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VOLUME 25 NUMBER 2 MAY 2008

CONTENTS RICHARD BREHENY A New Look at the Semantics and Pragmatics of Numerically Quantified Noun Phrases

93

141

JEAN-PIERRE KOENIG, GAIL MAUNER, BRETON BIENVENUE AND KATHY CONKLIN What with? The Anatomy of a (Proto)-Role

175

ANDREW KEHLER, LAURA KERTZ, HANNAH ROHDE AND JEFFREY L. ELMAN: Coherence and Coreference Revisited YURIE HARA: Evidentiality of Discourse Items and Because-Clauses TIM FERNANDO: Branching from Inertia Worlds

VOLUME 25 NUMBER 2 MAY 2008

EMMANUEL CHEMLA An Epistemic Step for Anti-Presuppositions

FORTH COMING ARTICLES

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VOLUME 25 NUMBER 2 MAY 2008

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JOURNAL OF SEMANTICS Volume 25 Number 2

CONTENTS RICHARD BREHENY A New Look at the Semantics and Pragmatics of Numerically Quantified Noun Phrases

93

EMMANUEL CHEMLA An Epistemic Step for Anti-Presuppositions

141

JEAN-PIERRE KOENIG, GAIL MAUNER, BRETON BIENVENUE AND KATHY CONKLIN What with? The Anatomy of a (Proto)-Role

175

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

Journal of Semantics 25: 93–139 doi:10.1093/jos/ffm016 Advance Access publication February 29, 2008

A New Look at the Semantics and Pragmatics of Numerically Quantified Noun Phrases RICHARD BREHENY University College London

This paper presents some arguments against a unilateral account of numerically quantified noun phrases (NQNPs) and for a bilateral account of such expressions. It is proposed that where NQNP give rise to at least readings, this is the result of one of the two forms of pragmatic reasoning. To that end, the paper develops an independently motivated account of specificity and existential closure involving diagonalization.

1 INTRODUCTION In this paper, the semantic and pragmatic properties of numerically quantified noun phrases (NQNPs) are considered. In particular, we will consider the status of implications like those in (1b) which are normally available from assertions of the example in (1a): (1) a. Two of the students did well on the test. b. No more than two of the students did well on the test. According to one commonly discussed view, NQNPs have a lowerbounding linguistic meaning giving rise to an at least interpretation.1 That is, an interpretation of (1a) based on an understanding of its linguistic meaning alone could be characterized according to the equivalence in (2)—where F denotes the set of sets of students and G denotes the set of sets of individuals who did well on the test: (2) Two of the students did well on the test. 5dX½jXj ¼ 2 ^ FðXÞ ^ GðXÞ
1

In what follows, single quotes (e.g. ‘two’) are used to make reference to expressions of English. Italics (e.g. ‘an at least two reading’) are used to make reference to particular interpretations.
The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected].

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Abstract

94 New Look at the Semantics and Pragmatics

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According to this view, where an upper-bounding implication as in (1b) arises it is made available through conversational implicature, based on a (neo-)Gricean Quantity maxim. While the same kind of account is widely accepted for quantified noun phrases such as ‘some students’ and ‘many students’, this view of NQNPs has never really commanded a firm consensus because their interpretation does not clearly conform to the analysis. In fact, there is a great deal of evidence which suggests that NQNPs would be better paraphrased using ‘exactly’. This evidence will be reviewed below. However, while the evidence is strong, no alternative to the standard view of NQNPs has been widely accepted. The challenge to any account of NQNPs as encoding an exactly interpretation stems from the fact that noun phrases containing numeral expressions still often give rise to at least readings. As such, any exactly account would be bound to explain the latter cases in terms of pragmatics. Until now, no such account has been forthcoming. In this paper, I will defend the exactly analysis of NQNPs and provide an account of the at least cases in terms of independently motivated pragmatic inferences concerning specificity and existential closure. We will also see that there is little independent motivation for arguing that NQNPs are simply ambiguous between the unilateral, at least interpretation and the bilateral, exactly one. As such, the bilateral-only account ought to be favoured. The proposals for NQNPs in this paper build on a set of ideas concerning specific uses of quantified noun phrases. In these cases, the speaker exploits a pervasive form of pragmatic reasoning best known in semantics as diagonalization. It will be argued that the same pragmatic account is independently required for exceptional scope data (which includes exceptional scope, at least readings of NQNPs) and for crosssentential anaphora (including anaphora dependent on specific NQNPs with at least readings). In the following sections, the standard, unilateral view of how sentences containing NQNPs are interpreted will be presented first. Subsequently, we will see that while a parallel unilateral view of NPs involving other quantity expressions would seem to be on the right track, the unilateral account of NQNPs has quite serious problems. It will be argued that, unlike other QNPs, NQNPs behave as though their linguistic meaning encodes the bilateral, exactly interpretation. We will then explore how, assuming a bilateral linguistic meaning, various semantic and pragmatic factors determine the different interpretations of utterances containing these expressions.

Richard Breheny 95

2 THE UNILATERAL VIEW There have been many proposals that the implication (1b) is an implicature premised on some Quantity maxim (Gazdar 1979; Levinson 1983; Horn 1989; van Rooij & Schulz 2006). Although these accounts differ, they are at one in ensuring that the implicature does not normally arise in downward entailing (DE) contexts; for example, that the implication in (1b) does not fall within the scope of the conditional in (3): (3) If two of Mary’s students did well on the test, then Mary won’t be fired.

(4) a. b. (5) a. b.

JohnF did well on the test. Some of the students did well on the test. If JohnF did well on the test, then Mary won’t be fired. If some of the students did well on the test, then Mary won’t be fired.

This makes sense from a Gricean perspective since implicatures based on the Quantity maxims turn on these being a more informative alternative utterance. In the case of ‘Some of the Fs have G’, this alternative is ‘All of the Fs have G’. Where there is embedding in a conditional, the alternative, ‘if All of the Fs have G then P is no longer more informative and so there is no ground for this kind of implicature. We can characterize a unilateral view as follows: Unilateral View: [two N] has unilateral lexical meaning (as suggested in (2)) and common upper-bounding implications arise as Quantity-based conversational implicatures.

3 PROBLEMS FOR THE UNILATERAL VIEW A great many observations have been made which suggest that numerals are different to other scalar items. It seems that NQNPs do

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This is reasonable when we look at other triggers for quantity implicatures. For instance, (4a) might often imply that no one other than John did well on the test. This exhaustive implication does not attach to the antecedent of the conditional in (5a). Mutatis mutandis, (4b) tends to imply that not all the students did well, while this implication disappears from the antecedent in (5b):

96 New Look at the Semantics and Pragmatics not behave as if they have unilateral meaning.2 Here, I will add some observations of my own (in section 3.1) in a survey of some of the points against the unilateral view to be found in Carston (1988, 1998), Horn (1992, 1996), Geurts (2006) and elsewhere.

3.1 DE contexts

(6) a. Everyone who has two children receives tax benefits. [Implies everyone who has three or more children receives benefits] b. Everyone who has two children received tax benefits. [Implies everyone who has three or more children receives benefits—but not so strongly] c. No one who has two children received tax benefits. [Does not imply no one who has three or more children received benefits] d. No one who has two children receives tax benefits. [May imply that everyone with three, four, etc. children receives benefits] If the unilateral view is right, these should all have implications along the lines of (6a). But they do not. In particular, (6d) seems to imply that people with more than two children receive benefits. Even 2 A note on terminology: The terms ‘linguistic meaning of a ’ or ‘meaning of a ’ will refer to the semantic interpretation(s) of a as determined by the semantic rules of the grammar as applied to the expression (in the imagined context under discussion). For instance, according to the unilateral account, the meaning of the NQNP [two students] can be given as kP:dX½jXj ¼ 2 ^ studentsðXÞ ^ PðXÞ
. The term ‘reading of a ’ will make reference to the interpretation of a when uttered in the imagined context under discussion. We will often use paraphrases to characterize readings and make reference to paraphrases in the short-hand terms noted above, viz. ‘an at least reading’ or ‘an exactly reading’. On the unilateral view, the typical reading of [[two students][failed]] could be paraphrased as j [ fX : studentsðXÞ ^ failedðXÞgj ¼ 2 (an exactly reading) due to the fact that the reading in question combines the interpretation as determined by the meaning of the sentence plus an upper-bounding implicature to the effect that no more than two students failed.

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As suggested in relation to (4) and (5) above, conversational implicatures based on a Gricean Quantity maxim ought not to arise where the triggering sentence appears in DE contexts (at least not without special intonation—see below). A brief consideration of (3) above suggests that the unilateral view of NQNPs would be confirmed in these kinds of contexts as well. However, a closer inspection of these cases reveals some more problematic data. Consider the examples in (6a–d):

Richard Breheny 97

the suggested implication of (6a) seems to turn on an implied or presupposed generalization concerning how tax benefit rules are devised.3 Consider (7) by contrast where no such covering generalization would normally be presupposed: (7) Everyone who has two children is happy.

(8) Everyone who has children or pets is happy. Indeed, it is easy to show how NQNPs should behave if the unilateral view is right by considering disjunction in contexts similar to those in (6). In each of (9a–d), the domain of quantification seems to include people who have children and pets. That is the negative quantifier in the (c) and (d) cases makes no difference: (9) a. b. c. d.

Everyone who has children or pets receives tax benefit. Everyone who has children or pets received tax benefit. No one who has children or pets received tax benefit. No one who has children or pets receives tax benefit.

These data should make us suspicious. If the unilateralist view is right, then we should understand all these examples with DE contexts in the same way as (9)—where ‘two Fs G’ has its unilateral interpretation. In fact, what we find for NQNPs is that only in those cases where we can make some kind of assumption about a covering generalization do we get an understanding that is consistent with the unilateralist view. This is brought home by considering (10a) in two contexts (10b) and (10c). In Context A, there is a suggestion that people who have more than three children are also unhappy, whereas 3 Throughout this paper, the terms ‘presupposition’ and ‘presuppose’ express thoroughly pragmatic concepts and are not meant in any way to be related to linguistic presuppositions. A pragmatic presupposition is an assumption that the speaker assumes is common ground among conversational participants, where ‘common ground’ is to be characterized in terms of structures akin to that of common knowledge or common belief (see Stalnaker 2002). (The only exception to this usage comes later in the paper in the context of mentioning van der Sandt’s and Geurts’ accounts—where their claim is that presupposition is linguistically driven.)

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It seems that on its most accessible reading, what (7) says would be true if John is miserable but has five children. Note that, by contrast with (7), (8) seems to quantify over people who have children and pets in addition to those who have only children and those who have only pets—as we would expect with the normal unilateral, inclusive interpretation of disjunction:

98 New Look at the Semantics and Pragmatics Context B pushes the invited implication the other way—that people with more than three children are happy: (10) a. No one who has three children is happy. b. Context A: People in the society under discussion tend to be more stressed the more children they have. c. Context B: The society under discussion is poor and more children means more prosperity.

