VOLUME 26 NUMBER 3 AUGUST 2009
CONTENTS
217
EMAR MAIER Proper Names and Indexicals Trigger Rigid Presuppositions
253
YINGYING WANG Counterfactual Donkey Sentences: A Response to Robert van Rooij
317
FORTHCOMING ARTICLES ALEX LASCARIDES AND MATTHEW STONE: A Formal Semantic Analysis of Gesture CHRISTOPHER DAVIS: Decisions, Dynamics and the Japanese Particle yo NINA GIERASIMCZUK AND JAKUB SZYMANIK: Branching Quantification v. Two-way Quantification
VOLUME 26 NUMBER 3 AUGUST 2009
ALAN C. BALE AND DAVID BARNER The Interpretation of Functional Heads: Using Comparatives to Explore the Mass/Count Distinction
JOURNAL OF SEMANTICS
JOURNAL OF SEMANTICS
VOLUME 26 NUMBER 3 AUGUST 2009
Journal of
SEMANTICS www.jos.oxfordjournals.org
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JOURNAL OF SEMANTICS A N I NTERNATIONAL J OURNAL FOR THE I NTERDISCIPLINARY S TUDY THE S EMANTICS OF N ATURAL L ANGUAGE
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BARBARA PARTEE (University of Massachusetts, Amherst) FRANÇOIS RECANATI (Institut Jean-Nicod, Paris) ROGER SCHWARZSCHILD (Rutgers University) ARNIM VON STECHOW (University of Tübingen) THOMAS EDE ZIMMERMANN (University of Frankfurt)
EDITORIAL BOARD: MARIA ALONI (University of Amsterdam) PRANAV ANAND (University of California, Santa Cruz) NICHOLAS ASHER (IRIT, Toulouse; University of Texas, Austin) CHRIS BARKER (New York University) SIGRID BECK (University of Tübingen) DAVID BEAVER (University of Texas, Austin) RAJESH BHATT (University of Massachusetts, Amherst) MARIA BITTNER (Rutgers University) PETER BOSCH (University of Osnabrück) RICHARD BREHENY (University College London) DANIEL BÜRING (University of California, Los Angeles) EMMANUEL CHEMLA (Institut Jean-Nicod, Paris; LSCP, Paris) JILL G. DE VILLIERS (Smith College) PAUL DEKKER (University of Amsterdam) JOSH DEVER (University of Texas, Austin) REGINE ECKARDT (University of Göttingen) MARTINA FALLER (University of Manchester) DELIA FARA (Princeton University) LYN FRAZIER (University of Massachusetts, Amherst) JEROEN GROENENDIJK (University of Amsterdam) ELENA GUERZONI (University of Southern California) MARTIN HACKL (Pomona College) PAULINE JACOBSON (Brown University) ANDREW KEHLER (University of California, San Diego) CHRIS KENNEDY (University of Chicago) JEFFREY C. KING (Rutgers University) ANGELIKA KRATZER (University of Massachusetts, Amherst)
PETER LASERSOHN (University of Illinois) JEFFREY LIDZ (University of Maryland) JOHN MACFARLANE (University of California, Berkeley) LISA MATTHEWSON (University of British Columbia) JULIEN MUSOLINO (Rutgers University) IRA NOVECK (L2C2, CNRS, Lyon) FRANCIS JEFFRY PELLETIER (University of Alberta) COLIN PHILLIPS (University of Maryland) PAUL M. PIETROSKI (University of Maryland) CHRISTOPHER POTTS (Stanford University) LIINA PYLKKÄNEN (New York University) GILLIAN C. RAMCHAND (University of Tromsoe) MARIBEL ROMERO (University of Konstanz) MATS ROOTH (Cornell University) ULI SAUERLAND (ZAS, Berlin) BARRY SCHEIN (University of Southern California) BERNHARD SCHWARZ (McGill University) BENJAMIN SPECTOR (Institut Jean-Nicod, Paris) ROBERT STALNAKER (Massachusetts Institute of Technology) JASON STANLEY (Rutgers University) MARK STEEDMAN (University of Edinburgh) MICHAEL K.TANENHAUS (University of Rochester) JOS VAN BERKUM (Max Planck Institute for Psycholinguistics, Nijmegen) ROB VAN DER SANDT (University of Nijmegen) YOAD WINTER (Utrecht University) HENK ZEEVAT (University of Amsterdam)
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Editorial Policy Scope Journal of Semantics aims to be the premier generalist journal in semantics. It covers all areas in the study of meaning, and particularly welcomes submissions using the best available methodologies in semantics, pragmatics, the syntax/semantics interface, cross-linguistic semantics, experimental studies of meaning (processing, acquisition, neurolinguistics), and semantically informed philosophy of language. Types of articles Journal of Semantics welcomes all types of research articles–with the usual proviso that length must be justified by scientific value. Besides standard articles, the Journal will welcome ‘squibs’, i.e. very short empirical or theoretical contributions that make a pointed argument. In exceptional circumstances, and upon the advice of the head of the Advisory Board, the Journal will publish ‘featured articles’, i.e. pieces that we take to make extraordinary contributions to the field. Editorial decisions within 10 weeks The Journal aims to make editorial decisions within 10 weeks of submission. Refereeing Articles can only be accepted upon the advice of anonymous referees, who are asked to uphold strict scientific standards.Authors may include their names on their manuscripts, but they need not do so. (To avoid conflicts of interest, any manuscript submitted by one of the Editors will be handled by the head of the Advisory Board, who will be responsible for selecting referees and making an editorial decision.) Submissions All submissions are handled electronically. Manuscripts should be emailed in PDF format to the Managing Editor [
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JOURNAL OF SEMANTICS A N I NTERNATIONAL J OURNAL FOR THE I NTERDISCIPLINARY S TUDY THE S EMANTICS OF N ATURAL L ANGUAGE
MANAGING EDITOR: ASSOCIATE EDITORS:
OF
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BARBARA PARTEE (University of Massachusetts, Amherst) FRANÇOIS RECANATI (Institut Jean-Nicod, Paris) ROGER SCHWARZSCHILD (Rutgers University) ARNIM VON STECHOW (University of Tübingen) THOMAS EDE ZIMMERMANN (University of Frankfurt)
EDITORIAL BOARD: MARIA ALONI (University of Amsterdam) PRANAV ANAND (University of California, Santa Cruz) NICHOLAS ASHER (IRIT, Toulouse; University of Texas, Austin) CHRIS BARKER (New York University) SIGRID BECK (University of Tübingen) DAVID BEAVER (University of Texas, Austin) RAJESH BHATT (University of Massachusetts, Amherst) MARIA BITTNER (Rutgers University) PETER BOSCH (University of Osnabrück) RICHARD BREHENY (University College London) DANIEL BÜRING (University of California, Los Angeles) EMMANUEL CHEMLA (Institut Jean-Nicod, Paris; LSCP, Paris) JILL G. DE VILLIERS (Smith College) PAUL DEKKER (University of Amsterdam) JOSH DEVER (University of Texas, Austin) REGINE ECKARDT (University of Göttingen) MARTINA FALLER (University of Manchester) DELIA FARA (Princeton University) LYN FRAZIER (University of Massachusetts, Amherst) JEROEN GROENENDIJK (University of Amsterdam) ELENA GUERZONI (University of Southern California) MARTIN HACKL (Pomona College) PAULINE JACOBSON (Brown University) ANDREW KEHLER (University of California, San Diego) CHRIS KENNEDY (University of Chicago) JEFFREY C. KING (Rutgers University) ANGELIKA KRATZER (University of Massachusetts, Amherst)
PETER LASERSOHN (University of Illinois) JEFFREY LIDZ (University of Maryland) JOHN MACFARLANE (University of California, Berkeley) LISA MATTHEWSON (University of British Columbia) JULIEN MUSOLINO (Rutgers University) IRA NOVECK (L2C2, CNRS, Lyon) FRANCIS JEFFRY PELLETIER (University of Alberta) COLIN PHILLIPS (University of Maryland) PAUL M. PIETROSKI (University of Maryland) CHRISTOPHER POTTS (Stanford University) LIINA PYLKKÄNEN (New York University) GILLIAN C. RAMCHAND (University of Tromsoe) MARIBEL ROMERO (University of Konstanz) MATS ROOTH (Cornell University) ULI SAUERLAND (ZAS, Berlin) BARRY SCHEIN (University of Southern California) BERNHARD SCHWARZ (McGill University) BENJAMIN SPECTOR (Institut Jean-Nicod, Paris) ROBERT STALNAKER (Massachusetts Institute of Technology) JASON STANLEY (Rutgers University) MARK STEEDMAN (University of Edinburgh) MICHAEL K.TANENHAUS (University of Rochester) JOS VAN BERKUM (Max Planck Institute for Psycholinguistics, Nijmegen) ROB VAN DER SANDT (University of Nijmegen) YOAD WINTER (Utrecht University) HENK ZEEVAT (University of Amsterdam)
EDITORIAL CONTACT:
[email protected] © Oxford University Press 2009 For subscription information please see back of journal.
Editorial Policy Scope Journal of Semantics aims to be the premier generalist journal in semantics. It covers all areas in the study of meaning, and particularly welcomes submissions using the best available methodologies in semantics, pragmatics, the syntax/semantics interface, cross-linguistic semantics, experimental studies of meaning (processing, acquisition, neurolinguistics), and semantically informed philosophy of language. Types of articles Journal of Semantics welcomes all types of research articles–with the usual proviso that length must be justified by scientific value. Besides standard articles, the Journal will welcome ‘squibs’, i.e. very short empirical or theoretical contributions that make a pointed argument. In exceptional circumstances, and upon the advice of the head of the Advisory Board, the Journal will publish ‘featured articles’, i.e. pieces that we take to make extraordinary contributions to the field. Editorial decisions within 10 weeks The Journal aims to make editorial decisions within 10 weeks of submission. Refereeing Articles can only be accepted upon the advice of anonymous referees, who are asked to uphold strict scientific standards.Authors may include their names on their manuscripts, but they need not do so. (To avoid conflicts of interest, any manuscript submitted by one of the Editors will be handled by the head of the Advisory Board, who will be responsible for selecting referees and making an editorial decision.) Submissions All submissions are handled electronically. Manuscripts should be emailed in PDF format to the Managing Editor [
[email protected]], who will forward them to one of the Editors.The latter will be responsible for selecting referees and making an editorial decision. Receipt of a submission is systematically confirmed. Papers are accepted for review only on the condition that they have neither as a whole nor in part been published elsewhere, are elsewhere under review or have been accepted for publication. In case of any doubt authors must notify the Managing Editor of the relevant circumstances at the time of submission. It is understood that authors accept the copyright conditions stated in the journal if the paper is accepted for publication.
All rights reserved; no part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without prior written permission of the Publishers, or a licence permitting restricted copying issued in the UK by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1P 9HE, or in the USA by the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923. Typeset by TnQ Books and Journals Pvt. Ltd., Chennai, India. Printed by Bell and Bain Ltd, Glasgow, UK
JOURNAL OF SEMANTICS Volume 26 Number 3
CONTENTS ALAN C. BALE AND DAVID BARNER The Interpretation of Functional Heads: Using Comparatives to Explore the Mass/Count Distinction
217
EMAR MAIER Proper Names and Indexicals Trigger Rigid Presuppositions
253
YINGYING WANG Counterfactual Donkey Sentences: A Response to Robert van Rooij
317
Please visit the journal’s web site at www.jos.oxfordjournals.org
Journal of Semantics 26: 217–252 doi:10.1093/jos/ffp003 Advance Access publication April 1, 2009
The Interpretation of Functional Heads: Using Comparatives to Explore the Mass/Count Distinction ALAN C. BALE Concordia University
Abstract Comparative judgments for mass and count nouns yield two generalizations. First, all words that can be used in both mass and count syntax (e.g. rock, string, apple, water) always denote individuals when used in count syntax but never when used in mass syntax (e.g. too many rocks v. too much rock). Second, some mass nouns denote individuals (e.g. furniture) while others do not (e.g. water). In this article, we show that no current theory of mass–count semantics can capture these two facts and argue for an alternative theory that can. We propose that lexical roots are not specified as mass or count. Rather, a root becomes a mass noun or count noun by combining with a functional head. Some roots have denotations with individuals while others do not. The count head is interpreted as a function that maps denotations without individuals to those with individuals. The mass head is interpreted as an identity function making the interpretation of a mass noun equivalent to the interpretation of the root. As a result, all count nouns have individuals in their denotation, whereas mass counterparts of count nouns do not. Also, some roots that have individuals in their denotations can be used as mass nouns to denote individuals.
1 INTRODUCTION In this paper we seek to answer two questions. First, do functional heads that determine phrasal categories have a semantic interpretation? Specifically, in theories where lexical items are underspecified for syntactic categories such as mass and count, do nominal functional heads have an interpretation that is separate from lexical items? Second, what is the semantic nature of the mass–count distinction and what mechanisms are needed to explain this distinction? To answer these questions, we propose that there are two types of functional heads in noun phrases: one mass and the other count. These functional heads The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email:
[email protected].
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DAVID BARNER University of California, San Diego
218 Interpretation of Functional Heads
(1) a. Seymour Seymour b. Seymour Seymour
has has has has
more more more more
strings than Esme. rocks than Esme. string than Esme. rock than Esme.
The sentences in (1a) are evaluated in terms of number whereas those in (1b) are evaluated in terms of length, weight or volume. Our interpretation of the count functional head as a function from sets of aggregates/groups without individuals to sets with individuals guarantees two things. First, all count nouns denote individuals (i.e. are associated with denotations that have individuals as minimal parts; see Section 5.2.1 for details). Second, no lexical items or roots that can be used in count noun phrases denote individuals. Hence, when such lexical items are used as mass nouns, the mass noun phrases also do not denote individuals. These two consequences of the interpretation of the count-noun head explain the generalization mentioned above. The second generalization is that there are at least two types of mass nouns: those that allow for a comparison by number (such as furniture) and those that do not (such as water). This is demonstrated in (2). (2) a. Seymour has more furniture than Esme. b. Seymour has more water than Esme. In (2a), truth conditions rely on a comparison by number (number of pieces of furniture) whereas in (2b) truth conditions rely on a comparison by weight or volume. In comparative constructions, mass nouns like furniture behave exactly like count nouns. Below, our treatment of the mass functional head as an identity function allows for these two classes to exist. As long as the lexical items can be interpreted as sets of aggregates with individuals or without, so too can mass nouns.
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have interpretations that are independent of the lexical items with which they combine: both are interpreted as functions from sets of aggregates/groups to sets of aggregates/groups. The mass noun head is interpreted as the identity function, simply passing up the interpretation of the lexical root to the entire noun phrase. In contrast, the count noun head is a function from sets of aggregates that do not have individuals as minimal parts to sets of aggregates that do. The semantic nature of these functional heads accounts for two generalizations. The first generalization is that no mass nouns that have an associated count-noun usage ever allow for a comparison by number. This is best demonstrated by flexible nouns such as string and rock. There are clear differences in how we evaluate sentences such as those in (1a) compared to those in (1b).
Alan C. Bale and David Barner 219
2 THEORIES OF MASS–COUNT SEMANTICS In most discussions of the mass–count distinction, it is recognized that the use of a term in count syntax entails that at least part of its referent be discrete and/or bounded, and subject to being counted (Link 1983, 1998; Bunt 1979, 1985; Gordon 1985; Jackendoff 1991; Bloom 1999; Gillon 1999). The analysis of mass nouns, in contrast, has been the subject of much controversy. One of the most widely accepted proposals is that while count nouns always denote individuals, mass nouns never do (Quine 1960; Link 1983, 1998; Gordon 1985; Macnamara 1986; Bloom 1994, 1999; Wisniewski et al. 1996). For example, the theories of Link (1983, 1998) propose join semi-lattices with minimal parts as the denotation of count nouns, and semi-lattices without minimal parts as the denotation of all mass nouns. As a result, mass nouns, unlike count nouns, do not denote individuals. According to psychologists, such as Wisniewski et al. (1996: 271), this difference means that speakers ‘conceptualize the referents of count nouns as distinct, countable, individuated things and those of mass nouns as nondistinct, uncountable, unindividuated things’. As an alternative to this view of mass–count semantics, Gillon (1992, 1999) and Bunt (1985) argue that although count nouns denote individuals, mass nouns can be used to denote either individuals or nonindividuals. Whether or not a particular mass noun can be used to denote individuals is not specified linguistically, but rather is determined via the speaker’s inspection of the world. Thus, in the case of mass nouns like space, the speaker may encounter no units susceptible to enumeration and conclude that the term denotes continuous stuff (i.e. not individuals). In contrast, an inspection of the world may reveal that furniture is being used to talk about discrete-bounded physical objects,
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The outline of this paper is as follows. In Section 2, we briefly summarize current approaches to the semantic characterization of mass nouns and count nouns. In Section 3, we discuss different possible tests for evaluating the semantics of mass and count nouns, and argue that comparative constructions provide the most reliable test. In Section 4, we establish our two semantic generalizations with respect to mass and count nouns in greater detail. In Section 5, we present our proposal to account for these semantic generalizations, a proposal that crucially relies on providing an interpretation for nominal functional heads. In Section 5, we also provide a partial semantic analysis of comparative constructions such as those in (1) and (2), explaining how the nature of the noun denotation affects the truth values of the sentences.
220 Interpretation of Functional Heads
3 HOW TO EVALUATE THE DIFFERENT THEORIES OF MASS NOUNS Given the three alternatives discussed in Section 2, the following question arises: What empirical facts can differentiate the three views? and How can we tell whether mass nouns denote individuals? Below we review three methods that have been discussed in the mass–count literature: (1) countability, (2) predicates and distributivity and (3) comparative constructions. To inform the question of mass–count interpretation, a good method should yield reliable results that are independent of other grammatical factors. Two of the methods fail to meet this criterion and are confounded by other grammatical properties.
3.1 Why counting is unreliable for determining atomicity Countability, at first pass, sheds light on the relationship between nouns and individuals. Consider the sentence template in (3), in which 1 Chierchia only has semi-lattices with minimal parts. There are no continuous lattices. Also, he associates the entire semi-lattice with mass nouns and the entire semi-lattice minus the minimal parts with plural count nouns. However, he employs an operator that chooses the supremum of these lattices, thus making his theory essentially equivalent to Link’s and Gillon’s.
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such as tables and chairs, and thus denotes individuals [see Gillon (1999), for discussion of the similarities between his views and Bunt (1985)]. A third view extends these intuitions, and proposes that all mass nouns, and not just terms like furniture, have denotations with minimal parts and are inherently plural (Chierchia 1998).1 According to this approach, differences between mass and count nouns exist, but not along the dimension of minimal parts. As Chierchia (1998: 68) states, ‘. . . furniture is no less ‘‘atomic’’ (i.e. made up of discrete sets of singularities) than piece of furniture or, indeed, table . . . At any rate, since in subdividing something we always get to an end, there is no principled reason to maintain that the denotation of mass nouns (even those whose granularity is unclear) do not have an atomic structure’. Thus, things like furniture, mustard and even fun can be divided up only to a certain point before there is no more furniture, no more mustard and no more fun. In each case, individuals are part of the denotation, though they may vary in how easily they are identified. To summarize, we have reviewed three main views of mass-count semantics. Mass nouns may (1) have denotations containing only nonindividuals, (2) be unspecified with regards to individuation or (3) only have denotations containing individuals.
Alan C. Bale and David Barner 221
both mass and count nouns are syntactically possible replacements for X.2 (3) Seymour counted the X.
(4) #Seymour counted the anger/judgment/tolerance. Each potential sentence is odd since it is difficult to image how one could count anger, judgment or tolerance. However, a problem arises with respect to how counting is related to contextual factors independent of the mass–count distinction. Consider the sentence in (5). (5) Seymour counted the sugar but not the water. This sentence seems unacceptable in some contexts and acceptable in others. For example, the sentence is odd in a context in which there is a pitcher of water and a pile of sugar on the table. However, it is more acceptable in a restaurant where there are bottles of water and packets of sugar on the table. One can talk about ‘counting sugar and water’ when one counts sugar packets and bottles of water. There are two possible explanations of why the acceptability of the sentence changes with the context. First, it is possible that the type of nominal denotation changes as the context of use changes:3 the denotation of sugar might be continuous in one situation but have minimal parts in another. However, it is also possible that the denotation remains constant and 2 Alternative templates that explicitly involve a numeral, such as There is/are N X, are not informative since they can only be used with count nouns. To adequately evaluate all theories, a syntactically neutral template is needed, since it is possible that numerals only select for count nouns due to their syntactic selectional restrictions rather than semantic requirements (for evidence supporting this possibility, see Gillon et al. 1999). 3 This position is similar to Bunt’s (1985) proposal that the primary denotations of mass nouns do not contain atoms, yet in context of use, such denotations can be mapped to (secondary) denotations that do contain atoms.
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With respect to this template, a possible generalization can be stated as follows: If a mass noun can be used in such a sentence felicitously, replacing X, then its denotation contains individuals. If not, then its denotation does not contain individuals. Underlying this is the assumption that counting requires that the noun denote individuals. On the surface, classifying nouns in this way is productive. For instance, it classifies all count nouns correctly: every count noun can be used felicitously in place of the X. Also, there are mass nouns that cannot be used felicitously in such a sentence. For example, consider the potential sentences in (4).
222 Interpretation of Functional Heads
(6) Seymour counted the pens/markers/crayons. The sentence in (6) usually refers to counting the individuals that make up the minimal parts of the denotation of pens, markers and crayons. However, in a factory context where perhaps it is Seymour’s job to keep tract of the number of boxes of writing implements, the relevant units for counting are boxes of pens, boxes of markers and boxes of crayons. In this case, it is doubtful that the nature of the nominal denotation is changing in this context. The minimal parts of the count noun pens are always the individual pens in a given context. What is more likely is that the circumstances of evaluation select units for counting—that is, boxes on a conveyor belt. In summary, the possibility that counting is influenced by the circumstances of evaluation makes this way of classifying nouns less than ideal.
3.2 Distributivity is an unreliable test for atomicity Another possible way of determining whether a denotation denotes individuals is to observe how a predicate can be distributed over its subparts. For example, the sentence in (7) has two prominent readings. (7) The chairs in this room weigh 50 pounds. This sentence can mean that all the chairs taken together weigh 50 pounds or that each chair weighs 50 pounds. By the second reading, the predicate is distributed over individual chairs. Linguists like Bunt (1985) use such facts to argue that in a given context of use, certain nouns denote individuals. This line of reasoning rests on the assumption that if a noun supports distributivity in a given context, then it must denote individuals in that context. However, other evidence suggests that this
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that the circumstances of evaluation determine whether or not counting is permitted (i.e. evaluating the sentence requires counting, and therefore a prior division of the things/stuff into units in the situation). In this case, the nature of the nominal denotation might be irrelevant in deciding whether or not counting is appropriate or acceptable. If so, such sentences would be unhelpful in determining whether nouns do indeed denote individuals. There is some data that support the second explanation. By all accounts, count nouns should specify stable units of individuation. However, consider the sentence in (6), when uttered in a factory where there is a conveyor belt with boxes of pens, boxes of markers and boxes of crayons passing by.
Alan C. Bale and David Barner 223
assumption is not warranted. Distributivity of a predicate over an NP may have more to do with the predicate than the inherent divided reference of the noun (e.g. see Langendoen 1978; Gillon 1992; Schwarzschild 1996). Consider the sentences in (8). (8)
a. These spoons are priced at 100 dollars. b. This cutlery is priced at 100 dollars.
(9) That sugar is cubical. According to Bunt (1985: 175), since (9) is true when referring to cubic lumps of sugar in a bowl on the table, as opposed to the ungranulated mass, the phrase that sugar in such a context should behave like the phrase those sugar lumps. In other words, Bunt’s suggestion is that (9) demonstrates that the denotation of the NP in this situation has individuals as minimal parts. However, Bunt does not consider that (9) might only demonstrate a predicate’s ability to distribute over subgroups in the subject’s denotation: subgroups of the sugar that constitute the lumps. As noted with regards to (8), these subgroups need not be the same as the individuals that constitute the
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What one receives for 100 dollars depends on the context of use. For example, either sentence could refer to a bunch of spoons that costs 100 dollars altogether. Alternatively, the sentences could refer to a stack of spoon sets, each set in its own box and each box priced at 100 dollars. The sentences could even refer to individual spoons that cost 100 dollars each. The way that a predicate applies to its subject depends crucially on the context in which it is uttered and not on whether the noun in question—that is, spoon or cutlery—denotes individuals. It is possible that these different readings arise due to the denotation of the noun changing with the context. However, it is also possible that it is the predicate, or at least the way in which the predicate combines with the noun, that changes with the context, while the denotation of the noun remains constant. In other words, a predicate can be applied to the largest group in the denotation or to each member of a set of smaller subgroups, regardless of whether the denotation of the noun contains individuals. As a result, the subgroups over which the predicate is distributed need not be identical to the individuals in the noun’s denotation. By this analysis (outlined in Langendoen 1978; Gillon 1992; Schwarzschild 1996), predicate distribution is an unreliable test for evaluating whether a noun denotes individuals. For example, consider how Bunt (1985) treats the phrase that sugar in (9).
224 Interpretation of Functional Heads minimal parts in the noun’s denotation.4 Since it is difficult to tell whether the predicate distributes over minimal parts or over higher subgroups, this method of classifying nouns is unreliable.
3.3 Comparatives and noun phrases Another method for exploring individuation involves comparative constructions. An interesting fact about such constructions is that the dimension of comparison implicated by a construction changes according to the denotation of the noun phrase. Consider the sentences in (10). Esme has more chairs than Seymour has tables. Esme has more water than Seymour has juice. Esme has more rope than Seymour has string. Esme has more gold in her ring than Seymour has silver in his necklace. e. Esme has more anger than Seymour has sympathy.
In (10), the objects of comparison can be determined transparently for each sentence. In (10a), a measurement of Esme’s chairs is compared to a measurement of Seymour’s tables. In (10b), a measurement of Esme’s water is compared to a measurement of Seymour’s juice. And so on. In each case, the dimension of measurement shifts with the noun phrases. Specifically, the sentences in (10) can be evaluated on the basis of number, mass or volume, length, purity of materials and emotional intensity, respectively. Given the sensitivity of the comparative construction to the noun, it becomes possible to classify nouns in terms of the selected dimension of comparison, beginning with a distinction between nouns that permit comparison by number and those that do not. This method of classifying nouns is highly reliable. First, it systematically identifies number as the default measuring dimension for count nouns, as in (11). 4
An explanation of these phenomena that appeals to predicate distribution seems necessary when comparative constructions involving the same nouns are involved. Consider the sentence in (i): (i)
a. John has more sugar than the Queen of England. b. John has more sugar lumps than the Queen of England.
In a context in which John has several small lumps of sugar, and the Queen of England has one huge, giant lump of sugar sentence, (a) is false whereas (b) is true. This is because sugar fails to provide the same default dimension for measuring that sugar lumps does: number of individuals. In other words, sugar does not alone (or even in its context of use) provide criteria for identifying individuals, and thus for using number as a measuring dimension. As demonstrated in (i), comparative constructions distinguish between an NP’s ability to quantify over individuals and a predicate’s ability to distribute over an NP, whereas predication tests alone cannot.
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(10) a. b. c. d.
Alan C. Bale and David Barner 225
(11) a. Seymour has more apples than Esme. b. Esme has more parties than Seymour. c. Esme has more ideas than Seymour.
(12) a. Seymour has more water than Esme. b. Esme has more glue than Seymour. c. Seymour has more energy than Esme. To evaluate these sentences, what matters is a continuous dimension of measurement, rather than number. Thus, even in a situation in which Esme has three portions of water and Seymour has only one portion, Seymour has more water so long as his single portion is greater overall in volume. The same results follow for sentences (12b) and (12c), where in each case a measurement cannot be based on number. In most cases, the problems encountered by other methodologies do not affect the comparative method. For example, judgments elicited by comparative constructions are not affected by predicate distribution since comparisons do not involve dividing up a subject or object and applying it to a predicate. Also, comparative judgments are determined primarily by mass–count syntax even when the noun root and the context remain constant: (13) a. Seymour has more rock/brick/string than Esme does. b. Seymour has more rocks/bricks/strings than Esme does. The sentences in (13a) and (13b) can be used in the same contexts, but result in different judgments. For example, consider a context where there are four small rocks that belong to Seymour and two very large rocks that belong to Esme. Despite the fact that there are salient individuals in this context—namely the rocks, the truth conditions of (13a) and (13b) differ. Only the count noun usages allow for a
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Each sentence is evaluated on the basis of number, as opposed to other dimensions of measurement such as mass or volume. For example, sentence (11a) is true in the context in which Seymour has three apples and Esme has one, even if the combined weight or volume of his three (tiny) apples is less than the weight or volume of her one (gigantic) apple. The same is true for the sentences in (11b) and (11c), where the person with the greater number of individuals is judged to have more x, where x stands in for either apples, parties or ideas. Furthermore, this method reveals differences between mass and count nouns, demonstrating the sensitivity of these constructions to the mass–count distinction. Consider the mass noun usages in (12).
