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JOURNAL OF SEMANTICS Volume 23 Number 3

CONTENTS JACQUES JAYEZ AND LUCIA M. TOVENA Epistemic Determiners

217

ERIC MCCREADY Created Objects, Coherence and Anaphora

251

PHILIPPE SCHLENKER Scopal Independence: A Note on Branching and Wide Scope Readings of Indefinites and Disjunctions

281

Please visit the journal’s web site at www.jos.oxfordjournals.org

Journal of Semantics 23: 217–250 doi:10.1093/jos/ffl002 Advance Access publication April 10, 2006

Epistemic Determiners JACQUES JAYEZ ENS–LSH Lyon LUCIA M. TOVENA Universite´ Paris VII

The present paper offers a contrastive examination of French items that require some knowledge of the speaker and items that require some ignorance. We relate this difference in a systematic way to the well–known problem of ‘identifiability’ in epistemic logic. In addition to providing a more precise analysis, this identification-based investigation leads us to two findings. First, non-identification (‘ignorance’) is actually a particular manifestation of the more general phenomenon of free-choiceness, which has received much attention lately. Studying non-identification helps us to gain a better understanding of the varieties of free-choiceness. Second, identification (‘knowledge’) has to be distinguished from specificity, understood as wide scope of an existential quantifier, and to be evaluated in the perspective of a full-fledged epistemic theory including epistemic agents and descriptions. This questions the scope-based analyses of determiners like un certain in French and a certain in English and gives a central place to the phenomenon of relativity of description, whose importance is independently motivated in recent work on reference.

1 INTRODUCTION The motivation behind this article is to gain insight into the behaviour of epistemic determiners by comparing and contrasting items that require some knowledge of the speaker and items that require some ignorance. Determiners and pronouns sensitive to ‘knowledge of the speaker’ exist in different languages, as noted by Haspelmath (1997). Examples are un N quelconque, quelque and un certain N in French, un certo and un N qualunque/qualsiasi in Italian, some in English (Farkas 2002), irgendein in German (Krifka 1991, Kratzer and Shimoyama 2002), etc. Broadly speaking, they either require the speaker not to know the identity of the referent or require her to know it. These are the items to which we refer with the general term of epistemic determiners. For example, in
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Abstract

218 Epistemic Determiners (1a), the speaker cannot know the identity of the diplomat referred to, as evidenced by (1b), whereas, in (1c), someone—who might be the speaker—must be able to identify the diplomat.

This article focusses primarily on un quelconque (UQ) and un certain (UC), two determiners that look like the mirror image of one another to some extent. The content is organized as follows. In section 2, we provide basic data on UQ and in section 3 we start the analysis of its epistemic properties by relating them to the wellknown problem of ‘identifiability’ in epistemic logic. We show that UQ is subject to a general requirement of non-identification. Section 4 provides a deeper analysis, in connection with the issues discussed in the recent literature on so-called free choice (FC) determiners (such as any in English). In the case of UQ, the requirement of nonidentification has the effect of relativizing to an epistemic agent the equivalence among members of the restriction, a feature which is the hallmark of FC items in general. This yields an epistemic free-choice type of item. The indefinite (un ‘a’) that enters the determiner overtly also affects the distribution and interpretation of the whole. Finally, section 5 concerns pragmatic aspects of the interpretation of UQ. This is for the ‘ignorance’ side of epistemic determiners. We then move on to the ‘knowledge’ side. In section 6, we provide crucial data on UC (un certain), and we discuss problems they raise for existing analyses, most notably those that rely on specificity. Our account in terms of identification, echoing that of section 4, is proposed in section 7. We show that, contrary to what is the case for UQ, which requires non-identification, UC requires that the referent be identified. However, this requirement is not relativised to a specific agent. Furthermore, it does not involve the strong standard notion of identification. Pragmatic aspects of the interpretation of UC are then discussed in section 8. Section 9 summarizes the major findings of this article.

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(1) a. Marie a rencontre´ un diplomate quelconque ‘Mary met some diplomat or other’ b.
Marie a rencontre´ un diplomate quelconque, a` savoir mon fre`re ‘Mary met some diplomat or other, namely my brother’ c. Marie a rencontre´ un certain diplomate ‘Mary met a certain diplomat’

Jacques Jayez and Lucia M. Tovena 219

2 BASIC DATA ON UN QUELCONQUE

(2) a. ??Hier, j’ai rencontre´ ‘Yesterday, I met b. Susanne a e´pouse´ un que je ne ‘Susan married some whom I don’t

un ami quelconque some friend or other’ copain de fac quelconque, connais pas university friend, know’

This general prohibition against the identification of the referent extends to sentences with a modal/attitudinal operator. The odd examples in (2) and (3) become unproblematic if UQ is replaced by the indefinite un ‘a’, see (4). (3) a.
Marie a probablement loue´ une voiture quelconque, celle que je vois la`-bas ‘Mary probably rented some car or other, the one I see over there’ b.
Marie a e´te´ oblige´e de louer une voiture quelconque, celle que je vois la`-bas ‘Mary had to rent some car or other, the one I see over there’ c.
J’espe`re que Marie a loue´ une voiture quelconque, celle que je vois la`-bas ‘I hope Mary rented some car or other, the one I see over there’

1 As noted in Jayez and Tovena (2002), another determiner, quelque, is very similar to UQ. However, it sounds rather formal in modern French and will not be considered in this paper.

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Modern French uses the determiner UQ to express ignorance about
quelconque the referent.1 This form enters the two constructions un N
No clear and stable semantic difference between and un quelconque N. the two has appeared so far, hence we will consider the notation ‘UQ’ as referring to either one. The main observations on UQ can be divided into three blocks. First, UQ is not compatible with identification of the referent. This is why (1b) is anomalous and, more generally, why a UQ-phrase is strange whenever the sentence implies that the speaker is able to identify the referent under normal circumstances (2a). In contrast, when the speaker clearly has no idea about the referent, UQ is unproblematic (2b).

220 Epistemic Determiners (4) a. Marie a rencontre´ un diplomate, a` savoir mon fre`re ‘Mary meta diplomat, namely my brother’ b. Marie a probablement loue´ une voiture, celle que je vois la`-bas ‘Mary probably rented a car, the one I see over there’

(5) a.

Marie n’a pas lu un livre quelconque ‘Mary read absolutely no book’ b. Est-ce que Marie a lu un livre quelconque? ‘Did Mary read any book whatsoever’ c. Marie n’a pas duˆ rentrer un code quelconque, ce qui a bloque´ le syste`me ‘There must be some code or other that Mary failed to type in, which made the system freeze’ d.
Marie n’a pas duˆ rentrer un code quelconque, le 1233A, ce qui a bloque´ le syste`me ‘There must be some code or other, 1233A, that Mary failed to type in, which made the system freeze’

Finally, in generic sentences such as (6a), UQ is not appropriate when it occurs as restriction of the generic operator (6b), see the contrast with (6c) where UQ is in the nuclear scope. The discussion of this case is deferred to section 4.2. (6) a. Un animal doit eˆtre soigneusement nourri ‘An animal must be fed with care’ b. ??Un animal quelconque doit eˆtre soigneusement nourri ‘Any animal must be fed with care’ c. Un chat doit avoir un jouet quelconque ‘A cat must have some toy’

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The second set of data concern downward-entailing environments. UQ may take narrow or wide scope. When it takes narrow scope, it can be paraphrased as ‘absolutely no’ (5a), ‘any whatsoever’ (5b), etc. When it has wide scope, it is subject to the prohibition against identification, see (5c) v. (5d).

Jacques Jayez and Lucia M. Tovena 221

3 EPISTEMIC PROPERTIES OF UQ

(7) Marie espe`re avoir inte´resse´ un e´tudiant quelconque ‘Mary hopes to have interested some student or other’ a#. Mary hopes (dx (x is a student & Mary has interested x)) a$. dx (x is a student & Mary hopes (Mary has interested x)) (8) dx (speaker believes (x is a student & Mary hopes (Mary has interested x))) A constraint such as (9) suffices to predict the right readings of (7). Intuitively, it says that a sentence with UQ is anomalous whenever the speaker can pick a referent for UQ. We ignore non-assertive sentences for the moment. We assume that UQ contributes a variable, following standard file-card or DRT-based treatments for singular indefinites, see Farkas (2002) for an overview. (9) Let A be an assertive sentence with a tripartite logical form [UQ(x)] [R(x)] [S(x)]. A is anomalous under an interpretation of the form dx (speaker believes (R(x) & S(x))).3 However, this definition of (non-)identification does not allow us to say why (10) is anomalous although the speaker might not know who is Mary’s only colleague. UQ is not an isolated case in this respect. Certain free choice (FC) items exhibit the same restriction (11). (10) a.
Hier, Marie a rencontre´ un colle`gue quelconque, le seul qu’elle ait ‘Yesterday, Mary met some colleague or other, the only one she has’ 2

It is generally held that the connection between scope and the de dicto/de re distinction dates back to Russell (1905). 3 We defer the formulation of a more adequate constraint until section 4.2.

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In this section, we examine the prohibition against identification, a feature of UQ that is absolutely general, even if it has other properties, as well. To a certain extent, this prohibition amounts to banning the de re interpretation with respect to the speaker, at least if the de re reading is equated—as usually done in formal semantics2—with the fact that an existential quantifier has wide scope over a modal operator. Consider (7) and its two interpretations (7a#-a$). (7a#) is the traditional de dicto interpretation and (7a$) the traditional de re one. When the speaker is the relevant epistemic agent, the forbidden reading is expressed in (8), which says that, for some particular individual x, the speaker believes that x is a student whom Mary hopes to have interested.

222 Epistemic Determiners (11) b.
Marie a pu rencontrer n’importe quel colle`gue, le seul qu’elle ait ‘Mary may have met any colleague, the only one she has’ (12) Hier, Marie qu’elle ait ‘Yesterday, Mary one she has’

a rencontre´

un

colle`gue,

le

seul

met

a

colleague,

the

only

(13) The set from which individuals that satisfy the restriction must be picked cannot be a singleton. The choice constraint does not apply to standard indefinites, as shown by (12). The similarity between (10) and (11) prompts the question of the link between UQ and FC items, which we address next.

4 UQ AS A FREE CHOICE ITEM Morphologically, un quelconque associates the indefinite un and a free choice element quelconque (from Latin qualiscumque). The latter may also combine with plural indefinites such as des ‘someplural’, quelques ‘a few’, plusieurs ‘several’, or numerals. This type of association between an indefinite or a pronoun and an expression that conveys indetermination, indifference, unselectiveness, etc. has been observed in a number of languages. The pretheoretical intuition that unifies the various descriptions of FC items in the literature presents the members of the restriction domain as equivalent. Since equivalence does not make sense for empty or singleton domains, the origin of constraint (13) is intuitively clear. We propose to distinguish different dimensions along which this equivalence manifests itself, so that we can build a unified characterization and at the same time make room for empirical differences across and within languages. In the next subsection, we show that some FC determiners, e.g. n’importe quel, require the referent to be undetermined, whereas some other, e.g. un quelconque, require the referent to be unidentified. Furthermore, the fact that un quelconque is a composite expression made of an indefinite plus an FC element will be shown to have consequences for its nature and behaviour.

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In other words, UQ and these items seem to obey constraint (13) that spells out one condition for choice to be possible. Let us call it the choice constraint.

Jacques Jayez and Lucia M. Tovena 223

4.1 Irreferential and epistemic free choice determiners

(14) a. (Dans ce roman,) diplomate ‘(In this novel) diplomat b. J’espe`re diplomate ‘I hope diplomat

Marie quelconque Mary or other’ que quelconque that or other’

a

rencontre´ un

met

some

Marie a rencontre´ un Mary

met some

(15) a.
Dans ce roma, Marie a rencontre´ n’importe quel diplomate ‘In this novel Mary met any diplomat’
b. In this novel, Mary met any diplomat’ c.
J’espe`re que Marie a rencontre´ n’importe quel diplomate ‘I hope that Mary met any diplomat’ d.
I hope that Mary met any diplomat As shown at length in Jayez and Tovena (2005a), certain FC items (any, n’importe quel, tout) are irreferential. Roughly speaking, they are infelicitous when the set of members of the restriction that satisfies the scope is referentially determined. Reference is conceived in a broad way, since it is defined with respect to the world of evaluation at which the FC item is interpreted. This world can be the actual world, as in
Marie a rencontre´ n’importe quel diplomate, an imaginary world, as in (15a,b), or an attitudinal alternative, as in (15c,d), where the logical form corresponding to ‘Mary met any diplomat’ is evaluated at each world compatible with the speaker’s hopes in the actual world. The reader is referred to Jayez and Tovena (2005a) for details.

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Is UQ an FC item? Let us start by considering two points that go against a straightforward positive answer. First, UQ can occur in episodic sentences, see examples (1a) and (2b), but this type of environment is considered to be incompatible with FC items in much of the literature, cf. Jayez and Tovena (2005a) and references therein. Second, there are FC items for which an epistemic analysis is not appropriate, see Jayez and Tovena (2005a) for evidence and discussion. So the epistemic sensitivity of UQ does not automatically secure its membership in the class of FC items. Specifically, observe the contrast between (14) and (15), concerning all non-episodic sentences. FC items such as any or n’importe quel in French are not possible in there, whereas UQ is possible because these sentences do not force identification.

224 Epistemic Determiners

b.
Marie a rencontre´ un diplomate quelconque, qui ne peut pas eˆtre mon fre`re ‘Mary met some diplomat or other, who cannot be my brother’ c. Va voir ‘Go and

un diplomate quelconque see some diplomat or other’

d.
Va voir un diplomate quelconque, a` savoir mon fre`re ‘Go and see some diplomat or other, namely my brother’ e.
Va voir un diplomate pas eˆtre ‘Go and see some be

quelconque, qui ne mon diplomat or other, who my

peut fre`re cannot brother’

f.
Va voir un diplomate quelconque, a` savoir mon fre`re ‘Go see any diplomat, namely my brother g.
Go and see any diplomat, namely my brother

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UQ is not affected by referentiality, see (14). In this respect, one might argue that it is essentially an epistemic item based on nonidentification, as suggested in Jayez and Tovena (2002). As noted above, the members of the restriction of FC items are equivalent or freely interchangeable. In particular, no member of the restriction must be determined at speech time as satisfying or not satisfying the scope, since this would set it out. This requirement has two important external manifestations that give reason to explore thoroughly the possibility that UQ is an FC item. First, such a requirement prevents the restriction from being a singleton, in which case the notion of arbitrary choice or equivalence would not make sense. This corresponds to the ‘choice constraint’ (13) and we have established that UQ is subject to it. Second, imposing or excluding a member of the restriction in an explicit way produces infelicitous sentences. We observe that UQ patterns like irreferential FC items in this respect too, as shown by the episodic and non-episodic examples in (6), for which we assume a context where the speaker’s brother is a diplomat. (16) a.
Marie a rencontre´ un diplomate quelconque, a` savoir mon fre`re ‘Mary met some diplomat or other, namely my brother’

Jacques Jayez and Lucia M. Tovena 225

h.
Va voir n’importe ne peut i.
Go and see cannot

quel pas eˆtre any be

diplomate, qui mon fre`re diplomat, who my brother

(17) a. Pick any card b. John was entitled to consult any file (18) a. Prend une carte ‘Pick some card b. Jean avait le droit de ‘John was entitled to

quelconque or other’ consulter un dossier quelconque consult some file or other’

In certain cases, the difference is almost imperceptible. For instance, (17a) and (18a) both convey the idea that any card can be picked by the addressee. In (18a), however, this is an inference that can be obtained with a non-FC indefinite through standard Gricean reasoning; Pick a card implicates that the speaker leaves open the possibility that any card be picked, since, otherwise, she should have provided a more precise indication (Pick this card, Pick the king of spades, etc.). The FC morphology of UQ adds the information that the speaker is not aware of any particular card that the addressee is likely to choose. In other cases, the difference is perceptible or quite clear. (17b) and (18b) are not

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One can construct similar examples with possibility/permission modalities or evidentials. In view of this strong parallelism, it is reasonable to treat UQ as an FC item. The fact that, in addition, it prohibits identification suggests that it is an epistemic FC item. The difference between irreferential and epistemic items has important consequences. Irreferential items demand that any member of the restriction be equal to any other with respect to their actual possibility of satisfying or not satisfying the scope. This is conducive to universal readings. For instance, (17a) entails that every card may be picked by the addressee in the different alternatives (possible continuations of the current situation). Similarly, (17b) entails that John could consult every file. Epistemic items demand that any member of the restriction be equal to any other with respect to its possibility of satisfying or not satisfying the scope for the epistemic agent. This is conducive to non-identification, but, crucially, does not entail that every member of the restriction satisfies the scope in the actual world or in some alternative(s). It is enough that the speaker ignores which individual satisfies or does not satisfy the scope.

226 Epistemic Determiners synonymous. The former asserts that John was allowed to consult every file whereas the latter asserts that he was allowed to consult a file that the speaker does not identify.

4.2 UQ as an indefinite FC item

(19) a. Si l’e´lection est de´mocratique, nous accepterons n’importe quel re´sultat ‘If it is a democratic election, we will accept any outcome’ b. #Si l’e´lection est de´mocratique, nous accepterons un re´sultat (un re´sultat quelconque) ‘If it is a democratic election, we will accept an outcome (some outcome or other)’ c. Apre`s la collision avec le deute´ron b, nous pourrons suivre n’importe quelle trajectoire suivie par le deute´ron a ‘After the collision with deuteron b, we will be able to trace any trajectory followed by deuteron a’ 4

Concretely, these alternatives are the leaves of the modal tree growing from the current world. However, UQ strictly requires non-identification, whereas this is only the default option for standard indefinites, see (4). 5

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As seen above, UQ does not behave exactly like other FC items with respect to the choice constraint. This strengthens one’s doubts about the complete parallelism between UQ and irreferential FC items. Suppose that a sentence hosting an FC item is evaluated at world w, two cases obtain: Either the domain restriction is determined at w, in which case the item is not appropriate if the cardinality of the domain is 0 or 1. Or the domain restriction is determined at the different alternatives that form the relevant set of alternatives for truth-conditional interpretation,4 in which case UQ is not appropriate if the restriction is a singleton in every alternative, unlike irreferential FC items. For instance, suppose that after a long civil war, one of the political sides decides to comply with the result of a democratic election, whatever it is. The party can felicitously declare its intentions by means of (19a), whilst (19b) would be difficult to interpret. Analogously, assuming that one wants to describe the trajectory of a deuteron after its collision with another one, (19c) is an option, whereas (19d) is again possibly odd. In both cases, the problem is that the domain of the restriction, i.e. the set of outcomes or trajectories, is a singleton in each alternative. A garden-variety indefinite like un shows the same restriction.5

Jacques Jayez and Lucia M. Tovena 227

d. #Apre`s la collision avec le deute´ron b, nous pourrons suivre une trajectoire (une trajectoire quelconque) suivie par le deute´ron a ‘After the collision with deuteron b, we will be able to follow a trajectory (some trajectory or other) followed by deuteron a’ When the previous observation is put together with the contrasts in (2), and (3) v. (4), we see that there are actually three different classes.

From (b) and (c), we see that there are two scenarios that may affect UQ, if it is an indefinite and an FC item. First the information that the restriction is a singleton can be added to the current belief set. Standard indefinites implicate that the restriction is not a singleton, but this is only a default preference7 which can be overridden by a belief update, so standard indefinites are compatible with such an update (12). FC items are simply not compatible with a 1-element restriction set, and accordingly UQ is out in such cases, as observed for (10). Second, the information that the restriction is a singleton can already be present in the initial belief state. In that case, standard indefinites may be infelicitous, even when the restriction is evaluated at different worlds as in (19b,d). Summing up, exploring the hypothesis that UQ is an epistemic FC determiner, we have built a case for the contribution of the indefinite component of this composite determiner. UQ inherits constraints from the classes of standard indefinites and of FC items. Specifically, (i) like standard indefinites UQ is not compatible with certain contexts in which the restriction domain is a singleton, (ii) like FC items and unlike standard indefinites it obeys the choice constraint and keeps the members of the restriction on a par through non-identification. Two more pieces of evidence for the indefinite character of UQ are that, first, unlike irreferential FC items and like indefinites it does not have 6

As noted by a reviewer, mentioning unpublished work by Farkas, indefinites may be compatible with singleton domains. For instance, I am going to show you a film which won the Palme d’or at Cannes in 1976 can be used in a situation where it is clear that exactly one film won the Palme d’or that year. However, it is sufficient for our purpose to observe that UQ and standard indefinites are anomalous in configurations such as (19). 7 A generalized conversational implicature, in Gricean terms.

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(a) Irreferential FC items are not compatible with the information that the restriction is a singleton in the evaluation world, see (11). This is as expected since FC items require that a choice be possible. (b) UQ is not compatible with the information that the restriction is a singleton in the evaluation world, see (10). This is as expected if it is an FC item. (c) Indefinites in general may be problematic in a context where it is common knowledge that the restriction is a singleton set.6

228 Epistemic Determiners a universal interpretation in comparative clauses (20). Second, unlike irreferential FC items and like indefinites it combines with negation and gives rise to the two traditional wide scope v. narrow scope readings, as noted for (5a) above.

On the other hand, the observation that UQ does not enter the restriction of generic sentences goes against its characterization as a standard indefinite, see (6), because standard indefinites generally do. However, we know that UQ signals ignorance about the referent and we observe in (21) that the generic interpretation conflicts with a mention of ignorance. This is to be expected since genericity involves reference to a class or type, for which ignorance about the referent does not make sense. So the anomaly of UQ in generic sentences is in fact perfectly normal. (21) [generic reading impossible] a. Un animal, je ne sais pas lequel, doit eˆtre soigneusement nourri b. An animal, I don’t know which one, must be fed with care c. Animals, I don’t know which ones, must be fed with care From the foregoing discussion, we conclude that UQ is an epistemic FC indefinite. As an epistemic FC item it obeys the subset of constraints for non-referential situations given in Jayez and Tovena (2005a: def. 41, p.36). As an indefinite it obeys prohibitions against 1-element restriction domains. These prohibitions should not be confused with the implicature of non-uniqueness for indefinites discussed in the literature, e.g., Hawkins (1991), which concerns the intersection of the restriction and the scope, whereas we are considering only the restriction. Before giving the details of the constraint on UQ, let us explain semi-formally what kind of free-choiceness it is intended to capture. A sentence like (30) forbids any interpretation under which a particular book must be read or cannot be read. (22) Il est obligatoire que Jean lise un livre quelconque ‘John has to read some book or other’

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(20) a. Marie s’est mieux de´brouille´e que n’importe quelle autre fille dans sa classe ‘Mary got by better than any other girl in her class’ 0 ‘Mary got by better than every other girl in her class’ b. Marie s’est mieux de´brouille´e qu’une fille (quelconque) dans sa classe ‘Mary got by better than some girl or other in her class’ L ‘Mary got by better than every other girl in her class’

Jacques Jayez and Lucia M. Tovena 229

A DRT representation for (30) would be K ¼ [x : John(x) h[y : book(y) read(x,y)] ].

