reading to (130) and (131). Since the conjunction word he and negation meiyou appear in reverse order in the two examples, the interpretation that is assigned by both children and adults cannot be due to linear order. (130)

Yuehan meiyou dai pijiu he hongjiu qu jiuhui. John not bring beer and wine go party 约翰没有带啤酒和红酒去酒会。 ‘As for both beer and wine, John did not bring them to the party.’

(131)

Yuehan pijiu he hongjiu dou meiyou dai qu jiuhui. John beer and wine both not bring go party 约翰啤酒和红酒都没有带去酒会。 ‘As for both beer and wine, John did not bring them to the party.’

The findings are that English-speaking children differ from English-speaking adults, and assign the same interpretations as Mandarin-speaking children and adults. All three groups assign the neither reading to the English example John didn’t bring both beer and wine to the party and to the Mandarin examples (130) and (131). However, English-speaking adults prefer to assign the not both reading. English-speaking children and adults presumably differ because children adhere to the Semantic Subset Principle. Since the neither reading is true in a subset of the circumstances corresponding to the not both reading, the neither reading is expected to be the initial value of the Conjunction Parameter. The expectation of the logical nativist account is that this value will initially be adopted by children acquiring all human languages, even ones in which the relevant input to children is the alternative value. We suggested that the reason English-speaking children (and both Mandarin-speaking children and adults) assign the neither reading to negated conjunctions is that these speakers all initially analyze conjunction words

162  The case for logical nativism (English and, Mandarin he) as positive polarity items. If so, then sentences like (130) should be interpreted in the same way by English-speaking children and adults, and conjunction should revert to its Boolean meaning. In such sentences, negation is introduced overtly into the assertion, so the entailment is as given in (132). (132) (133)

Only John brought beer and wine to the party. Assertion: Everyone else didn’t bring both beer and wine.

According to the present account, the inverse scope reading of conjunction in negative statements is a surface phenomenon, and does not apply at the level of logical form. This is schematically represented in (134). (134)

Inverse scope is canceled pijiu he hongjiu [qita-ren meiyou dai pijiu he hongjiu qu jiuhui]

X

This prediction was investigated in a study conducted by Goro, Minai, and Crain (2006). The finding was exactly as expected on the logical nativist account. English-speaking children assigned the same interpretation (of the assertion) to Only John didn’t bring beer and wine to the party as English-speaking adults do, i.e., they generate the not both reading. That is, English-speaking children accept this sentence as long as everyone else (being contrasted with John) did not bring both beer and wine. In the assertion, the focus operator only introduces covert negation, and conjunction does not take scope over covert negation. This shows again that polarity sensitivity is a surface phenomenon, and does not hold at logical form. The same conclusion was confirmed in an experimental study of Mandarin. Consider example (135). If the Mandarin conjunction he is a PPI, as we have suggested, then it will appear under covert negation in the assertion associated with (135). This should render its polarity sensitivity inert, yielding the both not reading, rather than the neither reading that is generated for conjunctions in sentences with overt negation. This is exactly what was found. (135)

Zhiyou Yuehan chi-le pinguo he li. Only John eat-asp apple and pear 只有约翰吃了苹果和梨。 ‘Only John ate apple and pear.’ Assertion: Everyone else didn’t eat both an apple and a pear.

This section has shown the intricacies and abstractness of logical nativism. We have shown that hidden meaning units contributed by focus operators bring out the logical meanings of both disjunction words and conjunction words in

3.20 Where we are headed  163 human languages. The most important lesson is how this account differs in its expectations from those of the experience-based approach. 3.20

Where we are headed

In the following chapters, we report the results of experimental investigations of the emergence of knowledge of logical concepts and logical laws in two typologically distinct human languages, Mandarin Chinese and English. The next chapter is concerned with negative statements that contain disjunction or conjunction. Chapter 5 considers children’s acquisition of polarity-sensitive expressions. Finally, Chapter 6 reports the findings of studies of children’s mastery of the semantic intricacies of focus expressions. Although each of these phenomena is rich in complexity and in detail in its own right, we will barely scratch the surface in considering proposals about these phenomena that have been advanced by theoretical linguists. Hopefully, though, our discussions will pique your interest in pursuing these topics further, and possibly even in investigating them using experimental techniques to study how children, across languages, acquire linguistic knowledge in general, and knowledge of logic in particular.

4 Scope parameters

Children’s linguistic competence encompasses a variety of rich and interrelated linguistic and logical generalizations. Chapter 1 described one of the logical generalizations which is prominent in human languages. We began with the observation that disjunction generates a conjunctive entailment in the scope of negation in human languages. In some languages, disjunction only generates a conjunctive entailment when negation is in a higher clause than the clause that contains disjunction. In other languages, disjunction generates a conjunctive entailment even when negation and disjunction are in the same clause. One way or the other, all human languages, as far as we know, adhere to one of de Morgan’s laws: ¬(A ∨ B) ⇒ ¬A ∧ ¬B. This one of de Morgan’s laws is just the tip of a logical iceberg. We proceeded to demonstrate that disjunction generates a conjunctive entailment when it appears in the scope of expressions with a negative cast, such as the determiner no (but not some) and the determiner phrase nobody (but not everybody). We went on to demonstrate that disjunction even licenses a conjunctive entailment in other linguistic contexts that do not have a negative cast, including the antecedent of conditionals, and the subject phrase of the universal quantifier every. Based on a series of observations about where the conjunctive interpretation arises, and where it does not, we postulated the following generalization: Disjunction generates a conjunctive entailment when it appears in the scope of any downward-entailing expression Δ: ∆ ( A ∨ B) ⇒ ∆ (A ) ∧ ∆ (B)

The class of downward-entailing expressions in any human language proves to be a motley collection. In English, the downward-entailing expressions include negation, negative adverbs, prepositional phrases headed by without (but not the preposition with), the antecedent of conditionals (but not the consequent), verb phrases headed by forbid or doubt, the determiner no, verbs expressing minimum conditions such as suffice and be enough, comparatives 164

Scope parameters  165 such as stronger and taller, and many others. But if downward entailment is an innate natural class of linguistic expressions, encompassing all human languages, then logical nativism anticipates that downward-entailing expressions will manifest the same properties across languages. These properties include (a) the defining property, i.e., licensing inferences from sets to their subsets, (b) licensing negative polarity expressions such as English any, ever, and at all, and their counterparts across languages, and (c) generating a conjunctive entailment for disjunction. Although this cluster of properties appears to be unrelated, these linguistic phenomena must actually be variations on a theme. We discussed this, too, in Chapter 1, and we’ll return to this in Chapter 5. The prediction that downward-entailing expressions form a natural class in human languages has been confirmed, both within and across languages. In (1), we offer English examples of downward-entailing expressions that admit any. The examples in (2) show that these same expressions license a conjunctive entailment when they take scope over disjunction. (1)

a. b. c. d.

I don’t talk to any other linguists. I usually arrive at the gym before any other linguists wake up. If any linguists go to the gym, I go swimming. I forbid any linguists from going swimming.

(2)

a. b. c. d.

I don’t talk to linguists or philosophers. I usually arrive at the gym before the linguists or the philosophers. If a linguist or a philosopher goes to the gym, I go swimming. I forbid linguists or philosophers from going swimming.

The present chapter and the next investigate how children interpret disjunction when it is associated with downward-entailing operators. In the present chapter, we will first look at how children interpret disjunction (and conjunction) in negative sentences, both in Mandarin and in English. Then, we will examine children’s interpretation of disjunction in sentences with the temporal conjunction before. Examples (1b) and (2b) above indicate that before is a downwardentailing operator in English, since it licenses any and generates a conjunctive entailment when disjunction appears in its scope. In the next chapter, we examine children’s knowledge of the licensing conditions of negative polarity items. If downward entailment is a core property of human languages, as logical nativism contends, then these properties are expected to be manifested early in the course of language development by children acquiring different human languages. Our goal is to establish that downward entailment provides a unified account of disparate-looking linguistic phenomena, across languages (including child languages). This supports the proposition we made in Chapter 1 – that downward entailment is a core linguistic property.

166  Scope parameters The experience-based approach owes us an explanation of how this kind of unification – taking in a variety of linguistic contexts, in historically unrelated languages – can be achieved. The experience-based approach limits itself to generalizations that are based on information structure and/or discourse function. Because the class of downward-entailing operators is so varied, however, an account based on information structure and/or discourse function is ill equipped to deal with the phenomena governed by downward entailment, without invoking some notational variant of the concept of downward entailment itself. Of course, it is conceivable that such an account will be forthcoming. As for acquisition, perhaps the kind of piecemeal acquisition advocated by the experience-based approach could suffice for children to learn the environments in which any can appear, such as those in (1). Moreover, perhaps children could avoid producing any in other non-downward-entailing environments, simply because they do not encounter it in those environments (but see Chapter 2). But a more pressing question for the experience-based approach is how children could navigate through their linguistic experience to discover when disjunction licenses a conjunctive entailment, and when it does not. This is not a distributional phenomenon, since disjunction words are permitted in both downward-entailing and non-downward-entailing environments. It seems highly improbable to suppose, moreover, that every child has the requisite skills for keeping detailed records of differences in the interpretation of disjunction in different contexts. As we have seen, the kinds of linguistic contexts that are downward entailing are a motley bunch. Either children have cognitive capacities well beyond those of linguists, who have only recently uncovered the generalizations about downward-entailing expressions, using both positive and negative evidence and evidence from cross-linguistic research, or children would be expected to make mistakes. As we will see, children’s mistakes are rare, if they occur at all. The present chapter begins with a review of some of the relevant literature on children’s production and comprehension of disjunction in the scope of negation. The research we review was designed to establish that c-command is operative in children’s grammars and instrumental in determining how ­disjunction is interpreted in negative sentences. The experimental studies we review consider alternative ways in which children might decide how disjunction is interpreted. Two alternatives to c-command are considered: (a) linear order (negation precedes disjunction), and (b) proximity (negation is positioned close to disjunction). Although these structure-independent strategies are clearly not operative in the grammars of adult language users, it is important to also make certain that structure-independent strategies are not operative

4.1 Negated disjunctions  167 for children. We review two previous experimental studies that attempted to settle this issue. Following this, we describe the two scope parameters involving negation and conjunction/disjunction in more detail. Then, we report the findings of experiments designed to see if children assign the initial values of the parameters, as suggested by the Semantic Subset Principle introduced in Chapter 3. The findings of these studies prove critical in distancing logical nativism from the experience-based approach to the acquisition of the meanings of logical expressions. The findings undercut the kind of “meaning-is-use” approach to the acquisition of logical expressions that has been advocated by proponents of the experience-based approach. Finally, the chapter concludes with a report on experimental investigations of children’s interpretation of disjunction in sentences with the temporal conjunction before. This expression meets some of the diagnostics of downward entailment, both in English and in Mandarin Chinese. There are differences between languages, however, in the way disjunction is interpreted in sentences with the temporal conjunction before. In English, the disjunction word or licenses a conjunctive entailment when it appears in the scope of the temporal conjunction before. In Mandarin, when the disjunction word huozhe appears in the scope of zai…zhiqian ‘before’, it does not appear to license a conjunctive entailment, at least for many adult speakers. We are led to ask, therefore, how children acquiring Mandarin interpret disjunction words that appear in the scope of before. As with disjunction in the scope of negation, our conclusion is that disjunction is subject to parametric variation, such that it is a positive polarity item in adult Mandarin. Following the dictates of the Semantic Subset Principle, we are led to predict that Mandarin-speaking children should differ from Mandarin-speaking adults in the interpretation they assign to disjunction in sentences with zai…zhiqian. Mandarin-speaking children are expected to initially favor the −PPI value of disjunction, leading them to interpret disjunction in sentences with zai…zhiqian in the same way as English-speaking children and adults do. This proves to be the finding, providing another instance in which child and adult languages differ, due to a scope parameter. Once again, this kind of difference between child and adult language poses a challenge for the experience-based approach, on which child language is input matching. 4.1

Negated disjunctions

This section is largely a review of previous research findings from experimental investigations of children’s knowledge of downward entailment, beginning

168  Scope parameters with how children interpret disjunction in simple negative sentences, and then turning to studies of older children and more complex sentence structures. 4.1.1 A longitudinal study of 2-year-olds We start with the youngest children first. One recent study of young children was a longitudinal investigation with three 2-year-old children. These children were presented with negated disjunctions in carefully designed contexts which were devised to investigate the interpretation children assigned to the test structures (see Crain 2008; Notley, Zhou, Crain, and Thornton 2009). One experiment was an act-out task. On one trial, children were shown three toy dogs. There was a white dog, a brown dog, and a black dog. The experimenter pretended to be Kermit the Frog, and also manipulated the toys in the experimental workspace. Kermit indicated to the child that he wanted to play with a dog. The experimenter then held up the three dogs, and Kermit said: “I don’t want to play with the white dog or the brown dog.” According to de Morgan’s law, this statement generates a conjunctive entailment, so if the 2-year-olds knew this one of de Morgan’s laws, they were expected to give Kermit the black dog, because the statement entails that Kermit didn’t want to play with the white dog and that he didn’t want to play with the brown dog. This left only the black dog. Suppose 2-year-old children interpret disjunction as exclusive-or, or lack knowledge of the relevant one of de Morgan’s laws. Then, Kermit’s statement might be interpreted by children as meaning that Kermit didn’t want to play with the white dog or didn’t want to play with the brown dog. On this scenario, children might be expected to offer Kermit either the white dog or the brown dog, since it was just one of these dogs that he didn’t want to play with. Children might also consider offering Kermit the black dog, but there is no reason to expect children to consistently make the inference that Kermit wanted the black dog, unless they were adhering to de Morgan’s laws. In another condition, negated disjunctions were introduced in wh-questions. On a typical trial, an array of characters was introduced. On one trial, some characters had yo-yo’s, some had sponge balls, and some had strawberries. Then, a target wh-question was posed to children, e.g., Who doesn’t have a yo-yo or a sponge ball? Children who assigned the conjunctive interpretation to disjunction, as in de Morgan’s laws, were expected to consistently point to the toy figures who had strawberries. One of the youngest children consistently responded in this way beginning on the very first trial, at age 2;3. The other two children consistently produced adult-like responses to wh-questions with negated disjunctions by age 2;10, showing that they too assigned

4.1 Negated disjunctions  169

Figure 4.1. A 2-year-old being interviewed

the conjunctive interpretation of disjunction by this age. In short, before these three children were 3-years-old, all of them consistently produced responses to wh-questions with negated disjunctions that indicated knowledge that disjunction is inclusive-or, which is the basis of de Morgan’s laws. Despite this finding, the transcripts of parental input reveal that children experience little evidence that disjunction is associated with the truth conditions corresponding to inclusive-or. The evidential base for inferring that disjunction is inclusive-or is thin at best.1 The majority of the input to children consists of positive statements. In most positive statements, the use of or does not conform to classical logic. Instead, the use of or triggers a pragmatic implicature such that or implies exclusivity (the not both reading) although it does not entail it. Consequently, the vast majority of children’s experience is consistent with the conclusion that disjunction is exclusive-or, and not inclusiveor (see Crain, Goro, and Thornton 2006). For example, a survey of the input to children (from CHILDES) clearly shows that the overwhelming majority of adult utterances with disjunction are either subject to a scalar implicature of exclusivity or express mutually exclusive alternatives (e.g., Was it a big yard or a small yard?). This means that the vast majority of the input is consistent

170  Scope parameters with exclusive-or, so if exclusive-or were an interpretive option in human languages, many children would presumably adopt it. The fact that all three of the 2-year-olds who participated in the experiment under discussion had reached the conclusion that disjunction is inclusive-or invites the inference that the logical meaning of disjunction emerges in children’s grammars without decisive evidence from experience. 4.1.2 Children’s knowledge of scope in negated disjunctions Next we will review some experiments with children who are roughly 4- to 5-years-old. There have been several previous experimental studies of Englishspeaking children at this age. These studies have focused mainly on how children interpret disjunction in the scope of negation or negative determiners (Chierchia et al. 2001; Gualmini, Crain and Meroni 2001; Gualmini and Crain 2002, 2005; Crain et al. 2002). These studies have revealed that 4- to 5-yearold English-speaking children are aware of the conjunctive entailment of disjunction in the scope of several negative expressions. A representative example is an experiment by Crain et al. (2002). This study used the truth-value judgment task, in what is called the prediction mode (Crain and Thornton 1998). First, we will describe the task, and then indicate why the prediction mode of the task was chosen for many experiments that involve disjunction. A truth-value judgment task usually involves two experimenters. One experimenter acts out stories with toy characters and props, and the other experimenter plays the role of a puppet. The puppet watches the stories alongside the child subject. One variant of the truth-value judgment task is called the prediction mode. In the middle of each story, events come to a momentary halt, to give the puppet a chance to make a prediction about what he thinks will happen when the story resumes. This prediction made by the puppet constitutes the test sentence. Following the puppet’s prediction, the story continues until the final outcome is revealed. Once the story has concluded, the puppet repeats the prediction made earlier. Since the prediction was about the final outcome of the story, the puppet’s prediction can now be assessed by the child subject. The child’s task is to decide whether or not the puppet predicted the correct final outcomes. If the child judges that the puppet did not make the right prediction, then the child is asked to tell the puppet what really happened at the end of the story. To motivate the studies that have adopted the prediction mode of the truthvalue judgment task, a historical note is in order. The truth-value judgment task was introduced in the mid 1980s. Ever since, it has been used successfully to assess children’s knowledge of a variety of linguistic structures. Most

4.1 Negated disjunctions  171 noteworthy, it was first used to assess children’s knowledge of Principle C of the binding theory (see, e.g., Crain and McKee 1985; Crain and Thornton 1998). In these studies, the task was used to investigate children’s interpretations of statements made by a puppet after the completion of stories that were acted out in front of the child subject and the puppet. This is now referred to as the description mode of the truth-value judgment task, since the puppet’s statements are descriptions of past events. The description mode of the truth-value judgment task is not optimal in assessing children’s understanding of statements that contain disjunction. Often, disjunctive statements are pragmatically odd when they are used to describe events that have already transpired. Suppose you and a friend witnessed Ted order sushi at lunch earlier in the day. Later, you overhear your friend tell someone, Ted ordered sushi or pasta for lunch. Although the statement is true, it is weaker than the corresponding statement without disjunction, Ted ordered sushi for lunch. If your friend knows that Ted ordered sushi, then it is pragmatically odd to use the weaker statement. The reasons for this, and evidence that people abhor Weakening, were presented in Chapter 1. Suppose you and your friend know that Ted ordered both sushi and pasta. What would you think if, later, you overheard your friend tell someone Ted ordered sushi or pasta for lunch? Because your friend’s statement is weaker than the alternative statement in which disjunction is replaced by conjunction, i.e., Ted ordered sushi and pasta, you would probably wonder why your friend was being deceptive. By comparison, consider a different scenario. Suppose you and a friend are taking Ted to lunch. Neither of you know what Ted will order for lunch, but you both know from past experience that Ted is likely to order sushi or pasta. Your friend makes a prediction: Ted will order sushi or pasta. Now, even if it turns out that Ted orders both sushi and pasta, your friend’s prediction will still be considered to be correct, and not deceptive. Your friend had no reason to think that Ted would order both dishes, but in making a prediction, this possibility was not ruled out. In short, disjunctive statements are felicitous in contexts in which the outcome is not known in advance. The prediction mode of the truth-value judgment task is one such context, so this variant of the task is often adopted in assessing children’s knowledge of statements that contain disjunction. Let us briefly describe the study by Crain et al. (2002), which used the prediction mode of the truth-value judgment task. Twenty-two English-speaking children (mean age 5;1) participated in the experiment. The test sentences were produced by a wizard puppet, Merlin the Magician. On one trial, children were

172  Scope parameters

Figure 4.2. The tooth fairy story

told a story about two girls who had each lost a tooth. The girls knew that the tooth fairy would come during the night to reward them, in exchange for their lost teeth. One girl decided to go to bed right away, but the other girl decided to stay up late to see what the tooth fairy looked like. Later the tooth fairy arrived, with two jewels and two dimes. Figure 4.2 shows the tooth fairy with these rewards. At this point, the story was interrupted so that Merlin could predict what would happen when the story resumed. One group of children (n =11) heard (3), in which negation precedes and c-commands the disjunction operator or, while the second group of children (n = 11) heard (4), in which negation precedes but does not c-command the disjunction operator.2 (3) (4)

The girl who stayed up late will not get a dime or a jewel. The girl who didn’t go to bed will get a dime or a jewel. 

¬(A ∨ B) A∨B

This experiment was designed to see if children use linear order as the basis of their interpretation of disjunction in negative sentences. If linear order is how children decide, then (3) and (4) should be interpreted in the same way by the different groups of children. The alternative is that children know that the conjunctive entailment of disjunction is generated only if negation ­c-commands disjunction. In sentence (3) negation c-commands disjunction.

4.1 Negated disjunctions  173

did The

not girl

get who

a dime or a jewel stayed up late

Figure 4.3. Negation c-command disjunction = the conjunctive entailment

got The

a dime or a jewel girl who didn’t go to bed

Figure 4.4. Negation does not c-command disjunction

This is graphically represented in Figure 4.3. In this case, disjunction generates a conjunctive entailment, so the sentence means that the girl who stayed up late will not get a dime and the girl who stayed up late will not get a jewel. In example (4), negation is embedded in a relative clause, … who didn’t go to bed, which modifies the subject NP the girl… Because negation doesn’t c-command disjunction, as depicted in Figure 4.4, the interpretation of disjunction is the same as if it were in a sentence without negation. So, disjunction in example (4) receives disjunctive truth conditions. Disjunction in (4) would be subject to a scalar implicature if the sentence had been presented in the description mode of the truth-value judgment task. But since the sentence is presented in the prediction mode of the task, the scalar implicature is canceled, so sentence (4) is expected to be judged to be true if the girl gets a dime, or a jewel, or both. If children know the c-command constraint on the interpretation of disjunction, the experimental hypothesis is the following. If it were to turn out that only one reward, a jewel or a dime, is presented to the girl who stayed up late, the puppet’s prediction about what would happen, i.e., (3), would have turned out to be wrong. However, the prediction about what would happen, as given in (4), would be the correct prediction. As events ensued, the tooth fairy gave a

174  Scope parameters dime and a jewel to the girl that had fallen asleep. But the tooth fairy was disappointed to see that the other girl was still awake. The little girl explained that she stayed up to see what the tooth fairy looked like. The tooth fairy decided to give this girl a jewel, but not a dime. Following the completion of the story, Merlin reminded the child of his prediction, using either sentence (5) or sentence (6). (5) (6)

I said that the girl who stayed up late would not get a dime or a jewel. I said that the girl who didn’t go to bed would get a dime or a jewel.

Because of their structural differences, sentences (5) and (6) generate different entailment patterns. Example (5) licenses the conjunctive interpretation of disjunction. Therefore, for this sentence to be true, it must be the case that the girl who is referred to in the sentence did not get a dime and it must also be true that she did not get a jewel. Children who generated a conjunctive entailment are, therefore, expected to reject the sentence, and to justify this negative decision by pointing out that the girl had been given a jewel. This response by children would be evidence that (5) entails the conjunctive interpretation of disjunction, from which it follows that the girl received neither a dime nor a jewel. This response by children is also evidence that children assigned the inclusive-or interpretation of the disjunction operator or, as in classical logic. Sentence (6) is an accurate description of the same context, because it does not license the conjunctive entailment of disjunction. The main findings were that the group of child subjects who were presented with sentences like (5) rejected them 92 percent of the time, but the other group who were presented with sentences like (6) accepted them 87 percent of the time. Thus, the findings indicate that children distinguish between the entailment patterns associated with the disjunction word or in the two sentences. The findings show that linear precedence does not suffice to establish a downward-entailing environment for the interpretation of disjunction. In order to induce the conjunctive entailment of disjunction, negation must c-command disjunction. 4.1.3 Children’s knowledge of proximity in negated disjunctions The study by Crain et al. (2002) was designed to find out if children know that disjunction generates a conjunctive entailment only if it is c-commanded by negation. The study presented pairs of sentences to children in which negation preceded disjunction. So, if children assign an interpretation of disjunction based on linear order, they should have assigned the same interpretation to both members of the pair. On the other hand, if children know that c-command is

4.1 Negated disjunctions  175 relevant to the interpretation of disjunction, then one member of the pair was expected to generate a conjunctive entailment, but not the other. This was the finding. There was a worry with the study, however. The worry was that the two test sentences differed in the number of words that intervened between negation and disjunction: the pairs of operators were closer to each other in (5) than in (6). If linear precedence is a domain-general cue that children pay attention to, it is possible that “distance” played a role in influencing children’s decisions. Perhaps when negation and disjunction are close to each other, the conjunctive entailment is generated, but not when these operators are further apart. To investigate the role of linear distance in child grammar, a follow-up experiment was conducted by Gualmini and Crain (2002). In one condition, children were presented with sentences in which negation c-commanded the disjunction operator or, but ones in which these two operators were further apart than they were in the sentences used in the earlier Crain et al. (2002) study, as illustrated in (7). In the second condition, negation preceded but did not c-command disjunction, as illustrated in (8). (7) (8)

Winnie the Pooh will not let Eeyore eat the cookie or the cake. Karate Man will give the Pooh Bear he cannot lift the honey or the donut.

Following the completion of each of the stories, Merlin reminded the child of his prediction, as in (9) and (10). At that point, children judged whether Merlin had made the correct prediction or not. (9) I said that Winnie the Pooh would not let Eeyore eat the cookie or the cake. (10) I said that Karate Man would give the Pooh Bear he cannot lift the honey or the donut.

Negation precedes and c-commands disjunction in sentences (7) and (9). Thus the preferred reading of the target sentence, for adults, is that Winnie the Pooh would not let Eeyore eat the cookie and he would not let Eeyore eat the cake. This interpretation made the sentence a false description of the story, because Winnie the Pooh did allow Eeyore to eat the cookie.3 In short, the conjunctive interpretation of disjunction is generated despite the number of words that intervened between negation and disjunction. If children’s interpretation was governed by structural relations between not and or, they should reject the target sentences, without regard to the distance between the two logical operators. The sentences in (8) and (10) were designed to determine whether children in the Crain et al. study refrained from assigning the conjunctive interpretation of disjunction due to the number of words that intervened between the two

176  Scope parameters operators. Notice that sentences (8) and (10) end with the string of words … he cannot lift the honey or the donut. If children compose linguistic material into local constructions, then they might be expected to assign the conjunctive interpretation to or in these sentences, as well as in sentences (7) and (9) (cf. Crain and Pietroski 2002, p.174). We discussed the reasoning behind this experiment in Chapter 1, based on the examples in (11) and (12). (11)

Plato was bald.

(12)

The most famous teacher of Plato was bald. a.  [the most famous teacher of ] [Plato was bald] b.  [the most famous teacher of Plato] [was bald]

(13)

Who was Socrates [the most famous teacher of]?

In (11), the predicate phrase was bald is being attributed to Plato. Therefore, this is a well-formed construction in English, and one that children experience with considerable regularity. But when the same sequence of words Plato was bald occurs in a sentence with a different syntactic structure, as in (12), the predicate phrase was bald pertains to a different individual, viz., the most famous teacher of Plato, Socrates. In short, Plato was bald is not a meaningful unit of information in (12). The grouping of words, Plato was bald, is simply an accidental occurrence of what is a meaningful unit of information in example (11). It could be argued that the words Plato + was + bald are unlikely to be grouped together in (12), because the remaining words, the most famous teacher of, do not form a unit that corresponds to anything in children’s experience. But this isn’t so, as shown in (13). In wh-questions such as (13), the displacement of the question word who yields just this sequence, the most famous teacher of. It is at least conceivable that children could form such sequences into constructions, as long as they experience many exemplars of ‘preposition stranding’ in questions. So, there are two constructions in (13), the well-formed question Who was Socrates, and the preposition-stranding phrase the most famous teacher of. Clearly, this is not how grammars work. Constructions are not combined by “cut and paste” operations. Rather, a hierarchical syntactic structure underlies both statements like (12) and questions like (13). As we saw in Chapter 1, grammars adhere to Frege’s Principle of Compositionality, such that semantic interpretation piggybacks on syntactic structure. The Principle of Compositionality: the meaning of the whole is a function of the meaning of its parts, and their mode of combination.