(11) Two of the students did well on the test. 5j [ fX : FðXÞ^ GðXÞgj ¼ 2 In the case of (6a), the idea is that the example evokes a context where one is being informed about the tax benefit rules. To get the enriched . . . or more reading, we make a background assumption to the effect that tax benefit rules are normally couched in terms of a lower limit: Anyone who has a number of children above the lower limit also qualifies for the break. Given that the speaker would know that this is relevant and that the audience would assume that the speaker knows about such assumptions and that the speaker has done nothing to forestall such assumptions being made, it will become common ground that the speaker has made this assumption manifest. Hence, the assumption becomes what might be termed a background implicature and can be presupposed.4 Given the now presupposed background assumption and what has been asserted, the or more implication follows. In addition to the . . . or more implication, there is a further inference to be made that no one with just one child receives benefit. This inference is derived as a quantity implicature on the bilateral account: Given that, in context, a key implication of the assertion is clearly intended to be the proposition that two or more children is sufficient for a tax break, the question naturally arises whether one child is sufficient. Given the relevance of this question to the topic and given the speaker’s apparent knowledge of the tax laws and willingness to communicate them and the fact that the speaker could have used ‘one’ instead of ‘two’, one can infer that having one child is insufficient (by standard quantity-implicature reasoning). 4

See Grice (1975) and Sperber & Wilson (1986) where the ideas are introduced. See also Simons (2006) for some recent discussion of the connection between background implicatures and presupposition.

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Indeed, contrary to the unilateralist view, it seems that these data could be better explained if we assumed that the linguistic meaning of NQNPs is bilateral. That is, if instead of using the equivalence in (2) to gloss the literal interpretation, we use (11):

Richard Breheny 99

3.2 Implicature ‘intrusion’ under denial (cf. Horn 1996) Given that in many of these DE cases, our intuitions would be explained if we assume that NQNPs are interpreted bilaterally, there is another problem for the unilateral view: normally, bilateral interpretations of scalar terms in DE contexts involve a marked operation (needing focus or special contexts). Compare the exchange in (12a,b) and (12a,b#)—note: capital letters indicate special rising, contrastive intonation: (12) a. Mary: John got someF of the questions right. b. Bill: He didn’t get SOMEF of the questions right. b#. Bill: He DIDn’tF get some of the questions right. Assume that Mary utters (12a) with focus on ‘some’ and that she and Bill had been wondering how John would do on a particular test. In such

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Note that this quantity implicature is different from that which would be derived as a neo-Gricean ‘reverse scale’ scalar implicature, given the unilateral interpretation of NQNPs. In that case, the alternative, ‘Everyone with one child receives tax benefit’ is a more informative alternative and thus, only its negation would be implicated (see Levinson (2000) for an account of these ‘reverse scale’ scalar implicatures). In addition to not correctly deriving the lower-bounding quantity implicature for (6a), the unilateral view does not have anything at all to say about (6d) except that it should pattern with (6a) and so it should entail that no people with three, four, etc. children get tax benefits. In addition, it should scalar implicate that some people with one child get tax benefit. But (6d) does not pattern with (6a) at all. (6d) implies that no one with one child gets tax benefit and it can, in the right context, imply that everyone with three or more children gets tax benefit. Neither of these implications seems explicable on the unilateral view. However, on the bi lateral view, the implications are derived in the same way as those for (6a). According to the bilateral account, the same background assumptions about the structure of tax laws get to be presupposed (as above). Given this context, the assertion with the bilateral meaning for ‘two children’ implies that no one who has one child gets the tax break. Given this same context, one can notice that the speaker’s uttering the sentence, ‘No one with three children receives tax benefits’ would have been more informative since it would imply that both no one with two children and no one with one child receive benefits. Hence, by familiar quantity implicature reasoning, one can infer that the speaker did not utter this because it is not true and that having three children is sufficient for tax breaks.

100 New Look at the Semantics and Pragmatics a context, the implication that John did not answer all the questions would be available. The natural construal of (12b) is that Bill is suggesting John did not answer some and not all the questions but in fact he answered all the questions. No such construal of (12b#) is available. This would just be understood as a denial of the existential claim Mary has made.5 Now compare (12) with the parallel case in (13): (13) a. Mary: John got fourF of the questions right. b. Bill: He didn’t get FOURF (of the questions) right. b#. Bill: He DIDn’tF get four (of the questions) right.

3.3 Questions (see Horn 1992) Consider the possible answers to the question in (14a). The markedness of the answer to the at least construal of the question is in contrast 5

Why focus is required on the quantity expression in order to deny the upper-bounding implication is not a question which is settled. One popular account is that negation in this case is metalinguistic. See Horn (1989) for an early discussion.

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Here, Mary would naturally be understood to mean that John got just four questions right. But this time Bill’s response in either (13b) or (13b#) could be understood to be denying the proposition that John got just four questions right. Moreover, in (13b), it does not seem right to say that Bill is simply denying the upper-bounding inference that he got no more than four questions right; rather the contrastive stress would suggest simply that he got some other number (maybe five, maybe three) right. The intuitions are even clearer for these examples if Bill responds more naturally with the elided, ‘No he didn’t’. The idea that (13b#) might further imply that John did not get five, six or more questions right would only arise in a context where it is assumed that the test was quite difficult, that John was not expected to get as many as four questions right. However, if there were 100 questions and four are below expectations, then (13b) no longer has this implication. In summary, there is unexpected behaviour of NQNPs in DE contexts. In contrast to ‘some’ and ‘or’, it does not look like the favoured reading in DE contexts is the unilateral reading. It looks like the at least reading for NQNPs in DE contexts turns on special implicated generalizations. This weakens the case for the unilateral view since the at least reading should be the favoured or default reading in DE contexts. Where there is a bilateral interpretation of NQNPs in DE contexts, unilateralists would have to concede that some form of implicature intrusion is going on. However, this form of intrusion requires special intonation in the case of other quantity expressions but not numerals.

Richard Breheny 101

to the opposite pattern of markedness in the ‘some’ and disjunction cases. (14) a. Do you have three children? b. No. I have two. c. No. I have four. d. ?Yes. (In fact) I have four. (15) a. Do some of your friends have children? b. ?No. All of them do. c. Yes. (In fact) all of them do.

On a Gricean view of scalar implications, the oddness in (15) and (16) makes sense, since in the context of questions, the quantity maxims do not apply (questions in fact set the level of informativeness required). So, the pattern in (14) is unexpected if NQNPs have a unilateral meaning. 4 ALTERNATIVES TO THE UNILATERAL VIEW OF NQNPs As it becomes more widely accepted that the unilateralist position for NQNPs is not well supported, the question arises as to what alternatives are potentially available and whether any of these have been put forward. Although Horn (1992) provides much evidence for the fact that NQNPs are not the same as other scalar terms, no positive account is offered. Carston (1998) entertains two analyses of NQNPs. One is the bilateral account being defended here. The other is an underspecification account. According to the latter, whether a NQNP is understood as at least n, exactly n or at most n could be left unspecified by the meaning of ‘n Fs’—just as the relation between John and the book in ‘John’s book’ is unspecified by the meaning of the possessive construction. Although Carston expresses a mild preference for the underspecification account, she leaves the matter open. Regarding Carston’s favoured alternative, some of the data discussed above suggest that the underspecification account may not be correct. For example, consider the asymmetry in DE contexts. Given the underspecification proposal, it is open whether NQNPs have a unilateral or bilateral interpretation and only extra-linguistic, pragmatic

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(16) a. Did John or Mary pass the exam? b. ?No. They both did. c. Yes. (In fact) they both did.

102 New Look at the Semantics and Pragmatics

(17) a. kP:d!x½#x ¼ 2 ^ students0 ðxÞ ^ PðxÞ
b. kx½#x ¼ 2 ^ students0 ðxÞ
c. kP:dx½#x ¼ 2 ^ students0 ðxÞ ^ PðxÞ
It should be noted, however, that while (17a) is related to (17b) and (17b) to (17c) via the kind of coercion that can be found relating other descriptive expressions, (such as Geurts’ example, ‘students’) there is no way back from the predicational (17b) to the bilateral meaning (17a) via one of Partee’s ‘regular’ coercions. In fact, there is another of Partee’s type shifts that is available to operate on (17b) and that is THE. This operator yields the meaning of ‘the two students’. That (17a) does not 6 Carston’s proposal may seem to have an advantage over the current one since it also covers the at most reading of NQNPs that arises in modal and related contexts—e.g. (i):

(i)

I can fit four people in my car

However, it should be apparent that the at most reading can be derived as a quantity implicature given a bilateral meaning for NQNP (cf. the discussion of (6a,d) above). 7 Here quantification is over group individuals; # is a function from such individuals to the cardinality of the group and d!x[. . . reads, ‘there is a unique x . . .’].

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principles are the determining factor. Now it could be argued (see Winter 2001) that where there are two logically related candidate interpretations of an expression, the interpretation which is favoured, ceteris paribus, is that which makes the overall proposition expressed logically stronger. In the DE case, the stronger interpretation would be the unilateral interpretation. But intuition suggests that in DE contexts the bi lateral interpretation is favoured. That is, unless there is a supporting generalization, one reads NQNPs in DE contexts bilaterally. If, on the other hand it were not correct to assume that stronger interpretations are favoured, the underspecification account ought to predict no preference, contrary to intuition. Either way, these intuitions are problematic for the underspecification account.6 Geurts (2006) favours what is referred to as a polysemy account of ‘two’ whereby each of the three meanings is listed in the lexicon: a predicational meaning, a bi-lateral quantificational meaning and a unilateral, existential quantificational meaning. Geurts observes that these meanings are related to each other via type coercions that relate predicational and quantificational interpretations of descriptions generally (see Partee 1986). Starting with the bilateral quantificational meaning for ‘two students’ represented in (17a),ÿ7 we can derive the predicational meaning (17b) via the BE operator kFððetÞtÞ kx½Fðku:u ¼ xÞ
Þ and in turn the unilateral quantifier meaning (17c) via A ðkP:kQ½dx½PðxÞ ^ QðxÞ

):

Richard Breheny 103

(18) a. Those are exactly 50 books on descriptions. b. We need to gather 50 cows. Those are at most 20. So we need to find at least 30 more cows. Similarly, in as far as bare numerals can function as predicates in English, so can modified numerals: (19) a. We are three. b. We are exactly ten. c. If the guests arrive, they will be at most three. Given that predicates can be modified by ‘exactly n’ and ‘at most n’ and by the reasoning applied for bare numerals, there ought to be a reading of ‘exactly two students’ or ‘at most three cows’ which is derived by a form of existential closure on such a predicate. But, presumably, as a predicate,

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fit the regular Partee pattern squares with Geurts’ conjecture that the basic, underlying meaning of ‘two’ is the bilateral quantificational determiner meaning. One assumes that the other two understandings of ‘two students’ mentioned arise because it is normal in English (and other languages) that such shifts in meaning relate one sense of an expression to another. To illustrate this point, Geurts cites the case of the count/mass shift that can relate senses of ‘beer’ and ‘apple’. Each nominal has its own basic sense—respectively, mass and count. Yet via what might be called regular coercions one can derive the, respectively, count and mass meanings of the expressions. To sum up, even though the basic meaning of ‘two students’ is the bilateral, the expression is simply ambiguous between the three meanings described above. This ambiguity arises due to the presence of regular coercions in English. While this account looks neat, the argument involving regular coercions to motivate the polysemy account has an interesting and problematic corollary. Let us take another look at the structure of that argument: We grant that ‘two’ is a non-monotone determiner but we also have to recognize that ‘two’ can appear as a modifier in predicate constructions as in ‘those are two cows’. We recognize that, generally, modified nominals, like ‘brown cows’, which can appear in predicate position can appear in argument position and take on existential force, as in ‘Brown cows were standing in the field’. By analogy, we can reason that ‘two cows’ in argument position can undergo the same existential closure. Thus, ‘Two cows were standing in the field’ ought to have an at least meaning. While this line of reasoning may seem appealing, bear in mind that modified numerals can also appear as predicate modifiers:

104 New Look at the Semantics and Pragmatics

5 GENUINE UNILATERAL INTERPRETATIONS? Thus far, we have encountered a number of examples where NQNPs might be glossed using the forms ‘at least . . .’ or ‘. . . or more’ where it seems this gloss arises as a form of implicature given certain background assumptions. Let us reconsider (6a) which could be glossed, ‘Everyone who has two or more children . . .’: (6) a. Everyone who has two children receives tax benefits. It was suggested above that this at least reading could just as well arise given an exactly meaning of the NQNP via a background implication/ presupposition about the normal structure of tax laws. In addition, the unilateral view has nothing to say about the . . . or less reading of (6d) while it seems clear that this reading could be derived in the same way as the . . . or more reading of (6a) given the bilateral account.

