JOURNAL OF SEMANTICS Volume 23 Number 4
CONTENTS TANIA IONIN AND ORA MATUSHANSKY The Composition of Complex Cardinals
315
BENJAMIN RUSSELL Against Grammatical Computation of Scalar Implicatures
361
ROBERT VAN ROOIJ Free Choice Counterfactual Donkeys
383
Editor’s Note
403
Please visit the journal’s web site at www.jos.oxfordjournals.org
Journal of Semantics 23: 315–360 doi:10.1093/jos/ffl006 Advance Access publication November 16, 2006
The Composition of Complex Cardinals TANIA IONIN USC/UIUC ORA MATUSHANSKY CNRS/Universite´ Paris 8
This paper proposes an analysis of the syntax and semantics of complex cardinal numerals, which involve multiplication (two hundred) and/or addition (twentythree). It is proposed that simplex cardinals have the semantic type of modifiers (ÆÆe, tæ, Æe, tææ). Complex cardinals are composed linguistically, using standard syntax (complementation, coordination) and standard principles of semantic composition. This analysis is supported by syntactic evidence (such as Case assignment) and semantic evidence (such as internal composition of complex cardinals). We present several alternative syntactic analyses of cardinals, and suggest that different languages may use different means to construct complex cardinals even though their lexical semantics remains the same. Further issues in the syntax of numerals (modified numerals and counting) are discussed and shown to be compatible with the proposed analysis of complex cardinals. Extra-linguistic constraints on the composition of complex cardinals are discussed and compared to similar restrictions in other domains.
1 INTRODUCTION The goal of this paper is to propose an account of the cross-linguistic syntax and semantics of complex cardinals. While there has been much work examining the syntax and semantics of simplex cardinals such as three, complex cardinals, which involve multiplication (1) and/or addition (2), have not previously received much attention. (1) a. five hundred thousand b. quatre vingt four twenty ‘eighty’ (French) (2) a. three hundred and five b. twenty-seven c. tri ar ddeg three on ten ‘thirteen’ (Welsh)
Hurford (2003)
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Abstract
316 The Composition of Complex Cardinals d. sto sem’ hundred seven ‘a hundred and seven’ (Russian)
1 We use the term xNP rather than NP or DP to indicate that it is irrelevant which functional layers are projected and which aren’t.
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We will argue that complex cardinals are composed entirely in syntax and interpreted by the regular rules of semantic composition (i.e., construction of complex cardinals is done exclusively by linguistic means). This analysis is independently motivated by syntactic transparency of complex cardinals and their compositional semantics. The paper is organized as follows. In section 2 we argue that simplex cardinals have the semantic type of modifiers (ÆÆe, tæ, Æe, tææ) and show how this accounts for the internal composition of complex cardinals via iterative syntactic complementation. Existential force of cardinal-containing extended NPs (xNPs)1 in argument positions is also treated in this section. Section 3 addresses the semantic atomicity requirement imposed by cardinals on their complements, and shows that such morphosyntactic operations as Case-assignment and number marking in cardinal-containing xNPs provide evidence that complex cardinals are built in the syntax; this section also discusses extralinguistic factors in the composition of complex cardinals. Section 4 presents an analysis of complex cardinals like twenty-two in terms of coordination and discusses some ordering constraints. Section 5 concludes the paper and poses some questions for further research. The Appendices address some further issues in the syntax and semantics of cardinals. Since our goal is to provide an analysis that works for complex cardinals cross-linguistically, we draw upon data from a variety of (typologically different) languages. While some empirical phenomena (e.g. articles, morphological Case assignment, etc.) are visible only in a subset of languages, we will extend the analysis based on these phenomena to other languages, unless there are empirical reasons for not doing so. One caveat is in order: we focus primarily on nonclassifier languages in this paper; however, we show in section 3 that our analysis can be logically extended to classifier languages as well. Due to lack of space, we concentrate here on the semantics of complex cardinals, and discuss their syntax in a relatively superficial manner. More discussion of the thornier issues arising in our analysis can be found in Ionin & Matushansky (in preparation).
Tania Ionin and Ora Matushansky 317
2 SEMANTICS OF CARDINALS This section is dedicated to the semantics of complex cardinals involving multiplication. We ask how complex cardinals such as three hundred, four hundred thousand, etc., are composed semantically (on cardinals involving addition, such as forty-two, see section 4). The background assumption we start with is that the semantics of cardinals is the same cross-linguistically, at least in languages that have complex cardinals.2 We follow the natural hypothesis that complex cardinals are derived from simplex ones: that four hundred should be semantically related to four as well as hundred.3
Furthermore, we strive to capture the basic intuition that the four in (3a) is semantically the same as the four in (3b). The meaning of a complex cardinal should be derived in such a way that each cardinal inside it is also semantically compatible with a lexical xNP: the same four should be able to combine with books as easily as with hundred books.
2.1 Semantic type of cardinals: cardinals are modifiers The above intuition is captured straightforwardly if simplex cardinals have the semantic type of modifiers (ÆÆe, tæ, Æe, tææ). Although the proposal that cardinals are modifiers has been much discussed in the literature (see Link 1987; Verkuyl 1993; Carpenter 1995; Landman 2003, among others), no distinction has previously been made between simplex and complex cardinals. We propose that simplex cardinals are of type ÆÆe, tæ, Æe, tææ, and derive the meaning of xNPs containing complex cardinals compositionally. In order to derive the meaning of complex cardinals, we need full recursivity, which we derive from the semantic type ÆÆe, tæ, Æe, tææ, as illustrated in the structure in (4), where the lexical xNP is the sister 2
The semantics that we propose for simplex cardinals is necessary only for languages that have complex cardinals. The main motivation for the semantic type ÆÆe, tæ, Æe, tææ (see below) is the compositional semantics of complex cardinals; if a language has only simplex cardinals, they can be type Æe, tæ and combine with the lexical xNP via Predicate Modification—see section 2.2.2. It is quite likely that cardinals historically developed from type Æe, tæ (see also Hurford 2001); in some languages simplex cardinals originate as predicates synchronically as well, and are converted to the modifier type (see Ionin and Matushansky (in preparation)). Since the issue is orthogonal to our concerns, we will not address it here. 3 One option that we do not discuss here, in view of total lack of morpho-syntactic evidence for such a hypothesis, is that not all simplex cardinals inside a complex one have the same semantic type (i.e. that four is ÆÆe, tæ, Æe, tææ in (3a) and Æe, tæ in (3b)).
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(3) a. four hundred books b. four books
318 The Composition of Complex Cardinals of the innermost cardinal. (5) is a sample lexical entry for simplex cardinals.
ð4Þ
tæ
. kx 2 De . dS 2 DÆe,
tæ
[P(S)(x) ^ jSj ¼ 2 ^
S is a partition P of an entity x if it is a cover of x and its cells do not overlap (cf. Higginbotham 1981: 110; Gillon 1984; Verkuyl & van der Does 1991; Schwarzschild 1994): (6) P(S)(x) ¼ 1 iff partition S is a cover of x, and "z, y 2 S [z ¼ y _ :da [a
(i) C is a set of subsets of X (ii) Every member of X belongs to some set in C (iii) Ø is not in C The first two conditions amount to claiming that X is the union of all members of C ([C¼X). The last condition is superfluous for the definition in terms of (plural) individuals, since we do not assume empty individuals in the domain. 5 See section 3 for a discussion of the semantic and morphological plurality of the lexical xNP here.
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(5) ½½2 ¼ kP 2 DÆe, "s 2 S P(s)]
Tania Ionin and Ora Matushansky 319
b. kx 2 De . x is a plural individual divisible into 100 nonoverlapping individuals pi such that their sum is x and each pi is a book (8a) shows that hundred books, being of type Æe, tæ, can be a sister of a cardinal, such as two, which has the denotation in (5) and the type ÆÆe, tæ, Æe, tææ. We have therefore achieved full compositionality—and this gives us the denotation for two hundred books in (9a), with its informal variant in (9b).6
Having the semantic type of modifiers, cardinals necessitate an argument of type Æe, tæ. We have already shown that this can be an xNP argument, as in two books. We predict that a cardinal can also take a PP argument, as in two thirds of this book. (On regular partitives, see Ladusaw 1982; Hoeksema 1984, 1996; Barker 1998; Cardinaletti & Giusti 2005; Gawron 2002 and Ionin, Matushansky and Ruys to appear, among others; see Martı´ Girbau, in press, on whether they contain a null NP.) We can therefore analyse fractions as fully compositional and built on the structure of regular partitives (see Ionin et al., to appear, where we extend our analysis of cardinals to cardinal, measure and fraction partitives).
2.2 Ruling out alternative semantic types xNP-internal cardinals have also been treated as determiners (semantic type ÆÆe, tæ, ÆÆe, tæ, tææ—see Bennett 1974; Scha 1981; van der Does 1992, 1993 among others) or as predicates (type Æe, tæ—see Partee 1986). As shown below, these alternatives do not work for complex cardinals (for which they were never intended, to be fair). 2.2.1 Ruling out the determiner theory of cardinals. If simplex cardinals have determiner type ÆÆe, tæ, ÆÆe, tæ, tææ, then it is not possible to derive the semantics of complex cardinals, as shown by (10). If hundred is 6
Note that two/hundred on our analysis means exactly two/exactly hundred, rather than at least two/at least a hundred, since otherwise two hundred books would mean, roughly, ‘at least two sets of at least a hundred books’. See Krifka (1999) for other problems with the at least analysis of cardinals.
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(9) a. ½½two hundred books ¼ kx2De . dS [P(S)(x) ^ jSj¼2 ^ "s2S dS’ [P(S’)(s) ^jS’j¼100 ^ "s’2S’ ½½book (s’)]] b. kx 2 De. x is a plural individual divisible into 2 nonoverlapping individuals pi such that their sum is x and each pi is divisible into 100 non-overlapping individuals pk such their sum is pi and each pk is a book
320 The Composition of Complex Cardinals combined with books first, as we have proposed, the resulting NP is a generalized quantifier (type ÆÆe, tæ, tææ), which cannot then be combined with another cardinal of type ÆÆe, tæ, ÆÆe, tæ, tææ.
ð10Þ
2.2.2 Ruling out the predicate theory of cardinals The proposal that cardinals are predicates (type Æe, tæ) faces the same problem as the proposal that cardinals are determiners: semantic composition of complex cardinals would fail, unless additional assumptions are made. Unlike the proposal discussed in subsection 2.2.1, assuming that simplex cardinals are predicates does not lead to a type clash. The relevant interpretation rule for complex cardinals (Predicate Modification) does exist and treats the semantic composition of two predicates (type Æe, tæ) as conjunction (Heim & Kratzer 1998). This results in an xNP of type Æe, tæ, as shown in (11).
ð11Þ
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The problem would not be solved if hundred combined with two before combining with books. This would mean combining two determiners of type ÆÆe, tæ, ÆÆe, tæ, tææ. However, we have no semantic rules for combining two elements of type ÆÆe, tæ, ÆÆe, tæ, tææ and moreover, such combinations are independently disallowed—cf. the every book, no these books, etc. Though the proposal that (simplex) cardinals are determiners is usually associated with a syntactic structure where they are projected as heads (Ritter 1991; Giusti 1991, 1997; Zamparelli 1995, 2002), semantically, this view is indistinguishable from the theory that they occupy the specifier of some functional projection, since in both approaches they form a unit to the exclusion of the lexical xNP (see section 3.1 for discussion).
Tania Ionin and Ora Matushansky 321
However, Predicate Modification would result in incorrect truthconditions for complex cardinals, whatever semantics we assume for simplex cardinals. Suppose that we assume the very simple semantics in (12). The xNP two hundred books would then be self-contradictory, since nothing can simultaneously have the cardinality 100 (consist of 100 atoms) and the cardinality 2 (consist of 2 atoms).
(13) a. ½½two ¼ kx 2 De . dS [P(S)(x) ^ jSj¼2] b. ½½hundred ¼ kx 2 De . dS [P(S)(x) ^ jSj¼100] c. ½½200 books ¼ kx 2 De . dS [P(S)(x) ^ jSj¼2] ^ dS# [P(S#)(x) ^ jS#j¼100 ^ ½½books(x)] Once again, the standard approaches to cardinals treating them as a unit to the exclusion of the lexical xNP, don’t help: the order in which two, hundred, and books combine is irrelevant, since on the view discussed here all three are predicates.
2.3 Syntax and semantics of existential quantification If xNPs containing cardinals have the type of predicates (Æe, tæ) what happens to such xNPs in argument positions? We know that such xNPs may be part of definite or quantificational DPs, as in (14). The fact that cardinals can combine with determiners means that cardinals are not determiners, since semantic combination of two determiners is independently known to be impossible. (14) the two birds/every two birds/those two birds In cases like (14), the semantic composition is straightforward: the determiner (type ÆÆe, tæ, ÆÆe, tæ, tææ) combines with the xNP two birds (predicate type Æe, tæ), resulting in a generalized quantifier (type ÆÆe, tæ, tææ). (Alternatively, the definite article may map the predicate to a type e R-expression).
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(12) a. ½½two ¼ kx 2 De . jxj¼2 b. ½½hundred ¼ kx 2 De . jxj¼100 c. ½½two hundred books ¼ kx 2 De . ½½books(x) ^ jxj¼100 ^ jxj¼2 Suppose that we assume instead the semantics in (5), modified so that cardinals have type Æe, tæ, as shown in (13). The resulting reading for 200 books is also problematic: in order to simultaneously be divisible into 100 non-overlapping individuals and 2 non-overlapping individuals, it is sufficient for a plural individual to consist of just 100 books. This is clearly unsatisfactory.
322 The Composition of Complex Cardinals In a sentence like (15a), the xNP two birds is associated with existential force, but there is no overt element that could be judged responsible for it, unlike in (15b). (15) a. Two birds sang. b. A bird sang.
ð16Þ
On this proposal, a choice function f applies to the set of all plural individuals x, such that each x is divisible into two non-overlapping
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The standard view that (simplex) cardinals are determiners (Montague 1974; Bennett 1974; Barwise & Cooper 1981; Scha 1981; van der Does 1992, 1993; among others) attributes existential force to them as part of their semantics. However, we argued in section 2.2.1 that such an approach is untenable for complex cardinals. How is the existential force introduced in (15a)? We believe that any standard theory of indefinites can account for cardinals as well. One traditional view is that predicate xNPs can become generalized quantifiers (type ÆÆe, tæ, tæ) as a result of a type-shifting operation (see Partee 1986; Landman 2003). Another possible way of passing from the predicate reading of three birds to the generalized quantifier reading is suggested by Krifka (1999). While Krifka’s semantic analysis of cardinals, based on that of Link (1987), is different from ours, his proposal that the empty D head is interpreted as an existential quantifier is fully compatible with our view. Alternatively, the existential force is introduced via global existential closure, per Heim (1982). In view of the above, our analysis clearly can shed no new light on the availability of long-distance scope readings (cf. Fodor and Sag 1982 and much subsequent literature). In the vast literature on indefinites (see, among many others, Farkas 1981; Ludlow & Neale 1991; Ruys 1992; Winter 1997, 2001a, 2005; Kratzer 1998), indefinites containing unmodified cardinals (three birds, four books, etc.) have been shown to behave much like indefinites headed by a or some with respect to exceptional scope-taking abilities. Like a- and some-indefinites, cardinal indefinites can therefore be analyzed as choice functions. We can follow the analysis of Winter (2001a, 2005), where the existential force of indefinites comes from a phonologically null choice function operator in D0. Combined with our semantics this yields the structure in (16).
Tania Ionin and Ora Matushansky 323
(17) a. (a) hundred/thousand/million/ dozen books
semi-lexical cardinals
b. (a) twenty/thirty/five/twelve/one thousand books 7 In addition to the presence of an article, semi-lexical cardinals are characterized by their compatibility with plural morphology, unlike other cardinals ( Jackendoff 1977):
(i)
a. hundreds (of ) books b. twenties of books c. three hundred (of ) books
We believe that semi-lexical cardinals are semantic modifiers (type ÆÆe, tæ, Æe, tææ) whatever the lexical category of their complement. The correlation of overt plural marking with the inability to assign Case (and hence the appearance of an of-PP rather than an xNP complement) is languagespecific, as discussed in section 3.2. It should also be noted that though the presence of an article correlates with the ability to be a multiple in English, it does not do so in French (cent livres ‘one hundred books’). 8 Note that the possibility of adjectival modification provides additional evidence in favour of treating the combination of a cardinal and an NP as a predicate.
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individuals, each of which is a bird, and returns a single such x. A DP such as two birds thus has type e: it is a plural individual (consisting of two non-overlapping individuals, each of which is a bird), which is picked out by the choice function f from the set of such plural individuals. As a result, any standard theory of indefinites combined with the semantics in (5) yields the existential force of indefinite cardinalcontaining xNPs. However, the question arises why cardinal-containing indefinite xNPs behave like a/some-indefinites rather than bare plurals. Bare xNPs are known to generally have narrow-scope readings only (Carlson 1977; Chierchia 1998, etc.), which means that they cannot combine with either choice functions or existential quantification. If, as suggested above, the existential force of cardinal-containing indefinite xNPs comes from the null determiner, why is this not available for bare plurals? We do not have a straightforward answer to this question. However, we note that the status of the determiner is not the same in bare xNPs as in cardinal-containing indefinite xNPs, as shown by the fact that the latter but not the former are compatible with the indefinite article in English. The indefinite article appears obligatorily when the leftmost cardinal is one of the so-called ‘semi-lexical’ cardinals (hundred, dozen, etc.), exemplified in (17),7 and in the modified cardinal construction8 as in (18) (for more discussion of this construction see Jackendoff 1977; Babby 1985; Gawron 2002; Ionin & Matushansky 2004, in preparation). Nothing comparable happens with English bare plurals (but see Bennis et al. 1998 for indefinite article insertion in Dutch plurals).
324 The Composition of Complex Cardinals (18) a stunning one thousand/twenty five books modified cardinals (19) (a) (stunning) books
bare plurals
2.4 Summary The compositional semantics of complex cardinals necessitates that simplex cardinals have the semantic type of modifiers, rather than determiners or predicates. If cardinals were determiners or predicates, complex cardinals would have to be treated as un-analysable units (i.e. the entire cardinal two hundred would have to have the semantic type of a determiner or predicate), and we would lose the intuition that complex cardinals are semantically related to simplex cardinals. Importantly, though the hypothesis that cardinals are semantic modifiers requires a special mechanism introducing existential force for cardinal-containing indefinite xNPs in argument positions, this mechanism is provided by any standard view of indefinites. An alternative hypothesis is that complex cardinals are constructed extra-linguistically and thus belong to a completely separate system (see Wiese 2003 for arguments in favour of this hypothesis). Our objection to this theory is twofold. Firstly, if syntactic composition and semantic interpretation of complex cardinals can be seamlessly incorporated into
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We hypothesize that the appearance of the indefinite article does not correspond to any semantic operation but marks the fact that a semantic operation introducing existential force has applied (since it distinguishes between bare plurals and cardinal-containing indefinite xNPs). We leave aside here the question why modification triggers indefinite article insertion (see Ionin & Matushansky, in preparation), but note that a similar effect occurs in the post-copular position in French (Matushansky & Spector 2005) and in Dutch (de Swart et al. 2005) and in a number of languages with proper names (Sloat 1969; Matushansky, to appear). To sum up, we have argued that the existential force of cardinalcontaining indefinite xNPs in argument positions does not come from the cardinal involved. Instead, any standard theory introducing existential force (existential closure, type-shifting, choice functions, etc.) is applicable here. We have observed that cardinal-containing indefinite xNPs group with some and a indefinites rather than with bare plurals, and noted that this grouping correlates with the possibility of indefinite article insertion. While we can offer no simple explanation for when and why an indefinite article becomes obligatory, we believe that its presence marks rather than introduces existential force.
Tania Ionin and Ora Matushansky 325
standardly assumed syntax and semantics, such an appeal to an extralinguistic system is unnecessary.9 Secondly, in the next section we will show that complex cardinals are transparent to such morphosyntactic operations as Case-assignment and number marking, which means that they are constructed by regular linguistic mechanisms. Even though we have to make an appeal to extra-linguistic factors in order to explain certain ordering constraints in complex cardinals, we will argue that similar factors come into play in complex measure phrases, such as five feet five inches, for which an extra-linguistic analysis seems unwarranted.
A member of the set denoted by two books is a plural individual consisting of two atomic books. This is why for the semantics in (5) to work, the lexical complement of a cardinal has to be atomic—otherwise, a member of the set denoted by two books could have denoted a plural individual divisible into two sets of books (and thus a plural individual of unknown cardinality), which is not what we want. Likewise, two hundred books has the extension in (19b), where, crucially, each pk needs to be a single book rather than a set of books: (19) b. kx 2 De . x is a plural individual divisible into two nonoverlapping individuals pi such that their sum is x and each pi is divisible into 100 non-overlapping individuals pk such their sum is pi and each pk is a book Importantly, our compositional analysis of complex cardinals requires that the lexical xNP that a cardinal combines with denote a set of atoms. This permits us to immediately account for languages where a lexical xNP combining with a cardinal must be morphologically singular, despite the availability of plural morphology. This is illustrated by the Finnish examples from Nelson & Toivonen (2000) in (20). (20) Yhdeksa¨n omena-a puto-si maa-han. nine-NOM apple-PART.SG fall-PAST.3SG earth-ILL ‘Nine apples fell to earth.’ (Finnish) From our point of view, Finnish morphology conforms completely to what we expect: the lexical xNP is morphologically singular, 9 Cappelletti et al. (2001), Cappelletti et al. (2005) and Domahs et al. (2005), among others, claim to provide evidence for a double dissociation between numerals and other words in certain aphasiacs. However, these studies appear to have concentrated on the number words rather than on the syntax or compositional semantics of cardinals, and therefore can be argued to point merely to the loss of the lexical knowledge in a particular lexical semantic class.
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3 SYNTAX OF CARDINALS
326 The Composition of Complex Cardinals obligatorily so.10 The same phenomenon can be observed in Hungarian (Farkas & de Swart 2003), Welsh ((21) from Mittendorf & Sadler 2005), and Turkish. (21) y tair cath ddu hynny the.PL three.F cat.F.SG black.SG that.PL ‘those three black cats’ (Welsh)
3.1 The atomicity requirement Our semantics of cardinals requires that the lexical xNP complement of a cardinal denote an atomic set. We see two possibilities for ensuring this requirement: (1) a (null) classifier, and (2) a special constraint that would exclude plural lexical xNPs as complements of cardinals. Depending on the implementation of this atomicity requirement, different syntactic structures must be adopted. 3.1.1 Classifiers One standard assumption intended to distinguish between mass and count nouns is that only atoms can be counted 10 Note that the verb is singular in (20) and the determiner is plural in (21). For the effects of cardinals on number marking inside and outside the xNP, see Ionin & Matushansky (in preparation).