4.1 Negated disjunctions  177 The experiment under consideration was designed to see if children encode information using linear strings of words, as on the constructivist account, or if children assign hierarchical structure to sequences of words and, consequently, interpret disjunction in one way when it is c-commanded by negation, and in another way, when it is not. Supposing that children assign a structural representation to sentences, and that children adhere to the Principle of Compositionality, this will ensure that they assign a semantic interpretation in which negation does not c-command the disjunction operator in (10) such that … he cannot lift the honey or the donut does not form a meaningful unit of information. If so, then this will suffice to eliminate the conjunctive interpretation of disjunction in (10). In addition, notice that negation and disjunction are close to each other in (8) and (10), as compared to the test sentences used in the Crain et al. (2002)’s study. If proximity was a sufficient condition for the assignment of a conjunctive interpretation to disjunction, then children should assign the conjunctive interpretation to disjunction in (8) and (10). If so, then they should have rejected the test sentences, because the Karate Man had not given honey to the Pooh Bear that he could not lift. By contrast, if children take into account the structural relationship between the two operators, the absence of intervening words should be irrelevant to their interpretation of disjunction. If so, the conjunctive interpretation of disjunction will not be assigned, since negation fails to take scope over the disjunction operator, regardless of linear distance or the local well-formedness of the sequence of words.4 On this scenario, children are expected to accept the test sentences. Thirty children responded to sentences like (9). The child subjects rejected the target sentence on 51 out of 60 trials (85 percent). Thirty-five children participated in the experiment that used sentences like (10). These children accepted the target sentences on 56 out of 70 trials (80 percent).5 Thus, children did not assign the conjunctive interpretation to the disjunction operator or, despite the proximity between negation and disjunction, and despite the similarity of the local construction types to other linguistic expressions for which the conjunctive interpretation is imposed. This shows that proximity between these two operators is not relevant for children’s interpretation of disjunction; structure is what matters for children. The findings show that children, just as adults, do not assign scope using a structural independent notion such as linear precedence (see also Lidz and Musolino 2002). The findings are consistent with the view that children base their interpretation of sentences on abstract syntactic properties, and do not entertain the kind of shallow linguistic representations that figure prominently, for example, in the Conservative Learning

178  Scope parameters model proposed by Tomasello (2000). Finally, because no overt marking of these abstract properties is available in the primary linguistic data, children’s sensitivity to abstract properties such as c-command adds to the logical nativist’s arguments from the poverty of the stimulus. 4.2

Negation and disjunction/conjunction

The next series of experiments assessed children’s knowledge of the interpretation of disjunction and the interpretation of conjunction in simple negative sentences. Let us first discuss how adult speakers interpret negative statements with disjunction (English or, Mandarin huozhe) as well as negative statements with conjunction (English and, Mandarin he). One factor that renders the meanings of logical expressions opaque in human languages is the scope relations they may enter into in negative statements. In English, negation takes scope over disjunction in negative statements, but in Japanese and in Mandarin Chinese disjunction takes scope over negation. Similarly, negation takes scope over conjunction in negative English statements, but the reverse pattern is observed in Japanese and in Mandarin. It will pay to go through this slowly, with examples. Consider the English example (14) Ted didn’t order pasta or sushi. Here the disjunction word or generates a conjunctive entailment, so disjunction entails both of the following statements: Ted did not order pasta and Ted did not order sushi. In this respect, English conforms to one of de Morgan’s laws of propositional logic: ¬(A ∨ B) ⇒ ¬A ∧ ¬B. (14)

Ted didn’t order pasta or sushi.

Mandarin Chinese contrasts with English in the way that the disjunction word huozhe is interpreted in sentences with negation, meiyou. Example (15) is the Mandarin translation of (14). Adult speakers of Mandarin do not judge (15) to mean the same as (14) means in English. Rather, adult speakers of Mandarin judge (15) to mean that Ted didn’t order pasta or Ted didn’t order sushi. This is not the conjunctive interpretation assigned to (14) by English speakers. (15)

(Wo cai) Taide meiyou dian yidalimianshi huozhe shousi. (I guess) Ted not order pasta or sushi (我猜)泰德没有点意大利面食或者寿司。 ‘It’s either pasta or sushi that Ted did not order.’

The difference between English and Mandarin is one of scope. In the English example, Ted didn’t order pasta or sushi, English speakers interpret negation

4.3 A parametric account of scope  179 as taking scope over the disjunction word or. In the Mandarin example, the disjunction word huozhe is interpreted as taking scope over negation, meiyou. This is why the Mandarin example means that it is either pasta or sushi that Ted did not order. As in this paraphrase, disjunction has wider scope than negation in Mandarin. Languages also differ in the interpretation they assign to the words for conjunction. Consider the English example (15). A majority of English-speaking adults interpret (16) to be equivalent to the following disjunction of circumstances: Ted didn’t order pasta or Ted didn’t order sushi. On this reading, negation takes scope over conjunction. English conforms to another of de Morgan’s laws: ¬(A ∧ B) ⇒ ¬A ∨ ¬B. (16)

Ted didn’t order (both) pasta and sushi.

There are two ways to translate the English example (16) into Mandarin. One is a reasonably direct translation, as in (17), which mirrors the word order of English. Another translation of (16) is given in (18). Here, the quantificational adverb dou (meaning both or all) is used. The quantificational adverb dou takes scope over expressions to its left, so the conjunction word he in (18) precedes both dou and the negation word meiyou. (17)

Taide meiyou dian yidalimianshi he shousi. Ted not order pasta and sushi 泰德没有点意大利面食和寿司。 ‘As for both pasta and sushi, Ted did not order them.’

(18)

Taide yidalimianshi he shousi dou meiyou dian. Ted pasta and sushi both not order 泰德意大利面食和寿司都没有点。 ‘As for both pasta and sushi, Ted did not order them.’

Adult speakers of Mandarin interpret both statements in the same way, as meaning that Ted did not order either pasta or sushi. Abstracting away from word order differences, both negated conjunctions yield a conjunctive entailment: ¬(A ∧ B) ⇒ ¬A ∧ ¬B. This is the inverse scope interpretation of the negated conjunction in (17), since the conjunction word he must be ‘moved’ to take scope over negation. In (18), by contrast, the negated conjunction is assigned a surface scope interpretation, for adults. 4.3

A parametric account of scope

Why does negation in combination with words for disjunction and conjunction have different scope relations across languages? Pursuing a suggestion

180  Scope parameters by Szabolcsi (2002), and following a proposal by Goro (2004), this cross­linguistic variation in scope relations can be attributed to two parameters, which we will call the Disjunction Parameter and the Conjunction Parameter (also see Goro, Minai, and Crain 2005, 2006; Crain 2008; Crain, Goro, and Thornton 2006; Crain and Khlentzos 2008). 4.3.1 The Conjunction Parameter The parameter value with conjunction taking scope over negation is designated and = +PPI, and the value on which negation takes scope over conjunction is and = −PPI. English takes the −PPI value of the parameter, such that negated conjunctions like (19) generate a not both reading. In Mandarin and Japanese, disjunction is +PPI. Therefore, de Morgan’s laws fail to apply. Negative conjunctions like (20) and (21) are interpreted as meaning both not. The logical formula corresponding to (20) and (21) is ¬A ∧ ¬B. For ease of exposition, we repeat the relevant examples here. (19)

Ted didn’t order (both) pasta and sushi.

(20)

Taide meiyou dian yidalimianshi he shousi. Ted not order pasta and sushi 泰德没有点意大利面食和寿司。 ‘As for both pasta and sushi, Ted did not order them.’

(21)

Taide yidalimianshi he shousi dou meiyou dian Ted pasta and sushi both not order 泰德意大利面食和寿司都没有点。 ‘As for both pasta and sushi, Ted did not order them.’

The various aspects of the conjunction parameter are summarized in the schematic diagram in Figure 4.5. 4.3.2 The Disjunction Parameter The parameter value with disjunction taking scope over negation is designated or = +PPI, and the value on which negation takes scope over disjunction is or = −PPI.6 English takes the −PPI value of the Disjunction Parameter, such that negated disjunctions like (22) license a conjunctive entailment. In Mandarin and Japanese, disjunction is +PPI. Therefore, disjunction fails to generate a conjunctive entailment, as illustrated in (23). The logical formula corresponding to (23) is ¬A ∨ ¬B. (22)

Ted didn’t order pasta or sushi.

4.3 A parametric account of scope  181 Adult English ¬ (A ^ B) True = {A, ¬ B},{B, ¬ A} {¬A, ¬B}

Positive evidence: Superset value AND = –PPI

Mandarin & Child English ¬A ^ ¬B True = {¬A, ¬B} Initial setting: Subset value AND = +PPI

Figure 4.5. The Conjunction Parameter

(23)

(Wo cai) Ted meiyou dian yidalimianshi huozhe shousi. (I guess) Ted not order pasta or sushi (我猜)泰德没有点意大利面食或者寿司。 ‘It’s either pasta or sushi that Ted did not order.’

The various aspects of the Disjunction Parameter are summarized in the ­schematic diagram in Figure 4.6. The cross-linguistic differences in the scope relations between negation and conjunction and between negation and disjunction lead to significant predictions about the course of language development. The predictions were first made by Goro (2004) for the Disjunction Parameter. Goro began with the observation that the alternative values of the Disjunction Parameter stand in a subset/­ superset relation, with English and German exemplifying the subset value, and with Japanese and Mandarin exemplifying the superset value. This situation, Goro reasoned, would lead to a learnability dilemma for children acquiring languages like Japanese and Mandarin, unless children initially selected the parameter value that corresponds to English, or = −PPI. Adopting this value of the Disjunction Parameter would mean, for example, that Mandarin-speaking children would interpret the negated disjunction in (23) Ted meiyou dian yidalimianshi huozhe shousi in the same way as English-speaking children and adults interpret the negated disjunction in (22) Ted didn’t order pasta or sushi; that is, Mandarin-speaking children would assign the scope relations designated as not > or. This semantic interpretation is not attested in the input to children, because adult Mandarin speakers use the or = +PPI value of the parameter, hence they interpret negated disjunctions to have the opposite scope relations, or > not.

182  Scope parameters Adult Mandarin ¬A v ¬B True = {A, ¬B},{B,¬A} {¬A,¬B}

Positive evidence: Superset value AND = +PPI

English & Child Mandarin ¬(A v B) True = {¬A, ¬B} Initial setting: Subset value AND = –PPI

Figure 4.6. The Disjunction Parameter

4.4

The Semantic Subset Principle

Let us suppose that, across languages, children (and adults) have access to both readings of sentences that contain two logical operators, such as sentences with negation and disjunction, and ones with negation and conjunction. Since these are scope phenomena, it seems likely that both readings are available. To avoid subset problems, however, the language acquisition device (LAD) imposes an initial preference for the strongest reading, not > or for negated disjunctions, and both > not for negated conjunctions. Also note that these preferences are upheld only if negation is in the same clause as the other logical operator. If negation is in a higher clause than the one with disjunction or with conjunction, then there is no ambiguity: negation always has scope over the other logical expression, yielding the not > or reading and the not > both reading across languages. The LAD guides children by incorporating the Semantic Subset Principle (SSP) (Crain, Ni, and Conway 1994). The SSP enforces an ordering on the values of certain parameters, where one value makes a sentence true in a subset of the circumstances that make it true on the other value. To avoid learnability problems that would otherwise arise, the SSP compels children to adopt the subset value of the parameter as their initial interpretation; this value is abandoned only on the basis of positive evidence in the local language. In simple sentences with negation and disjunction, a parameter governs the scope relations between these two expressions. The SSP establishes the default preference, according to which negation has scope over disjunction. English retains the default setting, whereas speakers of Japanese and Chinese adopt

4.4 The Semantic Subset Principle  183 the ­alternative setting of the parameter, with disjunction having scope over negation; this makes it look as if these languages violate de Morgan’s law in simple negative sentences (see Goro 2004, for a complete analysis). Children’s initial preferences yield the preferred adult interpretations for negation disjunctions in English (not > or), and for negation conjunctions in Mandarin (both > not). Conversely, children’s preference for the not > or reading of negated disjunctions is the dispreferred scope assignment in Mandarin, and children’s preference for the both > not reading of negated conjunctions is the dispreferred scope assignment in English. These observations led us to the predictions that (a) Mandarin-speaking children would initially prefer the reading favored by English speakers, not > or, but not attested in Mandarin, and that (b) English-speaking children would initially prefer the reading favored by Mandarin speakers, but not attested in English. These predictions have been confirmed. So much the worse for experiencebased accounts. Another question to answer is how children converge on the final state. Is there positive evidence that will suffice to compel children to override their default assumption about the scope relations between negation and conjunction/­ disjunction? Because children start with the subset language, this ensures that there will be such positive evidence. The positive evidence for Mandarinspeaking children will be sentence/meaning pairs exhibiting the preference by Mandarin speakers for disjunction to take scope over negation. Because disjunction takes scope over negation, these sentences will typically engage a scalar implicature. So, negated disjunctions are used by Mandarin speakers primarily in circumstances in which only one disjunct is false, not both. So in Mandarin Peng didn’t order sushi or pasta means that it is either sushi or pasta (but not both) that Peng didn’t order. For children, both disjuncts must be false, not > or. So, the truth conditions assigned to negated disjunctions by adults are inconsistent with the truth conditions that correspond to children’s initial preference. Assuming that preferences take time to reverse, a number of negated disjunctions are needed before children are able to reverse their initial preference. A similar learning scenario can be given for negated conjunctions. In this case, English-speaking children initially prefer the scope assignment that corresponds to Mandarin, but adult input should suffice to reverse this preference. The requisite input for children involves either marked stress, as in Peng didn’t order sushi and pasta, or the presence of both, as in Peng didn’t order both sushi and pasta. Adult English speakers use both kinds of statements to convey the not > both (in fact, only one) reading, so they use it in circumstances that are inconsistent with children’s initial preference for the both > not scopal interpretation.

184  Scope parameters There is controversy surrounding the empirical adequacy of the Semantic Subset Principle. We think the controversy misses the mark. As pointed out by Williams (1983), one might just as well talk about the Semantic Subset Problem. If parameter values are in a subset/superset relation, then it would be problematic for children to initially favor the value that generates the superset language. If they did, then it is not clear how children would retreat to the subset value, if that is the value favored by adult speakers of the local language. On the other hand, if children initially favor the subset value, no problem arises, since there will be positive evidence informing them that the subset value is not favored by adult speakers. If the Semantic Subset Principle is not operative, then another mechanism, or another source of information, must replace it. So, in cases where the Semantic Subset Principle does not seem to hold, children are confronted with a subset problem. In the absence of plausible alternatives to the Semantic Subset Principle, we think it is reasonable to assume that it is descriptively adequate, with considerable predictive power. This is not to say that invoking the principle explains how it operates in children’s minds. There are various ways it might be instantiated, but we will not be concerned with deciding among them as part of these deliberations (see Gualmini and Schwarz 2009). 4.5

Child language

To summarize the experimental hypotheses, Japanese- and Mandarin-speaking children are expected to initially interpret negated disjunctions using the scope assignment licensed in English, and English-speaking children are expected to initially interpret negated conjunctions using the scope assignment licensed in Japanese and Mandarin. Both of these predictions have been confirmed. 4.5.1 Negated disjunctions in child Japanese The initial study in this line of research was conducted by Goro and Akiba (2004a, 2004b), with Japanese-speaking children. These researchers investigated children’s interpretation of negated disjunctions like (24). For adult speakers, (24) means that the pig didn’t eat the carrot or the pig didn’t eat the pepper. Despite the disjunction word ka appearing within the scope of negation, nakat, in the surface syntax, ka is interpreted by adults as having scope over negation. (24)

Butasan-wa ninjin ka pi’iman-wo tabe-nakat-ta. pig-top pepper or carrot-acc eat-neg-past ‘It’s the carrot or the pepper that the pig didn’t eat.’

4.5 Child language  185

Figure 4.7. Experimental design

Based on the reasoning behind the formulation of the Semantic Subset Principle, children acquiring languages like Japanese and Mandarin were expected to differ from adult speakers, and initially select the parameter value that corresponds to English, or = −PPI. Adopting this value of the Disjunction Parameter would mean, for example, that Japanese-speaking children would interpret the negated disjunction in (24) in the same way as English-speaking children and adults interpret the negated disjunction in the English counterpart to (24) i.e., The pig didn’t eat the carrot or the pepper; that is, children were expected to assign the scope relations designated as not > or. Thirty 3- to 6-year-old children’s understanding of sentences like (24) was assessed in the Goro and Akiba study, using a version of the truth-value judgment task. The children ranged in age from 3;7 to 6;3, with an average age of 5;3. The task had two experimenters. One acted out short vignettes in front of the child, and the other played a puppet, Kermit the Frog, who watched the vignettes along with the child subject. The vignettes were about twelve different animals. The children were told that animals love cake, so every animal was expected to eat cake on every trial. Cake was mentioned simply to have a positive lead-in statement, preceding the negative target sentence. Each animal was asked, in turn, if it was happy to eat two vegetables, a carrot and a green pepper. There was a reward system administered by the child.

186  Scope parameters First, if an animal ate both of the vegetables, the child was instructed to give it a gold medal. If an animal ate only one of the vegetables, then it received a blue medal. Finally, if an animal was not willing to eat either vegetable, then it received a black cross (a symbol of failure in Japanese culture). The vignettes continued until all twelve animals were presented with their rewards. Then the puppet proceeded to guess, based on the reward the animal had received, what each of the animals had eaten. The puppet considered each animal in turn, starting from the first one, and the vegetables had been removed from the experimental workspace. This feature of experimental design was implemented to make if felicitous for the puppet to produce statements with disjunction, such as (24). If the vegetables had been present, then a statement without disjunction would have been more felicitous, since it would have been clear which of the vegetables the animal had eaten. Consequently, a simpler statement that mentioned only the vegetable the animal had eaten would have been pragmatically warranted, for adult Japanese speakers. The crucial test cases were the puppet’s statements about the animals that had been given blue medals, that is, the ones who ate only one of the vegetables.7 A blue medal was awarded to animals that had eaten just one of the vegetables, but it was no longer obvious which of the two vegetables the animals had eaten. Therefore, it was reasonable for the puppet to use a disjunctive statement (e.g., The pig didn’t eat the pepper or the carrot) which is an accurate description of the situation, in Japanese, though not in English. As expected, the control group of Japanese-speaking adults accepted the test sentences 100 percent of the time. By contrast, children rejected them 75 percent of the time. The findings are even more compelling once the data from four children, who responded like adults, were set aside. The remaining twenty-six children rejected the target sentences 87 percent of the time. The negative judgments of the vast majority of children, combined with children’s explanations of these judgments, suggest that Japanese-speaking children are assigning the conjunctive interpretation to ka in simple negative sentences. That is, with respect to the interpretation of negated disjunctions, Japanesespeaking children are more like English-speaking children and adults than like Japanese-speaking adults. 4.5.2 Negated disjunctions in child Mandarin Based on the findings of Goro and Akiba (2004a, 2004b), and the observation that the Mandarin Chinese disjunction word huozhe is a positive polarity item, further evidence for the Disjunction Parameter was pursued. According to the SSP, children acquiring Mandarin should initially interpret the disjunction

4.5 Child language  187

Figure 4.8. The blue ribbon test of negated disjunctions

operator huozhe in conformity with de Morgan’s laws in simple negated ­sentences, despite the absence of this interpretation for Mandarin-speaking adults. This was tested by Jing, Crain, and Hsu (2005) in a study with twentyone 4- to 5-year-old Mandarin-speaking children who ranged in age from 4;4 to 5;3, with an average age of 4;10. These child subjects exhibited the same linguistic behavior as children acquiring Japanese. It is worth pointing out that Chinese and Japanese differ in word order. In Japanese, the word for disjunction, ka, comes before negation, nakat, as in (25). In Chinese, the word for negation, meiyou, comes before the word for disjunction, huozhe, as in (26). (25)

Butasan-wa pig-top

(26)

Tanglaoya meiyou Donald Duck not-past

ninjin pepper

ka or

pi’iman-wo tabe-nakat-ta carrot-acc eat-neg-past

ju-qi zhuozi lift-up table

huozhe dianshiji or TV

We have seen that adult speakers of both Chinese and Japanese interpret ­disjunction as having scope over negation (or > not). Since the ordering of disjunction and negation is reversed across these languages, it follows that the or > not interpretation, which adults assign in both languages, cannot be based on linear order. We also saw that children acquiring both Chinese and Japanese

188  Scope parameters initially adopted the opposite scope relations (not > or), with negation taking scope over disjunction. It follows that children were not assigning this interpretation based on linear order, since the ordering of negation and disjunction differs across these languages. In short, no principle of isomorphism could explain either the adult interpretation or children’s interpretation, across languages. For now, we will tentatively suppose that the Semantic Subset Principle is responsible. 4.6

Negated conjunctions

Turning to negated conjunctions, the logical nativist account predicts that English-speaking children initially select the value of the Conjunction Parameter which corresponds to Japanese and Mandarin, and = +PPI. Adopting this value of the parameter would mean, for example, that English-speaking children would interpret the negated conjunction in (27) as entailing that the pig failed to eat the carrot and failed to eat the pepper. This both not reading is not attested in the input to children, because adult English speakers use the and = −PPI value of the Conjunction Parameter, hence they interpret negated conjunctions to have the opposite scope relations, not > and. (27)

The pig didn’t eat both the pepper and the carrot. Context: The pig has a blue medal.

As with negated disjunctions, the crucial test cases were the puppet’s statements about the animals that had been given blue medals, that is, the ones who ate only one of the vegetables. A blue medal was awarded to animals that had eaten just one of the vegetables, but it was no longer obvious which of the two vegetables the animals had eaten. Therefore, (27) is an accurate description of the situation for adult speakers of English, but not for (either child or adult) speakers of Japanese and Mandarin. The experimental hypothesis was that children acquiring English would favor the both not interpretation favored by Japanese and Mandarin speakers, ignoring the evidence from adult speakers of the local language, English. Figure 4.9 shows Kermit about to produce a target sentence that contained a negated conjunction. To test the prediction, we assessed twenty-one 3- to 5-year-old Englishspeaking children’s understanding of sentences like (27), using the same task as in the Goro and Akiba study. The children ranged in age from 3;10 to 5;6, with an average age of 4;9. On one of the critical trials, the child subjects were asked to judge whether or not the negated conjunction in (27) was an accurate description of the circumstance, as in the Goro and Akiba (2004a, 2004b) studies, in which

4.6 Negated conjunctions  189

Figure 4.9. The blue ribbon test was used again for negated conjunctions

the pig had eaten the carrot but not the green pepper. Whereas a control group of English-speaking adults consistently accepted the target sentence in this circumstance, children resoundingly rejected it (98 percent), justifying their negative judgments on the grounds that the pig had eaten one of the foods. Mandarinspeaking children and adults have also been tested and, as expected, both groups consistently produced the same responses as English-speaking children. It should be noted that Mandarin uses two structures to express negated ­conjunctions. In one, the conjunction word he precedes negation (due to the presence of dou, which can only bind constituents to its left). This is illustrated in (28). Without dou, negation is permitted to precede conjunction, as in (29). In assessing Mandarin-speaking children, we found no difference in their interpretation of negated conjunctions. Regardless of the order in which negation and conjunction appeared, children (and adults) consistently assigned the same both not interpretation. This reinforces the conclusion that children base their interpretation of logical expressions on syntactic form, and do not use strategies based on linear order. (28)

Tanglaoya zhuozi he dianshiji dou meiyou ju-qi.  both > not Donald Duck table and TV both not-past lift-up 唐老鸭桌子和电视机都没有举起。 ‘Donald Duck did not lift up both the table and the TV.’

190  Scope parameters (29)

Tanglaoya meiyou ju-qi zhuozi he dianshiji. Donald Duck not-past lift-up table and TV 唐老鸭没有举起桌子和电视机。 ‘Donald Duck did not lift up the table and the TV.’

both > not

Across languages, children are expected to initially favor parameter values that generate scope relations that make sentences true in the narrowest range of circumstances. This ensures that children will have access to positive evidence if the local language favors alternative scope relations, which make sentences true in a broader range of circumstances. The findings are that children and adults differ exactly in ways in which adult languages differ, both for negated conjunctions and for negated disjunction. First, the interpretation of negated conjunctions assigned by English-speaking children is the same as that assigned by Mandarin-speaking children and adults, although it differs from the interpretation assigned by adult English speakers. Second, the interpretation of negated disjunctions assigned by Mandarin-speaking children is the same as that assigned by English-speaking children and adults, although it differs from the interpretation assigned by adult Mandarin speakers. These findings are in keeping with the Continuity Hypothesis. Finally, the observed differences between children and adults are difficult to explain on models that appeal to linguistic experience as the basis of children’s linguistic competence. There is another relevant observation for logical nativism. Although children and adults differ – child and adult Mandarin differ, and child and adult English differ – the initial assignments of meanings by children do not differ across languages. In interpreting negated disjunctions, both children acquiring Mandarin and ones acquiring English initially favor the not > or value of the parameter. And, in interpreting negated conjunctions, children acquiring both languages initially favor the both > not value. The interpretations assigned by children are evidence that children acquiring both English and Mandarin favor the subset value of the relevant parameters. These findings illustrate how cross-linguistic differences provide a unique testing ground for the alternative theories of language acquisition. The observed patterns of children’s non-adult semantic interpretations are consistent with the logical nativist account, but they are quite unexpected on the experience-based account. 4.7

Disjunction and the preposition before

The conjunctive interpretation of disjunction is generated in sentences with before, as in (30).

4.7 Disjunction and the preposition before  191 (30)

Jane arrived at the pool before Mary or Sue. ⇒ Jane arrived at the pool before Mary and Jane arrived at the pool before Sue.

This interpretation arises for reasons similar to the ones just outlined for the universal quantifier. This is because the temporal concept before introduces a covert universal quantifier which quantifies over the points-in-time that make up events (Anscombe 1964; Heinamaki 1972). That is, if an event A occurs before an event B, then at least one point-in-time in event A must have taken place before every point-in-time in event B. The covert universal quantifier in the semantics of before is the source of the conjunctive interpretation of disjunction. In example (30), event A is expressed in the main clause Jane arrived at the pool. Event B is expressed in the before clause which can be paraphrased as Mary arrived at the pool or Sue arrived at the pool. Since event B is a disjunction of events, event B contains two subevents, one denoting Mary’s arrival and the other denoting Sue’s arrival. For (30) to be true, some point-in-time in event A must have preceded every point-in-time in both of the subevents that comprise event B. So, Jane’s arrival must have preceded every point-in-time in the subevent of Mary’s arrival, and Jane’s arrival must have preceded every point-in-time in the subevent of Sue’s arrival. This is why the temporal conjunction before licenses the conjunctive entailment of disjunction. The meaning of before differs from that of its conceptual twin after. For an event A to occur after an event B, then all that is required is for at least one point-in-time in event A to follow at least one point-in-time in event B (Anscombe 1964). There is no covert universal quantifier. This means that when event B contains a disjunction of subevents, then at least one point-intime in event A has to follow at least one point-in-time in either of the subevents. Consider the sentence Jane arrived at the pool after Mary or Sue. Event A is Jane’s arrival, and event B is a disjunction of subevents, Mary’s arrival and Sue’s arrival. The sentence is true if there is a point-in-time in event A, Jane’s arrival, that follows one of these subevents, or a point-in-time in event A that follows them both. So, the sentence is true if Jane arrived after Mary (but not after Sue), or if Jane arrived after Sue (but not after Mary), or if Jane arrived after both Mary and Sue. Hence the temporal conjunction after does not license the conjunctive entailment of disjunction. 4.7.1 Scope ambiguity A potential scope ambiguity arises when disjunction resides in a clause that is headed by the English preposition before, or in its counterpart in Mandarin, zai…zhiqian. The English preposition before is downward entailing. To see this, notice that the English disjunction word or generates a

192  Scope parameters conjunctive interpretation in a clause headed by before. This is illustrated in (31). Example (31) is true only if the dog finished before the turtle and before the bunny. Example (32) shows that the English preposition after is not downward entailing. Example (32) is true if the dog finished before the turtle or before the bunny. So, the examples (31) and (32) comprise another asymmetric minimal pair of downward-entailing and non-downward-entailing linguistic contexts. (31) (32)

The dog reached the finish line before the turtle or the bunny. The dog reached the finish line after the turtle or the bunny.