(a) for every w 2 W, there exists a function h extending f # on y such that (i) h(y) ¼ a and (ii) ‘h(y) is a book’ and ‘f #(x) reads h(y)’ are true at Æw, h æ, or, (b) for every w 2 W, there exists a y-extension function h of f # such that (i) h(y) ¼ a (ii) ‘h(y) is a book’ is true at Æw, h æ and (iii) ‘f #(x) reads h(y)’ is false at Æw, h æ. The mention of speaker’s beliefs is not a detail. This may not be apparent from sentences like (22). Consider (23) instead. For (23) to be appropriate, it must not be the case that the speaker believes that there is a particular book that Mary thinks John must read. This prohibition affects the epistemic alternatives that the speaker attributes to Mary, not the alternatives Mary actually entertains. (23) Marie pense qu’il est obligatoire que Jean lise un livre quelconque ‘Mary thinks that John has to read some book or other’ Therefore, the constraint on UQ must take into account DRS epistemically relativized to the speaker. The easiest way to go is to require that the initial DRS K, corresponding to the sentence where UQ occurs, be transformed into a DRS that expresses the speaker’s beliefs, as in (24). One must exercise a little care, however, in order to keep the presuppositions at the highest level. For instance, if we assume, as is usually done in DRT, that proper names are declared in the main DRS, the correct epistemic relativization of (31) is:8 [x y : Mary(x) John(y) hbel,sp[ : hbel,x[ : hmust,y[z : book(z) read(y, z)]]]]. 8

Henceforth, the notation hM,a or )M,a denotes the necessity (possibility) modal operator with respect to the modality M and the agent a. For example, hbel,sp denotes the modal operator associated with the speaker’s beliefs.

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If K is interpreted at Æw0, f æ, it is true in a model if and only if, for some Æw0, f #æ such that f#(x) is John, it is the case that for every Æw, f #æ accessible from Æw0, f #æ there exists some f$ extending f# on y such that ‘f$(y) is a book’ and ‘f#(x) reads f$(y)’ are true at Æw, f $æ. Because y is introduced by UQ, the sentence is felicitous only if there is no individual a for which the speaker believes that it is a book that Jean must read or must not read. Formally, if W is the set of worlds deontically accessible from w0, there must not be any individual a such that the speaker believes that:

230 Epistemic Determiners (24) Let K be the DRS [x1. . .xn : /1 . . ./k], where the xi are discourse referents and the /j conditions. Suppose we have arranged the discourse referents and the conditions so that the first m referents and the first p conditions must remain in the main DRS. The epistemic relativization of K to the speaker is the DRS K#, defined by: K# ¼ ½x1 . . . xm : /1 . . . /p hbel;sp ½ : /p+1 . . . /k :

(25) Tu peux consulter un fichier quelconque ‘You may consult any file’ As explained in Jayez and Tovena (2005a), the restrictions on FC items must accordingly take into account all the accessible worlds. In practice, this is equivalent to treating every modal operator as a hoperator on the same set of accessible worlds. For example, in (25), if )perm is the permission operator and hbel the belief operator9, there are two offending configurations (add is the addressee): a. dx(hbel,sp(hperm,add( file(x) & consult(x)))) b. dx(hbel,sp(hperm,add( file(x) & :consult(x)))) Configuration a expresses the fact that there is a particular individual that the speaker believes to be a consulted file in all the worlds that represent what is compatible with the permissions the addressee has. Generalizing, for every epistemic relativization, we must transform the ) operators into their h counterpart. Let Kh be the result of this transformation on a DRS K. Finally, we have to make our constraint sensitive to local 9

The nature of the epistemic source is not important. The reader may prefer Kratzer-style approaches in terms of modal base-ordering source combinations (Kratzer 1981) or probabilistic approaches (Kaufmann, 2002).

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It is beyond the scope of this paper to offer a full treatment of the presuppositions embedded under the different modalities. The reader is referred to Geurts (1999) for a detailed proposal. In addition to epistemic relativization, we have to modify the modal operators in some cases. Saying that there is no identification is not sufficient, since there are cases where the speaker identifies the individuals that possess the modal properties described by the sentence. For instance, in (25) the speaker may know which files are allowed. What is required is that she do not know at speech time which file(s) will be consulted or not consulted.

Jacques Jayez and Lucia M. Tovena 231

DRS (and not only to the main DRS). This may raise a problem when quantification and modality are associated. Consider (26). (26) Tous les e´tudiants ont e´te´ oblige´s de lire un livre quelconque ‘Every student had to read some book or other’ Under the preferred interpretation, the speaker cannot identify any book that a student had to read. The DRS for (26) is: [ : [x : student(x)] 0 hobl[ y : book(y) read(x,y)]].

(27)

Each DRS is initially superscripted with an empty list and has the general form [<> Discourse Referents: Conditions]. Let KL be the result of superscripting the DRS K with L and the dot ‘.’ be the list concatenation operator. There are four types of conditions: – predicative conditions of the form P(x1. . .xn), – negative complex conditions of the form :K, where K is a DRS, – model conditions of the form hM(KhM.L) or )M(K)M :L ), where KL is a DRS, – complex conditions of the form K1LOP K2L, where L is the superscript of the smallest DRS containing the condition.

So, for instance, [L. . .:K#L 0 K$ L], [L. . .: Most (K#L, K$L)], etc, are well-formed DRSs. Note that if L is the modal superscript of a DRS K, K acquires a superscript of the form hbel,sp.L in the epistemic relativization of the main DRS containing K. Now we can go back to the constraints that regulate the behaviour observed for UQ. They are provided in (28). The first ensures that UQ behaves like an indefinite. The second prevents any identification of an individual.

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For every value of x, say a, we require that there be no book such that the speaker believes that a had to read this book. The DRS corresponding to the UQ phrase is the deepest one. To impose the correct requirement on this DRS we have to know that it is embedded under the hobl modal operator. How can we capture this modal sensitivity for each particular DRS? We have to keep a trace of the modal path we follow when evaluating a DRS. We slightly modify standard DRT syntax and add a modal list of operators to each DRS.

232 Epistemic Determiners

Let us review briefly how (28) predicts the observations made up to this point. Condition (28.1) bans cases like (19b,d), which cannot host un because the restriction is a singleton. Non-modal assertions violate (28.2a) whenever the referent is identified. For instance, the epistemic relativization of the DRS for (1b), ‘Mary met some diplomat or other, namely my brother’, is: [<> x y : Mary(x) brother(y) hbel,sp[hbel;sp z : diplomat(z) met(x, z) z ¼ y]]. In every model where this DRS is true, there is a particular individual that the speaker believes to be a diplomat and to have met Mary. (2a) and (5d) are anomalous for the same reason. For (3a) ‘Mary probably rented some car or other, the one I see over there’, we have the following DRS, assuming an appropriate resolution of the demonstrative pronoun: [<> x y : Mary(x) over-there(y) hbel,sp[hbel,sp : hprob,sp[hbel,sp.hprob,sp z : car(z) rent(x,z) z¼y]]] Clearly, every model that satisfies the DRS satisfies: dz(hbel,sp(hprob,sp(car(z) & rent( f(x), z)))), which violates (28.2a). A similar reasoning applies to (3b,c) and to the imperative case (16d). (28.2b) bans sentences that exclude some individual(s), as seen in (16b,e). For dependent variables, the general idea is that no particular individual must be identified for any value of the quantified variable. For example, for (26), the constraint is :dx(hbel,sp(hobl(book(x) & (:)read(a, x)))), where a is any student. As noted by our reviewers, representations that embed the restriction under the modal sequence might sound artificial. For instance, (7),

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(28) UQ is subject to the following two constraints. 1. UQ inherits the constraints of the singular indefinite un. 2. Let K ¼ [L x : R(x) S(x)] be a DRS, where R and S are the restriction and scope properties and x is the variable introduced by UQ. Let K0 be the main DRS containing K, K#0 be the epistemic relativization of K0 and K# the DRS corresponding to K in K#0h: Let f \x be the restriction of f to variables different from x. If K# is evaluated at Æ f, w æ and has the superscript hbel,sp.L#, UQ is appropriate under an interpretation I only if I does not entail: a. dx(hbel,sp.L#(f \x(R) & f \x(S))) or, b. dx(hbel,sp.L#(f \x(R) & :f \x(S)))

Jacques Jayez and Lucia M. Tovena 233

‘Mary hopes to have interested some student or other’, is predicted to be anomalous under interpretation (29), where m denotes Mary. (29) dx(hbel,sp(hhope,m(student(x) & interested(m, x))))

5 IMPLICATURE It is well-known that epistemic or FC determiners and pronouns can convey indifference or various derogatory values (see the remarks in Farkas 2002) for some, Giannakidou 2001 for opjosdhipote; Horn 2000 for just any; Jayez and Tovena 2005a for n’importe lequel; Kratzer and Shimoyama 2002 for irgendein; von Fintel 2000 for whatever). Clearly, these values are connected with the fundamental semantic intuition that pervades FC items: all the members of the restriction are equivalent. A recurring question is whether such values are semantically stable or rather defeasible implicatures. Kratzer and Shimoyama argue for instance that the equirepartition of possible values, characteristic of FC items and observed with the German determiner irgendein—which shares a number of properties with UQ—is in fact a conversational implicature. They follow Kadmon and Landman (1993) in assuming that irgendein induces widening of the domain of the

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(29) suggests that Mary hopes that somebody is a student and that she interested her. A more natural interpretation is that, for somebody that Mary believes to be a student, she hopes to have interested her. (28) could be modified to incorporate different scope geometries, but notice that the interpretation depends on the modal operator (L#), the lexical content of R and S, and the tense, i.e. on factors that deserve a separate study. Moreover, the felicity of UQ depends only on the fact that no individual satisfies the restriction and the scope in all the worlds that can be accessed from the current world by following the h-version of the sentence modal path. The issue whether the speaker or other agents believe that a given individual satisfies the restriction is tangential and should be settled in connection with a general theory of DRSs. Since (28) is meant to express a general prohibition, which does not commit us to any particular view on these more specific problems, we will leave it as it is. This closes our semantics analysis of UQ. For space reasons, the issue of the different perspectives that can be adopted cannot be tackled. The interested reader is referred to Jayez and Tovena (2002). We complete the discussion with a section on a more pragmatic facet of the meaning of UQ, namely its derogatory values.

234 Epistemic Determiners

(30) a. ??It is possible that John is a diplomat. He most certainly is a diplomat b. It is possible that John is a diplomat. In fact, he most certainly is a diplomat c.
Marie a rencontre´ un diplomate quelconque, en fait c’est mon fre`re ‘Mary met some diplomat or other, in fact he’s my brother’ d. #Marie doit e´pouser un diplomate quelconque. Et xca ne peut eˆtre que mon fre`re ‘Mary must marry some diplomat or other. And he can only be my brother’ e. ??Vu sa position sociale, Marie a l’obligation d’e´pouser un diplomate quelconque: et elle a l’obligation d’e´pouser mon fre`re ‘In view of her social status, Mary has to marry some diplomat or other: And she has to marry my brother’

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restriction. For example, irgendein Mann cannot denote a proper subset of ½½man and must denote the set of all men. The speaker may choose to widen the restriction domain for three reasons: strengthening her claim, avoiding a false claim, or a false exhaustivity inference. This proposal does not work for UQ. If the FC constraint in (28) were a conversational implicature, it should evaporate under appropriate updates, (see Geurts 1999; Horn 2001; Levinson 2000 for detailed discussions of the phenomenon). One might object that, as noted by Geurts (1999: 62–64), conversational implicatures cannot be cancelled ‘unceremoniously’. For example, (30a) is awkward, in contrast to (30b). In both cases, the first sentence conversationally implicates that the speaker has no evidence that John is a diplomat. Suspending this implicature requires a retraction indicator of some kind, such as in fact. But this is not the case in (30c). Moreover, we surmise that the French counterpart (30d) of the German example that Kratzer and Shimoyama use to prove that the distribution requirement of irgendein is a conversational implicature, can be explained without resorting to cancellation. There are two modal operators in (39d), corresponding to two different modal bases. According to the first (deontic) modal base, it is obligatory for Mary to marry a diplomat, whose identity remains undetermined. According to the second (epistemic or deontic) modal base, the diplomat is identified. For the discourse to be coherent it is necessary that the two modal bases be distinct. For instance, if both are deontic they might be moral and physical respectively. Whenever they are identical the discourse may sound almost contradictory (30e).

Jacques Jayez and Lucia M. Tovena 235

More generally, it seems that the main motivation behind pragmatic approaches is the connection between FC items and FC imperatives. This connection is made explicit by Aloni and van Rooij (2004), who try to derive the distribution of FC items from Gricean principles. Their approach raises two problems, which illustrate the tension between lexical instructions and pragmatic derivations. First, to construct the derivation, they have to make certain stipulations that go far beyond simple Gricean principles. Second, and more importantly, they do not explain why such ‘Gricean’ implicatures are indefeasible. Kamp (1978) and Zimmermann (2000) note that sentences like (31b) suggest that the usual interpretation of FC disjunctions is an implicature.

However, this is not true for UQ, nor for irreferential FC items (32). We conclude accordingly that the ignorance value, or, more generally, the FC value, is not an implicature. This does not mean that we rule out connections between pragmatically-driven cases and the semantics of FC items, an issue we cannot address in this paper, but see Jayez and Tovena (2005b) for more discussion. (32) a.
Tu peux prendre une route quelconque, mais j’ai oublie´ laquelle ‘You may take some route or other, but I forgot which’ b.
Tu peux prendre n’importe quelle route, mais j’ai oublie´ laquelle ‘You may take any route, but I forgot which’ UQ expresses also indifference of the speaker, like some, irgendein, quelque (Van de Velde 2000), or whatever. The indifference value is responsible for the oddness of sentences where (28) is not overtly violated. (33) is strange because it implicates that the speaker does not care about the desk lamp she would like for her birthday. (33) ??Pour mon anniversaire, je voudrais une lampe de bureau quelconque ‘For my birthday, I would like some desk lamp or other’

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(31) a. You may reach the island by boat or by plane [implicates: You may reach the island by boat AND you may reach the island by plane] b. You may reach the island by boat or by plane, but I don’t remember which [does not implicates: You may reach the island by boat AND you may reach the island by plane]

236 Epistemic Determiners The indifference value is not automatically triggered by UQ. Indeed, it is cancelled in the sentences in (34), for instance, where the identity of the referent is relevant. Accordingly, we consider the indifference value to be a conversational implicature.

Finally, let us add a word on the question of the status of the ‘widening’ value in negative polarity environments. We noted above that sentences of type (5a,b) have an emphatic paraphrase. This remains true when the domain of the restriction is limited (35a). We observe the same situation with typical French FC ‘tags’ such as quel qu’il/qu’elle soit ‘whoever/ whatever (he/it)/she is’ or que ce soit ‘whatever’, which can be rightadjoined to certain types of NP in negative polarity environments (35b,c).10 (35) a. Marie n’a pas lu un quelconque de ces trois livres ‘Mary did not read any of these three books whatsoever’ b. Marie n’a pas lu un livre quel qu’il soit (parmi ces trois livres) ‘Mary did not read any book whatsoever (among these three books)’ c. Marie n’a lu aucun livre que ce soit (parmi ces trois livres) ‘Mary did not read any book whatsoever (among these three books)’ This suggests that widening is a side-effect of free-choiceness. We saw that FC items indicate that the members of the restriction are all on a par with respect to the nuclear scope. This may constitute the basis of the following inference: if the speaker insists upon the interchangeability of the elements of a set X with respect to a property P, it may be because she accepts to include in the set of satisfiers of X \ P even elements of X that are only marginal candidates for satisfying P.11 Being 10

Their distribution is limited, but we ignore the details here. This kind of abductive reasoning from meaning to its possible motivations is current in pragmatics, and it is difficult to trace down its exact origin. It has received renewed attention in the context of relevance theory (Sperber and Wilson 1986) and Blutner’s bidirectional optimality theory (van Rooy 2003). 11

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(34) a. Marie a duˆ eˆtre mise au courant du projet par un employe´ quelconque, et il faudrait savoir qui ‘Mary must have learnt about the project from some employee or other and we need to know who he is’ b. La victime a force´ment entendu un bruit quelconque, mais je me demande bien quoi ‘Surely, the victim heard some noise or other, but I really wonder what’

Jacques Jayez and Lucia M. Tovena 237

abductive, inferences of this sort cannot be guaranteed and one may suspect that they become generalized conversational or conventional implicatures via some process of (partial) grammaticalization. The various values that have been noted for FC items, such as indifference, ignorance or concession all express possible motivations of a speaker for calling attention to the interchangeability of certain elements through the use of a FC item. In the case of UQ, we assume that widening is conventionalised in negative polarity environments. 6 UN CERTAIN

6.1 Basic data We will restrict ourselves to the following three points. First, UC and AC neither entail nor exclude identification of the referent by the speaker (36). (36) a. J’ai rencontre´ un certain diplomate, que je connaissais tre`s bien ‘I met a certain diplomat, whom I knew very well’ b. On m’a parle´ d’un certain diplomate, mais je ne vois pas qui c’est ‘I have heard of a certain diplomat, but I don’t see who he is’ Second, they do not necessarily have a specific reading. For example, (37a) only has a specific reading, but (37b) has a non-specific reading and is natural under any interpretation that provides a sort of ‘type’ for the piece of information that each spy detains. For instance, the examples might mean that every spy who detains whatever information about a new type of ground-to-air missile must be eliminated. (37) a. Jean vent e´pouser une certaine fille ‘Jean wants to marry a certain girl’

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Let us now consider an epistemic determiner for which some form of knowledge rather than ignorance seems required. Un certain (UC) has been claimed to be the mirror image of quelque, and of UQ by extension, because it demands that the referent be ‘determined’ (bien de´termine´: Van de Velde 2000: 57). There is a widespread intuition that UC, because it involves the adjective certain from the latin certus (‘fixed’, ‘discriminated’, ‘determined’), conveys at least specificity (Van de Velde 2000). A similar intuition is found in the literature on a certain (AC) (Hintikka 1986; Kratzer 1998), but it is sometimes strengthened to incorporate identification (Farkas 2002; Jayez and Tovena 2002).

238 Epistemic Determiners b. Tous les espions qui sont en possession d’un certain renseignement doivent eˆtre e´limine´s ‘Every spy who has a certain piece of information must be eliminated’

(38) a.
Apparemment, j’ai un certain virus non-re´pertorie´ sous mon microscope ‘It seems I got a certain virus non-documented under my microscope’ b.
It seems I got a certain non-documented virus under my microscope c.
Il vient juste d’y avoir un certain accident au carrefour ‘a certain accident just happened at the crossroad’ d.
A certain accident just happened at the crossroad Apparently, some of these data have gone unnoticed, but they are particularly relevant because they constitute stumbling blocks for available analyses of UC/AC. In the remainder, we expose these problems and then put forward a proposal that grows out of this more thorough assessment of the situation.

6.2 Two lines of analysis and their problems Recent analyses of UC and AC can be divided into two groups, accepting some simplification: those that insist on specificity (Hintikka 1986; Kratzer 1998) and those that insist on identification (Farkas 2002; Jayez and Tovena 2002).

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Should we conclude that UC and AC have no special property and are run-of-the-mill indefinites? Intuition resists this conclusion, which otherwise would leave open a major question: why is it that, in (37a,b) and many similar examples, specificity is very strongly preferred, if UC and AC are just plain indefinites? The third point is related to identification. Although UC and AC do not require identification by the speaker, they are not felicitous in contexts where there is only identification by the speaker (38). In (38a,b), the virus is (i) a particular organism (specificity), (ii) possibly identified by the speaker (minimally as ‘the virus she just found’) and not identified by anybody else (since the virus is not documented). The other example is in part similar, but the accident might be identified by other witnesses on the scene.

Jacques Jayez and Lucia M. Tovena 239

6.2.1 Specificity-based analyses Elaborating on Hintikka (1986), Kratzer (1998) proposes that (i) AC has only a specific interpretation and (ii) the choice function for AC has an additional argument which allows for the relativization of choice functions to individuals. For instance, example (39) receives the representation in (39#). The value of f must be a function that picks out a date, given an individual, i.e. a value for x, and the set of dates DATE. So, it is a relativized choice function.12 (39)

"x(x is a husband 0 x had forgotten f(x,

DATE))

The issue is how to determine the connection between the individual and f. According to Kratzer, the value of f is contextually determined. For (39), f must pick x’s wife birthday from DATE. Similarly, in a question like Is Richard dating a certain woman? (Kratzer’s example (11)), a likely anchor (the value of x) is the speaker and the choice function ‘picks out a woman that the speaker has in mind’ (Kratzer 1998: 169). Kratzer’s proposal exploits the intuition that AC is inherently specific and, accordingly, has to be relativized to some epistemic agent. Farkas (2002) and Jayez and Tovena (2002) criticise Kratzer’s proposal on several counts. Farkas claims that Kratzer’s analysis cannot explain the properties of AC in modal environments, for instance the fact that the ‘narrow scope’ (as she calls it) paraphrase of (40) is incompatible with AC. For clarity, we have listed the intuitive paraphrases provided by Farkas. We return to this example at the end of section 7. (40) John wants to catch a certain unicorn wide scope paraphrase: ‘there is a unicorn that John wants to catch’ intermediate scope paraphrase: ‘John wants to catch a unicorn (that he identifies and believes exists)’
narrow scope paraphrase: ‘John wants to catch a unicorn (that he does not identify)’ Jayez and Tovena (2002) note that Kratzer’s analysis is not sufficient because it does not address the problem of identification, which is 12 The fact that a choice function is relativized simply entails that it has a general form f(x, X), where x is the relativizer—an individual in the present case—and X the argument set.