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‘exactly two’ applies to collections of exactly two individuals while ‘at most two’ applies to collections containing two, one or zero individuals. This means that there ought to be a grammatically derived meaning of, ‘Exactly two students asked a question’ according to whose truth conditions the sentence is true where three students asked a question. There also ought to be a meaning of ‘At most two students asked a question’ which is false if no students asked a question and true if three students asked a question. All this is to suggest that the line of reasoning currently under consideration is problematic. What relationship there is between predicates modified by numerals in various ways and the homophonous argument noun phrases is not as straightforward as it may first appear. Another conclusion to draw from these considerations is that Partee’s coercions really cannot be considered sytematic, grammatically licensed shifts in meaning that simply apply across the board. Of course, Geurts’ proposal does not presume this. In fact, Geurts is explicit that the various senses of ‘two’ are listed separately in the lexicon. We can indeed separate out the proposal about the polysemy of ‘two’ from its motivation. However, in doing so we remove any independent motivation for the idea that ‘two cows’ in argument position is ambiguous between a bilateral and an existential unilateral meaning. We will return to the differences between bare NQNPs and modified versions like ‘exactly two students’ once we first flesh out the picture of how one could naturally derive the attested at least readings of NQNPs given a bilateral meaning. We begin with a survey of some further examples.

Richard Breheny 105

(6) d. No-one who has two children receives tax benefits. Some more evidence for this account of these examples can be found in a study of children’s understanding of rules such as the following, reported in Musolino (2003):

(21) Let’s see if Goofy can help the Troll. The Troll needs two cookies. Does Goofy have two cookies? Musolino notes that this new design is motivated by an example from Kadmon (2001) of the following type: (22) There are four chairs in the seminar room. Normally, an assertion of (22) would be understood to mean that there are exactly four chairs in the seminar room. However, in the kind of

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(20) If you get two hoops over the stick, you get a prize. Asked if they should reward a puppet who got three hoops over the stick, younger children in Musolino’s study tended to hold back the reward, while they were happy to reward puppets who got only two hoops over. Children of this same age group generally treat NQNPs bilaterally in truth-judgment tasks involving assertions such as ‘Three horses jumped the fence’. At the same time, these same children very strongly favour a non-bilateral interpretation of ‘some horses jumped the fence’—assenting to the statement when in fact all the horses jumped (Musolino 2003; Papafragou and Musolino 2003). The data suggest that, for whatever reason, children of 4 or 5 years find it difficult to derive implicatures of various sorts. On the other hand, it has been independently shown that children universally derive the unilateral reading of disjunction and ‘some’ in negative contexts such as the antecedent of conditionals (see Gualmini & Crain 2002). So if NQNPs had unilateral meanings, children ought not have trouble with Musolino’s task involving (20). But children do and it seems that while they start off with a unilateral meaning for disjunction and ‘some’, they start off with the bilateral interpretation for NQNPs. The reason for their odd responses for (20) would then be explained as a failure to derive the . . . or more implication via the background implicature about the structure of rules of such games. It is interesting that Musolino was able to get an at least response out of children of the same age group in a different kind of task. In this second study, one puppet requires two cookies for a certain purpose and seeks to buy them from a second puppet, Goofy. In the critical trials, Goofy has four cookies to sell and children in the age group tended to assent to the final question in the following discourse:

106 New Look at the Semantics and Pragmatics

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context Kadmon discusses, a person is looking for four chairs (needed for a meeting for instance) and tells you so. You utter (22) when all you know is that there are many more than four indistinguishable chairs in the seminar room. In this context, it seems clear that, for all we learn from the speaker, there could be more than four chairs in the seminar room. However, we in fact do not really learn from the speaker anything about any number greater than four. This kind of example is clearly different from (6a) and (20). In fact it is different to the extent that we would be reluctant to gloss what the speaker means using ‘or more’. That is, we would be reluctant to use ‘There are four or more chairs in the seminar room’ as a gloss of what the speaker means. Rather, what the speaker means is something like, ‘There are four chairs for you in the seminar room’ or ‘There are four chairs for your purpose in the seminar room’. In the other example, when we include the implicature the speaker means that if you have two or more children then you qualify. What we can say about the difference between the Kadmon example (22) and examples such as (6a) is that the former involves a form of domain restriction while the latter involve a form of conversational implicature. This would explain young children’s differential performance on tasks based on the different kinds of example: while children do not have difficulty with domain restriction (they must encounter quantificational phrases that require domain restriction all the time), they do have difficulty with genuine conversational implicature of the kind found in (6a). Having said that, it is legitimate to wonder what it would mean to say that there are four cookies for the puppet in the presence of six cookies that are equally available for sale. Which four cookies are at issue? The answer for the children in Musolino’s study may be that they partition the cookies in their mind yielding a set of four cookies for the puppet. In fact it ought not suprise us if a child playing this game insists on a certain four cookies when the puppet goes to collect his purchase. In general, we can see different collections of four cookies as being the ones that the puppet receives for its purchase and we can accordingly identify different potential goal states for the puppet—one for each possible set. But given that we do not know which four cookies the puppet will receive or even whether the puppet in fact does receive four cookies, how is it that we can talk about the four cookies for the puppet? The answer to this question that will be expounded at length below involves a form of pragmatic reasoning known variously as pragmatic assent, reflexivization or diagonalization (see Stalnaker 1978; Perry 2001). Effectively, the idea is that we take for granted that there

Richard Breheny 107

were four specific cookies already identified in making the assertion and, without knowing which four have been identified, see what would follow from the assertion. In this case, what follows from the assertion is that the puppet can realize its goals through a cookie purchase. A number of ‘at least’ examples discussed in the literature seem to pattern the same way. Consider the following example from Carston (1998): (23) A: If you have two children you qualify for child benefit. B: I have two children. (In fact I have three.)

(24) a. I predict twenty people will be there tonight. b. I bet that five women finish in the top one hundred in this year’s marathon. (25) a. You must take two cards. b. To qualify for this course, you must have two A grades. Probably the most accessible understanding of (24b) and (25b) is the at least one while (24a) and (25a) are more clearly ambiguous in that we can imagine contexts where they give rise to an exact reading just as easily as contexts where the at least reading is intended. Examples like (25b) pose a challenge to any bilateral account of NQNPs since here we seem to be able to obtain an at least reading where the NQNP is part of a necessary condition. Strictly speaking, having exactly two A grades as a necessary condition for qualification would seem to preclude having three. By contrast, having two children as a sufficient condition for tax breaks (as per (6a)) does not preclude having three children and qualifying. Whereas the addition of an implicature to the meaning of (6a) narrows down the overall interpretation in the appropriate way, it does not seem that a similar move would be possible in the case of (25b). To compound the challenge for the bilateral account, we can observe that the main quantity implicature for (25b) is that one does not need

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In a sense, we could gloss B’s response as, ‘I have two children for the purposes of fulfilling the child benefit rules’ and it is easy to see how, if NQNPs have a bilateral meaning, this reading could be derived along the lines of the Kadmon example. The strategy for the bilateral account then is to argue that at least readings can arise either through a kind of background implicature or via this process of reflexivization. An important class of cases to be considered involve modal contexts—(24a) is from Carston (1998), (25a) is from Geurts (2006):

108 New Look at the Semantics and Pragmatics

6 SPECIFICITY AND EXISTENTIAL CLOSURE

6.1 Preliminaries Suppose that, in talking about what happened in a popular park on a Sunday afternoon, the speaker utters (26): (26) Two men were walking in the park. You know that it is unlikely that the speaker is claiming that just two men were walking in the park; rather, the natural understanding of this kind of speech act is as a piece of discourse introducing two men. Which two? In some cases, but probably not so many, it may not matter which two and, as in Kadmon’s chair example, you can just assume that the two men are given and see what follows from that. In other cases, you might assume that the speaker stands in some kind of epistemic relation with two specific men and it is these that the discourse is about. These would be the two men the speaker has ‘in mind’ in producing this token of the noun phrase. The latter kind of specific reading comes to the fore where there are continuations involving anaphora: (27) Two men were walking in the park. They were whistling.

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more than two A grades to qualify. This is the implicature one would derive if (25b) were to be equivalent to hdx[#x ¼ 2 ^ A-grades(x) ^ you_have(x)], since the alternative, ‘You must have three A-grades’ would entail what is asserted and thus its negation would be implicated. Before getting too enthusiastic on behalf of the unilateral approach given this example, we should note first that, like (6a), the reading of (25b) needs the appropriate kind of background assumptions about the nature of the underlying rules. Secondly, the exactly readings of these examples, such as where (25a) is understood to mean you must take just two cards, are not derivable via standard Gricean reasoning given a unilateral meaning. At best, the examples could be seen as motivation for the ambiguity approach. It will be argued below that these examples can be seen as exploiting the same form of reasoning as sketched above for the Kadmon examples. Moreover, in cases such as these, the form of reasoning effectively constitutes a kind of pragmatically derived existential closure. Motivation will be provided in favour of this pragmatic route over the grammatically encoded route. The motivation will come from exceptional scope facts and facts about anaphoric relations—topics to which we now turn.

Richard Breheny 109

(28) They weren’t men, they were robots, and they weren’t walking, they were rolling on little wheels. So here we have a case where one might gloss a sentence containing an NQNP with ‘at least’ but where there is good reason to think that the NQNP itself is understood bilaterally but specifically. In this section, we will consider those at least examples discussed above that cannot be handled via the background implicature account to see if, like Kadmon’s example, they may be explicable as specific noun phrases that are interpreted by a pragmatic reflexivization process. In order to make the discussion more concrete, we first need to make some assumptions about what it means for ‘two men’ to have a bilateral meaning and for such a noun phrase to be understood specifically. This we will do now and in addition, we will go over the two-dimensional framework for representing the pragmatic reasoning behind (27), as introduced in Stalnaker (1978) and elsewhere. We assume that, as an argument NQNP, ‘two Fs’ is assigned a meaning by the semantic rules of English along the following lines:9 8 This is not the only problem facing the dynamic treatment of such examples and the reader should consult Stalnaker (1998), van Rooij (2001) and Breheny (2004) for more reasons to favour the specific analysis of the indefinites in these cases. 9 This way of representing the bilateral meaning of NQNPs as Generalised Quantifiers is the most ‘neutral’ in the sense that it allows for a reading of ‘Three men lifted the piano’ which is true if John single-handedly lifted the piano and Bill and Sam also did. We can also assume, following Schwarzschild (1996) and others that distributivity, when it occurs, is a property of the predicate, here G.