In English, disjunction is interpreted in the scope of before in sentences such as (31). Therefore, disjunction generates a conjunctive entailment, in keeping with the generalization that began the chapter: disjunction generates a conjunctive entailment when it appears in the scope of any downward-entailing expression Δ, as depicted below. ∆ ( A ∨ B) ⇒ ∆ (A ) ∧ ∆ (B)

The conjunctive entailment means that at least one point-in-time in the event mentioned in the main clause must precede every point-in-time in both events mentioned in the clause with before. A few remarks are in order about the Mandarin counterpart to English before, which is zai…zhiqian. The first observation is that zai…zhiqian validates inferences from general (set-referring) terms (linguists from MIT) to specific (subset referring) terms (Chomsky). So, if the statement in (33) is true, then so is the statement in (34). (33)

Wo tongchang zai laizi MIT de yuyanxuejia zhiqian daoda I usually at from MIT de linguists before arrive jianshenfang. gym 我通常在来自麻省理工大学的语言学家之前到达健身房。 ‘I usually arrive at the gym before the linguists from MIT.’

(34)

Wo tongchang zai Qiaomusiji zhiqian daoda jianshenfang. I usually at Chomsky before arrive gym 我通常在乔姆斯基之前到达健身房。 ‘I usually arrive at the gym before Chomsky.’

The second observation is that zai…zhiqian licenses the Mandarin negative polarity item renhe, at least for many speakers. Example (35) was judged to be acceptable by about half of the native speakers of Mandarin we interviewed.

4.7 Disjunction and the preposition before  193 (35)

Wo tongchang zai renhe qita yuyanxuejia zhiqian daoda jianshenfang. I usually at any other linguists before arrive gym 我通常在任何其他语言学家之前到达健身房。 ‘I usually arrive at the gym before any other linguists.’

This brings us to the interpretation of disjunction huozhe in sentences with zai… zhiqian. We saw that disjunction is a positive polarity item in some languages (see section 4.3.2), including in Mandarin. Because disjunction is a positive polarity item in these languages, it takes scope over negation, and fails to generate a conjunctive entailment in negated disjunctions. But, as noted in the introduction, we are seeking generalizations that extend to other downward-entailing operators, not just ones that are limited to negation. It is worth asking in this regard if cross-linguistic variation is also witnessed in sentences that contain before and disjunction. In languages in which disjunction is a positive polarity item, disjunction could take scope over the word that expresses the concept before. So, the truth conditions associated with disjunction in sentences with the word for before in these languages should be different than they are in the corresponding English sentences, because disjunction is −PPI in English. To illustrate, consider the Mandarin example in (36), where disjunction (huozhe) can take scope over zai…zhiqian ‘before.’ Based on judgments solicited from several adult native speakers, we have discovered that there is considerable uncertainty about the downward-entailing status of Mandarin zai… zhiqian. If disjunction takes scope over zai…zhiqian, then at least one pointin-time in the event mentioned in the main clause must precede every pointin-time in at least one of the subevents mentioned in the clause headed by before. The Mandarin-speaking adults we have interviewed do not uniformly access this interpretation of (36). Some adult Mandarin speakers we interviewed judge (36) to have the same meaning as the English sentence in (37). In other words, they generated a conjunctive interpretation of disjunction in sentences with zai…zhiqian, such that (36) is true only if the dog reached the finish line before the turtle and before the bunny. (36)

Xiaogou zai wugui huozhe tuzi zhiqian paodao-le zhongdian. dog at turtle or rabbit before reach-asp finish-line 小狗在乌龟或者兔子之前跑到了终点。 ‘The dog reached the finish line before the turtle or the bunny.’

(37)

The dog reached the finish line before the turtle or the bunny.

Figure 4.10 illustrates one of the circumstances in which these adult speakers judge (36) to be true. The other circumstance that makes (36) true just has the rabbit and the turtle exchanging places in the rankings.

194  Scope parameters

Figure 4.10. Truth conditions: before takes scope over disjunction

Many of the Mandarin-speaking adults we interviewed judged (36) to be true in a broader range of circumstances than the one depicted in Figure 4.10. According to these Mandarin speakers, (36) is true in three circumstances, where the dog reached the finish line either (i) before the turtle, but not before the bunny, or (ii) before the bunny, but not before the turtle, or (iii) before both the turtle and the bunny. Figure 4.11 illustrates one of the circumstances in which adult speakers judge (36) to be true. This freedom of interpretation by these Mandarin-speaking adults, as compared to English speakers and other Mandarin speakers, led us to conduct an experiment with both children and adults, in both English and Mandarin. 4.7.2 Before and the Semantic Subset Principle The cross-linguistic differences between English and Mandarin mirror the different scope relations between negation and disjunction. Due to scope ambiguities, languages can differ in the interpretation of disjunction in sentences with (at least) two different downward-entailing expressions, negation and before. Cross-linguistic differences like these provide a testing ground for the alternative theories of language acquisition. It is clear from our earlier

4.7 Disjunction and the preposition before  195

Figure 4.11. Truth conditions: disjunction takes scope over before

discussion that the before > or reading is true in a subset of circumstances corresponding to the or > before reading. Following Goro (2004), we adopted the Semantic Subset Principle as a guide in making empirical predictions. This principle led us to predict that, regardless of the interpretation assigned by adult speakers, Mandarin-speaking children would initially favor the parameter value according to which disjunction is −PPI, as in English. If so, then, Mandarin-speaking children are expected to interpret zai…zhiqian as taking scope over disjunction, just as before does in English. So, the experimental hypothesis was that Mandarin-speaking children would initially analyze zai…zhiqian as having scope over the disjunction word huozhe, since this generates the truth conditions associated with the subset reading of the Disjunction Parameter in Mandarin. Our interest is in seeing whether Mandarin-speaking children differ from adults in their interpretation of disjunction in sentences with before, as they did in interpreting disjunction in simple negative sentences. If children’s interpretations are based on input from adults, then children acquiring both English and Mandarin would be expected to interpret disjunction in the same way as adults do in these languages; English-speaking children would be expected to assign

196  Scope parameters the conjunctive interpretation to disjunction, but Mandarin-speaking children would be expected to assign disjunction a ‘disjunctive’ interpretation. However, if children are guided by the Semantic Subset Principle, then only children learning English would be expected to pattern like adults, assigning the conjunctive interpretation to disjunction in simple sentences with before. Children acquiring Mandarin, by contrast, would be expected to differ from adults in the interpretation they assign to disjunction in simple sentences with before. Mandarin-speaking children would be expected to entertain the same semantic hypotheses as English-speaking children, but to differ from adult Mandarin speakers in their interpretation of disjunction in sentences with before. 4.8

Before and child language

The experimental hypothesis is that Mandarin-speaking children will side with English-speaking children and adults, but not with Mandarin-speaking adults. To test this prediction, Notley, Zhou, Jensen, and Crain (2012) designed an experiment to investigate the interpretations of sentences with zai…­zhiqian and the disjunction operator huozhe, by both child and adult speakers of Mandarin. As controls, the same experiment was conducted on both child and adult speakers of English. As far as possible, the contexts for both Mandarin and English were the same. On a typical trial, there was a running race between three animals, a dog, a turtle, and a bunny. In the end, the bunny came in first, the dog came in second, and the turtle finished last – the conclusion of the scenario depicted in Figure 4.11 above. When the story concluded, the puppet being manipulated by one of the experimenters produced either test sentence (38) or (39). (38)

The dog reached the finish line before the turtle or the bunny. Xiaogou zai wugui huozhe xiaotuzi zhiqian paodao-le zhongdian. dog at turtle or rabbit before reach-asp finish-line 小狗在乌龟或者兔子之前跑到了终点。 ‘The dog reached the finish line before the turtle or the bunny.’

(39)

The bunny reached the finish line before the turtle or the dog. Xiaotuzi zai wugui huozhe xiaogou zhiqian paodao-le zhongdian. rabbit at turtle or dog before reach-asp finish-line 小兔子在乌龟或者小狗之前跑到了终点。 ‘The bunny reached the finish line before the turtle or the dog.’

The child’s task was to decide whether the puppet’s statement was an accurate description of the story: “was the puppet right or wrong?” The basic idea is

4.8 Before and child language  197 that if Mandarin-speaking children initially hypothesize that zai…zhiqian has scope over the disjunction word huozhe, then they should interpret sentences like Xiaogou zai wugui huozhe xiaotuzi zhiqian paodao-le zhongdian (‘The dog reached the finish line before the turtle or the bunny’) as having the meaning that ‘the dog reached the finish line before the turtle and the dog reached the finish line before the bunny.’ In this case, they should be expected to reject test sentences like (38) in the given scenario, because the dog came after the bunny. And they should be expected to accept sentences like those in (39), because it is true that the bunny reached the finish line before the turtle and the dog. We tested twenty Mandarin-speaking children, ranging in age from 4;6 to 5;4, with a mean age of 4;7. In addition, we tested twenty-four English-speaking children ranging in age from 3;4 to 5;1, with a mean age of 4;4. We also tested twenty Mandarin-speaking adults and twenty English-speaking adults, as controls. Here are the main findings. In response to test sentences like those in (38), Mandarin-speaking adults accepted them 25 percent of the time, whereas Mandarin-speaking children rejected them 100 percent of the time. In the given scenario, children justified their rejection by pointing out that the bunny reached the finish line first. This kind of response pattern was also obtained from English-speaking children and adults. The English-speaking children rejected the test sentences 88 percent of the time, and English-speaking adults rejected them 98 percent of the time. In response to test sentences like those in (39), the rate of rejection by Mandarin-speaking adults was 40 percent. They consistently justified these rejections by pointing out that the sentences would be better with he, rather than huozhe. Presumably for these adult speakers, disjunction huozhe scopes over zai…zhiqian in the relevant sentences, thereby licensing a scalar implicature. That is, although both or and and are truth-conditionally true, and is pragmatically more felicitous than or, because and is more informative than or in the relevant situations. By contrast, Mandarin-speaking children accepted the test sentences 100 percent of the time. Similar response patterns were obtained from English-speaking children and adults. Both English-speaking children and adults accepted the test sentences to a high degree (91 percent for children, and 100 percent for adults). The results of this experiment show that Mandarin-speaking children behave more like English-speaking children and adults than like Mandarin-speaking adults. This is evidence that Mandarin-speaking children are guided by the Semantic Subset Principle in acquiring the meaning of disjunction. That is, children initially analyze zai…zhiqian as having scope over disjunction huozhe, because this generates the truth conditions associated with the subset

198  Scope parameters reading of the Disjunction Parameter in Mandarin. These findings also provide evidence against an experience-based account of language development, since Mandarin-speaking children are clearly not using adult input as the basis for their interpretation of disjunction huozhe. To wrap up, the parallels between human languages and classical first-order logic run much deeper than one of de Morgan’s laws, according to which disjunction generates a conjunctive entailment when it appears in the scope of negation: ¬(A ∨ B) ⇒ ¬A ∧ ¬B. The conjunctive interpretation extends to any downward-entailing expression. The parallels between the truth conditions associated with expressions of classical logic and those associated with the corresponding expressions in human languages have not been spelled out in detail until recently. Neither have the truth conditions of the logical expressions of human languages been thoroughly investigated in child language until recently. As we have seen in this chapter, from the early stages of language development, and across languages, children adopt a semantics for certain logical expressions that parallels the semantics of the corresponding expressions in logic. They adopt these meanings without decisive evidence in their favor in the input, and sometimes with considerable evidence against them, and in favor of alternative meanings that are never even considered by children. This constitutes a compelling case for the existence of an innate logic faculty, as proposed by logical nativism.

5 How something can be both positive and negative

English and Mandarin Chinese are typologically distinct languages, yet they share several core linguistic properties. These core properties govern the assignment of interpretations to logical expressions, individually and in combination. For example, both English and Mandarin have downward-entailing expressions. Downward-entailing expressions are important in teasing apart the alternative accounts of language acquisition, because such expressions tie together clusters of linguistic properties, including fixing the interpretation of disjunction. Both English and Mandarin possess logical expressions that are similar in meaning to the corresponding expressions in logic, including the inclusive-or interpretation of disjunction, to cite just one example. The inclusive-or interpretation of disjunction serves as the basic meaning of disjunction in classical logic and forms the basis for the logical entailments in de Morgan’s laws. The previous chapter reviewed several experimental investigations of children’s knowledge of the syntactic and semantic constraints on the interpretation of disjunction words (English or and Mandarin huozhe). The findings from these investigations demonstrated that, in responding to sentences with disjunction, children acquiring English and Mandarin (and Japanese) initially assigned interpretations that coincide with the laws of logic. If downward entailment is an innate property of human languages, then we would expect downward-entailing expressions to also manifest another of its characteristic properties, both within and across languages, namely the licensing of negative polarity expressions such as any, ever, and at all, and their counterparts in other languages. Although the licensing of negative polarity items and the conjunctive entailment of disjunction appear to be unrelated, we observed in Chapter 1 that these linguistic phenomena are really variations on a theme, which explains why they are both associated with the class of downward-entailing expressions. The prediction that these expressions form a natural class in human languages has been confirmed, both within and across languages. In the present chapter, we report the 199

200  How something can be both positive and negative findings of experimental investigations of children’s competence in producing and understanding polarity-sensitive items. As noted, polarity-sensitive items can be partitioned into negative polarity items, such as English any, and positive polarity items, such as English some. We review what we have found out from experimental investigations of the acquisition of both kinds of polarity-sensitive items. We begin with a brief discussion of their linguistic behavior in adult languages. 5.1

Polarity-sensitive items

In English, the negative polarity expression any and the indefinite article some are semantic twins. Like twins in a human family, these expressions can sometimes appear to be quite unrelated, but at other times are hard to tell apart. Both any and some are indefinite existential expressions, with a meaning that corresponds, in large part, to the existential quantifier in first-order logic (i.e., ∃). Despite being similar in meaning, any and some are generally tolerated in different linguistic contexts. Negative polarity items like any (and its ilk – ever, at all) are restricted to downward-entailing linguistic contexts. By contrast, the existential indefinite some is accepted in upward-entailing contexts, and although it can appear in the surface scope position under negation, it must be interpreted as taking scope over negation at the level of semantic interpretation (i.e., Logical Form). In short, some is a positive polarity item, and any is a negative polarity item. That said, any and some overlap both in distribution and interpretation in certain linguistic contexts. One linguistic context in which some and any are assigned similar interpretations is when negation appears in a higher clause than the clause that contains the indefinite expression (some or any). This is illustrated in (1). Notice that the italicized embedded sentence in (1) may contain either of the sentences (1a) or (1b), without a noticeable change in meaning. That is, the logical forms for (1), both with some and with any, are the same, with both some and any in the scope of negation. The difference in meaning between some and any re-emerges, however, once the statements are taken out of this linguistic context. So when the simple negative statements themselves are extracted from (1), as in (1a) and (1b), they have different logical forms. Sentence (1a) implies (but does not entail) that Julia touched some of the kangaroos. (1)

You’ll never convince me that Julia didn’t touch some/any of the kangaroos. a. Julia didn’t touch some of the kangaroos ∃ > not b. Julia didn’t touch any of the kangaroos not > ∃

5.1 Polarity-sensitive items  201 Another linguistic context in which both some and any may appear, with the same interpretation, is in the antecedent of conditionals. This is illustrated in (2). (2)

If Julia touches some/any of the kangaroos, Max will touch a crocodile.

From the perspective of first-order logic, it is no accident that some and any are interpreted in much the same way in the antecedent of a conditional. Essentially, an occurrence of some/any within the antecedent of a conditional is within the scope of a negation operator, from the standpoint of first-order logic. The reason is that A → B is logically equivalent to ¬A ∨ B. Here is a simple illustration of the semantic negation inherent in the antecedent of conditionals (p.c. Gennaro Chierchia). Observe first that the following two sentences are strongly deviant: (3) (4)

* There are any cookies left. * If you are wondering what to munch on, there are any cookies left.

Sentence (3) is ungrammatical and, unsurprisingly, it retains its ungrammatical status when it appears in the consequent of a conditional, as in (4). This is attributed to the observation that words like any need to be licensed in a negative environment, as in (5)–(6): (5) (6)

There aren’t any cookies left. If you are wondering what to munch on, there aren’t any cookies left.

However, if we move the deviant positive sentence (3) *There are any cookies left to the antecedent of a conditional, all of a sudden it becomes perfect, without any overt negation operator. This is illustrated in (7). And, as (8) illustrates, the meaning of any in (7) is similar to that of some. (7) (8)

If there are any cookies left, we’ll have something to munch on. If there are some cookies left, we’ll have something to munch on.

The acceptability of the otherwise deviant string with any, as in (3), when it is inserted into the antecedent of a conditional, as in (7), is attributed to the fact that the antecedent of a conditional shares with negation the property of being downward entailing. Based on the examples we have discussed so far, we can reach some general conclusions. First, the expressions some and any are two sides of the same coin. Both are indefinite existential expressions, close in meaning to the existential quantifier in first-order logic. But the licensing environments of any and some are somewhat different. Some is licensed in both positive and in negative sentences, whereas any is licensed only in negative sentences. Moreover, when

202  How something can be both positive and negative some appears in simple negative sentences, it is interpreted as taking scope over negation. There are contexts, however, in which these expressions receive almost the same interpretation. It is reasonable to view some and any as morphological variants, allomorphs, of the same morpheme. There is some subtle but compelling evidence that some and any are allomorphs in English. This evidence comes from their behavior in VP ellipsis. The examples in (9) and (10) can be used to illustrate. In (9), the indefinite some appears in the first clause, which makes a positive statement. The indefinite some serves as the antecedent for any in the elided VP of the second clause, because the VP is in the scope of negation. Notice that some cannot simply be repeated in the elided VP, due to the presence of negation. (9)

Ted ordered some sushi but Max didn’t. Ted ordered some sushi but Max didn’t *order some sushi/ order any sushi

Example (10) illustrates the reverse pattern. The indefinite any in a positive statement serves as the antecedent of some in the elided VP since, in this case, negation is absent. (10)

Ted didn’t order any pasta but Max did. Ted didn’t order any pasta but Max did *order any pasta/ order some pasta

On the analysis proposed here, the local linguistic environment strictly determines the selection of some versus any. Underlyingly, the two expressions are variants of the same abstract morpheme, ∃. Here is the proposal in a bit more detail. Consider, first, the derivation of (9) Ted ordered some sushi but Max didn’t. The derivation of the VP ellipsis structure in (9) takes place in three steps, as shown in (11). At Step 1, the contents of both clauses are overt, and both clauses contain the abstract morpheme ∃. At Step 2, the VP of the second clause is elided, including ∃. The elision of the second VP is permitted under identity, since both clauses contain the abstract morpheme ∃. Finally, at Step 3, the abstract morpheme ∃, is phonetically realized as some, because the first clause is positive. (11)

Step 1: Ted ordered ∃ sushi but Max didn’t order ∃ sushi Step 2: Ted ordered ∃ sushi but Max didn’t order ∃ sushi Step 3: Ted ordered some sushi but Max didn’t

The derivation of (10) reveals the reverse pattern, as shown in (12). At Step 3, the allomorph any is selected as the phonetic realization of ∃, because the VP in the first clause is in the scope of negation.

5.1 Polarity-sensitive items  203 (12)

Step 1: Ted didn’t order ∃ pasta but Max did order ∃ pasta Step 2: Ted didn’t order ∃ pasta but Max did order ∃ pasta Step 3: Ted didn’t order any pasta but Max did

In Chapter 1, we concluded that the existential indefinite some is logically equivalent to disjunction, when the domain of individuals is fixed. For example, the existential statement (13) Someone laughed and the disjunctive statement (14) Ted laughed or Max laughed have the same truth conditions in a conversational context in which Ted and Max are the only individuals in the domain of discourse. We also argued, following Karttunen (1977), that wh-questions were logically related to existential statements. The wh-question Who laughed? can be viewed as a search question, where the objective of the search is to identify the referent(s) of the existential indefinite someone in the corresponding statement Someone laughed. English (13) Someone laughed. (14) Ted laughed or Max laughed. (15) Who laughed?

Russian puts these expressions together in a transparent way, and so does Japanese and many other languages. Russian directly reveals the semantic kinship between disjunction, wh-words, and existentials. For example, the English existential indefinite someone is approximated in Russian by combining the question word kto ‘who’ and disjunction to ‘or’ to form kto-to, and the existential indefinite something is formed by combining čto ‘what’ and to ‘or,’ yielding čto-to ‘something.’ Example (16) illustrates the use of the disjunction word to in a declarative sentence, and as part of the existential indefinite kto-to ‘someone.’ Russian (16) Kto-to ne to shel, ne to exal. ‘Someone was either walking or riding (it’s not clear which).’

Finally, we pointed out that, across languages, negative polarity items are often formed by combining disjunctive words and wh-words. For example, we have seen that a reduplicated combination of wh-word plus disjunction constitutes a negative polarity item in Malagasy, as illustrated in (17). Malagasy (17) Tsy hitako na aiza na aiza ny ondriko. neg find.1sg or where or where det sheep.1sg ‘I can’t find my sheep anywhere.’

204  How something can be both positive and negative In Mandarin Chinese, the disjunction word is suppressed in forming negative polarity items, leaving wh-words alone to serve as existential indefinites, akin to negative polarity items. As expected, wh-words function like negative polarity expressions in downward-entailing contexts. For example, sentence (18) contains the negative quantificational expression meiyouren ‘nobody,’ which is downward entailing on its predicate phrase. In the scope of meiyouren, then, the wh-word shenme ‘what’ is interpreted as an existential indefinite expression, resembling English any and Mandarin renhe. The crucial observation is that the speaker is making an assertion in (18), and is not asking a question. (18)

Zai jiuhui shang meiyouren chi-guo at party prep nobody eat-asp 在酒会上没有人吃过什么水果。 ‘Nobody at the party ate any fruit.’

shenme shuiguo. what fruit

In non-downward-entailing contexts, by contrast, the appearance of the same wh-word shenme ‘what’ makes its ordinary semantic contribution, that of marking the sequence of words as a question. For example, when the Mandarin question word shenme appears in the predicate phrase of the universal quantifier meigeren ‘everybody,’ as in (19), the speaker is asking a question. This is because the predicate phrase of meigeren is not downward entailing. (19)

Zai jiuhui shang meigeren chi-le shenme shuiguo? at party prep every-cl person eat-asp what fruit 在酒会上每个人吃了什么水果? ‘What kind of fruit did everybody eat at the party?’

In short, the interpretation that is assigned to Mandarin wh-words like shei ‘who’ and shenme ‘what’ depends on whether or not they appear in downwardentailing linguistic environments. In downward-entailing contexts, these whwords are similar in interpretation to negative polarity items, such as Mandarin renhe or English any. Later in this chapter we report the findings of experimental investigations of Mandarin-speaking children’s knowledge of these licensing conditions for wh-words, to see if children, like adults, know that downward-entailing environments license the NPI renhe, and turn the wh-words shei and shenme into indefinite expressions, rather than question markers. We will now review the literature on children’s sensitivity to polarity items, beginning with child English. 5.2

Existential indefinites as negative polarity items

The first production study that investigated children’s use of PPIs and NPIs, as far as we know, was by O’Leary and Crain (1994). These researchers made

5.2 Existential indefinites as negative polarity items  205 an unexpected discovery, that children produced the PPI some in contexts in which an NPI is appropriate. We will report on that in section 5.5. Our concern in the present section is children’s knowledge of the licensing conditions on NPIs, as revealed in their productions. The study by O’Leary and Crain used a truth-value judgment task, in the description mode. Recall that in this variant of the task, the puppet Kermit the Frog is played by one of two experimenters. Kermit produces the test sentences following the completion of stories acted out by the other experimenter. As mentioned before, one of the virtues of the truth-value judgment task is that, whenever a child subject judges that Kermit “said the wrong thing,” the child can then be asked to explain to Kermit “what really happened in the story.” Ordinarily, what the child says is recorded to make sure that the child has rejected Kermit’s statement for the right reasons. In the O’Leary and Crain study, by contrast, the child’s explanations about why Kermit was wrong provided the means for assessing children’s linguistic knowledge about the licensing conditions on NPIs. To prod children towards producing PPIs instead of illicit NPIs, O’Leary and Crain manipulated the contexts preceding Kermit’s statements. The child subjects in the NPI component of the study were eleven children between the ages of 4;4 and 5;4. Prior to the experiment, the children had been familiarized with the task both in groups (in the classroom, during circle time) and individually (in a research room, away from the classroom). Each child was tested individually. They were presented with several kinds of test sentences. One set of sentences contained the NPIs any and anything. On each of the test trials, the sentences produced by Kermit the Frog were inaccurate descriptions of the stories that preceded them. Therefore, the children were expected to reject Kermit’s statements. Whenever children correctly rejected Kermit’s statement about the story, we proceeded with the elicitation component of the task. That is, we then asked the child subjects to explain to Kermit “what really happened.” Their ensuing descriptions of what really happened provided the relevant production data that served as the basis for evaluating their knowledge of the constraints on the use of the NPIs any and anything. The first type of target sentences contained the negative determiner none and the NPI anything. Following the story, Kermit the Frog produced a sentence with none. Let us call these Type 1 sentences. In one story, some Ninja Turtles were waiting up on Christmas Eve, to see if Santa had any presents for them. Although it looked like none of the Ninja Turtles would receive a present from Santa, in the end one of them did. By hypothesis, children should have corrected Kermit by producing an affirmative sentence that mentioned the Ninja Turtle that had received a present from Santa. Since affirmative sentences

206  How something can be both positive and negative are upward entailing, children’s productions were not expected to contain an NPI, but they could contain the indefinite expression something, which is licensed in upward-entailing linguistic contexts. When the story concluded, the experimenter produced the target sentence (20). The children’s corresponding responses are indicated in italics. Type 1 (20)

Kermit: None of the Ninja Turtles got anything from Santa. Child: No, this one found something from Santa.

Another type of test sentence contained the NPI anything in the predicate phrase of a sentence with the focus operator only. An example is illustrated in (21).1 These are called Type 2 sentences. In the stories that preceded these sentences, every character performed the action mentioned in the sentence. In the story corresponding to (21), four reindeer went to find something to eat. In the end, all the reindeer found something to eat. By hypothesis, therefore, children’s responses to Kermit’s incorrect description of the story should have contained a universal quantifier, every, which is upward entailing on its predicate phrase. If children know this fact about the universal quantifier, then they would not be expected to repeat the NPI anything that had just been used in the sentence produced by Kermit. Rather, children should be expected to replace the NPI anything with the indefinite expression something, which is licensed in the predicate phrase of the universal quantifier. Type 2 (21)

Kermit: Only one of the reindeer found anything to eat. Child: No, every reindeer found something to eat.