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(39#)

Each husband had forgotten a certain date – his wife’s birthday (Hintikka’s example (3))

240 Epistemic Determiners apparent in (38). Nothing prevents us from binding the variable introduced by UC/AC in such cases too in the way suggested by Kratzer. For instance, (38a,b) would be associated with the logical form in (41). One might then suppose that f picks out a new virus that the speaker has in mind, certainly the virus she just discovered. Yet the sentence remains strange. So, finding a plausible choice function is not enough to construct a plausible interpretation for the sentence. (41) righ-now-under-mic( f(x,

NON-DOCUMENTED VIRUSES))

(42) Chacun avait recxu de son instructeur une certaine taˆche a` exe´cuter ‘Each person had received from her instructor a certain task to carry out’ 6.2.2 Identification-based analyses Farkas’s (2002) and Jayez and Tovena’s (2002) approaches depend on the notion of identifiability and identification respectively. Farkas proposes that AC introduces a non-identified but ‘identifiable’ referent, by which she means that the context to which the AC phrase contributes can in principle be updated until all the available assignment functions give the same value for the variable introduced by AC. Farkas’s approach raises two problems. (i) The condition that the referent be non-identified is too strong. This condition can be interpreted in two different ways. Either the current context is the common ground13 and (43) should then be anomalous, or the current context is the speaker’s belief state and (36a,b) should be anomalous. 13

This is probably the correct interpretation in the context of Farkas’s approach.

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One might point out that a really important intuition can be derived from the Hintikka-Kratzer approach, namely that AC is ‘specific’. What must be specific (i.e. have wide scope in the logical form) is the choice function, as illustrated in (39#). However, other data show that the case of (39) cannot be generalized. For instance, (42) is compatible with an interpretation under which different instructors assign different types of task to the person they have in charge. The different tasks assigned were determined in advance by the instructors and, then, identified at the moment they were chosen. Under this interpretation, there is no unique choice function that would calculate the task assigned to the person.

Jacques Jayez and Lucia M. Tovena 241

(43) a. J’ai des proble`mes avec un certain article que tu vois sur mon bureau ‘I have problems with a certain paper that you can see on my desk’ b. I have problems with a certain paper that you can see on my desk

(44) [contexts: for (44a) and (44b), the speaker is not going to master or even to understand string theory; for a (44c) and (44d), computer is calculating the solution of a complex (but solvable) problem] a. Il y a un certain re´sultat en the´orie des cordes qui montre qu’il existe une infinite´ d’univers ‘There is a certain result of string theory which shows that there is an infinite number of universes’ b There is a certain result of string theory which shows that there is an infinite number of universes c.
Demain, l’ordinateur me fournira une certaine nouvelle solution que je vous communiquerai ‘Tomorrow, the computer me will provide a certain new solution, that I will pass on to you’
d. Tomorrow, the computer will provide me with a certain new solution, that I will pass on to you

14 In such examples, the identifying property may be conceived as ‘the property of being the solution that the speaker will find on the next day’.

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(ii) Moreover, Farkas assumes that the referent must be identifiable by means of some property in some possible evolution of the common ground projected by the speaker. This requirement is difficult to assess. On the one hand, if the speaker is mentioning a topic about which she is likely to remain incompetent, how could she acquire the knowledge necessary for identification (44a,b)? Yet her understanding is necessary for the common ground to converge towards an identification of the theorem. On the other hand, the variant in (44c,d) shows that, even when the speaker is bound to identify the referent, owing to the computer, and to disclose its identity, UC and AC are not felicitous if no other agent can identify it. Intuitively (44c,d) are odd because (i) the speaker has no idea of the solution at speech time and (ii) no other agent can identify it at speech time, as it is presented as new.14

242 Epistemic Determiners 7 ANALYSIS The various proposals we have been reviewing contain ingredients that may help us to find out how to make more robust the solution we proposed in Jayez and Tovena (2002). Let us recall the intuitive motivation for this solution, by discussing the elementary example (1c), repeated below. (1) c. Marie a rencontre´ un certain diplomate ‘Mary met a certain diplomat’

(45) a. Hier, un certain Paul est venu me voir ‘Yesterday, a certain Paul came to see me’ b. Yesterday, a certain Paul came to see me Third, the identification may be anterior or posterior to the time of the eventuality referred to by the sentence. For example, the speaker of (1c) or another agent may have known the diplomat before or after Mary met her.16 Fourth, the notion of identification has to be weakened. Farkas’s and Jayez and Tovena’s approaches use the standard, strong, 15 The sensitivity of identification to descriptions is by now a well-established idea, see, for example, Aloni (2001), Dekker (1998), Gerbrandy (1998). 16 In Jayez and Tovena (2002), we claimed that the speaker must identify the referent, a condition that is symmetrical to Farkas’s and that is equally too strong, see (36c,d).

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There is a strong intuition that the diplomat is not just ‘the diplomat that Mary met’, even if this description is uniquely identifying. The diplomat in question is presented as known under another guise. This is a quite general feature: the referents UC and AC introduce are given as identified in a way that is distinct from the way in which they are described in the sentence.15 For instance, uttering A certain glass fell and broke is strange unless one supposes that the glass in question is remarkable in some respect, because of its nature (it is very rare), or of an event where it played a special role, etc. This is tantamount to saying that the glass cannot been singled out by the property of being ‘the glass that fell and broke’. Accordingly, the condition we associate with UC and AC is that these determiners communicate that the speaker believes that there exists an agent who identifies the referent under a description other than the one provided by the sentence. The identity of the agent and the nature of identification are underspecified. First, this agent may or may not be the speaker. Second, the agent cannot be said to be necessarily known to the speaker, see (45a,b) where the speaker may have no idea about who knows Paul.

Jacques Jayez and Lucia M. Tovena 243

(46) a. Marie a rencontre´ un certain diplomate ‘Mary met a certain diplomat’ b. Chacun a rencontre´ un certain diplomate ‘Each met a certain diplomat’ c. Marie croit qu’un certain diplomate l’espionne ‘Mary thinks a certain diplomat is spying on her’ (46a) corresponds to the DRS [x: diplomat(x) Mary-met(x)]. UC and AC are appropriate just in case the speaker believes that there is an agent who (weakly) identifies a diplomat that Mary met through an independent description. (46b) corresponds to K ¼ [K1 ¼ [x : person(x)] 0 K2 ¼ [y : diplomat(y) met(x,y)]]. If it is evaluated at Æ f, w æ, K is true if and only if for each x-extension f # of f there is a y-extension f$ of f # such that f$(y) is a diplomat and f #(x) ¼ f$(x) met f$(y). UC and AC are appropriate just in case the speaker believes that everyone met an independently identifiable diplomat, that is, for each yextension f$ that satisfies K2, there is a function g$, differing from f$ at most on y, that satisfies K2 and assigns to y an independently identified individual. Why not consider directly the function f$ instead of the additional function g$? Because (46b) is compatible with an interpretation under which each person met several diplomats, who are

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notion of identification: an agent identifies a referent by means of a certain description D in an epistemic state s (a set of epistemic alternatives) if and only if there is a unique entity of the interpretation domain, say d, such that D(d) is true at every world of s. We saw at the end of section 6.2.1 that this is too stringent a requirement in certain cases. Generalizing, we observe that, in other cases, this condition is not necessary either. For example, imagine that the speaker (a) of (1c) knows that the diplomat met by Mary is the very same diplomat he has been told about by another agent (b) and that b knows this diplomat only as ‘the unique person who has been able to stop the recent civil war in Zizania’. If b has never seen or spoken to the diplomat in question and if we assume that speaker a has b’s ‘identification’ in mind, why should one need strong identification? It is enough to postulate that b believes that there is a unique entity that obeys a certain description, or, in symbols, hbel,b[d!x(diplomat(x) & stopped-war(x)]. In the following, when we speak of ‘identification’ we have in mind this type of ‘weak’ identification. To motivate the formal definition, let us consider briefly the three basic configurations in (46): an independent variable (a), a dependent variable (b) and a modally dependent variable (c).

244 Epistemic Determiners

(47) Marie croit qu’un certain diplomate l’espionne, mais elle ignore si c’est son colle`gue ou son chef a` l’embassade ‘Mary believes that a certain diplomat is spying on her, but she does not know whether it’s her colleague or her boss at the embassy’ (48) Marie croit qu’un certain diplomate l’espionne. Elle n’a aucune ide´e de qui xca peut eˆtre, mais, tu vois a` qui je pense, hein? ‘Mary believes that a certain diplomat is spying on her. She has no idea who it might be, but you see who I have in mind, right?’ Summarizing, this brief intuitive review shows that the constraint on UC and AC is that, in the speaker’s view, for every individual that satisfies the DRS where UC and AC occur, there is a (possibly identical) individual that (i) satisfies the DRS, too, and (ii) is independently identified. Before constructing the final constraint, we need a definition of ‘independence’. If P and P# are two (possibly complex) properties we define their independence in (49), which means that neither property entails the other one. (49) P and P# are independent at w, in symbols P ) P#, iff ½½Pw ? ½½P#w and ½½P#w ? ½½Pw. 17

We will see below that this is actually an oversimplification.

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not all independently identified. One cannot ensure in general that a function that provides a value for the diplomat will select precisely one of the independently identified diplomats. A similar analysis holds for (46c). This sentence corresponds to K ¼ [x : Mary(x) hbel,x[y : diplomat(y) spy-on(y,x)]]. K is true at Æ f, w0 æ if and only if for every epistemic alternative of Mary Æ f, w æ, there is a y-extension f # of f such that f #(y) is a diplomat who spies on Mary at w. UC and AC are appropriate just in case the speaker believes that a diplomat who spies on Mary is independently identified in each epistemic alternative.17 Since f #(y) is not necessarily an independently identified diplomat, we must again introduce an additional function g#. One might object that (46c) entails the existence of a unique independently identified diplomat. However this is only a preferred interpretation, as shown by the variant in (47). (47) entails that Mary believes that the spy might be her colleague or her boss. It is even possible that the existence of an independent identification is ascribed to the speaker instead of Mary, as in (48). The speaker reports that she has a particular candidate-spy in mind whereas Mary has not.

Jacques Jayez and Lucia M. Tovena 245

The formal constraint is spelled out in (75), where f  x f# means that f and f # differ at most on the value they assign to x.

The fact that K is evaluated in an epistemic relativization has the effect that the truth-conditions of the world w are ultimately dependent on the speaker, as for UQ. Paraphrasing (50) in more detail, we see that if the restriction and the scope are satisfied at Æf, w æ: a. there is an assignment function f # that returns a value for x satisfying the restriction and the scope. b. The speaker believes that there is an agent a and a description D such that: b1. D and R & S are independent. b2. a believes that a unique entity satisfies D. b3. f #(x) is identical to one of the individuals that a considers as possible candidates for satisfying D. Point b3 is made necessary by the weak nature of identification: since different individuals may satisfy D in the different epistemic alternatives of a, one can only require that f #(y) be identical to one of them. Let us examine two major consequences of (50). First, there is no constraint on the public or private status of identification. The condition does not determine whether identification is common ground or not, whether the speaker has any belief as to its informational fate, etc. All configurations are a priori possible. This tolerance provides the leeway one needs to address examples like those in (38). Consider (38a,b). Since the virus is new, the speaker is the only epistemic agent available. She identifies the virus as the one she

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(50) UC and AC are subject to the following constraint. Let K ¼ [x : R(x) S(x)] be a DRS, where R and S are the restriction and scope properties and x is the variable introduced by UC or AC. Let K0 be the main DRS containing K and K#0 be the epistemic relativization of K0. Let f\x be the restriction of f to variables different from x and sp be the speaker. UC and AC are appropriate under an interpretation I only if I is compatible with the following condition. If K is evaluated at Æ f, w æ with respect to K#0, Æ1w z ( f(R) & f(S)) æ1 0 Æ2df #(3 f #  x f & w z ( f #(R) & f #(S)) & hbel,sp(4dadD(D ) ( f #\x(R) & f #\x(S)) & hbel,a(d!xD(x)) & dy()bel,a(D(y)) & y ¼ f #(x))))4)3 æ2.

246 Epistemic Determiners

(51) a. L’anne´e dernie`re j’ai de´couvert un certain virus non re´pertorie´ dont je n’ai parle´ a` personne ‘Last year I discovered a certain non-documented virus about which I didn’t talk to anybody’ b. Last year I discovered a certain non-documented virus about which I didn’t talk to anyone Second, scope variations are unproblematic under the present analysis. Let us reconsider Farkas’s example (40), and translate the paraphrases she proposes into the terms of (50). Wide scope readings correspond to an identification by an agent, who may be different from the speaker. Possible paraphrases are ‘The speaker knows the unicorn that John wants to catch’ or ‘Someone knows the unicorn that John wants to catch’. The intermediate scope corresponds to the fact that John is one of the agents who possesses an identifying description of the unicorn. The narrow scope corresponds to the absence of identification, which is predicted to exclude UC and AC. Finally, let us recall that UC is sensitive to differences linked with the varying nature of the nouns it combines with, namely with abstract nouns such as tristesse ‘sadness’, e´tonnement ‘surprise’ or temps ‘time’. We have addressed in Jayez and Tovena (2002) this important phenomenon often disregarded in the literature.

8 PRAGMATIC EFFECTS We finally turn to the pragmatic effects of UC and AC. First, in most cases, the existence of a previous identification is trivial. Most entities

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discovered. Presumably, she entertains some representation of the virus (e.g., its shape) which she constructed in discovering it. For her to have an independent description, we should suppose that she has constructed a different representation of the virus. This is, of course, not impossible but very unlikely because the interval between the speech time and the discovery is extremely short. By considering a larger interval, we raise the plausibility of a different representation and the status of the sentence improves. In (51a,b), the speaker describes the virus as the non-documented virus she discovered last year. In the meantime she may have developed different trains of thought about the virus, have made extensive research, etc. In short, she probably entertains different descriptions of the virus, and this assumption is sufficient to license UC and AC.

Jacques Jayez and Lucia M. Tovena 247

(52) [Context: the person who phoned is known to A and B] A – C’e´tait qui, qui m’a te´le´phone´? ‘Who called me on the telephone? ’ B – Ah, Ah! Une certaine personne. . . ‘Ah, ah! A certain person’ Martin (2005) notes that examples like (53) are infelicitous and considers the possibility of an ignorance constraint with UC. (53) [Context: the speaker wants to introduce a colleague of hers to the addressee] a.?? Je te pre´sente un certain colle`gue, que je connais depuis longtemps ‘Please, meet a certain colleague whom I have known for a long time’ b.?? Please, meet a certain colleague whom I have known for a long time We account for such examples as follows. Since the hearer meets the colleague for the first time, she cannot be the identifier. So the 18 As we saw, Farkas (2002) proposes a non-identification constraint, which is an attempt to capture the same intuition.

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we deal with in everyday life are identified by many agents under many perspectives. The role of UC and AC is to underscore that the speaker has a particular reason to mention the existence of a previous identification. Obvious motivations include reminding the hearer that the entity has a certain importance or salience, letting her know that the speaker has a certain dgree of acquaintance with it, etc. Second, our approach also takes into account the intuition that UC and AC may indicate a desire to ‘hide’ a referent by holding back its identification. This interpretation may emerge whenever the description that is supposed to identify the referent remains implicit.18 We noted in Jayez and Tovena (2002) that the extra-identification required by UC or AC sheds light on the arch use mentioned by Strawson (1950), whereby a speaker does not disclose the identity of an entity while making it manifest that the entity has been identified and letting the hearer think that the speaker and/or the hearer are/is a possible identifier. In (52) A teases B by not giving the name of the caller.

248 Epistemic Determiners preferred interpretation presents the speaker as alluding to a previous identification of the colleague. However the identifying property remains implicit and it is unclear why the speaker takes the trouble to mention the existence of this property, which does not seem to play any role in the introduction rite, hence the marginal status of (53).

9 CONCLUSION

Acknowledgements We are grateful to the reviewers and the associate editor Yael Sharvit for their stimulating and fruitful comments and criticisms. We thank Bart Geurts for his careful reading of the prefinal version.

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In this article, we have discussed a variety of epistemic determiners that exploit the possibility v. impossibility of identifying the referent of the NP they contribute to form. Several major findings have emerged from this investigation. First, contrasting un quelconque with semantically cognate FC items such as n’importe quel, we have shown that the equivalence between members of the restriction set, which is the general characteristic of FC items, can manifest itself along different dimensions. In the case of UQ, the impossibility of referring is relativized to an agent. Second, both the indefinite and the free choice components of the complex determiner un quelconque are shown to contribute to its behaviour and to affect the nature of its freechoiceness. Third, contrasting the results on un quelconque and un certain, we can observe that the epistemic sensitivity of these items cannot be reduced to ‘knowledge of the speaker’. In addition to the complication introduced by the possibility of taking different perspectives ( Jayez and Tovena 2002), there is the fact that un certain invokes a scenario structure of ‘previous acquaintance’ which may involve several agents and be independent from the speaker. Hence, the knowledge at hand is a weak form of identification. Fourth, the intuition that un certain highlights the existence of a particular identification cannot be captured by assuming a form of specificity. Specificity relies on the way of identification provided in the sentence, whereas UC and AC signal the existence of a different way. Giving up specificity opens the way to an account for the frequent use of un certain in combination with common nouns such as moment, point, etc., as pointed out in Jayez and Tovena (2002).

Jacques Jayez and Lucia M. Tovena 249 LUCIA M. TOVENA UFR Linguistique Case 7031 2, Place Jussieu 75005 Paris France [email protected]

First version received: 03.03.05 Second version received: 25.10.05 Final version accepted: 05.12.05

REFERENCES Aloni, M. (2001) Quantification under Conceptual Covers. Ph.D. dissertation Amsterdam, ILLC. Aloni, M. & van Rooij, R. (2004) ‘Free choice items and alternatives’. To appear in Proceedings of KNAW 2004. Dekker, P. (1998) ‘Speaker’s reference, description and information structure’. Journal of Semantics 15: 305–334. Farkas, D. (2002) ‘Varieties of indefinites’. Proceedings of SALT XII, 59–83. Gerbrandy, A. (1998) Bisimulations on Planet Kripke. Ph.D. dissertation, Amsterdam, ILLC. Geurts, B. (1999) Presuppositions and Pronouns. Elsevier. Amsterdam. Giannakidou, A. (2001) ‘The meaning of free choice’. Linguistics and Philosophy 34: 659–735. Gondret, P. (1976) ‘Quelques, plusieurs, certains, divers: une e´tude se´mantique’. Le Franc xais Moderne 2: 143–152. Grice, P. (1975) ‘Logic and conversation’. In P. Cole & J. Morgan (eds), Syntax and Semantics. Vol. 3, Speech Acts. Academic Press, New York, 41–58.

Grice, P. (1978) ‘Further notes on logic and conversation’. In P. Cole (eds), Syntax and Semantics. Vol. 9, Pragmatics. Academic Press, New York, 113–128. Haspelmath, M. (1997) Indefinite Pronouns. Oxford University Press. Oxford. Hawkins, J. (1991) ‘On (in)definite articles: implicatures and (un)grammaticality predictions’. Journal of Linguistics 27: 405–442. Hintikka, J. (1986) ‘The semantics of ‘‘a certain’’ ’. Linguistic Inquiry 17: 331–336. Horn, L. R. (2000) ‘Pick a theory, not just any theory’. In L. Horn & Y. Kato (eds), Negation and Polarity. Oxford University Press, Oxford, 147–192. Horn, L. R. (2000) A Natural History of Negation, 2nd edition. Stanford: CSLI Publications (originally published by Chicago University Press, 1989). Jayez, J. & Tovena, L. M. (2002) ‘Determiners and (un)certainty’. In Proceedings of SALT XII, 164–183. Jayez J. & Tovena, L. M. (2005a) ‘Freechoiceness and non individuation’. Linguistics and Philosophy 28: 1–71.

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JACQUES JAYEZ ENS-LSH 15, Parvis Rene´ Descartes BP 7000 69342 Lyon France [email protected]

250 Epistemic Determiners Levinson, S. C. (2000) Presumptive Meanings. MIT Press, Cambridge. Martin, F. (2005) ‘??Oh! Un lapin bien pre´cis’. Talk presented at Indefinites and Weak Quantifiers, Brussels, 6–8 January 2005. Russell, B. (1905) ‘On denoting’. Mind 14: 479–493. Sperber, D. & Wilson, D. 1986, Relevance: Communication and Cognition. Basil Blackwell, Oxford. Strawson, P. (1950) ‘On referring’. Mind 59: 320–344. Van de Velde, D. (2000) ‘Les inde´finis comme adjectifs’. In L. Bosveld, M. Van Peteghem, and D. Van de Velde (eds), De l’inde´termination a` la qualification. Les inde´finis. Artois Presses Universite´, Arras, 203–272. van Rooy, R. (2003) ‘Relevance and bidirectional optimality theory’. In R. Blutner and H. Zeevat (eds), Optimality Theory and Pragmatics, Palgrave MacMillan. Basingstoke and New York, 173–210. von Fintel, K. (2000) ‘Whatever’. In Proceedings of SALT X, 27–39. Zimmermann, T. E. (2000) ‘Free choice disjunction and epistemic possibility’. Natural Language Semantics 8: 255–290.

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Jayez J. & Tovena, L. M. (2005b) ‘When ‘widening’ is too narrow’. In Proceedings of 15th Amsterdam Colloquium, 131–136. Kadmon N. & Landman, F. (1993) Any. Linguistics and Philosophy 16: 353–422. Kamp, H. (1978) ‘Semantics versus pragmatics’. In F. Guenthner & S. J. Schmidt (eds), Formal Semantics and Pragmatics for Natural Language. Reidel. Dordrecht, 255–287. Kaufmann, S. (2002) ‘The presumption of settledness’. To appear in Proceedings of CLS 38. Kratzer, A. (1981) ‘The notional category of modality’. In H. Eikmeyer & H. Rieser (eds), Words, Worlds and Contexts. Amsterdam: Mouton de Gruyter, 38–74. Kratzer, A. (1998) Scope or pseudoscope? Are there wide-scope indefinites. In S. Rothstein (ed.), Events and Grammar. Dordrecht, Kluwer, 163–196. Kratzer, A. & Shimoyama, J. (2002) ‘Indeterminate pronouns: The view from Japanese’. Third Tokyo Conference on Psycholinguistics, 1–25. Krifka, M. (1991) ‘Some remarks on polarity items’. In D. Zaefferer (ed.), Semantic Universals and Universal Semantics. Groningen–Amsterdam, GRASS, 150–189.

Journal of Semantics 23: 251–279 doi:10.1093/jos/ffl003 Advance Access publication July 17, 2006

Created Objects, Coherence and Anaphora ERIC MCCREADY Department of English, Aoyama Gakuin University

Abstract

1 INTRODUCTION Many authors have discussed existence entailments resulting from verbs of creation (Dowty 1979; Parsons 1990; von Stechow 2001, i.a.), particularly as they relate to sentences in progressive aspect such as (1). The basic problem is that the existence of something that can be called a ‘house’ depends on the completion of the building event it results from. (1)

John was building a house.