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If Welsh, Finnish, Turkish and Hungarian morphology correctly reflects the semantic atomicity of the lexical xNP, what happens in languages like English and Russian, where the lexical xNP in two books is morphologically plural? In section 3.1, we will discuss the two possible answers to this question: (1) the plural marking reflects semantic plurality (books in two books denotes a set of plural individuals) and some operation extracts atoms out of the plural xNP; or (2) the plural marking here is misleading: books in this context really means book (i.e. its extension consists of singular individuals (atoms)) and an additional operation marks the lexical xNP as plural. In section 3.2, we will show that number marking favours the first option and therefore a particular syntax of cardinals, and in section 3.3 we demonstrate that Case-assignment argues for a different syntax and thus for the second option. We will argue that the second option is preferable to the first (except in classifier languages), and propose how it can account for both the number marking and Case assignment facts. Finally, section 3.4 addresses the role of various extra-linguistic conventions in the composition of complex cardinals.
Tania Ionin and Ora Matushansky 327
11 Chierchia (2004) proposes a variant of the structure in (4), where the atomization operation is written directly into the lexical entry of each cardinal. This makes it necessary to relativize the definition of an atom to include such entities as hundred books. However, the property of being a ‘non-plural atom’ (necessary, for example, for the quantifier each or for plural/singular marking) then has to be redefined. This approach also has to deal with the number mismatches discussed in section 3.2 for the structure in (22a). 12 It could be argued that a third structure is available, where the classifier is a head, as in (22a), but the cardinal is a specifier, as in (22b). Such a structure can be excluded on the grounds of semantic redundancy: the cardinal in a specifier position requires a complement denoting an atomic set, i.e. another classifier. 13 The idea that cardinals occupy [Spec, NumP/QP], while Num0/Q0 holds number features can be found, with some variation, in Selkirk (1977), Jackendoff (1977), Li (1999), Haegeman & Gue´ron (1999), Gawron (2002) and Ga¨rtner (2004), among others. Zabbal (2005) proposes that though complex cardinals are interpreted by dedicated semantic principles, they are nonetheless constructed as maximal projections in regular syntax; Num0 contains an operator mediating between the lexical xNP and the numeral.
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(Kratzer 1989; Chierchia 1998). Under most standard approaches, a cardinal combines with an xNP denoting a set of entities and returns a subset of this set: those members of it that have the relevant cardinality (cf. (12)), i.e. contain the relevant number of atoms. Since mass individuals have an undefined number of atoms, the notion of cardinality is not defined for them. This approach is not enough for our semantics because the lexical entry in (5) requires the sister of a cardinal to be a singular count noun (which denotes an atomic set, i.e. a set of entities of the cardinality 1), rather than just a count noun (plural or singular). On the surface, however, a cardinal might have a morphologically plural complement, as in two books. If books in two books is a semantically plural predicate, we need to convert it into a semantically singular predicate (denoting an atomic set). Such an atomizing conversion is usually associated with classifiers (see Chierchia 1998; Kobuchi-Philip 2003, and references cited therein). The atomicity requirement imposed by cardinals on their lexical xNP sister can now be explained by positing a null classifier in languages like English, which exhibit plural marking inside cardinalcontaining xNPs (see Borer 2005 for a similar proposal). In languages like Finnish, Welsh, Turkish or Hungarian, no such operation would be necessary. The question arises where in the structure this classifier appears. One possibility is that it appears between the lexical xNP and the lowest (simplex) cardinal, as in (22a) (cf. Cheng & Sybesma 1999).11 In this configuration the classifier must have the semantic type of a modifier (ÆÆe, tæ, Æe, tææ). The alternative is that the classifier is a complement of the innermost simplex cardinal and the lexical xNP is merged as the sister of the entire complex cardinal, as in (22b).12 In this case, the classifier is a predicate (type Æe, tæ).13
328 The Composition of Complex Cardinals
ð22aÞ
Both structures result in roughly the same semantics as in (9) in section 2.1, though the order of composition is not the same. Importantly, the assumption that the interpretation of the lexical xNP as an atomic set is achieved via a classifier does not distinguish between the iterative complementation structure in (22a) and the specifier structure in (22b) in languages without overt classifiers.14 We believe, nonetheless, that the classifier analyses should not be applied to such languages. The reason is that the presence of overt classifiers in a language has been linked to the lack of a singular/plural and mass/count distinction (Sanches & Slobin 1973; Chierchia 1998; Borer 2005, among others; see Cheng & Sybesma 1999 for objections). This connection is weakened if languages with plural morphology have null classifiers. 14 We will not attempt here the discussion of the syntax of cardinals in classifier languages. Although the classifier generally follows the cardinal, the cardinal-classifier sequence combines with the lexical xNP in a variety of ways (see Downing 1984, 1996; Muromatsu 1998, among others, for Japanese facts; Cheng & Sybesma 1999 for Chinese facts; and Simpson 2005 for cross-linguistic facts). This suggests that more than one structure may be available in a given language and cross-linguistically. From the semantic point of view, our analysis can be easily extended to classifier languages. Following Chierchia (1998, 2004), we assume that lexical xNPs in classifier languages are massdenoting. For the structure in (22a) this means that a classifier maps the denotation of a massdenoting xNP onto a set of atoms. In addition, an overt classifier in a language like Chinese or Japanese also has additional constraints on which atoms to consider (e.g. humans, groups of humans, long cylindrical objects, etc.—see Downing 1984). The reason that cardinals in classifier languages cannot combine directly with an xNP is that cardinals require atomicity of their complements and thus cannot take mass-denoting xNPs as complements (see Chierchia 2004). Once a classifier has converted the mass xNP denotation into an atomic one, combination with a cardinal is possible. For the structure in (22b), the combination of the lexical xNP and the cardinal (via Predicate Modification) yields the intersection of the denotation of the lexical xNP with the set of plural individuals of a particular cardinality.
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ð22bÞ
Tania Ionin and Ora Matushansky 329
3.1.2 Countability If we don’t assume the presence of classifiers in complex cardinals, how can we ensure that the lexical xNP denotes an atomic set? We propose modifying not the definition of an atom (cf. Chierchia 2004) but the constraint on what can be counted: informally, only individuals of the same (known) cardinality can be counted. Formally, this means that the complement of a cardinal can only denote a set of individuals x such that there exists a number n such that for every x, jxj¼n: (23) ½½2 ¼ kP 2 D Æe, tæ . kx 2 De . dS [P(S)(x) ^ jSj¼2 ^ "s2S P(s)] ½½2(P)(x) is defined only if dn"z [P(z) / jzj¼n]
(24) a. # There are 17 people and chairs in this room. b. There are 17 women and children in this room. 15 One remaining issue is that of dual and trial marking. The approach suggested here incorrectly predicts that a cardinal should be able to combine not only with a singular xNP or an xNP headed by another cardinal (a base), but that the lexical xNP complement of a cardinal could also be a dual or a trial (since a dual or a trial xNP denotes a set of individuals of the same cardinality). A simple way to exclude this issue is to suggest that (non-singular) syntactic number, including dual and trial, is projected as Num0, while a cardinal combines with a bare xNP. However, this idea would not be able to explain the plural marking on intermediate cardinals in languages that have it (see section 3.2), which should be due to the presence of a NumP. We therefore hypothesize that a dual or a trial xNP cannot be a complement of a cardinal for the same reason a cardinal such as seven cannot: it is a not a multiple. A simple morpho-syntactic realization of this hypothesis is to assume that the dual/trial is a head taking the lexical xNP as a complement, exactly as a nominal two or three does. We note that duals and trials are as much of a problem for the null classifier approach in section 3.1.1 and for Chierchia’s analysis mentioned in footnote 11: on both analyses, there is an operation extracting atoms from a set, and there is no reason why atoms cannot be extracted from the set denoted by a dual or trial xNP.
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The constraint in (23) ensures that true plurals cannot combine with cardinals: a plural such as books denotes a set of individuals x where each x is a plurality of books, and such pluralities do not necessarily have the same cardinality. This means that to be interpretable, the lexical xNP in two books has to be semantically singular, despite appearances. (We come back to where the number marking on the lexical xNP comes from in section 3.2.) Cardinals can of course combine with singular xNPs: the singular xNP book denotes a set of atomic individuals, which by definition all have the same cardinality.15 At the same time, a cardinal can combine with an xNP headed by another cardinal, such as hundred books: since such an xNP denotes a set of plural individuals divisible into one hundred books, all members of the set have the same cardinality. The presupposition in (23) is probably due to pragmatics, since counting pluralities of an unknown size is pointless. A similar constraint prohibits counting of dissimilar entities:
330 The Composition of Complex Cardinals While (24a) is odd, (24b) is rescued by the fact that women and children saliently qualify as human beings. It is tempting to hypothesize that plural individuals with different cardinalities cannot be similar in the relevant respect, but given that a single shared property (e.g. being a human being) suffices, it is not clear whether the presupposition in (23) can be derived from the same source as the contrast in (24).
3.2 Number morphology
(25) a. one CL books b. four book In the specifier structure in (22b), the number marking on the xNP can be attributed straightforwardly to Spec-head agreement. The only possible source of singular marking in a cardinal-containing xNP would then be the cardinal one; otherwise plural marking has to be used. Thus both (25a) and (25b) would be impossible. A minor problem with this theory is that if number marking is due to agreement, there is no apparent need to project a classifier. This solution is not available for the configurations in (4) and (22a). Even if agreement between a head and its complement is available, in (22a) a classifier intervenes between the lowest cardinal and the lexical xNP, and so agreement is blocked syntactically. Conversely, if plural marking in cardinal-containing xNPs reflects semantic plurality, then to exclude (25a) it is necessary to assume that one takes a singular NP rather than a ClP and to exclude (25b) it becomes necessary to stipulate that a cardinal can combine only with another cardinal or ClP. In (4), on the other hand, in order for the agreement to take place it is necessary to show that cardinals are syntactically plural—and this is
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In the previous sub-section we have proposed the semantic means of accommodating the fact that our semantics requires the sister of the innermost cardinal to denote an atomic set. Three syntactic structures are compatible with this constraint: the simple iterative complementation structure in (4), the classifier structure of (22a), which is identical to (4) with the exception of a classifier between the innermost cardinal and the lexical xNP, and the classifier structure of (22b), where (4) contains a classifier and resides in the specifier of the functional projection NumP. In all three structures, it is necessary to ensure the correct number marking, ruling out number mismatches as in (25), which are compatible with our semantics. We will show that it is easy to do so in the specifier structure in (22b), while the complementation structures, (4) and (22a), require additional stipulations.
Tania Ionin and Ora Matushansky 331
not at all obviously the case: (a) they don’t have to bear plural marking (cf. (26)), and (b) it is not clear whether a semantic notion of plurality can be defined for objects of the semantic type ÆÆe, tæ, Æe, tææ. (26) a. two dozen(s) books b. three hundred(s) people c. four score(s) and seven years ago
English
(27) a. drie liter water three liter water ‘three liters of water’ b. driehonderd meisjes three.hundred girls ‘three hundred girls’ (28) dvadcat’ millionov knig twenty-NOM million-GEN.PL book-GEN.PL ‘twenty million books’
Dutch
Russian
However, as noted by an anonymous reviewer, it is not clear how this approach fits into the Agreement Hierarchy (Corbett 1983),
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An alternative, also suggested by Farkas & de Swart (2003: 47), is applicable to both (4) and (22a). Suppose that the source of the plural marking on the lexical xNP is the semantic plurality of the entire cardinal-containing xNP, which would denote a plural individual with all cardinals but one. The number marking in cardinal-containing xNPs is then a result of semantic concord—a phenomenon where part of an xNP agrees with the entire xNP, also observed with features other than [6 plural] (see Corbett 1983; Wechsler & Zlatic 2003). Support for this theory comes from the fact that, both cross-linguistically and within the same language, number marking in cardinal-containing xNPs is not uniform. Thus in English, cardinals in cardinal-containing xNPs must be morphologically singular; in Dutch this is true for cardinals and measure nouns (the Dutch examples in (27) are due to Eddy Ruys, personal communication), whereas in Russian, semantic concord is all-pervasive (except for cardinals between 21 and 99 in oblique cases, as noted by an anonymous reviewer). Finally, in Turkish, Welsh, Hungarian and Finnish, the lexical xNP must be singular (see (21) above). This crosslinguistic variation would be difficult if not impossible to explain if plural marking reflected genuine semantic plurality.
332 The Composition of Complex Cardinals
3.3 Case assignment with cardinals Contrary to most standard views, we assume that simplex cardinals belong to one or another open lexical class available in a language, and that it is not necessarily the case that all simplex cardinals belong to the same lexical class. Specifically, we agree with Hurford (1975, 1987, 2001, 2003) that the vast majority of cardinals are singular nouns,16 with lower cardinals being sometimes adjectival (but see Moser & Marlett 1994 for a discussion of Seri, where cardinals start out as verbs). This hypothesis explains why simplex cardinals do not have their own declensional paradigm, but decline like adjectives or nouns,17 but even more relevantly, it is also compatible with the behaviour of Caseassignment within a complex cardinal. Besides the fact that in many languages cardinals are Case-marked, simplex cardinals are also able to assign Case (Genitive in Russian, Partitive in Finnish). For an unclear reason, for most cardinals in both languages, Case-assignment is only visible in direct Cases (Accusative/ Nominative), while in an oblique Case the entire xNP is marked with 16 The hypothesis that the vast majority of cardinals are singular nouns is supported for instance by the fact that they can require a singular article or take overt plural marking. Another possible candidate for nouns with the semantic type of modifiers (and with similar behaviour with respect to Case) is measure nouns, such as pound or liter (see Chierchia 2004 for an ÆÆe, tæ, Æe, tææ analysis of measure nouns) and vague measure nouns (a bunch of roses, a can of olives, etc.), discussed by Dodge & Wright (2002) and Doetjes et al. (1998). 17 Note also that if simplex cardinals belong to standard lexical classes it makes the hypothesis that they are constructed extra-linguistically even less likely.
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governing the application of semantic concord. We discuss the problem and possible solutions in Ionin & Matushansky (in preparation). To conclude, for languages where number morphology is present in cardinal-containing xNPs, the specifier structure in (22b) appears to be preferable to both (4) and (22a). However, this structure comes with the additional assumption that a null classifier is available in such languages. Importantly, the presence of number marking on simplex cardinals inside complex ones, as in Russian, strongly suggests that complex cardinals are transparent to syntax and therefore cannot be constructed entirely in the lexicon, as required by extra-linguistic theories of cardinals (e.g. Wiese 2003) and by the hypotheses that cardinals are syntactic heads (e.g. Ritter 1991, Giusti 1991, 1997; Zamparelli 1995, 2002). An additional argument against these hypotheses comes from Case-marking in cardinal-containing xNPs discussed below. We will show that the Case-marking facts provide support for the structure in (4) over both structures in (22).
Tania Ionin and Ora Matushansky 333
that oblique Case (see Mel’cˇuk 1985; Franks 1994; Hurford 2003, among others): (29)
dvumja- stami pjat’judesjat’ju ˇsagami Russian two-INSTR hundreds-INSTR five-INSTR ten-INSTR steps-INSTR ‘(with) two hundred and fifty steps’
3.3.1 Case assignment by simplex cardinals In Russian and Inari Sami, cardinals assign Case to their sister nouns, and the Case depends on the cardinal. In Russian, the lower (adjectival) cardinals ½, 1½, 2, 3 and 4 (but not one) assign Paucal,19 while the higher cardinals assign Genitive, as shown in (30). In Inari Sami, cardinals 2 through 6 assign Accusative while the higher cardinals assign Partitive, as shown in (31) (Nelson & Toivonen 2000). Similar facts from other languages can be found in Hurford (2003). (30) a. cˇetyre ˇsaga´ four step-PAUC ‘four steps’ (Russian) ˇsagov b. ˇsest’ six step-GEN.PL ‘six steps’ (Russian) 18 We discuss Russian Case assignment in more detail in Ionin & Matushansky (in preparation); see also Babby (1985), Mel’cˇuk (1985), Halle (1994), Franks (1994, 1995) and Corbett (1983, 1993, 2000) for discussions of the complexity of the issues involved, and Bailyn & Nevins (2004) for the evidence that Paucal is a Case in its own right. 19 The syntactic configuration between an adjectival cardinal and its sister is far from obvious. On the one hand, adjectives are generally assumed to be maximal projections (adjoined to the xNP or merged as specifiers, depending on the framework). On the other hand, Russian adjectival cardinals assign (Paucal) Case to their sisters, which can only be a property of heads. Finally, if the xNP sister of an adjectival cardinal is its complement, we expect the entire maximal projection to be an xAP, which is clearly not the case. In Ionin & Matushansky (in preparation) we propose that adjectival cardinals can have both sets of properties since they are simultaneously heads and maximal projections.
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Taken in itself, this pattern of Case-marking is compatible with all the three structures under consideration, on the condition that simplex cardinals don’t require Case (which would entail that they are not nominal, against overwhelming cross-linguistic evidence (see Hurford 1975, 1987, 2001, 2003)). However, as discussed below, the behaviour of complex cardinals in direct Cases is only compatible with (4); we rely on Franks (1994) to explain the pattern in the oblique Cases.18
334 The Composition of Complex Cardinals (31) a. kyehti/ kulmaˆ/ nelji/ vittaˆ/ kuttaˆ pa¨a¨rni two/ three/ four/ five/ six child-ACC.SG ‘two/three/four/five/six children’ (Inari Sami) b. cˇicˇcˇaˆm/ ka´vci/ ovce/ love/ ohtnuba´loh/ seven/ eight/ nine/ ten/ eleven/ kyehtnuba´loh/ cˇyeti. . . pa¨rnid twelve/ hundred child-PART.SG ‘seven/eight/nine/ten/eleven/twelve/one hundred. . . children’ (Inari Sami)
ˇsagov (32) a. cˇetyre tysjacˇi step-GEN.PL four thousand-PAUC ‘four thousand steps’ (Russian) ˇsagov b. pjat’ tysjacˇ five thousand-GEN.PL step-GEN.PL ‘five thousand steps’ (Russian) The same argument can be constructed outside Slavic. In Finnish, cardinals 2 and above assign Partitive to the lexical xNP, as in (33a), from Hurford (2003), and in (33b). Partitive Case assignment in Finnish also takes place within complex cardinals, as shown in (34). (33) a. kolme saapasta three-NOM boot-PART ‘three boots’
b. viisi kirjaa five-NOM book-PART ‘five books’
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In languages where cardinals are responsible for Case assignment, the structure in (4) receives support over the structures in (22). In (4), the lowest cardinal assigns Case to its sister, the lexical xNP. In (22a) a classifier projection intervenes between the lowest cardinal and the lexical xNP, and so additional stipulations are required. Finally, in (22b) the complex cardinal is in the specifier and cannot assign Case due to the fairly standard assumption of both GB and Minimalist frameworks that maximal projections cannot assign Case. Importantly, Case assignment within Russian complex cardinals behaves just like Case assignment from cardinals to lexical xNPs. In a complex cardinal like four thousand or five thousand in (32), the case on thousand depends on the preceding cardinal. While four assigns Paucal Case to thousand, five assigns Genitive. The fact that the syntactic process of Case assignment takes place within a complex cardinal shows that Russian complex cardinals are constructed in syntax.
Tania Ionin and Ora Matushansky 335
(34) a. kolmekymmenta three-NOM.ten-PART ‘thirty’
b. viisisataa¨ five-NOM.hundred-PART ‘five hundred’
We conclude that Case-assignment within complex cardinals provides evidence against the hypotheses that they are syntactic heads (Ritter 1991; Giusti 1991, 1997; Zamparelli 1995, 2002) and therefore against extra-linguistic analyses of complex cardinals.
(35) a. son Mary b. liter water We propose that cardinals are exceptional nouns in the same way the adjectives worth, like and near are exceptional (see Maling 1983) in that they assign (Accusative) Case to their arguments, as illustrated in (36). As a result, the structure in (4) becomes possible. (36) a. It’s worth five dollars. b. It’s near the house. None of the possible alternatives is preferable. If we continue to assume that English cardinals are nouns and do not assign Case, then the standard assumption that nouns need Case will be violated in cardinal-containing xNPs whatever structure is adopted: a cardinalcontaining xNP would contain at least two nouns with only one Case (the one assigned to the entire xNP from the outside). If cardinals are
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3.3.2 The role of overt morphology Given the facts of Case assignment by and within complex cardinals discussed above, we conclude that languages with morphological Case assignment, such as Russian (and Slavic in general), Inari Sami, and Finnish must have the syntax in (4). On the other hand, languages like English, where Case assignment is not morphologically overt, could in principle have the syntax in (22a) or (22b), and still be compatible with the semantics that we have proposed for complex cardinals (with (22b) preferable to (22a) in languages like English, which have number marking on the lexical NP—see above). English, however, presents an additional complication. It is generally assumed that only prepositions and verbs can assign Case in English, which correctly predicts that nouns should be unable to take nominal complements, as illustrated in (35). Since we agree with Hurford (1975, 1987, 2001, 2003) that English cardinals are nouns, the structure in (4) should be ruled out in English for the same reason examples (35) are.
336 The Composition of Complex Cardinals
3.4 The role of convention in complementation Leaving aside the issues of the constituent structure of an xNP containing a complex cardinal, the analysis of complex cardinals as iterative complementation overgenerates, predicting the possibility of the complex cardinals in (37). However, cross-linguistically, only the higher simplex cardinals can function as complements to other cardinals (henceforth, multiples). (On the ordering of multiples see section 4.3.) (37) a. two twenty b. two [seventy five]
¼ 40 ¼ 150
The class of multiples usually contains most powers of the base (usually 10, but 20, 15 and 5 are also attested),20 and a small set of 20 Note that not all powers of 10 may serve as multiples. For instance, though 10 is a mathematical base, three-ten is not a possible complex cardinal of English, but is perfectly fine in Finnish (see (34)).
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adjectives, the status of semi-lexical cardinals becomes unclear. Finally, if they are neither adjectives nor nouns, we need to assume a new lexical category for them, which is not preferable to the theory that cardinals are nouns that exceptionally assign Case. We conclude that lack of overt Case-marking does not tell us which syntactic structure is appropriate for English. As a result, it is preferable to postulate the same syntactic structure across languages, and thus we must fall back on Russian data. This outcome seems to lead to an impasse, since Russian yields contradictory evidence for the syntactic structure of cardinal-containing xNPs: Case-marking is only compatible with the structures in (4) and in (22a), while number-marking is most easily accounted for in the specifier structure in (22b). We propose to make use of the independently motivated generalization that classifiers are not available in the presence of number morphology (Sanches & Slobin 1973; Chierchia 1998; Borer 2005, among others). If correct, this means that even for languages where no overt Case is visible, the structure in (4) should be preferred. We suggest therefore that morphological number marking in cardinal-containing xNPs is due to semantic concord. Even though the structure in (22b) allows for a simpler analysis of number-marking, it is incompatible with the Case-assignment facts, while the structure in (4) permits us to account for both Case and number-marking (see Ionin & Matushansky, in preparation).