Here are the main findings. First, in response to the Type 1 sentences, with the determiner none, children produced 44 affirmative sentences, none of which contained an NPI. Twenty-two of the children’s sentences contained an indefinite expression, e.g., something, and 22 were other responses. In response to the Type 2 sentences, with the focus operator only, children produced 44 sentences. Thirty-two of them had an upward-entailing determiner, usually all. As predicted, the vast majority of these sentences (31/32) contained an existential indefinite, e.g., something. The twelve remaining sentences were other responses. In short, out of the children’s 88 responses to sentences produced by Kermit (which contained the NPI anything), only one sentence by one child contained a repetition of the NPI anything. The O’Leary and Crain study represents compelling evidence that, by age 4 or so, children know the licensing conditions of NPIs. More specifically, one thing the study revealed is that, by 4- or 5-years-old, English-speaking children appear to know that a subject

5.3 Children’s comprehension of negative polarity items  207 phrase with the universal quantifier every or all does not license NPIs in the predicate phrase. In Chapter 1, we used the schematic in (22) to represent this knowledge. (22)

Every SUBJ[ ….……. ] PRED[…*any…]

What makes this finding of particular interest is that (22) represents a negative fact; children appear to know where NPIs are not tolerated. Nativists have long pointed to such facts in their arguments for innateness. The reason is that, in the absence of negative evidence, it is difficult to see how children could learn where NPIs are not licensed. Of course, this does not prove that a learning-theoretic account will not be forthcoming, but it does pose a challenge to the experience-based approach. At the very least, advocates of the approach owe us a story about how children achieve this kind of knowledge. 5.3

Children’s comprehension of negative polarity items

In a comprehension study, Thornton (1995) tested children’s interpretation of two different types of questions with negation and with the NPI any. The experiment investigated children’s awareness of the subtle meaning differences that arise when any and negation exhibit different scope relations. Consider the examples in (23) and (24), and their corresponding logical semantic representations (i.e., Logical Forms). (23)

Did any of the turtles not buy an apple? Question: ∃ (x) [turtle(x) ∧ ¬ bought an apple(x)]

(24)

Didn’t any of the turtles buy an apple? Question: ¬ ∃ (x) [turtle(x) ∧ bought an apple(x)]

In (23), the existential indefinite any takes scope over negation. The question asks if there exists a turtle such that it did not buy an apple. In (24), on the other hand, negation takes scope over the existential indefinite any. The question asks if there do not exist any turtles that bought an apple. Consider the answers that might be given to these questions in the context illustrated in Figure 5.1. In response to the question in (23) Did any of the turtles not buy an apple? the appropriate answer is “yes.” Children who offer this answer may volunteer further information, pointing to the turtle furthest to the right, and they might say “This one didn’t.” The question in (24) Didn’t any of the turtles buy an apple? is also expected to elicit a yes response, but the child who volunteers further information is expected to justify this answer by pointing to the two turtles on the left, and to say “These two did.” In short,

208  How something can be both positive and negative

Figure 5.1. Context for questions (23) and (24)

while the correct answer to both questions is “yes,” the reason for answering “yes” in each case is different. To see whether children are aware of these differences in meaning in negative statements with the NPI any, Thornton tested children’s comprehension of questions like (23) and (24) using a modified truth-value judgment task. This time, the puppet was a snail, appropriately named Snail. At the end of each story, the experimenter asked Snail a question. Snail told the child that it was having difficulty answering the question (That’s a hard one …), and requested assistance from the child. To provide help for Snail, the child answered the questions. Ten children participated in the experiment. They ranged in age from 3;6 to 4;11. The scenarios used to test children’s comprehension of the questions in (23) were designed to be felicitous on either interpretation, (23) or (24). The stories all followed the same basic plot; two characters acted one way, and a third character acted in a different way. This step was taken to ensure that a plausible answer was always available. For example, the story accompanying the questions in (23) was about three turtles that went to the store to buy some food. Two of the turtles bought an apple and the third one, who didn’t care for apples, didn’t buy one. The main finding was that children did not experience difficulty interpreting any in the scope of negation. Questions like (23) evoked correct answers from children 93 percent of the time. Children’s replies to the follow-up question by Snail consistently demonstrated their adult-like understanding of the question. That is, in response to (23) Did any of the turtles not buy an apple?, in the ­context of a situation like that depicted in Figure 5.1, children pointed to the turtle farthest to the right and said “Yes, this one didn’t.” Questions like (24) Didn’t any of the turtles buy an apple? evoked 85 percent correct responses. In this case, also, children’s replies to the follow-up questions demonstrated adult-like understanding. In response to (24), children pointed to the

5.4 Wh-indefinites in Mandarin  209 two turtles that had bought an apple and said “Yes, these two did.” In summary, 3- and 4-year-old children are aware of the differences in meaning necessary to correctly assign scope relations between any and negation. So far, the evidence from the findings of production and comprehension studies of the NPI any supports the view that English-speaking children have sophisticated linguistic knowledge of the licensing conditions on NPIs. The studies we report next show that children acquiring Mandarin Chinese have similar knowledge, although it is manifested in a different way in Mandarin, as compared to English. 5.4

Wh-indefinites in Mandarin

The next study we describe assessed Mandarin-speaking children’s knowledge of wh-indefinites, e.g., the wh-words shei ‘who’ and shenme ‘what.’ We wanted to see if Mandarin-speaking children assign different interpretations to wh-words depending on whether these words appeared in downward-entailing environments as compared to non-downward-entailing environments. As discussed earlier, these Mandarin wh-words can function both as existential indefinites and as question words. When these words appear in downwardentailing environments, their default interpretation is as existential indefinites, similar in most respects, but not all, to the negative polarity expression renhe in Mandarin.2 When Mandarin wh-words function as existential indefinites (in downward-entailing environments), the string of words becomes a statement. However, when these same words appear in non-downward-entailing environments, they are interpreted as question words, so the string of words becomes a question. In order to investigate these differences in interpretation, we devised a task that could determine where children interpreted a test sentence as a statement or as a question. We call this new methodological technique the question/ statement task. The first experiment using the question/statement task examined children’s interpretation of the wh-word shenme ‘what’ in the predicate phrase of the negative quantificational expression meiyou ‘none.’ The experiment compared the interpretation of the same wh-word in the predicate phrase of mei ‘every,’ which is not downward entailing. Examples (25) and (26) illustrate this contrast. (25)

Meiyou xiongmao chi shenme shuiguo. not panda eat what fruit 没有熊猫吃什么水果。 ‘None of the pandas ate any fruit.’

210  How something can be both positive and negative (26)

Mei-zhi xiongmao dou chi-le shenme shuiguo? every-cl panda all eat-asp what fruit 每只熊猫都吃了什么水果？ ‘What kind of fruit did every panda eat?’

In (25), the wh-word shenme ‘what’ occurs in the predicate phrase of meiyou xiongmao ‘none of the pandas.’ Since this context is downward entailing, it licenses the interpretation of shenme as a negative polarity item for adult speakers of Mandarin. Therefore, sentence (25) expresses a negative statement, meaning none of the pandas ate any fruit. By contrast, the wh-word shenme ‘what’ in (26) appears in the predicate phrase of the universal quantifier phrase meizhi xiongmao ‘every panda.’ This is not a downward-entailing context, so the wh-word shenme ‘what’ is interpreted as a question word by adult speakers, thereby rendering the sentence with a question reading, asking What kind of fruit did every panda eat? The research question is how Mandarin-speaking children interpret shenme in these different linguistic contexts. If Mandarin-speaking children know that the predicate phrase of meiyou ‘none’ is downward entailing, then they are expected to interpret sentences like (25) as statements. And if Mandarin-speaking children know that the predicate phrase of meizhi ‘every’ is not downward entailing, then they are expected to interpret sentences like (26) as questions. These were the experimental hypotheses. To evaluate the experimental hypotheses, Su, Zhou, and Crain (2011) used the question/statement task. The task involves two experimenters. One acts out stories using toy characters and props, and the other plays the role of a puppet that watches the stories alongside the subject. After each story, the puppet attempts to tell the subject what he thought had happened in the story, using a test sentence. However, sometimes the puppet doesn’t pay close attention to the story and thus is not sure about what happened. If this is the case, then the puppet asks the child a question, using a test sentence. On each trial, the child subject’s task was to decide whether the puppet accurately said what happened in the story or asked a question about the story. Whenever the puppet said what happened in the story, the subject was instructed to judge whether the puppet was right or wrong. But if the puppet asked a question about the story, the subject was instructed to answer the question and then ask the puppet to pay closer attention to the next story. We tested twenty-eight Mandarin-speaking children between the ages of 3;5 and 4;9 (mean age 4;2). A typical test scenario is depicted in Figure 5.2. As shown in the figure, three pandas went to have breakfast and, in the end, one panda had an egg, a pear, and a strawberry, and the other two pandas had both an egg and a strawberry.

5.4 Wh-indefinites in Mandarin  211

Figure 5.2. Pandas at breakfast

After the experimenter acted out the scenario, the puppet presented sentences like (25) and (26) (repeated here). The child subject then judged whether the puppet accurately described what happened in the story or, if the puppet asked a question about the story, the child was instructed to answer the question. (27)

Meiyou xiongmao chi shenme shuiguo. not panda eat what fruit 没有熊猫吃什么水果。 ‘None of the pandas ate any fruit.’

(28)

Mei-zhi xiongmao dou chi-le shenme shuiguo? every-cl panda all eat-asp what fruit 每只熊猫都吃了什么水果？ ‘What kind of fruit did every panda eat?’

There were two main findings. First, children interpreted sentences like (27) as statements 100 percent of the time. In the example scenario, they rejected (27) on the grounds that the pandas all ate some fruit. Second, children interpreted sentences like (28) as questions 100 percent of the time. In the scenario, they provided an answer to sentence (28), pointing to the fruit that each panda ate. These results clearly show that children analyze the wh-word

212  How something can be both positive and negative shenme ‘what’ as a negative polarity item in the predicate phrase of meiyou ‘none,’ whereas they interpret it as a question marker in the predicate phrase of meizhi ‘every.’ Using the question/statement task, a second experiment, by Zhou and Crain (2011), investigated children’s understanding of wh-word shei ‘who’ in the antecedent clause versus the consequent clause of a dou-conditional. As we have seen, the antecedent clause of a dou-conditional is downward entailing. It therefore licenses the negative polarity interpretation of wh-words in adult Mandarin. By contrast, the consequent clause of a dou-conditional is not downward entailing. Therefore, a wh-word that appears in this linguistic environment is interpreted as a question marker in adult Mandarin. The present experiment looked at children’s knowledge of this asymmetry between the two clauses of dou-conditionals. The test sentences included (29) and (30). (29)

Eyu qu yao shei, maotouying cunzhang dou zhao-le crocodile go bite who owl village-head all find-asp zhizhuxia bangmang. Spiderman help 鳄鱼去咬谁，猫头鹰村长都找了蜘蛛侠帮忙。 ‘Whoever Mr. Crocodile went to bite, Mr. Owl asked Spiderman for help.’

(30)

Eyu qu yao xiaozhu, maotouying cunzhang dou zhao-le crocodile go bite pig owl village-head all find-asp shei bangmang? who help 鳄鱼去咬小猪，猫头鹰村长都找了谁帮忙? ‘Who did Mr. Owl ask for help when Mr. Crocodile went to bite Mr. Pig?’

In (29), the wh-word shei (who) is in the antecedent clause of the dou-conditional. It is expected to be interpreted, therefore, as a negative polarity item, making the sentence express a statement meaning Whoever Mr. Crocodile went to bite, Mr. Owl asked Spiderman for help. By contrast, the wh-word shei ‘who’ is expected to be interpreted as a question marker in (30), because it resides in the consequent clause of the dou-conditional, which is not a downward-entailing linguistic context. Consequently, (30) poses the question Who did Mr. Owl ask for help when Mr. Crocodile went to bite Mr. Pig? Forty-five Mandarin-speaking children were tested in this experiment (ranging in age from 3;5 to 5;0, mean age 4;3). Here is a typical scenario. The experimenter first introduced the characters, and the problem: This story is about a small village. There are four guys living in this village. One is the village head, Mr. Owl, and there are three villagers: Mr. Rabbit, Mr. Pig and Mr. Cat. The villagers lived a happy life until last week,

5.4 Wh-indefinites in Mandarin  213

Figure 5.3. The villagers and the unwanted intruder

when a bad guy started coming to the village. His name is Mr. Crocodile. Mr. Crocodile always came at night to try to bite the villagers. When the village head, Mr. Owl, found out about this, he came up with an idea.

At this point in the story, the situation is depicted in Figure 5.3. As the story unfolded, the village head, Mr. Owl, recruited assistance from two superheroes, Batman and Spiderman, as depicted in Figure 5.4. The experimenter continued to tell the story, as follows: Mr. Owl asked two of his super friends, Spiderman and Batman, to protect his villagers. The next night Mr. Crocodile came to Mr. Pig’s house. Mr. Owl found out, and called Spiderman. Just when Mr. Crocodile was about to bite Mr. Pig, Spiderman came down from the roof and ran Mr. Crocodile out of the house. As a reward, Mr. Owl gave Spiderman a purple shell. The next night Mr. Crocodile came to Mr. Pig’s house again. He wanted revenge. Mr. Owl found out, and called Spiderman again. When Mr. Crocodile jumped towards Mr. Pig, Spiderman came out from behind the door and ran Mr. Crocodile out of the house. Mr. Owl rewarded Spiderman with another purple shell. The following night, Mr. Crocodile decided not to try to bite Mr. Pig, because Spiderman always came to help. So he went to Mr. Rabbit’s house. Mr. Owl found out again and, this time, he called Batman. When Mr. Crocodile

214  How something can be both positive and negative

Figure 5.4. Mr. Owl requests help from one of his super friends broke into the house, he found Batman standing right in front of him. Again Mr. Crocodile was run out of the house. Mr. Owl gave Batman a white shell as a reward. After that, Mr. Crocodile left the village and never came back.

When the story had concluded, the puppet produced either sentence (29) or (30). Each sentence was presented to a different group of children. The child’s task was to decide whether the puppet accurately described what happened in the story, or to answer a question about the story. The main finding was that 37 out of 42 children3 consistently rejected the puppet’s statements like (29) (88 percent of the time). In the scenario, they said “no” to sentence (29) by pointing out that Batman also came to help. In response to sentences like (30), children provided an accurate answer to the question (100 percent of the time). In the story under consideration, they answered “Spiderman” in response to sentence (30). The findings are compelling evidence that children interpret the wh-word shei ‘who’ as an existential indefinite (similar in meaning to a negative polarity item) when it occurs in the antecedent of a dou-conditional. And children interpret the wh-word shei as a question marker when it appears in the consequent of a dou-conditional. Based on the findings of these two experiments, we conclude that, by age 4, Mandarin-speaking children know that downwardentailing environments turn wh-words into existential indefinites, rather than question markers.

5.5 Existential indefinites as positive polarity items  215 To conclude, the findings of the studies we have reported provide evidence that young children, across languages, know that (i) disjunction yields a conjunctive interpretation in downward-entailing environments, but not in nondownward-entailing environments; and (ii) downward-entailing environments license words like any, and turn wh-words shei and shenme into existential indefinites. This is strong evidence against an experience-based model of language acquisition, because on this approach, the two phenomena are not seen to be related; therefore, it would be surprising to find that the knowledge about the interpretation of disjunction is mastered alongside the knowledge about the licensing of words like any, and alongside the interpretation of wh-words – which are interpreted as indefinites in downward-entailing contexts, but as question words in non-downward-entailing contexts. Early mastery of such facts is suggestive evidence of an innate logic faculty, which spells out the meaning of disjunction for young children, across languages, and which spells out the semantics for a variety of downward-entailing expressions. 5.5

Existential indefinites as positive polarity items

We saw that for adult English speakers the existential indefinite some takes scope over local negation – it is a positive polarity item (PPI). We have also seen that disjunction words are PPIs in Mandarin and in Japanese. For adult speakers, the Mandarin disjunction word huozhe and the Japanese disjunction word ka are assigned inverse scope readings in simple negative statements, despite being c-commanded by negation in the surface syntactic structure. For children acquiring Mandarin and Japanese, however, the interpretation of disjunction in negative statements was found to differ from that of adults. Rather than analyzing disjunction words as PPIs, taking scope over negation, children acquiring Mandarin and Japanese interpreted negation as taking scope over disjunction words. So, children acquiring Mandarin and Japanese assigned negated disjunctions the (−PPI) interpretation it receives in English. This was striking evidence for the Continuity Hypothesis, and against experience-based accounts of language development. The explanation we offered for the observed differences between child language and adult language invoked the Semantic Subset Principle (SSP). The SSP was introduced in Chapter 3, and developed further in Chapter 4. This principle pertains to scope relations between logical expressions. If one scope relationship between logical expressions yields an interpretation that makes sentences true in a subset of the circumstances that correspond to the alternative scope relationship, then the SSP dictates that children should initially

216  How something can be both positive and negative prefer the scope relationship that yields the subset reading. In the case of ­disjunction, one scope relationship has negation taking scope over disjunction (not > or). This yields the conjunctive entailment of disjunction under negation, i.e., the ‘neither’ interpretation, ¬A ∧ ¬B. On the alternative scope relationship, disjunction takes scope over negation (or > not). This interpretation is true when just one of the disjuncts is false, or when both disjuncts are false, ¬A ∨ ¬B. The not > or interpretation, with its conjunctive truth conditions ¬A ∧ ¬B, ­asymmetrically entails the or > not interpretation, with its disjunctive truth conditions ¬A ∨ ¬B. Therefore, the not > or interpretation is the subset reading. The SSP dictates that children acquiring all languages should initially favor this scope relationship, regardless of the scope relations favored by adults. On the default interpretation disjunction is not a PPI, so children learning English will initially assign the interpretation that is favored by adult speakers and, hence, will mirror adults. Although children acquiring languages in which disjunction is a PPI will initially differ from adults, they will encounter positive evidence that their default assignment of scope relations does not match that of adult speakers of the local language. The critical evidence will consist of sentences of the form Not A or B in circumstances in which either A is true, but not B, or in which B is true, but not A. A similar learning scenario is expected for negated statements that contain an indefinite existential that is a PPI, such as English some. For adults, the indefinite some takes scope over local negation. This yields the ∃ > not reading. The alternative, non-PPI reading of the indefinite some yields the not > ∃ reading. The non-PPI reading asymmetrically entails the PPI reading, since not > ∃ entails ∃ > not, but not vice versa. In kicks the Semantic Subset Principle, dictating that children learning all languages adopt the –PPI (not > ∃) scope relations for negated statements with the indefinite some. The expectation, then, is that English-speaking children will differ from adults, and will initially interpret the existential indefinite some in the scope of negation, despite the absence of evidence for this interpretation in the input from adult speakers. But, again, children will encounter positive evidence informing them that the local language favors the alternate scope assignment, on which some is a PPI. The evidence will be negative statements of the form Not… some … presented in circumstances in which some, but not all, of the entities under consideration lack the property designated by the predicate. For example, one statement would be Julia didn’t touch some of the kangaroos, where Julia touched some, but not all of the kangaroos. This circumstance would be ruled out on children’s default analysis, so it would constitute evidence of a detectable mismatch between the child’s favored scope relationship and that of adults. Although the findings

5.6 Children’s production of existential indefinites  217 were somewhat unexpected at the time they were first reported, both production and comprehension studies have uncovered evidence that Englishspeaking children initially interpret the indefinite some in a non-adult fashion, as anticipated by the learning scenario just sketched out. We will report the production study first. 5.6

Children’s production of existential indefinites

Section 5.2 reported the findings of a production study by O’Leary and Crain (1994) assessing children’s knowledge of the licensing conditions on NPIs. The study revealed that children know, for example, that NPIs are not tolerated in the predicate phrase of sentences with a universal quantifier in the subject phrase. Because children know that the universal quantifier is not downward entailing on its predicate phrase, they correctly refrained from producing NPIs in the predicate phrase of their statements, despite having just heard an NPI in the predicate phrase of the test sentences produced by Kermit the Frog. The O’Leary and Crain (1994) study also investigated children’s production of PPIs. We turn to that part of the study now. As we saw, the study used the truth-value judgment task, with a production component. The NPI component of the study had two conditions, which we called Type 1 and Type 2. There were two further conditions in the study, so we’ll label them Type 3 and Type 4. As before, the test sentences were produced by a puppet, Kermit the Frog. The Type 3 target sentences contained the PPI something. In the stories that preceded these sentences, however, not all the characters performed the action mentioned in the target sentence. By hypothesis, children should have corrected Kermit, and responded by producing a sentence with negation or another downward-entailing expression. If so, their productions were expected to contain an NPI in place of the PPI that was used in the target sentence. The example in (31) illustrates the design features of the Type 3 sentences. Type 3 (31)

Kermit: Every dinosaur found something to write with. Child: No, this one didn’t find anything to write with.

Finally, Type 4 sentences contained the PPI some and the focus operator only. In the stories that preceded these sentences, none of the characters performed the action mentioned by Kermit. By hypothesis, children’s responses to Kermit’s incorrect description of the stories should have contained a downward-entailing

218  How something can be both positive and negative expression such as none or no one, and children were expected to replace the PPI some produced by Kermit, with an NPI equivalent, any. Type 4 (32)

Kermit: Only one of the friends had some presents for Gonzo. Child: No, none of the friends had anything for Gonzo.

Let us first report the findings for the Type 3 sentences, where children were expected to use a downward-entailing subject phrase, and to replace the PPI in the predicate phrase of Kermit’s sentence by an NPI. Children produced 44 sentences with a downward-entailing subject phrase or with negation. However, only 29 of these sentences with a downward entailing operator contained an NPI. Seven of them contained a PPI, and there were 8 other responses. In response to sentences of Type 4, children produced 44 sentences with a downward-entailing expression. Eighteen of these sentences had an NPI, but 10 of them had a PPI, and there were 16 other responses. Below are some examples in which children produced PPI some in contexts where it is not licensed in the adult grammar. (33)

a. b. c. d.

He didn’t get something to eat. Well, they didn’t get some food. None people had some presents. So he didn’t get some money.

(C.E.-K. 4;6) (E.E. 4;7) (E.P. 4;9) (E.G. 4;10)

As these examples illustrate, children used some or something in contexts where adults would have used any or anything to express the same message. Recall that the basic difference between some and any is that while the latter must be interpreted in the scope of negation, the former must be interpreted outside the scope of clause-mate negation. In other words, (33b) must be interpreted to mean that there exists some food that the characters in question didn’t get. In this case, some is interpreted outside the scope of negation. What (33b) cannot mean, however, is that the characters didn’t get any of the food, in which case some would be interpreted in the scope of negation. This difference is indicated in (34) below. (34)

They didn’t get some food. a. ∃(x) [food(x) ∧ ¬ they get (x)] b. * ¬∃(x) [food(x) ∧ they get (x)]

Summarizing the results, children did not seem to be aware of the interpretive restrictions on PPIs, since they often produced some and something in the scope of negation or a downward-entailing determiner, and assigned some a narrow scope reading (i.e. in contexts where adults would have used any or anything).

5.7 Children’s comprehension of existential indefinites  219 5.7

Children’s comprehension of existential indefinites

The last experiment we will review in this chapter was an investigation of children’s comprehension of the existential indefinite some in negative statements. Having witnessed the finding from the O’Leary and Crain (1994) study, where children had produced some N and something in linguistic environments where adults prefer any N and anything, the aim of this follow-up study was to determine whether or not children incorrectly interpret some in negative sentences. The experiment was conducted by Musolino (1998), who assessed children’s comprehension of sentences like (35), using a truth-value judgment task, in the description mode. (35)

The detective didn’t find some guys.

One of the two experimenters played the puppet Kermit the Frog. Kermit produced the test sentences following each story, which was acted out by the other experimenter. As usual, whenever a child subject judged that Kermit said the wrong thing, the child was asked to explain to Kermit what really happened in the story. The research question was to determine whether children would incorrectly interpret the existential indefinite someone in the scope of negation, as having the meaning of the corresponding NPI anyone. The misinterpretation that was anticipated was one in which children understand (35) to mean The detective didn’t find any guys. The experimental objectives called for situations in which both the surface scope and the inverse scope reading of (35) were felicitous, but which made Kermit’s statement false on the surface scope reading of someone, but true on the inverse scope reading of someone. So, in the situation, it was false that the detective didn’t find any guys (surface scope), but it was true that there were some guys that the detective didn’t find (inverse scope). If children correctly interpret someone as a PPI, taking scope over local negation, then they should accept (35) in this situation, but if children take some guys as an NPI, as if it meant anyone, then (35) would mean The detective didn’t find any guys, and children would be expected to reject (35). The subjects were thirty children ranging in age between 3;10 and 6;6. In the story under discussion, a detective and his two friends decided to play hide and seek. While the detective had his eyes closed, one of his friends hid behind a tree and the other friend hid under the seat of a covered wagon. Once the detective opened his eyes, he began walking around. First, he inspected the tree, then the covered wagon, and other hiding places, without finding either of his friends. Nevertheless, the detective didn’t give up. He decided to inspect

220  How something can be both positive and negative all of the hiding places again, more carefully. This time, the detective spots his friend who was hiding behind the tree, but he still did not see his other friend who was hiding inside the covered wagon. Kermit then produced his version of what had happened in the story, saying the following. That was a story about a detective and his friends. I know what happened in the story… The detective didn’t find someone.

In this situation, adults judge the statement by Kermit to be true, so adults say “yes.” This response is interpreted as indicating that adults assign inverse scope to someone, interpreting it to take scope over negation, as befits a PPI. If Kermit’s statement The detective didn’t find someone is interpreted to mean The detective didn’t find anyone, the expected response would have been “No,” since the detective had, in fact, found one of his friends. Here are the main findings. A control group of adult English speakers was tested using a videotaped version of the experiment, and these adult subjects always accepted the target sentences, showing that they analyzed someone as a PPI, and assigned it scope over negation (i.e., the inverse scope interpretation). Turning to the children, 14 of the 30 child subjects rejected the target sentences like (35) on at least three out of four trials. Overall, these children rejected the negative statements 88 percent of the time. When asked to tell Kermit “what really happened,” children pointed out that the detective did find someone, and they pointed to or mentioned the character hidden behind the tree. Thirteen of the 30 child subjects accepted the puppet’s statements on at least three of the four trials. Overall, this group accepted the target sentences 90 percent of the time. Finally, three children accepted the test sentences twice, and rejected them twice. Two analyses were conducted to determine whether age was a contributing factor in determining whether children accepted or rejected the target sentences. One analysis included the three inconsistent children (who accepted and rejected the test sentences equally often) in the group of children who consistently accepted the puppet’s statements. ANOVA revealed a significant difference between these groups (F1(1, 28) = 5.86, p < 0.03), with the younger group producing a higher rate of rejections. A second analysis assigned the three inconsistent children to the group that consistently rejected the puppet’s statements. Again, there was a statistically significant difference between the age groups (F1(1,28) = 12.51, p < 0.005). This is evidence that younger children tend to (incorrectly) assign surface scope interpretation to sentences like The detective didn’t find someone. Younger children, then, seem to be equating

5.7 Children’s comprehension of existential indefinites  221 the indefinite existential some and the negative polarity item any, at least when some occurs in the scope of local negation. As children get older, they begin to assign an inverse scope reading to some. Two accounts of children’s non-adult use of the existential indefinite some have been proposed. One account contends that younger children lack the computational resources to generate inverse scope readings of logical expressions. As children’s processing resources increase, they become better able to handle inverse scope relations. On this account, younger children experience difficulty with inverse scope readings, because the mapping between surface syntax and logical form is not one-to-one. Children prefer to compute on-line incremental interpretations, where what you see is what you get. Let us call this the isomorphism account. The alternative account supposes that young children have no difficulty computing inverse scope interpretations, but they are compelled by learnability considerations to initially favor the parameter setting according to which some is  –PPI. This value is initially favored to ensure that children’s initial scope assignments generate the subset reading of sentences with more than one logical expression. In short, the Semantic Subset Principle is invoked to explain children’s non-adult performance with negative sentences with some. On this account, it is noted that the reading on which The detective didn’t find someone takes someone to mean anyone is true in a subset of the circumstances which make the sentence true when someone is analyzed as a PPI. We have already reviewed a number of empirical findings that undermine the isomorphism account. One relevant finding was that English-speaking children differ from adults in interpreting negated conjunctions like (36). (36)

Ted didn’t order both pasta and sushi.

Adult speakers accept (36) in three circumstances, where (a) Ted ordered just pasta, where (b) Ted ordered just sushi, or where (c) Ted ordered neither sushi nor pasta. However, English-speaking children accept (36) in just one circumstance, where Ted ordered neither dish. The child’s both > not interpretation is based on the conjunction word and taking scope over negation. So this nonadult interpretation requires the computation of inverse scope relations between conjunction and negation. The same interpretation is assigned by Mandarin-speaking children and adults. There are two ways to translate the English example (36) into Mandarin. One of these ways mirrors the word order of English, as illustrated in (37). Here, negation meiyou precedes the conjunction word he, so the isomorphism account would expect children to assign the not > both surface scope reading.