The consensus therefore is that one should not build existence entailments into the semantics of creation verbs, at least not in such a way that they cannot be overridden by the progressive. For theories of discourse anaphora such as DRT (Kamp and Reyle 1993) or DPL (Groenendijk and Stokhof 1991), this boils down to the prediction that anaphora is not possible when the antecedent is an indefinite in the scope of a progressivized creation verb. Indeed, de Swart (1998) stipulates this directly in her semantics for aspectual coercion operators. And this move in fact seems right for examples like these. (2) a. Susan was writing a book. #It was long and interesting. b. John was building a house. #He moved into it. c. John was painting a picture. #It was a masterpiece. However, it has been shown that blocking anaphora from antecedents like these is not always desirable. McCready (2003) cites
The Author 2006. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected]

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This paper considers the possibility of anaphoric dependencies to the objects of creation verbs in progressive aspect. It is shown that such dependencies are possible in the right circumstances and a classification of the felicitous cases is proposed. A formal analysis making use of pragmatic information and discourse structure is given. Finally, some broader implications of the analysis are discussed.

252 Created Objects, Coherence and Anaphora examples like the following, in which although primie facie the first sentence in each of these discourses does not entail the existence of a completed house, book or whatever any more than the corresponding case in (2), anaphora is fine. (3) a. b. c. d.

John was building a house. His brother designed it. Susan is writing a book. It is coming together nicely. Jimmy is painting a picture. It might be a masterpiece. Bill is writing a program. It is in Prolog. (due to David Ahn)

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The aim of this paper is to provide a formal account of the distinction between examples like those in (2) and those in (3). The first steps toward doing so have already been taken in my earlier paper cited above, where I provided a typology of the good cases and a programmatic explanation of why they should differ from the bad ones. The present paper extends those observations and gives them a full formal treatment. The results speak to several larger issues within semantics. The first is the source of temporal information and constraints on temporal interpretation. At least two proposals can be distinguished in the literature on where temporal information comes from: according to one, temporal information is semantic and dictated by hard constraints within the grammar, while on the other, the placement of eventualities in a sentence within a larger temporal context is largely up to pragmatics. Within work concentrating on the discourse-level phenomena which are my focus, Kamp and Reyle (1993) exemplify the first approach, and Lascarides and Asher (1993) the second. The facts discussed in this paper show that, in fact, both sources of information are needed. Neither information from semantics alone or pragmatics alone is enough to induce the correct interpretations for the examples I will look at. In addition, information of both types is needed to rule out infelicitous examples. This, I think, has important consequences for the shape of theories of temporal semantics, and also for the placement of the divide between semantics and pragmatics more generally. The second is that the phenomenon I explore relates to other verb classes. Section 4 presents some related examples involving what I call verbs of choice, such as pick, choose and decide (on). These examples are similar to verbs of creation in that their object is not determinate until the event is complete, though they differ in that the object in question clearly has concrete existence before the event is complete (as well as in certain other respects). Both verb types bear parallels with intensional verbs, as discussed by Zimmermann (1993) and Moltmann (1997). In this respect, the facts I discuss relate directly to larger issues within the semantics of verbal classes.

Eric McCready 253

The paper is organized as follows. The next section summarizes the typology and discussion I gave in my earlier work, which relies on the fact that objects of creation verbs are incremental themes, for some cases, and on interactions with larger discourse processes in others. Section 3 shows how this treatment can be formalized in a theory of discourse semantics that involves a rich notion of discourse structure. Section 4 discusses some issues raised by the analysis and parallels with other verb classes, and section 5 concludes. 2 A TYPOLOGY OF (IN)COMPLETE OBJECT ANAPHORA

2.1 Existence entailments As noted above, the existence of the object of a creation verb—in concrete form at least (see below)—depends on the progress of the creation event. As the event proceeds, bits of the created object come into existence. It is possible to model this through use of a homomorphism between events and objects (Krifka 1992), which is independently necessary for verb classes such as verbs of consumption. On this sort of account, each subpart of the object affected by the event corresponds to a subpart of the event affecting it. Thus, in (4a), a part of the apple is consumed with each part of the eating event, and in (4b), a part of the house comes into existence with each part of the creation event: (4) a. eat an apple . . . b. build a house . . . This idea can be instantiated for particular verbs by assigning their objects a special thematic role, the incremental theme (I-Theme), defined in (5); this definition is essentially the one given by von Stechow (2001) and is specific to the creation verb case. Here f is an elementary embedding that holds between continuous subparts of the event and object, specifically for those subparts of the event and object which have been completed.1 (5) I-Themeðe; xÞ4df "e#½e#8e/ð f ðe#Þ8x ^ :ExistsðBEGðe#Þ; f ðe#ÞÞ ^ ExistsðENDðe#Þ; f ðe#ÞÞÞ
1 Here I use both existential quantifers and an existence predicate; introduction of the existence predicate is done only to simplify the formula and has no impact on the main point.

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I begin with a bit of background on creation verbs and the progressive. This will help when we come to consider the problem at issue. I then introduce the typology.

254 Created Objects, Coherence and Anaphora

(6) Progressive Axiom "P"x"e#[Prog(e#, ke[P(x)(e)]) > de$M e#[P(x)(e$)]] We thus get the logical form (7b) for the sentence in (7a). Because y is an I-Theme of e and e is progressivized, it is entailed that no complete object satisfying the predicate book# exists as a result of the creation event. (7) a. John was writing a book. b. de#dt[t < now ^ s(e#) ¼ t ^ Prog(e#, ke[writing#(e) ^ Agent(e, John) ^ dy[book#(y) ^ I-Theme(e, y)]])] Note, however, that this logical form does entail that some object exists.4 2

It would also be possible to define incremental themes by making use of axioms in the way done by Krifka or Pin˜o´n (2005). This way of doing things probably gives a better picture of what elements of the meaning of creation verbs are shared with other lexical classes. Still, since this issue is not my main focus, I will take the simpler, construction-specific route here. 3 Specifically, it fits well with any theory that gives the progressive a temporal component, such as those of Dowty (1979), Landman (1992), and Bonomi (1997), if combined with an analysis of English modals that also includes a temporal component. 4 This is so on the assumption that the preparatory phase (Moens and Steedman 1988) of the creation event is not part of the event itself; since no progress is made on the creation itself in the preparatory phase, no actual object is forced to correspond to it by the homomorphism. My intuitions indicate that—in general—preparatory phases are not considered when we talk about events. For instance, buying a pen is not, for me, part of writing a letter, at least when I think about letter-writing in the absence of additional context. For this reason, I will let the axioms above stand. However, it does seem to be the case that when context primes interpretation in particular ways it becomes more natural to include preparatory phases in the event proper. If this is right, then this question also speaks to the influence of pragmatics on temporal semantics; I will leave the issue here. Thanks to David Beaver and an anonymous reviewer for helping me clarify this point.

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In words, x is an I-Theme of e iff there is a function that maps every subevent of the creation to a subpart of its object, and, until the completion of each subevent, its corresponding object subpart does not exist. I will follow von Stechow in requiring this function to be a bijection.2 I will take the objects of creation verbs to be I-Themes in what follows. I will give the progressive the following semantic representation. This is a variation on the progressive semantics given in Asher (1992), which I use for concreteness; I do not think that the facts I discuss provide a way to choose between existing theories of the progressive, and my analysis is compatible with most other theories as well.3 The axiom crucially relies on the nonmonotonic conditional >. Informally, the axiom states that for any progressivized sentence S, an eventuality exists which partially realizes an eventuality of the type of S and which normally continues to an eventuality of that type. Normally e# will actually be stative, which is reflected in the DRT representations in section 3.

Eric McCready 255

2.2 Classifying the subcases At this point, we can consider the felicitous cases in (3). McCready (2003) argues for three distinct categories, organized by the object the pronoun depends on for its interpretation. The first class is made up of cases of reference to ‘partial’ objects whose existence is entailed by the combination of I-Theme and the progressive operator. In the second class, the pronoun is dependent on an abstract object, which the creation is intended to realize. In the final case, the temporal properties of modals and progressive operators induce felicity. I will discuss each type briefly in turn.

(8) a. John is building a house. It is right over there. b. Bill is painting a picture. It is on the easel. Certain predicates, like masterpiece, seem to require a complete object; such predicates are not felicitous in this first case. The reason, intuitively, is that it is not clear whether something is a masterpiece until it is finished; the artist could easily ruin the work at any point at which it is still in progress. This restriction seems to hold for the predicates in (2) as well.5 (9)

John is building a house. #It is a masterpiece.

2.2.2 Case 2: Abstract objects In cases of the second category, the pronoun is dependent on an abstract object, a target or goal. Such objects are available as one reading of created-object nominals; as McCready (2003) shows, predicates that describe properties of the 5 Ora Matushansky (p.c.) has pointed out to me, however, that the presence of adverbial already can help examples with, e.g., long significantly. The reason presumably is that in creation event size is ‘monotonic’; in general, size only increases as we keep building, and length only increases as we keep writing. These generalizations are of course often violated, but language seems to act as if they consistently hold.

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2.2.1 Case 1: Partial objects Begin with the first category. Here, the object that the pronoun depends on is partial, and is entailed to exist by I-Theme and the progressive operator: since the progressive guarantees that some portion of the progressivized event has taken place and I-Theme introduces a homomorphism between that event and its object, existence of the portion of the object corresponding to the completed part of the event is derived. This object has no known properties other than being a partial house, book, etc. Consequently, in general predicates applying to anaphoric pronouns with denotations in this class can apply to anything that has a physical existence.

256 Created Objects, Coherence and Anaphora

2.2.3 Case 3: Operator licensing The final case is the most complex. Here the temporal properties of modal operators and the progressive itself are involved in licensing. Note that (12a) contains masterpiece, which, as noted above, cannot apply to partial objects. This indicates that it in this discourse must refer to the completed picture. How can this be? (12) a. John is painting a picture. It might be a masterpiece. b. John is painting a picture. #It is a masterpiece. (13) a. John was building a house. He was working hard on it. b. John was building a house. #He worked hard on it. The answer lies in the semantics of temporal reference. As Hinrichs (1986) showed, progressivized sentences behave like statives in discourse; they overlap temporally, and reference time does not advance. Modal sentences, however, advance reference time when the modal complement is eventive (Condoravdi 2002). The result is that the complement of the modal is interpreted at a future point. (14) a. John might be sick. (present or future interpretation available) b. John might get sick. (future interpretation only) There are thus two possibilities for interpretation of a modal complement with respect to the event described by a preceding progressivized sentence: the complement can be interpreted at a time following the completion of the progressivized event, or one before it. This choice is dictated primarily by world knowledge. The interpreter will naturally select the interpretation that maximizes the coherence of the discourse.

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design to be realized can be used of them, as with (10) when used in the context of discussing a blueprint. (10) This house has two and a half bathrooms. There are a number of different predicate types that can be used in this case: predicates selecting explicitly for an abstract object (11a), ambiguous predicates (11b), and predicates referring to the medium in which something is produced (11c). (11) a. John is building a house. His brother designed it. (Bernhard Schwarz, p.c.) b. John is building a house. It is a Spanish-style villa. c. John is writing a book. It is in English. Note that in all of these cases the intentions of the creator play a role. (11b), for instance, is false if John is building something other than a villa; similarly, (11a) is false if John plans to deviate from his brother’s plans halfway through the construction.

Eric McCready 257

For (12a), this is the one on which the painting is already finished. But the other reading can also be selected, as in the following discourse. (15)

John is building a house. He might take a break for a while.

(16)

a. John was building a house. Then he painted it blue. b. John was building a house. #Then he was working hard on it.

With these basic observations in place, it is time to proceed to the formal analysis, which I will lay out in Segmented Discourse Representation Theory (SDRT; Asher and Lascarides 2003). 3 FORMAL ANALYSIS This section will present a formalization of the facts and informal analysis presented above. I will use SDRT, as it allows a straightforward treatment of the interaction of world knowledge and discourse information. As we will see, using it also yields a simple and natural

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Here again discourse coherence is key: when the house is finished, John no longer has anything to take a break from, as far as the interpreter knows. McCready (2003) does not attempt to formalize these observations, but they can be extended to an analysis making use of discourse structure and constraints on coherence. In the formal analysis to follow, I will characterize the discourse types discussed above as binary relations—Narration and Elaboration—on discourse segments, here sentences, following Mann and Thompson (1986) and Asher and Lascarides (2003), among many others. Formal definitions will be introduced later: but the essential point is that Elaboration implies temporal overlap of the events denoted by the two segments, while Narration implies temporal precedence. Since progressive operators function as statives, sequences of them will be understood as temporally overlapping and thus felicitous with Elaborations. Modals, however, can be interpreted either as shifting the interpretation time to a point within the interval at which the progressive sentence holds (Elaboration), or to one after it (Narration), and so to be compatible with both types. Additional support for this generalization comes from use of discourse particles. The particle then forces a Narration reading between the two sentences or clauses it connects. Given this fact, the account predicts that discourses without a modal in the second sentence will be felicitous if then is used, if world knowledge is compatible, but will be infelicitous when used with the progressive due to clashing temporal facts. This prediction is borne out.

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account of the interaction of modals and progressives. The presentation in this section will follow that above: I will begin with partial objects, continue to abstract objects, and close with a discussion of the modal and progressive cases. The first case does not require an appeal to the resources of SDRT; but the other two do, for reasons to be clarified below. I will use SDRT for all three for consistency. A bit of background on SDRT before we go to the analysis. In SDRT, each discourse segment is treated as a speech act which introduces a label that marks its propositional content. Through a complex reasoning process involving nonmonotonic inference over discourse content, lexical information and world knowledge, binary discourse relations are inferred as holding between these labelled speech acts. The structure inferred is an acyclic graph which puts important constraints on anaphora: informally stated, for an anaphoric expression introduced in a given discourse segment K, only discourse referents introduced in segments which are connected to K by some (sequence of ) discourse relations are available. This basic picture should be sufficient for the time being. I will introduce more details as they become necessary. I should note that, although I state the account in terms of SDRT, I think the account is compatible with most other theories of discourse structure as well. Possibilities include van den Berg and Polanyi (1996), Kehler (2001), and Webber et al. (2003), among many others. Crucially, though, the account will translate only if the particular theory of discourse structure allows discourse relations themselves to have semantic content; thus, if (for instance) in a particular theory discourse relations do nothing more than constrain anaphora and have no effect on interpretation, the account to be presented will not go through. The reason is that, on the present account, discourse relations mainly serve to model the intrusion of pragmatic reasoning on semantic content, and this won’t work if the relations themselves lack content completely. We saw above that use of the progressive with verbs of creation entails the existence of a partial object. The reason is that I-Theme entails the existence of a subpart of the progressivized event’s object. It is possible to derive this fact in a systematic way from the Krifka semantics, as we have already seen. For this sort of story to go through, however, we need to make an assumption about the progressive and how it interacts with anaphoric accessibility in a theory like DRT, on which SDRT is based. In standard DRT as presented in Kamp and Reyle (1993), the progressive is taken to simply modify an eventuality: any internal arguments associated with the verb are simply scoped outside the progressive operator, yielding representations that state, effectively, letter(x) ^ PROG(write( j, x)) for sentences like John is writing a letter

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6

The progressivized event itself is not available for anaphora, on this analysis. This seems to be right, as made clear by the following example, due to an anonymous reviewer (slightly modified). (i) John is building a house. It has taken three months (so far). Here it clearly refers to the partial house-building, i.e. the object represented by the discourse referent that tags the progressive operator.

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(abstracting away from tense). But this is clearly not what we want, for it asserts that the object being written is already a letter, as Kamp and Reyle themselves note. This approach is modified by de Swart (1998), who stipulates that internal arguments of creation verbs stay in the scope of the progressive, while all others scope out. This is empirically correct, it seems, but not very attractive theoretically. In this paper I will take a different approach. I will simply assume that the progressive is transparent to anaphora quite generally. However, the conditions associated with internal arguments remain in the scope of the progressive: this ensures that a letter that is being written is not yet a letter. On this assumption the partial object corresponding to the internal argument of the progressivized verb is always available for later anaphors, though nothing more is known about it (at the predication time) than that it exists. How should we state this transparency in DRT? De Swart (1998) assumes that the progressive introduces a subordinate DRS K that contains the eventuality description, and that internal arguments of extensional verbs introduce discourse referents and conditions into the DRS that immediately contains K. She further assumes that internal arguments of creation verbs introduce their discourse referents and conditions inside K, as already mentioned in section 1. I will make use of something like this account, but modify it in two ways. First, I will assume that the conditions associated with a particular internal argument are always introduced in the subordinate DRS modified by the progressive. In the case of extensional verbs, the semantics of the verb itself will guarantee that these conditions are verified by the embedding function for the entire DRS (as shown in detail by McCready 2003); in the case of verbs of creation, they will not be realized until the completion of the creation event, as desired. We need not assume the ‘split analysis’ of de Swart to make the semantics come out right. I will deviate further from de Swart by assuming that the discourse referent associated with internal arguments is always introduced outside the scope of the progressive. This move ensures that the referent of the progressive object is always available to later anaphors. But this discourse referent is associated with further conditions only within the scope of the progressive.6 The

260 Created Objects, Coherence and Anaphora

(17) a. John is married. #She is a nice person. (Heim 1988) b. Nine of the ten balls are in the bag. #It is under the couch. (Barbara Partee; cited in Roberts 1989) Anaphora here is not very good, but certainly the existence of an object is entailed. Here we have a real conflict: allowing entailments to introduce discourse referents gives the right results in the progressive creation case, but exactly the wrong ones for the examples in (17). It is not clear how this problem should be solved or even what kind of solution one would want. For the present, I restrict myself to providing a way to get discourse referents for the progressive case as discussed above (and in the Appendix). A progressivized creation sentence like (18a) will, on this analysis, be represented as in (18b). Here o indicates temporal overlap. Note that this representation is labelled by a tag p: this indicates that it is an individual SDRS, which will be embedded within a larger SDRS in an actual speech situation. The reader familiar with SDRT will note that I deviate from standard SDRT practice by representing temporal information independently of discourse relations, which entail temporal relations and are usually the only means within SDRT of representing temporal content. The reasons for this will become clear 7

Thanks to a reviewer for helpful comments on this approach.

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particular construction rule I assume (a modified version of de Swart’s) is given in Appendix A. One might try other ways of modelling this transparency, of course. One possibility might be to introduce a discourse referent in the global DRS via a meaning postulate, and connect it to the discourse referent in the scope of the progressive by a subpart relation; thus, x in the global DRS would relate to y in the scope of the progressive by a condition x 8 y, also in the scope of the progressive. This way of doing things is not completely satisfactory for various reasons: we would need a similar condition for events, and also the postulate actually introduces a potentially infinite series of incomplete objects, which is not what we want.7 One might also think that since I-Theme itself entails the existence of a partial object, there is no need to make any special assumptions about how discourse referents are introduced. I agree that this is what should happen, and in fact the derivation in McCready (2003) summarized above was meant to show exactly this. There is a problem, though: this kind of entailment alone is not enough to introduce discourse referents in theories like DRT, as shown by these well-known examples.

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below. Note also that I have represented the progressive eventuality as s, following normal DRT practice. As a reviewer points out, there is an apparent conflict here with the Progressive Axiom in (6) in that the axiom makes use of e, a type (ev) ordinarily associated with events, not states; this is not a problem if we read e as the type of eventualities, which includes statives.

Two things should be noted about this representation. First, the object that over there is predicated of corresponds to the future house, but is not itself anywhere asserted to be a house (at the time of s). All that’s known about the object denoted by x (using ‘denoted’ loosely) is that it exists in the actual world. The second thing to note, however, is that if the natural course of events is uninterrupted in Dowty’s sense, this object will become a house; this is guaranteed by the semantics of the progressive and the condition I-Theme(e, x) in the scope of the progressive.

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Now, if the continuing predicate is of the right type, it will be able to apply to the existing object x, and anaphora will turn out to be good, as illustrated in (19).

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8 Unless the object contains a variable which would become unbound were it scoped out; see Asher (1993) for extensive discussion of these cases. 9 Pin˜o´n also introduces templates for events and times, but I will not need them here. 10 Pin˜o´n does assume that templates must be physically located, in the sense that he requires them to be derivatively instantiated, meaning that they must be represented by some physical object in the world. This object could be something like a blueprint, or simply an image in the brain of a designer. The point for us is that templates need not be instantiated in the sense defined in the main text immediately below. 11 This notion corresponds somewhat to the idea of realization in Kamp (n.d.), but, unlike realization (as formulated there), does not depend directly on the presence of an attitude.

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However, since the object is partial, predicates like masterpiece cannot apply to it. Thus this representation captures the intuitive facts. Next I will discuss anaphora to the abstract object reading of the indefinite. We first must decide what kind of object the abstract object is. Intuitively it is a kind of template: something like a blueprint, in the case of a house, or a plot sketch, for a novel, or an idea about structure and melody, in the case of a song or symphony. It is not completely clear how best to formalize this intuition. There are at least two options: enriching the ontology with a special type for templates, or making use of some sort of abstract object. I am not deeply committed to either, but I need to choose one in order to make concrete the analysis of my main concern, the influence of pragmatics on the selection of particular readings for anaphors. In earlier versions of this paper I took the first approach, analysing these objects to be properties; doing so had the advantage that abstract objects have been analyzed as taking widest scope within DRT (Asher 1993),8 which immediately puts them out of the scope of the progressive and so available for later anaphors without having to worry about the effect of I-Theme. But there are problems with this, most notably that this analysis predicts verbs of creation to behave like ‘other’ intensional verbs (e.g., want or seek, at least on one analysis (Zimmermann 1993)) in terms of entailments; but it is not clear that they really do. This sort of analysis also runs into problems with the definition of I-Theme, as one might expect; specifically, since I-Theme is designed for objects of type e it doesn’t apply to properties at all. Therefore I will use a separate type for the abstract objects in question in this paper. I will follow Pin˜o´n (2005). Pin˜o´n introduces a distinct type m for templates of individuals, used along with the more standard DRT inventory of ordinary individuals, times, and eventualities.9 These objects are meant to exist independently of the creation of a physical object that actually realizes them.10 I will use the convention of writing variables of type m in boldface: x. We will also make use of a relation of instantiation: x 8[ x iff x is constructed according to the template x.11

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The instantiation relation is irreflexive, asymmetric and intransitive, and further must satisfy the following axiom. Here 8 is the subpart relation on individuals and 8# is the corresponding relation on individual templates. (20)

Mapping from Templates to Instantiations "a"m"m#[a 8 m ^ m# 8#[m) / db[b 8 a ^ b 8 m#]]

(21)

a. The house is near the center and was designed by John’s brother. b. John is building a house. It is near the center and his brother designed it.

In (21a) we see that the house is predicated of by two VPs: is near the center, which requires the concrete object reading (as made clear by the fact that templates don’t have a location) and was designed by his brother, which needs the template reading. (21b) shows that both readings are available simultaneously in the antecedent of the two pronouns, each of which selects for a different reading. Thus the situation looks more like a case of polysemy than one of actual ambiguity. True cases of ambiguity do not allow for this sort of reading, as shown by (22). (22)

a. The bank is where I left my canoe and has a lot of money in its basement. b. John went to the bank. It is where I left my canoe and it has a lot of money in its basement.

If these sentences are to be interpretable at all, we must understand bank as a financial bank where I, for some reason, left my canoe. The intended interpretation corresponding to (21), on which I left my canoe at the riverbank and there is money at the financial bank, is 12

(21b) is due to an anonymous reviewer.

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We now have a representation for our abstract objects (henceforth I will simply call them templates). Should we take nominals denoting created objects to be ambiguous between an object-oriented reading and a template-oriented reading, so that there are two distinct semantic objects (e.g. book1 and book2)? Presumably not. First, such nominals do not behave like ordinary ambiguous expressions, in that they allow for copredication on their two readings (Pustejovsky 1995; Asher and Pustejovsky 2005). Copredications are situations in which multiple predicates apply to the same object; we find that created object nominals allow for predication of both their readings simultaneously. Consider the examples in (21).12

264 Created Objects, Coherence and Anaphora simply not available. This is a first indicator that ambiguity is not the right way to go. The second problem for an ambiguity account is deeper. The issue is that—generally speaking—when one creates something one probably has something in mind that is the intended result. This ‘something in mind’ is a template, or (in the case of building construction and the like) the derived instantiation of a template. This is made clear by considering sentences like the following. (23) John built the house his brother designed.

d

d

(24) Dot Exploitation If both / and w take a discourse referent x as an argument, where / types x as type t1 and w restricts x to type t1 t2, then d

13 Although examples like (21) provide evidence for a dot object treatment, giving a formal derivation of them in type theory is beyond the scope of this paper. It requires a detailed exploration of the logic of the type composition logic of Generative Lexicon theory. See Asher and Pustejovsky (2005) for an account. In particular, the discussion of the examples in their (55) (p. 37) as they relate to the Coordinate d-Introduction Rule is relevant.

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Here John is not just piling bricks on mortar; he is also working to realize his brother’s template. This is also, in a sense, a case of copredication. We would be in error to divorce the two readings completely. I propose to make use of dot objects, objects of complex type, as a way to derive these readings. Within Generative Lexicon theory (Pustejovsky 1995), dot objects have been used extensively to account for polysemous expressions. Dot objects have complex types consisting of two (possibly incompatible) consistuent types. In the case at hand, the dot type is formed from the two types e and m, yielding type e m. Particular predications then select for one of these two types, or for the more general dot object; with this, a fairly general account of polysemous expressions becomes available. On this account, there is nothing wrong with simultaneously using predications that select for different sorts: each predicate simply picks out a different part of the dot object.13 It should be noted to avoid confusion that dot objects, as types, are not represented in the SDRS as such. They come into play only in the interpretation. However, they do have a DR-theoretic reflex, which is derived by the rule of Dot Exploitation from Asher and Lascarides (2001). O-Elab is essentially a subtype relation (presumably meant to abbreviate ‘Object Elaboration’). O-Elab(x,y) states that the type of y is the same as one coordinate of the -type x.

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a new discourse referent v of type t1 is introduced such that O-Elab(x,[v) and x is uniformly replaced by v in /. (Asher and Lascarides 2001)

d

14

Asher and Pustejovsky’s (2005) rule of d-Exploitation would serve equally well in this context. I use Dot Exploitation instead for expository reasons, as it is considerably simpler. 15 I will not provide a semantics for this latter reading in the present paper, since it is orthagonal to my main point, and not at all trivial. This project will have to be left to a later time. See, however, section 5 for some discussion, and Pin˜o´n (2005) for an extensive treatment rom a different perspective.

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This rule allows for the cases of copredication by rewriting the variables within the DRS-conditions when they have incompatible types. Dot Exploitation tells us to replace the dot type with one of its subtypes when we have a type conflict. I will make use of this rule in what follows.14 On this analysis, verbs of creation are ambiguous, while nominals denoting created objects are polysemous. Build, for instance, has a reading where it describes the building of an actual house; here it takes an object of type e, but on the reading on which it describes the realization of an abstract object, it must take an object of dot object type itself.15 House is a dot object of type e m; when combined with a verb like design, which selects for an object of type m, Dot Exploitation will allow the predication to go through. Now we are ready to return to the analysis of anaphora. Consider again our familiar example (11). The representation of the first sentence is identical to what we saw in (18). Addition of the second sentence yields the SDRS in (25b).

266 Created Objects, Coherence and Anaphora The predicate design selects for an object of type m, a template. The discourse referent x is a dot object of type e m, so it can serve as antecedent after Dot Exploitation is applied in order to derive a new discourse referent y from x, that is related to it via O-Elab. We now have the desired interpretation and have also avoided type clashes. There is still an issue here, however. What is the predication time of e#? The facts about the progressive initially tell us that e#[o s should hold. However, this is incompatible with world knowledge about the ‘realization verb’ reading of build, on which the abstract object being realized must exist before the time building event. This observation about world knowledge can be spelled out more precisely in a system like SDRT (Asher and Lascarides 2003), which makes crucial use of rhetorical connections between utterances to explain other semantic phenomena. In this system, defeasible axioms derived from world knowledge trigger inference of twoplace rhetorical relations between discourse constituents. These relations then influence the semantic interpretation given to the discourse. In this framework, the intuition above can be captured using an axiom on world knowledge, which states that if two discourse segments are being connected, one describing a house being built and the other describing the design of the same house, the event described by the second segment is a precondition for the occurrence of the first. Here, me picks out the main eventuality of a discourse segment, while k indicates the discourse structure of which the constituent a is a part, and to which b must be connected via some rhetorical relation. Here > is a nonmonotonic ‘normality’ conditional (for details, see Asher and Lascarides 2003), and the condition ?(a, b, k) indicates that a and b are connected by some rhetorical relation ? in the larger discourse structure k. d

The following axiom describes one of the consequences of Precondition, that the event described by the segment which is a precondition temporally precedes the event described by the segment to which it is the precondition (a represents temporal succession). 0 indicates a nondefeasible consequence in the logic of discourse interpretation. (27) Temporal Consequence of Precondition Precondition(a, b) 0 me(b) 6 me(a)) Now the correct representation for (11) may be derived. The axiom (26) will apply, and then the Axiom on Precondition will cause the second sentence to be interpreted as occurring before the first, giving the following final representation for (11).

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(26) ?(a, b, k) ^ (building, x, y, me(a)) ^ (designing, z, y, me(b)) > Precondition(a, b)

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It should be noticed here that the object that work-hard-on is predicated of in the subDRS introduced by the second progressive 16 I omit this because Elaboration simply states that there is temporal overlap, as seen in (33a): this does no more than duplicate what the progressive does in this particular case.

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Let’s now move on to the cases involving the progressive and modals. I begin with the progressive case. Hinrichs tells us that two stative sentences in sequence will be taken to overlap temporally. As the progressive is stative, two successive progressive sentences will instantiate this: they will overlap, and reference time will not advance. This will give us the following (standard) DRT representation for a felicitous discourse where the anaphora licenser is a progressive operator. Note that, in the full SDRT system that I am using, all information in the DRS in (29b) will be retained, but the content of the two segments will be separated into distinct speech acts between which the discourse relation Elaboration holds.16

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The condition t < t# indicates that the modal complement must be interpreted at a time no earlier than the present moment (the reference time). What though is the meaning of AT (t#,[/)? This part of the analysis is taken directly from Condoravdi (2002). The formula can be unpacked as follows.  de½uðeÞ ^ sðeÞ4 t
if u is eventive ð31Þ ATðt; uÞ ¼ de½uðeÞ ^ sðeÞ o t
if u is stative (Condoravdi 2002) As seen in (31), AT describes conditions on the temporal location of eventualities of various types. According to AT, the eventuality described 17

See also Asher (2002) for a related analysis that does not incorporate Condoravdi’s theory.

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operator is y, which is dependent on the partial object whose existence is entailed by the event-object homomorphism. Intuitively, this is correct; if the house was already complete, John would no longer be working on it. The partial object is available because of the fact that the progressive doesn’t advance narrative time, causing the two progressivized states to temporally overlap, as stated by the condition s o s#. In the modal case, however, the time of interpretation advances, and a completed object becomes available, as shown in section 2. I capture this fact using an adaptation of the system of Condoravdi (2002). First, I assume that the modal auxiliary induces a binary relation on SDRSs, which is interpeted by having the first SDRS act as the restrictor of the second. Essentially, this is a reconstruction within SDRTof the analyses of modality of Geurts (1995) and Frank (1997). This line of analysis is partly intended as a DRT reinterpretation of Kratzer’s (1981) theory of modals, in which the modal is analyzed as having a covert restrictor. On the analysis here, this restrictor is provided by the first argument of the R) relation.17 I also assume that the modal auxiliary introduces certain conditions into the SDRS which is the second argument of the modal relation. Thus, the modalized sentence It might be that / receives the following form:

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d

Consequence of R) R) ða; bÞ0)Kb

We can now make precise the earlier observations about the reference time of modal complements. As noted, the condition t < t# allows for overlap with the utterance time, and also for a future interpretation. Either reading will be available for stative complements, for the state is required only to hold at the speech time or later by the condition s(e) o t. However, the condition s(e) 4 t in the interpretation of the predicate AT requires the eventuality to be completely contained within t#, which will rule out the simultaneous reading. Now we are in a position to consider the representation that the modal cases of continuation will receive. Here is one with its associated SDRS (though this is a first approximation, which will be revised slightly below):

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by modalized stative sentences must overlap with the utterance time, while the eventuality described by event-denoting sentences must be included in the utterance time. However, such inclusion is impossible if t denotes the instant at which the sentence is uttered; for both t < t# and s(e) 4 t to hold, t must be interpreted as an interval beginning at the utterance time and extending into the future (for an indeterminate distance which, at minimum, is large enough to hold the entire runtime of the event /(e)). One thing remains to do. We have not yet guaranteed a modal meaning for the second element of R). I introduce the following condition on the relation, which states that the content of the second argument of the relation, written Kb , is modified by a possibility modal. We now have a Frank/Kratzer-style analysis within SDRT.

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For the discourse we are currently considering, it is clear that Narration is the relevant discourse relation. Now we need to axiomatize the bit of world knowledge that leads us to that conclusion. The following axiom will do the job:19 (34) ?(a,b,k) ^ (building,x,y,me(a)) ^ (painting,x,y,me(b)) > Narration(a,b) This axiom states that for any two discourse segments, if the main event of the first one is a building of an object and the main event of the second is a painting of that object, then Narration normally holds between the two segments. This seems plausible. With this axiom, we will be able to infer Narration, as needed. If Narration holds between these two constituents, further, it will be required that the first temporally precede the second (by Spatiotemporal Consequence of 18

Though, of course, it is possible to paint an unfinished house: it is just not very smart. The predications of the main events of a and b here have nothing to do with the progressive; they simply indicate the type of the event. 19

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Here y has been equated with x. Although everything that has been said up to now is consistent with the selection of x as antecedent, there is a point that still remains to be clarified about doing so. Our knowledge of the world tells us that painting houses is usually done after their construction is complete, and this isn’t consistent with painting x on its interpretation as unfinished object, much less the abstract object version.18 But we have another option. Since the modal is evaluated at a time later than the utterance time, we can resolve the time of evaluation to a time after the completion of the event of creation. At this point, the discourse referent x will become identical to the completed object y because of the event-object homomorphism, and no inconsistency willl result from selection of x. But how to guarantee that the temporal advancement induced by the modal moves forward to a point at which the creation event is complete? Here too we can make use of discourse structure. For the case in question, two rhetorical relations may hold between the two sentences in addition to the modal relation: Narration and Elaboration. Narration implies that the eventualities described by the sentences appear in narrative sequence, while Elaboration implies temporal overlap. This can be stated as follows, following Asher and Lascarides (2003) (where, again, me picks out the ‘main eventuality’ of a discourse segment): (33) a. Temporal Consequence of Elaboration Elaboration(a, b) 0 Part-of(meb, mea) b. Spatiotemporal Consequence of Narration Narration(a, b) 0 overlap(prestate(meb), poststate(mea))

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Narration). Thus, we can derive the correct reading. The final SDRS for this example will be the following:

(36)

?(a,b,k) ^ (building,x,y,me(a)) ^ (work-hard-on, x, y, me(b)) > Elaboration(a, b)

With this axiom, the SDRS for the progressive-licensed example considered above becomes the following:

Again, this is precisely the representation we want.

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Now that the necessary tools have been introduced, it is time to update our analysis of discourses licensed by the progressive to include discourse relations. Before we can infer the correct representation, however, we need an additional axiom on world knowledge to capture the intuition that putting finishing touches on a building is generally part of the building event and so elaborates on it:

272 Created Objects, Coherence and Anaphora Above we’ve seen felicitous examples of both types. One important fact should be noted about these discourses. In them, adding the information about rhetorical relations to the SDRT representation did not conflict with the temporal information given by the semantics, and so the SDRSs were coherent and thus felicitious. But this is not always the case. To see this, consider the following two discourses, which were discussed in the previous section. There it was stated that the reason for their infelicity was a conflict between world knowledge and temporal information.

We are now in a position to make this precise. Let’s begin with (38). In our system, it will be represented as follows:

Here, the temporal semantics of the progressive operators dictate that the two eventualities labelled by p and p# must overlap. However, Narration is inferred through the axiom in (34), and the semantics for Narration entail that me(p) a me(p#). Because of this a straightforward contradiction is derived and the discourse is incoherent, just in case the underspecified condition y ¼ ? is resolved to x. In other words, the discourse is unproblematic if the pronoun is not taken to refer to the unfinished house, which accords with intuitions. However, on the anaphorically dependent reading, its infelicity is accounted for.

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(38) John is building a house. #He is painting it blue. (39) John is building a house. #He might put the finishing touches on it.

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The analysis of (39) exhibits precisely the converse pattern. With the axiom previously defined in (36), we can derive the following representation for (39):

4 DISCUSSION There are two points in this analysis that bear a bit of discussion. First, I have deviated from ordinary SDRT practice in giving an overt representation to the temporal conditions on standard narrative discourse discussed by Hinrichs and Kamp and Reyle. Within SDRT, information about the temporal relation between discourse segments is standardly taken to derive directly, and exclusively, from the

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This SDRS tells us the following about the temporal structure of the situation described. First, from the semantics of Elaboration we get me(p) o me(p#), where me(p#) is the event of putting the finishing touches on the house. Now, the semantics for the modal and of the predicate AT tells us that put-ft-on( j,y) holds at a time t# that is fully distinct from the speech time t at which the progressive holds. But this contradicts the semantics of Elaboration if y is equated to the referent x, for since t# is subsequent to the completion of the progressivized event, temporal overlap will be impossible. Consequently, the discourse is incoherent if the anaphoric pronoun is taken to be dependent on the (partial) house.

274 Created Objects, Coherence and Anaphora discourse relations that hold between them. The reason is examples like (42). Here, Max’s falling is ordinarily taken to result from John’s pushing; this means that me(b) must precede me(a). Standard DRT would predict the opposite. This is one of the original motivations for introducing discourse relations into the formalism. (42) Max fell (a). John pushed him (b).

(43) a. John picked a straw. It was the long one. b. John is picking a straw. #It is the long one. (Bernhard Schwarz) While the objects of creation verbs are incomplete until the event described finishes, the objects of verbs of choice are complete, but their identity is indeterminate. Until a choice is made, what object will be chosen cannot be ascertained (barring rigged games and the like). For verbs like this, the class of predicates that cannot be used in later sentences is different for that of creation verbs. Whereas in the creation verb case the infelicitous predicates were those that didn’t allow partial objects, for indeterminate verbs the problem will lie in verbs that select for a specific object, as in (43b) and (44). (44) John is deciding on an answer (to the question). #It is wrong.

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The reason for representing this information should be clear. Without doing so, we would be unable to derive the temporal interpretations we need for the discourses at issue. For, if this temporal information was not present, no contradiction would result in the bad cases, and thus no infelicity. This analysis therefore suggests that, at least in some cases, temporal information should not be derived exclusively from rhetorical structure, but should instead be represented in the SDRS as well. Secondly, a final comment should be made about the infelicitous discourses. I have marked them as pragmatically infelicitous (using a ‘#’). But, as a reviewer points out, their infelicity is only commonsense: it is not impossible for someone to paint an unfinished house, only inefficient and uncommon. The use of default conditionals in the axioms that are used to derive this infelicity reflects this situation. Before closing this section, I would like to point out another class of verbs that are temporally opaque in a different way. These verbs also don’t allow anaphora to their objects when progressivized. These are verbs like pick, choose and decide. I will call this class verbs of choice; they are a subclass of the ‘verbs of obtaining’ discussed by Levin (1993).

Eric McCready 275

In both (44) and (43), the infelicity comes out of the fact that the object John chooses is not yet determinate. In (44), John may still pick the (or some) right answer, so wrong does not necessarily apply; this is a simple selectional restriction, as an indeterminate answer cannot (yet) be wrong. Likewise, in (43b), there is only one longest straw, but until John has finished picking, it cannot be known whether that will be the straw he picks. The above suggests that predicates applying to the entire group of objects which are being picked from will be felicitous, for no matter what object is selected, it will verify the predicate. (45) seems to provide some support for this idea: John is picking a straw. It is in Bill’s hand.

It is also possible to license anaphoric dependencies using modals with verbs of choice, as in (46). (46)

John is picking a straw. It might be the long one.

The reason is clear, given our discussion of the creation verb case: use of might allows the evaluation time of the modal complement to advance to a point at which the straw has already been picked and its identity is determinate. The resultative verbs of Moltmann (1997) also seem to have some of the properties in question. Moltmann characterizes this class as ‘verbs which imply that, as a result of the event described by the verb, some entity acquires the property conveyed by the complement NP’ (Moltmann 1997: 45). Some examples of this class are appoint and hire. Moltmann also mentions choose as an instance of this class, which suggests that there is some overlap between resultative verbs and my verbs of choice. To see that the verbs of choice are not a subclass of the resultatives, note that pick, for instance, is certainly not resultative, in that John picked a straw does not imply that any individual acquired the property of being a straw.20 Finally, let me mention another possible analysis. On an E-type account of anaphora, the infelicity of anaphora here might be explained in terms of the presuppositions of definite descriptions. For use of a definite to be felicitious, it must refer to a unique object existing in 20

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There are actually some examples in which this generalization doesn’t hold, like this one: John picked the winner.

(David Beaver, p.c.)

Here John’s picking does result in the selected individual becoming the winner, at least on one reading. At present I do not know exactly why this example differs from the straw case, but presumably it has got something to do with the particular predicate involved.

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276 Created Objects, Coherence and Anaphora the model. Seen in this light, the facts about these two kinds of verbs (when progressivized) can be understood as presupposition violations. In the case of creation verbs, the existence presupposition is violated, for no object yet exists; with pick-type indeterminate verbs, the uniqueness presupposition is violated, because there isn’t yet any unique object that satisfies the description. I did not take this route here in part because of my decision to make use of SDRT, which assumes a dynamic account of anaphora; still, I think the ideas behind the analysis I have given are also compatible with an E-type approach.

In this paper I began by summarizing my earlier (2003) characterization of the semantic characteristics of indefinite objects of creation verbs in the progressive. I went on to provide a formal analysis within SDRT; the result of this analysis proved to be extendable to anaphora involving the objects of verbs of choice under the progressive. The analysis has the consequence that temporal content must be given a semantic representation but, at the same time, be induced by pragmatic reasoning (in the present case, by discourse relations). If correct, this has significant implications for the structure of theories of temporal semantics. Further, I suggested that verbs of creation can be related to what I called verbs of choice, and both to the larger class of intensional verbs, though neither correspondence is complete. It seems worthwhile to further explore the issues raised by these comparisons, for it seems likely that a better understanding of the points these verb types have in common with, and the points that are distinct from, more wellunderstood classes of intensional verbs would deepen our understanding of modally and temporally intensional verbs. Several issues have been left untouched, however. First, the exact relationship between the ‘creation reading’ and the ‘realization reading’ of creation verbs remains to be discussed in detail. It seems that in general when something is created it is made after some sort of template, or simply to realize a plan. The axiom on instantiation in (20) guarantees that any partial object partially realizes a plan; this goes some way toward clarifying the relation between the two, but is certainly not exhaustive, especially when one considers other kinds of verbs. I think some additional light would be shed on the subject by working out a detailed theory of the application of dot objects in the creation verb case; more generally, it is interesting to consider the sort of connections that can hold between the different aspects of a dot

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5 SUMMING UP

Eric McCready 277

Acknowledgements I would like to thank Nicholas Asher, David Beaver, Christopher Pin˜o´n, and Bernhard Schwarz for extensive discussions on this topic. Thanks also go to David Ahn, Pascal Denis, Bart Geurts, Hans Kamp, Alexis Palmer, Brian Reese, Carlota Smith, Linton Wang, audiences at WCCFL 22, CLS 39, the Workshop on Existence in Nancy, the University of Texas at Austin, and Osaka University. I would also like to thank the two anonymous reviewers for this journal for extremely useful and detailed comments. This research was supported in part by Japan Society for the Promotion of Science Grant #P05014.

APPENDIX: CONSTRUCTION RULE FOR THE PROGRESSIVE This rule is stated following de Swart (1998: 378–379). De Swart, however, does not make her assumptions about introduction of internal argument discourse referents explicit in her construction rule, which I will attempt do do here. (48)

Given a progressive sentence of the form Prog(S): a. Introduce in UK a new discourse referent s. b. Introduce in ConK: s : PROGð K1 Þ

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object. Second, much work remains to be done on characterizing the various kinds of predicates that can apply to unfinished and abstract objects. I gave a preliminary survey above, but a more systematic approach with an eye to explanation rather than description needs to be taken to the data. Another predication-related issue involves the contribution of temporal adverbials (already mentioned in footnote 5). Consider the following minimal pair (due to Ora Matushansky). (47) a. John was building a house. #It was quite large. b. John was building a house. It was already quite large. Already seems to make the discourse perfectly felicitous. Intuitively, it allows us to evaluate the size of the partial house at the present moment, while at the same time eliminating the inconsistency that results from trying to apply the predicate large, which is interpreted most naturally as predicating the house in its completed state. I speculate that already allows the unfinished house to be packaged as a finished object for the purposes of predication. But this issue is also one that must be left for future work.

278 Created Objects, Coherence and Anaphora c. Introduce in UK1 a new discourse referent e. d. Introduce in ConK1 : e: e:S e. For any internal argument NP of S : a. Introduce in UK a new discourse referent x. b. Introduce in ConK1 a condition of the form P(x), where P is the property conveyed by NP. Received: 16.09.05 Revised version received: 21.12.05 Final version received: 18.05.06

REFERENCES Asher, N. (1992) ‘A default, truthconditional semantics for the progressive’. Linguistics and Philosophy 15:463–508. Asher, N. (1993) Reference to Abstract Objects in Discourse. Kluwer Reidel, Dordrecht. Asher, N. (2002) ‘Modality, quantification and discourse structure’. Paper presented at In the Mood, Johann Wolfgang von Goethe-Universita¨t Frankfurt am Main. Asher, N. & Lascarides, A. (2001) ‘Indirect speech acts’. Synthese 128: 183–228. Asher, N. & Lascarides, A. (2003) Logics of Conversation. Cambridge University Press. Asher, N. & Pustejovsky, J. (2005) ‘Word meaning and commonsense metaphysics’. Ms., UT-Austin and Brandeis University. Available from Semantics Archive.

Bonomi, A. (1997) The progressive and the structure of events. Journal of Semantics 14:173–205. Condoravdi, C. (2002) Temporal interpretation of modals. In D. Beaver, L. C. Martinez, B. Clark & S. Kaufmann (eds), The Construction of Meaning. CSLI Publications. Stanford. de Swart, H. (1998) ‘Aspect shift and coercion’. Natural Language and Linguistic Theory 16:347–85. Dowty, D. R. (1979) Word Meaning and Montague Grammar: The Semantics of Verbs and Times in Generative Semantics and Montague’s PTQ. Number 7 in Studies in Linguistics and Philosophy. Kluwer. Dordrecht. Frank, A. (1997) Context Dependence in Modal Constructions. Ph.D. thesis, University of Stuttgart. Geurts, B. (1995) Presupposing. Ph.D. thesis, University of Stuttgart.

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ERIC McCREADY Department of English Aoyama Gakuin University 4-4-25 Shibuya Shibuya-ku Tokyo-to 150-8366 e-mail: [email protected]

Eric McCready 279 Groenendijk, J. & Stokhof, M. (1991) ‘Dynamic predicate logic’. Linguistics and Philosophy 14:39–100. Heim, I. (1988) The Semantics of Definite and Indefinite Noun Phrases. Outstanding dissertations in linguistics. Garland. New York. 1982 doctoral dissertation. Hinrichs, E. (1986) ‘Temporal anaphora in discourses of English’. Linguistics and Philosophy 9:63–82.

Kamp, H. & Reyle, U. (1993) From Discourse to Logic. Kluwer. Dordrecht, Reidel. Kehler, A. (2001) Coherence, Reference and the Theory of Grammar. CSLI Publications. Stanford, CA. Krifka, M. (1992) ‘Thematic relations as links between nominal reference and event domains’. In I. Sag & A. Szabolcsi (eds), Lexical Matters. CSLI Publications. Stanford, CA. Landman, F. (1992) ‘The progressive’. Natural Language Semantics 1:1–32. Lascarides, A. & Asher, N. (1993) ‘Temporal interpretation, discourse relations and commonsense entailment’. Linguistics and Philosophy 16: 437–493. Levin, B. (1993) English Verb Classes and Alternations. University of Chicago Press. Mann, W. & Thompson, S. (1986) ‘Relational propositions in discourse’. Discourse Processes 9:57–90.

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Kamp, H. n.d. ‘Stechow on creation verbs: Some comments from a DR-theoretical perspective’. MS, Universita¨t Stuttgart.

McCready, E. (2003) ‘Anaphora and (un)finished objects’. In Proceedings of WCCFL 22. Cascadilla Press. Moens, M. & Steedman, M. (1988) ‘Temporal ontology and temporal reference’. Computational Linguistics 14:15–28. Moltmann, F. (1997) ‘Intensional verbs and quantifiers’. Natural Language Semantics 5:1–52. Parsons, T. (1990) Events in the Semantics of English. MIT Press. Pin˜o´n, C. (2005) ‘Verbs of creation’. To appear 2007 in Event Structures in Linguistic Form and Intepretation. Mouton de Gruyter. Pustejovsky, J. (1995) The Generative Lexicon. MIT Press. Cambridge, MA. Roberts, C. (1989) ‘Modal subordination and pronominal anaphora in discourse’. Linguistics and Philosophy 12:683–721. van den Berg, M. & Polanyi, L. (1996) ‘Discourse structure and discourse contexts’. In P. Dekker & M. Stokhof (eds), Proceedings of the Tenth Amsterdam Colloquium. von Stechow, A. (2001) ‘Temporally opaque arguments in verbs of creation’. In C. Cecchetto, G. Chierchia & M. T. Guasti (eds), Semantic Interfaces: Reference, Anaphora and Aspect. CSLI Publications. Stanford, CA. Webber, B., Stone, M., Joshi, A. & Knott, A. (2003) ‘Anaphora and discourse structure’. Computational Linguistics 29:545–588. Zimmermann, T. (1993) ‘On the proper treatment of opacity in certain verbs’. Natural Language Semantics 1: 149–179.

Journal of Semantics 23: 281–314 doi:10.1093/jos/ffl005

Scopal Independence: A Note on Branching and Wide Scope Readings of Indefinites and Disjunctions PHILIPPE SCHLENKER UCLA & Institut Jean-Nicod

Hintikka claimed in the 1970s that indefinites and disjunctions give rise to ‘branching readings’ that can only be handled by a ‘game-theoretic’ semantics as expressive as a logic with (a limited form of) quantification over Skolem functions. Due to empirical and methodological difficulties, the issue was left unresolved in the linguistic literature. Independently, however, it was discovered in the 1980s that, contrary to other quantifiers, indefinites may scope out of syntactic islands. We claim that branching readings and the island-escaping behaviour of indefinites are two sides of the same coin: when the latter problem is considered in full generality, a mechanism of ‘functional quantification’ (Winter 2004) must be postulated which is strictly more expressive than Hintikka’s, and which predicts that his branching readings are indeed real, although his own solution was insufficiently general. Furthermore, we suggest that, as Hintikka had seen, disjunctions share the behaviour of indefinites, both with respect to island-escaping behaviour and (probably) branching readings. The functional analysis can thus naturally be extended to them.

1 INTRODUCTION On two occasions in the recent history of semantics, indefinites were taken to pose a challenge to standard theories of scope. First, in the early 1970s, the philosopher Jaakko Hintikka claimed that indefinites interact scopally with universal quantifiers so as to yield ‘branching’ readings which cannot be captured within the ordinary semantics of first-order logic (e.g. Hintikka 1974). By contrast, he claimed, these readings are naturally explained if a game-theoretic semantics is adopted. As it turns out, Hintikka’s game-theoretic semantics can itself be translated into a fragment of (ordinary) second-order logic which comprises all formulas of the form df1 . . . dfn u, where df1 . . . dfn is a prefix of existential quantifiers over Skolem functions, and u is an ordinary, first-order formula (a Skolem function f is simply a function that takes i individual arguments x1, . . . , xi and returns an individual
The Author 2006. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected]

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Abstract

282 Scopal Independence

1 This is a slight simplification of the history. In fact, the problem of branching quantifiers was discussed in the literature on plurals (e.g. Barwise 1979, Sher 1991, Schein 1993, Beghelli et al. 1997), although Hintikka’s original problem, which involved first-order quantifiers rather than plurals, was rarely discussed per se. 2 We prefer the term ‘island-escaping’ to the adjective ‘specific’ because the latter has the disadvantage of pre-judging the issue of how these indefinites should be analyzed. By ‘island-escaping indefinites’, we will refer to expressions that give the impression of scoping out of syntactic islands (in our analysis, they don’t literally do so), and we will use the term ‘specific indefinites’ with the same definition.

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f(x1, . . . , xi)). In this way, Hintikka’s plea for a game-theoretic semantics could be reinterpreted as an argument for analysing indefinites in terms of a somewhat constrained form of existential quantification over Skolem functions. Hintikka further applied his device to the analysis of disjunction—to my knowledge, with some conceptual but no linguistic arguments. For empirical and methodological reasons, the matter was left unresolved and was somewhat forgotten in the linguistic literature of the 1980s and 1990s.1 At the same time, however, another problem became the object of acute scrutiny: contrary to what was predicted by syntactic theories of Quantifier Raising, certain indefinites (sometimes called ‘specific indefinites’) appeared to scope out of syntactic islands.2 This seemed remarkable because other quantifiers did not display such a behaviour. Reinhart 1997, Kratzer 1998, Winter 1997, and Matthewson 1999 (among others) suggested that the problem should be solved by resorting to second-order quantification over Choice functions, a proposal that has been developed in various directions in recent research (a Choice function F is a function that takes as argument a—possibly complex—predicate-denotation P, and returns an individual F(P) which satisfies P; special provisions must be made for the case in which P is empty). In this note, we show that branching and island-escaping readings are two sides of the same coin: when the latter problem is considered in full generality, mechanisms must be postulated which predict that branching readings should indeed exist. The point is worth making for conceptual but also for empirical reasons. The data that served to motivate Hintikka’s analysis were controversial. We will address some of the methodological objections that were raised against them, but our own examples will remain highly complex; on the other hand the connection between branching readings and the island-escaping behaviour of indefinites will provide an indirect argument in favour of Hintikka’s empirical claim. Specifically, we follow much existing research in analyzing island-escaping indefinites in terms of quantification over General Skolem Functions (Winter 2002, 2004; Schlenker

Philippe Schlenker 283

2 INDEFINITES I: BRANCHING

2.1 Scope and game-theoretic semantics In the early 1970s, Jaakko Hintikka claimed that the standard (‘Fregean’) notion of scope should be replaced with a different one, which naturally falls out from a ‘game-theoretic’ semantics. To see what the issue is, it is easiest to start from the intuitive account of scopal interaction that one may give for (1a): for any x that you care to choose, I can associate a y so that P(x, y) will be true. (1)

a. "x dy P(x, y) b. df "x P(x, f(x))

3 To my knowledge, the term ‘General Skolem Functions’ is due to Winter. Chierchia 2001 calls these ‘Skolemized Choice Functions’.

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1998; Chierchia 2001; Kratzer 1998). These can be seen as Choice Functions which, in addition to their predicate argument, take any number of individual arguments3 (thus a General Skolem Function G takes n individual arguments d1, . . . , dn and a predicate-denotation P, and returns an individual G(d1, . . . , dn, P) which satisfies P if P is nonempty; here too special provisions are needed when P is empty). But the availability of General Skolem Functions leads one to expect that branching readings should exist as well, which provides an indirect vindication of Hintikka. We will also suggest, somewhat cautiously, that the same analysis can be extended to disjunctions, which appear to display island-escaping readings and possibly branching readings as well. Despite this defence of Hintikka, however, we will see that his particular implementation of his insight within game-theoretic semantics was insufficiently expressive to account for all the possible readings, whereas full quantification over General Skolem Functions yields more adequate predictions. The rest of this note is organized as follows. In Section 2, we lay out the problem of branching readings of indefinites and we seek to address some of the methodological objections raised against Hintikka. In Section 3, we show that when the problem of island-escaping indefinites is considered in full generality, it requires quantification over General Skolem Functions, which in turn predicts that branching readings should exist. Finally, we consider the case of disjunction in Section 4, where we give limited arguments in favour of Hintikka’s empirical claims.

284 Scopal Independence

(2) a. "x dy "z dt Q(x, y, z, t) b. df dg "x"z P(x, f(x), z, g(x, f(x), z)) c. df dg "x"z P(x, f(x), z, g(x, z))4 Intuitively, in (2a) the choice of the witness y depends on the choice of x, and similarly the choice of the witness t depends both on the choice of x and the choice of z. This intuition is formally captured in the second-order translation given in (2c), where the second argument of P (¼ f(x)) is a function of a single variable, x, while the fourth argument of P (¼ g(x, z)) is a function of two variables, x and z. At this point it is natural to ask, with Hintikka, whether we could find a first-order formula whose translation was a Skolem form in which each of the functional arguments contains a single variable, as in the following: (3) df dh "x"z P(x, f(x), z, h(z)) The answer is that First-Order Logic contains no formula that is equivalent to (3). Why? Intuitively, sequences of two quantifiers "x dy and "z dt must be ordered somehow, and thus one of the existential quantifiers—say, dt—must end up in the last position of the sequence, i.e. in the scope of the two universal quantifiers. It then follows from the traditional semantics of First-Order Logic that the ‘choice’ of the witness may depend both on x and on z, so to speak (see 4

Clearly, (2c) entails (2b). Conversely, if a pair of functions f, g satisfies "x"z P(x, f(x), z, g(x, f(x), z)), then by defining g# ¼ kxkz g(x, f(x), z), we obtain a pair of functions f, g# that satisfies "x"z P(x, f(x), z, g#(x, z)).

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The underlying intuition is that of a game in which you (¼ the Falsifier) try to pick an x that makes the formula false. Then I (¼ the Verifier) try to pick a y that makes the formula P(x, y) true. Seen in this light, (1a) is true just in case I, the Verifier, have a winning strategy for the game we are playing; this means that there exists a function f associating ys to xs in such a way that, no matter what your choice of x is, P(x, f(x)) will be true. The latter paraphrase, formalized in (1b), is the ‘Skolem Normal Form’ of (1a), arrived at through a game-theoretic metaphor (a Skolem Normal Form starts with a prefix of existential quantifiers over Skolem Functions, followed by a series of universal quantifiers over individuals, followed by a quantifier-free formula). Of course the procedure may be repeated for more complex formulas, such as that in (2a), whose Skolem Normal Form is given in (2b), which can be further simplified to (2c):

Philippe Schlenker 285

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A Game of perfect information a. Formula: "x dy P(x, y) b. Move 1a: Falsifier chooses an x (call it x1). c. Move 1b: Verifier chooses a y (call it y1) d. If P(x1, y1) is true, Verifier wins; if P(x1, y1) is false, Falsifier wins. e. (a) is true iff the Verifier has a winning strategy, i.e. iff there is a function that pairs ys (¼ the Verifier’s choices) with xs (¼ the Falsifier’s choices) so as to make P(x, y) true, iff df<1> "x P(x<1> f(x)) (5) Another game of perfect information a. Formula: "x dy "z dt P(x, y, z, t) b. Move 1a: Falsifier chooses an x (call it x1). c. Move 1b: Verifier chooses a y (call it y1) d. Move 2a: Falsifier chooses a z (call it z2) e. Move 2b: Verifier has access to the value of x1, y1, z2, and chooses a t (call it t2) 5 One proof goes like this. We observe that when P is replaced by certain formulas, (3) singles out models that cannot be characterized by any First-Order sentence. For instance, the formula in (i) below asserts the existence of a function f and a function h such that (i) f is 1
1, (ii) h is constant, and (iii) the unique value of h has no antecedent by f.

(i)

df dh "x"z (( f(x) ¼ f(z) 0 x ¼ z) & h(x) ¼ h(z) & f(z) 6¼ h(z)))

This condition is equivalent to: there is an injection from the universe into a proper part of itself, a statement that is true precisely in infinite models. But a well-known consequence of the compactness theorem for First-Order Logic is that there is no formula which is true if and only if the domain is infinite.

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Hintikka 1996 for a proof that (3) is not equivalent to any first-order formula).5 What is remarkable, however, is that formulas such as (3) are in fact expressible when the game-theoretic metaphor is taken seriously. Let us first consider some simple examples. Hintikka suggests that the firstorder formulas in (1a) and (2a) can be given a semantics in terms of games of perfect information, in which the Verifier (who is to pick ‘witnesses’ for the existential quantifiers) has at each point access to all the choices made in preceding rounds of the game by the Falsifier (who chooses values for the variables bound by the universal quantifiers). The truth of a formula is then defined by the existence of a winning strategy for the Verifier; such a winning strategy will comprise a series of functions f1, . . ., fn, such that for each round i of the game, fi specifies which element the Verifier should pick given the elements that the Falsifier picked in the preceding rounds. Here are two simple examples of this analysis (we will henceforth write f for a Skolem function that takes n individual arguments):

286 Scopal Independence f. If P(x1, y1, z2, t2) is true, Verifier wins; otherwise Falsifier wins. g. (a) is true iff the Verifier has a winning strategy, iff df<1> dg<2> "x "z P(x, f<1>(x), z, g<2>(x, z))

(6) A Game with imperfect information a. Formula: b. Move 1a: Falsifier chooses an x (call it x1). c. Move 1b: Verifier chooses a y (call it y1) (with information about x1) d. Move 2a: Falsifier chooses a z (call it z2) e. Move 2b: Verifier choose a t (call it t2) (with information about z2 but not x1) f. If P(x1, y1, z2, t2) is true, Verifier wins; otherwise Falsifier wins. g. (a) is true iff the Verifier has a winning strategy, iff df<1> dg<1> "x "z P(x, f<1>(x), z, g<1>(z))6 6

It should be observed that the Skolem translations of Hintikka’s formulas always involve (i) a purely existential prefix of quantifiers over functions, followed by (ii) a first-order formula (in fact, a purely universal formula, i.e. a prefix of universal quantifiers followed by a quantifier-free formula). This is no accident—the existential quantifiers over functions assert the existence of a winning strategy for the entire game, and thus have scope over all other quantifiers, yielding what is called a R11 formula. As is summarized in Hintikka & Sandu 1997, the following theorem follows from results due to Enderton, Hintikka and Sandu: Theorem (Sandu 1991, Hintikka 1995, Enderton 1970) Every first-order sentence of Hintikka’s Independence-Friendly Logic is equivalent to a R11 formula. Conversely, every R11 formula is equivalent to a first-order sentence of Hintikka’s IndependenceFriendly Logic. This result is important because, as we will see, the kind of quantification over Skolem functions that is needed to model indefinites (and, if we are right, disjunction as well) is less restricted than Hintikka thought, and takes us outside the class of R11 formulas.

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But here is now the salient point of Hintikka’s analysis: without quantifying explicitly over Skolem functions, the truth conditions of (3) can be obtained by specifying that the game played is one of imperfect information, in which the Verifier has no access in the second round to the value picked by the Falsifier in the first round (for instance because in the two rounds the role of the Verifier is filled by two players that are on the same side but cannot communicate; or because the Verifier suffers from memory loss between the first and the second round). Thus without explicitly quantifying over Skolem functions, Hintikka manages to give truth conditions for a formula equivalent to (3), which he writes in a first-order syntax by indicating that the quantifier sequences "x dy and "z dt are unordered with respect to each other:

Philippe Schlenker 287

2.2 Branching Readings

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a. Some relative of each villager and some relative of each townsman hate each other b. Some book by every author is referred to in some essay by every critic c. Some official of each company knows some aide of each senator

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a.

b. df<1>dg<1>"x "z ((author(x) & critic(z)) 0(book-by( f<1>(x)) & essay-by(g<1>(z)) & referredto( f<1>(x), g<1>(z))))

7

See Janssen 2002 for arguments against this view.

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On the assumption that the truth conditions of (3) and (6) are indeed instantiated, Hintikka’s semantics is definitely more adequate than a standard first-order analysis, which cannot derive these truth conditions at all. It is also arguably more elegant than a second-order analysis, which doesn’t explain in a natural way why what seem to be first-order quantifiers (some and every) can interact scopally so as to yield branching readings. For the sake of argument, we will grant that if these readings exist, Hintikka’s analysis is indeed adequate in the simple cases7 (the qualification in the simple cases is added because, as we shall see shortly, Hintikka’s analysis turns out to be insufficiently expressive for more complex examples). Still, the question remains whether branching readings are indeed instantiated in English. Hintikka claims that they are. Some of his examples are reproduced in (7). To illustrate, (7b) has according to Hintikka the truth conditions represented in (8a) (game-theoretic semantics, firstorder quantification) or, equivalently, (8b) (normal semantics, secondorder quantification):

288 Scopal Independence Since the innermost formulas in (8) are admittedly cumbersome to read, it may be helpful to introduce a restricted quantifier notation for Hintikka’s system. We may then re-write (8) as (9): (9) Branching Reading (Hintikka) a.

The intended semantics for (9a) is that of a game in which the Falsifier is constrained to pick x’s that are authors and z’s that are critics. The Verifier’s task is then to find a y that is a book by x and a t that is an essay by z which satisfy the inner-most formula. In case there are no books by x or no essays by z, the Verifier has automatically lost. In (9b), we introduce the device of n-ary General Skolem Functions (Winter 2002, 2004; Chierchia 2001): (10) F is an n-ary General Skolem function for restricted quantification if for any n-tuple of objects and any set E, F(d1, . . . , dn, E) 2 E if E 6¼ Ø, F(d1, . . . , dn, Ø) ¼ # if E ¼ Ø. We may interpret # as triggering a presupposition failure. When we take this step, however, we run the risk of departing from Hintikka’s original truth conditions. For instance, if # projects in a certain way, (9b) will yield a presupposition failure where (8b) simply produces a falsehood, e.g. in a situation where there are critics, and there are authors who didn’t write any books (in this case (8b) is false because no function f<1> exists that satisfies the consequent of the conditional; while (9b) may yield a failure because under some assignments F<1>(x, ky book-by(y, x)) denotes #). For present purposes, a convenient alternative is to take # to be an object of which no atomic predicate is true. In this way, we get the desirable result that (9b) comes out as false when some author has written no books (but only poems) or some critic has written no essays (but only reviews). (See Winter 1997 for further considerations on what should be done with General Skolem Functions whose predicate argument is empty; we

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b. dF<1>dG<1>["x: author(x)]["z: critic(z)]] referred-to (F<1>(x, ky book-by(y, x)), G<1>(z, ky essay-by(y, z))

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a. dF<1> dG<1> "x "z R(x, F<1>(x), z, G<1>(z)) b. dF<1> dG<2> "x "z R (F<1> (x), G<2>(x, z))

(11a) is the Skolem translation of a branching reading, while (11b) is the translation of a non-branching reading. Now it is clear that (11a) implies (11b)—if there is a unary Skolem function with the right properties in (11a), then of course there is a binary Skolem function with the same properties ( just make the dependency on the second argument vacuous). And this situation is quite general: Hintikka’s branching readings are systematically stronger than some non-branching ones. For instance, (9) asymmetrically entails ["x: author(x)][dy: book-by(y, x)]["z: critic(z)][dt: essay-by(t, z)]referred-to(y, t). This is the source of the difficulty: whenever a situation satisfies the branching reading, it also satisfies a non-branching reading whose existence is uncontroversial (since Hintikka does not claim that some English 8

Two remarks should be made about the status of #. (A) When # is seen as an object which is not in the extension of any atomic predicate, a Logical Form with General Skolem functions can systematically be translated back into a notation with simple Skolem functions. The key is to replace atomic formulas such as admire(x, F0<1>(x, ky professor(y)) (where F0<1> is a General Skolem Function) with conjunctions of the form (professor(f0<1>(x)) & admire(x, f0<1>(x))) (where f0<1> is a simple Skolem Function). To give an example, (ib) below is translated as (ic): (i) a. Every student admires some professor. b. dF0<1> ["x: student(x)](admire(x, F0<1>(x, ky professor(y))) c. df0<1>"x(student(x) 0 (professor(f0<1>(x)) & admire(x, f0<1>(x)))) (B) Such a solution has a cost, however. In particular, we make counter-intuitive predictions about, say, ‘I did not invite a certain Moldavian king’, which should have a true reading with wide scope existential quantification over General Skolem functions (dF0<0> I did not invite F0<0>(ky Moldavian-king(y))): since ky Moldavian-king(y) has an empty extension, F0<0>(ky Moldavian-king(y)) denotes #, hence the result. (Similar problems are discussed in Geurts 2000).

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do not attempt to give a serious solution to this problem in the present note).8 Be that as it may, the problem of branching quantifiers as we have outlined it was left more or less unresolved at the end of the 1970s and at the beginning of the 1980s. There seem to have been at least two reasons for this. First, Hintikka’s judgments were called into question by several researchers (e.g. Fauconnier 1975, Boolos 1984), and given the complexity of the crucial examples it proved difficult to reach a clear empirical verdict. Second, Fauconnier (1975) raised a methodological objection against Hintikka’s argument. As Fauconnier noted, branching readings systematically entail non-branching ones. This appears most clearly when we look at the relevant Skolem translations:

290 Scopal Independence sentences must have a branching reading, only that they may). Thus, on the basis of intuitions of truth alone, we cannot prove that branching readings exist, since any situation that makes the branching reading true will make a non-branching reading true as well. What about intuitions of falsity, then? The difficulty is that a charitable interpreter who has a choice between interpreting a sentence S as (11a) or as (11b) should be very reluctant to deem S false when (11a) is false but (11b) is true. Charity requires that the interpreter maximize the truth of the speaker’s utterance, and thus assume that the speaker meant (11b), not (11a). As a result, it is exceedingly difficult to prove that the reading in (11a) really does exist.

However Fauconnier’s methodological objection can be circumvented by embedding the relevant sentences in environments that reverse the order of entailments. Thus if a sentence P has two readings, a Strong Reading S and a Weak Reading W, where S entails W, it is clear that in It is not the case that P the reading corresponding to W will in fact entail the reading corresponding to S (because negation reverses the order of entailments). This example is still not ideal, because negation may be construed as meta-linguistic, which complicates further an already thorny issue. A better solution is to embed P in an if-clause or—to avoid issues that arise from the non-monotonicity of conditionals—in a when-clause. This attempt was carried out in Schlenker 1998, where it was suggested that there is an empirical difference between the following sentences, the first of which involves the indefinite ‘a dissident’ (or: ‘a certain dissident’), and the second of which involves a modified indefinite ‘at least one dissident’. The claim was that only the former allows for an embedded branching reading, i.e. a reading in which existential quantification over Skolem Functions has scope inside the antecedent of the conditional. My original example was improved by Eklund & Kolak 2002, and thus I shall cite their version of it (this is the example in (12a). I add some controls to obtain minimal pairs): (12) Context: We are fighting for human rights in China and as part of that campaign we are trying to get a representative from each country to fight for the release of one dissident from each (Chinese) prison. I make the following prediction: a. If a (given/certain) representative from each country fights for the release of a (certain) dissident from each prison, our

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2.3 Improvement

Philippe Schlenker 291

Suppose we are in the following situation: (i) every country did in fact select a representative who went to each prison to lobby for the liberation of a dissident, but (ii) for a given prison, different representatives lobbied for the liberation of different dissidents, i.e. they did not co-ordinate their actions. Suppose the campaign fails. Does this mean that I necessarily lied when I made the claims in (13)? There appears to be a difference between the sentences involving at least one dissident and those involving a (certain) dissident. If I asserted the former, it seems that I necessarily lied. If I asserted the latter, by contrast, there is a construal of what I said that makes it compatible with the facts. Why should this be? Clearly, in all the relevant readings a representative is scopally dependent on every country, and similarly a certain/at least one dissident is dependent of every prison. Thus the Logical Form of the antecedent clause should be one of the following,9 where R(y, t) stands for: y fights for the release of t. (14)

a. ["x: country(x)]["z: prison(z)][dy: rep.-from(y, x)] [dt: dissident-from(t, z)] R(y, t) b. ["x: country(x)][dy: rep.-from(y, x)]["z: prison(z)][dt: dissident-from(t, z)] R(y, t) c. ["z: prison(z)][dt: dissident-from(t, z)] ["x: country (x)][dy: rep.-from(y, x)]R(y, t)

9 For reasons that are discussed in Section 2.4, Hintikka’s particular implementation is in fact not adequate to represent embedded branching readings. We disregard this point in the present section.

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campaign will be a success. (Eklund & Kolak 2002, modified from Schlenker 1998) b. If a (given/certain) representative from each country fights for the release of at least one dissident from each prison, our campaign will be a success. (13) Context: We have been fighting for many years for human rights in China. I recount the story of our failures and successes, and say: a. Whenever a (given/certain) representative from each country fought for the release of a (certain) dissident from each prison, our campaign was a success. b. Whenever a (given/certain) representative from each country fought for the release of at least one dissident from each prison, our campaign was a success.

292 Scopal Independence d.

d#. dF<1> dG<1> ["z: prison(z)]["x: country(x)] R(F<1> (x, ku representative-from(u, x)), G<1>(z, ku dissident-from (u, z)))

(15) a. A situation that satisfies the Branching Reading (14d) (and thus also each Non-Branching Reading)

b. A situation that satisfies the Non-Branching readings (14) but not the Branching Reading (14d)

The kind of situation illustrated in (15a) is the hallmark of branching readings. There must be a group S of representatives (those that are assigned by one of the functions to the countries) and a group D of dissidents (assigned by the other function to the prisons) such that each of the representatives in S stands in the designated relation to each of

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As we just saw, there is a reading of the sentence that requires coordination between the representatives, so that, for each prison, the ‘choice’ of the dissident, so to speak, does not depend on the country. (14b) is too weak to enforce this (because [dt: dissident-from(t, z)] is in the scope of both universal quantifiers). Since (14a) is weaker than (¼ asymmetrically entailed by) (14b), it too is too weak to represent the reading in question. By contrast, the branching reading in (14d–d#) specifies that the condition for success is that the representatives coordinate their actions, as is the case in (15a) but not in (15b):

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I conclude that the branching reading in (14)d-d# is the only plausible contender to analyze the ‘coordination’ reading we started out with.

2.4 Beyond Hintikka There is something ironic about the preceding discussion. In essence, we have claimed that Hintikka’s initial observation about branching readings was correct, but hard to prove on his own examples because a formula of the form df<1> dg<1> "x "z R(x, f<1> (x), z, g<1> (z)) is

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the dissidents in D (this is what Sher 1991 calls a ‘massive nucleus’). Why? Because by virtue of the existence of the functions whose existence is asserted by the initial prefix of the Skolem translation, the universal quantifiers over countries and representatives quantify also, indirectly, over the representatives associated to countries and the dissidents associated to those prisons; and thus each of these representatives must stand in the relevant relation to each of these dissidents, and vice versa. In particular, for each of these dissidents it must be the case that each representative lobbies for him; there must thus be a co-ordination so as to apply maximum pressure on the Chinese authorities. The conclusion at this point is that the branching analysis correctly handles the ‘co-ordination’ reading; the logical forms in (14a) and (14b) do not. But what about the logical form in (14c)? It correctly imposes that for each prison one of its dissidents receive the support of every country. But this logical form suffers from a different problem: it makes [dy: representative-from(y, x)] scopally dependent on ["z: prison(z)]. However with the modifiers given or certain in a given/certain representative, this reading is very difficult to obtain. If two representatives of Country 1 have divided the job among themselves, so to speak, and if the campaign is a failure, I could plausibly maintain that I did not lie because each prison was to be pressured by the same representative from each country—a condition which is not met in (16):

294 Scopal Independence

(17) 10

Schlenker 1998 failed to see this point, as did Eklund & Kolak 2002.

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logically stronger than the formula df<1> dg<2> "x "z R ( f<1>(x), g<2>(x, z)), which represents an uncontroversial reading of the sentences under study. In order to circumvent this difficulty, we had to embed the test sentences within a downward-monotonic environment, which had the effect of reversing the order of entailments. In so doing, however, we produced readings that are indeed branching, but which Hintikka’s system cannot account for.10 To see this, observe that the sentences we used were of the form If P, Q, where P had a branching reading and was thus equivalent to df<1> dg<1> "x "z R(x, f<1>(x), z, g<1>(z)). For simplicity, let us analyse conditionals as material implications, and assume that Q is a contradiction. The result is then equivalent to :df<1> dg<1> "x "z R(x, f<1>(x), z, g<1>(z)) (we could have obtained this result more directly by embedding P under negation, but as was mentioned earlier negation introduces problems of its own). However, the logic that corresponds to Hintikka’s gametheoretic semantics, ‘Independence-Friendly Logic’, is not closed under ordinary (contradictory) negation. This is because, as was mentioned earlier, this logic is equivalent to a fragment of Second-Order Logic (call it FIF) which includes all the formulas that contain (i) a prefix of existential quantifiers over Skolem functions, followed by (ii) a firstorder formula. But in general :df<1> dg<1> "x "z R(x, f<1>(x), z, g<1>(z)), which is equivalent to "f<1> "g<1>:"x "z R(x, f<1>(x), z, g<1>(z)), is not equivalent to any formula of this form. In fact, Barwise 1979 proves that the negation of a formula P of FIF is itself expressible in FIF just in case P is expressible in First-Order Logic. But in general the formula dF<1> dG<1> "x "z u is not expressible in first-order logic, from which it follows that its negation is not expressible in FIF. Now Hintikka does give game-theoretic rules for a negation, but as he points out this is not ordinary, contradictory negation. The rule is that :IFS is true iff S is true when the roles of the Verifier and of the Falsifier are reversed, whereby we do obtain the result that the negation Hintikka defines for IF does not take us out of IF, since :IFS also asserts the existence of a strategy for one of the players (in the second-order translation, this will indeed yield a formula of FIF). But there are cases in which neither the Verifier nor the Falsifier has a winning strategy. Consider the following formula, where "x and dy are scopally independent:

Philippe Schlenker 295

3 INDEFINITES II: ISLAND-ESCAPING BEHAVIOUR It must be granted that the semantic judgments on which the argument of the previous section is based are rather subtle. Much more robust, on the other hand, are some data that have given headaches to syntacticians working on theories of ‘Quantifier Raising’. As we will see, these data provide strong indirect evidence for Hintikka’s claim that branching

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The Verifier has a winning strategy for this formula just in case for some y whose choice does not depend on the Falsifier’s choice of x, x 6¼ y. Clearly no y can satisfy this requirement. For his part, the Falsifier has a winning strategy just in case he can choose an element x such that, no matter what element y the Verifier chooses, x ¼ y. Again no element x has this property when the domain contains at least two individuals. Thus Hintikka’s definition of negation does not give us contradictory negation, since the contradictory negation of P should be true whenever it is not the case that P is true, and this fails to be the case in this example. Now Hintikka does discuss the possibility of introducing contradictory negation in his logic to obtain what he calls an ‘extended IF first-order language’. The rule is simply: :S is true iff S is not true, otherwise false. As he points out, ‘no game rules can be used to define contradictory negation’ (Hintikka 1996: 148); and furthermore, ‘contradictory negation can syntactically speaking occur only in front of an entire sentence (closed formula)’, for if it were prefixed to an open formula, ‘you would need a game rule to handle a substitutioninstance of that open formula when you reach it in a semantical game’. Clearly this is not what happens in natural language, and I conjecture that the problem is in fact completely general: to the extent that there are branching readings to begin with, it would appear that those can be obtained within the scope of any operators that one cares to choose. If so, the challenge for supporters of IF who take linguistic data seriously is to show how embedded branching readings can be obtained. Of course the problem does not arise if instead of a game-theoretic semantics one adopts an analysis with existential quantifiers over Skolem functions that are not constrained to have widest scope. This is what we shall do in what follows. (This analysis has the additional advantage of being immediately compatible with the theory of generalized quantifiers, which Hintikka did not consider in his analysis; see, however, Robin Clark’s ‘Quantifier Games and Reference Tracking’ for an analysis of generalized quantifiers within game-theoretic semantics).

296 Scopal Independence readings exist. Furthermore, the problem raised for Hintikka by embedded branching readings has a direct counterpart with islandescaping indefinites that take embedded scope. If the present approach is on the right track, this is unsurprising, since island-escaping indefinites and branching readings are two sides of the same coin.

3.1 The original discussion

(18)

a. If some relative of mine dies, I will inherit a house a#. [some relative of mine]i [if xi dies, I will inherit a house] b. If we invite some philosopher, the party will be a disaster (Reinhart 1997, slightly modified) b#. [some philosopher]i [if we invite xi, the party will be a disaster] c. Most linguists have looked at every analysis that solves some problem c#. [Most linguists]i [some problemj xi have looked at every analysis that solves xj]

We will follow the literature (especially Reinhart 1997) in assuming that (a) the behaviour illustrated in (18) is shared by indefinites headed by ‘a’ as well by numerals (‘one problem’, ‘two problems’, ‘three problems’, etc.), and that (b) modified numerals (‘at least one problem’, ‘more than two problems’, etc.) generally do not display an islandescaping behaviour, for reasons that we do not investigate in the present note. Finally, (c) unless otherwise noted, we take the adjective ‘certain’ (or ‘specific’) to help bring out readings that are available but sometimes difficult to obtain in its absence. If the indefinites in (18) give the appearance of escaping syntactic islands, why not assume that they literally do so at Logical Form? Granted, this would require a stipulation, since other quantifiers do not escape syntactic islands; but after all every analysis ends up having to stipulate something about indefinites, so this might not be such a bad thing in the end. However this theoretical line raises two additional problems: (i) Unlike indefinites that overtly have wide scope, plural specific indefinites are claimed by Reinhart 1997 not to give rise to distributive readings (see Winter 1997; Ruys 1992; the version

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As is well known, indefinites give the appearance of scoping out of syntactic islands, as in the following examples, cited in Reinhart 1997 (see also Farkas 1981, Abusch 1994, Kratzer 1998, Ja¨ger 2006):

Philippe Schlenker 297

below is from Geurts 1999b). Thus (19a) can be read as (19b) but not as (19c): (19) a. If three relatives of mine die, I will inherit a house. b. There are three relatives of mine such that, if they all die, I will inherit a house. c. There are three relatives of mine such that, if any of them dies, I will inherit a house. (The generality of these judgments has sometimes been called into question, e.g. by Matthewson 1999 and Geurts 1999b.) In addition, there is a much stronger argument against a solution based on unrestricted Quantifier Raising for indefinites. The crucial point is that there are indefinites whose restrictor contains a bound variable, and yet which in some sense appear to have wider scope than the binder of this variable: (20) a. If each of my guests comes with a certain friend of his, the party will be disaster b. If [each of my guests]i [a certain friend of hisi]k xi comes with xk, the party will be a disaster c. [a certain friend of hisi]k If [each of my guests]i xi comes with xk, the party will be a disaster Intuitively, (20a) means something like this: there is a way to associate each of my guests to a friend of his such that, if each guest comes with the friend associated to him, the party will be a disaster.11 But all the unrestricted QR analysis can deliver is (20b) or (20c). In (20b) I am committed to the claim that the party will be a disaster if each of my guests comes with any friend of his—which is much stronger than the intended reading of (20a). By contrast, (20c) commits me to the much weaker claim that individual i has a friend such that, if each of my guests invite him, the party will be a disaster—which is clearly not the intended meaning of (20a) (where ‘a certain friend’ covaries with ‘each of my guests’).

3.2 General Skolem Functions vs. Choice Functions As it turns out, however, we already have a mechanism at our disposal to formalize the intended reading of (20a). Using General 11

B. Geurts (p.c.) notes that the relevant reading is unavailable when ‘certain’ is deleted from (20a). To my (non-native) ear, this observation is correct, but it does not extend to minimal variants of (20a) in which ‘a certain friend of his’ is replaced with ‘some friend of his’ or with ‘one of his friends’.

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(ii)

298 Scopal Independence Skolem Functions, (20a) may be given the Logical Form in (21) (to be refined below): (21) dF<0> [if [each of my guests]i xi comes with F<0>(kx x a friend of hisi), the party will be a disaster12 Using the same device, we may also account for the other cases of island-escaping indefinites that were discussed earlier. (18a) can be analyzed as in (22a), and (18c) as in (22b) or (22b#) (which yield the same truth-conditions): (22)

General 0-ary Skolem Functions are called Choice functions. So far the latter are sufficient to handle our examples. Several versions of the Choice Function analysis have been offered in the literature: (i) Reinhart 1997 suggested that existential closure over Choice Functions could be performed at any (propositional) level of a syntactic derivation. (ii) By contrast, Kratzer 1998 suggested that Choice Function variables are not existentially quantified, but that their value is provided by the context. She further suggested that these functions may take additional individual arguments, and thus that they should be General Skolem Functions rather than simple Choice functions. (iii) Matthewson 1999 suggested against Kratzer that Choice Functions should be existentially quantified. However against Reinhart she claimed that the existential closure need only occur at the highest level. 12

Note that in this example the General Skolem Function need not take any individual argument, because in any event the restrictor friend of his contains a bound variable, which allows variation between the friends and the guests (since different guests may have different sets of friends, the function F<0> may select different individuals from these sets). Still, as has been observed repeatedly in the Choice Function literature, this analysis is still wanting (see for instance Geurts 2000). Suppose that two of my guests G1 and G2 have exactly the same friends. Does it follow that the function quantified over in (21) select the same friend for G1 and G2? The Logical Form in (21) predicts that this is indeed the case. If this is incorrect, as has been claimed in the literature, we need to replace F<0>(friend of hisi) with the expression F<1>(i, friend of hisi), which may associate to different individuals i and i’ different friends f and f’, even if i and i# happen to have exactly the same friends: (i)

dF<1> [if [each of my guests]i xi comes with F<1> (i, friend of hisi), the party will be a disaster

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a. dF<0> [if F<0>(kx x a relative of mine) dies, I’ll inherit a house] b. [most linguists]i dF<0> xi has looked at every analysis that solves F<0>(kx x a problem) b#. dF<1> [most linguists]i xi has looked at every analysis that solves F<1>(xi, kx x a problem)

Philippe Schlenker 299

By contrast, we will suggest that (i) quantification over General Skolem Functions is needed, and that (ii) the existential quantifiers over functions sometimes need to have scope under other operators. Importantly, these are exactly the conclusions we reached on the basis of branching readings in Section 2.13

3.3 Functional readings Reinhart’s Choice Functions cannot handle the following examples (Schlenker 1998; Dekker 2002; Winter 2004): (23)

Consider (23), and assume the following situation: (i) every student made progress in some area he was already good in, but (ii) I still flunked some of the students. It seems that in such a situation I could have uttered (23a) without lying; but had I asserted (23b), my utterance could not have been construed as true. In other words, (23a) has the reading given in (23c), which can be paraphrased as: There is a distribution of areas per student such that if every student makes progress in the area that is assigned to him (say, the one that he is weakest in), then nobody will flunk the exam. (23b) lacks such a reading. On the relevant reading of (23a), the choice of the area is clearly dependent on the choice of the student. As observed by R. Schwarzschild (p.c.), the functional reading can be brought out by continuing the discourse with: ‘John must make progress in Binding Theory, Mary must make progress in Case Theory, . . .’ . This continuation is much more difficult with ‘at least one area’ than with ‘some/a certain area’.

13 See Ja¨ger 2006 for an entirely different solution, in which indefinites are analysed as variables with certain definedness conditions imposed by their restrictor.

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[Context: Every student in my syntax class has one weak point—John doesn’t understand Case Theory, Mary has problems with Binding Theory, etc. Before the final, I say:] a. If each student makes progress in some/a(certain) area, nobody will flunk the exam. Intended Reading: There is a certain distribution of fields per student such that if each student makes progress in the field assigned to him/her, nobody will flunk the exam. b. 6¼ If each student makes progress in at least one area, nobody will flunk the exam c. dF<1> if ["x: student x] x makes progress in F<1>(x, ky area y), nobody will flunk the exam.

300 Scopal Independence To analyze (23a), Reinhart has no choice but to insert an existential quantifier over Choice functions under the universal quantifier, which is itself in the scope of the if-clause—as in (24): (24) If ([each student]i dF<0> [xi makes progress in F<0>(area)]), nobody will flunk the exam

(25) [Context: Every student in my syntax class has two weak points—John doesn’t understand Case Theory and LF, Mary has problems with Binding and Theta theory, etc. Before the final, I say:] a. If each student makes progress in two (specific) areas, nobody will flunk the exam b. If each student makes progress in at least two areas, nobody will flunk the exam c. dF<1> if ["x: student x] x makes progress in F<1>(x, ky two(y) & areas(y)), nobody will flunk the exam. Once we have at our disposal all the expressive power afforded by General Skolem Functions, we may try to constrain the system by requiring that the existential closure always have maximal scope—a position which would mesh nicely with Hintikka’s original analysis, and also with Matthewson 1999. But this won’t work. Whatever readings are obtained in (23a) can be replicated in the scope of a variety 14 One could try to save Reinhart’s system by postulating that the example in (23a) contains concealed pronouns, along the lines of (i):

(i)

If each student makes progress in some/a(certain) area , nobody will flunk the exam.

Apart from the fact that such a mechanism is ad hoc, it also makes incorrect predictions. For if it is generally available, there is no reason it could not be used in (23b) as well. But this generates a reading that this sentence does not normally have: (ii)

If each student makes progress in at least one area , nobody will flunk the exam.

If such a reading were available, I could assert (23b) truthfully and still flunk students who did make progress in (any) one area. This does not seem to be the case.

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But this now yields the wrong truth conditions, for (24) predicts that in case each student makes progress in any area, I am not allowed to flunk anybody. This is clearly not the reading we are after. By contrast, the additional dependency offered by 1-ary Skolem functions in (23c) suffices to solve the problem.14 Exactly the same argument can be extended to unmodified numerals, which can be analyzed in terms of General Skolem Functions that take as predicate argument a property of pluralities ([ky (two y & areas y] denotes the set of groups of (at least) two areas):

Philippe Schlenker 301

of operators, including non-monotonic ones. This point was made forcefully by Chierchia 2001, 2003 with respect to quantification over Choice Functions. Starting with (26a), which exhibits a specific indefinite, Chierchia observes that (26b) can be used to deny (26a), and that similarly (26c) may attribute to Lee the denial of (26a). (26)

It would appear, then, that existential quantification over General Skolem Functions must be allowed to occur at any propositional level in a sentence. This is also the conclusion reached independently by Winter (2002, 2004). Winter emphasizes the analogies between the use of Skolem Functions in (a) the analysis of indefinites, (b) functional readings of definite descriptions, as analyzed in particular by Jacobson 1994 and Sharvit 1999, and (c) the theory of functional and pair-list readings of interrogatives. This is an important theoretical step because these readings provide independent evidence for a formal device (quantification over functions) which, up to this point in our discussion, has been a pure stipulation. Consider first functional readings of definite descriptions. Jacobson argues that (a variant of ) (27a) involves quantification over functions as in (27c) rather than quantification over individuals as in (27b): (27)

a. The only woman that no man loves is his mother-in-law.16 b. [no x: man x] [[the only y: woman y & x loves y] ¼ x’ s mother-in-law.]

15

While the operators in (26) are all monotonic, the same point applies to non-monotonic environments as well, as in (i): (i)

Exactly two linguists studied every solution that some problem might have.

And lest the reader think that this applies only to those non-monotonic quantifiers that can be analyzed as a conjunction of monotonic quantifiers (e.g. exactly two students ¼ at least two students and no more than two students), I give in (ii) an example in which this strategy won’t work (because an odd number of students cannot be obtained as a conjunction of monotonic quantifiers—see Gamut 1991, Vol. 2, p. 329) (ii)

An odd number of linguists studied every solution that some problem might have.

See also the discussion in Chierchia 2001 for further relevant observations. 16

(i)

Examples of this sort are originally due to Dahl 1981. Jacobson 1994 discusses (i): The only woman that no Englishman will invite for dinner is his mother.

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a. Every linguist studied every solution that some problem might have b. Not every linguist studied every solution that some problem might have c. Lee said that not every linguist studied every solution that some problem might have15

302 Scopal Independence c. [if: f is a natural function & f maps men to women & [no x: man x] x loves f(x)] ¼ [kx: man x. xs mother-in-law]

(28) Which dish did every guest make? a. (Every guest made) his favourite dish. b. Al (made) the pasta; Bill, the salad; and Carl, the pudding. (29) Which dish did most/several/a few/no guests make? a. Their favourite dish. b. #Al the pasta, and Bill the salad. (28) allows both for a pair-list and for a functional reading of the question, in the sense that it allows for a list of pairs of guests and dishes that they made, and also for a single answer that defines in a natural way a function from guests to dishes they made. By contrast, (29) only allows for a functional reading, and thus the pair-list answer in (29b) is simply impossible. For later reference we note (i) that the contrast between these two examples stems from the nature of the quantifier that has scope over the interrogative word (‘every guest’ in (28), ‘most’/ ‘several’/‘a few’/‘no guests’ in (29), and (ii) that in (29) the functional readings do not allow for unrestricted quantification over all the functions there are, but only over those which are presented as being, in some sense, ‘natural’ (this presumably accounts for the deviance of (29b): what is called for in the answer is the description of a natural function rather than an arbitrary pairing between individuals and dishes). In particular, all the non-upward monotonic quantifiers allow only for a functional reading, and never for a pair-list reading (see Winter 2004 for further discussion).

3.4 A Problem of Overgeneration? Schwarz 2002 argues that an analysis of specific indefinites based on Skolem Functions is bound to overgenerate miserably (see also Bende-Farkas & Kamp 2001). The problem arises in configurations such as [. . .dF. . . O . . . F. . .], where the existential quantifier

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Jacobson (who attributes this point to Dahl 1981 and Hornstein 1984) observes that (27b) does not yield the right truth conditions. As summarized by Winter 2004, we may ‘consider a situation in which John is a man who loves both his wife and his mother-in-law. In this situation [(27b)] is false. However, [(27a)] [and (27c) -PS] may still be true, as long as also other men do not love only their mother-in-law’. (Other arguments against (27b) are offered in Jacobson 1994 and Sharvit 1999) Next, consider questions:

Philippe Schlenker 303

over Skolem Functions binds ‘across’ an operator O which is not upward-monotonic. This is the case in (30b), which—if we are right— should be a possible logical form for (30a). The difficulty is that (30b) predicts truth conditions that are not attested. (30)

Assuming that there are indeed books that I recommended (so as to avoid the ‘empty restrictor’ problem), (30b) is true if and only there is at least one pairing f of students and books such that no student read the book assigned to him by f; and in turn this is true just in case no student read every book that I had recommended, as is laid out in (30d). How serious is this problem? As Schwarz himself points out, the natural solution is to claim that the existential quantifier does not range over all the functions there are, but only over the ‘natural’ ones. Furthermore, we already saw that in the case of questions the nonupward-monotonic quantifiers only allow for functional readings, where quantification is restricted to ‘natural’ functions. If the same constraint is at work for indefinites, we would in fact expect that (30a) should not have the reading in (30b), because it requires quantification over all the functions there are rather than only the ‘natural’ ones. Pending further investigation, then, I conclude that Schwarz’s objection can be circumvented.

4 DISJUNCTION As is well-known, disjunctions and existential quantifiers share the same algebraic properties (both are ‘joins’ in a Boolean algebra). In fact, a disjunction p or q can be seen as an existential statement there is a proposition in fp, qg which is true. It was even proposed by Rooth and

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a. No student read a book I had recommended. b. dF<1> [[no x: student x] x read F<1>(x, ky [book y & I had recommended y])] c. No student read every book I had recommended. d. Suppose that none of the restrictors are empty, and call B the set of books I had recommended. Then: b 0 c: let f be a function that witnesses the truth of b; then f(_, B) associates to each student a book I recommended which he didn’t read. The existence of such a function shows that c. is true. c 0 b: Construct f(_, B) so that for each student x, f(x, B) is a book I had recommended and that x did not read. f witnesses the truth of b.

304 Scopal Independence Partee 1982 that disjunction should literally be analyzed as an indefinite because it gives rise to ‘donkey’-style readings: (31) If John lost a watch or a compass, Mary found it (Rooth and Partee 1982) Rooth and Partee observe that the consequent means something like Mary found what John lost, a reading that they analyse by treating the disjunction as a DRT-style indefinite bound by an unselective universal quantifier: (32) "i[(watch xi or compass xi) & John lost xi] Mary found xi

(33) a. First-Order Notation: b. Second-Order Translation: df<1> dg<1> "x "z ((P(x, f<1>(x), z) & g<1>(z) ¼ 0) v (Q(x, f<1>(x), z) & g<1>(z) ¼ 1) a#. First-Order Notation: "x dy "z (P(x, y, z) v Q(x, y, z)) b#. Second-Order Translation: df<1> dg<2> "x "z ((P(x, f<1>(x), z) & g<2>(x, z) ¼ 0) v (Q(x, f<1>(x), z) & g<2>(x, z) ¼ 1) It is useful to think of the functions g<1> and g<2> in (33b–b#) as making a ‘choice’ between the two disjuncts. Consider for example (33b). If g<1>(z) ¼ 0, the only way the innermost formula can be true 17 In more complex cases, an enriched syntax must be used for branching readings involving disjunctions, in order to indicate which formulas the disjunction v is supposed to apply to (the notation in (33a) would lead to ambiguities if there were more than two formulas). Such a syntax is developed for instance in Sandu and Va¨a¨na¨nen 1992 and Hintikka 1996. I will stick to the simpler notation in what follows.

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(see Stone 1992 for some difficulties with this approach). Hintikka’s ‘Independence Friendly’ Logic treats disjunctions on a par with existential quantifiers, in terms of a game-theoretic semantics whose second-order translation involves quantification over Skolem functions. In particular, like existential quantifiers disjunctions allow for branching readings such as the one represented in (33a), whose second-order translation is (33b) (where it must be assumed that g ranges, among others, over the functions that have f0, 1g as their range). It should be noted that the disjunction in (33a) plays the role of the existential quantifier dt in our earlier example (6a).17 For comparison, I include in (33a#–b#) a standard first-order formula in which a disjunction has scope under two universal quantifiers:

Philippe Schlenker 305

4.1 Island-escaping behavior Larson 1985 suggested that disjunction can have scope only as far as the word ‘either’ in the construction ‘either. . . or. . .’ can go. In other words, ‘either’ may optionally mark the site of the covert scopal movement of ‘or’. This conclusion is suggested by the following paradigm: Mary is looking for a maid or a cook (. . . but I don’t know whether it’s a maid or a cook that Mary is looking for) (Rooth & Partee 1982, also cited in Winter 1998) (35) a. Mary is looking for either a maid or a cook. b. Either Mary is looking for a maid or a cook. c. Mary is either looking for a maid or a cook. d.??Either Mary isn’t looking for a maid or a cook. e.??Mary either isn’t looking for a maid or a cook. f. Mary isn’t looking for (either) a maid or a cook can’t be interpreted as: ‘Mary isn’t looking for a maid or isn’t looking for a cook’. (34)

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is if the first disjunct (and hence P(x, f<1>(x), z)) is true; while if g<1>(z) ¼ 1, the innermost formula can be true only if the second disjunct (and hence Q(x, f<1>(x), z)) is true. Of course the choice of the values 0 and 1 is entirely arbitrary; all that matters is that the domains of the quantifiers dg<1> and dg<2> include functions with at least two elements in their range, so as to enforce a ‘choice’ between the two disjuncts. As the Skolem translations given in (33b–b#) make clear, the branching reading entails the corresponding non-branching logical form (though the converse need not be the case): if some pair of functions , g<1>> witnesses the truth of (33), then , g#<2>> witnesses the truth of (33b#), where for all x, z, g#<2>(x, z) ¼ g<1>(z). This is exactly the pattern we saw earlier when we discussed the branching readings of indefinites. To my knowledge, Hintikka did not provide arguments to establish that English disjunctions must indeed be analyzed in this way. In the following sections, we try to fill this gap. The rough generalization appears to be that disjunctions generally share the behaviour of indefinites in that they too escape syntactic islands, and give rise to functional readings—and probably also to branching readings. But the readings in question tend to be harder to obtain than in the case of indefinites—a fact that should ultimately be derived. As a result, the data about branching readings, which were already quite difficult with indefinites, are outright unclear when it comes to disjunctions. I shall thus start the discussion with island-escaping readings, where the judgments are somewhat easier.

306 Scopal Independence Larson’s precise generalization is stated in (36): (36) Larson’s Generalization (cited in Winter 2001) a. In or co-ordinations without either, as well as in either coordinations with either undisplaced, the scope of or is confined to positions where either can potentially appear. b. When either is displaced, it specifies the scope of or to be at that displaced position. As is suggested by Larson, ‘either’ certainly cannot move out of syntactic islands—for instance the following is ungrammatical:

However, contrary to what Part (a) of Larson’s generalization predicts, I believe that there are cases in which a disjunction can give the appearance of scoping out of a syntactic island. Let us first consider the clearest data, which involve parentheticals: (38) Students taking the exam have a choice of two options: Greek or Latin a. Not a single student who picked some/a certain option (I don’t remember which) passed the exam. b.#Not a single student who picked at least one option (I don’t remember which) passed the exam. c. Not a single student who picked Greek or Latin (I don’t remember which) passed the exam. d. Not a single student who picked Greek or picked Latin (I don’t remember which) passed the exam. Reading: For some x 2 fGreek, Lating, not a single student who picked x passed the exam. I use the behavior of indefinites as a baseline, and note that (i) the parenthetical in (38a) help bring out the relevant island-escaping readings, while (ii) the same parenthetical in (38b) is incompatible with modified indefinites, which are independently known not to escape islands. I then use the same parenthetical strategy in (38c) to force wide scope readings of disjunctions. The result is similar to (38a) rather than (38b), which suggests that the parenthetical helps bring out an islandescaping reading of disjunction.

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(37)  Either not a single student who picked Greek or Latin passed the exam (cannot mean: Not a single student who picked Greek passed the exam or not a single student who picked Latin passed the exam).

Philippe Schlenker 307

Without parentheticals, a special intonation is sometimes needed to obtain an island-escaping reading (it has been noted that intonation can also help indefinites take scope outside of islands; it is too early to tell whether it is the same intonational pattern that does the trick in both cases): (39)

Not a single student who picked Greek OR Latin passed the exam.18

The phenomenon appears to be quite general. Although there are three ways to form disjunction in French, all of them yield island-escaping readings with a parenthetical or a special intonation (or both):19 a. Pas un seul e´tudiant qui a choisi le grec OU le latin ( je ne rappelle plus) (n#) a re´ussi l’examen. Not a single student who has picked the Greek OR the Latin (I don’t remember) NE has passed the exam b. Pas un seul e´tudiant qui a choisi le grec OU BIEN le latin ( je ne me rappelle plus), . . . Not a single student who has picked the Greek OR-WELL the Latin (I don’t remember) c. Pas un seul e´tudiant qui a choisir SOIT le grec, SOIT le latin ( je ne me rappelle plus), . . . Not a single student who has picked BE-IT the Greek OR-WELL the Latin (I don’t remember)

As was the case with indefinites, it appears that island-escaping disjunctions can take scope under other operators, including nonupward-monotonic ones. Again I use examples involving indefinites as a baseline, and observe that with the right intonation the disjunction, like the indefinite, can take scope outside of the island but in the scope of the subject quantifier (and in 41 it can be checked that prefixing the sentence with not can indeed yield the contradictory negation of the initial sentence, as was pointed out for indefinites by Chierchia 2001). (41)

18

a. (Not) Every logician presented every proof that some theorem has (modified from Chierchia 2001.) b. Exactly four logicians presented every proof that some theorem has.

Emphasis of ‘or’ can also give rise in this example to an exclusive reading of the disjunction, a reading which is irrelevant for our purposes. 19 Example (40c) shows that the wide scope reading is not obtained through a kind of metalinguistic afterthought (‘I said Greek, but maybe I should have said Latin instead’). This line wouldn’t work for the soit . . . soit. . . construction, since one half of the construction only (soit . . .) wouldn’t yield a grammatical sentence.

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(40)

308 Scopal Independence c. (Not) Every logician presented every proof that the Completeness Theorem OR the Incompleteness Theorem has. d. Exactly four logicians presented every proof that the Completeness Theorem OR the Incompleteness Theorem has. (Two French logicians focused on the Completeness Theorem and two German logicians focused on the Incompleteness Theorem).

(42) a. Exactly four logicians studied every conceivable proof that the Completeness Theorem or the Incompleteness Theorem might have. b. [¼4x: logician x] dF<0> [every y: y proves F<0>(fthe Completeness Theory, the Incompleteness Theoremg] (x studied y) (43) a. Not a single student who picked Greek or Latin passed the exam. b. dF<0>[no x: student x & x picked F<0>(fGreek, Lating] (x passed the exam)20 Our conclusion accords with the theory of Winter 2004, who suggested (pp. 157–159) that his Choice/Skolem Function mechanism should be applied to disjunctions (be they propositional or not). We leave it for future research to determine in greater detail how the syntax/semantics interface works in these cases.21 20 As noted by an anonymous reviewer, this mechanism should presumably be extended to cases of predicate and propositional disjunction, where the data appear to be somewhat similar:

(i)

Not a single student who picked Greek or picked Latin (I don’t remember which) passed the exam. b. Not a single student who picked Greek or who picked Latin (I don’t remember which) passed the exam. 21 One problem is to determine how a General Skolem Function can come to take as one of its arguments the set of the disjuncts. In Winter’s framework, the solution is to take disjunction to have its normal Boolean meaning (¼ join), and to take a Choice/Skolem function to select one of the minimal elements of the denotation of the disjunction. Thus Winter 2004 analyses (ia) [with a wide scope disjunction] as in (ib): (i)

a.

a. If Bill praises Mary or Sue then John will be happy. b. df [CH( f ) & [d(min(M [ S)) (kx. praise#(x)(b#)) / happy#( j#)]] where min(M [ S) is the set of the minimal sets of which the generalized quantifier M [ S is true—i.e. min(M [ S) ¼ ffm#g, fs#gg.

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Given the mechanisms that we have already used for indefinites, a simple analysis suggests itself, in which a General Skolem Function takes as argument the set of the disjuncts, in addition to n individual arguments (in the next two examples, n ¼ 0; we discuss below examples for which n ¼ 1).

Philippe Schlenker 309

4.2 Functional Readings To go one step further, I will now suggest that disjunctions can also, somewhat marginally, allow for functional readings. As with other island-escaping readings, a special intonation on ‘or’ can be helpful. In addition, we can once again use Schwarzschild’s suggestion about possible continuations of the discourse to bring out the functional reading. (44)

The functional reading in (44a) can be analysed with 1-ary General Skolem Functions, as is shown in (45): (45)

dF<1> if ["x: student x] x makes progress in F<1>(x, fsyntax, semanticsg), nobody will flunk the exam.22

4.3 Branching? Do disjunctions give rise to branching readings? If the previous observations are correct, they should, since the expressive power of quantification over Skolem functions is necessary to handle functional 22

Using the notation of (33), we may also analyze this reading as follows: (i)

df<1> if ["x: student x] (x makes progress in syntax & f<1>(x) ¼ 0 or x makes progress in semantics & f<1>(x) ¼ 1), nobody will flunk the exam.

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Context: Every student in my linguistics class in syntax or in semantics. Before the final, I say: a. If each student makes progress in syntax OR in semantics, nobody will flunk the exam. ( John must make progress in syntax, Mary must make progress in semantics, . . .) Intended Reading: There is a certain distribution of fields (syntax or semantics) per student such that if each student makes progress in the field assigned to him/her, nobody will flunk the exam. b. If each student makes progress in some area, nobody will flunk the exam. (John must make progress in syntax, Mary must make progress in semantics, . . .) Intended Reading: There is a certain distribution of fields (syntax or semantics) per student such that if each student makes progress in the field assigned to him/her, nobody will flunk the exam. c. 6¼ If each student makes progress in at least one area, nobody will flunk the exam. (<#>John must make progress in syntax, Mary must make progress in semantics . . .)

310 Scopal Independence readings of (stressed) disjunctions. As was the case for indefinites, this predicts that branching readings of disjunctions should indeed be available, as is expected in Hintikka’s system. The judgments are, if anything, more difficult than in the case of branching readings of indefinites. My impression is that the semantic judgments for (46a) are closer to those we obtain in (46b) than in (46c) (in order to avoid difficulties that may arise from the non-monotonic nature of conditionals, the examples can be refined so as to replace the if-clause with a past tense when-clause):

a. If a given representative from each country fought fights for the release of the youngest inmate OR the oldest inmate from each prison, our campaign will be was a success. b. If a given representative from each country fights for the release of a certain inmate from each prison, our campaign will be a success. c. If a given representative from each country fights for the release of at least one inmate from each prison, our campaign will be a success. On the assumption that a given representative has scope over each prison, the crucial question is what happens if the campaign fails because representatives from different countries sent conflicting signals to a given prison—some of them asking for the release of the youngest inmate, while others asked for the release of the oldest inmate. Does this entail that I lied when I asserted (46a), (46b) or (46c)? It seems to me that I could more easily claim that I did not lie if my utterance was (46a) or (46b) than if it was (46c), but of course the data are difficult to assess. If this empirical claim is correct, it can be explained by positing the logical form in (47), which involves existential quantification over Skolem Functions which each take a single individual argument and a single set argument: (47) dF<1> dG<1> ["z: prison(z)]["x: country(x)] R(F<1>(x, ku representative-from(u, x)), G<1>(z, fthe u: youngestinmate-from(u, z)), the u: oldest-inmate-from(u, z))g) Importantly, the availability of such a logical form is exactly what is expected on the basis of our earlier observations about the existence of

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(46) Context: We are fighting for human rights in China and as part of that campaign we are trying to get a representative from each country to fight for the release of one dissident from each (Chinese) prison. I make the following prediction:

Philippe Schlenker 311

island-escaping and functional readings of disjunctions.23 As in our discussion of indefinites, then, the surest way to vindicate Hintikka’s original insight is thus to make a detour through island-escaping and functional readings of disjunctions: the existence of functional readings suggests that existential quantification over Skolem functions is available, which in turn leads one to expect that branching readings should be real as well. 5 CONCLUSION

(i) When the full array of data is taken into account, Hintikka’s problem of branching readings and the syntactic problem of island-escaping readings turn out to be two sides of the same coin. In particular, data from functional readings of islandescaping indefinites motivate a semantic mechanism of quantification over Skolem functions, which in turn predicts that branching readings should be real. (ii) It is likely that disjunction shares the behaviour of indefinites with respect to island-escaping readings and possibly with respect to branching as well. This is natural both given Hintikka’s theory and given other observations that suggest that the analogies between disjunction and indefinites are quite systematic. (iii) Hintikka’s particular analysis suffered from the same drawback as analyses of island-escaping indefinites based on wide scope existential closure. Theses analyses are too restrictive and should allow for intermediate existential quantification over General Skolem Functions. On the other hand we leave it for future research to determine why indefinites can have Skolem Function readings in the first place (and why modified indefinites generally cannot).

23

This conclusion could be avoided, but only at the cost of a rather unnatural stipulation. One would have to posit that if a General Skolem Function G(R, _, . . ., _) appears in the scope of a quantifier Qx, then x must be an argument of G. This would rule out branching readings, since the latter involve Skolem Functions that fail to encode a dependency with some quantifiers they are in the scope of. Thus in (i), F<1>(R, x) and G<1>(S, y) are in the scope of two individual quantifiers, but they take only one individual argument (x and y respectively, since R and S are the predicate arguments): (i)

dF<1> dG<1> ["x: ___] ["y: ___] . . . F<1>(R, x) . . . G<1>(S, y). . .

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Although several aspects of the analysis remain tentative, this note has sought to establish the following points:

312 Scopal Independence Acknowledgements This note is a very distant descendent of Schlenker 1998. I wish to thank the following for critical comments and suggestions: Denis Bonnay, Serge Bozon, Paul Dekker, Paul Egre´, Kai von Fintel, Bart Geurts, Irene Heim, Hans Kamp, Ed Keenan, Gabriel Sandu, Barry Schein, Roger Schwarzschild, Benjamin Spector, Anna Szabolcsi, Klaus von Heusinger, and two anonymous reviewers. The author gratefully acknowledges the financial support of the American Council of Learned Societies (‘Ryskamp Fellowship’) and of UCLA.

First version received: 11.6.04 Accepted: 28.11.04 Second version received: 25.4.06

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PHILIPPE SCHLENKER Department of Linguistics, UCLA 3125 Campbell Hall Los Angeles CA 90095-1543 USA

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