Tania Ionin and Ora Matushansky 337
3.5 Summary In this section, we have argued that the lexical xNP sister of a cardinal must be semantically singular, and have discussed two possible accounts 21
This said, in some languages being a multiple does appear to correlate with certain such properties, but not in any way that promises a straightforward solution. As mentioned above, simplex cardinals do not behave the same: the higher a cardinal, the more it behaves like a noun with respect to concord, the presence of an article, Case assignment and Case-marking (see Hurford 2003; Ionin & Matushansky, in preparation, for details). This makes it possible to say that higher cardinals behave more like nouns also in being able to appear in the complement of another cardinal. However, (a) it is not at all clear in what way being a noun is a gradable property and (b) being a multiple does not map directly into any of these properties. Finally, even if we just postulate a [6 multiple] feature, it would not be able to account for such complex cardinals as the French quatre-vingt ‘eighty’, where vingt ‘twenty’ can be a multiple with quatre ‘four’ only. Importantly, the issue of multiples arises irrespectively of which linguistic analysis is adopted for complex cardinals.
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others (12, 20, 60. . .), which may be subject to further constraints. For example, 20 serves as a multiple productively in Mixtec, Yoruba and Celtic languages, where 20 is a base, and sporadically in Danish and French, where it is not (Hurford 1975, 2003). This is exactly a situation where our arguments against the extralinguistic nature of cardinals do not apply: whereas syntactic phenomena inside complex cardinals (such as Case assignment or number marking) show that they are combined in syntax, the distinction between multiples and non-multiples does not correlate with any syntactical or morphological property relevant to the computational system.21 The cross-linguistic and intra-linguistic variation as to which cardinals are simplex or complex is equally large. For instance, in Russian, sorok ‘forty’ is linguistically simplex, and is derived from the Old Nordic sekr ‘furs’ (see Wiese 2003, chapter 3), while dvenadcat’ ‘twelve’ is complex (lit. ‘two on ten’). In English, sixty is arguably derived from six-ten, but given the phonological changes, it may be preferable to treat it as a simplex cardinal (the same holds for forty, eighty, etc.). We consider the issue of which cardinals are simplex and which are complex to be extra-linguistic as well. To summarize, any syntactic analysis of complex cardinals needs to be supplemented by extra-linguistic constraints (see Ionin & Matushansky, in preparation, for a discussion of extra-linguistic constraints in such non-numeric areas as measure phrases, names and titles). The alternative of treating the composition of complex cardinals as entirely extra-linguistic fails to account for Case assignment and numbermarking, as well as the similarities between cardinals and measure nouns.
338 The Composition of Complex Cardinals
4 COMPLEX CARDINALS AND COORDINATION We have so far been concerned with complex cardinals involving multiplication (two hundred), which we analyzed as complementation (cf. (4)). We now turn our attention to complex cardinals involving addition, like twenty-two, two hundred and two, etc. Examples like (38) show that simplex cardinals can be combined into complex ones via coordination, which is then interpreted as addition. (38) a. one hundred and two b. laba iyo toban two CONJ ten ‘twelve’ (Somali) c. seven and two thirds 22
Saeed (1999)
An anonymous reviewer draws our attention to the interpretation of NP-ellipsis with cardinals: (i) Mary bought two hundred books, and Peter – three. a. three books b. three hundred books
Although the preferred interpretation of the elided xNP in (i) is (ia), the majority of the speakers we have asked also accept (ib), in particular if two in the first conjunct is stressed, although we have also found minor speaker variation in function of the multiple (e.g., million is preferred to hundred ). The fact that ‘intermediate’ NP-ellipsis is possible lends further support to the iterative complementation structure and is incompatible with the specifier approach, but further work is required to determine why (ib) is dispreferred or unavailable for some speakers (including the reviewer in question).
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for the presence of plural morphology in two books in English, Russian, etc. The first one depends on the presence of an atomizer, which is either part of the lexical entry of cardinals, or syntactically projected as a classifier. The second option is that plural marking with cardinals reflects number agreement in some form. We then discussed some of the syntactic phenomena inside complex cardinals, since it is the syntactic transparency of complex cardinals that lends weight to our claim that they are constructed in syntax. The behaviour of morphological Case and of number marking in cardinal-containing xNPs lead to opposite conclusions about their internal structure, even within the same language, which is why we sketched some arguments in favour of the iterative complementation structure in (4) crosslinguistically (except maybe in classifier languages).22 Finally, we showed that although certain phenomena in the syntax of complex cardinals must be attributed to extra-linguistic constraints, there is evidence that their semantic and syntactic composition is nonetheless done by standard linguistic means.
Tania Ionin and Ora Matushansky 339
d. zweiundzwanzig two and twenty ‘twenty-two’ (German) e. Her husband was a grave looking young man of five or six and twenty ( Jane Austen, Sense and Sensibility, chapter 19)
(39) a. six feet six inches of finest silk b. six feet and six inches of finest silk (40)
a. two dollars (and) seventy-five cents b. two dollars (and) seventy-five In addition, coordination without an overt conjunction is attested cross-linguistically, as noted by Payne (1985) (via Winter 1995), Stassen (2000) and Drellishak (2004): nipita ni’ (41) n˜e niyo’j be.PST her.brother her.aunt her.sister ‘It was her aunt, her brother, and her sister.’ (Andoke (Macro-Carib, Witotoan)) from Stassen (2000: 5) via Drellishak (2004) As noted by Drellishak (2004), asyndetic coordination means that an overt conjunction is optional. In addition, in some languages and under some circumstances, an overt conjunction is impossible, as is the case for VP-coordination in the West-Papuan language Abun (Berry & Berry 1999 via Drellishak 2004). This is consistent with the fact that in some languages (e.g. Russian), numerical expressions never contain an overt conjunction, while in others (e.g. Arabic), an overt conjunction is obligatory for addition (Zabbal 2005).
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We propose that this analysis can be extended to complex cardinals not involving overt conjunction (e.g. twenty-two) by appealing to the notion of asyndetic coordination—the phenomenon where the semantics of coordination is obtained in the absence of an overt conjunction. (See Hurford 2003 for a discussion of other means of expressing nonmultiplication arithmetic operations, also exemplified in (2c)). Asyndetic coordination is also attested in the domain of measurements, as illustrated by (39a) (from Gawron 2002), which is truthconditionally equivalent to (39b). In addition to showing that asyndetic coordination is not specific to complex cardinals, (39) points to an extra similarity between measure nouns such as foot/inch and cardinals (see also footnote 16), and (40) illustrates the effect for monetary units.
340 The Composition of Complex Cardinals However, treating addition as coordination (whether asyndetic or overt) is not enough. We also need to establish where in the xNP containing a complex cardinal the coordination takes place and to derive compositionally the correct interpretation of such an xNP.
4.1 The syntax of coordination
4.1.1 Right-node raising or NP-deletion? The first possibility is that coordination in complex cardinals involves right-node raising of the lexical xNP, as shown in (42) (for analyses of right-node raising as rightward movement, see Ross 1967, Postal 1974, Abbott 1976, Grosu 1976, Sabbagh 2003, among others).
ð42Þ
Right-node raising can also account for the example in (39), which could be derived from right-node raising of the common PP, as shown in (43). ð43Þ An alternative possibility is that coordinated cardinals are derived via PF-deletion of the NP in the first conjunct, as shown in (49a). The
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Given the syntax and semantics that we have proposed, in two hundred twenty books, each coordinated cardinal must contain an instance of the lexical xNP books: two hundred books and twenty books. There are two ways in which two hundred books and twenty books could be converted into two hundred and twenty books: (1) right-node raising of the lexical xNP; and (2) PF-deletion of the lexical xNP in the first conjunct. We discuss both possibilities below, and note that both strategies are in principle available: some languages use right-node raising, others use PF-deletion, and still others utilize both strategies.
Tania Ionin and Ora Matushansky 341
measurement cases in (49b) can be dealt with in the same way (PF-deletion of the of-PP):
ð44Þ
(45)
onid un mlwydd cant Hurford (1975: 198) but one years hundred ‘ninety years Æoldæ and nine. . .’ (Genesis 17.1, 24)
For the purposes of the present paper the choice of xNP-deletion vs. right-node raising is irrelevant: either mechanism can derive complex cardinals involving addition. However, it should also be observed that if the specifier structure in (22b) is adopted, the question need not arise when the classifier is null. This would have been an argument in favour of (22b) were it not the case that in at least some languages, more than one instance of the lexical xNP is present with a coordinated cardinal, as shown below. 4.1.2 Evidence in favour of multiple xNPs Our overall proposal that coordinated cardinals are derived from coordinated xNPs (whether via 23 (45) exemplifies the use of a regular preposition to express subtraction (also known as ‘overcounting’; see Menninger 1969 and Hurford 2003). The remaining arithmetical operation, division, is also used albeit rarely, and once again regular linguistic means are employed. We leave overcounting and division aside here but see Hurford (2003).
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Different options may be adopted in different languages. In Ionin & Matushansky (in preparation), we argue that cross-linguistically both processes are attested: we show that the behaviour of Russian and Biblical Welsh cardinals are best explained under the xNP-deletion view, while the right-node raising view can account for the behaviour of cardinals in English and Inari Sami. Furthermore, German appears to utilize both mechanisms, and Hurford (1975) discusses Biblical Welsh data with the lexical xNP appearing in the middle of the complex cardinal (cf. also three score years and ten):23
342 The Composition of Complex Cardinals right-node raising or NP-deletion) finds support in Luvale (Zweig, to appear) and Biblical Hebrew, where the lexical xNP may appear in both conjuncts of a coordinated cardinal, as in (46)–(49) (see also Hurford 1975 for the same effect in Biblical Welsh). (46) mikoko makumi atanu na-mikoko vatanu sheep ten five and-sheep five ‘fifty-five sheep’ (Luvale)
ˇsanıˆm ˇsana (48) ˇsaloˆˇs warba me oˆt three year-PL and four hundred-PL year ‘ÆAnd Salah lived after he begat Eberæ four hundred and thirty years. . .’ (Genesis, 11.15) ˇsanıˆm ˇsana. . . (49) teˇsa umatayim nine year-PL and hundred-DU year ‘ÆAnd Peleg lived after he begat Reuæ two hundred and nine years’ (Genesis, 11.19) The multiple lexical xNP facts provide evidence in favor of treating twenty-two books in English as having the underlying form twenty books and two books, and also against the specifier structure in (22b), which does not lead us to expect multiple instances of the lexical xNP.
4.2 The semantics of coordination On our analysis, an xNP like twenty-two books involves the coordination of twenty books and two books, where both are predicates over semantically plural individuals. It is easy to show that the standard Boolean semantics of and (Partee & Rooth 1983), type-lifted to apply to predicates, does not yield the expected result for this xNP: (50) ½½and ¼ kf 2 DÆe,
tæ
. kg 2 DÆe,
tæ
. kx 2 De . f(x) ^ g(x)
(51) ½½and (½½two books) (½½twenty books) kx . ½½twenty books(x) ^ ½½two books(x) The reading in (51) is not available for the xNP twenty-two books. This absence is fully expected for pragmatic reasons, since nothing can be
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ˇsana ˇsana me oˆt u-sˇl oˇsˆım (47) t ˇsa nine hundred-PL year and-thirty year ‘ÆAnd all the days that Adam lived wereæ nine hundred and thirty years’ (Genesis, 5.5)
Tania Ionin and Ora Matushansky 343
simultaneously 20 books and 2 books (cf. section 2.2.2).24 Instead, we obtain a considerably more complex meaning: (52) ½½twenty-two books ¼ kx . dy, z [x¼y4z ^ ½½twenty books(y) ^ ½½two books(z)] The first observation that can be made in this respect is that this effect is not restricted to cardinals. As shown by Krifka (1990a), Lasersohn (1995), and Winter (1996, 1998, 2001b), the standard view of Boolean coordination leads to problems with plural predicates, and Heycock & Zamparelli (2000, 2003) show that the same issue arises for plural predicates inside DPs:
(54) His friends and colleagues came to the party.25 a. A set of people each of whom is his friend and his colleague came to the party. b. A set of people each of whom is his friend or his colleague came to the party. What is relevant for us here is the fact that coordination of two plural predicates may result in a split reading (54b) (term due to Heycock & Zamparelli 2000, 2003). Heycock & Zamparelli (2000) propose to derive this reading by assuming that and returns a set-product, as defined in (55).26 (55) Set-product (SP) SP (A1, . . .An) ¼def fX : X¼a1 [ . . . [ an, a1 2 A1, . . . an 2 Ang The split reading in (52), however it is achieved (see Krifka 1990a; Lasersohn 1995; Winter 1996, 1998, 2001b for alternative proposals to Heycock & Zamparelli 2000), is what we need for coordination inside an xNP like twenty-two books: a set of plural individuals that are each a sum of two plural individuals such that one of them is in the denotation of two books and the other is in the denotation of twenty books. 4.2.1 The role of pragmatics in coordination An important observation made by Heycock & Zamparelli (2000, 2003) concerns the possibility 24
The absence of the reading in (51) means that a cardinal-containing xNP such as two books has an exactly-reading only—if the at least reading were available, then a single plural individual could have been at least two books and at least twenty books simultaneously. See also fn. 6. 25 That the ambiguity of the conjunction occurs at the level of NP predicates is even clearer when the DP is placed in the predicate position, as in They became his friends and colleagues. 26 The definition in (55) can be adapted to plural individuals.
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(53) a. The books are old and new. b. These men and women met in the park.
344 The Composition of Complex Cardinals of overlap in the split reading of (54b). The situation where no individual may be both a friend and a colleague is called a full split reading. This reading is most salient in (53b): no single individual can be simultaneously a man and a woman. Strikingly, with coordination of xNPs containing cardinals, only the full split reading seems available: (56) Twenty-two people came to the party. a. A plural individual that is simultaneously 20 people and 2 people. . . b. A plural individual that contains 20 people and 2 people. . .
(57) a. Twenty people and two people came to the party. b. Twenty professors and seven deans came to the party. c. All professors and several deans came to the party. The lack of overlap is also clearly seen when measurements or money are considered: (58a) cannot be about a mere six feet of silk (with the six inches included inside the six feet), and (58b) cannot be about only five dollars (with the seventy-five cents included in the five dollars). (58) a. I bought six feet (and) six inches of finest silk. b. This cost five dollars (and) seventy-five cents. Other examples where and means ‘in addition to’ and that do not involve cardinals come from Hofweber (2005) and Carlson (1987): (59) She only had an apple and dessert.
Hofweber (2005)
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The absence of the joint reading (56a), on which a plural individual is 20 people and two people at once, is fully expected (see above). More puzzlingly, the reading in (56b) must be a full split reading: no overlap is possible. This cannot be ruled out pragmatically: in principle, a plural individual containing 20 people and two people may contain the totality of 20 people, or of 21 people. However, twenty-two people clearly cannot denote a predicate over a plural individual with fewer than 22 subparts. So why is overlap impossible for cardinal-containing predicates, while it is allowed elsewhere? By our hypothesis, (56) is derived from (57) by right-node raising or NP-deletion. We note that to the extent that (57) is acceptable, overlap is equally impossible in it. Furthermore, the same lack of overlap occurs even when the lexical xNPs in the two conjuncts are different: only a mathematician set on devising a puzzle would treat (57b) as being about twenty people. Finally, the situation is not specific to xNPs containing cardinals: we see the same lack of overlap in (57c).
Tania Ionin and Ora Matushansky 345
As Hofweber (2005) observes, ‘A usual utterance of this wouldn’t be true if she just had an apple, even though fruit is perfectly fine dessert.’ In other words, the lack of overlap is not limited to coordinated cardinals containing a single overt lexical xNP. Furthermore, it is not even limited to coordination of xNPs, as shown by (60). Carlson (1987) observed that while in isolation John did something amazing can be true by virtue of there being a token event of John pulling a rabbit out of a hat, in (60), this phrase must denote something different from the rabbit-pulling event.
What is the reason behind this lack of overlap across constructions? We suggest a pragmatic explanation of these facts, along the following lines. When the denotation of one of the coordinated xNPs (two people, six inches, etc.) is totally or partially included in the denotation of the other (twenty people, six feet, etc.), a pragmatic principle prevents the use of a coordinated structure. A good candidate is the Gricean maxim of Manner (Grice 1975), which basically requires that all professors and several deans should not be used when all professors is a simpler alternative; the same principle rules out twenty-two people when twenty people is an accurate (and simpler) description. Basically, a conversational maxim prevents the speaker from using two coordinated xNPs unless she knows that the denotation of neither of them is contained inside the denotation of the other. 4.2.2 Supporting evidence: availability of overlap If the lack of overlap is pragmatic in nature, then it should be possible to override it. Indeed, we note that overlap does become possible in certain environments. For instance, in (61a), the question is open as to whether professors who have joint appointments in linguistics and psychology may be counted twice. Similarly, in (61b), the quorum requirement may be satisfied if a total of ten professors, five of whom are deans, are present. (61) a. Each applicant is required to meet with three professors from linguistics and two professors from psychology. b. We need ten professors and five deans for a quorum. Likewise, Carlson’s example (60) allows overlap under certain circumstances: for instance, if to marry the princess John needs to do something amazing and to pull a rabbit out of a hat, he may be able to persuade the princess that one action fulfills both conditions.
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(60) John did something amazing and he pulled a rabbit out of a hat. Carlson (1987)
346 The Composition of Complex Cardinals
(63) We need twenty books and two books. We propose that in this case, the relevant entity also appears in two guises: the guise of a book that our French friends recommended, and the guise of a book that our British friends recommended. This reading appears to be facilitated by stress on the conjunction (which then has to be overt). 4.2.3 The role of an overt conjunction There is a subtle difference between the readings of (56) and (57a): (57a), to the extent that it is 27 The possibility that things more abstract than entities can be counted suggests a reanalysis of the well-known ambiguity of examples like (i), from Krifka (1990b):
(i) Four thousand ships passed through the lock last year. The so-called event-related reading of (i), purported to count the events of ships passing through the lock, can instead be surmised to count stages of ships passing through the lock. An immediate advantage of such a hypothesis would be that it would permit the standard uniform semantics to be maintained for cardinals. Due to the lack of space, we leave a detailed discussion of this matter for future research.
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Eddy Ruys, personal communication, suggests that the pragmatic constraint against overlap is overruled in these examples because the same individuals or events are presented in different guises: e.g. on the overlap reading of (61b), the same person is presented under the guise of a professor as well as the guise of a dean. On the other hand, the guise strategy is unavailable when we are talking about twenty people and two people in (57a) (or twenty-two people in (56)), since the lexical nouns in the two conjuncts are identical. The guise strategy is similarly unavailable for six feet and six inches in (58a), since no measure unit can be in the guise of a foot and the guise of an inch at the same time. Further evidence in favour of a pragmatic approach based on guises can be drawn from the fact that a plural cardinal-containing xNP can denote a single individual: (62) a. It is as if she is really three different people. b. These two very different people ( Jekyll and Hyde) are really one person. Both examples in (62) are concerned with different guises of the same individual, which permits the same entity to be counted more than once. We believe that this is also what takes place in (61), where the same entity can be counted under different guises.27 Likewise, overlap does seem (marginally) possible for an xNP containing a coordinated cardinal if the two conjuncts have different implicit restrictions: in (63), it is possible that we need the twenty books that our French friends recommended, plus the two books that our British friends recommended, and there is overlap between the two sets.
Tania Ionin and Ora Matushansky 347
4.2.4 Summary We have shown that the lack of an overlap reading with an xNP containing a coordinated cardinal (twenty-two books) in fact extends well beyond this phenomenon to coordination of two separate xNPs and even coordination of entire events. We have argued that the lack of overlap is pragmatic in nature, and shown that, like any pragmatic constraint, it is overruled under certain conditions. The issue still remains of why overlap is easily available in the absence of a cardinal, as in (54). Since the question of how genuine semantic plurals are affected by the pragmatic considerations discussed above extends beyond the scope of the paper, we leave it to future research.
4.3 The role of convention in coordination Two new questions arise now that we have a semantics for coordinated cardinals. The first one is what determines whether addition or multiplication is at work. For instance, why is (a) hundred fifteen never interpreted, through multiplication, to mean 1500? Conversely, why is fifteen hundred never interpreted, through addition, to mean 115? The second question is that of the ungrammaticality of coordinated cardinals such as twenty-seventeen (with the meaning ‘37’), which are overgenerated by our system (Philippe Schlenker, personal communication). We follow Hurford (2003) for our data and the conclusion that, just as for the constraints on complementation discussed in section 3.4, the answers lie in extra-linguistic conventions. 4.3.1 Addition v. multiplication As shown in Hurford (2003), there are cross-linguistic mathematical constraints on the order of cardinals
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acceptable, suggests that a group of 20 people and a separate group of two people arrived at the party separately, while (56) suggests nothing of the kind. We believe that the difference is once again due to pragmatics: while (56) and (57a) have the same truth-conditions, (56) is the conventional way to talk about twenty-two people. If one chooses to use (57a) (the unconventional way) instead, one should have a good pragmatic reason for doing so: the most natural reason is to separate the groups of twenty people and two people in space and/or time. (Another reason is to assign different guises, as in (62) and (63).) Without such a reading, (57a) is pragmatically odd. This relationship between (56) and (57a) can probably also be accounted for under the maxim of Manner: (57a) is a lengthier, more cumbersome way of saying what can be more succinctly expressed by (56). Like any conversational maxim, it can be overridden by pragmatic considerations—e.g. the need to separate the two groups.
348 The Composition of Complex Cardinals with addition v. multiplication. In the case of multiplication, in most languages, the higher cardinal follows the lower cardinal: thus, 200 is read two hundred, not hundred two. In the case of addition, in the absence of an overt conjunction, the high cardinal nearly always precedes the low cardinal: thus, 22 is read twenty-two, not two-twenty; 102 is read a hundred two, not two hundred, though the reverse order, two and twenty, where the overt conjunction unambiguously signals addition, is also attested, e.g. in German (38d).
Exceptions can be found for both generalizations. Thus in Scottish Gaelic cardinals 11 through 19 exhibit the order low-high. In many other languages (e.g. English), these cardinals form a single word, with the internal order low-high (nine-teen). On the other hand, the first generalization is violated by a number of languages, among which are Sinhala and Maori, where the ordering of cardinals in multiplication is high-low.28 4.3.2 Non-standard coordination We propose that cardinal coordination is not constrained semantically but rather that extra-linguistic, arithmetical, constraints are involved: for instance, languages which use a base-ten system typically disallow the coordination of two simplex cardinals whose value is at least 10 but below 100 (hence the impossibility of twenty-seventeen, forty-thirty, ninety-ten), though there are exceptions (e.g. the French soixante-dix, lit. ‘sixty-ten’, for 70). Interestingly, the presence of an overt coordination alleviates the constraints on which cardinals can be coordinated: (64) a. twenty seventeen books asyndetic coordination b. #twenty and seventeen books overt conjunction As indicated by the grammaticality judgments, in the presence of an overt conjunction, convention can sometimes be overridden. This is used in the following line from a children’s poem by the Russian poet Taffy: (65) tridcat’- tri i dva kota i cˇetyre kosˇki Russian thirty three and two cat.M-PL and four cat.F-PL ‘Thirty-three and two tomcats and four tabbycats.’ 28
Unlike in Shona and Yoruba, where cardinals follow nouns and it can therefore be argued that the NP is head-final, in Sinhala and Maori cardinals precede nouns and this argument is not available (see Hurford 2003; Ionin & Matushansky, in preparation, for details and discussion).