222  How something can be both positive and negative But just as English-speaking children favor the inverse scope reading, so do child and adult speakers of Mandarin. (37)

Taide meiyou dian yidalimianshi he shousi. Ted not order pasta and sushi 泰德没有点意大利面食和寿司。 ‘As for both pasta and sushi, Ted did not order them.’

Another way to translate the English example (36) into Mandarin is given in (38). Since, as we have seen, the quantificational adverb dou (meaning ‘both’ or ‘all’) can only take scope over expressions to its left, the conjunctive phrase in (38) must precede dou and, consequently, it must also precede the word for negation meiyou. So, the surface syntax of example (38) corresponds to the preferred scope interpretation. In short, there is isomorphism between surface word order and logical form. (38)

Taide yidalimianshi he shousi dou meiyou dian Ted pasta and sushi both not order 泰德意大利面食和寿司都没有点。 ‘As for both pasta and sushi, Ted did not order them.’

The critical observation is that both examples (37) and (38) are assigned the same interpretation in Mandarin. This rules out the possibility that Mandarin speakers use precedence (linear order) to determine scope relations. Another series of experiments have led to findings that cannot be explained on the isomorphism account. The structures in the experiments were pseudoclefts such as (39). (39)

A teddy or a dice is what no child chose.

Although disjunction precedes negation in (39), children interpret disjunction to license a conjunctive entailment in such sentences, so (39) entails that no child chose a teddy and no child chose a dice. At Logical Form, therefore, negation has scope over disjunction, as in one of de Morgan’s laws: ¬(A ∨ B) ⇒ ¬A ∧ ¬B. In a recent experiment, we have tested Mandarinspeaking children and adults using the same materials on Mandarin sentences like (40). (40)

Xiaoxiong huozhe shaizi tamen (dou) mei na. Teddy or dice they all not take 小熊或者色子他们都没拿。 ‘A teddy or a dice is what they all did not take.’

Again, neither children nor adults interpreted (40) in the way that would be expected on the isomorphism account, by assigning the surface scope reading.

5.7 Children’s comprehension of existential indefinites  223 Instead, children and adults assigned the inverse scope reading, with and without dou, where disjunction generates a conjunctive entailment. Based on these observations from the literature, and many related observations, we conclude that children’s default non-adult interpretation of the existential indefinite some – as taking scope under negation – is motivated by the Semantic Subset Principle, and does not reflect a general tendency for young children to attempt to map the surface syntax as directly as possible to logical form, as advocated by the isomorphism account. This invites the conclusion advocated by the logical nativism account, that the acquisition of semantic knowledge is constrained by universal principles of language, and by principles of language learnability in the absence of negative evidence. The fact that children are found to differ from adults, but only in ways in which adult languages differ from each other, is one of the guiding tenets of logical nativism, the Continuity Hypothesis. The difference between child and adult language resists explanation on the experience-based approach to the acquisition of cognitive skills, including logic and language.

6 Two logical operators for the price of one

Child language acquisition proceeds without the benefit of the vast array of data available to linguists. In developing linguistic analyses, linguists consider many kinds of evidence that are not available to children, including cross­linguistic data, as well as both positive and negative evidence (i.e., the kinds of sentences that are ungrammatical in a particular language). These data permit linguists to disconfirm hypotheses, and formulate better ones. Despite the lack of cross-linguistic data and negative evidence in children’s experience, by the time they have reached their fourth birthday, every normal child has mastered many, perhaps most, of the linguistic and logical principles that have been uncovered by linguists and logicians over the past few decades of research. The principles children master in the first few years of life include nontrivial generalizations. For example, we have seen that downward-entailing operators tie together clusters of apparently unrelated linguistic phenomena in particular languages, like English, and we have seen that the same phenomena are governed by downward- entailing operators in other languages around the globe. We have also seen that, although these phenomena appear unrelated at first glance, it turns out that, upon closer scrutiny, these phenomena are related at a deeper level of analysis. In the absence of an alternative account of these regularities – i.e., lacking a learning-theoretic account of how young children come to know these phenomena – it seems reasonable to conclude that humans are innately endowed with the universal principles and parameters of grammar, and that children only acquire languages that conform to these principles and parameters. Furthermore, many of these principles and parameters involve logical expressions and their interactions. So it is reasonable to suppose that logical principles and parameters (e.g., scope parameters) are part of the innate genetic endowment of the species. Much of this book has been about downward-entailing operators, and the present chapter is no exception. This is because downward entailment is a prime candidate for being a core property of human languages. It is expected to be manifested in all human languages, and it ties together clusters of seemingly 224

Two logical operators for the price of one  225 unrelated linguistic phenomena. Downward-entailing expressions manifest several semantic properties. By definition, downward-entailing operators license inferences from sets to their subsets. In addition, downward-entailing operators license negative polarity expressions, and when downward-entailing operators take scope over disjunction, disjunction generates a conjunctive entailment. Although this cluster of linguistic phenomena appears to be unrelated, we tried to show in Chapter 1 that these phenomena are variations on a theme. In Chapter 4, we reported two instances in which children’s initial assignments of scope relations differed from those of adults. First, Mandarin- and Japanese-speaking children’s interpretation of negated disjunctions are not attested in the input to children by adult speakers of Mandarin or Japanese. Adult speakers of these languages analyze disjunction words as positive polarity items, which take scope over negation in simple negative sentences. By contrast, children acquiring Mandarin and Japanese initially interpret disjunction within the scope of negation. So, children initially favor an interpretation that is different from the one that is favored by adult speakers of these languages. A second disparity between the languages of children and adults was the finding that English-speaking children initially interpreted negated conjunctions in a way that is consistent with the interpretations assigned by Mandarin-speaking and Japanese-speaking children and adults, but unlike the scope assignments that are made by adult speakers of English. Clearly, children’s initial scope assignments in both cases are not based on the input they receive from adults. We argued, following Goro (2004), that cross-linguistic variation in the interpretation of disjunction and conjunction in negative sentences is due to a pair of scope parameters, and a principle of learnability – the Semantic Subset Principle. In the absence of negative evidence, it is to be expected that children’s initial hypotheses about scope relations are based on the Semantic Subset Principle, which entreats children to favor interpretations that make sentences true in the narrowest range of circumstances. In the case of negated disjunctions, the subset reading is the one on which negation takes scope over disjunction. In the case of negated conjunctions, this is the reading on which conjunction takes scope over negation. The fact that children’s initial assignments of scope relations sometimes fail to match those they encounter in the input is problematic on the experience-based approach, but the finding that child language can differ from adult language (in limited ways) is consistent with the Continuity Hypothesis. According to the Continuity Hypothesis, child language may differ from the local language, but the differences are circumscribed by the parameters of the human logic faculty. The differences between child and adult language mirror differences that are manifested between adult languages.

226  Two logical operators for the price of one The main subtext of this book is that both child and adult languages are logical, in the sense that they draw upon first-order logic. To supplement the conclusion that human languages are logical, we pointed to a range of linguistic structures where all child and adult languages, as far as we know, conform to the laws of classical logic. These are putative linguistic universals. One candidate for a linguistic universal is when negation appears in a higher clause than the clause that contains disjunction or conjunction. In these structures, the polarity sensitivity of disjunction and conjunction is canceled. Therefore, English, Mandarin, and Japanese (and all other human languages as far as we know) pattern alike, and all languages conform to de Morgan’s laws. In the present chapter, we return to a discussion of another linguistic structure that illustrates that human languages are logical, again by showing that, once the polarity sensitivity of logical expressions is canceled, the interpretations of these expressions revert back to the meanings of the corresponding expressions in classical logic. The linguistic structure that is the topic of this chapter involves focus operators (e.g., English only, Japanese dake, Mandarin zhiyou). Focus operators are of particular interest to us, because they cancel polarity sensitivity. The reason for this is that focus operators are (partially) downward entailing, as we will explain. Focus operators generate a covert negation as part of their meaning. When conjunction and disjunction are incorporated in sentences with focus operators, the covert negation of focus operators generates logical entailments that mirror de Morgan’s laws for negated conjunctions and negated disjunctions. This shows that the basic meanings of disjunction and conjunction are the same in human languages as they are in classical logic. And sentences with focus operators reveal another linguistic universal that comports with the laws of classical logic. This makes the linguistic universal a prime candidate for innate specification. To further assess this possibility, we turn to the child language laboratory. This chapter reports the findings of experimental studies of children’s knowledge of the laws of propositional logic. These experiments demonstrate that children know these laws as early as they can be tested. This is achieved by putting disjunction and conjunction in sentences with focus operators. The conclusion that human languages, including child language, adhere to the laws of classical logic is expected on the logical nativist approach to language development. Moreover, the fact that focus operators generate covert negation represents another semantic property of human languages that is difficult to reconcile with the experience-based approach to language development. On the other hand, children’s early mastery of basic laws of logic provides further evidence

6.2 The two meaning components of focus operators  227 for the conclusion that human languages build upon an innate logic faculty that consists of universal linguistic and logical principles and parameters. 6.1

Focus operators

Linguistic investigations of focus operators (e.g., English only, Mandarin zhiyou) have led to a number of insights about the meanings of logical expressions in human languages. In some languages, logical expressions like some, and, and or are positive polarity items, and must be interpreted outside the scope of local negation. As a consequence, these logical expressions yield inverse scope interpretations in simple negative statements. The scope relations are the reverse of what would be expected if scope was determined by the surface syntax. This makes them take on the appearance of violating rules of classical logic, which does not have rules for interpreting logical expressions outside the brackets within which they are positioned in logical formulas. The presence of focus operators in human languages often cancels the inverse scope interpretations that are assigned to the corresponding logical expressions, resulting in an alignment between human languages and classical logic. We will review some of the effects of focus operators in the following sections, to bolster the case that human languages are logical. Another of our concerns will be how children acquire the meanings of focus operators. Many researchers have reached the conclusion that children and adults sometimes differ in the interpretations they assign to sentences with focus operators, but the nature of the difference remains controversial. The main issue of contention is whether children compute both meaning components of sentences with focus operators: the presupposition and the assertion. We begin, then, by discussing in more detail these two meaning components of focus operators. We will use the English focus operator only as the main example, and then we will compare its properties with those of Mandarin zhiyou, in order to compare the interpretations of logical expressions in typologically different languages. The conclusion we reach is that children acquiring both languages have access to the semantic intricacies of sentences with focus operators, and that these sentences reveal the logical structure of human languages, including both child and adult languages. 6.2

The two meaning components of focus operators

As proposed by Horn (1969), the meaning of a sentence with the focus operator only, such as (1), can be decomposed into two conjoined propositions.

228  Two logical operators for the price of one The first proposition pertains to the focus element, Bruce. The content of this proposition is the truth-conditional meaning of the original sentence, minus the focus operator, only. So (2) represents the first meaning component of (1). We will call this meaning component its presupposition. (1) (2)

Only Bruce speaks a Romance language. Bruce speaks a Romance language.

The second meaning component is a proposition that is entailed by sentences with focus operators, such as (1). We call this meaning component the assertion. Much of the content of the assertion is contributed by the meaning of the focus operator only. Of course, the content of the assertion contains the focus element, Bruce, and the property being attributed to him, …speaks a Romance language. But the assertion contains more than this. First, the assertion introduces a contrast set. Focus operators are felicitous only if there is a set of entities that stands in contrast to the focus element.1 In addition, the assertion contains a covert negation. Essentially, the assertion of a sentence with a focus operator denies that anyone else who is being contrasted with the element in focus (Bruce) has the property that is being attributed to the element in focus (… speaks a Romance language). So, the assertion of (1) can be represented as in (3).2 (3)

For all x ≠ Bruce, x does not speak a Romance language.

Notice that the assertion, but not the presupposition, introduces negation. The assertion consists of the denial that the property being ascribed to the element in focus can be attributed to any member of the contrast set. Although negation is part of the meaning of the focus expression only, it remains covert, in the sense that it does not appear in the surface phrase structure of sentences like (1). 6.3

Covert negation is downward entailing

To verify that only contributes a covert negation, it is worth applying a couple of diagnostic tests for the presence of negation. We know that negation is downward entailing, so the properties that are associated with downward-entailing expressions will provide evidence that only introduces negation. Downwardentailing expressions generate certain kinds of entailments. The present task, then, is to see if only generates these entailments. We will consider both meaning components of example (1) Only Bruce speaks a Romance language, one at a time, beginning with the presupposition.

6.3 Covert negation is downward entailing  229 The first question is whether only is downward entailing in the presupposition. By definition, downward-entailing expressions endorse inferences from claims about sets of things to claims about subsets of those things. So, if only is downward entailing in the presupposition, it should be possible, salva veritate, to substitute a subset-referring expression, such as French, for the set-referring expression, Romance language in the example under consideration, repeated here as (4). The substitution is made in (6). (4) (5) (6)

Only Bruce speaks a Romance language. Presupposition: Bruce speaks a Romance language. #Bruce speaks French.

As a matter of record, English speakers typically deny that (4) entails (6). People reject this entailment on the grounds that Bruce could speak Spanish or Italian, and not French. In other words, there are circumstances in which (4) could be true, but (6) is false. In short, the endorsement of inferences from sets to subsets does not hold for the presupposition associated with the focus operator only. Based on observations such as this, von Fintel (1999) argues that the first meaning component of only, the presupposition, is not downward entailing. What about the second meaning component of only? Is the assertion downward entailing? Returning to example (4), the assertion is given in (7). The assertion contains the set-referring expression Romance language. In example (8), we have substituted the subset-referring expression French for Romance language. The question is whether (4) (and (7)) entails (8). The answer is affirmative. If only Bruce speaks a Romance language, then it could not be the case that anyone being contrasted with Bruce speaks French, or any other Romance language. (7) (8)

Assertion: For all x ≠ Bruce, x does not speak a Romance language. For all x ≠ Bruce, x does not speak French.

The fact that (4) Only Bruce speaks a Romance language entails that everyone else does not speak French means that the assertion associated with the focus operator only passes one of the diagnostic tests of downward entailment. Although (4) lacks an overt downward-entailing expression, the assertion made by (4) contains negation, which is downward entailing. For completeness, let’s apply another diagnostic test of downward entailment, to see if either the presupposition or the assertion passes another test. The second diagnostic involves disjunction (English or): as we have seen, when a disjunctive word appears in the scope of a downward-entailing expression, it

230  Two logical operators for the price of one licenses a conjunctive entailment. First, let’s consider an example with negation in the surface string, but without a focus operator: Ted didn’t order pasta or sushi. If this statement is true, then it follows that Ted didn’t order pasta, and it also follows that Ted didn’t order sushi. So, if Ted didn’t order pasta or sushi, then Ted didn’t order pasta and Ted didn’t order sushi. This shows that disjunction licenses a conjunctive entailment when it appears in the scope of negation, at least in English. Now let’s apply this same assessment of the interpretation of disjunction to the focus operator only. Consider example (9), which lacks negation in the surface string. The presupposition associated with (9) is given in (10) and the assertion is given in (11). (9) (10) (11)

Only Bruce speaks French or Spanish. Presupposition: Bruce speaks French or Spanish. Assertion: For all x ≠ Bruce, x does not speak French or Spanish.

Now we can ask whether the disjunction word or in (9) licenses a conjunctive entailment in either the presupposition or the assertion. It is clear that disjunction does not license a conjunctive entailment in the presupposition. To see this, we need only imagine a circumstance in which (9) Only Bruce speaks French or Spanish is true, but where it is false that Bruce speaks French and Bruce speaks Spanish: (12)

#Bruce speaks French and Bruce speaks Spanish.

A circumstance that makes (9) true, but not (12), is one in which Bruce speaks just French, but not Spanish. So, disjunction in the presupposition of sentences with only does not generate a conjunctive entailment. Hence, the presupposition of sentences with only is not downward entailing. We can move then to the assertion made by (9) Only Bruce speaks French or Spanish. The question is whether the disjunction word or in (9) generates a conjunctive entailment in the assertion. If so, then (9) must entail that everyone else (being contrasted with Bruce) doesn’t speak French and everyone else doesn’t speak Spanish. That is, in every possible circumstance in which (9) is true, the conjunctive statement in (13) must also be true. This is clearly a valid inference. (13)

For all x ≠ Bruce, x does not speak French and x does not speak Spanish.

So, we have applied two diagnostic tests of downward entailment, and we have found that the assertion of sentences with only passes both tests. We conclude that the focus operator only introduces a downward-entailing expression, negation, in the assertion. We also saw the presupposition of only fails both of

6.4 Polarity-sensitive expressions  231 these diagnostic tests, so we might say that the focus operator only is partially downward entailing.

6.4

Polarity-sensitive expressions

In sentences with focus operators, such as English only, the assertion introduces negation and a contrast set. Negation is part of the meaning of only, and it is introduced at the level of semantic interpretation (i.e., Logical Form), as part of the assertion. Negation need not appear in the surface string of sentences with only. Let us refer to the negation that is introduced into the semantic representation of sentences with only, covert negation. In this way, we can compare covert negation with overt negation, i.e., when a negative expression (e.g., not) actually appears in the surface string, and is pronounced. Interestingly, the distinction between overt and covert negation is quite dramatic. When negation is overt, polarity-sensitive items like English some are interpreted as taking scope over negation at the level of semantic representation. However, when negation is covert, as in sentences with only, polarity­sensitive items like some are interpreted within the scope of negation. We will take advantage of this property of only as a means of assessing the basic meanings of logical expressions across languages. Towards this end, we need to discuss polarity-sensitive items in more detail. We have discussed two kinds of polarity-sensitive items, negative polarity items (NPIs) and positive polarity items (PPIs). As their names suggest, they can be considered to be polar opposites. An NPI is an expression that must be licensed by a downward-entailing operator, such as English any and Mandarin renhe. For example, English any is accepted in sentences with negation, such as (14), Julia did not touch any of the kangaroos. The semantic interpretation of this sentence is given in (15). As this analysis indicates, the NPI any is translated as an existential quantifier ∃ that appears inside the scope of negation, ¬. For sentence (14) to be true, there do not exist kangaroos that Julia touched. In view of the Logical Form assigned to example (14), as in (15), let us refer to this scope relationship between negation and the NPI any as the not > ∃ reading. This indicates that negation takes scope over any. This is also called the surface scope reading, since the order in which not and any appear in the surface string is the same as the order in which they appear at Logical Form. (14) (15)

Julia did not touch any of the kangaroos.  ¬∃(x)[Kangaroo (x) ∧ Touch (Julia, x)].

not > ∃

232  Two logical operators for the price of one A PPI assigns the opposite scope relations, as compared to an NPI. A PPI must take scope over local negation at the level of semantic interpretation (i.e., Logical Form). An example of a PPI is English some. Consider (16) Julia did not touch some of the kangaroos. The sentence has the semantic representation in (17). Notice that some is also analyzed as an existential quantifier ∃ in (17), just as any was in (15). In this case, however, the existential quantifier takes scope over negation, so (16) can be paraphrased as (18) There are some kangaroos that Julia didn’t touch.3 In view of this logical form, we will refer to this scope relationship between negation and some as the ∃ > not reading. This is also called the inverse scope reading, since the order in which not and some appear in the surface string is opposite to the order in which they appear at Logical Form. (16) (17) (18)

Julia did not touch some of the kangaroos.  ∃(x)[Kangaroo (x) ∧ ¬Touch (Julia, x)] There are some kangaroos that Julia didn’t touch.

∃ > not

Comparing some and any, there are two further points to note. First, notice the difference in the meanings of (14) and (16).4 The meaning difference follows from the fact that some and any are assigned different scope relations with respect to negation. Notice also that both some and any are interpreted as existential quantificational elements in the logical representations in (15) and (17). That is, some and any are allomorphs. They are both words for expressing the same underlying concept, ∃, but they are in complementary distribution in the semantic interpretations that are assigned to the simple negative statements that contain them, with some being interpreted outside the scope of negation (the inverse scope reading), and any being interpreted inside the scope of negation (the surface scope reading).

6.5

How to cancel polarity sensitivity

There are linguistic contexts that cancel the polarity sensitivity of PPIs. When the English PPI some appears in these contexts, therefore, it no longer has the inverse scope reading. The reading that remains is the surface scope reading. In these contexts, then, the meaning difference between some and any vanishes. This vindicates the analysis of both expressions as referring to the same logical concept, ∃ (Chapter 1). We have already witnessed one context that cancels polarity sensitivity. This is when negation resides in a higher clause than the clause that contains the PPI.

6.5 How to cancel polarity sensitivity  233 We illustrate this with English some, as in (19) and (20). In these examples, some and any are logically equivalent. Any residual difference in meaning is quite nuanced, and does not reflect a difference in scope. Both are true if the speaker is not convinced that there exist kangaroos that Julia touched. That is, both examples receive the surface scope, not > ∃, interpretation. (19) (20)

You didn’t convince me that Julia touched some of the kangaroos. You didn’t convince me that Julia touched any of the kangaroos.

not > ∃ not > ∃

The second linguistic context that cancels polarity sensitivity of PPIs is focus operators, such as English only and Mandarin zhiyou. The canceling effect is due to the fact that focus operators introduce covert negation in the assertion meaning component. Because negation is introduced covertly, at the level of semantic interpretation (or Logical Form), PPIs are not required to take scope over them, as they would if negation were overtly expressed. This suggests that polarity sensitivity is, in part, a phonological process, involving two expressions (e.g., negation and a PPI) that are spelled out at the level of phonetic form (PF). Let us take this argument one step at a time, beginning with the PPI some in example (21). The example has the focus operator only, but there is no word expressing negation anywhere in the surface string. The presupposition for (21) is given in (22), and the assertion, with covert negation, is given in (23). (21)

Only Julia touched some of the kangaroos. Cf. Only Julia touched any of the kangaroos.

(22)

Presupposition:   Julia touched some of the kangaroos. ∃(x)[Kangaroo (x) ∧ Touch (Julia, x)]

(23)

Assertion:   For all w ≠ Julia, there do not exist kangaroos that w touched ∀(w) [w ∈ cont(Julia) → ¬∃(x)[Kangaroo (x) ∧ Touch (w, x)]

There are a few noteworthy details about the meaning of (21). First, note how some is interpreted in the presupposition. The presupposition of (21) is roughly the sentence minus the focus operator, as indicated in (22). Logically speaking, both the original statement and the assertion are true in circumstances where Julia touched all of the kangaroos. Because some is analyzed as an existential quantifier, as indicated in the logical formula associated with (22), the possibility that Julia touched all of the kangaroos is not ruled out, from a logical point of view. However, few people would accept (21) (or (22)) in a circumstance in which Julia touched all of the kangaroos. The reason is that the use of some in (21) invokes a scale: < some, many, most, all >. The expression some is the weakest term on the scale. Because the speaker of (21) selected

234  Two logical operators for the price of one to use the weaker expression (some), rather than a stronger expression (many, most, or all), hearers infer that the speaker was not in a position to assert a statement that contained a stronger expression (many, most, or all). This inference follows from the Principle of Cooperation, a pragmatic principle dictating that speakers attempt to make the strongest statement they can. When speakers select a weaker term, like some, hearers infer that the speaker was not in a position to use any of the stronger terms. Therefore, (21) induces an implicature for hearers – that Julia did not touch all of the kangaroos. So, the presupposition corresponding to (21) can be paraphrased as Julia touched some, but not all, of the kangaroos. Example (21) does not assert that Julia didn’t touch all of the kangaroos, but the speaker is taken to imply this. A similar observation can be made about the assertion. The critical observation is that negation takes scope over the existential quantifier in the assertion corresponding to (21), as represented in (23). The assertion yields the not > ∃ reading. It follows that it is more accurate to paraphrase the assertion, using the NPI any, rather than using the PPI some, as indicated in (24). (24)

For all w ≠ Julia, w didn’t touch any (*some) of the kangaroos.

Why is some not tolerated in (24)? Suppose the variable w in (24) ranges over a guy named Tony. Then, if the statement in (24) were to include some, then (24) would entail the statement Tony didn’t touch some of the kangaroos. But the statement Tony didn’t touch some of the kangaroos is interpreted to mean that there are some kangaroos that Tony didn’t touch, and this, in turn, triggers a scalar implicature. It implies that there are some kangaroos that Tony did touch. The implicature arises because, as a PPI, some is interpreted outside the scope of negation. From that position, some triggers a scalar implicature. Attesting to the implicature is the fact that most people explicitly exclude the none interpretation of a sentence like Tony didn’t touch some of the kangaroos. Logically speaking, the use of the expression some not is valid in circumstances in which the stronger expression all not is true. The reasoning for excluding the all not reading is the same as before, although the example is slightly more complicated, due to the presence of negation. The use of some invokes a scale < some, many, most, all > (from weaker to stronger) and this leads, by implicature, to a derived meaning that negates the stronger terms on the scale (many, most, all). One of the stronger assertions is that all of the kangaroos are such that Tony didn’t touch them; in other words, Tony didn’t touch any of the kangaroos. This is the assertion associated with sentences with the focus operator and the PPI some, but it is not considered to be equivalent in meaning to the same sentence absent the focus operator, due to the scalar implicature.

6.5 How to cancel polarity sensitivity  235 Here is the upshot. If the PPI some is introduced in the assertion, as in (25), this generates the wrong interpretation. The overt negation brings out the PPIstatus of some. If the PPI some is used in the assertion of sentences with the focus operator, as in (25), then the inverse scope interpretation is similar to the interpretation that is assigned to simple negative statements such as Tony didn’t touch some of the kangaroos. (25) #Assertion with some: For all w ≠ Julia, there exist kangaroos that w didn’t touch. ∀(w) [w ∈ cont(Julia) → ∃(x)[Kangaroo (x) ∧ ¬Touch (w, x)]

Although the PPI some appears in the original example, Only Julia touched some of the kangaroos, if it is spoken aloud in the assertion, it functions as a PPI, and takes scope over negation. So, some cannot be overtly pronounced in the assertion, since this would result in an overt negation which, in turn, would trigger the inverse scope reading, ∃ > not. It is clearly incorrect to render the assertion as ∃ > not. Rather, the assertion is not > ∃. To express this reading, the NPI any must be used, rather than the PPI some. In summary, the covert negation introduced by focus operators cancels the inverse scope relations between negation and PPIs, at the level of semantic interpretation. The fact that covert negation cancels the polarity sensitivity of PPIs points to a learnability dilemma for children. If adults attempt to instruct children about the assertion of sentences with focus operators, they must do so without repeating, verbatim, the predicate phrase of the sentence with the focus operator. We illustrate the dilemma in the following imaginary dialogue. (26)

Mother: Only Julia touched some of the kangaroos. Child: Does that mean that Tony didn’t touch some of the kangaroos? Mother: No, it means that Tony didn’t touch any of the kangaroos.

This dialogue develops two points. First, it shows that polarity sensitivity is a linguistic phenomenon that pertains to logical expressions that are pronounced aloud, but not to logical expressions that are generated covertly, e.g., as part of the assertion of focus operators. The fact that covert negation cancels the polarity sensitivity of PPIs invites the conclusion that polarity sensitivity is strictly a surface phenomenon. The superficiality of polarity sensitivity is underscored by the previous observation that PPIs are only interpreted outside the scope of negation if these two logical expressions both appear in the same clause. A second point is that the PPI some and the NPI any receive the same semantic analysis in sentences with focus operators. This reinforces the analysis of both expressions as allomorphs, both of them referring to the same logical concept, ∃.

236  Two logical operators for the price of one 6.6

Focus operators across languages: the case of Mandarin

The inner workings of focus operators are similar in Mandarin and in English, though there are some subtle differences. Consider example (27). The English counterpart would be Julia didn’t eat some kangaroo, where kangaroo is a mass term, referring to kangaroo meat. We have chosen to translate the English phrase … some kangaroo, as … yi-kuai[+/–]spec daishurou, which means ‘…a piece of kangaroo meat.’ (27)

Zhuliya meiyou chi yi-kuai[+/–]spec daishurou Julia not eat one-cl kangaroo-meat 茱莉亚没有吃一块袋鼠肉。 ‘Julia didn’t eat a piece of kangaroo meat.’