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While this way of looking at things suggests that ‘two men’ is bilateral and specific, someone who is tempted by either the unilateral account or the ambiguity account could claim that (26) and (27) both involve the existential, unilateral meaning of ‘two men’, as per Geurts’ proposal in (17c) above. The proposal would be that in (27), the quantifier is dynamic, binding the plural pronoun in the second discourse segment (see Groenendijk & Stokhof 1991; Kamp & Reyle 1993; Chierchia 1995 for some ideas of how this might work). However, this type of example has been discussed at length in the literature on dynamics and anaphora where it has been observed that a simple dynamic binding relation between ‘Two men’ and ‘they’ cannot capture the fact that the anaphoric relation is mediated by the specificity of the antecedent and the definiteness of the anaphor (see Stalnaker 1998; van Rooij 2001; Breheny 2004). For example, while a natural continuation of (27) by an interlocuter might involve so-called pronominal contradiction, as in (28), this cannot be accounted for in any kind of dynamic binding approach:8

110 New Look at the Semantics and Pragmatics (29) kG: j [ fZ : FðZÞ ^ GðZÞgj ¼ 2

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Turning now to the question of specific noun phrases, there have been a number of proposals in the literature about their formal treatment. Most notably, specific indefinites have been analysed semantically using choice functions (see Reinhart 1997; Kratzer 1998; Winter (2004) and Schlenker 2006 among others). Among these, we can distinguish between Kratzer’s account and the others. For Kratzer, specifics introduce a free choice-function variable while for other accounts a mechanism of existential closure is employed in deriving the semantic interpretations of sentences containing specifics. We will discuss existential closure accounts as they would apply to NQNPs a little later. Among non-choice-function accounts, that which is found in Schwarzschild (2002) is in interesting way similar to Kratzer’s. Schwarzschild (2002) advocates the ‘singleton indefinite’ approach. Effectively, Schwarzschild’s proposal is that indefinites are quantified noun phrases but, when they are specific, they are understood to have a contextually restricted domain of quantification containing just one individual. So, ‘a man’ is understood specifically where the domain of quantification is taken to have been reduced to a unit set. In the case of ‘two men’, the idea would be that the domain of quantification is a singleton collection, but, given the meaning in (29) above, this singleton collection would be of two men. Although Schwarzschild’s proposal is formally distinct from that of Kratzer (1998) the two have an important property in common when contrasted with other choice function accounts. This is that they presume that the speaker can express a proposition in context knowing that the audience cannot grasp what that proposition is through ignorance of the value of some kind of contextual parameter. For Schwarzschild, all one knows about the contextually restricted domain of quantification for the indefinite is that its extension consists of just one member. But Schwarzschild acknowledges (following Stanley & Szabo 2000) that quantified noun phrases require that one supply the intension of the domain for a full interpretation. For example, where the speaker uses ‘every student’ intending to quantify over students in Bill’s class, then what context supplies is not simply the set of individuals in Bill’s class but a function from worlds to the set of whoever is in Bill’s class. Thus, on Schwarzschild’s account, the audience often does not know what the full, contextually determined interpretation of ‘some student’ is when it is used specifically. In a similar vein, on Kratzer’s account, when ‘some student’ is understood specifically, the noun phrase is analysed so that a choice

Richard Breheny 111

10

In fact this is one of the three principles proposed in that paper. Although Stalnaker suggests his principles are all broadly Gricean in spirit, his motivation for the principle in question stems also from the idea that the meanings of expressions are not generally up for grabs in conversation. 11 In ‘Logic and Conversation’, Grice (1975) reserves a special category of implicatures which turn on the open flouting of maxims. In these cases, the implicatures ‘repair’ the violation not at the level of what is literally said but at the general communicative level.

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function variable is sister to the nominal predicate—understood as providing the argument for the choice function. Thus, when a speaker uses ‘some student’ specifically, in order to grasp what proposition is expressed, one has to know which function serves as the value of the variable and hence one should know which individual the indefinite denotes. But often one does not, as we will see shortly. Normally, it is expected of the speaker that the audience can grasp the full set of truth conditions for the sentence he/she utters. For example, if ‘John’ is used, then the speaker should ensure that, in context, the audience can figure out which John is referred to. Similarly, the audience should be able to infer the referents of pronominals and demonstratives and the domains of quantified noun phrases. These expectations are summed up in Grice’s Manner maxims enjoining clarity and the avoidance of ambiguity. In two-dimensional terms, Stalnaker (1978) proposes a principle of conversation which also captures this expectation: this is the principle that the speaker express the same proposition in each context alternative.10 In following Schwarzschild’s or Kratzer’s suggested analysis, here we should note that their proposals imply that speakers openly violate these expectations in the case of specifics. This raises the question why such violations are condoned in this kind of case. We can get an answer to this question by noting firstly that in openly violating the expectation, the speaker is at least at some level being clear (about not being clear). Second, as suggested in the discussion of Kadmon’s example, it is not always necessary to determine exactly what proposition is expressed. Sometimes, one can take the truth of that proposition for granted (without knowing exactly what it is) and see what follows from that. If what does follow for the hearer is sufficient for the conversational purpose at hand then, in some sense, the speaker has respected the Gricean principles at the level of what is implied (or implicated) if not what is said.11 Among the more frequently discussed uses of specific indefinites are those that give rise to exceptional scope effects—to be examined below—and those that introduce individuals into discourse—as in (27). Arguably, in both these cases, the exploitation of the conversational principles is an efficient means to an end which is not easy to realise otherwise. Similarly, it is being argued

112 New Look at the Semantics and Pragmatics

12

At this stage, nothing precludes using Kratzer’s approach to derive many of the readings to be discussed. However, doing so would introduce an unnecessary ambiguity into NQNPs. This point will be taken up in the final discussion.

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here that this form of exploitation is an efficient means to getting across at least readings of NQNPs in many contexts. In what follows, the reasoning behind the exploitation of specifics (including specific NQNPs) will be cast in Stalnaker’s two-dimensional framework (see Stalnaker 1978, 1998). In that framework, the set of worlds in which what is common ground is true is called the ‘context set’. Speech acts have the affect of changing the context set in two ways: The facts about the speech act can affect the context set and, once the speech act is accepted, this also results in a change to the context set. For example, when the speaker utters S in order to assert some proposition p, the effects include the elimination of alternatives in which p is not true in addition to the elimination of alternatives in which the speaker does not utter S. As a preliminary, it will be worthwhile to work through the account of the discourse in (27) in the two-dimensional framework. We will be using Schwarzschild’s approach while treating NQNPs as bilateral quantified noun phrases.12 In the context described for (27), where it is assumed that the speaker is introducing two indivduals into the discourse rather than making a claim about the totality of men walking in the park, one assumes that the noun phrase is specific. Adopting Schwarzschild’s approach, we can say that the NQNP’s domain of quantification is implicitly restricted so that one collection of individuals remains. Just how implicit domain restriction arises is a matter of some debate (see Stanley & Szabo 2000 among others) but it seems clear that it is an independent phenomenon. As such, we follow Schwarzschild and simply assume that such restrictions occur. However, for the purposes of discussion in what follows, we will make this implicit restriction explicit along the following lines. Where a noun phrase like, [two men] is specific, we talk about its interpretation as if the form of the noun phrase is really [two men who have P] where P is a to-be-specified predicate. As the noun phrase is taken to be specific, it is presupposed that P applies to just one collection (of two men). Given that the speaker has uttered the first sentence of (27) clearly intending the noun phrase to be understood specifically in this way, we can reason as follows: The speaker is violating the pragmatic principle that he/she expresses the same proposition in each context alternative. In fact, as far as can be presupposed, P could denote any singleton set containing a collection of two men and so the speaker’s utterance causes the set of possible context alternatives to proliferate with different

Richard Breheny 113

(30) dX½jXj ¼ 2 ^ menðXÞ ^ walking in the parkðXÞ
Strictly speaking, though, in the context of the utterance having been made (with alternatives now discriminated according to different values for P), the diagonal proposition in fact entails (30). In some cases, this difference may not be so important since the distinction between alternatives that turn on choices of values for P may not be so relevant and indeed the existentially quantified proposition may be taken to be the main point of the utterance. So far so good. We have an account of how, for instance, the Kadmon examples come out seeming to involve unilateral 13

In fact, strictly speaking, the alternatives proliferate in a more fine-grained way than is suggested here since it is really properties that context has to identify in resolving for P. In the case at hand, it is not necessary to take this level of fine-grainedness into account. Later, in modal contexts, it will be.

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collections of two men in the denotation of P in different alternatives.13 We can assume that, in flouting the pragmatic principle, the speaker is inviting us to see what follows on the assumption that the proposition she expresses is true. So at this point, we can repair the principle that the speaker expresses the same proposition in each alternative by assuming that in each currently live alternative the speaker expresses the proposition that what he/she says in that alternative is true. That is, in each alternative, the speaker expresses what Stalnaker calls the diagonal proposition. The diagonal is true at a world, w, if what the speaker says at w is true. It is to be noted that, conceptually, the repair takes place after the utterance of the specific is made. That is, in updating the context with the diagonal proposition, we are considering alternatives which we discriminate in terms of different denotations for P—among other things. So, let us consider two live context alternatives, w and w# in both of which m1 and m2 are the two men in the collection P picks out. The difference between w and w# is that in w, but not w#, m1 and m2 were walking in the park. In updating the context with the diagonal proposition, we eliminate w# and keep w. But notice that in w#, there could just as well have been two or more men walking in the park (just not both m1 and m2). So, in updating the context set with the diagonal proposition, we may be eliminating context alternatives where two men are walking in the park. However, if we individuate alternatives as they were prior to the speaker’s utterance, for any two men, mi and mj, we retain every alternative in which mi and mj walk in the park. This means that the overall effect is almost the same as updating the pre utterance context with the existentially closed proposition given in (30):

114 New Look at the Semantics and Pragmatics

(31) dX½jXj ¼ 2 ^ menðXÞ ^ walking in the parkðXÞ ^ whistlingðXÞ
Again, if we do not care too much about what P expresses, we may understand the speaker’s main point to be this implication of his or her utterance. It may seem that, in this way, we derive an interpretation which is virtually equivalent to that which is derived by simple dynamic binding. However, Stalnaker’s assumptions about the pronoun ‘they’ are too weak.15 To see this, consider that the following discourse is infelicitious: (32) Two boys were playing cricket in my garden. #He hit a shot and broke one of my windows. If we assume that in each alternative, ‘he’ in the second utterance simply refers to a uniquely salient individual, there is nothing to stop us individuating alternatives whereby one of the two boys mentioned in the first utterance is uniquely salient and other alternatives where the other is uniquely salient. The resulting interpretation would be the same as having said, ‘One of them hit a shot . . .’. Given that the continuation would have been otherwise perfectly coherent it seems we must conclude that the pronoun carries with it more than simply the presupposition of unique salience. It seems indeed that the definiteness of the pronoun brings with it some kind of additional indentifiability constraint. One apparent way to satisfy that constraint is 14

The motivation for the presupposition of unique salience comes from examples like, ‘John is married. ?She is French’ and Partee’s notorious marble example. 15 This point is developed at greater length in Breheny (2006a).