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(38) d. zweiundzwanzig two and twenty ‘twenty-two’ (German)
Tania Ionin and Ora Matushansky 349
The possibility of (65) argues that the constraints on coordination can be overridden when there is some reason to separate two pluralities, and this requires an overt coordination. Again, we draw a parallel with measure phrases (cf. (39)). Convention dictates that the larger measurement unit (feet) appears before the smaller one (inches), as in (66a); with asyndetic coordination, the reverse order is impossible (66b). However, when an overt conjunction is used, convention can be overridden: both orders are possible, as indicated by (66c–d). For (66d) to be acceptable, it is helpful to clearly separate the six inches of silk from the six feet of silk in space and/or time. This is parallel to what happens with cardinals in (65). feet six inches of blue silk. inches six feet of blue silk. feet and six inches of blue silk. inches and (then) six feet of blue silk.
We speculate that an overt conjunction changes the prosodic properties of the cardinal-containing xNP and makes it compatible with the new interpretation. 4.3.3 Cross-linguistic and intra-linguistic variation Complex cardinals differ as to whether they use asyndetic or overt coordination, within the same language, as well as between languages. For instance, in English, twenty-two disallows an overt and, while one hundred and one requires it, and in three hundred (and) fifty, it is optional. We note that similar differences exist in other coordinated structures as well. For instance, consider times: when minutes and seconds are coordinated, overt conjunction is optional (68a), while when years and days are coordinated, overt conjunction is obligatory, or at least strongly preferred (68b). Thus, coordinated cardinals in which an overt conjunction is obligatory vs. optional have a parallel in other types of coordinated structures. (68) a. She ran the race in five minutes (and) ten seconds. b. She lived there for five years (and) ten days. We note that the arithmetic constraints on coordination of cardinals have to be part of any theory of complex cardinals, not just ours. For instance, take a theory that treats complex cardinals as morphological compounds, constructed entirely in the lexicon: it would have to assume the role of arithmetic constraints on compound formation. We do not see why assuming arithmetic constraints in morphology is any more explanatory than assuming them in syntax. Furthermore, given the facts in (66), the morphological compound view would have to treat complex measure phrases such as six feet six inches as compounds
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(66) a. I bought six b. ??/I bought six c. I bought six d. I bought six
350 The Composition of Complex Cardinals as well, which does not seem particularly desirable. The advantage of our syntactic view is that, once the extra-linguistic factors are taken into account, arithmetic operations can be done via entirely linguistic means, consistently with cross-linguistic data. 5 CONCLUSIONS AND NEW QUESTIONS
Acknowledgements We owe a heartfelt one thousand and one thanks to Dominique Sportiche, Eddy Ruys, Francis Corblin, Francxois Recanati, Gennaro Chierchia, Irene Heim, Joost
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We have proposed that simplex cardinals are semantic modifiers and complex cardinals are constructed by regular syntactic means (complementation and coordination, for the languages discussed here). This analysis allows us to satisfactorily account both for the semantics of complex cardinals and for their cross-linguistic syntax. In Ionin & Matushansky (2004), we show that this analysis also allows us to account for the (seemingly) special properties of the English modified cardinal construction in (18). For non-classifier languages, we propose that complex cardinals do not form a constituent to the exclusion of the lexical xNP (until right-node raising or NP-deletion). The data presented indicate that multiplication and addition in language use entirely linguistic means: standard syntax as well as independently attested principles of semantic composition. We show that properties of cardinals that do not follow from standard syntax and semantics can be accounted for by extra-linguistic constraints, which are necessary under any theory of complex cardinals and play a role in nonnumerical areas. On the other hand, a theory that treats the composition of complex cardinals as entirely extra-linguistic fails to account for number marking and Case assignment within complex cardinals. Some questions remain open for further study. We have suggested that a reconciliation between the conflicting structures suggested by the patterns of number marking and Case assignment can be derived via semantic concord. This means that the interaction of semantic concord and the Agreement Hierarchy must be examined in detail. We also need to address the question of number agreement and concord with cardinalcontaining xNPs, since different patterns are attested cross-linguistically (singular or plural marking on the lexical xNP, on the verb and on the determiners and modifiers in the cardinal-containing xNP). Ordinals and non-nominal cardinals also need to be explored more deeply, as do non-multiplication arithmetic operations, exemplified in (2c) and (45).
Tania Ionin and Ora Matushansky 351 Zwarts, Philippe Schlenker, Yael Sharvit and two anonymous JoS reviewers for dozens of helpful comments, precisions and counter-proposals, to Ida Toivonen and Elsi Kaiser for information about cardinals in Inari Sami and Finnish, respectively, and to Jim Hurford for information about cardinals in various languages. We are also thankful to the audiences of the se´minaire du volet DP (programme Architecture de la phrase, Fe´de´ration TUL), the UCLA semantics lunch (spring 2004), GURT 2004, Workshop on Numerals in the World’s Languages, Studientag Noun Phrases—Typology and Theoretical Problems (Freie Universita¨t Berlin), WCCFL 23, the Linguistic Perspectives on Numerical Expressions workshop, and the USC Ling 635 syntax seminar (fall 2004), where earlier versions of this paper were presented, for their substantial input. The second author gratefully acknowledges the partial support of her research by Fe´de´ration Typologie et Universaux du CNRS, programme 4.
We now consider some other issues in the syntax of numerals in order to show that they can be successfully treated under our analysis: modified numerals and cardinals inside arithmetic expressions. APPENDIX 1: MODIFIED NUMERALS Constructions such as (69a–c) (Kadmon 1987; Krifka 1992, 1999; Corblin, to appear) and (69d) (Corver & Zwarts 2004) are usually assumed to involve modification of the numeral, before it has combined with the lexical xNP:29 (69)
a. b. c. d.
[[more than ten] books] [[at least ten] books] [[exactly ten] books] [[just about ten] books]
standard bracketing
However, the syntax that we have proposed for cardinals requires them to have the seemingly counter-intuitive bracketing structure in (69): the cardinal must combine with the lexical xNP before combining with the quantifier: (70) a. [more than [NP ten books]] b. [at least [NP ten books]] 29
Corblin (to appear) argues that while at least combines with an xNP and denotes a relation between two sets, more than is cardinal-internal and denotes a relation between two numbers. If correct, his proposal can be used as an argument in favour of the specifier structure in (22b).
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APPENDICES: OTHER ISSUES IN THE SYNTAX OF NUMERALS
352 The Composition of Complex Cardinals c. [exactly [NP ten books]] d. [just about [NP ten books]] There is in fact independent evidence against the bracketing in (69). First of all, for this bracketing to work, the PP must be linearized before the constituent to which it is attached (i.e. the cardinal), as in (69d), an order unattested elsewhere in English. Secondly, two books can be replaced by an xNP such as the predicted number of books—supporting our proposal that two books in the constructions in (70) is a constituent: [more than [the predicted number of books]] [at least [the predicted number of books]] [exactly [the predicted number of books]] [just about [the predicted number of books]]
Thus, at least in English, an analysis of modified numerals and prepositional numerals does not necessitate that more than ten, exactly ten, etc. form a maximal projection to the exclusion of the lexical xNP.30 The same result can be obtained for other languages. APPENDIX 2: COUNTING We have been arguing against the standard assumption that a complex cardinal is a unit to the exclusion of the lexical xNP complement. The question arises how we can deal with mathematical examples like (72), where cardinals (simplex as well as complex) function as arguments. (72) a. Two and two is four. b. Seven times seven is 49. c. Twenty-five plus seventy-four is ninety-nine. (73) a. I added two/this number to two. b. I multipled seven/this number by seven. In examples like (73), cardinals behave like xNPs of the semantic type e in that they appear in normal argument positions. The question is which of the two forms is the basic one. One answer is that the counting form, as in (72)–(73), is the basic one, and the xNP-internal form is derived from it. On this view, an item such as two hundred and four refers to a particular number (an abstract entity). 30 If our approach is correct, then we predict that argument positions, usually considered to be reserved for xNPs, can be filled by PPs ([PP Between 20 and 30 people] arrived). This is not necessarily a problem, given that PPs can appear in the subject position of copular predicates (Under the bed is a weird place to sleep).
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(71) a. b. c. d.
Tania Ionin and Ora Matushansky 353
On our approach to the semantics of cardinals exactly the opposite has to be true. Two questions therefore have to be answered: (a) what is the mechanism allowing the transition from the use of cardinals as singular terms (74a) to their xNP-internal use (74b),31 and (b) is there any independent motivation for assuming that the xNP-internal use of cardinals is basic? (74) a. The number of moons of Jupiter is four. b. Jupiter has four moons.
(75) a. Two are for you, and two for me. b. Two are more than none. c. Two and two are four. His concrete proposal is that semantically bare determiners involve implicit quantification: (75) b#. For whatever X, two X are more than no X. c#. For whatever X, two X and two (more) X are four X. We concur with this proposal and assume that NP-internal cardinals are the basic form, and mathematical cardinals are nominalizations. Independent evidence for this view comes from the fact that while mathematical cardinals always behave as nouns, xNP-internal cardinals don’t: as Hurford (2001) observes, cross-linguistically, lower cardinals are often adjectives. It depends on the language whether a particular xNP-internal cardinal behaves like a noun or like an adjective, so if mathematical cardinals are treated as the basic form and xNP-internal cardinals are derived from them, an additional stipulation is required to account for the categorial diversity of the latter. Our account is therefore more economical, and also relies on the transition from a less abstract meaning (the property of a set) to a more abstract one (a theoretical entity). 31
Hofweber (2005) calls this question Frege’s other puzzle (Frege 1884).
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The answer to the first question is provided by Hofweber (2005). Hofweber compares NP-ellipsis with numerals (75a) to generic statements involving ‘bare determiners’ (75b). He observes that in both cases, cardinals (except for one) trigger plural agreement, and suggests that generic statements involving ‘bare determiners’ involve ellipsis as well, although of a slightly different kind. In particular, Hofweber argues that generic statements like (75b) can be unified with the arithmetic statements like (75c):
354 The Composition of Complex Cardinals Our account differs from Hofweber’s concerning cases where singular agreement is used, as in (75d). In such cases, Hofweber claims, we’re not dealing with bare determiners but with singular terms, and the copula is one of identity. (75) d. Two and two is four.
(76) a. Two hours in the alien ship was/were clearly not enough. b. 10 miles separate(s) the castle from the dragon lair. Either plural or singular agreement can be used with bona fide cardinal-containing xNPs when the subject is an abstract measure xNP. This informal description certainly applies both to the ‘bare determiners’ in (75c) and ‘mathematical cardinals’ in (75d). The slight preference for the singular agreement can be assimilated to the same preference with more abstract predicates: (77) a. Two hours is/?? are such a short time, really. b. 10 miles is/?? are not much of a distance. We conclude that Hofweber’s implicit quantification view, in combination with the known variation in agreement, can account for mathematical cardinals on the basis of regular syntax. The behaviour of plus and minus, which would seem to be purely mathematical expressions, lends further support to the intuition that simple arithmetic operations are expressed via standard linguistic means. Besides their mathematical sense, they also have a regular linguistic meaning of (xNP-connecting) as well as and excepting, as shown by their use in informal contexts (all my friends plus my colleagues came to the party). Nonetheless, historically, plus and minus started out in many languages as purely mathematical terms and their informal use is a back-formation. This back-formation is inexplicable without a most natural assumption that mathematical (and other scientific) usage always rests on standard linguistic means—back-formation is then driven by parallelism with other terms. However, this natural assumption also forces us to conclude that the mathematical use of numerals is derived from the xNP-internal one.
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Hofweber suggests that the transition from (75c) to (75d) involves ‘type lowering’, from operations on determiners (type ÆÆe, tæ, ÆÆe, tæ, tææ) to operations on entities. This ‘cognitive type coercion’ is required for cognitive reasons, unlike the more familiar type shifting. We suggest that this last step is unnecessary, and the cases in (74c) and (74d) should be treated the same. Our motivation for this proposal comes from the following variation:
Tania Ionin and Ora Matushansky 355 TANIA IONIN University of Southern California Department of Linguistics GFS 301 3601 Watt Way Los Angeles, CA 90089. e-mail:
[email protected]
Received: 26.03.06 Revised version received: 19.06.06 Final version received: 21.09.06
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ORA MATUSHANSKY Universite´ Paris VIII UMR 7023 (D-327) 2 rue de la Liberte´ 93526 Saint Denis CEDEX France. e-mail:
[email protected]
356 The Composition of Complex Cardinals Grammar approach to English measure phrases’. In J. Larson & M. Paster (eds), Proceedings of the 28th Annual Meeting of the Berkeley Linguistics Society. Berkeley Linguistics Society. Berkeley. 75–86. van der Does, J. (1992) ‘Applied quantifier logics’. Unpublished PhD thesis, University of Amsterdam. van der Does, J. (1993) ‘Sums and quantifiers’. Linguistics and Philosophy 16:509–550. Doetjes, J., Neeleman, A. & van de Koot, H. (1998) ‘Degree expressions and the autonomy of syntax’. UCL Working Papers in Linguistics 10: 323–368. Domahs, F., Bartha, L., Lochy, A., Benke, T. & Delazer, M. (2005) ‘Number words are special: Evidence from a case of primary progressive aphasia’. Journal of Neurolinguistics 19:1–37. Downing, P. (1984) ‘Japanese numeral classifiers: A syntactic, semantic and functional profile’. Unpublished PhD thesis, University of California, Berkeley. Downing, P. (1996) Numeral Classifier Systems: The Case of Japanese. John Benjamins. Philadelphia. Drellishak, S. (2004) A Survey of Coordination Strategies in the World’s Languages. MA thesis, University of Washington. Farkas, D. (1981) ‘Quantifier scope and syntactic islands’. Chicago Linguistics Society 17. 59-66. Farkas, D. & de Swart, H. (2003) The Semantics of Incorporation: From Argument Structure to Discourse Transparency. CSLI Publications. Stanford, CA. Fodor, J. D. & Sag, I. (1982) ‘Referential and quantificational indefinites’. Linguistics and Philosophy 5:355–398. Franks, S. (1994) ‘Parametric properties of numeral phrases in Slavic’. Natural
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Tania Ionin and Ora Matushansky 357 Unpublished PhD thesis, University of Massachusetts, Amherst. Heim, I. & Kratzer, A. (1998) Semantics in Generative Grammar. Blackwell. Oxford. Heycock, C. & Zamparelli, R. (2000) ‘Plurality and NP-coordination’. In M. Hirotani, A. Coetzee, N. Hall and J. Kim (eds) Proceedings of NELS 30. University of Massachusetts, GLSA. Amherst, Massachusetts. 341–352. Heycock, C. & Zamparelli, R. (2003) ‘Friends and colleagues: Plurality, coordination, and the structure of DP’. MS, University of Edinburgh/ Universita` di Bergamo. Available at http://semanticsarchive.net/Archive/ mRhN2FlN/fc-heycock-zamparelli03. pdf Higginbotham, J. (1981) ‘Reciprocal interpretations’. Journal of Linguistic Research 1:97–117. Hoeksema, J. (1984) ‘Partitives’. MS, University of Groningen. Hoeksema, J. (1996) ‘Introduction’. In J. Hoeksema (ed), Partitives: Studies on the Syntax and Semantics of Partitive and Related Constructions. Mouton de Gruyter. Berlin. 1–24. Hofweber, T. (2005) Number determiners, numbers, and arithmetic. The Philosophical Review 114:179–225. Hurford, J. (1975) The linguistic theory of numerals. Cambridge University Press. Cambridge. Hurford, J. (1987) Language and Number: The Emergence of a Cognitive System. Blackwell. Oxford. Hurford, J. (2001) ‘Numeral systems’. In N. J. Smelser & P. B. Baltes (eds), International Encyclopedia of the Social and Behavioral Sciences. Pergamon. Amsterdam. 10756–10761. Hurford, J. (2003) The interaction between numerals and nouns. In F. Plank (ed), Noun Phrase Structure in the Languages of Europe. Typology of
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358 The Composition of Complex Cardinals Krifka, M. (1992) ‘Definite NPs aren’t quantifiers’. Linguistic Inquiry 23: 156–163. Krifka, M. (1999) ‘At least some determiners aren’t determiners’. In K. Turner (ed), The Semantics/PragmaticsInterface from Different Points of View. Current Research in the Semantics/Pragmatics Interface 1. Elsevier Science. 257–291. Ladusaw, W. (1982) ‘Semantic constraints on the English partitive constructions’. In D. Flickinger, M. Macken and N. Wiegand (eds), Proceedings of WCCFL 1. Stanford Linguistics Association. Stanford. 231–242. Landman, F. (2003) ‘Predicate-argument mismatches and the adjectival theory of indefinites’. In M. Coene & Y. D’hulst (eds), The Syntax and Semantics of Noun Phrases. Linguistics Today 55. John Benjamins. Amsterdam and Philadelphia. 211–237. Lasersohn, P. (1995) Plurality, Conjunction and Events. Kluwer. Dordrecht. Li, Y. A. (1999) ‘Plurality in a classifier language’. Journal of East Asian Linguistics 8:75–99. Link, G. (1987) ‘Generalized quantifiers and plurals’. In P. Ga¨rdenfors (ed), Generalized Quantifiers. D. Reidel. Dordrecht. 151–180. Ludlow, P. & Neale, S. (1991) ‘Indefinite descriptions: In defense of Russell’. Linguistics and Philosophy 14:171–202. Maling, J. (1983) ‘Transitive adjective: a case of categorial reanalysis’. In F. Heny & B. Richards (eds), Linguistic Categories: Auxiliaries and Related Puzzles. D. Reidel. Dordrecht. Martı´ Girbau, N. (in press) ‘Partitives: one or two nouns’. Rivista di Grammatica Generativa. Matushansky, O. (to appear) ‘Why Rose is the Rose’. In O. Bonami & P. Cabredo Hofherr (eds), Empirical Issues in Formal Syntax and Semantics 6.
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Languages in Europe 7. Mouton de Gruyter. The Hague. Ionin, T. & Matushansky, O. (2004) ‘A singular plural’. In B. Schmeiser, V. Chand, A. Kelleher & A. Rodriguez (eds), WCCFL 23: Proceedings of the 23rd West Coast Conference on Formal Linguistics. CSLI. Stanford. 399–412. Ionin, T. & Matushansky, O. (in preparation) ‘Issues in cross-linguistic syntax and semantics of complex cardinals’. Ionin, T., Matushansky, O. & Ruys, E. G. (to appear) ‘Parts of Speech: Toward a unified semantics for partitives’. In C. Davis, A. R. Deal and Y. Zabbal (eds), Proceedings of NELS 36. University of Massachusetts, GLSA. Amherst, MA. Jackendoff, R. (1977) X-bar Syntax: A Study of Phrase Structure. MIT Press. Cambridge, Mass. Kadmon, N. (1987) ‘On unique and non-unique reference and asymmetric quantification’. Unpublished PhD thesis, University of Massachusetts, Amherst, MA. Kobuchi-Philip, M. (2003) ‘On the syntax and semantics of the Japanese numeral quantifier’. Unpublished PhD thesis, CUNY, New York, NY. Kratzer, A. (1989) ‘An investigation of the lumps of thought’. Linguistics and Philosophy 12:607–653. Kratzer, A. (1998) ‘Scope or pseudoscope? Are there wide scope indefinites?’ In S. Rothstein (ed), Events and Grammar. Kluwer. Dordrecht. 163–196. Krifka, M. (1990a) ‘Boolean and nonBoolean and’. In L. Ka´lman & L. Polos (eds), Papers from the Second Symposium on Logic and Language. Akade´miai Kiado´. Budapest. 161–188. Krifka, M. (1990b) ‘Four thousand ships passed through the lock: Objectinduced measure functions on events’. Linguistics and Philosophy 13:487–520.
Tania Ionin and Ora Matushansky 359 Partee, B. H. & Mats Rooth (1983) ‘Generalized conjunction and type ambiguity’. In R. Bauerle, C. Schwarze & A. von Stechow (eds), Meaning, Use and Interpretation of Language. Mouton de Gruyter. Berlin. 361–383. Payne, J. R. (1985) ‘Complex phrases and complex sentences’. In T. Shopen (ed), Language Typology and Syntactic Description. Complex Constructions, vol. 2. Cambridge University Press. Cambridge. 3–41. Postal, P. (1974) On Raising. MIT Press. Cambridge, Mass. Ritter, E. (1991) ‘Two functional categories in noun phrases: Evidence from Modern Hebrew’. Perspectives on Phrase Structure. Syntax and Semantics 25. Academic Press. New York. 37–62. Ross, J. R. (1967) ‘Constraints on variables in syntax’. Unpublished PhD thesis, MIT. Ruys, E. G. (1992) ‘The Scope of Indefinites’. Unpublished PhD thesis, Utrecht University. Sabbagh, J. (2003) ‘Ordering and linearizing rightward movement’. In G. Garding & M. Tsujimura (eds), Proceedings of WCCFL 22. Cascadilla Press. Somerville, MA, 436-449. Saeed, J. (1999) Somali. The London Oriental and African Language Library 10. John Benjamins. Amsterdam and Philadelphia. Sanches, M. & L. Slobin (1973) ‘Numeral classifiers and plural marking: An implicational universal’. Working Papers in Language Universals, vol. 11. Stanford University. Stanford, California. 1–22. Scha, R. (1981) ‘Distributive, collective and cumulative quantification’. In J. Groenendijk, M. Stokhof & T. M. V. Janssen (eds), Formal Methods in the Study of Language. Mathematical Centre Tracts 135. Mathematisch Centrum,
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360 The Composition of Complex Cardinals Winter, Y. (1995) ‘Syncategorematic conjunction and structured meanings’. In M. Simons & T. Galloway (eds), Proceedings of Semantics and Linguistic Theory (SALT) 5. CLC Publications, Department of Linguistics, Cornell University. Ithaca, New York. 387–404. Winter, Y. (1996) ‘A unified semantic treatment of singular NP coordination’. Linguistics and Philosophy 19:337–391. Winter, Y. (1997) ‘Choice functions and the scopal semantics of indefinites’. Linguistics and Philosophy 20:399–467. Winter, Y. (1998) ‘Flexible Boolean Semantics: coordination, plurality and scope in natural language’. Unpublished PhD thesis, Utrecht University. Winter, Y. (2001a) Flexibility Principles in Boolean Semantics: Coordination, Plurality and Scope in Natural Language. MIT Press. Cambridge, MA. Winter, Y. (2001b) ‘Plural predication and the Strongest Meaning Hypothesis’. Journal of Semantics 18:333–365. Winter, Y. (2005) ‘On some problems of (in)definiteness in flexible semantics’. Lingua 115:767–786. Zabbal, Y. (2005) ‘The syntax of numeral expressions’. MS, University of Massachusetts, Amherst. Zamparelli, R. (1995) ‘Layers in the Determiner Phrase’. Unpublished PhD thesis, University of Rochester. Zamparelli, R. (2002) ‘Dei ex machina’. MS, Universita` di Bergamo. Zweig, E. (to appear) ‘Nouns and adjectives in numeral NPs’. In L. Bateman & C. Ussery (eds), Proceedings of NELS 35. University of Massachusetts, GLSA. Amherst, Massachusetts.