226 Interpretation of Functional Heads
4 COMPARATIVES AND THE MASS/COUNT DISTINCTION
4.1 Data Previous investigations have used comparative constructions to evaluate the semantics of noun phrases. This paper adds two new generalizations to the literature. These generalizations, as we show, have profound consequences for the semantics of the mass–count distinction. First, for common mass and count nouns, the comparative methodology yields results that are consistent with all existing theories of the mass–count distinction: (14) a. Esme has more cups/plates/candles than Seymour. b. Esme has more butter/water/toothpaste than Seymour. The sentences in (14a) are true if Esme has a greater number of individual things (i.e. cups, plates and candles) than Seymour, even if his things are bigger or heavier than Esme’s. Since each noun is a count noun, number is specified as the dimension of comparison. In (14b), the sentences are true if Esme has a greater volume of stuff, even if the stuff is divided into discrete portions. Thus, if Esme has one large bottle of water and Seymour has three bottles, Esme still has more water than Seymour. These intuitions can be extended to nouns that can appear in both mass and count contexts. For all such nouns, the count usage always 5 Although context cannot force a comparison by number when the noun phrase does not permit such a comparison, the context can influence other types of measurement. For example, whether an object has more gold than another often depends on the context. Where purity matters, the comparison will be evaluated in terms of the percentage of gold in the object. However, where the overall amount of gold matters, the comparison will be evaluated in terms of mass.
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comparison by number even though individuals are contextually salient in both cases.5 Based on these observations, we submit that the comparative methodology offers the most reliable way of assessing mass–count semantics, since judgments are almost exclusively affected by alternations in mass–count syntax. In taking this view, we follow McCawley (1979), and psychologists such as Gathercole (1985), and Barner and colleagues (Barner & Snedeker 2005, 2006; Barner et al. 2008), who have all used comparative constructions to test the semantic distinction between mass and count nouns (see also Cresswell 1976, who used comparatives to support his proposal that NPs are essentially measurement relations).
Alan C. Bale and David Barner 227
specifies comparison by number, and the mass usage never does (i.e. some continuous dimension is selected): (15) a. Esme has more ropes than Seymour. b. Esme has more strings than Seymour. c. Esme has more stones than Seymour. (16) a. Esme has more rope than Seymour. b. Esme has more string than Seymour. c. Esme has more stone than Seymour.
(17) Generalization 1: No term that can be used in count syntax can also be used in a mass syntax to denote individuals. It is important to note that this generalization cuts across subcategories of mass nouns and count nouns. Distributionally, nouns can be classified according to whether they are more amenable to count syntax (such as dog, cake, apple and ideas), more amenable to mass syntax (such as water, mud, darkness and coffee) or equally acceptable in either category (such as paper, rock, stone, thought and judgment). No matter the category preference, if a noun can appear in both categories, it will denote individuals as a count noun but not as a mass noun. Thus, conceptual factors that might influence whether a noun is used as mass or count more frequently do not affect this generalization. Also, Generalization 1 is true regardless of the type of semantic coercion that is associated with the noun’s syntactic flexibility. It is true
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In (15), Esme has more ropes, strings or stones if she has a greater number of individuals. This is true regardless of how big Seymour’s objects are. However, in (16), the basis for judgments is clearly different, and is consistently based on other dimensions of measurement such as length, mass, volume or area. For example, (16a) is true if Esme has one ten-foot rope and Seymour has three one-foot ropes. In this same context, (15a) is false. The results of the comparative judgment shift systematically according to the syntactic status of the noun as mass or count, independent of the context, and despite the fact that perfectly good individuals are present in both cases [see Barner & Snedeker (2005, 2006), for evidence that adults, 3-year-olds, and 4-year-olds shift quantity judgments according to mass–count syntax for terms like string and stone, and for novel mass and count nouns used to refer to discrete physical objects]. Based on these examples and others like them (e.g. paper-papers, rock-rocks, tile-tiles, coffee-coffees, chocolate-chocolates), we propose Generalization 1:
228 Interpretation of Functional Heads for so-called ground-noun coercion as in (18). In these cases, there is coercion from denotations containing individuals to denotations consisting of the stuff those individuals are made of. It is true of packaging coercion, as in (19). Here, there is coercion from substances to portions of substances. It is also true of individuation-by-cause coercion, as in (20). In these examples, coercion is from denotations of emotions or mental states to denotations individuated in terms of the cause of those emotions or mental states. Finally, the generalization applies to individuation-by-instance coercion, as in (21), in which coercion is from nouns that denote a mental capacity or activity to nouns that denote instances of the capacity or activity in use.
(19) a. too much water vs. too many waters b. too much beer vs. too many beers c. too much coffee vs. too many coffees (20) a. too much anxiety vs. too many anxieties b. too much fear vs. too many fears c. too much hope vs. too many hopes (21) a. too much thought vs. too many thoughts b. too much judgment vs. too many judgments c. too much kindness vs. too many kindnesses Regardless of other idiosyncratic relationships between the interpretation of mass and count usages, wherever there is mass–count flexibility, the count noun always denotes individuals whereas the mass noun never does. Taken in isolation, Generalization 1 seems to support theories of the mass–count distinction like that of Link (1983), which specify two distinct semantic domains for mass and count nouns, respectively. However, theories such as this cannot explain the data in (22): (22) a. Esme has more furniture than Seymour. b. Esme has more equipment than Seymour. c. Esme has more footwear than Seymour. Each of these comparative sentences contains a mass noun. However, unlike the terms in (14) or (16), these mass nouns support comparisons based on number. For example, (23a) can be paraphrased as ‘Esme has more pieces of furniture than Seymour’. Similarly, (14b) is equivalent
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(18) a. too many apples vs. too much apple b. too many dogs vs. too much dog c. too many bricks vs. too much brick
Alan C. Bale and David Barner 229
to ‘Seymour has more pieces of equipment than Esme’ and (14c) to ‘Esme has more shoes and boots than Seymour’.6 Although such mass nouns are by no means in the majority, examples are not uncommon, and include luggage, underwear, company, glassware, wildlife, silverware, cutlery, mail, inventory, waterfowl, jewelry and artillery, among others. In each case, the mass noun specifies comparison by number. These results lead us to propose our second generalization regarding mass– count semantics:
Mass nouns that can have individuals in their denotation like furniture and jewelry (henceforth ‘object–mass’ nouns), differ from mass nouns like water or mustard, which never can, no matter what the context or situation [see Barner & Snedeker (2005) and Barner et al. (2008) for psychological tests demonstrating this difference between object–mass nouns and mass nouns like mustard; see also Barner & Snedeker (2006) and Barner & McKeown (2005) for evidence regarding the origin of object–mass nouns in language acquisition]. Paradoxically, the nouns that best denote individuals when used as mass nouns are the nouns that are most resistent to count syntax in English: (24) a. b. c. d.
*Esme has some furnitures/equipments/footwears. *Those furnitures/equipments/footwears belong to Esme. *She has many furnitures/equipments/footwears. *She has five furnitures/equipments/footwears
Together, the facts subsumed by Generalizations 1 and 2 are problematic for all three of the theories of mass–count semantics 6 According to McCawley (1979), mass nouns like furniture sometimes do not specify comparison by number. Instead, what is important is the extent to which the function of furnishing, for example, is satisfied. For example, he judges the sentence ‘Fred has more furniture than me’ to be true in cases where I have a greater number of individuals but Fred has more types of furniture. However, type readings of this kind are accessible for most nouns, including count nouns. For example, McCawley notes that (ii) can be true if Fred has more types of clothes despite having fewer articles of clothing.
(i)
Fred has many more clothes than I do.
Furthermore, the same judgments hold for French where the translation of furniture is the count noun meuble. (ii) Fred a plus de meubles que moi. Based on these considerations, it seems that McCawley’s examples highlight a type/individual ambiguity present in nouns like furniture (and indeed in most nouns), but that they do not provide evidence against the claim that certain mass nouns quantify over individuals (for discussion, see Barner et al. 2008).
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(23) Generalization 2: Some mass nouns (in the context of use) have individuals in their denotation and others do not.
230 Interpretation of Functional Heads outlined above. They require a theory that allows mass nouns to denote individuals, but that prohibits them from doing so whenever the noun can also be used in count syntax. A corollary of this is that the theory must prevent mass nouns that denote individuals from also appearing in count constructions.
4.2 Problems with alternative accounts
4.2.2 Inherent plurality Like Link (1983), Chierchia (1998) argues that all mass nouns share a common semantic domain. However, in contrast to Link, Chierchia proposes that all mass nouns have 7
Also supporting this view, Wisniewski et al. (1996: 295) claim that:
. . . on a particular occasion, we may conceptualize a swan, several ducks, and a heron on a lake as an unindividuated group called waterfowl, and not think of them individually as birds.
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4.2.1 Uniform semantic domains for mass nouns The theories of Link (1983), Bloom (1994, 1999) and many others argue that mass nouns denote unindividuated quantities. While these accounts can explain the conversion facts, they do not predict the existence of object–mass nouns like furniture, which denote individuals. Thus, such theories can provide a natural explanation for Generalization 1 but are incapable of accounting for Generalization 2. In response to this problem, some have suggested that although object–mass nouns name phenomena that are discrete individuals, they do not represent them as such, but instead lead speakers to construe their referents as unindividuated (e.g. Bloom 1994; Wisniewski et al. 1996). According to Bloom (1994: 45), ‘mappings relevant to the study of linguistic competence must be between grammatical classes and cognitive classes—not classes of entities in the world’. While chairs and tables are individuals and count as instances of furniture, the word furniture does not pick them out as individuals, but leaves them unindividuated.7 Accepting this logic, we are still led to conclude that mass nouns like furniture denote individuals. Note that the comparative method does not lead to judgments based on number whenever discrete individuals in the world are named. As demonstrated in (15) and (16), the interpretation of nouns like string and stone shift as the nouns change between mass and count, even when the entities in the world remain constant (and clearly qualify as discrete individuals, as evidenced by their status as such when named by count nouns). Comparative judgments are sensitive to shifts in mass–count syntax and nonetheless indicate that at least some mass terms denote individuals.
Alan C. Bale and David Barner 231
(28) Esme has more rice than Seymour. The sentence in (28) is false so long as Seymour has more rice in mass or volume, no matter how much it is emphasized that Esme has more grains or bags.10 Vagueness also fails to make the correct prediction for words that vary in mass–count usage cross-linguistically. In French, one speaks of des e´pinards (roughly ‘some spinaches’), des cheveux (‘some hairs’—even in the context of washing it/them) and des paˆtes (‘some pastas’). In each case, the French word is a count noun, but the equivalent English word is a mass noun. Using the comparative methodology, Inagaki and Barner (2009) showed that French speakers base comparative judgments for spinach, hair, toast, pasta, etc., on number, while English speakers base 8
We assume that Chierchia is using the term ‘vague’ in much the same sense as Quine (1960: 126), where what counts as a minimal part is ‘left unsettled’. 9 ‘What set of atoms generates the extension of a mass noun can be quite vague (though for mass nouns like furniture it isn‘t substantially more vague than for table) and typically varies from context to context’. (Chierchia 1998: 70) 10 Another significant problem for Chierchia is that it is unclear why vagueness should systematically affect mass nouns but not count nouns. Many count nouns suffer greatly from vagueness. As Quine (1960: 126) notes in his discussion of the count noun mountain, ‘it is not clear when to declare a saddle to be in the middle of one mountain and when between two mountains. The issue makes all the difference between one mountain and two’. Nonetheless, unlike mass nouns it is never acceptable to base comparative judgments for a term like mountain on mass or volume.
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denotations with minimal parts. As a result, his theory is unable to differentiate object–mass terms from other mass nouns. Chierchia provides at least one mechanism by which his theory might account for different types of mass nouns. He suggests that mass nouns like water differ from those like furniture according to their relative vagueness.8,9 What counts as individuals for a particular mass noun on a given occasion is not specified linguistically but rather is determined contextually. The difference between object–mass nouns and other mass nouns is determined by how readily one can identify the individuals that make up the minimal parts. However, vagueness seems unable to account for Generalizations 1 and 2. As Chierchia notes, the effects of vagueness are normally mitigated by providing details in the context. In speaking about the sentences ‘The rice is from Italy’ and ‘The grains of rice are from Italy’, Chierchia (1998: 85) states, ‘what counts, in context, as minimal parts has to be made clear. In a situation where it is clear that only whole grains of rice count as rice then [the two sentences above] will have the same truth conditions’. Yet no matter how explicit the context is for sentences like the one in (28), there can never be a comparison by number.
232 Interpretation of Functional Heads judgments on continuous dimensions like mass and volume. Thus, the sentences in (29a) lead to judgments based on total mass or volume, whereas those in (29b) lead to judgments based on number: (29) a. Esme has more spinach/hair/pasta than Seymour. b. Esme a plus d’e´pinards/cheveux/paˆtes que Seymour.
4.2.3 Multiple domains for mass nouns Theories that support two or more semantic domains for mass nouns, such as Bunt (1985) and Gillon (1992, 1999), provide an account of the Generalization 2, but fail to account for the conversion facts as stated in Generalization 1. By claiming that the denotations of particular mass nouns are underspecified, both theories allow mass nouns to denote sets of ‘ensembles’ (for Bunt) or ‘aggregates’ (for Gillon) that may or may not be composed of individuals.11 According to these authors, the nature of a noun’s denotation is determined via an inspection of the world: when discrete individuals are present, the mass noun will denote individuals, but where no individuals exist, it will not (see Bunt 1985: 130; Gillon 1999: 9). Hence, it is predicted that some nouns should denote individuals while others should not. This is the essential data point summarized in Generalization 2. However, these proposals provide no account of why mass nouns like stone and string should fail to denote individuals as mass nouns but not as count nouns. They also fail to account for cross-linguistic variation such as the difference between French and English demonstrated in (29). In all such cases, discrete physical objects may exist in the world, but only the count usages lead to comparative judgments based on number. In general, these theories offer no account of the conversion facts of Generalization 1 or the observation that certain words denote 11
In Bunt’s (1985) theory, the denotation of a mass noun has minimal parts only when it is interpreted in the context of use. The primary denotations do not have minimal parts, but can be mapped to secondary denotations that do have minimal parts, given the appropriate context.
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In English, if Esme has more individual leaves of spinach, this does not mean that she necessarily has more spinach than Seymour. Seymour could still have a greater mass or volume. However, the opposite is true in French (though mass or volume may act as a proxy for number when the leaves are not countable in a context). Such examples suggest that discrete individual things do exist in the world, and that these things can be encoded linguistically. However, no amount of contextual specification in English permits comparison by number in these cases. The semantic difference appears to be purely grammatical.
Alan C. Bale and David Barner 233
individuals as count nouns but not as mass nouns despite the things in the world remaining constant. 5 INTERPRETING FUNCTIONAL HEADS
5.1 Syntactic assumptions Features distinguishing mass from count Before providing an interpretation for mass and count NPs, let us first note our syntactic assumptions.12 Three facts are relevant to our analysis. First, certain quantifiers/determiners only select count nouns—for example, many, several, a few, every, and the numerals two, three, four, etc. Second, certain quantifiers/determiners only select mass nouns—for example, much and little. Third, quantifiers such as a lot of, this, the, all and some can be used with either kind of noun. Minimally, a syntax for the mass– count distinction should account for these facts. These facts can be explained by a framework that assumes that lexical items are unspecified for syntactic categories [a hypothesis first defended for a subset of lexical items by Chomsky (1970); for an extension of this view, see Halle & Marantz (1993); Marantz (1997); Harley & Noyer (1999); Barner & Bale (2002, 2005); Borer (2005)]. By this approach, lexical items become nouns or verbs in the syntax by 12 Our syntactic structures are similar to those proposed by Borer (2005). Only the labelling of categories is different. The quantifier facts that motivate our syntactic structures are also used to motivate Borer’s structures. However, we will leave facts about classifiers in Mandarin Chinese out of the present discussion.
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The problem posed by Generalizations 1 and 2 is how to describe the lexical and syntactic sources of individuation. Generalization 1 requires an account of how count syntax specifies reference to individuals. In contrast, Generalization 2 requires an account of how some mass nouns can denote individuals while others do not. In this section, we provide an interpretation for the functional heads of count-noun and massnoun phrases that accounts for these facts. We begin by outlining what we take to be the basic syntactic form of such phrases. We then proceed to outline a detailed functional interpretation of these forms, focusing on the interpretation of root lexical items and the functional heads that determine the category of the phrases. Next, we explain how these functional interpretations can be combined in comparative constructions to yield the data presented above. Our syntax and the general strategy of our semantic approach are similar to Krifka (1995) and Borer (2005), with important differences in the details.
234 Interpretation of Functional Heads
a. n,c
Figure 1
b. Root lexical item
n
Root lexical item
The tree in (a) shows the basic structure of a count noun phrase whereas the tree in (b) shows the basic structure of a mass noun phrase.
a.
n,c
b.
√cat
n
√furniture
Figure 2 The tree in (a) shows the basic structure of the count noun phrase cat whereas the tree in (b) shows the basic structure of the mass noun phrase furniture.
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combining with nominal and verbal heads. Similarly, mass and count nouns can be distinguished syntactically by features of the functional head in which the noun appears. Minimally, two features are required. One feature, which we call ‘n’, determines whether or not the phrase is nominal. The second feature, which we call ‘c’, determines whether or not the phrase is count. When appearing together, these features are bundled under the same syntactic head. This system permits two syntactic possibilities for noun phrases (Figure 1): one in which a root lexical item combines with just the nominal feature ‘n’ and another in which a root combines with ‘n’ and the count feature ‘c’. The example in (a) represents a count-noun functional head, and the example in (b) a mass noun functional head. We represent lexical items (or roots) with the root symbol ‘O’ preceding the canonical orthographic representation of the word [see Pesetsky (1994), for a similar use of this symbol]. Thus, the lexical item associated with furniture is Ofurniture (and cat is Ocat). The mass noun furniture and the count noun cat are represented as in Figure 2. By this account, the distribution of quantifiers/determiners can be easily explained. First, since all quantifiers/determiners apply to nouns, they all require that their complement have the feature ‘n’. Second, quantifiers/determiners that only apply to count noun phrases (such as several) require that their complement also have the feature ‘c’. Third, quantifiers/determiners that only apply to mass noun phrases (such as much) require that their complements do not have the feature ‘c’.
Alan C. Bale and David Barner 235
Finally, quantifiers/determiners that apply to both count nouns and mass nouns (such as all) have no requirements or restrictions with regard to ‘c’. This exhausts all possible combinations of features.
5.2 Interpretations
5.2.1 The interpretation of roots Following an influential tradition established by Link (1983), we adopt an algebraic semantics for NPs. Specifically, we assume that roots are interpreted as join semi-lattices. Such structures have proven to be useful for providing a semantic analysis of how quantifiers and determiners interact with count and mass nouns while also accounting for their referential properties (see Bunt 1985; Gillon 1992, 1999; Chierchia 1998, etc). The join semi-lattices relevant to our semantics implicate sets of aggregates. Aggregates (sometimes also called pluralities, sums, groups, collections or ensembles) can be quantities of individuals or of substances, energies, ideas, etc. We will represent aggregates by using a sequence of lowercase letters (e.g. abc, bc, a, b). As is commonly noted in the literature on aggregates, an ordering relation can be defined through a sum/join operator (4) that maps any two aggregates to a single aggregate that is a combination of the two (cf. Link 1983).13,14 Definition of 4: For all aggregates x and y: x 4 y ¼ xy.15 With this operator, one can define the aggregate-part-of relation, symbolized by ‘<’. Definition of <: For all aggregates x and y, x < y if and only if (x 4 y) ¼ y. 13 Sets and aggregates are often interchangeable due to their similar structural properties: both can form join semi-lattices. Here, we prefer aggregates since their representation is more amenable to the representation of atomless semi-lattices, which might be crucial for interpreting a large class of mass nouns. 14 Alternatively, a sum operator can be defined through a given ordering relation. 15 Note that this operator is idempotent (for any aggregate x, x 4 x ¼ x), commutative (for all aggregates x and y, x 4 y ¼ y 4 x), and associative (for all aggregates x, y and z, (x 4 y) 4 z ¼ x 4 (y 4 z) ).
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With the syntactic forms specified in Section 5.1, we can now explore the interpretation of roots and functional heads. As outlined below, we propose that roots are interpreted as semi-lattices (sets of aggregates/ pluralities). The mass noun functional head is interpreted as an identity function, whereas the count noun functional head is interpreted as a function from semi-lattices without individuals to semi-lattices with individuals.
236 Interpretation of Functional Heads
Definition of ‘minimal part’: an aggregate x is a minimal part for a set of aggregates X iff x 2 X and for any aggregate y, such that y 6¼ x and y 2 X, it is not the case that y < x. This definition of minimal parts might appear weaker than most, since by our account minimal parts are not necessarily atoms. Often it is assumed that two distinct minimal parts cannot share aggregates. However, according to the definition above, two minimal parts could share aggregates. For example, consider the following set X ¼ fac, ad, bc, bd, acd, abc, abd, bcd, abcdg. The set X is closed under sum and forms the lattice depicted in Figure 3. abcd
abc
ac
Figure 3
abd
ad
acd
bc
bcd
bd
The join semi-lattice X ¼ fac, ad, bc, bd, abc, abd, acd, bcd, abcdg. Note this lattice can be generated from the minimal parts fac, ad, bc, bdg.
16 It is simple to prove that < is a partial order. Reflexivity: For all aggregates x, (x 4 x) ¼ x and hence x < x. Anti-symmetry: For all aggregates x and y such that x < y and y < x, it follows that x 4 y ¼ y and y 4 x ¼ x. By commutativity, (y 4 x) ¼ y and hence by substitution x ¼ y. Transitivity: For all aggregates x, y and z, if x < y and y < z, then x 4 y ¼ y and y 4 z ¼ z. Since y 4 z ¼ z, it follows that (x 4 y) 4 z ¼ z by substitution. By associativity, (x 4 y) 4 z ¼ x 4 (y 4 z). By substitution, x 4 (y 4 z) ¼ x 4 z. Since (x 4 y) 4 z ¼ z, it follows that x 4 z ¼ z. Hence, if x < y and y < z, then x < z.
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Due to the properties of 4, the relation < represents a partial order (that is to say, it is reflexive, anti-symmetric and transitive).16 For our semantics, the interpretation of every root R is a set of aggregates X. Thus ½½R ¼ X. Furthermore, for all aggregates x and y that are members of X, their sum x 4 y is also a member of X. In other words, the interpretation of every root is closed under sum. Also, since the members of X are partially ordered by <, the interpretation of each root is a (sum/join) semi-lattice. There are three types of semi-lattices that are relevant for a discussion of mass and count nouns. In the first—a limited semi-lattice—every member of the semi-lattice is composed of minimal parts. A minimal part is defined as follows:
Alan C. Bale and David Barner 237
Definition of ‘individual’: an aggregate z is an individual for a set of aggregates X iff z is a minimal part for X and for all aggregates y 2 X, either (i) z < y or (ii) there is no w < z, such that w < y. This definition guarantees that an individuated semi-lattice will not have minimal parts that share an aggregate. An example of an individuated semi-lattice is given in Figure 4. In this structure, no part of a minimal part can appear in another aggregate without all of its parts appearing in that aggregate. The notation in Figure 4 makes this point seem trivial, since the minimal parts are represented by single letters (e.g. a, b, c or d). However, we can replace the aggregates a, b, c and d with complex aggregates such as ef, gh, ij and kl without changing the classification of the minimal parts as individuals. An example is shown in Figure 5.
abcd
ab
abc
abd
acd
bcd
ac
ad
bc
bd
a
b
c
d
cd
Figure 4 The semi-lattice X ¼ fa, b, c, d, ab, ac, ad, bc, bd, cd, abc, abd, acd, bcd, abcdg. Note this lattice can be generated from the set of individuals fa, b, c, dg.
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In this lattice, the minimal parts share aggregates. For example, the aggregate a is part of both ac and ad. Similarly, c is part of ac and bc. This type of lattice can represent roots that denote aggregates with nonhomogeneous components, such as Osuccotash [an example from Sharvey (1979)]. All succotash contains lima beans and corn, but it would be unusual to call a piece of corn succotash if it were not paired with at least one bean. Thus, the lattice in Figure 3 could represent an amount of succotash in which a and b are portions of beans and c and d are portions of corn. The second type of lattice relevant to our account is an individuated semi-lattice, which has individuals as minimal parts, where individual is defined as follows:
238 Interpretation of Functional Heads efghijkl
efghij
efgh
efghkl
efijkl
ghijkl
efij
efkl
ghij
ghkl
ef
gh
ij
kl
ijkl
The important point is that the relation of the minimal parts to other members of the lattice defines what counts as an individual in the lattice. For example, since ef is a minimal part in Figure 5, and since no subpart of ef appears in any other aggregate without all of ef appearing in that aggregate, the aggregate ef is an individual in the lattice. These individuated semi-lattices can be used to represent denotations that contain individuals, as is required for object–mass nouns like furniture. Unlike limited and individuated semi-lattices, the third type of semi-lattice has no minimal parts and hence no individuals either. We call this semi-lattice a continuous semi-lattice. Unlike the others, these lattices cannot be easily represented graphically or symbolically. However, they are nonetheless well-defined mathematical objects. A set of aggregates X is a continuous semi-lattice iff X is closed under sum and X has no minimal parts. In other words, for every aggregate x that is a member of the lattice X, there is another aggregate y in X such that y < x and y 6¼ x. Intuitively, this means that for any aggregate in X, there is an even smaller part of that aggregate that is also in X. Continuous semi-lattices can be used to represent lexical roots such as Ospace, whose denotations might not contain minimal parts. Whether continuous semi-lattices are needed [as suggested by Link (1983)] or whether every lattice must have minimal parts [as suggested by Chierchia (1998)] is not crucial to our remaining discussion, nor for our proposal regarding the role of functional heads in NP interpretation. What does matter is that there is a difference between individuated lattices on the one hand and non-individuated lattices on the other (whether ‘continuous’ or simply ‘limited’).
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Figure 5 The lattice X ¼ fef, gh, ij, kl, efgh, efij, efkl, ghij, ghkl, ijkl, efghij, efghkl, efijkl, ghijkl, efghijklg. Note this lattice can be generated from the set of individuals fef, gh, ij, klg.
Alan C. Bale and David Barner 239
5.2.2 The interpretation of functional heads There are two functional heads that require an interpretation: the mass noun head represented by the feature ‘n’ and the count noun head represented by the bundle of features ‘n, c ’. By our account, the mass noun head is interpreted via an identity function. As a consequence, the interpretation of mass nouns is identical to the interpretation of the root in isolation. Interpretation of the mass noun functional head: ½½n ¼ i, where i maps every set onto itself.
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Determiners such as the and that (among others) operate on the unmodified semi-lattice that represents the denotation assigned to the root. For instance, as suggested by Link (1983), the can be represented as a (partial) function from semi-lattices to the supremums of the semilattices (the largest and top-most aggregate in the lattices). This function is partial since it requires that each semi-lattice in its domain have a unique largest and top-most aggregate. As discussed in Link (1983), this representation predicts both the determiner’s presuppositions and truth conditions. As another example, the interpretation of the determiner that can be interpreted as a function from semi-lattices to a member of that lattice—in effect, a choice function that is sensitive to contextual cues such as proximity, pointing and topics in the previous discourse. For clarity, consider an example. Suppose we are in a room with two tubs of water and several pieces of furniture (a few chairs, a table and a sofa). The denotation of the root Owater would be the set of all the aggregates of water (all the parts of water), called W. This denotation might be a limited semi-lattice or a continuous semi-lattice. Whatever the choice, the denotation will have a top-most member (all the water in both tubs taken together). Call this member a. Also, the denotation will have as separate members all the water in one tub (call it b) and all the water in the other tub (call it c). Suppose also that b is contextually emphasized (perhaps by someone pointing to it). Note that in this context, the supremum a is identical to the aggregate bc. In this situation, the phrases the water and that water have the denotations in Figure 6. In the same context, the denotation of Ofurniture would be the set of furniture and furniture pluralities. Thus if a, b and c were the chairs; s the sofa, and t the table, then the denotation would be the set F ¼ fa, b, c, s, t, ab, ac, as, at, bc, bs, bt, cs, ct, st, abc, abs, abt, acs, act, ast, bcs, bct, bst, cst, abcs, abct, abst, acst, bcst, abcstg. This is an individuated semi-lattice. Given this denotation, the phrases the furniture and that furniture have the interpretations in Figure 7.