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interpretations of the NQNP. In fact, the account just given recapitulates in two-dimensional terms the more informal line of reasoning sketched in section 5 for this kind of example. We begin to depart somewhat from Kadmon’s favoured dynamic treatment of these cases when we look at pronominal anphora. Let us continue with the second segment of (27), which contains the pronoun, ‘they’. In line with the assumptions in Stalnaker (1998), we could assume that such expressions are simple variable terms of direct reference, which come with a presupposition that their referents are uniquely salient.14 At the point where the second utterance is made, we currently have active alternatives in which the collection of two men in the denotation of P was walking in the park. Taking the pronoun to be referring to this collection, we update the context by eliminating alternatives where the men in question are not whistling. The result is a kind of extended diagonal proposition which entails (31):

Richard Breheny 115

6.2 More non-specific specifics and the pragmatics of existential closure Anyone familiar with the literature on specific indefinites and exceptional scope will recognize our treatment of the Kadmon-style examples above as applicable to often discussed cases of exceptional scope indefinites. Consider for instance (33): (33) Mary will accede to the throne if two old uncles die before she does. An approximate gloss of the relevant reading of this example is that there are two old uncles who are such that Mary accedes if they die before she does. The example is referred to as a case of exceptional scope since it is assumed that the reading in question ought not to arise if normal grammatical constraints on scope are functioning. Most treatments of this kind of example aim to derive the relevant interpretation while assuming that there is no movement of the noun phrase out of the subordinate clause (see Reinhart 1997, Kratzer 1998 a.o.). Such examples are discussed in Breheny (2006b) where the no-movement view is taken and where it is shown that these cases can be handled via diagonalization. In the case at hand, even if we assume that ‘two old uncles’ is interpreted bilaterally, it is a straightforward matter to account for the understanding in question if the NQNP is understood specifically (i.e. as ‘[two old uncles who have P]’) and it is assumed

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by identifying individuals as those the speaker has in mind in uttering a given noun phrase. In the case we are considering, the utterance of ‘two men’ in the first segment is understood to be traceable via a causal chain to a collection of two men whose activities serve as the grounds for the speaker’s utterance. To say that the individuals are identified in this way is to say that P is identified with a token-reflexive property ‘being the collection s had in mind in producing u’ (where u is the utterance of the noun phrase). Having identified P in this way, the distinction between context alternatives is no longer irrelevant as it is in the Kadmon example and thus the strengthened proposition is taken to be expressed, i.e. that the collection of individuals that s had in mind in producing u whistled. That this is an acceptable way of identifying individuals is motivated by the pronominal contradiction examples, like (28) above, where one can talk about the specific individuals introduced by dicourses such as (27) independently of the descriptions used by the speaker (see van Rooij 2001 and Breheny 2004 for more evidence of this kind).

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(34) a. Mary will accede to the throne if just two old uncles die before she does. b. Mary will accede to the throne if exactly two old uncles die before she does. Note that, according to the non-specific construal of (34a,b), Mary’s accession is triggered by the death of any two old uncles, so long as there are no more than two. This is not the same as the specific ‘exceptional scope’ readings of these examples. That these exceptional scope facts fall out of the same account as that given for the Kadmon-style examples and the dynamic binding cases adds support to the proposal that apparent unilateral, existential understandings of NQNPs are derived in this way, starting with bilateral NPs understood specifically.17 But there is more motivation 16 It should be granted that (34b) in particular requires a little context to justify the use of ‘exactly’, but not too much. For instance, one can easily get the reading in question if (34b) is a response to a vague claim about the accession, for instance that there are ‘not many’ people standing between Mary and the throne. 17 The connection between ‘dynamic binding’ and exceptional scope cases is made in van Rooij (1998). That paper builds on van Rooij (1997) and explores the issues of implementing the pragmatic technique of diagonalization into a dynamic semantics for a formal language and does not explore the case of NQNPs.

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that the speaker intended to convey the diagonal proposition—as above. The result after updating with the diagonal is that, in each context alternative, the two old uncles in the denotation of P are such that their death leads to Mary’s accession. Given that we have included no other information about P in our update, we can see that the overall effect of the utterance is to inform us that there is a way of choosing a pair of old uncles such that their death prior to Mary’s leads to her accession. It is relevant at this stage to note that, on the diagonalization account of exceptional scope examples like (33), it is not necessary to assume that the speaker is communicating that it is two old uncles s/he has in mind that stand between Mary and the throne. However, in contexts where it is relevant, it may be that the speaker is optionally conveying this extra information about whoever satisfies P and this information can be accommodated. Without this extra assumption, diagonalization would have the effect that the simple existentially closed proposition is being conveyed. In Breheny (2006b), it is argued that it is a virtue of the diagonalization account over contextualist accounts such as Kratzer’s that it accommodates the intuition that sometimes examples like (33) can be understood in a purely existential way. It is also relevant to note at this point that other types of noun phrases that are bilateral can give rise to the same understanding:16

Richard Breheny 117

that this general pragmatic approach to deriving existential closure is the correct one once we look at a popular alternative involving a mechanism of free existential closure. As mentioned above, a popular analysis of indefinites involves the use of choice functions. Building on earlier work in Reinhart (1997) and Winter (1997), recent work (see Winter 2004 and Schlenker 2006) has seen the need to interpret indefinites using choice functions of variable adicity—along the following lines (where # is an object of which no predicate is true):

For reasons discussed in Kratzer (1998) and elsewhere, examples such as (36a) below need to be analysed using a unary General Skolem Function whose domain is the set of linguists. This analysis is represented in (36b): (36) a. Every linguist has studied every analysis that has been proposed for some problem. b. dF<1>[[Every linguist]i [has studied every analysis that has been proposed for F(xi, problem)]]. While Kratzer (1998) leaves the skolemized choice function variable free, Schlenker (2006) and Winter (2004) both advocate a mechanism of free existential closure of such free variables. Important motivation for this move can be found with examples such as (37a,b), discussed in Chierchia (2001): (37) a. Not every linguist has studied every analysis that has been proposed for some problem. b. No linguist has studied every analysis that has been proposed for some problem. Chierchia argues against Kratzer (1998) that (37a) need not be understood as if the skolemized choice function variable has been given a particular referent by context (as shown in (38a) below) but as if some kind of existential closure has occured immediately within the scope

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(35) F is an n-ary General Skolem Function if for any n-tuple of objects and any set E, Fðd1 ; . . . ; dn ; EÞ 2 E if E 6¼ ; Fðd1 ; . . . ; dn ; ;Þ ¼ # if E ¼ ; (Schlenker 2006, p. 288)

118 New Look at the Semantics and Pragmatics site of the binder of the implicit variable of the function—as represented in (38b): (38) a. [[Not every linguist]i [has studied every analysis that has been proposed for F(xi, problem)]] b. [[Not every linguist]i dF<1> [has studied every analysis that has been proposed for F(xi, problem)]]

(39) Exactly two students read every paper that some professor wrote. While one can imagine contexts where (39) is understood according to the intermediate scope gloss in (40a), there is no reading of this example that corresponds to widest scope existential closure— represented in (40b) below—which is equivalent to (40c) (see Schwarz 2002 and Breheny 2006b for details): (40) a. [[exactly 2 students]x dF<1>[x read every paper that F(x, ku.professor(u)) wrote]] b. dF<1>[[exactly 2 students]x [x read every paper that F(x, ku.professor(u)) wrote]] c. [At least two students]x [[some professor]y [x read every paper that y wrote]] and [At most two students]x [[every professor]y [x read every paper that y wrote]] 18

In this example, the noun phrase ‘exactly two students’ should not be understood specifically but rather it should be assumed that the domain of quantification (of students) is given—say the students in the course the speaker is teaching.

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This is not to say that (37a,b) cannot be understood as if there were a particular kind of problem in question—as where the indefinite is modified with ‘a certain’. But it also seems clear that Chierchia’s point stands that these examples can be independently understood in the manner suggested in (38b) where there are potentially different kinds of problem for different linguists. So it seems that some mechanism of local existential closure is required for these examples. However, in Breheny (2006b) it is argued that the nature of that mechansim is pragmatic and derives from the same kind of reasoning (using diagonalization and accommodation) as employed in the examples already discussed. Below, we will see how this kind of account can be extended to derive the intermediate scope existential closure reading of (37a) glossed in (38b). But first we should note that any account positing a mechanism of free existential closure (such as Winter’s or Schlenker’s) has problems of its own in that it over generates. This problem is discussed at length in Schwarz (2001, 2002) and can be illustrated using the following example:18

Richard Breheny 119

The general observation in Schwarz (2002) is that the mechanism of free existential closure of a choice function variable generates unattested readings where closure is allowed at the root-clause level in all cases except where the binding quantifier is monotone increasing—as in (36a). In Breheny (2006b) it is argued that the effect of intermediate existential closure can be achieved pragmatically and that the manner in which this effect is derived precludes the widest scope closure reading.19 The account can be illustrated by considering (41a), which has an intermediate scope reading—glossed in (41b):

As before, we proceed by assuming that the NQNP is specific as suggested in (42) and following the diagonalization path: (42) It’s not true that Mary will accede to the throne if [two old uncles who have P] die before she does. The mechanism that gives rise to the intermediate scope effect involves accommodating a further assumption about P. Recall that in the discourse example (27), the definiteness of the anaphoric pronoun triggered a further accommodation about the identity of P—that it applied to the collection of individuals that the speaker had in mind. Recall also that such an accommodation can be optionally made for examples such as (33). Now, by accommodating a different kind of assumption about P, one can derive the intermediate scope effect for (41). The accommodation in question is that P picks out a ‘first among equals’ collection of uncles; to wit, a collection of two uncles which are such that if any pair of uncles’ deaths trigger Mary accession, the deaths of the collection of two uncles P picks out trigger her accession. In general, if we have the NQNP in the scope of some operator, [O1. . . [two Fs who are P] . . .], and this whole construction is in the scope of another operator, [O2. . . [O1. . . [two Fs who are P] . . .]], then 19

Recall that we derived the widest-scope readings of examples such as (33) via diagonalization but that reading was derived as a relevant implication of the diagonal proposition. Recall also that the diagonal proposition was not equivalent to the existentially closed proposition but entailed it. In cases where the indefinite is in the scope of DE or other non-monotone quantifiers, the un-enriched diagonal would still entail the existentially closed proposition but that implication is generally not so relevant and not considered a reading by informants.

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(41) a. It’s not true that Mary will accede to the throne if two old uncles die before she does. b. It’s not true that dF<0> [Mary will accede to the throne if F(two old uncles) die before she does]

120 New Look at the Semantics and Pragmatics we can always accommodate a ‘first among equals’ assumption about P so that we can have the intermediate scope effect without movement. Suppose / is the result of extracting the NQNP from within the scope of the operator, O2. That is, if the interpretation of [O2. . . [O1. . . two Fs who are P . . .]] is represented as O2#(w1(two_Fs_who_P#(w2))) where two_Fs_who_P# is an (((e,t),t),t) operator and w2 is possibly null, then / is kX[w1(kQ[Q(X)](w2))]. In that case, and where P is type ((e,t),t) the ‘first among equals’ presupposition is as follows: (43) :ðdX½jXj ¼ 2 ^ FsðXÞ ^ uðXÞ
Þ _ dX½PðXÞ ^ uðXÞ


(44) a. Not every student read every paper that two professors wrote. b. [Not every student]i dF<1> [read every paper that F(xi, two professors) wrote] c. [[Not every student]i [read every paper that [two professors who have P(xi)] wrote]] The relevant ‘first among equals’ accommodation is given in (45): (45) "u½students(u)/:(dY½jYj ¼ 2 ^ professors(Y) ^ "y 2 Y½"z ½paper(z) ^ wrote(z)(y) / read(z)(u)


)_dX[P(X)(u) ^ "y2 Y½"z ½paper(z) ^ wrote(z)(y) / read(z)(u)


Given (44c) and (45), we learn that not every student read every paper that the collection of two professors paired with them by P wrote; and in addition that P pairs each student, x, with a collection of two professors all of whose papers x has read, if there is any such collection. Thus, together, (44c) and (45) tell us just what (44b) tells us.

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In the example under discussion, / is kU[Mary will accede to the throne if U die before she does]. Then, given that P is presupposed to pick out just one collection of two uncles, the assertion of (42) contradicts the right disjunct of (43) leaving us with the left disjunct of (43) being implied. A similar story can be told for the derivation of the reading (44a) represented in (44b). One difference lies in the nature of the implicit modification. Again we follow Schwarzschild (2002) in observing that, generally speaking, one quantified noun phrase’s domain of quantification can be dependent on another. As this is an independent phenomenon we can, for the purposes of this discussion, simply assume that the implicit restriction can be functional and is so in this case. Thus (44a) is understood as if the form were more like in (44c) where P is understood to pair each student in the domain of quantification with just one collection (of two professors):

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6.3 At least readings in modal and other embedded contexts We can now return to some of the other examples discussed in the last section which seemed to motivate an ambiguity account: (24) a. I predict twenty people will be there tonight. b. I bet that five women finish in the top one hundred in this year’s marathon. (25) a. You must take two cards. b. To qualify for this course, you must have two A grades. It should be clear at this stage how the account of the narrow scope existential readings of these kind of examples ought to go. There is one refinement that needs to be made to the way we have been thinking about diagonalization so far. In cases where the NQNP is in the scope of modal expressions it matters what property P expresses. Thus, what we need to consider are context alternatives that differ according to which property P expresses. So to take (25a) as an example, the relevant first-among-equals assumption about P would be that, given a context alternative, w, P expresses a property, Pw, which is such that in each permissable alternative accessible to w, either there is no collection of two cards you take or you take the collection that Pw picks out. Thus,

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At this stage, one could ask what would cause anyone to make such an assumption as in (43) or (45). One answer is simply that there is no other way to obtain the relevant scope reading due to the abovementioned grammatical constraint on scope relations. But more to the point, the answer lies in the fact that the pragmatic reflexivization process is quite general. It is the discourse-level existential-closure mechanism and one good reason for thinking so concerns the fact that the effect of the unattested widest scope existential closure cannot be obtained in this way. To see this, consider how we might try to extend the scope of / to include also negation. That is, consider what happens if / is kU[It’s not true that Mary will accede to the throne if U die before she does]. If we plug this into (43), given that P is presupposed to pick out just one collection of two uncles, we get a disjunction whose right disjunct says the same as what is asserted while the left disjunct merely contradicts what is asserted. So the ‘first among equals’ presupposition adds nothing in this case. Similar considerations apply to (39) and (44c) (see Breheny 2006b). So, seeing discourse-level existential closure in this pragmatic way helps us to understand why the unwanted readings generated by free closure are not available.

122 New Look at the Semantics and Pragmatics in updating the context with the diagonal proposition, we retain the context alternative, w, just in case you take two or more cards in each deontic alternative accessible from w. An obvious candidate for P in (25a) would be something like, ‘being the first two cards chosen’ but in other cases, such as (46), a more general first-among-equals presupposition is required: (46) You must not take two cards.

(47) "w#½w#Rw/(:dX½jXj ¼ n ^ F(X) ^ G(X)
_ dX½Pw(X) ^ G(X)
)
Here, G represents the scope of the existential closure. For both (25a) and (46), this would be kX.You take X. Note that with the relevant first-among-equals accommodation, an utterance of (25a) could be compared with an alternative utterance of ‘You must take three cards’ in terms of informativeness. Under these conditions, the un-uttered sentence would have been more informative and, if it would have been relevant, a quantity implicature to the effect that you need not take three cards would follow. Hopefully, it should be clear by now that in following through the pragmatics of specificity and diagonalization, we can account for all the various at least readings of NQNPs discussed.

7 SPECIFICITY, DIAGONALIZATION AND ANAPHORIC RELATIONS In this section, we will explore what kinds of anaphoric relations can exist between NQNPs and pronominals. We will see that where the NQNP antecedent has the at least reading, the approach being promoted in this paper gives a better account of the facts than any alternative account which just says that NQNPs are ambiguous. To get things started, let us return to the discourse in (27): (27) Two men were walking in the park. They were whistling. We have seen how to derive the relevant interpretation of this discourse by starting out with a specific bilateral NQNP. It was also mentioned

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So, considering the general class of modal contexts exemplified in (24) and (25), we can give the general scheme for the first-among-equals presupposition in (47), where w is a context alternative and Pw is the property expressed by P in w and R is the relevant accessibility relation for the modal:

Richard Breheny 123

that there is good reason to think that the pronoun in the second sentence forces an identifiability condition, satisfied in this case by thinking about the possible specific collections of individuals as those the speaker has in mind. It is this extra dimension of the interpretation of such discourses that the simple dynamic binding account misses. Problems for dynamic binding multiply when we consider that exceptional scope indefinites can give rise to similar anaphoric relations: (48) Mary will accede to the throne if two uncles die before she does. Fortunately for Mary, they are very old.

(49) They are not uncles. They are second cousins. This is handled in a straightforward manner by the diagonalization account: At the point where the second utterance of (48) is made, in each alternative we have a collection of two uncles in the denotation of P and Mary accedes if these die before her. As with the discourse above, the definiteness of the pronoun forces one to identify the collection in question independently—the most natural way being to think about them as the collection the speaker has in mind. We then understand the correction in (49) as an injunction to alter what is presupposed, so that the collection the speaker has in mind are second cousins not uncles. As an alternative implementation of the unilateral analysis of NQNPs, we could think about them along the lines of the choice function account whereby the argument NQNP consists of a variable over choice functions as a sister to the plural predicate, kX:jXj ¼ 2 ^ unclesðXÞ and there is free existential closure of this choice-function variable. Trying to make this quantification dynamic would run into the same problems as before since dynamic binding of a choice function variable would require that ‘they’ in the second sentence of (48) have an implicit predicate. This predicate would have

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Simple dynamic binding as discussed in DRT and elsewhere precludes binding from within the antecedent of a conditional. So, one option here for a dynamic unilateral account might be to follow Geurts (2000, forthcoming) in thinking about exceptional scope in terms of presupposition projection. In Geurts’ favoured DRT framework, this would mean introducing a discourse referent plus the condition that it denote a collection of two uncles outside of the scope of the conditional. This discourse referent then would be accessible for the discourse referent introduced by the pronoun in the second sentence. But note that this approach still faces the problem of pronominal contradiction. For instance, an interlocutor could follow up (48) with (49):

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(50) There are four chairs in the next room. You can borrow them overnight but if you return them after 10am, you will be charged. Considering Kadmon’s favoured dynamic treatment of this example, we could envisage the construction of a Kamp-style discourse representation structure (DRS) where the discourse referent introduced for the first sentence is identified with the DR in the antecedent of the final conditional (see Kadmon 2001 and Kamp & Reyle 1993 for suggestions of how this could be done). But note that the resulting structure says something weaker than the full force of the super’s reply. The DRS would only tell us that there are four chairs in the next room which are such that if you return them late you will be charged. However, the force of the super’s utterance is that whichever four chairs you choose, they are such that if you return them late you will be charged. We can get a good account of this example by considering the diagonalization treatment: After the first sentence is uttered and the context updated, we are faced with context alternatives in each of which a collection of four chairs is the denotation of the implicit restriction of the NQNP and these four chairs are in the next room. The second sentence contains a pronoun which has a salience presuppposition, hence, in each alternative, the pronoun denotes the set of four chairs in the denotation of the specific’s restriction. But the pronoun also has an identifiability condition. In this case, we cannot satisfy the condition with the property of being the collection the speaker has in mind (because the speaker has no particular chairs in mind). But we can satisfy the condition with the property of being the

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to be recovered from its antecedent (possibly along the lines of Elbourne 2005). But then the pronominal contradiction cases become difficult to handle. As a non-dynamic alternative, one could suppose that in uttering the first sentence of (48), the speaker makes it clear that he/she has a particular choice function in mind and hence a particular collection of individuals in mind. This collection could then be the referent of the pronoun in the second sentence. So, there is a way to account for the anaphoric relation in (48) via this modified unilateral account of NQNPs (using choice functions and free existential closure). But, being static, this account misses some essential properties of dynamic binding which the diagonalization approach retains. To see this, let us return to a Kadmon example. Consider a case where a building superintendent is asked by a staff member about getting four chairs needed for a meeting. The superintendent replies as follows (knowing there to be many more than four indistinguishable chairs in the next room):

Richard Breheny 125

four chairs that the addressee takes in realizing her goals. We can get a sense that this is the kind of description that most readily comes to mind by noting the mild infelicity of the following alternative reply by the super where we interpret ‘four chairs’ as before, in the at least way (i.e. it is clear the super has no particular chairs in mind): (51) There are four chairs in the next room. You can borrow them.

(52) dF<0>[in the next room(F(kX.jXj ¼ 4 ^ chairs(X)))] The definite pronominal in the second sentence requires both a salience condition and an identifiability condition to be met. Recall that, for some previous examples, to meet the salience condition it would have sufficed to suppose that the speaker intends to raise the objects he/she has in mind to salience. However, in this case, the speaker does not have a set of four chairs in mind and so there is no particular collection of four chairs being raised to salience in this way. An alternative idea might be to assume that the noun phrase ‘four chairs’ is implicitly restricted in some way and the pronoun in the second setence is understood as an E-type—i.e. it denotes the total set of chairs in the next room under discussion. The natural restriction for this example would be along the lines of ‘There are four chairs you can take in the next room’. Thus, the pronoun in the second sentence could be understood as, ‘the four chairs in the next room you can take’. However, there could just as well be more than four chairs in the next room that you can take. So this way of restricting the NQNP still does not single out four chairs four future pronominal reference. It seems only one kind of restriction would work in this case and that would be

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On the account under consideration, the reason why this seems strange is that we want to understand ‘them’ as ‘the four chairs you borrow’ and yet then the utterance would be taking for granted that for which permission is being given. Having understood the second utterance of (50) as just suggested, the correct understanding of the conditional sentence follows automatically: we eliminate alternatives where the audience does not return the four chairs they borrow before 10 and do not get charged. The choice function-plus-free-closure account that we are still considering would have severe difficulty deriving this reading without making use of the style of reasoning that is employed in the alternative two-dimensional account being offered here. This is so because it is in the nature of these Kadmon-style contexts that no determinate set of chairs becomes salient for future reference. To see this, let us suppose that the first sentence could be analysed along the following lines:

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8 DISCUSSION Let us compare what is being proposed with a modification of Geurts’ ambiguity account. On this modification, ‘two students’ can be understood as a predicate expression (possibly, as Geurts 2006 suggests, due to a regular type coercion from the bilateral noun phrase meaning). Predicate nominal expressions (like ‘brown cows’) can find their way into syntactic argument position as sister to a (possibly skolemized) choice function variable. Mandatory existential closure ensures that [brown cows] or [two cows] have existential force but (in line with the free-existential-closure account) existential closure does not necessarily occur at the level of the noun phrase nor does it have to occur at the level of the root clause. So far we have come across three kinds of problem with this account. Firstly, if we follow this reasoning we should admit that ‘exactly two’ and ‘at most two’ have grammatically derived existential monotone readings (respectively, at least two and at least one).20 Secondly, as discussed in section 6, the account generates 20 Of course, the account defended here makes it in principle possible that ‘exactly two’ has a pragmatically derived existentially closed reading. This issue will be taken up shortly.

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along the lines of ‘there are four chairs you will take in the next room’. But to put this restriction into an existential claim would mean taking for granted that you do take four chairs. In two-dimensional terms, this means that in each context alternative, there is a particular set of four chairs the audience takes. In other words, to get the anaphora facts right in this case, one has to take for granted that there are four chairs that you take under discussion. Given that this same form of reasoning can be employed to deliver the effect of free existential closure and without the need to posit a formal ambiguity in NQNPs then it seems clear that the univocal bilateral account is conceptually more appealing here. To sum up this discussion: By considering relations between NQNPs with at least readings and pronominal anaphora we reveal again that the apparent existential closure effect comes with a form of pragmatic reasoning whereby we take for granted that there is a specific collection at issue and see what follows from that. This form of reasoning makes this specific collection available for subsequent pronominal reference. Thus, close consideration of the anaphora data further motivates the idea that when NPs are used in this specific way, the discourse becomes implicitly modal—in the manner that Stalnaker’s two-dimensional framework supposes.

Richard Breheny 127

(53) a. John gave an A to every student who recited a difficult poem by Pindar. b. dx[Pindar_poem(x) ^ "y[student(y) ^ read(x)(y) / John_ gave_A_to(y)]] In addition to this type of problem, we have seen that dynamic binding as found in DRT and elsewhere does not capture many of the subtle facts which are brought to light by the diagonalization account. In fact, following from Stalnaker (1998) and van Rooij (2001), the facts here suggest that simple dynamic binding rather imperfectly recreates what goes on at the pragmatic level when anaphoric relations between indefinite noun phrases and pronominal anaphora are being established. Once we consider the variety of cases in which at least readings of NQNPs surface, it seems very plausible then that they could well be dealt with as cases where a bilateral NQNP is understood specifically and the relevant pragmatic reasoning follows. The phenomena we have looked at here have manifestations independently of NQNPs, occuring

21 A fourth problem for this account stems from the fact that bare plurals, like ‘brown cows’, tend to resist exceptional scope readings (although such readings are perhaps not impossible).

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unattested wide-scope existential readings where the NQNP is in the scope of a non-upward monotone quantifier. Thirdly, as just discussed, anaphoric relations are problematic for this account.21 It seems plausible on the other hand that this otherwise mysterious existential closure mechanism is really just the pragmatic reflexivization process. Such a process accounts not only for exceptional scope facts but also for cross-sentential anaphoric facts and it naturally accounts for all the at least readings of NQNPs that appeared to challenge the bilateral account. An alternative ambiguity account would suggest that the unilateral version of ‘two students’ is dynamic and exceptional scope is a matter of presupposition projection as formally specified in van der Sandt (1992), Geurts (1999) and elsewhere. As Geurts (2000) admits, such an account of exceptional scope re-creates noun phrase movement at the level of discourse representation. As such, it faces the problems raised in Schwarzschild (2002) concerning its insufficient specificity. For example, a simple wide-scope analysis of (53a) below, as represented in (53b), is much weaker than the intended interpretation since it would only take one obscure poem by Pindar that no student recited for it to be true:

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22

Note that this dilemma for the pragmatic account of the derivation of at least readings is similar to that raised for those accounts that derive the at least readings via a systematic, grammatically determined existential closure process. However, it is not as severe in the current case since the at least readings are pragmatically derived and therefore have to be justified according to rational principles of conversation. In the grammatical case, the readings in question just ought to be available unless blocked by a further rule.

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with all kinds of indefinite or ‘weak’ noun phrases (see Breheny 2006b for a discussion). The fact that NQNPs pattern in the same manner as other nondefinites with regard to exceptional scope allows us to make some observations about the merits of analysing indefinite noun phrases generally as singular terms consisting of a choice-function variable as sister to a predicate. On the one hand, we could reserve this analysis for specifically used noun phrases only and suppose that non-specific indefinites are quantificational. In that case, one could argue that Schwarzschild’s singleton indefinite proposal coupled with the diagonalization account of apparent existential closure obviates the need to posit this formal ambiguity. On the other hand, we could suppose that all indefinites are singular terms and that free existential closure can be invoked to handle non-specific cases as well as exceptional scope cases. In addition to the problems for this line of thinking already mentioned here (and in Schwarz 2002), there is good reason to think that non-specific NQNPs really are bi-lateral nonmonotonic quantifiers (see the discussion around (6a–d)). As such, NQNPs would not be subjectable to this uniform analysis. But then, as non-definites, NQNPs seem no different from other indefinites in terms of their potential for exceptional scope and specific readings. The ‘singleton indefinite’ account does make a uniform analysis of NQNPs possible and this fact provides another reason to think about nondefinites generally as quantifiers and not singular terms. At this stage, a few words are in order about the modified NQNPs ‘exactly two’, ‘just two’ and so forth. According to what has been claimed so far, these noun phrases are understood as quantifiers with the same meaning as the unmodified NQNP (as suggested in (29)). This being the case, one could legitimately wonder why these noun phrases resist at least readings even though such readings ought in principle be derivable via the same process as for the unmodified case. Why for instance, in Kadmon-style contexts, the building super’s saying, ‘There are exactly four chairs in the next room’ cannot be understood in the same way as his saying ‘There are four chairs in the next room’?22

Richard Breheny 129

In answering this kind of query, one should first note that at least readings of these modified NQNPs are available in exceptional scope contexts. Consider again (34a,b) repeated below:23 (34) a. Mary will accede to the throne if just two old uncles die before she does. b. Mary will accede to the throne if exactly two old uncles die before she does.

23 Note that, as with (33), the exceptional scope reading of examples like (34a) is really at least reading. To see this, we should modify the example so that it reads ‘Mary will accede to a throne . . .’. With the NQNP specific, the speaker is understood to be talking about Mary’s accession via the death of a particular collection of uncles. It does not preclude Mary standing in more than one line of accession with yet more old uncles preceding her.

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It is to be conceded that (34a) has a more accessible exceptional scope reading than (34b). But one could argue that this has to do with how easy it is to see a reason for modifying the NQNP: ‘just two’ emphasizes perhaps how small the number is, how close Mary is to the throne. The suggestion in the text above was that the exceptional scope reading for (34b) would be more prominent if ‘exactly’ was clearly being used to emphasize the precision of the claim. For example, if (34b) is a response to someone vaguely mentioning that ‘one or two’ or ‘a few’ relatives stand between Mary and the throne, then the specific, exceptional scope reading becomes more prominent—especially where the modifier, ‘exactly’ or ‘two’ is stressed. These considerations suggest the beginnings of an explanation for why these modified NQNPs normally resist the at least interpretation in many other contexts: If the semantic rules of English determine that ‘two students’ and ‘just two students’ or ‘exactly two students’ contribute the same function to the determination of truth conditions, then the use of ‘just’ or ‘exactly’ ought to be otiose—since people prefer to express a given semantic content in as few words as necessary and they prefer not to have to parse unnecessary constituents. In fact, if one used the modified form instead of ‘two’ for no reason, one would be violating a Gricean maxim enjoining brevity. Thus, the use of ‘just’ or ‘exactly’ ought to prompt one to find a reason for that usage. Now it seems that ‘just’ and ‘exactly’ have different shades of nontruth-conditional meaning that makes their use conditions slightly different. For example, ‘just flat’ and ‘exactly flat’ cannot be appropriately used in the same set of situations. ‘The countryside for the cycle race was just flat’ seems to presuppose that there was an expectation that the countryside was otherwise (in parts at least). ‘The countryside for the cycle race is exactly flat’ suggests a degree of

130 New Look at the Semantics and Pragmatics

(54) a. Take 200g of butter. b. Take exactly 200g of butter. One can imagine that the instruction in (54a) allows for different degrees of lassitude depending on whether the recipe is for a fine pastry (low degree of slack) or a butter sauce (higher degree of slack). Accordingly, the modification by ‘exactly’ in (54b) has different slackness regulation effects in the different examples. Another typical case where ‘exactly’ would function as a slackness regulator would be in the case of round numbers. As Krifka (2007) observes, round numbers are very often used in an approximative way. (55a) below would often be acceptable if one or two students more or less than 20 were taking the class. Thus, (55b) forestalls such pragmatic loosening: (55) a. Twenty students are taking the advanced syntax class. b. Exactly twenty students are taking the advanced syntax class. It is also well-known that using a non-rounded number often has the opposite effect—that of being precise. Where the context question is ‘How many students are in the advanced syntax class?’ (56a) below is understood as being as precise. But if there is no need for slackness

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precision in the statement that would not have been conveyed had the modifier not been present. As suggested in Lasersohn (1999), ‘exactly’ seems to function as a ‘slack regulator’ in these cases. Lasersohn’s idea is that predicates like ‘flat’ are often applied to referents of which they are not strictly true. Although the resulting assertion is literally false, Lasersohn observes that the utterance is judged acceptable up to contextually defined limits of lassitude. The function of a slack regulator, according to Lasersohn, is not to affect truth conditions but to narrow down the degree of acceptable lassitude. On the question of whether ‘exactly’ functions as a slackness regulator for NQNPs, Lasersohn claims that it does so only in the case of telling the time. He suggests that generally speaking, ‘exactly’ modified NQNPs do not have the same literal truth-conditional content as unmodified NQNPs. If in contrast to Lasersohn we accept the arguments in this paper that unmodified NQNPs are already bilateral, we can consider whether ‘exactly’ ever functions as a slackness regulator for NQNPs in non-time-telling contexts—and the answer of course is that they do. Consider, for example, the following instructions in a recipe:

Richard Breheny 131

regulation in this case (56b) ought to give rise to some other kind of effect, according to the pragmatic account of the function of ‘exactly’ modification of NQNPs sketched above: (56) a. Twenty one students are taking the advanced syntax class. b. Exactly twenty one students are taking the advanced syntax class.

(57) There are exactly four chairs in the next room. You reason as follows: Given that the unmodified utterance would have sufficed to inform me that I can get the chairs I need from the next room, in using ‘exactly’ the super must have wanted to convey some information over and above what the unmodified utterance would have conveyed. While the unmodified utterance would have addressed my immediate concerns, it would not have given any information about whether there are four, five, etc. chairs in the next room. Although this question is relevant only to a secondary degree, I can see no reason for the use of the modification other than to raise the salience of this question. I thereby assume that the superintendent wished to address this question in addition to my concerns. The utterance would address both these issues if it was non-specific; therefore, I conclude that it is the non-specific reading that is intended.

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Indeed intuition suggests that the speaker of (56b) would be attempting to convey something else about the figure mentioned—for example, that he/she has obtained it on good authority or that he/she is using the official figure. The fact that ‘exactly’ can function as a slackness regulator with NQNPs provides further indirect evidence for the bilateral account. For if, as Lasersohn supposes, the function of ‘exactly’ applied to cardinals is to make unilateral NQNPs bilateral, then it literally encodes a different function to his slackness regulator. Thus, it is somewhat curious that ‘exactly’ modification still functions as a slackness regulator in many cases. In addition, we have seen that modification of already precisely understood NQNPs (as in 56b) drives the search for further effects. This is to be expected on the Manner maxim-based account of NQNP modification but somewhat mysterious if we assume ‘exactly’ has truth-conditional significance when applied to cardinals. We are now in a position to address the dilemma raised at the beginning of this discussion of modified NQNPs. Suppose that you tell the superintendent that you are looking for four chairs and he replies as in (57) below:

132 New Look at the Semantics and Pragmatics So the strategy for the bilateral-plus-diagonalization account would be to consider contexts where the at least reading typically arises to see whether the effects of modification can be accounted for on pragmatic grounds. A straightforward case would involve modifications of examples like (6a). In these cases, the or more reading results from a background implicature and should persist even where the NQNP is modified. This seems to be right—especially in the case of (58b). (58c) perhaps requires a little more context in order to give the modifier some motivation. For example, if the audience has just uttered: ‘I have exactly two children’ to the benefits officer:

For (58b,c) the at least readings can be derived via the background implicature given the non-specific reading of the modified NQNP. By contrast to the above examples, in the context of necessary conditions we saw that the at least reading has to come via the specific reading plus diagonalization. The account we are considering suggests that one ought to be able to derive at least readings for modified NQNPs—so long as there is an independent contextually established purpose for the modification. The following context seems to work fine for ‘just’ in (59a) but perhaps not so well for ‘exactly’ in (59b): (59) a. Normally, at this university you have to have three A grades to qualify for entry to a graduate programme, but for this Linguistics Masters degree, you have to have just two A grades from your undergraduate course. b. Normally, at this university you have to have three A grades to qualify for entry to a graduate programme, but for this Linguistics Masters degree, you have to have exactly two A grades from your undergraduate course. However, a better context for ‘exactly’ NQNPs would involve a typical use of this modification—such as slackness regulation associated with round numbers. Consider the following example with the additional background information that beach clubs are normally fairly lax in enforcing their own rules (such as for dress codes): (60) In order for this beach club to recognise you as an official lifeguard, you have to attend exactly twenty training days on the beach under the guidance of a senior life-guard.

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(58) a. If you have two children, you qualify for this benefit. b. If you have just two children, you qualify for this benefit. c. If you have exactly two children, you qualify for this benefit.

Richard Breheny 133

(61) A: John ate three cookies. B: Therefore John ate two cookies. (62) A: Two students drank beer. B: Therefore, two students drank some alcoholic beverages. (63) A: Two male students drank beer. B: Therefore two students drank beer. Note that, the bilateral-plus-diagonalization account as well as the ambiguity account imply that the monotonicity inferences for NQNPs exemplified in (62–63) are acceptable only on the at least reading of B’s utterance. 24

Thanks to Anna Szabolcsi for drawing my attention to the Hungarian data. However, see also the discussion in the next section of the possibility that in some languages (Hungarian being one of them), NQNPs in fact encode an at least meaning. 25

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Obviously, (60) does not preclude your official recognition if you do more than 20 days training. Whether this would be the whole story about the difference between modified and unmodified numerals is an open question. While it is at least plausible that the difference between the two types of expression can be accounted for along these pragmatic lines, it may be that, in addition, the use of ‘exactly’ modified NQNPs is associated with a kind of processing bias whereby the non-specific reading is made initially most prominent to the audience. The existence of such a processing bias would not rule out the at least readings for the modified form in principle but it would make such readings far less accessible—in the sense that they would require a lot more contextual support and inferential work to derive. The point at which a processing bias transforms into a hard rule of grammar is perhaps not so easy to pin down and it is an open question whether in a given language, a marker such as ‘exactly’ actually blocks the specific-plus-diagonalisation reading. Such may be the case in Hungarian where NQNPs in focus position are apparently mandatorily understood according to the exactly reading (see Kiss 2007).24,25 The next point of discussion leads on from the question of modification and concerns monotonicity. Given that the bilateral account here is able to derive apparent at least readings by way of the speaker expressing a (possibly enriched) diagonal proposition, we do not have any problems predicting that there is a way to construe the following discourses in a coherent manner:

134 New Look at the Semantics and Pragmatics A number of commentators have suggested that data concerning negative polarity items raise potential problems for the bilateral-plusdiagonalization account and the ambiguity account.26 It seems that examples such as (64a) below have become accepted as felicitous in the NPI literature (see van der Wouden 1997, Ladusaw 1996). In contrast, (64b) is not regarded as acceptable: (64) a. Exactly two students asked any questions at the workshop. b. Two students asked any questions at the workshop.

(65) ?Exactly two million people have ever visited this forest. Rothschild also notes that there are other non-monotonic environments in which NPIs are clearly infelicitous. He cites (66a) but others such as (66b,c) are not difficult to find: (66) a. ?An even number of students ever handed in their assignment. b. ?Approximately five students ever handed in their assignment. c. ?Precisely two pints of blood was ever taken from his body. These data suggest that the condition that weak NPIs be in a nonupward monotone environment is at best a necessary condition and that other factors determine the acceptability of weak NPIs. Without wishing to provide an exhaustive account for the differential judgements surrounding (64a,b) in this brief discussion, it 26 In particular, I acknowledge an anonymous Journal of Semantics referee and Daniel Rothschild for putting this issue on the agenda for both the bilateral and the ambiguity accounts.

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Accepting the judgments as they stand (even though almost all native speakers of English I have interviewed have judged (64a) in addition (64b) to be of low acceptability), these facts are not necessarily problematic for the accounts we are considering. However, the accounts come into conflict with any proposal that the licensing condition on these weak NPIs is that they be in non-upward monotone environments. If this in fact was the licensing condition, then the unmodified NQNP should just as well license NPIs. One reasonable response for either the ambiguity proponent or the bilateralist is to observe that the non-upward monotone proposal for (weak) NPIs looks to be very strong and not without problems of its own. For example, even informants who judge examples like (64a) to be potentially acceptable do not always judge NPIs to be acceptable in the scope of ‘exactly’ modified NQNPs. As discussed in Rothschild (2006) large numbers tend to degrade the acceptability of NPIs:

Richard Breheny 135

is worth noting that informants are happier to judge the examples in (67a,b) as felicitous—where there are different modifiers on the NQNP: (67) a. Just two students ever handed in their assignment. b. As few as two students ever handed in their assignment.

9 SUMMARY AND CONCLUSIONS We started out by considering NQNPs as encoding solely a unilateral meaning and Gricean or neo-Gricean quantity implicatures as accounting for cases where these noun phrases have a bilateral, exactly reading. The evidence against this type of account that was reviewed also strongly suggests that it is more likely that NQNPs encode a bilateral semantics with the other readings being derived in some way from there. The main purpose of this paper has been to set out just what kind of pragmatic reasoning would be involved in deriving the at least readings if NQNPs were univocally bilateral. In addition, it has been argued that the reflexive-style of reasoning appealed to here is recruited independently, in mediating anaphoric relations between non-definite noun phrases and anaphora and in exceptional scope cases. In fact, this form of reasoning is in all likelihood ubiquitous in conversation, perhaps to an extent comparable to quantity implicature (see Perry 2001, Stalnaker 1978 for some further cases). It should be noted, however, that there has been no argument in this paper that NQNPs have to have bilateral semantics, only that NQNPs in English encode a bilateral meaning and that the various at least readings are derivable via pragmatic reasoning. It is conceivable that in other languages the correlates of NQNPs are unilateral in some way and that they give rise to a different pattern of readings. For instance,

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The difference between the modifiers in (67a,b) and ‘exactly’ and ‘precisely’ seems to be that the former suggest more strongly an expectation that more students would hand in their assignments. In such contexts, they would also pattern with ‘only’ in emphasizing or foregrounding the inference that no more than the number mentioned handed in their assignment. Just why these weak NPIs are acceptable in these environments is an open question but it does not seem unreasonable to suggest that their licensing requires the overt presence of an element which realizes the relevant foregrounding function. It is possible that informants who judge (64a) to be acceptable can see ‘exactly’ being put to this use also. This possibility is also motivated by the small-number constraint.

136 New Look at the Semantics and Pragmatics

Acknowledgements I would like to thank Nicholas Allott, Bart Geurts, Daniel Rothschild, Philippe Schlenker, Anna Szabolcsi, Deirdre Wilson and two anonymous Journal of Semantics referees for helpful and stimulating feedback on earlier versions of this paper.

REFERENCES Breheny, R. (2004), ‘Indefinites and anaphoric dependence—a case for dynamic semantics or pragmatics?’ In

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Anna Szabolcsi (personal communication) points out that the pattern of readings found for English in (6a) and (6d) does not obtain in Hungarian. As also mentioned above, Kiss (2007) suggests that focussed NQNPs in Hungarian are mandatorily given exactly readings. So it may be that there is a different system in Hungarian and other languages for realizing the at least and exactly readings. This is a matter for further research. The main and obvious competitor to this proposal for English NQNPs is to say that they are ambiguous in some fashion. In the course of the paper, a number of versions of the ambiguity story were encountered. The focus of Geurts polysemy story is on the fact that quantified noun phrases of a certain class can be coerced into to predicate expressions and predicate expressions can be coerced into existential quantifiers (using, respectively, BE and A). However, it was found that Geurts’ appeal to the apparent regularity with which these coercions occurred does not carry so much force since, if Partee’s type shift were really an independent phenomenon in the grammar—driving interpretation—and not merely a post hoc description of what happens in specific cases, then ‘exactly n’ and ‘at most n’ ought also to be polysemous. In addition to these considerations, Geurts’ proposal as it stands does not make the link between the at least readings of NQNPs, the cross-sentential cases and the exceptional scope cases. Other ambiguity accounts which manage to make this link (dynamic quantifier and free-existential closure accounts) were found to be wanting in other ways and, at best, merely offer different and orthogonal formal descriptions of the effects of the pragmatic reflexivization process when it is recruited in the interpretation of specific noun phrases.

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138 New Look at the Semantics and Pragmatics Schwarz, B. (2001), ‘Two kinds of long distance indefinites’. In R. van Rooij and M. Stokhof (eds.), Proceedings of the Thirteenth Amsterdam Colloquium. ILLC Publications. Amsterdam. Schwarz, B. (2002), Two kinds of long distance indefinites. Unpublished MS, University of Texas. Schwarzschild, R. (1996), Pluralities. Kluwer. Dordrecht. Schwarzschild, R. (2002), ‘Singleton indefinites’. Journal of Semantics 19.3:289–314. Simons, M. (2006), Presupposition without common ground. Unpublished MS, Carnegie Mellon University. Sperber, D. & D. Wilson (1986), Relevance: Communication and Cognition. Blackwells, Oxford. Stalnaker, R. (1978), ‘Assertion’. In P. Cole (ed.), Syntax and Semantics Vol. 9: Pragmatics. Academic Press. New York. 315–32. Stalnaker, R. (1998), ‘On the representation of context’. Journal of Logic, Language and Information 7:13–9. Stalnaker, R. (2002), ‘Common ground’. Linguistics and Philosophy 25:701–21. Stanley, J. & Z. Szabo (2000), ‘On quantifier domain restriction’. