Lexical Meaning in Context: A Web of Words

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Lexical Meaning in Context This is a book about the meanings of words and how they can combine to form larger meaningful units, as well as how they can fail to combine when the amalgamation of a predicate and argument would produce what the philosopher Gilbert Ryle called a “category mistake”. It argues for a theory in which words get assigned both an intension and a type. The book develops a rich system of types and investigates its philosophical and formal implications, for example the abandonment of the classic Church analysis of types that has been used by linguists since Montague. The author integrates fascinating and puzzling observations about lexical meaning into a compositional semantic framework. Adjustments in types are a feature of the compositional process and account for various phenomena including coercion and copredication. This book will be of interest to semanticists, philosophers, logicians, and computer scientists alike. n i c h o l a s a s h e r is Directeur de Recherche CNRS, Institut de Recherche en Informatique de Toulouse, Universit´e Paul Sabatier, and Professor of Philosophy and of Linguistics at the University of Texas at Austin. He is author of Reference to Abstract Objects in Discourse (1993) and co-author of Logics of Conversation (2003) with Alex Lascarides.

Lexical Meaning in Context A Web of Words NICHOLAS ASHER CNRS, Institut de Recherche en Informatique de Toulouse and University of Texas at Austin

cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, S˜ao Paulo, Delhi, Dubai, Tokyo, 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/9781107005396
C

Nicholas Asher 2011

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 2011 Printed in the United Kingdom at the University Press, Cambridge A catalogue record for this publication is available from the British Library ISBN 978-1-107-00539-6 Hardback

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

page viii

Preface

PART ONE

FOUNDATIONS

1

1

Lexical Meaning and Predication 1.1 Types and presuppositions 1.2 Different sorts of predication 1.3 The context sensitivity of types 1.4 The main points of this book

3 4 10 18 21

2

Types and Lexical Meaning 2.1 Questions about types 2.2 Distinguishing between types 2.3 Strongly intensional types 2.4 Two levels of lexical content 2.5 Types in the linguistic system

25 25 27 34 44 49

3

Previous Theories of Predication 3.1 The sense enumeration model 3.2 Nunberg and sense transfer 3.3 Kleiber and metonymic reference 3.4 The Generative Lexicon 3.5 Recent pragmatic theories of lexical meaning

61 62 64 69 71 87

PART TWO

95

4

THEORY

Type Composition Logic 4.1 Words again 4.2 The basic system of types

97 101 103

vi

Contents 4.3 4.4 4.5

Lexical entries and type presuppositions The formal system of predication A categorial model for types

106 114 121

5

The Complex Type • 5.1 A type constructor for dual aspect nouns 5.2 Some not-so-good models of • types 5.3 The relational interpretation of • types 5.4 Subtyping with •

130 130 137 149 160

6

• Type Presuppositions in TCL 6.1 How to justify complex type presuppositions 6.2 Applications 6.3 • Types and accidentally polysemous terms

163 163 169 185

PART THREE

189

DEVELOPMENT

7

Restricted Predication 7.1 Landman’s puzzle 7.2 More puzzles 7.3 Extensional semantics for as phrases 7.4 A new puzzle 7.5 As constructions in TCL 7.6 Proper names in as phrases revisited 7.7 An aside on depictives

191 193 194 195 197 201 211 213

8

Rethinking Coercion 8.1 Re-examining the data 8.2 Coercion and polymorphic types 8.3 Discourse and typing 8.4 Discourse-based coercions in TCL

214 214 219 236 240

9

Other Coercions 9.1 Noise verbs 9.2 Coercions from objects to their representations 9.3 Freezing 9.4 Cars and drivers, books and authors 9.5 Verbs of consumption 9.6 I want a beer 9.7 Evaluative adjectives 9.8 Coercions with pluralities 9.9 Aspectual coercion and verbal modification

246 246 247 248 249 251 252 256 261 262

Contents

vii

10

Syntax and Type Transformations 10.1 The Genitive 10.2 Grinding 10.3 Resultative constructions 10.4 Nominalization 10.5 Evaluating TCL formally

272 272 280 281 284 296

11

Modification, Coercion, and Loose Talk 11.1 Metonymic predications 11.2 Material modifiers 11.3 Loose talk 11.4 Fiction and fictional objects 11.5 Metaphorical predication

300 300 301 305 309 312

12

Generalizations and Conclusions 12.1 Integrating ordinary presuppositions 12.2 Conclusions: a sea of arrows

315 315 318

PART FOUR References Index

321 323 331

CODA

Preface

Just over fifty years ago with the publication of “Two Dogmas of Empiricism”, W. V. O. Quine launched a persuasive and devastating attack on the common sense notion of word meaning and synonymy, according to which two terms were synonymous just in case they had the same meaning. Quine’s legacy continues to hold sway among much of the philosophical community today. The theory of word meaning is often thought either not to have a subject matter or to be trivial—dog means dog. What else is there to say? Well, it turns out, quite a lot. Linguists like Charles Fillmore, Igor Mel’cuk, Maurice Gross, Beth Levin, Ray Jackendoff, James Pustejovsky, and Len Talmy— to mention just a few, as well as researchers in AI who have built various on-line lexical resources like WORDNET and FRAMENET, have provided rich and suggestive descriptions of semantic relations between words that affect their behavior. And this has led to several proposals for a theory of word meaning. Against this rich descriptive background, however, problems have emerged that make it not obvious how to proceed with the formalization of lexical meaning. In particular, something that is commonly acknowledged but rarely understood is that when word meanings are combined, the meaning of the result can differ from what standard compositional semantics has led us to expect: in applying, for instance, a property term ordinarily denoting a property P to an object term ordinarily denoting a, the content of the result sometimes involves a different but related property P applied to an object b that is related to but distinct from the original denotation of a. While the choice of words obviously affects the content of a predication, the discourse context in which the predication occurs also affects it. The trick is to untangle from this flux a theory of the interactions of discourse, predication, and lexical content. That is what this book is about.1 1

I owe many people thanks for help with this book: Alexandra Aramis, Alexis, Elizabeth, and Sheila Asher, Tijana Asic, Christian Bassac, David Beaver, Stephano Borgo, George

Preface

ix

In this book, I argue that the proper way to understand the meaning of words is in terms of their denotations and the restrictions that other words impose on them. And it is the latter that govern how words interact semantically. I begin with the widely accepted observation according to which a predication will succeed only if the selectional restrictions the predicate imposes on its arguments are met. I provide an analysis of selectional restrictions by assigning words types. Meeting a selectional restriction is a matter of justifying a lexical presupposition, the presupposition that a term has a certain type. This analysis yields a theory of lexical meaning: to specify the type and the denotation of a word is to give its lexical meaning. The mechanisms of presupposition justification developed in dynamic semantics in recent years lead to an account of how predication adds content to the “ordinary” contents of the terms involved, which will provide my account of meaning shifting in context. The theory I will develop in this book has implications for compositional semantics, for example for the architecture of verbal and nominal modification. It also unifies analyzes in compositional semantics of presuppositions with my analysis of type presuppositions; for instance, the presuppositions of factive verbs or definite noun phrases are just special cases of type presuppositions. The idea that there are non-trivial semantic interactions between words that affect the content of a predication is intuitive and perhaps obvious. But working out a precise theory, or even an imprecise one, of this phenomenon is difficult. I begin with some basic questions, distinctions, and observations. What is a word? In some sense the answer is obvious: words are the things dictionaries try to define. On the other hand, the answer is not so simple. Words in many languages come with inflection for case, for number, for gender, among other things. Furthermore, there are morphological affixes that can transform one word into another like the nominalization affixes in English: an Bronnikov, Robin Cooper, Denis Delfitto, Pascal Denis, Tim Fernando, Pierdaniele Giaretta, John Hawthorne, Mark Johnson, Hans Kamp, Chris Kennedy, Ofra Magidor, Alda Mari, Claudio Masolo, Bruno Mery, Friedericke Moltmann, Philippe Muller, David Nicolas, Barbara Partee, Sylvain Pogodalla, Franc¸ois Recanati, Christian Retoret, Antje Rossdeutscher, Sylvain Salvati, Magdalena Schwager, Stuart Schieber, Torgrim Solstad, Tony Veale, Laure Vieu, Kiki Wang, Laura Whitten, and participants of the seminars on lexical semantics at the University of Verona, the University of Texas at Austin, the University of Stuttgart, and the Summer Institute of the Linguistic Society of America at Stanford, where some of this material was presented. I want especially to thank Hans Kamp and members of the SFB 732 at the University of Stuttgart for their generous invitation to spend three months there to work on this project during the summer of 2008. Special thanks are also due to Julie Hunter and Renaud Marlet who reread much of the manuscript and offered many helpful comments and to James Pustejovsky, who got me to work on the subject of coercion and dot objects in the first place. Finally, I’d like to thank Andrew Winnard, Sarah Green, Gillian Dadd, Alison Mander, and Elizabeth Davey from Cambridge University Press for their help with the manuscript. The book is dedicated to Tasha, my darling little cat who didn’t manage to live to see the end of this project.

x

Preface

affix like -ion turns a verb like afflict into the noun affliction. Morphological affixes and prefixes can often affect the meaning of a word; they can also determine how their host words combine with other words, as we shall see later on in this book. Even inflections like the plural are not always semantically innocent. Thus, the notion of a word quickly becomes a theoretical term; the meaningful parts of the lexicon may include things that we ordinarily would think of as bits of words, and basic word stems (the elements to which affixes and prefixes attach) may not end up looking like ordinary words at all. Despite these complications, I will continue to speak (loosely) of words. What is it to give the meaning of a word? There are a number of answers in the literature on lexical semantics or theories of word meaning. Cognitive semanticists like Len Talmy and Tom Givon, among others, think that meanings are to be given via a set of cognitively primitive features—which might be pictorial rather than symbolic. According to these semanticists, a lexical theory should provide appropriate cognitive features and lexical entries defined in terms of them. Others in a more logical and formal framework like Dowty (1979) (but also Ray Jackendoff, Roger Shank, and other researchers in AI) take a specification of lexical meaning to be given in terms of a set of primitives whose meanings can be axiomatized or computationally implemented. Still others take a “direct” or denotational view; the function of a lexical semantics is to specify the denotation of the various terms, typically to be modelled within some model theoretic framework. All of these approaches agree that a specification of lexical meaning consists in the specification of some element, whether representational or not, formal or not, that, when combined with elements associated with other words in a well formed sentence, yields a meaning for a sentence in a particular discourse context. Whatever theoretical reconstruction of meaning one chooses, however, it should be capable of modelling inferences in a precise manner so that the theory of lexical meaning proposed can be judged on its predictions. In addition, the theoretical reconstruction should provide predictions about when sentences that are capable of having a truth value are true and when they are not. This drastically reduces the options for specifying lexical meaning: such a specification must conform with one of the several ways of elaborating meaning within the domain of formal semantics; it must specify truth conditions, dynamic update conditions of the sort familiar from dynamic semantics (Kamp and Reyle (1993), Groenendijk and Stokhof (1991), Asher (1993), Veltman (1996)), or perhaps provability conditions of the sort advocated by Martin-L¨of (1980) and Ranta (2004), among others. For proponents of a direct interpretation of English, a denotational approach to lexical meaning suffices. Most semanticists, however, use a logical language

Preface

xi

to state the meanings of natural language expressions. The logical representations of sentential meanings are typically called logical forms. Within such a framework a lexical entry for a word should specify a logical representation that when combined together with the contributions of other words in a well-formed sentence will yield a logical form with well-defined contents. I shall follow formal semantic tradition and use a logical language with a welldefined model theoretic interpretation to provide as well as to construct logical forms.2 Thus, at a minimum, lexical semantics should be concerned with the lexical resources used to construct logical forms in a language with a precise model theoretic interpretation. But what are those resources? Clearly the syntactic structure of a clause is necessary for constructing a logical form for the clause, but that is not the province of lexical semantics. One that is, however, is argument structure. Most words—verbs, adjectives, nouns, determiners, and adverbs—have arguments, other words or groups of words, that they combine with; and the meaning of such words must specify what other kinds of words or groups of words they can combine with to provide larger units of meaning. But an account of lexical meaning must do more than this; it must also specify what the process of combination is when the representation of one word meaning combines with other word meaning representations licensed by their argument structures. It must couple its representation of a word’s meaning with a mechanism for combining this representation with the representations of the meanings of its arguments or of the words to which it is an argument. The construction of logical form and the lexical resources used to construct it thus inevitably involve the notion of predication; when one bit of logical form functions as an argument to another, a predication relation holds between a property denoting term and its argument. A satisfactory theory of lexical meaning must yield an account of predication, and the choice of a model of predication affects the choice of how to represent lexical meanings. I turn now to a basic formal model of predication and the representation of lexical meaning.

2

Cognitive semantics lexical theories will not figure in this book, because they do not really have the resources to provide logical forms for sentences capable of defining truth conditions or update conditions. G¨ardenfors (1988) has provided a formal model of the cognitive semantics view of lexical meaning by taking the cognitive features to form the basis of a vector space. Lexical meanings are then represented as vectors or sets of vectors in this space. Such a theory can give us a potentially interesting measure of similarity in meaning by appealing to distances between points in this feature space. Certain lexical inferences can also be accounted for as G¨ardenfors (1988) shows. But the compositional problem, that is, the problem of showing how these meanings compose together to get meanings of larger units, is unsolved, and it is not at all obvious how one could solve it within the vector or feature space framework for anything more than the simplest of fragments of natural language.

PART ONE FOUNDATIONS

1 Lexical Meaning and Predication

To build a formal model of predication and to express lexical meaning, I will use the lambda calculus. The lambda calculus is the oldest, most expressive, and best understood framework for meaning representation; and its links to various syntactic formalisms have been thoroughly examined from the earliest days of Montague Grammar to recent work like that of de Groote (2001), Frank and van Genabith (2001). Its expressive power will more than suffice for our needs.1 The pure lambda calculus, or λ calculus, has a particularly simple syntax. Its language consists of variables together with an abstraction operator λ. The set of terms is closed under the following rules: (1) if v is a variable, then v is a term; (2) if t is a term and v a variable, then λvt is also a term; (3) if t and t are terms, then the application of t to t , t[t ], is also a term. We can use this language to analyze the predication involved when we apply a predicate like an intransitive verb to its arguments. The meaning of an intransitive verb like sleeps is represented by a lambda term, λx sleep (x); it is a function of one argument, another term like the constant j for John that will replace the λ bound variable x and yield a logical form for a larger unit of meaning under the operation of β reduction. β reduction, also known as β conversion, is a rule for inferring one term from another. β reduction is the formal counterpart in the λ calculus of the informal operation of predication. One can also think of reduction as the rule governing application, and so I shall call it the rule of Application.2 I’ll write such a rule in the usual natural deductive format. 1

2

There are other formalisms that can be used—for instance, the formalism of attribute value matrices or typed feature structures with unification. This formalism, however, lacks the operation of abstraction, which is crucial for my proposals here. Besides Application, there are other rules standardly assumed for the λ calculus—for example, α conversion, which ensures the equivalence of bound variables, rules for equality, and the following rules which validate a rule of Substitution that I shall introduce subsequently:

4

Lexical Meaning and Predication

• Application: λxφ[α] φ( αx ) The λ calculus as our representational language tells us in principle what our lexical entries should look like. For example, if we decide that a word like cat is a one place predicate, then our lexical entry for this word should have the form λx cat (x), where cat is an expression in our language for logical forms that will, when interpreted, assign the right sort of denotation to the word and contribute to the right sort of truth conditions for sentences containing the word. Of course, there are lots of decisions to be made as to what cat should be exactly, but we will come back to this after we have taken a closer look at predication.

1.1 Types and presuppositions Sometimes predications go wrong. This is something that lexical semantics has to explain. (1.1) a. ?That person contains an interesting idea about Freud. b. That person has an interesting idea about Freud. c. That book contains an interesting idea about Freud. d. That person is eating breakfast. e. That book is red. f. #That rumor is red. g. # The number two is red. h. # The number two is soft. i. # The number two hit Bill. j. The number two is prime. k. John knows which number to call. l. *John believes which number to call. The predications in (1.1f,g,h) or (1.1i) are malformed—each contains what Gilbert Ryle would have called a category mistake. Numbers as abstract objects can’t have colors or textures or hit people; it’s nonsensical in a normal • t = t → t[t ] = t [t ] • t = t → f [t] = f [t ] • t = t → λx t = λx t Church (1936) shows how to encode Boolean functions within the λ calculus, once we have decided on a way of coding up truth functions.

1.1 Types and presuppositions

5

conversation to say something like the number two is red, soft, or that it hit Bill.3 The mismatch between predicate and argument is even more blatant in (1.1l). One has to exercise some care in understanding why a predication like (1.1a) sounds so much odder than (1.1b–d). In some sense people can contain information: spies have information that they give to their governments and that counter-spies want to elicit; teachers have information that they impart to their students. But one can’t use the form of words in (1.1a) to straightforwardly convey these ideas. The predication is odd; it involves a misuse of the word contain. If it succeeds at all in making sense to the listener, it must be subject to reinterpretation. It’s important to distinguish between necessary falsity and the sort of semantic anomaly present in (1.1a) and (1.1f–i). In the history of mathematics, many people, including famous mathematicians, have believed necessarily false things. But competent speakers of a language do not believe propositions expressed by a sentence with a semantically anomalous predication. (1.1a) or (1.2c,d) are semantically anomalous in a way that (1.1b–d) or (1.2a,b) below are not.4 (1.2) a. Tigers are animals. b. Tigers are robots. c. #Tigers are financial institutions. d. #Tigers are Zermelo-Frankel sets. Many philosophers take (1.2a) to be necessarily true and (1.2b) to be necessarily false.5 Nevertheless, according to most people’s intuitions, a competent speaker could entertain or even believe that tigers are robots; he or she could go about trying to figure this out (e.g., by dissecting a tiger). It is much harder to accept the possibility, or even to make sense of, a competent speaker’s believing or even entertaining that tigers are literally financial institutions, let alone ZF style sets. Thinking about whether a competent speaker could entertain or believe the proposition expressed by a sentence gives us another means to distinguish between those sentences containing semantically anomalous expressions and those that do not. 3

4 5

As the attentive reader may have already guessed, besides “normal” conversations, there are also “abnormal” discourse contexts—contexts that would enables us to understand these odd sentences in some metaphorical or indirect way, or that even enable us to reset the types of words. More on this later. Thanks to Dan Korman for the first two examples. The reason for this has to do with a widely accepted semantics of natural kinds due to Hilary Putnam and Saul Kripke, according to which tigers picks out a non-artifactual species in every possible world.

6

Lexical Meaning and Predication

The reason why (1.1a), (1.1f–i) or (1.2c,d) are semantically anomalous, while the other examples above are not, is that there is a conflict between the demands of the predicate for a certain type of argument and the type of its actual argument. People aren’t the right type of things to be containers of information, whereas tapes, books, CDs, and so on are. Rumors aren’t the right type of things to have colors, and tigers aren’t the right type of things to be sets or financial institutions. We can encode these humdrum observations by moving from the pure lambda calculus to a typed lambda calculus. The reason why some predications involve misuses of words, don’t work, or require reinterpretation, is that the types of the arguments don’t match the types required by the predicates for their argument places. (1.1a) involves a misuse of the language. Contain, given the type of its direct object, requires for its subject argument a certain type of object—a container of information; and persons are of not of this type—they don’t contain information the way books, journal articles, pamphlets, CDs, and the like do. On the other hand, there is no such problem with (1.1b); books are the sort of object that are containers of information. (1.1c) is also fine, but that is because the verb have doesn’t make the same type requirements on its arguments that contain does. The typed lambda calculus, developed by Church (1940), assumes that every term in the language has a particular type. This places an important constraint on the operation of Application. Assume that every term and variable in the lambda calculus is assigned a type by a function type. • Type Restrictied Application: λxφ[α] φ( αx ) provided type(x) = type(α). λxφ[α] is undefined, otherwise. In what follows, I’ll encode type with the usual colon notation; α: a means that term α has type a. The typed lambda calculus has many pleasant semantic and computational properties. This has made it a favorite tool of compositional semanticists since Montague first applied it in developing his model theoretic notion of meaning in the sixties. I will model predication as type restricted application and lexical entries as typed lambda terms. This will require that each term gets a type in a given predicational context. Moreover, each term will place restrictions on the type of its eventual arguments. The data just discussed indicates that the set of

1.1 Types and presuppositions

7

relevant types for a theory of predication and lexical meaning are quite finegrained; in the next chapter we will see how this data and other data lead to the hypothesis of a great many more types than envisaged in Montague Grammar or standard compositional semantics. Before addressing questions about types, I want to investigate some implications of Type Restricted Application for a theory of predication. There is a compelling analogy between the way types and type requirements work in the typed lambda calculus and the linguistic phenomenon known as presupposition. Linguists take certain words, phrases, and even constructions to generate presupposed contents as well as “proffered” contents; the latter enter into the proposition a sentence containing such items expresses, whereas the presupposed contents are conceived of as constraints on the context of interpretation of the sentence. For instance, in (1.3) The dog is hungry the definite determiner phrase (DP) the dog is said to generate a presupposition that there is a salient dog in the discourse context. If such a presupposition is satisfied in a discourse context, the presupposition is said to be bound; if it cannot be bound, the presupposition is accommodated by making the supposition that the discourse context contains such a salient dog. However, there is a certain cost to such suppositions; if there really is no salient dog in the context, (1.3) is difficult to interpret. Frege and Strawson proposed that in cases where no salient dog can be found, a sentence like (1.3) cannot be literally interpreted and fails to result in a well-formed proposition capable of having a truth value.6 This view of presupposition, though it has its detractors, is well established in linguistics and has received a good deal of empirical support and formal analysis (Heim (1983), van der Sandt (1992), Beaver (2001)). Type Restricted Application says something very similar to the doctrine of presupposition: a type concordance between predicate and argument is required for coherent interpretation. If an argument in a predication cannot satisfy the type requirements of the predicate, then the predication cannot be interpreted and fails to result in a well formed logical form capable of having a truth value. There are other similarities between presupposition and type requirements. A common test for presupposition is the so-called projection test: presuppositions “project” out of various operators denoting negation, modality, or mood. So if the type requirements of a predicate are a matter of presupposition, then semantically anomalous sentences like (1.1g,h) should remain anomalous 6

This is known as the “Frege-Strawson” doctrine.

8

Lexical Meaning and Predication

when embedded under negation, interrogative mood or modal operators. This is indeed the case: (1.4) a. # The number two could have been red. b. # Is the number two soft? c. # The number two didn’t hit Bill.7 The sentences in (1.4) all convey presuppositions that are absurd and that cannot be met—namely, that the number two is a physical object. Other tests for presuppositions concern the non-redundancy of presupposed content and the inability to make certain discourse continuations on presupposed content.8 These tests apply to type requirements of predicates as well. It is not redundant to say the abstract object two is prime instead of two is prime, and it seems impossible to make discourse continuations on the type requirements, since the latter are not even propositional contents. Thus, it seems that the type requirements of predicates provide a kind of presupposed content. I shall call these type presuppositions. Two features of presuppositions will be very important for the study of predication in this book. The first is the variability among terms that generate presuppositions to license accommodation. It is standardly assumed that the adverb too generates a presupposition that must be satisfied in the given discourse context by some linguistically expressed or otherwise saliently marked content. Thus, in an “out of the blue” context, it makes no sense to say (1.6) Kate lives in New York too. even though as a matter of world knowledge it is clear that the presupposition of too in this sentence is satisfied—namely, that there are other people besides Kate who live in New York. Even if the proposition that there are other people besides Kate who live in New York is manifestly true to the audience of (1.6), (1.6) is still awkward, unless the presupposed content has been made salient somehow in the context. The presupposed, typing requirements of the predicates in (1.1) and (1.4) resemble the behavior of the presupposition of too; they 7

8

A presuppositional view should allow that this sentence has a perfectly fine reading where the negation holds over the type requirements as well. But typically such readings are induced by marked intonation. If this sentence is read with standard assertion prosody, then it is as anomalous as the rest. The continuation test says that one cannot elaborate or explain or continue a narrative sequence on presupposed content. Thus, one cannot understand the example below as conveying that John regretted that he yelled at his girlfriend and that then after fighting with her he went to have a drink.

(1.5) John regrets that he fought with his girlfriend. Then he went to have a drink.

1.1 Types and presuppositions

9

have to be satisfied in their “predicative” context in order for the sentences containing them to receive a truth value. Accommodation of these type presuppositions is impossible. The sentences that fail to express a coherent proposition capable of having a truth value do so, because the relevant type presuppositions cannot be satisfied, given that the arguments and predicates therein mean what they standardly mean and have the types that they standardly do. On the other hand, some presupposition introducing phrases like possessive DPs readily submit to accommodation. For instance, Sylvain’s son presupposes that Sylvain has a son, but this information is readily accommodated into the discourse context when the context does not satisfy the presupposition. (1.7) Sylvain’s son is almost three years old. Other definite descriptions can be satisfied via complex inferences. The example below, which features a phenomenon known as “bridging,” features such an inference; the definite the engine is “satisfied” by the presence of a car in the context—the engine is taken to be the engine of the car: (1.8) I went to start my car. The engine made a funny noise. In the following chapters we will see cases of type presuppositions that can either be satisfied in complex ways like the bridging cases or can be accommodated via a “rearrangement” or modification of the predicative context, if the latter fails to satisfy the type presuppositions in a straightforward way. Figuring out when presupposed typing requirements can be accommodated and when they cannot will be a central task of this book. Another important property of presuppositions is their sensitivity to discourse context. For instance, if we embed (1.7) in the consequent of a conditional, the presupposition that projects out from the consequent can be bound in the antecedent and fails to project out further as a presupposition of the whole sentence (1.9): (1.9) If Sylvain has a son, then Sylvain’s son is almost three years old. A similar phenomenon holds for type presuppositions. Consider (1.4a) embedded as a consequent of the following (admittedly rather strange) counterfactual. (1.10) If numbers were physical objects, then the number two could have been red. The presupposition projected out from (1.4a) is here satisfied by the antecedent of the counterfactual and rendered harmless. Thus, category mistakes for the most part must be understood relative to a background, contextually supplied set of types, a background that may itself shift in discourse.

10

Lexical Meaning and Predication

1.2 Different sorts of predication Having introduced types as part of the apparatus of predication, let me come back to predication itself. I have spoken so far of predication as a single operation of applying a predicate to its arguments. But in fact predication takes many forms in natural languages, some particular to particular languages, others more general. Even among ordinary predications, linguists distinguish between: • predication of a verb phrase to a subject or a transitive verb to an object • adjectival modification with different types of adjectives—e.g., evaluative adjectives like good rock, bad violinist, material adjectives like bronze statue, paper airplane, and manner adjectives like fast car, slow cigar • adverbial modification and modification of a verb phrase with different prepositional phrases or PPs—e.g., the distinction between load the wagon with hay and load the hay on the wagon. Beyond these are more exotic forms of predication: • metaphorical usage (extended predication) (1.11) John is a rock. • restricted predication (1.12) John as a banker makes $50K a year but as a plumber he makes only $20K a year. • copredication (1.13) The lunch was delicious but took forever. (1.14) The book has a purple cover and is the most intelligible introduction to category theory. (1.15) #The bank is rising and specializes in IPOs. • loose predication (1.16) That’s a square (pointing to an unpracticed drawing in the sand). • resultative constructions (1.17) a. Kim hammered the metal flat. b. * Kim hammered the metal gleaming. (1.18) depictives a. Pat swims naked. b. *Pat cooks hot. • the genitive construction

1.2 Different sorts of predication

11

(1.19) a. Kim’s mother b. Kim’s fish • noun noun compounds (1.20) a. lunch counter b. party favor Each one of these forms of predication presents its own challenges for lexical and compositional semantics; the lexical theory must assign to the words in these constructions the right sort of meaning and postulate the right sort of composition rules for predication so as to get the right result. In addition, a lexical theory must specify what morphological processes and elements affect meaning and how; it must give those processes and elements a meaning. A lexical theory using the typed lambda calculus can provide the right sort of picture to tackle these issues. Let’s consider these forms of predication in a bit more detail. Loose predication is a difficult and well-known problem in philosophy.9 But other forms of predication mentioned above, which linguists think also provide challenges for lexical theory, have not received so much philosophical scrutiny or formal analysis. Copredication, for instance, which is a grammatical construction in which two predicates jointly apply to the same argument, has proved a major challenge. Languages, as we shall see in the next chapter, distinguish between events and objects; the predicates that apply the one type do not apply in general to the other type literally. It turns out that some objects, however, are considered both events and physical objects in some sense. Consider, for instance, lunches. Lunches can be events but they are also meals and as such physical objects. As a result, lunch supports felicitous copredications in which one predicate selects for the event sense of lunch while the other selects for the physical object or meal sense. (1.21) Lunch was delicious but took forever. It turns out that many words behave like lunch in (1.21) and denote objects with multiple senses or aspects. I will call predications like those in (1.21) aspect selections, and I will analyze these predications as predications that apply to selected aspects of the object denoted by the surface argument. In trying to account for instances of copredication that involve aspect selection like (1.21), standard, typed theories of predication and lexical semantics confront some difficult if not unanswerable questions. How can a term have two incompatible types, as is apparently the case here? How can one term 9

Loose predication is related to vagueness, and vague predication might be considered another form to be studied. But I shall not do that here.

12

Lexical Meaning and Predication

denote an object or set of objects to which apply two properties demanding different, even incompatible types of their bearers? It would have to be the case then that such an object must have, or belong to, two incompatible types. But how is that possible? Proponents of standard type theory have only one clear recourse, and that is to claim that terms associated with two incompatible types are ambiguous. But that deepens the mystery about copredications involving aspect selections: if lunch in (1.21) is ambiguous between a physical object reading and an event reading, then we must disambiguate the term in one way to make sense of the first predication but disambiguate it in a second way to make sense of the second predication; and the problem is that, on the surface at least, we have only one term to disambiguate—we have to choose a disambiguation, but such a choice will inevitably cause one of the predications in (1.21) to fail. At this point we might try a strategy of desperation and postulate a hidden “copy” of the problematic term, rewriting (1.21) in effect as (1.21 ) Lunch was delicious but lunch took forever. This copying strategy now allows the proponent of standard type theory to proceed to disambiguate the two occurrences of lunch in different ways allowing the two predications to succeed. But the promise of the copying strategy is shortlived. Copying expressions will get us incorrect truth conditions in many cases. Consider (1.22), where last applies to events, while tasted applies only to objects (you can’t taste events except metaphorically): (1.22) A lunch was gingerly tasted by Mary and then lasted three hours. The copying strategy forces us to interpret (1.22) as (1.23) A lunch was gingerly tasted by Mary and then a lunch lasted three hours. It’s easy to see that (1.22) and (1.23) have different truth conditions; (1.22) is true only in those situations where Mary gingerly tasted the same lunch that lasted three hours, while (1.23) can be true in situations where Mary gingerly tastes one lunch but another lunch lasts three hours. Thus, it is not obvious how to deal with examples of copredication even from the standpoint of compositionality, if one’s lexical theory produces a rich system of types. Montague himself noted that there were copredications that were puzzling even within his much more impoverished system of types. In (1.24) temperature seems to have two aspects, one of which is a number on a scale, while the other is a function from times to numerical values. (1.24) The temperature is 90 and rising.

1.2 Different sorts of predication

13

We’ll see many more examples of copredications and how to analyze them in chapters 5 and 6. Restricted predications like the main predication in John as a banker makes $50K a year seem to predicate properties of certain parts or aspects of the “restricted argument” (in the example at hand, John). But it is not clear in what sense we should understand the word part. In the example, it’s not as though we’re predicating the making of a salary to some physical part of John, as in John’s right arm has a bruise. Restricted predication thus introduces some puzzles of its own. Resultative constructions are another form of complex predication. (1.17a), for example, involves two predications on the term the metal—one by the adjective flat and one by the verb.10 But this construction also introduces a third predication, which features the causal relation between the hammering and the flatness of the metal. Genitive constructions also introduce a predication in which some relation is predicated of the objects described by the two noun phrases or DPs that make up the genitive construction. Sometimes this relation is given by the head noun as in (1.19a) but sometimes it is not as in (1.19b). The predication in the genitive also seems to add to or to change the content of the words in the construction. Finally, the semi-productive predication construction in English, known as noun-noun compounding, also seems to add to or transform the meanings of its constituents—sometimes in radical ways so as to produce idioms whose meaning is not derivable from the meanings of its constituent terms like party favor. Besides these forms of predication, there are other factors that can influence the content of a predication. One is number. Some predicates with plural arguments require a collective or group predication, which requires the argument to be described in a certain way. Consider (1.25) a. The students surrounded the building. b. The students mowed the whole meadow. (1.25a,b) exemplify collective predications where a property is predicated of the whole set of students but not of each student individually. Contrasting with collective predication is distributive predication, which occurs when a property or relation is predicated of each element of a plural group, as in (1.26) The boys each worked hard. There is a grammatically marked distinction between plurality and singularity, about which most lexical theories have nothing to say. Nevertheless, they 10

Syntacticians take the structure of this sentence to be quite complex, involving what is called a “small clause,” the metal flat, and the verb hammer.

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Lexical Meaning and Predication

should, because an account of the lexical meaning of the word disperse or surround must mark it as requiring an argument that, if plural, must be interpreted collectively. In many predications, interactions between the type presuppositions of the predicate and the types of its arguments also affect the content of the predication. (1.27) provides examples of this phenomenon, which is known as coercion in the literature. Coercion is so called because it appears that one word coerces another word (usually the second word is an argument of the first) to have a different meaning from its usual one. (1.27) a. good lunch, good children b. Mouse isn’t very tasty unless you’re a cat. c. John started a cigarette, started a car, began the sonata, finished the novel. d. John liked the dress with the flowers/ liked the garden with the flowers. The phenomenon observed with the adjectival predications in (1.27a) is a very general and diverse one. The predications therein show how adjectival modification can affect the type and meaning of the resulting noun phrase. A good lunch is one that tasted good. Pustejovsky (1995) and others have proposed that an adjective like good selects a component of the meaning of its argument— roughly, its purpose or telic role. Nevertheless, as many have noted, such adjectives also apply to arguments that don’t have purposes. For instance, children in and of themselves don’t have fixed purposes; yet when good modifies children, we understand different things: when someone says those are good children, we understand that the children are behaving well or that they have certain laudatory dispositions to behavior. There is a subtle, though undeniable, shift in meaning in these predications. A theory that simply says that good denotes the property of being good, that children denotes children and lunch denotes a meal and that says nothing about how these meanings combine in predication other than that the objects denoted by the one term have the property denoted by the other cannot make any headway explaining these nuances in meaning. Unfortunately, many philosophers and some linguists still hold such a theory to be true (for instance, see Fodor and Lepore (1998)). (1.27b) shows how the bare singular use of a count noun can in many circumstances change the type of the noun phrase from count to mass. This transformation is known as grinding in linguistics. The examples in (1.27c) show how aspectual verbs coerce their arguments into denoting some sort of event. Aspectual verbs require or presuppose that their direct object is some event involving their subject; when their direct objects are not event-like, a felicitous coercion sometimes occurs, and we infer defeasibly that some sort of

1.2 Different sorts of predication

15

activity involving the subject of the aspectual verb serves as its internal argument. Thus, we understand John started the car as John’s started the running of the car’s engine. To start a cigarette is typically to start to smoke a cigarette. (1.27d) shows that coercions can happen with prepositional phrases—the dress with the flowers has at least one interpretation where a representation of flowers is stitched, printed, or drawn on the fabric of the dress, while the garden with the flowers does not have that interpretation, at least not nearly so saliently.11 As we shall see, there are subtle differences with respect to the presuppositions in the typing requirements of various aspectual verbs and other coercing predicates. Are such coercions really part of lexical semantics? That is, is it a defeasible but a priori inference that if John started the car, John started the engine of the car or that if Julie enjoyed the book, then (defeasibly) she enjoyed reading it? Do such inferences follow solely from one’s linguistic mastery of the language? Fodor and Lepore think that none of these inferences belong to lexical semantics but are rather part of encyclopaedic or world knowledge. However, most people can distinguish between the largely automatic interpretations that these predications seem to entail and those that require more conscious effort. One might take that to be a mark of the information as being present even during predication rather than inferred afterwards using background, nonlinguistic beliefs. It is notoriously difficult to distinguish between what is properly a part of lexical meaning and what is world knowledge. Quine’s attack on lexical meaning can be seen as starting from the point that one cannot make this distinction in a principled way. Part of the difficulty is that, to some extent, the division between word meaning and world knowledge is a theory-internal distinction. For instance, if you’re an externalist for whom the meanings of two singular or natural kind terms t and t are determined by their reference, it may be a fact of meaning that t = t or not. Thus, water is H2 0 would be a fact of meaning, and hence analytic, on such a view! Despite these difficulties, there is are tests one can use to see whether it is certain information conventionally associated with particular word meanings rather than just general world knowledge that gives rise to these inferences. For one thing, it seems pretty clear that the infierences given in (1.27c) are tied to particular predicates, particular verbs. Let’s suppose that cigarette, like lunch, always has associated with it a possible event reading. It should then be possible to access that appropriate event reading with other predicates that take events.

11

This example is due to Marliese Kluck.

16

Lexical Meaning and Predication

(1.28) a. Nicholas’s smoking of that cigarette will begin in 2 minutes. b. Nicholas’s cigarette break will begin in 2 minutes. c. ??Nicholas’s cigarette will begin in 2 minutes. It’s quite clear that (1.28c) is semantically strange. The event associated with cigarette in enjoy the cigarette, begin the cigarette, finish the cigarette, just isn’t available with other event predicates. This strongly suggests that there is some particular conventional meaning that issues from the predication of the properties these verbs denote to the objects denoted by their arguments that isn’t available in other predicational contexts. That is, the eventuality of smoking isn’t just accessible with any predication involving cigarette; it is the result of combining cigarette as an object or internal argument of an aspectual verb or a verb like enjoy. It is not only that such inferences are tied to particular verbs; they are tied to them independently of what the verb’s object is. Consider the use of a nonsense word like zibzab. 12 To say (1.29) John enjoyed the zibzab is to say that John enjoyed doing something to the zibzab. At this point, it’s really hard to understand how the inference to an event reading is part of world knowledge. It becomes clear that it is an a priori truth that to enjoy something is to be involved in some interaction with it—some eventuality. When the direct object argument of a verb like enjoy does not denote an eventuality as part of its standard meaning, coercion introduces somehow an appropriate eventuality. This militates strongly for placing coercion within the realm of linguistic knowledge, not contingent factual information about what the world is actually like. A further question concerns how this eventuality involved in predications like those in (1.27c) is specified. While we’ll see that this is not true in all cases, some nouns like cigarette help to specify the eventuality induced by coercion when they are in the direct object of a coercing verb. To see this, consider replacing the word cigarette with the relevant part of its entry in Webster’s New World College Dictionary, which should at least roughly have the same content as the word cigarette. (1.30) a. Nicholas enjoyed a cigarette. b. Nicholas enjoyed a small roll of finely cut tobacco wrapped in thin paper. 12

Thanks to Chris Kennedy for these sorts of examples.

1.2 Different sorts of predication

17

Speakers immediately get the defeasible interpretation of (1.30a) where Nicholas smokes a cigarette but not in the second case. These alternations appear pretty systematic with a small class of words like book, novel, sonata, and so on, indicating that indeed such defeasible interpretations are a part of lexical semantics.13 Coercions, as Aristotle said of all familiar things, are easy to see but hard to understand. Some linguists have argued that in fact coercions are what they appear to be. They indicate that the meaning of terms fluctuates from context to context, and some have taken the moral of these observations to be some sort of radical contextualism about meaning (for instance, Recanati (2004, 2002, 2005)). Pustejovsky (1995) also seems to endorse such a view in emphasizing the “generativity” of the lexicon. But these conclusions do not follow from the evidence. They are also vastly counterintuitive: when I say that I enjoyed the cigarette, does the word cigarette now all of a sudden change its meaning to mean smoking a cigarette? It does not seem so. Fodor and Lepore (1998) and more recently Cappelen and Lepore (2004) correctly, in my view, crticize such an approach to coercion in their criticisms of Pustejovsky (1995). Furthermore, despite many claims that the lexicon is in fact generative or context sensitive in some radical way, I do not know of any formally worked out proposal of this view.14 As we shall see in chapter 3, the generative lexicon of Pustejovsky (1995) has static lexical entries that do not change during coercion. When it comes to technical developments, I shall show that in fact basic word meanings cannot change if we are to be able to derive any predictions at all about lexical meaning. If that approach to coercion is wrong, however, what is the right approach? Coercion is a ubiquitous, attested phenomenon in natural language. One has to be able to give an analysis of it in any remotely viable theory of predication and lexical meaning. In order to explain the data one has to do one of two things: either one has to develop a theory of lexical meaning where the lexical entries themselves change in context, or one has to complicate one’s notion of predica13

14

Laura Whitten and Magda Schwager independently observed to me that using such dictionary definitions is problematic, because Gricean maxims would predict that there are some special reason that the more complex formulation is used. This special reason would block the standard associations with the content. But if the inference here concerns nonlinguistic knowledge, we wouldn’t expect the flouting of the Gricean maxim to block such an inference. A Gricean explanation of why the inference fails for (1.30b) occurs precisely because that inference is based on lexical content, not world knowledge. Although one possibility for formalisation would be in a connectionist approach, where word meanings are thought of as vectors of strengths of associations with other words that get recalculated every time the word occurs. This is very far from either Pustejovsky’s generative lexicon or Recanati’s relevance theory approach. It’s also philosophically and conceptually extremely unsatisfying, as such an approach doesn’t begin to tell us anything about lexical meaning or lexical inference or about how meanings compose together.

18

Lexical Meaning and Predication

tion and logical form. Since I do not see how the first option can be developed in any detail that does justice to the composition of sentential or discourse meaning from lexical content, I will investigate the alternative that coercion phenomena call for a reanalysis of predication. When I say that I enjoyed a cigarette, the word cigarette does not change its meaning but what I enjoyed is doing something with the cigarette. That is, coercions involve a more complex act of predication than one might have thought. The reason that this is so, I will argue, is that in coercions type presuppositions have to be accommodated and, as with accommodation at the level of contents, type accommodation typically introduces new material into logical form.15 Viewed from this perspective, coercion is not really a problem about meaning change in the lexicon; it’s a problem about compositionality—about how lexically given meanings combine together in the right sort of way. I argue for a similar conclusion for dual or multiple aspect nouns like lunch, book, temperature, and so on; the process of justifying type presuppositions with the types assigned to these nouns will complicate the process of logical form construction and may add new content to logical form. To account for many features of predication, the logic of meaning composition has to be rethought and revamped considerably from the standard approach to predication that underlies Montague Grammar. This is the task to which I devote myself for most of this book.

1.3 The context sensitivity of types We want a theory of lexical information that offers a framework within which empirical research will yield a correct account of lexical content. I have argued that a lexical theory has to do two things to reach this goal: give an account of the meanings of lexical items and an account of the operation of predication needed to derive truth conditions for clauses. But in order to capture the observations and intuitions of most of those who have worked in the field of lexical semantics, we need to do this in a particular way: we need to construct a theory of lexical meaning and predication that can exploit features of the discourse context. In particular this means a context sensitive theory of typing. Observations that confirm this last claim have been around for years. Nevertheless, there have been few attempts in the literature to account for these observations. Lascarides and Copestake (1995) noticed that the event readings of the object of a verb like enjoy can depend on discourse factors. Normally enjoy coerces its object or theme argument that has the type book into an expression 15

GL says little about predication. Because it fails to carry through on either way of analyzing the data, we shall see that GL fails to account for coercion.

1.3 The context sensitivity of types

19

that involves an event of reading the book as in (1.31a). But this reading depends on the assumption that Julie is a person, someone capable of reading the book, because this reading is not available with (1.31b). It becomes available if (1.31b) occurs in the context, say, of a fairy tale in which goats have been established as capable of reading. This is a matter of linguistic knowledge, of how the discourse context affects the analysis of (1.31b), not a matter of world knowledge—it is completely unintuitive to assume as a general matter of world knowledge that goats can read in fairy tales (it has to depend on the particular fairy tale!). (1.31) a. Julie enjoyed the book. b. The goat enjoyed the book. Most stories about coercion (Pustejovsky (1995), Nunberg (1979), Egg (2003), Asher and Pustejovsky (2006)) assume that the object argument of enjoy is some sort of eventuality, which is the result of a typing adjustment due to a clash between the type of argument the verb demands and the type of argument that is in fact its direct object; the verb enjoy requires an event as object argument and so coerces the direct object into giving an argument that is of some event type. Regardless of the details of how this coercion process actually works, (1.31a,b) shows two things. First, the inference from enjoy the book to enjoy reading the book must be defeasible. Second, the fact that we can get the reading that the goat enjoyed the book in (1.31b), given a discourse context in which goats talk, shows that the typing and typing adjustment rules must be sensitive to information in discourse. Danlos (2007) has shown that aspectual verbs are also sensitive to discourse context. Aspectual verbs take some sort of eventuality as an object or theme argument. The GL framework claims that these eventualities are given by the lexical entries of nouns. But Danlos’s examples show that this is not the case: (1.32) a. ??Yesterday, Sabrina began with the kitchen. She then proceeded to the living room and bedroom and finished up with the bathroom. b. Yesterday Sabrina cleaned her house. She began with the kitchen. She then proceeded to the living room and bedroom and finished up with the bathroom. c. Last week Sabrina painted her house. She started with the kitchen. She then proceeded to the living room and bedroom and finished up with the bathroom. The examples in (1.32) show that the eventuality is not, at least in all cases, given by the lexical entry of a noun in the theme argument of the verb or some

20

Lexical Meaning and Predication

adjoined PP. When a discourse is not clearly about any particular eventuality as in (1.32a), the coercions induced by the presence of aspectual verbs are rather bad; there is no way to recover an associated eventuality to serve as the theme argument of the aspectual verbs. On the other hand, when the discourse is clearly about some eventuality, then these aspectual verbs naturally get associated with that eventuality. Skeptics at this point might say that this is not a matter of linguistics at all but cognitive psychology and world knowledge.16 The judgements in (1.32) might be a matter of the interpreter’s being primed with a recent mentioning of some event that can be used to fill in the needed event arguments to the aspectual verbs. However, if these judgements were merely a matter of priming, then the structure of the prior discourse shouldn’t affect the judgements. Yet it does. Contrast (1.32c) with (1.32d): (1.32d) ?Last week Julie painted her cousin’s house. Then this week she started with the kitchen. She then proceeded to the living room and bedroom and finished up with the bathroom. This discourse is once again much more problematic and resembles (1.32a) in that it’s no longer clear what is the event argument of the aspectual verbs start, proceed, and finish up. (1.32c) and (1.32d) form a minimal pair and provide strong evidence that furnishing an event argument to these aspectual verbs is a linguistic matter that involves an interaction between the discourse context and how it is structured, lexical meaning, and the construction of the meaning of an individual clause. It is not a matter of language independent world knowledge or of psychological priming. It’s not just the aspectual verbs whose coercive force is sensitive to discourse context. Discourse context can push us to reinterpret many expressions:17 (1.33) a. I went to the gallery after the robbery. The elephant had been stolen. b. I went to the zoo after the robbery. The elephant had been stolen. Discourse context also affects the interpretation of other forms of predication. The genitive is one such predicational construction where there is a relation inferred to hold between variables or constants introduced by the DPs in that construction. Sometimes this relation is specified by a relational noun in the genitive construction—e.g., John’s mother. However, Asher and Denis (2004) note that discourse-based information can override the relation provided by the lexical meaning of relational nouns: 16 17

Jerry Fodor put this point to me on a related matter after a lecture on discourse structure at Rutgers in 2005. These examples are inspired by examples from Marliese Kluck.

1.4 The main points of this book

21

(1.34) [Context: Picasso and Raphael both painted a mother with a child.] Picasso’s mother is bright and splashy —a typical cubist rendition. It makes Raphael’s mother look so somber. And where no relational noun is involved, discourse context can also affect how to interpret the underspecified relation introduced by the genitive: (1.35) a. All the children were drawing fish. b. Suzie’s salmon was blue. As Asher and Denis (2004) and a number of other researchers (Vikner and Jensen 2001, Partee and Borshev 1999) have argued, the genitive construction seems to be one that is partially determined by the lexical entries of the nouns involved—and Asher and Denis argue that in particular it is the types of the nouns involved that help determine the relation. But the examples above show once again that the meaning of this construction is discourse sensitive in a way that previous analyzes of the interaction between discourse and the lexicon (cf. Lascarides and Copestake 1996) were unable to capture. These examples of discourse sensitivity show something of much more general interest as well. The eventualities that are inferred to be the arguments of the aspectual verbs in, for example, (1.32b,c) are inferences that are not based on general conceptual or world knowledge but on information that is conveyed linguistically in prior discourse. This must be so, since if these inferences were driven by non-linguistic knowledge, then (1.32a) should be fine when it isn’t. We haven’t shown, of course, that these mechansims cannot be guided by nonlinguistic information; but we have shown that they are not themselves simply a matter of world knowledge. The discourse sensitivity of the mechanism shows us something that the simple predicational examples cannot do straightforwardly (though see the last paragraph of the last section of this chapter); the coercion mechanisms are part of the linguistic system.

1.4 The main points of this book Examples of coercions with simple predication like those in (1.27a,c) have received an extensive discussion in the lexical semantics literature (Pustejovsky (1995), Kleiber (1999), Egg (2003), Recanati (2005)). But a satisfactory formal analysis of coercion, copredication, or restricted predication and how these phenomena affect the composition of content is lacking. Further, no one to my knowledge has really investigated the interactions between discourse and lexical meaning of the sort introduced in the previous section. I will develop a

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Lexical Meaning and Predication

theory of predication and lexical meaning and an account of how these interact with discourse structure in this book. I will use the theory to investigate phenomena like copredication, restricted predication, and coercion. The guiding idea, already implicit to some extent in Pustejovsky (1995), but made much more explicit in Asher and Pustejovsky (2006), is that almost all words will have single and simple lexical entries. Words like the nouns cat, lunch, book or the verbs kill, read, and master denote simple properties or relations, and so accordingly the logical forms that specify their denotations are very simple. For instance, cat has the lexical entry λx cat(x), while master is a simple transitive verb that denotes a relation between its subject (or external) and object (or internal) arguments. If words have simple entries and make simple contributions to truth conditional content, they come with a rich amount of information about the types assigned to the lambda terms and the variables within them. These types will guide predication and be responsible for fine-grained differences in lexical meaning. When words are combined together to form clauses, sentences, and discourses, the types associated with various terms will interact in complex ways. I will introduce operations of type adjustment in response to type mismatches between predicate and argument that correspond to the accommodation of a type presupposition, or more generally speaking the justification of such a presupposition. I will tell a similar story about morphological processes with semantic import; in effect the application of semantically rich morphology to a word stem is also a matter of type driven predication, which may bring with it various type adjustments. The effects of these type adjustments at logical form is that the logical form for the clause will contain elements that are not present in the lambda terms for the constituent words themselves. Predication involves not only applying a function to an argument but also operations of adjustment corresponding to type presupposition justification. Coercion and the sort of problematic copredications that I introduced earlier will invoke particular sorts of presupposition justification. As we will see, however, predication is not simply a matter of putting well formed lexical meanings together and adjusting them when they do not fit; type information is also to some extent dependent on the discourse context. The theory I will present will provide a framework for investigating the context sensitivity of type assignments. While I will use the framework of the typed lambda calculus, I will extend the typed lambda calculus beyond the usual set of simple types and functional types to include two complex types. These complex types furnish the basis for my analysis of problematic cases of copredication and coercion. One complex type, the • type, will be used to analyze terms of which we can predicate

1.4 The main points of this book

23

properties of two different aspects of the same thing (what I call aspect selection). Most of these terms are nouns, and I will call them dual aspect nouns. I will argue that this kind of predication requires a special metaphysical conception of the objects whose aspects are the bearers of the properties predicated. The type adjustment with dual aspect nouns is, in some sense, just a shifting of emphasis or a reconceptualization of the very same object. Coercions like those induced by verbs like enjoy, shift the predication entirely away from the original object to some other object of a different type—for instance, an eventuality associated with the original object. Such coercions, unlike aspect selection, do not affect the way the objects denoted by the term that is subject to the coercion are counted or individuated. I will model coercions with another sort of complex type, something that I shall call a polymorphic or dependent type. I will provide rules for dealing with the types I introduce in the analysis of predication when they occur either as type presuppositions of predicates or as types on arguments of predicates that require some other type. Rules for type presupposition justification will allow us to select the appropriate type of the argument for the requirements of the predication at hand. In addition I will show how the type system is sensitive to the discourse context. By integrating a theory of discourse structure and discourse contexts from earlier work (Asher (1993), Asher and Lascarides (2003)) within the theory of predication, I will show how discourse can transform and constrain type assignments and type transformations. The type system is dynamic and evolves as discourse proceeds in a way similar to the way that linguists and philosophers have argued that the semantics of discourse evolves dynamically. My approach crucially distinguishes the logical forms constructed during predication from the types that guide and constrain predication. When we accommodate, say, a type presupposition of a predicate that demands an event as an argument but is given something of type physical object, justifying the presupposition will require not only an adjustment in types but, typically, an adjustment at the level of logical form as well. We need types to construct logical form, but we also need the logical forms as distinct semantic citizens, for it is they, not the types, that are the vehicles of model theoretic content. I will argue for a “two stage” or two level semantics for lexical meaning: a level with the usual intensions for the expressions of logical form, and a level with a proof theoretic semantics for the types. The nature of types and the argument for my two level theory will occupy much of the next chapter. The development of the system of complex types and the two-stage theory of semantics and its applications will occupy the rest of the book. Besides the analyzes of copredication and coercion, I will show how the system yields an analysis of restricted predication and the genitive

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Lexical Meaning and Predication

construction. Though topics like metaphor and poetic license outrun the scope of this book, I will tentatively offer an application of my system to these topics at the end of the book. We’ll see that types in the theory of predication are closely linked to metaphysical principles of individuation and counting. Thus, the types used to guide predication will be of a quite general nature. The system of types, however, involves more types than those just needed for checking predication. Finegrained differences in types can affect the content of a predication and can account for at least some analytical entailments—entailments that are a priori and follow from the meanings of the “non logical” words of natural language. More speculatively, types will provide a linguistic foundation for a theory of concepts and of internally available contents and inferences. The approach is thus anti-Quinean (and also contra Fodor and Lepore (1998), Cappelen and Lepore (2004)). Nevertheless, I have taken to heart the warnings of Fodor and Lepore about lexical semantics. For instance, my type-driven theory of predication is agnostic about lexical decomposition beyond what is demanded by morphology and syntax.

2 Types and Lexical Meaning

The typed lambda calculus and its operation of type restricted application are familiar to anyone who has worked in formal semantics. But there are largely unexamined questions about the nature of types, their relations to formulas of logical form, and the effect of rules of type shifting on logical form. We need to look at these questions in detail.

2.1 Questions about types Let us first turn to questions about types. For one thing, are our types all atoms or are there types that have a structure and that are constructed from “type constructors” together with other types? Another question is, what is the interpretation of our types? Montague Grammar has an answer to our questions. Montague Grammar starts with two basic types, the type of entities e and the type of truth values t and then closes the collection of types under the recursive rule that if a and b are types, then so is a ⇒ b.1 The type a ⇒ b is one that, given an argument of type a, produces an object of type b. Montague Grammar converts these extensional types into intensional types as follows: if a is an extensional type, then s ⇒ a is its intensional correlate, where s is the type of worlds or more generally indices of evaluation. Montague Grammar has an extensional set theoretic model of types: the primitive types are identified by their inhabitants, the set of objects of that type relative to some domain of interpretation, while the set 1

The notation → for the functional type constructor is standard. But as I will distinguish this functional type constructor from its related cousin, the implication constructor for logical forms, → and from the usual way of defining a function ( f : a → b), I will use the slightly nonstandard ⇒.

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of functional types over types a and b is modelled as the function space or set of all functions from a into b, { f : a → b}. When Montague developed his theory, his use of the typed lambda calculus served a logical purpose. Turing (1937) had shown that the untyped lambda calculus had a model in the set of computable functions, but the application of such a theory in formal semantics was problematic. When terms of the untyped lambda calculus include the standard truth functional operators essential to semantics, it is easy to form terms like λx¬x[x], which is the property of not applying to oneself—the Russell Property. Applying the Russell property to itself (note that we’re using untyped Application here) produces the following result, which is uninterpretable when negation is understood as in classical logic: (2.1) λx¬x(x)[λx¬x(x)] = ¬(λx¬(x)[λx¬x(x)]) The typed lambda calculus avoids this problem, since the Russell Property does not have a consistent type in the typed lambda calculus. It is, in other words, not a well-formed term. The typing of expressions allows one to combine the lambda calculus with the operators of classical logic; it also ensures that the theory is consistent if set theory is. The typed lambda calculus avoids paradox in a simple and pretty much cost free way. Since the work of Dana Scott and Gordon Plotkin in the early seventies (Scott (1972)), we have abstract models of the type-free lambda calculus. But they have certain drawbacks for the purpose of studying natural language semantics. The models used by Scott require that the values of lambda terms be continuous functions in the sense that one can compute their value in the limit given some long enough run of values. But it is precisely the operators of classical logic like ¬, ∀, or ∃ that fail to be continuous in the requisite sense. While the untyped lambda calculus has various uses in mathematics and computer science,2 there are compelling linguistic reasons to adopt a typed lambda calculus in constructing logical forms. The models of a Montagovian typed lambda calculus together with the standard quantifiers and connectives are unproblematic set theoretic constructions. Furthermore, the typed lambda calculus provides a tight connection between syntactic categories and semantic 2

For example, in representing fixed points or recursion. In recursion, a function or term takes itself as an argument. Turner (1989) has argued that in natural language terms, in particular property terms, can take themselves as arguments as well:

(2.2a) Being nice is nice. (2.2b) It’s bad to be bad. I will argue in chapter 10, however, that examples like (??) don’t argue against a typed notion of predication.

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types, as has been shown in the field of categorial grammar. There is a natural homomorphism from categories to types that paints a compelling picture of the interaction between syntax and semantics and yields a simple computational process for the derivation of a logical form for a clause. A third reason is that the typed lambda calculus has just the right expressive power. There is a natural distinction between properties and objects crucial to the intuitive conception of predication (where one predicates a property of an object)— properties are functions whereas objects are the arguments of functions. It’s less obvious how to model traditional predication in an untyped system, since the basic distinction between objects and properties isn’t reflected in the semantics of expressions. A typed system yields a natural explanation of semantic well-formedness and semantic anomalousness too, while untyped systems don’t. Nevertheless, typed systems are expressive enough to define the operations relevant to the analysis of predication as well as semantic correlates of the morpho-syntax of word formation. Examples include: nominalization— the operation from higher types into e (e.g., is square −→ the property of being square), grinding (the operation that takes a count noun like rabbit and transforms it into a mass), the operation from type e into a quantifier type to handle coordinations like John and three students went to the party, the operation from types of transitive verbs as types of first-order relations into higher types (should we wish it), the operation from individual denoting terms into collection denoting terms, and the transformation from mass/count arguments into activity/telic eventualities (e.g., drink wine vs. drink three glasses of wine). In a minute, we are going to complicate Montague’s vision of types considerably. I turn now to some reasons for this move.

2.2 Distinguishing between types An analysis of predication that uses a rich system of semantic types is only promising if there is good evidence that languages encode such a system. Luckily, there is evidence that information about types is conventionalized; it even affects the case system in some languages. There are many ontological categories that languages reflect in their grammar: the distinction between questions and propositions, for instance, or the distinction between abstract objects and concrete or physical objects. These distinctions permit us to distinguish between the malformed predications in (1.1f–j) and well-formed predications in which the types of the predicate and its arguments match.

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2.2.1 Events vs. objects Many other distinctions between types of objects exist. What follows is a partial list. The distinction between eventualities (events, processes and states) and non-eventualities (other sorts of objects) allows us to predict general patterns of predication. Events occur at times but objects don’t; adverbs of manner of motion go well with events, but their adjectival counterparts fail to predicate felicitously of many noneventualities, as the minimal pairs below in (2.2) and (2.3) demonstrate: (2.2) a. John’s birth occurred at 10 am this morning. b. #John occurred at 10 am this morning. (2.3) a. The tree grew slowly. b. ?The tree was slow. Languages like Japanese reflect the distinction between eventualities and objects in the grammar within the system of particles. Chinese reflects the distinction between eventualities and objects within the system of classifiers. Linguists have also shown that languages are sensitive to the differences among eventualities. Dowty (1979) and Vendler (1957), among others, have observed that punctual events like achievements don’t go well with adverbials that express the fact that the event they modify took place over an extended interval of time. On the other hand, activities fit well with such adverbials.3 (2.4) a. #John died for an hour. b. John ran for an hour. Thus, further distinctions between different sorts of eventualities help explain patterns of predication involving temporal adverbials. The distinction between states and other eventualities shows up in other parts of the grammatical system. For instance, verbs that denote states in general do not accept the progressive form in English, while verbs that denote events do. (2.5) a. #Samantha is knowing French. b. Samantha is running. c. Arnold is dying. Japanese marks a distinction between animate and inanimate in its predicative verb structure, which is related to the difference between event types and non-event types (but does not exactly correspond to it). • iru(x), x: animate • aru(x), x: inanimate (event) 3

See also Krifka (1987), Rothstein (2003) for more discussion of this data.

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2.2.2 Locations vs. objects Another example of a grammatically grounded distinction between types in natural language concerns the distinction between locations and physical objects. Places are fixed elements in the terrestial reference frame, while objects typically have a complex internal structure and can move with respect to the terrestial reference frame. Some evidence for this distinction comes from Basque, where the grammar encodes differences between location and objects via two genitive cases -ko and -ren; locations in general easily take the genitive -ko but not -ren, while objects in general do the reverse. Aurnague (1998) distinguishes the following types: places (e.g., valley, field, river, mountain, hill), objects (e.g., apple, glass, chair, car), and mixed objects (e.g., house, church, town hall). Of particular interest are the “mixed objects” and the behavior of their expressions in Basque. The terms for mixed objects readily accept both forms of the Basque genitive. So if we accept the encoding hypothesis for Basque, mixed objects like houses would appear to belong to two types, or two ontological categories, at the same time—location and physical-obj—neither of which is a subtype of the other (it is neither the case that the properties associated with physical objects are inherited as properties of places nor that the properties associated with places are inherited as properties of physical objects). (2.6) Maite dut etxeko atea haren paretak harriz eginak direlariak. (Michel Aurnague p.c.) I like the door of (locational genitive) the house the walls of (physical object genitive) which are made of stone. Prepositions in English serve to distinguish between places or locations and physical objects, though the distinctions are less clear cut than in Basque (Asher 2006).

2.2.3 Mass vs. count The mass/count distinction is another type distinction marked in many languages. Chinese marks this distinction in its system of classifiers, whereas other languages like English mark the distinction with determiners and to some extent within nouns (although many nouns can receive both a count and noun interpretation). Certain determiners in English are designated as mass determiners—e.g., much, as in much water, much meat. They do not go with count nouns in general—e.g., much person, much people are malformed. Other determiners like many, every, the apply both to count nouns and mass nouns but

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require special interpretations when put with mass nouns.4 Thus every water, many waters must range over contextually given portions of water or perhaps kinds of water. Languages also distinguish “determiner phrases” (DPs) denoting quantized portions of matter like many waters or the water from DPs with ordinary count nouns. (2.7) You can take two piles and put them together to make a bigger pile. (2.8) Two little waters make one large water. (in a restaurant) Piles pick out portions of matter as does the expression two waters. But you can’t put two dogs together to make a bigger dog. This last observation holds for all count nouns.

2.2.4 Kinds vs. individuals Another universal distinction in language is the distinction between kinds and individuals. Kinds are often expressed in English with a bare plural noun phrase (e.g., cats, numbers, people) but can also be expressed with other constructions: (2.9) The Mexican fruit bat is common in this area. Linguists take the definite noun phrase in sentences like (2.9) to refer to a kind rather than to range over individual members of the kind. They argue, quite sensibly, that the predicate is common in this area (but also others like is extinct, is widespread) cannot hold of an individual but only of kinds or species. Thus, most languages encode a three way distinction between the types of masses, countable individuals, and kinds. Chinese, once again, encodes the distinction between kinds and individuals in the classifier system. (2.10) Moby Dick shi yi tiao / *zhong jing. Moby Dick be one Cltail /*Clkind whale. Moby Dick is a whale (individual).

2.2.5 Containers vs. containables A more subtle type distinction encoded in the system of prepositions within English involves containers and containables. In general anything that desig4

Borer (2005a) argues that the mass/count distinction is to be located in a classifier-like syntactic projection and that nouns are by default mass. She cites as evidence the fact that nouns without classifiers in Chinese are interpreted as mass.

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nates a specific volume or enclosure can be a container. Many physical objects can serve as containers, although some cannot. (2.11) b. c. d.

a. The water is inside the pitcher. The keys are inside the car. John put the keys inside his pocket/inside the drawer. # John threw the keys inside the air. (Versus: John threw the keys in the air.) e. # John put the wine inside the water. (Versus: John put the wine in the water.)

2.2.6 Plurality Plurality also introduces type distinctions. Research on plurals, as I briefly outlined in chapter one, distinguishes at least two types of plural predication: distributive and collective. Distributive predication occurs when a property or relation is predicated of each element of a set as in (2.12) The boys each worked hard. On the other hand, (2.13a,b) exemplify collective predications where a property is predicated of the whole set of students but not of each student individually. (2.13) a. The students surrounded the building. b. The students mowed the whole meadow. Sometimes collective predication occurs with singular nouns (and so this semantic phenomenon must be distinguished from the syntactic phenomenon of number). (2.14) The committee is meeting in the lounge. (collective predication) Some predicates, finally, put no requirements on how their plural arguments are to be understood. 5 (2.15) Three girls danced with four boys. (2.15) makes no claims about whether the boys distributively or collectively danced with the girls, only that there were three girls and four boys and that dancing went on between them. 5

These are called cumulative predications.

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The distinctions between types of predication mark distinctions in type presuppositions. For instance, an account of the lexical meaning of the word disperse or surround must mark it as requiring an external argument that is of group or collective type, which means that the argument must denote a group of individuals or range over groups of individuals. Verbs like disperse or surround do not go well with inherently distributive quantifiers like most students, whereas they apply perfectly to plural noun phrases that can be interpreted as denoting groups: (2.16) a. ?Most students surrounded the building.6 b. The students in the square surrounded the building. Other predicates like work must be interpreted distributively and impose type presuppositions on their arguments to that effect.

2.2.7 Types and specific lexical items Some verbs have quite specific type requirements encoded in their selectional restrictions. (2.17) a. John weeded (mulched, hoed . . . ) the garden (lawn, area, tomatoes, peas, plants . . . ). b. John hoed (mulched) the weeds. c. # John mulched, hoed, weeded the water. d. #John shoveled the closet. You can’t weed, hoe, or mulch certain types of locations—bodies of water, for instance. Locations that can be weeded have to have dirt or soil in them. And you can only shovel a location open to the elements. This is not a matter of world knowledge but a matter of grammar, broadly construed: one can perfectly well imagine someone cleaning a body of water like a lake of floating algae or water plants, but we don’t call that weeding. Given the fine-grained type distinctions made by the language, it should not be surprising that when predicates combine with arguments of different types, the meaning of the predicate shifts in the resulting predication. Consider the following. (2.18) a. John swept (shoveled, wiped . . . ) the closet (room, walkway, kitchen, fireplace, floor, counter . . . ). b. John swept (shoveled, wiped . . . ) the dirt (debris, manure, sand, slush, litter, shavings, cinders, dust . . . ). 6

Note that the partitive DP most of the students does admit of a collective interpretation, unlike the straight quantified DP most students.

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Predications involving sweep have a different content depending on whether the direct object is a location, a place, or a surface (we can assimilate all of these here to the type location), or whether the direct object is a portion of matter. The resulting meanings for sweep, for instance, are so different that they don’t license copredication or ellipsis: (2.19) b. c. d.

a. John swept the kitchen and Mary the entryway. John swept the dust and Mary the leaves. #John swept the kitchen and Mary the leaves. # John swept the kitchen and the dust.

Another example of an apparent meaning shift in a predicate because of a shift in type of its argument comes from communication verbs. The meaning of verbs like whisper, whistle, whine, etc. varies with respect to whether it has an object argument; furthermore, the type of this argument can also affect the verbal meaning. (2.20) a. John shouted (whispered, whistled, whined . . . ). (activity) b. John shouted (whispered, whistled, whined . . . ) a warning. (accomplishment) c. John shouted (whispered, whistled, whined . . . ) at the animal. (accomplishment or activity) d. The bullets whistled past John. (accomplishment) Such so called verbal alternations have occupied linguists for many years.7 They offer us another means for seeing how languages encode a sophisticated system of types. But they also clearly pose a challenge for lexical semantics that resorts to types: how can we account for the shifts in the meaning of a verb given its different arguments? Other well-known verbal alternations involving prepositions show subtler shifts in meaning. (2.21) b. c. (2.22) b. c. d. 7

a. John treated Mary to dinner. John treated Sam for cancer. John treated the cancer. a. John loaded the hay on the wagon. John loaded the wagon with the hay. John sprayed the paint on the wall. John sprayed the wall with the paint.

For a comprehensive bibliography and discussion, see Levin (1993).

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To state the generalizations as to how these predications behave, we must recognize distinct types accorded to arguments of these transitive verbs. Predicating the verb treat of a living entity such as a person, animal, or even a plant means something quite different from when the verb is predicated of a direct object that denotes a disease. The type of the object of the prepositional phrase modifying the verb also will make a difference to what the predication ends up expressing; for instance, we infer that all of the hay is on the wagon in (2.22a) but not in (2.22b), whereas (2.22b) conveys that the wagon is fully loaded, or at least prepared, whereas this is not the case in (2.22a). Sensitivity to argument type is not just a property of verbs and prepositions. We’ve seen how determiners interacting with different nouns can deliver different types of DPs. Adjectives have a similar behavior. Consider the difference in the meaning of the adjectives flat (due to Partee (1984)) and red in the following: (2.23) b. c. d. (2.24) b. c. d.

a. flat tire flat beer flat water flat country a. red meat red shirt red pen red wine

I could go on and on with the list of type distinctions made in language and that affect the contents of predications. There is a lot of evidence that natural languages encode a rich system of types that are used to guide predication. For each type distinction, I will try to establish syntactic or lexical alternations to distinguish between types. That is, positing a type distinction in a lexical theory will require linguistic evidence: there must be a linguistic construction that accepts expressions of one type but not the other. This is at least a minimal condition.

2.3 Strongly intensional types Supposing that we enrich the type system with a suitable collection of subtypes of e, can we still retain Church’s and Montague’s simple set theoretic model of types? The answer is no. The set theoretic model isn’t right for several reasons. First, we need to distinguish between a type and the type’s extension or inhabitants in order to have a coherent notion of subtyping. Consider, for example,

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the relation between the type of physical properties (physical-object ⇒ t, or p ⇒ t) and the type of all first-order properties e ⇒ t. It is intuitively obvious that the type of physical properties is a subtype of the type of all first-order properties. But if we think of types as sets and identify the relation of subtyping with the relation of subset, then this intuitive connection is lost: the set of functions from physical objects to truth values is disjoint from the set of functions from entities generally to truth values, as long as there are some entities that are not physical objects. That is, these two sets of functions have distinct domains and so their intersection is 0, even though the physical properties are subfunctions of the first-order properties. No element of the set of inhabitants of p ⇒ t is an element of e ⇒ t. But we can’t simply do without the notion of subtyping. We need the usual subtyping relation between physical properties and first-order properties to state a suitable form of application, according to which the application of a determiner, which requires its first argument to be some first-order property, to a noun phrase denoting a physical property or physical kind yields a semantically well-formed content. The set theoretic interpretation of functional types is a disaster for the compositional construction of logical forms once we posit subtypes of e. We might try to reinstate the set theoretic interpretation by taking p ⇒ t and e ⇒ t to be sets of partial functions. This gets things wrong for a different reason. Consider the obvious truth that physical properties like height, weight, mass, length, and so on are not properties of abstract objects. Yet on the partial functions view, they are and necesssarily so! They are simply everywhere undefined on the domain of abstract objects. Can we limit our interpetation of types then to be just certain sets of partial functions? Perhaps, but which ones? Do we want to consider as a physical property some property that is only defined for very few types of physical objects? More importantly, if we exclude the empty partial function as an inhabitant of any functional type, then our sets of “nice” partial functions may not be closed under operations that we would like for types, like joins and meets (or unions and intersections if you think set theoretically). Furthermore the empty partial function is just ∅. So if we ban empty partial functions from the set of partial functions, the set of types loses its lattice and even semi-lattice structure. This threatens the whole structure of the lexical type hierarchy and with it the analysis of predication and lexical meaning. The whole attempt to save the set theoretic model begins to look very gerrymandered. Another reason we need to move away from the extensional conception of types is that sets are not a faithful representation of some types that we need. Consider, for example, the set of fictional entities. Let us take seriously the idea that fictional objects are indeed fictional and so they don’t exist; they are not

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part of the domain of interpretation. Further, fictional objects not only don’t exist in the actual world; they don’t exist in possible worlds either—i.e., other ways in which the world could be. A fictional creature like a hobbit is not at all like the sister that I might have had; the latter exists in a possible world, the former does not. That’s what it is to be fictional. So on a view that identifies types with their inhabitants, types corresponding to fictional objects and the absurd type would be the same type, since they have the same extension or the same set of inhabitants, namely the empty set. But types of fictional objects are intuitively distinct from ⊥. Whether a term describes a fictional character or not certainly appears to make a difference as to how predications are understood. Within fiction, there is no question of checking or wondering whether the predication actually results in a literal truth. It is even quite controversial among philosophers who have written on fiction whether terms that appear to refer to fictional entities refer in fact to anything at all. On the other hand, fictional talk differs from metaphorical or loose talk; fictional talk is literal—the trees in The Lord of the Rings literally speak (see 2.25) whereas in metaphorical talk (2.26) the predications aren’t to be taken at face value. (2.25) Look! the trees are speaking. (Lord of the Rings) (2.26) These trees are really speaking to me. I’m going to paint the living room green. To make sense of this difference in predicational behavior, we should distinguish a type of fictional objects. And it should be distinct from the absurd type no matter what the circumstances of the actual world are. This leads me to adopt the thesis that types are neither to be identified with their actual inhabitants (extensions) nor even their possible inhabitants (standard semantic intensions). They are “hyper-intensional.”8 If types are intensional entities, they are not intensions as semantics standardly conceives of them—i.e., as functions from indices (possible worlds or sequences consisting of a world, time, context, and other appropriate elements) to extensions.9 Modulo a certain understanding of fictional objects, I have established that types aren’t to be identified with extensions, intensions, or sets thereof. So where do types fit into an ontology of abstract entitites? We need to think about the relations between the following sorts of abstract entities: • types 8 9

Reinhard Muskens in Muskens (2007) also argues for a hyper-intensional construal of types. The extension (at an index) of an individual constant is an individual; the extension of a 1-place predicate is a set; and an extension of a closed formula is a truth value.