∃ > not, not > ∃

The subscript [+/–]spec indicates that the Mandarin example is ambiguous, depending on the scope of the phrase relative to negation. If … yi-kuai[+/–]spec daishurou is +spec, then this phrase takes scope over negation. The result is the ∃ > not reading. According to this reading, there must be a piece of kangaroo that Julia didn’t eat. On the other hand, if … yi-kuai[+/–]spec daishurou is –spec, then this yields the not > ∃ reading, and the sentence is true only if Julia didn’t eat any of the kangaroo meat. Now we can introduce the Mandarin focus operator zhiyou, which corresponds to English only. As with English only, Mandarin sentences with zhiyou, like (28), can be partitioned into a presupposition (29) and an assertion (30). The critical observation is that the assertion introduces a covert negation, and this eliminates one of the possible interpretations that was available in the sentence without zhiyou (25). The reading that is eliminated is the inverse scope reading, ∃ > not. So, everybody being contrasted with Julia didn’t eat any (*some) kangaroo meat. (28)

Zhiyou Zhuliya chi-le yi-kuai daishurou. Only Julia eat-asp one-cl kangaroo-meat 只有茱莉亚吃了一块袋鼠肉。 ‘Only Julia ate some kangaroo meat.’

(29)

Presupposition: 茱莉亚吃了一块袋鼠肉。 ‘Julia ate some kangaroo meat.’

(30) Assertion: Qita mei-ge-ren dou meiyou chi renhe Other every-cl-person all not eat any daishurou kangaroo-meat 其他每个人都没有吃任何袋鼠肉。 ‘Everyone else didn’t eat any kangaroo meat.’

not > ∃

6.7 Conjunction and disjunction are PPIs in some languages  237 (31) # Assertion: Qita mei-ge-ren dou meiyou chi yi-kuai+spec Other every-cl-person all not eat one-cl daishurou ∃ > not kangaroo-meat 其他每个人都没有吃一块袋鼠肉。 ‘There’s some kangaroo meat that everyone else didn’t eat.’

Because the covert negative operator introduced by zhiyou cancels the inverse scope reading, the assertion must be glossed using Mandarin NPI renhe (English any). The numeral+classifier yi-kuai cannot be used to express the meaning of the assertion, for the same reason that English some could not be used in expressing the assertion for (21). If either of these expressions is used in the assertion, the ambiguity re-emerges, since Mandarin yi-kuai and English some are PPIs. In several important respects, then, Mandarin and English share a common semantics for sentences with focus expressions, despite the fact that these languages are historically unrelated. The common semantics is attributed to principles of the innate logic faculty. So far we have established that polarity sensitivity is a surface phenomenon and that focus operators cancel the inverse scope relations associated with PPIs. These observations can be turned into a diagnostic test for the polarity sensitivity of logical expressions, as well as a means for establishing the basic meanings of such expressions. We will use what we have learned about focus operators to investigate the basic meanings and scope possibilities for the expressions for conjunction and disjunction across human languages. 6.7

Conjunction and disjunction are PPIs in some languages

This section begins with a very brief review of the two scope parameters described in Chapter 4, i.e., the Disjunction Parameter and the Conjunction Parameter. Then we review some relevant experimental findings from studies of child language showing that the inverse scope readings generated by one value of these parameters is canceled in sentences that contain focus operators. The two scope parameters proved to be of particular interest in adjudicating between the logical nativist approach and the experience-based approach. This is because these parameters involve default settings that are not attested in some languages. Therefore, the logical nativist approach, but not the experience-based approach, anticipates that children acquiring these languages will favor scope relations that are not attested by adult speakers. The default setting of the Conjunction Parameter corresponds to languages including Mandarin and Japanese, whereas English and German adopt the

238  Two logical operators for the price of one alternative value. In languages like Mandarin and Japanese, conjunction is +PPI, and takes scope over local negation. This generates a stronger reading than the reading that corresponds to the –PPI value of the Conjunction Parameter, as in languages like English and German. Based on considerations of language learnability, the logical nativist account predicted that English-speaking children should initially favor the setting that corresponds to Mandarin and Japanese, rather than the setting that is used by adult English speakers. This was experimentally confirmed. The Disjunction Parameter partitions the same language families, but in the opposite way. In languages like Mandarin and Japanese, disjunction is +PPI, and takes scope over local negation. In this case, however, disjunction generates a weaker reading than the reading that corresponds to the –PPI value of the Disjunction Parameter, as in languages like English and German. Based on considerations of language learnability, the logical nativist account predicted that Japanese- and Mandarin-speaking children should initially favor the setting that corresponds to English and German, rather than the setting that is use by adult English speakers. This was also experimentally confirmed. Taken together, these findings are compelling evidence that children are not guided by experience in postulating their initial interpretations of the scope relations of logical expressions. Rather, children are initially guided by innately specified principles and parameters. One of the main goals of this book has been to show that human languages and classical logic adopt the same meanings for disjunction and conjunction, as well as some other logical expressions. In classical logic, the logical connectives for negation, ¬, disjunction, ∨, and conjunction, ∧, make specific contributions to the truth of the formulas that contain them. These truth conditions are the basis of entailments, as stated in de Morgan’s laws of propositional logic. In human languages, counterparts to these logical connectives appear, such as the English expressions not, or, and and, and the corresponding Mandarin Chinese expressions mei, huozhe and he. Conventional wisdom maintains that these expressions in human languages differ in important respects from the corresponding expressions in classical logic. In our view, the differences reside in the scope relations that different languages assign to combinations of these logical expressions. In contrast to classical logic, there are two possible scope assignments in human languages for the logical expressions not and or, as well as for not and and. When human languages appear to violate the laws of logic pertaining to negated conjunctions and negated disjunctions, appearances are deceiving according to the logical nativist account. To show this, we will now discuss a linguistic structure that cancels the scope relations that are

6.8 Covert negation cancels polarity sensitivity  239 manifested in human languages, but not in classical logic. Doing so clears the decks for an unobstructed view of the commonalities of human languages and classic logic. 6.8

Covert negation cancels polarity sensitivity

We have seen that English-speaking adults interpret (32) in conformity with one of de Morgan’s laws of propositional logic: ¬(A ∧ B) ⇒ ¬A ∨ ¬B. Englishspeaking children differ from adults in how they interpret negated conjunctions. Children assign the logical form ¬A ∧ ¬B to sentences like (32). (32)

John didn’t eat both an apple and a pear.

We have also seen that English-speaking children and adults interpret (33) in conformity with another of de Morgan’s laws: ¬(A ∨ B) ⇒ ¬A ∧ ¬B. (33)

John didn’t eat an apple or a pear.

That is, English disjunction licenses a conjunctive entailment when it appears inside the scope of negation. Next, it will be useful to consider how Englishspeaking adults interpret sentences with the focus operator only. An example sentence with only and and is (34), and one with only and or is (35). These examples differ from the negated conjunction in (32) and the negated disjunction in (33) in two ways. First, they include the focus operator only. Second, they do not include overt negation. (The point is that negation is introduced covertly, in the assertion.) The presupposition of (34) and (35) pertains to the focus element, John. The meaning of the presupposition is roughly the same meaning that would be assigned to the sentence if the focus operator was removed. (34)

Only John ate both an apple and a pear. Presupposition: John ate both an apple and pear. Assertion: Everyone else didn’t eat both an apple and a pear: ¬(A ∧ B) ⇒ ¬A ∨ ¬B

(35)

Only John ate an apple or a pear. Presupposition: John ate an apple or pear. Assertion: Everyone else didn’t eat an apple or a pear: ¬(A ∨ B) ⇒ ¬A ∧ ¬B

The critical meaning component in these examples is the assertion. The assertion of (34) remains consistent with de Morgan’s laws, and so does the assertion of (35). So, adding a focus operator does not alter the scope relation that obtained in negated conjunctions, and in negated disjunctions, in

240  Two logical operators for the price of one languages in which conjunction and disjunction are –PPI, at least for adults. English-speaking children, however, were found to interpret conjunction as +PPI. If focus operators cancel polarity sensitivity, then English-speaking children are expected to pattern like their adult counterparts in interpreting sentences such as (34). Not only would this finding be evidence in favor of the analysis of the Conjunction Parameter as a scope parameter, if we find that English-speaking children interpret (34) in the same way as adults, it would also constitute evidence that children adhere to the relevant one of de Morgan’s laws: ¬(A ∧ B) ⇒ ¬A ∨ ¬B. What happens in languages in which adult speakers interpret conjunction and disjunction as +PPI? As we have seen, the Mandarin Chinese expressions for conjunction, he, and disjunction, huozhe, are both +PPI for adults. As such, these expressions take scope over negation in negative sentences, as illustrated in (36) and (37). In exact opposition to adult English, negated conjunctions have the logical form ¬A ∧ ¬B in Mandarin, and negated disjunctions have the logical form ¬A ∨ ¬B in (adult) Mandarin. Mandarin-speaking children differ from their adult counterparts in the interpretation that they assign to negated disjunctions. Children assign the logical form ¬A ∧ ¬B, as in English, whereas adults assign the logical form ¬A ∨ ¬B. (36)

Yuehan meiyou chi pinguo he li. John not eat apple and pear 约翰没有吃苹果和梨。 ‘It’s an apple and a pear that John didn’t eat.’

(37)

Yuehan meiyou chi pinguo huozhe li. John not eat apple or pear 约翰没有吃苹果或者梨。 ‘It’s an apple or a pear (or possibly both) that John didn’t eat.’

When focus operators enter the picture, massive changes in interpretation are expected. The covert negation that is introduced in the assertion of sentences with focus operators is predicted to cancel the inverse scope interpretation that is assigned to PPIs in sentences with overt negation. 6.9

Conjunction and focus

Based on the discussion in the previous section, here is the first prediction. The covert negation introduced in the assertion of sentences with focus operators should take scope over conjunction, even in languages like Mandarin and Japanese, where conjunction takes scope over negation in sentences with overt negation. Let us follow up this prediction, before we proceed to the second

6.9 Conjunction and focus  241 prediction, about the interpretation of disjunction. Consider the Mandarin example in (38). (38)

Zhiyou Yuehan chi-le pinguo he li. Only John eat-asp apple and pear 只有约翰吃了苹果和梨。 ‘Only John ate an apple and a pear.’

Example (38) differs from the negated conjunction in (36) in two ways: it includes the focus operator zhiyou, but does not include overt negation. The presupposition of (38) pertains to the focus element, Yuehan. The meaning of the presupposition is roughly the same meaning that would be assigned to the sentence if the focus operator was removed, as in (39). (39)

Zhiyou Yuehan chi-le pinguo he li. 只有约翰吃了苹果和梨。 Presupposition: John ate both an apple and a pair.

The assertion is the critical meaning component. The assertion pertains to the contrast set. As we have seen, everyone in the contrast set must lack the property being attributed to the focus element. The property being attributed to Yuehan is the content of the verb phrase. The assertion entails that everyone else lacks this property. The assertion is given in (40). In the assertion, negation takes scope over conjunction, so the assertion conforms to the relevant one of de Morgan’s laws: ¬(A ∧ B) ⇒ ¬A ∨ ¬B. Recall that this law was not operative for the negated conjunction in (36), because conjunction took scope over negation in that case. Note in this regard that the assertion of (40) is not as shown in (41), where conjunction takes scope over negation. The interpretation in (41) would be expected if conjunction he was analyzed as +PPI. (40)

Zhiyou Yuehan chi-le pinguo he li. 只有约翰吃了苹果和梨。 Assertion: Everyone else didn’t eat both an apple and a pear: ¬(A ∧ B) ⇒ ¬A ∨ ¬B

(41)

Zhiyou Yuehan chi-le pinguo he li. 只有约翰吃了苹果和梨。 #Assertion:  It’s an apple and a pear that everyone else didn’t eat. ¬A ∧ ¬B

The conclusion is that Mandarin sentences with zhiyou, with its covertly negated conjunction, adhere to the relevant one of de Morgan’s laws after all. This is another outcome in favor of logical nativism.

242  Two logical operators for the price of one 6.10

Disjunction and focus

The second prediction is about the interpretation of disjunction in sentences with focus operators. The covert negation introduced in the assertion of sentences with focus operators should take scope over disjunction, even in languages like Mandarin and Japanese, where conjunction takes scope over negation in sentences with overt negation, at least for adult speakers. That is, disjunction words – which are PPIs in ordinary negative statements – should lose their PPI-hood in the assertion of Mandarin sentences with the focus operator zhiyou, and in the assertion of Japanese sentences with the focus operator dake. Consider example (42), which can be compared to the earlier example of a simple negated disjunction, repeated here as (43). (42)

Zhiyou Yuehan chi-le pinguo huozhe li. Only John eat-asp apple or pear 只有约翰吃了苹果或者梨。

(43)

Yuehan meiyou chi pinguo huozhe li. John not eat apple or pear 约翰没有吃苹果或者梨。 ‘It’s an apple or a pear (or possibly both) that John didn’t eat.’

Again, the example with the focus operator (42) differs from the negated conjunction in (43) in two ways. Example (42) includes the focus operator zhiyou, but does not include overt negation, as in (43). The presupposition of (42) pertains to the focus element, Yuehan. The meaning of the presupposition is indicated in (44). (44)

Zhiyou Yuehan chi-le pinguo huozhe li. 只有约翰吃了苹果或者梨。 Presupposition: John ate an apple or a pear.

The assertion pertains to everyone in the contrast set. As we have seen, everyone in the contrast set must lack the property being attributed to the focus element. The assertion entails that everyone in the contrast set lacks this property. The assertion is given in (45). In the assertion, negation takes scope over conjunction, so the assertion conforms to the relevant one of de Morgan’s laws: ¬(A ∨ B) ⇒ ¬A ∧ ¬B. This law was not operative for the negated disjunction in (43), because conjunction took scope over negation in that case. So, the assertion of (42) is not as shown in (46), with disjunction taking scope over negation. The illicit assertion in (46) would be expected if disjunction houzhe was analyzed as +PPI. (45)

Zhiyou Yuehan chi-le pinguo huozhe li. 只有约翰吃了苹果或者梨。 Assertion: Everyone else didn’t eat an apple or a pear: ¬(A ∨ B) ⇒ ¬A ∧ ¬B

6.11 Focus operators in child language  243 (46)

Zhiyou Yuehan chi-le pinguo huozhe li. 只有约翰吃了苹果或者梨。 #Assertion: It’s an apple or a pear that everyone else didn’t eat: ¬A ∨ ¬B

The conclusion is that Mandarin sentences with zhiyou and houzhe adhere to another of de Morgan’s laws. This is further reassurance for logical nativism. 6.11

Focus operators in child language

Everyone agrees that children are able to compute the presupposition of sentences with focus operators. This is hardly surprising, since the presupposition is the meaning that is generated by the sentence without taking into account the contribution of the focus operator. So, children will compute a meaning that is equivalent to that of the presupposition even if they fail to understand the semantic contribution of focus operators. Controversy surrounds children’s understanding of the second meaning component, the assertion. As we have seen, the assertion requires the computation of a set of elements being contrasted with the element in focus. It has been proposed that children’s limited computational resources prevent them from computing such contrast sets. As a consequence, the proposal goes, children fail to generate the assertion associated with focus operators. The controversy boils down to a disagreement on whether children differ from adults because children fail to compute the assertion, or rather because children and adults select different focus elements. This section briefly reviews some experimental evidence that addresses this controversy. It has become clear, based on recent experimental findings that we review in the following sections, that children do compute the assertion, and that they differ from adults in the selection of the focus element. Let us begin by illustrating how children and adults differ in responding to sentences with focus operators. Consider a situation in which a cat and a duck are both holding flags, and the duck is also holding a balloon. Suppose someone makes the following statement as a description of the situation: Only the cat is holding a flag. For adults, this statement is not an accurate description of this situation, since the assertion entails that no member of the set of alternatives to the focus element (the cat) has the property being attributed to the focus element, holding a flag. The fact that the duck is holding a flag falsifies the assertion. It has been found, however, that many young English-speaking children accept this sentence as a description of the situation under consideration. Based on such experimental findings, Crain et al. (1994) conclude that some children initially associate pre-subject only with the VP in sentences like

244  Two logical operators for the price of one Only the cat is holding a flag. The claim is that children interpret the sentence Only the cat is holding a flag in the same way as the sentence The cat is only holding a flag, where the focus operator only has been moved to a position immediately preceding the VP. In both sentences, the focus operator is associated with the VP, holding a flag. So, children understand the assertion to be that the only thing the cat is doing is holding is a flag, or the only thing the cat is holding is a flag. An alternative account of children’s non-adult responses has been advanced by Paterson, Liversedge, Rowland, and Filik (2003), who suggest that children generate the presupposition associated with only (in the present example, the cat is holding a flag), but are unable to generate the assertion (no one else is holding a flag). Essentially, Paterson and colleagues conclude that young children cannot mentally represent contrast set information. To support this conclusion, Paterson et al. (2003) conducted several experiments aimed at controlling for what they call the VP Scope analysis advanced by Crain et al., according to which children associate the focus operator with the verb phrase in sentences with pre-subject only. The VP Scope analysis is contrasted with the proposal that children fail to process the assertion, i.e., the No Scope ­analysis. These researchers found that in response to test sentences with presubject only (e.g., Only the fireman is holding a hose), 4- to 5-year-old children produced a pattern of responses to six pictures that was uniquely consistent with the No Scope analysis 25 percent of the time, whereas children produced a pattern of responses uniquely consistent with the VP Scope analysis only 5 percent of the time. In response to test sentences with pre-verbal only (e.g., The fireman is only holding a hose), children again produced a high percentage (38 percent) of No Scope responses. Similar patterns of results were obtained for older children. Paterson et al. argue, on the basis of these findings, that the primary reason that children produced non-adult responses to sentences with only in previous studies was because they had also failed to process the assertion. It is likely that non-adult responses to only sentences were evoked from children due to a failure to compute the assertion in the Paterson et al. study. However, it is unlikely that this was the source of children’s non-adult responses in other research. In retrospect, it seems that Paterson et al.’s task artificially induced an abnormally high proportion of No Scope responses, as well as other kinds of erroneous responses. A closer examination of the results reveals that, for the most part, there was no recognizable pattern of correct or incorrect responses by any of the groups of children that were tested (up to age 12) or even by the adult control group. This suggests that the task was quite confusing for both children and adults. Moreover, both child and adult subjects

6.11 Focus operators in child language  245 showed relatively high proportions of another type of unexpected response, an NP Scope response, in which pre-verbal only was associated with the subject NP. The youngest children (4–5 years) produced this response 12.5 percent of the time and adults produced this response 9 percent of the time, which was just as often as 6- to 7-year-old children. These relatively high levels of NP Scope responses provide a clue as to why subjects found the task confusing. Namely, the pictures that were used were more pragmatically felicitous for associating the focus operator with the subject rather than with the VP. Two characters (e.g., a fireman and a policeman) appeared in every picture, and these characters were holding some object (e.g., a hose or a ladder). Moreover, there were never any extra objects in the background. This context apparently led to erroneous NP Scope responses from both children and adults, regardless of the surface position of the focus operator only in the test sentences. Another finding is worthy of note. Even in contexts that favored the subject NP as the focus element, some children displayed a pattern of responses uniquely consistent with the VP Scope analysis, though adults never showed this non-adult pattern of behavior.5 In sum, the No Scope response is a possible response pattern by children, but the higher proportion of this type of response – as compared to the VP Scope response – was probably due to task demands in the Paterson et al. study, rather than being due to children’s inability to compute contrast sets. In subsequent work, Paterson et al. (2005) acknowledged that the scenarios used in their earlier (2003) study were pragmatically infelicitous. In the later study, Paterson et al. changed the task demands and elicited substantially fewer No Scope responses than in the earlier study. Several research findings invite the conclusion that children are able to ­construct contrast sets in response to sentences with only. We will review some of the relevant literature in the next section. In those studies, however, there were no VP Scope responses by children, due to certain design features of the experiments. So, before we turn to those studies, it will be useful to report the findings of a study of 3- to 6-year-old Mandarin-speaking children which evoked VP Scope responses to sentences with focus operators (Jing et al. 2005). In this study, children were presented with sentences with dou-shi ‘only’ in Mandarin, such as (47), which corresponds to the English sentence Only workers that are wearing hats took a hammer or a pair of pliers. In the context, there were three workers wearing hard hats and one without a hat. The workers with hard hats had a hammer or pliers, one of these three workers also had a wrench, and the worker without a hat had a hammer. For adults, the sentence Only workers that are wearing hats took a hammer or a pair of pliers was

246  Two logical operators for the price of one false as a description of this situation, because the worker without a hat had a hammer. (47)

Dou-shi dai-zhe maozi de gongren na-le chuizi huozhe foc-cop wear-prog hat de worker take-perf hammer or qianzi. pliers 都是戴着帽子的工人拿了锤子或者钳子。 ‘Only workers that are wearing hats took a hammer or a pair of pliers.’

The children in the study rejected the test sentences 87 percent of the time. Children’s rejections were not justified in the same way as adults’ were i.e., by reference to the worker without a hat. On 60 percent of the trials, children justified their rejections on the grounds that one of the workers wearing a hat was in possession of a wrench, not just a hammer or a pair of pliers. So, the interpretation children assigned to (47) was the same as the interpretation that would be given to the English sentence The workers that are wearing hats only took a hammer or a pair of pliers, where the focus operator dou-shi ‘only’ is positioned immediately preceding the VP. In other words, Mandarin-speaking children appear to be constructing a contrast set based on the content of the VP rather than being based on the content of the subject NP, as in adult Mandarin. Based on that finding and the findings of previous studies, we proposed that, when children assign VP Scope, they analyze only as a sentential adverbial which c-commands both the subject NP and the VP in the syntactic structure. The analysis we attribute to children is graphically depicted in example (48). In adult grammars, the focus operator and the subject NP form a constituent, which eliminates the VP scope interpretation. To explain why children and adults differ, we point out that many English adverbs of quantification (e.g., always, sometimes) tend to take sentential scope, regardless of their syntactic position (e.g., (Sometimes) a man who owns a donkey (sometimes) beats it), and this phenomenon is witnessed across the world’s languages. The claim is that children initially analyze focus adverbs such as only as taking sentential scope. Positive evidence informs children that their analysis must be abandoned, if necessary. Thus, this learnability scenario is consistent with the Continuity Hypothesis – the proposal that children’s linguistic analyses are restricted to ones that characterize adult languages (e.g., Crain 1991; Pinker 1984). In the experiments we review next, the protocols successfully eliminated the VP Scope interpretation. Once this interpretation was no longer under consideration, children clearly demonstrated their ability to compute the assertion of sentences with focus operators, in Japanese, in English, and in Mandarin.

6.12 Disjunction and focus in child language  247 (48)

IP ADV

IP

Only NP

I′

John I VP

ran the marathon

6.12

Disjunction and focus in child language

There have been a number of recent studies of how child and adult speakers of English, Japanese, and Chinese interpret disjunction and conjunction in sentences with focus operators (English only, Japanese dake, Chinese zhiyou). We will look first at experiments that presented the statement in (49) to children acquiring Japanese and to ones acquiring English. (49)

Only Bunny Rabbit ate a carrot or a pepper.

To understand the design of the experiments, we will make reference to the semantics of the statement in (49). This statement expresses two propositions, the presupposition and the assertion. The presupposition is derived simply by deleting the focus operator from the original sentence. This yields Bunny Rabbit ate a carrot or a pepper. For many speakers, there is an implicature of exclusivity not both in the presupposition. In any event, the presupposition is true if Bunny Rabbit ate either a carrot, or a pepper, but not both. Children’s understanding of the presupposition was investigated in one experimental Condition 1. The second proposition is the assertion. While holding the information from Condition 1 constant (Bunny Rabbit ate a carrot), experimental Condition 2 investigated children’ understanding of the assertion of (49). The assertion concerns individuals that are not mentioned in the sentence. To derive the assertion, the sentence can be partitioned into (a) a focus element and (b) a contrast set. Focus expressions are typically associated with a particular linguistic expression somewhere in the sentence. This expression is the focus element, and more often than not, the focus element receives phonological stress. In the sentence Only Bunny Rabbit ate a carrot or a pepper, the focus element is Bunny Rabbit. Condition 2 investigates children’s knowledge of the assertion, namely what

248  Two logical operators for the price of one is true or false of individuals in the contrast set. The members of the contrast set are individuals in the domain of discourse that are taken by the speaker and hearer to be alternatives to the focus element. These individuals should have been introduced into the conversational context before the sentence was produced; their existence is presupposed. In the present example, the contrast set consists of individuals being contrasted with Bunny Rabbit. The sentence would not be felicitous in the absence of this contrast set. In the present discourse, the contrast set consists of Winnie the Pooh and Cookie Monster. The assertion is about the contrast set. The assertion states that the members of the contrast set lack the property being attributed to the focus element. In Only Bunny Rabbit ate a carrot or a pepper, the assertion is the following claim: everyone else (= Winnie the Pooh and Cookie Monster) did not eat a carrot or a pepper. The critical point is that the assertion contains disjunction in the scope of a local downward-entailing operator, e.g., negation or its semantic equivalent. Because disjunction appears under a downward-entailing operator in the assertion, a conjunctive entailment is licensed: everyone else didn’t eat a carrot and didn’t eat a pepper. To recap, the circumstance presented in Condition 1 was designed to examine children’s interpretation of the presupposition. Children are expected to accept the sentence Only Bunny Rabbit ate a carrot or a pepper in the circumstance in which Bunny Rabbit ate the carrot but not the pepper. In Condition 2, the Bunny Rabbit again ate the carrot. So, if children access the presupposition, but not the assertion, then their response in Condition 2 should be based on what the Bunny Rabbit ate, and not on what Winnie the Pooh and Cookie Monster ate. However, if children compute the assertion, as well as the presupposition, then their response to Condition 2 should reflect their assessment about Winnie the Pooh and Cookie Monster. The assertion entails that Winnie the Pooh and Cookie Monster did not eat either the carrot or the pepper. In the circumstance corresponding to Condition 2, Cookie Monster ate a pepper. Therefore, if children compute the assertion, they should reject the sentence Only Bunny Rabbit ate a carrot or a pepper in Condition 2. The same conditions were presented to children acquiring Japanese, and to children acquiring Mandarin. Despite the linguistic differences, English sentences with only, Mandarin sentences with zhiyou, and Japanese sentences with dake are all analyzed in the same way, as in (50). (50)

Only Bunny Rabbit ate a carrot or a pepper. Usagichan-dake-ga ninjin ka piiman-wo taberu-yo. rabbit-only-nom carrot or pepper-acc eat-dec Presupposition: Bunny Rabbit ate a carrot or a pepper. Assertion: Everyone else did not eat a carrot or a pepper.

6.12 Disjunction and focus in child language  249

Figure 6.1. Condition 1

The interpretation children assign to English disjunction or and to Japanese disjunction ka was investigated in sentences with focus operators in a series of experiments by Goro, Minai, and Crain (2005, 2006; Minai, Goro, and Crain 2006). In one experiment, twenty-one English-speaking children (mean age = 5;0) and twenty Japanese-speaking children (mean age = 5;4) participated. Condition 1 was designed to see if children assign ‘disjunctive’ truth conditions to or/ka in the presupposition of sentences with only/dake. As we just described, the test sentences were presented following a story in which Bunny Rabbit ate a carrot but not a pepper. The other characters in the story, Winnie the Pooh and Cookie Monster, did not eat either a carrot or a pepper. The circumstance associated with Condition 1 is summarized in the table in (51), and graphically depicted in Figure 6.1. (51)

Condition 1: The presupposition Carrot

Pepper

Winnie the Pooh

*

*

Bunny Rabbit

√

*

Cookie Monster

*

*

250  Two logical operators for the price of one Condition 2 was designed to see if children generate a conjunctive entailment in the assertion of sentences with only/dake. The test sentences were presented (to different children) following a story in which Bunny Rabbit ate a carrot and Cookie Monster ate a pepper. This condition is graphically represented in (52). (52)

Condition 2: The assertion Carrot

Pepper

Winnie the Pooh

*

*

Bunny Rabbit

√

*

Cookie Monster

*

√

In Condition 2, Cookie Monster ate a pepper. Because only/dake are downward entailing in the assertion, the test sentences were expected to generate a conjunctive entailment. The assertion is that everyone else (Winnie the Pooh and Cookie Monster) did not eat a carrot and did not eat a pepper. Therefore, children were expected to reject the test sentences in Condition 2, on the grounds that Cookie Monster ate a pepper. Children responded exactly as predicted. In Condition I, both Englishspeaking children and Japanese-speaking children accepted the test sentences over 90 percent of the time. The high acceptance rate in Condition 1 suggests that children assigned disjunctive (not both) truth conditions to or in the presupposition. In contrast, the same children rejected the test sentences in Condition 2 over 90 percent of the time. (Adult controls accepted Condition 1 sentences 100 percent of the time and rejected Condition 2 sentences 100 percent of the time in both languages.) The high rejection rate by children in Condition 2 suggests that both children acquiring Japanese and ones acquiring English know that the disjunction operator or creates conjunctive entailments in the assertion of sentences with only/dake. The findings invite the inference that children have adult-like knowledge about the semantics of only/dake, and are able to compute its complex semantic interaction with disjunction. Similar experiments have been conducted with Chinese-speaking children, with the same pattern of results (Jing et al. 2005). We interpret the findings as compelling evidence against the claim in the literature that children lack the computational resources to compute the assertion meaning component of sentences with focus operators (e.g., Paterson et al. 2003). We wish to make three concluding remarks about the interpretation of disjunction in sentences with focus operators. First, it is likely that sentences with

6.12 Disjunction and focus in child language  251 disjunction in the scope of focus expressions generate conjunctive entailments in all human languages. This is advanced as a putative linguistic universal by Crain (2008): disjunction generates a conjunctive entailment in the assertion of focus expressions. This leads to the second point. Supposing that all human languages are such that disjunction generates a conjunctive entailment in sentences with focus operators, then all human languages adhere to one of de Morgan’s laws: ¬(A ∨ B) ⇒ ¬A ∧ ¬B. The third point is subtle, so we will take it in steps. The issue is how the meaning of the assertion component of focus operators is acquired by children. We have seen that, in the assertion of sentences with focus operators, disjunction is assigned the inclusive-or truth conditions of classical logic, even in languages where disjunction is a PPI in negative sentences. By examining their interpretation of sentences with focus operators, we discovered that both child and adult speakers of these languages know that disjunction is inclusive-or. We conclude this because speakers of Japanese and Mandarin interpret disjunction to generate a conjunctive entailment in sentences with focus operators, just as speakers of English do. The question becomes, then, how do children come to know that if covert negation c-commands disjunction, its polarity sensitivity is rendered inert? It seems unlikely that parents provide the necessary input to inform children that disjunction generates a conjunctive entailment in sentences with focus operators. Here is why. To provide this information, parents would have to provide children with evidence that the meaning of the assertion of sentences with focus operators generates a conjunctive entailment. But how could parents convey this information? Recall that in Japanese and Chinese, the translation of a simple negative statement with disjunction (e.g., Bunny Rabbit didn’t eat the carrot or the pepper) does not generate a conjunctive interpretation. Rather, adult speakers of these languages judge the corresponding sentences to mean that Bunny Rabbit didn’t eat the carrot or Bunny Rabbit didn’t eat the pepper. But now consider the interpretation of the assertion of the sentence with the focus operator: Only Bunny Rabbit ate the carrot or the pepper. The assertion is about the contrast set, and it asserts the proposition that everyone else did not eat the carrot or the pepper. Here is the rub. Suppose adult speakers of Chinese or Japanese try to provide input to children about the meaning of the assertion. It is difficult to see how they can accomplish this. The problem is, if adults actually produce the assertion, then they must use overt negation. But disjunction does not generate a conjunctive entailment in the scope of overt negation, whereas it does in the scope of covert negation. To appreciate the learnability dilemma, notice

252  Two logical operators for the price of one that the Japanese sentence in (53) and the Chinese sentence (54), with overt negation, do not generate a conjunctive interpretation, because these are simple negative statements with disjunction and negation in the same clause. The sentences (53) and (54) mean that everyone else didn’t eat a carrot or didn’t eat a pepper. (53)

Usagichan igai-no zen’in-ga ninjin ka piiman-wo tabe-nakat-ta. rabbit except-gen everyone-nom carrot or pepper-acc eat-neg-past ‘Everyone except Bunny Rabbit didn’t eat a carrot OR didn’t eat a pepper.’

(54)

Qita meigeren, tamen meiyou chi huluobo huozhe qingjiao.6 other everyone they not eat carrot or pepper 其他每个人他们没有吃胡萝卜或者青椒。 ‘For everyone else, they didn’t eat a carrot or they didn’t eat a pepper.’

So, adult speakers of Japanese and of Chinese are in a bind if they want to instruct their children about the assertion of sentences with focus operators. If they produce the assertion verbatim, they must use overt negation. But if parents use overt negation, then disjunction is no longer interpreted in the scope of negation. In the presence of overt negation, disjunction is +PPI, so it takes scope over negation, and no longer generates a conjunctive entailment. Rather, the interpretation is disjunctive – everyone being contrasted with Bunny Rabbit didn’t eat a carrot, or didn’t eat a pepper, or perhaps neither one. But the both not reading is just one of the truth conditions adults assign to sentences like (54). Moreover, a scalar implicature becomes operative when disjunction is outside the scope of negation, so the both not reading is disfavored. It remains, then, to explain how children could learn the meaning of the assertion of sentences with focus operators from their primary linguistic data. We leave this as another challenge for the experience-based approach. Of course, on the logical nativist approach, there is nothing to learn. The hidden entailment is part of the meaning of focus operators for all speakers of all human languages. 6.13

Conjunction and focus in child language

The next structure to cover is children’s interpretation of and in sentences with focus operators. A series of experiments have been conducted to test children’s access to the Boolean not both interpretation of the conjunction operator and within the covert negative proposition associated with sentences containing focus operators. The experiments employed the truth-value judgment task in the description mode. The storylines of the experimental trials were similar, so we will describe just one experimental protocol. The story involved a magic competition, in

6.13 Conjunction and focus in child language  253 which three would-be magicians (Aladdin, Neptune, and Genie) attempted to perform feats of magic. In one experiment, toy figures of the three would-be magicians were manipulated by one experimenter, while another experimenter coordinated a computer-generated animated presentation of feats of magic, which was implemented as the toy figures pronounced their magic words. The subject witnessed the three would-be magicians uttering magic words as they gestured towards objects displayed on a computer screen. Subsequently, objects were animated by the experimenter working the computer (e.g., boxes shook and opened, cars flipped over, a frog turned into a princess). Each of the magicians was awarded a prize if he succeeded in performing one of the feats of magic. These prizes served as reminders for children whose task was to judge the truth or falsity of the test sentences. The test sentences were produced by a puppet, Kermit the Frog (manipulated by a third experimenter), who watched the magic competition along with the child subject. At the end of each trial, Kermit the Frog said what he thought happened on the trial, using one of the test sentences. In (55) we give an example of an English test sentence, with only and and. (55)

Only Aladdin opened the blue box and the black box. Presupposition: Aladdin opened the blue box and the black box. Assertion: Everybody else did not open both the blue box and did not open the black box.

The main interest is children’s interpretation of the assertion. If the conjunction word and takes scope over negation, as it does for English-speaking children in simple negated conjunctions, then they should assign the both not (neither) interpretation to (55). That means that children should judge the sentence to be false if someone other than Aladdin (say Genie) succeeded in opening one of the boxes, but not the other. However, the sentence is true in that same circumstance on the not both interpretation of and, since Genie didn’t open both of the boxes. So, if children assign the not both interpretation, as in classical logic, then they should accept (55) as an accurate description of the situation. Notice, finally, that the presupposition (that Aladdin opened both boxes) is satisfied in this condition. This condition is schematically represented in (56). (56)

Condition 1 blue box

black box

Aladdin

√

√

Neptune

*

*

Genie

√

*

254  Two logical operators for the price of one In addition to Condition 1, there were two control conditions. These control conditions were included to ensure that children did not give the right answers for the wrong reasons. This is an important feature of all of the experiments we conduct with children. Controls are especially critical in cases where the experimental hypothesis is confirmed by children’s acceptance of the test sentences. It is well known that subjects who are unsure about the task, or misunderstand the sentences presented to them, tend to be overaccepting and produce “Yes” responses. Or children might say “Yes” in response to Kermit’s target sentences, simply because they like Kermit. It is important to include control conditions in which children produce negative judgments about Kermit’s descriptions of the stories. In this way, the experimenter can identify children who say “Yes” consistently, so that these children can be eliminated from the data analysis. As usual, when children indicate that Kermit said the wrong thing, they are asked to explain why. The production data obtained from this component of the task provides a further check to ensure that children understand the task, are paying attention, and are basing their decisions on the events that transpired in the story. In the present study, there were two control conditions, both of which were expected to evoke negative responses from children. One of the two control conditions examines children’s understanding of the presupposition Aladdin opened the blue box and the black box. Condition 2 falsified the presupposition, because Aladdin was successful in opening only one of the boxes, but not the other. This condition is represented in the table in (57).7 (57)

Condition 2 blue box

black box

Aladdin

*

√

Neptune

*

*

Genie

√

*

As in Condition 1, Condition 3 satisfied the presupposition, but not the assertion. This time, Genie successfully opened both boxes. So the assertion that everyone else didn’t open at least one of the boxes was resoundingly falsified. Still, children had to be computing the assertion, and not just the presupposition, in order to render a negative judgment in response to the test sentence in this condition.

6.13 Conjunction and focus in child language  255 (58)

Condition 3 blue box

black box

Aladdin

√

√

Neptune

*

*

Genie

√

√

Twenty English-speaking children (ages 3;10–6;3, mean age = 4;11) participated in the experiment. The overall results were highly consistent with the experimental hypotheses. Children accepted Kermit’s statements in Condition 1 95 percent of the time, but only 15 percent of the time in Condition 2, and only 10 percent of the time in Condition 3. The pattern of responses by adults was the same as that of children. The most important finding is that children consistently accepted the test sentences in Condition 1. This response pattern is consistent with the relevant one of de Morgan’s laws: ¬(A ∧ B) ⇒ ¬A ∨ ¬B. And it revises the scope relations between negation and conjunction that were observed when children responded to negated conjunctions, as in (60), thereby showing that focus operators bring to the surface children’s adherence to the laws of classical logic, but introducing negation covertly rather than overtly. (59) Only Aladdin opened the blue box and the black box. Assertion: Everybody else didn’t open the blue box and the black box: ¬A ∨ ¬B (60)

Aladdin didn’t open both the blue box and the black box. ¬A ∧ ¬B

Children’s adherence to the interpretation of conjunction has also been demonstrated in children acquiring Japanese in a study by Goro et al. (2005, 2006). These researchers found that Japanese children consistently accepted the not both interpretation of Japanese conjunction …mo…mo when it appeared in the scope of the covert negation that is associated with sentences containing the focus operator dake (only). Like disjunction ka, Japanese conjunction …mo… mo is never interpreted by adults to be within the scope of local negation in simple negative sentences (see Goro 2004). Therefore, the vast majority of the input to Japanese-speaking children fails to exemplify the logical character of …mo…mo; nonetheless, children acquiring Japanese proved to be aware of the logical character of conjunction, and the relevant one of de Morgan’s laws: ¬(A ∧ B) ⇒ ¬A ∨ ¬B We have recently replicated these experiments with children acquiring Mandarin, using the focus operator zhiyou, and the pattern of results is exactly

256  Two logical operators for the price of one as expected on the logical nativist account. The experience-based approach (e.g., Goldberg 2003; Tomasello 2000) owes us an explanation of this uniformity across languages, as well as an explanation of how the logical interpretations of disjunction and conjunction arise in sentences with focus operators like English only, Japanese dake, and Mandarin zhiyou. 6.14

Quantification without qualification

This brings us to the final topic of the present chapter. The concluding piece concerns children’s knowledge of the different truth conditions that disjunction bears in downward-entailing contexts versus in non-downward-entailing contexts. This difference in meaning sometimes arises even in the same sentence. As we observed in Chapter 1, downward entailment comes with a twist in sentences with the universal quantifier, e.g., English every. In sentences with a pre-subject universal quantifier, the subject phrase of the sentence is downward entailing, but the predicate phrase is not. To see this, consider the following inference: if every cow ate a vegetable, then every brown cow ate a vegetable. This inference strikes English speakers as logically valid. In this inference, a general term in the subject phrase, cow, has been replaced by a more specific term, brown cow. The same kind of substitution is not valid, however, if we attempt the same substitution in the predicate phrase of the sentence with pre-subject every. Consider the following inference: if every cow ate a vegetable, then every cow ate a green vegetable. This inference is clearly not valid, yet we have simply replaced the general term, vegetable, by a more specific term, green vegetable. In short, the subject phrase of sentences with pre-subject every validates inferences from expressions referring to sets of things to expressions referring to subsets of those things. By contrast, the predicate phrase of sentences with pre-subject every does not validate such inferences. The same asymmetry arises in conditional statements. In the antecedent of conditionals, it is valid to replace a general term with a specific term, but the same replacement is not valid in the consequent of conditionals. The asymmetrical nature of these linguistic structures extends to the interpretation of disjunction and to the licensing of negative polarity items. We will use disjunction to illustrate. As we just mentioned, the antecedent of a conditional is downward entailing, but the consequent is not. As a result, disjunction gives license to a conjunctive entailment when it appears in the antecedent, but not when it appears in the consequent. This can be verified by looking at the examples in (61) and (62).

6.14 Quantification without qualification  257 (61) ANT[If Ted ordered pasta or sushi], CON[then Max ordered pizza] a. If Ted ordered pasta, then Max ordered pizza and b. If Ted ordered sushi, then Max ordered pizza (62) ANT[If Max ordered pizza], CON[then Ted ordered pasta or sushi] a. If Max ordered pizza, then Ted ordered pasta or b. If Max ordered pizza, then Ted ordered sushi

The same asymmetry holds for sentences with a pre-subject universal quantifier. This is shown schematically in (63) and (64). Examples were laid out in Chapter 1. (63) (64)

Every SUBJ[ … or … ] PRED[………….….]  Every SUBJ[ ….…….……] PRED[…. or …….]

= Conjunctive = Disjunctive

Another asymmetry is witnessed when we compare quantificational expressions that are downward entailing on their predicate phrase, versus ones that are not. For example, the quantificational expression nobody is downward entailing on its predicate phrase, but the quantificational expression everybody is not. The contrast is illustrated in (65) and (66). (65) (66)

Nobody who became ill Pred[ordered pasta or sushi] Everybody who became ill Pred[ordered pasta or sushi]

= Conjunctive = Disjunctive

According to logical nativism, these kinds of asymmetries should be manifested across languages. Mandarin is our litmus test, as usual. In Mandarin, the quantificational phrase corresponding to English nobody is meiyouren. Like English nobody, meiyouren is downward entailing on its predicate phrase. So, the Mandarin word for disjunction, huozhe, generates a conjunctive entailment when it appears in the predicate phrase of meiyouren, as shown in (67), just as we noted in (65) that English or generates a conjunctive entailment in the predicate phrase of nobody. (67)

Zai jiuhui shang meiyouren chi-guo shousi huozhe yidalimianshi. at party prep nobody eat-asp sushi or pasta 在酒会上没有人吃过寿司或者意大利面食。 ‘Nobody at the party ate sushi or pasta.’ = Conjunctive

The Mandarin counterpart to English everybody is the quantificational expression meigeren. The Mandarin disjunction word huozhe does not generate a conjunctive entailment in the predicate phrase of meigeren. This is verified in (68).

258  Two logical operators for the price of one (68)

Zai jiuhui shang meigeren chi-le shousi huozhe yidalimianshi. at party prep every-cl person eat-asp sushi or pasta 在酒会上每个人吃了寿司或者意大利面食。 ‘Everybody at the party ate sushi or pasta.’  = Disjunctive

Children must distinguish between structural positions in order to determine which positions are downward entailing and which are not. Until children can make these necessary distinctions, they could easily be led – by analogy – to make false generalizations. One possible error would arise from assuming that disjunction has a uniform interpretation in sentences with a pre-subject universal quantifier, i.e., in the predicate phrase, as well as in the subject phrase. Likewise, children might mistakenly permit negative polarity items in the predicate phrase, as well as in the subject phrase, in such sentences. It is important therefore to investigate whether or not children make the correct syntactic distinctions, leading to the correct semantic generalizations. The expectation of the nativist approach is that mistakes by children will be rare, or even nonexistent, because language acquisition is circumscribed by universal principles, and supplemented by innate knowledge of syntactic structure, as well as innate knowledge of the concept and consequences of downward entailment.

6.15

Asymmetric quantification in child language

Several studies have used the truth-value judgment task to investigate the truth conditions children associate with disjunction in the subject phrase versus the predicate phrase of the universal quantifier. For example, studies by Gualmini, Meroni, and Crain (2003) used the truth-value judgment task, in which children were asked to evaluate sentences like (69) and (70), posed by Kermit the Frog. (69) (70)

Every woman bought eggs or bananas. Every woman who bought eggs or bananas got a basket.

In one condition, sentences like (69) were presented to children in a context in which some of the women bought eggs, but none of them bought bananas. The child subjects consistently accepted test sentences like (69) in this condition, showing that they assigned a disjunctive interpretation to or in the predicate phrase of the universal quantifier every. In a second condition, children were presented with sentences like (70) in a context in which women who bought eggs received a basket, but not women who bought bananas. The child subjects consistently rejected the test sentences in this condition. This finding is evidence that children generated a conjunctive interpretation for disjunction in the subject phrase of every. This asymmetry in children’s responses in

6.15 Asymmetric quantification in child language  259

Figure 6.2. Every dog versus No dogs

the two conditions demonstrates their knowledge of the asymmetry in the two grammatical structures associated with the universal quantifier, i.e., the subject phrase and the predicate phrase. The findings represent a challenge to the experience-dependent approach to language acquisition. The challenge is posed by the asymmetry in the interpretation of the same disjunction, or, in the subject phrase versus the predicate phrase of the universal quantifier, since the distinction is one of interpretation, not the distribution, of the logical expression. The same asymmetrical pattern of responses has been found in other comparisons of downward-entailing environments and non-downward-entailing environments. In one experiment (with Esther Su), we investigated Mandarinspeaking children’s interpretation of disjunction huozhe in the predicate phrase of the downward-entailing quantificational expression meiyouren ‘nobody.’ We compared this to children’s interpretation of huozhe in the predicate phrase of the non-downward entailing quantificational expression meigeren ‘everybody.’ Twenty-four children participated in the study. They ranged in age from 4;01 to 5;03, with a mean age of 4;09. They were tested using the truth-value judgment task. Children were presented with sentences like (71) and (72) in a context that is graphically depicted in Figure 6.2. There were four dogs in the story and

260  Two logical operators for the price of one Minnie Mouse. Minnie Mouse put out lots of things for the dogs to choose from, including jewels of different colors. There were red jewels, green jewels, and purple jewels. Several dogs thought about taking a purple jewel, but in the end each dog chose a red jewel or a green one. As Figure 6.2 indicates, two dogs picked red jewels, two picked green jewels, and Minnie Mouse picked one of the purple jewels for herself. Following the story, Kermit the Frog produced the test sentences in (71) to one group of children, and (72) to a different group of children. (71)

Meiyou xiaogou zhai-guo baoshizihua huozhe baoshihonghua. not dog pick-asp purple jewel or red jewel 没有小狗摘过宝石紫花或者宝石红花。 ‘None of the dogs picked a purple jewel or a red jewel.’

(72)

Mei-zhi xiaogou dou zhai-le baoshilühua huozhe baoshihonghua every-cl dog all pick-asp green jewel or red jewel 每只小狗都摘了宝石绿花或者宝石红花。 ‘Every dog picked a green jewel or a red jewel.’

Children rejected the test sentences with meiyou, such as (71), 90 percent of the time. They justified their rejection of this particular sentence by pointing to the two dogs that had picked red jewels. This finding is evidence that children computed the conjunctive interpretation of disjunction in (71), so the sentence entailed that the dogs did not pick purple jewels and did not pick red jewels: ¬A ∧ ¬B. On the disjunctive interpretation, the sentence would mean that none of the dogs picked a purple jewel, or none of them picked a red jewel. Since none of the dogs picked a purple jewel, the sentence is true on this interpretation: ¬A ∨ ¬B. So, if children allowed the sentence to have a disjunctive reading, they would have accepted it. By contrast, children accepted sentences with mei-zhi…dou, as in (72), 94 percent of the time. This sentence is true on the disjunctive interpretation, according to which every dog picked a red jewel or a green jewel, or possibly both. This context for the control sentence, with every, was chosen to make sure that children do not conflate or and and, as suggested by some researchers (Paris 1973). In this regard, we would note that children did not require every dog to choose both a red jewel and a green jewel. Instead, they accepted (72) in the circumstance in which each dog picked one or the other. So, the conjunctive entailment was not licensed by children in response to sentences like (72).8 This asymmetry in children’s responses demonstrates their knowledge of the different assignment of truth conditions to the disjunction word huozhe when

6.15 Asymmetric quantification in child language  261

Figure 6.3. Disjunction in the subject phrase

it appears in the predicate phrase of a downward-entailing quantificational expression, versus when it appears in the predicate phrase of a non-downwardentailing quantificational expression. By the age of 4, then, Mandarin-speaking children know that downward-entailing expressions generate the conjunctive interpretation of disjunction, and that non-downward-entailing expressions do not. Mandarin Chinese patterns like English in many other respects. In both languages, the subject phrase of a sentence with a pre-subject universal quantifier is downward entailing, whereas the predicate phrase of the same sentence structure is not downward entailing. According to the logical nativist account, children acquiring Mandarin are expected to exhibit asymmetrical responses to disjunction in these two environments. This expectation was investigated using the truth-value judgment task. The endpoint of a typical trial is depicted in Figure 6.3. In the story that led up to this circumstance, there were five dogs and a bunny rabbit. The bunny rabbit distributed rewards to the five dogs, according to which kind of flower or plant they chose. Two of the dogs chose red flowers, and they were given butterflies. Two dogs chose white flowers, and they were given balls. One dog

262  Two logical operators for the price of one chose a green branch, and was given a star. Following the story, Kermit said what he thought happened in the story using the test sentence in (73). (73)

Mei-zhi zhai-dao xiaohonghua huozhe xiaobaihua de xiaogou Every-cl pick-asp red flower or white flower de dog dou dedao-le hudie. dou get-asp butterfly 每只摘到小红花或者小白花的小狗都得到了蝴蝶。 ‘Every dog that picked a red flower or a white flower got a butterfly.’

In sentence (73), the disjunction word huozhe appears in the subject phrase, so it is expected to generate a conjunctive entailment. If so, then the sentence entails that every dog that chose a red flower got a butterfly, and every dog that chose a white flower got a butterfly. Clearly, the circumstance depicted in Figure 6.3 makes (73) false on this interpretation. Accordingly, the child subjects rejected the test sentence 91 percent of the time. They were invited to tell Kermit why he was wrong. They explained to Kermit that he said the wrong thing because the two dogs that had chosen white flowers got balls, and not butterflies (Su and Crain 2009). In the second condition, the Mandarin disjunction word houzhe was placed in the predicate phrase of a sentence with a pre-subject universal quantifier, mei. In a typical story, there were five brave princesses out on an adventure to take back what had been stolen from them by a wicked witch. For protection, one princess brings along a magic bird and each of the four other princesses brings a dog. The witch happens to go away and all five princesses find lots of treasure to steal back: five jewels, five rings, one flower, and one star. The princess who has the magic bird quickly decides to steal back the blue flower. Two of the princesses with dogs say, “Jewels are more precious then flowers!” and each of them takes back a jewel. The other two princesses say, “Jewels are pretty, but rings are even better!” These two princesses each take back a ring. The final outcome is illustrated in Figure 6.4. After the story, Kermit produced the test sentence (74). Notice that (74) is true if children assign disjunctive truth conditions to huozhe. On a disjunctive reading, the sentence is true if every princess with a dog took back a jewel or a ring (or possibly both). However, if children fail to distinguish the two arguments of mei, they could reject sentence (74). There are at least two analyses of the test sentences that would result in negative judgments by children. A negative judgment could result if children understood huozhe ‘or’ to mean he ‘and.’ In this case, children would have taken sentence (74) to mean that every princess with a dog stole a jewel and a ring, so they would have rejected (74) on the grounds that each of the princesses with dogs took only one thing.

6.15 Asymmetric quantification in child language  263

Figure 6.4. Disjunction in the predicate phrase

There is a second analysis in which children would have rejected (74). If children analyzed both the subject phrase and the predicate phrase of the universal quantifier mei to be downward entailing, it would license a conjunctive entailment of disjunction in the predicate phrase, just as it does in the subject phrase. If so, the children’s interpretation of (74) would require every princess with a dog to have stolen both a jewel and a ring, contrary to fact. (74)

Mei-ge dai-zhe gou de gongzhu dou tou-le baoshi Every-cl carry-asp dog de princess dou steal-asp jewel huozhe jiezhi. or ring 每个带着狗的公主都偷了宝石或者戒指。 ‘Every princess who carried a dog stole a jewel or a ring.’

Children accepted the test sentences 95 percent of the time. This is evidence that children assigned disjunctive truth conditions to huozhe in the predicate phrase of mei, a non-downward-entailing context. These experimental findings resemble those reported earlier in studies of English-speaking children (e.g., Boster and Crain 1993; Gualmini et al. 2003). Taken together, the findings of the studies we have reviewed in this section show that, in typologically distinct languages, young children know that disjunction yields a conjunctive interpretation when it occurs in the subject phrase of the universal quantifier, but not in the predicate phrase of the universal quantifier. They also know that disjunction licenses a conjunctive entailment in the predicate phrase of certain downward-entailing quantificational expressions,

264  Two logical operators for the price of one such as meiyouren ‘nobody.’ The finding that children acquiring Mandarin and children acquiring English are sensitive to these structural asymmetries in the interpretation of disjunction in different structural positions shows that children have considerable knowledge of both syntax and semantics. Both structural position (syntax) and the meanings of logical expressions (semantics) are used by children to determine the different truth conditions associated with disjunction in downward-entailing contexts versus non-downward-entailing contexts. It is worth mentioning in this regard that the basic ingredients of the experience-based approach, communicative function and information structure, appear to be largely irrelevant in accounting for what children know. This is not to say that conditionals and sentences with the universal quantifier do not have communicative functions. They do. But communicative function and information structure do not seem relevant for children’s knowledge of the asymmetries in the interpretation of disjunction words in the linguistic structures we have investigated. 6.16

Conclusions

Children have demonstrated adult-like knowledge of the different truth conditions that are relegated to disjunction in different linguistic environments. These findings augment those reported in previous sections and in previous chapters, showing early emergence of semantic competence. We have described how the semantic property of downward entailment provides a unified account of disparate-looking linguistic phenomena. Chapter 4 reported the findings of several experimental assessments of children’s knowledge that English or and Mandarin huozhe yield a conjunctive interpretation when these expressions appear in the scope of negation. Chapter 5 reported the findings of several studies of children’s knowledge of the licensing conditions for English any and Mandarin renhe, as well as the licensing conditions governing the interpretation of Mandarin wh-words like shei ‘who’ and shenme ‘what.’ It turned out that the interpretation children assigned to Mandarin whwords shei and shenme depended on whether or not they are in a downwardentailing linguistic environment, just as it does for adults. Because downward entailment is the critical ingredient in the linguistic phenomena described in both Chapter 1 and Chapter 4, children were expected to master both phenomena early in the course of language development, and across human languages. This prediction was confirmed. Advocates of the experience-based approach, such as Croft (2001), contend that the categories of the child’s grammar are learned “inductively,” based on

6.16 Conclusions  265 the taxonomy of language-specific constructions that the child accrues. If so, not only could children interpret disjunction as exclusive-or, they should be expected to do so, in view of their experience. The prediction of the logical nativist account, by contrast, is that both English-speaking children and Mandarinspeaking children (and children acquiring any other language) should interpret disjunction differently when it appears in a downward-entailing linguistic context, as compared to when disjunction appears in a non-downward-entailing linguistic context. We have seen that, despite the fact that the majority of children’s experience is consistent with the exclusive-or interpretation of disjunction, there is abundant experimental evidence showing that children do not interpret disjunction as exclusive-or. On the experience-based approach, children’s early mastery of the interpretation of disjunction calls for explanation, as does children’s early adherence to the licensing condition for words like English any and Mandarin renhe, and children’s early appreciation of the distinction in the interpretation of whwords shei and shenme, as indefinites in certain contexts, and question words in other. Early mastery of these linguistic phenomena would be expected only to the extent that abundant evidence is available to children in the input. The availability of abundant input seems highly implausible, in view of the inherent complexity of the structures involved. In view of these observations, the fact that children have been found to rapidly master this cluster of complex properties, across languages, poses a challenge to experience-based approaches. It is incumbent on advocates of the experience-based approach to explain the findings from child language, as well as the fact that a range of apparently unrelated phenomena are manifested in typologically distinct languages, such as English and Mandarin.

Notes

1

Logic and human languages

1 In first-order logic, quantification is restricted to variables that range over individuals, the entities in the domain of discourse. In second-order logic, quantifiers are also able to bind variables that range over properties of individuals (sets of individuals), and to bind variables that range over functions. There are several linguistic phenomena that require the expressive power of (at least) second-order logic. In addition, second-order logic has proven useful in providing a compositional account of the meanings of sentences with quantificational expressions (Montague 1974). While we acknowledge that several phenomena in human languages require the resources of second-order logic, we will limit our discussion in this book to linguistic phenomena that can be handled using first-order logic. 2 The one exception is the discussion in Chapter 3, where we demonstrate how principles of syntax could be extended to discourse. 3 If disjunction is interpreted as exclusive-or, then a statement of the form ¬(A ∨ B) is true (i) if either A alone is true, (ii) if B alone is true, and (iii) if both A and B are true. If disjunction were exclusive-or in English, then the statement John didn’t see Ted order pasta or sushi would be true if John saw Ted order both dishes. No human language generates these truth conditions for disjunction in the scope of negation, as far as we know (cf. Crain and Khlentzos 2008; Jennings 2001). 4 More formally, negated disjunctions generate a conjunctive interpretation, in accord with de Morgan’s laws: ¬(A ∨ B) ⇒ (¬A ∧ ¬B). So, a negated disjunction ¬(A ∨ B) is true in only one circumstance, where ¬A and ¬B. However, a negated conjunction ¬(A ∧ B) is true in three circumstances where (i) ¬A and B, (ii) ¬B and A, and (iii) ¬A and ¬B. Since circumstance (iii), ¬A and ¬B, makes both statements true, it follows that a negated disjunction is true in a subset of the circumstances that corroborate a negated conjunction. 5 The representation of any as the universal quantifier having scope over negation is advanced by Quine (1986). There are reasons to doubt the analysis Quine proposes (see Carlson 1980). To take a simple counterexample, consider the meaning of the statement delivered on every international flight (following the safety instructions): If you are not sure about anything we have told you, please ask a flight attendant. According to Quine’s analysis, this statement should convey the message that you should ask the flight attendant if everything you were told was not clear to you. Clearly, the intended message is that you should ask the flight attendant if something you were told was unclear to you. 266

Notes to pages 22–43  267   6 The same asymmetry occurs in dou-conditionals in Mandarin.   7 Of course, it is also possible to give both negative and plural answers to wh-­questions, e.g., Nobody took Max’s iPhone, and Jon and Bill took Max’s iPhone. To accommodate such answers, we can partition the possible answers to wh-­questions into two sets – one that meets the existential presupposition (E), and one that does not. The Existential Presupposition is ∃x.ιy(iPhone[y] ∧ Owns [Max,y] ∧ Took [x,y] ∧ x≠Max), where ι is Russell’s iota operator roughly corresponding to English the. The set of E-positive answers = {a, b, c, …, {a, b}, {a, c}, …, {a, b, c}, …} and the set of E-negative answers = {Ø}.   8 The set of possible answers to the question Who took Max’s iPhone? would be the set containing the propositions a1 took Max’s iPhone, a2 took Max’s iPhone, a3 took Max’s iPhone … an took Max’s iPhone. More formally, the meaning is ∀P i=1Vi=n (P = ), which is the n-placed disjunction of all identities of the form P = < aj took Max’s iPhone>, so P = or P = or P = or … or P = . Since the meaning of a wh-question is formed by quantifying over a set, the meaning of wh-questions is not strictly speaking first-order.   9 Malayalam exhibits a similar pattern to Japanese (Jayaseelan 2001; Madhavan 1988, 1997). 10 Existential quantifiers that are formed by combining wh-words and disjunction often have a semantic restriction – these expressions are only felicitous when the identity of the person or thing is unknown to the speaker. This is true in Japanese and in Malayalam. By contrast, indefinites like English someone/something have no such restriction. The exceptions to this, in English, are indefinites that incorporate a whword, such as somewhere and somehow. In most circumstances, these expressions are used when the speaker is unaware of the exact location of an individual or entity (e.g., I left the book somewhere in the study), or is unaware of the reason why something happened (e.g., Max solved the problem somehow). In languages where the subject is the Topic, the opposite meaning restriction holds, i.e., indefinites in Topic position must be referring expressions (a.k.a. specific indefinites). For example, in Hungarian it is not acceptable to say something like An unknown person called: *Egy ismeretlen ember felhívott. 11 Again, we are passing over technical details. For example, if the wh-word is an unbound variable, then the question arises how it, by itself, can be interpreted as an existential quantifier. This is typically handled in the literature by invoking a covert operator, which has scope over the entire sentence and supplies existential force to the wh-word, or the existential force is attributed to a process called existential closure. 12 As noted, example (112) does not entail (113): (112)

No vet who treated every dog in town was vaccinated. LF = ∀x((Vx ∧ ∀y(Dy → Txy)) → ¬Ix) [Ix = x was vaccinated]

(113)

No vet who treated every collie in town was vaccinated. LF = ∀x((Vx ∧ ∀y(Dy ∧ Cy → Txy)) → ¬Ix) [‘collie’ is taken to be elliptical for collie dog: Dy ∧ Cy]

268  Notes to pages 53–72

Consider the following unacceptable pair of sentences, *Any dog/collie in town was vaccinated. There are two relevant points to make about these examples. First, they become acceptable when embedded under No vet who treated… This is shown in (112a) and (113a). The second point is that (112a) entails (113a). So, replacing every by any reverses the entailment relations such that the set-referring term dog can be replaced by the subset-­referring term collie, salva veritate.

(112a)

No vet who treated any dog in town was vaccinated. LF = ∀x∀y((Vx ∧ (Dy → Txy)) → ¬Ix)

(113a)

No vet who treated any collie in town was vaccinated. LF = ∀x∀y((Vx ∧ (Dy ∧ Cy → Txy)) → ¬Ix)

13 Goldberg only explicitly mentions the law governing negated disjunctions, but the logic of her argument extends, without qualification, to the law governing negated conjunctions. 14 All things are not equal, however, since the evidence for de Morgan’s laws is not clear in simple sentences in many human languages. For example, English-speaking children interpret Ted did not order both pasta and sushi to mean that Ted ordered neither dish. We will argue that this is not a violation of de Morgan’s laws, but it does show that one cannot know in advance the meanings that people will assign to complex statements involving several logical expressions. 2

Competing approaches to language and logic

  1 Another experience-based model of language acquisition is the Competition model of MacWhinney and Bates (1989). This model invokes a connectionist architecture, according to which learners extract relevant information and form generalizations on the basis of cues that are in the input. Examples of cues include word order, morphological agreement between linguistic items, and semantic plausibility. The learner places more or less weight on these different cues according to their availability in the linguistic environment. These differences account for cross-linguistic variation and for variation among speakers of the same language.   2 Other terms are sometimes used to describe the shallow linguistic structures that children devise in response to the linguistic input. These include schemas, templates, and constructs. As these are essentially the same as constructions, we will make no attempt to distinguish among them, and will use the terms interchangeably.   3 The term conservative learning is not intended to extend to the model of language development proposed by Snyder (2007). Snyder’s parametric approach contends that children are innately equipped with the principles and parameters of UG. Nevertheless, Snyder embraces grammatical conservatism, leading to his insistence that children’s spontaneous speech has privileged status as a source of evidence about children’s grammars. For a review of the model proposed in Snyder (2007), see Thornton (2008).   4 One needs to distinguish between explicit corrective feedback (You cannot say that) and more subtle substitutes for negative evidence that children might encounter (e.g., the fact that adults never produce a construction in similar circumstances,

Notes to pages 90–117  269 where the child would expect it to be used if it were consistent with the grammar of the local language). This is referred to as indirect negative evidence. It is important to note, however, that indirect negative evidence is an unlikely source for children’s mastery of complex linguistic structures. 5 Some notable exceptions include matrix wh-questions with how come, as in How come she left? (cf. *How come did she leave?). Other wh-structures that lack inversion include exclamatives (e.g., What dives she hangs out in!) and, as noted earlier, indirect questions, such as I’ll have what she is having. 6 Another Italian wh-phrase, come mai, patterns much like perché, but for ease of exposition, we will limit our discussion to perché. 7 If perché is immediately followed by the subject NP, as in (i) below, then perché must be construed locally. To see this, note that the question in (i) is asking why Gianni said something, not why he resigned, as in (31). (i)

Perché Gianni ha detto che si dimetterà (non a Piero)? why Gianni have-3sg said that self resign-3sg/future (not to Piero) ‘Why did Gianni say that he will resign (not to Piero)?’

8 A.L. also used subject/auxiliary inversion in rhetorical questions and in jokes. See Thornton (2008) for further details. 9 There have been few empirical studies attempting to demonstrate the specific forms and meaning that children are unable to acquire as part of their first language. One notable exception is a study by Hunter and Lidz (in preparation), which shows that children have difficulty understanding words as determiners if the word violates the semantic constraint on determiner meanings, known as conservativity (a.k.a., the lives on relation). 3

The case for logical nativism

1 Other referring expressions include definite descriptions like the Prime Minister and the woman with red hair. We will just use names wherever possible. 2 We discuss the possibility that children have access to this kind of information, called negative evidence, in section 3.15. 3 For simplicity, we have chosen to omit the syntactic process whereby the dummy auxiliary verb do is introduced, and is raised from its original position to one that precedes the subject NP. 4 The representation in (27) is a simplification of Merchant’s (2004) analysis. On his account, the prepositional phrase to Chuckie’s house moves to a focus position, and the remainder of the structure is deleted (i.e., he sent the letter). 5 Some of the non-coreference effects hold only for non-predication constructions. We will simply ignore predicational pseudoclefts and focus on what are called specificational pseudoclefts, where non-coreference is dictated. 6 For alternative so-called reconstruction accounts see Heycock and Kroch (1999), Bošcović (1997), and Bachrach (2003). There are also accounts that abandon Principle C altogether. 7 This example was selected to show that Mandarin and English are governed by the same c-command constraint on interpretation. In section 3.13 we argue that (for

270  Notes to pages 117–123

adults, but not for children), the Mandarin disjunction word huozhe takes scope over negation in ordinary negative statements, such as in example (107) below. In example (41), however, the negated modal bu hui dedao ‘will not get’ blocks the inverse scope reading that is usually assigned. If the negated modal bu hui dedao is replaced by mei dedao ‘didn’t get’, then adults revert to the inverse scope reading, as in example (42). Regardless of whether disjunction is c-commanded by either hui dedao or mei dedao, we have found that young Mandarin-speaking children consistently assign the surface scope reading to negated disjunctions, so disjunction licenses a conjunctive entailment for children regardless of the preferred interpretation assigned by adults (see section 3.13, and Chapter 4).   8 There are other, related phenomena, which we will not be concerned with here (see Schlenker 2003, and the references therein).   9 The acceptability of Type 2 pseudoclefts with negative polarity items like any is somewhat controversial. At all events, negative polarity items pattern in acceptability like their fragment answer counterparts. So, (46) seems as acceptable as the following question/fragment answer pair:

q: What did Max refuse to order? a: Any dessert.

10 Appearances were deceiving. When English-speaking children rejected sentences with every, it was not because they generated a conjunctive entailment at all, but because they wanted all of the characters to perform the same action (e.g., to take a teddy). A follow-up experiment confirmed that children consistently accepted sentences like (51) in this kind of context. This finding has been reported previously, by Boster and Crain (1993), in an early investigation of children’s interpretation of disjunction in sentences with the universal quantifier. 11 The requisite underlying structure for (52) with dou is: [Tamen dou mei na xiao­ xiong huozhe shaizi] [tamen dou mei na]. Because dou binds expressions to its left, however, dou takes scope over tamen in the clause that contains the elided material in (52), whereas dou takes scope over the disjunctive phrase xiaoxiong huozhe shaizi in the surface syntactic structure. Interestingly, if the elided material is expressed overtly, i.e., Tamen dou mei na xiaoxiong huozhe shaizi, Mandarin speakers revert to the ‘disjunctive’ reading, with disjunction taking scope over negation. This suggests that, in pseudoclefts, PPIs are rendered inert for movement, because negation is introduced covertly. This provides further support for an analysis of focus operators discussed in section 3.19, and in Chapter 6. The result is the conjunctive entailment of disjunction is generated in negated disjunctions with dou by Mandarin-speaking children and adults alike. 12 Levinson argues that some languages fail to enforce non-coreference except in the sentences with pronouns and referring expressions. On the syntactic account, such difference across languages would be relocated to a parameter, or perhaps a series of parameters. Nevertheless, learnability considerations would lead to the expectation that children, across languages, initially hypothesize the strongest version of Principle C, which enforces non-coreference for all types of NPs, not just pronouns.

Notes to pages 125–177  271 13 Some name-like expressions pick out different individuals at different times, e.g., Mr. Universe, and Miss Australia. These are clearly not rigid designators. 14 The semantic (polarity) status of wh-words in Mandarin is far from clear, because wh-words also appear to function as positive polarity items in other downwardentailing linguistic environments. We are currently conducting experiments with Mandarin-speaking children to determine their preferred interpretation of wh-words in these downward-entailing environments. 15 We would not put too much weight on the similarity between wh-words and negative polarity items in Mandarin. There are notable semantic differences. For one thing, wh-words sometimes allow a small amount (or insignificant amount) interpretation that is not available for true negative polarity items such as renhe. 16 This study was conducted in collaboration with Takuya Goro and Anna Notley. The Mandarin counterpart to the study was conducted by Peng Zhou. 17 The closest human language counterpart to material implication in classical logic is the If…, then… conditional, in English. There are some important ways in which the If…, then… conditional in English resembles the conditional of classical logic. But, in other respects, conditionals in human languages lack essential properties of conditionals in classical logic. The findings of some experimental studies of children’s interpretation of conditionals are reported in Crain and Thornton (1998). Although there is little research on conditionals in child language, the findings appear to reinforce ways in which conditionals are similar in human languages and in ­classical logic. 18 This is a descriptive generalization, but it is overridden in some languages, in certain cases. Discussion of the exceptions to the generalization, however interesting, would take us too far afield. 4

Scope parameters

1 The evidential basis for the inclusive-or interpretation of disjunction is even flimsier in languages like Japanese and Mandarin Chinese, since disjunction takes scope over negation in simple negative statements, yielding an implicature of exclusivity that is consistent with the exclusive-or interpretation of disjunction. 2 An expression A c-commands another expression B if there is a path upwards from the first branching node above A, and then downwards to B. 3 As in the Crain et al. study, we controlled the order of the disjunct that made the sentence false. On one trial, the target sentence was false because the sentence containing the first disjunct was false, as in the story just described; on the other trial, the sentence was false because the sentence containing the second disjunct was false. 4 As in the Crain et al. study, on half the trials, only the first disjunct needed to be parsed in order for subjects to decide the truth or falsity of the test sentences. However, on half of the trials, the truth or falsity of the sentence could only be decided if subjects parsed the entire disjunction, since the second disjunct was crucial for deciding the truth of the test sentences. 5 Why did children reject the target sentence 20 percent of the time? In 7 of the 14 cases, children’s explanations suggested they were failing to assign a relative clause

272  Notes to pages 180–232 structure. For instance, children sometimes rejected (10) by saying that in the story it had not been established whether Pooh could lift the honey or the donut. In our view, this kind of response could arguably be excluded. If so, then the rate of acceptance would be 89 percent (56/63). 6 Other languages that take disjunction to be inside the scope of negation in simple negative sentences include French, Greek, Romanian, Bulgarian, and Korean (Szabolcsi 2002). Other languages in which disjunction is interpreted as taking scope over negation include Hungarian, Russian, Serbo-Croatian, Slovak, and Polish (Goro and Akiba 2004a, 2004b; Szabolcsi 2002). 7 The statement with disjunction is true, according to the logical principle of Weakening. However, most people judge statements that are generated by Weakening to be pragmatically odd (see Crain and Khlentzos 2008). 5

How something can be both positive and negative

1 In Chapters 3 and 6, we present evidence that the assertion of sentences with focus operators is downward entailing, in the sense that the assertion contains a “covert” negation operator. It is this negation operator, presumably, that licenses the NPI any in the test sentences used in the present experiment. 2 There are some structures, including negative statements, where shenme is ambiguous and, depending on intonation, can be interpreted either as an existential indefinite or as a question marker. 3 The data from three children were excluded from the analysis, because they didn’t respond correctly to the control trials. 6

Two logical operators for the price of one

1 The contrast set could be properties of individuals, rather than individuals. Consider the sentence John only danced. The focus operator is only, but the focus element is danced. The entailment (the assertion) in John only danced is that every property being contrasted with dancing is not a property that John has. For simplicity, and because no one has investigated this issue with children, in the remainder of the chapter we will limit discussion to examples with contrast sets that are made up of individuals, rather than properties of individuals. 2 Everyone agrees that the second proposition (ii) is directly asserted/entailed by the original sentence, but the status of the first meaning component is more controversial: Horn (1969, 1996) and von Fintel (1999) argue that it is a presupposition, whereas Atlas (1993, 1996) and Herburger (2000) take it to be an assertion. We will adopt Horn’s terminology. We will refer to the first proposition, about the focus element, as the presupposition, and we will refer to the second proposition, about the individuals being contrasted with the element in focus, as the assertion. We intend no theoretical commitment by adopting this terminology. 3 As will become clear in the paragraph that follows, there is an implicature in (18). This implicature arises because the existential indefinite some is interpreted outside the scope of negation. The derived meaning of (18) is ‘some, but not all, of the kangaroos are such that Julia didn’t touch them.’ It follows from this that she did touch some of the kangaroos.

Notes to pages 232–260  273 4 For discussion of linguistic contexts that cancel polarity effects, see Baker (1979); Krifka (1991, 1995); Kroch (1979); Jackendoff (1969); Jespersen (1917); Linebarger (1987); Szabolcsi (2002, 2004). 5 Thanks to careful controls introduced by Paterson et al., it is clear that these responses (5 percent from 4- to 5-year-old children) show an association of pre-subject only with the VP. 6 We conducted an experiment to verify that adult Mandarin speakers interpreted the disjunction word huozhe as having scope over negation meiyou in sentences like (54). We interviewed sixteen adult native Mandarin speakers. They assigned the +PPI reading to disjunction over 95 percent of the time. 7 Different objects were used in each of the conditions in the experiment. The labels blue box and black box are used in the tables in (57) and (58) for expository purposes. 8 In other studies, the same kinds of sentences were presented in different contexts. This enabled us to find out the range of circumstances in which children accept disjunctive statements with downward-entailing expressions, and without them. We have chosen to discuss just one context here, for ease of exposition.

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Index

a priori truth, 52; see also contingent truths accidental occurrence, 42, 176 acquisition of passives, 78 acquisition of relative clauses, 79 adjunct wh-questions, 87 ambiguity of scope, 56 argument wh-questions, 87, 93 assertion of focus, 160, 235, 251 asymmetric quantification, 258 bare wh-words, 87 binding theory, 102, 103, 142; see also c-command backwards anaphora, 121, 128, 129, 130, 134 non-coreference, 106, 114, 115, 117, 118, 126, 127, 143 Principle B, 71, 121, 135, 142, 156 Principle C, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 113, 114, 115, 118, 119, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 139, 142, 144, 171, 269, 270 pronominal binding, 108 brain imaging research, 6 c-command, 102, 103, 104, 105, 106, 108, 109, 110, 111, 114, 115, 116, 117, 118, 119, 120, 121, 122, 129, 130, 134, 139, 142, 143, 144, 166, 172, 173, 174, 177, 178, 269; see also binding theory branching node, 103, 271 contra-indexation, 123, 125 Coalition model, 74, 75 communicative function, 41, 67, 264 Competition model, 75, 268 compositionality, 42, 176, 177

condition of plausible dissent, 61 felicity conditions, 61 conditionals, 10, 17, 18, 21, 22, 23, 33, 34, 49, 57, 59, 62, 63, 145, 164, 201, 212, 256, 264, 267, 271; see also material implication negated conditional, 38, 40 ruguo, 14, 15, 22 Conjunction Parameter, 152, 180 conjunctive interpretation, 7, 34, 117, 121, 143, 164, 168, 174, 175, 177, 178, 186, 190, 191, 192, 193, 196, 198, 215, 251, 252, 258, 260, 261, 263, 264, 266, 270 conjunctive truth conditions, 13, 36, 37 connectedness, 112, 119 in pseudoclefts, 115, 116, 117, 119, 270 question-in-disguise, 117, 118, 120 conservativity, 61, 269 constructivist theory, 66, 68 contingent truths, 50; see also a priori truths Continuity Hypothesis, 70, 80, 81, 82, 83, 84, 85, 86, 92, 95, 101, 154, 190, 215, 223, 225, 246; see also linguistic generalizations contrast set, 158, 160, 228, 231, 241, 242, 244, 246, 247, 248, 251, 272 core linguistic principles, 72, 77, 102 deep-seated regularities, 77, 102 covert negation, 160, 162, 226, 228, 231, 233, 235, 236, 240, 242, 251, 251, 255 cross-linguistic generalizations, 68, 75, 100 cross-linguistic variation, 93, 100, 180, 193, 225 crossover questions, 107, 108, 109, 132, 133 deictic pronoun, 107, 129, 131 demonstrative expression, 28, 30

285

286  Index Disjunction Parameter, 120, 150, 152, 195, 198, 237, 238 disjunctive truth conditions, 13, 36, 143, 159, 173, 216, 262, 263 domain widening, 25, 27, 32 domain-general approach, 65 do-support, 88, 89 downward entailment, 10, 12, 14, 22, 24, 27, 33, 42, 62, 63, 99, 144, 145, 146, 165, 166, 167, 199, 224, 229, 230, 256, 258, 264; see also upward entailing downward-entailing contexts, 23, 25, 26, 27, 33, 45, 137, 147, 204, 215, 256, 264 downward-entailing expressions, 10, 17, 18, 145, 146, 164, 165, 166, 194, 199, 215, 228, 229, 261, 273 elicited production task, 85 entailment relations, 3, 4, 5, 6, 10, 45, 137, 157, 268 exclusivity, 8, 9, 56, 59, 138, 169, 247, 271 existential presupposition, 19, 20, 267 existential quantification, 26, 27, 30, 31, 147, 148 experience-based approach, 49, 57, 59, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 75, 77, 78, 79, 80, 82, 84, 86, 91, 96, 97, 98, 99, 102, 148, 153, 155, 163, 166, 167, 207, 223, 225, 226, 237, 252, 256, 264, 265 analogical processes, 67, 68 conservative learners, 69, 70, 71, 97 item-based construction islands, 66 lexically specific patterns, 66, 91 shallow linguistic representations, 65, 102, 177 statistical learning algorithms, 67 Feynman, Richard, 24 focus domain, 67 focus element, 158, 228, 239, 241, 242, 243, 245, 247, 248, 272 focus expressions, 6, 160, 163, 237, 251 generative grammar, 66, 148 Goldberg, A. E, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 62, 66, 67, 68, 72, 100, 256, 268 how-questions, 91 human reasoning, 1, 2, 3, 4, 56

implicature, 8, 9, 19, 20, 56, 126, 137, 138, 159, 169, 173, 183, 197, 234, 247, 252, 271, 272 inclusive disjunction, 7, 50, 51, 58, 100 inclusive-or, 7, 8, 9, 13, 17, 23, 34, 38, 44, 52, 53, 55, 56, 57, 58, 59, 121, 144, 150, 157, 169, 170, 174, 199, 251, 271 indefinite article some, 18, 200 indirect negative evidence, 97, 269 indirect wh-questions, 132 innate linguistic principles, 103 isomorphism, 151, 188, 221, 222, 223 linear order, 151, 161, 166, 172, 174, 187, 188, 189, 222 Kermit the Frog, 128, 131, 138, 168, 185, 205, 217, 219, 253, 258, 260 language acquisition device (LAD), 182 language faculty, 5, 76, 82 language learnability, 35, 223, 238 linguistic contexts, 10, 13, 18, 21, 23, 25, 26, 35, 63, 146, 164, 166, 192, 200, 206, 210, 232, 265, 273 linguistic generalizations, 67, 68, 75, 104; see also Continuity Hypothesis learning mechanisms, 57, 67, 98 logical connectives, 4, 26, 58, 66, 83, 84, 238 long-distance questions, 87, 95 material implication, 37, 271; see also conditionals The Meno (Plato), 64 negative evidence, 155 negative polarity items (NPI), 18, 20, 22, 25, 26, 27, 32, 33, 45, 99, 116, 117, 143, 146, 147, 148, 165, 199, 203, 204, 256, 258, 271 renhe, 18, 21, 22, 23, 24, 25, 26, 33, 99, 116, 146, 147, 148, 193, 204, 209, 231, 236, 237, 264, 265, 271 parametric account of scope, 179 positive polarity items (PPI), 160, 162, 231 pragmatics, 8, 46, 123, 124, 127; see also Principle P conversational context, 19, 29, 107, 108, 109, 113, 123, 124, 158, 203, 248 information-structure, 67

Index  287 pragmatically infelicitous, 44, 55, 245 theory of guises, 123, 125, 126 prepositional phrase-preposing (PP-preposing), 133, 134, 136 Principle of Cooperation, 8, 20, 234 Principle P, 123; see also pragmatics prosody, 74, 139 question/statement task, 209, 212 referring expressions, 103, 104, 109, 110, 114, 115, 121, 122, 123, 124, 126, 127, 267, 269, 270 relative clause, 79, 80, 131, 173, 271 Semantic Subset Principle (SSP), 120, 152, 153, 154, 155, 161, 167, 182, 184, 185, 188, 194, 195, 196, 215, 216, 221, 223, 225 Socrates, 42, 64, 176 strengthening, 43 structure-independent rules, 98; see also Yes/ No question surface scope, 151, 179, 200, 219, 220, 221, 222, 231, 232, 233, 270 symmetrical response, 60, 61

Tomasello, M., 66, 67, 68, 69, 70, 72, 73, 90, 178, 256 truth-value judgment task, 119, 170, 185, 208, 252, 259 description mode, 171, 173, 205, 219, 252 prediction mode, 170, 171, 173 Universal Grammar, 64, 70, 72, 73, 76, 77, 78, 81, 82, 83, 86, 87, 98, 101, 106, 123, 127, 134, 155 upward entailing, 43, 200, 206; see also downward entailment usage-based approach, 4, 84; see also experience-based approach validity, 3, 4, 45, 47, 56 VP Scope analysis, 244, 245 wanna contraction, 88, 96 Wason card selection task, 3, 56 Weakening, 26, 28, 43, 44, 45, 171 Yes/No question, 30, 31, 112; see also structure-independent rules