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Journal of Semantics 23: 361–382 doi:10.1093/jos/ffl008 Advance Access publication November 22, 2006
Against Grammatical Computation of Scalar Implicatures BENJAMIN RUSSELL Brown University
Recently, several authors have argued that Gricean theories of scalar implicature computation are inadequate, and, as an alternative, one author has proposed a grammatical system for computing scalar implicatures. The present paper provides arguments, counter to the claims of these authors, that Gricean reasoning can account for the implicatures of certain complex sentences and does not generate undesirable implicatures for others. Moreover, it is shown that a putative advantage of grammatical scalar implicature computation, that it informs a theory of intervention in negative polarity item licensing, is spurious. These arguments, plus general conceptual advantages of Gricean theory, lead to the conclusion that scalar implicature computation is not carried out in the grammar.
1 INTRODUCTION Scalar implicatures, according to a theoretical tradition that goes back to Grice (1975) and is elaborated and formalized by Horn (1972, 1989), Gazdar (1979), Sauerland (2004), Blutner (2004), and van Rooij & Schulz (2004), have been understood as inferences of the following (somewhat abbreviated) form: (1) Speaker A said /, and could as easily have said w, which is stronger. Because A is co-operative, she makes the strongest true statement possible, so w can’t be true. The key to the reasoning in (1), and to Gricean pragmatics generally, is co-operation: it is co-operative to be informative, so scalar implicatures are the product of the distinctly extralinguistic behaviour of agents working together towards a common goal. The idea that such inferences may be attributed to co-operation rather than grammar has been crucial for the development of modern semantic theory. Because the literal meaning of linguistic expressions need not provide a complete description of the understood message of utterances, the theory of grammar only needs to assume a bare-bones model-theoretic semantics The Author 2006. Published by Oxford University Press. All rights reserved. For Permissions, please email:
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Abstract
362 Against Grammatical Computation of Scalar Implicatures that delivers literal meanings which may then be used by co-operative agents to convey more nuanced information. In recent years, several challenges to this Gricean view of scalar implicatures have been raised. These arguments take two forms: (a) that there are observed scalar-type inferences that the Gricean theory is unable to compute, and (b) that the Gricean theory generates implicatures that are not observed. In particular, it is argued that the Gricean theory makes wrong predictions about the following types of sentence:
(3) Gricean analysis incorrectly predicts: a. George ate some of the fries or the apple pie. , = George did not eat all of the fries or the apple pie. (This entails George did not eat the apple pie.) (Chierchia 2004) b. John has more than three children. , = John has exactly four children. (Fox & Hackl to appear) A number of theories of scalar implicatures, departing in various ways from Grice’s theory, have ensued, developed by Carston (1988), Landman (2001), Levinson (2001) and Recanati (2003), among others. Recently, Chierchia (2004) has proposed a particularly radical departure from the Gricean theory: scalar implicatures, he argues, are not the product of rational behaviour between co-operative conversants as in (1), but rather are computed automatically in the grammar by means of special semantic composition rules and lexical scales. The main argument that has been made against a global, Gricean framework and in favour of a local, grammatical computation mechanism is an empirical one: that a Gricean theory does not generate the set of observed scalar implicatures. Because the Gricean theory follows, without significant further stipulations, from the uncontroversial assumption that speakers co-operate, nobody argues on a theoretical basis that a stipulated mechanism for grammatical implicature computation is
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(2) Gricean analysis fails to predict: a. George believes that some of his advisors are crooks. , George believes that not all of his advisors are crooks. (Chierchia 2004) b. George knows that some of his advisors are crooks. , Not all of his advisors are crooks. (Chierchia 2004) c. It is better to eat some of the cake than it is to eat all of it. It is better to eat some but not all of the cake than it is to eat all of it. (Carston 1988, Levinson 2001, Recanati 2003)
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2 GRICEAN COMPUTATION OF IMPLICATURES OF COMPLEX SENTENCES
2.1 Apparent embedded implicatures Chierchia identifies a range of observed scalar implicatures that are not obviously generated by Gricean principles. The most compelling of these are apparently embedded implicatures of kind in (4a). (4) George believes some of his advisors are crooks. a. , George believes not all of his advisors are crooks. b. , It is not the case that George believes all of his advisors are crooks. Chierchia argues that Gricean reasoning cannot generate the observed implicature in (4a): if scalar implicatures are derived by the kind of reasoning in (1), hearers can only make conclusions about the negation 1 There is one exception to this: Fox and Hackl (to appear) argue that a global theory relies crucially on stipulated Horn scales. And, since Horn scales are stipulated formal, linguistic objects (with no apparent function except their use in scalar implicature computation), we may just as well stipulate a grammatical mechanism. I argue briefly below in Section 3 that Horn scales are just a way to specify a class of competing utterances for Gricean reasoning in the absence of a principled theory of competition. Further, even if Horn scales must be assumed, it is still more parsimonious to suppose the lexicon is organized into competition classes (something we have considerable psycholinguistic evidence for) than to introduce a new set of rules into the grammar.
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superior to Gricean computation.1 For this reason, the argument for a general Gricean framework in this paper will consist of demonstrations that claims of over- and under-generation by a purely Gricean theory are unfounded. That is, observed implicatures that have been claimed to be outside the scope of Gricean pragmatics will be derived within such a theory, and claims that Gricean reasoning generates undesirable implicatures will be countered. There is a second, indirect argument against global Gricean implicature computation provided by Chierchia: he develops a theory of the otherwise mysterious phenomenon of intervention in negative polarity item licensing (Linebarger 1987) that depends on the tools of grammatical implicature computation. In Section 3 I show that this theory does not actually make the right predictions about intervention, and suggest that any theory of intervention based on scalar implicatures is likely to fail. So, in the absence of empirical evidence of the Gricean theory’s inadequacy, I conclude that the adoption of a more complex, stipulative grammatical system for the computation of scalar implicatures is unjustified.
364 Against Grammatical Computation of Scalar Implicatures
(5) George has not yet formed an opinion about all of his advisors, but, at this point, he believes some of them are crooks. Here, the strongest implicature drawn is that it is not the case that George believes all his advisors are crooks; this is because the default context, in which George is opinionated, is explicitly ruled out. The enrichment of weak implicatures with contextual inferences in a global, Gricean framework correctly mirrors the observed fine-grained context-sensitivity of scalar implicatures. And the fact that Gricean inferencing can generate ostensibly embedded implicatures as well as weaker global implicatures obviates the need Chierchia tries to establish here for a grammatical system of implicature computation.3 Scalar terms embedded under factive verbs and other elements with presuppositions are a bit more complex. 2 This way of deriving a stronger implicature from a weaker one based on assumptions about an agent’s beliefs is akin to the strengthening of epistemic weak implicatures (it is not the case that the speaker believes . . .) to epistemic strong implicatures (the speaker believes it is not the case that . . .). See Section 2.3 below for details. 3 Incidentally, Chierchia’s system, which introduces implicatures at each type t meaning, could handle this case, canceling the strong implicature generated for the embedded clause, but not the weaker implicature generated at the matrix clause level. The point here is not that Chierchia’s system is inadequate for such cases, but that it is not needed.
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of competing utterances, not embedded clauses within those utterances, and so they should only infer (4b). On the other hand, in Chierchia’s system, the implicature of some of his advisors are crooks is computed to give a strong meaning of some of his advisors are crooks and not all of his advisors are crooks, which subsequently composes up to give a strong meaning of George believes some of his advisors are crooks and not all of his advisors are crooks. Thus, by grammaticizing the process of scalar implicature computation, Chierchia is able to compute embedded scalar implicatures like (4a). But notice that (4a) follows from (4b) in every context where George has some belief about whether all of his advisors are crooks: if it is not the case that George believes that all of his advisors are crooks, and George has some belief about whether all of his advisors are crooks, then George must believe that not all of his advisors are crooks.2 Speakers I’ve consulted readily agree that ‘Either George thinks all his advisors are crooks or he thinks they’re not all crooks’ has to be true, suggesting that this is a ‘default’ background assumption. It might follow from the assumption that George has a belief about each of his advisors’ criminality; indeed, in a context where this assumption is explicitly denied, the ‘embedded’ implicature is not generated:
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(6) George knows some of his advisors are crooks. This is entailed by the alternative: (7) George knows all of his advisors are crooks. Chierchia observes that an utterance of (6) implies not just the negation of (7), as predicted by Gricean reasoning, but also the negation of its presupposition: (8) All of George’s advisors are crooks.
(9) a. Asserted: George believes some of his advisors are crooks and not all are. b. Presupposed: Some of George’s advisors are crooks and not all are. This accords well with intuitions, at least initially. But contexts where the ‘‘implicature of the presupposition’’ is defeated and yet the ordinary scalar implicature still arises pose a serious problem for this analysis. Consider (6) in the following slightly richer context: (10) The public has long been aware that every last one of George’s advisors is a crook. And now (even) George knows that some of his advisors are crooks. Here, the right theory will predict that the implicature that George believes not all of his advisors are crooks can still go through while the inference that not all of the advisors are crooks does not. In Chierchia’s theory, clauses with scalar terms become ambiguous: they may be strengthened or not. In other words, either the embedded implicature is cancelled (and is found neither in the presupposition nor the assertion), or not (and is found in both).4 There is no room for the 4 Cancellation, in Chierchia’s system, is a re-analysis of a sentence whereby mechanisms for adding implicatures are inactive.
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Chierchia claims that his system makes the right predictions about such sentences: implicatures are added an expression’s meaning by the compositional semantics at each type t meaning (extensionalizing). This means that, in building (6), the embedded sentence is computed to have the strong meaning some of his advisors are crooks and not all of his advisors are crooks. When this combines with the predicate know, this meaning makes two contributions: it enters into the belief relation with George, and it becomes presupposed content, to be projected through the semantic composition by whatever means ordinary presuppositions project. At the end of the day, then, (6) has the following content:
366 Against Grammatical Computation of Scalar Implicatures
(11) a. George knows that some of his advisors are crooks, and (in fact) they all are. b. Some of George’s advisors are crooks, and #(in fact) they all are. This suggests, not surprisingly within a Gricean framework, that the inference that not all the advisors are crooks is not generated by the same mechanisms as ordinary scalar implicatures. And, since they are apparently distinct from scalar implicatures, it is beyond the scope of this paper to provide a comprehensive Gricean theory of such ‘presuppositional implicatures’—I will, however, make a brief speculation. The source of the inference, made by only some speakers, might be the assumption that George is well-informed about the integrity of each of his advisors. (As an anonymous reviewer points out, this assumption would depend on the speaker’s using know, rather than believe: in canonical (non-downward-entailing) environments, know, unlike believe, presupposes its subject is well-informed about the propositional content of its complement, and it therefore seems reasonable to suppose it implies its subject is well informed about related propositions.) This assumption, plus the implicature that it is not the case that George believes all his advisors are crooks, licenses the inference that not all of George’s advisors are crooks. Interestingly, such inferences seem to project beyond negation (I’ve used examples with possible/certain because of potential positivepolarity effects getting in the way with some): (12) George doesn’t know that failure in Iraq is possible. implies Failure in Iraq is not certain.
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intermediate interpretation found in (10) where the presupposition’s ‘implicature’ is cancelled but the assertion’s is not. A rule could be formulated to selectively remove implicatures within the presuppositional system, but this is an extra stipulation, and it makes Chierchia’s system still more complex. A Gricean analysis of such inferences must begin with a careful consideration of their status. Perhaps the first thing to notice is that they are relatively weak compared with scalar implicatures. Indeed, many speakers I consulted do not have the intuition that (6) implies that not all the advisors are crooks at all, but only that it is compatible with such a situation. Such sentences are apparently equally felicitous whether or not all of the advisors are crooks—an expression like in fact is not needed to cancel that supposition like it is to cancel an ordinary scalar implicature.
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(13) Utterance assertion: : George believes failure is possible. Utterance presupposition: Failure is possible. Alternative’s assertion: : George believes failure is certain. Alternative’s presupposition: Failure is certain. Notice that, whereas the alternative’s assertion is weaker than the utterance’s, its presupposition is stronger. The speaker, then, could have uttered a sentence with a weaker assertion with a stronger presupposition, but chose not to. The reasons for making such a conversational move will depend on context in ways that are too complex to explore in this paper; but we can say, roughly, that whenever the difference in content between an utterance’s presupposition and its alternative’s presupposition is of more interest than the difference between the corresponding assertions, we predict a ‘presuppositional implicature’. This line of argument is not meant to be a full-fledged Gricean analysis of such inferences; nonetheless, it should suggest that such an analysis is possible, and that its account of sensitivity to context would be more explanatory than a grammatical theory. A related example has been discussed by Carston (1988), and Recanati (2003), who argue that scalar terms like some sometimes have not all as part of their meaning (what Carston calls explicature).5 Specifically, it seems that some is interpreted as some but not all in the following sentence: (14) It is better to eat some of the cake than it is to eat all of it. 5
This is, of course, different from Chierchia’s position: in Chierchia’s system, a grammatical rule is responsible for scalar implicature generation, so the syntactic environment a scalar term appears in determines whether an implicature is generated. In contrast, Carston’s proposed ambiguity means discourse context determines which some is being used, so some can mean some and not all in any environment. In this paper, I’m arguing specifically against doing it by grammatical rules, but the arguments can be taken as counterarguments to non-grammatical non-Griceans like Carston as well.
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Certainly know in such an environment does not presuppose or imply that its subject is well-informed about anything, let alone that George is well-informed about the odds of failure in Iraq. So such sentences will need to be treated some other way—perhaps through Gricean reasoning about presupposed content. It is plausible that Gricean reasoning incorporates such information: if speakers are aware of competing utterances, they should be aware of the presuppositional content of those utterances as well as their assertoric content. In a case like this, a speaker, considering the alternative George doesn’t know that failure in Iraq is certain, might choose to use a sentence with a weaker presupposition because she does not want a stronger one to be accommodated. Spelling this out, we have:
368 Against Grammatical Computation of Scalar Implicatures
(15) Any cutoff for good that makes to eat all of the cake count as good also makes to eat some of the cake count as good. What makes an infinitive like to eat all of the cake count as good? Bare infinitives in present tense have been analysed as generics (Chierchia 1984)—that is, a set of typical worlds or situations in which a ‘generic’ individual eats all of the cake. So to eat all of the cake counts as good if this set of situations is included in the extension of good. This means that (15) is true iff the generic situations in which all of the cake is eaten are in the extension of good only if the generic situations in which some of the cake is eaten are in the extension of good. Because situations in which some cake is eaten range from worlds where just a crumb is eaten to those where all is eaten, the extension of the generic to eat some of the cake will plausibly exclude situations at either end of the scale, including those where not all the cake is eaten. Therefore, if more restrictive extensions for good include situations where less cake is eaten, then (14) comes out true, without appeal to scalar implicatures at all. If this analysis is right, genericity should be crucial for the acceptability of sentences like (14). Indeed, this prediction seems to be borne out: similar sentences in the (usually) non-generic past tense are considerably degraded. (16) #It was better to eat some of the cake than it was to eat all of it.
2.2 Downward-entailing operators It has been widely observed that implicatures associated with weak scalar terms like some are not generated when those terms are located
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Many speakers find such sentences felicitous; critics wonder how that can be if all entails some. King and Stanley (2006) provide a potential answer to this criticism. They note that (14) requires focal stress on some, and they develop a semantics of the restriction of quantification over worlds based on focus. That is, the fact that some is focused leads to the restriction of the set of worlds considered by better to those where some and not all of the cake are eaten. This analysis seems to be a reasonable solution to this problem. But a potentially simpler solution is available. That is, (14) is simply a comparative—standard semantics for comparatives (Cresswell 1976; Schwarzschild & Wilkinson 2001) gives it a meaning roughly paraphrasable as:
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below a downward-entailing (DE) operator6 (Horn 1972); Fauconnier 1975; Gazdar 1979): (17) If George eats some of his vegetables, he’ll get dessert. , = It is not the case that if George eats all of his vegetables, he’ll get dessert. Further, scalar terms appearing below DE operators have a reversed pattern of observed implicatures:
As Levinson (2001) notes, this fact is predicted by a Gricean theory. Suppose d is a DE environment, and r and x are equally marked, with r x. Then, by the definition of downward-entailing, d(x) d(r)—that is, a sentence S with semantics d(r) is weaker than (entailed by) the alternative where r is replaced by x. This means that an utterance of S, which contains a stronger scalar term, implicates the negation of the sentence with the weaker term, a reversal of the usual pattern. So Gricean theory explains the reversal of scalar implicatures by DE operators, and therefore makes the correct predictions about the implicatures of conditionals like (18). Chierchia’s grammatical theory, in contrast, has to stipulate a special rule for downward-entailing operators: they remove the grammatically computed scalar implicatures of expressions they combine with. Because it is a stipulation, this rule explains nothing—it could just as well have been upward-entailing operators that remove implicatures.7 Both Chierchia’s theory and a Gricean one make the same predictions about scalar terms within the scope of downward-entailing operators: scalar implicature patterns will be reversed; the Gricean theory, however, explains this behaviour, while Chierchia’s accounts for it by a special rule.
2.3 Scalar terms inside disjunction Chierchia argues that the Gricean theory makes the wrong predictions about the interaction of multiple scalar terms in a single sentence: the 6 I use if for these examples—despite the fact (according to most modern theories of conditionals) that if is not itself a downward-entailing operator (see, for example, von Fintel 1999)—since, under the correct circumstances, antecedents of conditionals are downward-entailing environments. That is, with a universal modal in the second conjunct, the antecedent is (Strawson) DE, just like the restrictor of a universal quantifier; but with existential modals, the antecedent may be upwardentailing. 7 Thanks to Polly Jacobson for suggesting this way of making this point.
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(18) If George eats all his vegetables, he’ll get dessert. , It is not the case that if George eats some of his vegetables, he’ll get dessert.
370 Against Grammatical Computation of Scalar Implicatures reasoning in (1) incorrectly predicts that (19) implicates (19b), not (19a). (19) George ate some of the fries or the apple pie. a. ,It is not the case that George ate all of the fries. b. , = It is not the case that George ate all of the fries or the apple pie.
(20) Speaker A said /, and could as easily have said w, which is stronger. Because A is co-operative, she makes the strongest true statement possible, so A must not know w is true (:Kw). That is, scalar implicatures are inferences of the form /,:Kw, rather than the stronger /,K:w. Given these weaker inferences, corresponding strong inferences of K:w may be generated when the hearer assumes that the speaker knows whether w is true (Kw _ K:w)—i.e. when the speaker is competent with respect to the truth of w. Treating scalar implicatures as this kind of two-stage inference is not only more faithful to Grice’s theory; it also provides a solution to Chierchia’s puzzle, for (19) now has the implicature in (21), which does not have the bad entailments of (19b). 8 A related proposal can be found in van Rooij & Schulz (2004), who present a theory that depends on relevant alternative meanings rather than competing utterances for Gricean reasoning. This is a potentially innocuous departure from classical Gricean reasoning, and I cannot address its consequences here.
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The second implicature, which the Gricean theory is supposed to generate, entails that George did not eat the apple pie; this is, of course, undesirable. Following Sauerland (2004), I propose that a reconsideration of the epistemic status of implicatures provides a solution to this problem within Gricean theory.8 Sauerland’s particular implementation of this solution involves the stipulation of two unrealized lexical items (L and R) which serve as scalar alternatives to and and or, as well as the formal apparatus of crossing scales. The analysis presented here, though related to Sauerland’s, does not rely on stipulated covert lexical items, and is therefore perhaps a clearer demonstration of the applicability of a purely Gricean theory to the complex sentences at issue. The key to both the analysis presented here and Sauerland’s is a closer consideration of the epistemic status of scalar implicatures. Horn (1989) and Soames (1982) have pointed out that the Gricean reasoning for scalar implicature computation is not accurately given in (1); instead, Gricean agents are only justified in drawing the weaker conclusion in (20).
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(21) :K George ate all of the fries or the apple pie. And (21) entails the following two epistemic facts about the speaker. (22) a. :K George ate all of the fries. b. :K George ate the apple pie.
(23) K: George ate the apple pie. This can be explained in Gricean terms: a sentence’s scalar implicature cannot be strengthened if this leads to contradiction with another of its basic implicatures. First, notice that p and q are stronger than (entail) p _ q, and p and q are each certainly easier to say than p or q, so if a speaker has chosen to use p or q, she must not know that either p or q is true. So the weak implicatures in (24) should be generated along with the weak implicatures in (21).9 (24) a. :K George ate some of the fries. b. :K George ate the apple pie. These implicatures, combined with the uncontroversial assumption that speakers believe what they say (25a) (Grice’s maxim of quality), are enough to ‘‘block’’ the strengthening of (22b) to (23). The derivation is as follows: (25) a. K (George ate some of the fries _ George ate the apple pie) (from (19)) b. K (: George ate the apple pie / George ate some of the fries) (equivalent to (25a)) c. K: George ate the apple pie / K George ate some of the fries (from (25b), assuming a distribution axiom for knowledge modality) d. :K George ate some of the fries / :K: George ate the apple pie (contrapositive of (25c)) e. :K George ate some of the fries (from (24a)) f. :K: George ate the apple pie (modus ponens) 9
These implicatures are labeled clausal, rather than scalar, implicatures by Gazdar (1979).
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In contexts where the hearer can assume the speaker is competent—i.e. knows whether George ate all the fries—(22a) can be strengthened, yielding the desired implicature in (19a) (in all other contexts, (22a) is predicted to be the strongest implicature drawn, which is very much in keeping with my intuitions). Why isn’t (22b) strengthened to the obviously undesirable inference (23)?
372 Against Grammatical Computation of Scalar Implicatures The conclusion in (25f ) contradicts, and therefore blocks, (23), so the observed implicature (19a) is generated by the Gricean theory without any undesirable consequences. The Gricean theory is again capable of generating the right implicatures for complex sentences, counter to Chierchia’s argument that the observed implicatures of sentences like (4) and (19) are not generated by a global theory.