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• concepts • properties Given the relatively well-understood analysis of properties in formal semantics and pragmatics as semantic intensions (or as functions from indices to extensions), types cannot be properties. In addition, properties are typically understood to be mind-independent entities, entities whose existence is not dependent on the existence of minds. Types, however, given their role in guiding predication, are part of the conceptual apparatus necessary for linguistic understanding. They are mind-dependent representations of mind-independent properties and individuals. This leads us to the hypothesis that types are concepts, which I take to be mind-dependent entities as well. This hypothesis has some promising support. Concepts come at different levels and granularities. They form a hierarchy, just as types do. There are concepts of what it is to be a property, what it is to be an individual, what it is to be a physical object, and so on. There are also much more specific concepts: the concept of red, the concept of S´egol`ene Royale or of Hillary Clinton. Like types, concepts are the internal, mind dependent reflection of mind independent properties and individuals they are concepts of. Concepts (and types) have their own “internal” semantics which has to “track,” in the appropriate way, the properties and individuals they are concepts of. It is in virtue of such tracking that a concept is a concept of some object or property. For example, the concept of red tracks the property of being red. A concept red of the color red is triggered by something at a particular location l in the conceiver’s visual field, typically when the conceiver is perceptually aware of something at l that is in fact red in color. Though this tracking is generally reliable, it can occasionally fail. For instance, if there were something wrong with a conceiver’s visual apparatus or the circumstances of the perceptual event were very non-standard, the concept red could be introduced as holding of some object when the object of which the conceiver is perceptually aware is in fact green in color. Another way the tracking could go wrong is that the object is in fact red but the concept fails to be triggered. Although making this notion of “tracking” precise is a book-length project on its own, I can say a few words here. I understand this notion in terms of how the rules for the application of the concept in the conceptual system function. In fact it is these rules that define the concepts and give them their content. These rules look something like natural deduction rules. A concept has certain “introduction rules” and certain inference rules that it licenses. The introduction rules stipulate that an object must satisfy certain conditions for its falling under a certain concept; these conditions may be determined by the sensory system

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of the organism or by other associated concepts. Talk of satisfying the application conditions of a concept can be replaced by the notion of something’s being provably of that type, giving an intuitionist flavor to the interpretation of types.10 There are more complex combination rules as well that determine how one concept interacts with others. It is these same rules that determine whether an object is of a basic type like cat or not. Type presuppositions and the rules for type presupposition justification are instances of rules of type and concept combination. This system of rules supplies what computer scientists call an internal proof theoretic semantics of a term and these rules define or give the content of concepts and a fortiori of types. This internal semantics contrasts with the mind-external, denotational semantics of the terms, which involve real world objects, properties, and so on. The two are connected by the tracking mechanism. Linking concepts and types together helps us understand both: concepts get a rigorous framework from type theory, while types are now linked to the agent’s sensory interactions with his environment and as well as the interactions between other concepts/types in the linguistic system. It is plausible that humans in a given speech community share concepts and a type system. They must do so in order to communicate, to exchange information.11 The internal semantics conceived as a system of proof or computation rules allows us to make sense of a shared conceptual system. If your concept of red and my concept of red have the same internal semantics, then we can be said to have the same concept of red, and similarly for other concepts. We can prove of two such proof or computational systems whether they are the same or not, using several different criteria. The crudest one is input/output equivalence; roughly two systems are input/output equivalent, just in case they give the same results in the same cases. With respect to the conceptual/type system, this would mean that the same linguistic actions and judgments are observed in the same contexts. Demonstrably, members of the same speech community have systems that are largely input/output equivalent. There is also the criterion of trace equivalence, where for each computation, the same sequence of actions is observed in the two systems. Finally, there is the criterion of bisimulation, according to which for each point in the computation there are the same possible continuations. Because the rules that make up the internal content of concepts are in general defeasible, concepts cannot determine reference to mind independent entities or properties independently of the context of their application. My notion of a concept thus differs from Frege’s notion of a sense.12 On a standard Fregean 10 11 12

More on this below. A proof of this fact is to be had in Lewis (1969). Peacocke (1992) uses concepts as constituents of thoughts to account for informativeness and

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view, senses compose together to yield thoughts, which determine on their own the truth conditions of sentences and discourses. I need a different view. A proposition is the result of the compositional interpretation of logical forms for the words that make up the sentence or discourse. But the compositional interpretation of a logical form results for me, as for most semanticists, in an intension—a function from indices to truth values. Since concepts don’t determine extensions, let alone intensions, concepts cannot be the constituents of propositions.13 Philosophers might take intensions to be simply formal standins for what propositions “really are.” But even then, if sentences are typically about mind-independent objects and the properties and relations these objects stand in, then the “real propositions” such sentences express will not contain concepts either— at least not of the sort I have in mind, mind-dependent entities with an internal semantics. More concretely, consider basic referential expressions: indexicals, proper names, demonstratives. The content of these terms, intuitively, has to do with the individuals they denote, not some proof object or set of rules for defeasibly determining whether a given object is in their denotation. The content of the type associated with you consists of rules for determining who the audience is in a particular context. But that’s not the contribution of you to the content of a clause in which it occurs. Its semantic content in this sense is the audience itself. Forceful externalist arguments given by Kripke (1980), Putnam (1975), and others show that our concepts associated with names of individuals and natural kinds do not suffice to determine the extensions or intensions of these expressions. If one looks to the behavior of such terms in modal contexts, there is compelling evidence that their meanings are not in general determined by “what is in the head” of a competent speaker of the language. In this respect too, types resemble concepts; they are tied via the expressions they type to properties and real world entities, but they are not identical to properties or real world entities, nor to sets thereof. They are part of our conceptual apparatus used to guide predication. To show how the externalist arguments affect types, let’s consider a typical Twin Earth scenario, familiar from the externalist literature cited above. Oscar on Earth and his twin “Twin Oscar” on Twin Earth speak syntatically identical languages and are type identical down to their molecular constitution. In

13

Frege style puzzles about the substitution of coreferential terms; he takes concepts to be something like Fregean senses. In fact, on the standard semantic conception of propositions, propositions don’t have “constituents” except in a set theoretic sense—and these would be sets of n-tuples of worlds, other indices, and truth values.

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keeping with general physicalist principles then, they have the same internal make up, the same thoughts, the same conceptual system. In particular their linguistic judgements about semantic well-formedness will be the same. Thus, when Oscar and Twin Oscar each interpret the strings water is wet and water is a tree, they assign the same syntactic form and the same semantic types to each expression; for the first string they will each construct a coherent logical form using the tools of the theory of predication, while for the second they will not. But whereas they marshal the same type system and conceptual resources when dealing with their languages, the languages of Oscar and Twin Oscar are different—they have a different semantics. On Earth water picks out the kind H2 0, or real water, whereas on Twin Earth the string water has a different semantics—it denotes a chemical compound distinct from H2 0, which, so the story goes, is XYZ or “twin water.” Water in English picks out a different substance from water in Twin English. Thus water makes dramatically different contributions to truth conditions in sentences of English and Twin English like: (2.27) Water is H2 0. (2.27) is true (and necessarily true) in English but false (and indeed necessarily false) in Twin English. Such Twin Earth scenarios are well established in the philosophical literature, and intuitions about them are relatively robust. They constitute powerful evidence that as internal reflections of properties and individuals, concepts, and types are not identical with mind-independent properties or individuals nor do they determine them, although they are associated with them through the tracking mechanism. If concepts, and a fortiori types, are not constituents of propositions, they can nevertheless compose together. Making the linguistically relevant types a subset of the set of concepts allows us to use the logical framework of types to explore concepts. Types associated with properties are functions from one type into another; when given an appropriate type as argument, types associated with properties return a new type. We can even compose types or concepts together to give us types associated with propositions or semantic intensions.14 I shall call the type corresponding to a proposition a thought. If there are as many types as there are distinct word stems in the language, then the hypothesis that types are concepts and compose together to yield thoughts gains in plausibility. Let us look a bit more closely at the composition of thoughts. Once we 14

Composition allows us to talk of concepts as constituents of thoughts, though this talk should be interpreted with care. It is true that concepts compose together to form thoughts, but that does not necessarily mean that the finished product will actually contain those concepts. Nevertheless, because I shall identify thought contents at least in part with the derivation of the thought from its constituents through composition, that’s pretty close to constituency.

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distinguish between subtypes of the type e of entities non-extensionally, we must think of the complex types in a more fine-grained way as well. Just as we have different subtypes of the type e, we also have different subtypes of e ⇒ t, or even t itself, the type of propositions. For instance, the concept or type red associated with the nominal modifier red combines with other concepts to form more complex concepts like red pen, red apple, and so forth. This is their “proffered” internal content that they contribute to the thoughts of which they are constituents. The nominal modifier red has a type that is a subtype of (e ⇒ t) ⇒ (e ⇒ t). Apple itself has a type that is a subtype of e ⇒ t. Later we will see how these “proffered,” as opposed to presupposed types affect the calculation of logical form. It is important to separate these proffered types from the type presuppositions of these terms. Both red and apple have type presuppositions on their arguments in logical form. For red its argument must be a physical object; for apple its λ bound variable must be an offspring of a plant. This allows such terms to enter into semantically well formed predications that are necessarily false (on an externalist semantics) like (2.28) Apples are vegetables (2.29) Those are apples (said by someone pointing to pears) but prevents the following from being well-formed predications when the words are understood literally: (2.30) #Apples are rocks. (2.31) #Those are apples. (said by someone pointing to cars) Here’s an approximation of the logical forms I shall assign to red and apple, with their type presuppositions expressed as restrictions on the λ bound arguments: • λP: e ⇒ t λx: p (red(x) ∧ P(x)) • λy: plant-offspring apple(y). This means that apple is defined when it applies to fruits other than apples to yield a truth value (it yields the truth value “false” in such cases).15 The fine-grained type apple is a function that when applied to an individual returns a “proof” that the object is an apple, if that object meets the conditions of application, and it returns a “refutation” that the object is an apple, 15

This is illustrative only. Nothing hangs on the particular choice of the type presupposition for apple, only that it must have one.

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if it fails to meet the conditions of application.16 It is this fine-grained type that is the internal proffered content of the term apple and that enters into the composition of thoughts. The same is true of all primitive types. The basic, primitive types like cat, dog, animal are analogous to the defined types like integer in mathematical applications of the λ calculus. The difference is that concepts and a fortiori types don’t seem to have easy definitions in the ordinary sense, although there are computations that humans have mastered that enables them to use concepts/types correctly. When I write where v is a variable, v: apple, I mean that the object denoted by v relative to an assignment meets the application conditions that are constitutive of the type apple; thinking of these application conditions as a proof or computation, this means that when the computation takes the value of v as input, it terminates and yields the value true. The notion of “object” within the internal semantics also requires explanation, as these are individual concepts.17 What about the fine-grained type red? red is a functor that when applied to a subtype of p returns another subtype of p—exactly which subtype of p depends on the fine-grained type of its argument. The type red thus has an argument place in it for a physical type. When the functor is applied to apple, we get the physical subtype: • red(apple) We now define the fine-grained type and internal semantics of the word red vis-`a-vis the polymorphic type red. red is a polymorphic type because the particular type of red depends on the type of the modifier’s argument. We may go further and require red to be a dependent type, as in (2.32) John hates everything red—red meat, red apples, red shirts, and so on. The exact type given by red will in this case depend on the value of the variable. While most of the time adjectives can be understood as having polymorphic types in this book, we will need dependent types to handle quantificational examples like (2.32). red presupposes that its argument be a subtype of p. If the modifier’s argument meets this type presupposition, then red(α), the application of red to α, is the value. Then the word red has the following type in this context: 16

17

This differs from what advocates of Type Theory like Martin-L¨of (1980) and Ranta (2004) take the denotation of a λ term to be; in type theory the denotation of a term is the collection of “positive” proofs. This corresponds closely to the notion of a classical extension. My view allows it to be the case that we can neither determine that something is an apple or that it is not an apple, but I will not investigate these refinements here. Cardelli (1988) takes an object is essentially a collection of functions or attributes with values, but there are other construals of individual concepts that are compatible with this approach.

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• (α ⇒ t) ⇒ (red(α) ⇒ t) The way to understand the internal semantics of the term is again to use the proof theoretic idea, in the large sense of proof. Red takes any type that gives proof application conditions for entities that are of type α p and returns a new type that gives application conditions for what it is to be a red α. The fine-grained types of verbs are similar to red in that they are functors taking a sequence of types (the sequence represents their arguments) and returning another type. It is natural to think of verbs as the “glue” that binds the other types in a thought together. This means we must introduce more complex types for verbs than is usual in standard formal semantics. As we’ll see, it is the DP rather than its head noun that furnishes the type of the argument to the verb, since determiners are often responsible in a language like English for saying whether the argument of a verb is count or mass, or a plural that is collectively interpretable or only has a distributive interpretation. The type of a verb takes DP types (or the types associated with the DP’s values) as arguments to give us a proposition. Thus, intransitive verbs will be functors from one DP type to propositions, while transitive verbs will be functors from two DP types. We will represent differences in verb alternations by the differences in the output that a particular instance of the polymorphic or dependent type yields. To figure out what a DP type is, we must turn our attention to determiners. Their conceptual role is to state relations between types in terms of the individual concepts that satisfy the application rules for these types. Each determiner with a distinct logical function will give rise to a distinct determiner concept. For instance, the determiner every has a fine-grained type every that when applied to a subtype of count e returns a functional type that, given a subtype of count, returns a thought, or a subtype of the type of propositions. The thought expressed by applying every first to α and then to β is the thought that every individual concept that satisfies the application rules of α also satisfies the application rules of β. The internal semantics of every is a type theoretic version of a Barwise and Cooper (1981) generalized quantifier. An intransitive verb or VP type takes such a generalized quantifier type as an argument and provides it with a subtype of e ⇒ t to yield a thought. For example, the sentence in (2.33a) has the corresponding thought described by the fine-grained type in (2.33b): (2.33) a. Every dog barks. b. (every(dog))(bark) c. ∀x(dog(x) → bark(x)) From (2.33b) we determine the type of bark. It is the function from DP types α

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to the fine-grained type α(bark), which is a subtype of the type of propositions. This generalizes straightforwardly to other grammatical categories. This develops the idea proposed by Howard (1980), the so-called “CurryHoward isomorphism,” according to which each lambda term corresponds to a type, which encodes a proof. These proofs determine the internal meaning of the term and its natural language correlate. To go back to our example, the λ term corresponding to the English expression every dog is: • λP∀x(Dog(x) → P(x)) The type of this term is (e ⇒ prop) ⇒ prop, where prop is the type of propositions. The interpretation of the term itself is one which is a function from proofs to proofs; given a property P or a proof from individuals to truth values, the lambda term denotes a proof that every dog has that property P. To apply this term to the lambda term λx bark(x) successfully is to produce a proof procedure for proving that every dog barks. The internal semantics is given in terms of the proof theoretic apparatus of the logical system, not in terms of some externally given values provided by an independent model. The notion of proof can be suitably generalized to an abstract mathematical sort of construction of the sort that intuitionists have worked on for many years, known as Topos theory.

2.4 Two levels of lexical content Let me summarize the discussion so far. I’ve argued that types are concepts, mind-dependent entities with a fine-grained content. Types have an internal semantics that is given at least in part in terms of the rules by which they combine with other types; they are proof theoretic objects.18 Types can be associated with other types—what we might think of as traits; each trait we associate with a type is a constraint on the introduction rule for the type. If there are concepts other than the linguistic types that I focus on here, I speculate that they have the same sort of internal content, specified by rules of combination, introduction, and elimination. Types as proof objects provide an internal semantics for natural language sentences and discourses that complements the external semantics given by ordinary intensions. We can even distinguish between different conceptualizations of the same physical object or of the same property, so in some respects the structure of types has the capacity to make finer distinctions in meaning 18

For similar ideas, see Fernando (2004)’s automata theoretic analysis of verb meanings, which amounts to a constructive theory for their types.

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than intensional semantics can.19 But the purpose of the internal semantics is not the same as that of the external semantics. Intensions are the soul of a theory of meaning—they are needed to determine truth, reference, and other external, semantic properties that link language to the world we talk about. Types and their adjustments are the heart of a theory of predication and responsible for other properties of meaning. The construction of logical form depends on type checking, and it is the clash of general, high-level types that lies behind failures of predication. This is semantics but it is an internal matter, something that speakers do “in their heads.” Types, and type presuppositions in particular, are responsible for our intuitions about semantic well-formedness and, I will argue below, for analytical entailments and for generalizations about word meaning. Types also serve a computational and theoretical need in lexical semantics and in the theory of predication. They simplify considerably the task of checking whether a syntactically acceptable sentence is semantically well formed or not; the property of semantic well-formedness for a sentence corresponds to the property of producing a normalized logical form for it, a logical form in which no more applications can be performed; and in a typed system with types like the one I will propose, this property is not only decidable but polynomial in complexity.20 Much of this book will be devoted to examining the interactions between internal semantics given by types and the external semantics for logical forms. For, as I’ll argue below when I look in detail at models of complex types, it is precisely in the rules that determine how type shifts from complex types to constituent types affect the logical form that various complex types will distinguish themselves. In other words, a division between the internal semantics and the type system and the external semantics allows us to get at the right semantics for complex types, since the semantics for these types is in part determined by what they do to logical form. It’s not usual in semantics to postulate two systems of meanings for words and the complex constituents made out of them. Martin-L¨of’s intuitionistic Type Theory (Martin-L¨of (1980), Ranta (2004)) identifies types and proofs and the semantic contents of terms; the internal semantics thus emerges as the only meaning of the logical forms, and the external semantics drops out. The meaning of a term in Type Theory is just the collection of its proofs. 19

20

In classical semantic systems, the interpretation of types needs to be distinguished from that for logical forms, since types do not convey enough information to provide truth conditions. Montague Grammar’s simple set theoretic model of types assigns types a very impoverished semantics compared to that given to logical forms. The types of the extensional typed lambda calculus do not, for instance, distinguish between any entities or between the truth values. Even in an intensional setting, Montagovian types do not distinguish between propositions or between different one place properties, for instance—all one place properties are of the same type. One complication to this claim concerns nominalization. I discuss this in chapter 10.

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Given the arguments in the previous section concerning the independence of the semantics of concepts and thoughts on the one hand and the semantics of propositions on the other, we cannot simply replace our intensional semantics of terms in the lambda calculus with the internal semantics of types. This move would run afoul of very basic intuitions about semantic content, as I argued above. To collapse the level of types and its conceptual, internal semantics with the level of logical forms and its intensional semantics is to miss the intentional nature of language in the Husserlian sense, according to which the semantic denotations of most expressions consist in mind-independent entities. The system of types and mind-dependent concepts is per force no substitute for external, mind-independent contents.21 There are also technical problems with the conception of meaning at the core of Type Theory. Consider a statement that has no proof, say because it is false. Its semantic value is the same as a sentence whose proof cannot be constructed say because of a type clash of the sort we saw in the last chapter. There seems to be no way in Type Theory to distinguish between statements that have no proof because they are false and statements that are semantically anomalous. Since this distinction is fundamental to the approach taken in this book, I cannot follow the philosophical and conceptual view laid out in Type Theory. But I can use their technical developments to fashion my internal semantics, while rejecting Type Theory’s conceptual and philosophical claims about meaning. Crucial to my enterprise is the distinction between objects in the internal semantics and objects in the external semantics. With this we can use a type theoretic view of the internal semantics to explain semantic anomalousness. If there is no proof that results from applying a type corresponding to a property to an internal object or individual concept, this is because there is a type inconsistency between the type assigned to the object and the type presupposed by the function representing the property applied to it. Statements without proofs in an internal semantics are those with a type inconsistency, and it is the lack of any positive proof in the internal semantics that defines semantic anomalousness. This “internal falsity” is of course distinguished from ordinary falsity in the external semantics; if a λ term is false in this sense in the internal semantics, it cannot even be evaluated in the external semantics. But a statement’s having a non-empty set of proofs from its internal semantics does not entail external truth outside of mathematical contexts; it may not 21

It seems to me that the simplest statements about the external world like you’re hungry pose problems for purely proof theoretic approaches to meaning. Externalist arguments of the sort examined in the previous section constitute powerful evidence that concepts, and a fortiori types, our internal mental reflections of real world properties and things, don’t suffice to determine denotations or intensions. A theory that identified the meanings of terms with the internal semantics of types has no means for accounting for these arguments.

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even be consistent with external truth, as I’ve already argued.22 Furthermore, my internal semantics distinguishes between the types needed for constructing a proof of well-formedness (a normalization)—these are the types involved in type presuppositions, and the fine-grained types assigned to lexical expressions as part of their proferred content. Hence, there is in prinicple room in the internal semantics for a distinction between semantic anomalousness and (internal) falsity. Type Theory isn’t the only monostratal proposal for lexical meaning. There’s also what I call the Sortal Theory. The Sortal Theory claims that type information is really just a part of the language of logical forms that is singled out by selectional restrictions. Type information is really just information about sorts. Semantic ill-formedness is the result of using the semantic and proof theoretic apparatus of the language of logical forms to derive a contradiction based on meaning postulates about sorts. At first glance, the distinction between the Sortal Theory and a typed theory of logical forms looks to be one of notational variance. The typed lambda term of the bistratal theory I propose in (2.34a) has the very similar looking Sortal Theory analogue in (2.34b) (φα is the object level formula associated with the type α). (2.34) a. λx: α ψ(x) b. λx (ψ(x) ∧ φα (x)) But here appearances deceive. Sorts, as predicates in logical form, have a set theoretic semantics; and they provide no constraints on the construction of logical form. Without any types at all, we have all the inconveniences of doing compositional semantics in a type-free environment. Furthermore, without types, we have no account of semantic ill-formedness, which my theory accounts for in terms of the failure of the type presuppositions of terms to be justified and hence for a failure of normalization. According to the Sortal Theory, there aren’t any syntactically well-formed sentences that are semantically ill-formed; those sentences that are predicted to be ill-formed because of type clashes on the typed view are just false on the Sortal Theory. The Sortal Theory can no longer explain the projection of selectional restrictions either. These problems count, to my mind, as strong evidence against the Sortal Theory. Matters are no better with coercion. Selectional restrictions are just like any other predicate on the monostratal Sortal Theory; so the literal meaning of 22

There is here a delicate but well-studied matter about how the internal semantics deals with the acquisition of new information about internal objects. Computer scientists have labelled this the problem of side-effects.

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most of the cases of coercion that we have seen is inconsistent. Thus, on the Sortal Theory, coercion must be a matter of content revision. But I have no idea how such a revision would go, and, I suspect, neither does anyone else. The Sortal Theory has nothing promising to say about coercions. Those who don’t believe in a linguistic level of lexical meaning separate from general world knowledge will be attracted to the Sortal Theory. Quineans or philosophers with a minimalist view of lexical conent will think that the Sortal Theory makes entirely the right identification between coercion and belief revision. But it seems to me to be an entirely inadequate alternative to the two levels of lexical content I have set out here. The two-level theory of lexical content has tantalizing implications for a general theory of content. Types offer an interesting approach to problems that motivate the Fregean picture of language by developing a two-factor theory of content in a rigorous way. An internal semantics for the types will allow us to construct an “internal semantics” for language, which could be the internal reflection of externalist, model theoretic conceptions of content. That is, a proof theoretic, internal semantics gives content to concepts and thoughts which are linked through the logical forms to the externalist semantics of intensions.23 We have seen that we might want the meaning of the type hesperus to come apart from the meaning of the name Hesperus. In this way we can in principle make sense of the informativeness of certain true identity statements as well as acknowledge their necessary truth. Indeed, having two semantics associated with formulas (one albeit indirectly) gives us the tools to make sense of puzzles about belief as well as paradoxes of informativeness.24 We want to have something like a Fregean picture where two distinct types or concepts may correspond to the same referential meaning or intension. Unlike Frege’s senses, however, types and concepts do not determine the referential or standard, intensional meaning of terms. At best there is a homomorphism from concepts to sets of intensions that preserve the structures relevant to predication—i.e., the relations between types.

23

24

Many people have followed the view in the philosophy of mind (see for instance Burge (1979), Tye (1999), Dretske (1981)) that the contents of thoughts like the contents of many expressions in natural language are often determined by external factors, but it is hard to deny that there is an internal component to thoughts as well. For the beginnings of such an exploration, see Asher (1986, 1987, 1989).

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2.5 Types in the linguistic system 2.5.1 Type checking in predication Types are designed to affect semantic well-formedness and felicitous predication. The general idea is that predicates place type presuppositions on their arguments, which their arguments must satisfy or at least be compatible with. In the lambda calculus representations of word meanings that I shall use, almost every word is a predicate with one or more lambda abstracted variables. So most words have type presuppositions. But not all types play this role. There is good evidence that finely individuated types do not play a role in the type checking relevant to predication. Consider again these examples from the first chapter: (2.35) b. c. d.

a. Tigers are animals. Tigers are robots. #Tigers are financial institutions. #Tigers are ZF sets.

One might hypothesize that types at the upper end of the type hierarchy are relevant to type checking. animal is pretty clearly at the upper level of the type hierarchy (D¨olling 2000). robot is a subtype of artifact, which is also at the upper level. And most type hierarchies would take animal and artifact to be incompatible types. This assumption would predict that (2.35b), (2.35c), and (2.35d) are all equally semantically anomalous. But they are not, even though they are all false, indeed necessarily false, given the widely accepted externalist semantics for natural kinds like tigers. The clash between the type demands of the predicate and the type of its argument in these examples has to do with rather deep metaphysical principles like individuation and counting conditions. Sets, especially of the ZF kind, have simple individuation criteria based on the axiom of extensionality and are all built out of a single object, the null set, on the standard, cumulative conception. Tigers share nothing with ZF sets with respect to individuation conditions. Financial institutions are more abstract than standard physical objects— they are relational structures that depend on various physical individuals but not any particular ones (the employees of the institution can change, so can its physical locations while the financial insititution continues). While the individuation conditions of financial institutions are murkier than those for ZF sets, once again tigers are not counted or individuated in anything like the way that financial institutions are. Robots and animals, on the other hand, are close enough in terms of identity and counting conditions that we can make sense of (2.35b); we can imagine a competent speaker believing such a proposition.

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(2.35c,d) are much harder to make sense of without a big background story. And, as one would expect if one adopts the presuppositional perspective, a big enough background story may lead to a type coercion making the predication once again acceptable. The type checking associated with well-formedness of predication is sensitive to those types that have different individuation and counting conditions. A semantic anomaly will result only when the type requirements of the predicate and argument give rise to incompatible individuation conditions. The discussion of the type presuppositions of (2.35b) suggests that the type presupposition of the predicate are robots must be simply that the argument is of type p or physical object. In other words, in order for the predication to succeed, the argument can be any sort of physical object; it is not restricted to things of type artifact, let alone robot. Thus, the type presupposition that robot contributes as a check on predication is quite general. The types with distinctive individuation conditions relevant to type checking are somewhat diverse from the perspective of standard type hierarchies. They include very general types—like physical object, informational object or abstract object, mass, count, plurality, singularity, and eventuality. But there are also relatively fine-grained distinctions in types that predication is sensitive to: the distinction between state, activity, accomplishment, and achievement, as well as the distinction between different types of locations, and the distinction between portions of matter and normal countable individuals. Assuming that seemingly closely related types like activity and accomplishment are interchangeable, for instance, leads to a type clash; adverbials like in an hour and for an hour are sensitive to the defining and differentiating features of these types of eventualities and accept one type but not the other for their arguments. I shall assume that such distinctions also point to distinctive differences in individuation conditions. On the other hand, it’s hard to find a predicate similarly sensitive to the defining and differentiating features of tigers and robots. If only types with distinctive individuation conditions perform an important role in the type checking of predication and are part of the type presuppositions of a term, what role do the more fine-grained types play in the grammatical system? Fine-grained types and the internal semantics can affect logical form when combined with functor types. These functor types may provide different fine-grained value types when they take arguments of different fine-grained types. For instance, in section 2, I distinguished between:

2.5 Types in the linguistic system (2.36) b. c. d. e.

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a. red(apple) red(shirt) red(pen) red(meat) red(wine)

Each of the modifying predications in (2.36) are distinct. When we predicate a color of an apple, we predicate it typically of the skin. We can call an apple truly red even if most of it, its flesh, is white. On the other hand, this won’t do for red shirt. A shirt is red only if the entire shirt, or very nearly so, is red. We may call a pen red if it writes in red ink; the color of the visible surface of the pen may not be relevant at all for that predication to succeed. Finally, red meat refers to a kind of meat, e.g., beef, lamb, and the like, which may not be at all red on the surface, say, when it shows up on the dinner plate. While the adjective red like other color words is typically analyzed as an intersective adjective (according to which the red X is both an X and red), it appears to become subsective (according to which the red X is an X but not necessarily red) when combined with meat or pen. That is, the following sentences are not necessarily false: (2.37) The red pen is not red. (2.38) That piece of red meat is not red. (2.39) This red wine isn’t really red; it’s more of a very deep purple. Even though there is no type incompatibility here between the type of the color adjective and the type of the common noun it modifies, there is a subtle shift in meaning and semantic behavior of the adjective noun combination. This observation extends to many adjectives, in particular gradable adjectives: thus small robot has a different meaning from small mountain, small hill, and so on. This shift arises from the interaction of the fine-grained types or internal semantics of words, I contend. These subtle shifts in the resulting predication make it plausible that in principle each word stem, even each word, could give rise to a distinct concept, a distinct fine-grained type that can play a role in the grammatical system. Without such fine-grained differences, we cannot explain the differences in meaning noted above. The fine-grained types associated with verbs also find a use in the grammatical system. Recall, for instance, the difference between the two transitive uses of a verb like load in John loaded the wagon with hay (the wagon is completely full) versus John loaded hay on the wagon (the wagon is not necessarily completely full). By feeding different types into the functor type, we can output different types of propositions that describe different relationships between the

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wagon and the hay. Of course, this is only a framework for a worked out analysis, but it is general enough to accommodate, for instance, a sophisticated approach like that of Krifka (1987). We must thus distinguish two uses of types in the grammatical system. To check the felicity of predications, we must resort to type presuppositions, while to understand the shifts in meaning, we resort to the fine-grained types associated with words. The fine-grained types are part of the type hierarchy, and to check whether one meets the type presuppositions of a predicate it suffices to use the relation on types. For instance, suppose that Hesperus and Phosphorus, two names for the planet Venus, give rise to two different concepts, two distinct fine-grained types. For the purposes of type checking in predication, even for the predicate of identity, the distinctness of these concepts or finegrained types doesn’t matter. What matters is the following subtyping chain. (2.40) hesperus, phosphorus heavenly-body physical-object e. If we have a predicate P that requires the relevant argument to be occupied by something of type physical-object, then the predication Pt should succeed if t has the type hesperus; the type presuppositions of P should be met by any subtype of physical-object, in particular hesperus (or phosphorus).

2.5.2 Lexical inference Fine-grained types also provide a basis for lexical inference or analytical entailment. The issues of lexically based inference and analytical entailment are murky ones, and one can study the problems of constructing logical forms and the phenomena concerning predication that motivate this book without taking a position on them. The data concerning lexically driven inferences are also controversial. Fodor and Lepore (1998), for instance, question the robustness or legitimacy of the data as really part of semantics. Among most working linguists and lexicographers, however, the intuitions are strong if not entirely systematic that there are many analytical entailments. The question I want to pursue briefly here is whether, and if so how, the type mechanisms I have devised for the construction of logical form give us purchase on the often debated but little resolved issues of lexical inference and analytical entailment. In so doing, I shall also show how the internal semantics distinguishes analytic truth and analytic falsity from semantic well-formedness and semantic ill-formedness. Roughly, while it is the type presuppositions and the mechanisms for justifying them that determine well- or ill-formedness, it is the connections between the fine-grained types of proferred content that determine analytic truth or falsehood.

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Simply studying predication and arriving at a logical form tells us little about analytical entailments. Analytic entailments are entailments of the logic underlying logical forms; they are valid and so true in all models for the language. But unless we add certain information based on the links between non-logical words, we reduce the class of analytic entailments to the set of logical consequences in the language of logical form. If the lexicon is to add anything to the class of analytic entailments, it must do so in virtue of one of the following possibilities. (1) Certain lexical entries for words are logically complex and thus give rise to entailments using the logic validated by the models for the logical forms. (2) The lexicon contains axioms relating the meanings of words and thus adds to the logical theory of compositional semantics. (3) The rules for the analysis of predication, in particular the rules for handling complex types and the relations between types, add information to logical form that the underlying logic can exploit to provide analytic entailments beyond the entailments provided by the underlying logic alone. Linguists and philosophers have for the most part pursued the first track under the rubric of providing a “decompositional” semantics (Jackendoff (1990) comes prominently to mind). Even our quite minimal hypothesis that every word stem or root gives rise to a distinct type leads to at least some decomposition: distinct words with the same stem but formed using semantically rich morphological affixes and suffixes should have common bits of logical form; that is, the logical form of some words of the same root must be constructed out of the logical forms of at least one of the other words of the same root. For instance, many linguists have argued that sink’s syntactic behavior as a transitive but also intransitive verb indicates that its lexical meaning consists of two facts, one describing an underspecified action on the part of an agent, and the second describing the resulting state of that action, namely that the theme of the sinking is sunk. This yields a host of analytic entailments, some of which are not completely trivial: (2.41) a. The enemy sank the ship with a torpedo −→ the enemy used a torpedo to sink the ship −→ the ship sank −→ the ship was sunk. b. The enemy sank the ship with a torpedo −→ the enemy’s torpedoing the ship was the cause of its sinking. Asher and Lascarides (1995, 2003) explore such decompositional analyzes for a variety of verbs, including causatives and psych verbs. Here is the decomposition of Asher and Lascarides (2003) for sink. It involves a causal relation between two facts—one determined by an underspecified action marked with a question mark, and the other by a property of being sunk instantiated in a state that is posterior to the action.

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(2.42) sink: λxλeλy(?(y, x, e) CAUSE ∃s(sunk(x, s) ∧ e ≺ s)) To handle the alternation between causative and intransitive sink, Asher and Lascarides assume that unsaturated arguments of the causing fact can be existentially closed off at the final stages of constructing the logical form for a clause containing such a verb. This decompositional analysis, together with analyzes for use and gerunds, validates all the entailments in (2.41). Levin (1993) contains a comprehensive list of verbs which invite similar decompositional analyzes. They include verbs like:25 bake, build, braid, brew, burn, carve, cast, chirp, cook, crochet, dig, draw, drill, fold, hum, knit, mumble, murmur, paint, sing, shoot, sketch, weave, shout, whisper, whistle, write, sink, break, open, close...

The following examples indicate how these very different verbs obey the same syntactic alternations as sink, suggesting a similar analysis. (2.43) a. The bottle broke. (intransitive/causative transitive) b. John broke the bottle. (2.44) a. The window opened suddenly. (intransitive/causative transitive) b. Mary opened the window suddenly. Asher and Lascarides (2003) generalize their decomposition to the class of psych verbs. They also all have an underlying causal structure, where some unspecified action by the subject causes the patient (the direct object of the psych verb) to have the state denoted by the past participle form of the verb. Thus, all actions denoted by psych verbs decompose into an event with a particular result state involving an adjectival form of the root lexeme. Such a decomposition obviously does not give a complete analysis of a verb like bother (it couldn’t since it relies on the meaning of bothered to specify the meaning of the verb), but it is a useful way of portraying the similarity in meaning of psych verbs. Decomposition in this limited sense can show how the same basic lexical meaning can lead to several syntactic realizations and thus serves a useful purpose. These limited decompositions also provide for limited analytical entailments. Nevertheless, the decompositional approach has received substantial criticism (Fodor 1971). Fodor assumed that if a decompositional approach to lexical semantics, for example one in which kill is analyzed as cause to die, is psychologically real, then it should take longer to process words with more com25

For a treatment of some of these, see van Hout (1996) or Bittner (1999).

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plex meaning representations than those with simpler representations. However, many experiments have shown that this is not the case for the pair kill and die. Note, however, that kill does not support syntactic alternations like the ones above.26 Strongly decompositional approaches to word meaning have in general failed dramatically to provide plausible results for lexical meanings.27 One major problem is that it is not clear what the primitives out of which all lexical meanings are built should be. In a few areas of lexical research such as the work on spatial and temporal expressions, decomposition has led to more promising results. Researchers have largely agreed on the need for certain topological primitives (contact and weak contact, or equivalently parthood and weak contact) and geometrical ones. For time, the primitives required to construct linear orders are well known and axiomatized. More recently, the topological and even geometrical primitives have been axiomatized within a project to analyze the meanings of spatial, more precisely topological, prepositions (Aurnage and Vieu (1997), Vieu (1997), Muller (2002)). Such work is extremely important for lexical semantics, because it gives a concrete meaning to the primitives, determining what sorts of models for the logical form language are the admissible ones (Asher and Vieu (1995), Donnelly (2001)). Such an axiomatization yields a wealth of analytic entailments that go well beyond those given by the axiomatization of the first-order connectives and quantifiers. There have also been, following Jackendoff’s seminal work, thorough investigations of motion verbs (Asher and Sablayrolles (1995), Muller and Sarda (1999)), though correspondence theorems continue to be lacking for the motion verb primitives of goal, source, and path. In most other areas of lexical meaning, the sort of thorough investigation that lexical research on temporal and spatial expressions has delivered is lacking. Axiomatizations are at best partial, and more often than not characterizations of lexical meaning rely on notions that are part of the background language in which one characterizes the reference of these terms and hence the models; and this frequently amounts to little more than a restatement of intuitions. 26

27

It is true that kill takes different adverbials, in particular adverbials involving process like sadistically, with a knife, and so on from die. These, so the argument goes, modify the process of killing (Pustejovsky (1995)). Pustejovsky (1995) takes these adverbials to be evidence that kill involves a process and a result state. This is not really convincing, however. What these adverbial modifiers show is that there must be a type distinction between events of killing and events like dying, not that there must be a decomposition involved, though indeed it does seem to be an analytical entailment that if Sam killed Pat then Pat died. However, recent experiments by Gail McKoon on activity, stative, change of state, and indirect causation verbs does provide evidence for the hypothesis that there is increasing representational complexity for these types as we go from one category on the left to the next on the right, as hypothesized by Levin and Rappaport (1994). McKoon discussed these experiments during her seminar at the LSA summer school in Stanford, California, 2007.

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There is of course a reason why axiomatizations in these areas don’t exist. In the case of space and time or space-time, the mathematical structures underlying the meanings of various words in natural language were clear thanks to thousands of years of reflection on these topics by philosophers, mathematicians, and physicists. It was relatively easy, though still not straightforward, to build a qualitative theory that characterizes that structure as it’s reflected in language. But there’s no guarantee that other areas of lexical meaning are amenable to such treatment. There have been hasty general treatments of lexical primitives like Shank’s (1974) conceptual dependency paradigm. Such a description might lead to an abstract underlying structure and then perhaps an axiomatization. But one would need a much more detailed descriptive analysis, and there are no guarantees that an abstract structure or that an axiomatization would emerge therefrom. I don’t know what the abstract structure of buying and selling is; looking at formal treatments in ontology of various concepts, one gets the feeling that either there are no interesting structures worth axiomatizing or that research has somehow gotten off on the wrong track. It may simply be utopian to think that every part of the lexicon will end up looking like the parts concerning spatial and temporal expressions. Perhaps the best we can hope for is a partially decompositional analysis with some primitives properly understood. A type system encodes analytic entailments without full axiomatization or decomposition. Some entailments are just type presuppositions. For instance, (2.45) Kim is a bachelor −→ Kim is male, Kim is adult, Kim is human (2.46) Kim is not a bachelor −→ Kim is male, Kim is adult, Kim is human are natural inferences most people would make. I take these inferences to show that bachelor puts detailed type presuppositions on its argument when used predicatively. To say exactly what these are, we need to appeal to an operation on types , which is a meet operation and is defined by appealing to the given subtyping relation : Definition 1 σ τ = the greatest lower bound of σ and τ in the partial order

on types. I will assume that for any two types σ and τ, there is at least one type that is a subtype of both and that’s the type ⊥. So the term bachelor looks like this: λx: adult male Bachelor(x), where the typing on x provides the type presuppositions. These presuppositions translate back out into logical form via the following, natural principle: • Type Presupposition Inferences

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Suppose ψ dynamically implies28 δ(t) where t has the type presupposition α. Then ψ dynamically implies φα (t), where φα is the translation in logical form of the type α. Since each word stem gives rise to a type, there is no problem about assuming the existence of a φα . Type Presupposition Inferences enables us to infer that if Kim is a bachelor, then Kim is male and Kim is adult, as desired. Moreover, these are plausibly analytic entailments. On the other hand, not all analytical entailments based on lexical meaning are presuppositional. Some, in fact many, have to do with the fine-grained types that are part of proferred, internal content. The type tiger is a subtype of animal, and so that should be an analytic entailment. But being an animal is not presupposed of the bound variable in the logical form for tiger. If it were, then it would be as crazy to think that tigers are robots, as it is crazy to think that they are financial institutions or ZF sets. This entails that there are semantically well-formed sentences that are analytically false. Similar remarks apply to bachelor. While Kim is a bachelor entails that Kim is not married, Kim is not a bachelor fails to entail that Kim is unmarried. Thus, unmarried, assuming such a type exists, is not part of the type presuppositions of bachelor. But it is an analytic entailment based on lexical meaning that bachelors are unmarried. To express this entailment using the type hierarchy, we exploit the subtyping relation on types. If α β then anything of type α is also of type β, and this is itself a conceptual truth. To capture such entailments we need to be able to translate from the type hierarchy into logical forms or into the language of thoughts introduced in the last section. It is commonly assumed that is a partial ordering on the type hierarchy. And so a type hierarchy T together with the usual axioms for partial ordering will allow us to deduce subtyping relations. I’ll call this deduction relation, T , for a given type hierarchy T . We can now provide an obvious method for producing analytic entailments: • From Types to Entailments: Suppose for a type hierarchy T , T α β. Then: 1. it is a conceptual truth that every(α, β) 2. it is an analytic truth that ∀x(φα (x) → φβ (x)) From Types to Entailments provides a simple way of inferring analytic entail28

Dynamic notions of implication carry bindings from premises to conclusions. In particular in dynamic semantics ∃xφ dynamically implies φ(x). For details on a dynamic system, see Groenendijk and Stokhof (1991).

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ments. For instance, we can easily encode the entailment that a bachelor is unmarried via the following type constraints:29 • bachelor unmarried Type hierarchies and From Types to Entailments yield a host of analytic truths. (2.47) b. c. d. e. f.

a. Tigers are animals. Chairs are physical objects. Stories are informational objects. Everything that has a color is a physical object. A physical property is a property. If it’s Tuesday, it can’t be Wednesday.

(2.47a–d) are straightforward consequences of the type hierarchy used to check predication. (2.47e) is perhaps a less straightforward consequence of the type system. Expressions that pick out days of the week pick out different days. This is a matter of what these expressions mean. The type hierarchy encodes these facts by using the meet operation : • tuesday monday = ⊥ There are some plausibly analytic entailments that the type hierarchy doesn’t encode directly. For example, consider the entailment from (2.48) Kim killed Sandy to (2.49) Sandy died. To capture this entailment, we would have to suppose that the complex type or thought kill(kim, sandy) is a subtype of die(sandy). But this would predict that adverbs that go with die can then go with kill, and this is not the case; one can say that Sandy died peacefully, but one can’t use these verbal modifiers in the same way with kill: (2.50) Kim killed Sandy peacefully. 29

If types are concepts, then linking types via the relation really amounts to conceptual analysis, a time honoured approach to philosophy. In a type hierarchy entailments can be captured without requiring any definitional reduction of one type to some Boolean combination of other types. Nor do we have to take on board the dubious entailments of a profligately decompositional approach.

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To capture such analytic entailments without resorting to decomposition, we need to look at the rules of application for Kim’s killing Sandy in our internal semantics of types. Since the rules that sanction the application of the type of Kim’s killing Sandy to a situation will also sanction the application of the type Sandy’s dying to that situation, the analytic entailment seems secure. Similarly, one can argue that Kim bought a computer from Sandy analytically entails Sandy sold a computer to Kim and vice versa, even though neither fine-grained type is a subtype of the other.30 Note that these observations do not lead to the generalization that any term of propositional type that has a non empty set of proofs as its internal content is an analytic statement. Once again, the presence of such proofs in general demonstrates only that the typing constraints involved in the term are coherent; it entails only that the term of propositional type is capable of having an (external) truth value. However, if we can show using with the fine-grained internal meanings for the primitive types that any proof object in the internal meaning of α is also a proof object for β, we have an analytic entailment. The type hierarchies linguists use are a simplified expression an approximation of those fine-grained internal meanings. Thus, we get to the following generalization of From Types to Entailment, where I represents the proof relation over the type meanings. • If x: α I x: β, then φα analytically entails φβ . Many analytic entailments follow simply from the type system we need to analyze predication. Others follow from the types associated with the proferred internal contents of lexical expressions. Types and their internal semantics thus offer a simple way of modeling lexical entailments without having to resort to an extraneous set of meaning postulates or dubious lexical decompositions. I will argue below that in cases of coercion or copredication, new entailments based on lexical meaning and predication can arise from the adjustments in types needed to satisfy type presuppositions and to make the predication work. By using type presupposition justification rules to add information 30

If these two fine-grained types were subtypes of each other, we would expect them to have the same inhabitants. So any event of Sandy’s selling a car to Kim is identical to an event of Kim’s buying a car from Sandy and vice versa. This would predict that any adverbial modification of one should hold of the other. But that isn’t true. For instance, (2.51a) does not entail (2.51b), nor does (2.52a) entail (2.52b):

(2.51) a. Kim bought a car from Sandy for Bo. b. Sandy sold a car to Kim for Bo. (2.52) a. Kim bought a car from Sandy with a credit card. b. Sandy sold a car to Kim with a credit card.

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to logical form, we end up modeling all sorts of entailments that don’t follow simply from the meanings of the syncategorematic or logical words of the language. Some of them could even be defeasible entailments such as start a cigarette ∼ | start to smoke a cigarette. For these it is the mechanisms of predication that introduce the entailment into logical form. Assuming that every lexical root has its own unique type as I do thus doesn’t preclude having a non-trivial theory of lexical inference encoded in the type hierarchy. Subtyping relations between types enable us to encode entailments based on lexical meaning. And having a type associated with each word root doesn’t preclude a decompositional analysis of various words in terms of the root type—consider the case of psych verbs, whose meaning is analyzed in terms of their adjectival correlates. It’s thus a logically unsupported step to conclude, as Fodor and Lepore (1998) do, that an anti-decompositionalist approach to lexical semantics precludes any interesting theory of lexical or analytic entailment. This is clearly not enough to lay the issue of analytical entailment to rest, but it shows some of the resources of a typed approach.

3 Previous Theories of Predication

With this discussion of some of the philosophical background for a typed theory of lexical meaning, I now turn to examining some precursors of the theory to be proposed here. All of these precursors take some sort of stand concerning the representation of lexical meaning and the sort of phenomena that are the focus of this book—various forms of predication both at the clausal and morphological levels, copredication, and coercion. A basic issue concerning lexical representation is lexical ambiguity. Some people distinguish between monomorphic and polymorphic languages, which correspond to two different ways of thinking about ambiguity. A monomorphic language (or lexicon for a language) is one in which each word has a unique type and syntactic category. Ambiguous words on this view are analyzed as words with the same orthography but each with a different sense. This is the view found in Montague Grammar or even in HPSG, and it corresponds to an approach to ambiguity according to which ambiguous expressions are represented by the set of their disambiguations. A polymorphic language (or lexicon for a language) is one in which each word may have multiple types or underspecified types that may be further specified during the composition process. Underspecification is a tool or method devised by linguists working on ambiguity in sentential and discourse semantics. Underspecification produces underspecified logical forms for ambiguous discourses For instance, suppose we have to give the truth conditions of a sentence with multiple quantifiers like (3.1): (3.1) Every nurse examined a patient. (3.1) has two readings: one in which the universal quantifier introduced by every nurse takes wide scope over the existential quantifier introduced by a patient, and one in which the existential quantifier has wide scope over the universal quantifier. An underspecified logical form for (3.1) would introduce

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“holes” in the formula (Reyle 1993, Bos 1999), keeping the λ terms for the two quantifiers separate from the verb but also introducing relations between the terms to encode constraints on how λ conversion should go—for instance, the underspecified logical form for (3.1) will encode the fact that both quantifiers determine arguments for the main verb. But the scope of operators is only one source of underspecification. There are many anaphoric or context dependent phenomena in natural language—for instance, pronouns, tenses, presuppositions—for which a determinate semantics cannot be supplied independently of the discourse context. Underspecified logical forms are used to represent the semantic contribution of these words and morphemes. Take a pronoun like he. Its meaning is supplied by the antecedent it is linked with in a particular discourse context. One cannot specify a lambda term conveying the meaning of such an expression without resorting to underspecification. However, with underspecification, specifying a lambda term is relatively straightforward; Asher (1993), for instance, has the following lambda term for he— λP∃x(P(x) ∧ x =?), where ? marks the “hole” to be filled in by a term provided by the pronoun’s antecedent.1 Thus, underspecification provides a natural and powerful tool for representing certain kinds of ambiguity in lexical semantics. The λ calculus extends naturally to a treatment of such underspecification, as Pogodalla (2004) argues.

3.1 The sense enumeration model The most orthodox model of lexical meaning is the monomorphic, sense enumeration model, according to which all the different possible meanings of a single lexical item are listed in the lexicon as part of the lexical entry for the item. Each sense in the lexical entry for a word is fully specified. On such a view, most words are ambiguous. This account is the simplest conceptually, and it is the standard way dictionaries are put together. From the perspective of a typed theory, this view posits many types for each word, one for each sense. Predication may select for a subset of the available senses for a predicate or an argument because of type restrictions. While conceptually simple, this approach fails to explain how some senses are intuitively related to each other and some are not. This is not only a powerful intuition shared many linguists and lexicographers; there are also linguistic tests to distinguish between word senses that are closely related to each other and those that are not. Words or, perhaps more accurately, word occurrences 1

See Pogodalla (2004) for a completely typed version of this expression in which holes are introduced as a special type.

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that have closely related senses are called logically polysemous, while those that do not receive the label accidentally polysemous or simply homonymous. Cruse (1986) suggests copredication as a test to distinguish logical polysemy from accidental polysemy: if two different predicates, each requiring a different sense, predicate properties of different senses of a given word felicitously, then the word is logically polysemous with respect at least to those two senses. Another test is pronominalization or ellipsis: if you can pronominalize an occurrence of a possibly ambiguous word felicitously in a context where the pronoun is an argument of a predicate requiring one sense while its antecedent is an argument of a predicate requiring a different sense, then the word is logically polysemous with respect to those senses.2 Contrast (3.4a–b) and (3.4c–e): (3.4) a. #The banki specializes in IPOs. Iti is steep and muddy and thus slippery. b. #The bank specializes in IPOs and is steep and muddy and thus slippery. c. Lunch was delicious but took forever. d. He paid the bill and threw it away. e. The city has 500,000 inhabitants and outlawed smoking in bars last year. Bank is a classic example of an accidentally polysemous word. As (3.4a–b), show, both the pronominalization and copredication tests produce anomalous sentences, which confirm its status as accidentally polysemous. On the other hand, lunch, bill, and city are classified as logically polysemous, as (3.4c–e) witness that they pass the tests of copredication and pronominalization. The distinction between accidental and logical polysemy isn’t absolute. There are degrees of relatedness that the felicity of copredications and pronominal tests reflect. Contrast (3.4d–e) with (3.5a,b), for instance: (3.5) a. ?My janitor uses a brush and so did Velazquez. b. ?The city outlawed smoking in bars last year and has 500,000 inhabitants. 2

Of course, there are other tests for ambiguity, such as the so-called contradiction test, according to which a particular sentence with an ambiguous word ω may be consistently judged both true and not true in the same context since an interpretation may access different senses of ω. Read with contrastive stress, sentences like

(3.2) The bank specializes in IPOs (3.3) The book is beautiful can be understood as true and false in the same context. Nevertheless, the contradiction test is not a sure fire indicator of real ambiguity. Books are both informational and physical in some sense even though we can select each one of these aspects within a predication. We can also access both meanings simultaneously.

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(3.5a,b) aren’t as good as (3.4c–e); (3.5a,b) are rather zeugmatic. Their zeugmaticity results from different factors; (3.5b) as opposed to (3.4e) involves the same two lexical senses but in a different order. This suggests that copredications are subject to discourse effects. On the other hand, (3.5a) involves two relatively unrelated senses of brush—paint brushes and cleaning brushes have for the most part very different properties—different functions, sizes, and so on. In some languages like French, these two senses have different translations, pinceau and brosse. These senses don’t cohere together in the way that the distinct senses for lunch, bill, book, and city do. Though a full explanation promises to be complex, sense enumeration models have no way of explaining the differing degrees of success that copredications appear to have. Sense enumeration models fare even worse with the phenomenon of coercion. We have seen that coercions are context sensitive; the exact meaning of a phrase like begin with the kitchen is often determined by discourse context. According to the sense enumeration model, this would require begin or kitchen to have a distinct sense for each one of the contextually specified meanings of begin with the kitchen. This seems highly unintuitive; further, it threatens to make a specification of lexical meaning practically impossible, as discourse contexts can coerce such phrases in unpredictable ways.

3.2 Nunberg and sense transfer In contrast to the sense enumeration model of word meaning is the view that lexical semantics consists of a set of lexical entries, while pragmatics furnishes a set of maps from one lexical meaning to another. These maps specify, inter alia, coercions. Frege’s theory of meaning includes coercions. He thought that intensional operators like verbs of saying or of propositional attitudes induced a meaning shift of the terms within their scope. He stipulated that the meaning of terms when they occur within the scope of an intensional operator shifted from their reference to their sense. The intensional operator coerces a meaning shift, a shift from customary meaning to non-customary meaning. Predication for Frege had to involve type checking in order to discard the application of, say, a belief relation to the simple extension of its clausal argument. Depending on whether one subscribes to the many levels of sense interpretation of Frege or not, one can say that such coercions are carried through the sense hierarchy as the depth of embeddings under intensional operators increases. Generalizing Frege’s strategy, Nunberg (1979, 1995) proposes that lexical meanings are subject to shifts in predication. A lexical entry specifies a denotation for a referring expression or for a predicate according to Nunberg.

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While Nunberg isn’t completely explicit about what the specifications of lexical meanings look like, his ideas fit within the standard framework in which the denotations of terms are expressed by lambda terms.3 These terms will then have their standard interpretation in a model. For instance, the word cat will have as its lexical entry an expression λx cat(x) and its interpretation in the intended model will be that function that for any given world w and time t returns 1 if x is assigned as a value something that is a cat at w and t, and returns 0 otherwise. Sometimes such lexical entries can be transformed via a general rule like grinding or by a more specialized rule transferring the normal interpretation of a term to some salient associated entity when predication demands this. Nunberg applies such a notion of transfer to definites and indexicals (thus it would appear that Nunberg adopts a version of a type driven theory of predication). Some examples Nunberg and others have found to motivate this view are quite vivid:4 (3.7) I’m parked out back. (3.8) The ham sandwich is getting impatient. The basic idea is intuitive. In these examples, applying a particular predicate whose argument is required to have type α to an argument whose type is β, where α β = ⊥ forces either the argument term or the predicate term or both to change their meanings so that the predication can succeed. For instance, ham sandwiches can’t literally get impatient; and if I’m standing in front of you, I can’t literally be out back. So what happens is that we shift the meaning of the terms so that the predications succeed: it’s my car that is parked out back, and it’s the guy who is eating the ham sandwich who is getting impatient. The problems lie in the details. When exactly is the sense transfer function introduced? The transfer function could always be optionally available but that would lead to vast overgeneration problems: (3.9) The ham sandwich that hasn’t been eaten is on the counter. (3.9) would be predicted to have a reading on which the eater of the ham sandwich that hasn’t been eaten is on the counter. Let’s suppose with Sag (1981) that Nunberg’s sense transfer functions work 3 4

For instance, see Sag (1981) for a formal development of his view. Note that the “parking” examples are felicitous with all sorts of subjects:

(3.6) a. John is parked out back. b. The students are parked out back. c. Most students park out back.

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on lexical entries for common noun phrases or N . The result we want for (3.8) is clear. The ham sandwich should have the following logical form: (3.8’) λP the(x) ( f (ham sandwich)(x) ∧ P(x)) where f is the transfer function mapping ham sandwiches to people who are eating them or who have just eaten them. The problem is that we only become aware of the need for a type adjustment mechanism in building the logical form of the sentence when we try to put the subject noun phrase together with the verb phrase, and at that point it is no longer straightforward to add the transfer function to work over the contribution of the common noun.5 Indeed, if we think of the process of predication here as building up a denotation for the sentence in compositional fashion, then it is hopeless to try to apply the transfer function where Sag and Nunberg would like; the common noun denotation is simply no longer available at this stage of composition. If we think of the process of predication as building a logical form rather than a denotation, then the contribution of the common noun is in principle available, but specifying the scope of the transfer function is not straightforward. It cannot be always a common noun that should be shifted in coercion cases. We have to generalize Sag’s assumption to get an analysis of (3.7): either the full DP or the verb will have to undergo sense transfer. But if it is the entire noun phrase or, in the language of syntax, the DP (determiner phrase) that is shifted, we get incorrect truth conditions. Consider (3.10):6 (3.10) George enjoyed many books last weekend. A straightforward application of the Nunberg strategy yields the following logical form: (3.10’) f (many books(x)) ∃e(enjoy(g, x, e) ∧ last weekend(e)) The transfer function shifts the meaning of the entire quantifier, and so presumably the quantifier ranges over the elements in the image of the transfer function, namely some sort of eventualities. Of course, we don’t know what those are. Perhaps, for the sake of concreteness, we could assume that they are events of reading books. But if (3.10’) says that there were many book reading events that George enjoyed over the weekend, this is compatible with there being just one book that George read over and over again that weekend. Clearly, this is not a possible reading of (3.10), and so we cannot implement Sag’s proposal for Nunberg’s idea straightforwardly for all coercions without a lot more 5 6

See Egg (2003) for even more extreme examples, where the coercion isn’t clearly needed until subsequent sentences of discourse are processed. Thanks to George Bronnikov for this example.

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work. In fact, this observation about (3.10) will constitute a problem for many extant accounts of coercion, Pustejovsky’s GL account included, as we’ll see below. Nunberg himself did not investigate coercions involving enjoy. But the DPshifting approach has general empirical problems. Consider the difference between the two minimal sentences in (3.11): (3.11) b. (3.12) b.

a. Everyone is parked out back and is driving an old volvo. # Everyone is parked out back and is an old volvo. a. ??John was hit in the fender by a truck and will cost a lot to repair. John’s car was hit in the fender by a truck and will cost a lot to repair.

(3.11a) is fine but relies on the fact that the subject DP does not shift. Were there shifting going on, then (3.11b) should be good, but it is plainly not. Similarly if the DP had actually shifted meaning, then (3.12a) should have a reading that is equivalent to (3.12b), but it does not. (3.12a) is simply semantically anomalous. Kleiber (1999) argues that the sense transfer model as I’ve specified it doesn’t pass the anaphoricity and copredication tests. For example, consider the examples below where anaphor and its antecedent are forced by the predication contexts to have two different senses linked by a transfer function of the sort Nunberg countenances. (3.13) a. George Sand est lue par beaucoup de monde, bien qu’elle soit disparue depuis longtemps (George Sand is still read by many people even though she died long ago). b. ?George Sand est lue par beaucoup de monde, bien qu’ils ne soient plus e´ dit´es (George Sand is still read by many people even though they (the books she wrote) are no longer in print). Taking their cue from such examples, Kleiber and others reject Nunberg’s analysis of logical polysemy using reference shifters. They conclude that examples like (3.7) and (3.8) point to a different sort of phenomenon from the logical polysemy exemplified by the classic coercion cases involving aspectual verbs.7 To avoid some of these problems, the sense transfer model can resort to 7

Kleiber’s observations have some force. Nevertheless, once again judgments in acceptability reveal a not completely black and white distinction. The following examples from Abusch (1989) show that Kleiber’s examples don’t give us the full story. In some cases we can get anaphoric links between two expressions whose meanings are related by a sense transfer function of the sort that Nunberg envisions.

(3.14) a. The mushroom omelet left without paying, because he found it inedible. b. ? The mushroom omelet is eating it with gusto.

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an alternative transfer strategy: shift the meaning of the verbs rather than the meaning of common nouns or DPs.8 This can in principle avoid the problem noted with (3.10) and with the problem noted by Kleiber. But this shift leads to another set of difficulties. Consider the following ellipsis facts.9 (3.16) b. c. d.

a. I’m parked out back, and Mary’s car is too. ? I own a car that is parked out back and Mary’s car does too. Mary enjoys her garden and John his liquor. ?Mary enjoys digging in her garden, and John his liquor.

If we transfer the sense of parked out back to the property of owning a car that is parked out back to account for the parking examples, then the ellipsis in (3.16a) should be odd or it should give rise to the following reading: Mary’s car does not own a car that is parked out back as well. But the ellipsis is fine, and it lacks this reading. Similarly if we transfer the sense of enjoy to something like enjoy digging to make sense of the predication that Mary enjoys her garden, then we should predict that the ellipsis in (3.16c) should be bad much the way (3.16d) is. But the ellipsis in (3.16c) is fine. If we do not apply meaning transformations at the level of denotations, we must spell them out at the level of logical form. And we can’t do this in the obvious way without predicting that (3.16a,b) are equivalent—similarly for (3.16c,d). That is, we cannot simply replace the contribution of parked out back, which I’ll assume is a 1-place predicate here, to one that looks like this: λx∃z (parked-out-back(z)∧owns(x, z)). This means that simply applying transfer functions to verbal meanings is unworkable. Even if we can get this proposal to work using techniques like underspecification,10 many questions about this proposal still remain. For instance, is the And it appears that sometimes copredication works as well in these cases. (3.15) is somewhat zeugmatic but passable, I think: (3.15) Plato is one of my favorite authors and is on the top shelf to the right. 8 9 10

Nunberg (1993) suggests this as a possibility. Thanks to Alexandra Aramis for suggesting these sorts of examples. If one makes use of underspecification and of ways of resolving underspecifications in ellipsis which are not part of Nunberg’s proposal and which were not really understood at that time, one gets a much more plausible proposal, which is in fact that of Egg (2003).

• λx parked-out-back(x) −→ λx∃z (parked-out-back(z)∧?(x, z)) • λyλx enjoy(x, y) −→ λxλy∃z (en joy(x, z)∧?(z, y)) The ? stands for a relation that must be filled in from the discourse context. Crucially, as Asher (1993) argues, such underspecifications in ellipsis contexts can be resolved one way in the source of the ellipsis and another way in the target. This explains why (3.16a,c) are good and distinct from the degraded ellipses in (3.16b,d). This gets us something like the right logical form for sentences such as (3.10) and other examples of coercion.

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shift at the level of logical form really to be described as a change of meaning of the verb in these predicational contexts? Is it really conceptually plausible that these verbs shift their meaning but that other words do not? Exactly which sentential constituents can be arguments of the sense transfer function? Exactly what triggers the application of the function? A more serious problem with this account is that it doesn’t answer the question, “Why this meaning transformation and not another?” There are no constraints on when a sense transfer function can be introduced at all. It’s clear that one can’t invoke an arbitrary function whenever predications break down, for then we could not predict that any sentences are semantically anomalous. The whole type system has become otiose in that case. But neither can we appeal to some function that’s salient in the context. Here’s an example from Kleiber (1999), where it’s perfectly clear what the transfer function should be in the context that would make this predication acceptable. The function takes us from pianos to the noise they make or from the verb parvenir to a verbal meaning which means something like make a sound that comes. Nevertheless, we cannot get (3.17) to mean that we heard the sound of the piano which came to us floating over the waters of the lake. The sense transfer model has no explanation why. (3.17) Nous entendˆımes le piano, qui nous parvenait flottant par-dessus du lac (We heard the piano which came to us floating over the waters of the lake). More generally, there’s no account of what would validate the application of transfer functions. Why should we be permitted to make such transfers in some cases but not in others? The sense transfer model, moreover, doesn’t address the distinction between logical and accidental polysemy. We need a more semantically based account to handle this distinction. Nevertheless, postulating a set of maps amongst lexical meanings is a good idea. The sense transfer model just doesn’t develop it at the right level. In the theory I propose, something like these maps will operate over types and will be part of a lexical entry.

3.3 Kleiber and metonymic reference Kleiber (1999) proposes another model under the rubric of “metonymic reference” to account for coercion.11 This model assumes part–whole relationships to be the basis of coercion and many examples of predication. Properties of some parts of objects can be “coerced” into predications of the whole. In 11

Kleiber’s model is similar to Langacker’s notion of “active zones.” See for, instance, Langacker (1990).

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Kleiber’s model, we can include as parts of an object things commonly associated with it. But this makes the part–whole relation no longer the usual one, and so the model becomes rather mysterious. We clearly don’t want to consider John’s car to be part of John in any standard mereological sense! (3.18) a. Paul est bronz´e (Paul is tanned). b. Les am´ericains ont d´ebarqu´e sur la lune en 1969 (The Americans landed on the moon in 1969). c. Le pantalon est sale (The trousers are dirty). d. Le stylo est rouge (The pen is red). e. John was hit in the fender by a truck. Modifications of some of these examples show that part–whole relations sometimes figure in copredications: (3.19) a. Paul est bronz´e et tr`es athl´etique (Paul is tanned and very athletic). b. Les am´ericains ont d´ebarqu´e sur la lune en 1969 et ont men´e une sale guerre en indochine (The Americans landed on the moon in 1969 and waged a dirty war in Indochina). c. Le pantalon est sale et trou´e (The trousers are dirty and torn). d. Le stylo est rouge et tr`es cher (The pen is red and very expensive). However, the part whole relation can’t cover all the cases of logical polysemy— recall (3.18e). To consider another example, it’s not clear that we want to say that part of the lunch was delicious and part of the lunch took forever in (3.4c), repeated below: (3.4c) Lunch was delicious but took forever. While there is no doubt that predication may take advantage of a part–whole relation, one needs more details as to how the compositional construction of logical forms proceeds in Kleiber’s case as well. When does the metonymic shift occur and why does it occur? Kleiber’s view isn’t sufficiently developed in order for us to be able to answer these questions. The examples of metonymy are not examples of semantic, type coercion. It is in principle possible from the perspective of conceptual coherence that, for instance, the entire population of America landed on the moon in 1969. Of course, that’s false and unbelievable, but that’s not a semantic matter. In the Nunberg examples or the examples of coercion involving aspectual verbs, something like sense transfer or type coercion has to take place for semantic reasons: the predicate and the argument can’t as they stand combine without producing a semantic anomaly. Kleiber nevertheless extends his model to deal with coercion cases involving

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aspectual verbs. Kleiber sensibly enough postulates a temporal interval argument for begin that has a well-defined initial part and then a continuation (typically expressed by an accomplishment verb with telicity and durativity). For any direct object or internal argument of begin not expressed by a phrase including an accomplishment verb, there must be a homomorphism from the accomplishment structure to the internal argument. This implies that begin must have something like an accomplishment as its object. But now how does this relate to the metonymic model? It is not obvious that the relationship between an eventuality (Laurence’s smoking a cigarette) and one of its participants (the cigarette) is one of part and whole, since the cigarette as a spatio-temporal entity is not included completely in the event, nor is the event included in the cigarette. Still less is it clear that such constraints are sufficient to capture many relevant cases. Consider for example: (3.20) a. Paul a commenc´e de d´econstruire son livre. Marie a commenc´e le sien aussi (Paul began to deconstruct his book. Mary began hers too). b. Paul a commenc´e de d´econstruire son livre. Marie a commenc´e a` d´econstruire le sien aussi (Paul began to deconstruct his book. Mary began to deconstruct hers too). One can construct a homomorphism from the deconstruction of the book to a temporal structure that captures accomplishments. Then Kleiber’s model would predict that (3.20a) has a reading that is a paraphrase of (3.20b). But it does not.

3.4 The Generative Lexicon The last approach to polysemy that I shall treat here is by far the most developed of the ones I have surveyed. That is the model given by the Generative Lexicon or “GL.” The present approach draws its inspiration from many of the ideas in GL as developed by Pustejovsky (1995) and others. GL is motivated by the phenomena of coercion and logical polysemy. It aims to preserve compositionality as much as possible while giving an account of these phenomena beginning with a single lexical entry for logically polysemous words. Pustejovsky (1995) thinks that specific lexical meanings are generated in the meaning composition process from interactions of type constraints and something like a sens g´en´eral, a general, perhaps underspecified meaning for all the uses of the word that can be specialized via predication. The hard work is to figure out an appropriate format for a sens g´en´eral and the procedures that in appropriate contexts will specify this underspecified meaning.

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1. Argument Structure: Specification of number and type of logical arguments. 2. Event Structure: Definition of the event type of a lexical item. Sorts include state, process, and transition. 3. Qualia Structure: A structural differentiation of the predicative force for a lexical item. 4. Dot Objects: they are invoked to explain copredications. In Pustejovsky (1995) they are part of the qualia structure. 5. Lexical Inheritance Structure: this part of the lexicon specifies the type hierarchy. GL avails itself of the formalism of attribute value matrices, or AVMs, combined with types known as typed feature structures (TFS), a very good formal account of which can be found in Carpenter (1992). In effect, a TFS can be thought of as a type with a bit of information attached via “attributes” whose values are more types. Formally, in the language of type theory, this amounts to associating with the “head” type of the TFS a record or collection of types. Since there is a natural translation from feature structures to first-order formulas, the use of TFSs for lexical entries allows one to combine type information with information that naturally goes into the logical form of a lexical entry. The two most innovative aspects of GL are qualia structures and dot objects. Following Moravscik (1975), GL postulates that many nouns contain information about other objects and eventualities that are associated with the denotation of the noun in virtue of something like the Aristotelian explanatory causes, or αιτια. The qualia structure of a word specifies four aspects of its meaning: • • • •

constitutive: the relation between an object and its constituent parts; formal: that which distinguishes it within a larger domain; telic: its purpose and function; agentive: factors involved in its origin or in “bringing it about.” ⎡ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎣

⎤

⎥⎥⎥ door(x,y) ⎥⎥⎥ ⎥⎥⎥ const : aperture(y) ⎥⎥⎥ ⎥⎥⎥ formal : physobj(x) ⎥ telic : walk through(e’,w,y) ⎥⎥⎥⎥⎥⎥ ⎥⎦ agentive : make(e,z,x)

Figure 3.1 Qualia structure of door

3.4 The Generative Lexicon ⎡ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎣

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⎤

⎥⎥⎥ cigarette(x) ⎥⎥ const : tobacco(x, y) ⎥⎥⎥⎥⎥⎥ formal : physobj(x) ⎥⎥⎥⎥⎥ telic : smoke(e, x, y) ⎥⎥⎥⎥⎥⎥ agentive : roll(e’, x, y) ⎥⎦

Figure 3.2 Qualia structure of cigarette

Pustejovsky and his students hypothesize that in predications like (3.21), the verbs begin and enjoy, which require an eventuality for their internal arguments, select as their arguments the eventualities encoded in the qualia structures of nouns like cigarette. (3.21) a. begin a cigarette (i.e., smoking) b. enjoy the book (i.e., reading) According to GL, the observations about coercion with verbs like enjoy, begin, and finish indicate a rich type structure in which objects of a given type α conventionally associate with objects of other types relevant to an object of type α’s production or function; this type structure is accessible to and guides the composition process. Pustejovsky (1995) also uses observations about coercions involving certain prenominal adjectival modification constructions to motivate qualia-based typing information: (3.22) a. fast car b. fast motorway c. fast water To explain these data, Pustejovsky and Boguraev (1993) argued that fast selects for the telic-role of the NP head, sometimes acting coercively. For most of the above Adj-N combinations, we arrive at interpretations such as “cars that are fast moving” and “motorways that permit fast traffic.” Bouillon (1997) discusses a wide range of phenomena which are handled by reference to qualia in such constructions. Another application of qualia-based typing has been to account for certain denominal verb formation cases, as discussed in Hale and Keyser (1993). Hale and Keyser’s canonical examples are illustrated in (3.23) below. (3.23) a. John put the books on the shelf. / J. shelved the books. b. John sent the letter by fax. / J. faxed the letter. c. John put the wine in bottles. / J. bottled the wine.

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GL proposes the following analysis of these observations: the noun-to-verb transformation is licensed in just those cases where the noun’s telic role involves an object that matches the verb’s direct object. For example, from the noun shelf, whose telic makes reference to the relation of holding books (and related objects), the verb shelve is licensed, because its direct object shares the argument referenced in the noun’s telic value. Climent (2001) discusses this idea in more detail. I turn now to a critical examination of the framework. First of all, we can quickly dispense with the idea of meaning generation during the composition process. There is no generation of meaning in the process of meaning composition in GL; meaning composition simply selects components of lexically specified meanings in the analysis of the coercion or copredication phenomena. The exploitation of qualia in the purported explanation of the various phenomena just listed simply focuses on a particular component of the lexical meaning of a noun and unifies this with the typing requirement of a predicate of the noun phrase or higher projection thereof (e.g., DP). The generative lexicon should rather have been called the “selectional” or “specificational” lexicon. Nevertheless, a selectional process in meaning composition is an interesting idea. How far does it take us? It turns out that the notion of a selectional meaning composition process is not well developed in GL and breaks down rather rapidly in the face of recalcitrant data and formal scrutiny. First, it is often difficult to understand exactly what the values of the qualia are supposed to be. Is the telic role of a shelf, its purpose, really just to hold books? Presumably not. Shelves can hold all kinds of things—wine glasses, ski boots, outboard motors, clothes. So we should predict that sentences like (3.24) a. John shelved his sweater b. Mary shelved her glasses have a similar meaning to John shelved the books, but if (3.24a–b) make sense at all, they involve a shift to a metaphorical sense of shelve—something similar to shelve an idea. Furthermore, this analysis predicts denominal verbs that don’t exist: (3.25) a. John poured the wine in the glasses. / # John glassed the wine. b. John put the roast in the oven. / #John ovened the roast. The analysis for denominal verb formation vastly over generalizes. The criterion proposed by GL isn’t sufficient for explaining the observations. And GL’s claim that having the right qualia structure is a necessary condition for denominal verb formation isn’t right either. For example, the classic examples of

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denominal verbs like lunch and snack have intransitive uses in which there are no direct objects that could be referenced in the telic roles associated with the nouns lunch, snack, and so on. An additional problem is that the qualia values seem to shift depending on the examples analyzed. For instance, to get the right meaning for fast car, which is a modal meaning (has the ability to go fast), we have to say that the car’s telic role is to be able to drive or to be able to transport people. But if we modalize the value of the telic quale, then we should expect John enjoyed the car to mean something like John enjoyed the ability of the car to drive or to transport people, and we wouldn’t expect the much more natural reading—John enjoyed driving / looking at the car. Similarly for the telic role of motorway. In spite of these worries, the telic roles of many nouns are nevertheless quite clear. It is much less clear what the constitutive or formal qualia are for many objects. Consider, for instance, the constitutive quale for door vs. tobacco. For tobacco the constitutive is something like an Aristotelian material cause, the matter out of which the object is constructed, but that is hardly the interpretation of the constitutive quale for door, which GL takes to be an aperture. Apertures are not matter—they are precisely the lack of matter. These remarks might seem quibbling, but there is a general point behind them. If the qualia are not defined in a precise way, then the theory can postulate anything for the values of qualia and thus loses explanatory power. The general unclarity concerning what the qualia structure of a given noun is extends from the particular values of qualia to their types. What exactly is the type of the qualia object? This is a legitimate question for GL since it makes heavy use of types. An aspectual verb like begin seems to take an event type as its object argument or at least some sort of intensional event description, as it is perfectly coherent to say: (3.26) a. John began to read that book, but he never finished (reading) it. b. John began that book, but he never finished it. If the logical form of the first clause of either (3.26a) or (3.26b) were something like (3.26’) ∃e∃e (begin( j, e, e ) ∧ read that book(e)) then we would predict that (3.26a,b) imply that there was a reading of the book and that that event was incomplete or unfinished, which seems quite problematic, and perhaps even contradictory. Assuming that the infinitival contributes a property of events or event types as the argument of begin avoids this problem

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and invites a straightforward intensional analysis of (3.26a,b) along the lines of well-known modal analyzes of the progressive (Dowty 1979, Asher 1992).12 On the other hand, we don’t have imperfective paradox-like phenomena with the verbs enjoy or finish. If it’s true that I enjoyed smoking my cigarette, then I did smoke my cigarette. Notice also that enjoy doesn’t, unlike the aspectual verbs, subcategorize for infinitival clauses, at least in English. (3.27) b. c. d. e.

a. Nicholas enjoyed smoking a cigarette. Nicholas enjoyed a cigarette. #Nicholas enjoyed to smoke a cigarette. Nicholas finished a cigarette. #Nicholas finished to smoke a cigarette.

However, in GL the distinction between event types and events isn’t clear at all. Some interpreters of GL (Egg 2003) have taken the object of the coercion verb to be an event type; others (Asher and Pustejovsky (2006), or Copestake and Lascarides 1996)) have taken the arguments to be events. The truth seems to lie somewhere in the middle, and to depend on the verb. Our discussion of event types versus events as qualia values brings us to problems in the compositional semantics. In fact, the interaction between compositional semantics and lexical semantics is hardly ever discussed in GL, and this leads to problems—not surprisingly if you believe, as I do, that a theory of lexical meaning has to also specify a method of meaning composition or an account of predication. For instance, some authors like Kleiber have claimed that GL does not account for the data concerning anaphoric availability. That is, the sort of coercions induced by aspectual verbs are alleged to fail the pronominalization test. Suppose we introduce an element into discourse during coercion that has the type of an eventuality, as the telic roles for the AVMs for book, cigarette, and other artifacts do in GL. Then we should predict these eventualities to be accessible for future anaphoric reference, if none of the well-known semantic or syntactic principles barring anaphoric links obtain. However, the marginal acceptability of (3.28a) translated from Kleiber (1999) and (3.28b) appear to put this hypothesis in jeopardy. (3.28) a. Paul has started a new book. ??It (that) will last three days. b. ?Paul enjoyed his new book, though it was quick. It’s clear what is intended in these examples: an anaphoric reference to the reading event. Of course, if we distinguish between the types of objects for 12

Assuming that an infinitival provides an event type or a property of events would also be in keeping with the compositional semantics of infinitivals. See Asher (1993) for a discussion.

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aspectual verbs like start and verbs like enjoy as I did above, then accounting for the difference in acceptability of (3.28a,b) is straightforward. Other examples, however, show that an event is anaphorically available in coercion examples, when the discourse context is right. (3.29) a. Paul has started a new book, but that won’t last.13 b. Paul has started a new book. His reading will take him three days. (3.28a,b) and (3.29a,b) all require an event denoting expression to be accessible to the pronoun. I take it that (3.29a,b) are acceptable. The contrastive construction in (3.29a) makes the event more salient. The use of a definite description in (3.29b) also makes it easier to pick up the event of Paul’s doing something with the book. However, other, similar uses of aspectual verbs as in (3.30) also support anaphoric reference to events without difficulty when the discourse context is of a special kind. (3.30) Last week Julie painted her house. She began with the kitchen. That didn’t take very long. She then proceeded to the bedroom and the living room. That took forever, because she painted friezes on the walls in those rooms. In this use of aspectual verbs anaphoric reference to the events of painting the rooms is easy. Such examples also pass the copredication test when we use relative clauses: (3.31) Yesterday Julie painted her house. She began with the kitchen which didn’t take very long. She then proceeded to the bedroom and the living room, which took forever, because she painted friezes on the walls in those rooms. These examples show that the pronominal test with coerced eventuality readings does succeed, though the reasons for this success have to do not with qualia but with complex interactions between discourse structure and clausal logical form. It’s not clear what, if anything, GL predicts about the possibility of referring anaphorically to an event within the qualia structure. It had better not be the case that all the eventualities mentioned in the qualia are all available as anaphoric antecedents. That would give plainly false predictions. A more sensible hypothesis, empirically speaking, is that the terms denoting eventualities in the qualia structure only become available as anaphoric antecedents when they become the arguments of the coercion predicate, giving them as it were some sort of linguistic realization. But when that happens, does 13

Thanks to Elizabeth Asher for this example.

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Previous Theories of Predication ⎡ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎢ ⎢⎢⎣

⎤

⎥⎥⎥ cigarette ⎥⎥⎥ ⎥⎥⎥ sem arg1 : [1] ⎥⎥⎥ ⎥⎥⎥ Pred : cigarette ⎡ ⎤ ⎥⎥⎥⎥ ⎢⎢⎢ ⎥⎥⎥ ⎥⎥⎥ ⎢⎢⎢ smoke ⎥⎥⎥ ⎥⎥⎥ telic : ⎢⎢⎢⎢⎢ Pred : smoke ⎥⎥⎥⎥⎥ ⎥⎥⎥⎥⎥ ⎢⎢⎣ sem arg1 : [2] ⎥⎥⎦ ⎥⎥⎥⎥⎥⎦

Figure 3.3 Partially rewritten qualia structure of cigarette

that mean that the original object of the coercion predicate is no longer linguistically realized? Is it no longer available for anaphoric reference? That seems plainly wrong. Figuring out a principled view of what is going on, however, will require much more attention to the details of composition and interpretation than is available in GL. Let’s look at some of the formal details. Qualia structures appeal to the formalism of typed feature structures, or TFSs. A typed feature structure is a function from a type to a set of pairs of attributes and values. These values may either be constants (these are in fact types), variables with indices that are to be identified with values of some other attributes, or typed feature structures themselves. Values are thus recursively defined. The standard language of feature structures has a modal semantics (Blackburn (1997), Lascarides et al. (1996)). The models for TFSs correspond to directed acyclic graphs (DAGs). Following Blackburn (1997), one can define the semantics of TFSs by thinking of features as modal operators that label arcs between the nodes of a DAG types as propositions holding at nodes, and constraints on types as conditionals. Notice that the types themselves don’t have any particular structured semantics in this analysis. All types, that is, are considered as atoms. This is already an important limitation: we cannot state type presuppositions for higher types. Despite the appeal of the ideas in GL, there is more than a bit of “grunt work” to get everything to work out as advertised, as many have noted. The exposition in Pustejovsky (1995) is rather lax and informal and uses first-order formulas, as we saw above in the examples of qualia structures, instead of the proper formalism for TFSs. To represent the feature structure for cigarette properly, we would need to rewrite the qualia structure for cigarette as in figure 3.1. In addition, we need the value of the telic quale in the qualia structure for cigarette to be defeasible, since it may be that when we say that Max enjoyed the cigarette, he enjoyed eating it (it might be a chocolate cigarette). To reflect this fact we would need to add the default type assignments of Lascarides et al. (1996).

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We have now expressed qualia properly in TFSs, but we are still not quite done. The operation of unification over TFSs is a binary operation that returns a new TFS where the old values in the common arguments of two TFSs are replaced with their meets (greatest lower bounds in the type hierarchy) and then adds all the argument value pairs that are not shared. Typed unification is unification checked by typing; for instance, we can unify the feature structure for cigarette with the feature structure for enjoy, provided that the object argument’s type in the TFS for enjoy (the object argument in the TFS for enjoy is just a variable that will be replaced under unification with the feature structure for cigarette) has a meet with cigarette (the type) that is not the absurd type ⊥. By hypothesis, however, the object argument for enjoy is an event, while cigarette is a subtype of physical object and has no non-absurd meet with the event type. So the composition crashes here, unless we can coerce either the type of the appropriate argument slot of the verb or the type of cigarette. GL’s idea is that in this case, one of the qualia types of cigarette should be substituted for cigarette. But how is this done? How do we in fact shift the predication to hold of the telic value when we have a phrase like enjoy the cigarette? How exactly is the predication in coercion cases involving aspectual verbs or verbs like enjoy supposed to work in terms of unification? Does one unify the variable in the argument place of the verb with something of the appropriate type in the AVM or feature structure associated with the element that is supposed to fill the argument position? Something like this must be going on, but such a rule is not part of unification standardly construed. Neither a defeasible version of unification like that in Lascarides et al. (1996) nor GL itself provides rules suitable to the analysis of coercion. The unification formalism underlying TFSs is not by itself sufficient to get the appropriate bit in the logical form as the argument for a coercing predicate like enjoy. We need some way of manipulating the feature structure so that we get the event in the telic quale as the argument of enjoy. In feature structure terms, this means stipulating a special lexical rule that transforms the original feature structure into one of the appropriate sort. This now looks very much like the sense transfer function of Nunberg. Alternatively, we can see the feature structure with qualia to be a disjunction of a primary sense (the basic word meaning) and associated senses (the meanings associated with the qualia); predication selects among the associated senses when necessary. Now that we have brought the structures of GL into familiar territory, we see that they have the familiar problems. The qualia constrain but also pack Nunberg’s sense transfer function into the lexical entries for nouns. That strategy brings with it the problems that we’ve seen already with the sense transfer function. For example, this strategy threatens to get the wrong truth conditions

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for sentences with coercions and quantification like (3.10) repeated below; we want the coercion to affect the argument of enjoy but we don’t want the quantifier many books to be coerced into the quantifier many book readings, even though the coercion based on a type clash can only be identified once we are at the stage of combining the whole DP with the verb. (3.10) George enjoyed many books last weekend. Putting the sense transfer function into the noun seems to be precisely the wrong strategy to deal with coercions, since doing so shifts the domain of quantification in (3.10) on a standard compositional analysis of the DP many books. This wrongly predicts that (3.10) is true if there are many events of reading one book over the weekend. We should rather think of the transfer as doing something to the verb as I argued earlier. Perhaps one could implement something like this idea with special lexical rules for TFSs (although all GL approaches are, as far as I know, mute on this subject), but it would look extremely ad hoc and be highly non-compositional. Hopefully, there is a better alternative! Pustejovsky and Moravscik exploit the Aristotelian explanatory causes of traditional metaphysics to handle coercion. Aristotle of course takes the αιτια to be universal features of being. However, it doesn’t take long to realize that qualia aren’t a universal feature of all types of substances in todays “common sense” metaphysics. Types associated with terms that denote natural kinds— e.g., water, h2 o, wood, gold, birch, elm, penguin, etc. do not plausibly have any associated agentive or telic qualia.14 Pustejovsky (2001) tries to turn this problem into advantage for GL by defining the type artifact as any type whose associated feature structure has agentive and telic qualia. For such substances their origin or the event of their construction as well as their purpose are pertinent to understanding what they are. This certainly seems plausible. So it should follow that only artifacts give rise to the sort of coercions with the aspectual verbs and verbs like enjoy that motivate GL. Nevertheless, even this restricted qualia hypothesis runs into trouble, and on two counts. First, it would seem that one can enjoy some natural substances even without turning them into artifacts; climbers can enjoy a cliff; many people can enjoy the mountains or the sea, the beach, the forest, the wilderness, the wide open spaces, and so on. Nevertheless, these would all appear to be objects that are not artifacts. On the other hand, for some artifacts like door, the associated agentive and telic qualia don’t work with verbs like enjoy in the way that the associated qualia of 14

At least not unless the terms “acquire” a use or purpose in a particular context. Pustejovsky (p.c.) noted occurrences of spoiled water, which would indicate that the water was spoiled for some purpose like a lab experiment.

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cigarette do. What would the telic role of door be? One might think that it is to be walked through, or closed. But if I say (3.32) John enjoyed the door this sounds very strange; and if it means anything, it certainly doesn’t mean that he enjoyed closing the door or walking through it. In a somewhat similar vein, consider (3.33) John enjoyed the vegetable garden. Vegetable gardens are artifacts; they are created by human for the purpose of growing food, as their name implies. Nevertheless, it’s hard to get a reading for this according to which John enjoyed growing vegetables in the vegetable garden or that he enjoyed creating the vegetable garden. At least equally available is the much more generic “enjoyed looking at” reading. Such counterexamples abound with artifacts. Kitchens, bedrooms, lamps, forks, knives are all artifacts that can be enjoyed, but the GL predicted reading of, say, John enjoyed the lamp—the reading that John enjoyed turning on the lamp or using it to illuminate something—is not there. The list of artifacts that don’t behave in the way GL predicts is much longer than the list of those that do.15 It does not help, as Pustejovsky and Bouillon (1995) or Godard and Jayez (1993) do, to appeal to aspectual clashes between the demands of the aspectual verbs or enjoy and the eventualities contained in the qualia to explain away counterexamples to GL’s account of coercion. They argue that the qualia for door, lamp, or kitchen involve eventualities that do not meet the demands of the aspectual verbs for some sort of accomplishment as an object argument; therefore, it’s no surprise that the qualia don’t show up as the values of the coercion. But notice that the aspectual verbs or enjoy are relatively catholic in their requirements on the type of eventuality they can take. (3.35) a. John enjoyed/began/finished/started swimming/sleeping/drinking. (activities) b. John enjoyed/began/finished/started swimming three laps/crossing the street/drinking three beers. (accomplishments) 15

Here is another counterexample from Kleiber (1999) with respect to the coercion data. GL should predict that (3.34a,b) have at least one common reading, since one thing one typically does with bulletin boards is read them. Nevertheless, (3.34a) can’t be readily interpreted as (3.34b).

(3.34) a. Paul a commenc´e le tableau d’affichage (Paul began the bulletin board). b. Paul a commenc´e a` lire le tableau d’affichage (Paul began to read the bulletin board).

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These verbs don’t take states or achievements as arguments. One could try to argue that kitchen’s, door’s, and lamp’s telic or agentive qualia are all states or achievements. But this seems a dubious stipulation. A plausible telic quale for lamp is to illuminate an area; and this is, by the usual aspectual tests, an activity. It would appear that the agentive quale of all of these objects is some sort of a creation event, which is an accomplishment. Thus, either the eventualities associated with the telic and agentive qualia of these terms are not the intuitive ones (in which case what use are they?) or the theory fails to make the right predictions for a vast number of ordinary cases. In any case, the inadequacy of qualia to make the right predictions does not just affect the account of coercions involving aspectual verbs. It also threatens the account of adjectives. Consider (3.22c). Water that is moving fast is the desired interpretation of this adjectival modification, but it is one which does not seem to involve reference to any of the inherent qualia of water. As Fodor and Lepore (1998) point out, and as we’ll see in detail later, there are many types besides those given in a classic qualia structure that are relevant to coercion. More importantly, GL is far too inflexible to handle certain examples that show that what eventualities are selected is sensitive to information already present in the context derived from preceding discourse. (3.36) Paul a commenc´e de tapisser sa chambre. Marie a commenc´e la sienne aussi (Paul has started to wall paper his room. Mary has started hers too). These examples pattern with examples like (3.30), in which the particular eventuality selected as the argument of the aspectual verbs is inferred from the discourse context. There are other ways types get affected as well. In GL only the verb is involved in the coercion of its arguments; for instance, the aspectual verbs and enjoy coerce their object argument to be of event type, and the event type is specified by one of the qualia. But this is empirically incorrect. For instance, the subject of an aspectual verb may determine what the type of its theme or event argument is. (3.37) a. The janitor has begun (with) the kitchen. b. The cleaners have started the suits. c. The exterminator has begun (with) the bedroom. In each of these there is a coercion to a particular type of event for the object argument of the aspectual verb. Yet it is obvious that the noun phrases in object

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position do not by themselves supply the requisite events, as the minimal pairs in (3.38a–c) lack the salient readings of (3.37a–c).16 (3.38) a. Jan has begun (with) the kitchen. b. Kim and Pat have started the suits. c. Sam has begun (with) the bedroom. We need information about the subject or agent of the aspectual verb to get the preferred readings for (3.37a–c). In GL, it’s totally unclear how the agent of the verb affects the selection of the event argument. GL cannot explain the effects we have noted. And for those who would argue that these are readings based on “pragmatic” inferences, they are at least as robust as the readings of the coercion cases that motivate GL. Secondly, they don’t depend on anything in the “context” other than the arguments of the verb! To be sure, these inferences are defeasible as well as the ones for the basic qualia. As far as I can tell, there’s no argument to say that qualia are part of lexical semantics if these aspects of meaning are not.17 There are many more instances of coercion that don’t fit in very well in the GL framework of qualia. The coercions in (3.39) involve the (defeasible) inference to a particular type of object of drink, namely alcohol. This phenomenon is known as “lexical narrowing.” (3.39) a. Chris likes to drink. b. Chris drinks all the time. c. Chris is a heavy drinker. d. Let’s have a drink. Qualia cannot model this sort of coercion, as they are tied to nouns denoting substances—mainly certain kinds of artifacts. We need to generalize the type system considerably in order to capture this data. Other coercion phenomena, like the metonymic examples of Kleiber, don’t find a proper home in GL. In Chinese, there are clear examples of part–whole shifts in the classifier system, where we shift from kinds to members of the kind. Here is an example where there is an anaphoric link between two DPs, and a metonymic shift due to the classifiers.18 16 17 18

Of course, (3.38a–c) have readings on which the agents have begun constructing or fabricating the objects. For a similar criticism of GL, see Vespoor (1996). This example is due to Laurent Pr´evot; see Pr´evot (2006).

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(3.40) a. ni kan zhe zhu hua. you look that CL.plant flower (Look at that flower.) b. jian liang duo gei wo ba. cut two CLbloom give me EXCL (Cut two blooms for me.) One might attempt to assimilate these metonymic coercions to the qualia via the constitutive role, but then the constitutive ceases to have a clear definition— is it truly the material cause or not? In addition it’s far fetched to suppose that a qualia structure will list all the parts of an artifact as complex as a passenger jet, for example. Vikner and Jensen (2002) have argued that perhaps qualia might be used to interpret the English Saxon genitive construction. They hypothesize that the qualia tell us what relation there is between the noun phrase or DP with the genitive marking and the head noun. However, here too an appeal to qualia doesn’t help very much. A quick survey shows that the number of relations involved between these two expressions is vast indeed. (3.41) a. Bill’s mother b. Mary’s ear c. Mary’s team d. The girl’s car e. The car’s design f. Mary’s cigarette (i.e., the cigarette smoked by Mary) g. Bill’s cake (the cake baked by Bill or the cake eaten by Bill) h. The wine’s bottle i. A mother’s boy j. The rapist’s victims k. Japan’s economy l. The economy’s sluggishness m. The economy’s performance n. Sunday’s meeting These examples illustrate that the relation between the DP in the genitive and the head noun is often determined by the meaning of the nouns in the construction—sometimes by the argument structure of a relational noun or a deverbal noun. With respect to GL, qualia appear to affect the genitive if the head noun is not intrinsically relational—e.g., (1.19e) (telic), (1.19d) (formal), (1.19f,g) (telic or agentive)—cf. Vikner and Jensen (2002). On the other hand, the head noun and the noun in the DP with genitive case can affect the relation (not just the head N), and furthermore, many relations present in the genitive construction don’t fall under any qualia — e.g. (1.19k,n) (spatial or temporal

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location), (1.19l) (“predicational”), 1.19c (set membership), (1.19b) (ownership or control). Qualia are at best a partial predictor of what’s going on with the genitive construction. The determination by the syntax/semantics interface of the relation involved in the interpretation of the genitive is defeasible. Information from the discourse context can overrule, for example, the determination of the relation by a relational noun like mother: (3.42) [Context: Picasso and Raphael both painted a mother with a child.] Picasso’s mother is bright and splashy —a typical cubist rendition. It makes Raphael’s mother look so somber. Some might object that this example involves extrananeous elements. The terms mother instead of Madonna suggest a special meaning. But Recanati (2004) offers the following example to show that contextual effects override the semantic import of relational nouns for the treatment of the genitive: (3.43) a. Ok. I just heard from John and Bill who are working at the old folk’s home. b. We need some supplies right away. c. John’s grandmother needs a wheelchair, and Bill’s grandmother a bedpan. Here we can perfectly well access the interpretation where John and Bill are in charge of certain aged persons. And it overrides the relational interpretation of grandmother and grandfather. GL’s introduction of qualia structures to analyze coercion looks very different from Nunberg’s sense transfer model. But in the end it packs the sense transfer function into the lexical entry for nouns, which just gives the wrong results when we implement it precisely. Moreover, the data show that the qualia model is insufficiently general and too inflexible to succeed. What about dot objects, another idea within GL? The underlying idea is again intuitive; copredications indicate that a word may have two independent senses in some sense at the same time. But this intuition is in need of development as well as defense. And once again, we don’t have the right formal framework to investigate this intuition. Pustejovsky’s introduction of dot objects to model copredication is an additional overload on the overtaxed AVMs with the typed feature structure and unification-based framework. Dot objects actually introduce considerable complexities into the type formalism and involve a rather subtle metaphysical analysis, as I’ll show in detail in the next chapter.

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In Pustejovsky (1995), one can glean a proposal for exploiting terms of complex • type. The proposal is to take an object of complex type and then “select” one of the constituent types at hand. It is in fact a simple coercion story but uses a different apparatus from qualia. Suppose, as Pustejovsky does, that book is a complex object of type informational object • physical object. By using such projection operations, we can coerce book to the appropriate type for examples like: (3.44) a. The book is interesting. b. The book weighs five pounds. On the other hand, it’s not at all clear, since it appears that the projection operation is destructive, how one can either account for copredication as in (3.45a) or the anaphoric coreference in (3.45b), where the pronoun it refers back to an informational type object while the predication in the main clause forces book to be of type physical object or p for short. (3.45) a. The book is interesting but very heavy to lug around. b. John’s Mom burned the book on magic before he could master it. In (3.45a), on the other hand, we need to use the informational type to handle the first predication and the physical type to make the second predication go through. But once we retype the book from physical object • informational object or p • i to, say, i, then how can we recover the physical type? This problem receives no solution in the GL model of dot objects. However, matters are worse. Suppose p p • i = ⊥; that is, suppose that the complex type physical object • information and the type physical object are inconsistent, and so their meet is ⊥. Then, GL’s theory of dot objects goes inconsistent. After selection, what happens is that instead of (3.46) book(x), x : p • i (where x : p • i is an assignment of the type p • i to x) you get, after one of the selection rules, (3.47) book(x), x : p But this is inconsistent with the basic typing rules for book. If one decides that the meet of the two types is consistent, it would still produce a funny typing of book. It would imply, for instance, that the i part of this retyped p•i object is not there or empty, and that would lead to very strange interpretations. Moreover, we would not be able to handle simple sentences like (3.45). Something has to be done to fix this.

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We have now surveyed both empirical and formal problems with GL. Despite its intuitive appeal and its undoubted success in making coercion and copredication central problems of lexical semantics, GL is in big trouble. The core claim that meanings are generated during the composition process is at best misleading. The posited complex lexical structures consisting of qualia and dot objects either don’t make sense as they stand or fail to make the right predictions on a relatively massive scale. It’s also not clear how to work out the ideas in the TFS formalism. Much of what Pustejovsky (1995) wants to do with dot objects, for instance, doesn’t make sense in the typed feature structure formalism, where types are atoms—whatever dot types are, they are not atoms. The TFS formalism supplies neither rules nor a semantics for such type constructors as •. And so no analysis of copredication is forthcoming in such a formalism. TFSs also fail to do justice to coercion, because it provides no general rules for doing what has to be done to get coercion to work. The main problem with GL is that it postulates an elaborate theory of lexical meaning without providing a theory of predication and meaning composition over that implicit in the theory of unification. To get an adequate explanation of the data, we need to do both. We also need to think much harder about the conceptual underpinnings of dual aspect nouns and the types that help us understand them. GL gives us a rich set of problems to think about, but we will have to build a replacement theory pretty much from the ground up. And we will have to use a different framework from that of TFSs.

3.5 Recent pragmatic theories of lexical meaning In contrast to GL’s attempt to locate the mechanisms for coercion and aspect selection within the lexical semantic entry for particular words, there is a pragmatic approach to such phenomena, exemplified on the one hand by Stanley and Szabo’s hidden variables approach (Stanley and Szabo (2000)) and on the other by relevance theorists Sperber and Wilson (1986), Recanati (2002), or Carston (2002). Broadly speaking, such approaches attempt to analyze phenomena such as coercion or aspect selection as involving pragmatic reasoning. For Stanley and Szabo the pragmatic reasoning involves finding contextually salient values for hidden variables; for the relevance theorists, it involves a process of enrichment of logical form. (3.48) It’s raining. (3.49) I’ve had breakfast.

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By postulating a hidden location or temporal variable, Stanley and Szabo can account for the conveyed content that these sentences typically have in a particular discourse context. For instance, uttering it’s raining conveys the content that it’s raining at some salient place of utterance. I’ve had breakfast conveys that I’ve had breakfast during some salient interval of time. Discourse context can of course affect salience: in (3.50), for instance, the salient location is that of the mountains in (3.50a), while it is a location on the way to the mountains in (3.50b). (3.50) a. We can’t go into the high mountains today. It’s snowing too hard, and we won’t be able to see anything. Let’s go for a hike around here instead. b. We can’t go into the high mountains today. It’s snowing too hard and the roads are a mess. Stanley and Szabo provide, however, no mechanism for determining the salient locations with which to bind the variable they introduce in logical form.19 The Stanley–Szabo proposal can be adapted to deal with coercions.20 One would need to postulate for each coercing predicate λxφ two hidden variables, one higher-order relational variable and another that will end up being related to x. Enjoy, which is understood to take an event as a direct object, would now look something like this: (3.51) λyλeλz enjoy(z, e) ∧ R(e, y) When no coercion is present R could be resolved to identity, but when the direct object of the verb involves denotations to non-event-like objects, then R would be resolved to some contextually salient property. So, for instance, enjoying playing a soccer game intuitively involves no coercion, and the variable introduced by the DP that ranges over playing soccer game events would be identified with the event variable that is the direct object argument of enjoy. However, Laura enjoyed a cigarette would involve a coercion; in this case the variable introduced by the DP ranging over cigarettes would be related via some contextually salient relation R like smoking to get the logical form: (3.52) ∃y∃e (enjoy(l, e) ∧ smoke(e, y) ∧ cigarette(y)) This isn’t quite right, as the lexical entry doesn’t specify that enjoy is a control verb. Additional stipulations, however, will fix the problem. 19 20

For examples like (3.50), one could appeal to the formulation of relevance in van Rooij and Schulz (2004) to define the salient binder for the variable. In effect Egg (2003) develops such a proposal. This is just the proposal used in the underspecified approach I suggested would be a possible option for the sense transfer strategy.

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This approach has an advantage over GL or the sense transfer view as developed by Sag and Nunberg, in that it gets the quantification cases right: enjoying many books does not, on this view, mean that one enjoys many events of reading books. On the other hand, this generalization of the Stanley–Szabo approach has several fundamental flaws. The first is that it has nothing to say about when coercion takes place. The typed approach I will provide does: when there is a type mismatch, there will be an attempted type adjustment, which, if successful, will in turn lead to a justification of the type presupposition. Without this sort of restriction on coercion due to type mismatch, the Stanley–Szabo approach predicts interpretations for enjoyed playing the soccer game that do not fit the facts. It predicts the possibility of all sorts of strange relations between this event and the event that is actually enjoyed—like, for instance, that the event enjoyed was different from the one that involves the playing of the soccer game. Such interpretations are not attested at all, regardless of context. In addition, consider the following example, due to Vespoor (1996): (3.53) a. Last night, my goat went crazy and ate everything in the house. b. At 10 p.m., he started in on your book. b . At 10 p.m., he began to eat your book. b . #At 10 p.m. he began your book. (3.53b ) is plainly bad even though we are primed in the context to understand that the eventuality to be coerced to is an eating event. The salient value for the hidden variable is clearly salient. Thus, the account is too weak and predicts coercions where there are none, unless we add to it a type-driven theory of predication. This approach also operates at the wrong level. Not all coercions are alike. While begin, start, and finish all coerce some arguments —e.g., start a cigarette, begin a cigarette, and finish a cigarette, they are not all equally happy in their coercive capacity with other direct objects. And one and the same ergative verb may license coercion in its internal or direct object argument, whereas it does not in its intransitive form. The aspectual verbs all work this way. (3.54) b. c. d. e. f. g. h.

a. I started your book this morning. I began your book this morning. I finished your book this morning. #The book started/finished this morning. #The book finished this morning. The reading of the book started this morning. The reading of the book finished this morning. The meeting started/began/finished this morning

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Begin, start, and finish all accept event denoting DPs in their theme argument in their intransitive use (3.54f–h), but they do not coerce non-event denoting DPs in that position into DPs that denote events (3.54d,e). In contrast, they support coercion of their theme argument position when they are used transitively. It’s very unclear how simply postulating a variable at the level of logical form will be able to explain these observations. Coercions are sensitive to actual lexical items and not to general pragmatic principles. Aspectual verbs like stop and finish have a clearly related meaning, but their behavior with respect to eventuality coercion is quite different. (3.55) b. c. d. e. f. g. h.

a. Mary finished eating the apple. Mary finished the apple. Mary stopped eating the apple. Mary stopped the apple. Jules finished smoking the cigarette. Jules finished the cigarette. Jules stopped smoking the cigarette. Jules stopped the cigarette.

Whereas (3.55a,b) have interpretations in common (in (3.55b) Mary could have finished doing other things to the apple), (3.55c,d) do not. (3.55d) only has a reading that (3.55c) lacks, in which Mary stops some physical motion of the apple, like its rolling off the table. (3.55a,c) have similar meanings, although (3.55c) does not entail that she ate the whole thing whereas (3.55a) does. (3.55b,d) have quite dissimilar meanings: finish the apple cannot mean stopping some physical motion of the apple. Aspectual differences between these verbs can account for the differences between the similar meanings of (3.55a) and (3.55c), but the differences between (3.55b) and (3.55d) cannot be so explained.21 Further, stop and finish don’t license the same coercions. (3.56) a. John has finished the garden (the kitchen). b. #John has stopped the garden (the kitchen). (3.56) is perfectly natural and means that John has finished doing something to the garden, like preparing it or digging it up. It’s very unclear what (3.56) means at all in an “out of the blue” context. There are similar though less striking differences between start and begin. Further, the coercion effects of these verbs are less easily interpretable with many consummable direct objects than the coercion effects of finish. 21

As far as I know no one has looked at these minimal pairs.

3.5 Recent pragmatic theories of lexical meaning (3.57) b. c. d. e. f.

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a. Mary started eating her apple. ?Mary started her apple. Mary started eating her sandwich. Mary started her sandwich. Mary began eating the apple. ??Mary began the apple.

These examples sound more or less good depending on their arguments. I have a harder time getting the eating event associated with fruits with these verbs than with constructed foods like sandwiches or candy.22 When start or begin take natural foodstuffs as their direct objects, I do not find that the coercions pick up an eating event, even when the example is primed in the context. Finally, the aspectual verb end hardly seems to induce event coercion at all. (3.58) b. c. d. e.

a. ?Mary ended the cigarette. ??Julie ended the apple.23 Alexis ended the sonata with a flourish. Lizzy ended the sonnet with a wonderful image. Mary ended the meeting (the discussion, the negotiations).

When we use the verb finish with a consummable, a coercion is possible; but this is not the case when the coercing predicate involved is end. The coercive capacities of end are quite restricted, in fact to things that are informational artifacts or entities that are or have eventualities of some sort as aspects (e.g., things like films). Event coercion is very much a matter of the verb’s fine-grained meaning, in particular its presuppositions, not a general pragmatic mechanism. The Stanley–Szabo approach attempts to explain coercion at the wrong linguistic level. Further evidence that this last charge is warranted comes from the observation that coercion seems to be linguistically constrained. Consider these examples due to James Pustejovsky: (3.59) a. Isabel has a temperature. b. Check Isabel’s temperature. c. Every physical object has a temperature. 22

23

I didn’t find any citations on Google for starting apples, starting peaches, or the like. And begin the fruit sounds even weirder to me. I did find one citation involving starting a peach candy. With vegetables like carrot, there are many citations involving products derived from carrots like carrot juice, but no citations for started a carrot by itself. There seem to be no sensible uses of this on Google, though someone might attempt to convey the proposition that Mary killed the apple by using this sentence. There seems to be an alternative to this aspectual use of end for all sorts of objects that can be destroyed, which is put an end to. This might be responsible for blocking the coerced reading of (3.58a,b).

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(3.59a) conveys that Isabel has a fever, an abnormally high temperature, whereas of course (3.59b,c) do not. Why should pragmatic processes of enrichment be blocked in these cases? It is not clear what sort of answer there could be, unless it has to do with the conventional meanings of words and, more importantly, certain linguistic, more specifically type, constraints on coercion. If the Stanley–Szabo account does not seem promising for coercion, it has even less to say about dual aspect nouns. It has no account of the complex cases of copredication that motivated GL’s introduction of “dot objects” or Cruse’s idea of perspectives. Finally, it has no account of predication failure. If hidden higher-order variables are present in all predications, we should be able to coerce verbs like hit. But that doesn’t seem to be possible. (3.60) Bill hit the number two. The Stanley–Szabo view is not the only pragmatic approach to lexical meaning. Relevance theorists (Sperber and Wilson (1986), Recanati (2004, 1993)) attempt to capture these inferences by appealing to a pragmatic process of free enrichment. Interpreters will add to the content of (3.48) and (3.49) in order to make the information conveyed optimally relevant, according to the principle of relevance. Free enrichment is a local, optional process in which literally encoded meanings are added to by a pragmatic inferential process to form enriched meanings that then combine to form the proposition that expresses the conveyed truth conditions of a sentence. Relevance theorists point to phenomena like lexical narrowing as support for their theory. Similar examples resembling lexical narrowing involve the specialization of a broad general meaning to a particular argument. (3.61) a. The ironing board is flat. b. My neighborhood is flat. c. My country is flat. It is indeed true that each of these uses of flat specializes a general meaning, as we can see from our ellipsis test. (3.62) ?This ironing board is flat and my country is too. However, these cases can fit into the Stanley–Szabo approach, if we assume that flat involves a hidden degree variable (Kennedy (1997)); the subject of the predication could in principle dictate a particular degree of flatness relevant to the subject’s type. In fact, given Kennedy’s work, it appears relatively straightforward to give a semantic account of the differences in (3.61). Nevertheless, relevance theorists can also attack examples like (3.61) using the principle of relevance.

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There are a number of problems with the proposal of free enrichment (and processes that relevance theorists take to be similar, like Nunberg’s sense transfer). First of all, free enrichment and sense transfer, as they’re usually formulated, predict the wrong truth conditions for many coercion cases involving coercion (recall the discussion of (3.10), just as Sag’s (1981) precisification of Nunberg’s sense transfer model does. Second, if these processes are optional, they will have the same problems as the Stanley–Szabo account in overgeneralizing cases of coercion. Finally, general pragmatic mechanisms do not account for the sensitivity of coercion and aspect selection to particular words and particular predicational contexts. The data I have provided here strongly suggests that coercion and aspect selection have to do with the semantics of particular words; they are driven by type mismatches, not by optional, general pragmatic mechanisms, though the latter may be eventually needed to fill out underspecified constraints provided by the justification of type presuppositions. A final difficulty with the relevance-based accounts is the lack of precision in the notion of relevance.24 The formulation of the principle of relevance requires an appeal to unknown mechanisms of inference and processing cost. It’s unclear how these mechanisms, or an appeal to speaker intentions, can constrain predication in a precise fashion. For instance, we should expect on the enrichment view that we could always make sense of predications in which there are, from my perspective, type clashes. There should be little difference between the classic coercion cases and cases where no coercion is possible such as some of the examples in (1.1), repeated below: (1.1g) The number two is red. One could imagine a speaker intending to convey with (1.1g) that the number two guy in some procession is wearing red. But such a pragmatic interpretation of (1.1g) just doesn’t seem possible because of the constraints put on predication by the meanings of the individual words. Pragmatic approaches also fail to say anything relevant about the cases of coercion like John enjoyed his glass of wine or Mary enjoyed her cigarette in out of the blue contexts. On the free enrichment approach, sense transfer or the hidden variable approach, we should either expect no definite answer in out of the blue contexts or variation. However, speakers are remarkably constant in their interpretations of such sentences. Such theories have difficulty in saying anything about the interaction between semantics, predication, and the pragmatic principles they use to analyze coercion. There simply isn’t enough detail 24

See Asher and Lascarides (2003) or Merin (1999) for a more detailed look at Relevance Theory.

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in extant pragmatic theories to see how they could make substantive predictions or how they could exploit the semantic content of lexical items. In short, there is no pragmatic substitute for a lexical semantic theory. Let us take stock. We have seen that previous accounts in general do not provide formally or materially adequate accounts of phenomena that a lexicon theory must address. They all attempt to shift the meaning of various terms to account for coercion. Nunberg and the pragmatic approaches leave the shifting mechanism completely unconstrained, providing little explanatory force, while GL makes the shifting mechanism too rigid to account for the data and appears to get the wrong truth conditions for quantified sentences involving coercion. Turning to copredications, none of these theories has an account that begins to get the facts right. More generally none of these theories can account for how previous discourse context can affect predication. The approach I will flesh out in the next chapters attempts to remedy these weaknesses while retaining some of the flexibility of pragmatic approaches.

PART TWO THEORY

4 Type Composition Logic

I have surveyed the main, extant proposals for lexical semantics and have argued that these do not meet the demands for a satisfactory theory of lexical meaning. I propose a new framework here, a context sensitive model of typedriven lexical semantics, that builds on the insights of previous accounts but attempts to remedy their inadequacies. This framework, the type composition logic, or TCL, assigns to each word stem a type. Some word stems like stone, which are ambiguous between a verbal and a nominal meaning, will have a complex type to represent that ambiguity. Such word stems may not have a distinct logical form until the syntactic environment or a morphological suffix1 selects for the verbal or nominal sense. The lexical entries for word stems will take seriously the idea that predicates place type presuppositions on their arguments, presuppositions that must either be satisfied by the types of the arguments or accommodated if the predication is to be semantically well-formed. I will thus distinguish between type presuppositions that predicates place on their arguments and the types that the term arguments introduce as part of the proffered content. When putting terms together in a predication—be it in a standard predication, a nominal or verbal modification, the application of a determiner to a noun phrase, or even semantically rich morphological processes—extra contributions to logical form can arise when there is a type clash between a predicate and one of its arguments and a type presupposition must be accommodated. This means the account of predication must involve more than the simple application of a property to an object or a relation to its terms. It must involve accommodation mechanisms that will introduce material into logical form to make the predication succeed in certain cases. In addition, I will make these mechanisms sensitive not only to the presuppositions introduced within local predication—the application of 1

For example, in German Bank is ambiguous just as its English homynym is; however, plural morphology allows us to distinguish B¨ancke (benches) from Banken (financial institutions).

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the predicate to its arguments—but also to the discourse context in which this predication takes place—hence the “context sensitivity” in the context sensitive model of lexical content. My proposal brings the theory of predication and lexical content into line with a general tendency towards dynamics in semantics and pragmatics that has developed over the last quarter century. Dynamic semantics has proved extremely useful in analyzing the semantics of anaphoric elements in language like pronouns and tenses and of expressions that generate presuppositions that must be integrated into the given discourse context (e.g., Kamp (1981), Heim (1982, 1983), Asher (1986, 1987), van der Sandt (1992), Asher (1993), Kamp and Reyle (1993), Groenendijk and Stokhof (1991), Veltman (1996), Beaver (2001)), and extensions of this idea to include richer ideas of discourse structure and pragmatics have also proven useful (Asher and Lascarides (2003)). Dynamic semantics treats the meaning of a formula as a relation between information states, an input information state, and the output information state. The input information state represents the content of the discourse context to date while the output information state represents the content of the previous discourse context integrated with the content of the formula. The interpretation of a discourse involves the relational composition of constituent sentences’ relational meanings. In dynamic semantics for natural languages, as well as in the dynamic semantics for programming languages, the interpretation of a formula can either function as a test on the input context or can transform the context. So, for example, John is sleeping in dynamic semantics would yield a formula that functions as a test on the input context, which we can think of as a set of elements of evaluation. If an element of evaluation verifies the proposition that John is sleeping, then it is passed on to the output context; if it does not verify the proposition, it does not become part of the output context. Operators like conditionals form complex tests on an input context C: an element of evaluation e will pass the test defined by If A then B just in case any output o from A given e will yield an output from B (given o as an input). Some sentences, for instance those containing indefinite noun phrases, output a context that is distinct from the input one. They transform elements of the input context; in particular they reset or extend the assignment functions that are parts of elements of the context to reflect the information they convey. On a view that treats assignments as total functions over the set of variables, an indefinite has the action of resetting an assignment that is part of the point of evaluation for formulas, as in Tarskian semantics. On a view where assignments are treated as partial functions, the interpretation of an indefinite extends the assignment with a value to the variable introduced by the indefinite

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in logical form. This reset or extended assignment becomes part of the output context. In dynamic semantics presuppositions constitute a particular sort of test on the input context. Consider a sentence like (4.1) Jack’s son is bald. The presupposition generated by a definite noun phrase like Jack’s son (namely, that Jack has a son) must be satisfied by the input context, if the interpretation of the rest of the sentence containing the definite is to proceed. One way of satisfying the presupposition in (4.1) occurs is for it to be already established in the context of utterance of (4.1) that Jack has a son. This can occur, for instance, when (4.1) is preceded by an assertion of Jack has a son. Presuppositions can also be satisfied by contexts within the scope of certain operators, as in (4.2), even though it has not been established in the discourse context that Jack has a son:2 (4.2) If Jack had a son, then Jack’s son would be bald. In dynamic semantics the content of the antecedent of the conditional is encoded into the input context for the interpretation of the consequent and the presupposition it generates. Thus, the satisfaction of the presupposition by the antecedent of the conditional in (4.2) means that the presupposition places no requirement on the input context to the whole conditional, the context of utterance. The satisfaction of the presupposition by elements of the discourse context entails that the presupposition does not “project out” as a requirement on the context of utterance. Thus (4.2) is consistent with the assertion that in fact Jack has no son. On the other hand, dynamic semantics predicts that if we change (4.2) just slightly so that the antecedent does not provide a content that satisfies the presupposition, the presupposition will project out as a requirement on the input context to the whole conditional: (4.3) If Jack were bald, then Jack’s son would be bald too. What happens when a presupposition cannot be satisfied by the discourse context? It depends on what sort of presupposition is at issue. Some presuppositions, such as those introduced by definite noun phrases, are easily “accommodated.” In dynamic semantic terms this means that the input context 2

One of the great successes of Dynamic Semantics has been to show that the behavior of presuppositions introduced by material within the consequent of a conditional follows straightforwardly from the conception of the conditional as a complex test on the input context and thus offers a solution to the so-called projection problem.

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is altered in such a way so that the presupposition is satisfied. Other presuppositions, such as that generated by the adverbial too, are much less easily accommodated, as I mentioned at the beginning of this book. Given that operators like conditionals can add “intermediate” contexts between the context of utterance and the site where the presupposition is generated, we need a theory of where and how to accommodate in case the input context does not satisfy the presupposition. In some theories of presupposition that operate on semantic representations like that of van der Sandt (1992), accommodation simply involves adding a formula for the presupposition to an appropriate part of the representation for the discourse.3 Van der Sandt stipulates that one tries to accommodate at the outermost context first and if that fails then one tries to accommodate at the next outermost context. The constraints on accommodation are that the addition of the presuppositional material be consistent with the discourse context. So, for instance, one cannot add the presupposition that Jack has a son to a context where it is established that Jack does not have a son. I will develop a theory of presupposition satisfaction and accommodation for type presuppositions that is related to the clausal theory of presupositions as developed in van der Sandt (1992). To implement a theory of presupposition at the level of types, we need three things: a theory of types, a theory of the relations between types, and an account of type presupposition satisfaction and type presupposition accomodation. The theory of type presupposition satisfaction is simple. Normal predication involves a test on the types of the expressions involved in the predication. If the type of the functor and its argument are related in such a way that the argument’s type is a subtype of the type presupposition placed by the functor on its argument, then the predication is licensed and the construction of logical form can proceed via application. That is, the presupposition induced by the functor is satisfied. Matters become more complex when complex types like • are involved; a type presupposition might be satisfied by one of the constituent types of a • type. I will study this issue in detail in chapter 6. On the other hand, when such presuppositions are not satisfied, there are several ways to accomodate the presupposition. One way is reminiscent of classic accommodation at the clausal level: we simply add the type requirements of the predicates to the types of the arguments via the least upper bound operation . But there are other sorts of accommodation that depend, for instance, on the 3

In other theories like that of Heim (1983), the accommodation procedure is not really well developed; but see Beaver (2001) for a detailed account of accommodation in a Heimian approach to presupposition.

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types of the arguments and the types of the predicate. In chapter 8 we will look at a particular type of accommodation that occurs when coercion takes place. We must integrate type presuppositions within our representation of the lexical meaning of words. We will do this by adding another parameter to our terms, one for type contexts that will carry information about the type presuppositions of various terms. As we shall see, applying a predicate to its arguments may change the extant presuppositions or indeed the logical forms of the predicate or the argument if accommodation is involved. I will set out in this chapter and in chapter 6 a composition logic that determines how the types of lambda terms can combine, and how type presuppositions can be accommodated. First, however, I set out a preliminary set of types and the relation of subtyping on them.

4.1 Words again With the adoption of a dynamic framework at the lexical level, we must revisit the issue of lexical ambiguity and the units of lexical semantics. Traditionally, ambiguity is a matter of individuating expressions. In the structural case, individuation is often provided on independent syntactic grounds. For example, morphosyntax provides at least two derivations for sing, dance, and drink— one on which these lexical items are analyzed as intransitive verbs, one on which they are treated as transitive verbs. These different expressions are represented via bracketing, labelled trees, syntactic terms, or some other means, with different representations standing for different expressions. For lack of independent natural candidates, the “structures” underlying lexically ambiguous expressions like bank are then represented in some arbitrary fashion. According to this traditional picture, it is expressions, not surface forms, that serve as inputs to semantic interpretation; there is a sharp distinction between “logical” polysemy and “accidental” polysemy, in that the latter is invisible to semantics. The traditional treatment of accidentally polysemous words is analogous to the treatment of pronouns in traditional semantics: the choice of the pronoun’s antecedent is “invisible” to the interpretative component; traditional semantics solves this problem by indexing the pronoun with its antecedent as an input to logical form construction. The use of a dynamic approach with underspecification however, allows one to investigate the resolution of anaphoric constructions as part of the interaction between underspecified, compositional content and discourse context.4 A similar observation should be made at the 4

The literature concerned with DRT is replete with such investigations. See, for instance, Kamp and Reyle (1993).

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lexical level. Many word stems in English like inquire, hear, own, woman, and sister come with a determinate type structure, which also determines their argument structure. But other word stems do not. Word stems like stone, sink, boat, and dog can be determined to be of nominal or verbal type depending on their local “predicational” environment.5 Because there is a close connection between types and syntactic categories, the choice of type will determine the syntactic category and will allow such word stems to combine with functional or closed class lexical elements like determiners, or verbal morphology.6 Accidentally polysemous words like bank in English, which can be disambiguated by the predicational context and the selectional restrictions of the predicates they combine with, are a special case of word stems with an underspecified type. Below I will introduce a restricted set of disjunctive types in the system; roughly, if α and β are subtypes of some determinate type, then the disjunctive type α ∨ β is also a type. Such disjunctive types can serve as least upper bounds of two types, when upper bound for the two constituent types exist in the hierarchy. But even when this doesn’t occur, the semantics postulates disjunctive “objects” that serve to model underspecifications or accidental ambiguities. For instance, stone will denote in the internal semantics a disjunctive object involving a basic type stone and a transitive verbal type as one of its other disjuncts.7 Intuitively, this object does not correspond to a determinate type in the hierarchy, however. The word stem bank will have be assigned the disjunctive object financial institution ∨ river border ∨ transitive verb. This use of disjunctive objects is analogous at the type level to the use of underspecification at the level of compositional content; we can exploit the predicational context and discourse context to disambiguate lexical entries with disjunctive types, just as those who use underspecification at the compositional level use discourse context to disambiguate anaphors or relative operator scopings. For example, bank in the following sentences must be a verb; only if it combines with the infinitival complementizer to do we get a grammatical sentence and a 5

6 7

Borer (2005a,b) has an extreme version of this view, on which all open class lexical elements have in effect an indeterminate type. She conceives of the content of such words as being outside the linguistic system. TCL can accommodate the motivating cases for her view, without denying that the lexicon also contains entries for lexical stems with a determinate type structure. In a review of Borer’s work, Potts uses data from tagging of large corpora to argue that in fact most English words have some determinate type structure. He notes that of the 40,000 word types in the Brown corpus, only 11.5% are even 2-ways ambiguous. Marantz (1997) and Angelika Kratzer in an unpublished manuscript contain competing approaches to Borer’s view but also maintain that it is morphosyntax and the functional lexemes and their projections that determine argument structure, not the lexicon. Plural morphology can also help in picking out the appropriate type of the item, as in the case of German Bank and its two, different plural forms that provide a disambiguation. This follows the suggestion of Asher and Denis (2005).

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well-formed predication: John wanted to bank his check that very day or Mary wanted to bank the airplane.

4.2 The basic system of types Let us begin by examining simple, functional, and disjunctive types, as well as the types that carry presuppositions. Thus, we have • Simple or Primitive Types: e, t, physical object, etc. • Presuppositional Type: Π, another base type that carries the type presuppositions of terms. • Disjunctive Types: If σ, τ, and ρ are types, σ ρ and τ ρ, then (σ ∨ τ) is a type. • Functional Types: If σ and τ are types, then so is (σ ⇒ τ). • Quantificational Types: If σ is a simple type, and τ is any expression denoting a type and x is a variable ranging over types, then ∃x σ τ is a type.8 To illustrate, a term t is of this quantificational type if there is a subtype x of σ such that t is of type τ[x]. The set of simple types, ST, forms the core of the system. It contains the basic types countenanced by Montague Grammar, e, the general type of entities, and t, the type of propositions, along with a finite set of subtypes of e and a countable set of subtypes of t. Another distinguished subtype is ⊥, the absurd type. When there is no type in the type hierarchy γ such that α γ and β γ, α ∨ β represents a disjunctive object that is the internal semantics of an accidentally polysemous term that must be resolved to assign the term a determinate type. Functional types represent properties. ST comes with the subtyping relation , which forms a semi-lattice over ST with ⊥ at the base.9 Using on the simple types, we define a greatest lower bound operation for elements of ST. Definition 2 Greatest Lower Bound: α α = β iff β α and β α and there is no γ  β such that β γ and γ α and γ α . has the usual properties—e.g., idempotence, commutativity, and α β iff α β = α. TCL captures incompatibility between types in terms of their 8 9

x is, I realize, close to an individual level variable x. I strived for typographic consistency making all type formulas in small caps. Hopefully this will not cause too much confusion. As we will see, the subtyping relation as defined in the next section will entail that  is not the supremum of the lattice. In fact  is not a type. Note that the fact that  is not a type in the hierarchy does not stop us from using the tautology  in logical forms. These are quite different objects.

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common join, ⊥. We can also define a dual to greatest lower bound, least upper bound, or : α  β = γ iff γ is the least general type in the hierarchy such that α  γ and β  γ = γ. Note that  may not be always defined, since there may be no type that is the least upper bound of arbitrary types α and β

4.2.1 Subtyping In the previous chapter, we saw that the standard set theoretic model of types fails to provide a coherent notion of subtyping for functional types, once we admit a rich set of subtypes of the type of entities e. To summarize the difficulty, recall that according to set theory, the set of physical properties or functions of type p ⇒ t, that is, the set of all functions from objects of physical object type to propositions, and the set of first-order properties or functions of type e ⇒ t (the set of all functions from entities to propositions) are disjoint, even though p e in the lattice of simple types and even though every function in p ⇒ t is a subfunction of some function in e ⇒ t. There is no coherent notion of subtyping for higher-order types, where subtype is understood as subset, once we admit multiple subtypes of e. Type theory and the categorial models that I develop below provide a coherent notion of subtyping for all types, in the sense that, together with the rules of the simple, typed λ calculus, they generate a consistent logic or system of proof. We need such a notion of subtyping to specify an appropriate rule of application for β reduction: roughly one can apply a λ term λxφ to a term t if the type of t is a subtype of the type of x. I will specify subtying using a restricted, intuitionistic notion of deduction or proof for types, Δ . • From subtyping to logic: α ST β α Δ β In particular, the model will verify: Fact 1

Subtyping for functional types: α α β β (α ⇒ β) (α ⇒ β )

Subtyping for functional types implies that e ⇒ t p ⇒ t. This makes sense from a proof theoretic or computational point of view: if you have a proof that given a proof of an entity, you have the proof of some proposition, then you have a proof that given a proof of an entity of a particular type (say

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a physical object), you have a proof of a proposition. But we cannot derive p ⇒ t e ⇒ t. This seems not to get us what we want for our type hierarchy, since this implies, on the usual conception of first-order properties, that the type of first-order properties is a subtype of the type of physical properties.10 In light of this, we must re-examine what we mean by a first-order property. In a system with many subtypes of e, something is a first-order property just in case it is a function from some subtype of e into the type of propositions. To spell this out, our types must be defined in a second-order language for types. The type of first-order property would thus not be what we naively take it to be, namely e ⇒ t, but rather something that is implied by all function types taking as inputs subtypes of e and returning a proposition. That is, the type of a first-order property is: (4.4) ∃x e (x ⇒ t) Anything from whose type declaration we can “prove” (4.4) is a first-order property. To get anywhere, we must provide subtyping rules for existentially quantified types. To get a sensible notion of subtyping as deduction, my subtyping rules follow the standard introduction and elimination rules for ∃. In particular, where A is any type expression with an occurrence of β and B a type expression where β does not occur, then • Type theoretic ∃ introduction: β α A (∃x α A( Xβ )) • Type theoretic ∃ “exploitation”: β α, A B (∃x α A( xβ )) B This enables us to get the right facts about first-order properties. In particular, take the λ expression for black dog, whose course grained, denotational meaning is a function from physical objects to propositions. The NP has the type p ⇒ t, from which we can easily prove (4.4) using the ∃ introduction rule. We can now combine black dog with a determiner whose type presupposition 10

This has disastrous consequences for the construction of logical form. Consider the rule of application in the λ calculus which is like Modus Ponens—given a type α and a type α ⇒ γ, we get γ. Now take the case of a determiner which is something of type (e ⇒ t) ⇒ ((e ⇒ t) ⇒ t) and it must combine with something of p ⇒ t. We have by assumption that e ⇒ t p ⇒ t. But we cannot now apply the determiner meaning to its restrictor; application is not sound in this case, just as β α does not allow us to conclude: β → γ, α γ.

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on its first argument is that given by (4.4). We also have the general type of physical properties, ∃x p (x ⇒ t), the general type of informational properties, ∃x i (x ⇒ t), and so on. The subtype hierarachy for these will be the intuitive one. (4.4) is the type presupposition of anything that intuitively takes a first-order property as an argument—e.g., a determiner or DP. Any expression that expresses a particular first-order property will satisfy this presupposition in the sense of entailing it. Thus: Fact 2 Any ordinary physical property (e.g., mass, shape, weight, color, etc.) is a first-order property and any property of informational objects (e.g., the property of being interesting, intelligible, etc.) is a first-order property. In addition, applying a physical property to an object of non-physical type is not defined (yields a type clash), and similarly applying a property defined only on entities of abstract object type, i.e., of type i, to something of type p is not defined.

4.3 Lexical entries and type presuppositions In the simply typed lambda calculus, type checking is done automatically during the moment of application. In the system developed here, however, a clash between the type requirements of a predicate and the types of its arguments may require adjustments to the predication relation and to logical form. Doing this directly within the typed λ calculus led Asher and Pustejovsky (2006) to unwanted complexity, and so I have chosen a different route, separating out those operations involving type presupposition justification from the core of the simply typed λ calculus. To pass presuppositions through properly from predicates to arguments, I add a presuppositional parameter to each type as de Groote (2006) and Pogodalla (2008) do to handle dynamic contexts.11 Each term has an extra argument for a presupposition element that can be modified by the lexical item. For instance, the standard lexical semantic entry for tree looks like this: (4.5) λx: p tree(x) 11

Since I’m not trying to embed dynamic semantics in the λ calculus, I do not resort to their continuation style semantics. They add two parameters of interpretation, but I shall add only one. I use standard dynamic semantics for passing type values across discourse spans. Nevertheless, everything I do here should be fully compatible with other approaches to dynamic semantics.

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The predicate’s type presupposition is that its argument must have type p. My revision to the entry for tree adds another λ bound variable π of type Π, which ranges over presuppositional elements. These presuppositional elements carry typing requirements from a predicate to its arguments. The addition of a type presupposition encoding parameter to terms complexifies the system of types in a predictable way. The type of propositions in TCL moves from Montague’s t to Π ⇒ t, and DPs and determiners shift predictably, given the more complex types for first-order properties. Although we cannot yet capture completely the presuppositions of determiners, let’s suppose for now that the type presuppositions of determiners are quite weak at least with respect to the higher-order variables: these range over all types that satisfy the definition of a first-order property in (4.4). Thus all DPs will have the general type: (∃x e (x ⇒ (Π ⇒ t)) ⇒ (Π ⇒ t)). I’ll abbreviate this type to dp. I’ll abbreviate the polymorphic property argument for a DP, ∃x e (x ⇒ (Π ⇒ t)), to be simply 1 (for a first-order property). Accordingly, determiners will have the type 1 ⇒ (1 ⇒ (Π ⇒ t)). Because the type presuppositions of the higher-order variables don’t vary with the lexical entry, I’ll assume from now on that all capital variables of the form P, Q, R, P1 , etc. are of type 1. Scripted variables P, Q, etc. will range over modifiers or objects of type 1 ⇒ 1, or mod. Capital Greek letters Φ, Ψ, etc. will range over objects of DP type. Let’s go back to the entry for nouns. In a standard typed system a noun is an argument of modifier forming an NP. An NP denotation furnishes an argument to a determiner to form a DP. DPs in turn take verbs or VPs as arguments. But the behavior of type presuppositions shows that the view of semantic composition that is encoded in the standard functional types for these categories is not quite right. Modifiers only combine with nouns if they satisfy the type presuppositions of the latter; modification by any subsective adjective preserves the type of the noun it syntactically modifies.12 For example, heavy must justify the typing requirements of dog; that is, a heavy dog is still a dog. Or to take a more extreme example, a red number, to the extent that it can be interpreted at all even given contextual help, still seems to be a number, whatever else it might be. Thus, the type presuppositions of the noun must percolate to the modifier. In order to pass the presupposition from the noun to the modifier, I will make 12

That is, anything that satisfies an NP in which a subsective adjective X applies to an NP Y always satisfies Y as well. This is problematic for non-subsective modifiers: wooden nutmegs aren’t real nutmegs (though they look very much like them), and former soldiers are normally no longer soldiers. Nevertheless, even former soldiers might carry the same type relevant to the predication as current soldiers. We will revisit this issue in chapter 11, where I shall argue that these modifiers are more subsective than they might seem.

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use of the presupposition parameter.13 Nevertheless, I will also follow tradition and assume that modifiers take first-order properties as arguments of the sort traditionally associated with nouns. Thus, letting P be a variable of modifier type, the functional type from first-order properties to first-order properties, the lexical entry for tree looks like this:   (4.6) λPλxλπ P(π ∗ argtree 1 : p)(x)(λvλπ tree(v, π ))

argtree stands for the “first” argument position of the predicate; this argument 1 position is always associated with the referential or denoting argument; the first argument position of a transitive verb will be its subject, while the second argument position will be filled by its direct object or internal argument. π ∗ argtree 1 : p says that, in addition to the type constraints π already encodes, whatever fills the first argument position of tree must have a type that justifies the type p. This includes the variable v in the lexical entry (4.6), but it may also include a variable contributed by the modifier. So summing up, (4.6) says that a noun like tree takes a modifier as an argument in order to pass along its type presupposition requirements to the modifier. In order for the modifier to combine with the noun, it must justify the presupposition that is appended via * to its presupposition parameter argument. The modifier also takes a simple first-order property, in this case λvλπ tree(v, π ), as an argument. This way of doing things may look complicated in comparison to the usual type declarations in the λ calculus, but we will need the flexibility provided by this formalism when we have to justify presuppositions. Presupposition parameters range over lists of type declarations on argument positions for predicates. To save on notational clutter, I’ll often just write argi when the predicate is obvious, or just list the type when the argument position and predicate is obvious. By integrating this λ term with a determiner and a verb, more type presuppositions will flow onto the presupposition parameter π. I haven’t said what the type of x is explicitly in the entry for tree. Because we want to allow for flexible justification of presuppositions, the type presupposition of x should be very weak. I shall take it to be of type e. When these presuppositions are to remain local to the term but not already specified, I’ll use the standard notation of the λ calculus for readability, but these presuppositions should be understood as generated by the predicate and stored in the local presuppositional parameter. Thus, the final entry for a tree will be:   (4.7) λP: mod λx: e λπ P(π ∗ argtree 1 : p)(x)(λvλπ tree(v, π ))

In practice, I will omit the typings of terms when they are obvious. More gen13

This acts just like the left context parameter in de Groote (2006).

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erally, for any noun Nn, we have the following entry, where PreNn encodes the type presuppositions of Nn. (4.8) λP: mod λz: e λπ P(π ∗ PreNn )(z)(λuλπ Nn(π, u)) Given these abbreviations, the general type of nouns shifts from the standard e ⇒ t to mod ⇒ 1. For NPs I will have the relatively simple type schema, α ⇒ (Π ⇒ t), where α is a subtype of e. I suppose that when no adjective is present, P in (4.8) applies to the trival subsective adjective, λPλx: eλπP(π)(x), and so gives a predictable type for a simple NP. I deal with multiple adjectival modifiers through type raising to form a complex modifier; the exact logical form for such raised NPs will be a matter of meaning postulates.14 In general predicates must pass their typing presuppositions onto their arguments. More specifically, a VP should pass typing presuppositions to its subject, and a transitive verb should pass its typing requirements to its object. For example, in The book is heavy, the type requirements made by the verb phrase on its subject argument should be satisfied or accommodated in order for the predication to succeed. In keeping with standard assumptions about the syntax–semantics interface, this means we must rethink the entries for our lexical entries to track these presuppositions and to put them in the right place. Consider an intransitive verb like fall. We want its type presuppositions to percolate to the subject. We can do this by assuming that an intransitive verb, or more generally a VP, is a function from DP denotations to propositions.15 This function will feed the appropriate type presuppositions to the subject DP in the same way that nouns feed their presuppositions to their modifiers. In order to do this properly, we must make our verbal predicates relatively catholic as to the type of DP they accept. The specific type requirements that verbs will place on their arguments will not be placed on the DP itself, but be placed rather in the presupposition slot so that it may be propagated to a local justification site and justified there—i.e., on the individual argument term furnished by the DP, if that is possible. If the higher-order types 1, dp etc. shift in type, it is usually because of a shift of one of their constituent types, from one subtype of e to another. It is quite difficult to shift higher-order terms directly, as we can see from the lack of coercions, say, from propositions to questions or from propositions to properties. 14

15

The issue of multiple adjectival modification gets complicated when we have a subsective combined with a non-subsective adjective as in fake, yellow gun or yellow, fake gun. It seems that both of these NPs have the reading of denoting an object which is a fake gun and yellow; nevertheless, standard compositional accounts will not be able to provide this reading for fake, yellow gun without resorting to meaning postulates as well. This applies the same trick used to handle transitive verbs taking generalized quantifier arguments—which makes the latter functions from DP denotations to VP denotations.

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We need presupposition checking on the type of the individual variable bound by the determiner in the DP in order to make the system function well. For instance, we need this to explain how the ambiguity in the meaning of an accidentally polysemous word like bank gets resolved when it combines with a VP like offered subprime loans in: (4.9) Many banks offered subprime loans in those days. The quantifier in (4.9) quantifies over banks that are financial institutions, not river banks. This happens because the type presupposition of the VP is passed directly onto the variable that many binds and because this variable inherits the disjunctive type, river-bank ∨ financial-institution. I assign the type to the noun bank, the type mod ⇒ ((river-bank ∨ financial-institution) ⇒ (Π ⇒ t), which means that the variable bound by the determiner in the DP will get the type river-bank ∨ financial-institution and it is the type of the variable that will be disambiguated by the type presupposition of the VP on its subject argument, which is financial-institution. The alternative, that the ambiguity is resolved at the level of the higherorder properties of the NP or DP directly, gives the wrong results. To see this, consider what would be, on this view, the type of many banks. It should be a function from properties of banks, considered either as river banks or financial institutions, to propositions. A property of banks is presumably a disjunctive type formed from two functional types, one of the form river-bank ⇒ (Π ⇒ t) and one of the form financial-institution ⇒ (Π ⇒ t). Given our reconstrual of subtyping and interpreting type disjunction as akin to logical disjunction, the type of the NP is then equivalent to ((river-bank financial-institution) ⇒ (Π ⇒ t)), which means that the variable bound by the determiner gets the type river-bank financial-institution. This last type is, however, presumably equivalent to the type ⊥ and so the quantification in (4.9) is vacuous, which goes completely contrary to intuitions and is a disastrous prediction. We might try to salvage this approach by making the type presuppositions of the VP hold only at the level of the DP type itself. This type presupposition would be (financial-institution ⇒ (Π ⇒ t)) ⇒ (Π ⇒ t), while the DP’s type is ((river-bank financial-institution) ⇒ (Π ⇒ t)) ⇒ (Π ⇒ t). Given Subtyping for Functional Types, the type presupposition of the VP on the subject is a subtype of the DP’s type, and so should be satisfied. But now we don’t resolve the ambiguity! The DP continues to quantify over riverbanks and over financial institutions, and the word bank remains ambiguous! This again goes contrary to intuitions. Thus, for an intransitive verb like fall, we have the following lexical entry where π ∗ argfall 1 : p specifies the type assignment for fall on its first argument

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place to be of type p or of physical type. This first argument place is ultimately filled by the variable bound by the quantifier that is the translation of the DP in subject position. The variables that will end up as subject place arguments for the verb can be determined from the syntax of the λ term for the predication. In particular, the variable introduced by the DP Φ will be one; and in the representation below, y is one as well.   (4.10) λΦλπ Φ(π ∗ argfall 1 : p)(λy: pλπ fall(y, π ))

The type of an intransitive verb or a VP, which in Montague Grammar has the type e ⇒ t, now has the more complex type, dp ⇒ (Π ⇒ t), or the functional type from general DP types to propositional types. Transitive verbs look very similar. The presuppositions of the predicate must percolate to the internal (direct object) arguments as well as the external (subject) arguments, which brings us to the following translation for a verb like hit. (4.11) λΦλΨλπ Ψ(π ∗ arg1 : p){λx: pλπ Φ(π ∗ arg2 : p)(λy: pλπ hit(x, y, π ))} I’ll usually abbreviate this to: (4.12) λΦλΨλπ Ψ(π ∗ arg1 : p){λxλπ Φ(π ∗ arg2 : p)(λyλπ hit(x, y, π ))} The typing on x and y, which I’ve omitted in (4.12), are easily inferrable from the typing on the first and second arguments of the verb; they are both of type p. Such lexical entries for verbs permit a lexical treatment of a wide scope reading for the direct object or internal argument quantifier. The following, slightly different entry for the verb suffices: (4.13) λΦλΨλπ Φ(π ∗ arg2 : p){λyλπ Ψ(π arg1 : p)(λxλπ hit(x, y, π ))} Let’s now go back to determiners. All singular determiners require their head noun phrases to be first-order properties. Most determiners, however, also carry type presuppositions on the sort of individuals they quantify over. For instance, the mass determiner expressions in English much and a lot of require that the elements in the domain of quantification be masses or portions of matter, another subtype of e. For instance, much requires the variable it binds to range over masses. The determiner a on the other hand requires the variable it binds to range over quantized or countable objects. These presuppositions interact with the presuppositions conveyed by the NPs with which determiners combine. Consider (4.14) I’ll have a Chardonnay (a water, a coffee).

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(4.14) means that I’d like a particular quantity of Chardonnay, water, or coffee— a glass, a cup, perhaps even a bottle. Conversely, mass determiners impose portion of matter readings: (4.15) There was a lot of rabbit all over the road. (4.15) means that there was a considerable quantity of rabbit portions of matter all over the road. This leads me to suppose that the determiner imposes a type presupposition on the individual argument that interacts with the type presupposition of the NP. In the next section, we’ll see how. Linguistically, this is interesting, because it appears that many NPs are in fact underspecified with respect to the mass/count distinction; the mass/count distinction is imposed by the determiner in English (and in other languages, like Chinese, by the classifier).16 Just as with complex clausal presuppositions, there is an order in which these presuppositions must be integrated into logical form. In particular, the presupposition introduced by the determiner must be satisfied or accommodated by the NP prior to dealing with the presupposition introduced by the predicate that makes up the nuclear scope of the determiner. This leads to an explanation of the judgements in (4.16). (4.16) a. A water has 12 ounces in it. b. *Much water has 12 ounces in it. Once we have integrated the mass presupposition on the variable bound by the determiner, it can no longer go with the obligatorily count property in the VP. Further evidence for the ordering of presuppositions and their justification comes from looking at complex cases of coercion. Consider (4.17) a. The Chardonnay lasted an hour. b. *Much Chardonnay lasted an hour. The preferred reading of (4.17a) is that a particular quantity of chardonnay participated in some event (presumably drinking) that lasted an hour. We provide the whole noun phrase some sort of event reading only after the determiner presupposition has been integrated into logical form and been justified by the predicate in the restrictor. The fact that lasted an hour requires for successful coercion a quantized event leads to uninterpretability when the bound variable has received the type mass from the determiner. These observations lead to the following entry for a : (4.18) λP: 1λQ: 1λπ ∃x(P(π ∗ arg1P : count)(x) ∧ Q(π)(x)) 16

In this TCL agrees with the “exoskeletal” approach of Borer (2005a,b).

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When building up a λ term for a DP, we will typically get a sequence of type presuppositions on the variable bound by a determiner: those given by the verb will have to be justified jointly with those given by the head NP and by the determiner. It is instructive to see what would happen if, instead of the proposal given here, we restricted the variables P and Q in the case of the determiner a to the type count ⇒ (Π ⇒ t). How could we apply such a determiner to a simple physical property like λxλπ dog(x, π ∗ p)? There is no subtyping relation between count first-order properties and physical properties, and so the application of a count determiner denotation to a physical property is not sound. As we’ll see below, we can use accommodation to adjust type presuppositions so that application may proceed. Roughly, accommodation allows us to take both type presuppositions and take their meet and assume this meet is the type of the argument and the λ bound variable it is supposed to replace in the operation of application. So far so good. But given our general facts about subtyping for functional types, the meet of a count property presupposition and a physical property will not be (count p) ⇒ (Π ⇒ t) but rather: (count  p) ⇒ (Π ⇒ t). This meet makes a wrong prediction about what the variable of a DP like a dog ranges over: the prediction is that it ranges over anything that is an inhabitant of count  p and this includes abstract objects, masses, etc. This does not at all accord with intuitions. But I see no other way of making the alternative way of construing the type presuppositions of determiners work out.17 Thus, a determiner places only weak type presuppositions of the sort I have given here on its property arguments and places the more particular type presuppositions on the bound variable the determiner introduces. The lexical entries chosen determine how presuppositions percolate through the derivation tree, and they predict that presuppositions will be justified typically locally to the argument’s typing context (the π that determines the typing of the argument). For instance, when we combine a determiner and an NP to form a DP that is an argument to another predicate φ, then φ conveys presuppositions to the NP or the DP’s restrictor. If such a presupposition is justified in the restrictor of a DP, it will also be justified in the nuclear scope. The converse, however, does not hold. This leads to a distinction between global justification (justification in the restrictor) versus local justification (justification in the nuclear scope). As we shall see, there is a preference for binding justifications of presuppositions at this “global” level, but this preference can be overridden 17

The same reasoning that I have given here applies to the view of types as partial functions, though I have argued this is not a viable alternative to TCL’s strongly intensional view of types.

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when it is impossible to justify a presupposition at that site.18 Furthermore, notice that just as with clausal presuppositions (see (4.19) where his father is bound to the presupposed content of the proper name John), one presupposition can justify another: the type presuppositions on the nouns car and tree justify, indeed satisfy, the presupposition of the verb hit, which wants a subject and object argument of type p in (4.20). (4.19) John’s son loves his grandfather. (4.20) A car hit a tree. Our understanding of subtyping via deduction or entailment enables us to extend and accordingly and  through the higher types. We can use our general notion of subtyping to derive easily some welcome facts. For one, we can prove that any specific noun is a subtype of noun,19 any specific modifier is a subtype of mod,20 any specific NP is a subtype of np,21 any specific DP is a subtype of dp,22 and so on, which is all to the good.

4.4 The formal system of predication In this section, I introduce the formal system of predication in TCL that exploits the notion of presupposition projection via λ bound parameters and the lexical entries elaborated in the previous section. This includes a composition logic with complex types, a logic that tells us how to compose bits of logical form together, taking account of type presuppositions, to form the logical form for a clause or a sentence. In standard formal semantics, a composition logic is used to build logical forms for clauses or sentences of a natural language. It assumes a syntactic structure for the clause to be composed and basic lexical entries for each word, with perhaps some morphological decomposition. A composition logic 18

19

20 21 22

The way I have set up the lexical entries, together with the preference for global binding, predicts as a default a principle that was stipulated in Asher and Pustejovsky (2006). The principle is the Head Typing Principle: Given a compositional environment X with constituents A and B, such that the logical forms of A and B, A and B have the types: A: α, B: β with α β = ⊥, then if A is the syntactic, lexical head in the environment, then the typing of A must be preserved in any composition rule for A and B producing a type for X  . The Head Typing Principle tells us that the head type in the construction should remain. For example, tree has the type mod ⇒ (p ⇒ (Π ⇒ t)), while noun is of the type mod ⇒ ∃x(x ⇒ (Π ⇒ t)). Assume that the type corresponding to tree is given. Then assuming mod we need to show that ∃x(x ⇒ (Π ⇒ t)), which follows from p ⇒ (Π ⇒ t) by ∃ introduction. This is trivial, since all modifiers are of type mod by definition. Once again this is proved by ∃ introduction. This is trivial, since specific DPs are all of the type 1 ⇒ (Π ⇒ t).

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exploits the rules of the lambda calculus to produce a normalized logical form giving the semantic content of the clause in a logically perspicuous language, usually that of higher-order intensional logic. The semantics of terms in the usual composition logic is just that of higher-order intensional logic, and so the composition process is not isolated as a special system. Since even first-order intensional logic is of course undecidable, we cannot prove that the composition process has any interesting computational properties, unless we separate out the composition logic from the general semantic framework. If we separate the compositional logic from its standard intensional, external semantics, and endow it with its internal interpretation, then we can show that the process of constructing logical form does have interesting computational properties. Formulas in our TCL have an external semantics given by the intended interpretation of the formulas of higher-order intensional logic, but these formulas also have an internal semantics via their types. This semantics is used to guide and to verify the composition process. A predication is well formed iff it has a normalization, and two formulas are equivalent just in case they reduce to the same normal form. The categorial interpretation of the types provides the internal semantics for our formulas. This internal semantics does not of course determine the external semantics, but it does capture certain general features of the external semantics—for instance, the aspectual nature of nouns that have a • type. We will check that the rules of TCL are sound with respect to the categorial interpretation. Because TCL concerns only type assignments, shifts in logical form due to type assignments and β reductions that are guided by a syntactic tree, the logic will turn out to have some interesting properties, which I’ll examine in chapter 10. Our lexical entries furnish the terms of TCL. These terms are formulas of λ2 , the higher-order typed lambda calculus. The rules of TCL are designed to deliver normalizations for logical forms for clauses or sentences, given a syntactic parse of the clause or sentence. Thus, TCL derivations are a quite restricted subset of all possible derivations of λ2 . The syntactic parse is a tree structure and dictates how the normalization procedure should go and also dictates what should be the types associated with the terms of the leaves: we begin with the leaves and then compute the result of combining lower nodes. The close correspondence between syntactic categories and semantic types, which has been part of semantics since the beginning of Montague Grammar and is part of compositional interpretation, means that normalization will succeed unless an unresolvable type clash occurs during application. TCL rules divide into those that deal with types generally, the “simple rules of TCL,” and those rules that are specific to handling presuppositions. The first simple rule for TCL is Application and its dual Abstraction. I have adopted

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a slightly more permissive version of application than was introduced in the first chapter where the argument and λ bound variable were required to be type identical. Instead I have allowed, given our complex system of types, a version in which one can do Application if the argument is a subtype of the λ bound variable or vice versa. This makes sense in terms of presupposition theory: if one can deduce the presupposition from what is given in the context, then this is a classic case of binding, and there should be no adjustment necessary to the presupposition or to the context to which it is applied. φ( xt ) is the result of replacing every occurence of x in φ with an occurence of t. Below I state Application by applying λ term to a term with a type assignment— t: τ means that t has type τ. (4.21) Application λx: αφ[t: γ], λxφ: α ⇒ β, γ α φ( xt ): β (4.22) Abstraction x: α, t: β λxt: α ⇒ β Application is a slight generalization of Modus Ponens and incorporates as well the principle of strengthening of the antecedent; it corresponds to the inference valid in classical, intuitionist ,and linear logic:23 φ ψ ψ → χ, φ χ In addition to these two rules, it is convienient to add the derived rule of Substitution. Let −→β denote the reduction relation between formulas using the rules of TCL. Then: (4.23) Substitution t −→β t 

φ −→β φ( tt ) I turn now to the rules for presuppositions. The rule Binding Presuppositions provides an account of binding with respect to lexical type presuppositions encoded in π. Suppose our context π contains the type α that is supposed to be placed on some argument position i of a predicate but that argument position already has the type γ assigned “locally” and γ α.24 It is clear that 23 24

In effect, I have incorporated here a version of subtype coercion. See Luo (1999). In practice, the local type assignment will always be the last on the string of type assignments appended to the local presuppositional parameter, or at least outside those typing requirements imposed by other terms.

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the local typing on the argument position satisfies the type requirement α. At this point the type presupposition α, like a bound, clausal presupposition, just “disappears”. In the rule below, I assume that the type assignments on argiP can either occur within a concatenated sequence or in separate parts of logical form. (4.24) Binding Presuppositions γ α, argiP : α, argiP : γ argiP : γ Sometimes presuppositions can’t be bound. With clausal presuppositions, when a presupposition cannot be satisfied, its content is accommodated or added to a place in the discourse structure if it is consistent to do so. Something similar holds in TCL for type presuppositions. Suppose that an argument position i for some predicate P has type α but there is a presupposition imposed on it from another term that it have type β. In this case, the local presupposition parameter π will look like this: π ∗ argiP : α ∗ argiP : β. If α β  ⊥, then the type presupposition will simply be added to the typing of t. This is what the rule of Simple Type Accommodation states: (4.25) Simple Type Accommodation

α β  ⊥, argiP : α ∗ argiP : β argiP : α β Binding is a special case of Simple Type Accommodation (since α β = α, if α β). There is a general consensus that clausal presuppositions should be bound locally and accommodated typically globally (i.e., at a level that outscopes all proffered content). Simple Type Accommodation, however, is very close to binding, and so we will treat both here locally. In general, type presuppositions are to be justified locally; only when this fails must the justification take place at some other place in the derivation tree. Simple Type Accommodation makes sense of the interactions of determiner type presuppositions and the type presuppositions of the NPs that go in for the restrictor arguments. Consider (4.14), for instance, repeated below. (4.14) I’ll have a Chardonnay. Let’s suppose that Chardonnay has the type presupposition wine.25 That is, I 25

Actually Chardonnay will most likely have a complex type that allows for the following sorts of copredications:

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will suppose that if someone tries to apply the word Chardonnay to something like a rock or even a liquid like milk, he simply has failed to make a predication (and hasn’t understood the meaning of the word). Thus Chardonnay has the lexical entry λPλπ P(π ∗ wine)(λxλπ chardonnay(x, π )). In integrating this with the trivial modifier, and then the resulting first-order property expression with the determiner a and using Simple Type Accommodation to take care of the type presuppositions, I predict the variable introduced by the DP a Chardonnay to have the type of wine count portion of wine, which is, intuitively, what is desired—the noun phrase is a property of properties of quantities or portions of wine. The same applies mutatis mutandis to other interactions between the type presuppositions of determiners and the presuppositions of their arguments. Let’s now turn to a derivation for a simple sentence like (4.27) to illustrate our simple rules. (4.27) A car hit a tree. I begin with the determiner entry which is a count determiner. From here on out I will abbreviate the type count to ct. (4.28) a. λP: 1λQ: 1λπ1 ∃v: e (P(π1 ∗ arg1P : ct)(v) ∧ Q(π1 )(v)) b. Here again is the entry for tree: : p)(w)(λvλπ tree(v, π )) λP: mod λw: e λπ P(π ∗ argtree 1 We must combine tree and the trivial modifier, λP: 1λx1 : eλπ1 P(π1 )(x1 ), using Application and Substitution several times (I will put the argument to which Application is about to apply in square brackets for readability): (4.29) b. c. d. e. f. g.

  a. λPλwλπ P(π ∗ argtree 1 : p)(w)(λvλπ tree(v, π ))[λPλx1 λπ1 P(π1 )(x1 )] λwλπλPλx1 λπ1 P(π1 )(x1 )(π ∗ argtree : p)(w)[λvλπ tree(v, π )] 1   λwλπλx1 λπ1 λvλπ tree(v, π )(π1 )[x1 ](π ∗ argtree 1 : p)(w) λwλπλx1 λπ1 λπ tree(x1 , π )[π1 ](π ∗ argtree : p)(w) 1 λwλπλx1 λπ1 tree(x1 , π1 )(π ∗ argtree 1 : p)[w] λwλπλπ1 tree(w, π1 )[π ∗ argtree 1 : p] λwλπ tree(w, π ∗ argtree : p) 1

Combining the result of that reduction with the determiner, another use of Application yields a formula for the DP (since type(λw: pλπ2 tree(w, π2 )) 1): (4.26) Chardonnay has enjoyed international acceptance due to its versatility both in growing and in wine production, and is, for many casual drinkers, the quintessential white wine. (slightly adapted from http://www.wisegeek.com/what-is-chardonnay.htm). But I will abstract away from the issue of complex types here.

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tree : ct)[v] ∧ (4.30) λQλπ1 ∃v (λwλπ2 tree(w, π2 ∗ argtree 1 : p)(π1 ∗ arg1 Q(π1 )(v))

Two more uses of Application and Substitution get us: : ct ∗ argtree (4.31) λQλπ1 ∃v (tree(v, π1 ∗ argtree 1 1 : p) ∧ Q(π1 )(v)) At this point we can use Simple Type Accommodation and resolve our presuppositions on the variable v as well as on the variable w (noting that p ct  ⊥). : p ct) ∧ Q(π1 )(v)) (4.32) λQλπ1 ∃v (tree(v, π1 ∗ argtree 1 Let’s now build the VP. In adding the verb’s contribution to the VP, I do not specify the types of x and y below as they can be inferred from the typing on the first and second arguments of hit.   hit   (4.33) λΦλΨλπ Ψ(π∗arghit 1 : p)(λxλπ Φ(π ∗arg2 : p)(λy1 λπ hit(x, y1 , π ))) tree [λQλπ1 ∃v (tree(v, π1 ∗ arg1 : p ct) ∧ Q(π1 )(v))]

That is, the verb hit requires that its arguments be of physical object type. But first let us combine the verb’s contribution with the DP logical form in square brackets. Since Φ is of type dp, we can use Application:  tree (4.34) λΨλπ Ψ(π ∗ arghit 1 : p)(λxλπ λQλπ1 ∃v (tree(v, π1 ∗ arg1 : p ct)  hit   ∧Q(π1 )(v))(π ∗ arg2 : p)[λy1 λπ hit(x, y1 , π )])

We use Application and Substitution to eliminate the higher-order variable Q (which is of type 1):  tree (4.35) λΨλπ Ψ(π ∗ arghit 1 : p)(λxλπ λπ1 ∃v (tree(v, π1 ∗ arg1 : p ct)    hit ∧λy1 λπ hit(x, y1 , π )[π1 ][v])[π ∗ arg2 : p])

(4.35) now reduces via 3 instances of Application and Substitution (using the bracketed arguments) to:   hit tree : p ct) (4.36) λΨλπΨ(π ∗ arghit 1 : p)(λxλπ ∃v (tree(v, π ∗ arg2 : p ∗ arg1  hit ∧ hit(x, v, π ∗ arg2 : p)))

We notice now that the second argument of hit and the first argument of tree are the same (the variable v). So we can now reduce this formula via an instance of Binding and Substitution to:   tree (4.37) λΨλπΨ(π ∗ arghit 1 : p)(λxλπ ∃v (tree(v, π ∗ arg1 : p ct)  ∧ hit(x, v, π )))

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Let’s now continue the derivation by constructing a logical form for the subject DP. (4.38) a. λP: 1λQ: 1λπ∃y(P(π ∗ arg1P : ct)(y) ∧ Q(π)(y)) [λuλπ car(u, π ∗ argcar 1 : p)] b. which reduces to: λQλπ∃y (car(y, π ∗ argcar 1 : p ct) ∧ Q(π)(y)) We now integrate the subject DP’s logical form with that of the VP in (4.36c) to get:   tree (4.39) a. λΨλπ Ψ(π ∗ arghit 1 : p)(λxλπ ∃v (tree(v, π ∗ arg1 : p ct)    car ∧ hit(x, v, π )))[λQλπ ∃y (car(y, π ∗ arg1 : p ct) ∧ Q(π )(y))]

b. Application yields:  hit λπλQλπ ∃y (car(y, π ∗ argcar 1 : p ct) ∧ Q(π )(y))(π ∗ arg1 : p)   tree  [λxλπ ∃v (tree(v, π ∗ arg1 : p ct) ∧ hit(x, v, π ))] c. Application and Substitution yield:   λπλπ ∃y (car(y, π ∗ argcar 1 : p ct) ∧ λxλπ ∃v (tree(v, π ∗   hit argtree 1 : p ct) ∧ hit(x, v, π ))(π )(y))[π ∗ arg1 : p] d. Another use of Application and Substitution yields: car   λπ∃y (car(y, π ∗ arghit 1 : p ∗ arg1 : p ct) ∧ λxλπ ∃v (tree(v, π ∗  hit argtree 1 : p ct) ∧ hit(x, v, π ))[π ∗ arg1 : p][y]) e. Another two uses of Application and Substitution yield: car hit λπ∃y (car(y, π ∗ arghit 1 : p ∗ arg1 : p ct) ∧ ∧∃v (tree(v, π ∗ arg1 : p∗ hit argtree 1 : p ct) ∧ hit(y, v, π ∗ arg1 : p))) We can now check the presuppositions of hit on its subject. Hit requires its first argument to be of type p. This presupposition has to be satisfied by y, which it clearly is. Thus (4.39e) reduces via Binding and Substitution to: car tree : ct (4.40) λπ∃y (car(y, π ∗ argcar 1 : p ct) ∧ ∃v (tree(v, π ∗ arg1 : p ∗ arg1 p∗) ∧ hit(y, v, π)))

Let us now look at an example of adjectival modification involving the intersective adjective heavy. Heavy has the lexical entry in (4.41a). Note that it does not impose special typing requirements on its property argument P or on x:

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(4.41) a. λP: 1 λx: e λπ (P(π )(x) ∧ heavy(x, π ∗ argheavy : p)) b. Applying the lexical entry for tree to (4.41a), we obtain: heavy λzλπλPλxλπ (P(π )(x) ∧ heavy(x, π ∗ arg1 : p)) tree   (π ∗ arg1 : p)(z)(λuλπ tree(u, π )) c. After several uses of Substitution and Application, we get: tree : p∗ λzλπ (tree(z, π ∗ argtree 1 : p) ∧ heavy(z, π ∗ arg1 heavy

arg1 : p)) d. Binding and Substitution reduce the presuppositional contexts: tree : p)) λzλπ (tree(z, π ∗ argtree 1 : p) ∧ heavy(z, π ∗ arg1 In (4.41b), we had two compatible typings on the same variable. When we attempt the same derivation for the modification heavy number, we get an irresolvable type clash in the presuppositions. In particular, we will have the following constraints on the parameter π: heavy

: abstract ∗ arg1 (4.42) π ∗ argnumber 1

: p.

We cannot justify the type presuppositions of the noun and the adjective with any of our rules. TCL thus predicts the attempted modification in heavy number to crash; no well-formed lambda term corresponds to this noun phrase and it has no proof-theoretic interpretation.

4.5 A categorial model for types I turn now to the semantic setting for this calculus. Church’s simple set theoretic model of types is not available to us because of problems with the subtyping relation and the hyperintensional nature of types as proof objects. There are two ways we can proceed with alternative models. One is to follow out the proof theoretic intuition that I laid out in identifying types with concepts. The proof theoretic paradigm has developed into Type Theory thanks largely to the work of Martin-L¨of (1980), and Ranta (2004), as well as Girard (1971). Work by Luo and his collaborators (Luo (1994), Luo and Callaghan (1998)) shows how to analyze the existentially quantified types within that formalism, originally introduced by Strachey in the 1980’s and elaborated in considerable detail by Reynolds (1983). The other way is to examine a more abstract model of proof or computation using category theory. I take a categorial construction to be a model for types and as an abstract way of specifying a certain conception of the proof theoretic, internal semantics for λ terms. But we can also use it to reflect the structure of objects in the type. In this section, I briefly review some of the basics of category theory and show how a proof theoretic

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interpretation is reflected in the categorial model, and I show the soundness of the basic rules for subtyping in the model. For a detailed presentation of the relevant material, see Asperti and Longo (1991)’s very beautiful introduction to category theory or Goldblatt (1979). Those who don’t want to look at these details can skip this section. The category theoretic notion of a closed cartesian category, or CCC, has the resources within which to model the quantifier free types introduced so far and furnishes a connection with the underlying logic of Type Theory (Lambek and Scott (1986)). It does not give a model of the full system of quantified types (Chen and Longo (1995)), nor does it give us by itself a satisfactory analysis of subtyping. Nevertheless, we can begin with CCC’s. To understand what a CCC is we need some definitions. Categories are a collection of objects and maps between objects that are related both to graphs and deductive systems as explained below. Definition 3 A graph consists of a set of objects (points) and a set of arrows between points (edges). In addition, there are two maps from Arrows to Objects, one labeled Domain and the other Co-Domain, which pick out the collections of first arguments and second arguments of arrows respectively. Definition 4 A deductive system D is a graph in which for each object A in D, there is an arrow 1A , which is the identity map on A, and for each pair of arrows f : A → B and g : B → C, g ◦ f : A → C, the composition of g with f , is defined. Objects can be identified with formulas and arrows with proofs. The closure under composition gives us a rule of inference. Definition 5 A category is a deductive system where ∀ f : A → B, g : B → C and h : C → D: • f ◦ 1A = f = 1 B ◦ f • (h ◦ g) ◦ f = h ◦ (g ◦ f ) In category theory one can define certain constructions over objects in a category. Products, for instance, are one such construction. Definition 6 Let A be a category and a, b be objects in A. Then a × b is the categorial product of a and b, which comes with two arrows π1 : a ×b → a and π2 : a ×b → b such that for any arrows f : c → a and g: c → b in A there is a unique h: c → a × b such that h ◦ π2 = g and h ◦ π1 = f . Category theorists typically display a categorial product using the following

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diagram where all the arrows commute: c D f zzzz DDDDg z h DDD zz D"  |o z z / a a × b π2 b π1 In the category of Set, product constructions correspond to Cartesian products. Other constructions of interest in category theory are those of an initial and terminal object. Definition 7 An object 0 is an initial object in a category C iff for all objects c in C, there is a unique arrow f : 0 → c in C. An object 1 is a terminal object in C iff for all objects c in C, there is a unique arrow f : c → 1 in C. Terminal objects are the duals of initials. Duality in category theory reverses the directions of the arrows in a construction. Categorial coproducts are the dual of products and correspond to disjoint union in set theory. They give rise to the following commuting diagram: c z< O bDDD f zzz DDg z h DDD zz D z z / a+b o a π2 b π1 A cartesian category is one that contains a terminal object and that is closed under the product construction. Duality ensures that a cartesian category also contains coproducts. Another notion from category theory that we need in order to give the basic model of types is the notion of an exponential, which corresponds to the function space construction in set theory. Definition 8 Let C be a cartesian category with objects a, b in C. The exponent of a and b is object ba in C together with a map eval: ba × a → b such that for all maps f : c × a → b there exists a unique h: c → ba such that (h × id) ◦ eval = f . Note that h × id: c × a → ba × a. Exponent objects of the form ba have a domain Do(ba ) = a and a co-domain Co(ba ) = b. A cartesian closed category, or CCC, is a cartesian category that is closed under the exponent operation. If the basic objects of a CCC are the basic types, then the exponent objects correspond to the functional types; the initial object corresponds to ⊥ and its dual is the terminal object, though it does not correspond to a type in the type hierarchy. Furthermore, coproduct

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provides us with a natural model of disjunctive types and disjunctive objects. There are many mathematical examples of CCCs. In terms of logic, we have conjunction and arrow corresponding to the type operations of product and exponent. More specifically, we can model both the introduction and elimination rules for ∧ and →. Since a CCC is closed under products, given a and b, we have a × b and b × a, which corresponds to the conjunction introduction rules on formulas that correspond to types: A, B A∧ B. The projection π1 given with a product object corresponds to a conjunction elimination inference rule: A ∧ B A. Similarly the projection π2 yields A ∧ B B . Using these, we can easily show a × b  b × a (where  denotes isomorphism), so conjunction is commutative. Turning to the → rules, suppose ac and bc are exponent objects, then ac × bc is isomorphic to (a × b)c ; this corresponds to the rule on formulas C → A, C → B C → (A ∧ B). The map eval given with exponent objects provides a categorial model of modus ponens, while the unique function h defined for exponent objects provides a model for conditional proof. This suffices to show: Fact 3 The positive implicational fragment of intuitionistic logic has a model in a CCC (e.g., Lambek and Scott (1986)). We can include an interpretation of the type quantifiers within a categorial model once we move to a construction known as a topos, thanks to the work of William Lawvere.26 A topos is a category with a terminal object, a subobject classifier, and closed under pull backs (Crole (1993), Asperti and Longo (1991)). While subobjects are a category theoretic rendition of the familiar set theoretic notion of subset (see Asperti and Longo (1991)), pull backs, or fibre products, are special category theoretic constructions that will prove extremely useful when we come to complex types. Here is their definition. Definition 9 Let C be a category and let a, b, c be objects in C, with morphisms r : a → c, t : b → c. The pull back with respect to r and t, denoted a×c b, is an object in C with two morphisms π1 : a×c b → a and π2 : a×c b → b satisfying t ◦ π2 = r ◦ π1 , such that for any d ∈ C and morphisms f : d → a and g : d → b satisfying t ◦ g = r ◦ f , there exists a unique morphism h: d → a ×c b such that f = π1 ◦ h and g = π2 ◦ h. If a category C admits of pull backs for all arrows r and t of C, then it admits 26

For a very nice explanation of how quantifiers are interpreted in a topos, see Goldblatt (1979).

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of products for all objects a, b of C. Here is a picture of a pull back: d

f h

" a ×c b

π1

'/

a

g

.

π2

  b

r  /c t

It is the structure of the whole pull back with its different maps that tells us about the objects in the type. In the category of set, a pull back forms sets of those pairs in a Cartesian product a × b that project down to the same element in c via the maps given from a to c and from b to c. It thus yields a set of equivalence classes of pairs. Fact 4 Within a topos the standard laws of intuitionistic quantification are sound.27 I will specify a particular kind of topos to model the type system and to provide the internal semantics of λ terms of TCL. This topos, call it T , includes all the basic types in ST, the simple semi-lattice of types provided for the langauge.28 The basic subtype relation of ST is modelled by stipulating that our topos include an arrow from α to β whenever ST contains α β. Given that T is a category, this ensures that the subtyping relation over simple types is transitively closed. A topos is also closed under product, coproduct and pull back as well as their duals, as well as the structures needed to interpret quantification. Thus, the topos T contains all functional types and all restricted quantified types. To extend the basic relation of subtype given by ST to more complex types, I will build a partial order within T using the arrows that model ST. I will use a restriction of the deduction relation given by Fact 4 to capture the subtyping relation.29 Essentially, this restricts the arrows that are used to define the subtyping relation. I associate the logical formula T r(α) with the type α. Principally, I need to eliminate theorems that would cause trouble for the subtyping 27 28 29

For details, see Goldblatt (1979). In subsequent chapters, I shall add a limited number of complex types as elements of the topos. There are in fact many notions of subtype that one can explore in a categorial setting. One might be to use retracts, as defined in Asperti and Longo (1991). But this seems to not give us a sensible notion of deduction, which I take to be important in defining the subtyping relation.

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relation; e.g., since A → A, then using deduction to model subtype without restrictions would give us β α ⇒ α, for any α and β.30 We don’t want that! Let stand for the consequence relation defined in Fact 4, and let Δ and Δ be defined as follows: Definition 10

Restricted deduction: α β ∈ ST T r(α) → T r(β) ∈ Δ Δ, T r(α) T r(β) and Δ  T r(β) T r(α) Δ T r(β)

Since the underlying logic is sound with respect to a topos, then so is Δ , as long as Δ itself is consistent. Definition 11

Subtyping: α β iff α Δ β.

As to the interpretation of and , let a b be the product type of a and b, which models conjunction. Given this interpretation, a b a (and b) and always exists. I will model a  b, when it exists in the type hierarchy, as the disjunctive object a ∨ b or coproduct a + b, and ⊥ as the initial object.  corresponds to the terminal object, but as is evident from the definition of subtyping, we cannot prove for any type α that α , because in the underlying logic

. Hence, I will not take  to be an element of the type hierarchy, though the categorial models all contain terminal objects. Many pleasing facts follow from the definition of subtyping and Δ . First, it is simple to prove a version of cut for Δ : X, T r(α) Δ T r(β), Y, T r(β) Δ T r(γ) X, Y, T r(α) Δ T r(γ) This means that the subtyping relation is transitive. It is also reflexive.31 In view of the internal semantics, proof theoretic equivalence implies identity and so is also anti-symmetric, as desired. Furthermore, because the subtyping relation is now based on a notion of inference within T , we can validate all of our basic rules. Fact 5 Application, Abstraction, and Substitution are all sound in a CCC and hence in the topos T .32 30 31 32

Thanks to Zhaouhui Luo for pointing this out. This follows in Δ because  is not a type. Interpret Application via Eval, Abstraction via the unique function h associated with a exponent object. Substitution is the identity rule.

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The rule from From Subtyping to Logic yields a reasonable logical relation for . In particular, Fact 6 The rule Subtyping for Functional Types is sound in a CCC and hence in T .33 The definition of subtyping also yields a converse of the Subtyping for Functional Types Rule. Fact 7

(a) α ⇒ β α ⇒ β iff α α and β β . (b) α ∨ β α ∨ β iff (α α or α β ) and (β β or β α ) (c) α β α β iff (α α and β β ) or (α β and β α )34

This implies that only functional types of the same -arity are subtypes of other functional types; more generally, is a structure preserving morphism over exponents, products and coproducts in a CCC or T . Fact 8

Simple Accommodation is sound in a CCC and hence in T .35

These facts show the quantifier free fragment of TCL to be sound and make clear the natural correspondence between category theoretic models and the proof theoretic interpretations of Type Theory or the looser application rule systems that I have appealed to in discussing the nature of concepts. We shall see extensions of this correspondence as we move on to consider more complex categorial constructions. Finally, using the constructions in a topos, we can prove: Fact 9 Type theoretic ∃ Introduction and Type theoretic ∃ Exploitation are sound in T .36 If the quantifiers are bounded in such a way as to be restricted to finite collections of types, bounded existential quantifiers reduce to finite disjunctions 33

34

35

36

The rule assumes that a a and b b . Given the intuitionistically valid deduction A ⇒ A, B ⇒ B , A ⇒ B A ⇒ B , since T r(a ) Δ T r(a) and T r(b ) Δ T r(b) by assumption, and assuming A ⇒ A, B ⇒ B  A ⇒ B , we have A ⇒ B Δ A ⇒ B . Consider the case where α and β are simple types and assume that α ⇒ β α ⇒ β . We must have proven α ⇒ β from α ⇒ β and this requires a Δ proof from α to α and from β to β , which can only be given by the subtyping relation in Δ. We can generalize this result by induction over all complex types. Note that we Δ is a restricted fragment of positive intuitionist logic. An even simpler intuitionistically sound argument suffices to prove: a ∨ b c ∨ d iff (a c or a d) and (b c or b d). Similar reasoning proves the last item in this fact. Accommodation says that if a term t must meet two type presuppositions α and β that are compatible, then t must meet their product type. This is guaranteed by the intuitionistically valid law: A → (B → (A ∧ B)). See Goldblatt (1979) and Luo (1994), among others.

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and bounded universals to finite conjunctions corresponding to finite coproducts and products that already exist within a CCC).37 Let me now turn to the internal semantics of TCL formulas. TCL makes use of the standard recursive type assignments from terms to types or objects in the categorial model given for the ordinary typed λ calculus, with type expressions denoting types. However, TCL has a special type π, which is a parameter of all terms derived from the lexicon. We must give some sort of semantic value to this type. π puts type constraints on argument positions; in effect π puts type constraints on the variables that end up occupying those positions. The effect of π semantically, then, is to make the assignment of types to variables not a single valued function from variables to types but a function from variables to a set of types. Thus, π’s semantic value is a function from variables to sets of types. The assignment of types to expressions should ideally obey the following constraint on coherent assignments. Definition 12 Coherent assignment: f is a coherent type assignment to the term λv1 . . . λvn λπφ iff ∀vi ⊥  f (π)(vi ) and f (λv1 . . . λvn λπφ) = β1 ⇒ (β2 ⇒ . . . ⇒ (βn ⇒ ( f (π) ⇒ α) . . .) only if ∀γ ∈ f (π)(vi ) βi γ. I assume that lexical entries are constructed in such a way that there is always a coherent assignment for the λ term for the entry that ensures that the λ term has a definite type. Presupposition type justification reduces the set of types assigned to each variable in f (π) to a singleton set or single valued function from variables to types, if it is successful. Lemma 1 A TCL term t has a type assignment iff there is a single valued type assignment to variables in t.38 Thus, TCL terms have a value in the internal semantics just in case the type presuppositions are all justified in the λ term reduction process. This is exactly what we need to make sense of semantic anomaly and semantic well37

38

To prove the correctness of the two subtyping rules for  finitely bound existentially quantified types, let us suppose that ∃x α A is understood  as β α {Aβ }. Clearly, there is the requisite morphism from each element of the family to β α {Aβ }, since each element is a subtype of itself. This suffices to prove the ∃ introduction rule. For the ∃ elimination rule, if there is a requisite morphism from A( xβ ) into B (this is what subtype guarantees), where β does not occur in B, then  there also exists a relevant morphism from each element of {Aβ } to B and hence from β α {Aβ } to B. Note that this also suffices to show Fact 2 as well as its generalization to all generalized property types. From left to right suppose that t: σ but that there is no single valued assignment to variables in t. Because of the mechanisms of type presupposition justification, this means that for every type assignment f there is some variable vi such that f (vi ) = {α, β} such that α β = ⊥. Computing the type of t recursively shows us that it cannot have a type. The right to left direction is proved by an induction on the complexity of TCL terms, using Fact 5.

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formedness. Since I have shown that the basic rules of TCL are sound in the model, we can now show: Fact 10 Any λ term t with a coherent assignment f in a structure A such that  for all variables vi in t, f (π)(vi )  ⊥, will have a definite type in A. To prove this fact, note that the lexical entries are assumed to have a definite  type by hypothesis. The condition that f (π)(vi )  ⊥ for all variables vi in t ensures that either Binding or Accommodation will reduce the type presuppositions assigned to the π parameters in t to singletons. Lemma 1 now entails the result. Another interesting model is the set of computable functions or computations over a countable domain closed under function space and cartesian product. This is another way of thinking of the proof theoretic model. I’ll call this model F . We can define an interpretation τ of types and of in F recursively: • • • • •

τ(⊥) = the empty function For a simple type α, τ(α) = {(a, 1): for some inhabitant a of α} τ(α ⇒ β) = { f : τ(α) → τ(β)} τ( ) = λx, y ∀ f ∈ y∃g ∈ x g ⊆ f Application is interpreted as the operation of applying a function to an argument. • Abstraction is interpreted as the operation of function construction.

Fact 11

The basic rules of TCL are valid in F .

In this section, I have set out an abstract, categorial model for types as proof objects which abstracts away from the details of the proof system. I’ve also gestured at a more concrete model F . This model ensures the soundness of the rules of TCL presented so far. In the next chapter, I take a look at a particular type constructor that also has a categorial interpretation.

5 The Complex Type •

An important question about TCL remains open from the last chapter: what sort of general type constructors do we need for investigating the meaning shifts evident in coercion, aspect selection, and copredication? The simply typed lambda calculus distinguishes between simple types and functional types, and TCL requires the existence of bounded quantified types. But we need other complex types to model aspect selection and copredications involving aspect selection, which are the subject of this chapter. A theory that invokes complex types has to say how these types get used in the analysis of the phenomena. And to do that, we need to provide a way of exploiting complex types and deciding what information flows from them— i.e., what are their effects on logical form and truth conditions. Underlying this system of type manipulation must be a semantics or model of what such complex types are. Given the nature of the type system and the separation between logical forms and types, two questions need to be answered: (1) How does the semantic conception of such complex types interact with the type hierarchy? And (2) how does information about types interact with logical form? In this chapter I investigate answers to these questions with respect to the complex type •, which has received the most scrutiny in Asher and Pustejovsky (2006) and Cooper (2005).

5.1 A type constructor for dual aspect nouns Do we need a separate type constructor to model the predication of properties to selected aspects, or to model the behavior of dual aspect nouns? I claim that we do, since aspect selection is a distinct form of predication from others. The intuition is that objects like books or lunches have two distinct aspects. Books, for instance, appear to have both a “physical” aspect and an “informational”

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aspect; which is selected in a predication depends on the type restrictions imposed by the predicate on its arguments. Books have a “dual” nature—two conceptualizations, if you will, that are equally “true of” or “faithful to” the object. Book is a paradigm example of a dual aspect noun. In one sense, almost every noun is a dual aspect noun. Consider (5.1) Ducks lay eggs and are common to most of Europe. (individual and kind) (5.2) Snow is common this time of year and all over my back yard. (kind and mass) (5.1) and (5.2) instantiate a general pattern—a copredication that involves predication on a kind as well as a predication on an individual or portion of matter. That is, while predicates like lay eggs apply to individuals, predicates like is common or is extinct apply, not to individuals, but to species or what linguists since Carlson (1977) have called kinds. In English the bare plural construction and the simple definite or definite DPs, a N or the N, where N is any noun, can, given a suitable predicate of which it is an argument, refer to a kind or provide some sort of quantifier over individuals. Note that kinds and individuals are incompatible aspects in the sense that they have different, even incompatible, metaphysical individuation and identity conditions. Besides the kind/individual duality, there are many examples of more specific, dual aspect nouns:1 (5.4) Mary picked up and mastered three books on mathematics. (physical object and informational content) (5.5) Je ne suis qu’un roseau mais je suis un roseau pensant. (Pascal) (physical object and thinking agent) (5.6) That is a lump of bronze but also Bernini’s most famous statue. (portion of matter and artifact) (5.7) Le prix Goncourt is 10000 euros and a great honor not accorded every year. (amount of money and prize and winner-person) (5.8) The lecture (interview, speech) lasted an hour and was very interesting. (event and information) (5.9) The bank (location) is just around the corner and specializes in sub prime loans. (physical object/ location and institution) 1

These copredications happen at the level of speech acts as well.

(5.3) Could you pass the salt please? Asher and Lascarides (2001) argue that please types its sentential argument as a request, while the syntax of (5.3) types the clause as a question, and this forces the discourse constituent introduced by (5.3) to have a complex type question • request. Asher and Reese (2005) and Reese and Asher (2007) extend this notion to biased questions which are both assertions and questions.

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(5.10) The canvas is immense, and, as an example of a bygone school, interesting to all art lovers. (adapted from an article of the New York Times, March 24, 1894) (physical object and informational object) (5.11) The promise was made but impossible to keep. (speech act (event) and proposition) (5.12) The belief that all non-Christians are immoral is false but persists in many parts of America. (informational content and state) (5.13) Mary’s testimony occurred yesterday and is riddled with factual errors and inconsistencies. (event and information content) (5.14) The very same thought that caused Mary to shudder amused Kim. (event and information content) (5.15) The house contains some lovely furniture and is just around the corner. (physical object and location) (5.16) Most cities that vote democratic passed anti-smoking legislation last year. (population and legislative entity) (5.17) Lunch was delicious but took forever. (food and event) We’ve seen evidence that such dual aspect nouns are ambiguous according to the contradiction test. However, dual aspect nouns and their aspects are certainly distinct from accidentally polysemous nouns like bank which don’t support copredication. Intuitively, dual aspect nouns should have a type in which both constituent types, the types of the aspects, are in some sense present. The copresence of these two types can lead to different individuation criteria for the same objects, as we saw in the last chapter and as we’ll see in the next. Nevertheless, postulating a new complex type for dual aspect nouns is controversial. The traditional story about the data involving dual aspect nouns is that there is a sort of coercion going on. For (5.4a) the story postulates that books are physical objects but that they have associated with them an informational content. Sometimes predicates apply to books properly speaking while some predicates apply to the associated informational content. These cases, many argue, are examples of sense transfer. Why should we need anything else? One objection to this proposal is that sense transfer functions don’t tell us that there’s anything special about lunches, books, and other elements that seem to have two constitutive types at once. Real books have to exist in some physical form (even e-books), but they also have to have some information content. The physical and informational aspects of books bear a very different relation to each other from the weak association that holds between me and a vehicle I am driving. If sense transfer functions capture the latter, they fail to

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explain what’s special about books, lunches, and other objects that I claim are of • type. In general it’s not easy to tell when a term is a dual aspect term. The linguistic test for such terms has two parts: first they must support copredications; secondly, predications that pick out a particular aspect of the objects associated with these terms must be able to affect the way such objects are counted or individuated. This second property of dual aspect terms is not shared by terms in standard coercive contexts. Consider the sentences below involving book, question, and newspaper, all of which are claimed to denote objects with multiple aspects in the literature. (5.18) a. The student mastered every math book in the library. b. The student carried off every math book in the library. (5.19) a. The teacher answered every student’s question. b. The teacher repeated every student’s question. (5.20) a. John bought two newspapers yesterday. (physical object reading) b. Rupert Murdoch bought two newspapers yesterday. (institution reading) The quantification over books in (5.18) is sensitive in one case to its informational aspect, and in the other to its physical aspect. In (5.18a), we simply quantify over all informationally distinct individuals without reference to the instantiations of these informational units; it is entirely unnecessary, for example, for the student to have read every distinct copy of every book in the library. In fact all of the math books in the library could have been mastered without the student’s ever having gone to the library at all—he could have read and mastered them via Google Books. In (5.18b), however, every physical individual must have been taken in order for the sentence to be true. Similar remarks hold for the distinction in (5.19b): one act of answering the same question posed on multiple occasions will count as an answer to each question; this is not the case with the act of repeating the question, however, since this refers to copying each individual speech act rather than providing the informational content of the answer. The same remarks apply to the pair in (5.20). Finally, the ability of almost any noun to refer to a kind or to a set of individuals entails that most nouns pass the quantification test with respect to their kind and individual aspects. Now contrast these examples with cases where coerced type shifts have been postulated, either of the Nunberg variety or the GL kind:

134 (5.21) b. (5.22) b.

The Complex Type • a. Everyone is waiting to go home. Everyone is parked out back. a. John enjoyed many cigarettes last night. John enjoyed no cigarettes last night.

In neither (5.21a) nor (5.21b) do we quantify over cars. (5.21b) says something like everyone came in a car that’s parked out back. And in (5.22a), while the object of enjoy is plausibly an event, it’s the event of smoking many cigarettes; the meaning of (5.22a) is not that John enjoyed many smokings of a cigarette or cigarettes. If coercions changed the denotation of the object noun phrase or DP, we would predict (5.22a) to be true when John enjoyed many smoking events that involved just a few cigarettes. The meaning or denotation of the object noun phrase or DP, and the things it quantifies over, don’t change; rather the argument of the verb becomes some meaning related to the noun phrase. Similar remarks apply to (5.22b). So the logical form associated with the object DP doesn’t shift when the coercion takes place. In contrast, the logical form of the whole noun phrase involving dual aspect nouns does seem to shift when we predicate a property of an aspect of an object. So predications involving aspects and predications involving coercions are not the same thing. One could attempt to use Nunberg’s transfer functions on different terms to simulate this behavior. To handle coercion, transfer functions could apply to arguments of verbs; whereas to handle aspect selection, transfer functions apply to the head noun phrase within the DP. This gets the counting arguments right, but copredication is going to be a problem. By either using the standard denotation or the shifted denotation of the head noun book on magic, we can satisfy the type requirements of one of the coordinated verbs. But we can’t satisfy them both. (5.23) John’s mother mastered and then burned the book on magic. If the use of transfer functions on terms does not look promising, then alternatively we can exploit standard approaches to ambiguity and postulate two senses of book: the basic physical book and “informational books” which have the following logical from: (5.24) i-books: λx: i∃y: p (book(y) ∧ info(y) = x) The ambiguity approach hypothesizes that book is ambiguous between i-book and p-book. Although standard tests for ambiguity indicate sometimes that dual aspect nouns are ambiguous, it would be wrong to treat all ambiguous terms in the same way. We’ve already seen that accidental and logical polysemy differ

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in several linguistically discernible ways—for instance, logically polysemous words pass the copredication and anaphora tests, while accidentally polysemous terms don’t. Furthermore, logical polysemy is not just a matter of association. The association between cars and individuals who drive them is at least as clear as the informational relation between physical objects and informational objects, but we can’t say (5.25) I’m parked out back and am an old Volvo anymore than we can say the bank specializes in IPOs and has eroded because of the recent floods. Nor is the peculiar predicative behavior of dual aspect terms versus other terms that undergo coercion a matter of semantic versus pragmatic ambiguities or type shifting. The Nunberg examples are often taken to be examples of a pragmatic shift, whereas the sort of type shifting or ambiguity postulated for books and lunches are taken to be semantic. Nevertheless, this can’t be the whole story, as there are semantically ambiguous words like bank that function equally badly with coopredication. Metaphysically, there is a big difference between objects that are of • type and objects that are not. Books are equally physical and informational objects, but there is no sense in which I am equally a person and my car. Such big metaphysical differences should be and are reflected in our conceptual scheme, that is, in the system of types. This is one principal motivation for introducing a complex type • for such objects. Let’s examine the ambiguity thesis and the postulated difference between ibooks and p-books a bit further. The distinction between i-books and p-books may seem a bit strange but it corresponds to a distinction between types and tokens. Barbara Partee has suggested (p.c.) that one might handle the quantificational ambiguity seen above with read and carry off by treating the entire phenomenon as an instance of the type/token distinction. According to this suggestion, (5.18a) makes reference to the type while (5.18b) refers to the token. There appear to be several problems with this solution. Simply reducing the above phenomenon to an ambiguity between i-books and p-books or types and tokens does not solve the problem of how the copredication works. In copredications involving the informational and physical aspects of books, we would have to say that one simultaneously accesses a type or i-book as well as a token or p-book. We would still in that case have to have a relational analysis of the token to the type and we would need to complicate our analysis of copredication in the same ways as we are presently envisioning for aspect selection. Furthermore, there are cases where reference seems to be made to more

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objects than are available under a simple type/token analysis. For example, in (5.26b), quantification is over informational tokens which are distinct from the actual physical object tokens that would be available. (5.26) a. John hid every Beethoven 5th Concerto score in the library. b. John mastered every Beethoven 5th Concerto score in the library. Hence, for an object of complex type, if there are type and token interpretations available for each component type of the dot, then the underlying typing is more complex than originally countenanced. I can sharpen this observation. Consider examples of real quantification over kinds. (5.27) a. John has stolen every book there is. b. Frances has grown every wildflower in Texas. While there are (improbable) interpretations exploiting the token reading of the quantified expression in each example above, the type interpretation is more felicitous. Let’s now see what a kind interpretation of the quantifiers in (5.18) would be. The verb carry off in (5.18b) would select for physical instantiations, or tokens, of kinds of books, while master would select for kinds of books. But then we will postulate a separate “book kind” for War and Peace, Anna Karenina, as well as for Pride and Prejudice. This stipulation, according to which we have a kind for each particular informational object, would get us what we want but this notion of kind is quite distinct from what we take to be kinds of books (novels, philosophical tracts, etc.), which group many particular informational objects together. The standard type reading of every book is distinct from the quantification over the particular informational content interpretation of the dot object in sentence (5.18a). Furthermore, making the dual aspect nouns ambiguous with respect to their type leads to real problems in the analysis of copredications. Which type for book do we choose in dealing with (5.4), for instance? Neither one on its own will do. So we must also postulate either sense transfers or ambiguities among the predicates of such objects. For instance, we could make master ambiguous between its normal sense where it requires an object of informational type and one where it takes an object of physical type as in (5.28): (5.28) p-master: λx: pλy∃z: i (master(y, z) ∧ info(x) = z) Alternatively, we could have an informational pick up.2 We now have multiplied ambiguities manyfold in the theory. We have i-books and normal books 2

This sense does indeed seem to exist, but it’s not the one at issue in the example (5.4).

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(or, vice versa, books as basic informational objects and p-books) and we also have normal mastering and p-mastering, or normal pickings-up and i-pickingup. In fact we can’t even choose between these alternatives; the dual nature of books says both are equally important. So we have in fact a “second-order” ambiguity in this analysis. A great many ad hoc decisions have to made now in lexical semantics. Moreover, books and lunches have only two constitutive aspects, but what about cities and other things that have more than two aspects? To be sure these are not “expensive” ambiguities; it’s easy to understand how one sense is related to the other, provided we spell out the functions linking them appropriately. But English and other natural languages don’t seem to exhibit these ambiguities. Worse, the account predicts that intuitively a priori false or odd sentences can be true. Consider, (5.29) John burned a book and then mastered it. Let’s suppose that the pronoun must find an antecedent with an i-book sense because master takes as a direct object something of informational type. This forces us to understand book in the “i-book” sense. Suppose now that burn requires as a direct object something of physical type. To handle the copredication, we must postulate a shift in the type of burn to an i-book sense: John burned some copy of an i-book. The trouble is many physical books may be instantiations of the same i-book. So this theory predicts a reading of (5.29) where John burns one copy of some i-book, and then masters a different one, which is perfectly possible. Perhaps there are other ways of resolving the ambiguities to get the right truth conditions for (5.29), but there are no principled ways of ruling out incorrect readings like the one I’ve just described. The traditional theory has to stipulate that books are ambiguous between physical books and i-books, and it also has to stipulate an ambiguity with respect to predicates of books; and this leads to problems. Thus, I will postulate • types for empirical and conceptual reasons.

5.2 Some not-so-good models of • types Now that I have motivated the need for a new complex type, let us return to the two questions with this chapter began: (1) How does the semantic conception of such complex types interact with the type hierarchy? And (2) how does information about types interact with logical form? Let’s see how these questions play out with the complex type •.

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5.2.1 • types as intersective types There is one model for • types already available to GL. Within the typed feature structure framework, types are modelled as propositions true at nodes; therefore, complex types have no natural interpretation, if the complex typeforming constructor has no apparent propositional operator correlate. The only possible propositional operator correlate is conjunction or (if one thinks of propositions in terms of sets of indices) intersection. This would mean that • types would in effect be intersective or conjunctive types (Coppo and Dezani 1978), with the following axiom governing conjunctive types of the form α β: • Conjunctive Types Axiom: x : α β iff x : α ∧ x : β This model of • adopts the following conjunctive types hypothesis (CTH). Let’s assume, as most work in lexical semantics does, that the type hierarchy forms a semi-lattice in which greatest lower bounds are assured to exist. Then: • Conjunctive Types Hypothesis: α • β := α β = glb{α, β}3 To see how CTH fares, let’s first see how the outlines of an account of copredication might go. Consider once again a classic copredication like (5.30): (5.30) The book is interesting but very heavy to lug around. Without going into too many details at this point, let’s imagine that the coordinated adjectival phrases place a conjunctive type requirement on the subject of the verb phrase—in this case, the subject must be both of type p and of type i. Now if we assume, again without going into details, that the type assigned to book, which is also by hypothesis p ∧ i, percolates up to the complete noun phrase as a whole, then the types match and the copredication succeeds. The problem CTH faces, however, is fundamental and stems from the basic axiom for conjunctive types. In particular, for certain dual aspect nouns that assign a variable x the type α • β, saying that x : α and x : β will entail that x can denote no object, because α and β may be inconsistent types. Two types α and β are inconsistent just in case assigning these types to any term t would make the denotation of t have incompatible properties. But hence according to CTH, α • β = glb{α, β} = ⊥, where ⊥ is the absurd type. If glb{α, β} = ⊥ in virtue of incompatible properties that objects of those types necessarily have, then no such complex type can have any inhabitants; that is, if x: ⊥, then the 3

This is of course how conjunction of types is also modelled in the internal semantics of types developed in chapter 4.

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interpretation of x relative to any points of evaluation is empty, because otherwise this semantic value or denotation of x would have to have incompatible properties that cannot be co-instantiated. ⊥ is a type with no inhabitants. Consider terms of • type like lunch or book. The term lunch supports copredications and is of the complex type that consists of a meal, an object with parts (courses, dishes), and an event, the eating of the meal. Events and physical objects have different, in fact incompatible, properties.4 Objects, from our commonsense point of view, perdure through time while events have a duration; objects are wholly present at each moment in time while events have temporal parts. So there is a strong reason to think that events and physical objects are disjoint types of entities. I’ve also already presented linguistic evidence that events and physical objects are distinct types. But that evidence points to a stronger conclusion—namely, that events and physical objects are incompatible types. Nothing is wholly an event and wholly an object, for they have incompatible essential properties: events have temporal parts, but objects don’t; objects perdure through time, but events do not; the whole event is not present at one of its temporal parts, whereas a ball or a person is fully present at each temporal instance in which it exists. These are straightforward truths of commonsense ontology. Thus, the intersection of the types event and physical object is empty. But if lunches, as I’ve argued, have the type physical object • event, then • is not to be understood as the intersection of two types or their meet, unless we want to say that there are no lunches. Similarly, one can argue that the population of a city is not at all identical to the legislative body that runs the city; a city like Austin has a million inhabitants but its legislative body consists of the mayor and the city council which has eight people in it. More generally, legislative bodies are a strict subset of the citizenry, unless we have a direct democracy where all the inhabitants constitute the legislative body. Books receive the type in TCL of physical-object • informational-object. Is it the case that physical-object informational-object = ⊥? The argument may be a bit harder to make here, but it would appear that informational objects and physical objects also have incompatible individuation properties. For instance, one important thing about informational objects is that they can have multiple concrete instantiations. Individual physical objects cannot have multiple concrete instantiations. This leads to different counting principles for informational objects and physical objects, which, as we shall see later, are at the heart of what Pustejovsky and I called “quantificational puzzles.” Moreover, these modal properties are incompatible and so it would appear that the 4

Though of course some philosophers, so-called four dimensionalists, don’t shrink from identifying all objects with event-like four-dimensional objects that course through time.

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intersection or meet of the two types is empty. Nevertheless, books are in some sense both informational and abstract objects. (5.31) a. Chris burned a controversial book. b. Chris read every book he burned. There are obviously books. So if we assume that books have a dual nature, CTH must be wrong. Intersective types don’t furnish the right model even when the two constituent types in a • type have a glb that is not ⊥, as in for example (5.32a,b). (5.32) a. The apple is red. b. The apple is juicy (is delicious). The apple as a physical object or as a food has a certain part, its skin of which one can make certain predications, viz., about its color, that don’t hold of the entire object. But if we think about types intersectively and as sets of objects, then the intersection of the type skin and food just gives us the skin of the food, and that’s not what tastes delicious or is juicy. So once again a simple analysis of a • type as an intersective or conjunctive type is incorrect. It just seems wrong to model objects of • types as instersections of types. Of course, this is an extensional construal of intersective types and I have assumed an intensional theory. But it stands to reason that such intensional intersective types should determine extensional meets in the type structure. I conclude that whatever • types are, they cannot be conjunctive types.

5.2.2 • types as pair types Another way to think of • types is as a pair or a product of types. We can consider the product construction to issue (as it does for the category of set) in a collection of pairs. • Pair Types Hypothesis: α • β := (α, β) If we think of objects of • type as inhabitants of such a collection of pairs, then each object of complex type would correspond to a pair, consisting of a component of each constituent type. This leads us to consider the Pair Types Hypothesis (PTH). Pair types can account for some of our intuitions about the different individiuation conditions of informational and physical objects.5 Suppose that 5

Thanks to Tim Fernando for this point.

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a. there are exactly two copies of War and Peace, two copies of Ulysses, and six copies of the Bible on a shelf. b. Pat has read War and Peace and Ulysses, and no other book. c. Sandy has read the Bible, and no other book. Now, consider the questions: • • • •

(Q1) How many books are there on the shelf? (Q2) How many books has Pat read? (Q3) How many books has Sandy read? (Q4) Who has read more books, Pat or Sandy?

My guess is that most people would answer: • • • •

ten to (Q1) two to (Q2) one to (Q3) Pat to (Q4)

The pairing approach gives us for the situation 10 pair objects consisting of a physical object represented by a number of the physical copy and an information content represented by the title of the book or an abbreviation thereof: • (1, W&P), (2, W&P), (3, U), (4, U), (5, Bible), (6, Bible), (7, Bible), (8, Bible), (9, Bible), (10, Bible) Given that the second element of these pairs are informational objects, it should be noted that, e.g., Bible stands for the same information content or informational object in the last six pairs. To answer (Q2)–(Q4), what matters are the second elements, the information contents, to counting how many books a person has read. Counting the first components or whole pairs is relevant for answering (Q1), but not for (Q2)–(Q4). Simple copredications are not the problem for this model. To handle copredication in the pair model, we proceed as with conjunctive types, with the difference that instead of requiring a conjunctively typed argument, the conjoined predicates of different types α, β require a pair typed argument (α, β), which is provided by a DP with a dual aspect noun in its head. But this model does have a problem, a big problem, with simple predications that require only one of the constituent types as in (3.44b), repeated below: (3.44b) The book weighs five pounds.

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The predicate weighs five pounds requires that its argument be of physical type, i.e., of type p. As p and i (the type of informational objects) are objects of a category, the product type p × i exists and furnishes a model of the complex type of book. Given categories p and i , the morphisms for the product type are guaranteed to exist. • π1 : p × i −→ p • π2 : p × i −→ i These morphisms appear to be what we need, to adjust the type book so that its type matches up with the type of the predicate in (3.44).6 Indeed, we need such a morphism or something like it to switch the type of the DP to get the right counts and the right answers to the questions I posed two paragraphs ago. It’s not enough just to be able to prove that the variable can have the appropriate type; it has to have the right type in order to quantify over objects of the right domain. Suppose, however, we use the projection π1 to isolate the p component of the book; thus, we retype the variable supplied by the DP the book as of type p. This manoeuvre coerces the term to pick out just one component of a complex object and leads to an analysis for (3.44). But it completely fails to give an adequate account of examples like those in (5.33) or (5.34). The problem is that when we use such a type projection, we end up losing the information that the variable introduced by the book is also of type i, information that we need to handle predications that occur in other clauses or with expressions that are anaphorically dependent upon the DP the book. (5.33) John’s Mom burned the book on magic before he could master it. (5.34) Mary bought a book that contradicts everything G¨odel ever said. It will not do to simply retype the term that had the • type with one of its constituent types. If we shift the book on magic to p so as to make the predication in the main clause of (5.33) succeed, then the anaphoric pronoun in the subordinate clause will not have an antecedent of an appropriate type. By being anaphorically linked to the book on magic, which now picks out an object of type p, it will also have the type p and this will lead to a type clash in the predication in the subordinate clause of (5.33). Alternatively, if we try to coerce the object of master back to an informational object, we get a typing conflict with the typing requirements of burn.7 6 7

Pustejovsky (1995) seems to have this in mind. One might think that an appeal to a sort of bridging inference could be made to rescue the view. That is, one might claim that the pronoun refers to the information content associated with the object of type p. Indeed, this seems plausible. But at the level of types, this will not

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Even worse, given the category theoretic notion of product, assigning book a product type entails that it also has the type both i and the type i. This lands us back with all the problems of intersective types. I conclude that PTH at least under such a construal cannot be right. The crucial insight needed to solve this difficulty is that the projections from complex types to the constituent types go with different terms, not the original term. So in addition to our projections on pair types, we must have function symbols f1 and f2 , which will give us new terms associated with t. We must modify the PTH to include the following axiom concerning these function symbols: • Separate Terms Axiom (STA): t : α • β iff f1 (t) : α ∧ f2 (t) : β With the relevant details now omitted, the analysis of (5.35) The book weighs five pounds and is an interesting story. under PTH and STA would have the following logical form: (5.35 ) ∃!x: p×i (book(x)∧ weighs five pounds( f1 (x))∧ interesting story( f2 (x))), where f1 (x) : π1 (p × i), f2 (x) : π2 (p × i) Unlike simple PTH, PTH + STA provides different terms for the complex object, its physical aspect and its informational aspect. No term has two incompatible types nor does any term have the intersection of the two constituent types of a • type. This approach is certainly an improvement over our previous attempts to understand •, but it complicates PTH; the projections associated with product types cannot be interpreted as providing sound typing information about a term t with a • type but rather provide information about other terms than t itself.

5.2.3 Relations between objects and their aspects Another problem remains with this analysis. STA assumes a functional relationship between an object of complex type and its aspects. This implies that there are always at least as many objects of complex types as aspects. The problem is, how do we count objects of complex types? We have seen that books as objects of complex type can be counted relative to the individuation criterion do. There simply is no way to recover the i type from the physical type projection. This would require that there be a map from arbitrary physical objects to i type objects and that does not exist. One would have to know that what one has is in effect a physical component of an object that has an informational component as well, but the formalism provided by PTH does not guarantee this. My proposal, discussed in the next section, will provide just this information.

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provided by the informational component type. They can also be counted relative to the criterion provided by the physical component type. Consider the relation between physical aspects a and a of a book b considered as a complex • type. It makes sense for us to say in the presence of a and a that: (5.36) a and a are copies of the same book b. We can have many physical copies of the same book (informationally speaking). So the individuation conditions for books in their informational aspect and in their physical aspect are different: if we count books with respect to their informational content, we get one number; if we count books with respect to their physical manifestations, we get a different number. Indeed, such individuation conditions offer yet another sort of argument for why we cannot consider physical object • information as an intersective type, as objects of informational type have different individuation conditions (and hence a different essential property) from objects of physical type. Can we count objects of complex type, where the constituent types provide two distinct criteria of individuation, using both criteria of individuation? The answer is “no,” since this yields absurd results. Consider once again a shelf of books, where there are three copies of the Bible and one copy of Jane Austen’s collected works, which contains Pride and Prejudice, Emma, Mansfield Park, Sense and Sensibility, Persuasion, Northanger Abbey and Lady Susan.8 In answering the question, How many books are there on the shelf? a person might say four counting physical volumes; but she might also answer eight, using the informational type to individuate the domain. Which of these will depend on context, certainly. But taking the pair types hypothesis as an ontological thesis—namely each pair of a distinct physical book and a distinct informational content constitutes a countable object—would yield the crazy count of 10 books. From the current perspective, that’s counting using two different principles of types, determined by two incompatible types. Thus, we can’t count objects of type α • β according to the combination of the principles of counting determined by the types α and β. We can only count according to one coherent principle of counting, one coherent individuation criterion. The cases where individuating criteria conflict calls into question the functionality of aspects presupposed by STA. Suppose we count books relative to the informational criterion. Then, as we’ve seen the relationship between books and physical aspects cannot be functional; one informational book may have several physical copies or aspects. On the other hand, if we consider the Jane Austen case again, then we see that books individuated phyiscally may have 8

Thanks to Julie Hunter and Laure Vieu for giving me this example.

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multiple informational aspects. Once again functionality fails to hold. STA presupposes something that cannot be satisfied in many cases. Further evidence for a nonfunctional relation between aspects and objects of complex type comes from the quantificational puzzle examples, which involve quantification over different aspects. I repeat the illustrative example (5.18) below. (5.18) a. The student mastered every math book in the library. b. The student carried off every math book in the library. The quantification over books in (5.18) is sensitive in one case to its informational aspect, and in the other to its physical aspect. In (5.18a), we simply quantify over all informationally distinct individuals without reference to the instantiations of these informational units. There are, typically, many different copies of certain math books in a library. It is not necessary, for example, for the student to have mastered the books by reading every distinct copy of every math book in the library—or even any physical copy of a book in the library in order for (5.18a) to be true. When we individuate books relative to their information content, there will be no functional relation between the variable ranging over books and the term ranging over the physical aspects of books. These considerations show that the relationship between objects of p • i and the physical books of type p is not a functional one, nor is it a relation of types to tokens. Instead we have two different types involved with two different counting principles, two ways of talking about tokens. STA has to be modified and complicated. In our model of • with product types, we have focussed on the set theoretic implementation of this idea. Like many others who have thought about this subject, I have implicitly assumed a naive isomorphism from the model of types to the ontological structure of objects along lines of figure 5.1. The problem is how to interpret the projection at the level of types from the complex type α • β to its component types α and β. Such projections are basic to the product construction, but we cannot interpret these projections as telling us that if x: α • β, then in virtue of the projections we have x: α or x: β. We must use STA. I have also shown that we cannot “read off” a similar projection over terms, let alone their denotations. The categorial product model of types, especially in its realization in the category of sets, helps us in understanding neither the typing of dual aspect nouns nor the nature of the objects that inhabit these types. However one might want to explicate the notion of pair object, the example of the shelf of books with Jane Austen’s collected works shows that understanding objects of • type as pairs of objects of the constituent types in the set theoretic sense yields absurd results when we attempt to count such

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π1

αO

Types:

x

βk

type

Terms:

type

f1 (t)

s

f2 (t) k

Objects:

o f

α•β

O

type

f1

denotes



π2

O

f2

t

denotes



o k

denotes



o

Figure 5.1 Naive isomorphism from types to objects

objects with the pair model. For according to the standard identity criteria for pairs, two books formalized in terms of their informational and physical aspects as a, b and c, d will be identical just in case a = c and b = d. In the Jane Austen example above, such individuation criteria would yield the unintuitive result that there are 10 books on the shelf.9 Even putting aside the arguments against having a functional relation between objects of complex type and their aspects, there is still the question, what is the interpretation of the pairing function at the level of truth conditional content and what is the analysis of the link between the semantic values of fi (t) and t? How do we spell out concretely the analogues of the morphisms π1 and π2 at the level of metaphysical constitution? We want fi (t) and t in the analysis of (5.30) to refer in some sense to the same book, but PTH + STA give us no clue by themselves. What is it to be an object of a pair type? If we knew the answer to this question, we could make progress on the relation between the values of fi (t) and t, where fi (t) is one of the terms for the projections postulated by STA. It’s not that the object is itself a set or a pair of objects! When I copredicate two properties of a book in (5.30), I refer to just one object, not two. Furthermore, that object is not a set; if it were, it could not be a physical object, which it is! The problem is that it’s in some sense once again both an informational and a physical object; we have not made much headway in understanding this puzzle. One suggestion is that we understand the dependence of the object of simple type on the object of complex type in terms of the parthood relation. In terms of 9

Of course, there is a dependence of identity criteria here: if book a is identical with book b on the physical individuation criterion, then of course they will have the same informational content as well.

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the notation of STA, fi (t) would be construed as a part of the semantic value of f .10 A lunch, for example, is part event and part food; it is the singular fusion of its parts. But normal parts of objects have names and can be referred to. This isn’t true of the inhabitants of • types like lunches. This should lead us to be suspicious of this view. Such suspicions point to a deeper problem. The presence of different individuation conditions for an object of • type like book militates against a simple mereological conception of objects of complex type as being the mereological sum of objects of the constituent types. For on such an account, such objects would have different identity conditions depending on which part one used to determine the criterion of individuation. We can formalize this situation using a relation of identity relative to some type providing a principle of individuation. Consider again two physical copies of the same book (individuated informationally). Letting = p stand for the identity relation relative to an individuation criterion appropriate for physical objects and letting =i stand for the identity relation relative to the criterion appropriate for informational objects, we have: (5.37) a. b1 =i b2 b. b1  p b2 In mereological terms, this implies that b1 and b2 have a common informational part but distinct physical parts. But then by the axioms of mereology, we have in terms of an absolute identity relation (in standard mereology two objects are equal just in case they have exactly the same parts): • b1  b2 This mereological approach predicts that in the example with the collected works of Jane Austen, we get once again the implausible count of 10 distinct objects! Thus, the mereological conception, like the pair conception of objects of complex type, seems fatally flawed. Another proposed analysis11 construes objects of complex type as collections like groups or orchestras. The latter suggestion certainly seems on the wrong track. Singular nouns that refer to groups can support plural anaphoric reference: (5.38) a. The orchestra got ready. Then they started to play the Bach suite. b. The battalion was in trouble. They were receiving heavy fire from the enemy. They called in for tactical air support. 10 11

Robin Cooper (p.c.), for instance, claims that lunches are composite objects with an event component and a food component. Also due to Robin Cooper, p.c.

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But plural anaphoric reference with lunch is crazy: (5.39) The lunchi for Chris Peacocke was very nice. Theyi pleased him too. Arguably, nice and please can take both events and meals as arguments, so we should be able to predicate this jointly of both the event and the meal. But the plural anaphora is semantically uninterpretable when the coreference is stipulated as above. Since a singular use of lunch cannot support plural anaphora, this strongly suggests that it does not refer to a plurality, in the way orchestra, battalion, and team arguably do. The alternative is to claim that an inhabitant of a • type is single but composite. Perhaps one can just bite the bullet about the counting argument given above. But mereological talk seems distinctly out of place when trying to make sense of objects like lunches. For ordinary objects like lunches, we have something like Benaceraff’s problem: an analysis of such objects in terms of a theoretical apparatus like mereology just seems wrong. (5.40) Part of the lunch is an event and part of the lunch is a meal. We readily make sense of a parthood relation among objects of the same type. Physical objects have physical parts; an apple has various physical parts, the core, the skin, the flesh, and so on. At least some events also have readily identifiable event parts. Such homogenous objects easily have causal interactions as well. A much vaguer notion of parthood must be invoked to explain the inhabitants of • objects on the mereological view. Unrestricted mereological composition aside, we normally do not think of objects as having parts of different types. Substance dualist positions concerning persons are an example of such, but much of the unintuitiveness of this view comes precisely from our inability to have a clear conception of how the various parts interact causally. Furthermore, in order to accommodate a mereological conception of the inhabitants of • types, we would have to suppose substance multi-ism. Not only would we have to worry about minds and bodies as being parts of the same person; we would have to worry about events and foodstuffs being parts of the same object, information and paper as being part of the same object, and so on. Dualism would be simple in comparison to the metaphysical view being proposed. In each case we would have to elaborate some sort of special causal or other relation telling us how changes in one part might affect another. But this seems crazy for inhabitants of • types. When I tear pages out of a book, an alteration in the physical part doesn’t cause a change in the informational part; my action changes both the physical and the information content together; it’s not that there are two parts—there just one object, the book, with two aspects. The part–whole model, at least where we understand such talk in its physical,

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spatio-temporal sense, is not the appropriate one for lunches or other objects of • type.12

5.3 The relational interpretation of • types In the previous section, we’ve seen problems for the PTH + STA hypothesis. We need to do away with the functional relation between the objects that inhabit a type that is a constituent of a • type and inhabitants of the • type. We also have a more general problem, which is making conceptual sense of an object with multiple aspects. Rather than try to ride roughshod over our intuitions about ordinary and familiar objects, I will complicate the notion of predication in “co”-predication. Predication typically involves the attribution of a property to an object considered under a certain conceptualization, which is what an aspect is.13 Aspects may be quantificationally complex: the true informational aspect of a book is an informational object of a certain kind that has one or more physical realizations. This will allow several physically distinct books to have the same informational aspect. In addition, natural language does not give a pre-eminent status to physical objects as opposed to non-physical ones. Thus, the “informational aspect” of book is just as much an object of good standing as the physical aspect of book. It is these thick individuals (Kratzer 1989) that we count and quantify over.14 Our primary ontological objects are thick or clothed objects as opposed to bare particulars. Nevertheless, aspects depend on bare particulars; an aspect is, metaphysically speaking, a bare particular combined with some property or some property instance that it has (Asher 2006). We can speak of a mereological or constituent relation over these aspects, if we wish. But crucially this is not a parthood relation over the object itself, for an object is not the sum of all its aspects. Given the way I have defined aspects, the sum 12

This is not to say that mereological relations don’t support copredications; they do (the apple was red and juicy). Further, predications based on part–whole relations sometimes lead to different counting principles. Here is an example due to Magda Schwager that exemplifies this. Suppose that a company makes computers with dual processors, two CPUs for each machine. Then it appears that there are two ways of counting (CPUs or dual CPU machines) suggested for computers in the following sentence.

(5.41) The company has produced 500 computers. 13

14

Perhaps then computer in this case might count as a dual aspect noun. It is also, I maintain, what lies at the bottom of restricted predication. To consider a book as a physical object is to think of it under a certain aspect; to consider the book as an informational object is to think of it under another aspect—similarly, for other objects of • type. For details see the next chapter. Thanks to Magda Schwager for pointing out that this is related to the proposal of Aloni (2001) concerning conceptual covers for quantification.

150

The Complex Type •

of an object’s aspects cannot be identical to the object itself (since each aspect contains the object together with some property that it has).15 A lunch object is wholly an event (under one aspect) and wholly food (under another aspect). When we speak or think of lunches as food, there’s no “other part” of the lunch itself that’s left out and that is an event. The view that I propose then is not substance multi-ism but a property multiism. These properties together with objects comprise aspects, which are essential to our naive conception of objects. In ordinary language we count and quantify over objects with respect to some property—i.e., it is the aspects that determine our quantification and counting. Some objects, namely those of • type have two or more perhaps incompatible aspects and so give rise (according to context) to two or more principles of counting. But when counting or quantifying over objects of • type with two or more incompatible constituent types, we must choose one of these to guide counting and individuation. Thus, predication is constitutive of the domain of quantification. As we have seen, aspects are not parts. To say that objects are the mereological fusion of their aspects would make their aspects count essentially toward their individuation conditions. There are some aspects like information aspects or physical aspects that are constitutive of objects like books, but, as we saw, mereology predicts counting principles of objects denoted by dual aspect terms that don’t fit the facts. Another way in which parts and aspects differ is this. If an aspect of a thing exists, then the thing itself must exist as well, but this is not true of parts in general. This gives us an explanation of why something like STA is needed. Aspects are dependent upon the objects of complex type. I will codify the relation between aspects and the objects of which they are aspects with the relation o-elab, which stands for Object Elaboration. When I write o-elab(x, y), I mean x is an aspect of y, or x “elaborates” on the sort of object y is. This discussion of aspects enables us to amend our conception of • types and of the relation of the type structure to the metaphysical nature of aspects and the individuals they are aspects of. Our formal product model of • types suffered formal problems at the level of typing, but is also led to misconceptions concerning the inhabitants of a • type. The essence of • types is to provide for a morphism to an aspect in a particular predicational environment, a morphism that in fact leads to the creation of a new object that is related to the one of • type. As this object is not identical to the one of • type, this morphism does not entail the problematic typing information associated with products— namely, that if x: α • β, then x: α and x: β. Furthermore, this morphism may 15

Contra Asher (2006).

5.3 The relational interpretation of • types

151

entail a switch in individuation criteria and that hence the relation between an aspect and its parent object, construed relative to a certain individuation criterion, may not be functional. For instance, several informational aspects may be contained in one physical volume with regard to books, and one informational aspect of a book may be instantiated in many physical copies. I take a given predicational environment to license a transformation from one topos to another. A transformation maps objects in one category to objects in the other as well as the arrows of the first to the arrows of the second in such a way as to preserve the structure of the first category: Definition 13 Let C and D be categories where C has objects Obj(C) and arrows Ar(C). A transformation or functor from C into D is a pair of maps (F o , F→ ), Fo : Obj(C) → Obj((D), F→ : Ar(C) → Ar(D) such that for each f : a → b, g: b → c in Ar(C), F→ ( f ): Fo (a) → Fo (b), F→ (g ◦ f ) = F→ (g) ◦ F→ ( f ) and F→ ida ) = idFo (a) . I distinguish a particular class of transformations; I’ll call them Aspect, or A, from one topos that has • types C to another D.16 I use product to simulate the type of a functor and its argument. A takes the product of a functor type, an exponent of the form γα (or γβ ), and its argument in the initial category, a • type object α • β, into the same product in the target category D. However, in D there is a pair of morphisms, id and aspect from γα × α • β to the product of γα with a pull back. Apart from this potentially new arrow aspect, C and D are the same. Exactly what this pull back is depends on the relationship R between the aspects α and β, a relationship that I take to be constitutive of the • type. When R and its converse are not functional in both directions, the pull back will be of the form α ×P(β) P(β)[R]; this happens whenever α and β have extensionally different individuation conditions (conditions that can issue in different counts of objects and different domains). The arrow aspect moves us from a • type to a type in which one of the constituent types is available via projection to be the type for the argument of the functor γα . This move is not innocent, however, as it does transform the original • type into a different type, a different conceptualization. Hence, a new term is needed for the co-domain of aspect. To define the co-domain of aspect, we need one more definition, that of a restricted product α × β[R] for a given relation R. Definition 14 α × β[R] is the restriction of the product α × β such that for the projections π1 and π2 of α × β π1 (x) = y and π2 (x) = z iff R(y, z). 16

I need topoi here as the basic categorial construction because theses are closed under pull backs.

The Complex Type •

152

Restricted pull backs are a straightforward generalization of restricted products. We can now graph the natural transformation A and its associated arrow, aspect, as in (5.2). Assume that the natural relationship constitutive of α•β is R. A ◦ aspect ◦ πi , where π1 is the projection from the pull back to the chosen type, A ga × a • b

-

ga × a • b

. id × asp .



ga × a ×P(b) P(b)[R]

C

D

Figure 5.2 The natural transformation A and its associated arrow aspect

provides an appropriate type for our argument of the predicate represented by the exponent in the figure. Given that a • type licenses such a transformation, this tells us something about the inhabitants of a • type. Such objects are capable of showing any of their aspects in the right predicational environment. Each of the aspects has a complex relationship exhibiting the relations between the chosen aspect and collections of the other aspect. That is, under the influence of a predicational environment, an object of bullet type comes to have a pull back structure of a particular kind. Figure (5.3) once again provides a picture of a generic pull back. The pull backs I use to model • types are special in two ways. First, they are degenerate, in that the “c” objects in figure 5.3 are always isomorphic to the power object of either the “a” or the “b” objects.17 If c at the right bottom corner of the square in the picture above is the power object of b, then it will be the elements in the co-domain of π2 ◦ t (or equivalently π1 ◦ r) that count the inhabitants of the complex type. Secondly, they are restricted via the natural relation that is used to define the • type. The view is that a×P(b) P(b)[R] models a • b in its a guise, and P(a) ×P(a) b[R−1 ] models the type in its b guise. 17

This construction requires a topos.

5.3 The relational interpretation of • types d

153

f h

!

a ×c b

π1

'/ a

g

.

π2

r

 

b

 /c t

Figure 5.3 The generic pull back

Let’s consider a • type that concerns us, the type p • i. The natural relations between informational and physical aspects that restrict the pull back are exemplification and its converse, instantiation. As we’ve seen, these natural relations are not necessarily functions, but become partial functions once we lift them to power objects P(p) and P(i); i.e., instantiates: p → P(i) and exemplifies: i → P(p). Partial functions or partial arrows from a to b in the categorial setting are just the composition of a function from a subobject of a together with another total function. Given the restricted pull back structure for the aspect associated with the p • i, the “projection” functions π1 and π2 in the restricted pull back provide the relevant subobject to define the partial functions of exemplification and instantiation. More concretely, if a book is subject to a predicational environment where an i aspect is needed, the transformation A yields a pull back individuated relative to information content. Each “i-book” will map onto the collection of its physical aspects in P(p). The pull back P(p)×P(p) i[Ex], where Ex stands for the exemplification relation, counts as the same all those perhaps physically distinct books that have the same information content—thus corresponding to books informationally construed, while p ×P(i) P(i)[In], where In stands for the instantiation relation, counts as the same all those books that have perhaps differing information contents but occur in the same physical volume. Let’s consider first the “informational” pullback of p • i in figure 5.4, with Ex again standing for the exemplification relation. Given the id map from P(p) to itself, the characteristics of pull backs force π1 = π2 ◦ exemplifies and π2 to

The Complex Type •

154 U

x h

%

P(p) ×P(p) i[Ex]

/) P(p)

π1

y

.

π2

id

 / P(p)

 

i exemplify

Figure 5.4 The “I” pullback

be a monomorphism; this means that the • type acts like an i type; in particular, p • i under this transformation is counted in the same way as i.18 When we individuate books relative to their physical aspect, we have a slightly different pullback (figure 5.5) in which the individuation conditions for physical aspects of books determine the number of inhabitants of the type (by determining the number of the elements of the elements of the image of P(P) under π1 ◦ t). The “physical” pullback of p • i restricted by the instantiation relation In in figure 5.5 forces π1 to be a monomorphism. When both U x h

%

P ×P(i) P(i)[In]

π1

)/

P

y

.

π2

instantiates

 

 / P(i)

P(i) id

Figure 5.5 The “P” pullback

aspects are exploited in the predicational environment as in copredication, we 18

Note that each inhabitant in the type is understood as an arrow from the type to the terminal object.

5.3 The relational interpretation of • types

155

have two pullback squares off a common • type, and the counting principles for objects may well be different in the two squares. Thus, counting principles for inhabitants of • types will shift with the local predicational environment. Two other examples may be useful. Consider the type of lunch, which is event • p. The natural defining relationship between these two types for this type is the one according to which the objects in p are constituents of the events in event. A predicational environment in which this type is required to be event, or evt, licenses the transformation A and the introduction of the aspect arrow leading to a restricted pull back, evt ×P(p) P(p). The constituenthood relation guarantees functionality from the restricted collection of event objects to the restricted collection of physical objects but not vice versa, and hence we must use the power object construction. This construction shows that we cannot infer in this particular case that lunch also has the type p but only the type of its power object; that is, the aspect we have chosen is of some type that picks out a collection of physical objects (in this case a singleton object), which is what we want.19 Contrast this last example with one where we have α and β with the same individuation criteria. An example of this we’ll see later is person • banker. There is a functional relationship between the two; there is a function f from John to his banker aspect whose inverse is functional as well. So here aspect provides us with the simpler restricted pullback person • f banker. If pull backs serve as a suitable interpretation of • types after the natural transformations, we should be careful not to conclude that an object of • type has the internal structure of a pull back in the category of sets; we don’t want to say that an object of complex type is a restricted set of pairs any more than it is a set of pairs or a pair. The virtue of category theory is that we are not forced to this set theoretic model; we can use the pull back structure to model the relationship between an object of • type and its aspects directly. That’s the virtue of a categorial model. A final point is that • types are not product types; neither are they subtypes of product types. They produce projections only after transformation, and the projections have a distinguished term realization from the • type—that’s what the aspect morphism requires.

19

The pair type interpretation of • types must somehow block the typing inference to physical objects in this relevant case, and how to do this is not obvious in the categorial setting. Zhaohui Luo suggests a mechanism of coercive subtyping, which may be an alternative method.

156

The Complex Type •

5.3.1 Model theoretic consequences of the relational interpretation I haven’t said much about the models of the logical forms with terms of • type in the external semantics. There is one modification that we must make to the standard models in order to accommodate the inhabitants of • types. Because I have introduced terms that refer to both thick individuals (aspects) and thin individuals (individuals of complex type), we must have both in the domain. In the quantificational puzzles, we saw that counting and quantification may be directed over physical aspects or informational aspects of books, or over books as objects of complex type, depending on the predicational restriction. There is ample evidence to suggest that we count or quantify over aspects or thick individuals in the relevant circumstances as well over thin individuals. To model this, I must postulate domains for each type. Domains Dα for simple types α have their own individuation and counting criteria provided by α. But what about the inhabitants of • types? Could they simply be identical to those that inhabit the simpler types? To answer this question, we have to investigate the relation between types and their inhabitants. The following axiom, implying that identified terms must have identical types, seems right: • t1 = t2 → (t1 : α ↔ t2 : α) or, given that typing contexts are functions from terms to types: • (ITID) t1 = t2 (π) → typeπ (t1 ) = typeπ (t2 ), where π is the type parameter for the formula t1 = t2 . In fact ITID follows from TCL as a theorem, if we assume the following lexical entry for is identical to: • is identical to: λxλyλπ x = y(π ∗ type(x) = type(y)) However, in general, α • β  α; the aspect is only created under the transformation, and the morphism that links the aspect to the object requires a separate term. In particular, if α β ≡ ⊥ and hence α × β ≡ ⊥, then α • β  α, because objects of • type have some properties incompatible with the properties of the objects of type α. Together with the principle of identical types for identicals, we now see if x : α • β and y : α in any typing context C, then we can immediately infer x  y. Now suppose that Dα•β and Dα have a common inhabitant. This should make (5.42) true: (5.42) ∃x: α∃y: α • β x = y We now derive an immediate contradiction from ITID. So the inhabitants of

5.3 The relational interpretation of • types

157

α • β must be disjoint in this case from the inhabitants of α and β. This result does not follow if α and β are in fact compatible and license the same counting and individuation conditions. This leaves us with a very rich universe of objects when we consider complex types. But there is yet another complication. As we have seen, to count individuals we need a principle of counting given by a simple type. We cannot coherently count objects of • type except with respect to one of the constituent types’ counting criterion, at least if the constituent types suggest two distinct criteria. So we mustn’t count the physical aspect of a particular book and the informational aspect of a book as two different books. But we can count books either as informational or as physical objects (though not coherently as both). • one way of counting: informational object with a physical realization • another way of counting books: physical object with an informational content Let’s now see how this account fares with the counting arguments. Consider the Jane Austen case again, where we have one physical volume containing Jane Austen’s seven published novels together with three copies of the Bible on a shelf. We have a domain of objects of p • i type together with the i type and p type inhabitants. We should expect that given what we have determined, the principle of counting will determine the number of p • i inhabitants. We will have four with the p type criterion and eight according to the i criterion. The counting criterion here determines the cardinality of the model! If we graph the Jane Austen situation using lines for the o-elab relation (the solid lines show the individuating aspects while the dotted lines determine the relevant aspect collections in the power object), we have the picture in figure 5.6 for the case where we individuate the p • i inhabitants, b1 , b2 , . . . via the p type. If we individuate with respect to the i type, we have the picture in figure 5.7. The number of p•i inhabitants individuated physically is in 1–1 correspondence with the physical aspects of the p • i objects while the inhabitants of p • i type are in 1–1 correspondence with the i inhabitants, the informational aspects of the book objects. This is a consequence of how we have treated • types in our categorial setting. Does this mean that we have in effect two models with two different sets of inhabitants for book, depending on which criterion of individuation is chosen? Not necessarily. But it does force us to the position that counting requires a criterion of identity and individuation, which is part of the doctrine of relative identity.20 The bare objects of • type are counted and individuated relative to 20

Thanks to Magda Schwager for this suggestion.

The Complex Type •

158 bH  1+ C

bO 2 C

 + CC C  + C  + C + C  C +  C + C  + C  C + C  + C

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i2

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C

C

7

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7

C

7

C

7

+

+

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+ + 7 C + 7 C C 7 + C 7+ C 7+ C 7

i8

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p1

p2

p3

p4

Figure 5.6 Books individuated physically

bO 11 . .

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Figure 5.7 Books individuated informationally

one of their constituent types. Typically, criteria of relative identity are typically understood as equivalence relations over the basic individual, but this is not an option generally from the perspective of natural language metaphysics. Fine (1982) takes physical individuals to be basic in a theory that has some similarities to what I have proposed. But as we’ve seen in some of our examples, there might not be enough physical individuals to get the right counting conditions for objects individuated in another way. And it’s not clear that physical objects should be the basic sort of individuals in natural language metaphysics. Finally, this makes our aspects complex set theoretic constructs, equivalence

5.3 The relational interpretation of • types

159

classes of basic objects, and this seems objectionable for the reasons that I’ve discussed earlier; this view also has the very unintuitive consequence that the abstract object now changes when some of the physical copies are destroyed.21 Perhaps a better way to understand my perspective on relative identity is that different predicational contexts will make available different criteria of individuation. We should relativize the domain of quantification in a world to a criterion of individuation, and for objects of • type the choice of individuation criterion will depend on the predicational environment. In fact, we should predict that the same discourse may select distinct criteria of individuation for the same • type. With some contextual help, this seems to be possible. We can switch counting criteria in mid discourse using expressions that refer back to the same objects, as in (5.43) or as in (5.44). (5.43) There are three copies of the Bible, three copies of Emma, and four copies of Formal Philosophy on the shelf. Thus there are ten books on the shelf. Fred has read Emma, the Bible, and Formal Philosophy, that is, three books. Yet Fred has read all of the books on the shelf. (5.44) The Best of Thomas Hardy is three books in one.22 This is predicted by the categorial model: successive applications of the natural transformation A will yield two different pull back squares, each selecting a different counting principle. Different counting principles will go with different predicational environments. Thus, we see that discourse context, and in particular the predicational context, can shift the cardinality associated with the domain of a • type by shifting the criterion of individuation.23 Lest one think that only p • i objects cause problems with domain shift, consider the following cases.24 Suppose that a county must by law have five judges each with a different jurisdiction. John happens to fill two of those functions, the other three by three distinct people. Are there five judges? Has the law been fulfilled? It would seem so; there are five judges, but only four people. But that is because the individuation conditions for a judgeship’s being filled given by the law are different from the individuation conditions for personhood. Counting problems arise whenever aspects come with distinct individuation conditions.25 21 22 23

24 25

A criticism that was made of Frege’s definition of number, where, e.g., the number 2 was identified with the set of all two element sets. Thanks to Louise McNally for this example. For a view of how to handle • type phenomena without such a type, see Bassac et al. (2010). I don’t think this approach does justice to the counting arguments I’ve advanced here and leans towards an ambiguity solution, which as I’ve argued above isn’t satisfactory either. Thanks to Julie Hunter for this example. Another example has to do with the much discussed statue/lump of clay object, Lumpel. That said, not all complex types introduce distinct or even incompatible individuation and

160

The Complex Type •

There doesn’t seem to be any special criterion of individuation or counting for aspects in general. In fact if you stop to think how many aspects objects have, it’s in general impossible to answer this question. This is because aspects involve a conceptualization of the object and they can be created almost at will from any property that an object has in principle—this is what happens in fact with restricted predication, as I’ve already said and will develop in detail in chapter 7. So in general it doesn’t make sense to say that there are just so many thick individuals in our models. However, we could perhaps force such a counting by introducing a type aspect into the theory, but this is not part of the normal system of types—it’s kind of like counting sakes.26

5.4 Subtyping with • I’ve given an abstract model of • types using the natural transformation A and pull backs. In fact, we can take • types to be defined by the double square of pull backs and the transformation A. Given our general notion of subtyping outlined in the previous chapter, we can apply this to •, if we make use of our interpretation of subtype in category theoretic models. So we need to see how Δ applies to pull backs and then to • types. A natural extension of Δ consists in adding to Δ the arrows that define how the • type interacts with its predicational environment. The transformation A for aspect selection, however, is peculiar in that it has the effect of introducing a new term linked to the one with • type. The arrows introduced in Δ are then of the form: A(α•β)×γα → α. To check that a • type α is a subtype of a • type β, we need to check that whenever the transformation A applies to one • type α, it applies to β and yields an equivalent pull back. And for our particular type of pull backs, this means that the arrows in the two pull backs must match; the projections for α must be subtypes of the projections in β.27 From the definitions in chapter 4, it follows immediately that in general a • type is not a subtype of one of its

26

counting criteria. In chapter 7, I argue that as phrases introduce complex types. But many, indeed most, of these don’t change individuation conditions. Consider the complex types given by as a janitor and as a salesman on e-Bay. We do not want to count John as a janitor and John as a salesman on e-Bay in two different ways, and we don’t have to, since janitors and salesmen on e-Bay arguably have the same individuation and counting criteria as persons. While we don’t count aspects, we can conjoin two restricted predications to denote a plural collection of aspects demanding plural agreement with its predicate, as pointed out to me by David Nicolas.

(5.45) John as a gay stripper and John as a banker are a weird combination. 27

This provides additional support that aspects are indeed objects in the model. This corresponds to the type overloading notion in Chen and Longo (1995), Longo (2004).

5.4 Subtyping with •

161

constituent types, nor are the constituent types subtypes of it. The • types have their own subtype hierarchy. There is one peculiar case of subtyping that involves the type γ • γ. In this case, A does not yield a distinct construction depending on the predicational environment. The natural relation here between γ and itself is that of identity, and so the pull back associated with γ • γ is γ ×γ γ[=]. Given the definition of a restricted pull back, we have a unique projection from γ ×γ γ[=] into γ. This morphism counts for establishing : Fact 12

Closure of a type γ under pull backs: γ ×γ γ[=] γ.

Recall that is a partial order. Thus, α = β if α β and β α. Fact 13 Idempotence: α • α = α.28 Fact 14

Simple types to •: α, β γ → α • β γ.29

Fact 15

Converse to Simple types to •: α • β γ → α, β γ.30

An immediate consequence of this is that, for all α, β e, α • β e. Fact 16 1. 2. 3. 4. 28 29

30 31

32

33

34

Subtyping and • Types

α • β = β • α.31 α • ⊥ = ⊥; α • β = α, provided α β.32 α β, γ δ iff α • γ β • δ, provided the • types exist.33 (α • β) (γ • δ) = (α γ) • (β δ), provided these both exist.34 This follows directly from our discussion of Closure under pull backs. The assumption guarantees there are structure preserving morphisms f : α → γ and g: β → γ. Composing these functions with the projections given by the pull back for α • β yields a pair (π1 ◦ f, π2 ◦ g) which provides the required morphism from α • β into γ ×γ γ[=], or γ • γ. Closure under pull backs gives us the rest. Given that α • β γ means that α • β γ • γ, we must have α γ and β γ by the structural requirements on subtyping. Neither the transformation A nor pull backs are sensitive to the order of the constituent types, though the pull backs are sensitive to which predicational environment is in force, and which projection from the • type is selected by A. Proving that ⊥ α • ⊥ and α α • β follows from Simple Types to •. Given Idempotence, we can show that α (i.e., α • α) is a subtype of the degenerate pull back α ×α β[μ] by using the maps id and the map μ provided by the subtyping relation from α into β. From left to right, the morphism from α • γ to β • δ is given by the pair of arrows ( f, g), where f, g are the morphisms given by the premise. The structural features of the objects are preserved by the construction and by the assumption that α β and γ δ. For the right-to-left direction, given α • γ β • δ, we have a morphism h from one • type to the other, and given our requirements, this means there must be morphisms from the co-domains projections of one to the co-domains of the projections of the other. By definition, (α • β) (γ • δ) α • β and also (α • β) (γ • δ) γ • δ. Now given that we have a subtyping relation between (α • β) (γ • δ) and a • type, (α • β) (γ • δ) must itself be a • type, say X • Y. Using 16.3 in the right-to-left direction, we haveX α and X γ; i.e.,

162

The Complex Type •

5. (β • δ) γ = ((β γ) • (δ γ)), provided these both exist.35 6. If α β = ⊥, then α • β α = ⊥ and α • β β = ⊥ if they are defined.36 In view of 16.6, p • i  p and p • i  i, which is as desired. Also p • i  ⊥. This can be expected whenever the individuation and identity conditions for things of type α are incompatible with the individuation conditions of things of type β. Finally, while book artifact, p • i, a supertype of book, is not. The theory leaves open the possibility that there are “natural” objects of the • type. From a proof theoretic perspective, these facts make sense. Consider 16.2. Given that from a proof that an object has the type α • γ we can get a proof that it has type β • δ, then for any aspect of the object for which we can prove that it is of type α, that aspect must also be of type β. Similarly, for any aspect of type γ, it must be of type δ. We cannot, however, in general infer that given t: α • β, t: α(β).37 What the presence of the projections provide is the inference: t: α • β t : α(β), where t is the term for an aspect of the • type. At the type level, this is expressed using the transformation A and the arrow from A(α•β)×γα to α×γα . This means that we will need to treat • terms in a special way when it comes to exploiting • types in justifying type presuppositions, a way that I turn to now.

35 36 37

X α γ. Similarly, Y β δ. Using Fact 16.3 in the left-to-right direction now, we have: X • Y ((α γ) • (β δ)), which is what we needed to show. Assuming that (β • δ) γ exists, ((β • δ) γ) = ((β • δ) γ • γ). By 16.3, we now have the equivalence desired. Assume to the contrary that α • β α = γ  ⊥. So γ (α • β). But by our requirements, γ β. But this means that α β  ⊥, which is contrary to assumption. So coercive subtyping is not valid in this system.

6 • Type Presuppositions in TCL

Having motivated and studied the properties and semantics of • types, I now turn to the way they influence the TCL rules for composition and presupposition justification. So in addition to the types we defined in chapter 4, I add to the TCL set of types a finite set of types of the form α • β, where α and β are well defined types. From the perspective of the λ calculus rules of application, • types behave pretty much like simple types; while they affect the subtyping relation in the way discussed in the last section, the effects of the internal structure of the complex type on the basic rules of the λ calculus are otherwise nil. The role of • types in type presupposition justification, however, is much more involved; the rules of • type presupposition justification exploit the internal structure of the • and introduce terms for its aspects. I turn to this now.

6.1 How to justify complex type presuppositions The reader may have wondered why I bothered with the system of type presuppositions. Everything done up to now in TCL could be done in a slight extension of the λ calculus to take account of Simple Type Accommodation. However, • types present another way of justifying a type presupposition; and to make this sort of justification clear and cogent, we need the flexibility of TCL. Suppose, for instance, that a predicate passes a presupposition to its argument that it needs something of type p. If the argument is itself of type p • i, the predication should work, if the predication is interpreted as applying to an aspect of the argument of type p. This is a distinct sort of presupposition justification. In such a case, we cannot appeal to Simple Type Accommodation (which, as we saw, generalizes Binding). Simple Type Accommodation takes two type presuppositions and combines them using the meet operation. But,

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• Type Presuppositions in TCL

as we’ve seen, it can happen that α • β α = ⊥, if α β = ⊥. This implies that type requirements involving • types are not satisfiable using Simple Type Accommodation, even though intuitively they should be satisfiable. Moreover, this sort of presupposition justification cannot be done simply by shifting the type of one term without violating the presuppositions of a basic lexical item or running afoul of the copredication and anaphora data. We need a different rule for • type presupposition justification. In virtue of our discussion of the Seperate Terms Axiom and the natural transformation A, we know that this justification must move us, in the case we are considering, from one topos to another, and from a term of type p • i to a term of type p, which the justification process must introduce. Let’s consider, for example, the compositional interpretation of the noun phrase in (6.1). (6.1) a heavy book The interpretation of interest is the predication of the property of being heavy to the book qua physical object. Since a phrase like heavy book is clearly felicitous, some sort of adjustment should be made to allow λ conversion to take place so as to construct a logical form for the NP. In chapter 5, I introduced a lexical entry for nouns of higher type than usual so that it could convey its type presuppositions to its modifiers. The entry for book is this: : p • i)(x)(λvλπ book(v, π )) (6.2) λP: mod λx: eλπ P(π ∗ argbook 1 where mod is 1 ⇒ 1. This combines via Application with heavy’s entry, which is given in (6.3): heavy

(6.3) λP: 1λuλπ1 (heavy(u, π1 ∗ arg1

: p) ∧ P(π1 )(u))

(6.2) and (6.3) combine to give us: heavy

(6.4) λxλπλPλuλπ1 (heavy(u, π1 ∗ arg1 : p) ∧ P(π1 )(u)) book  [π ∗ arg1 : p • i](x)(λvλπ book(v, π )) Two uses of Application and Subsitution give us: heavy

(6.5) λxλπλP (heavy(x, π ∗ argbook : p • i ∗ arg1 : p) ∧ 1 book   P(π ∗ arg1 : p • i)(x)) (λvλπ book(v, π )) : p•i is, recall, an instruction that this type must be satisfied by the types argbook 1 assigned to the variables going in for that argument of book. The problem is that u is both the first argument to heavy and the first argument of book. So it has to obey incompatible typing requirements.

165

6.1 How to justify complex type presuppositions

Given that we take aspects seriously, heavy should be predicated of the physical aspect of book. Our metaphysical underpinnings and categorial model of • types justify this move: if an aspect of a thing exists, the thing itself must exist as well. By the transformation A, given an object of complex type, a relevant aspect of it must exist when the predicational environment demands it. When heavy applies to the variable introduced by book, we are in the right predicational environment for A to apply. A then moves us to a structure in which we have the object of complex type and a different but related object of the type of the aspect. This entails a change to the logical form once A has taken place, but it is the fact that the modifier is an argument of the noun that determines what sort of change must take place. It is the adjective that must justify the type presupposition of the noun. We must justify the • type presupposition of book by adding material to the predicational environment provided by the adjective. And our mechanism of percolating presuppositions via π tells us exactly which predication to attend to. The effects of the transformation A on our • type are to introduce a functor for the term that can’t justify the presupposition so as to turn it into one that can. The term that causes the problem is: heavy(x, π ∗ argbook :p • i ∗ 1 heavy

arg1

: p). Via Abstraction this is equivalent to: λv: pλπ1 heavy(v, π1 )(π ∗

heavy : p)(x). We will apply a functor to the abstracted term argbook : p • i ∗ arg 1

1

which is a physical first-order property to turn it into a property of p • i type objects that will justify the presupposition. This means that we must add a variable of type p • i and relate it to a variable of type p that can be the argument of our abstracted predicate. Our functor has the following form: (6.6) λPλw: p • i λπ3 ∃z: p (P(π3 )(z) ∧ o-elab(z, w, π3 )) The whole term in (6.6) has the type of a function from physical properties into properties of • type objects. Let’s now return to (6.5) and the derivation of a heavy book. (6.5) is equivalent via Abstraction to heavy

(6.7) λxλπλP (λvλπ1 heavy(v, π1 )(π ∗ argbook : p • i ∗ arg1 1 book   ∧ P(π ∗ arg1 : p • i)(x))(λvλπ book(v, π ))

: p)(x)

The application of the functor in (6.6) to the term, λvλπ1 heavy(u, π1 ), yields: (6.8) λPλwλπ3 ∃z (P(π3 )(z) ∧ o-elab(z, w, π3 ))[λvλπ1 heavy(v, π1 )] (6.8) reduces in the following way:

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166

(6.9) a. λwλπ3 ∃z (λvλπ1 heavy(v, π1 )(π3 )[z] ∧ o-elab(z, w, π3 )) b. −→β λwλπ3 ∃z (λπ1 heavy(z, π1 )[π3 ] ∧ (o-elab(z, w, π3 ))) c. −→β λwλπ3 ∃z (heavy(z, π3 ) ∧ o-elab(z, w, π3 )) Let us now reintegrate the result in (6.9c) into the context of (6.7): :p • i (6.10) λxλπλP(λwλπ3 ∃z (heavy(z, π3 ) ∧ o-elab(z, w, π3 ))(π ∗ argbook 1 heavy

∗arg1

: p)(x) ∧ P(π ∗ argbook : p • i)(x))(λvλπ book(v, π )) 1

Substituting the new modifier meaning for the original one satisfies the presuppositions of the head noun, since the variable filling the argument of book, w, is now of the right type and furthermore the argument of heavy, z, is no longer also the argument of book. Using our standard rules (Application and Subtitution) over and over again, we get the desired λ term for the NP heavy book. Eliminating the higher-order variable from (6.10) we get: : (6.11) a. λxλπ (λwλπ3 ∃z (heavy(z, π3 ) ∧ o-elab(z, w, π3 ))(π ∗ argbook 1 heavy

p • i ∗ arg1 : p)(x) ∧ λvλπ book(v, π )[π ∗ argbook : p • i](x)) 1 : b. −→β λxλπ (λwλπ3 ∃z (heavy(z, π3 ) ∧ o-elab(z, w, π3 ))(π ∗ argbook 1 heavy

p • i ∗ arg1 : p)(x) ∧ book(x, π ∗ argbook : p • i)) 1 c. Via Binding and Substitution: λx: p • i λπ(λwλπ3 ∃z (heavy(z, π3 ) ∧ o-elab(z, w, π3 )) heavy [π ∗ argbook : p • i ∗ arg1 : p][x] ∧ book(x, π)) 1 d. Again using Application and Substitution twice: heavy : p • i ∗ arg1 : p) λxλπ(∃z (heavy(z, π ∗ argbook 1 heavy

∧ o-elab(z, x, π ∗ argbook : p • i ∗ arg1 1

: p)) ∧ book(x, π))

heavy

and z is in arg1 , we can use Binding to satisfy the Since x is in argbook 1 presuppositions and simplify the result in (6.11) to: (6.12) λx: p • i λπ∃z: p (heavy(z, π) ∧ o-elab(z, x, π) ∧ book(x, π)) We can now apply the determiner meaning to (6.10) and get our completed logical form for a heavy book: (6.13) λQλπ∃u: p • i ct ∃z: p (heavy(z, π) ∧ o-elab(z, u, π) ∧ book(u, π) ∧ Q(π)(x)) Let’s now look at the justification of • type presuppositions when the subject is a complex • type and the predicate selects for one of the constituent types. Consider (6.14):

167

6.1 How to justify complex type presuppositions (6.14) The book is heavy.

The presupposition that the verb phrase introduces, that its argument be of type p, must be justified by the noun phrase book, which has an objectual variable of type p • i. To justify the presupposition provided by the VP at the NP in subject position, we need apply a functor to the NP logical form similar to the one we had for the adjective. This time, instead of shifting a property of physical objects to a property of objects of p • i, we must do the reverse: we must provide a functor from a property of type (p • i) ⇒ t to a property of type p ⇒ t. This is easily done now that we have the general outline of the problem before us. Let’s suppose that the verb phrase has roughly the same type translation as the intransitive verb fall. Our earlier derivations show us how to integrate the presuppositions (via Application, Simple Type Accommodation, and Substitution) into their proper places in logical form. heavy

(6.15) λPλπ∃x (book(x, π ∗ arg1

: p ∗ argbook : p • i ct) ∧ heavy(x, π)) 1 heavy

The type requirements on x are inconsistent. But book(x, π ∗ arg1 : p • i) is equivalent via Abstraction to: argbook 1 heavy

(6.16) λyλπ book(y, π )(π ∗ arg1

:p ∗

: p ∗ argbook : p • i ct)(x) 1

To resolve the type mismatch, we need to predicate is heavy of an aspect of the book, its physical aspect. Thus, we need to apply to the λ term in (6.16) the functor in (6.17) that takes a property of • type objects and returns a property of physical objects: (6.17) λP: (p • i) ⇒ (Π ⇒ t) λv: p λπ ∃w: p • i (P(π)(w) ∧ o-elab(v, w, π)) Applying (6.17) to λyλπ book(y, π ) we get: (6.18) a. λPλvλπ∃w(P(π)(w) ∧ o-elab(v, w, π))[λyλπ book(y, π )] b. −→β λvλπ∃w(book(w, π) ∧ o-elab(v, w, π)) When we replace (6.18b) for the original λ term in (6.16), the typing of v and w in (6.18a–b), satisfies all of the binding requirements placed on π in (6.16). heavy The reason is the same as before: w is in argbook but not v, and v is in arg1 1 but not w. Furthermore, w and v are specified to be of the right type to satisfy their respective type requirements. We get as our final result: (6.19) λπ∃x: p∃v: p • i ct (book(v, π) ∧ o-elab(x, v, π) ∧ heavy(x, π))

• Type Presuppositions in TCL

168

Generalizing from these examples, there are two cases of presupposition justification particular to • types depending on which term provides which type presupposition: one where we require a functor for justification that takes us from a property of • type objects (or a property of a property of • type objects) to a property of objects of a constituent type (or a property of a property of objects of a constituent type) and one where we require a functor for type presupposition justification that takes us in the other direction. Both of them implement the effects of the transformation A and the arrow aspect, but at different levels. I now give a general statement of the two kinds of functors. Let φ be a formula with π and v free, and let π carry the information that argiP is of locally type α or β—something I will write as φ(π ∗ argiP : α/β). Suppose that π also carries the information that argQj is of type α • β. This means that the information on π looks like this: π∗arggQ : α•β∗argiP : α/β. Note that a sequence of type assignments can carry this information even if the types actually assigned to these argument positions are more specific, something which we have captured with the deductive relation on types Δ . Thus: Definition 15 A presupposition parameter π carries the sequence of type assignments β1 ∗ . . . ∗ βn iff for some π , π = π ∗ α1 ∗ . . . ∗ αn and αi βi for 1 ≤ i ≤ n. Now in addition to our assumption suppose that v is both in argiP and in argQj . Then we can introduce our F (“going forth” to the complex type) functor. Definition 16

Justifying a • type

φ(v, π), π carries argiP : α • β ∗ argQj : α/β, v ∈ argiP ∩ argQj F (λwλπ1 φ(w, π1 ))(π)(v) To define justification of a presupposition of a constituent type on a term that features a • type argument, we apply the B functor, which takes us “back” from a property of objects of • type to a property of objects of one of its constituent types. Definition 17

Justifying a constituent type of a • type

φ(v, π), π carries argQj : α/β ∗ argiP : α • β v ∈ argiP ∩ argQj B(λwλπ1 φ(w, π1 ))(π)(v) These justification rules say that when there is a type conflict involving a

6.2 Applications

169

• type, we can justify the relevant type requirement by applying to functors that allow for predications to aspects of objects of complex type. Justification rules for • types are sensitive to the type of the lambda term that needs to be adjusted, but it is a mechanical matter to adjust the functor in the right way.1 To see that these rules are correct, note that the transformed type contexts postulated by these rules must exist in our semantics if the input contexts exist. Our transfer rules fix the relation between the variables whose types stand in the projection relation α • β → α(β) to be the one provided for by the categorial semantics. The categorial semantics insures that given the predicational environment requiring α (β) and the type α • β, there is a term of type α (β) that will serve as a suitable argument. This is precisely what the transfer function together with the • exploitation rules determine. Our transfer functions say that the aspects are related to the object in the appropriate way and are thus sound.2

6.2 Applications Given our tests, almost every noun has two aspects—a kind and an individual aspect, and many nouns have more than one sort of individual aspect. Hence I assume that most nouns are typed α • κα , where κα is the kind associated with α, and α may itself be a • type. Some predicates will select for a predication of the kind while others will prompt a predication over individuals of type α. I turn now to some details of how TCL fares in its predictions concerning the quantificational test and copredications involving dual aspect nouns. 1

As a special case, consider names, which carry and can justify type presuppositions in TCL. Consider

(6.20) War and Peace is over 500 pages long. Assuming that is over 500 pages long is a property of the book in its physical aspect and that the name War and Peace is of p • i type, then we must accommodate the type presupposition of the VP within the subject DP somewhere. How we carry this out depends exactly on how we translate proper names into logical form. If we take the standard Montagovian treatement and say that the proper name introduces a quantifier λPP(wp), where wp is the constant introduced by the name, then we will supply a functor over the entire DP to get a variable of the right type to combine with the predicate. If we take Discourse Representation Theory’s (Kamp and Reyle (1993)) analysis of the contribution of a name to logical form, λPλπ∃x(x = wp(π) ∧ P(x, π)), we don’t need to postulate an extra functor type. In the case of (6.20), the functor from properties of • type objects to properties of constituent typed objects would have the following effect: (6.20) λPλπ∃x∃v(v = wp(π) ∧ o-elab(x, v) ∧ P(x, π)) 2

These rules improve upon the rules of Asher and Pustejovsky (2006) considerably. They are simpler and demonstrably sound. They enable us to prove versions of the substitution rules developed in Asher and Pustejovsky (2006).

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• Type Presuppositions in TCL

6.2.1 Anaphora and quantificational effects of presupposition justification The rules of TCL provide a treatment of complex examples involving • types like those given in the quantificational puzzle, as well as the basics of a treatment of copredication. They also allow for the anaphoric reference both to the object of • type as well as its aspect. (6.21) John’s mother burned the book on magic before he mastered it. The verb burn’s object argument must be a physical object, and so the derivation of a logical form for the main clause follows the one we did for the book is heavy. Using the B functor allows us to justify the presupposition of the verb. The subject of (6.21) satisfies the presuppositions placed on it by the verb, and integrating it into the logical form is straightforward.3 The only interesting part of the derivation of a logical form for (6.21), then, is the construction of the logical form for the VP. Let us pick up the derivation at the stage where we have put the verb and the object DP together: (6.22) λΨλπ Ψ(π ∗ argburn : p)(λy1 λπ3 ∃x (book(x, π3 ∗ argburn : p ∗ argbook : 1 2 1 burn p • i ct) ∧ burn(y1 , x, π3 ∗ arg2 : p))) The type constraints on π3 cannot be satisfied. But by Abstraction, the subformula of (6.22), book(x, π3 ∗ argburn : p ∗ argbook : p • i ct), is equivalent to 2 1   burn book λuλπ book(u, π )(π3 ∗ arg2 : p ∗ arg1 : p • i ct)(x). Using the Justification Rule for a Constituent Type, we apply the B functor, which recall is (6.23) λPλw: pλπ1 ∃z: p • i (P(π1 )(z) ∧ o-elab(w, z, π1 )), to λuλπ book(u, π ) to get: (6.24) λw: pλπ1 ∃z: p • i (book(z, π1 ) ∧ o-elab(w, z, π1 )) : p ∗ argbook : p • i ct and Applying (6.24) to the arguments x and π3 ∗ argburn 2 1 using Substitution on (6.22), we get: (6.25) λΨλπ Ψ(π ∗ argburn : p)(λy1 λπ3 ∃x∃z (book(z, π3 ∗ argburn : p ∗ argbook : 1 2 1 burn book p • i ct) ∧ o-elab(x, z, π3 ∗ arg2 : p ∗ arg1 : p • i ct) : p))) ∧ burn(y1 , x, π3 ∗ argburn 2 The presupposition introduced by burn can now be satisfied. So by Binding and Application we can reduce (6.25) to: 3

I’ll gloss over for now the details of the genitive construction John’s Mom.

6.2 Applications

171

: p)(λy1 λπ3 ∃x∃z (book(z, π3 ) (6.26) λΨλπ Ψ(π ∗ argburn 1 ∧ o-elab(x, z, π3 ) ∧ burn(y1 , x, π3 ))) Integrating the subject noun phrase, we now get:4 (6.27) λπ∃y(mom(y, j, π) ∧ ∃x∃z (book(z, π ) ∧ o-elab(x, z, π) ∧ burn(y, x, π))) We now must apply the logical form of the adverbial phrase before he could master it to the result we have. To do this properly, we should introduce event or time variables into our logical form, but this will further clutter our already complicated logical forms. So I’ll simply assume that before links two terms of type Π ⇒ t. Omitting some inconsequential details, what we get is this: (6.28) λπ before(∃y(mom(y, j, π) ∧ ∃x∃z(book(z, π) ∧ o-elab(z, x, π) ∧ : i) ∧ master(u, v, π))) burn(y, x, π))), ∃u∃v: i (u =?(π) ∧ v =?(π ∗ argmaster 1 The ? indicates that anaphoric antecedents for u and v introduced by the pronouns he and it respectively have not yet been found. What we’ve derived is the reading that the physical manifestation of the book has been burned, though the dot object book remains accessible5 for discourse binding as an anaphoric antecedent. Moreover, TCL predicts that the informational aspect dot object can be selected as the antecedent of v, as desired. A consequence of TCL’s presupposition justification mechanism is that in those cases where the predicate selects an aspect of an argument of complex type, quantification over aspects always has scope over the quantification over the object of complex type. This has certain effects. Consider (6.29) Three books by Tolstoy are heavy. This sentence has two conflicting predications. Intuitively, by Tolstoy modifies an informational aspect of book. We have not dealt with prepositional phrases so far; but they are complements of an NP, and hence modifiers of NPs. So I will assume that, with respect to type presuppositions, they behave similarly to other NP modifiers like adjectives. Following the derivation above for (6.14), we get a logical form for the DP in subject position like this:6 (6.30) λπ1 λQ∃3 v: p • i ∃u: i ((book*(v, π1 ) ∧ o-elab(u, v, π1 ) ∧ by(t, u, π1 )) ∧ Q(π1 )(v)) 4

5 6

Note that technically ct only applies to the variable x since it flows from the determiner, but it should also apply to z as well. A slight emendation to the statement of the presupposition justification rules will get that right. At least according to dynamic semantics. Book* is a predicate that can apply either to individuals or to collections thereof. See Link (1983).

172

• Type Presuppositions in TCL

When we come to integrate the verb phrase, we will get a presupposition requirement which is incompatible with the type presuppositions of the DP, forcing us to use the B functor again, which results in a shift of the quantificational domain of the DP: (6.31) λπ∃3 v: p ∃x: p • i ∃u: i (book*(x, π) ∧ o-elab(u, x, π) ∧ by(t, u, π) ∧ o-elab(v, x, π) ∧ heavy(v, π)) On a distributive reading (6.31) is satisfied iff there are three physical aspects p1 , p2 , p3 each of which is of some informational book by Tolstoy and each of which is heavy. Nothing in our semantics forces the three aspects to be aspects of the same informational book. So (6.29) has two readings—one where we have three physical aspects of different informational books, and one where we have three physical aspects of the same informational book.7 The reading that there are three physical aspects of one physically individuated book is ruled out by a natural ordering principle on aspects. This principle entails that predications pick out aspects of objects of complex type that are maximal. Let  denote the partial ordering on aspects. Then: • Partial ordering on aspects: Provided z, x, and y obey the same individuation criteria, (α β ∧ x: α ∧ y: β ∧ o-elab(x, z) ∧ o-elab(y, z)) → y  x Given this principle, if o-elab(p1 , b) and o-elab(p2 , b), then we have p1 = p2 , which contradicts the meaning of the quantifier. On our semantics of o-elab, this subformula of the logical form of (6.29) can only be satisfied if there is a distinct book (understood physically) for each distinct physical aspect. The shift in the quantificational domain of some DP due to TCL’s mechanism of type presupposition percolation and justification of • type presuppositions makes some interesting predictions. Consider (6.32), which quantifies over physical aspects of dot objects. Suppose that we assert (6.32) in a context in which some books from the library have been stolen and others borrowed. (6.32) Every book is now back in the library. TCL predicts (6.32) to be equivalent to a universal quantification over physical aspects of all books in some contextually specified domain, which presumably 7

For instance, someone might say these three books by Tolstoy are heavy while carrying three copies of Anna Karenina. One could object to the speaker with the reply, they’re all copies of Anna Karenina, but the speaker could respond with they’re all by Tolstoy. Nevertheless, there is a tendency to individuate books in (6.29) informationally. Why is the reading of three physical aspects of the same informationally individuated book difficult to get? It does seem that the modifier by Tolstoy does set the individuation criterion, which would indicate that we are dealing with an object of i • p rather than p • i. This would account then for the preferred three aspects of three informationally individuated books.

6.2 Applications

173

is the domain of books normally in the library. On either individuation of book (informational or physical), TCL predicts (6.32) to be true if and only if all the books that are normally in the library are back in it, as intuitions dictate. That is, suppose that the library contains five copies of Anna Karenina, six copies of The Possessed, and four copies of Madame Bovary, but only one copy of each has been returned. TCL predicts that (6.32) is neither ambiguous nor indeterminate in this context but false, which again accords with intuitions. These observations imply that TCL also accounts for the quantificational puzzles, an example of which is repeated below. (6.33) a. The student read every book in the library. b. The student carried off every book in the library. First let’s tackle (6.33a). Read is one of the few verbs that requires its direct object to be of • type, specifically p • i. So we do not need to apply either F or B to justify the type presupposition imposed by the verb on its object. We do, however, need to use the F functor to combine the NP book with its complement modifier, in the library. I’ll assume that libraries are dot objects as well, of type p • l, where l is short for location. The preposition in types its first argument as p and takes an argument of l type as its second argument:8   in (6.34) λΦλQλyλπ1 (Φ(π1 ∗ argin 2 : l)(λvλπ in(y, v, π )) ∧ Q(π1 ∗ arg1 : p)(y))

We can combine this with the DP the library using Justifying a Constituent Type and the “going back” functor B to get a locational property, to get: (6.35) λQλyλπ∃z: l ∃x: p • l (library(x, π) ∧ in(y, z, π) ∧ o-elab(z, x, π) ∧ Q(π ∗ argin 1 : p)(y)) This is now a modifier of a noun that can combine with book, this time using the Justifying a • Type rule, as the type presupposition of book must be justified by the type of y in (6.35). Applying the Back functor again to convert a property of objects of type p to one of objects of type p • i, within (6.35), we follow our previous derivations to get the following term with the appropriate typings of all the individual variables displayed below:9 8

9

We saw earlier that locations and physical objects belong to different, even incompatible, types, although it is an a priori truth that every physical object has a location. Note also that the entry I give here will not get the intuitively correct wide scope reading for the DP in the PP— every book in two libraries was stolen seems to mean that there were two libraries from which every book was stolen. I leave aside these difficulties here, as the points I want to make here do not involve these details. Recall, however, that, technically, all this information is encoded in π. The notation below is solely for convenience.

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(6.36) λPλπ ∀v: p • i (∃u: p∃z: l∃x: p • l (library(x, π ) ∧ in(u, z, π ) ∧ o-elab(z, x, π ) ∧ book(v, π ) ∧ o-elab(u, v, π )) → P(π )(v)) We can now apply the entry for read to (6.36). I assume that the first argument of read is typed in such a way that student justifies it and that the second argument is typed as p • i. We now use the basic rules of TCL including Simple Type Accomodation and Binding to get a finished logical form for the sentence (6.33a): (6.37) λπ ∃w (student(w) ∧ ∀v: p • i (∃u∃z∃x (library(x, π ) ∧ in(u, z, π ) ∧ o-elab(z, x, π ) ∧ book(v, π ) ∧ o-elab(u, v, π )) → read(w, v, π ))) As (6.37) shows, we get the desired quantificational reading for the direct object. That is, we have a quantification over p • i objects, not physical objects only, as desired. We now have to choose the criterion of counting and individuation appropriate to the quantificational domain. If we choose the i criterion, which is perhaps more plausible, then we get the reading that the student read every (informational) book of which there is a physical copy in the library. Note that we predict, as seems plausible, that the student could have read every book in the library even without having opened a single physical copy that is in the library. On the other hand, we could also take the criterion of counting and individuation provided by physical objects. This yields the less plausible reading that the student read every physical volume in the library. Now let us contrast this with the sentence in (6.33b). The derivation is the same down to the evaluation of the presupposition of the transitive verb on its object. Carry off, which I’ll abbreviate to cy below, presupposes of its internal argument that it is of type p. The application of the verb meaning to the direct object DP yields: cy

(6.38) λΨλπ Ψ(π ∗ arg1 : p){λwλPλπ ∀v(∃u∃z∃x (library(x, π ) ∧ in(u, z, π ) ∧ o-elab(z, x, π ) ∧ book(v, π ) ∧ o-elab(u, v, π )) → P(π )(v)) cy (π ∗ arg2 : p ∗ argbk 1 : p • i)(λv1 λπ3 carry-off(w, v1 , π3 ))} cy

To satisfy the type requirements in arg2 , we must apply the B functor on the restrictor of (6.36) to get something of type p from a property of p • i objects. Following earlier derivations, we get the following logical form for (6.33b): (6.39) λπ ∃y (student(y) ∧ ∀v: p (∃w∃u∃z∃x (library(x, π ) ∧ in(u, z, π ) ∧ o-elab(z, x, π ) ∧ book(w, π ) ∧ o-elab(u, w, π ) ∧ o-elab(v, w, π )) → carry off(y, v, π )))

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(6.39) doesn’t say that all the copies in the library were carried off, though it entails this. We can recover this reading completely by identifying the copies that are in the library with the physical aspects of the books quantified over. If the PP in the library helps to determine the domain of quantification for the DP, then this identification is warranted, and we can simplify (6.39) to: (6.40) λπ ∃y (student(y) ∧ ∀v: p (∃w∃z∃x (library(x, π ) ∧ in(v, z, π ) ∧ o-elab(z, x, π ) ∧ book(w, π ) ∧ o-elab(v, w, π )) → carry off(y, v, π ))) Had we used master instead of read in (6.33b), we would have quantified over informational objects only. The TCL formalism thus captures the subtleties of the quantificational puzzles.

6.2.2 Copredication revisited Let’s now return to the copredication examples. Here’s a classic example of copredication. (6.41) John picked up and mastered three books. We suppose that the phrasal verb pick up must take a physical object as its internal argument and that the verb master must take an informational object. The problem here is that we have two incompatible presuppositions that both have to be satisfied by the same direct object argument. How can this be done? As is well known, when transitive verbs are conjoined we have to ensure that they have common arguments. One standard way to do this is to suppose, as Montague did, a special coordination rule. For transitive verbs, it looks like the rule below in TCL. Since we don’t know what the types are for the coordinated verbs, I’ll just write Preφ2 to denote the appropriate type requirement of φ on its second argument. • Coordination Rule for and: – Given a λ term of the following form [λΦλΨλπ Ψ(Preφ1 (π))(λuλπ1 Φ(Preφ2 (π))(φ))] and [λΦλΨλπ Ψ(Preψ1 (π))(λuλπ1 Φ(Preψ2 (π))(ψ))], – one may rewrite the construction as the following λ term: λΨλΦλπ Ψ(Preψ1 (Preφ1 (π))) (λuλπ1 Φ(Preψ2 (Preφ2 (π))) (λxλπ2 (φ(π2 )(x)(u) ∧ ψ(π2 )(x)(u))) A similar rule holds for coordinated disjunctions. I will assume a generalized conjunction operator that allows us to conjoin two λ-terms as long as they have the same arity.

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• Type Presuppositions in TCL

I now turn to a formal treatment of example (6.41). Let’s ignore the subject argument and concentrate on what goes on at the VP. The problem is that the presuppositional requirements of the two coordinated verbs are inconsistent; they cannot be jointly satisfied by any argument, for this argument would have to be of two incompatible types. Such copredications are felicitous, however. I take this to mean that the presuppositions of the two verbs must be accommodated somehow. The Montague-like coordination rule given above works fine, provided the presuppositional requirements of the two verbs are consistent. When they are not, as in (6.41), we must justify them in different spots. The idea that presuppositions may be justified at different spots in a semantic representation or a derivation is an important and integral part of theories of presupposition. All theories of presupposition in dynamic semantics hold that presuppositions can be justified in different contexts: for instance, a presupposition that is generated in the consequent of a conditional can be justified there, in the antecedent of the conditional, or in the “global” context in which the conditional occurs. Something similar happens with type presuppositions. The type of the argument must somehow justify the type presupposition that its predicate imposes, and we prefer that the justification take place where it is imposed: on the argument of the predicate. However, in some cases of copredication, this preference for type presupposition justification cannot be satisfied, and a different context of presupposition justification must be found. The Copredication Rule provides for two additional predications closer to the verbal complex—those predications φ and ψ are each applied to the variable x introduced by the argument of the coordinated predicates. The syntactic structure in figure 6.1 shows graphically with the mark † where the justification of type presuppositions takes place. The following rule exploits these additional locations for presupposition justification. Definition 18 Local Presupposition Justification in Coordinated Constructions Suppose Preψ (Preφ (π)) is unsatisfiable. Then: Φ(Preψ (Preφ (π)))(λxλπ1 (φ(π1 )(x) ∧ ψ(π1 )(x))) Φ(π)(λxλπ1 (φ(Preφ (π1 ))(x) ∧ ψ(Preψ (π1 ))(x))) A similar rule holds for copredications with disjunction. With the possibility of local justification in place, I now return to (6.41). I assume that both verbs presuppose an argument of type p for their subject (which means we can simplify our notation considerably) and that pick up, abbreviated to pk below, requires its object argument to be of type p while master, abbreviated to ms,

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6.2 Applications

DP

w ww ww w w ww

IP H H

HH HH HH H

I’ GG

GG GG GG G

w ww ww w w ww  V y EEE EE yy y EE yy EE y yy

V1 (xi )†

and

VP G

GG GG GG G

DPi

V2 (xi )†

Figure 6.1 Local type presupposition justification sites

presupposes an object argument of type i. Given the coordinated construction, these two type requirements are placed on a common direct object and are hence unsatisfiable. Local Justification, combined with our rule for coordination (note the type abbreviation given on the DP’s presupposition parameter), yields: (6.42) λΨλπ Ψ(π∗p)(λuλπ1 ∃3 w (book(w, π1 ) ∧ λx: eλπ3 (λvλπ4 pick-up(u, v, π4 ) pk [π3 ∗ arg2 : p ∗ (p • i) ct][x] ∧ λvλπ4 master(u, v, π4 )[π3 ∗ argms 2 : i ∗ (p • i) ct][x])[π1 ][w])) Using the Application and Substitution several times, this term reduces to: pk

(6.43) λΨλπ Ψ(π ∗ p)(λuλπ1 ∃3 w(book(w, π1 ) ∧ pick-up(u, w, π1 ∗ arg2 : p ∗ (p • i) ct) ∧ master(u, w, π1 ∗ argms 2 : i ∗ (p • i) ct))) The sequence of type assignments on π1 triggers Justification of Constituent Types. This invokes a use of our B functor on the two verbal predicates with the two different type requirements in the two distinct predications. (6.44) a. λPλv1 : p • iλπ5 ∃z: p(P(π5 )(z) ∧ o-elab(z, v1 , π5 )) b. λPλv1 : p • iλπ5 ∃z: i(P(π5 )(z) ∧ o-elab(z, v1 , π5 )) Following the rule for Justification of Constituent Types, we now apply the functors to the abstracted terms λw1 λπ3 pick up(u, w, π3 ) and λvλπ4 master(u, v, π4 ) pk and then apply the result to the original arguments w and π1 ∗ arg2 : p in the

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• Type Presuppositions in TCL

first case and w and π1 ∗argms 2 : i in the second. After β reductions we substitute the result in (6.43) to get: pk

(6.45) λΨλπ Ψ(π∗p)(λuλπ1 ∃3 w (book(w, π1 )∧ ∃z: p(pick-up(u, z, π1 ∗arg2 : p) pk

∧ o-elab(z, w, π1 ∗ arg2 : p)) ∧ ∃z: i (master(u, z, π1 ∗ argms 2 : i) ∧ o-elab(z, w, π1 ∗ argms : i)))) 2 The presuppositions of the two verbs can now be locally satisfied. So using Binding, Application, and Substitution, we get: (6.46) λΨλπ Ψ(π ∗ p)(λuλπ1 ∃3 w: p • i (book(w, π1 ) ∧ ∃z: p( pick-up(u, z, π1 ) ∧ o-elab(z, w, π1 )) ∧ ∃z: i( master(u, z, π1 ) ∧ o-elab(z, w, π1 )))) We can now combine this with the subject DP’s logical form to finish off the derivation. (6.47) λπ∃u(u = j(π) ∧ ∃3 w: p • i(book(w, π) ∧ ∃z: p (pick-up(u, z, π) ∧ o-elab(z, w, π)) ∧ ∃z : i (master(u, z , π) ∧ o-elab(z , w, π)))) This approach generalizes to all instances of coordinated verbal copredications, as long as the DP to be distributed quantifies over objects of • type.10 This same strategy can be used on modifiers as well as verbs and VPs. For instance, consider the coordinated modifiers in (6.48): (6.48) an often purchased but dull novel The conjoined adjectives in (6.48) are a coordinating construction and should be treated similarly to verbal coordinations like (6.41). We can follow the derivation of a logical form for (6.41), using the rule of Justifying • Types and the F functor instead of the B functor and the rule of Justifying Constituent Types to get an appropriate logical form for these coordinations. In fact we can treat any sequence of modifiers in this way, even when no coordinating conjunction is present.

6.2.3 Verbs and modifiers with • type presuppositions So far, all our examples of type presuppositions involving • have been a matter of adjusting lexically given presuppositions to the demands of predicates. However, sometimes predicates can force on their arguments a complex type. That is, some predicates coerce their arguments to be of complex type. Asher 10

So, for instance, TCL predicts that a derivation of a normal form for every dog is eating and is numerous will not succeed, despite the fact that dog is of • type with dog and κdog as constituent types, because the quantifier already selects only for the individual type. No local justification of the kind type presupposition for the second VP is possible.

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and Pustejovsky (2006) argue that the verb read is such a predicate. Consider the following data: (6.49) b. c. d.

a. Mary read the book. John read the rumor about his ex-wife. Mary read the subway wall. Mary illuminated and then read the subway wall.

The coercion phenomena in (6.49) involve subtle shifts in meaning. One can hear rumors and spread rumors, which one cannot do with books (even if you’re listening to a book on tape); on the other hand, one can’t see or look at rumors whereas one can see or look at a book. In contrast, one can see a subway wall or look at it, without getting any informational content. However, in (6.49b,c) the arguments of read change their meaning. For instance, (6.49c) implies that the subway wall is a conveyor of information, and the only way to understand (6.49b) is to assume that the rumor has been printed or exists in some physical medium. These examples suggest that read coerces its arguments into objects of the same type as book. For both (6.49b) and (6.49c) the predicate coerces its complement to the appropriate type, that of an informational object with physical manifestation. In each of these cases, there is a “missing element” to the complex type: for (6.49b) the coercion effects the introduction of the physical manifestation to the otherwise informational type; for (6.49c) the coercion results in the introduction of an informational component to an otherwise merely physical type. Read also enters into copredications that exploit one of the constituent types of the • as seen from (6.49d). As the presuppositional approach predicts, this phenomenon is peculiar to particular words. Words that presuppose • types of their arguments are relatively rare. Besides read, there are closely related words like decode, decipher, peruse, make out, pore over, scan, study, and translate that arguably induce complex types for some of their internal arguments. For some quite closely related verbs like master, the possibility of coercion to a complex type is degraded. For instance, (6.50b) is a lot less felicitous than its (6.49) counterpart: (6.50) a. Mary mastered the book. b. ??Mary mastered the subway wall. Furthermore, coordinate predication or copredication, which often requires a • type as an argument, doesn’t license the introduction of such a type. (6.51) is anomalous and hard to give a meaning to. (6.51) ?? John built and mastered the wall.

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• Type Presuppositions in TCL

More striking still is the way the verb write fails to pattern with read. Although what writing produces is an object of complex type p • i, write cannot easily convert to • type internal arguments that are lexically typed of physical type:11 (6.52) b. c. d.

a. Mary wrote the book. John wrote (up) the rumor about his ex-wife. #John wrote the subway wall. #John wrote the stone, the typewriter paper.

This asymmetry is quite remarkable, and the explanation for why this transformation is possible with arguments of read but not with write is quite involved. Part of the explanation lies in the fact that write produces an object of • type from an object of i type. Writing is a process that begins with a physically unrealized informational object and then issues in the creation of a physical instantiation of the informational object. Since write is a verb of creation, its object does not exist (physically) beforehand and so cannot be typed p. But when we predicate write of an object inherently typed p, this means that the writing process applies to something that is already, prior to the writing process, a physical object, but at this point it’s not clear what the creation process of writing is doing. If an informational object already has a physical instantiation, then it can’t be written—i.e., have its physical aspect created by the writing process. At this point we have an unrecoverable type clash between the type requirements of the predicate and its argument. On the other hand, we can apply write to something that is inherently informational, like a rumor; the process of writing transforms the informational object into an object of complex type. With respect to read, we make a presupposition as to the type of its object —it must be of type p • i. This presupposition can be more easily accommodated, as many sorts of objects can have information stored on them (people write on stones and on subway walls); and it is this information that we accommodate. Unlike writing, the process of reading does not turn an argument that was not of • type into one that is, and there is no incoherence between the information accommodated and the proffered information imparted by the verb. Up to now, we have examined two sorts of cases of presupposition justification with • types: one where the • type presupposition of a predicate is justified directly by the type of its argument (via Binding or Simple Type Accomodation), and one where the predicate presupposes a type of an aspect of an argument of • type. In both cases, the justification of the presupposition is 11

You can also write a rumor, however. A quick check on Google reveals several attested instances.

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conceptually straightforward. Justifying • types via B or F is similar to binding, or its generalization Simple Type Accommodation, in that the information needed to justify the presupposition is already available in the context. However, when a predicate presupposing a • type, say α • β, applies to an argument of a constituent type, say α, the justification is less straightforward. The argument of the verb does not carry the requisite type information in any sense; the requisite information has to be imposed on the argument in order for the predication to go through. The presupposition is no longer justified solely in virtue of the inherent typing of the argument; we have to add something “extra” to our understanding of the argument. I shall call the sort of presupposition justification that occurs when an argument of type α or β takes on a • type α • β in response to the type presuppositions of a predicate, • accommodation. • accommodation and the binding-like justifications involving • examined earlier have different effects on quantification. We’ve seen that objects of • type have complex individuation conditions that can vary, as we saw in the cases of the quantificational puzzle, with the predicational context—viz., when the predicates select for different aspects of an object of • type. Does this mean that when a lexical item like read introduces a • type on an otherwise simply typed object, we can individuate that object relative to both informational and physical individuation criteria? In other words, can such predications give rise to versions of the quantificational puzzle? The answer is no, which is somewhat surprising, given that terms that are lexically typed as dual aspect nouns permit us to use criteria of individuation appropriate to each constituent type of the •. Consider the following examples. (6.53) a. Mary read every screen. b. Mary read three books. c. Mary read three rumors about her ex-husband. Mary has to read all the physical screens in order for (6.53a) to be true. In a situation where many screens have the same information on them, (6.53a) is true only if Mary read each and every physical screen, not just the few screens that jointly convey all the information on the screens in the situation. Similarly Mary must read three informationally distinct rumors about her ex in order for (6.53b) to be true. In other words (6.53b) cannot have the meaning Mary read a (the) rumor about her ex three times. On the other hand, for Mary to have read three books, she may have read three informationally distinct books or three physically distinct ones, as we have seen. If she carried three books home, she has to have carried three physically distinct books, and if she mastered three books, she has to have mastered three informationally distinct books.

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• Type Presuppositions in TCL

The way in which the objects read are individuated affects the individuation of the events of reading. Reading three books comprises three events, one for the reading of each book. But these events may be individuated either in terms of three physical books or three informational books (without regard to how many physical books were involved in the reading events). This is not true for (6.53a,c). The events are individuated relative to the set individuation conditions of the original type of the arguments. This means that physical screens and the informational rumors have to be involved in the reading events themselves somehow in order to individuate the events in the appropriate way. • accommodations thus never shift the counting principles or the individuation criteria for the objects whose types are shifted. In this • accommodations resemble classic coercions, which don’t change counting principles for the objects that fall under the coerced term either. • accommodations nevertheless differ from classic coercion cases. Accommodating a presupposition of • type on a noun phrase really does in some sense tell us more about the type of its argument; a stone that can be read is no longer a mere stone, but a conveyor of information. Something like the Rosetta Stone, a very famous stone conveying information, can be destroyed simply by wiping out the inscriptions on it, whereas a normal stone can remain the same stone after considerable erosion. Now contrast the case of the Rosetta Stone with a classic example of coercion. To say that Mary enjoyed her glass of wine doesn’t in any way tell us more about the intrinsic nature of the glass of wine, only that Mary enjoyed doing something with it, presumably drinking it. There is a subtle but unmistakable distinction between the two cases.12 The upshot of this discussion is that not all predicates project their presuppositions in the same way. Presuppositions of • types introduced by verbs or modifier predicates behave differently from those introduced by nouns. This is to be expected. Traditional presuppositions have quite different binding and accommodation behavior. Some presuppositions, like those of definite descriptions, are easily accommodated, while the presuppositions of adverbials like too are much less so. Furthermore, different presupposition triggers produce presuppositions with specific instructions on how they are to be integrated into 12

In Asher (2007) I argued that the preposition at might introduce a complex p • l (l is recall short for the type location) in constructions like:

(6.54) Mary is at the chair. (6.54) is possible in contexts where Mary is playing some sort of game where pieces of furniture are used as waypoints or locations. I now think that at is probably not a • type introducer but functions rather more like the coercions with the aspectual verbs or enjoy. In this situation the chair remains a chair, while also serving as a location. The intrinsic nature of the chair is not altered.

6.2 Applications

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proffered content. For instance, Hunter and Asher (2005) argue that indexicals and definite descriptions generate presuppositions with different instructions on how they are to be justified. The presuppositions generated by indexicals require binding at a global level, while the presuppositions generated by definite descriptions can be bound or accommodated at various positions in the discourse context. TCL already predicts a difference between the ways presuppositions of modifiers and nouns are to be justified. Consider (6.55) below: (6.55) John turned off every readable screen. The adjective readable imposes the type p • i on its individual level argument. The noun screen imposes the type presupposition on any modifier that it be a physical property. Using the B functor on the modifier meaning will, after β reduction, produce the following noun phrase logical form. (6.56) λx: p λπ∃v: p • i (readable(v, π) ∧ o-elab(x, v, π) ∧ screen(x, π)) When the determiner meaning is applied, we will get a quantification over all physical screens that can be read, which accords with intuitions. What about • accommodations involving verbs? With one restriction, these will have a correct analysis in TCL as well. The application of the “back” and “forth” functors, B and F , in the rules for • type presupposition justification is triggered by a sequence of type justifications of the form . . . α ∗ (α • β), or . . . β ∗ (α • β), where the • type is always introduced by the noun, the local predicate in a verbal predication, or the non-modifier in a modifier predication. Suppose we make this observation a part of our • justification rules. Then a • type presupposition from a verb cannot trigger the Justifying a • Type rule, because it is neither a local predicate nor is it involved in a modifier predication. But this means then that the type presupposition cannot be justified. As with coordinate constructions, when justification fails, we attempt a type justification at an adjusted site, closer to the verb itself. That is, the type presupposition of the verb applies, not to an argument of its DP argument but only to the nuclear scope of the DP—i.e., on the verbal predicate itself, as in the case of presupposition justification for coordinate constructions involving predicates with incompatible type presuppositions. At this point, however, the • type is provided by a local predicate. So the Justifying a • Type rule applies, and we can justify the type presupposition. With this modification, TCL entails that when • type presuppositions are imposed by a verb on one of its arguments, these presuppositions must be justified, if they are to be justified at all, at an alternative site, and not on the argument itself as is the case with ordi-

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nary • presupposition justification. This immediately predicts the differences in quantificational behavior between • accommodation and • justification. Consider, for example, (6.49c). Given the reformulation of the Justifying a • Type rule, the presupposition of read cannot be justified when it applies to the whole object DP. So we must resort to local justification, where the type presupposition of the verb applies only on the second nuclear scope argument of the determiner of the object phrase—i.e., the verb itself. However, at this point the type presupposition of the noun has already been conveyed to the verb. Hence we have for (6.49c): (6.57) λΦλπ Φ(π ∗ agent)(λvλπ1 ∃x (subway-wall(x, π1 ) ∧ read(v, x, π1 ∗ p ∗ p • i))) At this point, the type requirements imposed by read and the restrictor of the DP look familiar and trigger the Justifying a • Type rule. We use B and Justifying a Constituent Type of a • Type, but we apply the functor below to λy1 π3 read(v, y1 , π3 ). (6.58) λPλπ (λu: p∃z: p • i (o-elab(u, z, π ) ∧ P(z, π ))) Using Justifying a Constituent Type with this functor, Substitution, plus several uses of Application and Binding, gives us for the VP meaning: (6.59) λΦλπΦ(π ∗ agent)(λvλπ1 ∃x (subway-wall(x, π1 ) ∧ ∃z (o-elab(x, z, π1 ) ∧ read(v, z, π1 )))) The type presupposition justification in • accommodation involves a local adjustment of types for the purposes of the predication, but the effects do not percolate up to the full DP and thus do not affect the quantificational domain, in contrast to • justification. (6.59) implies that there is an object of complex type of which the subway wall is the physical aspect, but we do not change the type or individuation conditions of subway walls in so doing—which accords with intuitions. The quantification in the DP remains over whatever it was lexically specified to be by the head of the common noun phrase. Verbs like read seem to be largely lacking for the other • types instantiated in the lexicon. There are no verbs that presuppose complex types like event • i or prize • amount of money, portion of matter • artifact as far as I am aware.13 There are some grammatical constructions that license • accommodation and thus introduce • types. In chapter 7, I’ll argue that restricted predications like 13

Renaud Marlet pointed out to me that one can say paint a canvas or cast a bronze, and this is evidence that these verbs might presuppose that their internal arguments be of type portion of matter • artifact. However, Google searches show that bronze and canvas are themselves complex types supporting the sort of copredications that one would expect.

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185

(6.60), depictives like (6.62), and resultative constructions like (6.61) introduce complex types involving both an object and an aspect of it that results after the completion of some process. (6.60) This film as a work of art is very mediocre. (6.61) Sam wiped the table clean. (6.62) Sam drove home drunk. These grammatically licensed cases of • type accommodation will induce a local justification of the type presupposition.

6.3 • Types and accidentally polysemous terms Now that we’ve examined logically polysemous types like • involving multiple aspects, let’s turn briefly to accidentally polysemous words. Such words have coproducts, or disjunctive objects, for their internal meanings. Coproducts exist for arbitrary types α and β in a CCC and a Topos, and Δ enables us to establish some straightforward facts about the type construct α ∨ β when it denotes a type in the type hierarchy. Fact 17 Subtypes with disjunctive types: a. b. c. d.

α α ∨ β and β α ∨ β Given α γ, β γ, α ∨ β γ (α ∨ β) (δ ∨ γ) = (α δ) ∨ (β γ) ∨ (α γ) ∨ (β ∨ δ) α∨β=β∨α

Let us see how to use ∨ to deal with accidental ambiguities. For instance, consider a word like bank. Let’s assume for a minute that bank is simply ambiguous between a riverbank and a financial institution sense and so corresponds to the following disjunctive type: (p • l) ∨ inst (since both constituent types are subtypes of e, the two elements of the co-product are types and have the requisite property of disjointness; and so this disjunctive type exists). A predication like (6.63) The bank specializes in IPO’s specifies the coproduct to one of its proper types via Accomodation in TCL in virtue of the observations about and disjunctive types. That is, the predicate specializes in IPO’s types its argument as inst (institution), and this can combine with the accidentally polysemous subject. Thus, Type Accommodation functions as a type disambiguator.

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• Type Presuppositions in TCL

Type Accommodation does not add any variables to logical form or have anything like the complexity of the • justification rules. Thus, TCL predicts that accidentally polysemous terms will share little in the behavior of their logically polysemous cousins: we should not get the same patterns of anaphora resolution or of copredication. Compare the anaphoric possibilities of accidentally polysemous expressions with those of logically polysemous ones: (3.45b) John’s Mom burned the book on magic before he could master it. (6.64) The bank specializes in IPO’s and it slopes gently down to the river. Once a disjunctive type α∨β is specified to the type of one of the disjuncts, say α, because of predication and a use of Simple Type Accomodation, accidentally polysemous expressions do not support anaphoric reference to objects of type β. In the logical form for (6.64) with the types as hypothesized, once we have specified the type of the subject to inst, there is no variable of the appropriate type from the first clause to serve as the binder for the pronoun it. This contrasts with TCL’s treatment of (3.45b) where • justification rules furnish just such a binder for the pronoun. Similar observations hold for the failure of copredication with simple disjunctive types. Many accidentally polysemous words like bank may also be logically polysemous. As many have observed, the financial institution sense of bank has two aspects: an institution aspect and a p • l aspect. Thus bank can support copredications of the right kind. (6.65) The bank is just around the corner and has specialized in subprime loans for the last few years. Thus, the λ bound variable x in λx bank(x) would have the type constraint x: (inst • (p • l)) ∨ p • l, assuming that river banks are locations as well as physical objects. We can now no longer use Simple Type Accommodation to resolve the ambiguity, as inst•(p•l) is not a subtype of inst. But if we think of the * operation on π as telling us that something has to meet two type constraints, there is a natural way to proceed. From the underlying logic and categorial semantics, we know that α∨β, γ α γ∨β γ. So the type constraints that need to be satisfied χ φ “distribute” across disjunction in the following sense: from argk : δ∗argi : α∨β we get argχk : δ ∗ argφi : α ∗ ∨ argχk : δ ∗ argφi β, where the disjunction amounts to two possible TCL derivations, one where the type restriction α is used and the other where β is employed. If one of these fails to provide a coherent result, then we disambiguate the disjunctive type in favor of the other alternative disambiguation. This follows from the observation that α ∨ ⊥ = α. If both

6.3 • Types and accidentally polysemous terms

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disambiguations yield consistent results, then the ambiguity remains, and two logical forms can issue. Let’s see how disjunctive types work in a concrete example of copredication. Consider: (6.66) The bank has eroded because of the floods and specializes in IPOs. As the types of the two VPs conflict (one selects for p, the other for inst), we resort to local justification,14 where the presuppositions of the two verbs in the verb phrases remain local to the verb phrases themselves. In particular we will use here the Local Justification in Coordinated Constructions rule that we used for our other examples of coordinated predication. Applying this rule to our example and proceeding as in our earlier analysis of copredication, we get for the coordinated verbs: (6.67) λΨλπ Ψ(π)(λvλπ (λuλπ3 eroded ...(π ∗ argerode : p • l)(v) ∧ 2 specialize

λuλπ4 specializes ...(π ∗ arg2

: inst)(v)))

We can now apply this to the subject DP the bank. To simplify notation, let the type of bank be just p ∨ (p • inst), leaving out the locational type. The rules of TCL yield: (6.68) λπ∃!w (bank(w, π) ∧ λuλπ3 eroded ...(π ∗ argerode : p ∗ argbank p 2 1 specialize

∨(p • inst))(w) ∧ λuλπ4 specializes ...(π ∗ arg2 p ∨ (p • inst))(w)) argbank 1

: inst∗

Factoring out the disjunctions, we get: (6.69) λπ∃!w (bank(w, π) ∧ λuλπ3 eroded ...(π ∗ p ∗ p ∨ (p • inst) ∗ p)(w) ∧ λuλπ4 specializes ...(π ∗ p ∗ inst ∨ (p • inst) ∗ inst)(w)) For the first coordinated verb, both resolutions of the ambiguity remain open. The first disambiguation makes w of type p and the second makes w of complex type and introduces an extra variable for the aspect of type p using the Justifying a Constituent Type rule. But now we have to see how these types fare in the second disjunct in (6.69). The predication in (6.69) knocks out the first disjunct, as inst p = ⊥. So only the second typing is available, according to which w: p•inst. Since the complex type works for both conjuncts, it is this one that survives the justification process. TCL thus predicts a reading for (6.51): 14

Our assumption that these two types have no greatest lower bound makes sense in view of the fact that institutions have different individuation and identity conditions from things that are physical objects and locations.

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• Type Presuppositions in TCL

there is a physical bank building that has eroded because of the recent rains, and the financial institution that owns or occupies the building specializes in IPOs. This interpretation is quite remote from most interpreters’ minds, but it is possible. Nevertheless, the derivation shows that the copredication does not and cannot simultaneously access the interpretation of bank as a river bank and as an institution.

PART THREE DEVELOPMENT

7 Restricted Predication

In this chapter I investigate how grammatical constructions like restricted predication, or the qua construction, license the accommodation of • types. The idea is that the construction DP as a NP introduces a variable from the head DP whose complex • type is determined by the restricted predication construction— from the head DP and the NP that is the argument of as. Thus, John as a banker introduces a variable for predication of the type human • banker. But first let’s get some background. The sentences in (7.1) share a property with attitude reports in that the substitution of coreferential proper names does not preserve truth.1 (7.1) a. Superman as Superman always gets more dates than Superman as Clark Kent does. b. ?? Superman as Superman always gets more dates than Superman as Superman does. (7.2) a. Chris hit Superman as Clark Kent, but he never hit Superman as Superman. b. ?? Chris hit Clark Kent as Clark Kent, but he never hit Clark Kent as Clark Kent. (7.3) a. Lois slept with Superman as Clark Kent before she slept with Clark Kent as Clark Kent. b. ?? Lois slept with Superman as Clark Kent before she slept with Superman as Clark Kent. The (a) versions of the above examples all seem satisfiable, perhaps even true, and to convey non-trivial information. They differ intuitively from their substitutional variants in (b), which seem necessarily false. These intuitions about 1

These examples are adapted from Saul (1997).

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the truth conditional status of (7.1a–7.2a) versus (7.1b–7.2b) imply a semantic rather than pragmatic difference between the (a) and (b) variants; that is, there is intuitively a difference in the truth conditional status of the (a) and (b) variants, which should follow from the semantic interpretation of their logical forms. First a bit of terminology. I’ll be concerned with sentences of the form (7.4) φ as ψ χ where χ is a predicate on an argument introduced by φ. I’ll call the predication in χ the main predication and the predication derived from ψ the restricting predication.2 A first thought is that as phrases function like attitude contexts to force the constituents within their scope to take on something like Fregean senses as semantic values. But attitude contexts and as phrases function quite differently with respect to inferences involving identity, suggesting that we cannot have a single account for both phenomena. Proper names in as phrases like those in (7.1) have a different intensional behavior from names in other intensional contexts. (7.1a–d) remain “informative” and even true in spite of the fact that the identity between CK and S is known or part of the background context, while the “uninformative” counterparts are false. Thus, the following propositional attitudes seem completely consistent: (7.5) a. John believes that Superman = Clark Kent. b. John believes that Superman as Superman always gets more dates than Superman as Clark Kent does. The lack of substitutivity within as phrases is striking when we compare it to the epistemic transparency of other predications inside attitude contexts. Suppose that (7.6a–b) are both true. (7.6) a. John believes that Hesperus is Phosphorus. b. John believes that Hesperus is dim and that Hesperus is a planet. Then it seems to be a valid inference that (7.6c) John believes that Phosphorus is dim and that Phosphorus is a planet. If one quibbles with the inference from (7.6a–b) to (7.6c), it is enough for my purposes that one accept that John ought to believe that Phosphorus is dim and that Phosphorus is a planet if (7.6a–b) are true. The reason this argument is valid is that thoughts should support the customary logical inferences; so if 2

There’s considerable evidence that as constructions are clauses and involve predications, as Jaeger (2003) and Szabo (2003) argue. I take their view of the syntactic facts to be basically right, though I’ll add a few details in section 3 below.

7.1 Landman’s puzzle

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you believe that a = b and you believe φ(a), you believe, or at least ought to believe, that φ(b). But now what about as phrases? Suppose that in the spirit of traditional Fregean approaches to meaning we adopt (1) a compositional theory of senses, according to which the sense of each meaningful, syntactic constituent of a sentence S becomes itself a constituent of the meaning of the proposition or thought that S expresses; so the meaning of a is F is the proposition in which the sense of F is applied to the sense of a. Suppose further that (2) we analyze propositional attitudes as a relation between a proposition and an agent, and finally that (3) the names Clark Kent and Superman are syntactic constituents of the as phrases in (7.5b) (something which seems undeniable). Then we land into the following difficulty. By (1) the embedded proposition in (7.5a) can be represented as the application of a complex concept to the senses of the proper names in the complements of the as phrases. Now since thoughts support the customary logical inferences, from (7.5a) and (7.5b) it follows by the laws of identity that (7.7) John believes that Superman as Superman always gets more dates than Superman as Superman does. So from a pair of intuitively consistent beliefs and some minimal assumptions, we infer that John should believe something necessarily false, as long as thoughts obey the “laws of thought.” This is clearly counter to intuitions.3

7.1 Landman’s puzzle Landman (1998) provided a set of intuitive postulates for sentences containing as phrases. These postulates suggest an extensional analysis. However, Landman’s postulates, which I present informally, also reveal a deep problem with our intuitions about restricted predication. Landman’s Postulates: 1. John as a judge is John. 2. If John as a judge is corrupt and John as a judge is well-paid, then John as a judge is corrupt and well paid. 3. If taking bribes implies being corrupt, then if John as a judge takes bribes, then John as a judge is corrupt. 3

We could try resorting to a hierarchy-of-senses view: the complement of the as phrase in (7.5) would then be assigned a second-level sense. Then, even while the first-level sense of Superman might be identical to the first-level sense of Clark Kent, they could differ in second-level senses. But now suppose that John believes that Superman is Clark Kent (7.5a), and that he also believes that he believes that Superman is Clark Kent. The counterintuitive conclusion now follows once again.

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4. John as a judge is not both corrupt and not corrupt. 5. If John as a judge is corrupt, then John is a judge. 6. John as a judge either takes or doesn’t take bribes. These axioms are plausible but lead to the following problem: • • • • •

From (5): If John as a judge is John, John is a judge. From (1): John as a judge is John. So from (1, 5): John is a judge. But similarly from (5): If John as a non-judge is John, John is a non-judge. So by parallel reasoning from (1): John is a non-judge—i.e., John is not a judge.

Putting both arguments together, we start from what appear to be uncontroversial premises to arrive at a contradiction.

7.2 More puzzles Adding to the puzzles about as phrases is the way the copula and proper names function within these restricting predications.4 In standard predications, when we use proper names in predicative constructions and a definite NP in subject position, as in (7.8) a. That man is Mark. b. The prettiest city in the world is Paris. the predication is naturally construed as one of identity. However, as predications appear to be different. Consider (7.9) a. John as Sam was interesting. b. John as Sam earns more than $50K. These examples sound strange; whatever they are, the restricted predications involving a proper name do not function like their counterparts with the copula. Names with “descriptive content” or that designate roles like Lear, Macbeth, Hamlet, or Superman and Clark Kent in complements of as phrases help us see what’s going on. (7.10) John as Lear was fantastic, but John as Hamlet was boring. 4

Jaeger (2003) notices that as phrases are not synonymous with is predications, but he does not discuss the case of proper names.

7.3 Extensional semantics for as phrases

195

If the phrases as Lear and as Hamlet in (7.10) functioned the way the predications do in (7.8), then logic would dictate that Hamlet = Lear. But clearly this does not follow from (7.10), and so it would appear that proper names do not have a normal predicative role when they are complements of as phrases. Similar intuitions about the use of proper names obtain for the examples (7.1). In so far as (7.9a) sounds OK, it’s because we’re saying that John is playing at being Sam—he dresses like him, talks like him, acts like him. This is of a piece with other predicative uses of names. (7.11) He’s an Einstein. (7.12) You’re no Jack Kennedy. As phrases with proper names function similarly. They predicate properties associated with the bearer of the name to the head of the construction. This discussion reveals yet another reason to reject a simple Fregean approach to as constructions. A Fregean approach to intensional contexts changes only the reference of the expressions within the context and not the nature of the predication. But we see that as clauses require precisely another account of predication. We must supplement the basic Fregean idea with some view of how as would link the sense of its complement with its subject. These puzzles involve a problem with predication, not just an analysis of as phrases, since as phrases affect the interpretation of the main predication. As we shall see, the mechanisms of TCL are well suited to deal with them.

7.3 Extensional semantics for as phrases To say that John as a judge is corrupt is to say, roughly, that John is corrupt insofar as or when he is a judge. This temporal gloss invites an extensional semantics for as phrases. Jaeger (2003) and Szabo (2003) construct a semantics for as phrases that makes crucial use of situations or eventualities, both of which are temporally extended entities. Both accounts take as phrases to restrict the main predication to some temporal span of the subject. On these views, predication depends on a hidden situation or eventuality argument. Jaeger (2003) stipulates that as phrases hold in a “small” situation or part of the world of evaluation. He also observes that John as a judge is corrupt presupposes that John is a judge.5 Jaeger reformulates the formulation of the Landman axioms to filter out the presuppositions; Jaeger’s reformulation of 5

The standard tests for presupposition in questions and with negation seem to suggest that Jaeger is right: (i) It’s not true that John as a judge is corrupt still implies that John is a judge; (ii) any answer to the question Is John as a judge corrupt? implies that John is a judge.

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the axioms avoids Landman’s puzzle. To ensure the validity of his reformulated axioms, however, Jaeger has to make some further stipulations. For instance, to capture axiom 5, the predications in the as phrases must be upwards persistent, in the sense that if John is a judge in a “small” situation, John is also a judge in a larger situation. To account for the restriction of the main predication by the as phrase, Jaeger uses Van der Sandt’s (1992) theory of presupposition binding, according to which the presuppositional content of as phrases will move to get “bound” at an appropriate site in the logical form of the sentence. Jaeger appeals to a hidden argument in the main predication to which the presupposition will bind; for example, John as a judge is corrupt becomes after presupposition binding: John is corrupt when he is a judge. As Szabo (2003) notes, however, this would imply that this hidden argument can be explicitly bound by another adverbial as in (7.13a). In that case we would predict that the presupposition given by the as phrase is simply accommodated and plays no role in the main predication. But this prediction turns out to be wrong. Consider (7.13b), which is due to Szabo (2003), and which has an explicit restriction on the putative, hidden argument of the main predication as well as an as phrase. It only has the interpretation that John as a judge makes money that would be considered good for a janitor. Thus, contrary to Jaeger’s account, the as phrase plays a restricting role even in the presence of the adverbial for a janitor. (7.13) a. John makes good money for a janitor. b. John as a judge makes good money for a janitor. Szabo (2003) bases his account of as phrases on a Neo-Davidsonian analysis of predication according to which predications are relativized to “states” or other eventualities and then adds a partial ordering over states. On his analysis, as phrases are sentential (IP) adjuncts with the following truth conditions: • John as a judge is φ is true just in case there are states s0 and s s0 such that 1. John is a judge in s0 ; 2. φ holds of John in s; 3. φ holds of John in all states s1 such that s s1 or s1 is a state in some contextually salient alternative to John’s being a judge (such as being a janitor). According to this semantics, John as a judge makes $50K says that only in states of being a judge does John make $50K. It also implies that John is a judge at the actual world or maximal state of John’s and it avoids Landman’s

7.4 A new puzzle

197

problem by relativizing the predication of John’s being a judge and his being a non-judge to two distinct states. Szabo also avoids positing a hidden argument for the main predication and in this respect his analysis seems more satisfactory than Jaeger’s. Another feature of Szabo’s account is that it contains a sort of focus constraint, capturing the intuition that the as phrase’s predication of a property P to its subject implies that the subject has other properties than P (this constraint also makes the content of the as clause presupposed, which captures Jaeger’s observations about presuppositionality). In the jargon of the semantics of focus, John as a judge implies other alternatives, John’s being P, to John’s being a judge. This effectively captures the intuition that as phrases restrict the main predication to some particular, restricted aspect of the subject.

7.4 A new puzzle While Szabo’s account seems promising, there are problems lurking. First, it’s not clear how to get the truth conditions that Szabo wants compositionally from the meanings of the sentence’s constituent expressions.6 The real difficulty with the extensional accounts comes from the underlying Neo-Davidsonian view of predication, according to which all predications are relativized to some sort of eventuality. In Neo-Davidsonian semantics, if I say that I am happy now to be going home but unhappy now that I have such a long flight ahead of me, then you can infer: (7.14) a. I am unhappy now. b. I am happy now. Can one be simultaneously in a happy and an unhappy state? Perhaps, because we interpret these as two restricted predications; but in general this strategy is unavailable and the contradiction inescapable for many pairs: (7.15) a. John makes $100K a year. b. John makes less than $70K a year. In (7.15) we cannot recover from this pair a non-contradictory meaning. The intuition is that one cannot be in two states with contradictory properties at 6

As phrases appear to be sentential or IP adjuncts. While syntactic techniques allow some variable binding across an IP and IP adjuncts (by, for instance, raising a noun phrase to some higher position like the specifier in CP), Szabo’s semantics requires that the as phrase constrain the eventuality (state or event) argument of the main verb. To do this the as phrase would have to take scope over the asserted predication and somehow constrain the eventuality of the main predication, even though in standard compositional theories of the syntax–semantics interface the eventuality variable introduced in the main VP is existentially bound by the time we interpret IP adjuncts of the main clause.

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the same time. In fact, one might go so far as to suppose (where Ot signifies temporal overlap): • State Consistency Principle: (∃sφ(s) ∧ ∃s φ(s ) ∧ sOt s ) → ∃s (φ ∧ ψ)(s ) Though intuitively correct, the State Consistency Principle is not part of standard Neo-Davidsonian semantics. And it cannot be added, as we will see, to Szabo’s approach. Instead, Szabo modifies the standard Neo-Davidsonian view of predication by requiring that such predications hold not only of some state at the present moment but in all states that include that one, up to and including the object of predication’s maximal present state, unless they are states supporting alternatives of those singled out by the predication. Let us call this principle the Persistence of predications.7 But now suppose that John works two jobs and thus that (7.16) is true: (7.16) a. John is a judge. b. John is also a janitor. According to Persistence, John will then be both a judge and a janitor in his maximal present state. So far so good: this seems to be true of people who hold two jobs at once.8 The other piece of the puzzle has to do with whether the main predication applies to all states that satisfy the restricted predication. Szabo’s last constraint implies that this is so. The same intuition that underlies Szabo’s fix of the standard Neo-Davidsonian view of predication leads us to accept the view that the main predication should hold in all those states in which the restricted predication holds. I call this constraint universality: • Universality: If φ as ψ χ holds, then in any state s in which φ has the property expressed by ψ, the property expressed by χ applies to φ in s as well. That is, if John as a banker is corrupt is true, then in all states in which John is a banker, he is corrupt. Further support for Universality comes from the fact that if it fails to obtain, then the truth conditions of (7.17a,b) are jointly satisfiable in Szabo’s account. (7.17a) would be true just in case there is some state s in which John is a judge 7 8

Note that Jaeger also adopts something like Persistence. Although being a judge and being a janitor may be alternatives to each other for Szabo, they can both clearly apply to John in his maximal present state. Thus, I conclude that Szabo’s constraint really does not affect persistence or else it gets the wrong results.

7.4 A new puzzle

199

and some substate s of s in which John is honest. This semantic analysis of (7.17a) is compatible with John’s being corrupt in some, many, or even most situations when he is a judge. (7.17) a. John as a judge is honest. b. John as a judge is corrupt. Intuitions belie this prediction. If it’s true that John as a judge is honest, then it’s not true that there are situations where John is a judge and he is corrupt. Universality and Persistence together with Szabo’s account yield a contradiction. It’s not hard to see why. If as constructions allow us to predicate contradictory properties of some object under different restrictions, and the restricted predications are upwards persistent and universality holds, then we will predicate contradictory properties of the object in the same state. To make the problem concrete, suppose further that the following intuitively satisfiable claims are true. (7.18) a. As a judge, John makes $50K. b. But as a janitor, John only makes $20K. Assuming (7.16a,b), Persistence implies that John is a judge and a janitor in the maximal state of John (at the present time). According to Universality, the main predications in (7.18a,b) should hold of every state that satisfies the predication in the as clauses, But then, the maximal present state s of John must be such that John makes $50K in s and such that John makes only $20K in s, which is impossible. Our argument has shown that there is no restriction on the main clause predication by the as clause: John as a φ ψ’s is just equivalent to John ψ’s. And this means that (7.18a,b) are inconsistent given the perfectly innocuous assumption that John works both jobs. This is clearly a terrible prediction for an analysis of as phrases to make. One might want to deny an inference from (7.18a) to (7.16a) and from (7.18b) to (7.16b). The New Puzzle, however, relies not on such inferences but just on the possibility that (7.18a,b) and (7.16a,b) can all be jointly true. What can an extensionalist do? He could give up the possibility that (7.16a,b) and (7.18a,b) are jointly satisfiable, but that runs counter to quite robust intuitions. This would be to accept the conclusion of the puzzle—and to acknowledge, as we have seen, that restricted predication plays no essential role. He could reject Persistence; the restricting predication need not hold in superstates of those states in which it holds. But then, we must countenance in our present case the fact that there are some superstates of John’s being a judge where he is not a judge. Since the logic is classical, it appears that we have no other option. But then it appears that we cannot say in this case that John is a judge, unless

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we are willing to say that he is not a judge as well. Either we say nothing or we say something contradictory. Neither of these options seems plausible. Another unpalatable way out of this puzzle is to give up Universality. But then one can’t make sense of the intuitive incompatibility of (7.17a,b), and the account of restricted predication suffers a similar difficulty as the standard Neo-Davidsonian view of predication. The new puzzle infects any putative analysis of the restricted predication as containing hidden restricted predications. It seems impossible to distinguish situations or states in which Clark Kent is Superman from those in which Clark Kent is Clark Kent, if indeed Clark Kent is identical to Superman. If we cannot distinguish these states, then none of the sentences in (7.1) is satisfiable. Persistence and Universality imply that we must evaluate all claims about Superman as Superman and all claims about Superman as Clark Kent at the same maximal state of Superman. But then we cannot ascribe incompatible properties to Superman as Superman and to Superman as Clark Kent; the examples in (7.1) are predicted to be false. Finally, the New Puzzle affects the presuppositional part of the extensionalist accounts as well. It appears that the following sentence, though awkward, can be true: (7.19) John as a judge is severe, but as a non-judge he is quite easy going. Extensional accounts like Szabo’s and Jaeger’s predict that there must be a presupposition failure with (7.19) since the presupposition that John is a judge and the presupposition that John is not a judge must hold of John’s present maximal state. As they cannot both be justified, they predict (7.19) to be semantically anomalous. To most English speakers’ ears, however, it sounds fine. Although the extensionalists are right in trying to modify the notion of predication in order to understand restricted predication, the New Puzzle shows that we need a fundamentally different approach. Restricted predication is fundamentally different from non-restricted predication. But Neo-Davidsonians assume that restricted and standard predication are in effect the same; restricted predication only puts extra constraints on the eventuality underlying the predication. The State Consistency Principle, which I take to be a fundamental principle guiding predication, cannot be consistently added to the extensionalists’ view of restricted predication. This shows that something else must be going on in restricted predications. I conclude that states as we ordinarily understand them are simply the wrong sort of object to analyze restricted predication. There is something irreducibly intensional about restricted predication, though the intensionality is of a different sort from the intensionality of attitude constructions.

7.5 As constructions in TCL

201

7.5 As constructions in TCL My view is that restricted predications single out an aspect of an object to which the main predication applies, and that such aspects are intensional objects of a particular kind. As predications pick out individuals under the guise of a property contributed by the as clause’s complement. An individual considered under the guise of a certain property or description is an aspect, and it is that aspect that figures in the predications of the main clause of a sentence containing an as phrase. Such aspects present the individual under some conceptualization, as we saw earlier. The approach using aspects analyzes restricted predication as a phenomenon involving individual objects and clearly separates this from verbal predications involving eventualities. As such it is no surprise that adverbial adjunct modification is not a possibility in restricted predication. The properties in the as phrase complement thus play a very special role in predication. They specify types that characterize the aspect of the object under discussion. The function of an as phrase is to introduce a type picking out an aspect of an object with several aspects. Many of the inferences that seem unproblematic for states need re-examination in this intensional setting. In TCL aspects are objects whose types are constituents of • types. While • types are introduced by lexical items like nouns, they can also be introduced by a grammatical construction of which the as phrase construction is one example. As phrases are • type introducers and coerce their subjects into something with several aspects, one of which the complement or object of the as phrase serves to define. In terms of the model of predication with complex types, an as clause requires the use of • introduction transforming the type of its subject into a complex type, one constituent type of which is determined by the predication in the as phrase. In addition, as phrases force a restriction of the main clause predication to that metaphysical part of their subjects that is described in the as phrase. So for example, John as a judge is corrupt coerces John into having a complex type, one constituent of which is the type of being a judge, and it says that there is an aspect or metaphysical part of John—his being a judge—and that part is corrupt. As phrases are a productive means for producing new • types. We don’t normally consider books as having an aspect of being paddles. Nevertheless, an as phrase can introduce such an aspect. (7.20) This book as a paddle is useless. It’s a fine piece of literature though. (7.20) says that this book has an aspect (among others) of being a paddle. Notice, however, that the book isn’t just a paddle; the anaphoric pronoun refers

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back to the book in its normal nature, not its paddling aspect. This is an example where we exploit the complex type in anaphora resolution. As phrases also modify predications in which one term denotes a collection or plurality as in:9 (7.21) a. John and Mary as a couple are a pain to have at a party, though John and Mary individually are fine. b. The students as individuals are well behaved, but as a group they are not well behaved. This illustrates a new type of • type, a collection • set of individuals type, for conjoined DPs or plural definite DPs. (7.20) shows that the • types that as phrases introduce are often linked to contingent properties, rather than essential properties like that of being a physical object, an informational object, or a place. The book will not cease to exist if it ceases to function as a paddle. The typing of an object via an accidental property is not solely a peculiarity of restricted predications, of course; linguists often appeal to the type food, but one could argue that something’s being a food is a contingent property of the thing itself. Nevertheless, because of the close link between types and individuation conditions, we should not expect quantifier domain shifting with all restricted predications. As Jaeger and Szabo noted, the restricted predication construction makes the book’s being a paddle presupposed, and this puts limits on the acceptability of various restricted predications. In (7.22) we see an attempt to presuppose information that is essentially incompatible with the basic type of the head noun: (7.22) a. #The rock as an abstract object is interesting. b. #The cigarette as an event lasted only 4 minutes. Rocks aren’t abstract objects, and cigarettes though artifacts aren’t events, and they’re essentially not events. It is thus impossible to accommodate such a presupposition, resulting in the infelicity of these examples. I will explain such examples by appealing to the presupposition as a presupposition about type: in order for (7.22) to be evaluable for truth or falsity, the type constraints of the as clause must be satisfiable by the subject. In this case they are not. Although aspects of things are not parts of those things, they still, recall, have an ordering. Consider the aspects denoted by John as a banker, and John as a banker in Toulouse. John’s being a banker in Toulouse is a more specific aspect than the aspect of John’s being a banker. Further, there is only one aspect of John’s that is his banking aspect. This follows from our assumptions about 9

Thanks to Friederike Moltmann for this example.

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individuation (that bankers and people have the same individuation criteria) and the ordering principle on aspects of chapter 6, which I repeat below: • Partial ordering on aspects: Provided z, x, and y obey the same individuation criteria, (α β ∧ x: α ∧ y: β ∧ o-elab(x, z) ∧ o-elab(y, z)) → y  x Furthermore, our partial ordering says that John as a banker in Toulouse is a subaspect of John the banker (tout court). At the level of logical form, the complement of an as phrase specifies a type for a variable u that serves as the argument in the main clause predication. But the as phrase also changes the type of the subject into a • type, relating the term introduced by the subject in logical form to u via o-elab, making u an aspect of the subject. This means that the type presuppositions of the as construction must apply to the subject DP, which is what we should expect, given that as introduces a predication over the subject. As phrases introduce a complex type, because they imply the aspect they single out for predication in the main clause is one of several. When we speak of John as a judge as opposed to John simpliciter, we are speaking about a restricted aspect of John, and we imply that John has other aspects besides that one singled out by the as phrase. TCL captures this implication by having as phrases retype their subjects as having a complex, but not completely determined, type and by having one aspect of the complex type specified by the complement of the as phrase. As Szabo suggests, the as construction has a comparative or contrastive element as well as something presuppositional: an as phrase presupposes that the subject has an aspect of the type it specifies. The logical form for John as a judge is corrupt looks like this: (7.23) λπ∃u: judge (o-elab(u, j, π) ∧ judge(u, π) ∧ corrupt(u, π)), where j: ? • judge While as phrases involve a predication semantically, the distributional facts suggest that they are not small clauses: as seen in (7.24), standard small clauses are restricted to certain argument positions and subject to strong restrictions on movement. (7.24) b. c. d. e.

a. The doctor examined the patients naked. ?The patients naked the doctor examined. John squashed the book flat. ? The book flat John squashed. *John gave the book flat to Mary.

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On the other hand, as clauses can modify many arguments and can move freely within the sentence. As phrases more closely resemble contrastive or comparative clauses, as the examples in (7.25) attest: (7.25) b. c. d. e. f.

a. John gave the book as a present to Mary. John gave the book to Mary as a present. As a present John gave the book to Mary. John gave the book rather than the stereo to Mary. Rather than the stereo, John gave the book to Mary. John gave the book to Mary rather than the stereo.

Comparatives (Kennedy (1997)) are usually analyzed as involving a degree function that plays a role in the main predication. As phrases don’t have degrees but they have a similar structure, introducing an aspect that plays a role both in the main and secondary predication. I assume that as takes a DP that plays a role in the main clause—this is the as clauses’s subject—and a complement to form a modifier that is adjoined to the main IP, much like a comparative. As takes its complement DP and the main clause IP as arguments—something which is necessary since as affects or places constraints on all of these elements semantically. The DP whose trace is in the subject of the as clause, I assume, undergoes quantifier raising so that it contributes an argument to the logical form both of the small clause and the main clause, as is depicted in the tree in figure 7.1.10 As phrases in English place restrictions on their DP complements. They take definites and also possessive constructions as well as indefinites in English but not other determiners. (7.27) b. c. d. e.

a. John as a doctor is competent. John as the winner of the race is happy. John as Fred’s father is mean. ??John as every (any) doctor is competent. ??John as many things is competent.

In other languages like French and Spanish, the corresponding constructions don’t allow DPs in complement position at all: (7.28) a. Jean comme m´edecin (*un m´edecin, *le m´edecin, *tout m´edecin). b. Maria como avogada (*una avogada). 10

The trace can either be in subject position, as is the case in most of our examples, or in other argument positions of the main verb as in (7.26):

(7.26) John loves Mary as a janitor.

7.5 As constructions in TCL

y yy yy y yy

DP

Q(xi )

as

{{ {{ { { {{

{{ {{ { { {{

205

CP C

CC CC CC C

PP

{{ {{ { { {{

IP A

AA AA AA A

DP

DP

φ

xi

}} }} } } }}

IP A

AA AA AA A I’

VP

Figure 7.1 Syntactic structure of as phrases

This suggests that the complement of the as phrases contribute a property, not a full DP, to interpretation. The property conveyed by the object NP of the as phrase’s complement DP determines a type that picks out an aspect of the subject of the as phrase. So the entry for as is: (7.29) λP: 1 λQ: 1 λΦ: dp λπ Φ(π∗? • ty+ (P)) (λu∃v: ty+ (P) (P(π)(v) ∧ o-elab(v, u, π) ∧ Q(π)(v))) The function ty+ takes a lambda term of type 1 and returns the most specific type it imposes on its object type argument, which is just the fine-grained type associated with that property in the internal semantics. We now can derive the logical form of John as a judge is corrupt. To interpret quantifier raising, the IP minus its DP furnishes a λ abstract: (7.30) λxi λπ corrupt(xi , π ) Assuming that the complement of the as phrase, the DP a judge, contributes the property term λuλπ0 judge(u, π0 ), which goes in for the λ bound P in (7.29), that (7.30) goes in for the λ bound Q, and that the λ term for John saturates the dp type variable in (7.29), the usual TCL rules of Application and Substitution now yield: (7.31) λπ∃xi : ? • judge (john = xi (π) ∧ ∃z: judge (judge(z, π)∧ o-elab(z, xi , π) ∧ corrupt(z, π))) On this analysis, as phrases serve principally to type the DP argument and to

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introduce an aspect of that DP denotation. But they also of course are factive predications, as the logical form makes clear. My story is similar to the extensionalist view. An intensional version of Univerality holds on my account, and trivially so since the as phrase always picks a unique aspect of John of that type; thus, if John as a judge is corrupt, we cannot consistently say that John as a judge is also honest. However, Persistence does not hold when we move a predication from an aspect to the whole object of complex type, and this is essential for solving the New Puzzle in this framework. John may be corrupt as a banker but not as a janitor, and we can’t infer in this account that John himself is corrupt simpliciter, unless by that we simply mean that there is some aspect of John and John under that aspect is corrupt. Predications on aspects of an object do not automatically transfer into predications of the object of complex type. To say of a book that it weighs five pounds is only to say of its physical aspect that it has that property; its informational aspect does not have that property. Predicating properties of aspects thus allows both presuppositions in (7.19) to be consistently accommodated; the presuppositions generated by the two as phrases on my account, in contrast to the extensional accounts, are that there is an aspect of John that is a judge and an aspect of John that is a non-judge. The big difference between TCL’s account of restricted predication and an extensionalist one lies in the difference between aspects and eventualities and the role these play in predication. A Neo-Davidsonian account takes all predications to involve eventualities, and holds that restricted predications pick out eventualities that are parts of eventualities picked out by unrestricted predications. Aspects, once again, are not parts. All of a book (in its material aspect) is a material object, and all of the book (in its informational aspect) is also an informational object. This means that we have to be careful with negated claims with aspectual predication; sometimes the negation acts normally and takes narrow scope, as in (this book is not heavy), but sometimes the negation takes “wide” scope over all aspects. For example, to say that something is not a material object, on this view, is to say that the object has no aspects that are material objects; and so, it is impossible to establish from a restricted predication picking out an informational aspect of a book that the book itself is not a material object at some time, state, or location. Similarly, from the fact that John has both a judge and a non-judge aspect we cannot conclude from this that John is not a judge at some time or place. Restricted predications, as well as aspect selecting predications, allow us to predicate incompatible properties of different aspects of objects; they also allow us to predicate properties of certain aspects that would be false of other aspects, indeed necessarily false, even if these predications hold at the same time. • types always give rise to a restricted

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predication when we ascribe to an object some property that is compatible only with one of several constituent types. One might argue that my account of predication is too weak to be plausible. Consider again (7.22). What blocks the accommodation of the complex type on rocks? We’ve seen that read can introduce a term of complex type involving information when it is predicated of something of purely physical type. Nevertheless, read, recall, does not affect the intrinsic nature or the individuation principles of its objects when it coerces them to have • type; that is why it does not affect the interpretation of the quantification in the object DP— subway walls remain physical objects even when the presupposition of read is justified locally within a VP like read the subway wall. Matters are otherwise with as phrases; they do modify the intrinsic nature of the DP, and in order for that to happen, the DP must range over objects that already at least potentially can have an aspect of the sort the as phrase specifies. It is simply impossible to construe rocks as having an aspect of type abstract object. There are also some restrictions with regard to restricted predications because of the logic of aspects: it is impossible for John as a banker to be both corrupt and not corrupt. Matters are otherwise with predications that are not restricted according to the grammar. Consider any pair of apparently contradictory sentences like I am happy now and I am unhappy now. Doesn’t my account make these automatically compatible? On my account such predications may, or may not, be restricted predications. They are contradictory predications of me if they are unrestricted. But the preferred interpretation of a sentence like (7.32) I am happy and unhappy now is one according to which we infer two restricted predications; i.e., there is an aspect of me that is happy and one that is unhappy; when we get incompatible predications on a single term, we read them as restricted predications. Indeed, this should not surprise us: one of the basic messages of this book is that many predications in natural language cannot be taken at face value; what appears to be a simple predication is often one restricted to an aspect of an individual. Nevertheless, (7.32), while not contradictory, feels incomplete; the interpreter awaits a specification of the aspects in which I am happy and I am not happy. As I have noted, this is not always an available strategy—viz., for (7.15) repeated below. (7.15) a. John makes $100K a year. b. John makes less than $70K a year. Some inferences that fall under a persistence-like principle do go through. Consider (7.33) and (7.34).

208 (7.33) b. (7.34) b. c.

Restricted Predication a. John as a judge makes $50K a year. John makes at least $50K a year. a. John as a judge in town A makes $50K a year. John as a judge in town B makes $60K a year. John as a judge makes at least $110K a year.

Some predicates persist as predications from parts to larger parts or wholes. If an aspect or part of John makes $50 K a year, then that part makes at least $50K, and making at least X is upward persistent in the relevant sense. The partial ordering I’ve defined over aspects or tropes allows us to define for additive properties (like salary) a homomorphism from the collection of properties to a domain of quantities so that we can sum up properties across aspects. But in general whether such persistence applies to other properties, like that of being a judge, will depend on the different sorts of restricted predications attributed to the object. In addition consider the following sentence:11 (7.35) John as a banker is the same person as John and the same person as John as a salesman. This example, though a bit unnatural, is perfectly intelligible. Given how different aspects can collapse relative to certain identity critera, this truth is something that is compatible with the TCL analysis of restricted predication. Furthermore the truth of (7.35) follows with a few assumptions. Let’s assume that if for aspects a and b a  b, then at least defeasibly it follows that if φ(a), then φ(b). In other words, this partial order over aspects resembles the subtyping relation itself, in that it supports defeasible inheritance. Now clearly Sameperson( j, j) (John is the same person as John). Assume now, as is plausible, that Same-person(x, y) is not only reflexive but also transitive and symmetric. Given defeasible inheritance, it follows at least defeasibly that Same-person(b, j), where b is the banker aspect of John and also that Same-person(s, j), where s is the salesman aspect of John. Given the properties of the predicate Sameperson, it quickly follows that Same-person(b, s), as desired. The partial order on aspects functions with respect to inheritance of properties in much the same way as the subtype relation does, which is not surprising as one is defined in terms of the other. If α β, an inhabitant of α normally has all the properties that an inhabitant of β does, but not vice versa. For instance, housecat cat; and Tasha, a house cat, inherits many properties associated with cat, the properties of having fur, being four-legged, having retractable claws, being able to climb trees. An element of the general type won’t have 11

Thanks to Gabriel Uzquierro for this example.

7.5 As constructions in TCL

209

many of Tasha’s properties—being gray and white, weighing five and one half pounds, and so on. Sometimes, more specific properties associated with the subtype block the inheritance of properties of the supertype. For instance, cheetah is also a subtype of cat, but cheetahs don’t inherit the property of having retractable claws. The same thing holds of aspects. If John is a person, then John the banker is also a person, and John the banker is even the same person as John. But the persistence of properties in general fails; more “general” aspects, higher up in the partial ordering (recall that the object of complex type is at the top of this partial order), often fail to inherit the properties of more specific aspects. But note this doesn’t mean that our language is non-classical, because predications for objects with aspect is always relative to one or more aspects. So, for instance, in cases where we have aspects of John as a banker and John as a non-banker, it still is OK to say that John is a banker—it’s just that this means that John, an object of complex type, has an aspect that is; furthermore, the object of complex type also has an aspect that is not a banker. Just as languages relativize many predications to particular times, worlds, and sometimes discourse contexts, on the view that I propose predications to objects of complex type are relativized to aspects. TCL’s treatment of as phrases makes sense of recursively embedded as phrases where one as phrase falls within the scope of another.12 (7.36) John made good money as a chimneysweep as a youth.13 Such embedded as clauses produce an aspect of an aspect; there is an aspect of John, John as a chimneysweep, and an aspect of that, which I’ll call John as a young chimneysweep. Given the partial ordering on aspects, we have: • John  John as c  John as young c The properties of John as a chimneysweep are defeasibly inherited by the aspect of John the chimneysweep in his youth, but not the other way around. For instance, John as a chimneysweep in his youth is a chimneysweep, but John as a chimneysweep is not necessarily young. Temporal aspects like that picked out by as a youth will pick out a temporal slice of John, and this affects predication roughly in the same way as a temporal adverb does but by a rather different mechanism. Thus, John as a chimneysweep in his youth will be temporally located within the time when he was a young man. How do the Landman axioms fare on this view? Consider axiom 2: 12 13

Although as phrases are similar to comparatives in a number of respects, they differ in one important respect. Contrastives do not embed happily one within another. Thanks to John Hawthorne for this example.

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Restricted Predication

2. If John as a judge is corrupt and John as a judge is well-paid, then John as a judge is well-paid and corrupt. The logical form for the antecedent of the conditional will yield: (7.37) λπ∃x: ? • judge (∃y: judge (x = j(π) ∧ judge(y, π) ∧ o-elab(y, x, π) ∧ corrupt(y, π))∧∃z: judge (judge(z, π)∧ o-elab(z, x, π)∧ well-paid(z, π))) By our axioms on types, as they are both o-elaborations of the same object and have logically equivalent types, y = z. And this yields the desired conclusion: (7.38) λπ∃x∃y (x = j(π) ∧ judge(y, π) ∧ o-elab(y, x, π) ∧ corrupt(y, π) ∧well-paid(y, π)) Axioms 3, 4, and 6 just follow as simple inferences or instances of theorems of classical logic or by the persistence axiom for types. The only problematic axiom is axiom 1, at least if we assume that the is in its formulation is the is of identity: 1. John as a judge is John. What we get for (1) is the following logical form: • λπ∃x: ? • judge ∃y: judge (judge(y, π) ∧ o-elab(y, x, π) ∧ y = x(π)) This is not valid. The aspect involving John that the as phrase picks out isn’t in general identical to the object of complex type. The presupposition of as phrases is that John has other aspects than that of being a judge, aspects whose type may be incompatible with judge. In that case we know that the judge aspect cannot be an inhabitant of the complex type ? • judge. Rejecting such instances of axiom 1 is essential for correctly characterizing the behavior of proper names in this framework. (7.39) Superman as Clark Kent is Superman. (7.40) Superman as Superman is Superman. Suppose that (7.39) yields as a logical form (7.41), where φCK (y) stands for whatever formula involving y we see fit to represent the contribution of the name Clark Kent when it occurs as a complement in an as phrase, and where R is any relation between y, which is the subject of the as predication, and the whole sentence’s subject s, which is Superman. (7.41) ∃y(φCK (y) ∧ R(y, s) ∧ y = s)

7.6 Proper names in as phrases revisited

211

Suppose that (7.40) yields an analogous logical form. Now reconsider (7.1a), according to which Superman as Superman gets more dates than Superman as Clark Kent does. Using the logical forms for (7.39) and (7.40), we’ll be able to substitute within (7.1a) Superman everywhere for any guise of Superman; in particular, we’ll be able to substitute Superman for the Clark Kent aspect of Superman. But this now yields that Superman gets more dates than Superman, which is necessarily false.14 Finally, Landman’s axiom 5 must be understood in a certain way. It does follow that if John as a judge is corrupt (ignoring presuppositions), then John is a judge. But the predication in John is a judge is still a restricted predication; all that really follows in this account is that there is some aspect of John under which we can truly say that he is a judge.15

7.6 Proper names in as phrases revisited I return now to the role of proper names within as phrases. On the one hand, TCL takes names, like all other linguistic elements, to have an internal semantics and thus a specific type. They can be used predicatively and in restricted predications in particular. On the other hand, the individual concept or type paired with a name in the internal semantics doesn’t clearly pick out any as14

15

We could interpret the is in, e.g., (7.39) not as the is of identity, but as the is of constitution. Thus, John as a judge is John would say that the part of John that is a judge is a part of John. This doesn’t seem that controversial, though the notion of parthood here needs to be explained. The view here provides an interesting consequence. Aristotle, who perhaps discovered restricted predication, holds a view in Sophistical Refutations 167a7–9 according to which (7.42a) is false but (7.42b) is true (Szabo, 2003).

(7.42) a. An isosceles triangle as such (i.e., as an isosceles triangle) is such that the sum of the interior angles = 180 degrees. b. An isosceles triangle as a triangle is such that the sum of the interior angles = 180 degrees. The logical form for these sentences is not entirely clear. Many read the predication as giving necessary and sufficient conditions for something’s being an isosceles triangle qua isosceles triangle or at least a necessary condition— i.e., the predication is that of an “iff” or of an “only if” statement. On my account of restricted predication, the definitional reading yields as logical forms for (7.42a,b) (assuming some sort of unselective quantification over x and ignoring type assignments): (7.42a ) ∀x, y((isos-trian(x) ∧ o-elab(y, x)) → (isos-trian(y) ↔ the sum of the interior angles(y) = 180◦ )) (7.42b ) ∀x, y((isos-trian(x) ∧ o-elab(y, x)) → (trian(y) ↔ the sum of the interior angles(y) = 180◦ )) (7.42b ) is clearly provable and necessarily true, whereas (7.42a ) is not (at least not in the right-to-left direction). If these are the right logical forms, then we have an explanation of Aristotle’s intuitions about these sentences.

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pect; for instance, John as John doesn’t seem to pick out any particular aspect of John’s. Some names, however, do pick out well defined aspects: names that are associated explicitly with roles in plays—Hamlet, Lear, Faust, Aunt Augusta, etc. Other names associated with more or less well-defined sets of individuating properties, like Superman and Clark Kent, Hesperus and Phosphorus or to give a more down-to-earth example, Jesse Ventura and The Body, which was Ventura’s moniker as a pro-wrestler, also work this way. As phrases thus coerce the meaning of proper names in their complements: ordinarily such names denote an individual, but in such contexts they denote an aspect of the individual, when that aspect is defined.16 This immediately blocks substitution of coreferential names within type designations, because coreferentiality of names doesn’t imply anything about the equivalence of the aspects associated with them; the fact that a = b doesn’t imply that the aspects picked out by the types associated with the names are the same. In this my analysis of as phrases is Fregean in spirit. But my analysis (with a standard, intensional analysis of propositional attitudes added) also implies that the thought that a = b doesn’t imply that x as a is intensionally equivalent to x as b. In this my analysis differs importantly from a Fregean one of the sort discussed earlier. On the other hand, property denoting complements of as phrases aren’t predicted to be opaque in the same way, as no coercion to a aspect denotation is required. Logical relations between predicates are reflected in the partial order on types and our axioms for aspects will allow substitution of logically equivalent predicate expressions. Following the outlines of the derivation of (7.31), we get where s and ck stand for Superman and Clark Kent respectively: (7.1a.1) λπ∃y: ? • s (s = y(π) ∧ ∃z: s (s-aspect(z, π) ∧ o-elab(z, y, π) ∧ ∃x: ? • ck (s = x(π) ∧ ∃w: ck (ck-aspect(w, π) ∧ o-elab(w, x, π) ∧ gets more dates than (z, w, π))))) Using Accommodation and in view of the facts proved in chapter 5 that α•α = α and (α • β) (γ • δ) = (α γ) • (β δ), we can simplify (7.1a.1) to: (7.1a.2) λπ∃y: ? • s • ck ∃z: s (s = y(π) ∧ s-aspect(z, π) ∧ o-elab(z, y, π)∧ ∃w: ck (ck-aspect(w, π) ∧ o-elab(w, y, π) ∧ more dates(z, w, π))) So Superman, in virtue of the aspects that the names Superman and Clark Kent can pick out in restricted predications, turns out to have several aspects and these aspects are what play a role in the main predication of (7.1a). Superman is forced, if this sentence is true, to have the types ?•α and ?•β, which naturally 16

This is a vindication at least in part of a Neo-Fregean approach: the predication involving a proper name is one of ascribing a role of some kind.

7.7 An aside on depictives

213

yield the type ? • α • β for Superman. The as phrases each pick out a relevant part of the individual, which serve as the arguments in the main predication. This semantic analysis of as phrases is compositional, avoids the problems of the New Puzzle, and explains why proper names behave strangely in otherwise apparently extensional contexts. It is a natural application of the conception of thick and thin individuals needed for copredication. In fact, the Saul examples show us that thick individuals are common subjects of predication. Restricted predication is a much more widespread phenomenon than one might think.

7.7 An aside on depictives Depictive constructions are similar to restricted predications in that they make two predications of an object. That is, in (7.43a) John has the property of being drunk and of driving home. (7.43) a. John drove home drunk. b. The doctor examined the patients naked. These examples are often treated (cf. Rothstein 2003, Kratzer forthcoming) using event semantics. The idea is that this construction introduces two events linked in a variety of ways. Within event semantics, it seems that we need to stipulate the relations between the events introduced in order to get the right temporal connections—namely, that John drove home while drunk. A bit of syntactic ingenuity is also needed to make John in (7.43a) the argument of the adjunct drunk. Our type driven approach to predication provides an alternative approach to these constructions, according to which depictives are restricted predications. In depictive constructions, IP adjoined modifiers have very similar semantics to as phrases to determine aspects. These modifiers pick out an aspect of the subject that is then the argument to the main predication and modify the type of a DP in the sentence. So in (7.43a) driving home is predicated of John as drunk. This would immediately license the desired temporal relations between the state of John’s being drunk and his driving home. Depending on which quantifier is raised in (7.43b), TCL predicts that the depictive may characterize the doctor or the patients.

8 Rethinking Coercion

With the framework of TCL and the formal analysis of • types in place, I turn now to coercion. The classic cases of coercion involve some sort of “shift” in a predication from the predication of a property to an object to the predication of a property to an eventuality of some kind. Here is a motivating example. (8.1) Sheila enjoyed her new book. (8.1) has the preferred reading that Sheila enjoyed reading the book. In this chapter I will present a formal analysis of such shifts. I will also provide an account of how such shifts are sensitive to the discourse context. For example, if the discourse context makes contextually salient that Sheila is an author, then the possible reading of (8.1) is that Sheila enjoyed writing the book. If the discourse context makes contextually salient that Sheila is the name of a cat, then the event enjoyed is perhaps something like clawing, scratching, biting, or sleeping on the book. GL, which attempted to predict the different readings for the predication with the coercion from the qualia associated with the direct object of the verb, was unable to model these context dependent inferences.

8.1 Re-examining the data Coercions involving a shift from a predication involving an argument that is not an eventuality to a predication involving an argument of eventuality type are widespread. Adjectives and other verbs that take syntactically given arguments of type e but that presuppose arguments of eventuality type sometimes force a predication over an eventuality that is related in some way to the denotation of the syntactically given argument. Some coercions, however, are much better than others.

8.1 Re-examining the data

215

(8.2) a. That person is slow (in understanding things, in running, etc.). b. The slow animal (the animal that is moving slowly) c. ?The slow tree (the tree that grows slowly) d. The event lasted an hour. e. John lasted an hour (e.g., John’s playing tennis, John’s running). Even when a noun has no clearly associated eventualities like those stipulated by GL and Pustejovsky (1995), aspectual verbs still coerce a predication on eventualities. It is just that we don’t know what these eventualities are, though appropriate discourse contexts can make precise the eventuality enjoyed in say (8.3): (8.3) John enjoyed the bathroom. Coercion depends on many factors. In (8.1), (8.2), and other classic examples of coercion, the predicates are responsible for coercing a predication on an eventuality related to their internal arguments, though they don’t determine which sort of events end up being introduced. We tested this hypothesis in chapter 1 using made-up words like zibzab inserted in the internal argument position of one of these predicates. (8.4) Sam enjoyed (started, finished) the zibzab. When hearers are asked about this sentence, most of them report that he enjoyed/started/finished doing something with the zibzab, but they have no idea what. The event interpretation can’t derive from the lexical meaning of the noun, since it’s made up and has no lexical meaning. The event interpretation, underspecified as it is, must come from the verb or from a predicate which presupposes that its argument be of eventuality type. If a coercing predicate is a prerequisite for coercion, the specification of the content of the coerced predication typically depends on several factors: on the discourse context, and on other arguments of the coercing predicate. Recall these examples from chapter 1: (8.5) a. #Smith has begun the kitchen. b. The janitor has begun (with) the kitchen. c. The cleaners have started the suits. d. The exterminator has begun (with) the bedroom. e. The painters have finished the windows. Which eventualities end up being the internal arguments of the verbs begin, start, and finish in (8.5) is not just a function of the direct objects or the coercing arguments themselves. The subject argument also plays an important role in determining the eventuality internal arguments.

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Given the theory of type presuppositions and their possible sites for binding and accommodation sketched in chapters 4 and 6, we should expect the verb to license the adjustment to the predication. The main verb of a clause is the main predicate, and type presuppositions flow from predicates to their arguments in TCL. However, the coercive shift in the predication from a syntactically given argument to another one of different type is different from the sort of type presupposition justification involving • types. No intuitions support the view that kitchen or any other noun referring to an artifact or natural kind is a dual aspect noun with an eventuality and an artifact aspect. Kitchen is different in nature from, say, lunch or interview. The linguistic evidence for this intuition is that while lunch takes all sorts of predicates of eventualities straightforwardly, kitchen does not: (8.6) a. The lunch starts/finishes at 12:30. b. ??The kitchen starts/finishes at 12:30. Eventuality readings of the kitchen in (8.6b) are difficult but perhaps possible, especially if a particular discourse context is invoked—one, say, in which a visit to the kitchen is scheduled. The difference between (8.6a) and (8.6b) is subtle though clear. The nouns in (8.5) are not plausibly artifact/eventuality dual aspect nouns and do not involve a selection of an aspect. We have also seen a difference in the behavior in the selection of quantificational domains for dual aspect nouns versus traditional coercions. Coercions induced by aspectual verbs and the like do not give rise to versions of the quantificational puzzle, examined in chapter 6. They do not affect the interpretation of the DP argument itself, something we observed in chapters 3 and 4 by looking at pairs like the following. (8.7) George enjoyed many books last weekend. (8.8) Fred stole every book from the library. (8.7) means that George enjoyed doing something with many books last weekend, presumably reading them. The coercion does not affect the quantification in the DP but only the way the variable introduced by the DP is related to the argument of the verb enjoy. In (8.8) the predication that forces the type shift on book from p • i to p affects the interpretation of the entire DP. Another difference between coercion and aspect selection concerns the robustness of the presupposition justification involved. Dual aspect nouns are compatible with any predicate that selects one of their aspects. But only some predicates that presuppose eventuality types for their arguments license coercion, and sometimes these predicates license coercion only in certain syntactic configurations. Eventuality coercions involving predicates like start with

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nouns like book as an internal argument are not available in every syntactic configuration. (3.54) b. c. d. e.

a. The reading of the book started at 10 a.m. #The book started at 10 a.m. John started the book. John started the reading of the book. John started at 10 a.m. (started to run, to bicycle, to climb.)

(3.54b) is weird in comparison to (3.54a) or (3.54c–e). As I argued in chapter 1, this suggests that event interpretations should not be part of the noun’s meaning. It would be difficult to deny phrases like the book an event reading if events were associated with book in the lexicon, as is the case in GL, or as is the case in TCL with dual aspect nouns like lunch. This would lead to incorrect predictions, like saying that (3.54b) is fine, when it is not. My position concerning nouns like book and event coercion is this: only certain predicates with particular argument structures that have eventuality presuppositions license the introduction of an associated eventuality with nouns like book. For the aspectual verbs start, begin, finish, and end, event coercion is only possible if there is an agent explicitly given as an argument in addition to the argument that undergoes coercion. The coercive behavior of aspectual verbs is not uniform either. While aspectual verbs like stop and finish have a clearly related meaning, their behavior with respect to eventuality coercion is quite different. They have different meanings when they combine with the same arguments: (3.55) b. c. d.

a. Mary finished eating the apple. Mary finished the apple. Mary stopped eating the apple. Mary stopped the apple.

There are aspectual differences between these verbs that account for the differences in meaning between (3.55a) and (3.55c); but, as I argued, contra attempts in GL, no explanation using event aspect for the differences between (3.55b,d) is forthcoming, as both verbs select for internal arguments with largely the same aspectual types. Stop and finish also don’t license the same coercions. (8.9) a. John has finished the garden/the kitchen. b. #John has stopped the garden/the kitchen.

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(8.9a) is perfectly natural and means that John has finished doing something to the garden, like preparing it or digging it up. It’s very unclear what (8.9b) means at all in an out of the blue context. Stop also has different control properties from finish or enjoy. Like these verbs, stop controls syntactically explicit agent argument positions of complements like (8.10a,b); but unlike finish and enjoy, it does not control any argument positions with coerced DPs. (8.10) b. c. d.

a. I’ve stopped smoking. I’ve stopped to smoke. I’ve stopped the smoking. I’ve stopped cigarettes.

(8.10d) can mean that I’ve stopped smoking cigarettes, but it can also mean that I’ve stopped cigarettes at the French Andorran border if I’m a custom’s agent; it can mean that I’ve stopped cigarettes from rolling off the table, etc. Start and begin also differ from finish or enjoy. The coercion effects of start and begin are less easily interpretable with many consummable direct objects than finish. (3.57) b. c. d. e. f.

a. Mary started eating her apple. ?Mary started her apple. Mary started eating her sandwich. Mary started her sandwich. Mary began eating the apple. ?Mary began the apple.

These examples sound more or less good depending on their arguments. I have a harder time getting the eating event associated with fruits with these verbs than with constructed foods like sandwiches or candy. Google searches support this intuition.1 When start or begin take anything but natural foodstuffs as their direct objects, the coercions they induce do not describe except with difficulty an eating event.2 While begin, start, and finish all coerce some arguments — e.g., start a cigarette, begin a cigarette, finish a cigarette—they are not all equally happy in their coercive capacity. 1

2

I didn’t find any citations on Google for starting apples, starting peaches, or the like, and begin the fruit sounds even weirder to me. I did find one citation involving starting a peach candy. With vegetables like carrot, there are many citations involving products derived from carrots like carrot juice, but no citations for started a carrot by itself. This generalization would seem to explain the observations of Vespoor (1996) below.

(8.11) a. Last night, my goat went crazy and ate everything in the house. b. At 10 p.m. he started in on your book. c. At 10 p.m. he began to eat your book. d. #At 10 p.m. he began your book.

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Yet another aspectual verb end hardly seems to induce event coercion at all on its own. (8.12) b. c. d. e.

a. ?Mary ended the cigarette. ??Julie ended the apple.3 Alexis ended the sonata with a flourish. Lizzy ended the sonnet with a wonderful image. Mary ended the meeting/the discussion/the negotiations.

When the verb finish takes a consummable as its internal argument, it describes a consumption of the object, whereas this rule does not work with end. The coercive capacities of end are restricted to things that are informational artifacts—i.e., things of type p • i or entities that are or have eventualities of some sort as aspects (e.g., things like films). Event coercion is very much a matter of the verb’s fine-grained meaning, as well as of its type presuppositions.4

8.2 Coercion and polymorphic types Coercion is, on my view, a matter of adjustment in predication due to the justification of a type presupposition. Coercion arises because of a type conflict: a predicate demands a certain type α of one of its arguments but the argument is of type β and α β = ⊥, and, furthermore, neither α nor β are constituent types of the other (i.e., neither one is a • type containing the other as a constituent). So the methods of type justification surveyed so far do not apply. What is special about coercing predicates is that, in addition to imposing a type presupposition on its argument, the predicate licenses a map from β to some possibly underspecified subtype of α. This map ensures that the presupposition of the predicate is satisfied, provided that the underspecification can be filled in. The map licensed is another transformation from one category to another.

3

4

(3.53d) is plainly bad even though the context primes the reader to interpret the coerced eventuality as an eating event. Vespoor (1996) postulates that coercion specifications get to be part of the semantic content, even though they are defeasible at the outset. If the generalization observed above is correct, we would not need to resort to this complication. There seem to be no sensible uses of this on Google, though someone might attempt to convey the proposition that Julie killed the apple by using this sentence. There seems to be an alternative to this aspectual use of end for all sorts of objects that can be destroyed, which is put an end to. This might be responsible for blocking the coerced reading of (8.12a,b). The qualia of GL associated with a food like apple thus explain little concerning the coercions just discussed.

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As with • types, a particular predicational configuration licenses the transformation and the result of this transformation is what satisfies the type presuppositions of the functor. However in aspect selection, it is the • type of the argument together with a functor that takes as an argument one of the • type’s constituents that licenses the transformation; in coercion, it is the fine-grained functor type together with an argument of the right type that licenses the transformation. The output of the transformation is a type B that is a function of that argument’s type, as well as other arguments of the functor. The value of B is specified not only by the types of these arguments but by the discourse context. In figure 8.1 is a general diagram for coercion involving an argument β of type β that is triggered by a functor of type δα and where a specification of B is a subtype of β and depends on α. We’ll look at many examples of such coercion. BC β

δα × α × γ

-

β

δα × α × γ

. id × id × dep .

β



δα × α × B(α, γ)

C

D Figure 8.1 β Coercions

This transformation invokes polymorphic types with underspecification. I used underspecification of types in the last chapter to analyze restricted predication. A polymorphic type encodes a general dependency between one type α of some term and the type of the term’s argument, which I’ll call a parameter. We will be looking at particular “instances” of the dependency relative to particular parameters. Our transformations in fact require dependent types, since they may depend not only the type of another term but on the semantic value (in the internal semantics) of that term. For instance, consider (8.13) John enjoyed everything last night,

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where the term involved in the coercion is a quantifier. If a term t is assigned a dependent type, then it will have a general, quantified type; its instantiations will have the types specified when the parameter types are substituted for the bound variable types. Whereas functional types denote a simple arrow object, dependent types denote an indexed family of arrow objects in the abstract, category theoretic model for types (Barr and Wells (1990), Asperti and Longo (1991), Chen and Longo (1995), Longo (2004)).5 For example, the finegrained type red can be considered as a map from objects of type p to p, but we can also consider it as a polymorphic type—a type whose value is dependent upon the type of its argument (or the value of its argument in the internal semantics). Types like meat, pen and shirt map to different output types— red(meat), red(pen), etc.— with quite distinct application conditions, which specify the internal semantics of these types. Constraints on such types are represented with quantification over types as in (8.15) with a type restriction on the output:6 (8.14) ∀x  p red(x) p) Here again is the type of red: (8.15) ∃x p ((x ⇒ t) red(x) ⇒ t) In TCL, polymorphic types may be either universally or existentially quantified types. What interests us for the most part are their instantiations. Given a dependent type θ of the form ∃x1 α1 . . . ∃xn αn A(x1 , . . . xn ) α, every instantiation of θ, θ(β1 , . . . , βn ), where βi αi , is a subtype of α. All coercions involve at least polymorphic types on my analysis. In fact, coercions involve dependent types in light of examples like (8.13), but most of the simpler examples familiar from the linguistic literature require only polymorphic types, so I’ll develop the analysis with this in mind. Predications involving the aspectual verbs (begin, start, continue, finish, end) and verbs like enjoy license polymorphic types that can justify their type presuppositions. These polymorphic types map the types of the grammatically given arguments of the verb to a subtype of event, or evt. Thus, these verbs presuppose their internal arguments to have an event type, but they also license a polymorphic type, all of whose instances are subtypes of evt. I use this polymorphic type, or rather the instance given by instantiating the quantifiers to the types given 5

6

These types are also similar to the records used by Cooper in the framework of Type Theory (Cooper 2002, 2005). Records are functions from types to other types or even type assignments. Of course, if the set of subtypes of p is finite, these restricted universal type expressions denote product types in the categorial semantics, just as restricted existential type expressions denote coproducts.

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by the verb’s arguments, to justify the type presupposition of the verb. Polymorphic types justify type presuppositions in something like the way bridging inferences can serve to justify presuppositions.7 In some cases the value of the polymorphic type may be lexically specified, but often it is only determined by the predicational context (by which I include the other arguments of the coercing verb) or the discourse context. It is because of this indeterminacy, or polymorphism from the type theoretical point of view, that it is expedient to use polymorphic types rather than simple functional types. To state the type presuppositions of coercing predicates, I use the function + ty , introduced in the last chapter. ty+ picks out the most specific type associated with a λ term. The value of the underspecified, polymorphic types licensed by coercing predicates depends on the head type of the DP arguments of the verb—that is, the type of objects over which they are defined. I define head(Φ), or hd(Φ) as follows, where Φ is of type dp and of the form λQλπ Quantifier x (φ(x, π), Q(x, π)). Definition 19

hd(Φ) = ty+ (φ)

Let’s now look at the entry for a coercion verb like enjoy. As we expect from the discussion, it is structurally similar to the entry for read. enjoy

enjoy

: ag)(λv Ψ(π ∗ arg2 : evt − (hd(Φ), hd(Ψ)) (8.17) λΨλΦλπ Φ(π ∗ arg1 (λy1 λπ3 ( enjoy(v, y1 , π3 ) ∧ ag(y1 ) = v(π3 ))))) A gloss of some of the new elements in (8.17) is in order. Enjoy requires that its subject be an agent or of type ag. Enjoy, like the aspectual verbs, is also a control verb; the formula ag(y1 ) = v specifies that the agent of the eventuality y1 is the same as the agent of enjoy. The internal argument type presupposition for enjoy must be of event type or evt, but the type presupposition also conveys the information that it licenses a presupposition justification via the instantiation of the polymorphic type  given by the head type of its arguments. The type  is a function of two types that returns a subtype of evt. However, the instantiation of  relative to the arguments of enjoy in a particular predicational context may or may not be unspecified. In cases where the conventional types of arguments do not specify the coerced underspecified types, the discourse context 7

Here is an example of a bridging inference that justifies the presupposition introduced by a definite description.

(8.16) I started my car. The engine made a funny noise. The DP the engine has a presupposition that the entity it denotes be linked to some salient individual in the discourse context. By making the inference that the engine is part of my car, the presupposition of the definite is justified. For discussion, see Asher and Lascarides (1998a).

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may do so. It is up to a theory of discourse structure and interpretation to specify how this is to be accomplished. If the eventuality type remains unspecified even with the discourse context is taken into account, then the predication is not felicitous, since the underspecified type does not justify the type presupposition of enjoy. It is similar to the effect of an unresolvable anaphor such as the pronoun in (8.18) when uttered in an “out of the blue” context without any salient antecedent: (8.18) He’s silly.

8.2.1 Polymorphic type presupposition justification The presuppositions of predicates that license eventuality coercion resemble those of predicates like read that can force an accommodation of a • type (recall the discussion of read the subway wall from chapter 6). Our discussion of 8.7) above sharpened the resemblance between coercion generally and the behavior of read on its internal argument. In neither case, does the justification of presuppositions affect the interpretation of the DP; it affects only the local predication involving the verb. Hence, the lexical entry that encodes the presuppositions for coercing predicates must introduce a type presupposition that triggers Local Presupposition Justification, our rule introduced in chapter 6. This will ensure that the type presupposition receives a justification close to the verb and not in the restrictor of the DP. It will thus not shift the quantificational domain or the change the objects the DP is in some sense intuitively about. Let’s look at an example where enjoy applies to a DP like many books as in (8.19) which is a slight simplification of (8.7). (8.19) George enjoyed many books. Constructing a logical form for the DP and applying it to the entry for enjoy gives us: enjoy

(8.20) λΦλπ Φ(π ∗ ag)(λv λQ many(x) (book(x, π ∗ arg2 : evt − (hd(Φ), book book ct) ∗ arg1 : (p • i) ct), Q(π)(x)) (λy1 λπ1 (enjoy(v, y1 , π1 ) ∧ ag(y1 ) = v(π1 )))) Following the stipulation that polymorphic type presuppositions must be justified locally and abbreviating our type constraints on x and y1 , we get: (8.21) λΦλπ Φ(π ∗ ag)(λvλQ many(x) (book(x, π), Q(π ∗ evt − (hd(Φ), book ct))(x))[λy1 λπ1 (enjoy(v, y1 , π1 ) ∧ ag(y1 ) = v(π1 ))])

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Continuing the reduction, we get: (8.22) λΦλπ Φ(π ∗ ag)(λv many(x) (book(x, π), enjoy(v, x, π ∗ evt − (hd(Φ), book ct)) ∧ ag(x) = y1 (π ∗ evt − (hd(Φ), book ct)))) The presuppositions in the nuclear scope of the quantifier cannot be satisfied as they stand. But the dependent type in the type presupposition of the verb licenses a transformation of the sort I diagrammed earlier and the introduction of a polymorphic type functor with a polymorphic type to justify the presupposition. The functor will apply to the λ abstract in the consequent given by the verb, λy1 λπ1 (enjoy(v, y1 , π1 ) ∧ ag(y1 ) = v(π1 )), just as we have seen with other cases of adjusted presupposition justification. The functor resembles the one used for aspect selection in that it shifts the type of the property that will combine with the verb; but instead of introducing the relation o-elab, which relates an aspect and its bearer, the functor introduces an underspecified relation that in the context of a felicitous predication will specify the event relating the variable introduced by the object DP, and other arguments of the verb. The functor thus introduces the an eventuality of underspecified type (α, β). The formula reflecting this type in the logical form is given by the term φ(α,β) (e, x, y). The functor instantiated for our example looks like this: (8.23) λPλuλπ (∃z: (ag, book ct) ∃z1 : ag(P(π )(z) ∧ φ(ag,book ct) (z, z1 , u, π ))) Applying the functor on the designated λ term within (8.22) and using Substitution, Binding, Application, and Substitution, we get: (8.24) λΦλπ Φ(π ∗ ag)[λv many(x) (book(x, π), ∃z∃z1 (enjoy(v, z, π)∧ ag(z) = v ∧ φ(ag,book ct) (z, z1 , x, π)))] We can now integrate the subject into (8.24) and exploit the fact that ag is a function to get the finished result: (8.25) λπ∃y(y = g(π) ∧ many(x) ( book(x)(π), ∃z: evt( enjoy(y, z, π)∧ ag(z) = y ∧ φ(ag,book ct) (z, y, x, π)))) This eventuality can be specified by the predicational context. For example, in the given predicational context the polymorphic type may map an object of type cigarette to an event of type smoke(agent, cigarette). In this case we can specify the eventuality involved in the coercion and in turn specify φ(ag,book ct) (z, y, x, π) with the formula smoke(z, y, x, π). We’ll see how to do this in a minute. The type of functor in (8.23) suffices to handle all cases of event coercion with verbs whose presuppositions are sensitive to both the type of the subject

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and object. I’ll call this the E functor. In what follows, I assume that α and β are inconsistent with the value of the dependent types  and δ. Much of the notation below is familiar from the rules of presupposition justification for • types. argQj : α/β is shorthand for the j-th argument of Q being either of type α or of type β, and to say that v ∈ argiP ∩ argQj is, recall, to say that v is a variable that is both the i-th argument of P and the j-th argument of Q. These are conditions that are needed for the introduction of the E functor: • Type Accommodation with Polymorphic Eventuality Types (EC) φ(v, π), π carries argiP : (α, β) ∗ argQj : α/β, v ∈ argiP ∩ argQj E(λwλπ1 φ(w, π1 ))(π)(v) Since such type accommodations are the properties of lexical items, we can generalize our accommodation strategy for event coercion to arbitrary dependent type coercions: • Type Accommodation with Polymorphic Types δ (δC) φ(v, π), π carries argiP : δ(α, β) ∗ argQj : α/β, v ∈ argiP ∩ argQj D(λwλπ1 φ(w, π1 ))(π)(v) Polymorphic types in event coercion describe a morphism from types of objects to dependent types of eventualities involving those objects, and the E reflects that morphism from objects to eventualities in logical form. Why should this transfer principle and type shift from objects to eventualities be sound? The answer has to do with the presuppositions of the particular words that allow for this morphism, like, e.g., the aspectual verbs and enjoy. Enjoying a thing, for instance, presupposes having interacted in some way with the thing, and that interaction is an event. The verb enjoy, however, doesn’t specify what that event is. The event could be just looking at the object as in enjoy the garden or perhaps some other activity. Similarly, one can’t finish an object unless one is involved in some activity with that object, whether it be creating it or engaging in some other activity towards it. That is why such transformations are lexically based; it is the lexical semantics of the words that license the coercion and that makes the rules sound. Note that if polymorphic types were not so lexically constrained, the whole system of types might collapse. If arbitrary polymorphic or dependent types are allowed, then compositionality becomes trivial and the type hierarchy becomes meaningless. In TCL, however, the polymorphic types licensed are part of a

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lexical entry’s information. And so TCL predicts lexical variation of coercions, as the data show. Polymorphic types permit us to model how the sort of eventuality that is coerced from the meaning of the verb’s direct object in classic cases of event coercion often depend on other arguments of the verb, as in the case of (8.5) above. They also account for the judgement in (8.26) where the eventuality that is enjoyed is underspecified, unless the context, for instance, makes clear that what Lizzy enjoys about rocks is climbing them: (8.26) Lizzy enjoyed the rock. How should we think of the specification process of ? Pustejovsky’s GL is right that the types of the objects involved in  are important in specifying the eventuality involved in the coerced predication.8 In reviewing criticisms of GL, however, we saw that the use of qualia, even when restricted to artifacts, didn’t cut the coercion data at the joints. The examples in which telic and agentive function as GL predicts are captured by a different classification, one that uses modal types like consummable together with a type like artifact. To enjoy or to begin/finish a consummable artifact (e.g., a prepared food or beverage but not limited to such ) almost always has the reading that one enjoyed, began, or finished consuming the consummable. One could then specify the particular type of event of consumption based on the particular type of consummable. It seems reasonable to postulate types like container and containable, or polymorphic types like contain, which permit us to specify the following subtype relations: bottle, can contain(liquid). These capture the “figure/ground” alternations that have been noticed in the linguistic literature. As noted in Lascarides and Copestake (1995), world knowledge or discourse information can help specify the meaning of coercions. In TCL this means that discourse context contributes to specifying types like . We have also seen that such information, as well as information about other parameters in , may defeat default lexical specifications for  like those postulated for the qualia in 8

The qualia of GL are, from the perspective of TCL, polymorphic types of one argument. They are partial functions from types to types. They classify various events as agentive, telic, and so on with respect to a certain parameter type—the type with which they were associated in GL. To capture the intuitive aspects of GL’s story about coercion, we just need to stipulate the following components in our type hierarchy:

(8.27) a. write agentive(p • i) b. roll agentive(cigarette) c. smoke telic(cigarette) d. read telic(p • i) e. drink  telic(beverage) f. play, listen-to telic(music)

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GL. How should defeasibility enter into our type inferences that derive from this sort of coercion? We could assume a notion of defeasible inheritance in which subtypes inherit associated types or traits from their supertypes but in which information associated with more specific types may override information inherited from more general types— as is the case in Lascarides et al. (1996).9 Rather than make our type justification rules defeasible, however, I will defeasibly specify values for the partial function  in a background logic. This logic will contain defeasible type specification rules that give appropriate defeasible values for  or for its particular instantiations. This allows us to use information from the discourse already present in a limited way to infer information about the type of the associated eventuality, and we avoid having to incorporate defeasibility into any of the type coercion rules. Separating the reasoning about the values of dependent types from the type composition process simplifies the type justification rules and allows them to remain monotonic. Our logic here for specifying types is a universal fragment of a modal logic with a weak conditional operator > which contains variables over types, constants for atomic types, function symbols for dependent types and • types, and non-logical predicate symbols like , . Our axioms can all be written out in a universal fragment of first-order logic, which is amenable to quantifier elimination and a proof that its validity predicate is decidable.10 The semantics, proof theory, and licensing of defeasible inferences of such a fragment is well understood (Asher and Morreau 1991, Morreau 1992, Morreau 1997, Asher and Mao 2001). The truth definition for this language is completely standard except for formulas of the form A > B, which is true roughly just in case if A then normally B. While modus ponens is not a valid rule for >, the semantics for > allows us to defeasibly infer B from A > B and A. The logic also supports a form of specificity reasoning: conditionals with logically more specific antecedents “win” over those with less specific antecedents. So the following inference pattern is defeasibly valid: (A ∧ B) > C, A > ¬C, A ∧ B ∼ | C, where ∼ | represents the defeasible inference relation. This is essentially the same logic used by Asher and Lascarides (2003) in reasoning about discourse structure, though applied to a different language. It is easily extended to incorporate information about discourse structure into it. Here are some sample defeasible specifications of  that we might want to adopt. Let ev stand for the type of an aspectual verb or enjoy Many more such axioms exist that depend on suitable discourse information. 9 10

In an earlier version of TCL developed by Asher and Pustejovsky (2006), defeasibility was part of the type coercion rules themselves. See Lascarides and Asher (1993) for a discussion.

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(α human ∧ β p • i) → (ev(α, (α, β)) > (α, β) = read(α, β)) (α author ∧ β p • i) → (ev(α, (α, β)) > (α, β) = write(α, β)) (α goat ∧ β p • i) → (ev(α, (α, β)) > (α, β) = eat(α, β)) (α janitor ∧ β p) → (ev(α, (α, β)) > (α, β) = clean(α, β))

We can also simply deny certain equalities as in • (α goat ∧ β p • i) > ¬(α, β) := read(α, β) As I argued in chapter 1, these default rules are part of the lexicon, part of word meaning and the theory of predication. It will undoubtedly be a tricky business to write these default specifications. But these could be gleaned perhaps from data about word collocations across corpora. Undoubtedly, many of these result from language users’ sensitivity to the frequency of collocations. As the data suggests, there are many possible values for instantiations of underspecified, polymorphic types like . A big advantage of the polymorphic type approach is that it allows us to specify associated eventualities by taking into account arguments other than the internal argument of the licensing verb. This will allow us to specify many cases of coercion that we have already examined and that fall outside the scope of traditional qualia. This also suggests a further refinement: an instantiation of parameters in  may yield a type that may be further specified in certain discourse situations;  might even involve a non-deterministic choice element, choosing an eventuality out of a set of potential candidates with a certain frequency. The defeasible specifications given enable us to eliminate the underspecification remaining in (8.25). With the first rule of default identities, we can now specify the dependent type (agent, book ct) to read(agent, book ct). In turn this allows us to specify further the type description of the eventuality φ(agent,book) to read. When we retrace the derivation that for (8.7) above, we get as a final analysis: (8.28) λπ∃y(g = y(π) ∧ manyx (book(x)(π), ∃z (enjoy(y, z, π) ∧ read(z, y, x, π) ∧ y = ag(z))))11 We thus derive the reading that George enjoyed an event that is associated with many books, and that event is by default an event of his reading those books. Similarly, we predict Elizabeth enjoyed the sonata to mean that Elizabeth enjoyed listening the sonata. This default can be overridden if the context makes another sort of eventuality salient. 11

The careful reader will have noticed that the predicate read above is not the same as that introduced by the verb in TCL, because it contains an additional event argument. I come back to events and their relation to verbs in the next chapter.

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Given that the polymorphic type presuppositions of coercing verbs are to be accommodated locally, we predict that copredications should occur with coercion verbs. This is indeed the case.12 (8.29) John bought and then enjoyed an apple. (8.29) can mean that John bought a physical apple and then enjoyed eating it. If we suppose that the two coordinated verbs follow our alternative coordination rule, then we should expect a local accommodation of the type pressuppositions and the analysis will follow very closely to the analysis for coordination seen in chapter 6. Crucially, what allows the copredication to work with coercions is that an additional variable is introduced for the eventuality of eating the apple that is linked to the variable introduced by the DP an apple by the application of a functor to the λ term that accommodates the presupposition. My analysis of coercion makes use of the Separate Term Axiom and shares this feature with my analysis of aspect selection. In general it is the use of separate terms related together that distinguishes logical polysemy from accidental polysemy. This in fact predicts that copredications should work with all cases of logical polysemy. According to my proposal, it is the presuppositions of enjoy, finish, and other predicates that provide the justification for the event coercion. TCL predicts that event coercion generalizes: any predicate that licenses a polymorphic type whose instances are subtypes of evty will give rise to event coercion. However, TCL predicts that not all coercions are equally good. Presupposition justification using polymorphic types does not in general determine a specific eventuality type as the value of the morphism for a given object. When such eventualities cannot be defined by the context or by other predicational parameters, TCL predicts that it’s not clear what’s being said; there is no fully formed logical form for such a sentence, much like a case of an unresolved anaphor. For example, in (8.30), the predication is predicted to be odd or incomplete, much in the same way as he’s silly uttered in a context where an antecedent for the pronoun isn’t readily available expresses an incomplete proposition: (8.30) John enjoyed the door. (8.30), though not very felicitous by itself, needs only a bit of context to become good again. In the next section, we will see how discourse context can specify the underspecified types introduced by EC. 12

Note that GL cannot handle such examples, if one is to select the qualia value as the contribution to logical form of apple. It will run into exactly the same difficulty that GL’s account of copredication with • types did.

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TCL predicts that different coercing verbs may suggest different specifications for the dependent types they license, and they may even put requirements on the type of eventuality they license. For example, finish and enjoy certainly behave differently at the level of the default identities; to enjoy a garden suggests that one enjoyed looking at a garden, whereas to have finished a garden conveys that one has finished constructing the garden or digging it up. Finish in its transitive usage takes an accomplishment type eventuality, whereas enjoy or stop need not.13 Finish also requires that its accomplishment argument be a action by the subject that directly affects the object. This is not true of enjoy either. Verbs like last also give rise to a version of event coercion, though it’s different from that with enjoy. Last presupposes that its subject is involved in some temporally bounded state or activity—e.g., of existence or some more contextually defined state or activity. Earlier we saw that finish and stop also behave differently. Mary finished the apple and Mary stopped the apple have very different readings. Recall also the pair: (8.9) a. John has finished the garden/the kitchen. b. #John has stopped the garden/the kitchen. I take the differences between stop and finish to be a matter of their type presuppositions—in particular, the sort of dependent types they respectively license. An agent’s finishing X presupposes that the agent was involved in some sort of accomplishment or activity involving X. Finish in its transitive use has a presupposition that its subject is performing an action that directly affects the direct object and it is that eventuality that the agent finishes, whereas stop lacks this presupposition. When an agent stops X, where X is a DP, the presupposition is just that X was involved in some sort of event or process that the agent puts a stop to, not that the agent puts a stop to some event that he and X were involved in.14 13

Consider, for instance:

(8.31) a. I’ve stopped smoking cigarettes. b. ?I’ve finished smoking cigarettes. c. I’ve stopped smoking five cigarettes. d. I’ve finished smoking five cigarettes.

14

(8.31a) implies that I’ve stopped doing an activity, the activity of smoking cigarettes. (8.31b) does not have this reading. Instead (8.31b) seems almost to force an accomplishment structure on the event of smoking cigarettes. The pair (8.31c,d) is also interesting: finish naturally combines with a gerund denoting an accomplishment, whereas stop does not. (8.31c) seems to coerce the naturally telic predicate into an activity in which one is smoking five cigarettes at the same time. Agents can of course stop doing something to X, in which case there is a presupposition that the agent was doing something to X.

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In TCL, stop does not license a dependent type of eventuality involving its internal argument and its subject. It licenses a dependent type of eventuality only on the internal argument. Hence the particular transfer functor for this coercion will differ from that for finish or enjoy. For John stopped the apple, the type presupposition for stop is (apple) and accommodating this presupposition will give rise to an event description in which an agent argument is lacking and thus there is nothing for John to control in John stopped the apple. Generalizing from the data surveyed earlier, if the object argument X is typed p, then the process involving X must be a physical motion. The language for type specifications that serves to specify default values for the dependent type  can also specify this constraint: (8.32) stop(agent, (p)) → (p) phys-process Thus, TCL predicts that it’s hard to accommodate the relevant presupposition for (8.9b), because it’s unclear what physical process the garden or kitchen could be undergoing that John could put a stop to. This predicts also a difference in the control behavior of a verb like stop exhibited in the examples (8.10). For a gerund with a subject argument position, we predict that control is possible. But if a DP is used the control phenomenon disappears, since the dependent type licensed by stop does not contain an agentive parameter. Begin and start have particular presuppositions about the type of arguments they permit. When their internal arguments are not of event type, begin and start require arguments that are constructed or fabricated consummables— sauces, pastas, cigarettes; in addition, start accepts as a non-event argument anything that has an engine (motorcycles, buses, airplanes, cars, etc.). Like enjoy and finish, they license the justification of their presuppositions via a dependent type that involves an agent parameter. With this assumption, TCL predicts that in their intransitive uses, where no agent is specified, these verbs will not license coercions, because an argument is missing to the licensed dependent type. When an agentive subject argument is not present, the dependent type licensed by, say, start, begin, and finish, is not defined and so no predication has taken place. The data confirms this prediction. (8.34b) below is quite bad, although (8.34d) is better.15 15

Intransitive coercions involving start are acceptable when the coerced event is made explicit, say, by an infinitival phrase or gerund:

(8.33) a. The pasta started to boil. b. The pasta started boiling. These point to a complex compositional problem; what these examples mean is that the

232 (8.34) b. c. d. e.

Rethinking Coercion a. The reading of the book started (began, ended) at 10 a.m. #The book started (began, ended) at 10 a.m. The eating of the pasta started (began, ended) at 6 p.m. ?The pasta started (began, ended) at 6 p.m. The cooking/preparation of the pasta started (began, ended) at 6 p.m.

Begin and start license polymorphic types with specific restrictions on arguments. They are, for example, quite restrictive with respect to non-event and non-physical arguments. They share this behavior concerning arguments of abstract object type with other eventive verbs like last, but not, curiously enough, with enjoy. (8.35) #John has started/begun the fact (the thought, the proposition) that he is hungry/the number 2/ the cumulative hierarchy of sets.16 (8.36) John has started/begun thinking about the fact that he is hungry/the number 2/the cumulative hierarchy. (8.37) John started the rumor that Mary is sleeping with Sam. (8.38) John enjoys the cumulative hierarchy/the number π. (8.39) John enjoys the fact/ the thought that you are unhappy. It’s of course weird to say that John enjoys the proposition that you are unhappy, though presumably not that John enjoys entertaining the proposition that you are unhappy. This points to a fine-grained use of the defaults in TCL. It appears to be a linguistic fact that for certain abstract object type arguments, the dependent type (agent, prop) introduced in coercion is not defined. More formally, we can add to our axioms about types, where the predicates ↑ ((α, β)) and ↓ ((α, β)) mean that the map postulated by (α, β) is undefined and defined respectively.17 • ↑ (agent, prop) • ↑ begin((agent, i))18

16 17 18

pasta’s boiling or sizzling started. These form an interesting object of study like other verb transformations or alternations. This is quite different from John has started on the number 2/the cumulative hierarchy, etc.), which I find quite acceptable. Note, however, that being defined does not necessarily imply being specified! A potential counterexample is story. Some have claimed that story is a subtype of i, which is inhabited by abstract objects. However, there are many examples attested on Google of stories lasting. Last typically holds of events or states:

(8.40) Maybe that wasn’t the rustle of pages you heard while this story lasted, but Peter Pan himself, listening in. (8.41) Although the story lasted until the very last issue of Monster Fun, it did not make ... The story lasted for just 19 issues... These examples would suggest that story is perhaps of a complex type—evty • i or in other uses p • i.

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•  >↑ start((arg1 , i)), but ↓ start((arg1 , rumor)) TCL’s account of coercions using dependent types captures these distinctive behaviors of different coercing verbs. Event coercions occur not only with verbs but with adjectives, as in (8.42) quick cigarette TCL’s treatment of modifiers leads to a straightforward analysis. We have the following lexical entries for cigarette and quick:19 cig

(8.43) λPλxλπ P(π ∗ arg1 : p-art)(x)(λuλπ cigarette(u, π )) quick

(8.44) λQλvλπ (quick(v, π ∗ arg1

: evt − (hd(Q))) ∧ Q(π )(v))

Adjectives like quick, as well as its lexical semantic neighbors like rapid and slow, license unary dependent types whose values are events and whose parameter is the head type of the first-order property of the adjective. Applying (8.43) to (8.44) and using Application and Substitution, we have: (8.45) λxλπ (quick(x, π ∗ p-art ∗ evt − (p-art)) ∧ cigarette(x, π)) The type presupposition on the adjective’s argument cannot be justified as it stands because of the requirement that the argument of quick be an event and evt p-art = ⊥. But quick(x, π ∗ p-art ∗ evt − (p-art)) is equivalent to λx λπ1 quick(x , π1 )(π ∗ p-art ∗ evt − (p-art))(x). We now apply a unary version of the functor E to λx λπ1 quick(x , π1 ) to change this into a term that will satisfy all the type requirements. Applying the result of the application of the functor to λx λπ1 quick(x , π1 ) to the arguments π ∗ p-art ∗ evt − (p-art) and x and substituting the result in (8.45) gives us the finished logical form for the noun phrase, after several uses of Application, Substitution, and Binding: (8.46) λx: p-artλπ (∃z (quick(z, π) ∧ φ(cigarette) (z, x, π)) ∧ cigarette(x, π)) Using defeasible rules to specify the underspecified type (cigarette), since cigarettes are consummables, will get us to the desired reading of a quick consumption of the cigarette or a quick smoking of a cigarette for the noun phrase. TCL’s analysis preserves the type of the noun in the DP. Thus, TCL predicts that the quantification in the DP of John had two quick cigarettes is over objects rather than events. This prediction makes sense of more complex predications like (8.47) Mary drank a quick cup of tea 19

Cigarette has the type presupposition p artifact, which I’ll abbreviate to p-art, though its fine-grained type is consummable, or perhaps even cigarette.

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in which Mary is obviously drinking cups of tea not quick events of drinking tea. (8.47) reveals an interesting interaction between type presuppositions and presuppositions at the level of the contents of formulas. As it stands, TCL does not identify the quick drinking event to be the event of drinking described by the main verb. However, this would be a consequence of treating the information introduced by the type adjustment process as presuppositional at the level of content as well. That is, supposing that the quick drinking eventuality inferred by TCL is part of presupposed content, then if possible, we should bind this bit of information to some bit of proferred content. The main verb provides just such a binder. Presupposition theory also tells us that such binding will occur unless there is either no potential binder or binding results in an inconsistency with the semantics. We don’t always want it to be a property of quick that it modifies the main event. Consider: John drove a quick way home, but he went very slowly and it took him a long time is perfectly consistent and grammatical. As with coercing verbs, adjectives that support coercions license other dependent types besides eventualities. Consider the adjective fast. Fast licenses a coercion using a dependent type that involves a disposition, or some sort of modal property. A fast car is a car that can go fast; a fast highway is one on which one can drive fast; fast food is food that can be eaten quickly or that normally doesn’t take much time to prepare. It may be that fast sometimes also selects for an eventuality, as we saw earlier in discussing fast water. The type specification logic allows us to put multiple constraints on polymorphic types; we can formulate rules for an adjective such that it licenses one kind of polymorphic type given one argument, and another sort of polymorphic type in another. For instance, if δ is a general underspecified polymorphic type, then we could say for fast that its type presupposition is evt − δ(α) with further constraints like evt − δ(vehicle) evt − disp(vehicle), and evt − δ(water)

evt − (water), where disp is an underspecified disposition of vehicles. The availability in TCL of coercion with types other than eventualities mitigates the problem of event anaphora, which we saw was a big problem for other accounts. As we saw earlier, the eventuality introduced by coercion is sometimes not available for anaphoric reference:

(8.48) ?Paul was starting a new book. That lasted for three days. The TCL approach to coercion using dependent types makes these eventualities available for coreference, when eventualities are the appropriate type of

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object selected for by the coercing predicate.20 Some examples of eventuality anaphora sound bad because of the intensional use of certain aspectual verbs like start and with the fragile nature of their presuppositions.21 Start has some content in common with the imperfective mood; one can start something without finishing it. If these intensional uses involve event types and not events as arguments, this suffices to explain the awkwardness of anaphoric references to events with such coercion predicates. The aspectual verbs with the stronger presuppositions do support event anaphora. (8.50) a. John has finished a new book. That took three years out of his life. b. John has finished a new book. The writing took three years, and then the efforts to find a publisher three more. I find both of these examples fine, when the pronoun in (8.50a) refers to the creation or writing of the book. The anaphoric data with enjoy remains more problematic. It appears difficult to pick up an event with an anaphoric pronoun even when we put in a lot of discourse context to help with the anaphor, though individual judgements are quite variable on this score. Most native speakers find (8.51b) better than (8.51a). (8.51) a. ?James is enjoying a cigarette. It started just now. b. James is enjoying the smoking of a cigarette. It started just now. c. ? James enjoyed the book. But it only lasted a couple of days. So he needed to get some other mysteries to entertain himself after work during the Summer School. d. James enjoyed the book. His reading of it lasted a week. As we shall see, polymorphic types allow us to model many cases of coercion besides the classic eventuality coercions: the coercions brought about by material adjectives, sound verbs, the Nunberg style examples, grammatically encoded coercions like grinding (the conversion of an object into a portion of matter or mass), or nominalization.22 The formalism when extended to dependent types is flexible enough to model any relation of any arity between ob20 21

I noted earlier that the problems with the anaphora test seem limited to the class of verbs that take event types as arguments. The fragility of these presuppositions has to do with their projectbility:

(8.49) a. John has not started (begun) making dinner. b. Has John started (begun) making dinner? 22

These do not entail that dinner is being made or that John is doing anything about dinner. One can also think of Partee and Rooth (1983) style type shifting in this vein.

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jects. They can also be made dependent on contextually specified information, allowing us to solve the discourse based examples of coercion.

8.3 Discourse and typing With the basic coercion story in place, it’s time to integrate context dependence at the discourse level. We have seen how to integrate information relevant to the coercion of an argument from other arguments of a functor using the > logic. Now we turn to the problem of integrating factors from the larger discourse. There is considerable evidence that type coercion depends at least in part on discourse context. The eventuality involved in enjoying a book, for example, will depend on discourse context. To go back to our example, goats normally enjoy eating books; but within a fairy book context, goats can enjoy reading books. Standard predicational restrictions can be relaxed or wholly rewritten. How do we do this? Lascarides and Copestake (1995) offer one approach with their “discourse wins” rule, but we need to place this kind of operation squarely within the lexicon. In order to do this, we need to take a detour through a theory of discourse structure. I turn to that now. Segmented Discourse Representation Theory, or SDRT, offers a formal account of the hypothesis that discourse has a hierarchical structure upon which interpretation depends. For our purposes I will need the following features of SDRT.23 • SDRT’s semantic representations or logical forms for discourse, SDRSs, are recursive structures. A basic SDRS is a labelled logical form for a clause, and a complex SDRS will involve one or more discourse relation predications on labels, where each label is associated with a constituent, i.e., a perhaps complex SDRS. • An SDRS for a discourse is constructed incrementally within a logic of information packaging that uses several information sources and that is responsible for the final form of the SDRS. The logic of information packaging, which reasons about the structure of SDRSs, is distinct from the logic of information content, in which we formulate the semantic consequences of an SDRS. • The rules for inferring discourse relations are typically rules that exploit a weak conditional >. They form part of the Glue Logic in SDRT, which allows us to “glue” new discourse segments together with discourse relations to elements in the given discourse context. This logic has exactly the same 23

For details, see, e.g., Asher (1993), Asher and Lascarides (2003).

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rules as the logic for specifying values for dependent types, though the language of types and the language for describing discourse logical forms are distinct. • The discourse relations used in SDRT, which have semantic (e.g., spatiotemporal, causal, etc.) effects, are either coordinating (Coord) or subordinating (Subord). Examples of subordinating relations are Elaboration, where the second constituent describes in more detail some aspect of some eventuality or some fact described in the first constituent. Some coordinating relations like Narration (where constituents describe a sequence of events) and Continuation (where linked constituents elaborate simply on some topic) require a topic; i.e., there must be a simple constituent, a common “topic,” that summarizes the two related constituents and that is linked to them via the subordinating Elaboration relation. If this third constituent has not been explicitly given in the previous discourse, it must be “constructed.” Discourse structure affects the way semantically underspecified elements are resolved. Sometimes the temporal structure of a discourse is more elaborate than what is suggested by a semantic analysis of tenses such as that found in DRT Kamp and Reyle (1993). There are clearly temporal shifts that show that the treatment of tenses cannot simply rely on the superficial order of the sentences in the text. Consider the following discourse (from Lascarides and Asher 1993).24 (8.52) b. c. d. e.

a. (π1 ) John had a great evening last night. (π2 ) He had a great meal. (π3 ) He ate salmon. (π4 ) He devoured lots of cheese. (π5 ) He then won a dancing competition.

(8.52c–d) provides “more detail” about the event in (8.52b), which itself elaborates on (8.52a). (8.52e) continues the elaboration of John’s evening that (8.52b) started, forming a narrative with it (temporal progression). Clearly, the ordering of events does not follow the order of sentences, but rather obeys the constraints imposed by discourse structure, as shown graphically below. Thus the eventualities that are understood as elaborating on others are temporally subordinate to them, and those events that represent narrative continuity are understood as following each other. The relevant parameter for interpreting tenses is discourse adjacency in the discourse structure, not superficial 24

My apologies for the potential confusion on variables. SDRT uses π, π1 , . . . to denote discourse constituents and α, β, . . . function as variables over constituents, while in TCL π picks out a presuppositional parameter in the type system and α and β range over types. I hope that context will make it clear which uses of these variables is in question.

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adjacency. A theory like SDRT (Asher (1993), Asher and Lascarides (2003)) provides the following discourse structure for (8.52) and this allows us to get a proper treatment of the tenses therein. Here π6 and π7 are discourse constituents created by the process of inferring the discourse structure.25 Note that π1 and π2 serve as topics for the Narrations holding between π2 and π5 and π3 and π4 . π1



Elaboration

π6 } AAA } AA }} AA }} } } Narration A / π5 π2



Elaboration

π7 A }} AAA } AA } A }} }} Narration A / π4 π3 Figure 8.2 SDRT graph for (8.52)

Temporal relations between events introduced by verbs with certain tenses are underspecified in a language like English, and discourse structure is an important clue to resolving this underspecification. SDRT predicts that discourse structure affects many types of semantic underspecification. Nearly two decades of work on ellipsis, pronominal anaphora, and presupposition has provided evidence that this prediction is correct (Asher (1993), Hardt, Busquets and Asher (2001), Asher and Lascarides (1998b, 2003)). My hypothesis here is that discourse structure also helps resolve underspecification at the level of types and hence contributes to content in predication. To see how this comes about, we need to examine discourse coherence and its relation to discourse structure. In SDRT, as in most theories of discourse interpretation, to say that a discourse is (minimally) coherent is to be able to derive a discourse structure for it. Discourse coherence is a scalar phenomenon, however. It can vary in quality. Following Asher and Lascarides (2003), I say that an sdrs τ1 is more coherent than an sdrs τ2 if τ1 is like τ2 , save that τ1 features strictly more rhetorical connections. Similarly, τ1 is more coherent 25

See Asher and Lascarides (2003) for details.

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than τ2 if τ1 is just like τ2 save that some underspecified conditions in τ2 are resolved in τ1 . But for now, let’s focus on the perhaps simplistic position that discourse coherence is maximized by “maximizing” the rhetorical connections and minimizing the number of underspecified conditions. We can define a principle that will govern decisions about where one should attach new information when there’s a choice. It will also govern decisions about how other forms of underspecification get resolved. And the principle is: the preferred updated sdrs always maximizes discourse coherence or MDC (Asher and Lascarides 2003). The degree-of-coherence relation ≤ thus specified is a partial ordering on discourse structures: other things being equal, the discourse structures which are maximal on ≤ are the ones with the greatest number of rhetorical connections with the most compelling types of relation, and the fewest number of underspecifications. MDC is a way of choosing the best among the discourse structures. It’s an optimality constraint over discourse structures that are built via the glue logic axioms. Asher and Lascarides (2003) examine in detail how MDC works in picking out the intuitively correct discourse structure for (8.52), as well as many other examples. We won’t be much concerned here with exactly how discourse relations are inferred, but we will need from time to time to refer back to this background logic. To get a feel for how MDC works in tandem with underspecification, consider the example from Asher and Lascarides (2003), (8.53):

(8.53) a. I met an interesting couple yesterday. b. He works as a lawyer for Common Cause and she is a member of Clinton’s cabinet.

The pronouns he and she introduce underspecified formulas into the logical form for this discourse. They could be bound deictically to salient individuals in the context, but that would not allow us to infer a tight connection between (8.53a) and (8.53b). The discourse would lack coherence. On the other hand, if he and she are linked via a “bridging” relation to the DP an interesting couple, then we can infer a strong discourse connection between (8.53a) and (8.53b). MDC predicts that this anaphoric interpretation of the two pronouns is preferred because it leads to the preferred discourse structure.

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8.4 Discourse-based coercions in TCL Armed with SDRT’s notion of discourse structure, we can return to the examples with the aspectual verbs. I will use the speech act discourse referents π0 , π1 , π2 , . . . to isolate the minimal discourse units in these examples. (8.54) a. ??Yesterday, Sabrina began with the kitchen (π1 ). She then proceeded to the living room and bedroom (π2 ) and finished up with the bathroom (π3 ). b. Yesterday Sabrina cleaned her house (π0 ). She began with the kitchen (π1 ). She then proceeded to the living room and bedroom (π2 ) and finished up with the bathroom (π3 ). c. Last week Sabrina painted her house (π0 ). She started with the kitchen (π1 ). She then proceeded to the living room and bedroom (π2 ) and finished up with the bathroom (π3 ). While I see reasoning about discourse structure and lexical semantics as largely separate modules, aspectual verbs like begin (with), proceed, and finish up incorporate a certain bit of discourse information that is then used by the SDRT inference system, or glue logic, to build a discourse structure.26 They are, from an SDRT perspective, Narration introducers. A sequence of clauses in which begin with, continue with or proceed with, and finish up with occur in sequence constitute a strong indication that these clauses should be linked with Narration. The second argument of such a verb contributes the event description of one of the constituents that make up the narration. I’ll take this argument to be specified by an event property of type agent ⇒ evt, which if it is not given in the syntax remains unspecified. Here is a lexical entry for proceed that formalizes these points: proceed

proceed

: ag)(P(π ∗ arg2 (8.55) λPλΨλπ∃β∃α (α: {Ψ(π ∗ arg1 evt))} ∧ Narration(β, α) ∧ β =?)

:

For example, given such a logical form, Sabrina proceeded to clean up the kitchen would have the following logical form: (8.56) λπ∃β∃α (α: ∃y∃e (kitchen(y, π) ∧ clean-up(s, e, y, π)) ∧ Narration(β, α) ∧ β =?) 26

Actually, it’s more proper to say that the glue logic imposes constraints on discourse structure; typically, a discourse will have more than one acceptable discourse structure. For more on “discourse verbs,” see Danlos (2007). For more on the SDRT inference system and its logical properties like decidability, see the chapters on the glue logic in Asher and Lascarides (2003).

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The typing requirement of proceed on the property is satisfied by the fact that clean up the kitchen can be understood as an event description, something which I have explicitly introduced or “reified” in the logical form. Using these lexical entries together with the SDRT axioms for discourse connectives like then,27 the logical form for (8.54a–c) will specify a discourse structure containing the information Narration(π1 , π2 ) and Narration(π2 , π3 ). In SDRT Narration(π1 , π2 ) and Narration(π2 , π3 ) imply that there is a topic discourse constituent that π1 , π2 , and π3 elaborate on. This topic discourse constituent is explicit in (8.54b,c), and it is intuitively this topic that specifies in (8.54) what the object arguments of the aspectual verbs are. The eventuality type of the second argument of begin with can sometimes be specified by the object in the PP via our default type specification rules. Consider: (8.57) Jane began with a cigarette and then proceeded to a glass of wine. (8.58) Jane began with a fried oyster appetizer (π1 ) and then proceeded to the osso buco (π2 ). In these examples, the discourse verbs together with the discourse connector and then both specify that the two verb phrases must be linked via the Narration discourse relation in the sdrs for the discourse. However, in (8.57) and (8.58), the resolution of the underspecified dependent types proceeds independently from the construction of the discourse structure thanks to the type specification rules in the lexicon, and in fact it is these resolutions that serve in (8.58) to construct a topic for the discourse, as required by the fact that Narration holds between π1 and π2 : the topic is something like Jane’s meal for (8.58); for (8.57) it’s something more diffuse, which makes sense since we expect (8.57) to occur within a larger discourse, say about Jane’s evening or something like that. In (8.54a) we must construct a topic as in (8.57) or (8.58) that elaborates the constituent containing π1 , π2 , and π3 linked by Narration. In order to do this, we need to look at the eventualities involved in the Narration and try to generalize from them to construct a topic. However, the relevant eventualities are those provided by EC, and their type is underspecified—-they are of type (agent, kitchen). The problem is that  doesn’t return a determinate value when applied to kitchen and the type of agent, at least as far as our lexically given type specification rules are concerned. In this respect kitchen is different from cigarette, novel, or words associated with • types like lunch (meal • evt). 27

The adverbial then functions as a further clue for Narration, something that SDRT’s glue logic formalizes (Asher and Lascarides (2003)). It is up to the glue logic in SDRT to find an appropriate value for β in the lexical entry for proceed and for the logical forms that are derived from it.

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If this eventuality cannot be specified, then we cannot specify the topic for the Narration. The discourse is thus lacking in coherence, not only because of the underspecified eventualities involved in the sequence but also because of the lack of topic. On the other hand, in (8.54b,c), by linking the underspecified conditions describing the eventualities in the logical forms for the clauses π1 , π2 , and π3 with the condition describing the eventuality in π0 , we can easily infer Elaboration between π0 and the constituent containing π1 , π2 , and π3 , thus satisfying the requirements of Narration, provided we resolve the underspecified eventualities to the one described in π0 . MDC favors this resolution, as the result allows us to construct a more coherent discourse structure. As with other resolutions of underspecifications in SDRT, the resolution of the underspecification and the construction of the discourse structure are codependent tasks. By filling in the underspecified types in a particular way, we can build the discourse structure—we can have a fully specified topic that we elaborate on with the second and third constituents, which are linked by Narration. And by building such a discourse structure we resolve the under specifications. MDC will pick the discourse structure with the underspecifications resolved as the preferred one. Lascarides and Copestake (1995) as well as Asher and Lascarides (2003) point out that the qualia based predictions of GL are easily overturned in suitable discourse contexts. I repeat that moral here again with an example very similar to the discourse examples above. (8.59) a. Last week Suzie worked on a number of paintings of consummables. b. On Monday she began a cigarette; on Tuesday she began and finished a glass of wine. c. On Wednesday she finished the cigarette, and started on a plate of tacos. d. Thursday she finished the plate of tacos. e. I really enjoyed the plate of tacos. The event readings posited by the qualia of GL aren’t available in this discourse context. MDC and the process of discourse construction overrules any of the defeasible conclusions that issue from the specification logic for underspecified dependent types. Here is another example involving a precisification of the coercion involving enjoy: (8.60) Nicholas and his older daughters had a great time skiing at Alta. Lizzy enjoyed the chutes, while Alexis and Nicholas enjoyed the back bowls. The discourse sensitivity of coercion has its limits, and so we have to limit the TCL specification mechanisms or they will overgenerate acceptable sen-

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tences. Particular difficulties emerge with particles and quasi idiomatic expressions like eat up. One can, it seems, say (although perhaps tellingly there are no cited examples on Google of this idiom): (8.61) The dog enjoyed eating his food up in about 15 seconds. But one cannot say: (8.62) *The dog enjoyed his food up in about 15 seconds. The TCL type presupposition accommodation mechanism specifies a semantic relation, not a word or string of words. Thus it can’t specify part of an idiom, and eat in eat up is part of an idiom. At the discourse level, this observation also holds: (8.63) Everyone was enjoying taking their shirts off with the warm weather. Mary enjoyed taking her shirt off, Sam enjoyed taking his shirt off, and Jenny enjoyed her shirt off too. Whatever it means (if it means anything), the last clause in (8.63) cannot mean that Jenny enjoyed taking her shirt off, though I have primed for that reading by setting up an explicitly parallel structure under an Elaboration. Parts of idioms or lexical units can’t be specified, because they aren’t a matter of composition; the meaning of eat up is not a matter of composing the meaning of eat and up, nor is it clear that take off is the result of composing the meaning of off with take in any obvious way. For have off, the explanation is a bit different. Have can take a state as a second argument, which is what off produces when it is applied to a DP argument. The problem here is that this is not of the right type to be a specification of the dependent type of enjoy, which must be a relation between the object and subject argument of the verb. It is also important to note that the TCL mechanisms do not change the syntax of the coerced noun phrase. Adjoining the adverb or the PP to the logical form for the DP does not give the adverb access to the eventuality introduced in coercion; it can only modify the DP as a whole. But a manner adverb like rapidly must modify a verb or some projection thereof, in contrast to temporal adverbs which can apparently modify DPs directly: (8.64) a. A cigarette now means trouble later on. b. An airplane now would be a huge financial burden on the company. (buying) c. *A cigarette rapidly is no fun. d. Smoking a cigarette rapidly is no fun.

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More generally, while discourse structure can affect the resolution of underspecified eventualities provided by the type adjustment mechanisms, the type adjustments required by certain verbs don’t pattern with other underspecifications that are sensitive to discourse structure. Parallel and contrasting discourse constituents help guide the resolution of pronominal anaphors, ellipsis, and the scoping of operators and quantifiers (Asher (1993), Hardt et al. (2001)). Such structures affect the resolution of the underspecified elements in coercions involving the aspectual verbs, as one would expect, but they don’t easily affect coercions involving enjoy. The readings of the underspecified eventualities induced by discourse structure are given in parentheses. (8.65) Sabrina began painting the kitchen. She began the living room at the same time too (painting), so there were paint supplies all over the place. (8.66) Sabrina has finished painting the kitchen. But she hasn’t begun the living room yet. (painting) (8.67) Sabrina prepares the vegetable garden somewhat reluctantly, but she really enjoys the flower beds. (?preparing) (8.68) Sabrina prepares the vegetable garden somewhat relunctantly, but she really enjoys doing the flower beds. (preparing) Causal and narrative discourse relations also show a clear difference between enjoy and aspectual verbs like finish. (8.69) Sabrina began painting the kitchen, after she finished the living room. (painting) (8.70) Sabrina enjoyed painting the kitchen, and then she equally enjoyed the living room. (??painting) (8.71) Sabrina enjoyed painting the kitchen, and then she equally enjoyed doing the living room. (painting) (8.72) Sabrina began painting the kitchen because she had already finished the living room. (painting) (8.73) Sabrina agreed to paint the living room because she had so enjoyed the kitchen. (#painting) (8.74) Sabrina agreed to paint the living room because she had so enjoyed doing the kitchen. (painting) Elaborative discourse structures like the ones we have examined seem to do the best job of specifying eventualities introduced by the type adjustment mechanism with enjoy. Enjoy’s lack of sensitivity to narrative, causal, and even contrastive discourse structure is somewhat of a mystery. It may have to do with the fact that the aspectual verbs have a temporal and anaphoric content that can contribute indepedently to discourse structure. But more research is needed on

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this point, in particular an empirical investigation of the discourse contexts involving enjoy. Radical pragmaticists like Recanati claim that contextual effects are to be found everywhere. The view I have elaborated here is more cautious, but TCL predicts discourse effects to be possible wherever there is underspecification in lexical and compositional semantics. Given the discussion of the coercion data, lexical underspecification might be quite common. It will also surface in the analysis of certain constructions like the Saxon genitive, which I discuss in chapter 10. I also should mention that discourse structure has other effects too; for instance, discourse structure affects copredications in the sense that some copredications have a more sensible discourse structure than others. (8.75) The paper, which was founded in 1878, documents in detail the international news on a daily basis. (8.76) ??The paper, which weighs typically about 2 lbs, was founded in 1878. (8.77) ?The paper, which documents in detail the international news on a daily basis, was founded in 1878. (8.78) The paper, weighs typically about 2 lbs, documents in detail the international news on a daily basis. I leave the analysis of discouse effects in copredication, however, to another time.

9 Other Coercions

So far we’ve analyzed examples of coercion involving events and aspectual verbs or verbs like enjoy. But there are many other examples of coercion that dependent types can model. I survey some in this chapter.

9.1 Noise verbs The class of verbs that comprise hear, deafen, drown out, and so on are coercing predicates. (9.1) a. We hear the piano two floors down. b. The orchestra drowned out the piano. c. The guitar was deafening. d. The airplane was deafening. Verbs requiring “noise” arguments assimilate to the analysis of stop given in the last chapter. They license a form of event coercion triggered by a dependent type like that licensed by stop, except that the dependent type for noise verbs given parameters yields an eventuality that makes a noise. As with other examples of eventuality coercion, it is the verb that does the coercion. Though we may not understand exactly what’s going on in (9.2) and we can’t specify what eventuality is involved, we infer that some eventuality involving the stone that makes noise was deafening. (9.2) The stone was deafening. Moreover, this inference is a matter of presupposition. We make the inference even when sentences like (9.2) are negated: (9.3) The stone was not deafening.

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Once again, we have to address the implications of the TCL view on which noise making events are introduced by mechanisms for presupposition accommodation. Recall Kleiber’s (3.17), repeated below: (3.17) Nous entendˆımes le piano, qui nous parvenait flottant par-dessus du lac (We heard the piano which came to us floating over the waters of the lake). TCL predicts that (3.17) only has a nonsensical reading, because in TCL neither the syntax nor the meaning of the noun or its containing DP shifts. The noun piano, and the noun phrase le piano retains its normal type, and so the relative pronoun must agree in type with it. This predicts that the only possible reading of (3.17) is one on which the piano is itself floating over the waters of the lake. On the other hand, true anaphoric uses of pronouns should be good according to my analysis. (9.4) a. We hear the piano two floors down. It starts every evening around 10 and goes on for a couple of hours. b. The guitar was deafening. It hurt my ears. TCL predicts both of these examples have a reading on which the pronoun picks out the noise made by the object that is the argument of the noise coercion predicate in the previous sentence. This accords with intuitions.

9.2 Coercions from objects to their representations Depiction verbs also function as coercion verbs. (9.5) (9.6) (9.7) (9.8) (9.9)

John is drawing a fish. Suzie is painting a landscape. Pat sculpted a lion. This program models buildings in 3D. Chris sketched his hand.

All of these verbs introduce a dependent type that ends up making their internal semantic argument some sort of representation of the syntactically given internal argument. Like the noise verbs and stop, these verbs introduce a unary polymorphic type ∃x p representation-of(x) p with its one parameter given by the type of the syntactically given object argument. This polymorphic type does not introduce an eventuality but another kind of entity, a representation, which is a special kind of physical object.

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Coercion involving depictions also works with prepositional phrases. Consider the following pair (due to Marliese Kluck): (9.10) a. The garden with the flowers was especially beautiful. b. The dress with the flowers was especially beautiful. The head noun provides a preferred interpretation of the prepositional phrase. This example is interesting because there is no type conflict between the head noun and the prepositional phrase. There is a reading on which the dress could have been grouped with real flowers, though it’s not the preferred reading. There’s even a representational reading of the whole noun phrase—that is, the picture of the garden with the flowers of the picture of the dress with the flowers. These examples are not captured within TCL because TCL type shifts are guided by type conflicts. A natural extension of the TCL system to capture such examples, however, is to make the justification of type presuppositions sensitive to considerations of plausibility, something which has been suggested for the justification of ordinary presuppositions, as Asher and Lascarides (1998b) and Asher and Lascarides (2003) argue. More specifically, if a particular way of justifying a type presupposition makes the discourse more coherent because it enhances plausibility, then it will be that manner of justification that the system should select.

9.3 Freezing Another example of a coercion verb is freeze. Freeze requires that its theme argument be a liquid. It denotes a process whereby its theme argument, which starts out in a liquid state, ends up in a no longer wholly liquid state. However, freeze can apply to things that are not liquids, as in (9.11c). (9.11) a. The water froze. b. The river froze. c. The bottle froze. (9.11c) is clearly a case of object coercion. Bottles are not liquids. However, what they contain is often a liquid. We typically understand (9.11c) as a coercion: the contents of the bottle froze, contents which we force to be liquid or at least partially liquid (bodies and wet laundry can also freeze solid). (9.12) a. The bottle froze. [The liquid in the bottle] froze. b. The bottle of soda froze. [The soda] in the bottle of soda froze.

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A verb like freeze also licenses a dependent type for its internal argument— something of the form ∃x container contents(x) liquid— that is invoked when the direct object of freeze is not a liquid or is not a material that stiffens under cold and is rather a container. Drink is another verb like freeze that invokes the dependent type contents, when its object is not a liquid: (9.13) Nicholas drank the bottle. TCL predicts these coercions introduce new discourse entities or discourse referents in logical form involving liquids. Let’s see how such coercions fare with the anaphora test. (9.14) Nicholas drank the bottle. It was a delicious Corbi`eres red, a mixture of grenache, cabernet, and mourv`edre. (9.15) Nicholas drank the bottle, and he spilled none of it on himself for once. The anaphora test shows that the contents of containers are entities available as antecedents for anaphoric elements if the containers themselves are. This provides additional confirmation for the TCL approach.

9.4 Cars and drivers, books and authors TCL’s analysis of the Nunberg cases of coercion examined in chapter 3 also involve dependent types. (9.16) a. I’m parked out back. b. The ham sandwich is getting impatient. c. Plato is on the top shelf. Some of these are more difficult to interpret than others. (9.16a) for instance has a very easy interpretation with the coercion, whereas most speakers need a bit of help with (9.16b). With the “parking” examples, TCL assumes that the verb licenses the introduction of a vehicle type associated with the argument. If that’s the case, then we have just another lexical coercion introducing a dependent type, which in this case provides a map from the head type of the DP to the type of an associated vehicle. This vehicle argument is available for subsequent reference. (9.17) I’m parked out back. It’s a Volvo. (9.18) I’m parked over by the Esso FBO.1 It’s a Comanche. 1

An FBO is a flight base operation where planes can be parked.

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On the other hand, it is not just the particular verb park in the passive form that that can coerce the relevant type shift in such examples. (9.19) a. I’m out back. It’s a Volvo b. He’s out back. It’s a Volvo. c. John’s in front of the house. It’s a Volvo. The interpretation of the (9.19b) really depends on features of the discourse context. Consider the following two extensions of (9.19b): (9.20) a. I just saw John. He’s out back. It’s a Volvo. b. He’s in Paris. #It’s a Volvo. c. Hi. Can you get our cars for us? He’s out back. It’s a Volvo. I’m over on the left. It’s a Subaru. The car interpretation of (9.20a) feels more awkward than (9.19a) or (9.20c). And the it in (9.20b) is really very difficult to interpret when we take it to be an anaphoric pronoun, even when interpreters are primed to associate vehicles with agents. Such coercions seem to be triggered by the predication of a nearby location to agents unless the agent is not capable of owning a car. The polymorphic type is licensed by the presence of a lexical element—e.g., a verb like park—or a relevant context in which it’s easy to associate vehicles with agents in some way in nearby locations that the agent clearly does not occupy. (9.20b) fails to meet the discourse conditions that would trigger the coercion, and (9.20a) does so only with difficulty. This last condition on coercion is much more dependent on extra-lexical and predicational resources and may be why this coercion has a more pragmatic feel to it. Mutatis mutandis for the coercion from authors to their books and from dishes of food to the people eating them, although, as Kleiber notes, the anaphora test works less well with the author/books coercion. (9.21) George Sand is still widely read, although #they are (# it is, she is) no longer in print. (9.22) George Sand’s books are still widely read, although they are no longer in print. These data are to some extent of a piece with the problematic nature of event anaphora with the coerced argument of enjoy. They suggest that the content introduced by a dependent type in presupposition justification in some coercions is so “local” that it remains part of the content of the verb and so remains unavailable for anaphora. We’ll see another example of this phenomenon in the next section.

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TCL predicts that all of these coercions involve presupposition justification at a local site, just like the classic cases of event coercion surveyed in the last chapter. Thus, it predicts that copredications involving the coercing predicate and a predicate that combines normally with the argument can be felicitous. This prediction is confirmed. (9.23) b. c. d. e. f.

a. The guitar was a Strachey and was deafening. Nicholas drank and then broke the bottle. Susan is painting the fish she ate for dinner I’m parked out back and in a hurry. The ham sandwich that had too much mustard on it is getting impatient. Plato is my favorite author and on the top shelf

On the other hand, the TCL approach does not predict that the VP meaning itself is shifted in these coercions; what is shifted is the predication relation between the property provided by the verb phrase and the denotation of the subject. Thus, TCL predicts that examples with VP ellipsis like (9.24) I’m parked out back and Mary’s car is too have their intended interpretation: I own a car that is parked out back and Mary’s car is parked out back too. This constitutes a significant improvement over theories that attempt to shift the meaning either of the VP or the object to treat coercion.

9.5 Verbs of consumption Sometimes the type constraints of certain verbs on their object or internal arguments are so specific that we omit the internal argument. This is true of certain verbs of consumption. (9.25) b. c. d. e.

a. John smokes after dinner. John drinks a lot at parties. I’ve eaten. Nancy drove to work. Lizzy climbed well.

These are not exactly coercions, but they are related. These verbs assign defeasible type requirements to their internal arguments that are sufficiently precise that they contribute to truth conditional content. One naturally understands

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(9.25a) as meaning that John smokes cigarettes after dinner. This type assignment is defeasible; John could smoke a pipe or cigars, or non-tobacco products in the right context—marijuana, opium, crack, etc. But the latter are much less preferred. Similarly, (9.25b) is naturally understood as meaning that John drinks a lot of alcohol at parties, though in certain contexts we might infer John drinks something else habitually. TCL can model these implications within the default type specification logic. Doing so requires us to take smoke as licensing a dependent type with two parameters. We can now write the following constraint in the type specification logic: •  > ∃x e smoke(agent, x) = smoke(agent, cigarette) There remains the question of what information one should add to logical form when consumption verbs license dependent types. Is there, for example, a variable at the level of logical form standing for the internal argument? It appears that for smoking and eating, the induced internal arguments may be available for coreference, as the following examples show: (9.26) John smokes after dinner. They’re usually Balkan-Sobranies. (9.27) I’ve eaten. It was very filling. But for (9.25d) the anaphora test tells us that such arguments are not available for anaphoric coreference.2 (9.28) Nancy drove to work today. #It used a lot of gas. How to interpret the anaphora test in these cases is a delicate matter. Similar sorts of problems crop up in languages with incorporation, where incorporated nouns, though contributing to truth conditional content, serve only with difficulty as antecedents to anaphors. These cases, like some of the Nunberg coercions, may be closer to incorporation than other forms of coercion. How to handle incorporation within a dynamic framework, however, is not a settled matter; and I will leave the matter here.

9.6 I want a beer The interactions between a verb like want and a DP type complement provide an example of a coercing construction, rather than a purely lexically governed 2

These arguments, if they exist, are expected to be unavailable for coreference in the habitual uses of consumption verbs like John smokes, unless the modality introduced by the habitual is introduced with narrow scope only over the verb.

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coercion. Pustejovsky (1995) treats want like enjoy. Fodor and Lepore (1998) in general do not take coercion to be a phenomenon that is part of the grammar. But they do argue that want in (9.29) want a beer is an example of coercion. It coerces its arguments into something of the type denoted by inifinitival phrases, which in Asher (1993) I called a projective proposition, and which I’ll conflate with properties or VP denotations here. Fodor and Lepore (1998) make use of the light verb have to analyze this coercion. For them (9.29) means want to have a beer. As pointed out by Harley (2005), Fodor and Lepore’s proposal has problems because even the light verb have has some restrictions on its use that make this proposal not work as a general solution. She considers (9.30) a. John wants a compliment b. John wants a pat on the back which are perfectly fine but their synonyms according to the Fodor and Lepore strategy (9.31) a. #John wants to have a compliment b. #John wants to have a pat on the back aren’t particularly good. One should say John wants to get a compliment, receive a compliment, get a pat on the back, and so on. Harley (2005) offers a decompositional analysis of have and get to get the right relations between compliments and agents. Roughly she analyzes have as Phave + be while get is analyzed as Phave + become, where Phave is an unarticulated preposition whose meaning is something like possession. To want a beer, then, is analyzed as [WANT [be [Phave a beer]PP ]VP ]VP . Certain DPs like a compliment denote a punctual event and so are incompatible with stative component of have, namely the unarticulated verb be, but not with the accomplishment verb get. Nevertheless, Harley’s solution is unsatisfying as well. If get is in the syntax or logical form of the verb phrase wants a compliment, then why can’t we say wants off a shot with his gun or wants a letter off to the Dean? It’s perfectly acceptable to say (9.32) a. John wants to get a shot off with his gun b. David wanted to get a letter off to the Dean c. David wanted to get a letter to the Dean

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and moreover a shot with his gun denotes a punctual event. So Harley should predict that the ungrammatical (9.33a) and the marginal (9.33b,c) are fine. (9.33) a. *John wants a shot off with his gun. b. ?David wanted a letter off to the Dean. c. ?David wanted a letter to the Dean. Particles like off have to modify a verb; for example get, send, fire and be all combine with off. The examples in (9.33) show that the requisite verbs in Harley’s decomposition are simply not there in all cases. Furthermore, when Harley speaks of a decompositional analysis, it’s unclear what she is decomposing. If she’s decomposing the meaning of the verb want, then it is difficult to see how one could get the vasly preferred narrow scope reading for a compliment in (9.30a). In a decompositional approach to want, whatever one does with the verb, the object DP will combine with whatever one assigns as a logical form to the verb, and the rules of application will perforce yield something like this, which is unintuitive to say the least for (9.30a). (9.30a’) ∃x (compliment(x) ∧ wants( j,∧ get( j, x))) Harley has no way to derive the much more prominent de dicto reading of (9.31a) within her analysis. What Harley should say is that want imposes a syntactic environment around its internal argument, when the latter is not an infinitival phrase. There is evidence that something like this holds for want as opposed to the aspectual verbs or enjoy. Unlike the coercions with the aspectual verbs or enjoy, there is evidence that there are two verbs or verb-like elements in the syntax: (9.34) b. c. d. e.

a. John wanted his stitches out rapidly. ?The dog enjoyed his food rapidly. *John enjoyed his stitches out rapidly. James wants Jenny’s shirt off. *James enjoyed Jenny’s shirt off.

TCL predicts (9.34b) to be marginal; rapidly must modify some verb like element or its projection in the syntax, and in the syntax there is nothing that denotes the event of doing something with the food. There’s only the verb enjoy and that doesn’t combine well with rapidly. TCL also predicts that one cannot use coercion to infer a word that is a proper part of an idiom or lexical item and so predicts (9.34e) to be bad. But TCL type accommodation and binding mechanisms alone cannot explain the peculiarities of coercions with want: the adverb in (9.34a) clearly modifies a verb-like element describing the event associated with his stitches within the projective proposition that is the

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object of the verb, and want allows some reconstruction of idioms like have your stitches out, but not others like get a shot off. There is some intriguing evidence for the presence of a verb like have in the syntax as well. For instance, want like have refuses to allow particle shift: (9.35) b. c. d.

a. John has his shirt off. *John has off his shirt. The doctor wants John’s shirt off. *The doctor wants off John’s shirt.

This points to a peculiar interaction between syntax and semantics: want presupposes a particular structured complex type as its internal argument, something involving an underspecified verb type that can combine with verb particles like out and of or their PP (prepositional phrase) kin. The TCL framework can account for this observation by having want not only demand of its internal argument that it be a projective proposition or property but also license an underspecified polymorphic type that is a generalization of the type of a transitive verb. This type,which I’ll call τdp actually depends for its value on a parameter, a DP, that is not part of the entry. Thus, the transformation it licenses requires a DP type with which it will combine. When instantiated with the type of the variable bound by the subject DP, τ produces a fine-grained subtype of prop that affects logical form via δC. Here’s a lexical entry for want (abbreviated to wt in the superscript): wt ∧ (9.36) λPλΦλπ Φ(π ∗ argwt 1 : ag)(λz want(z, P(π ∗ arg2 : 1 − τdp (hd(Φ)))(z)))

In want to have a beer, the type of the infinitival justifies the second argument type presupposition of want without further ado, but with want a beer, we must justify this presupposition via τ and the transformation it licenses. The transformation introduces a particular functor that takes DP types as arguments. The appropriate functor in this case is the λ term in (9.37), which applies to the syntactically given internal argument DP in predications like that in (9.29 or (9.30a). As want is a control verb, the λ bound y will be saturated by want’s subject argument. (9.37) λΦ: dp λyλπ (Φ(π)(λxλπ1 φτ (y, x, π1 ))) Once the DP is applied to (9.37), we have something of the appropriate type satisfying the type presupposition of want. Note that both the DP’s contribution and the underspecified verbal contribution occur within the scope of the intension operator ∧ . The result for (9.30a) prior to the use of any of the defeasible specification rules is:

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(9.30a”) λπ wants( j,∧ (∃x (compliment(x) ∧ φτ ( j, x, π)))) TCL naturally gets the de dicto reading for a sentence like (9.30a). To get the de re reading, we resort to standard quantifying-in techniques. In TCL we could defeasibly assign the underspecified dependent type τ the type have. The type of the DP may override this specification and require a different dependent type and hence the introduction of a different verbal relation in intension linking the DP and subject of want. Now have can take a state as its second argument, which is what off applied to Jenny’s shirt yields. We thus predict with Fodor and Lepore (1998) and others that (9.34a,d) are acceptable, as these particles can combine with the internal argument of have to provide an appropriate state. Similar to coercions with want are coercions with believe. As noted for instance in Asher (1986), the verb believe, though it ordinarily requires its internal argument to be of proposition type, can sometimes take a noun phrase referring to an individual. (9.38) John believes Mary. (9.38) means that John believes some proposition associated with Mary, typically a proposition expressed by something she said, wrote, or that is somehow associated with her. The type of coercion that goes on here, like that with want, operates at the level of the higher-order types; there is a type clash between the type of the DP and the type presupposition of the verb. The presupposition produced by the verb are accommodated via a type like τ that is dependent on the head type of the syntactically supplied object DP. However, the dependent type here, call it σ, returns a proposition type not a property type. Corresponding to this is a functor from the individual to some proposition associated with her, which applies to DP of the verb believe and looks like this: (9.39) λΦ: dp λπ ∧ (Φ(π)(λxλπ1 φσ (x, π1 ))) The φσ in (9.39) stands for an underspecified property holding of the variable introduced by the DP; the result of applying the DP to this property yields a proposition that then serves as the true internal argument to the verb believe.

9.7 Evaluative adjectives Adjectival modification can also affect whether things have a function. We saw examples of these in chapter 1. In (9.40), we see some more examples. (9.40) good lunch, good rock

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It would be silly to assume that rock contains an intrinsic function for rocks as part of its meaning. Rocks are natural kinds with no natural or given function. But good can coerce the type of the natural kind into some sort of an artifact, for which one could argue the telic polymorphic type is well defined. The exact value of the polymorphic type is underspecified; the discourse context or what we typically think of as an adjunct modifier of the noun phrase can make clear what the purpose is. (9.41) This is a good rock for skipping/throwing/carving/chiseling, etc. Sometimes the polymorphic type is specified by a common noun. (9.42) This is a good skipping rock. Or it can be specified via a restricted predication: (9.43) This rock is good as a skipping stone. (9.41–9.43) seem roughly equivalent in meaning and so have roughly the same analysis. In (9.43), according to TCL’s analysis of restricted predication, good is predicated of an aspect. But what type is the aspect? To get a clearer idea, consider the contrast between these two predications: (9.44) a. Samantha is a mathematician. b. Samantha is a really good mathematician. There is a subtle distinction in the meaning of mathematician in (9.44a) and (9.44b).3 To say that Samantha is a mathematician typically means that she has a certain profession; being a mathematician is like being a banker or a lawyer. On the other hand, to say that Samantha is a really good mathematician is to say that she is good at what mathematicians do—proving theorems, solving combinatorial problems, coming up with interesting conjectures, and so on. While one can get the activity reading for (9.44a), the “profession” reading, the reading that Samantha has a particular profession, is difficult to get with (9.44b); the same observation holds for good lawyer, great writer, good salesman, etc. Similarly, to say that a rock is a good skipping stone is to say that it is good for the activity of skipping. The observation holds also for evaluative adjectives at the negative end of the scale: to say of Fred that he’s a lousy mathematician or a bad mathematician is just to say that he’s bad at doing math, or at the limit that he can’t do math. These readings resemble the disposition coercion readings for the adjective fast. To be a good mathematician is to have a certain disposition to certain 3

Thanks to Julie Hunter for discussions on this point.

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activities that are performed well. Similarly, to be a good skipping stone, a rock must be good for the activity of skipping. Dispositions are different from events. They are modal or quantificational properties; an object has a disposition to engage in an activity φ just in case in the appropriate circumstances the object normally does φ. That is, Samantha’s being good at math means that in the relevant circumstances she normally does what mathematicians do and she does it well. Thus, the evaluative adjective modifies an event but that event is under the scope of a generic operator, which Asher and Morreau (1995) and Pelletier and Asher (1997) define using a weak conditional > and first-order quantification. The dispositional reading comes from a justification of the type presuppositions of the adjective via an underspecified dependent type: there is a natural map from mathematician to the disposition to do math, and for every good mathematician x at time t, such a disposition must also exist for x at t (i.e., the map is everywhere defined). Positive evaluative adjectives thus give rise to a certain subsective property: if you’re a good mathematician, you’re a mathematician in that you have the ability to do math. But negative, evaluative adjectives like bad, terrible, and worthless do not. Consider: (9.45) That rock is a terrible skipping stone. In fact it’s not a skipping stone at all. If terrible skipping stone entailed that the rock was a skipping stone, then this discourse would be contradictory, or we would have to understand the second sentence as a correction by the speaker of his first claim. Negative evaluative adjectives do not imply that the object has the capacity for the activity associated with its description. On the other hand, the map from the activity of doing math to the profession sense of mathematician is not everywhere defined. Nor is the map from mathematicians to the activity of doing math everywhere defined, and so an event coercion involving mathematicians or stones is not guaranteed to be sound. This observation predicts that event coercions over mathematician should not give rise to the activity of doing math, unless a lot of context is provided. Putting mathematician as a direct object of an aspectual verb or enjoy partially confirms this prediction: the event of doing mathematics is not available to satisfy the type presuppositions of these verbs. (9.46) a. #Sam began that mathematician. b. Sam enjoyed that mathematician. c. Sam enjoyed mathematics at university. (9.46a) is pratically uninterpretable. 9.46b) entails the existence of some event involving a mathematician (performances, cannibalism, or sexual encounters

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come to mind), but only in a very particular context can it be an event of doing math (imagine that Sam is judging the performance of several mathematicians doing math). On the other hand, (9.47) Those were good oysters (9.48) That was a good cigarette have clear event readings associated with consuming oysters or cigarettes: there was an event of eating those oysters, and that event was good, or there was an event of smoking that cigarette and that event was good. Even the present tense (9.49) These are good oysters has both a dispositional reading and an event reading. This contrasts starkly with that was/is a good mathematician, which doesn’t have the event reading. To sum up, evaluative adjectives select for an event or disposition type. Whether an eventuality or a disposition is introduced to justify type presuppositions depends upon the type of the noun that is in the scope of the evaluative adjective and upon the content of an accompanying as or for adverbial phrase, if it occurs.4 TCL predicts that when the polymorphic type is not specified, we get an anomalous predication, just as we do in the classic cases of coercion: (9.50) a. #This rock is good as granite. b. #This rock is good. c. This rock is a good example of granite. Let us look at a lexical entry for an evaluative adjective. Following Kennedy (1997), I treat evaluative adjectives as functional relations over entities x and degrees with respect to a certain property of eventualities or dispositions involving x. So their lexical entry is something like this: (9.51) λP: 1λx: e λπ ∃d: degree Eval-Adj(P, x, d, π ∗ arg1 : ((evt  disposition) ⇒ t) These degrees can be positive or negative. The generalization is that if the degree d > 0, a degree given by positive evaluative adjectives, then EvalAdj(P, x, d, π) implies P(x). When d ≤ 0, then Eval-Adj(P, x, d, π) does not. When P must combine with a predicate that is not a property of eventualities or dispositions, the existence of a map from things of the type picked out by 4

The latter produces in TCL a restricted predication involving the subject and makes the eventuality or disposition an aspect of the individual. But as I’ve noted, almost anything can be an aspect!

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P to dispositions or activities introduces an appropriate polymorphic type that will locally satisfy the type presupposition of the adjective. Presupposition justification using δC will introduce a term that can combine with the abstracted term λx Eval-Adj(P, x, d, π ∗ arg1 : (evt  disposition) ⇒ t) so that the presupposition will be justified. This term involves a map from things of type hd(P) to an associated activity type of objects; in effect the noun simply contributes its head type, the most specific type of things it denotes, to evaluation. With this in mind, we can now proceed to a derivation for a common noun phrase like good mathematician. Assume that we have applied the noun’s lexical entry to the adjective, which yields: good

: (agent ⇒ t)∗ (9.52) λPλxλπ∃d good(P, x, d, π ∗ arg1 ((disposition  activity) ⇒ t))(λuλπ mathematician(u, π )) We must resolve the type clash on the argument of P (agent (disposition  activity) = ⊥) by locally justifying either a disposition type or an activity type. Supposing that the map from occupations to dispositions is defined for good but the map from occupations to activities is not, we can define dispositions in terms of a quantification over eventualities together with the weak conditional >. Assuming that the list of such typical activities has a finite subset from which all other activities can be inferred, we can take all the typical activities of a type P of person as a conjunction φ(hd(P)) . Hence, the appropriate functor a modifier of dispositions to one of properties of people to dispositions is something like this: (9.53) λP: mod λPλv P(λx: evt ∀u(P(u) > φ(hd(P)) (u, x)))(v)(π) We can apply this functor to good and apply a meaning postulate which uses the activities associated with mathematicians and links it to a degree. The result is the following: (9.52b) λPλxλπ∃d∀v: evt (φ(hd(P)) (x, v, π) > (d(v) > 0)) (λuλπ Mathematician(u, π )) Application and Simple Type Accommodation now yield a property of individuals that is a disposition to do good mathematics: (9.52c) λxλπ∃d∀v (φ(mathematician) (x, v, π) > (d(v) > 0)) The contrast between evaluative adjectives and coercions involving enjoy reinforces the observation we’ve already made: a coerced argument cannot be sensitive only to the type of the argument; it must be also sensitive to the type of predicate. The lexical entries for enjoy and good in TCL together with

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the use of polymorphic types provides an account that predicts the observed differences between evaluative adjectives and coercing verbs like enjoy.

9.8 Coercions with pluralities In a good theory of predication, we must distinguish those predicates that type for a collective predication of a plural type from those that type for a distributive one. That is, a predicate like disperse or gather takes a collectively understood plural argument. Many predicates go either way, but there is, intuitively, a big difference as to whether the predication is understood collectively or distributively. (9.54) Three students lifted the piano. When (9.54) is understood as a collective predication, then all three students are involved in lifting the piano together, whereas when understood distributively it says that each of the three students lifted the piano individually. This implies the existence of a map from groups to their members and back again that affects predication. For some predicates, the plural argument can be understood either collectively or distributively, whereas other predicates force their plural arguments to be understood in a particular way—for example, the determiner most is inherently distributive. Like almost all of maps that underly coercion, the map from collective to distributive and back again also supports copredication: (9.55) The students worked very hard (distributive) and mowed the whole meadow (collective). Making sure that an argument is collective ought to be a matter of type checking in a typed system, but it is a subtle matter how the argument is transformed by the composition process and by subsequent discourse (see Asher and Wang (2003) for details). For instance, a predicate like mow may be understood either collectively or distributively; its final interpretation depends on the nature of its arguments and the discourse context. It can sometimes be understood as both.5 (9.56) The students mowed the meadow on the left and the professors the meadows on the right. 5

Thanks to Ofra Magidor for this example.

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TCL predicts these sorts of examples to have their intended readings, because what is shifted is the predicational relation, not the meaning of the VP. Accordingly, the recovery of the target in ellipsis proceeds prior to the coercion steps, just as the recovery of a verb phrase with an anaphor must proceed prior to the assignment of an antecedent to the anaphor, as I argued in Asher (1993). In TCL, coercions thus allow for “sloppy” interpretations in ellipsis, just as anaphors do.

9.9 Aspectual coercion and verbal modification One of the truisms about the progressive is that stative constructions aren’t supposed to support a progressive aspect—for instance, (9.57a) supports this generalization. Nevertheless, (9.57b–d) are perfectly unproblematic. (9.57) b. c. d.

a. #John is knowing French. John is being silly. John is just being John. John’s being an asshole.

Contrast (9.57b–d) with their non progressive counterparts John is silly, John is John, John is French and it becomes obvious that the progressive form of be produces a coercion. Following the received wisdom concerning the analysis of the progressive, I will assume that when the progressive applies to a verb or verb phrase, the eventuality argument is required to be an eventuality that is not a state. However, when the progressive operator applies to a copular phrase, the constuction licenses the introduction of a dependent type mapping a state of type σ to a type of activity that when performed by an agent yields a result in which the agent is silly. This coercion is licensed, not by a lexical item, but by a particular predicational construction. This coercion is relatively robust. For example, it passes the anaphora test: (9.58) a. John’s being silly, and he’s doing it to annoy you. b. #John is silly, and he’s doing it to annoy you. The pronoun it as an argument to the verb do must pick up an event or event type in (9.58a), not a state; attempting to use the same construction to refer back in the state as in (9.58b) is impossible. While most of this book has examined modificational predication in the nominal domain, aspectual coercion occurs also with verbal modification. The progressive aspect is a modifier of a syntactic projection of the verb, the VP.

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Furthermore, other modifiers like temporal adverbs modify or “shift” the aspect of the verbal complex:6 (9.59) b. c. d.

a. John wrote a letter in an hour. John wrote a letter for an hour. John kissed Mary at 10 in the morning. John kissed Mary for an hour.

The temporal modifiers can change the aspect of the verbal complex from an achievement or accomplishment in (9.59a,c) to an activity in (9.59b,d). To analyze these, we need a theory of verbal modification. There is a very successful theory, or group of theories, of verbal modification known as event semantics. In event semantics eventualities of various sorts play many roles. Davidson (1968/69) proposed that action verbs have a hidden eventuality argument that could serve as an argument to adjuncts to the verb phrase. Since then, it has become standard practice in syntax following Abney (1987) and in semantics (e.g., Asher 1993) to extend this usage to all verbs and to suppose that verbal inflection binds these event arguments and localizes them in time. Davidson’s approach is highly intuitive when one thinks of simple sentences with action verbs like (9.60) Brutus stabbed Caesar with a knife on the steps of the Capitol. In (9.60) the event argument of stab is temporally localized by the past tense morpheme, spatially localized by the adverbial on the steps of the Capitol and modified by with a knife. All of these linguistic elements contribute properties of events and are linked conjunctively. The Davidsonian approach thus predicts that the order of the modifiers does not affect the content of the sentence, a prediction that has come under attack from Cinque (1999). Neo-Davidsonians like Kratzer (2005) go so far as to make subjects or external arguments predicates of events as well. For sentences with other verbs, however, the Neo-Davidsonian approach is conceptually less plausible. Consider sentences like (9.61) a. Two and two makes four. b. Peano arithmetic is undecidable. There is no event in any robust sense being described in either one of these sentences. Events are, most philosophers would agree, located in space-time, and neither (9.61a) nor (9.61b) are about regions of space-time. And nevertheless, there are verbal modifications in similar sentences: 6

For a good overview of aspect in several languages, see Smith (1991).

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(9.62) a. Two and two will always make four. b. The function approaches zero very quickly as its argument approaches two. Furthermore, there is a well-known problem for event semantics involving negation. A sentence like (9.63) No one talked has the intuitive content that there was no event of talking by any one in the domain of quantification. This is what a standard Davidsonian account predicts. However, sentences like (9.63) can receive verbal modification: (9.64) No one talked for an hour. Crucially, there is a reading of (9.64) in which the adverbial modification occurs outside the scope of the negation: (9.64) implies that there was no talking for an hour, not that every one had the property of not talking for an hour (but rather only five minutes). A Davidsonian approach seems to get the truth conditions for (9.64) wrong or can’t explain what is the argument of the modifier.7 Finally, the Neo-Davidsonian picture of verbal modification as an operation of conjoining two event predications doesn’t hold up. Some modifiers function semantically more like arguments of the verb than adjuncts. For some types of modifiers, a verb cannot have more than one modifier of that type, as Beaver and Condoravdi (2007) note. Consider, for example: (9.65) a. #Brutus killed Caesar with a knife with a hammer. b. #Brutus killed Caesar with a knife with a sharp knife. (read with no pause) c. Brutus killed Caesar with a knife and a hammer. With a knife and with a hammer are modifiers that fill in an instrumental role of the verb. One can coordinate instrumental modifiers as in (9.65c) and analyze these modifications using the mechanisms of copredication developed in TCL. But one cannot simply add them ad libidem. This is contrary to what a standard Neo-Davidsonian analysis would have us expect. If we treat such modifiers as optional arguments of the verb, we get a better analysis of the data. While this is compatible with standard syntactic treatments of VP modifiers,8 it is very different semantically from Davidsonian or 7 8

For more discussion, see Asher (1993). My semantics is also friendly to more complex syntactic proposals for verbal projections like that of Cinque (1999).

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Neo-Davidsonian semantics. I will suppose that a verb like kill takes an optional instrumental just in the way that a verb like wipe takes an optional direct object, according to Levin (1999) and Kratzer (2005).9 Once that instrumental argument is filled by an explicit instrumental modifier, it cannot be filled again. This is what the λ calculus derivation predicts. Similar observations hold for modifiers that provide a recipient role for a verbal complex: (9.66) b. c. d. e. f.

a. John loaded the hay on the wagon on the train. On the train, John loaded the hay on the wagon. John loaded the hay on the wagon and on the train. John loaded the wagon with the hay with the flour. #John wrote a letter to Mary to Sue. John wrote a letter to Mary and to Sue.

In (9.66a) on the train does not describe a recipient role of the loading and hence not a modifier of the verb load but is a modifier of the noun wagon. Fronting this PP makes it a modifier of the verb but it furnishes a location not a recipient. The only way to have the wagon and the train both be recipients is to use coordination. A similar moral holds for the write and its recipient role in (9.66e–f) and for the “contents role” of load type verbs in (9.66d). NeoDavidsonian approaches have no explanation for these observations. If these PPs saturate optional arguments, then we have a ready-made explanation of these facts. With regard to (9.66d) we have an infelicitous sentence because to adverbials do not combine with DPs whose head type is agent. and so the only way to understand (9.66d) is that we are trying to saturate one optional argument twice, which we can’t do in the λ calculus. Not all verbal modifiers saturate optional arguments. Some modifiers simply take the VP as an argument, as in Montague Grammar. Temporal and locative modifiers seem to fall into this class. We can have several temporal modifiers that simply narrow down the time at which the event described by the verbal complex took place. Locative modifiers work similarly. (9.67) a. On Monday Isabel talked for two hours in the afternoon between two and four. b. In Paris John smoked a cigarette on the train in the last second class wagon in seat number 27. The fact that temporal and perhaps other modifiers take the VP itself as an argument makes predictions in TCL. Predicates pass their type presuppositions onto their arguments in TCL, not the other way around. So TCL predicts that 9

For more discussion of this point see the section on resultatives in chapter 10.

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temporal adverbials can affect the type of the verbal complex, as seen in the examples (9.59) above. The temporal modifiers can change the aspect of the verbal complex from an achievement or accomplishment in (9.59a,c) to an activity in (9.59b,d). Furthermore, TCL predicts that temporal modifiers should not be affected by the type of the verb or the verbal complex. In examining verbal modification in TCL, I have been speaking of modification of the verbal complex. But what is that, semantically or type theoretically? With Neo-Davidsonians, we could stipulate that the verb projects an event variable to the tense and aspect projections. Alternatively, we can look to the fine-grained type structure of the verbal complex, which consists of the verb’s type, whose value when saturated by the types of its argument is a subtype of the type of propositions, or t. The specific type of the verbal complex is determined by the appropriate instance of the polymorphic type of the verb with its type parameters specified by the verb’s arguments. Thus, the type of an intransitive verb in (9.68) is a generalized function from subtypes of dp and a presuppositional context type to a subtype of prop. This is a refinement of the type, given in (9.68b), that TCL has given to intransitive verbs up to now. (9.68) a. ∃x dp (x ⇒ Π ⇒ iv(hd(x))) b. dp ⇒ Π ⇒ t A similar story holds for transitive and ditransitive verbs. The “tail” or value of the verb type in (9.68a) will yield different fine-grained types for different values of its parameters. The strategy is to let various adverbials, tense, and other modifiers modify this proposition; some modifiers force the introduction of an eventuality or a fact that realizes the propositional content.10 For simple action sentences, modification by, for example, manner adverbials produces a realizing eventuality for the content given by the verbal complex that the manner adverbial then modifies. But for verbal complexes modified by negation or various modal operators, tense or the presence of a locating adverbial like that in (9.64) may introduce a realizer that is a fact. Similarly, if the type of the verbal complex contains no action verbs but expresses simply a relation between informational objects as in (9.61), temporal adverbs or tense license a coercion that introduces a fact realizer of the content. This would predict that the temporal modification of (9.62a) means something like it will always be true that 2 and 2 makes 4. Thus, most modifications involve a coercion from the verbal complex’s internal semantic value, which is a subtype of prop, to an event or fact realizer. 10

For a discussion of facts versus eventualities, see Asher (1993).

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This strategy allows me to give a unified account of adverbial modifiers like manner adverbials and modifiers that take information contents as arguments. These are the so-called IP modifiers. (9.69) b. c. d.

a. John has evidently taken the VCR (since it’s not here). James clearly likes qualia. Julie has perhaps gone out this morning. Many Americans allegedly love only money.

Standardly, these adverbs are taken to adjoin to IP rather than to VP, but this postulates movement of the adverbial modifiers in many languages. Instead, I propose that they select directly for the propositional content determined by the verbal complex. Note that this can happen even though an adverbial within the propositional adverb’s scope has selected an eventuality as the value of the dependent type of the basic VP as in (9.69c). This suggests a complex coercion story that exploits the map from information contents to eventualities or facts; we’ve already tacitly appealed to this map in event coercion, where the verbal complex specifies an event.11 The value of the polymorphic type associated with a verb is an information content, but various modifiers can coerce this to an eventuality. In this way, TCL takes a middle course between the views of Davidson and Montague on adverbial modification. Let’s now take a look at a derivation with a simple verbal modifier. Consider the verb phrase (9.70) hit Bill with a hammer With a hammer is an instrumental, which is a kind of verbal modifier. The type specification logic contains axioms of the following form, where ty+ (tv)(x, y) is the value of the most specific instantiation of the polymorphic type of the transitive verb when applied to type parameters x and y: (9.71) ∃y p ∃x p with(ty+ (tv(x, y)), hammer)

instrument(ty+ (tv(x, y)), hammer) This axiom suggests the proper formula with which to combine the modifier: (9.72) λuλπ ∃x (hammer(x) ∧ instrument(x, u, π ∗ u: evt)) Similarly to the way TCL models modifiers for nouns, I add higher-order arguments to eventive verbal entries that are typed instrumental, manner, etc., 11

For more on the map from information contents to eventualities and facts, see Asher (1993).

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which are all subtypes of 1; the instrumental modifier is depicted in (9.73).12 If the instrumental argument isn’t realized its λ abstracted variable is applied to the identity property and no realizer is involved. However, a non-empty entry for the modifier as in (9.72) instrumental argument of the verbal complex forces the introduction of an eventuality realizing the verbal complex. This features another use of EC, or event coercion, but this time from prop to evt.  (9.73) λΦλP: instrumental λΨλwλπ (realizes(w,∧ {Ψ(π ∗ arghit 1 : p)(λxλπ Φ  hit   realize : evt)) (π ∗ arg2 : p)(λyλπ hit(x, y, π )))}) ∧ P(w, π ∗ arg1

After constructing the VP using the coerced (9.73) and integrating the entry for the DP Bill, we combine the modifier from (9.72) and allow tense to bind the resulting variable w. (9.74) λΨλπ ∃w: evt ∃t < now (holds(w, t) ∧ realizes(w,∧ {Ψ(π∗arg1 : p)(λxλπ hit(x, b, π ))}) ∧ ∃u (instrument(w, u, π ) ∧ hammer(u, π ))) This approach has several pleasing consequences. It predicts that two separate instrumental phrases cannot combine with a VP because the VP will have only one lambda abstract for instrumentals; once that argument is saturated, we cannot integrate another instrumental with that verbal complex. Second, it validates the Davidsonian simplification inferences, if we assume, as we did for nominal modifiers, that empty verbal modifier phrases are interpreted as the identity property. Third, it predicts that a verbal complex may modify the type of an instrumental by passing to it type presuppositions. Some evidence for this is the observation that different verbs lead to different interpretations of the instrumental: (9.75) paint a miniature with a brush (9.76) scrub the floor with a brush TCL also predicts that certain eventuality types may be derived from others. For instance, walk is an activity but walk to the store with a goal PP is an accomplishment. The type system can now model the hypothesis that accomplishments consist of an activity together with a natural endpoint, or telos (given by the goal PP). On the other hand, verbal temporal modifiers take the whole VP as an argument, and so can cause a local type justification of the verbal complex. For an hour takes a VP like hit Bill as an argument and imposes the type presupposition that the variable of complex and dependent type that it modifies must be 12

instrumental is defined as the type evt ⇒ ∃x instrument(evt, x). If we like, we can suppose that it is the syntactic operation of adding an Instrument Phrase that introduces the additional λ abstract over properties.

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of type activity. We now have a case of coercion since hit(p, p) is a subtype of achievement. A version of EC licenses an accommodation of the activity type presupposition by inserting an iteration operator over the VP, yielding an appropriate interpretation of hit Bill for an hour. TCL also predicts that temporal modifiers may lead to fine-grained shifts in meaning in the verbal complex. For example, consider: (9.77) a. She left her husband five minutes ago. b. She left her husband two years ago. In (9.77b), we have a very different sense of leave than in (9.77a). (9.77a) interprets her husband in a p • l sense whereas (9.77b) interprets her husband in a more institutional sense; that is, (9.77b) means that the subject has left her marriage. Conditional type constraints in the type specification logic can model the effects of the temporal adverbials on the predication. Intensional adverbs like clearly or allegedly select the propositional content introduced by the verbal complex. If we interpret them in situ, we must assume it that takes Tense as an argument and that the quantification over the propositional aspect has scope over TenseP. Thus, the entry for a modifier like allegedly is (Ψ combines the subject DP in the term below): (9.78) λP: vp λT : tense λΨλπ (alleged(∧ T (λvP(π)(Ψ)))) Even though the adverb is interpreted in situ, it has scope over the entire sentence. Without separate meaning postulates, allegedly φ does not entail φ. For other propositional adverbs like clearly, the lexical entry is a little bit different, allowing the entailment to φ.13 Finally, this approach predicts temporal modification to be possible for all sentences, including sentences with negation on the VP or monotone decreasing quantifiers like few people in subject position. Temporal adverbials outside the scope of negation coerce the introduction of a fact that realizes ¬φ, as does the application of Tense. Hence, TCL delivers a uniform account of temporal modification as predicates of realizers, unlike Davidsonian approaches. With this sketch of TCL’s view of verbal modification, let us return to aspectual coercion in the examples (9.57), one of which I repeat below. (9.57b) John is being silly. 13

Perhaps one less nice consequence of the TCL approach is that it does not predict without postulating type shifting the alleged order insensitivity of verbal modifiers (again, sed contra, see Cinque (1999)); e.g., John hit Bill with a hammer on the head is equivalent to John hit Bill on the head with a hammer. It does predict, however, order insensitivity between temporal modifiers and other modifiers.

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Because the types of the verbal complexes can be quite very fine grained, we can distinguish between verbal complex types whose realizers are facts, those whose realizers are events (here I have in mind paradigmatic event sentences like John kissed Mary), and verbal complex types whose realizers are facts or states but have a close connection with eventualities, activities, but don’t by themselves denote eventualities. In this last class fall examples that have been described as statives that accept progressivization, copular sentences that involve some stage level predicate like is silly, is stupid, is an asshole,.... (9.79) illustrate that these have a natural link to certain activities: (9.79) a. John was ridiculous to insist on fighting that guy b. John was stupid/insane/silly to give his money to that woman. c. John was an asshole in being so rude to that student. This construction doesn’t work with other stative predications like (9.80) #John knew French to give that speech/in making that speech. These constructions indicate copular predications with stative adjectives form a particular subtype of prop. While these predications are usually classified as statives by the usual tests of adverbial modification, they are special in that they have a very tight connection with activities of which they describe the result. This subtype is an argument to the progressive and then produces a particular kind of realizer after tense is applied. What the progressive does according to Dowty (1979) and Asher (1992) inter alia is introduce a functor describing some process that leads at least in the normal instances to the appropriate realizer of the proposition given by the verbal complex. While the progressive does not apply to what one might call “pure statives” like John know French, the progressivization of this special subclass of statives introduces an eventuality “realizer” of the verbal complex given by a VP produced from a copula with an adjective complement. When it combines with an adjective, the copula passes the presuppositions of the predicate to its DP argument. We could assume John is silly has a perfective or completed aspect; this might be what forces the introduction of a realizer. This realizer is of type state because of the presence of the copula which affects the fine-grained type of the verbal complex. I give the aspectual operator’s contribution first and then the end result. Below P is the type of the adjectival VP and Φ as usual is a variable of type dp. (9.81) a. λPλΦ λπ∃z: state realizes(z,∧ {Φ(Pre(argP1 )(π))(P(π))}) b. λπ∃z: state(realizes(z,∧ {silly( j, π)})

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Alternatively, we can follow the lead of Slavic languages in which there is no verb form for the copula in such sentences at all (and hence no aspect) and not introduce any realizer at all. This yields a very simple form for John is silly: (9.82) λπ silly( j, π) Now let us turn our attention to (9.57b). After constructing the logical form of the VP, we apply the progressive operator in Aspect. The progressive aspect also introduces a realizer but it must be an event type that is non-stative. So it demands a realizer that is an activity. At this point local justification is attempted by introducing a realizing eventuality for the verbal complex. A coercion takes place when the aspectual information combines with the verbal complex, prior to Tense, but here the coercion is more complex. The verbal complex still requires that any realizer be stative (it is a type presupposition of the verbal complex itself), so we need Aspect, together with the fine grained type of the verbal complex, which reflects the copula + adjective construction, to license a polymorphic type of the form activity(σ, α) whose parameters are σ state and the bearer of the state. The output or value of the polymorphic type is a type of activity or process involving an object of type α that results in a state of type σ. The associated functor for this polymorphic type is: (9.83) λPλeλxλπ∃s (φactvty(hd(P),hd(x)) (x, e, π) ∧ result(e, s, π) ∧ P(π)(s)(x)) We now use a version of EC to justify the progressive’s type presuppositions, and we get the following meaning for (9.57b): (9.84) λπ∃e: activity (e ◦ now ∧ ∃s (φ( j, e) ∧ result(e, s)∧ realizes(s,∧ silly( j, π)))) In words this says that John is doing some activity whose result state is s and s includes the temporal span of some aspect of John in which he is silly. If we take the view that there is no aspect forcing a realizer in John is silly, we get essentially the same logical form, but in this case we have a direct coercion to the result state interpretation from the propositional content ∧ silly( j, π). These are the intuitively right truth conditions for such a sentence. Our discussion has shown how aspectual coercion falls within the TCL approach to coercion.14 This discussion also shows us what is behind the polymorphic types that we used for simple event coercion; they are introducers of event realizers for an underspecified verbal complex. 14

See de Swart (1998) and Bary (2009) for a more extensive discussion of uses of coercion to describe different uses of the pass´e simple and imparfait in discourse. As far as I can tell, all of these coercions are of a piece with the story for aspectual coercion that I have spelled out here.

10 Syntax and Type Transformations

Coercions, as we saw in the last chapter, involve fundamentally a map or a family of maps from one type to another specified by the type structure of a lexical entry. In this chaper, I consider four syntactic and morphosyntactic constructions that invoke a map from one type to another and provide grammaticized examples of coercion: the genitive, grinding, resultative constructions, and nominalization. At the end of this chapter, I address some questions about the logical power and expressivity of TCL.

10.1 The Genitive Asher and Denis (2004) show that the genitive construction offers empirical evidence in favor of the more flexible typing system of TCL. They contrast their account with the one proposed by Vikner and Jensen (2002) that explicitly appeals to GL. Let’s start with some simple English examples of the genitive constructions: (10.1) a. Bill’s mother b. Mary’s ear c. The girl’s car Interpreting phrases like (10.1) requires one to establish a relation between the two nominal referents that are introduced respectively by the specifier NP (the genitive NP, or possessum) and the head noun (the possessor). This relation is often not explicitly specified by the grammar, and as a result these constructions give rise to many interpretations (i.e., many different relations can be inferred). For instance, depending on the context, the girl’s car can be the car owned/driven/dreamt about/designed. . . by the girl.

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273

10.1.1 Vikner and Jensen’s GL based account Vikner and Jensen (2002) argue that GL’s lexical semantics of the head noun is exploited during the interpretation of the genitive. According to them, the default relations found in the genitive constructions are provided by the different qualia roles associated with the head noun. More precisely, the idea is that the genitive NP, acting as the functor, is able to type-coerce the (monadic) denotation of head noun into a relation: crucially, this relation corresponds to one of qualia roles in the lexical entry of the noun. This approach has prima facie some empirical appeal, for one can indeed find examples corresponding to most of the qualia roles: (10.2) b. c. d.

a. const: The door’s wood (i.e., the wood the door is made of) formal: The car’s design telic: Mary’s book (i.e., the book read by Mary) agentive: Bill’s cake (i.e., the cake cooked by Bill)

This approach has a number of problems, as Asher and Denis (2004) argue. They claim that the telic is not part of the semantically licensed readings but rather a pragmatic one. If one goes along with their view, then this already indicates that the qualia aren’t a homogeneous set of types semantically associated with a word. Asher and Denis’s (2004) main criticism is that the qualia are simply not a reliable guide for inferring the genitive relation. They fail to find any plausible example of a true consitutive relation between a head and the genitive NP; there are lots of genitives that involve material constitution— e.g., the car’s metal, the sail’s fabric, the computer’s motherboard, but in these examples the quale constitution is introduced by the genitive NP, not the head. Trying to deal with this problem in the framework of GL leads to a familiar problem, the ad hoc redefinition of the const role; Vikner and Jensen (2002) must, and indeed do, propose that the const quale be interpreted as the part– whole relation. Because of this, Vikner and Jensen (2002) often adopt an extremely liberal view of qualia. For instance, they assume that the same qualia role (namely, the const role) is responsible for explaining both the interpretation of genitive like the girl’s nose (clearly a case of a part–whole relation) and that of the girl’s team (clearly, a case of set-membership). This makes the const role very unclear. There is a directionality problem: the part–whole relation is between the head N and the genitive NP, while the set-membership relation goes the other way around, in potential violation of the head principle which we have derived in TCL from the way presuppositions percolate through the derivation tree. That is, the girl is constituted in part by her nose in one case, but it is the

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team that is constituted in part by the girl. Another problem is that the part– whole and set-membership relations are rather different formally; the former is clearly transitive, while the latter is not. All of these problems can be avoided if we use polymorphic types to introduce the requisite relations. We can exploit the fact that nouns like nose and team have different types (body-part and group respectively) to predict that these cases will give rise to different types of relations. Another argument against qualia that Asher and Denis (2004) provide comes from morphologically rich languages that have grammaticalized certain genitive relations. Crucially, none of these languages have grammaticalized qualia roles therein. In Basque, for instance, there are two genetive postpositions, namely an unmmarked -(a)ren suffix and a marked -ko suffix that specifically encodes (spatial) localization and which thus requires that the type of the object denoted by the nominal in this genitive case be a location (see Aurnague (1998)). Below is a minimal pair from Basque that gives an illustration of the two genitives: (10.3) a. liburuko argazkia book-ko photo-def ‘the photo from/in the book’ b. liburuaren argazkia book-aren photo-def ‘the photo of the book’ The relation of localization whether temporal or spatial is not part of the qualia. Finally, the qualia by themselves fail to provide the relation own (i.e., material possession) that one finds preferred in many examples of the genitive (e.g., John’s car) across different languages.

10.1.2 Genitives within TCL GL’s qualia fail to give an adequate analysis of the genitive construction; they fail to have any privileged epistemic status. The more general notion of polymorphic type does much better. The syntax of the genitive construction is somewhat controversial. Asher (1993) assumed an Abney-like syntax for the genitive construction with a DP analysis (cf. Abney (1987)) in which the construction is headed by an empty functional D head, which assigns (genitive) case to the Spec, DP. Asher and Denis (2004) borrow den Dikken’s (1998) syntactic analysis of the genitive, which assumes a small clause structure in which the possessor is the complement of the predicate that is predicated of the possessum.

275

10.1 The Genitive (10.4) yy yy y y yy Spec

DP G GG GG GG GG

D

w ww ww w w ww

D’ G GG GG GG GG

NP

v vv vv v v vv

teacher

XP C CC CC CC C

X

{{ {{ { { {{

X’ B BB BB BB B

P

| || || | ||

PP E EE EE EE E John

This predicative structure is then selected by a determiner. At this point, various “spell-out” options predict the various word orders. In the case of the prenominal Saxon genitive, the P complement raises all the way up to Spec of DP. With Asher and Denis (2004), I’ll assume the following λ term provides the denotation for the predicative head X and I’ll treat the possessor DP John’s just like John in TCL. To lighten up the notation and since nothing much here rides on the complexities of the interpretation of the verbal complex, I will use the usual Davidsonian notation to stand for my talk of realizers of verbal complex; thus R(u, v, e) is shorthand for realizes(e,∧ R(u, v). (10.5) λΦ: dpλRλu: eλeλπΦ(π)(λv: eR(u, v, e)) X semantically resembles a verbal projection in which some propositional content is realized by an eventuality. The major difference between X and a lexical verb is that one of its arguments is a property, not a DP denotation. From these two entries, we derive the λ term in (10.6) for the X’ John’s. (10.6) λRλuλeλπ R(u, j, e, π ∗ e: evt − (hd(u), person)) Whatever the contribution of the head noun, we need to find an associated relation and an eventuality variable. In some cases like those involving deverbal nouns, the lexical entries will provide what we require. In other cases, I hypothesize that the genitive licenses a coercion supplementing, when needed,

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material to the denotation of the head noun to yield an object of complex, polymorphic type as well as a description of this entity via a saturation of R. In this the genitive is similar to a coercing verb like enjoy. So, associated with the typing of e in (10.6) is a licensing dependent type (hd(u), person).1 What is induced by the coercion is not just a value for the λ abstracted relation R but in fact something close to a realized verbal complex, since it comes with a variable that has an eventuality aspect. The use of eventualities has several advantages. It allows us to treat the genitive construction with EC, and the additional structure posited leads to a natural treatment of temporal NPs (cf., for example, Enc¸ (1986)). Consider a sentence like (10.7) John’s wife went to Yale. Interpreting this sentence properly assumes that we can temporarily relate the eventuality described by the genitive (i.e., that some individual is the wife of John) to the eventuality described by the whole sentence. Interestingly, this sentence has a preferred reading wherein John’s wife is interpreted at the utterance time; that is, wherein the state comes after the main eventuality. The simplest cases of the genitive construction are the ones in which the head noun is a relational noun. (10.8) a. John’s teacher (deverbal) b. John’s friend (relational) c. John’s laziness (deadjectival) To derive a logical form for John’s teacher, let’s assume that the deverbal noun teacher has the simple Neo-Davidsonian entry (forgetting about adjectival modification for the moment). (10.9) λyλxλeλπ teach(x, y, e, π) Using the syntactic structure of the genitive above, we apply the denotation for X’ to that of teacher: (10.10) λRλuλeλπ R(u, j, e, π ∗ e: evty − (hd(type(u)), person)) [λyλxλe λπ teach(x, y, e, π )] −→β (10.11) λuλeλπ teach(u, j, e, π) 1

Asher and Denis (2004) used a different system of types; the dependent types formalism used here is simpler and more general.

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277

The construction intuitively supplies only one argument to the determiner. So we have to existentially close off the variable e, which can be done straightforwardly by an Existential Closure operator of the form λPλu λπ ∃e P(π )(e )(u ).2 This leaves: (10.12) λuλπ∃e teach(u, j, e, π) When we combine this with the empty determiner at the top of the syntactic construction, we get: (10.13) λPλπ∃!u∃e (teach(u, j, e, π) ∧ P(π)(u)) The derivation of the λ term for John’s friend below proceeds analogously; the only difference is that friend introduces a state rather than an event variable into the λ term. (10.14) λPλπ∃!u∃s (friend of(u, j, s, π) ∧ P(π)(u)) Many examples of the genitive construction make reference to a state of an individual, e.g., John’s laziness. Asher and Denis (2004) assume that λ term for the deadjectival laziness is the following: (10.15) λxλs: state lazy(x, s) This denotation is not relational and consequently will not be able to combine with the denotation given above for X. This suggests that the genitive relation is not always relational, contrary to what most existing accounts assume. It can also have the logical form:3 (10.16) λΦλS λs: stateλπ Φ(π ∗ e: state − σ(hd(v)))(λvλπ S (v, s, π )) Combining this new λ term for X with the DP meaning yields for the X’ John’s: (10.17) λS λs S ( j, s) which can now combine with the NP laziness to yield: (10.18) λs: stateλπ lazy( j, s, π) A more interesting case of the genitive construction for analysis is where the interpretation of the relation between the possessive DP and the head NP comes from a dependent type associated with the head NP, as in: (10.19) John’s team 2 3

This formalizes a rule in the construction procedure of Asher (1993) for nominals. In TCL this means that X has a complex disjunctive type.

278

Syntax and Type Transformations

The lexical entry for team is λPλxλπP(π ∗ group)(λvλπ team(v, π )). Since there is no modifier, this just reduces to give λxλπteam(x, π) as the logical form for the head NP. Combining this with λ term for John’s leads to a type clash, since the latter demands an argument that is an eventuality, and it also requires a four-place relation. But here we can use EC and its associated functor on the λ term for the NP to resolve the conflict, turning the two-place noun entry into a description of a relation of the appropriate arity: (10.20) λRλuλeλπ R(u, j, e, π) [λxλyλvλπ team(y, π )∧ φ(hd(x),team) (x, v, y, π )] Using application and substitution, we now get: (10.21) λuλeλπ (team(u, π) ∧ φ(person,team) ( j, u, e, π )) Assuming the presence of a feature Gen or X for the context, we have the defeasible type specification: (10.22) X > (α, group) := belongs-to(α, group) We can now specify φ (person, team) to belongs to, which yields: (10.23) λuλeλπ (team(u, π) ∧ belongs-to( j, u, e, π)) Since we are now at a maximal projection, Existential Closure binds all the surplus variables (here, only the e variable): (10.24) λuλπ∃e (team(u, π) ∧ belongs-to( j, u, e, π)) Combining this with the empty determiner entry yields the expected DP logical form. The ownership/control reading is available in most cases of the genitive. The genitive construction makes this the default specification of the polymorphic type (α, β) in the genitive construction. TCL encodes this as a defeasible type specification: (10.25) X > (α, β) := poss(α, β) To get other specifications of the dependent type, I have to write axioms with logically equally specific or more specific antecedents. So while I assumed above that X > (α, group) := belongs-to(α, group), this axiom in view of the default possessor reading should be revised to: (10.26) (X ∧ β := group) > (α, β) := belongs-to(α, group) With these type specifications, the type specification logic of TCL now entails for a genitive like John’s dog:

10.1 The Genitive

279

(10.27) λuλπ∃e (dog(u) ∧ owned-by(u, j, e, π)) In the genitive construction, it is sometimes the head noun that helps specify the polymorphic type . (10.28) a. The painter’s sky b. The artist’s object c. The janitor’s room These are the equivalents of the following verbal coercion examples, which I discussed in chapter 8: (10.29) a. The janitor/The fumigator started (on) the room. b. The architect/The workers started (on) the house. TCL treats both sorts of examples in the same way using the type specification axioms. The appropriate type specification axioms yield the following representation for (10.28b): (10.28 ) λPλπ∃!y∃!x (artist(x, π) ∧ object(y, π) ∧ created-by(y, x, π) ∧ P(π)(y))

10.1.3 Discourse contexts and the genitive I now return to treat examples where the discourse context enables us to specify the appropriate eventuality and relation in the genitive construction. Here is the example from Asher and Denis (2004) I discussed earlier, repeated below. (1.35) a. All the children were drawing fish. b. Suzie’s salmon was blue. Here I draw on the theory of discourse structure, SDRT, discussed in chapter 8. SDRT posits that (1.35a) and (1.35b) stand in an Elaboration relation (Asher and Lascarides (2003)). But this will be so only if Suzie’s salmon is interpreted in a very particular way; namely, the salmon is the fish that Suzie is drawing. Without this link, we cannot make any clear discourse link between the two sentences, threatening the discourse’s coherence. To give some details, salmon introduces a term whose type is a subtype of the term introduced by fish—i.e., salmon fish. But that term is now connected to its predicate via a relation introduced by the dependent type picture-of, so that the type presuppositions of draw can be satisfied. We must now attend to the interpretation of the genitive. We could infer by default that Suzie owns the salmon, using our default rules for the genitive. But this wouldn’t lead us to infer any discourse relation between (1.35a) and (1.35b); on this resolution (1.35a,b) would lack coherence. SDRT’s principle of Maximize Discourse Coherence (MDC) forces us to

280

Syntax and Type Transformations

specify a polymorphic type invoked in (1.35b) for the analysis of the genitive in such a way so as to permit the computation of a discourse relation between (1.35a) and (1.35b). This is of a piece with the examples of discourse based event coercion we studied in chapter 8. That means we must choose an appropriate specification of the polymorphic type that provides the link between salmon and Suzie in the genitive construction. By specifying this type to the (complex) polymorphic type draw(suzie, picture-of(salmon)), we can compute an Elaboration and thus establish a good discourse connection between (1.35a) and (1.35b). Of course, this only follows if we also make the additional inference that Suzie is one of the children. This last inference, however, is simply a consequence of a general strategy for handling presuppositions: Suzie, as a referential expression, generates a presupposition that we endeavor to bind to some element given in the context. The children provides just such an appropriate element.

10.2 Grinding Grinding is another sort of coercion. It occurs when a bare count noun is required to have a mass interpretation. Grinding is triggered in part by the use of a bare noun in the singular or by a mass determiner applied to a count noun and partly by the demands of a predicate, and so they qualify as a type of coercion.4 There appear to be instances of copredication where we understand a bare noun both as a kind and as a mass. (10.30) Snow is frozen water and all over my yard right now.5 (10.31) I had free-range chicken last night.6 Grinding is another dependent type licensed by certain predicates. That is, the polymorphic type grind takes any physical object type or kind type as in (10.30) and converts it to a subtype of mass. The mechanism of polymorphic type coercion handles the copredications above in the same way as other copredications involving coercion. We can get fine-grained differences in grinding using types: (10.32) Rabbit is usually yummy but not when it’s all over your windshield. We have a coercion from the meat sense where we generically quantify over that to rabbit muck or a portion of rabbit matter. 4 5 6

As David Nicolas pointed out to me, grinding is not freely available, as bare singular nouns in English can have a kind or a mass interpretation. Thanks to Jeff Pelletier for this example. Thanks to Regine Brandt for this example.

10.3 Resultative constructions

281

10.3 Resultative constructions Resultatives are a syntactic construction that involve coercion. Here are some examples of this construction. (10.33) a. The bottle froze solid. b. Nicholas drank the bottle dry. c. Julie wiped the table clean. d. James hammered the metal flat. In such examples, the freezing results in the contents of the bottle being entirely solid. That is, the property of being solid is predicated of the contents of the bottle after and because of the freezing process. Similarly, the table has the property of being clean after and because Julie has wiped it. Wechsler (2005) and others, notably Kratzer (2002, 2005), Levin (1999), have made important contributions to the analysis of the resultative construction giving us reasons why only certain adjectives can go into the construction and have specified those verbs that permit this construction by isolating a class of core intransitive verbs. On the semantic front, things are less well developed. Accounting for this construction requires several stipulations when implemented in a standard event semantics. TCL provides us with a novel analysis of resultatives that has some advantages over approaches within event semantics. Unlike depictives or restricted predications, resultatives have a small clause syntax; the words the table clean in (10.33c), for example, form a syntactic unit (recall our discussion in chapter 7). The small clause modifies the verb, and it is always within the scope of VP adjoining adverbs: (10.34) a. John wiped the table clean at midnight with a sponge. b. *John wiped the table at midnight clean. Following Levin (1999) and Kratzer (2005), verbs like hammer and wipe are core intransitives, and the so-called internal argument adjoins to VP. I note that freeze is also a core intransitive, but it is the theme argument that occupies the subject position in the intransitive use. I’ll assume that the VP structure of freeze is much like that for wipe. These “small clauses” lack a tense or other event saturating element; they also lack a verb. They don’t denote elements of propositional type, as they fail to go with propositional attitude verbs; nor can the small clauses at issue combine with naked infinitive verbs. Finally, verbs that support the resultative construction don’t combine well with internal arguments that are other than of the DP category.

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Syntax and Type Transformations

(10.35) a. *Lizzy believes the table clean. b. Lizzy believes that the table is clean. c. *Alexis saw the table clean (where clean is understood adjectivally not verbally). d. ?Alexis saw the table be clean. e. *John wiped the table is clean In the light of this discussion, I tentatively propose the following syntactic structure for the VP of a resultative construction like that in (10.33b).

V

yy yy y yy yy

wipe

VP

u uu uu u u uu

VP I II II II II

DP

uu uu u uu uu

IP F FF FF FF F clean

the table

The meaning of the construction is intuitively clear: the main verb describes an event or activity that results in the DP having the property that the small clause states it to have. With this structure given above, however, we have some work to do. It is not straightforward in the syntax that the type presuppositions of the verb will flow to the DP in the adjoined position. Verbs that license such optional arguments put type presuppositions on them, as we’ve seen with freeze or with wipe—wipe requires its optional direct object argument to be of type p. To understand this flow of type presuppositions to adjunct-like elements, let’s examine the interpretation of core intransitives. They have a structure very much like that for resultatives, except that the DP is adjoined directly to VP. The question is, what does this adjunction mean semantically, other than a “less tight connection” between the predicate and its argument than with “true” transitives like sharpen? TCL fleshes out this intuition by Levin and Kratzer by interpreting the adjunction of an optional internal argument as linking the verb via an underspecified predicate to the new argument. In order to pass the verb’s presuppositions to these arguments, the verb’s lexical entry in TCL has λ abstracted variables for these optional arguments, filling them with the trivial modifiers in case the arguments are not explicitly given. In effect, I am applying TCL’s analysis of verbal modifiers like instrumentals to optional direct arguments, except that the optional argument does not have a grammatically

10.3 Resultative constructions

283

specified connection with the verbal complex the way an instrumental does.7 A core intransitive with an optional “direct object” argument thus looks very much like a normal transitive verb. The one crucial difference lies in the way the optional argument is linked to the verb. The entry for wipe is given below. (10.36) λΦλΨλvλπ (v: Ψ(π ∗ arg1 : p)(λxλπ wipe(x, π )) ∧ ∃w w: Φ(π arg2 : p)(λyλπ ?(y, π )) ∧ result(v, w, π)) The question mark in the logical form in (10.36) tells us that there is some underspecified property of y that is the effect of the content of v’s being realized. Unlike other underspecified elements, these are not induced by any type coercion but rather introduced by the syntactic construction itself. The variable v is a realizer of the propositional content that John did some wiping, because the discourse relation Result is veridical (it implies the truth of the formulas associated with both of its arguments). The variable w is another realizer of the content that y, the optional object argument of wipe, has some underspecified property. Such a construction specifies the relation between v and w to be the discourse relation Result; in effect v and w specify here discourse constituents, or occurrences of propositional content.8 When no direct object is given (10.36) combines with the identity term for properties, and existential closure gives us the bare existence of some unspecified wiped object. Without any specification at all, this object cannot be referred to anaphorically. In other words, anaphors subscribe to the slogan—no anaphoricity without identity.9 Let’s briefly look at the composition process for: (10.37) John wiped the table. Applying the meaning in (10.36) to the table, we get for the VP: (10.38) λΨλvλπ (v: Ψ(π ∗ arg1 : p) (λxλπ wipe(x, π )) ∧ ∃w w: ∃y (table(y, π) ∧ ?(y, π) ∧ result(v, w, π))) After integrating the subject DP, Tense will apply an existential quantifier to v yielding for (10.37): 7

8 9

Alternatively, as I suggested earlier for arguments like adverbial modifiers, it is the adjunction operation itself that introduces an operator that changes the functional type of the verb from an intransitive to a “partially transitive one.” The operator is straightforward in the typed λ calculus entries of TCL. The operator, which we can call adjoined-arg, takes something of the form dp ⇒ prop and returns something of the form dp ⇒ (dp ⇒ prop). The tricky part is spelling out the details of what adjoined-arg does with the added argument. Asher and Lascarides (2003) argue that causative verbs introduce Result relations between discourse segments. Core intransitive resultatives do the same thing. Although this identity may be supplied by the anaphor itself, if it’s a definite, via the process of bridging.

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Syntax and Type Transformations

(10.39) λπ∃t < now ∃v (holds(v, t) ∧ v: wipe( j, π) ∧ ∃w (w: ∃y (table(y, π) ∧ ?(y, π) ∧ result(v, w, π)))) (10.39) says that John wiped the table and that resulted in some so far underspecified property that the table now has.10 Having sketched the semantics of core intransitives, let’s return to resultatives. The small clause introduces a discourse constituent where a “verbalized” property is predicated of a DP. The discourse unit introduced by the small clause is linked to the discourse constituent introduced by the main clause via the discourse relation Result. The adjective in the complement position of the IP in the resultative construction ends up specifying a property and so we get for the IP a λ abstract over a discourse constituent. The operator adjoined-arg has a slightly different form because its output is slightly different: it takes an intransitive verb and yields something of type ip ⇒ (dp ⇒ prop). With all this in mind, consider again (10.33a). We can expect a justification of the type presupposition of the predicate freeze, which should apply to a liquid. Freeze licenses the introduction of a dependent type contents which will take the type of the object DP as its parameter. In the final logical form for (10.33a) I use α and β for discourse constituents and the usual syntax of the SDRT language, which corresponds straightforwardly to the TCL formalism given above. (10.33a ) λπ∃α∃β∃z (α: ∃x (bottle(x, π) ∧ contents-of(x, z, π) ∧ freeze(w, z, π)) ∧ result(α, β) ∧ β: solid(z, π))

10.4 Nominalization Various forms of nominalization involve a type shift that we can profitably study in terms of polymorphic and dependent types. Nominalization is a means for referring to entities that are not ordinarily understood to be elements of the domain of discourse—that is, of the type e. Nominalizations can arise from complementizers like that, with gerund forms or with various morphemes. Some nominalizations take verbs or adjectives and produce first-order properties. Examples include the verbal affixes -ion, -ment, -er, -ee and the adjectival suffix -ie (as in a quickie, a biggie). Some nominalizations take properties and produce subtypes of e; -ity, -om, and -ness are examples. Linguists have done 10

The account as it stands fails to get the implication that there is a change of state concerning the table. This has to do with the “propositional” presuppositions of change of state verbs, of which wipe would arguably be one. I return to this point in the last chapter.

10.4 Nominalization

285

considerable work on nominalization since the seventies,11 and here I can only give a brief overview of how this topic might receive an analysis in TCL. Verbal nominalizations provide maps from verbs to first-order properties.12 Some, like invention, can describe a property of an object that results from the event or change of state denoted by the verb stem invent. This object is also the verb’s internal argument, and so one can think of the nominalization operation denoted by -ion as operating on invent as selecting the internal argument to be the referential argument of the resulting noun. In other cases like destruction, -ion specifies the result state of the event denoted by the verb. The -ion suffix can also be used to refer to an event; invention and destruction can be used to refer to the event of inventing and of destroying respectively.13 There are differences between derived nominals, those nominalizations that result from some morphological or other transformation of a verbal or adjectival stem into a noun denotation, and nouns denoting events or other objects that do not have any such derivational history. Examples of the latter are race, walk, trip, change, collapse, design and slide. Grimshaw (1990) and Borer (2005b), among others, argue that verbs these classes differ with respect to argument structure: roughly, those in the former inherit much if not all of the argument structure of the verb, while those in the latter have little to no verbal argument structure. This is of course is not surprising if one takes the nominalization operation to be a matter of morphology, which many linguists do. In TCL the nominalizing morpheme maps the type of the verbal complex—i.e., a polymorphic type applied to the verb’s arguments as parameters—into a property of eventualities, of propositions, or of objects. The simple, non-derived nominals simply denote properties of various entities. The event readings of the derived nominals select for one aspect of the value of the verbal complex; but there are other verbs that select a more abstract aspect of this referential argument: (10.40) Economists predict an improvement of the economy in the coming year. In TCL, predict selects for the informational aspect of the entity introduced by an improvement in the economy, thus capturing the intensional nature of 11

12 13

Grimshaw (1990) is a good starting point for the earlier syntactic literature, and since her book many people have worked on the subject, including Alex Marantz, Angelika Kratzer, Hagit Borer, Helen Harley, to name a few. Asher (1993) proposes an analysis of gerunds, that clauses, and other means of forming nominalizations in the syntax. Those proposals are largely compatible with my proposals here. Asher (1993), for instance, contains a detailed analysis of these forms in English.

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the verb. If the event aspect were selected, simply predicting that an event happened would make the prediction come true!14 Nominalizers interact with the argument structure of the elements they modify; most nominalizers transform a verbal stem into a noun denotation whose referential argument (the variable that will end up being bound by the determiner it combines with to form a DP) is one of the arguments of the verbal stem. For example, consider the -er nominalization which takes a verb and picks out an agent or instrument that does the sort of action denoted by the verb. Here are some verbs that undergo this shift: (10.42) clean, carry, lie, bake, sell, report, buy, create, write, invent, perform, dance, cater, fight, box, fence, ski, climb, sail, port, auction, preach, demonize, photograph, paint, choreograph, teach, swim, wrestle, cut, weld, driller, dresser. In TCL the -er transformation is an arrow from the type of a transitive verb to the type of its subject argument. Sometimes this nominalization doesn’t worked or is “blocked” when there already is another word in the lexicon for an agent that does the activity denoted by the verb. For example, the -er nominalization of cook doesn’t denote someone who cooks, because there is already the noun cook that does this. A cooker is instead a pot or something one cooks in. -er nominalizations are examples of nominalizations of verbal stems that select one of the arguments of the verb to be the nominal’s referential argument. A polymorphic type formulation of the -er transformation for an entry of a “non-shifted” transitive verb V goes as follows. The type presuppositions of the verb that apply to its normal arguments also apply in the nominalization (tns is a type for tense operators). • The -er Arrow -er: dp ⇒ (tns ⇒ (dp ⇒ Π ⇒ V(hd(dp), hd(dp), Π))) → mod ⇒ (hd(dp) ⇒ (Π ⇒ V(hd(dp), hd(dp), Π)) V(hd(dp), hd(dp), Π) is a fine-grained type that is a subtype of prop, and so er maps a verbal meaning into a subtype of first-order properties. hd(dp) ⇒ (Π ⇒ (V(hd(dp), hd(dp), Π))) is a polymorphic type all of whose instances are subtypes of 1. The -er arrow is underspecified between object and subject abstraction, but an -er nominal never denotes the event that the verb describes. 14

Interestingly, as noted in Asher (1993), many of the non-derived, simple nominals given above also can denote both events and informational objects:

(10.41) The collapse of the Germans is a fact (what the Allies hoped for).

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The -er arrow says nothing about the other argument and how it is filled in. This depends on how we write the functor that gives the contribution of -er at the level of logical form. As Lieber (2004) notes, some nominalizations are more constrained than the -er one, though they still confirm our first generalization. For example, the -ee nominalizer requires the agent type internal argument of the verb it transforms to be its referential argument. The -ion nominalizer sometimes yields a referential argument that is not one of the arguments of the verbal stem to which it applies. An important distinction is the distinction between result and event nominals. Translation is a nominal that arguably has argument structure on both an event and a “result object” reading, even though its verbal stem translate does not have the result object of the translation as one of its arguments (unlike the verb invent). (10.43) a. The translation lasted for years. b. Fitzgerald’s translation of The Odyssey is a masterpiece of English literature. c. #The translation lasted for years but is a masterpiece of English literature. d. The translation took years to complete but is a masterpiece of English literature. Despite having both a result and an event reading, nominals like translation do not support copredication terribly well.15 In contrast, simple event nominals that have both result and event readings tend to support copredication. (10.44) a. The exam was two pages long. b. The exam lasted for three hours c. The exam was only two pages long but lasted three hours. These observations suggest a second generalization. Derived nominals do not have a • type with an event and a result object type as constituents; nor do they license coercive maps from events to result objects or in the other direction. Were either of these the case, we would find copredications with -ion nominals when we do not, and predications like (10.45b) below would be rescuable, when they are not. 15

Pascal Denis first observed that copredications with derived nominals is often difficult. Most putative examples of copredication involving derived nominals exploit the predicate took years or something similar as in this example (due to James Pustejovsky): Linnaeus’s classification took 25 years and contains 12100 species. But took years can be elliptical for took years to complete, which goes perfectly well with ordinary, physical object nouns (this table took years) and so doesn’t provide an convincing example of event and result object copredication involving derived nominals.

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Interestingly, nominalizations of verbs with an internal argument saturated by the result of the action described by the verb do not have result readings.16 (10.45) a. Benjamin Franklin’s invention was very popular. b. #The invention of the bifocals was very popular. Creation verbs like invent, construct, and create only have result readings when their internal argument is not realized. This last observation suggests a refinement of the first generalization: some nominalizers, like the -ion nominalizer, may transform verbs that don’t incorporate result arguments into their argument structure into nominalizations whose referential argument is a resultobject argument. But this transformation can only take place if the nominalization is not modified in such a way that the result argument is introduced and saturated. This last generalization shows that the realization of argument structure of derived nominals affects their denotation . But what happens to that structure when the arguments aren’t realized? Previous proposals concerning nominals17 postulated some form of existential closure for the verbal argument structure of the nominal once the NP involving it is formed, leaving only the referential argument of the nominal to be saturated by the application of the determiner. While it is undeniable that the argument structure of a nominal like cutter or an event nominal like destruction is present in “some sense” and can be saturated by arguments in prepositional phrases, as in (10.46) the destruction of Carthage by Rome these arguments are not present in a fuller sense in that when not made explicit they cannot be made the antecedents of anaphors that don’t license bridging. (10.47) a. The destruction was complete. #It was completely wiped out. b. The destruction was complete. The city was completely wiped out. Definite descriptions, it is well known, license “bridging inferences” that can connect the denotation of denotation to the city, as the object of the destruction. TCL offers an interesting option for exploring this observation. The -ion operator, applying as it does to a verbal stem, makes all the DP arguments of the verbal stem optional. When the DPs are syntactically realized, the normal type presuppositions of the verb stem apply; but when the DPs are not syntactically realized, then applying our nominalization to the identity property for DP arguments together with existential closure will yield unspecified objects that cannot be picked up by anaphoric elements. 16 17

Thanks to Chiara Melloni for pointing this out to me. Among these I include Asher (1993), Pustejovsky (1995), Rossdeutscher (2007).

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Let’s consider the nominal translation in more detail. Let us assume that the -ion nominalizer makes optional the internal or object (external) and (subject) arguments of the verb. As with core intransitives, this means then that the internal and external arguments are no longer directly related via the verbal predicate but rather stand in some underspecified relation to the verbal complex, which in this case consists just in a verbal activity. The -ion arrow then takes us from a standard verbal type involving a verbal type V (like that in the -er arrow) to a function f : dp ⇒ dp ⇒ prop, but the particular subtype of prop that is the tail of f involves an unknown and inaccessible saturation of the verbal complex conjoined with underspecified relations between that verbal complex meaning and the variables contributed by the DPs. In fact there are two ways, the -ion arrow can be further specified, which leads us to the following entries for the verb stem and the event and result object nominalizations:18 (10.48) translate: λΦλΨλwλπ Ψ(π ∗ arg1 : ag) (λxλπ Φ(π ∗ arg2 : p • i) (λyλπ translate(x, y, w, π ))) (10.49) translation (event): λΦλΨλv: evt λπ Ψ(π ∗ arg1 : ag) (λxλπ Φ (π ∗ arg2 : p • i)(λyλπ ∃w (translation(w, π ) ∧ ?(x, w, π ) ∧?(y, w, π ) ∧ realize(v, w)))) (10.50) translation (result): λΦλΨλv: p • i λπ Ψ(π ∗ arg1 : ag) (λxλπ Φ (π ∗ arg2 : p • i) (λyλπ ∃w (translation(w, π ) ∧ ?(x, π ) ∧?(y, π ) ∧ result(w, v)))) The term w in (10.49 denotes a “bare” verbal complex and hence is of type prop; in (10.50), w is coerced into a fact by the predicate result. The nominalization operator can do two things, both familiar operations of TCL. It can select for an eventuality in the event reading of the verbal complex—hence the presence of the realizes predicate linking the variable of complex type and the variable for the event aspect, or it can provide an object in the result reading. Hence the nominalization operator’s value is the disjunctive type evt ∨ result-object. If the DP arguments of the nominal are syntactically realized as in (10.51) Fitzgerald’s translation of The Odyssey matters are more complex. Some syntacticians have taken the view that the of PP merely provides an internal argument for the verb, thus realizing one of the optional arguments. Given our treatment of the genitive, it makes sense to take the DP in genitive case as furnishing another argument and realizing the 18

I do not concern myself here with the geometrical sense of translate or the somewhat archaic sense of the verb in which it means transform or move.

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optional external or subject argument. TCL then yields as a logical form for the event reading of the nominal:19 (10.52) λPλπ∃v∃!y∃w (translation(w, π) ∧ agent( f, w) ∧ theme(o, w) ∧ realize(v, w) ∧ P(v, π)) On the other hand, if the DP arguments are not realized, we apply the term translation to λPP twice and use existential closure to get the following logical form for the event reading of the translation: (10.53) λπ∃v: evtλπ∃w∃x∃y (translation(w, π) ∧?(x, π) ∧?(y, π) ∧realize(v, w)) The unrealized arguments of the nominal, being completely unspecified, are not available as anaphoric antecedents to anaphors like pronouns, according to my slogan “no anaphoric reference without identity.” Thus, TCL provides a promising start of an explanation for the behavior of -ion nominals. Since the nominalization has the disjunctive type evt ∨ result-object, TCL predicts the lack of copredications. TCL does predict that anaphoric reference to the event of translating with the result reading though.20 The TCL formalism also captures my three generalizations about the verbal nominalizations. So far, we have only examined nominalizations yielding entities that Asher (1993) called “saturated,” that is, entities like propositions, facts, and eventualities. The realm of nominalizations is much larger than this. Natural languages have sufficient resources to map most types realized by natural language expressions into a subtype of e, the type of abstract objects or informational objects i. In English, morphemes like -ity, -hood, and -ness do this job. English also has subjectless gerunds, arguably bare nouns, and constructions like the property of or the property such that constructions, as well to map expressions of higher-order type into e. (10.54) a. humility, elementhood, squareness b. the property of being triangular c. the concept of being red d. being triangular e. the property of properties such that for any property everything that is a man also has that property. Most of these nominalizations function like proper names. One could think of nominalization as a function from types into dp, but one could also think of 19

20

Alternatively, one can specify meaning postulates about how PPs combine with nominalizations as in Asher (1993). Lieber (2004) and Melloni (2007) also provide constraints on how argument structure may be realized. For a discussion, see Asher (1993).

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nominalizations as purely referential expressions, whose type is a subtype e. I shall do the latter (and I won’t bother with the composition of the property of constructions). All of these nominalizations make use of what I call: • The Property Nominalization “Arrow”:  ν: α −→ e, where α n∈N n where n is the type of nth order properties. We should distinguish the nominalizations of two types if the types are distinct. That is, ν should be a monomorphism into subtypes of e. This has an effect at the level of logical form; corresponding to ν is a function symbol that picks out the entity that corresponds to the object of higher type. At the cost of a little ambiguity, I’ll use ν to represent that function symbol as well. Sometimes these various nominalizations seem to denote the same sort of thing. (10.55) a. Humility is a virtue. b. The property of being humble is a virtue. c. Being humble is a virtue. However, Moltmann (2004) notes that these nominalizations can act differently. (10.56) a. John’s humility is greater than Mary’s humility. b. #John’s being humble is greater than Mary’s being humble. (10.57) a. John is looking for honesty. b. #John is looking for the property of being honest. c. Originality is highly prized at this conference. d. The property of being original is highly prized at this conference. e. I often encounter hostility. f. #I often encounter the property of being hostile. (10.58) a. #The property of being a cat is widespread. b. Cathood is widespread. c. Cats are widespread. Given Asher’s (1993) discussion of the scale of abstract entities, honesty, hostility can refer to something concrete (instances of these properties) whereas the property of construction cannot. The data also suggests that these nominalizations do not refer to eventualities, facts, or other sorts of entities that complete gerund phrases refer to. John’s being humble is a state of John but it doesn’t have the same properties as John’s humility. Moltmann (2004) claims that an -ity nominalization refers to an abstract

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entity a but predications over a apply only to instances of a, not to the property. Thus, she claims the following equivalence: • John is looking for honesty ↔ John is looking for instances of honesty. This claim is too strong. -ity nominalizations can refer to properties and we can make straightforward second-order predications of them: (10.59) Humility is a property I admire in Mary. (10.60) Avariciousness is a property that no one should aspire to having. Thus, contra Moltmann, these nominals can be coerced into pure property readings when required. We can have copredications involving both the property and instance readings of -ity nominalizations, which is our indicator for a logical polysemy rather than accidental polysemy. Copredications with the property of construction, however, do not occur. (10.61) a. Avariciousness is a property that no one should aspire to having but is encountered all the time today. (property and instances or tropes) b. #The property of being avaricious is a property that no one should aspire to having but is encountered all the time today. (10.62) a. Humility is an admirable property but in short supply amongst most philosophers. (property and instances) b. #The property of being humble is an admirable property but in short supply amongst most philosophers. In TCL nominalizations involving the -ity, -dom, and -ness morphemes have two aspects—a pure property aspect and an instance aspect. These aspects differ in ontological status; instances behave like masses whereas properties are abstract objects and behave like count nouns. The copredication tests show that it is the nominal and not the verb or predicate that licenses the property or instance reading. Thus, I propose that such nominals are of the complex type ν(1) • instance(1). instance is a polymorphic type from properties to concrete instances of them in the world. • instance: 1 −→ p The instance aspect of a property nominal is related to the property aspect of the object of complex type via the predicate realizes; instances are realizations of properties in just the same way that eventualities or facts are realizations of propositions. Predicates that presuppose an instance of a property type as a semantic argument will select the instance aspect of the denotation, while predicates that presuppose a pure property type argument will select for the

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other aspect. So, for example, (10.62a) has the logical form (little is the mass determiner corresponding to the count determiner few): (10.63) ∃x∃y(admirable property(x) ∧ little z (realizes(z, x) ∧ o-elab(z, y), philosophers have(z)) ∧ x = ν(λvhumble(v)) ∧ o-elab(x, y)) Nominalization enables a language to express predications to properties, and this capacity brings with it a capacity for self-predication. How does a strongly typed language represent what appear to be self-predications as in the following examples? (10.64) a. Being nice is nice. b. It’s bad to be bad. c. Humility is humbling. If such examples are cases where a property applies to itself, we cannot assign a well-founded functional type to the property. But are such cases really cases of self-application? No. What is really going on is that the property applies to a nominalization of the property. The nominalization is type theoretically significant and shifts the type of its argument. Thus, there is no problem of assigning an appropriate functional type (see also Chierchia (1984)). In a typed system, we cannot construct the Russell property or similar selfreferential objects. However, we can come close to expressing self-application as well as non-self-application once we have nominalization. Below is the lambda term for non-self-application as applied to properties of type 1. ν below gives the nominal correlate in e of the property in logical forms. (10.65) λP: 1 ¬P(ν(P)) (10.65) is a term of type 1 ⇒ prop, the type of a generalized quantifer or second-order property. It is the property of those first-order properties that do not apply to their own nominalizations. According to the definition of the Property Nominalization Arrow, (10.65) has a correlate in e, namely (10.66) ν(λP¬P(ν(P))) In the type free lambda calculus, the Russell paradox can be reconstructed, when (10.65) applies to itself. However, in the typed system even with a nominalization type shifter, this can’t happen. Applying (10.65) to its own nominalization isn’t even well formed, since (10.66) is of type e and (10.65) is of type 1 ⇒ prop.21 21

It’s important that the nominalization operator does not make e a universal type (as in Martin-L¨of’s original system, proved inconsistent by Girard (for a nice exposition, see Coquand (1986)). So there is no Burali-Forti paradox for the present system, although there are plenty of incompletenesses (Coquand 1986).

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Some properties, in particular all physical properties, emphatically do not apply to their nominalizations and so have the property (10.65). (10.67) a. The property of being a horse is a horse. b. The property of being triangular is triangular. c. The property of being red is red. The general observation is that properties of individuals do not apply to their own nominalizations, analytically. That is, the sentences in (10.67) are analytically false. TCL’s typing conventions explain this observation. By distinguishing between objects of type p and abstract or informational objects of type i, we know that predicates that are typed as physical properties (p ⇒ t) cannot apply to purely informational objects. Nominalizations of properties, however, must be informational objects; they are clearly abstract. So nominalizations of physical properties fail to meet the type requirements of the predicates. There are some properties that do apply to their own nominalizations. The relation of identity, for example, or, to use an example from the medieval philosopher Nicholas of Cusa, the relation of being not other than, have the property of applying to their own nominalizations.22 The property of being a property also has this property. (10.68) a. the property of being a property b. The property of being a property is a property. (10.68b), in contrast to the examples in (10.67) seems analytically true. We can derive (10.68b) as an analytical truth in TCL, if we make use not only of the rules for λ in TCL but also the rules for the connectives and quantifiers of the base language. Let’s go through the steps (I’ll omit the presupposition parameter, as it’s not relevant here). (10.69) is a property: λx∃P ν(P) = x (10.70) The property of being a property: ν(λx∃P ν(P ) = x) (10.71) The property of being a property is a property: We need to show: λx (∃P ν(P) = x){ν(λx∃P ν(P ) = x)} 1. ν(λx∃P ν(P) = x) = ν(λx∃P ν(P) = x) 2. ∃Q ν(Q) = ν(λx∃P ν(P) = x) 3. λx∃Q ν(Q) = x[ν(λx∃P ν(P) = x)] 22

Identity 1, ∃ introduction 2, Abstraction

Nicholas of Cusa proposed the following analogy for the Trinity: non aliud non aliud quam non aliud est.

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Similarly we can derive that the property of not being a property is a property is also an analytical truth. (10.72) the property of not being a property ν(λx¬∃P ν(P) = x) (10.73) is also a property: 1. ν(λx¬∃P ν(P) = x) = ν(λx¬∃P ν(P) = x) 2. ∃Q (ν(Q) = ν(λx¬∃P ν(P) = x) 3. λy∃Q ν(Q) = y[ν(λx¬∃P ν(P) = x)] We can model application or the relation of having as the inverse of the nominalization operation, if we assume a bijection from properties to their nominalized counterparts. So the following sentences are representable: (10.74) Many properties do not apply to their own nominalizations. (10.75) Many properties have the self applicative property. Because our quantification is limited to quantification over inhabitants of a given type, we cannot model: • there is only one relation of identity • the property of self application applies to itself. Were we to countenance unrestricted quantification over types in TCL at least in some circumstances, these would be representable.23 TCL also shows that there are certain predicates that necessarily do not apply to any objects. Consider the predicate that expresses the property of not having any properties. (10.76) λx∀P¬Px Suppose we now instantiate P = λx¬P0 x and let a be any object such that λx∀P¬Px[a]. By intantiating P to P0 and application, we get (10.77) λx¬P0 x(a) = ¬P0 (a)) But on the other hand, instantiating P = λx¬P0 x, we get (10.78) ¬λx¬P0 (a) ↔ ¬¬P0 (a) ↔ P0 (a) If the system is consistent, then there is no object (of any type) that has the property λx∀P¬P(x). If we think about this in set theoretic terms, however, this makes sense: there is no object of ZFU such that no set contains it in ZFU. 23

Thanks to Renaud Marlet for this point.

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One might wonder whether the system of types with a nominalization arrow remains consistent. A cardinality argument, for instance, threatens our approach. I have assumed a 1–1 map from higher types into their nominalized counterparts. But if one assumes that there are at least as many types or properties as there are subsets of the basic domain, and each one gives a distinct type, postulating such a 1–1 map violates Cantor’s theorem. This argument is easily dispensed with. The set of all types that can be produced with finite applications of ⇒ and the definable dependent types is at most countably infinite, given a countable set of atomic types (they correspond at most to the set of all finite sequences over ω). There is no cardinality problem at the level of types as long as e is at least countably infinite. The argument for properties is more delicate. There is a cardinality problem if there are as many properties as there are subsets of the domain of individuals. But why suppose that this is so with respect to natural language? There are only at most countably many definable properties and so at most countably many nominalizations of those properties. The general task of proving a relative consistency theorem for the type theory is more involved. The category theoretic model that I have used for TCL and that verifies the rules of TCL does not in and of itself provide an interpretation for the nominalization function ν. But it appears that we can add to the categorial model a monomorphism from n into e, picking out a countable subobject of i e, provided e, and i, are big enough. This does not make e a universal type, because the morphism does not serve in the definition of the restricted inference relation defining a subtype relation. Note that this does not make higher-order properties a subtype of e, only their nominalisations. Adding such a map to our categorial model would provide a categorial model for the whole type system as I have so far developed it. It would also make e “almost” a reflexive object as defined in, e.g., Asperti and Longo (1991).24

10.5 Evaluating TCL formally Let us return to the internal semantics of TCL formulas. Lemma 1 of chapter 4 shows that TCL terms have a value in the internal semantics just in case the type presuppositions are all justified in the λ term reduction process. This is exactly what we need to make sense of semantic anomaly and well-formedness, and we were able to show that every term involving type presuppositions without a type conflict would have a determinate type. Since chapter 4, I have 24

For the model F , the existence of a 1–1 function from one countable set (recall that the set of property types is countable!) to another is, of course, no problem. So F appears to give us a relative consistency proof.

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introduced special types like the • types and coercions. These provide natural transformations and a means for resolving type conflicts by extending the original categorial structure with arrows to types that permit a suitable typing. But we must investigate the effects of these natural transformations. A chain of natural transformations C0 → C1 → . . . → Cn produces in effect a chain of elementary substructures as each category’s structure on the left of an → is preserved in the category on the right. Thus, Fact 18 If a term t has a type α in Ci in a chain of natural transformations, it has type α in C j for i < j. Using Lemma 1 from chapter 4 and Fact 14 above, terms in which there is no conflict between type presuppositions preserve their type up the chain of structures linked by natural transformations. This allows us to strengthen Lemma 1 to deal with the cases of coercion and aspect selection:25 Lemma 2 A TCL term t in which all type conflicts in the assignment to the type presupposition parameter are resolved by a natural transformation has a definite type in the co-domain category of the transformation. I now turn to the complexity of the TCL calculus. TCL rules are for the most part just the rules of the typed λ calculus. In this investigation I will leave aside the calculation of the subtyping relation, which can be computed off line from the lexically given types. I will look at what computational costs are incurred by the presupposition justification process. It turns out not much is needed. To handle presupposition binding, • justification, and accommodation, I’ve added rules that allow us to eliminate type presuppositions, and rules for justifying type presuppositions via • type justification or via the rules for justifying dependent types. In addition, I’ve added certain rules like Local Justification that allows us to move presuppositions from one argument to another. This adds a certain amount of complexity to the λ calculus, though in the end not much. In order for the rules for presupposition justification to apply, presuppositions must be moved to the sites in logical form where they can be evaluated. We do this by (a) combining higher-order arguments (of DP type or higher) with their predicates (transitive and intransitive verbs) via Application and Substitution, and by (b) using Application and Substitution on presupposition terms. I call (b) the presupposition percolation process. Lemma 3 25

The presupposition percolation process terminates in at most

The proof of the lemma follows from Lemma 1, Fact 14, and the observation that type assignments are preserved through natural transformations and from the proofs of the soundness of the rules for • type presupposition justification and of the soundness of the coercion transformations.

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3mn−2 + 3mn−3 + . . . 3m + 3 steps for a λ term of complexity n and where the term and each of its subterms have at most m arguments, for n > 1. For n = 1 the proceedure stops in at most 3 steps. I define the complexity of a λ term via its tree representation in which the most complex predicate is at the top with its arguments immediately below it and the arguments of those arguments below them, and so on. Thus λ free terms have complexity 0, a λ term all of whose λ bound variables are subtypes of e or prop is of complexity 1, and a λ term whose λ bound variables range over terms of complexity at most n has complexity n + 1. I prove the lemma by induction on n. For the case where our term has complexity 1 looks like this: • λx1,1 : e . . . λx1,n : eλπ1 φ1 (π ∗ α)(v1,1 ) . . . (v1,n ) In this case we must use Application to get the presuppositions to the appropriate sites next to the φ1 , . . . , φm and perhaps then use local justification. At this point the process of presupposition percolation stops in at most 3 operations. For the case where the term τ has complexity 2, the worst case is where τ has m terms each of complexity 1. Then there will be at most 3m + 3 steps to finish the presupposition percolation procedure. Now for the inductive step. Assume we have a term of complexity n + 1 with m arguments of complexity n. Again, we will need to use Application and Substitution to get the presupposition to which the term applies in the sites next to its arguments with an additional move of local justification if necessary. By the inductive hypothesis, moving the presupposition to their innermost sites will take at most 3mn−2 + 3mn−3 + . . . 3m + 3 steps for each of the m arguments +3 more, which suffices to prove the lemma. The rules for presupposition justification can then apply. Only one application of • justification suffices for any one predication. The rules of presupposition justification that appeal to functors will add additional λ bound variables to the derivation but not many; the number of new λ bound terms, since the functors must combine with λ terms τ already present in the derivation and with τ’s own arguments, cannot exceed the number of λ bound variables in τ plus a λ bound variable for τ itself and one perhaps for what τ was supposed to combine with. We can then show by a similar combinatorial argument that for each λ conversion we have to do at most Abstraction, Simple Type Accommodation, Application and Binding, plus one use of Presupposition Binding. This yields: Lemma 4 The justification proceedure adds at most n(4m + 1) steps for n predications each with a maximal number of m arguments.

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Given the ordinary properties of the typed λ calculus and the assumption that the subtyping relation is itself decidable, this suffices to show the decidability of TCL. Any λ term in TCL can be shown to have a normal form within a finite number of steps, and if a normal form cannot be obtained, this will also be shown in a finite number of steps. We can further set a bound on the length of the derivations. TCL derivations and the terms therein form a strict subset of all possible derivations in the typed λ calculus, as they are completely determined by the syntactic structure of the sentence and the types of the lexical entries. They are linear in the sense that once formulas are combined using TCL rules, they are not used further. While λ operators introduced in the lexicon may capture some variables during the composition process, apart from that there are no new bindings in the β reductions of TCL. While adjectives, determiners, reflexives may introduce some non-linear terms into a deduction, as can constructions like coordination, secondary predication, or relative clauses, these non-linear terms do not increase the number of applications or the complexity of the derivation in more than a polynomial fashion; the higher-order variables are linear and the complexity of the terms never increases when doing application with these terms, and the duplicated terms are all specified lexically to be of no higher type than e. In virtue of the results of Aehling and Schwichtenberg (2000), TCL deductions yield a complete normalization in polynomial time relative to the complexity of the λ term and the maximal number of arguments of any subterm in it. Fact 19 Suppose a λ term τ has complexity n and each subterm of τ has at most m arguments. Suppose τ is formed from a grammatical syntactic analysis of a sentence with basic typings assigned by the lexicon to each λ bound variablee in τ. Then whether τ has a complete normalization or not is computable in TCL within a time that is a polynomial function of n and m over the complexity of the basic type checking process.

11 Modification, Coercion, and Loose Talk

The previous chapters investigated coercions that have received attention in the literature—coercions by nouns on their adjectival modifiers and coercions by verbal predicates on their arguments. There are also interesting coercions, however, that result from combining two nouns in a noun–noun compound or in certain cases from combining a noun with an adjective. These have received less attention but they tell us much about coercion. For instance, adjectives that constrain the denotations of the nouns they modify to be made out of a certain kind of matter or nouns denoting material that compound with other nouns, what I’ll call material modifiers have a coercive function. These have been discussed in the literature, but there are other kinds of adjectives that are also coercers but less studied. I will give an overview of these here. My analysis of the coercive function of adjectives will lead us to study what might be in fact another form of predication—-the predication the occurs in so called “loose talk.” Loose talk is a very common phenomenon but also very puzzling; it occurs when we predicate properties of objects that they only have in some approximate or “loose” sense. What that sense is, I’ll explain presently.

11.1 Metonymic predications Recall the following examples from chapter 3. (3.18) a. Paul est bronz´e (Paul is tanned). b. Les am´ericains ont d´ebarqu´e sur la lune en 1969 (The Americans landed on the moon in 1969). c. Le pantalon est sale (The trousers are dirty). d. Le stylo est rouge (The pen is red).

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Kleiber considers these to be coercions since the predicate applies to a part of the denotation of the argument. These predications meet many of our expectations about coercions. They support copredication. (3.19) a. Paul est bronz´e et tr`es athl´etique (Paul is tanned and very athletic). b. Les am´ericains ont d´ebarqu´e sur la lune en 1969 et ont men´e une sale guerre en indochine (The Americans landed on the moon in 1969 and waged a dirty war in Indochina). c. Le pantalon est sale et trou´e (The trousers are dirty and torn). d. Le stylo est rouge et tr`es cher (The pen is red and very expensive). There are also no quantificational puzzles here, though some of these copredications like (3.19b) may involve • types. We don’t individuate the trousers any differently in the first or second clauses of (3.19c), and we don’t get any counting differences either the way we did for books. Further, no type inconsistency is here to trigger coercion. The type presuppositions of the predicates are not violated in these predications. So for TCL these modifications do not count as coercions. I offer a different analysis: the metonymic effects observed here are the result of the application of a predicate of polymorphic type to the finegrained meaning; the polymorphic type of the predicate yields a different value depending on what the type of its input argument is. Just as flat yields a quite different meaning and type when it applies to beer from when it applies to tire, so too is tanned is a polymorphic type predicate that yields a different value for humans than it does (in English) for hides. Moreover, that value can be guided by plausibility. Since it’s not very plausible that all of the Americans landed on the moon, the output of the polymorphic type to The Americans yields a content in which representatives of the Americans landed on the moon. These are modifications of meaning but the “meaning shift” that some have observed here is accounted for by the mechanism of polymorphic types given by lexical items.

11.2 Material modifiers Material adjectives like wooden and nouns like glass, stone, metal, etc. supply the material constitution of objects that satisfy the nouns these expressions combine with, as in (11.1): (11.1) glass (wooden, stone, metal, tin, steel, copper) bowl

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According to the theory of qualia in GL, the material or constitution quale, the material out of which objects that satisfy the noun are made, is specified by the lexical entry of the noun. But in (11.1) it is not bowl that specifies the material constitution, but rather the modifier. This situation is in fact very common for artifacts, as they can be made out of many different materials. Material modification is unlike the adjectival modification considered thus far in this book. Adjectival modifiers like heavy and red are subsective; a red book is a book. However, material modification can affect the typing of the head noun. (11.2) b. c. d. e.

a. stone lion (vs. actual lion) paper tiger (vs. actual tiger) paper airplane sand castle wooden nutmeg

When the constitution of the object is given by an adjective whose denotation is not a possible type of constitution for the type of object denoted by the head noun, we get a shift in the type of the head noun. This shift is important because it supports different sorts of inferences. (11.3) a. A stone lion is not a lion (a real lion), but it looks like one. b. A stone jar is a jar c. ?A paper airplane is an airplane. As lions are living animals, they cannot be made out of stone; so a stone lion is not a real lion. Stone is no longer an intersective nor even a subsective modifier. In contrast, a stone jar remains a jar, as jars can be made out of stone. In this case stone is intersective. I am not sure whether a paper airplane is an airplane. If one thinks of airplanes as having certain necessary parts like an engine or on board means of locomotion, then most paper airplanes aren’t airplanes. On the other hand, many people tell me that their intuitions go the other way. Material modification and discourse structure reveal curious interactions with world knowledge. Consider, for instance, (11.3c). It is part of world knowledge that paper airplanes don’t have engines. Nevertheless, it appears that the engine gets interpreted in the same bridging way in the two examples below. (11.4) a. John closed the door to the airplane. The engine started smoothly. b. John made a paper airplane in class. The engine started smoothly. The bridging inference in (11.4b), in which the engine is inferred to be part of the airplane, would seem to go against world knowledge; the requirement to maximize discourse coherence and to resolve underspecified conditions trumps

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world knowledge. This seems to indicate that in fact paper doesn’t behave like stone in stone lion but rather remains something closer to intersective. Paper isn’t exactly intersective, because paper airplanes are in some halfway land —in principle they could have engines, as (11.4b) demonstrates, and even transport people and goods but typically they do not. The type of airplane has shifted, but not so much as with the shift from lion to stone lion. This presents us with a puzzle. Can such predications actually change the type of the modifier from subsective to non-subsective? Or is it rather that the modification actually changes the type of the head noun? If the type of the head noun is what changes, that would explain not only the cases like stone lion and stone jar but also the puzzling in-between cases like paper airplane, or perhaps also sand castle. To answer these questions, we need to specify how a material modifier specifies the matter of the objects satisfying the common noun phrase. Here is one straightforward, “extensionalist” proposal: (11.5) λPλxλπ(P(π ∗ p)(x) ∧ ∃u (mat(u, π) ∧ made-of(u, x, π))) This gets things wrong with stone lion or sand castle, because it has as a logical consequence that a stone lion is a lion. According to the type hierarchy lion is a subtype of animate. Our rules for lexical inference should preserve subclass/superclass relations, and so we infer from the fact that something is a stone lion the fact that it is animate. Similarly, we will infer from the fact that something is a sand castle to the fact that it is a habitation, a place where one lives. Both of these inferences seem unsound. Similar examples led Kamp and Montague to conclude that adjectival modification takes place at the level of intensions. On this view, an adjective is a function from noun phrase intensions to noun phrase intensions. In the TCL framework we would have (11.6) λP: s ⇒ 1λxλπ (∨ mat(P(π ∗ e)(x))) But this logical form prevents us from making the right inferences for many other cases of material modification; e.g., we want to be able to infer from the fact that something is a stone jar that it is a jar. A better account splits the difference between these two. I will take the material modifier to have a polymorphic type, and the value of that type is assigned to the variable to which the λ abstracted property applies. I will change the logical form (11.5) only slightly, assigning the polymorphic type value to the main variable. Formally, we change the typing context of (11.5) exploiting the head type of the argument of P.

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(11.7) λP λxλπ (P(π ∗ made of(hd(MAT), hd(P)))(x) ∧∃u(mat(u) ∧ made-of(u, x))) For instance, applying the adjective paper to airplane converts the type from simply airplane to an object of the type made-of(paper, airplane). Paper airplane would thus yield the following logical form: (11.8) λxλπ (airplane(x, π ∗ made of(paper, airplane)) ∧ ∃u (paper(u) ∧ made-of(u, x, π))) Material adjectives in TCL specify the matter of the satisfiers of the noun.1 The modification of the noun type by a material modifier shifts the type of the variable, that is, the lambda abstracted argument in the common noun phrase’s logical form. Normally, the onus of presupposition accommodation is on the modifier. But not so with material modifiers. To see why we have to do some metaphysics about essential properties. The polymorphic type made of(paper, airplane) suggests that the object is essentially made of paper. Why might this be a reasonable hypothesis? Recall the discussion of Kripke’s Naming and Necessity concerning the wooden lecturn. It turns out, if he’s right and I think he is, that wooden lecturns have different essential properties and hence individuation conditions from say plastic lecturns, in the sense that a wooden lecturn is necessarily made of wood and no wooden lecturn could remain the same lecturn if it were magically transformed into some other material. Similarly, paper airplanes are necessarily made of paper, which distinguishes them from airplanes generally.2 That is, using the reflection of the type hierarchy in logical form: • x : made of(paper) → ∃y(made of(x, y) ∧ paper(y)) TCL’s type specification logic precisifies the type made-of(α, β). Suppose that we associate with types another polymorphic type mat that is related to made of. But mat returns the matter out of which objects of a type may be composed. So for a type like jar we have the following subtype formulas: • stone mat(jar) • earthenware mat(jar) 1

2

Adjectival modification changes the information that would typically to be given by the qualia associated wtih the noun meaning in GL, showing yet again the sensitivity of types to the predicational context; material constitution, determined by qualia in GL, isn’t fixed by single lexical entries but dynamically evolves within the predicational context. It’s yet another reason for dispensing with qualia and moving to TCL’s underspecified types and more dynamic notion of typing. This also corrects that conflation in GL between the modal flavors of the different qualia. Such constitutive qualia contribute to individuation conditions in a very different way from say telic and agentive qualia.

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• glass mat(jar) • metal mat(jar) • wood mat(jar) The following type constraint further narrows down the types of objects that made-of gives us. (11.9) made-of(α, β) → (α mat(β) ↔ made-of(α, β) β) We can properly predicate jar of an object if in fact its type is compatible with that of being a jar. And our constraints above show this to be true for an NP like stone jar. To be precise, for stone jar, we have the following logical form: (11.10) λxλπ (jar(x, π ∗ made-of(stone, jar)) ∧ ∃u (stone(u, π) ∧ made-of(u, x, π))) Since stone is something jars can be made out of, a stone jar is literally a jar according to (11.9). Similarly for wooden airplanes, metal airplanes, even plastic airplanes. On the other hand, stone lions can’t be real lions, because the matter out of which real lions are made can’t be stone. So (11.9) doesn’t apply, and we can’t infer that stone lions are lions. Furthermore, this implies that there is a conflict between the type assignment to the variable and the demands of the predicate. And furthermore, none of the TCL rules allows us to resolve the conflict.3 Nevertheless, from the logical form of stone lion, the predicate lion still applies to a variable which has now a type that is incompatible with being a lion, since the variable picks out an object that is made out of a material that lions can’t be made of. In this case, we understand the predication of lion to the variable typed made-of(stone, lion) “loosely.” Noun phrases like stone lion or perhaps paper airplane are examples of loose talk.

11.3 Loose talk Loose talk, metaphor, poetic license are all ways that predications that don’t literally work can be reinterpreted. I’ll take loose talk to be generated by type clashes that occur within a certain kind of discourse context to be elaborated on shortly.4 3

4

Paper airplanes are arguably not airplanes really either, because airplanes can’t be made out of paper. Paper, or at least normal paper, lacks the required strength to weight ratio needed for an airplane to fulfill its functions. But we can also see why paper airplanes constitute an intermediate case, as it’s not completely ruled out that airplanes are made of paper. In what follows I won’t give an analysis of when we are to interpret a predicate loosely. Type mismatches, I hypothesize, are necessary. But not every type mismatch can be understood as

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Let’s first consider a simple geometric case. (11.11) (Pointing to a shape that a child has drawn) You’ve drawn a circle. (11.12) I need a circular table to put in that corner. We call things circles or circular when they only approximately resemble mathematical circles. When we do this, we are speaking loosely. To interpret such sentences loosely, we make use of a set of background alternatives. The loose interpretation of such sentences is the object drawn or the table that I need has a shape that is closer to that of a mathematical circle than any of the relevant alternatives—in this case, simple geometric shapes like that of a triangle or a square. There’s probably no way to accurately describe the geometric shape drawn by Pat, and saying You’ve drawn something that resembles a circle might well not meet the pragmatic requirements of the conversation. Two notions involved in this intuitive picture require analysis, the notion of a set of alternatives and the notion of closeness. Which set of alternatives is at issue depends on the predicate that is to be interpreted loosely. In general this is a matter of the internal semantics of the predicate, not its external denotation. We look to the lowest proper supertype in the type hierarchy to find the relevant alternatives. Thus, when the predicate circular is to be interpreted loosely, then we look to the supertype of that two dimensional shape. The alternatives are given by the other types just under this supertype—-square, rectangle, triangle, and so on. The notion of closeness involved in loose talk is a “measure” of the distance between some object that is paradigmatically, by definition, or prototypically a P and the object that we are calling loosely a P. We then compare that degree of closeness and the closeness of the object in question and a paradigm of P , where P is some relevant alternative to P.5 Where does the metric necessary for a measure of closeness come from? Is the metric to be located in extensions? No. The metric depends on features associated with the predicate that make up its internal semantics. Words for geometric shapes are some of the handful that have explicit definitions; in such cases, we can look to the definition to devise a metric that might be a dis-

5

an example of loose talk. Sometimes, there is no recovery from a type mismatch, as we saw with the examples that motivate a type-driven account. It is, I suspect, a complex business to give sufficient conditions for loose talk. Intentions and a certain amount of convention are involved. In keeping with this, I have not been able to find any reliable tests for loose talk in the literature. A very interesting article that develops some of the same points I make here is Partee (2004). Partee extends the claims I make about loose talk to so-called non-subsective adjectives like fake and imaginary. I find the argument compelling. I also think that there are interesting connections between loose talk and vagueness, but I will not pursue those here. I should note that loose talk is similar to vague predications in which a notion of closeness is often thought to be involved.

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crete measure suggested by the deformation function above or perhaps a more continuous measure. In the general case, it is superficial criteria, rather than the actual extension of the predicate, that define the metric. The denotation of lion for example is determined by the criteria for belonging to the same species, which is presumably some sort of DNA code. But I can judge whether something’s a stone lion, even though I have no idea really what the species identifying criterion for lions are. The DNA code is certainly not what I use to judge whether something’s a stone lion. My criterion is a superficial one, based on looks. Consider also the following example of loose talk: (11.13) (After tasting a very weak alcoholic drink, I exclaim, pointing to it) This is water! My predication is based on a superficial feature of water—that it’s tasteless. Such superficial features flesh out the internal semantics of predicates whose core is the TCL predication rules. Competent speakers judge as to whether a loose predication holds based on features that are part of the internal semantics of a predicate. These features rely on the fine-grained types of TCL, which have played a prominent role in determining the output of polymorpohic or dependent types and coercion. Examples of such types are lion, castle, circle, and so on. Some features associated with such types are types that exploit the subtype relation; recall that the subtype relation reflects universal generalizations: if α β, then in the object language ∀x(φα (x) → φβ (x)), where, recall, φα is a λ term expression in the language of logical form corresponding to the type α. So for a type like lion, one feature will be a supertype like animal. However, the type specification logic also contains > and so we could also defeasibly specify associated types. These correspond to the truth of a generic statement in the object language. Generic statements express the right sort of properties for figuring out whether something is closer to a lion than a giraffe— for instance, male lions have manes, adult lions have big strong paws, lions have whiskers, and giraffes have long necks are all statements that provide properties relevant to determining whether something loosely speaking is a lion rather than a giraffe. With these relations TCL can encode the requisite information for defining the metric pertinent to many loose predications. As with the case of circles, there is a certain amount of perceptual information relevant to determining whether a statue is, loosely speaking, a lion or not. Thus, in order to make sense of loose talk we would need, in many cases, links between types and perceptual information that lies outside the TCL system properly speaking. For example, using the deformation function for shapes together with the notion of alternatives, we can capture the notion of closeness. This metric is defined largely with respect to perceptual information.

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(11.14) That object qua circle is closer (count the number of iterations of the deformation function) to being a protoypical circle than to a prototype of any other geometric shape. Not all perceptual information and not all generic statements involving the predicate are relevant to predications of loose talk. To return to (11.13), it’s certainly a generic and even an analytic truth that water is a subtype of mass. Nevertheless, this is not relevant to the metric needed for evaluating the loose talk in (11.13). Loose talk relies on a set of distinctive and contingent characteristics associated with the typical satisfier of the predicate. Distinctive characteristics are associated with a type. We can encode these distinctive characteristics in TCL’s type specification logic. By counting characteristic traits or constructing a metric from perceptual information as in the case of shapes, we can define the “standard” bearers or “prototypes” that are used to anchor the metrics for loose talk. • A prototype of some type α is an object x such that there is no object qua α that fits more of the associated traits of α than x does. I now give the truth conditions for loose talk. • P(x) is satisfied loosely with respect to an assignment g at a world w in a structure A iff g(x) is closer to elements of PA than g(x) is to elements of QA , where Q is some relevant alternative to P. An important difference between this approach to loose talk and other possible approaches like those of Sperber and Wilson (1986) or Carston (2002) is that the actual extension of the loosely interpreted predicate does not change. If we change the actual extension of the loosely interpreted predicate, then we render false universal statements involving the predicate that are strictly and literally true. Here is one example: (11.15) All points on a circle are equidistant from a single point. This proposition remains true on the present account. In my account of loose talk, we end up making sense of stone lions as really a loosening of the predication relation involved; stone lions are lions only in that they resemble lions with respect to shape more than other alternatives— other common animals. Similarly, stone lions aren’t strictly speaking lions, but they are closer to lions on the relevant metric (here shape) than any of the alternatives suggested by lion. We can also make sense of the intermediate cases. When we say that paper airplanes are airplanes and sand castles are castles, this is also a stretch or a loosening of the predication involving the

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predicate airplane or castle. Sand castles aren’t really castles, but they look more like castles than anything else. So material modifiers are at least “loosely speaking” subsective. My analysis of loose talk applies to other troublesome adjectival modifications as Partee (2004) suggests. The troublesome adjectives I have in mind are the well-known non-subsective adjectives like fake, ersatz, and alleged. Like material modifiers, these modifiers modify in some way the type of the head noun’s argument. In effect we have a type downdate. That is a fake lion is no longer a lion but something fake. An alleged criminal is not a criminal but someone that is alleged to be a criminal and so on. For at least some of these it seems that we can use the analysis of loose talk developed here. Fake lions aren’t lions but they are more like lions with respect to some set of contextually salient features than any other alternative. The apparatus used to characterize loose talk applies to restricted predications or standard predications involving proper names. While there is no comparison of alternatives that goes on in examples like (11.16), they also invoke features associated with the name. (11.16) a. You’re no Jack Kennedy. b. He’s an Einstein. The predicative use of names indicates that names convey descriptive information. Dan Quayle qua Jack Kennedy has certain properties typically associated with the bearer of the name Jack Kennedy. To be a Jack Kennedy, you have to have certain properties we associate with John Kennedy—charismatic, being a leader, being a force for good. Similarly, to be an Einstein you have to possess properties associated with Einstein—being really smart. The properties or traits associated with the predicative use of the name can be gleaned from such generics, but once again not all properties of generics are relevant to the predication, for example those that follow from essential properties of Einstein like the property of being human. The predicative use of a name picks out a set of distinctive characteristics that are associated with the bearer of the name. These features are encoded via types in the TCL type specification logic.

11.4 Fiction and fictional objects Fiction and fictional objects present a challenge to a theory of predication. Things that aren’t possible according to the standard typing system become possible in fiction. Is fictional predication a kind of coercion? In cases of coercion we have

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seen that the basic types of terms are not changed but a local adjustment is made—and terms are added—to resolve the type conflict in the predication. Predication involving fictional objects is different. We really need to shift the types of individuals. For instance, goats can become creatures that read and talk in fairy tales. Trees literally talk in fairy tales or fantasy novels like The Lord of the the Rings. These predications should be precluded by normal type constraints, and we know that there are no reference preserving maps (in this world) from goats to talking agents or from trees to talking agents. Thus, something different from the sort of coercion processes that we have seen in the last two chapters is at work in predications to fictional objects. What are fictional objects anyway? Outside of a Meinongian framework where there are non-existent entities, fictional objects are puzzling. Fictional objects can’t be real objects, or objects that could exist in some possible world but not the actual one. Fictional objects are not possibilia; the sister I might have had is not the same type as a sister I made up to amuse people or to make excuses the way Algernon does with his made-up friend Bunberry in Oscar Wilde’s The Importance of Being Ernest. The type of fictional objects has no inhabitants, although it is a subtype of e. Furthermore, there are many subtypes of the type of fictional objects. Fictional horses are quite different from fictional cats or fictional sisters or fictional friends. However we analyze predication of fictional objects, our account must allow that fictional objects have, in some sense, many of the qualities of real objects of the same type. Perhaps fictional contexts introduce a dependent type mapping actually realized types into unrealizable counterpart types with the proviso at the very least that the generic properties we associate with inhabitants of the actually realized types carry over to their fictional counterparts. Thus, if Sherlock Holmes is a fictional object he is also a fictional man, and he has (in fiction) at least by default the qualities generically associated with men. He has two legs, two arms, wears a coat when it’s cold outside, sleeps at night, and works during the day. In fictional predication, the objects literally have the properties ordinarily expressed by predicates—something which is not the case in metaphorical predication or loose talk. In The Lord of the Rings the trees actually speak to one another, just as you and I would to our respective conversational partners. Another important difference is that in fiction objects come to acquire the properties they do in a matter of stipulation, at least in the fiction in which they are introduced. They have the properties they do in virtue of the predication of those properties to them in the story.6 Thus, predication to fictional objects must be marked in a particular way, as the evaluation of the logical form with 6

There can be even revision of those properties, so it may be not completely clear from a text whether a fictional object has property P or not.

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those predications will proceed in a quite different way from the way logical forms of non-fictional discourse is evaluated.7 Let us look a bit more closely at the way fictional discourse updates the discourse context contrasting it with discourse update in non-fictional discourse. In a dynamic semantics, where an information context is understood as a set of world assignment pairs,8 updates for non-fictional discourse proceed in two ways. Existential quantifiers in logical form will reset or extend the assignments in the context, while other elements of the logical form will eliminate worlds from the context. Thus, an update in non-fictional discourse adds information by eliminating possibilities and by resetting assignments to variables. Obviously, we don’t want updates in fictional discourse to perform these operations on real possibilities and we don’t want existential quantifiers in the logical form of a fictional discourse to make assignments to variables of objects since we’ve said that there aren’t any fictional objects in any possible world. The problem is that fictional discourse works an awful lot like non-fictional discourse from the dynamic semantic viewpoint. We need to have devices permitting long-distance anaphoric links between fictional noun phrases and pronouns. We learn more about fictional characters as the story proceeds and this learning procedure seems very similar to the elimination of possibilities in the course of non-fictional discourse update. So what can we do? It seems sensible in these cases to suppose a set of pseudo-possibilities, possibilities for this fictional story along with assignments to fictional objects in these pseudopossibilities, and update in the standard way of dynamic semantics.9 Truth for what is said about fictional objects just concerns what is established relative to all of the pseudo-possibilities for a given fictional context. It may be the case that a fictional context may be constructed from more than one fictional work; I leave that delicate but interesting question aside here, as it far outruns our questions concerning lexical meaning. To shift to pseudo-possibilities and these fictional objects that aren’t possibilia, we need a type shift that percolates “all the way up” to the top of the discourse. Thus I will postulate an “arrow” from any type to its fictional counterpart. This type shift changes all the denotations to pseudo-denotations in pseudo possibilities. Interestingly, this type shift leaves the associated generics unchanged—and thus the fine-grained conceptual content of fictional types remains similar to the non-fictional parts. Fictional discourse is an example of 7 8 9

Here we must be careful to distinguish fictional discourse from discourse about fiction! Pace complications about modals, and propositional attitudes. This seems to be the formal counterpart to the popular ”pretense” theory of fictional objects.

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“global coercion” and is enforced by a dependent type that comes from the initial discourse context and spans all the predications in the entire text.

11.5 Metaphorical predication Metaphorical predication is another form of predication that has been analyzed in terms of coercion; like coercions metaphorical predications involve a failure of type presupposition. Like loose predication, metaphorical predication doesn’t imply that the property or relation involved applies to its terms literally. There are some similarities between metaphor and loose talk as I defined it above. Consider Shakespeare’s almost too familiar metaphor: (11.17) Juliet is the sun. One can analyze that in the manner of loose predication: Juliet is more like the sun than anything else in the comparison class of heavenly bodies. The predicate gives the alternatives to the predication just as we saw with loose talk. Black (1962) proposed a theory vaguely along such lines, and more recently Asher and Lascarides (1999) proposed an analysis of metaphorical predication in which they tried to put some more meat on the notion of closest fit. They looked in particular at metaphorical interpretations of change of location verbs. They argued that in effect each type has a definition in terms of genus and differentiae. For change of location verbs like enter, the genus is the type change-of-location-verb, which is a subtype of change-of-state-verb. The differentiae that distinguish come from go, another change of location verb, concern the verbs’ pre- and post-conditions (the precondition gives the starting point of the motion, while post-conditions include at least the end point of the motion and may specify something about the trajectory from the starting point as well Asher and Sablayrolles (1995)). Thus, for a somewhat leaden metaphorical predication like (11.18) Nicholas went into a blue funk. Asher and Lascarides would claim that the differentiae of go persist—namely, that Nicholas was not in a blue funk prior to the metaphorical change of motion, but was in one after the change. What changes is that the genus is in fact reinterpreted replacing the type location with some sort of qualitative space pertaining to emotions. The problem with this view is that it does not do well with many metaphors, especially creative and powerful ones. The sun’s differentiae with respect to

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other heavenly bodies in Shakespeare’s language isn’t known to modern readers who still find the metaphor powerful, and modern differentiae distinguishing the sun from other stars and planets do not seem to give the metaphor its content. More importantly, this puts a heavy burden on lexical semantics in that it requires Aristotelian definitions for particular types with respect to other elements in their class. One might rightly be skeptical that many lexical items have definitions in the requisite sense. We have to go to a higher level of generality. More recent theories of metaphor speak of the predicate as giving a frame for the interpretation of the subject of the predication. Gentner and Markman (2006) and Bowdle and Gentner (2006) analyze metaphor by postulating the existence of a map from the subject term and its associated properties to the predicate and its associated properties to define metaphorical interpretation. This notion is much more general than what Asher and Lascarides proposed, because these associated properties need not be part of a definition of the term or a predicate. The problem is that it is unclear what these associated properties are, how metaphorical predication gives rise to such a mapping, or indeed how this mapping interacts with the linguistic system and what it does to linguistic interpretation. Furthermore, without a well-defined idea of associations, this idea is rather empty. An alternative suggests itself from the machinery of TCL that is general yet precise. Metaphors involve a failure of type presuppositions and a peculiar form of type accommodation. Suppose that we have a predication of t to t , t requires of the relevant argument that it meet type α, but t : β and α β = ⊥. Metaphorical predication forces us to consider t as an object of complex type in which both types are combined but where one has a certain metaphysical priority. To say of Juliet that she is the sun does not convert her into having an aspect that is literally a heavenly body massing more than a thousand Earths so as to support thermonuclear fusion at her core. But the metaphor tells us that she has an aspect in which she is very much like the sun. The suggestion is that metaphorical predications type the subject of the predication having a • type in which one constituent type has metaphysical priority. I’ll write such types with subscript types on the •; e.g., α •α β denotes a • type in which α has metaphysical priority. What does it mean to have metaphysical priority? For one thing, it means this: • α •α β α Thus, Juliet under the type woman •human sun remains a woman, a human being despite being assigned an aspect in which she shares some qualities of the sun.

314

Modification, Coercion, and Loose Talk

The aspect in which Juliet is the sun is the one that now requires interpretation. We can appeal to the fine-grained contents associated with types conveyed by true generics involving inhabitants of that type and to predications to objects of that type in prior discourse. To say that Juliet has an aspect in which she is the sun is to say that many of these predications apply mutatis mutandis to her. She has an aspect in which, speaking loosely, she is the sun. These predications have to be filtered or reinterpreted in order not to clash with the fact that Juliet is a human being. This interpretation process may not be rule bound and it may depend on different ways of using structural analogies on the associated conceptual information, something which Gentner was after. The TCL system by itself, however, does not have much to say about these notions. Indeed, they may lie outside the linguistic system altogether. Interestingly though, this sketch of an analysis of metaphorical predication gives us a way of understanding how the non-linguistic conceptual repertoire might eventually end up affecting lexical content (frozen metaphors) through the incorporation of this information into the type system. Viewing metaphorical predication as introducing aspects of the predicatae of the predicates has an interesting consequence. Complex types where one constitutent type has metaphysical priority, • types of the form α •α β, are not in general commutative. This predicts that metaphors should be asymmetric, which they are.10 For instance, these two metaphorical predications have vastly different meanings: (11.19) a. My surgeon is a butcher. b. My butcher is a surgeon.

10

Thanks to Tony Veale for this point and for the suggestion that metaphor might be modelled using some sort of complex type.

12 Generalizations and Conclusions

The TCL system, designed to deal with type presupposition justification, especially of the complex sorts found in coercion and aspect selection, has many other applications. It can analyze fine-grained shifts in meaning using finegrained types. It offers a novel perspective on adverbial modification. In dealing with resultatives and nominalizations, the system provides a natural treatment of optional arguments. We have also seen how it yields a new way of thinking about metaphor and about loose talk. It remains to be seen whether it can be used to say anything interesting about vague predication. At present I do not see anything special emerging from the TCL formalism.

12.1 Integrating ordinary presuppositions Throughout this book I have spoken of type presuppositions. And I’ve argued that the formulas introduced by presupposition justification are part of presupposed content. But what about content level presuppositions? Do they fit into the TCL approach? Many presuppositions come from particular lexical elements, the so-called “presupposition triggers.” Many lexical items are presupposition triggers. Most change of state verbs, like like buy, sell, loan, borrow, heal, etc. have lexical presuppositions, which are the preconditions that have to obtain before the actions or transitions they denote can take place. Their preconditions, e.g., of ownership or physical possession, obey all the classical tests for presuppositions; they take wide scope over various operators like negation or the operator associated with a question. Such change of state verbs also have post-conditions, the conditions that obtain after the event denoted by the verb has taken place. Post-conditions correspond to proffered content, while preconditions are another encoding of the linguistic notion of presup-

316

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position. All change of state verbs have pre- and post-conditions and hence generate presuppositions. There’s a question as to how a lexical system ought to represent such presuppositions. We have two choices: we can put this information into the lexical entry’s contribution to the logical form of the clause in which it occurs as is traditionally the case and is carried out in the work of Kamp and Rossdeutscher Kamp and Rossdeutscher (1994b,a) in their detailed work on the German verb heilen (to heal). Alternatively, we can stick such information in the type system. TCL already adds a presupposition parameter to all lexical entries and such a parameter can carry presuppositions that are ordinarily understood at the level of logical form. While the first option is pretty well understood, it leads to vast redundancy. Verbs like buy, acquire, and purchase have the same ownership pre- and postconditions, while buy, acquire, purchase, and steal have the same physical possession pre- and post-conditions. If the presuppositions or preconditions and post-conditions are entered for each lexical entry we miss important generalizations about the presuppositions as well as the post conditions of verb classes. This would suggest that such pre- and post-conditions are to be attached somehow to a general type like change of state verb and then inherited by the various subtypes.1 A second problem that TCL can potentially shed light on is the projection of propositions. Following van der Sandt (1992), most linguists working on presupposition have assumed a separate percolation proceedure for presuppositions as part of presupposition justification. The TCL predication mechanisms predict that presuppositions that are generated lexically are automatically carried up the derivation tree until they are justified (via binding) and then at top level they would be accommodated unless this is blocked by the usual constraints on accommodation. To specify the type change of state verb, for instance, and of presuppositions more generally, I place all “standard” presuppositions as type requirements on the proposition that is determined by the root verbal complex, which I’ll call here p. Given our idea of satisfaction, the type presupposition on the proposition p will be satisfied whenever the propositional content of p together with the discourse context entails the type presupposition, or more precisely, the formula associated with that type. Accommodation of this presupposition will occur when binding is not possible but the content of p is consistent with the type presupposition. To take a very simple example, let’s look at the presuppositions of a pronoun like he, which is that there must be in the context some person who is male that 1

Levin (1993) suggests such an approach.

12.1 Integrating ordinary presuppositions

317

is the binder of the variable introduced by pronoun, call that xi . Using dependent types we can specify the presupposition on the propositional argument, which I’ll label p, as male(binder(ty+ (xi ))). Thus, in (12.1) (12.1) A father kissed his daughter the presupposition generated by the object DP on the propositional variable is satisfied by the subject DP once that is integrated into logical form. Presuppositions involving types like binder involve a similar sort of “spell out” at the level of logical form that our polymorphic and dependent types used to model coercion or those of aspect selection. For presuppositions of anaphoric pronouns, the justification condition will involve an explicit binding of the variable introduced by the definite with the variable introduced by the antecedent. Presuppositions provided by definite determiners are similar.2 Now what about transclausal presupposition justification? Let’s consider a conditional: (12.2) a. If John doesn’t own a car, he’ll buy one. b. If John buys a car, he’ll be happy. The type presupposition of buy on the propositional argument that is in the consequent of (12.2) is that he does not own a car (assuming that the anaphora in one has been resolved). More generally, an acquisition verb V has the following presupposition on the propositional variable. V (12.3) ¬own(hd(argV 1 ), hd(arg2 ))

This presupposition on the propositional content is unresolved in the consequent. What we need is a mechanism that allows this presupposition to travel up the relevant contexts until it is satisfied or accommodated. Adopting a continuation style semantics of the sort provided by de Groote (2006) and Pogodalla (2008) can provide such a mechanism. Assuming such a mechanism is in place, the type presupposition automatically goes up to the antecedent of the conditional (which takes the presuppositional context of the consequent as its input). It is, however, satisfied there; and as we are dealing with clausal presuppositions, there is nothing more to do. By contrast buy in the antecedent of (12.2b) isn’t satisfied by the local propositional content, so that presupposition 2

Following Heim (1982, 1983), people have taken definite noun phrases and perhaps more generally referential expressions to give rise to presuppositions of familiarity. Using the discourse framework of SDRT and the analysis of presuppositions provided by Asher and Lascarides (1998b), Hunter and Asher (2005) show how to give the outlines of a general presuppositional account of referential expressions—at least including indexicals, definite descriptions, and proper names.

318

Generalizations and Conclusions

is passed on up to the higher context. It will be accommodated and expressed in logical form, if the context does not have the content to bind it. Presuppositions can sometimes induce coercion. Consider the following case involving acquisition verbs.3 Real-estate agents, used car salesmen, and stockbrokers will say (12.4) I sold three houses/ten cars/1 million shares this week. even though they did not in fact own in either a physical or legal or any other sense the objects that they sold. In fact what happened is that these agents do something that results in someone else’s change of ownership of whatever the theme of sell is. These contexts make salient a map from agents to a collection of people or companies they represent, which allows us to reinterpret the verb in the appropriate way. As usual, I suppose a particular dependent type representative from agents to agents or groups of agents. The context will license a coercion licensing the substitution in (12.3) of representative(agent) for agent. An application of δC will then make the appropriate change at the level of logical form. If for some reason the context cannot accommodate this information, then accommodation will have to be done locally, for at some point the presuppositions on p have to be spelled out.4

12.2 Conclusions: a sea of arrows The TCL framework presented in this book provides a general framework for predication and for lexical meaning. The basic idea is that word meanings are relatively simple, but predication can be quite complicated, because it involves operations of type presupposition justification. I have surveyed a number of constructions which make the story of predication complicated: predication involving dual aspect nouns, restricted predication, and various cases of coercion. To handle these phenomena I extended the standard typed lambda calculus with a new, complex type, • types, and with polymorphic types as well. All of these phenomena have a common thread: a conflict between the typing demands of a predicate and its argument in a predication lead to a justification of type requirements and subsequent adjustments in logical form. I modeled these type justifications and their accompanying adjustments in logical form using the framework of category theory. Maps from one type to another also figure in the analysis of coercion. The type justifications essential to coercion involve maps from one type of entity 3 4

Thanks to Julie Hunter for this point. This last is an additional stipulation to the general TCL treatment of presuppositions.

12.2 Conclusions: a sea of arrows

319

to another. For every multiple aspect noun of • type, there exists a map from the inhabitants of the • type to inhabitants of one of the constituent types. I argued that most nouns are dual aspect nouns in that they have an individual aspect and a “kind” aspect. I also surveyed other nouns with specific aspects: nouns that involve both an informational and a physical object aspect, nouns that involve an informational and an eventuality aspect, nouns that involve, for example, a location and a physical object aspect, nouns that involve a location, a physical object, and an institutional aspect like banks or cities. These maps are encoded with dependent types. The most studied and familiar of these is our type  that encodes a map from objects into processes involving them. This seems to reflect a basic metaphysical premise that objects are conceptualized in part by the processes they undergo or can undergo. There are many types of processes that objects can be mapped to—noise making events, events with result states, events that result in the coming to be of an object (a particular kind of result state), events that involve the use of the object (another particular kind of event with a result state). The qualia of GL pick out a small subset of the events that are involved in coercion. Coercions featured other maps as well. For instance evaluative adjectives made use of a map from types of objects to types of dispositions, which I analyzed in terms of a generic quantification over events. I postulated a polymorphic type that maps objects to dispositions involving them to analyze predication involving evaluative adjectives. Another important polymorphic type involved in grinding and in material adjectives is the map from objects to their matter. I also postulated maps from plural entities to their collective and distributive readings. with a pair of maps from groups (acting collectively) to sets (of the members of the group) and from sets to groups. Other polymorphic types represent the map from objects to representations of them or the map from objects to the associated traits of that object (used to handle material modification and loose talk). I also made use of maps from abstract entities to more concrete ones. Following the analysis of Asher (1993) of facts, there is a map from atomic and conjunctive facts to eventualities. By their nature, such facts are guaranteed to have a physical instantation. Thus, one can expect a map from facts to eventualities, at least for atomic facts. For negative facts, the situation is not so clear. Negative facts like the fact that no one coughed during the concert do not map onto any clear eventuality; they assert the lack of certain eventualities. There is, however, a map from a fact, even a negative one, into the times at which the fact holds. A final dependent type is involved in nominalization. Nominalization takes anything of some type and converts it into something of type e. Nominalization involves the polymorphic type ν : α → e. There must be some

320

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restriction on the size of the set of inhabitants of types in order for ν not to lead to paradoxes and some bounds on the number of subtypes in e. Nevertheless, there are no coercions for some things. For instance, there is no general map from a saturated abstract entity to a physical object. One could imagine the existence of such a map (many nominalists and physicalists try to specify such a map), but the map isn’t well defined in our common sense metaphysics. A coercion exists in a given typing context, if it can be established that a corresponding, well-defined map at the level of denotations exists, given the information in that context. It is the presence of such a map that makes the coercion sound. Coercions like those noticed by Nunberg, between drivers and their cars or between books and their authors or between individuals and the dishes they have ordered, may be felicitous only in certain contexts. These are more fragile and contextually determined than other coercion processes. It is, finally, a matter of considerable subltety and philosophical reflection as to when coercions are sound in a given context—i.e., when we can demonstrate the existence of a suitable map between objects of one type and objects of another. There is in any case a rich set of maps underlying lexical meaning. And this set of maps evolves and changes as discourse proceeds. It is this sea of maps and how it changes that constitutes the web of words, truly a marvelous creation of human kind.

PART FOUR CODA

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Index

• type, 137 • types, 86, 140 λ calculus, 3 B functor, 168 F functor, 168 abstraction, 115 accidental polysemy, 63 analytical entailment, 52 application, 115 aspect selection, 11, 130 Binding Presuppositions, 116 cartesian closed category, 123 categorial semantics, 121, 123, 125, 219 category theory, 122, 123 Church, A., 4 Closed Cartesian Category, 122 coercion, 14, 214 coercions with want, 253 concepts, 37 containable, 30 container, 30 copredication, 11 count, 29 De Groote, P., 106 dependent type, 42 depictive constructions, 213 disjunctive object, 102 disjunctive type, 102 dot objects, 72 dual aspect nouns, 23, 92, 131 dynamic semantics, 98 EC, 225 event nominal, 287 event semantics, 263 external semantics, 44 externalism, 39 fictional entities, 35 first-order property, 105

Fodor, J., 15, 60, 253 Fodor, Jerry, 54 Generative Lexicon, The, 71, 74, 78, 133 genitive construction, the, 84 Harley, H., 253 internal semantics, 44 Jaeger, G., 192, 195 kinds, 30 Kleiber, G., 69, 247 lambda calculus, 3 Lepore, E., 15, 60, 253 Levin, B., 33 lexical inference, 52 local justification, 185, 187, 223 logical polysemy, 63 loose talk, 306 Martin-L¨of, 45 mass, 29 material adjectives, 301 material modification, 302 monomorphic languages, 61 Montague Grammar, 25 natural transformation, 152, 219 nominalization, 284 Nunberg, Geoffrey, 64, 133 Object Elaboration, 150 persistence of predication, 198 plurality, 31 polymorphic languages, 61 polymorphic type, 42, 220, 225 predication, 10 presupposition, 7, 99, 316 product, 122 property nominalization, 291 pull back, 124 Pustejovsky, J., 71, 73, 86 qualia, 74, 78, 273

332

Index

qualia structures, 72 quantificational puzzle, 139, 145, 173, 175, 181, 216 Recanati, F., 92, 245 restricted deduction, 126 restricted predication, 191 result nominal, 287 resultative, 13 Russell property, 293 Segmented Discourse Representation Theory, 236 self-application, 293 self-predication, 293 semantically anomalous, 5 sense enumeration model, 62 sense transfer model, 64 Simple Type Accommodation, 117 simple types, 103 sortal theory, 47 Sperber, D., 92 Stanley, J., 87 State Consistency Principle, 198 substitution, 116 subtyping, 35, 104, 126 Szabo, Z., 87, 192, 195 TCL, 114 thoughts, 40 topos, 124 two-level semantics, 44 type checking, 49 Type Composition Logic, 97, 107 type presuppositions, 8, 107, 109, 116, 313, 316 type specification logic, 227 Type Theory, 45 type underspecification, 220 typed feature structures, 72, 78 typed lambda calculus, 6 types in language, 27 underspecification, 61 underspecified type, 226 universality, 198 verbal alternations, 33 verbal modification, 262 wide scope reading, 111 Wilson, D., 92 words, x, 101 zeugmatic, 64