240 Interpretation of Functional Heads a.
b.
[[the]] (W) = sup(W) = a
[[the]] = sup
[[n]] ( [[√water]]) = i(W) = W
[[n]] = i
[[that]] (W) = fTHAT(W) = b
[[that]] = fTHAT
[[√water]] = W
[[ n]] ( [[√water]]) = i(W) = W
[[n]] = i
[[√water]] = W
a.
b.
[[the]] (F) = sup(F) = abcst
[[the]] = sup
[[n]] ( [[ √furniture]]) = i(F) = F
[[n]] = i
[[√furniture]] = F
[[that]] (F) = fTHAT(F) = abc
[[ that]] = fTHAT
[[n]] ( [[√furniture]]) = i(F) = F
[[n]] = i
[[√furniture ]] = F
Figure 7 The root Ofurniture denotes the semi-lattice F ¼ fa, b, c, s, t, ab, ac, as, at, bc, bs, bt, cs, ct, st, abc, abs, abt, acs, act, ast, bcs, bct, bst, cst, abcs, abct, abst, acst, bcst, abcstg, whose top-most member is abcst. The lattice also contains the contextually prominent aggregate abc that is some distance from the speaker. The function fTHAT selects from any given set the contextually prominent aggregate that is further away from the speaker. (a) shows the compositional meaning of determiner phrase the furniture. (b) shows the compositional meaning of the determiner phrase that furniture.
In summary, mass functional heads do not alter the interpretation of root lexical items. If a root is interpreted as an individuated lattice, then the mass NP is interpreted as an individuated lattice.17 If the root represents an un-individuated lattice, then the mass NP does too. 17 In this way our theory differs from those of Sharvey (1979) and Borer (2005) who maintain that count syntax introduces a hidden classifier not present in mass syntax. Their theories provide no way of deriving a number interpretation for mass nouns like furniture. Our theory can be considered a simple expansion or addition onto their theories to account for the empirical facts discussed in this paper.
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Figure 6 The root Owater denotes the semi-lattice W whose top-most member is a. The lattice also contains contextually prominent aggregates b and c, where b is farther away than c. The function fTHAT selects from any given set the contextually prominent aggregate. (a) shows the compositional meaning of determiner phrase the water. (b) shows the compositional meaning of the determiner phrase that water.
Alan C. Bale and David Barner 241
The interpretation of the count noun head differs substantially from that of the mass noun head. It is not interpreted as an identity function but rather as a function that alters the type of semi-lattice it takes as an argument. Furthermore, it is only a partial function. Its domain consists only of semi-lattices that are non-individuated (continuous or limited) semi-lattices. This partial function maps these types of lattices to individuated semi-lattices.
Here, we set aside the details of how each lexical denotation is mapped to an individuated semi-lattice. For the present purposes, the important point is that there is a systematic relationship between mass and count usages of single lexical roots, like apple, fear, tile and rock. The count usages always denote individuals, whereas the mass usages do not. This observation suggests that each lexical root supports both kinds of interpretation, but is semantically underspecified, and requires mass– count syntax (i.e. IND) to select between interpretations. For example, by one account concepts like apple supply both a principle of application (which distinguishes apple-stuff from orange-stuff or banana-stuff) but also a principle of individuation (which indicates how much of this stuff, and in what arrangement, counts as one individual, or as two). The relationship between mass and count interpretations may depend on such conceptual factors, and thus the difference between them may vary idiosyncratically from one mass-count pair to another (for details, see Barner & Bale 2002, 2005). For example, the relation between the mass and count interpretations of water is quite different from the relation between those for chicken (the first can be called a ‘packaging’ relation, whereas the second a ‘grinding’ relation). Amidst these interesting idiosyncrasies, however, there is a systematic generalization, which is the focus of our discussion: IND maps lexical items that denote only nonindividuated semi-lattices to denotations of individuated semi-lattices (i.e. intensions that denote only non-individuated semi-lattices to intensions that denote only individuated semi-lattices; for simplicity we leave out the intensional talk). We assume that idiosyncrasies specified in the lexical concept help determine this mapping. By this proposal, all count nouns are derived from lexical items that denote non-individuated semi-lattices. Relevant to this hypothesis is the fact that lexical items differ with respect to categorical preference
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(Underspecified) interpretation of count noun functional head: ½½n, c ¼ IND, where IND is a function from semi-lattices to semi-lattices. The domain of IND does not include any individuated semi-lattices. The range of IND only includes individuated semi-lattices.
242 Interpretation of Functional Heads
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(although most lexical items can appear in either category). Some items are more natural as mass nouns (e.g. water) and some are more natural as count nouns (e.g. apple), while others seem fully flexible (e.g. tile, rock, stone and judgment). In our view, these differences in ‘preference’ cannot be explained by a grammatical system. Grammar can explain the possibility of flexible use, but not the frequency with which forms actually occur. In a previous set of papers (Barner & Bale 2002, 2005), we discussed this issue with respect to noun–verb flexibility in detail. Our main observation was that, given the capacity to generate novel nouns and verbs from words first heard as members of the opposite category, any grammar must account for noun–verb flexibility via grammatical rules. However, by all accounts, such rules cannot explain why one lexical item should appear more frequently (or seem more natural) as a noun or as a verb. The grammar specifies that both options are available without specifying a preference. The same is true for the mass–count distinction. Given the capacity to produce novel mass and count nouns, the grammar must include rules that generate flexibility, while allowing for differences in the frequency of mass and count usage across items. In our discussions of noun–verb flexibility, we suggested that such differences in usage may stem, in part, from extra-grammatical factors. For example, some possible uses may be blocked by existing vocabulary items, as noted by Clark (1993). Other possible uses may be pre-empted by potentially ambiguous homophony (for discussion, see Bauer 1973; Clark 1982, 1993; Rainer 1988). Furthermore, Dressler and Ladanyi (2000) list a number of additional factors that likely contribute to restricting grammatical productivity, including pragmatic incompatibilities related to reference (Bauer 1983; Corbin 1997), pragmatic selfevidence (e.g. bearded man v. *eyed man), stylistic convention and various socio-linguistic considerations. In short, we believe that the use to which words are put, and the availability of contexts for their interpretation, goes beyond the types of generalizations that we discuss here, and probably beyond the scope of a theory of grammar. Before discussing some examples of our interpretation of the functional heads, we would like to clarify that we are not suggesting that the mass noun interpretation is conceptually more basic than the count noun interpretation. The functional interpretation of the count noun head simply represents a mapping involving two different denotations. It does not represent a derivation of count-like concepts from mass-like concepts. The relation between mass and count concepts is a separate matter altogether which has little to do with the syntactic representation of nominal categories and their interpretations.
Alan C. Bale and David Barner 243
a.
b.
[[the]] (X’) = sup(X’) = abc
[[the]] = sup
[[n,c]]( [[√rock]]) = IND (W) = X’
[[n,c]] = IND
[[√rock]] = W
[[the]](Y’) = sup(Y’) = nmo
[[ the]] = sup
[[n,c]]( [[√apple]]) = IND (Z) = Y’
[[n,c]] = IND
[[√apple]] = Z
Figure 8 The root Orock denotes the non-individuated semi-lattice W while the root Oapple denotes the non-individuated semi-lattice Z. The function IND in this context maps W to X# ¼ fa, b, c, ab, ac, bc, abcg which is an individuated semi-lattice. Also, the function IND in this context maps Z to Y’ ¼ fn, m, o, nm, no, mo, nmog which is also an individuated semi-lattice. (a) shows the compositional meaning of determiner phrase the rocks. (b) shows the compositional meaning of the determiner phrase the apples.
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For clarity, consider an example. Suppose we are in a room filled with rocks and apples. Suppose W is the denotation of the root Orock and that Z is the denotation of the root Oapple. Thus, W contains any aggregate that consists only of rock-stuff and Z contains any aggregate that consist of apple-stuff. We assume that both W and Z are nonindividuated semi-lattices. In this context, certain amounts of rock-stuff form objects (i.e. they form rocks). Let’s represent the set of these objects as X ¼ fa, b, cg. The sub-lattice that has these objects as atoms would be the set X# ¼ fa, b, c, ab, ac, bc, abcg. Also in this context, certain amounts of apple-stuff (arranged in the appropriate way according to how apples are individuated) form objects (i.e. they form apples). Let’s represent the set of these objects as Y ¼ fm, n, og. The sub-lattice that has these objects as atoms would be the set Y# ¼ fn, m, o, nm, no, mo, nmog. Given this context, the interpretation of the noun phrases the rocks and the apples will be as in Figure 8. The function IND maps W to a lattice that contains all of the rocks in the room as individuals while it maps Z to a lattice that contains all the apples in the room as individuals. The determiner the then selects the supremum of this lattice. The interpretation of the singular morpheme is not crucial to our account, since only mass nouns and plural count nouns can appear in comparative constructions of the kind under consideration. Still, for completeness, we provide an interpretation for the singular count noun head. Like Link (1983) and Chierchia (1998), we propose that singular
244 Interpretation of Functional Heads nouns denote only a set of individuals without any higher aggregates. To do this, we exploit the IND function as follows: Interpretation of the singular head: ½½n, c, sg ¼ kP (fx: x is an individual in IND(P)g) Thus, singular nouns have denotations that only contain the atoms of the count noun denotation.
5.3 An account of generalizations 1 and 2
5.3.1 Truth conditions for comparatives To account for the truth conditions of comparative sentences, we must first outline a plausible interpretation for such sentences. For simplicity, we assume that more is a determiner that takes sets as arguments. Also, we assume that more can syntactically combine with either count or mass noun phrases (although not with singular count nouns). Furthermore, we will ignore issues concerning ellipsis in than clauses (see Bresnan 1975; Hoeksema 1983; Kennedy 1999; Lechner 1999), as well as quantifier movement (see Larson 1988; Kennedy 1999; Hackl 2000; Heim 2000) and general concerns with respect to compositionality (see Cresswell 1976; Kennedy 1999; von Stechow 1984; Larson 1988). These issues are important and can be empirically addressed; however, we will focus on the semantics of the noun phrase rather than other aspects of comparative semantics. What we outline is not a compositional semantics for comparatives sentences, but rather the truth conditions that reflect speaker intuitions. To do so, we will take the sentence schema in (23) as our basic sentence structure. (23) Y has more NP than Z has. Whatever the correct syntactic and compositional structure is for sentences that follow the schema in (23), we assume that the truth conditions are based upon a comparison of two sets: the set of things/ stuff that are in the denotation of the NP and that are possessed by Y compared to the set of things/stuff that are in the denotation of the NP that are possessed by Z. The interpretation of more specifies how these two sets are compared. Truth conditions for sentences that fit the schema in (23): ½½Y has more NP than Z does ¼ ½½more (fx: owns(½½Y, x) & ½½NP (x)g, fx: owns(½½Z, x) & ½½NP (x)g)
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In this section, we describe how our proposal explains the comparative data (Section 5.3.1), and thus how it explains the two generalizations in Section 4 (Section 5.3.2).
Alan C. Bale and David Barner 245
Interpretation of the determiner ‘more’: ½½more ¼ kX kY [l(X,Y)] Contextual conditioning of measure function l: l is interpreted as one of the set-comparison functions mz in the series Æm1, m2, m3, m4. . .mnæ such that the argument for l is in the range of mz. Furthermore, contextually mz is preferred to my if z < y. We make the comparison with more context dependent since the comparison is different for different types of NPs. Comparison is based on number for furniture and apples, on weight or volume for water and mud and on emotional intensity for anger and fear. As the type of denotation for the NP changes, the set-comparison functions in l also change. For now, let’s concentrate on comparisons by number. We will specify this comparison function to be the first in the series. It is the default comparison. Definition of the measure function m1: m1 is defined only for sets of aggregates that are individuated semi-lattices. When defined, m1(X,Y) ¼ 1 iff X and Y are join semi-lattices and jfx: x is an individual in Xgj > jfy: y is an individual in Ygj. The function m1 compares the number of individuals in each semi-lattice, where individuals are defined as above. According to our definition of m1, if the first argument has more individuals than the second, then the comparative sentence is true. Otherwise the comparative sentence is false. Note that m1 might not be the only function that makes use of the set of individuals in a lattice. Interpretations for other quantifiers such as 18 For simplicity, we present a non-conservative semantics for more. However, conservativity can be maintained if more is viewed as a three-place quantifier with the entire domain covertly serving as the third argument. See Keenan and Westerstahl (1997) for arguments and a discussion. Alternatively, more could be viewed as a modifier of a covert adjective, in which case it would not be subject to conservativity.
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Note that the two arguments of more are subsets of the denotation of the NP. In fact, the arguments are themselves join semi-lattices. Possession is closed under sums (if Y owns x and Y owns z, then Y possesses x 4 z) and possession is closed under the lattice part-of relation (if Yowns x 2 ½½NP, then for any z < x such that z 2 ½½NP, Y owns z). It follows from these two facts that if the NP denotation is an individuated semi-lattice, then both arguments to more are also individuated semi-lattices. Similarly, if the NP denotation is a nonindividuated semi-lattice, then both arguments to more are also non-individuated. Such consequences are crucial for our account. Given that more takes two semi-lattices as arguments, we define its semantics as follows.18
246 Interpretation of Functional Heads two might also rely on defining a set of individuals. However, other quantifiers, such as all, do not require such a set. We give possible interpretations for such quantifiers below. ½½two ¼ kX kY(jfx: x is an individual in Xg \ Y)j > 2) ½½all ¼ kX kY(fz: z 2 X \ Covg 4 Y), where Cov is a contextually defined cover as discussed in Gillon (1992) and Schwarzschild (1996).
(24) a. Seymour has more apples than Esme has. b. Seymour has more apple than Esme has. c. Seymour has more furniture than Esme has. According to our semantics, the truth of (24a) and (24c) depends on a comparison of the number of individuals that Seymour and Esme each own. The truth conditions of (24a) are given in (25). (25) ½½more (fx: owns(½½Seymour, x) & ½½apples (x)g, fx: owns(½½Esme, x) & ½½apples (x)g) ¼ m1(fx: owns(½½Seymour, x) & ½½apples (x)g, fx: owns(½½Esme, x) & ½½apples (x)g) ¼ jfx: x is an individual in fx: owns(½½Seymour, x) & ½½apples (x)ggj > jfy: y is an individual in fx: owns(½½Esme, x) & ½½apples (x)ggj Since apples is a count-noun, its denotation must be an individuated semi-lattice (according to the function IND). As a result, the two sets that serve as arguments for more are also individuated semi-lattices. This
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According to our truth conditions, comparisons of number operate on lattice theoretically defined individuals in two given sets. This means that more can only compare by number if its NP argument is interpreted as an individuated semi-lattice. Non-individuated semi-lattices must use another type of comparison, such as a comparison by weight. We will forego the details of how such a comparison is done for now, but we will assume that the comparison function m2 makes such a comparison. This proposal for implementing truth conditions differs from the proposals advanced by Cresswell (1976), Klein (1981) and Hackl (2000). These authors either do not address the multiple ways of comparing nominals or their proposals are incompatible with the lattice-theoretical approach explored in this paper. Still, extensionally speaking, the truth conditions presented above overlap significantly (if not completely) with all of these previous proposals. Given the truth conditions established thus far, let us consider examples like those mentioned in Section 3.
Alan C. Bale and David Barner 247
means that the two sets can be compared via the function m1. The result is that the comparison is true if the number of apples that Seymour has is greater than the number that Esme has. A similar analysis can be given for the sentence in (24c). For example, consider the truth conditions in (26).
The only difference between (25) and (26) is that furniture is a mass noun. As a mass noun, it has the same denotation as the root lexical item Ofurniture. However, this lexical item has an individuated semilattice as its denotation, unlike Oapple. As a result, the sets compared by more are individuated semi-lattices and hence the truth of the sentence relies on comparing the number of pieces of furniture owned by Seymour to the number of pieces owned by Esme. The truth conditions change dramatically for sentences like the one in (24b). The truth conditions for (24b) are presented in (27). (27) ½½more (fx: owns(½½Seymour, x) & ½½apple (x)g, fx: owns(½½Esme, x) & ½½apple (x)g) ¼ m2(fx: owns(½½Seymour, x) & ½½apple (x)g, fx: owns(½½ Esme, x) & ½½ apple (x)g) Unlike in (24a), the NP complement of more is a mass noun. Unlike in (24c), the mass noun does not denote an individuated semi-lattice. If it did, then the root could not appear in a count noun phrase as it does in (24a). As a result, the two sets compared by more are non-individuated semi-lattices and cannot be compared by the function m1. The next applicable function in l must be used instead, such as the function m2, which computes a comparison by weight. In summary, by exploiting the various options given for the noun phrase semantics provided in Section 5.2, it is possible to explain the different types of judgments for comparative sentences involving bare NP arguments. 5.3.2 Two generalizations explained Given the interpretation of functional heads presented here, the two generalizations in Section 3 can be explained. In Generalization 2, we noted that some mass nouns
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(26) ½½more (fx: owns(½½Seymour, x) & ½½furniture (x)g, fx: owns(½½Esme , x) & ½½furniture(x)g) ¼ m1(fx: owns(½½Seymour, x) & ½½furniture (x)g, fx: owns(½½Esme, x) & ½½furniture (x)g) ¼jfx: x is an individual in fx: owns(½½Seymour, x)&½½furniture (x)ggj > jfy: y is an individual in fx: owns(½½Esme, x) & ½½furniture (x)ggj
248 Interpretation of Functional Heads
6 CONCLUDING REMARKS We presented data from comparative constructions to investigate the semantic interpretation of mass and count nouns. The purpose of this investigation was to explore, via the case study of the mass–count distinction, how lexical and syntactic representations interact in the generation of phrase-level interpretations. Based on the data generated by comparative constructions, we established two empirical generalizations. First, we noted that nouns which can occur in either mass or count syntax undergo a shift in the dimension of comparison according to the syntactic context in which they are used. When used as count nouns, nouns specify comparison by number. When used as mass nouns, the very same nouns do not permit comparison by number. Second, we noted that, like count nouns, some mass nouns also specify comparison by number. To capture these two generalizations, we hypothesized that root nouns are not specified as
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denote individuals while others do not. As demonstrated by our discussion of comparative constructions, denotations that contain individuals allow for assessments or measurements based on number, whereas denotations without individuals do not. Thus, according to our proposal, Generalization 2 follows from the fact that lexical roots can be mapped either to individuated lattices (as in the case of Ofurniture) or to non-individuated lattices (as in the case of Owater and Oapple). Since the mass noun functional head is interpreted as an identity function, the resulting interpretation of mass nouns can be either individuated or non-individuated. Generalization 1 states that any lexical item that can be used as a count noun cannot denote individuals when used as a mass noun. This follows from our interpretation of the count noun functional head. This functional head is interpreted as a function from nonindividuated lattices to individuated lattices. Thus, not only do all count nouns necessarily have individuals as part of their denotation but corresponding root lexical items cannot have individuals in their denotations. Since the interpretation of the mass noun is identical to the interpretation of the root lexical item, the mass noun counterpart to any count noun cannot have individuals as part of its denotation. A further consequence of this semantic interpretation is that lexical items that are interpreted as individuated semi-lattices such as Ofurniture and Oequipment can never appear as count nouns. This explains why *three furnitures and *three equipments are not acceptable count noun phrases.
Alan C. Bale and David Barner 249
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mass or count. We argued that nouns are formed by combining roots with functional heads, and that root nouns can be associated with denotations that either do or do not contain individuals as minimal parts. The interpretation of the count noun head maps denotations that do not contain individuals to denotations that do. In contrast, the mass noun head is interpreted as an identity function. Thus, if the root noun is mapped to a denotation with individuals, then the mass noun version of this root will also be mapped to such a denotation. Also, since the count noun head only ranges over root nouns that are not associated with individuals, it follows that such nouns should never denote individuals when used in mass syntax. We argued that existing theories have difficulty accounting for these facts because they fail to provide a grammatical account that explains the comparative data. Theories like Link’s (1983), which posit separate semantic domains for mass and count nouns, do not distinguish between the subtypes of mass nouns, and assign all mass nouns a common type of denotation. Other theories, like those of Bunt (1985), Gillon (1999) and Chierchia (1998), which appeal to context or world knowledge to explain the interpretation of mass nouns, fail to explain why denotations of noun phrases change as mass–count syntax varies, when the contextual setting is constant. The fact that some mass nouns do not denote individuals even when they are present in a context (e.g. stone) indicates that comparative judgments require a grammatical explanation, rather than one that appeals to context or world knowledge. Thus, theories that posit a uniform mass semantics and theories that posit nonlinguistic mechanisms for explaining their heterogeneity fail to account for the data presented here. These data require a theory that predicts heterogeneous mass noun interpretations and explains them via grammatical representations. The current paper provides one way in which these requirements might be fulfilled, and establishes the minimal requirements for future theories of the mass–count distinction. Beyond the facts described here, the current proposal also has significant implications for the study of noun semantics crosslinguistically. Many languages feature comparative constructions akin to those in English, and thus permit their use for assessing mass and count interpretations. Languages vary considerably with respect to the frequency with which words are used as mass or count (if at all), and also with respect to which words denote individuals as mass nouns. As a result, analysing comparative judgments cross-linguistically will provide the strongest test for the current proposal and for any future theory as well. Our view predicts that languages with a mass–count distinction will exhibit the same generalizations as in English, regardless
250 Interpretation of Functional Heads of item-by-item differences in how words are used. So long as a word can denote individuals as a mass noun, it should not appear also in count syntax. Also, there should be no distinction between the interpretations of root nouns and the interpretation of mass nouns. Thus, in languages that lack count syntax (e.g. Japanese, Chinese), nouns should be interpreted like mass nouns in English, and receive both individuated an unindividuated interpretations. Acknowledgements
ALAN C. BALE Concordia University, H663 1455 de Maisonneuve Boulvard, West Montre´al, QC (H3G 1M8) Canada e-mail:
[email protected]
DAVID BARNER Department of Psychology University of California, San Diego 5336 McGill Hall 9500 Gilman Drive La Jolla, CA 92093-010 e-mail:
[email protected]
REFERENCES Barner, D. & Bale, A. (2002), ‘No nouns, no verbs: psycholinguistic arguments in favor of lexical underspecification’. Lingua 112:771–91. Barner, D. & Bale, A. (2005), ‘No nouns, no verbs? Rejoinder to Panagiotidis’. Lingua 115:1169–79. Barner, D. & McKeown, R. (2005), ‘The syntactic encoding of individuation in language and language acquisition’. In A. Brugos, M. R. Clark-Cotton & S. Ha (eds.), BUCLD 28: Proceedings of the 28th Annual Boston University Conference on Language Development. Cascadilla. Somerville. 61–72. Barner, D. & Snedeker, J. (2005), ‘Quantity judgments and individuation: evidence that mass nouns count’. Cognition 97:41–66.
Barner, D. & Snedeker, J. (2006), ‘Children’s early understanding of masscount syntax: individuation, lexical content, and the number asymmetry hypothesis’. Language Learning and Development 2:163–94. Barner, D., Wagner, L. & Snedeker, J. (2008), ‘Events and the ontology of individuals: verbs as a source of individuating mass and count nouns’. Cognition 106:805–32. Bauer, L. (1973), English Word Formation. Cambridge University Press. Cambridge. Bloom, P. (1994), ‘Semantic competence as an explanation for some transitions in language development’. In Y. Levy (ed.), Other Children, Other Languages: Theoretical Issues in Language
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We would like to thank Brendan Gillon, Gennaro Chierchia, Jesse Snedeker, Kyle Johnson, Heather Newell, Dana Isac, Mark Hale, Charles Reiss, the Concordia LSA and an anonymous reviewer for helpful comments. This research would not have been possible without grants from the Social Sciences and Humanities Research Council of Canada, grant numbers 752-2001-1304 and 756-2006-0484.
Alan C. Bale and David Barner 251 Cresswell, M. (1976), ‘The semantics of degree’. In B. Partee (ed.), Montague Grammar. Academic Press. New York. 261–92. Dressler, W. U. & Ladanyi, M. (2000), ‘Productivity in word formation (WF): a morphological approach’. Acta Linguistica Hungarica 47:103–44. Gathercole, V. (1985), ‘More and more and more about more’. Journal of Experimental Child Psychology 40:73– 104. Gillon, B. (1992), ‘Towards a common semantics for English count and mass nouns’. Linguistics and Philosophy 15:597–640. Gillon, B. (1999), ‘The lexical semantics of English count and mass nouns’. In E. Viegas (ed.), The Breadth and Depth of Semantic Lexicons. Kluwer. Dordrecht. 19–37. Gillon, B., E. Kehayia & V. Taler (1999), ‘The mass count distinction: evidence from psycholinguistic performance’. Brain and Language 68:205–11. Gordon, P. (1985), ‘Evaluating the semantic categories hypothesis: the case of the mass/count distinction’. Cognition 20:209–42. Hackl, M. (2000), Comparative Quantifiers. Ph.D. thesis, MIT. Halle, K. & Marantz, A. (1993), ‘Distributed morphology and the pieces of inflection’. In S. J. Keyser & K. Hale (eds.), The View from Building 20. MIT Press. Cambridge. 111–76. Harley, H. & Noyer, R. (1999), ‘Licensing in the non-lexicalist lexicon: nominalization, roots and the encyclopedia’. MIT Working Papers in Linguistics 32:119–37. Heim, I. (2000), ‘Degree operators and scope’. In Proceedings of SALT X. CLC Publications. Cornell. 40–64. Hoeksema, J. (1983), ‘Negative polarity and the comparative’. Natural Language and Linguistic Theory 1:403–34.
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Development. Lawrence Erlbaum Associates, Inc. Hillsdale. 41–76. Bloom, P. (1999), ‘The role of semantics in solving the bootstrapping problem’. In R. Jackendoff, P. Bloom & K. Wynn (eds.), Language, Logic, and Concepts: Essays in Memory of John Macnamara. MIT Press. Cambridge. 285–310. Borer, H. (2005), Structuring Sense, Volume 1: In Name Only. Oxford University Press. Oxford. Bresnan, J. (1975), ‘Comparative deletion and constraints on transformations’. Linguistic Analysis 1:25–75. Bunt, H. C. (1979), ‘Ensembles and the formal semantics properties of mass terms’. In J. Pelletier (ed.), Mass Terms: Philosophical Problems. Synthese Language Library, 6. D. Reidel. Dordrecht. 249–77. Bunt, H. C. (1985), Mass Terms and Model-Theoretic Semantics. Cambridge University Press. New York. Chierchia, G. (1998), ‘Plurality of mass nouns and the notion of ‘semantic parameter’’. Events and Grammar 70:53–103. Chomsky, N. (1970), Remarks on nominalization. In R. Jacobs & P. Rosenbaum (eds.), Readings in English Transformational Grammar. Blaisdell Waltham. 184–221. Clark, E. V. (1982), ‘The young wordmaker: a case study of innovation in the child’s lexicon’. In E. Wanner & L. R. Gleitman (eds.), Language Acquisition: The State of the Art. Cambridge University Press. Cambridge. 390–425. Clark, E. V. (1993), The Lexicon in Acquisition. Cambridge University Press. Cambridge. Corbin, D. (1997), ‘Entre les mots possibles et les mots existants: les unite´s lexicales a` faible probablite´ d’actualisation’. In D. Corbin (ed.), Mots possibles et mots existants. Universite´ de Lille, Silexicales 1. 79–90.
252 Interpretation of Functional Heads Link, G. (1998), Algebraic Semantics in Language and Philosophy. Center for the Study of Language and Information. Stanford. Macnamara, J. (1986), A Border Dispute: The Place of Logic in Psychology. MIT Press. Cambridge. Marantz, A. (1997), ‘No escape from syntax: don’t try morphological analysis in the privacy of your own lexicon’. University of Pennsylvania Working Papers in Linguistics 4: 201–25. McCawley, J. D. (1979), ‘Lexicography and the count-mass distinction’. In J. D. McCawley (ed.), Adverbs, Vowels, and Other Objects of Wonder. University of Chicago Press. Chicago. 165– 73. Pesetsky, D. (1994), Zero Syntax: Experiencers and Cascades. MIT Press. Cambridge. Quine, W. V. O. (1960), Word and Object. MIT Press. Cambridge. Rainer, F. (1988), ‘Towards a theory of blocking’. In G. Booij & J. van Marle (eds.), Yearbook of Morphology. Kluwer. Dordrecht. 155–85. Sharvey, R. (1979), ‘The indeterminacy of mass predication’. In J. Pelletier (ed.), Mass Terms: Philosophical Problems. Synthese Language Library, 6. D. Reidel. Dordrecht. 47–54. Schwarzschild, R. (1996), Pluralities. Studies in the linguistics and philosophy 61. Kluwer. Dordrecht. von Stechow, A. (1984), ‘Comparing semantic theories of comparison’. Journal of Semantics 3:1–77. Wisniewski, E. J., Imai, M. & Casey, L. (1996), ‘On the equivalence of superordinate concepts’. Cognition 60:269– 98. First version received: 24.12.2007 Second version received: 07.09.2008 Accepted: 10.11.2008
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Jackendoff, R. (1991), ‘Parts and boundaries’. Cognition 41:9–45. Keenan, E. L. & Westerstahl, D. (1997), ‘Generalized quantifiers in linguistics and logic’. In J. van Benthem & A. ter Meulen (eds.), Handbook of Logic and Language. Elsevier. Amsterdam. 837–93. Kennedy, C. (1999), Projecting the Adjective: The Syntax and Semantics of Gradability and Comparison. Garland. New York. Klein, E. (1981), ‘The interpretation of adjectival, nominal, and adverbial comparatives’. In J. Groenendijk, T. Janssen & M. Stokhof (eds.), Formal Methods in the Study of Language. Mathematical Center Tracts. Amsterdam. 381–98. Krifka, M. (1995), ‘Common nouns: a contrastive analysis of Chinese and English’. In G. Carlson & F. Pelletier (eds.), The Generic Book. University of Chicago Press. Chicago. 398–411. Inagaki, S. & Barner, D. (2009). Countability in absence of count syntax: Evidence from Japanese quantity judgments. In M. Hirakawa, S. Inagaki, Y. Hirakawa, H. Sirai, S. Arita, H. Morikawa, M. Nakayama, & J. Tsubakita (eds.), Studies in Language Sciences (8): Papers from the Eighth Annual Conference of the Japanese Society for Language Sciences. Tokyo. Kurosio. Langendoen, T. (1978), ‘The logic of reciprocity’. Linguistic Inquiry 9:177–97. Larson, R. (1988), ‘Scope and comparatives’. Linguistics and Philosophy 11: 1–26. Lechner, W. (1999), Comparatives and DP-Structure. Ph.D. dissertation, University of Massachusetts, Amherst. Link, G. (1983), ‘The logical analysis of plurals and mass terms: a lattice-theoretical approach’. In R. Ba¨uerle, C. Schwarze & A. Stechow (eds.), Meaning, Use, and Interpretation of Language. de Gruyter. Berlin. 302–23.
Journal of Semantics 26: 253–315 doi:10.1093/jos/ffp006 Advance Access publication June 11, 2009
Proper Names and Indexicals Trigger Rigid Presuppositions EMAR MAIER Radboud University Nijmegen
I provide a novel semantic analysis of proper names and indexicals, combining insights from the competing traditions of referentialism, championed by Kripke and Kaplan, and descriptivism, introduced by Frege and Russell, and more recently resurrected by Geurts and Elbourne, among others. From the referentialist tradition, I borrow the proof that names and indexicals are not synonymous to any definite description but pick their referent from the context directly. From the descriptivist tradition, I take the observation that names, and to some extent indexicals, have uses that are best understood by analogy with anaphora and definite descriptions, that is, following Geurts, in terms of presupposition projection. The hybrid analysis that I propose is couched in Layered Discourse Representation Theory. Proper names and indexicals trigger presuppositions in a dedicated layer, which is semantically interpreted as providing a contextual anchor for the interpretation of the other layers. For the proper resolution of DRSs with layered presuppositions, I add two constraints to van der Sandt’s algorithm. The resulting proposal accounts for both the classic philosophical examples and the new linguistic data, preserving a unified account of the preferred rigid interpretation of both names and indexicals, while leaving room for non-referential readings under contextual pressure.
1 INTRODUCTION Since Kripke and Kaplan introduced rigid designation as an alternative to the Frege/Russell analysis of referential terms as definite descriptions, there has been an ongoing debate between ‘descriptivists’ and ‘referentialists’, mostly focusing on the semantics of proper names. Beside the observation that the denotations of names and indexicals appear to be unaffected by modal and other embeddings, the strongest argument for the referentialist account is the intuitive contrast between sentences like (1a) and (1b): (1)
a. Mary is called Mary b. The person called Mary is called Mary
The first expresses a contingent proposition. It ascribes to Mary the contingent property that she was given a particular name, while the The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email:
[email protected].
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Abstract
254 Proper Names and Indexicals Trigger Rigid Presuppositions second expresses the tautological proposition that someone who is called Mary is called Mary. Descriptivists analyse Mary as the person called Mary and therefore cannot account for the observed contrast. Nowadays, however, descriptivists can draw on a much richer set of linguistic data, including examples of bound (2a) and accommodated (2b) proper names and of bound (2c), shifted (2d) and deferred (2e) firstperson pronouns:
‘Johni says that hei is a hero’ [Amharic, Schlenker 2003] e. I am traditionally allowed to order whatever I like for my last meal [Nunberg 1993] All the above have been used to argue against a simple referentialist semantics. Moreover, non-referentialist accounts of these phenomena have been proposed with the help of modern semantic machinery such as E-type syntax/semantics, Discourse Representation Theory (DRT), presupposition-as-anaphora (PA), morphosyntactic feature deletion/ transmission and monstrous context shifting. In section 2, I review in some detail the history of the debate between descriptivists and referentialists, focusing in particular on the crucial judgments that constitute Kripke’s contrast in (1). In section 3, I sketch the current state of the debate about proper names, arguing that the ‘neo-descriptivist’ proposals of Elbourne and Geurts can handle (2a) and (2b), but fail with respect to (1). In section 4, I turn to indexicals, focusing on the first-person pronoun. I discuss apparently bound indexicals like (2c) and show how to analyse those in a purely referentialist framework. In section 5, I discuss further differences between indexicals and proper names and discuss two neo-descriptivist DRT proposals that attempt to deal with (1) or (2d) and conclude that neither analysis can achieve both. In section 6, I propose a novel approach, combining an essentially referentialist, two-dimensional semantics with modern insights from the side of the descriptivists in Layered Discourse Representation Theory (LDRT). Appendix A analyses deferred indexicals like (2e) in the new LDRT framework, and appendix B gives formal details of the LDRT semantics.
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(2) a. If a child is christened Bambi and Disney Inc. find out about it, they will sue Bambi’s parents [Geurts 1997] b. If presidents were elected by alphabetical order, Aaron Aardvark might have been president [Bach 1987] c. Only I did my homework [Heim 1991] d.
Emar Maier 255
2 FROM FREGE TO KRIPKE AND KAPLAN
2.1 Proper names: a historical overview Proper names (Mary, Amsterdam, . . .) are commonly regarded as purely referential devices, that is, their function was taken to designate a certain individual and that is all there is to their meaning. Puzzles about unknown, mistaken and missing reference, however, led Frege to his distinction between Sinn and Bedeutung. In addition to reference (Bedeutung), proper names also have a real meaning (Sinn), some kind of descriptive content that allows the hearer to determine a referent. Frege’s ideas are now commonly cast in a possible worlds framework where Bedeutung is called extension, the term is referent in the actual world, while Sinn is modelled as intension, a partial function from possible worlds to extensions at those worlds. In this set-up, even if a name happens to lack a bearer or one has false or incomplete beliefs about the bearer, it will still have a fully functional meaning, namely, the intension. A point of substantial disagreement between Frege and the various later versions of the descriptivist thesis lies in the exact descriptive content associated with a given name. These range from the fully personal, contextual, ‘hidden’ descriptions like ‘the bright heavenly body I always see in the evening’, to a mere ‘the object called Hesperus’. Following Frege’s thesis of intersubjectivity of Sinn, I opt for the latter
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My analysis is couched in a two-layered fragment of LDRT in which proper names and indexicals trigger presuppositions in a k(ripke/)k(aplan) layer and want to be resolved therein. In the output LDRS, this kk -layer is semantically interpreted as providing a contextual anchor for the interpretation of the fr (egean) layer for descriptive content. The distributional differences between names and (pronominal) indexicals are partly explained by pragmatic blocking effects (in section 4). The remaining differences are adequately captured by assuming that the constraint of layer-faithful resolution is ranked much higher for indexicals than for proper names. Proper names, but not indexicals, can occasionally hop from kk to fr under severe contextual pressure, resulting in descriptive binding (2a) or accommodation (2b). The proposed hybrid analysis is thus shown to account for both the classic philosophical examples and the new linguistic data in a principled fashion, preserving a unified account of the preferred rigid interpretation of both names and indexicals, while leaving some room for variation with respect to non-referential readings.
256 Proper Names and Indexicals Trigger Rigid Presuppositions
(3) Some people think that Mary is called Martha The sentence says that the actual Mary is mistakenly represented in some people’s minds as bearing the name ‘Martha’. In formal semantic terms, the predicate called Martha is evaluated with respect to other people’s belief worlds (denoting the sets of people bearing the name Martha in those worlds), while the name Mary is interpreted with respect to the actual world (denoting the individual actually called thus). Henceforth, I will use the term immunity to embedding for this behaviour of referential terms. Kripke accounts for the felicity of (3) by analysing names as simple constants whose interpretation at any possible world of evaluation is the same, namely, the actual Mary, so that what is believed in (3) is that this individual has a certain property. Replacing Mary with the description the person called Mary would amount to ascribing people contradictory belief, unless we assume a mechanism by which such descriptions take widest possible scope: (4) There is a unique individual called Mary and some people think that she is called Martha In addition to being ad hoc and breaking compositionality (or positing an unmotivated kind of syntactic movement that takes Mary out of the complement clause and the quantifier), a wide scope 1 Nothing hinges on this particular description. The reader is free to interpret the proper name condition whichever way she likes, mutatis mutandis.
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and, for convenience, associate with every name a condition like ‘john(x)’ meaning ‘x is called John’.1 The 1970s saw a revival of the more basic analysis of proper names as simply referential. This is due in great part to Kripke’s (1972) famous argumentation against descriptivism, in favour of an enhanced account of names as directly referential devices. Kripke convincingly argues that names lack descriptive content and instead analyses names within a possible worlds framework as rigid designators, that is, as constants with a trivial, constant intension that has them refer to the same individual at all possible worlds. Thus, a proper name’s meaning and reference once again coincide. The main motivation lies in the observation that proper names differ from definite descriptions in the fact that the denotations of the former but not the latter are unaffected by embedding under (modal) operators. Take (3), where a name is embedded under a quantifier and a belief attribution.
Emar Maier 257
stipulation will not help against Kripke’s next argument, which involves a minimal pair of sentences without operators to take scope over: (5)
a. Mary is called Mary b. The person called Mary is called Mary
2
Formal definitions of tautology and contingency can be found at the end of section 2.2. As both sentences are grammatical and true, we might say that the contrast cannot belong to syntax or semantics and therefore must belong to pragmatics, but that is merely a matter of terminology. Readers who want to draw such a strict line between semantics and pragmatics may substitute ‘semantics/pragmatics’ or even ‘pragmasemantics’ for my use of the term ‘semantics’. 3
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Both are well-formed and true, though perhaps a little strange on account of their meager if not trivial informational content. Despite these semantic similarities, I claim, following Kripke, that there is a genuine semantic contrast between them. This difference lies in the modal status of the propositions expressed by the examples. In the case of (5a), where the subject is a proper name, the proposition expressed is contingently true. It is true in some worlds, including the actual one, but false in others, for instance the rather close world where Mary’s parents decide, at the last moment, that ‘Martha’ is a better name for the baby than their original idea ‘Mary’. In yet other worlds where Mary was never even born, we may assume that (5a) has no truth value. Now consider (5b) in which the proper name has been replaced by the corresponding description. On one salient reading at least, this variant expresses an analytic, tautological2 truth on a par with bachelors are unmarried or Mary ¼ Mary. What (5b) says, on this reading, is that the most salient individual with the name ‘Mary’, whoever it is, has the name ‘Mary’. This proposition is never false (though perhaps it lacks a truth value in some worlds where there is nobody with that name). It has been suggested that this type of ‘metaphysical’ judgment does not constitute bona fide semantic data. I take a Kripkean standpoint in assuming that a semanticist can and should consider intuitions beyond mere truth value judgments. In my mind, the contrast between (5a) and (5b) is as hard as some truth value judgments.3 I assume, with Kripke, that the judgment whether or not a sentence in a given context expresses a contingent proposition is derived from the ability to grasp propositions and evaluate those in different possible worlds. To elicit a judgment of contingency for (5a), we would (i) present an utterance of it to an informant, with whom we share acquaintance with a salient individual named Mary, (ii) ask her to determine what it means and (iii) ask if she can imagine possible circumstances in which what it means is false.
258 Proper Names and Indexicals Trigger Rigid Presuppositions
2.2 Indexicals Kaplan (1989) extends Kripke’s analysis to indexicals, which are similarly immune to all types of embedding: (6) It was so noisy that some people might have thought that I was not speaking at all The embedded I refers to the actual speaker/writer, me, Emar, not some possible speaking entity in a person’s belief worlds. If I simply referred to the speaker of the world of evaluation, this sentence would require possible worlds where a speaker is not speaking. One difference between names and indexicals is that indexicals do have a clear linguistic meaning other than mere reference. I, for instance, means something like ‘the speaker of the current utterance’. In fact, the extra-linguistic ‘reference-fixing’ that ties a name to its bearer (by a ‘baptism’) in the case of a proper name is taken care of by this lexically encoded meaning in the case of an indexical. The combination of meaningfulness and immunity to embedding naturally leads to a wide scope descriptivist analysis. However, the Kripkean knock-down argument against descriptivism for proper names applies here as well: (7) a. I am speaking b. The current speaker is speaking
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Put a little differently, the intuitive contingency of (5a) corresponds to the idea that bearing a certain name is only an accidental property of an individual. The individual referred to in (5a) may in fact have a scar on her left arm and bear the name ‘Mary’, but we can easily imagine her without the scar and with a different name. Note that we are not considering evaluating different possible utterances of (5a) in different worlds. It is hard to imagine a false utterance of (5a), the closest we can get is when uttered in a context where there is no (salient) Mary, in which case the sentence lacks a truth value altogether. Instead, we consider an actual, felicitous, utterance of (5a), then determine what it says, that is, what proposition it expresses, and finally evaluate that in different possible worlds. To finish Kripke’s argument: An analysis treating the name in (5a) as rigidly designating the actual Mary and the description in (5b) as an intensional object gets all these judgments right. The descriptivist on the other hand would predict the sentences to be completely equivalent. In this respect, referentialism beats the classic varieties of descriptivism. In what follows, I will use the contrast in (5) as a test for various modern descriptivist proposals.
Emar Maier 259
(8) ½½I : C / [W / D]; ½½I(c)(w) ¼ the speaker of c The predicate am speaking on the other hand denotes the same intension in every context: (9) ½½am speaking : C / [W / §(D)]; ½½am speaking(c)(w) ¼ the set of people that are speaking in w The character of the sentence I am speaking (¼(7a)) is then constructed from the characters of its constituents (8) and (9) as follows:
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These sentences exhibit the same contrast as (5): though neither is particularly informative, and both are true whenever uttered, (7a) is but contingently true (I might have remained silent) while (7b) (has a reading that) expresses a tautology. We conclude that I is not synonymous with a definite description, that is, does not have intensional content. Since indexicals do refer, this reference must be rigid, which immediately explains the immunity to embedding witnessed in (6). To account also for the obvious context dependence (your utterance of I does not denote the same individual as mine) and linguistic meaning (the use of I is governed by a lexical rule that states that it always refers to the speaker of the current utterance), Kaplan devises a two-dimensional semantics in which linguistic meaning is formalized as character, functions from contexts to intensions, which in turn are functions from worlds to extensions. In every context of utterance, I rigidly refers to the speaker of that context. If we now stipulate that linguistic operators are only sensitive to intensional content (Prohibition of Monsters), we can unite immunity to embedding with context dependence and lexical meaning. The formal system proposed by Kaplan, moreover, follows the interpretation process for deriving metaphysical judgments of necessity or contingency in addition to mere truth values. The new semantic notion in Kaplan’s logic is the character of an expression, meant to model its linguistic meaning, among other things. Formally, the character of an expression is a function from contexts to intensions, which in turn are functions from worlds to extensions. The characters of basic expressions are given by the lexicon, and the characters of complex expressions are compositionally derived from the characters of the constituents. For instance, we can capture the meaning of I as a rigid designator, denoting the speaker (2 D) of the context of utterance (c 2 C) in all possible worlds of evaluation (w 2 W):
260 Proper Names and Indexicals Trigger Rigid Presuppositions (10) ½½I am speaking : C/½W/f0; 1g; ½½I am speaking(c) (w) ¼ In the intuitive interpretation process sketched in section 2.1 above, we determined the proposition expressed by a particular utterance on the basis of its conventional, linguistic meaning. Formally, an utterance is a sentence uttered in a particular context, and a proposition expressed by a sentence in a context is its intension, that is, a (partial) function from worlds to truth values: The formal notions of contingency and tautology are defined as properties of a proposition. We say that the proposition expressed by u in c is contingent if it maps at least one world to 0 and one to 1. A proposition is a tautology if it maps no world to 0. Finally, we define the notion of a truth value of an utterance of u in c with respect to a possible world: (12) ½½ucw ¼ ½½uc ðwÞ Note that when eliciting truth value judgments, we are asking about the actual truth value of an utterance, which we define as ½½ucwc , the value of the proposition evaluated in the world of the context, wc. Applied to the crucial test examples, the proposition expressed by (7a) as uttered by me, that is, in a context c where I, Emar, am the speaker, is the function that maps any world w in which I exist and am speaking to 1, any possible world in which I exist but am silent to 0, and is undefined in any world in which I do not exist. Thus, Kaplan’s formal system models the intuition that (7a) expresses a contingent proposition. By contrast, the proposition expressed by (7b) in c maps any world w whose speaker is speaking to 1 and is undefined for any world in which there is no speaker, which makes it a tautology. We return to indexicals in section 4, but first we take a closer look at names. 3 NAMES AND OTHER DEFINITES The direct reference paradigm of Kripke and Kaplan seemed theoretically and empirically superior to the descriptivist alternatives of the time. However, new data and new insight in the semantics of definites and pronouns slowly led to interesting new descriptivist
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(11) ½½uc ¼ ½½uðcÞ : W/f0; 1g
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(13) I have a poodle named Horace. fHorace/Sheg is five years old [Geurts 1997] Note already that the analogy between names and pronouns is not perfect. For one, the distribution of proper names is generally more restricted. Once an individual is firmly established in the common ground, pronouns are usually the preferred way to pick it up.4 This might be explained as an effect of some ‘referential hierarchy’ (Prince 1981; Zeevat 1999), which in effect rules out a proper name when a pronoun would have been felicitous: (14) Mary thought fshe/*Maryg was safe We’ll return to this observation in section 4 to explain some of the distributional differences between names and indexical pronouns. Now back to the similarities, an important characteristic names share with pronouns is that they generally do not contribute to the truth-conditional content, the proposition expressed. We saw that the referentialists took this property as the starting point for their semantics of names, but now consider pronouns. Since bound pronouns are represented as bound variables and bound variables contribute nothing but their assigned referent to the truth conditions, this rigidity falls out automatically for this class. But how about non-c-commanded pronouns such as the one in (13) or in donkey sentences? (15) Every man who owns a donkey beats it 4 There are of course also cases where proper names are preferred, for instance when there are several possible antecedents equally salient and with the same gender and person features.
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proposals. In this section, we take a look at two accounts of proper names that take their cue from the similarities between names and third-person pronouns. Though this by itself does not put them in the descriptivist camp, it does constitute a move away from the direct reference paradigm in which they play fundamentally different roles: names refer to objects and (anaphoric) pronouns are bound variables. I argue that these two recent pronoun-based semantic analyses are truly descriptivist. Sommers (1982) was the first to note that, just like third-person pronouns, names tend to pick up their referent from the common ground, established by previous discourse or otherwise. It is hard to imagine that I go up to a stranger talking about ‘Horace’ or ‘she’ without prior introduction or pointing. First I need to introduce a particular individual in the conversation, after that I can use the name or a pronoun, as in the following mini-discourse:
262 Proper Names and Indexicals Trigger Rigid Presuppositions Here it depends on your semantic framework: in dynamic semantics this discourse binding is treated as variable binding as well, so the same idea would apply. In a more traditional static framework, these pronouns are sometimes referred to as ‘E-type’ which means they are analysed as hidden descriptions. Interestingly, the two different approaches to donkey pronouns have led to two distinct unified semantic theories of various definites (indexical, anaphoric and E-type pronouns, as well as definite descriptions and names) based on Sommers’ analogy between pronouns and names. I argue that both analyses fail to explain the contrast in (5), henceforth referred to as the Kripke test.
Elbourne (2006) provides a unified analysis of third-person pronouns, definite descriptions and proper names, in effect treating them all as descriptions. He starts from the well-known analysis of donkey pronouns as hidden descriptions, analysing the it in (15) as the donkey. With the help of a fine-grained situation semantics, this picks out exactly those donkeys made available by the restrictor of the quantifier, without letting go of the notion of binding as requiring c-command. Elbourne’s particular brand of E-type semantics holds that (i) a donkey pronoun has the syntax and semantics of the determiner the, and (ii) it is followed by a phonologically deleted NP at LF. The LF of (15) thus ends in . . . beats [it donkey], meaning . . .beats the donkey. To unify donkey pronouns with regular bound pronouns and overt definite descriptions, Elbourne adds indices. Numerical indices on hidden or overt descriptions at LF indicate whether they are bound (i > 0, coindexed), E-type (i ¼ 0) or referential (i > 0, free):5 (16) it,[it donkey]i,
[note: ½½it¼½½the]
lf: But what about proper names? Like pronouns and overt definite descriptions they are definite NPs and they occasionally exhibit donkey binding: (17) a. If a child is christened Bambi and Disney Inc. find out about it, they will sue Bambi’s parents [Geurts 1997] 5 I use the label ‘lf ’ to refer to a representation of the truth conditions of a sentence in some (firstorder) logic. LF denotes a purely syntactic representation of a sentence.
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3.1 Names as E-type pronouns
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b. Every woman who has a husband called John and a lover called Gerontius takes only Gerontius to the Rare Names Convention [Elbourne 2006]
(18) a. it , [it donkey]i b. the woman , [the woman]i c. Mary , [the Mary]i , [note: ½½Mary¼kx[mary(x)]]
We get the correct reading for the examples in (9), (15) and (17) if the bound pronouns and names bear the ‘E-type index’ 0. Syntactically bound pronouns are also taken care of, through co-indexing. The referential cases are supposedly handled by free indices. Elbourne does not talk much about referential pronouns (like I), and I will postpone my discussion to section 4, but for proper names he does claim a free index will indeed ensure rigidity. Let us apply our litmus test: can he account for Kripke’s contrast between Mary and the person called Mary? Following (18) we will see that the E-type analysis correctly assigns a necessary proposition to (5b) (by choosing index 0). However, his analysis does not produce the right reading for (5a): (19) Mary is called Mary [(5a)] LF: [the Mary]1 is called Mary lf: mary(1x[mary(x) ^ x ¼ x1]) ½½(19)wg ¼ 1 iff g(x1) defined and g(x1) is called Mary in w Under what conditions would this sentence be false? In order for it to have any truth value in w, the description must be defined, that is, there must be one (unique or most salient) x fulfilling its condition, which means g(x1) must be called Mary. But then that would immediately make it true, so the 6 The first occurrence in both examples is merely mentioned, even though it is not overtly marked as such (by quotation marks or the like).
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This is a crucial new piece of empirical evidence against Kripkean referentialism, for it shows a proper name (the second occurrence of Bambi/Gerontius)6 not used to refer to an individual in the actual world or even in the common ground representation thereof. It is further evidence for Sommers’ analogy between pronouns and names, for it shows that names, like pronouns (and definite descriptions), have referential as well as (donkey-) bound uses. Elbourne takes the bound proper name data as evidence for his unification of definites, which may be summarized thus:
264 Proper Names and Indexicals Trigger Rigid Presuppositions
(20) If presidents were elected by alphabetical order, Aaron Aardvark might have been president [Bach 1987] The name Aaron Aardvark here is probably not intended to refer to a particular entity already established in the common ground. Moreover, the descriptive content of the proper name (having that name) plays a crucial role in determining the proposition expressed: that the mere property of having that name might land you the presidency. This is not too different from the bound Bambi and Gerontius examples in which the name itself played a special, metalinguistic role, yet here there is no available antecedent to bind to. It seems as though we are forced to create such an antecedent on the basis of the surrounding discourse context and world knowledge. In this case, it is not hard to infer that in the hypothetical world with alphabetical elections there might be someone called Aaron Aardvark and if so, he might have been president. We have, so to speak, accommodated the descriptive content of the name in the antecedent of the counterfactual. 7 Note that, although names are not easily bound syntactically, pronouns are, so we cannot give up the second logical representation in light of the claimed unification. Furthermore, we cannot get rid of the third form by building rigidity into the semantics of name predicates because E-type uses like (17a) really require a descriptive interpretation of the predicate. Besides, definite descriptions are known to have rigid uses as well (Donnellan 1966), so we need a dthat for those anyway.
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sentence is predicted always to be either true or undefined, but never false. In reality, there are plenty of worlds where Mary (g(x1)) was given a different name and in which the sentence should come out false. The reason why the E-type analysis fails is that even with the addition of free indices the descriptive content associated with the proper name still enters the truth conditions, thus trivializing them. Diagnosed thus, a solution presents itself: in addition to the free index we must ‘rigidify’ the content of the proper name. As it happens, rigidification is standardly implemented in Kaplan’s two-dimensional semantics by means of a so-called ‘dthat’ operator that turns world evaluation into context evaluation: for any expression e, ½½dthatecw ¼ ½½ecwc . However, such a drastic measure defeats Elbourne’s purpose: a unified treatment of names and pronouns as definite descriptions. The equally unappetizing alternative is that all definites are three ways ambiguous, that is, we have three distinct uses each requiring a distinct logical representation: we have E-type uses (1x[mary(x)]), bound uses (1x[mary(x) ^ x ¼ xi]) and rigid uses (dthat1x[mary(x)]).7 In order to set the stage for the rival dynamic approaches below let me mention another objection, concerning accommodation. In his refutation of referentialism, Geurts (1997) cites the following as an example of a proper name neither directly referential nor bound:
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Elbourne cites another example, requiring a similar kind of accommodation: (21) John has four sons: Primus, Secundus, Tertius and Quartus. If he has a fifth, I’m sure Quintus will be bullied [Heim p.c. to Elbourne]
3.2 Names as presupposition triggers Dynamic semantics and presupposition theory have given rise to a fruitful analysis of proper names as presupposition inducers, on a par with other definites. In this section, we will see how far this can take us. Geurts’ (1997) neo-descriptivist semantics of proper names is couched in Kamp’s (1981) DRT with van der Sandt’s (1992) PA. Like Elbourne, Geurts follows Sommers’ idea that names behave rather like pronouns to arrive at a unification of names, definite descriptions and pronouns, but now all as presupposition triggers (in the sense of van der Sandt). By way of illustration of the framework and the theory, imagine a discourse context where a man and his poodle have been introduced. This is represented in DRT as follows: (22) John has a poodle named Horace
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Again, there really is no Quintus, but from the discourse and some background knowledge of Latin we can infer that the hypothetical fifth son will probably be named Quintus, thus creating a proper antecedent for the name to refer back to. Terminology is a bit murky here: we might say that the descriptive content of the name Quintus is accommodated in the antecedent of the conditional, but we could just as easily maintain that Quintus is (donkey-)bound to the hypothetical son with the socalled bridging inference that John’s fifth son would be named so. In any case, to turn this somewhat vague meta-semantic story into a real account, we need a framework that can deal with context change more naturally. This is where dynamic semantics and presupposition theory come in. In the next section, we will see how Geurts and others account for binding, as in (17), and accommodation, as in (20), in a principled and unified fashion.
266 Proper Names and Indexicals Trigger Rigid Presuppositions The DRS in (22) forms the input context for the interpretation of the rest of the discourse. A sentence is given a preliminary representation (PrelDRS) where the contribution of pronouns and other definites is marked as presuppositional. The next step is to merge input context and sentence representation and resolve the presuppositions of the latter, that is, try to bind presupposed discourse referents to already established ones by matching the associated contents: (23) Horace is three years old
(24) If a child is christened Bambi and Disney Inc. find out about it, they will sue Bambi’s parents
Whenever binding fails, PA predicts that we fall back on accommodation, that is, the creation of a suitable antecedent by simply
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The usual projection behaviour for presuppositions, as captured by PA, correctly predicts the Bambi reading:
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dropping the presupposed referent and content at a suitable position in the DRS. This accounts for the Aardvark example:8 (25) If presidents were elected by alphabetical order, Aaron Aardvark might have been president
8
PA in fact predicts a preference for global accommodation. In this particular example, that reading is contextually overruled as it is considerably less coherent than the intermediate accommodation reading depicted here.
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The benefits of this dynamic framework over static versions of descriptivism are threefold. (i) A big advantage over the static E-type analysis is the unified analysis of syntactic and donkey binding as simply variable binding (brought about by presupposition binding). This is the hallmark of dynamic semantics in general. The other advantages relate to the DRT + PA framework in particular. (ii) We derive the wide scope behaviour of names from the general pragmatic mechanisms of presupposition projection, fully worked out in the independently motivated theory of PA. Moreover, this is achieved without a need for ambiguities and with fully compositionally generated PrelDRSs. (iii) A final advantage is the sound and fully integrated treatment of accommodation in DRT + PA. As I mentioned already at the end of section 3.1, such an account is crucial for understanding (20) (¼(25)) and (21), but tends to be relegated to informal meta-semantics in other (static and dynamic) frameworks. It is precisely for these three reasons that my own account will be cast in a dynamic DRT + PA-based framework. My reasons for going beyond Geurts’ elegant proposal and adopting LDRT have to do with Geurts’ inability to deal with another big class of rigid designators, indexical pronouns, to be discussed in the next sections, and its failure to pass the Kripke test, the demonstration of which will take up the rest of this section. The Kripke test, as wielded against Elbourne’s E-type account, compares the truth-conditional/propositional contents expressed by two sentences. But in DRT, sentences, represented as PrelDRSs, do not express classical propositions at all, so, in its original form, the Kripke
268 Proper Names and Indexicals Trigger Rigid Presuppositions
(26) fMary/the person called Maryg is called Mary
[cf. (5)]
Since sentences with the same PrelDRS have the same context change potential and hence express the same dynamic meaning, Geurts cannot account for the Kripkean intuition that there is a semantic contrast in (5). The other way of adapting the Kripke test to DRT is by focusing on output DRSs. Unlike PrelDRSs, input and output DRSs have a static interpretation in possible worlds semantics. DRSs so interpreted are no more than notational variants of predicate logical formulas. So let us compare the output DRSs that we get from interpreting the test sentences with respect to the same input context. As we saw above, both sentences get assigned the same PrelDRS, represented in (26). Adding (26) to a context where a salient individual named Mary exists will have no truth-conditional impact at all, while adding it to a context without a Mary will lead to interpretation failure or, depending
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test does not apply. Still, intuitively Geurts’ account is a direct implementation of the wide scope descriptivist reduction of Mary to the person called Mary and as such fails to do justice to Kripke’s contrast. In principle, there are two ways to go about translating the Kripke test to the dynamic setting: we can compare the dynamic meanings assigned to the sentences and argue that they are unfit to capture the observed contrast, or we can look at the static meanings of output DRSs associated with the interpretation of the two sentences. To start with the first, the dynamic meaning of a sentence is given by its context change potential. In non-representational dynamic frameworks, sentences directly encode such a context change potential, formalized as a relation between contexts. In DRT, we have an intermediate representational level: a sentence is mapped onto PrelDRS which can be interpreted as encoding both restrictions on input DRSs and transformations from suitable inputs to output DRSs, reflecting the utterance’s presuppositions and contribution of information to the common ground, respectively. The subject terms in the Kripke test examples are both definites and therefore, on Geurts’ analysis, both analysed as presupposition triggers. Moreover, both terms trigger the same presuppositions, so the PrelDRSs for (5a) and (5b) are exactly the same:
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4 BINDING AN INDEXICAL We have seen how examples of non-referential proper names have been used in an attempt to reinstate a descriptivist analysis of these expressions and how eventually the subtle Kripke test proved too much for the neo-descriptivist proposals. However, Kripke’s direct reference approach cannot deal with the neo-descriptivists’ new data, so it is really a draw. In this section, we turn to indexicals to see if similar non-referential data exist. I discuss and refute a number of claims to the effect that Kaplan is wrong because first-person pronouns have bound uses, just like third-person pronouns. I explain part of the apparent distributional differences between names and indexicals by means of a pragmatic blocking mechanism.
4.1 Where to find a non-referential indexical? We are looking for bound indexicals, that is, either syntactic or donkey-bound examples. Unlike with proper names (27a), syntactic binding seems already quite easy because there is no Condition C or hierarchy favouring third-person forms over indexical first or second, as witness (27b): (27) a. Johni did f*Johni’s/hisig homework b. Ii did fmyi/*hisig homework However, there is no direct9 way of telling whether the possessive in (27) really is interpreted as a bound variable or simply as a coreferential 9 I discuss the syntactician’s way of teasing the two apart by studying sloppy readings in elliptical continuations in section 4.2 below.
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on the rest of the context, accommodation of this individual. In either case, contrary to Kripkean intuitions there is no distinction between the name and the corresponding definite description in static output truth conditions. To sum up: On Geurts’ analysis there is no semantic difference between the two test sentences, neither in dynamic sentence meaning, nor in admissible inputs, nor in static output truth conditions. I conclude that Geurts’ unified analysis of names and other definites as presupposition triggers, though superior to Elbourne’s with respect to accommodation and with respect to the unification of E-type and syntactic binding, still fails the Kripke test and therefore falls short of the mark.
270 Proper Names and Indexicals Trigger Rigid Presuppositions indexical: there is only one me, so both first-person indexicals could be referring to it independently. So, we should look for embedded cases where rigid reference and binding diverge. Outside the person domain, such cases have indeed been identified:
In these cases, there is an embedded indexical referring not to the actual speech context, but to a hypothetical/quantified situation introduced earlier in the sentence. We have here the analogues of the Bambi/Gerontius construction of section 3. However, I submit that (28) shows only that actual and here are not really (or not unambiguously) indexical. A very plausible explanation would be that they are simply anaphoric expressions that seek to be bound by the most salient possible world and place, respectively. This would put actual and here in the same category as there and that, which are commonly taken to have a ‘discourse deictic’ (i.e. anaphoric, nonreferential) use, perhaps in addition to a genuine indexical one. In any case, the one proven, unambiguous indexical we have been discussing in section 2.2, I, does not allow this kind of binding, as becomes apparent when we try to construct a Bambi case, (29a), or a quantifier binding (29b): (29) a. If a studenti is speaking, I*i am nervous b. Every speakeri has difficulty stopping when I*i should [Partee 1989] Or consider the following minimal pair, in which the speaker of this utterance picks out a counterfactual speaker while me picks out the actual speaker: (30) If you had been fthe speaker of this utterance/meg, everybody would have listened attentively Examples like (29) and (30) in addition to Kaplan’s modal embeddings exemplified in (6), p. 6, strongly suggest that I cannot pick out a hypothetical speaker distinct from the real one. Nonetheless, a little further digging (in the literature) reveals some candidates: (i) sloppily
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(28) a. If you had written some novels and people had rumoured that you hadn’t written any of the novels you actually had written you would be upset [Kratzer p.c. to Cresswell 1990: 44] b. If someone otheri than George Bush had won the election, the actual winneri would have been happy [Hunter & Asher 2005] c. Every time I take him to a new restauranti, he says he’s been [Hunter & Asher 2005] herei before
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bound my under only and in ellipsis (section 4.2.1), (ii) first-person de se belief reports (section 4.2.2) and (iii) shifted first-person indexicals (section 4.4). In section 4.3, I argue that (i) and (ii) provide insufficient basis for discarding Kaplan’s theory, by proposing alternative analyses that do not violate direct reference. The data to be presented in section 4.4 finally are not so easily accommodated in a strictly Kaplanian framework.
4.2 Heim’s bound I’s
4.2.1 Sloppy I under only and ellipsis The first, convincing description of a non-referential first-person pronoun in English is Partee’s (1989): (31) I’m the only one around here who will admit that I could be wrong [Partee 1989] Perhaps, the most plausible reading is the one in which I am the only one allowing for the possibility of being wrong. This is called the sloppy reading. The strict reading, by contrast, is the one in which I am the only one willing to admit that Emar could be wrong. The strict reading is readily accounted for in a Kripkean setting, but the sloppy one appears to be problematic because the I who is or is not doing the admitting is not the actual speaker, but rather ranges over everybody in the domain. Based on this observation Heim (1991) initiates the attack on Kaplan: [. . .] Kaplan’s analysis implies that when there are several occurrences of I (or its case forms me, my) in a sentence, each of them refers to the speaker. This is not true, 1st person pronouns are in fact just like 3rd person pronouns in that they can be interpreted as bound variables rather than referring terms [. . .] [Heim 1991]10
10 Note the parallel with Sommers’ (1982) likening names to third-person pronouns, and the subsequent neo-descriptivist developments of this idea in the previous section.
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Recently, the view that even the prototypical indexical, English I, has non-referential uses has been gaining attraction, as witness the influential recent work of Heim (2005) and Kratzer (1998, 2009), among others. These authors claim that first-person pronouns have bound variable uses, just like third-person pronouns. In section 4.2.1, I discuss the primary data and argumentation in favour of such bound or ‘fake indexical’ Is, which can be traced back to Heim’s (1991). In section 4.3, I will provide alternative referential analyses of these data.
272 Proper Names and Indexicals Trigger Rigid Presuppositions To bring out bound readings of indexical pronouns, Heim turns to sloppy readings: (32) a. I did my homework, but my classmates didn’t b. Only I did my homework [Heim 1991]
(33) a. [I did my homework] but [not [my classmates did my homework]] [strict] b. [I kx[x did x’s homework] but [not [my classmates kx[x did x’s homework]]] [sloppy] The same analysis explains the ambiguity with only (and other focus constructions): (34) a. [only I]kx[x did my homework] b. [only I]kx[x did x’s homework]
[strict] [sloppy]
But under what conditions can we get bound variable interpretations of my in (32b)? According to Heim, the possessive my can be bound under feature agreement: the features of possessive in (32) agree with those of the quantifier [only I] and therefore may be deleted at LF. Kratzer (1998, 2009) turns it around: the possessive is born and semantically interpreted as a ‘minimal’ (¼featureless) pronoun that gets its features during phonological spell out by rules of feature transmission. In either case, in the sloppy reading of (32b) the visible firstperson feature has become a purely morphosyntactic feature, not semantically interpreted. 4.2.2 First-person de re and de se belief reports The next argument against rigid I involves first-person belief reports in Kaplan’s mistaken self-identity scenario: Kaplan is thinking about the time he saw a guy on TV whose pants were on fire without him noticing it (yet). A second later he realized he was watching himself through the surveillance camera system and it was his own pants that were on fire. He reminisces: (35) I thought I was at a safe distance from the fire
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Assuming an ambiguity between bound variable and referential pronouns explains the ambiguity of (32a) under an analysis where semantically ‘matching’ VPs are phonologically deleted (Sag 1976): If the possessive in the first clause is referential, then so is the elided one, yielding a strict reading, as represented in (33a). If the first my is a bound variable, bound by the subject (through quantifier raising, say), then so is the second one, yielding a sloppy reading, (33b):
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What he thought at the time was ‘I am at a safe distance from the fire’, which makes (35) true de se (i.e. from a first-person perspective). However, the coreferential first-person report construction can also report a third-person de re belief that just happens to be about the subject himself: (36) I thought that I was remarkably calm
(37) Beli kx[safe(x)]
[lf of (35), de se]
In (36) on the other hand, the speaker simply believes the (singular) proposition expressed by the complement with its Kaplanian, rigid I. For uniformity, note that belief in a proposition can be reduced to selfascription of the property of inhabiting the worlds picked out by the proposition (Lewis 1979), so we get: (38) Beli kx[calm(i)]
[lf of (36), de re]
The key point is that the de se reading of a first-person report comes about by de-rigidifying and binding the embedded I. So, again, Heim has provided an example of a first-person pronoun I interpreted not as a rigidly referential expression, but as a bound variable.
4.3 Saving Kaplan’s rigid I Instead of giving up on Kaplan at this point, I would like to explore alternative analyses of the supposedly non-referential first-person indexicals of the previous section. I propose analyses of both sloppy and de se bound I that are consistent with Kaplan’s directly referential semantics and finally address a problem of overgeneration. 4.3.1 Sloppy ellipsis and only through higher-order unification I propose to reduce (32b) (only) to something like (32a) (ellipsis), which in turn is analysed with higher-order unification (HOU; Dalrymple et al. 1991). I show how such an analysis restores a transparent link between the outward, formal features of my (first person, singular) and their customary semantic interpretation (being the current speaker) in both of Heim’s alleged bound variable examples in (32).
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The reported thought here may be ‘That guy is remarkably calm!’ with that guy really referring to Kaplan, the belief subject himself. Chierchia (1989) postulates a syntactic/semantic ambiguity: the logical form of (35) features a k-abstractor binding the embedded I to turn the complement into a self-ascribed property (being at a safe distance from the fire) (Bel* denotes property self-ascription):
274 Proper Names and Indexicals Trigger Rigid Presuppositions First, we apply the unification approach of Dalrymple et al. (1991) to the ellipsis example. In this framework, the first conjunct can get just a compositional, Kaplanian interpretation: I did my homework , did_homework_of(i, i). In the second conjunct didn’t introduces a free, second-order variable P to be resolved by HOU at the next stage of interpretation. The compositionally derived ‘preliminary logical form’11 of the entire sentence thus looks like this: (39) I did my homework but my classmates didn’t [¼(32a)] did_homework_of(i, i) ^ "x[classmate(x, i) /:P(x)] [pre-lf]
(40) P(i) 8 did_homework_of(i, i) The HOU algorithm (Huet 1975) generates four distinct solutions (¼unifying substitutions) of this equation for P, whereupon we can discard another two (because the parallel argument position, the subject, is not abstracted over; cf. Dalrymple et al. 1991). We are left with the following two: (41) a. P 1ky[did_homework_of(y, y)] b. P 1ky[did_homework_of(y, i)] The last step is to apply these unifying substitutions to the preliminary lf of (39): (42) (39) , did_homework_of(i, i) ^ . . . a. "x[classmate(x, i) /:did_homework_of(x, x)] b. "x[classmate(x, i) /:did_homework_of(x, i)]
[sloppy] [strict]
Thus, we derive both the strict and the sloppy readings of (39), semantically, without having to resort to an ambiguity in the first conjunct, so, in particular, without the need for a non-referential my.
11
Terminology borrowed from DRT + PA, where sentence interpretation is modelled as a twostage process: (i) the compositional derivation of a PrelDRS and (ii) the resolution process that connects the sentence with the context, cf. section 3.2.
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The next step is to determine what it is that the classmates did not do, that is, to resolve the free variable P. This is done by first finding the parallel, contrasting elements in the two conjuncts. In general, recognizing such parallelisms is no trivial matter, but I will skip over the details here (see Dalrymple et al. 1991). In this case, there is a clear contrast: my classmates did not do P but I did. Moreover, it is stated that I did my homework, so we equate I did P with I did my homework to get a second-order matching equation:
Emar Maier 275
(43) Only I did my homework "x[x 6¼ i / :B(x)]
[pre-lf]
To resolve B we construct a suitable matching equation. The background applied to the focus corresponds to the sentence we see, which gives rise to the following equation, unifying substitutions and outputs: (44) B(i) 8 did_homework_of(i, i) [cf. (40)] a. B 1ky[did_homework_of(y, y)] [cf. (41a)] (43) , "x[x 6¼ i/: did_homework_of(x, x)] [cf. (42a), sloppy] b. B 1ky[did_homework_of(y, i)] [cf. (42b)] (43) , "x[x 6¼ i/: did_homework_of(x, i)] [cf. (42b), strict] Again, the semantic HOU approach allows my in (43) to be interpreted as a regular Kaplanian indexical (in the matching condition (44)), even in the derivation of the sloppy reading. Unlike in the overt ellipsis case, our agnosticism about the status of the information that I did my homework leads to a qualification of the claim that the possessive my here is really semantically represented as an indexical in the (pre-)lf. We might maintain that it is represented as such in the matching condition, but the main point is that we need not assume a bound–referential ambiguity in (43). The strict/sloppy ambiguity is
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With this alternative account of sloppy VP ellipsis in place we turn to only. As it happens, Pulman (1997) has already proposed to extend HOU analysis of ellipsis resolution of Dalrymple et al.’s to the interpretation of focus and focus particles like only. I will apply a simplified version to Heim’s only example. The simplest account would be a full reduction, analysing (32b) (¼(43)) literally as (32a) (¼(39)) to arrive at the strict and sloppy output lfs of (42). Those outputs are rather close to the intuited readings of the sentence, but one possible objection is that they assert rather than presuppose, derive or implicate that I did my homework. I wish to remain agnostic about this issue, so I will just leave that part out of the logical representation. In detail, the modified Pulman-analysis runs as follows. We assume that our sentence consists of a focus-sensitive operator (only) plus a focus (I, lf: i) plus a background (lf: B). We are going to use HOU precisely to determine that background because the asserted contribution of the only sentence depends on it: everybody distinct from the focus does not have the background property.
276 Proper Names and Indexicals Trigger Rigid Presuppositions no longer a matter of syntactic ambiguity in the first-person pronoun, but rather of semantic underspecification and pragmatic resolution inherent in HOU.
(45) I believe that I am P dR[R(i, i) ^ Beli kx[P(1y[R(x, y)])]] Paraphrase: I was acquainted with myself in a certain way (R) and I believed (through property self-ascription) that whoever I was Racquainted with had property P. The de se reading of (35) is verified by taking R to be equality, the non-de se reading required for (36) to, say, R 8 kxky[see_on_tv(x, y)]. This immediately brings out one of the main advantages of the relational approach over Chierchia and Heim: we need not postulate a syntactic ambiguity in coreferential reports to get both de re and pure de se truth conditions. I am well aware that subsequent data on the de re/de se distinction pose severe challenges not only for the relational approach (e.g. reports with PRO + infinitive, or only embedded reports) but also for the ambiguity approach (e.g. universally quantified reports). For an overview of these issues and a defence and further development of the relational approach, I refer to Maier (2006). I will currently restrict attention to constructions featuring allegedly bound occurrences of overt first-person pronouns.
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4.3.2 De re/de se unification through acquaintance relations Now that we have seen how to maintain a straightforward Kaplanian semantics of sloppy my under only and ellipsis, we take another look at the argumentation behind Heim’s claim that first-person de se I is a bound variable rather than a directly referential term (section 4.2.2). The argument clearly depends on Chierchia’s analysis of the de re/de se distinction. In this section, I describe an alternative report semantics, using acquaintance relations, that leaves the Kaplanian semantics of I intact. Based on Kaplan (1969) and Lewis (1979), Cresswell & von Stechow (1982) reduce the semantics of de re and de se reports to ‘relational lfs’ featuring acquaintance relations as modes of presentation of the object of belief. Thus, coreferential reports (x believes that x is . . .) are underspecified for belief modality (de re or de se): a report like (35) or (36) is true if the belief in question is held under any acquaintance relation that holds between matrix and embedded subject, where acquaintance relations can encode either the first-person perspective (de se) or any relevant second- or thirdperson one (de re). The lfs of both (35) and (36) are thus of the following form:
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For our purposes, the important thing to note is that on a relational analysis the embedded I is in effect moved outside the belief and represented logically as ‘i’ ‘‘the second one in the R(i, i) of (45)’’, that is, as a standard Kaplanian indexical. Thus, we get representations that correctly predict the felicity of both (35) (de se) and (36) (de re) without giving up Kaplan’s analysis of I as a rigid designator.
(46) Only John did John’s homework
[only strict]
The result is slightly odd due to a Condition C effect, but some context or just some extra stress on the first name will make such sentences perfectly felicitous. The relevant observation is that, if and when such sentences are felicitous they allow only a strict reading. This contrasts with Heim’s first-person variant, which also allows a sloppy reading. With ellipsis we find the same contrasts between coreferring names and indexicals. The referentialist using HOU to account for apparent binding under focus and ellipsis generates sloppy readings for any coreferring terms in such constructions, whether they are names, descriptions, anaphoric pronouns or indexicals. Heim on the other hand can simply assume Condition C to block the possibility of syntactically bound names and thereby derive the observed behaviour. To answer this challenge, I propose a pragmatic account to block the unwanted sloppy readings generated by HOU. The crucial observation is that I differs from John, not in being a pronoun, but in having no ‘lighter’ alternative means of expression. In other words, the marked Condition C violation in (46) has a perfectly fine paraphrase with a third-person pronoun: (47) Only John did his homework
[strict/sloppy]
On the HOU account (46) is semantically equivalent to (47), but to express the sloppy reading, a speaker will prefer the unmarked (47) over the
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4.3.3 Overgeneration and pragmatic blocking of sloppy and de se names It has been objected that the proposed pragmatic HOU analyses overgenerate sloppy and de se readings, in particular, when the pronouns are replaced with coreferring proper names. In this section, I explore these objections and give counterarguments, first for the strict/ sloppy examples, then for the de re/de se reports. Replace the pronouns of Heim’s only example with coreferential proper names:
278 Proper Names and Indexicals Trigger Rigid Presuppositions
Table 1
Derivation of sloppy name blocking in bidirectional optimality theory
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repeated proper name (and that over variants with demonstratives or definite descriptions coreferring to John). If the speaker would nonetheless choose a ‘heavier’ (e.g. more content, higher in the ‘referential hierarchy’ alluded to on p. 9) or otherwise more ‘marked’ (e.g. Condition C violation) form, she must have some ulterior motive for doing so. What could be the motive for repeating the name? Apparently the speaker wants to emphasize that it is John whose homework is under discussion, that is, that it is John’s homework that the others did not do: the strict reading. The pragmatic blocking mechanism can be captured in terms of bidirectional optimization (Blutner 2000). We have two forms ((46) and (47)) and two meanings/lfs (strict and sloppy). Condition C serves as a markedness constraint, establishing that (46) is a more marked form than (47). The faithfulness constraint is one that says that pronouns should be logically represented as variables, as in the sloppy lf, while names should be represented as referential terms, as in the strict lf. Table 1 depicts the preferences based on these markedness and faithfulness constraints as arrows between form-meaning pairs in the horizontal and vertical directions, respectively. The horizontal arrow in the top row of Table 1, for instance, indicates that, on account of the faithfulness constraint just formulated, the pair Æ(46),strictæ is preferred over the pair Æ(47),strictæ, that is, the strict interpretation is more faithfully expressed by (46) than by (47). The pair down-right in Table 1 is preferred in both directions and is therefore optimal ( ). The pairs that have arrows pointing to this optimal pair are ruled out because their meaning has a better alternative means of expression or their form has a more faithful meaning. The last remaining pair, top-left, is now also optimal because there are no longer any competing forms for its meaning or competing interpretations for its form. In our example, the result of bidirectional optimization is that the Condition C violation (46) gets only the strict reading, which is the result we were after. However, we immediately make the mirror image prediction: the unmarked variant, (47), gets only a sloppy reading. This prediction is not borne out. It is universally acknowledged that a sentence like (47) is ambiguous. I conclude that full bidirectional
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(48) Only John did that guy’s [pointing to John] homework
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optimization is too strong to model the intuition behind the blocking of the sloppy reading of (46). However, the problem we just ran into is an instance of a much more general problem, discussed for instance by de Hoop et al. (2004) as an ‘asymmetry of markedness’, or by Ga¨rtner (2004) as ‘partial iconicity’. It is a generally observed pattern that, although marked forms have only marked meanings, unmarked forms tend to be ambiguous, their interpretation depending entirely on the context. This is what we find in our case: the marked form (46) gets only a strict reading, but the unmarked form (47) is compatible with both, favouring a sloppy reading in our particular example only because world knowledge tells us it is quite unlikely that a group of students should even consider doing John’s homework. In a very specific context, or with a different predicate (e.g. Only John is allowed to drive his favorite Hummer), the strict reading will be favoured. The problem with standard bidirectional optimization is that it does not allow for any ambiguity: unmarked forms get paired with unmarked meanings, marked forms with marked meanings and the rest is discarded. Ga¨rtner (2004) suggests a number of explanations of the ‘partial iconicity’ pattern within the general architecture of optimality theory, one of which based on Zeevat’s (2000) version of bidirectional optimality where OT-syntax (the speaker’s perspective, represented by our vertical arrows) is asymmetrically ordered before OT-semantics (the hearer’s perspective, represented by our horizontal arrows), so that, in certain contexts, the marked form can be filtered out already by the syntax, leaving only the unmarked form for both interpretations. Skipping over the optimality-theoretic details of implementation, the main points of my analysis are the following. (i) HOU generates strict and sloppy readings based on mere coreference. (ii) The very fact that the coreferential name has a lighter pronominal alternative is what pragmatically blocks its sloppy reading. (iii) For coreferential firstperson pronouns there is no easier alternative means of expression. This explains why we find both strict and sloppy readings in Heim’s firstperson examples, but not with proper names. The pragmatic HOU + blocking analysis makes some interesting further predictions. First, an even heavier coreferring term, such as a demonstrative or description, is correctly predicted to force a strict interpretation (at best):
280 Proper Names and Indexicals Trigger Rigid Presuppositions Second, in languages that have lighter pronominal forms, the normal pronoun will get a strict interpretation. A case in point is Dutch where the reduced pronominal possessives m’n (‘my’), je (‘your’), z’n (‘his’), etc. compete with their full counterparts mijn (‘my’), jouw (‘your’), zijn (‘his’), etc. These reduced, or weak, forms are indeed much more likely to be read sloppily, an observation not explained by the competing syntactic account:12,13
[sloppy] [strict]
A similar story can be told for the de re/de se examples. It has been noted many times that coreferring third-person pronouns allow both de re and de se, just like the first-person case discussed in section 4.2.2, but with coreferential proper names, Chierchia (1989: 22) claims, de se readings are unavailable: (50) Kaplan thought fhe/#Kaplang was at a safe distance from the fire 12 A third prediction is that in dialects such as Motherese and Legalese, where certain repeated coreferential descriptions or names are decidedly less marked, we would get sloppy readings, as in, for example, Plaintiff may divide plaintiff’s time between opening and closing argument [www.courts.mo. gov/hosted/circuit13/Trials.htm] [and so may the prosecution], or Mommy can clap Mommy’s hands, and so can Baby! I will leave proper investigation of this prediction for future research. 13 As pointed out by the referees, further research is required, as there are still some recalcitrant data in this area for which the proposed account seems to overgenerates sloppy readings:
(i)
a. b. c.
Only here do people like the cheese that is produced here [other indexicals, *sloppy] Only a sister of [John]F’s loves him [no c-command, *sloppy] Du bist der einzige der deinen Sohn versorgt you are the only one who your.2sg.acc son take care of.3sg ‘You are the only one who is taking care of your son’ [Kratzer (2009): *sloppy]
However, note first that these data are far from clear. Roeper (2006), for instance, challenges the lack of sloppy readings for coreferential indexicals (ia) and names ((46)). Also, the literature on strict and sloppy identity in VP ellipsis provides plenty of examples that are straightforwardly handled by an HOU approach, but whose sloppy readings are beyond the syntactic approach discussed here (cf. Dalrymple et al. 1991; Hardt 1993; Kehler 2000). Some of these even translate into focus constructions: (ii)
a. b.
The police officer who arrested John insulted him, and the one who arrested Bill did too. [Wescoat (1989): no c-command, sloppy] Only the police officer who arrested [John]F insulted him. [?sloppy]
Finally, there are also relevant data that fall beyond both the current syntactic and HOU approaches, including constructions exhibiting a strict–sloppy ambiguity without focus or ellipsis: (iii)
I am someone who knows what I want
[strict/sloppy]
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(49) a. Alleen jij hebt je huiswerk gedaan only you have your.(weak).2sg homework done ‘Only you did your homework’ b. Alleen jij hebt jouw huiswerk gedaan only you have your.(strong).2sg homework done ‘Only you did your homework’
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The relational account defended in section 4.3.2 indeed overgenerates a true reading for the proper name variant because the logical form, (51), includes the possibility of an egocentric acquaintance relation of equality: (51) dR[R(k, k) ^ Beli kx[safe(1y[R(x, y)])]]
(52) a. # Kaplan thought that Kaplan was remarkably calm b. Kaplan thought that the guy on TV was remarkably calm I conclude that the Kaplanian I + HOU + pragmatic blocking account is not just a viable alternative to Heim’s syntactic ambiguity account; it also makes a number of interesting new and correct predictions.
4.4 Monsters and shifted indexicality The final candidate for a bound first person involves shifted indexicals in attitude reports, made popular by Schlenker (2003). A standard example is (53), but there are many others involving other indexicals in English (e.g. in two days), or first-person indexicals in other languages 14 In fact, reports like (52b) with descriptions that match the content of the reported belief as well as its ‘mode of presentation’ could well be classified as de dicto reports.
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The same pragmatic reasoning as above can block out this de se possibility. The violation of Condition C/referential hierarchy indicates that the speaker must have wanted to emphasize that it is Kaplan who was thought to be at a safe distance from the fire. This kind of emphasis seems appropriate only if the speaker wanted to report Kaplan as having a rather marked mistaken identity thought of the form ‘Kaplan is at a safe distance from the fire’. Such a thought, however, did not occur in the scenario described. What Kaplan thought was simply ‘I am at a safe distance from the fire’. Assuming that the marked/stressed name was meant to faithfully indicate that the name itself was a noteworthy constituent of the reported thought, we predict that (50) is indeed infelicitous in the given context. In the first-person case, there is no simpler alternative, which explains the difference between names and pronouns in allowing de se interpretations. Again, the blocking account makes a novel prediction, beyond the scope of Heimian syntactic accounts: a repeated proper name report does not just block de se, it also blocks most de re construals. In particular, though Kaplan does believe de re about himself that he was remarkably calm, we cannot report this with (52a). If we want to use a name or description rather than the unmarked, all-purpose (de re/de se) third-person pronoun, we have to use one that matches the actual acquaintance relation of the belief reported, as in (52b):14
282 Proper Names and Indexicals Trigger Rigid Presuppositions (e.g. Zazaki and Ancient Greek) (cf. Anand 2006, for a thorough overview and investigation): (53) ‘Johni says that hei is a hero’
[Amharic, Schlenker 2003: 68]
(54) a. John believes that I am a hero Belj kx[hero(x)]
[¼(53), pseudo-Amharic] [cf. (37)]
15 All theories of shifted indexicals discussed share the prediction that shifted I is always de se. This appears to be borne out (Schlenker 1999; Anand 2006).
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It looks like the embedded first person is interpreted as bound by the matrix subject John, more or less like the English third-person pronoun used to translate it. I argue that, unlike Heim’s, these examples indeed necessitate a substantial overhaul of Kaplan’s logic. Indeed, von Stechow (2002) proposes an analysis that de-rigidifies Amharic I in the same way Heim did with agreeing I is under only and belief reports. However, following Schlenker (2003), I argue that the problem lies in Kaplan’s report semantics, more specifically in his ‘Prohibition of Monsters’, rather than in the rigidity of indexicals. Below I briefly discuss both von Stechow’s and Schlenker’s analyses. For different treatments and more data, see Anand & Nevins (2004) and Anand (2006). Von Stechow (2002) takes up the Chierchia–Heim account and generalizes it to Amharic (among other things). In his analysis, attitude verbs introduce k-abstractors for each relevant indexical domain (first person, second person, place, time, etc.) that can bind embedded indexicals. Following Heim, von Stechow relies on feature agreement to restrict binding, which makes the right predictions for English de se reporting (whether in first, second or third person). In our Amharic example, however, the matrix subject (and thus the reporting verb) does not agree with the embedded subject that we would like to bind. For this purpose, von Stechow introduces the ‘Amharic parameter’, an extra deletion rule designed specifically to let attitude verbs bind nonagreeing embedded indexicals. This rule, presumably, is what sets apart the English and Amharic grammar of embedded pronouns. To make a long story short (by restricting attention to the person domain and skipping the morphosyntactic details), the resulting interpretation of (53) is exactly Chierchia’s dedicated de self, (54a),15 while the English counterpart comes out as a de re belief about the actual speaker, (54b) (cf. Section 4.2.2):
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b. John believes that I am a hero Belj kx[hero(i)]
[English] [cf. (38)]
c1c ¼1 (55) ½½Bel x kcu ¼ 1 iff for all c compatible with x’s beliefs: ½½u a. John believes that I am a hero [pseudo-Amharic] Bel j kc[hero(ic)] b. John believes that I am a hero [English] Belj kc[hero(ic )]
With this kind of explicit context quantification, it’s really the context argument of the indexical (subscripted in (55)), rather then the indexical itself, that gets bound. The difference is admittedly subtle, and of course Schlenker does change the semantics of indexicals by adding an explicit (and bindable) context parameter. The difference with von Stechow is that Schlenker’s I in both English and Amharic does not reduce to a mere variable but remains tied to a context. The conclusion we draw from this section is that bound variable uses of indexicals have yet to be found. On the other hand, the phenomenon of shifted indexicality does show that Kaplan’s twodimensional analysis of indexicals and/or speech reports needs refining. In the next section, we explore the possibility of a presuppositional account of indexicality analogous to Geurts’ analysis of names. This investigation will extend our data set, while a review of current presupposition-based proposals, though ultimately unsatisfactory, will provide some new theoretical insights to be incorporated in my own proposal in section 6. 5 INDEXICALS AS PRESUPPOSITION TRIGGERS Though traditionally analysed as directly referential, the literature provided at least some prima facie suspects for bound indexicals, so it is
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So, on von Stechow’s account Amharic I can indeed behave like a third-person pronoun and contribute no more than a bound variable to the lf. Schlenker proposes an alternative analysis that changes Kaplan’s report semantics rather than the indexicality of the first person. In his analysis attitude verbs are context quantifiers, shifting the context of interpretation to that of the reported speech act or belief. In principle, every indexical in the scope of an attitude operator can then be interpreted with respect to the reported context or the actual context (henceforth ‘c*’). Apparently, English strongly prefers the latter option for I, while Amharic I is allowed to pick a shifted context.
284 Proper Names and Indexicals Trigger Rigid Presuppositions
5.1 Accommodating indexicals At the end of section 4, we concluded that clear evidence of a bound indexical has yet to be found. Especially with I, the only convincing argument against Kaplanian rigidity across the board is the one based on indexical shifting in Amharic-type attitude reports. But, to argue against Kripke’s referentialist account of proper names, neo-descriptivists did not just find binding, but also accommodation of names. It turns out that this too is impossible with indexicals. Zeevat (1999) suggests that accommodating an indexical is impossible, by discarding some tentative accommodation examples. For instance, he argues that examples of true demonstratives (this/that), where the hearer, ‘listening to a conversation on a tape or through a key hole’ (p. 282), accommodates an unseen pointing gesture, are not really accommodation but rather a case of purely pragmatic (extra-semantic) repair, since the accommodation is not intended as such by the speaker.16 To prevent such unwanted accommodation in his semantics, Zeevat requires that his input contexts always contain a representation of the current speaker. This is quite a reasonable assumption since DRSs by definition represent the interpretation of a discourse, so the current 16 An even more extreme variant discarded in this way is his example of someone who comes upon a chance inscription of I am the greatest created in the sand by the wind, interpretable only by the ‘accommodation’ of an intentional agent. This is clearly an unintended accommodation and hence simply a repair (and this time an undesirable one).
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remarkable that neither Elbourne nor Geurts try to extend their unification of definite noun phrases to this subclass. Perhaps, this is due to the differences between names and indexical pronouns: (i) indexicals do not allow Bambi-style binding in the way that proper names do, while (ii) in ellipsis and focus constructions names do not allow the same sloppy readings as indexicals. Finally, (iii) indexicals appear much harder to accommodate than names, a fact to be discussed in section 5.1. Still, there are some attempts at extending Geurts’ dynamic framework to analyse indexicals more or less on a par with proper names and other definites, that is, as presuppositions. In section 5.2, I briefly discuss and discard a naive account, simply extending Geurts’ analysis to indexicals, by way of establishing a null hypothesis, before looking at the more sophisticated variant of Hunter & Asher (2005) in section 5.3. I conclude that this analysis too is flawed in various ways, for instance in failing Kaplan’s version of the Kripke test. I close the section with Zeevat’s (1999) discussion of which will spill over into the next section as it goes beyond descriptivism proper.
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utterance being interpreted must be highly salient, and therefore so must the contextual parameters of the utterance (its speaker, time and place). We return to Zeevat’s utterance DRSs below, but for now note that they render global accommodation of indexicals like I, here and now obsolete because there is now always a suitable candidate to bind to. Finally, how about local accommodation, like with Aaron Aardvark? Again, I know of no examples, that is, no examples where embedded I means whoever is the speaker at some embedded context.17 I tentatively conclude that I and its kin, unlike proper names and definite descriptions, do not accommodate at all.
On the naive account, indexicals trigger presuppositions whose content is given by the lexical, descriptive meaning of the indexical, just like any other definite: (56)
17
A possible example of local accommodation of an intentional (i.e. impure) indexical that springs to mind is the following: I’m waiting for a phone call from Mary, when Gerontius calls. I say: (i)
Oh, Gerontius, hi. I didn’t expect you. I thought you’d be Mary.
Binding this last you globally to the actual addressee, Gerontius, seems to give the wrong reading. Of course, I did not believe that Gerontius would be Mary. Indeed a possible explanation would be that you here is accommodated locally: I thought that the person I’d be addressing now would be Gerontius. However, an alternative Kaplan-proof solution is to analyse it as a de re belief about Gerontius, under the acquaintance relation ‘the person I’m addressing’ in the relational framework presented in section 4.3.2: I am acquainted with you, Gerontius, as the person I’m now addressing, and I believed that it would be the case that whoever I am so-acquainted with is Mary. This second explanation also extends to similar examples in first person: (ii)
She must have thought I was a burglar. That’s why she didn’t come to the door last night.
In this case, I does not refer to any speaker—real, hypothetical or imagined—so local accommodation fails. The de re account works fine: she is acquainted with me as the person knocking on her door and it must have been the case that she thought the person she is so-acquainted with is a burglar. This de re analysis however does not extend well to other, seemingly related, cases of descriptive indexicality outside attitude reports: (iii)
Why did you open the door without checking? You should be more careful! I could have been a burglar [Hans Kamp, p.c.]
In Appendix A, I present Nunberg’s (1993) analysis of such apparently descriptive (but not accommodated) uses of indexicals in terms of deferred reference. As suggested by an anonymous reviewer, an alternative explanation of Nunberg’s and Kamp’s examples above may be developed on the basis of Aloni’s (2000) conceptual covers, a different formalization of the idea of a mode of presentation than the acquaintance relations I use. This kind of framework could perhaps be extended to subsume the rest of the data regarding attitude ascriptions in a uniform fashion. I leave this pursuit for future research.
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5.2 A naive account of indexicals as presuppositions
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5.3 Hunter and Asher: indexicals as wide scope presuppositions Hunter & Asher (2005) propose a small modification of PA specifically for this end: they add an operator [ representing a preference for global over local resolution for actual, here and now, and an even more restrictive operator \, which forces the presupposition in question to be resolved at the outermost context, for English I. The account requires a variety of different, ad hoc operators meddling with resolution. More seriously, it treats Amharic I like here and now, as something that prefers global resolution but that does allow local binding (though not accommodation) under pragmatic pressure. This implies (i) a preference for the Kaplanian, English-style reading of the Amharic (53) and (ii) the possibility of shifting Amharic I outside attitude reports. Neither of these predictions are borne out. More seriously still, the proposed mechanisms only work in embedded contexts, so, like the naive theory (5.2) and the presuppositional account of proper names (3.2) it fails the Kripke test: it cannot generate distinct outputs for (57a) and (57b), given a suitable input context with a speaker (cf. 5.1):18
18 It may be objected that of course we get the same outputs when binding the speaker, but that accommodation of that presupposition is possible and indeed leads to a different output corresponding to the tautological reading. Indeed, there would appear a small representational difference, but without truth-conditional (i.e. semantic) significance. Below and in section 6.1 we consider Zeevat’s way to fix just this, by looking at difference DRSs and anchoring the input.
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As demonstrated with proper names in section 3, the advantages would be a unification with other definites, and an independently motivated mechanism of presupposition projection to generate widest possible scope outputs. However, presupposition resolution occasionally generates other outputs, for instance, local binding and accommodation. For proper names, examples corresponding to such resolutions were spotted in the wild, but our search for bound and accommodated indexicals has been unsuccessful. Conclusion: The naive theory of indexicals using standard PA overgenerates immensely, as the only readings that we actually find are those corresponding to global binding to the actual speaker/time/place (as represented in an input DRS). If we still want some of the unificational benefits of this theory, we need to restrict it somehow.
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5.4 Zeevat: Utterance DRSs Zeevat in his (1999) emulation of Kaplan in DRT + PA recognizes the naive theory’s problem of overgeneration and the problems related to the Kripke test. His proposal starts with the observation that every DRS input must contain representations for the current utterance being interpreted and its contextual coordinates (speaker, time, place, etc.). Such a proper input, with the current utterance singled out (let us use Schlenker’s asterisk: e*), is called an utterance DRS. Indexicals trigger presuppositions containing that special utterance referent, so that I is represented as the speaker of the actual utterance e*. The effect is equivalent to that of Hunter and Asher’s \, always forcing widest possible scope. As Zeevat himself notes, when interpreting the Kripke test examples ‘there is nothing that distinguishes [the outputs of] the two sentences and Kaplan’s argument is as destructive for our theory as for the widescope theory’ (p. 287). His solution: The presupposition associated with I and other indexicals will always resolve. In this way, though the resulting material is almost the same, in the case of indexicals we are dealing with old information. [. . .] The content of the sentence must be defined as the new information the sentence brings and should not contain
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As there are no embeddings, there is nothing to take scope over and the \ in the indexical PrelDRS will not affect resolution at all.
288 Proper Names and Indexicals Trigger Rigid Presuppositions conditions that were already sitting there. If descriptive content is old, it does not belong to the content of the sentence. The new material in the two examples is different, because the speaker—and not I—leads to new material in the DRS. [Zeevat 1999: 288]
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Looking at the difference DRSs we find that I in (58a) contributes none of its content (i.e. it is directly referential, in a sense), while (58b) as a whole contributes a tautology, as Kaplan would have it. Unfortunately, we cannot yet make sense of the semantic contribution of (58a), as its difference DRS corresponds to an open formula, which expresses no proposition. Zeevat proposes external anchoring to fix this last flaw and arrive at a faithful reconstruction of Kaplan. In the next section, we discuss this, along with the pros and cons of anchors.
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In other words, I gets bound while the speaker introduces new material, meaning it is getting accommodated. As shown in (58), if the speaker accommodates, the output DRSs may still be truth-conditionally equivalent, yet what matters, according to Zeevat, is not the output but what is newly contributed, that is, the differences between output and input. For this purpose, we define the difference DRS of a given sentence interpretation as the material in the final output DRS minus the old discourse referents and conditions from the input DRS:
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6 RIGID PRESUPPOSITIONS
6.1 Direct reference in DRT: anchors Kamp & Reyle (1993) already provide a way to incorporate a referential semantics of proper names in the otherwise descriptive framework of DRT using external anchors. Zeevat (1999) incorporates anchors in his DRT + PA analysis of indexicals. I argue that their notion of anchoring is too rigid and meta-semantic, and I propose a more integrated layered account of direct reference in DRT. Formally, anchors are partial assignment functions or embeddings as they are often called in DRT semantics, mapping discourse referents to individuals. We can interpret a DRS u relative to an anchor a containing the free variables of the DRS in its domain. Interpretation of an anchored DRS, Æu, aæ, proceeds as in vanilla DRT, but with the anchor restricting the set of verifying embeddings. Formal definitions can be found in Appendix B, but the idea of anchoring is that the semantic evaluation of a DRS with respect to a possible world, the determination of the proposition expressed, relies on certain variables already being fixed to certain individuals. This is basically the same idea as we saw in section 3.1 where free variables were interpreted as rigid designators whose reference was fixed by an assignment function. In DRT the mechanism of anchoring is primarily used to fix the reference of a proper name discourse referent. In dynamic terms, a proper name is said to trigger an extension of the anchor, linking the discourse referent from the name to the designated individual directly: (59) a. Mary is called Mary b.
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We have seen that descriptivism had problems deriving the wide scope behaviour and the ‘rigidity intuition’ highlighted by the Kripke test. The first is accommodated in more modern descriptivist analyses like Elbourne’s static E-type account, and Geurts’ and Hunter and Asher’s dynamic, presuppositional accounts. I have shown how the second problem still haunts these neo-descriptivist proposals, making them ultimately unsatisfactory. On the other hand, the occasional binding and accommodation of proper names is left unexplained by the referentialists but follows directly from Geurts’ neo-descriptivism in particular. To account for all these problems, I propose a synthesis of dynamic semantics with presuppositions and direct reference, inspired by the framework of LDRT and the notion of external anchoring.
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(60) input:
If we then compute the proposition expressed by the difference DRS relative to the current anchor, we get a proper Kaplanian semantics. The main improvement over the plain anchoring account sketched above is that we do find representations of the linguistic meaning, namely, as presuppositions in PrelDRSs. Also, anchors are added to the context DRSs on the basis of the participants’ perception of the utterance context, so that the interpretation of the utterance can
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This gives the correct, referentialist truth conditions: the DRS in (59) is true in a world, if there is a verifying embedding extending the anchor, that is, if there is an assignment that maps x to Mary and that verifies the condition of the DRS in w: f verifies (59) in w iff (i) f(x) ¼ Mary (anchor compliance), and (ii) f ~w mary(x) (content verification). So the sentence is true in w iff the actual Mary is, in w, named Mary. This gives us a contingent proposition about a fixed individual, Mary. By contrast, the representation of the unanchored, purely descriptive variant represents the existential proposition that there is at least one person named Mary. So, yes, anchoring solves DRT’s issues with the Kripke test, but at a cost, as we will see below, after a brief look at indexicals. By analogy with the above treatment of proper names, the simplest proposal would be to extend the anchor every time we hit an indexical. In doing so a major flaw of the anchoring mechanism becomes apparent: in these anchored representations the intuitive meaning associated with the indexical is lost completely. All that is left is a discourse referent, paired with an actual object. Note that this objection applies to the proper name case as well, though with indexicals it is especially problematic as they obviously have such a meaning (viz. the ‘linguistic meaning’ captured by Kaplanian character in the classic two-dimensional account of rigidity or by the presupposed content in neo-descriptivist proposals). Zeevat (1999) tries to combine the rigidity provided by anchoring with PA’s inherently descriptive, presuppositional meanings. Recall from section 5 that Zeevat switches from output DRSs to difference DRS in order to derive the Kripke–Kaplan contrast but that he ended up with an open DRS. His next step is to require that the current utterance marker e* and its coordinates in an utterance DRS be properly anchored:
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6.2 Layered DRT LDRT is a framework designed to model the interaction of distinct but not independent types of information contributed by an utterance. It introduces labels to store the information contained in a DRS at separate layers, which are connected by sharing discourse referents. The semantics presented below relativizes the interpretation of an LDRS to
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proceed rather straightforwardly through the independently motivated mechanisms of PA (with the addition of a wide scope argument (e*) or operator (\)). Nonetheless, I still have two general objections against anchoring: (i) being wholly in accordance with classic, Kripke/Kaplan referentialism, external anchoring is ‘too rigid’ to account for the nonreferential uses of names discovered by the descriptivists (cf. Bambi (17) and Aardvark (20)); and (ii) the notion of an external anchor is at odds with the representational architecture of DRT(+PA). Let me elaborate on these points. As to (i), what we get, at best, is a reconstruction of Kaplan in DRT, and to achieve that we give up the flexibility of PA. For instance, Zeevat’s e*-presuppositions force a widest possible scope reading (rigidified by the anchors in the context DRS), which means we can no longer account for, for example, Bambi and Aardvark sentences. As to (ii), in DRT + PA, DRSs form an intermediate representational level between the sentence and the model-theoretic interpretation. This level is not merely a helpful notation, but an integral part of the interpretation process. First of all, this is due to Kamp’s mentalistic philosophy (DRS representation as symbolic entities can, in a sense, ‘fit in the mind’), but, less philosophically, language interpretation, and presupposition resolution in particular, relies heavily on the manipulation of symbolic material in a DRS. It is unclear how anchors fit into this architecture, since an anchor consists of pairs of discourse referents and actual individuals from the domain, that is, it is a mixture of symbolic and modeltheoretic entities, obviously unfit as a genuine part of a representation. I propose to use the LDRT framework of Guerts & Maier (2003) to represent names rigidly in DRSs, without mixing object- and metalanguage (cf. anti-anchor objection (ii) above), instead retaining a representation of the descriptive meaning within the DRS (at a separate layer). Furthermore, my proposal works even without the introduction of difference DRSs (though it would be rather straightforward to accommodate them too). In section 6.3, I address objection (i) by combining LDRT with PA.
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(61) a. Mary is called Mary
b. The person called Mary is called Mary
But of course this is just symbols, we have to set up the semantics in such a way that the kk -marked content gets separated from the propositional contribution and provides an actual individual. This is achieved by turning the kk -content of a DRS into an anchor that restricts the embeddings for the fr -content. To do this, we first define the basic semantic notion of a verifying embedding: f, a partial function mapping discourse referents to individuals, verifies an LDRS with respect to a world and a particular label (f ~w,l u) iff f can be extended to an embedding that verifies all conditions labelled l. An LDRS is l-true in w iff the l-layer is verified by the empty embedding (or by the anchor, in case of an anchored LDRS). In other words, the semantics tells us to ignore everything not labelled l and then apply the regular DRT semantics to the rest. The condition ‘maryfr (x)’ in (61b), for instance, is verified by g with respect to w and fr iff g(x) is in the extension of the predicate ‘mary’ in w. An embedding f verifies the LDRS in (61b) as a whole iff it can be extended to an embedding g
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a specific layer, in effect ignoring everything labelled otherwise. Below I sketch the ideas behind LDRT and illustrate it by applying it to our crucial examples. All formal details can be found in Appendix B. For our current purposes, we need two layers, one for the truthconditional contribution, labelled fr (egean), and one for the reference fixing content that comes from proper names and indexicals, labelled k (ripke-)k (aplan). The syntax of this two-layered fragment is like regular DRT except that every discourse referent and every condition are marked with one of the two labels. If we assume that the content introduced by a directly referential term is labelled kk , while the rest is labelled fr , we can already distinguish the representations for Mary and the person called Mary, without anchors:
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19 To capture the fact that Mary is called Mary (or I am the speaker) is a priori true, that is, that Mary is always called Mary in the world of its context of utterance, we add a restriction to ‘proper contexts’ (cf. Kaplan 1989): A context c is proper iff the interpretation of an indexical or name predicate in c is a subset of the interpretation of that predicate in wc, the world associated with c, cf. Appendix B.
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including x in its domain that verifies all fr conditions, that is, iff g(x) is in the extension of ‘mary’ in w. This means that the empty assignment verifies the LDRS in (61b) with respect to fr and w iff w contains at least one individual called Mary. The fr -content is therefore the near tautological proposition that someone is named Mary, which I take to be correct (cf. section 3.2). It captures the intuition that (61) makes no significant truth-conditional contribution. The crucial test is the computation of the proposition expressed by (61a). We are really going to have to use the two layers to get the correct contingent proposition here. The idea is as follows: truthconditional contribution is the content expressed by the fr -layer. But if we zoom in on the fr -layer of (61a) we find only a condition containing an fr -free variable. Following Zeevat’s reasoning in sections 5.4 and 6.1, we could use an anchor to ‘close off ’ the open fr -layer in the semantics. But we do not want to assume an actual external anchor, developed separately alongside the representational (L)DRS. Instead, we have now a kk -layer containing precisely the information needed to properly anchor x to an individual. Given a proper semantic separation between context of utterance and evaluation index in the model, we can evaluate the kk -layer at a context to construct an anchor against which to interpret the fr -layer at an index. To illustrate the procedure, let us evaluate (61a) with respect to a context c and an index world w. We first look at the kk -layer. The semantic anchor construction involves finding the smallest truthful embedding of the kk -layer with respect to c which has the kk -labelled discourse referents in its domain. Here, this must be an embedding that maps x to an individual in the extension of ‘mary’ in c. If there are multiple such individuals, that is, people called Mary in c, there would be multiple embeddings of the same size and hence no minimal one. Thus, the kk -anchor at c is only defined if there is a unique person called Mary in c, and if defined it is the function that maps x to that unique person. We assume here that evaluating a predicate at a context is exactly like evaluating it at a possible world except that name predicates like ‘mary’ and all indexical predicates like ‘speaker’ get a singleton extension. This ensures that any kk -layer of an LDRS representing a felicitous discourse has at most one verifying embedding in a context c.19 Now we can evaluate ‘what is said’, the fr -content, against the background of this kk -anchor. The fr -layer of the LDRS is true in
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(62) a. I am speaking
b.
the speaker is speaking
The kk -anchor of (62a) in c is the function that maps x to the unique speaker of c (cf. footnote 19 and above). The fr -content expressed by (62a) in context c is the set of worlds w in which the kk -anchor in c maps x to a speaker in w, that is, the (contingent) proposition that the speaker of the context is speaking. For (62b), the anchor is empty and we get the near tautological proposition that there is a speaker. In conclusion, the LDRT semantics above accommodates rigidity while preserving representational, linguistic meaning by replacing anchors with explicit kk -descriptions at the DRS level. LDRT does not require separate anchors that uncomfortably fall in between the representational and the model-theoretic levels of interpretation. The kk -layer is fully representational, and as such fits with the mentalistic picture that motivated DRT is essentially representational level. Not until the moment of determining static truth conditions by interpreting the representational objects do we construct an anchor. The LDRT account thus counters the second objection against anchoring raised in
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a possible world w iff there is an extension of the kk -anchor at c that truthfully embeds the fr part of the LDRS in w. In the case at hand, the fr part is true in w iff the anchor provided by the kk -layer at c maps x to an individual in the extension of ‘mary’ in w. In other words, iff the unique individual called Mary in c is called Mary in w. Moreover, it is false if that unique individual bears a different name in w, and undefined if there is no unique Mary in c. The fr -proposition expressed by an LDRS in a context c is defined as a function from worlds to truth values, namely, the function that maps to 1 all the worlds in which the fr -part is verifiable with respect to the anchor provided by the kk -layer at c. This yields the correct, contingent proposition for (61a): one that maps all worlds where the Mary of the context exists and bears the name Mary to 1 and all worlds where she exists under a different name to 0. Note that this notion of fr -content, as restricted by an anchor built from the kk -layer and the extra-linguistic context c, still assigns a tautological proposition to the description example, (61b), because there the kk -layer, and hence the kk -anchor, is empty. The same computations apply to indexicals if we represent their meaning at kk :
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section 6.1 while still preserving an anchor-based notion of semantic rigidity and passing the Kripke test. This is only preliminary though, for we have not yet said how to derive these LDRSs from a given surface structure, to which we now turn.
6.3 Layers and presupposition
6.3.1 The presuppositions of proper names Assuming a lexically hardwired distinction between descriptive and rigid terms, the original Kripke test sentences’ PrelLDRSs will have to look like this: (63) a. Mary is called Mary
b. The person called Mary is called Mary
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Now that we have switched to a two-dimensional syntax and semantics for DRT the question becomes how to represent names, pronouns and descriptions in layered preliminary structures, and how to resolve those. Following Zimmermann’s (1991, 2004) ‘Hypothesis (L): lexical items are always deictic or absolute’, I take it that an expression’s reference either depends on the context and is intensionally rigid or has intensional content but is contextually inert. In LDRT terms, the representational content of an expression either wholly resides in kk , or in fr , and which of the two is specified by the (L)exicon and should therefore be reflected in the PrelLDRS. This implies that there are two kinds of presuppositions: kk -presuppositions triggered by lexically rigid items such as names and indexicals, and fr -presuppositions triggered by definite descriptions and other, non-NP triggers. In the following, I consider what this means for the representation and resolution of proper names and then indexicals.
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In an empty context, we would get (61b) for (63b), and (61a) for (63a), through accommodation. On second thought however, accommodating in kk does not really make sense conceptually. If an individual is available in the extra-linguistic utterance context c, it will presumably be represented at the representational input level, available for binding, which is preferable to accommodation. If, on the other hand, a suitable individual is not available in c, and we were to accommodate a kk -presupposition that there is such an individual, the resulting LDRS would simply be uninterpretable because we cannot create a proper anchor for the kk -layer in c. Thus, we have identified two new constraints on layered resolution: LAYERFAITH prevents layered presuppositions from binding or accommodating in other layers than the one they originated in; *kk ACCOMMODATE blocks accommodation of kk -presuppositions. Adding these constraints to the familiar constraints on presupposition resolution identified by van der Sandt (1992), with *kk -ACCOMMODATE ranked higher than LAYERFAITH, gives the right predictions, at least for the Kripke test sentences. The indexical Kripke test is passed in exactly the same fashion as the proper name version: I triggers a kk -labelled speaker presupposition that gets bound in a proper utterance context, yielding a contingently true output representing direct reference to the actual speaker, me. The speaker triggers a descriptive presupposition that, lacking an fr
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For layered resolution, I introduce a ‘layer faithfulness constraint’ to the effect that a layered presupposition must be resolved in its own layer, that is, bound to a referent whose associated content semantically matches with respect to that layer or added to that layer by accommodation. This makes the right predictions for (63). The most likely discourse context for (63) is one where some particular Mary is already salient. Such a context corresponds to an input LDRS with a Mary represented as such at kk . After merging with this input, the kk -presupposition of (63a) will naturally bind to that Mary and give the desired output shown in (61a). In this same input context, the fr presupposition of (63b) will accommodate, leading to the near trivial (64) (which is equivalent to (61b), apart from the material already present in the context):
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(65) If a child is christened Bambi and Disney Inc. find out about it, they will sue Bambi’s parents [¼(17a)]
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antecedent, will accommodate, giving something akin to Zeevat’s (58) (but, again, without requiring external anchors). In both the proper name and indexical versions of the Kripke test, LAYERFAITH currently does not allow the descriptive presupposition to bind to the rigid contextual individual represented at kk in (64), that is, it blocks the possibility of a contingent, name-like reading of (63b). In some cases, for stylistic purposes or otherwise, descriptive paraphrases seem to be used to pick up a contextually salient individual rather like the corresponding name would. There is an easy fix for this, by bridging: we do in fact accommodate at fr but add the inference that the fr accommodated Mary is in fact the same as the contextually given Mary. We also find the opposite LAYERFAITH violation, kk binding into fr . The first such example would be Horace (13) (p. 9). In that example, a proper name appears to be bound by a globally available ‘dog named Horace’ introduced at fr by the previous sentence. One way to get around this is to introduce a pragmatic layer-update mechanism that promotes fr objects, when sufficiently grounded, to kk . The motivation behind this is that after the dog in the first sentence is accepted into the common ground, it should get promoted from fr to kk , since the audience apparently accepts with the speaker that there is an actual dog. A notable, and appropriate, consequence of this approach would be that, if the dog named ‘Horace’ does not actually exist, the post-promotion LDRS lacks real, objective semantic content, as the kk -layer does not lead to a proper anchor. We return briefly to the grounding/promotion issue when we discuss the possibility of globally accommodating a name, but first we turn to intermediate resolution for Bambi and Aardvark. There are cases where LAYERFAITH is undeniably violated in the kk to fr direction. In particular, LAYERFAITH blocks the local resolutions needed to account for Bambi and Aardvark sentences. Consider Bambi first:
298 Proper Names and Indexicals Trigger Rigid Presuppositions Both definites (Disney and Bambi) are proper names and thus lexically specified as kk -presupposition triggers. Intuitively, we need to bind z (Bambi) to x (the hypothetical child called Bambi). In Geurts’ unlayered DRT this was possible because the two matched in content; here this would not work because with respect to kk interpretation they do not match (nothing is predicated of x as far as the kk -layer is concerned). We can thus derive only the absurd reading where Disney sues Bambi, the cartoon deer, available through encyclopaedic knowledge in the global context. To get any sensible output, we must violate LAYERFAITH. In other words, in order to prevent uninterpretability, ‘layer hopping’ of a kk -presupposition to fr is allowed as a last resort:
The same applies to the Aardvark sentence where a name, lexically specified as triggering a kk -presupposition, cannot possibly resolve in its own layer: (67) If presidents were elected by alphabetical order, Aaron Aardvark might have been president
Faithful resolution is impossible, because there is no kk-information to bind to, and accommodation in kk is forbidden by *kk -ACCOMMODATE. Note that giving up that constraint would not even help. Global kk -accommodation would yield an unintended reading about an actual Aaron Aardvark. Local (¼non-global) kk accommodation is ruled out on the more general grounds that
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(66)
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embedded kk -layers simply do not make sense in the current Kaplanian semantics of kk . This is appropriate given the fact that kk corresponds to, in a sense, ‘hyper-global’ information, that is, information that is truly contextual in the Kaplanian rather than the wide scope or discourse sense.20 The output we want is one where not the person but the name itself plays a role, which can only be achieved by accommodating the presupposition in fr : (68)
20
The ban on local kk -layers is in some sense the representational analogue of Kaplan’s Prohibition of Monsters. Therefore, it is not surprising that embedded kk -layers play a central role in my analysis of Amharic I below.
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We just saw that the proposed ordering of our two constraints predicts that accommodation of a name must be fr -accommodation. As I said in section 3, it is quite strange to use proper names of people that are not part of the common ground. But if it does happen, communication does not necessarily break down. A cooperative hearer should be able to globally accommodate the presupposition of a name. Now, imagine someone uttering I ran into Mary the other day in a context where nobody named Mary was previously introduced or otherwise salient. We cannot bind the name presupposition to anything, and kk accommodation is blocked by *kk -ACCOMMODATE, so, unless we stop here and proclaim the sentence uninterpretable, our only option is to break LAYERFAITH and accommodate globally in fr . But that means that we get a purely descriptive output, equivalent to I ran into someone named Mary the other day. In other words, we lose the contrast of the Kripke test: Mary means the person named Mary, rather than rigidly referring to a certain contextually salient individual. I am inclined to say that, as with the Bambi and Aardvark examples, this is as it should be. Note first that accommodation of names is quite marked. And if it does happen, how can we expect the name to function referentially, that is, to pick out an individual from the context? Just hearing an unfamiliar name is probably not enough for an addressee to ‘create’ an actual entity to serve as anchor for the use of the name. However, as the conversation continues and more becomes known about Mary, it might
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(69) [context: Gerontiusi is a friend of mine.] If someone elsej had been named Gerontiusfr , Gerontiusi/*j would be annoyed. Second, if we were to say that a definite is free to bind and accommodate in kk as well as fr , we would come dangerously close to giving up on Hypothesis L and ending up with a descriptivist Geurtsian account where there is no more distinction between directly referential terms and their descriptive counterparts. The third argument for LAYERFAITH is based on the behaviour of indexicals and the desire for a unified account in which the remaining differences between names and indexicals (after section 4.3) are captured by assigning different relative 21 One reviewer raises the question what happens if there is no salient Gerontius in the input context. Consider the following variants in such an empty context:
(i)
a. b.
If someone had been named Gerontius, Gerontius would be annoyed If John had been named Gerontius, Gerontius would be annoyed
The only reading I can get for (ia) is a Bambi reading, paraphrasable as if someonei had been named Gerontius, hei’d be annoyed. This is exactly what the theory predicts. There is no Gerontius in kk and kk -accommodation is blocked by the highly ranked *kk -ACCOMMODATE. Breaking LAYERFAITH, we hop to fr where local binding to ‘someone named Gerontius’ is the preferred option in PA. Intuitively, (ib) gets a rather different, Aardvark-type interpretation, that is, local fr -accommodation: If there had been some Gerontius and John had (also) been named Gerontius, (the first) Gerontius would be annoyed. This is also correctly predicted by the theory. As with (ia), faithful resolution is out. Hopping to fr we try binding first. In this case, however, the antecedent contains no discourse referent (John is represented globally in kk ), so local binding is out. Without global binding options, the next candidates are global and intermediate fr accommodation. Depending on the further discourse context, both are possible: with global accommodation the speaker tries to convey that there is in fact some original Gerontius who would be annoyed, while with intermediate option this original Gerontius is merely hypothetical.
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be that a contextual individual does emerge. We have briefly touched upon this hypothetical mechanism of fr to kk promotion by ‘grounding’ above. A more precise description of the dynamics of layers within the context DRS and of its complex interactions with the extralinguistic contexts is beyond the scope of the current paper. In any case, whatever happens to the context later in the conversation, I claim that the prediction that initially an accommodated name is interpreted purely descriptively is correct. It seems LAYERFAITH can be violated, but then why have it at all? In the remainder of this section, I provide a number of reasons for keeping it as an occasionally violable constraint on layered resolution. First of all, I believe that layer hopping is exceptional and allowed only in special cases where interpretation would otherwise grind to a halt. This is corroborated by the fact that, given an explicit choice between (global) kk and (local) fr , as in (69), the faithful output is greatly preferred over the Bambi reading:21
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strengths to a single constraint. Therefore, in order to finish our case for lexically encoded rigid presuppositions and LAYERFAITH, we now turn to indexicals.
22
Obviously, both of these alternative analyses require some extensions to the basic LDRT + PA framework (higher-order variables, k abstraction, unification, etc.), but these adaptations can be borrowed directly from the static formulations in section 4.1.
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6.3.2 The presuppositions of indexicals Looking back at the data and analyses of indexicals, I in particular, it seems that we always get genuine direct reference, that is, in LDRT terms, global binding to the kk -layer. In section 4, I showed that there are no direct analogues of the Bambi binding of names (cf. (29)) with pure indexicals. Furthermore, the local, syntactic binding of indexicals under only and ellipsis argued for by Heim was shown to be an unnecessary theoretical artefact. If we adopt the independently motivated HOU analysis, Heim’s sloppy readings are straightforwardly accounted for with only global kk -binding. Local binding in de se readings of first-person reports can likewise be discarded by adopting the relational approach to de re reporting.22 Finally, in our search for accommodated indexicals in section 5.1, nothing came up that would count as an fr -accommodated I, and, for reasons discussed above, kk -accommodation will be impossible to find due to the nature of the kk -layer and its two-dimensional semantics. The only possible exception to global kk -binding left is the case of shifty Amharic reports, to which we turn next. I show below that even this case can be analysed without breaking LAYERFAITH. I propose to analyse the Amharic report as a case of local binding in kk. Like any first-person indexical, Amharic I triggers a kk presupposition, which from now on will have the more general ‘centre’ predicate as its content, because I should be able to represent not just the speaker but also the agent or first-person experiencer of a thought, dream or action. Obviously, this presupposition can bind to the globally given actual speaker in the input, yielding the ‘English reading’, de re about the actual speaker. The special Amharic reading is derived, without breaking LAYERFAITH, on three assumptions: (i) the presupposition of I is triggered in situ, that is, in a subDRS embedded under the attitude operator; (ii) attitude representations are embedded two-layered LDRSs that always contain a unique centre in kk and (iii) English I differs from Amharic I in the fact that English but not Amharic has a preference for wide scope.
302 Proper Names and Indexicals Trigger Rigid Presuppositions As a first approximation, before going into all these assumptions at length, we would get: (70)
(71) John thinks I am a hero dR[R(j, i) ^ Beli kx[hero(1y[R(x, y)])]] Translating to LDRT, we would derive that reading as follows:23 23 In the translation, I have simplified the representation by leaving out the definite description operator. To ensure that v in the embedded LDRS is nonetheless unique, we could simply assume a general constraint on admissible acquaintance relations: we demand that an acquaintance relation is actually a partial function from individuals to the things they are R-acquainted with. Another simplification is that I conveniently forgo labelling higher-order and intensional discourse referents because I do not want to go into a discussion about whether they should be part of the proposition expressed or merely relevant at the reference fixing stage.
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This represents the shifty Amharic reading as the result of faithful but local kk-binding. The output should be read as something like John believes (the character/diagonal of) ‘I am a hero’ (semantic details below and in Appendix B). Now, let us discuss the underlying assumptions one by one. Ad (i): representing I in situ in the PrelLDRS seems the most natural thing to do, but in light of the discussion in section 4.2.2 it actually becomes rather problematic. In that section, I argued against Heim and Chierchia and in favour of a relational account of the de re/de se ambiguity in coreferential first-person reports. On this relational account, the res in a de re report is represented outside the attitude operator. To recap the relational account, the English sentence in (71), corresponding to a literal gloss and an attested reading of the Amharic (70), would be represented as follows:
Emar Maier 303
(72) John thinks I am a hero
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In words, the main context of the PrelDRS above states that there is an acquaintance relation R that holds between the subject, John, represented as a kk -presupposition, and the res, I, likewise represented as a kk -presupposition. In addition, there is a condition that ascribes a certain belief to the subject, John. This belief is represented again as an LDRS, stating the existence of a centre (u), representing John’s internal self, so to speak, and an object (v) with which that centre is R-acquainted, and which has the property of being a hero. In other words, the embedded LDRS represents a thought of the form I am R-acquainted with someone who is a hero, where R is given by the main LDRS context as the vivid acquaintance relation actually holding between John and the res. We might stop here and just say that the Amharic and English readings correspond to the distinct PrelLDRSs of (70) and (72), and we would be no worse off than Heim, Chierchia and Von Stechow, who also distinguish de re and de se outputs syntactically. On the other hand, I think that would count as an admission of defeat for the unificational idea behind the relational approach. What we really want is to reconcile the PrelLDRSs in (70) and (72) in such a way that we have a single PrelLDRS for the English and the Amharic reports, from which we can then derive both readings by two different, faithful resolutions of I, the global and local kk -binding. Indeed, Maier (2006: 308–24) provides just that: a unified, compositional PrelLDRS that can resolve to both a relational de re output and a local Amharic one. To see what kind of modifications this involves, let me briefly sketch the main points of that analysis. As pointed out above, such a unified analysis is desirable, but note that the argumentation of the current paper does not ultimately depend on it in the sense that the LDRT framework can also emulate a simple syntactic ambiguity analysis.
304 Proper Names and Indexicals Trigger Rigid Presuppositions
(73)
To get the English de re reading, resolution proceeds roughly as in (72), with the kk -presupposition w bound globally to the actual speaker x: (74)
In section 4.3.2, I said that vivid acquaintance relations are typically perceptual relations between individuals. In fact, we will assume that the only concept one is acquainted with is one’s self-concept. Because in the representation of John’s belief in (74), we have x ¼ _ i, where x is the actual speaker, equating i with John’s self-concept does not make
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We start with a relational PrelLDRS with the res presupposition triggered inside the belief box and an intensional referent ‘i’ representing the object of acquaintance (connecting top-level and embedded belief). An intensional discourse referent is one that refers not to an individual but to an individual concept, a function from worlds to individuals. Acquaintance with concepts generalizes the standard notion of acquaintance as a relation between individuals in the sense that a mere individual corresponds to the special case of a rigid concept (constant function). Finally, to reduce unnecessary intensionality I will use the familiar _ operator of intensional logic to map a concept to an individual, namely, the extension of that concept at the world of evaluation.
Emar Maier 305
any sense here. So we can restrict attention to extensional acquaintance relations, that is, ones that relate individuals to rigid concepts. When i is a rigid concept, the embedded condition x ¼ _ i is equivalent to i ¼ ^ x because an extensional variable like x is rigid too. This allows us to replace occurrences of i throughout with x’s. Likewise, we can introduce an extensional variable vkk to replace the rigid j. Thus, we arrive at (75), which corresponds to the English reading represented in (71)– (72), except for the fact that we have acquaintance with rigid concepts rather than individuals directly. (75)
(76)
According to (76), the subject (y) is acquainted with an intensional concept (i) that in all of his belief alternatives corresponds to himself (u). In other words, i must be the self-concept, the image John has of himself, which we will count as a (possibly non-rigid) concept with which John himself is thoroughly acquainted. Assuming that there is only one way (R) of being acquainted with one’s self-concept, it follows that j denotes the self-concept of u, the centre of John’s belief. Maier (2006), finally, shows how the addition of a principle of introspection to the effect that one believes the things one believes to believe allows us to simplify the rather bloated representation in (76) to uncover exactly the de se output shown in (70). Ad (ii): the interpretation of embedded, two-layered, centred LDRSs. In section 6.3.1, I remarked that embedded kk -layers do not make
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To get the shifted reading, we bind the presupposition (wkk ) locally (and faithfully) to the embedded kk -centre (ukk ):
306 Proper Names and Indexicals Trigger Rigid Presuppositions
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sense in the two-dimensional LDRT architecture. Thus, in order for the current proposal to work, that Kaplanian two-dimensional semantics needs refining. The problem was that the only way to make sense of local kk -layers is with local context parameters, which in turn imply monstrous operators. Since Schlenker (2003), it has become quite uncontroversial to assume monstrous operators, especially when considering shifty reports. Borrowing from Schlenker and others I propose a monstrous belief semantics for 2D LDRT: f verifies Belx u in w iff f(x) self-ascribes in w the diagonal proposition expressed by u. The diagonal proposition expressed by an LDRS is the set of contexts in which the LDRS would be true. This notion of truth in a context, finally, depends on the whole two-dimensional LDRT semantics discussed in section 6.2 (cf. Appendix B): u is true in c iff the world of c is contained in the fr -proposition expressed by u with respect to the kk -anchor at c. In other words, the diagonal of u is the set of contexts c in which the kk layer defines an anchor that can be extended to an embedding that verifies the fr conditions of u in the world of c. In still other words, the effect of diagonalization in the definition of belief in LDRT is to semantically merge, in a sense, the embedded layers to together form a sufficiently fine-grained description of the de se mental state of the believer. Ad (iii): postulating different resolution preferences for English and Amharic. There is a genuine typological difference between English and Amharic, the question is just how to describe it. The present proposal locates the difference not in some hidden shift operator (cf. Anand & Nevins 2004), nor does it de-rigidify the Amharic indexical (cf. von Stechow 2002). The only difference I stipulate is that the English indexical has a stronger preference for global resolution. To finish the formalism, I therefore propose to add Hunter and Asher’s \ to the English kk -presupposition to encode a ‘super-rigidity feature’ that transcends the kk labelling. I conclude that the combination of layer-faithful presuppositions and forced wide scope resolution of English I accounts for the different behaviours of English and Amharic in report contexts in a natural way. Important benefits over the account of Hunter and Asher of indexicals are that we correctly predict Amharic to shift only in report contexts and that we pass the Kripkean rigidity tests. Zeevat does not address Amharic, but benefits over his account include abandoning external anchors and difference DRSs. In short, the indexical data in particular strongly support the layer faithfulness constraint and thus the whole lexical rigidity account inspired by Zimmermann’s Hypothesis L. For names, however, this principle may occasionally be overruled under pragmatic pressure, as witness Bambi and Aardvark. Together with the blocking
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mechanism of section 4.3.3, the difference in relative strength of this constraint captures precisely the observed differences between names and indexicals, while preserving their most basic shared feature of rigidity.
6.4 Conclusion
APPENDIX A: DEFERRED REFERENCE As a final test case for the ‘rigid presuppositions’ account, we turn to a different class of apparent counterexamples to direct reference: Nunberg’s (1993) descriptive, or deferred, uses of indexicals, mentioned briefly in footnote 17, p. 31. The original examples are (1a), with I, and (1b), with another pure indexical: (1) a. I am traditionally allowed to order whatever I like for my last meal [Nunberg 1993: 21] b. Tomorrow is always the biggest party night of the year [Nunberg 1993: 29] In both cases, the indexical is naturally interpreted as referring to a concept, that is, as a synonymous with a description like prisoner on death row, for (1a). Note that (i) strict Kaplanian rigidity would yield nonsensical readings (it can hardly be a ‘tradition’ to grant the wish of the particular prisoner who actually uttered (1a)), and (ii) the
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The current paper provides a new analysis of names, indexicals and definite descriptions that respects the semantic differences between descriptive and rigid definites. The proposal uses a two-layered fragment of LDRT with separate layers for descriptive and reference-fixing content, interpreted by means of a two-dimensional Kaplan–Schlenker semantics. Furthermore, inspired by neo-descriptivist ideas and data, it complements this basic account of rigidity in LDRT with an analysis of definites as presuppositions. In effect it divides the class of definites in two: (i) descriptive definites triggering fr -presuppositions that want to bind or accommodate in the context’s fr -layer, and (ii) referential terms such as proper names and indexicals triggering presuppositions that want to bind in kk . Adjustments to the basic proposal include (i) pragmatic explanations of why we find strict/sloppy and de re/de se ambiguities with indexical pronouns but not with names, (ii) a difference in constraint ranking to model the ability of proper names, but not indexicals, to hop from their original kk -layer to fr if all else fails and (iii) an account of shifted indexicality based on local binding to the embedded kk -centre and an additional widest scope marker to distinguish English from Amharic I.
308 Proper Names and Indexicals Trigger Rigid Presuppositions descriptive content apparently associated with these uses of indexicals does not correspond to their linguistic meaning as encoded in the term’s character or presupposed kk conditions: A condemned prisoner is traditionally allowed to (2) a. The speaker of this utterance order whatever she likes for her last meal The Saturday before classes start is always the biggest b. The day after the day of this utterance party night of the year
24 Nunberg’s views have in fact changed somewhat between 1993 and 2004. My simple reconstruction will be a loose hybrid of both analyses, in my own terminology.
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The indexicals in (1a) and (1b) are interpreted as referring to concepts but apparently this ‘descriptivization’ does not arise from accommodation of the indexical’s lexical content (as was the case with the descriptive reading of the Aardvark example (25)). So, where do these concepts come from? And, if the indexicals here are neither directly referential nor equivalent to their descriptive lexical meanings, do these data refute all theories of indexicals discussed so far? Nunberg’s answer to the first question allows for a negative answer to the second, with reservations: we can maintain with Kaplan that I in (1a) refers directly and rigidly to the actual speaker of the utterance (Kaplan’s Principle 2), in virtue of having its lexical meaning pick out the speaker parameter of the context (Principle 1), but we have to add a second, more pragmatic mechanism of identifying individuals in a context. Let me reconstruct Nunberg’s (1993, 2004)24 diagnosis as to the source of these descriptive interpretations in more detail. It is clear that the descriptive meaning condemned prisoner for I in (1a) comes from the context. Rephrasing Nunberg, the context, provided by world knowledge, preceding discourse, but also the sentence itself, can induce an equivalence relation equating any number of somehow similar individuals whose differences are irrelevant to the issue at hand. In the case of (1a), we are interested in the rights of the speaker qua condemned prisoner, which will induce a relation of equivalence that equates everybody in the domain sharing that predicament. This allows us to associate with the actual speaker, the equivalence class consisting of everybody in the same role, that is, every condemned prisoner. It is then only a small step to say that the actual
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in choosing to refer to himself as ‘the speaker of this utterance’ rather than as I, the speaker conversationally implicates that he has some relevant reason for choosing that particular descriptive content—we’d infer that he means us to believe that the tradition about last meals applies to people in virtue of their roles as speakers, even if that doesn’t make a lot of sense. But there’s no analogous implicature when a speaker refers to himself as I. Inasmuch as the linguistic meaning of the expression doesn’t figure as part of the utterance content, we’re not obliged to construe it as conversationally relevant. [Nunberg 2004: 21] The rigid presuppositions account fits this explanation like a glove. The speaker triggers a fr -presupposition that will leave its content in the fr layer, contributing the speaker property to the output truth conditions. Now, conversational implicatures are computed on the basis of truthconditional content contributed by a sentence, which corresponds to the fr -layer in the system proposed here. As for the indexical I, its content ends up in kk , meaning that it is used in the reference fixing stage rather than contributing to the truth conditions, let alone to implicature computation.
25
To get the right reading, I’m further assuming that the predicate is traditionally allowed to . . . is consequently coerced to shift along with the its indexical argument. The deferred predicate should accept equivalence classes and mean that everything in such a class has the given property.
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Kaplanian reference of an indexical can be ‘deferred’ to the equivalence class associated with it.25 Kaplan (or, for that matter, the rigid presuppositions account) is saved by adding an extra mechanism of contextually inducing equivalence relations and the idea that reference can shift from the individual to the contextually induced class of individuals similar to it. This highly pragmatic solution however engenders a new problem: Why do we only get deferred interpretations with indexicals and not with (referential uses of) their descriptive counterparts? Given a preference for referential interpretation (in more presuppositional terms: global binding or global accommodation plus bridging, cf. p. 42), of the definite descriptions in (2), they too will bring us to the same contextually given individual, so why cannot the context then equate Aileen with all other inmates in the same position and force a deferred reading in those cases? Nunberg’s answer involves an appeal to conversational implicatures, resembling the pragmatic blocking analysis of section 4.3.3:
310 Proper Names and Indexicals Trigger Rigid Presuppositions This leaves a final problem, not addressed by Nunberg: How about proper names? We have assumed, with Kripke and Kaplan, that their content also does not usually end up in fr , that is, in the truth conditions. That would predict that Nunberg’s conversational implicatures will not have access to their content either, so deferred reference should be just fine. Consider an utterance of (3) in a context where the identity of Wuornos has already been firmly established, say a documentary about women on death row: (3) Aileen Wuornos is traditionally allowed to order whatever she likes for her last meal
APPENDIX B: LDRT In this appendix, I spell out the formal details of the syntax and semantics of LDRT. I give no separate definitions for regular DRT because it can be viewed as a special case of LDRT: a regular DRS corresponds to an LDRS in which everything is labelled fr and DRT’s semantic interpretation is LDRT interpretation relative to fr . I focus on the semantic interpretation of layers, so I will not go any deeper into PrelLDRS construction or the resolution process. I will also leave out some notions used exclusively in section 6.3.2, such as intensional (i) and higher-order (R) discourse referents, which can be treated exactly as in standard static frameworks.
Syntax (1) LDRT syntax a. primitive symbols: (i) discourse referents: x, y,. . . (ii) for each n a set of n-place predicates: john, like, speaker,. . . (iii) layer labels: fr , kk b. labelled discourse referents: if n is a discourse referent and l a label, nl is a labelled discourse referent 26
If it is not, perhaps we can again appeal to some implicatures based on the speaker’s choice of a more marked referential term (proper name, description) over a simpler alternative (pronoun) on a referential hierarchy (as in section 4.3.3).
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Like indexicals, names add nothing to fr , so neither would give rise to content-based implicatures and both would permit deferred reference equally. Further research will have to show whether this prediction is always borne out.26
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c. LDRS conditions: (i) if P is an n-place predicate, l a label, and n1, . . ., nn are discourse referents, then Pl(n1, . . ., nn) is an atomic LDRS condition (bearing label l) (ii) if u, w are LDRSs, l a label, and n a discourse referent, then u 0l w, u)lw and Belnl u are complex LDRS conditions (bearing label l) d. LDRS: if U is a set of labelled discourse referents and C a set of LDRS conditions then ÆU, Cæ is an LDRS if u ¼ ÆU, Cæ is an LDRS, U is called the universe of u, U(u), and C is called the condition set of u, Con(u). (3) a. l-conditions: c 2 Conl(u) iff c 2 Con(u) and c bears label l b. l-universe: n 2 Ul(u) iff nl 2 U(u)
(2)
free variables a. for LDRS condition c and label l, define: FVl(c) ¼ ; if c bears a label different from l, otherwise: (i) FVl ðPl ðn1 . . . nn ÞÞ ¼ fn1 . . . nn g (ii) FVl(u 0l w) ¼ FVl(u)lw) ¼ FVl(u) [ (FVl(w)\Ul(u)) (iii) FVl(Belnlu)¼FVl(u)[fng b. For an LDRS u and label l: FVl ðuÞ ¼ [c2Conl ðuÞ FVl ðcÞ \Ul(u)
Semantics (5)
model: M ¼ ÆD; W; C; I; Bel; <æ a. D is a (fixed) domain of individuals b. W is a set of possible worlds c. C is a set of contexts27 (i) there is a function that associates each c 2 C with a world wc 2 W (ii) for indexical and proper name predicates P 2 fjohn; mary; speaker; center; . . . g and c 2 C: I(P)(c) is a singleton or ; (but never empty with ‘‘center’’) and I(P)(c) 4 I(P)(wc)
27 In this framework, contexts are not structurally different from possible worlds, so W and C may well overlap.
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(4)
312 Proper Names and Indexicals Trigger Rigid Presuppositions d. I is an interpretation function if P is an n-place predicate, then IðPÞ : C [ W/§ðDn Þ e. Bel assigns each individual a belief set: Bel : D 3 ðW [ CÞ/§ðCÞ f. < is a relation of comparative similarity on worlds: if w, w#, w$ 2 W [ C then w# <w w$ means w# is at least as close to w as w$ is. (6)
a. if l is label, u an LDRS, f an l-proper embedding for u, w 2 W [ C, define: f ~w,lPl(n1. . .nn) iff there is a g Ul ðuÞ f such that g ~w,lc for all c 2 Conl(u) b. if l is label, c an LDRS condition bearing label l, f an l-proper embedding for c, and w 2 W [ C, define: (i) f ~w;l Pl ðn1 . . . nn Þiff Æf ðn1 Þ . . . f ðnn Þæ 2 IðPÞðwÞ (ii) f ~w,l u 0l w iff for all g Ul ðuÞ f with f ~w,l u, there exists h Ul ðwÞ g with g ~w,l w (iii) f ~w,l u )l w iff in one of the u-worlds maximally similar to w, w holds too, that is, iff there is a w# and a g U(u)f with (i) g ~w#,l u and (ii) for all w$: w# <w# w$ if g ~w$,l u, and there is an h U(w) g such that h ~w$,l w (iv) f ~w,l Belnl u iff for all Belðf ðnÞ; wÞ \\u\\ (cf. (14) for definition of \\. . .\\) (9)
basic layered contents: if u is an LDRS, l a label, f an l-proper embedding for u, w 2 W [ C, define:
a. ½½uw,l ¼ 1 iff ; ~w,l u (the empty embedding is an l-proper embedding for u that verifies the l layer of u in w) b. ½½ul : W/f0; 1g; w 1 ½½uw,l (10) anchored interpretation: if u is an LDRS a. a function a : FVl ðuÞ/D is an anchor for the l-layer of u b. if a is an anchor for the l-layer of u, Æu, aæ is an anchored LDRS c. if a is an anchor for the l-layer of u, ½½Æu, aæw,l ¼ 1 iff a ~w,l u (11) the kk -anchor: if u is an LDRS, c 2 C, define:
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(7) (8)
embedding: f is an l-proper embedding for an LDRS or labelled condition w iff Dom( f ) FVl(w) notation: f A g iff f g and Dom(f) A truth definition:
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!½½ukk ;c ¼ the smallest embedding f with Domðf Þ ¼ Ukk ðuÞ and f ~kk;c u (12) proposition: if u is an LDRS, c 2 C, define: ½½uc : W/f0; 1g; w1½½Æu; !½½uuc;kk æw;fr (13) utterance truth: if u is an LDRS, c 2 C define: an utterance of u in c is true iff ½½uc(wc) ¼ 1 (14) diagonal proposition: if u is an LDRS, define:
Acknowledgements I thank Corien Bary and Jennifer Spenader for commenting on an early draft. I thank Hans Kamp, Ede Zimmermann, Philippe Schlenker, Bart Geurts, Henk Zeevat, Nick Asher, Rob van der Sandt, Kees de Schepper and Helen de Hoop for valuable discussions about the issues covered in the paper. I thank the audiences of TaBu 2006 (Groningen), Rob’s Festshop (Nijmegen), LUSH (Utrecht), Sinn und Bedeutung XI (Barcelona) and the ESSLLI workshop ‘What syntax feeds semantics?’ (Hamburg) for comments on presentations of different parts of this work. Finally, I thank the editor and three anonymous referees for their reports, which have greatly benefited the paper. This research is supported by the Netherlands Organization for Scientific Research (NWO), mostly under grant 446-07-004.1c
EMAR MAIER Department of Linguistics Radboud University Nijmegen Nijmegen The Netherlands e-mail:
[email protected]
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Partee, B. (1989), ‘Binding implicit variables in quantified contexts’. In C. Wiltshire et al. (eds.), CLS, vol. 25. University of Chicago Press. Chicago. 342–65. Prince, E. F. (1981), ‘Toward a taxonomy of given–new information’. In P. Cole (ed.), Radical Pragmatics. Academic Press. New York. 223–55. Pulman, S. G. (1997), ‘Higher-order unification and the interpretation of focus’. Linguistics and Philosophy 20:73–115. Roeper, T. (2006), ‘Not only I: notes on the syntax of focus binding’. In P. Brandt et al. (eds.) Form, Structure, and Grammar: a Festschrift Presented to Gu¨nther Grewendorf on Occasion of His 60th Birthday. Akademie Verlag. Berlin. 73–115. Sag, I. (1976), Deletion and Logical Form. Ph.D. thesis, MIT. Cambridge, MA. van der Sandt, R. (1992), ‘Presupposition projection as anaphora resolution’. Journal of Semantics 9:333–77.
First version received: 19.6.2008 Second version received: 3.12.2008 Accepted: 18.12.2008
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Nunberg, G. (2004), ‘The pragmatics of deferred interpretation’. In L. Horn and G. Ward (eds.), Handbook of Pragmatics. Wiley. Malden. 344–64.
Schlenker, P. (1999), Propositional Attitudes and Indexicality. Ph.D. thesis, MIT. Cambridge, MA. Schlenker, P. (2003), ‘A plea for monsters’. Linguistics and Philosophy 26: 29–120. Sommers, F. (1982), The Logic of Natural Language. Clarendon Press. Oxford. von Stechow, A. (2002), ‘Binding by verbs: tense, person and mood under attitudes’. In M. Kadowaki and S. Kawahara (eds.), Proceedings of NELS 33. GLSA. Amherst. 379–403. Wescoat, M. (1989), Sloppy Readings with Embedded Antecedents. MS, Stanford. Zeevat, H. (1999), ‘Demonstratives in discourse’. Journal of Semantics 16:279–313. Zeevat, H. (2000), ‘The asymmetry of optimality theoretic syntax and semantics’. Journal of Semantics 17: 243–62. Zimmermann, T. E. (1991), ‘Kontextabha¨ngigkeit’. In A. von Stechow and D. Wunderlich (eds.), Semantik/Semantics: Ein internationales Handbuch der zeitgeno¨ssischen Forschung. Walter de Gruyter. Berlin. 156–229. Zimmermann, T. E. (2004), ‘Tertiumne datur?’ Possessive pronouns and the bipartition of the lexicon. In H. Kamp and B. Partee (eds.), ContextDependence in the Analysis of Linguistic Meaning. Elsevier. Amsterdam. 319– 32. German version appeared in Zeitschrift fu¨r Sprachwissenschaft 14 (1995). 54–71.
Journal of Semantics 26: 317–328 doi:10.1093/jos/ffp005 Advance Access publication June 2, 2009
Counterfactual Donkey Sentences: A Response to Robert van Rooij YINGYING WANG Sun Yat-sen University and University of Amsterdam
Robert van Rooij (2006) proposed an analysis of counterfactual donkey sentences by combining the Stalnaker–Lewis analysis of counterfactuals with standard dynamic semantics. This paper points out some problems with van Rooij’s treatment of counterfactual sentences in the language of first-order logic and provides a new interpretation using dynamic semantics.
1 VAN ROOIJ’S THEORY OF COUNTERFACTUAL DONKEY SENTENCES To analyse the interplay of indefinites, pronouns and epistemic modalities, Groenendijk et al. (1996) provide a dynamic semantics for a language of first-order modal predicate logic. This approach differs from the traditional static one in that the meaning of a sentence is identified with its context change potential rather than with its truth conditions. Or, as Robert van Rooij puts it: ‘According to the alternative dynamic view, we interpret sentences with respect to a context that is represented by a set of world-assignment pairs, and the meaning of the sentence itself can be thought of as the update of this context, where possibilities are eliminated when the sentence is false, and the assignment of the possibilities is enriched if a new variable, or discourse referent, is introduced by way of an indefinites.’ van Rooij (2006: 391) One of the characteristics of this dynamic system is the following equivalence: ðdxPxÞ/Qx [ "xðPx/QxÞ1 1
See Groenendijk et al. (1996: 198). The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email:
[email protected].
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Abstract
318 Counterfactual Donkey Sentences This equivalence makes it possible to translate donkey sentences into logical formulae corresponding to their surface structures. Thus, donkey sentences can be interpreted in a compositional way. However, donkey sentences do not only show up in the indicative mood, in which case they can be analysed using material implication; we have counterfactual donkey sentences as well. For instance, (1) If John owned a donkey, he would beat it. In order to deal with sentences like (1), a straightforward idea is to extend the dynamic system for modal predicate logic with counterfactuals. This is exactly what van Rooij did in van Rooij (2006):
To achieve this goal, van Rooij’s basic idea is to combine the Stalnaker– Lewis analysis of counterfactuals with the system of dynamic semantics that we just mentioned. More precisely, first, based on the comparative similarity relation between worlds <w used by Lewis–Stalnaker, van Rooij defined the comparative similarity relation <Æw;gæ between world–assignment pairs as follows: Æw#; g#æ <
Æw;gæ
Æw$; g$æ iff w# <w w$, g#, g$ g and g# ¼ g$.3
According to this definition, two possibilities are comparable to Æw, gæ just in case their assignments coincide and extend g. w# <w w$is read as ‘w# is closer to w than w$’. Likewise, Æw#; g#æ < Æw;gæ Æw$; g$æ is read as ‘Æw#, g#æ is closer to Æw, gæ than Æw$, g$æ’. Then, in line with the Stalnaker–Lewis definition of selection functions, van Rooij defined the selection function f* from sets of world–assignment pairs to sets of world–assignment pairs as follows: (///g) ¼ fÆw#, g#æ 2 ///g: for all the Æw$, g$æ 2 ///g, Æw#, g#æ <Æw;gæ Æw$, g$æg, where ///g ¼ [/](fÆw#, g#æ: w# 2 W & g# ¼ gg).4 Roughly speaking, ///g stands for the set of the world–assignment pairs in which / can be verified. Here the basic idea is that a selection 2 In van Rooij (2006), ‘>’ is used to represent the counterfactual connective. To unify the symbols in this paper, here we change all ‘>’ into ‘,’. 3 See Definition 1 in van Rooij (2006). 4 See Definition 2 in van Rooij (2006).
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‘. . . we would like to represent (1) abstractly as (dxPx) , Qx, while still being equivalent with "x(Px , Qx). The challenge is to account for this equivalence, without giving up our standard dynamic account of indefinites.’2 (van Rooij 2006: 391)
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function selects the closest antecedent possibilities based on the comparative similarity relation between world–assignment pairs which was defined earlier. Finally, just like Stalnaker–Lewis definition of the truth condition of a counterfactual, a counterfactual is defined to be true if its consequent can also be verified in these selected antecedent possibilities. The main result in van Rooij’s extended dynamic system is that the following equivalence in counterfactual mood holds: (dxPx) , Qx [ "x(Px , Qx)
(2) (3)
If Alex were married to a girl from his class, it would be Sue. If I had a quarter in my pocket, I would throw it into the meter.
According to van Rooij, the characteristic feature of identification counterfactual donkey sentences is that the indefinites in such sentences do not really introduce discourse referents; the reason for calling (3) ‘weak’ is that it does not require the speaker to put every quarter into the parking meter at a world where he has more than one quarter in his pocket. According to van Rooij, the reason why these two special types of examples fail to satisfy the above equivalence is obvious. It is too strong to say that (2) is true just in case for any individual, if that individual were from Alex’s class and married to him, it would be Sue, and the same also applies to (3). Given this, van Rooij has to find a way to avoid this strong reading. The trick he uses is first to introduce a set of variables X showing which variables in the antecedent are unselectively ; X bound and then to define the comparative similarity relation <Æw;gæ between world–assignment pairs as follows: ; X Æw$; g$æ iff w#<w w$, g#, g$ g and g#[X ¼ g$[X.5 Æw#; g#æ <Æw;gæ
g# [X and g$ [X in the above definition stand for the restriction of g# and g$ to X, respectively. Finally, by redefining the selection function 5
See Definition 3 in van Rooij (2006).
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This is exactly what he wanted to achieve. Consequently, he concluded that counterfactual donkey sentences can be interpreted in a natural and compositional way just like indicative counterfactuals. However, the above equivalence has its weaknesses. van Rooij himself points out that it cannot be applied to two particular types of counterfactuals: identification counterfactuals like (2) and weak counterfactual donkey sentences like (3).
320 Counterfactual Donkey Sentences ; X based on the current similarity relation <Æw;gæ in the same way as he did before, van Rooij claims that (2) can be predicted as expected if it is represented in such a way that X ¼ / just in case Alex is married to Sue (and only Sue) in the world closest to the actual one among the worlds where Alex is married to a girl from his class. His account of (3) proceeds along similar lines, but I will not describe it in detail here. In section 2, I hope to show that there is no need to think of (2) or (3) as special cases.
2 PROBLEMS
Scenario. There is one tiger t and one lion l in the zoo. Now it is found that the cage for t is open, but fortunately t is still sitting in it, and l is sitting in its own closed cage. Now the question is: would you accept the following sentence? (4) If an animal had escaped, it would have been a tiger.7 The answer seems to be ‘yes’. Because the cage for t is open, while the one for l is closed, it is very unlikely that l would have escaped. But according to van Rooij’s account for counterfactual donkey sentences, the answer is ‘no’, at least if we take the counterfactual at face value and
6
See van Rooij (2006: 393). Thanks to the anonymous reviewer who provided this example. It is much simpler than the one used in the first version of this paper, which was inspired by Kratzer (1989) and Williamson (2008), and went as follows: In the zoo, there are two tigers, t1 and t2, and one lion l. It is discovered that the tigers’ cage is open and that t1 escaped. t2 is still in its cage, as is l, whose cage is properly locked. Now the question is whether we should accept the statement, ‘Besides t1, if another animal in the zoo had escaped, then it would have been a tiger.’ 7
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Van Rooij believes that weak counterfactual donkey sentences are the exception rather than the rule. Generally speaking, a counterfactual donkey sentence is equivalent to a formula with wide scope universal quantification.6 Unfortunately, he does not supply an independent, syntactic criterion that tells us when we are dealing with an exceptional case. This means that classifying an example as ‘weak’ becomes an ad hoc decision, if not just a way to save his theory from falsification. Below, I will defend the view that the equivalence between (dxPx) , Qx and "x(Px , Qx) does not in general hold. There is no need to make a distinction between weak and strong counterfactual donkeys. Let us first take a look at the following scenario:
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treat it as a normal case, in which the key equivalence holds. The sentence gets the following translation: (5)
(dx(Ax ^ Ex)) , Tx8
According to van Rooij’s equivalence, we can safely assert that (5) is equivalent with the following formula, with wide scope for the universal quantifier: (6)
"x((Ax ^ Ex) , Tx)
8
A, E and T are predicates for ‘is an animal’, ‘escape’ and ‘is a tiger’, respectively.
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Thus, it is predicted that the sentence in question is false because in the course of verifying (6), we must consider assigning the lion l to the variable x, but in this case the closest worlds in which the lion l escaped, that is, Al ^ El holds, can never be the one where it is a tiger, that is, Tl holds, in the situation as described. Now, of course one might claim that this is an exceptional case and that the example should be treated as a ‘weak’ counterfactual. But rather than taking recourse to such an ad hoc manoeuvre we may wonder what has gone wrong. As far as we can see, the problem lies in the interaction of the anaphora with the selection of the closest antecedent worlds. As we explained earlier in section 1, the selection function defined by van Rooij is based on the similarity relation between world–assignment pairs rather than worlds. According to van Rooij’s definition of this kind of similarity relation, two world– assignment pairs are comparable only in case they have the same assignment, but this means that if there is one new variable introduced by the antecedent of a counterfactual, we should check for each individual in the domain separately which are the closest antecedent possibilities, and this is precisely the reason why the lion l has to be considered when evaluating the sentence in question above. Actually, the selection function needs to be independent of the details of the assignment function and so to choose the world– assignment pairs whose worlds are the closest to the evaluation world. This gives the right interpretation for (4) because the world closest to the real world where an animal escaped is the one in which t escaped but l did not; moreover, t is indeed a tiger there. So, in section 3, we will give a new interpretation of counterfactuals in dynamic semantics where the selection function will be defined based on the comparative similarity relation between worlds, rather than world–assignment pairs, just as in the original proposals by Stalnaker and Lewis. Counterfactuals will be treated in a unified way. In the following text, I will always use
322 Counterfactual Donkey Sentences the phrase ‘first-order counterfactuals’ as short for ‘counterfactuals in a language of first-order predicate logic’. 3 SOLUTION Our theory is based on the version of dynamic semantics given in Groenendijk et al. (1996). We will first introduce some of their basic notions, and then we will give the update condition for first-order counterfactuals based on these notions.
The language L0 is standard first-order language. A model M for L0 is a pair ÆW, Dæ, where W, the set of possible worlds, is a non-empty set of interpretation functions for the non-logical constants in L0, and D, the domain of discourse, is a non-empty set of individuals. Based on M, the notions of possibilities and information states are defined as follows: Definition 1 (Possibilities and information states) Let M ¼ ÆW, Dæ be a model for L0 and V be the set of variables in L0. (a) The possibilities based on M are a set I of pairs Æw, gæ, where w 2 W, and g is an assignment function from X (X 4 V) to D; IX ¼ fÆw, gæ 2 I: the domain of g is X, X 4 Vg. (b) The set of information states based on I is the set S such that s 2 S iff s 4 IX for some X 4 V. A possibility involves two ingredients: a possible world w and an assignment function g.9 An information state is a set of possibilities whose assignment functions have the same domain. From the following definition, we will see that a possibility contains enough information for the interpretation of the basic expressions in L0. Definition 2 Let a be a basic expression, i ¼ Æw, gæ 2 I, with X 4 V the domain of g, and I based upon W and D. The denotation of a in i, i(a), is defined as follows: (a) If a is an individual constant, then i(a) ¼ w(a) 2 D. (b) If a is an n-place predicate, then i(a) ¼ w(a) 4 Dn. (c) If a is a variable such that a 2 X, then i(a) ¼ g(a) 2 D, else i(a) is not defined. 9 We have simplified matters by leaving out the referent systems as they occur in the possibilities of the system devised in Groenendijk et al. (1996).
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3.1 Basic notions
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So, for a non-logical constant, its denotation in i is exactly what w assigns to it, while for the value of a variable, it is determined by the assignment function. The following resetting device will come in handy when we define the interpretation of existential formulae. Definition 3 Let i ¼ Æw, gæ 2 IX for some X 4 V; x ; X; d 2 D and s 4 IX. (a) i[x/d] ¼ Æw, g[x/d]æ. (b) s[x/d] ¼ fi[x/d]: i 2 sg.
Definition 4 (Subsistence)
Let s, s# 2 S, and i ¼ Æw, gæ 2 s.
(a) i subsists in s# iff di# ¼ Æw, gæ 2 s#: w ¼ w# and g 4 g#. (b) s subsists in s# iff all i 2 s subsist in s#. So, a possibility i subsists in a state s#iff there exists a possibility i#2 s# such that i# is the same as i except for the possible introduction of new variables (we shall call i#a descendant of i in s#); a state s subsists in a sate s# iff all possibilities in s subsist in s#. Now it is time to see the core of dynamic semantics—the update conditions for the formulae of L0. Definition 5 Let s 2 S be an information state, and / a formula of L0. The update of s with / is recursively defined as follows: (a) s[Rt1. . .tn] ¼ fi 2 s: Æ i(t1), . . ., i(tn)æ 2 i(R)g. (b) s[t1 ¼ t2] ¼ fi 2 s: i(t1) ¼ i(t2)g. (c) s[:/]¼ fi 2 s: i does not subsist in s[/]g. (d) s[/ ^ w] ¼ s[/][w]. (e) s[dx/] ¼ Ud2D(s[x/d][/]). Updating a state s with an atomic formula preserves those possibilities in s which satisfy the formula in a classical sense. The negation of / eliminates those possibilities that subsist after hypothetically updating s with /. Updating a state with a conjunction is done sequentially. Updating s with dx/ proceeds by collecting all the possibilities in s[x/d][/] for each object d in the domain. Now the following facts hold:
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An essential notion for the dynamic interpretation of a first-order language is the notion of subsistence.
324 Counterfactual Donkey Sentences (a) s[/ _ w] ¼ fi 2 s: i subsists in s[/] or i subsists in s[:/][w]g. (b) s[/ / w] ¼ fi 2 s: if i subsists in s[/], then all descendants of i in s[/] subsist in s[/][w]g. (c) s["x/] ¼ fi 2 s: for all d 2 D: i subsists in s[x/d][/]g. Now, the definitions of consistency and support for formulae in L0 are as follows: Definition 6 (Consistency and support) formation state, and / be a formula of L0.
Let s be an in-
(a) / is consistent with s iff s[/] exists and s[/] 6¼ /. A formula / 2 L0 is consistent with a state s 2 S if and only if updating s with / does not result in an empty set, and / is supported by s if and only if updating s with / adds no new information except for the possible introduction of new variables. Furthermore, we should mention that consistency and support now become the core concepts instead of truth and falsity because what matters in dynamic semantics is information about the world, rather than the relation between language and the world. For further discussion, see Groenendijk et al. (1996).
3.2 Dynamic interpretation of first-order counterfactuals Now we turn to the interpretation of counterfactuals in this dynamic system. Veltman (2005) proposed to treat the meaning of a counterfactual in dynamic semantics as a test. On this view, counterfactuals do not convey new information—not directly at least. Here is a quotation from his paper: £
‘By asserting £if had been /, would have been w , a speaker makes a kind of commitment: ‘given the general laws and the facts I am acquainted with, the consequent w is supported by the state I get in when I assume that the antecedent / had been the case’. Then the addressee is supposed to determine whether the same holds on account of his or her own information. If not, a discussion will arise, and in the course of this discussion both the speaker and the hearer may learn some new laws and facts, which could affect the outcome of the test.’ Veltman (2005: 171) According to Veltman’s proposal, the natural way to define the update condition for a counterfactual is this: s[/ , w] ¼ s if s[/]c ~ w; s[/ , w] ¼ ø, otherwise.
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(b) / is supported by s: s ~/ iff s[/] exists and s subsists in s[/].
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Definition 7 Let / be a formula of L0, and I a set of possibilities based on ÆD, Wæ. (a) A binary relation <w is defined on W, which is strictly partially ordered, strongly centered,11 almost connected12 and well founded. (b) For i 2 I, i is a /-possibility iff fig ~ /. S (c) ///g ¼ i 2 I#fig[/] (I# ¼ fi 2 I: i is a /-possibility whose assignment is gg). (d) the selection function f(///g, Æw, gæ) ¼ fÆw#, g#æ 2 ///g: for all Æw$, g$æ 2 ///g, w# <w w$g. S (e) s[/]c ¼ Æw, gæ 2 sf(///g, Æw, gæ). Let us explain this definition. First, a comparative similarity relation with the properties listed above is defined on W. With these properties, we can say that w# is closer to w than w$ if w# <w w$.13,14 Then, the notion of /-possibility is introduced: i is a /-possibility iff / is supported by the state fig. The set ///g is defined to guarantee that if / introduces some new variables, all of them are interpreted in these possibilities, that is, when / does not introduce new variables, all the 10 Here we deviate from Veltman (2005), who does not start from a fixed comparative similarity relation to define s[/]c. 11 Strong centering: "w, v: w 6¼ v 0 w <w v. 12 Almost connected: "u, v, w, z: u
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We assume that s[/]c in above informal definition is the subordinate state where we get in when assuming that the antecedent / had been the case. Then Veltman’s definition says that if w is supported by this subordinate state, updating a state s with / , w leaves the state s unchanged; otherwise, the update results in the empty set. In our theory, we will adopt this update condition for counterfactuals. Then in the following, we will explain what this subordinate state really is. Our strategy is to apply the Stalnaker–Lewis account of counterfactuals to the dynamic framework.10 More precisely, we will define the state we get in when assuming that / had been the case to be the set obtained by taking each possibility i in s the /-possibilities closest to i. To formalize this idea, we need to introduce the following auxiliary notions:
326 Counterfactual Donkey Sentences
So now, formally, we can give the following update condition for counterfactuals in dynamic semantics: Definition 8 (Counterfactuals as tests) formulae of L0, s 2 S.
Let / and w be
s[/ , w] ¼ s, if s[/]c ~ w, s[/ , w] ¼ ø, otherwise. With these technicalities out of the way, let us now see how the problems discussed above can be handled. 4 ILLUSTRATION We construct the following model for the zoo scenario: D ¼ fd1, d2g, W ¼ fw0, . . ., w3g, wk(t) ¼ d1, wk(l) ¼ d2, wk(A) ¼ fd1, d2g, wk(T) ¼ fd1g (0 < k < 3) and the denotations of E are different in each wk (as in the table below). Obviously, w0 is the real world. Then, it is reasonable for us to define the following binary relation <w0 on W: w0 <w0 w2 <w0 w1 <w0 w3 . Suppose that the real information state s is fÆw0, gæg and that the domain of g is empty. E(t)
E(l)
w0
0
0
w1
0
1
w2
1
0
w3
1
1
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elements in ///g are /-possibilities with the same assignment g, but when / does introduce new variables, the elements of ///g are /-possibilities whose assignments only differ from g in that these newly introduced variables are interpreted. Then the selection function f(///g, Æw, gæ) is defined to pick out the possibilities in ///g whose world is the closest to w. Following Stalnaker and Lewis, we call these possibilities the /-possibilities closest to Æw, gæ. Note that the choice of the closest antecedent possibilities now only depends on the comparative similarity relation between the worlds involved; unlike in van Rooij’s definition, assignments play no role. Finally, we define the counterfactual update function. From this, we can obtain the collection for each possibility Æw, gæ in the state s the /-possibilities closest to Æw, gæ. And this is exactly what we want.
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The formula under evaluation is as follows: (5)
(dx(Ax ^ Ex)) , Tx
What we are going to check is whether (5) is supported by the information state s. According to our theory, first, we need to work out all the possibilities in /dx(Ax ^ Ex)/g: /dx(Ax ^ Ex)/g ¼ fÆw1, g[x/d2]æ, Æw2, g[x/d1]æ, Æw3, g[x/d1]æ, Æw3, g[x/d2]æg.
15 van Rooij (2006) deals with two more issues in conditional logic: one is the intuitive plausibility of SDA ((((/ _ w) , v) / ((/ , v) ^ (w , v)))), and the other is the appropriateness of the negative polarity item any in the antecedents of counterfactuals. [See details in section 3.2 of van Rooij (2006).] van Rooij claimed that these two problems can be solved in his framework. But as far as we can see, both of his solutions on these two problems rely on the general equivalence between (dxPx) , Qx and "x(Px , Qx). Without this equivalence, his proposal cannot stand. We will propose different solutions to these two problems in a forthcoming paper on counterfactuals in dynamic context.
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All these possibilities are antecedent possibilities whose assignments are the same as g except that the variable x is interpreted. Now the selection function can do its job. According to our definition, the possibility we have to pick out is Æw2, g[x/d1]æ because this possibility is the one whose world is the closest to w0 among the possibilities in / dx(Ax ^ Ex)/g. Since the denotation of x is d1, and d1 is a tiger, we can conclude that (5) is supported by the information state s, which means that the counterfactual in question is acceptable according to our theory. This is the right result. Turning to identification counterfactual donkey sentences like (2), since van Rooij has already showed that there is no problem if the set of unselective binding variables is empty (the comparative similarity relation between world–assignment pairs reduces to the one between worlds in this case), (2) is explained by our analysis as well, for the comparative similarity relation defined in our theory is always between worlds. For the same reason, it is also easy to see that weak counterfactual donkey sentences like (3) are handled correctly, too. To conclude, we have argued that a counterfactual donkey formula like (dxPx) , Qx should not be equivalent to "x(Px , Qx) and offered a semantics in which they are not. What is expressed by a dynamic formula of the form (dxPx) , Qx cannot be expressed by any static formula, or so it seems. Our dynamic interpretation can be used as a unified way to account for first-order counterfactuals, especially the donkey ones.15
328 Counterfactual Donkey Sentences Acknowledgements This paper was written under the supervision by Prof. Frank Veltman when I was studying in Amsterdam as a guest research student. My indebtedness to him is immeasurable. I further benefited from helpful discussion and criticism by Robert van Rooij, Johan van Benthem, Timothy Williamson, Dick de Jongh, Shier Ju, as well as two anonymous reviewers. I would like to thank all these people. Of course, none of them is responsible for any errors that remain.
REFERENCES Groenendijk, J., M. Stokhof, & F. Veltman (1996). ‘Coreference and modality’. In S. Lappin (ed.), The Handbook of Contemporary Semantic Theory. Blackwell. Oxford. 179–213. Kratzer, A. (1989). ‘An investigation of the lumps of thought’. Linguistics and Philosophy 87:3–27. Lewis, D. (1973). Counterfactuals. Blackwell. Oxford.
van Rooij, R. (2006). ‘Free choice counterfactual donkeys’. Journal of Semantics 23:383–402. Veltman, F. (2005). ‘Making counterfactual assumptions’. Journal of Semantics 22:159–180. Williamson, T. (2008). The Philosophy of Philosophy. Blackwell. Oxford. First version received: 09.07.2008 Second version received: 07.01.2009 Accepted: 08.03.2009
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