2.4 More than n phrases
(26) Bill has more than four kids. Gricean reasoning, Fox and Hackl claim, predicts that this should implicate (27) Bill has exactly five kids. Why? Because (28) is a stronger scalar alternative to (26), and it’s probably equally marked. (28) Bill has more than five kids. Therefore, (28) should be inferred to be false, yielding the interpretation in (27). This example, however, is amenable to the Gricean treatment given to Chierchia’s disjunctive case in the previous section. That is, Gricean reasoning, in fact, only licenses the epistemic weak inference: (29) :K Bill has more than five kids. And it is reasonable to suppose that there is another highly salient competing utterance for (26): namely, (27) itself. This means a basic scalar implicature of (26) is: (30) :K Bill has exactly five kids. Because of this, (29) cannot be strengthened, as this would contradict (30). This leaves the intuitively correct implicature that all the speaker knows is that Bill has more than four kids. Again, the Gricean theory, carefully applied, does not make the bad predictions that critics claim it does. 3 A CAVEAT: COMPETING UTTERANCES It is crucial in the reasoning in (1) and throughout this paper that the hearer and speaker are sensitive to a relation of easiness, or markedness,
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Fox and Hackl (to appear), who develop their own grammatical scalar implicature computation mechanism, discuss data that initially seem problematic for the Gricean theory. Consider the following sentence:
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that determines which utterances compete with each other. If this were not the case, scalar implicatures would be generated in great excess. In particular, because every sentence S is entailed by an utterance of S and the sky is blue, every sentence would implicate that the speaker does not believe the sky is blue. This is clearly not the case. But, because markedness is a key aspect of Gricean reasoning, this fact may be readily explained: for any sentence S, S and the sky is blue is a lot harder to say than S, so neither hearers nor speakers consider S and the sky is blue a competing utterance for S (except, perhaps, in certain bizarre contexts). Gricean reasoning is limited to stronger competing utterances—things a speaker might just as easily have said. It is not within the scope of this paper to provide a worked-out theory of which utterances compete—nonetheless, I assume that such a theory could be developed, and speculate briefly about what such a theory would look like in this section. A possible (but probably incorrect) theory of competition is a purely phonological one: one expression competes with another iff it has fewer syllables (a theory like this is advanced by McCawley (1978) and refuted in Horn (1978)). A more principled theory of competition has not been widely pursued—Matsumoto (1995) contains the bestdeveloped theory, and even this provides only rudimentary first steps, albeit promising ones. Instead, theories of implicature have taken competition to be determined by stipulated lexical scales (often called Horn scales) such as Æsome, allæ and Æpossibly, certainlyæ; two utterances compete with each other if their differences are limited to substitution of scalemates—i.e. they are scalar alternates. But this should not be understood to mean (as suggested by Fox and Hackl (to appear)) that Gricean pragmatics depends on the stipulation of lexical scales. From a Gricean perspective, although it is uncontroversial that scalar alternates are equally marked expressions, and therefore can enter into the type of reasoning given in (1), it is also clear that stipulated Horn scales provide just one of many possible theories of competition (and not a particularly interesting or principled one). Furthermore, there is no clear sense in which Horn scales must be in the lexicon—rather, they are generalizations about the lexicon: certain lexical items compete with others; saying two items are Horn scalemates is just a way of saying they are competitors (with the particular semantic relation of asymmetric entailment), and it is wellknown that scalar implicatures may be generated based on contextually-determined competitors (see Hirschberg 1991 on ‘on-the-fly’ construction of Horn scales). Finally, there is psycholinguistic evidence that shows that speakers reason about competing utterances (see, for
374 Against Grammatical Computation of Scalar Implicatures example, Sedivy 2003 and Grodner and Sedivy (to appear)). Because of this, assuming competition exists, and therefore that not all stronger utterances are ruled out by Gricean reasoning, is a less costly assumption than the alternative—that there are grammatical mechanisms for scalar implicature computation. 4 SCALAR IMPLICATURES AND INTERVENTION
(31) a. Condoleeza didn’t drink any Coke and a milkshake. (cf. Condoleezadidn’t drink any Coke or a milkshake.) b. George didn’t believe Condoleeza had ever eaten a McRib and Dick had ordered a McDLT. (cf. . . .Condoleeza had ever eaten a McRib or Dick had ordered a McDLT.) c. Dick doubts everyone would lift a finger to help him finish his McNuggets. (cf. Dick doubts George would lift a finger to help him finish his McNuggets.) In (31), the negative polarity items any, ever, and lift a finger appear within the scope of downward-entailing operators (doubt and negation), yet the sentences they appear in are ungrammatical. Chierchia develops a theory of NPI licensing based on Kadmon & Landman’s (1993) semantics of any that provides a putative solution to the intervention puzzle. Kadmon & Landman propose that any means approximately the same thing as some or a: it is an existential quantifier. any, however, requires a wider domain of quantification than some: if some quantifies over, say, the set of regular bun-and-beef-patty burgers, any quantifies over a wider domain, including McDLTs, veggie burgers, lamburgers, month-old Big Macs in the garbage, and so on. This aspect of any ’s meaning is called Widening. A consequence of Widening is that it makes any semantically weaker than some, or ½½some ½½any. To Widening, Kadmon and Landman add a
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Ladusaw (1979) made the following seminal proposal: negative polarity items (like any, ever, and drink a drop) are only licensed when they fall within the scope of a downward-entailing operator. Many subsequent theories of NPI licensing have tried to explain (Lee & Horn 1994; Kadmon & Landman 1993; Krifka 1995; Lahiri 1997) and made refinements to (Linebarger 1987; Zwarts 1996; Giannakidou 1998) this generalization. One particular refinement to this generalization (due to Linebarger 1987) has apparently stumped researchers: an NPI is not licensed by a DE operator if it is in the scope of every or contained in one of the conjuncts of and (where every and and are also within the scope of the DE operator).
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(32) a. George ate any McNuggets. b. George ate some McNuggets. So, given Widening, any used in upward-entailing environments should be predicted to be (factoring in its implicatures) an existential over fringe cases: (32a) should mean that George did eat McNuggets, if you’re lenient about what counts as McNuggets (allowing, say, limited edition McNuggets made from beef parts), but imply he didn’t eat normal McNuggets in a normal way. So Strengthening doesn’t follow from pragmatic principles plus the weakness of any, so if it is the right constraint, it seems it might have to be stated as part of the grammar. Moreover, Kadmon & Landman recognize that their theory doesn’t quite capture Ladusaw’s generalization: Ladusaw proposed NPIs were licensed by downward-entailing operators; but Strengthening as stated
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quasi-pragmatic condition called Strengthening: any is not licensed unless it strengthens the meaning of the sentence it is in. That is, a sentence Sany containing any must entail the corresponding sentence Ssome obtained by substituting some for any. Since ½½some ½½any (Widening), Strengthening (½½Sany ½½Ssome) is not satisfied unless any finds itself in a downward-entailing environment. So Kadmon & Landman make roughly the same prediction as Ladusaw: any only appears in downward entailing environments. And, since the intervention environments found in (31) are downward-entailing, they make the wrong predictions about intervention cases. Before dealing with intervention, however, a few comments about Kadmon and Landman’s theory are in order. Kadmon & Landman’s theory is particularly attractive because its two aspects are relatively well-motivated: Widening by intuitions about the meaning of any and its use in discourse (see Kadmon & Landman for details), and Strengthening by general pragmatic considerations: what would be the point of using any if it didn’t lead to a more informative sentence? But, as attractive as this picture is, the Strengthening condition cannot be purely pragmatic in this way. After all, the theory of scalar implicatures provides an obvious answer to the question just raised: the point of a speaker using a weaker term might be that the speaker does not have evidence to support the entailments of the stronger term. For this reason, assuming Widening, uttering a sentence like (32a) should be perfectly grammatical, and it should (in most contexts) have a scalar implicature: that the speaker was not in a position to make the stronger assertion in (32b).
376 Against Grammatical Computation of Scalar Implicatures above predicts they should be licensed in downward-entailing environments. The former, not the latter, makes the right predictions about NPIs embedded below two downward-entailing operators (negation and the restrictor of the quantifier every): they are licit. (33) Donald didn’t think that everyone who left any fries on their tray would get fired.
(34) ½½Condoleeza didn’t drink some Coke and a milkshakes ½½Condoleeza didn’t drink some Coke and a milkshake, but Condoleeza drank some coke or a milkshake Chierchia’s idea is that Kadmon & Landman’s Strengthening condition is too permissive: it only requires any to strengthen ordinary meanings of corresponding some sentences. Instead, why not make it strengthen strong meanings, disallowing any unless it yields a sentence that is stronger than the corresponding some sentence plus its scalar implicatures. Chierchia’s Strong Strengthening condition, then, is ½½Sany ½½Ssomes; in prose, the condition is that any is not licensed unless the meaning of a (possibly embedded) sentence with any is stronger than
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The global environment any appears in (33) is upward-entailing. This fact, which Chierchia calls the roofing effect, is crucial: it means NPIs are licensed below the root clause level. It also means that any process that affects NPI licensing must also be available below the root clause level. Chierchia argues that scalar implicatures affect the licensing of NPIs, specifically in intervention cases, and that this fact requires a theory like his that computes scalar implicatures in embedded environments. Chierchia’s argument is as follows: every and and are strong scalar items, with weaker alternatives some and or, respectively. When these scalar items appear in NPI-licensing downward-entailing environments, the sentences that contain them have scalar implicatures. Chierchia’s idea is that these scalar implicatures are what prevent the licensing of any in intervention environments; that Kadmon & Landman’s Strengthening condition should be strengthened, requiring any to strengthen not only the ordinary meanings of their counterparts with some, but also their scalar implicatures. Sketchy details of his implementation of this idea are as follows. Chierchia adapts Kadmon & Landman’s theory, introducing into it a modified Strengthening condition that depends on scalar implicatureenriched strong meanings. A strong meaning is the conjunction of the regular semantics of an expression with its locally-computed scalar implicatures; given an expression a, the strong meaning of a is notated ½½as; to illustrate:
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10 Here’s a sketch of a proof: let d be a downward-entailing environment that a strong scalar term r (with weaker counterpart x) and any are embedded below. Schematically, then, Sany is d(r, any), and imp(Sany) ¼ :d(x, any). Ssome is, correspondingly, d(r, some), and imp(ssome) ¼ :d(x, some). Now, since some any, and d is DE, d(x, any) d(x, some), so imp(Ssome) ¼ :d(x, some) :d(x, any) ¼ imp(Sany). 11 As Chierchia formulates the Strong Strengthening condition, ordinary meanings of any sentences must entail strong meanings of some sentences. But the quasi-pragmatic reasoning given for Strong Strengthening should require the strong meaning of an any sentence to entail the strong meaning of the corresponding some sentence (i.e. ½½Sanys ½½Ssomes). Apparently, such a condition would not definitively rule out intervention cases. Here are consistent denotations for Sany, Ssome, and their grammatically computed scalar implicatures from (31a) that satisfy this flavour of Strong Strengthening: ½½Ssome ¼ fw1, w2, w3, w4g, ½½Sany ¼ fw1, w3g, imp(Ssome) ¼ fw3, w4, w5g, and imp(Sany) ¼ fw2, w3, w4, w5g, so we have ½½Sanys ¼ fw3g and ½½Ssomes ¼ fw3, w4g. The interested reader can check to make sure all necessary entailment relations hold. Given the untenable nature of this alternate Strong Strengthening, only Chierchia’s actual formulation of Strong Strengthening will be considered in the rest of the paper.
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(entails) the strong meaning of the corresponding sentence with some. Now, in 4, ½½Ssomes ½½Condoleeza didn’t drink some Coke and a milkshake, but she drank some coke or a milkshake, so, in particular, for any to be licensed, Sany—i.e. (31a)—must entail Ssome’s scalar implicature, Condoleeza drank some Coke or a milkshake. Sany does not entail this (not drinking both doesn’t entail drinking one), so Strong Strengthening is not satisfied, and (31a) is ungrammatical. Crucially, Strong Strengthening must reference the implicatures of an embedded sentence; so if Strong Strengthening is right, scalar implicatures must be available below the root clause level, indirect evidence for Chierchia’s grammatical theory of scalar implicature computation. But Chierchia’s Strong Strengthening condition does not stand up to close scrutiny. Remember that Strong Strengthening requires Sany to entail not only Ssome , but also the scalar implicatures of Ssome. In Chierchia’s system, Sany has a grammatically computed scalar implicature as well; this is roughly equivalent to that of Ssome, except it is weaker—i.e., imp(Ssome) imp(Sany).10 So, as long as Sany doesn’t entail its own scalar implicature, it won’t entail the implicature of Ssome. And sentences, in Chierchia’s system, don’t entail their own implicatures: implicatures are negations of stronger, non-null alternatives. This means that when a DE operator has a strong scalar term and an NPI in its scope, an implicature will be generated, Strong Strengthening will not be satisfied, and the NPI will not be licensed. This all means that, in Chierchia’s theory, and and every are interveners simply because they have scalar implicatures when they are below downward-entailing operators.11 This solution makes two incorrect predictions about intervention. First, every scalar item that has scalar implicatures when embedded below a downward-entailing operator (i.e. every non-weakest scalar
378 Against Grammatical Computation of Scalar Implicatures term) is predicted to be an intervener. So, in addition to and and every, the set of interveners should include every strong scalar term, like necessarily, required to, and excellent, because no sentence with one of these items below a single downward-entailing operator will satisfy Strong Strengthening. But this prediction is contradicted by empirical data: (35) a. I don’t think Donald will necessarily eat any cheeseburgers. b. Donald doesn’t believe George is required to inform anyone before he supersizes his meal.
12
Chierchia also discusses numerals, which his theory predicts will intervene unless they are the lowest element of some relevant scale. He cites the following contrast as evidence that this prediction is borne out: (36) a. I didn’t meet eleven people that read some/any of my poetry. b. I never had eleven kids who won any championship. (said by a soccer coach) To my ear and my informants’, the contrast is not so sharp (I never had eleven kids who won a championship, which Chierchia does not mention, is much better than (36b)). Furthermore, the prediction that numerals are interveners depends on a scalar analysis of numerals, an assumption that there is considerable evidence against (see Horn 1992 and references therein for arguments). Because of this evidence, I’ve left arguments involving numerals out of the present paper for the most part, and won’t address in depth any possible intervention facts that involve them.
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In (35a), Ssome implicates I think Donald will possibly eat some cheeseburgers; in (35b), Ssome implicates Donald believes George is allowed to inform Congress. Strong Strengthening requires that each corresponding Sany—i.e. (35a) and (35b)—entail these implicatures, respectively. But, of course, they do not: these are roughly the implicatures, not entailments, of (35a) and (35b). So strong scalar terms are not, in general, interveners, a fact that is incompatible with the Strong Strengthening theory of NPI licensing. Chierchia notices in his paper that few, predicted by Strong Strengthening to intervene, does not; he invokes a difference between primary and indirect implicatures to account for this. But no such distinction is apparent in the scalar terms in (35); indeed, it is hard to imagine a theory of intervention that is based on the strong scalarity of and and every that does not predict necessarily and required to also intervene.12 The second incorrect prediction made by Chierchia’s theory of intervention is that whenever an NPI and a non-weakest scalar term are within the scope of a downward-entailing operator, the scalar term will intervene in the licensing of the NPI, regardless of their relative configuration. This is because a scalar implicature will be generated when the expression containing the scalar term and the NPI combines with the downward-entailing operator, and so this expression will have a non-trivial strong meaning that it must entail. Since such an entailment, i.e. the entailment by a sentence of its own implicature,
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never goes through, NPIs in such configurations are expected never to be licensed. But they can be perfectly grammatical:13
13 An anonymous reviewer wonders whether anyone in examples like these could be free choice any, failing to show intervention effects because it scopes outside negation. But, by the usual diagnostics, free choice any is not licensed in these environments:
(37) Colin does not think nearly anyone has eaten a Big Mac and a Quarter Pounder. Moreover, the possibility of the NPI ever, which has no free choice counterpart, in this environment provides additional evidence that it is, in fact, an NPI-licensing environment: (38) Colin does not think anyone has ever eaten a Big Mac and a Quarter Pounder.
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(39) a. If you ever order every item on the Value Menu, you’ll be appointed Secretary of Great Deals. b. Colin does not think anyone has eaten a Big Mac and a Quarter Pounder. In (39b), e.g. Ssome implicates Colin thinks someone has eaten a Big Mac or a Quarter Pounder, which, in turn, is not entailed by (39b), and so Strong Strengthening is not satisfied. A correct theory of intervention should only predict that an NPI is not licensed when it is in the scope of an intervener, not whenever an NPI and an intervener are both in the scope of a licensor. The incorrect characterization of the class of interveners and the scope conditions necessary for intervention is not an accident of Chierchia’s way of formalizing Strong Strengthening. It is a consequence of the conceptual basis of the theory. Strong Strengthening is supposed to be an explanation of intervention: that it is a consequence of ‘the interplay of the general licensing condition on any (it must lead to strengthening with respect to some), and the way strong meanings (i.e., implicatures) are computed.’ (p. 90) But any can’t (strongly) strengthen a constituent that has a grammatically-computed scalar implicature, so strong scalar elements, which generally have implicatures in NPI-licensing environments, are incorrectly predicted by Strong Strengthening to always be interveners. Likewise, the presence of grammatically-computed scalar implicatures in a constituent is unaffected by the relative scope of the NPI and scalar term, so Strong Strengthening is, in principle, insensitive to scope. The facts that many strong scalar terms are not interveners and that intervention is sensitive to scope casts doubt on the claim that Strong Strengthening, or anything like it, can explain intervention. It is not within the scope of this paper to propose an alternate theory of intervention in NPI-licensing. But the facts presented in this section suggest that it is not the scalar implicatures associated with and and every that are responsible for their behavior as interveners in the
380 Against Grammatical Computation of Scalar Implicatures grammatical process of NPI licensing. Indeed, it seems unlikely that a successful theory of intervention in NPI licensing will be based on scalar implicatures, and so intervention does not provide a reason to think that scalar implicatures are grammatically computed. 5 CONCLUSION
Acknowledgements This paper has benefitted from conversations with Polly Jacobson, Chris Barker, Dan Grodner, Julie Sedivy, Larry Horn, Robert van Rooij, Danny Fox, Brian Weatherson, and the audience at the ESSLLI 2004 workshop on Implicature and Conversational Meaning. I am especially grateful to Bart Geurts and two anonymous reviewers for their extremely thorough and helpful critiques of earier drafts of this paper.
BENJAMIN RUSSELL Brown University Department of Cognitive and Linguistic Sciences Providence RI 02912, USA, e-mail:
[email protected]
First version received: 1.12.05 Second version received: 7.7.06 Accepted: 18.10.06
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Chierchia’s proposal to grammaticize the computation of scalar implicatures is a radical departure from Gricean pragmatics. If Chierchia is right, scalar implicatures have nothing to do with rational principles of co-operation in conversation. Instead, this broad class of inferences that can be explained by the simple assumption that speakers co-operate is redundantly generated by a stipulated grammatical mechanism. Arguments for the radical shift to a grammatical theory of implicature computation depend on two claims: the first is that there are observed, apparently scalar inferences the Gricean theory can’t generate, as well as undesirable inferences that Gricean reasoning does generate. I’ve argued that a very general global Gricean theory (compatible with specific formalisms of this theory recently advanced in the literature) makes the right predictions about such inferences. The second argument, recently advanced by Chierchia, is that a semantic theory of intervention in NPI licensing depends on grammatically computed scalar implicatures; I’ve argued that any theory that depends on scalar implicatures to exclude intervention cases is too stringent, failing to license any in many grammatical sentences. I conclude that a departure from Gricean pragmatics is unwarranted, and we can, at least at this stage of the game, keep scalar implicatures out of the grammar.
Benjamin Russell 381
REFERENCES Hirschberg, J. (1991) A Theory of Scalar Implicature Garland Publishing Company. New York. Horn, L. (1992) ‘The said and the unsaid’. Proceedings from Semantics and Linguistic Theory II, Cornell University, Ithaca, New York, pp. 163–192. Available from CLC Publications, Department of Linguistics, Morrill Hall, Cornell University, Ithaca, NY 14853-4701. Horn, L. R. (1972), On the Semantic Properties of Logical Operators in English. PhD thesis, University of California, Los Angeles. Horn, L. R. (1978) ‘Lexical incorporation, implicature, and the least effort hypothesis’. In D. Farkas (ed.), Papers from the Parasession on the Lexicon. Chicago Linguistics Society. Chicago, 196–209. Horn, L. R. (1989) A Natural History of Negation. Chicago University Press. Chicago, IL. Kadmon, N. and Landman, F. (1993) ‘Any’. Linguistics and Philosophy 16(4):353–422. King, J. C. and Stanley, J. (2006) ‘Semantics, pragmatics, and the role of semantic content’. In Z. Szabo (ed.), Semantics vs. Pragmatics. Oxford University Press. Krifka, M. (1995) ‘Focus and the interpretation of generic sentences’. In G. Carlson and F. J. Pelletier (eds), The Generic Book. Chicago University Press. Chicago, IL, 238–264. Ladusaw, W. A. (1979) Polarity Sensitivity as Inherent Scope Relations. PhD thesis, University of Texas, Austin. Lahiri, U. (1997) ‘Focus and negative polarity in Hindi’. Natural Language Semantics 6(1):57–123. Landman, F. (2001) Events and Plurality: The Jerusalem Lectures, Vol. 76 of
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Blutner, R. (2004) ‘Pragmatics and the lexicon’. In L. Horn & G. Ward (eds), Handbook of Pragmatics. Blackwell. Carston, R. (1988) ‘Implicature, explicature, and truth-theoretic semantics’. In R. Kempson (ed.), Mental Representations: The Interface Between Language and Reality. Cambridge University Press. Cambridge, England, 155–181. Chierchia, G. (1984) Topics in the Syntax and Semantics of Infinitives and Gerunds. PhD thesis, University of Massachusetts. Chierchia, G. (2004) ‘Scalar implicatures, polarity phenomena, and the syntax/pragmatics interface’. In A. Belletti (ed.), Structures and Beyond. Oxford University Press. Cresswell, M. J. (1976) ‘The semantics of degree’. In B. H. Partee (ed.), Montague Grammar. Academic Press. New York, 261–292. Fauconnier, G. (1975) ‘Pragmatic scales and logical structure’. Linguistic Inquiry 6(3):353–375. Fox, D. & Hackl, M. (to appear) ‘The universal density of measurement’. Linguistics and Philosophy. Gazdar, G. (1979) Pragmatics: Implicature, Presupposition, and Logical Form. Academic Press. New York. Giannakidou, A. (1998) Polarity Sensitivity as (Non) Veridical Dependency. John Benjamins. Amsterdam. Grice, H. P. (1975) ‘Logic and conversation’. In D. Davidson and G. Harman (eds), The Logic of Grammar. Dickenson Publishing Co. Encino, California, 64–75. Grodner, D. & Sedivy, J. (to appear) ‘The effect of speaker-specific information on pragmatic inferences’. In N. Pearlmutter and E. Gibson (eds), The Processing and Acquisition of Reference. MIT Press. Cambridge.
382 Against Grammatical Computation of Scalar Implicatures Schwarzschild, R. and Wilkinson, K. (2001) ‘Quantifiers in comparatives: A semantics of degree based on intervals’. Natural Language Semantics 10(1):1–41. Sedivy, J. (2003) ‘Pragmatic versus formbased accounts of referential contrast: Evidence for effects of informativity expectations’. Journal of Psycholinguistic Research 32(1):3–23. Soames, S. (1982) ‘How presuppositions are inherited: A solution to the projection problem’. Linguistic Inquiry 13:483–545. van Rooij, R. and Schulz, K. (2004) ‘Exhaustive interpretation of complex sentences’. Journal of Logic, Language and Information 13:491–519. von Fintel, K. (1999) ‘NPI licensing, Strawson entailment, and context dependency’. Journal of Semantics 16(2):97–148. Zwarts, F. (1996) ‘Three types of polarity’. In F. Hamm and E. Hinrichs (eds), Plurality and Quantification. Kluwer. Dordrecht, 177–238.
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Studies in Linguistics and Philosophy. Kluwer Academic Publishers. Lee, Y.-S. and Horn, L. (1994) Any as indefinite plus even. Manuscript, Yale University. Levinson, S. C. (2001) Presumptive Meanings. The MIT Press. Cambridge, MA. Linebarger, M. C. (1987) ‘Negative polarity and grammatical representation’. Linguistics and Philosophy 10(3):325–387. Matsumoto, Y. (1995) ‘The conversational condition on Horn scales’. Linguistics and Philosophy 18(1):21–60. McCawley, J. D. (1978) ‘Conversational implicature and the lexicon’. In P. Cole (ed.), Syntax and Semantics 9: Pragmatics. Academic Press. New York, 245–258. Recanati, F. (2003) ‘Embedded implicatures’ Philosophical Perspectives 17(1):299–332. Sauerland, U. (2004) ‘Scalar implicatures in complex sentences’. Linguistics and Philosophy 27:367–391.
Journal of Semantics 23: 383–402 doi:10.1093/jos/ffl004 Advance Access publication July 17, 2006
Free Choice Counterfactual Donkeys ROBERT VAN ROOIJ University of Amsterdam
Abstract
1 INTRODUCTION During the 1970s, semanticists were busy dealing with counterfactuals. In the 1980s and early 1990s semanticists were heavily occupied taming donkeys, while in recent years every semanticist seems to develop his or her own pet analysis of free choice items. The main aim of this paper is to show that we can straightforwardly analyse counterfactual donkey sentences, by combining the Lewis/Stalnaker analysis of counterfactuals with standard dynamic semantics. This proposal is closely related to — and motivated by — Alonso-Ovalle’s (2004) analysis of counterfactuals with disjunctive antecedents, but is, I believe, more straightforward, and fully compositional. I also show in this paper that the main idea behind the proposed analysis of counterfactual donkey sentences helps us to account for a number of related problems involving disjunctions and the use of any in counterfactuals and permission sentences as well. This paper is organized as follows. In section 2 I discuss the problems of free choice permission, counterfactuals with disjunctive antecedents and the use of any, and counterfactual donkey sentences, while in section 3 I propose closely related solutions to these problems. I conclude with section 4. 2 PROBLEMS
2.1 Permissions and the free choice effect Lewis (1970/9) and Kamp (1973, 1979) have proposed a performative analysis of command and permission sentences involving a master and The Author 2006. Published by Oxford University Press. All rights reserved. For Permissions, please email:
[email protected].
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We propose a straightforward analysis of counterfactual donkey sentences, by combining the Lewis/Stalnaker analysis of counterfactuals with standard dynamic semantics. The main idea is to define a similarity relation between world-assignment pairs such that two such pairs are unconnected if their assignments differ. We show that with the help of this ordering relation we can also account for a number of related problems involving disjunctions and the use of any in counterfactuals and permission sentences.
384 Free Choice Counterfactual Donkeys
1
Although Lewis (1970/9) and Kamp (1973) account for the effect of permission sentences in rather different ways, both might be called performative analyses in the sense that their effect is to change the permissibility set. 2 In this paper I assume a performative analysis of command and permission sentences. There exists, of course, a whole literature of proposals as to how to account for the free choice inference without adopting a performative analysis. To mention just a few: Zimmermann (2000), Kratzer and Shimoyama (2002), Aloni (2003), Schulz (2004, 2005), Alonso-Ovalle (2005), and Geurts (2005). My favourite analysis along those lines is the proposal made in Schulz (2004, 2005), because it is the only analysis (as far as I know) that is able to fully preserve the standard analysis of disjunction and the standard analysis of the modals. In terms of this analysis, the free choice effect of the following examples (mentioned by one reviewer) can all easily be accounted for: (i) (ii) (iii) (iv)
John said/thinks that Bill may take an apple or a pear. According to the rules, you may take an apple or a pear. John can/is able to bake you a cake or a pie. At that point, Jones could have become a doctor or a lawyer.
I will ignore such examples in this paper, although they suggest (as argued by Schulz) that having a performative explanation is not enough to account for all free choice effects. 3 Here, and in the rest of the paper, I ignore the fact that the interpretation function ‘[]’ should be related to a (modal) model. 4 What if the new command is incompatible with one or more of the earlier ones? In that case we might make use of change by revision to be discussed below.
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his slave. Following Austin’s classical analysis of speech acts, Lewis and Kamp argued that such sentences are not primarily used to make true assertions about the world, but rather to change that what the slave is obliged/permitted to do.1,2 According to this account, if the master commands John to do / by saying ‘You must do /’, or allows John to do / by saying ‘You may do /’, it is typically not yet the case that the proposition expressed by / is respectively a superset of, or consistent with, John’s permissibility set, P, represented by a set of possible worlds. However, the performative effect of the command/permission will be such that in the new context what is commanded is a superset of, and what is permitted is consistent with, the new permissibility set. Thus, in case the command or permission is not used vacuously, the permissibility set, P#, of the new context will be different from P, so that the obligation/permission sentence will be satisfied. Our problem is to say how command and permission sentences govern the change from the prior permissibility set, P, to the posterior one, P#. For commands this problem seems to have an easy solution. If the command ‘You must do /’ is given by the master, the new, or posterior, set of permissible futures for John, P#, is simply P \ [/], where [/] denotes the proposition expressed by /.3,4 However, things are more complicated for permission sentences. It is clear that if / is allowed, P# should be a superset of P such that P# \ [/] 6¼ ;. It is not clear, however, which /-worlds should be added to P. Obviously, we cannot simply say that P# ¼ P [ [/]. By that suggestion, giving
Robert van Rooij 385
def
P ¼ fv 2 Wj "u : v < ug In terms of this set of ideal worlds we can determine whether according to the present state / is obligatory or just permitted. For instance, / is obligatory iff P 4 [/]. But this ordering relation contains more information than just what the set P of ideal worlds is, and in terms of this extra information we can determine the new permissibility set P#. If the master permits the slave to make / true, we can assume that P contains no /-worlds, i.e. none of the /-worlds is ideal. But some /-worlds are still better than other /-worlds. We can now propose that the effect of allowing / is that the best /-worlds are added to the old permissibility set to figure as the new permissibility set. The best /-worlds are the worlds ‘closest’ to the ‘ideal’ worlds P where / is true. This set will be denoted as P/ and defined in terms of the relation < as follows: def
P/ ¼ fu 2 ½/j "v 2 ½/ : u < vg To implement this suggestion, we can say that the change induced by the permission ‘You may do /’ is that the new permission set, P#, is just P [ P/ : Thus, according to Kamp’s (1979) proposal, command and permission sentences change a context of interpretation as follows 5 Reflexive: for all w : w < w; transitive: for all w, v and u: if w < v and v < u, then w < u; connected: for all w and v, w < v or v < w.
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permission to / would allow everything compatible with /, which is certainly not what we want. But how then should the change from P to P# be determined if a permission is given? This is Lewis’s problem about permissions. One possible way to solve Lewis’s problem about permissions is to assume that we not only have a set of best, or ideal, worlds, but also an ordering that says which non-ideal worlds are better than others (cf. Kamp, 1979). Thus, to account for the performative effects of commands and permissions, we need not only a set of ideal worlds, but rather a whole preference, or reprehensibility, ordering, <, on the set of all possible worlds. On the interpretation that u < v iff v is at least as reprehensible as u, it is natural to assume that this relation should be reflexive, transitive, and connected.5 In terms of this preference order on possible worlds we can determine the ideal set P as the set of minimal elements of the relation <:
386 Free Choice Counterfactual Donkeys (where I assume that John is the relevant agent, and P his permission state): def
UpdðMustðJohn; /Þ; PÞ ¼ P \ ½/6 def
UpdðMayðJohn; /Þ; PÞ ¼ P [ P/
6
This is, in fact, just P/ ; if it is assumed that / is compatible with P. Notice that according to this entailment relation we do not predict that we can infer May(j, / _ w) from May(j, /), and thus that Ross’ paradox does not arise. 7
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Note that according to our performative account it does not follow that for a permission sentence of the form ‘You may do / or w’ the slave can infer that according to the new permissibility set he is allowed to do any of the disjuncts. Still, Kamp’s analysis can give an explanation why disjuncts are normally interpreted in this ‘free-choice’ way. To explain this, let me first define a deontic preference relation between propositions in terms of our reprehensibility relation between worlds, <. We can say that although both / and w are incompatible with the set of ideal worlds, / is still preferred to w, / 6 w, iff the best /-worlds are at least as close to the ideal worlds as the best w-worlds, dv 2 [/] and "u 2 [w] : v < u. Then we can say that with respect to <. / and w are equally reprehensible, / w, iff / 6 w and w 6 /. Because, as it ¼ P/ [ Pw iff / w, Kamp can turns out, it will be the case that P/_w explain why normally disjunction elimination is allowed for permission sentences. For simple disjunctive permission sentences like ‘You may do / or w’, it is not unreasonable to assume that when performatively used, the master has no strict preference for the one above the other. If we make the same assumption for command sentences, it follows that from ‘You may/must take the apple or the pear’ we can conclude that the hearer may take the apple and that he may take the pear. Kamp (1973) argues that just as we can define an inference relation between propositions, we might also define an inference relation between performatively used permission sentences, which he called ‘pentailment’. In terms of our framework, he proposes that permission sentence May(j, w) is p-entailed by permission sentence May(j, /), iff for every appropriate initial permissibility ordering <, no new worlds would be added to the set of ideal worlds through the use of May(j, w) after the initial permissibility set was ‘updated’ through the use of May(j, /). On the assumption that < can only be an appropriate initial permissibility ordering for the performatively used May(j, / _ w) iff / w, we can derive the free choice inference in terms of the notion of p-entailment.7 Notice that Kamp’s notion of p-entailment is rather
Robert van Rooij 387
8 9
At least, we end up with this package deal effect if P is inconsistent with / and with w. Thanks to Manfred Krifka (p.c.) for this kind of example.
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close to Veltman’s (1996) fixed-point notion of entailment between speech acts. Unfortunately, Kamp’s performative analysis of permission sentences gives rise to some problems, though some of these are more easily solved than others. A first worry, discussed at length in Merin (1992), is that it seems to make the wrong predictions for conjunctive permissions. Indeed, it is the case that if we update context P to interpret ‘You may take the apple and the pear’ by P [ P/^w ; we either end up with a permission set where the hearer may take neither the apple nor the pear, or with a permission set where the hearer may take both of them: the package deal effect.8 This is wrong, because, intuitively, the speaker also allows the hearer to take the apple, without taking the pear. Fortunately, this problem can be solved easily once we allow the conjunction to take wide scope over the permission (van Rooy, 2000). A more serious problem is that the performative analysis seems to be limited to the free choice inference for permissions and commands, but cannot account for the similar inference when epistemic necessity or possibility is involved, i.e., the fact that we typically infer from ‘Ede must/might be in Berlin or in Frankfurt’ that the speaker thinks it is both possible that Ede is in Berlin, and that he is in Frankfurt (cf. Zimmermann 2000). A final problem is that the explanation of the free choice problem makes use of a strong assumption: the assumption that the disjuncts are equally reprehensible. The worry here is that one might say ‘You may take the apple or even the pear’, where the focus particle ‘even’ suggests that in the conversational context (before the utterance was made), taking the apple was taken to be less reprehensible than taking the pear.9 Intuitively, however, from this permission the hearer would still infer that he is allowed to take the pear. Similarly, it is unclear how this analysis can account for the intuition that ‘You may take any apple’ is felicitous, and that the hearer can conclude from it that the speaker doesn’t care which apple he takes, whatever was the reprehensibility ordering before the permission was given. The inference problem should be obvious now, but it is also unclear what licenses the use of any here. I want to propose that the example involving epistemic might can be solved easily once we also adopt a performative analysis of such statements. Traditionally (e.g. Veltman 1996), a statement of the form ‘It might be that /’ is analysed as being true, or asserted appropriately, when / is compatible with the common ground. Although there is not so much wrong with this analysis, it clearly can’t be the whole story,
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2.2 Counterfactuals with disjunctive antecedents Stalnaker (1968) and Lewis (1973) gave the following well-known analysis of (counterfactual) conditional sentences represented by / > w: / > w is true at w if some / ^ w-worlds are closer to w than any / ^ :w-worlds: The notion ‘closer /-world to w than’ can be explained in terms of an ordering relation on the accessible worlds (but let us assume that all
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because it would make such statements rather pointless. Intuitively, what such a statement does is that it brings the possibility that / is true to the attention of the hearer. This doesn’t mean that before the utterance was made the hearer ruled out that / is possible, but just that among the worlds compatible with what is presupposed, or believed, by the hearer, the possibilities where / is the case were not very salient. The performative effect of the possibility statement is then exactly to increase the salience of such possibilities. We might account for this formally in just the same way as we accounted for the performative effects of permission sentences. The only difference is that the set P now is not the set of admissible worlds, but rather those worlds among the ones that are compatible with what is presupposed that are most salient. The performative effect of ‘It might be that /’ is now just to update the set of most salient worlds from P to P [ P/ : Obviously, if we assume that / was equally (un)salient as w, the free choice inference that it might be that / and it might be that w follows from statements of the form ‘It must/might be that / or w’. I find this performative analysis of epistemic statements appealing. Unfortunately, however, it only increases the last mentioned problems discussed above. How can we now account for the fact that ‘Ede might be in Berlin, or even in Frankfurt’ and ‘Ede might be anywhere’ give rise to the free choice inferences that seem impossible to cancel? This is just as problematic as the fact that the free choice inferences seem to be impossible to cancel from sentences of the form ‘You may take the apple, or even the pear’, and ‘You may take any apple’. Moreover, it is unclear how we can account for the licensing of any in epistemic possibility statements on the standard reading of the modal. In the following, I will concentrate on permission sentences, assuming that the epistemic variant can be accounted for in a similar way. Before we come to our proposal, however, let me discuss in the next few sections some other problems that are very closely related, and for which I would like to propose a similar solution.
Robert van Rooij 389
worlds are accessible). The ordering relation ‘<w’ between worlds is required to obey the following conditions: reflexivity, transitivity, connectedness, and strong centreing.10 The intuitive meaning of u <w v is that u is at least as close, or similar, to w as v is. Accepting the limit assumption, i.e., [/] 6¼ ; 0 fv 2 [/] : "u 2 [/] : v <w ug 6¼ ; (or limiting our analysis to the finite case), we can reformulate the semantics of counterfactuals in terms of a selection function. Let us define a selection function f in terms of the similarity relation as follows: fw([/]) ¼ fv 2 [/]j "u 2 [/] : v <w ug. The proposition expressed by the conditional / > w is now the following set of possible worlds:
That is, / > w is true in w iff w is true at every closest /-world to w, or / is impossible.11 It seems reasonable that any adequate theory of counterfactuals must account for the fact that at least most of the time instantiations of the following formula (Simplification of Disjunctive Antecedents, SDA) are true: ðSDAÞ ðð/ _ vÞ > wÞ/ðð/ > wÞ ^ ðv > wÞÞ For instance, intuitively we infer from (1a) that both (1b) and (1c) are true: (1) a. If Spain had fought on either the Allied side or the Nazi side, it would have made Spain bankrupt. b. If Spain had fought on the Allied side, it would have made Spain bankrupt. c. If Spain had fought on the Nazi side, it would have made Spain bankrupt. The Lewis/Stalnaker analysis cannot account for these inferences because SDA is not a theorem of its logic. In fact, if we would change the logic by making SDA valid, i.e. by saying that fw([/ _ v]) ¼ fw([/]) [ fw([v]), the theory looses one of its most central features, its nonmonotonicity. As noted by Warmbrod (1981), by accepting SDA, we can derive MON on the assumption that the connectives are interpreted in a Boolean way. 10
strong centering; "v : w 6¼ v 0 (w <w v and v Fw w). Of course, Stalnaker’s analysis is still stronger, because he makes the additional assumption that for all [/] 4 W and w 2 W : fw([/]) is always a singleton set. In terms of the similarity relation between worlds, this means that Stalnaker assumes that <w obeys trichotomy: "u, v : u <w v or v <w u or u ¼ v. 11
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def
½/ > w ¼ fw 2 W : fw ð½/Þ4½wg
390 Free Choice Counterfactual Donkeys ðMONÞ ð/ > wÞ / ððð/ ^ vÞ > wÞÞ
(2) If any man would have seen it, we would have known about it. On Ladusaw’s (1979) hypothesis this would mean that we would like to have an analysis of counterfactuals that predicts that their antecedents are downward entailing. Obviously, antecedents don’t behave that way according to Lewis and Stalnaker: this is exactly what their non-monotonic analysis of counterfactuals amounts to. In contrast to their analysis, however, a strict conditional analysis of counterfactuals immediately accounts for the appropriateness of (2), because antecedents of strict conditionals are predicted to be DE contexts.12 I this paper I don’t want to question that (something like) a strict conditional account can explain our intuitions involving the use of disjuncts and (certain) negative polarity items in antecedents of counterfactuals. However, an analysis as strict conditional must make the meaning of counterfactuals extremely context dependent where accommodation is the rule, rather than the exception. In this paper I don’t want to argue against a strict conditional analysis of counterfactuals, but just want to show that sentences like (1a) and (2) don’t force us to give up our well-known non-monotonic analysis of counterfactuals along the lines of Lewis and Stalnaker.
2.3 Counterfactual donkey sentences Until now we have assumed that the meaning of a sentence can be represented adequately by a set of possible worlds. It is well-known, however, that this leads to problems for the analysis of indefinites and pronouns, especially in donkey sentences. Of course, Kamp (1981) and 12 Among others for this reason, a (context-dependent) strict conditional account has been argued for by Kadmon and Landman (1993) and von Fintel (1999, 2001).
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The reason is that from / > w and the assumption that connectives are interpreted in a Boolean way, we can derive ((/ ^ v) _ (/ ^ :v)) > w. By SDA we can then derive (/ ^ v) > w. Warmbrod (1981), followed by a number of other authors (e.g. Frank, 1997), have responded to this problem by abandoning the non-monotonic analysis of counterfactuals in favour of a (context dependent) strict conditional one, according to which both SDA and MON are valid. In fact, such a strict conditional account has an additional—and closely related—advantage as well. As is well-known, the negative polarity item any is licensed in antecedents of counterfactuals (cf. Heim, 1984).
Robert van Rooij 391
(3) If John owned a donkey, he would beat it. Representing counterfactuals as / > w like before, we would like to represent (3) abstractly as dx[Px] > 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. Suppose that we want to interpret a sentence of the form dx/ > w in possibility Æw, gæ. According to the standard Lewis/Stalnaker analysis of counterfactuals, we should then select among those possibilities that verify dx/ the ones that are closest to Æw, gæ and check whether they also make w true. Because / might contain free variables that should be interpreted by means of g, the natural context of interpretation of dx/ is the set W(g) ¼ fÆv, hæ : v 2 W & h ¼ gg.14 After the interpretation of dxPx, for instance, we end up with a set of world-assignment pairs like Æv, hæ where variable x is in the domain of assignment h, and h(x) is an element of the set denoted by P in world v. Let us denote this set of 13
I assume here that assignments are partial functions. Just like Lewis (1973), we might want to limit the worlds considered by means of an accessibility relation. I will ignore this possibility in this paper. Also, I will assume for simplicity that all worlds have the same domain. 14
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Heim (1982) showed that we could maintain a uniform analysis of indefinites and pronouns, and still get the truth conditions of donkey sentences right, while Groenendijk and Stokhof (1991) and others have demonstrated that such an analysis is actually no threat to compositionality, if we are willing to change our static possible-world conception of the meaning of a sentence. 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 indefinite.13 According to this analysis, the formula dx½Px/Qx is predicted to be equivalent with "x½Px/Qx, which means that we can account for (standard) donkey sentences in a systematic and compositional way. Although a considerable amount of attention has been devoted to donkey sentences in the past, only a particular branch of donkey sentences were actually inspected: indicative ones. To account for these indicative donkey sentences it was no problem to assume that conditional sentences should be analyzed (basically) in terms of material implication. But donkey sentences not only show up in indicative mood; we have counterfactual donkey sentences as well:
392 Free Choice Counterfactual Donkeys
3 SOLUTION
3.1 Counterfactual donkey sentences Fortunately, there is a natural way to define an ordering ‘<’ between world-assignment pairs in terms of the ordering relation between worlds used by Lewis and Stalnaker:17 Definition 1 Given a Lewis/Stalnaker similarity relation <w between worlds, we define the similarity relation < Æw;gæ between worldassignment pairs as follows: Æv,hæ < Æw;gæ Æu, kæ iffdef h ¼ k g and v <w u. Notice, first, that in case the antecedent / of a counterfactual doesn’t introduce new variables, or discourse markers, all the elements of ///g are world-assignment pairs with assignment g. Thus, in that case ‘<’ comes down to ‘<’, because we can now ignore the 15 We don’t have to assume that in order for the counterfactual / > w to be true in possibility Æw, gæ, the counterfactual (/ ^ v) > w also has to be true. 16 In terms of our framework, this is essentially what the proposal of Alsonso-Ovalle (2004) comes down to. Still, Alonso-Ovalle’s paper was the main impetus for the solution I propose in the next section. 17 The same ordering has been used in Schulz and van Rooij (to appear) to account for some apparent problems of exhaustive interpretation.
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world-assignment pairs by /dxPx/g. To check whether dx[Px] > Qx is true in Æw, gæ we have to select among the possibilities in /dxPx/g those that are closest to Æw, gæ, and see whether they also verify Qx. But this means that we need an ordering relation, < Æw;gæ , between worldassignment pairs with respect to possibility Æw, gæ : Æu, kæ < Æw;gæ Æv, hæ. Let us assume that we can analyse counterfactuals in terms of selection functions, as before, and that / > w is true in possibility i just in case w is true in all selected /-possibilities closest to i, i.e. in all j 2 fi ð=/=g Þ: It ð=dxPx=g Þ to be is clear what we want the result to be: we want fÆw;gæ [d 2 D fÆw;gæ ðfÆv,g½x =d æ : d 2 Iv ðPÞgÞ: On such an analysis, we would be able to account for (3) without necessarily giving up on a nonmonotonic analysis of counterfactuals.15 On the other hand, it is clear 16 that we don’t want to define fÆw ,gæ ð=dxPx=g Þ to be the desired set. For in that case, our analysis wouldn’t be compositional anymore. What we want, instead, is to first determine the (dynamic) interpretation of dxPx, i.e. /dxPx/g, and then define the selection function f, or the ordering relation < Æw,gæ ; such that the set of selected world-assignment x pairs is identical with [d 2 D fÆw ,gæ ðfÆv; g½ =d æ : d 2 Iv ðPÞgÞ:
Robert van Rooij 393
assignment function. But suppose that / is of the form dxPx. In that case, all the assignments in /dxPx/g differ from g in that they also assign an object to x. Let Æv, hæ and Æu, kæ be two possibilities in /dxPx/g. According to definition 1, to check whether the one is more similar to Æw, gæ than the other only makes sense in case h assigns the same individual to x as k, h(x) ¼ k(x).18 But this means that we check for each individual d separately what are the closest possibilities to Æw, gæ that make Px true. We define the selection function as follows:
def
ð=A=g Þ ¼ fÆv;hæ 2 =A=g : :dÆu;kæ 2 =A=g : Æu;kæ < Æw;gæ Æv;hæg; fÆw;gæ
where =A=g ¼ ½AðfÆv; hæ : v 2 W & h ¼ ggÞ; and j < i k iff j < i k but not k < i j: It is easy to see that it now follows that fÆw;gæ ð=dxPx=g Þ comes out x to be equivalent with [d 2 D fÆw;gæ ðfÆv; g½ =d æ : d 2 Iv ðPÞgÞ: As we have seen above, this is exactly what we want, but now we don’t define the selection function this way (which would give rise to a noncompositional analysis), but we still end up with the same happy result that dx[Px] > Qx is equivalent with "x[Px > Qx].19,20,21 I conclude that we can account for counterfactual donkey-sentences in a natural and compositional way.
3.1.1 Identifying and weak counterfactual donkey sentences Although I believe that a counterfactual donkey sentence is in general equivalent to a formula with wide scope universal quantification, there is a particular 18
Though the relation ‘<’ is connected, ‘<’ is not. To be sure, this equivalence holds for many-ary donkey sentences as well: if ~ x is an n-ary tuple of variables and / and w are n-ary predicates, our analysis predicts that d~ x½/ð~ xÞ > wð~ xÞ is equivalent with "~ x½/ð~ xÞ > wð~ xÞ: 20 Notice that this would also be true if we would make Stalnaker’s uniqueness assumption. 21 In contrast to Lewis, Stalnaker assumed that indicative conditionals should be treated in the same way as counterfactuals. Adopting that view, one might expect that the standard dynamic analysis of standard donkey sentences would come out as a special case of our analysis. This is not exactly the case. On our analysis, for dx[Px] > Qx to be true in world w where P has a non-empty extension it is not enough that all individuals in the extension of P also have property Q. However, if we limit the domain of quantification in the indicative case to the individuals that have property P, the standard dynamic analysis is only a special case. 19
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Definition 2 Given a similarity relation < Æw;gæ between worldassignment pairs as defined in definition 1, we define the selection function f from sets of world-assignment pairs to sets of worldassignment pairs as follows:
394 Free Choice Counterfactual Donkeys type of example for which this equivalence seems rather dubious: what I would call identifying counterfactual donkey sentences:22 (4) a. If Alex were married to a girl from his class, it would be Sue. b. If a boy from our class had married a girl from our class, he would have married Sue (and only Sue). c. If Ed was talking to a woman at the Ling. Department’s front desk, he would have realized that it was Kathryn.
22
The following examples were provided by a reviewer of this paper, but Frank Veltman gave similar examples. 23 Martin Stokhof suggested that we call this the ‘epistemic’ reading of the counterfactual.
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Isn’t it obviously too strong a claim to say that (4a), for instance, is true just in case for any individual (e.g. Mary), if that individual were from Alex’s class and married to him, it would be Sue? Yes, this would be too strong if we assume that the individuals in the domain have essential properties, like ‘being Mary’. If we give up that assumption, however, the reading is, I claim, much more natural.23 Alternatively—although it would implement a similar intuition—we could say that not all indefinites introduce discourse referents and that the indefinites used in the antecedents of (4a)–(4c) are of this type. The anaphora used in the consequents of (4a) and (4c) are then descriptive pronouns. But I don’t want to sell my analysis only to anti-essentialists, or to those who don’t mind indefinites and anaphora to be ambiguous, and will allow for weaker readings of counterfactual donkey sentences such that (4a)–(4c) receive acceptable truth conditions also from a more essentialist’s and standard dynamic semantics’ point of view. The donkey equivalence in standard DRT and dynamic semantics depends on the assumption of unselective binding. I made that assumption in the previous section, and will make it in the rest of this paper as well. However, this gives rise to the problem of how we can account for weak readings of donkey sentences (‘If I have a dime in my pocket, I throw it into the parking meter’) and for asymmetric readings of adverbs of quantification (the proportion problem). The standard way to solve those problem in dynamic semantics (going back to Root (1986) and also defended in Dekker (1993)) is to give up unselective binding for all variables involved. The idea is to unselectively bind only a subset of all the variables introduced in the antecedent of the conditional, and for those where you don’t do this, the weak reading follows. The nice thing about this solution is that (i) one still treats all indefinites in the same way, and (ii) the indefinite whose introduced
Robert van Rooij 395
variable is not unselectively bound can still be picked up anaphorically in the consequent (this is relevant for examples (4a) and (4c) above.) So, how does this work for counterfactual donkey sentences? Well, we will represent a counterfactual in general by a formula / >X w, where / and w are as expected, and X is the set of variables introduced by / that is unselectively bound. Notice that even if / contains an indefinite, X might still be the empty set. Now we are going to slightly redefine the ordering relation between possibilities as follows:
X X Æv; hæ < ;X Æw;gæ Æu; kæ iff def h; k g; h[ ¼ k[ ; and v < w u:
where h [X denotes the restriction of h to X, and thus that h [X ¼ k [X iff "x 2 X : h(x) ¼ k(x). What this definition comes down to is a weakening of definition 1, because it now allows for a comparison between possibilities where the assignments are not the same. In particular, if X ¼ ; it immediately holds that the assignments are irrelevant for the ordering relation: Æv; hæ < ;; Æw;gæ Æu, kæ iff v <w u. If one makes the assumption that one can only be married to one girl, or that Ed was talking to at most one woman, this small, but independently motivated, change already accounts for all of the examples (4a)–(4c) discussed above, without making the assumption that indefinites are ambiguous. If we redefine the selection function as follows: ;X ð=/=g Þ ¼ fÆv;hæ 2 =/=g : :dÆu;kæ 2 =/=g : Æu;kæ < ;X fÆw;gæ Æw;gæ Æv;hæg;
example (4-a), for instance, is predicted to be true if represented such that X ¼ ; just in case Alex is married to Sue (and only Sue) in the world(s) closest to the actual one where Alex is married to a(ny) girl from his class. But what should we do about counterfactual variants of weak donkey sentences? (5) If I had a dime in my pocket, I would throw it into the meter. To account for weak readings of counterfactual donkey sentences, we have to assume that there are possibilities closest to the actual world where I have more than one dime in my pocket. What is required to
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Definition 3 Given a Lewis/Stalnaker similarity relation <w between worlds, we define the similarity relation < ;X Æw;gæ between worldassignment pairs as follows:
396 Free Choice Counterfactual Donkeys account for such cases is to lump together all of the possibilities where the difference in assignment doesn’t matter, and say that only one of those assignments has to be taken into account for the interpretation of the consequent. Let us first say that Æv, hæ;X Æu, kæ iff v ¼ u and h[X ¼ k[X. Then we say that / >X w is true in Æw, gæ iff ;X ;X "Æv, hæ 2 fÆw;gæ ð=/=g Þ : dÆu; kæ 2 fÆw;gæ ð=/=g Þ : Æu; kæ;X Æv, hæ and Æu, kæ verifies w. Now we can account for the truth of the weak counterfactual donkey (5) where in the closest counterfactual world(s) I have more than one dime in my pocket. In the rest of this paper I won’t come back to identifying or weak readings of counterfactual donkey sentences and will always assume unselective binding.
Now we know how to account for counterfactual donkey sentences, it becomes straightforward how to account for counterfactuals with disjunctive antecedents. The reason is, of course, that disjunctive sentences can simply be represented by existential sentences (cf. Alonso-Ovalle 2004). Let ‘P’ denote the property that Spain fought on the x-side. In that case we can represent (1a) by dx[Px ^ (x ¼ allied _ x ¼ nazi)] > Spain bankrupt.24 (1a) If Spain had fought on either the Allied side or the Nazi side, it would have made Spain bankrupt. Given our analysis of counterfactual donkey sentences above, it is quite clear that we now predict that from (1a) we can indeed infer that (1b) and (1c) follow. (1b) If Spain had fought on the Allied side, it would have made Spain bankrupt. (1c) If Spain had fought on the Nazi side, it would have made Spain bankrupt.
24 In the main text I illustrate the proposal to account for the problem of simplication of disjunctive antecedents in terms of donkey anaphora in counterfactuals by means of disjunctions of type e. But this is for illustrative purposes only: the analysis works for disjunctions of any type. And this is needed as well: as mentioned by one reviewer, from an example like ‘If John had bought a car or borrowed a motorcycle, he’d be on time’ we intuitively infer ‘If John had bought a car, he’d be on time and if John had borrowed a motorcycle, he’d be on time’. In fact, Alonso-Ovalle (2004) proposed his analysis for disjunctions of type Æe, tæ.
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3.2 Counterfactuals with disjunctive antecedents
Robert van Rooij 397
25 McKay and van Inwagen (1977), however, present the following example, which shows that we don’t want SDA to be valid in general: from (i) we don’t want to conclude (ii):
(i)
If Spain had fought on either the Allied side or the Nazi side, it would have fought on the Nazi side. (ii) If Spain had fought on the Allied side, it would have fought on the Nazi side. I conclude that counterfactuals with disjunctive antecedents do not falsify the Lewis/Stalnaker account: we cannot conclude If /, then w from all instantiations of (subjunctive) conditionals of the form If / or v, then w. On the analysis suggested in section 3.1 this means that either not all counterfactuals with disjunctive antecedents should be represented by means of existential quantifiers (see Alonso-Ovalle 2004 for this type of move), or that the variable introduced by the quantifier representing the disjunction is irrelevant for the ordering relation (as proposed in section 3.1.1). On neither analysis, SDA is guaranteed to be valid. One reviewer noticed that for counterfactuals of the form ‘:(/ ^ v) > w’ we typically make an SDA-type of inference: :/ > w and :v > w, although that is not (immediately) predicted by the proposed analysis: (iii) If Jack had not seen both Mary and John, he would be unhappy. To account for such examples—as also suggested by the reviewer—I could, and would, either represent them as I would represent (iv), i.e. as (v): (iv) If Jack had not seen Mary or had not seen John, he would be unhappy. (v) dx[:Px ^ (x ¼ m _ x ¼ j)] > w. or would represent them more in line with their surface form, in which case the simplification inference is not guaranteed to go through, but depends on the ordering relation. 26
Alonso-Ovalle (p.c.) has the intuition that ‘Might’-counterfactuals of the form (/ _ v) > )w should intuitively entail both / > )w and v > )w. Neither his own analysis from 2004, nor my analysis can account for this. Fortunately, there is an easy way out of this problem. In the main text we have assumed that fÆw;gæ ð=/=g Þ is a set of world-assignment pairs. But we might redefine the selection function such that it rather denotes a set of sets of world-assignment pairs: + fÆw;gæ ð=/=g Þ ¼ ffÆv; hæ 2 =/=g : :dÆu; kæ 2 =/=g : Æu; kæ <Æw;gæ Æv; hæg : h 2 Gg: If we now assume + ð=/=g Þ, this still gives rise to that / > w is true in Æw, gæ iff w is entailed by each set in fÆw;gæ a compositional analysis, but one where ‘Might’-counterfactuals have Alsono-Ovalle’s desired truth conditions (at least, if disjunctions are analysed in terms of dynamic quantification).
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Our analysis explains why counterfactuals with disjunctive antecedents allow for simplification of the antecedent.25,26 Let us now turn to example (2) and see whether our new analysis can account for the appropriateness of negative polarity item any in the antecedent of a counterfactual. Obviously, we cannot account for the licensing of any on the standard DE-analysis: although we slightly changed the analysis of counterfactuals, it is still not predicted on our analysis that the antecedent of a counterfactual forms a downward entailing context. Fortunately, the DE-analysis is not the only analysis of NPI-licensing around. For both empirical and conceptual reasons, Kadmon and Landman (1993) and Krifka (1995) have argued in favour of a more pragmatic analysis of licensing NPIs. Kadmon and Landman (1993), for instance, have argued that the semantic meaning of any is just the same as that of an indefinite like some—i.e. that of the existential quantifier—but with a wider domain of quantification. To account for licensing, they claim that the NPI any can be used
398 Free Choice Counterfactual Donkeys
3.3 Permission sentences As it turns out, a very similar change of the ordering relation relevant for the (performative) analysis of permission sentences as what we used above for counterfactuals solves our remaining problems in section 2.1 as well. Let us represent ‘You may take any apple’ by a formula of the form ‘May( j,dxPx)’. As above, I will assume that existential quantifiers should be analysed dynamically. This means that /dxPx/g is not the set of possible worlds where there is an object that has property P, but rather the set of world-assignment pairs, Æv, hæ, where the object h(x) has property P in v. Given that the truth-set of an existential formula involves not only worlds but also assignments, we are forced to adjust our performative analysis of permission sentences as sketched in section 2.1, because that analysis was based on an ordering relation ‘<’ that involves worlds only. Fortunately, just as for the analysis of counterfactuals, also now there is a natural way to define an ordering ‘<’ between world-assignment pairs in terms of our previous ordering relation between worlds: we define Æv, hæ < Æu, kæ iffdef h ¼ k and v < u. We will still assume (for simplicity) that the permission set P is represented by a set of worlds, and define the set of / worlds ‘closest’ to the ‘ideal’ worlds P where ///g holds as follows:
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appropriately just in case the interpretation of the sentence after domain widening is stronger than before widening. Because domain widening of existential quantifiers in downward entailing contexts results in stronger assertions, the DE-analysis is explained rather than simply assumed. But the widening analysis of NPIs is not only more explanatory, it is also more general, because it can account for the appropriateness of sentences involving any although the NPI (or FC item) does not occur in a DE context (cf. Kadmon and Landman 1993 and, e.g. van Rooij 2003). Indeed, domain widening also explains why any is licensed in antecedents of counterfactuals. Let us represent a sentence like (2) by a formula like dxD[Px] > q where D is the domain of quantification. Notice that on our analysis it straightforwardly follows that if D# D, dxD#[Px] > q is strictly weaker than dxD[Px] > q. For instance, if D# ¼ fd1g and D ¼ fd1, d2g, then dxD[Px] > q has the same truth conditions as the conjunction ðPðd1 Þ > qÞ ^ ðPðd2 Þ > qÞ, while dxD#[Px] > q just means Pðd1 Þ > q, and is thus weaker (I assume here that d is the name of d). But this means that according to the widening analysis, in combination with our analysis of counterfactual donkey sentences, any is predicted to be licensed in antecedents of counterfactuals, just as desired.
Robert van Rooij 399 def
¼ fv 2 Wjdh : Æv;hæ 2 =/=g :dÆu;kæ 2 =/=g : Æu;kæ < Æv;hæg: P=/= g
27 Just as for counterfactuals with disjunctive antecedents, this dual reading might be a virtue rather than a vice: the free choice inference involving disjunctive permissions might be cancelled.
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This minor adjustment has the important consequence that if the domain of quantification involves only three apples, a1, a2, and a3, the permission ‘You may take any apple’, represented abstractly by ‘May(j, dxPx)’, is predicted to give rise to the inference that the hearer may take apple a1, apple a2 and may take apple a3 whatever the reprehensibility relation is. Thus, the permission is predicted to give rise to the free choice inference and this inference cannot be cancelled anymore. The reason is that although the reprehensibility relation ‘<’ might be such that a world w where only apple a1 is taken is less reprehensible than the best world v where, for instance, only apple a2 is taken, this doesn’t matter because in that case the possibilities Æw, kæ and Æv, hæ are not ‘<’-ordered with respect to each other, because k(x) ¼ a1 and h(x) ¼ a2, and thus k ¼ 6 h. Just as our analysis of counterfactual donkey sentences suggested a way to solve the problem involving counterfactuals with disjunctive antecedents, our analysis of permission sentences involving existential quantifiers immediately suggests a similar proposal of how to account for the strength of free choice inferences of disjunctive permission sentences. The idea is, of course, that disjunctions are just existential sentences. Let us represent a sentence like ‘John takes (apple) a1 or a2’ by something like ‘dx[Take(j, x) ^ (x ¼ a1 _ x ¼ a2)]’. Notice that this formula has the same truth conditions as the standard representation of the sentence: ‘Take( j, a1) _ Take( j, a2)’. With a dynamic interpretation of the existential quantifier, however, the truth-sets of the two formulas differ, because the assignments involved in the former set, but not the ones in the latter, have the variable ‘x’ in its domain. This distinction is crucial once we use these truth sets for the analysis of permission sentences. If worlds where a1 is taken by John to be less reprehensible than the best worlds where a2 is taken, P=Takeðj; a1 Þ _ Takeðj; a2 Þ=g contains no worlds where John takes apple a2. The minimal worlds where /dx[Take(j, x) ^ (x ¼ a1 _ x ¼ a2)]/g holds, Pdx½Takeðj; xÞ ^ ðx¼a1 _ x¼a2 Þ=g , on the other hand, contains not only worlds where John takes apple a1, but also worlds where John may take apple a2. Hence, the free choice inference is predicted if the disjunctive permission sentence is represented as May(j, dx[Take(j, x) ^ (x ¼ a1 _ x ¼ a2)) but not if it is represented as May(j, Take(j, a1) _ Take(j, a2)).27 Remember that according to Kamp’s notion of p-entailment mentioned in section 2.1, ‘You may take the apple’ and ‘You may
400 Free Choice Counterfactual Donkeys
4 CONCLUSION The purpose of this paper was rather limited: I wanted to show that we can straightforwardly analyze counterfactual donkey sentences in a fully compositional way, by combining the Lewis/Stalnaker analysis of counterfactuals with standard dynamic semantics. Moreover, I wanted to show that the main idea behind this analysis also helps us to account for a number of related problems involving disjunctions and the use of any in counterfactuals and permission sentences. Of course, having shown that some particular phenomena can be accounted for in a more straightforward way than perhaps realized before in some wellestablished theories, doesn’t save these latter theories from other problems. It is obvious that the Lewis/Stalnaker analysis of counterfactuals, the dynamic analysis of meaning, the performative analysis of imperatives, and the widening analysis of any face problems where my suggestions made in this paper are of no help. Fortunately, these problems were not the topic of this paper.28 Acknowledgements I would like to thank Luis Alonso-Ovalle for sharing with me his intuitions on counterfactuals with disjunctive antecedents, Kai von Fintel for pointing me to some literature on counterfactuals and NPIs, Katrin Schulz for general discussion, and the reviewers and editor of this paper for stimulating comments. This paper was presented
28
In a follow up of this paper, though, I will take up some of these problems and propose to analyze Dayal’s (1998) modal ‘any’ and free relatives like ‘whatever’ as counterfactual donkey sentences (in disguise) and compare that with recent analyses of ‘any’ like that of Chierchia (ms).
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take the pear’ follow from ‘You may take the apple or the pear’ only if taking the apple and taking the pear were equally strongly reprehensible. We have seen that this is perhaps too strong an assumption to make. On our new analysis of permission sentences however, both May(j, dx[Take(j, x) ^ x ¼ a1]) and May(j, dx[Take(j, x) ^ x ¼ a2]) are p-entailed by May(j, dx[Take(j, x) ^ (x ¼ a1 _ x ¼ a2)]), irrespective of the initial ordering relation. This means not only that the free choice inference is predicted to be uncancellable, but also that domain widening of the existential quantifier used in permissions results in a stronger permission. Thus, using Kadmon and Landman’s analysis of any (for both the NPI and the FC reading), we have straightforwardly explained why this item is licensed in permission sentences.
Robert van Rooij 401 in a Lego-talk in Amsterdam. I would like to thank the audience of this meeting, and in particular Paul Dekker, Martin Stokhof, and Frank Veltman.
ROBERT VAN ROOIJ Institute for Logic, Language and Computation (ILLC) University of Amsterdam Nieuwe Doelenstraat 15 1012 CP Amsterdam e-mail:
[email protected] http://staff.science.uva.nl/;vanrooy/
First version received: 21.2.06 Second version received: 08.05.06 Final version accepted: 18.06.06
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Journal of Semantics 23: 403–405 doi:10.1093/jos/ffl011
Editor’s Note
Maria Aloni Jennifer Arnold Ana Arregui Harald Baayen Giosue Baggio Rainer Ba¨uerle Sigrid Beck Walter Bisang Jonathan Bobaljik Lewis Bott Emmanuel Chemla Brady Clark Ariel Cohen Cleo Condoravdi Walter Daelemans Zachary Estes Martina Faller Donka Farkas Tim Fernando Annette Frank Jon Gajewski Richard Gerrig Jeroen Groenendijk Martin Hackl Robert Harnish Jack Hoeksema Janneke Huitink Michela Ippolito Ó The Author 2006. Published by Oxford University Press. All rights reserved. For Permissions, please email:
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We wish to express our gratitude to the following colleagues who are not members of the Editorial Board of the Journal but have kindly helped us in the past year with the refereeing of papers submitted:
404 Editor’s Note
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Gerhard Ja¨ger Jacques Jayez Lara Jones Laura Kallmeyer Laszlo Kalman Stefan Kaufmann Ji-yung Kim Katalin Kiss Michael Klein Nathan Klinedinst Utpal Lahiri Fred Landman Alex Lascarides Peter Lasersohn Rochelle Lieber Inderjeet Mani Friederike Moltmann Reinhard Muskens Diarmuid O’Seaghdha Terence Parsons Orin Percus Manfred Pinkal Christopher Pin˜on Massimo Poesio Monika Rathert Arndt Riester Craige Roberts Susan Rothstein Kjell Johan Saeboe Uli Sauerland Roger Schwarzschild Scott Schwenter Katrin Schulz Julie Sedivy Peter Sells Ben Shaer Junko Shimoyama Ronald Smyth Benjamin Spector Penka Stateva Carol Tenny Satoshi Tomioka
Editor’s Note 405
John Trueswell Jan van Eijck Frank Veltman Laurence Vieu Thomas Werner Yoad Winter Rachel Yang Malte Zimmermann
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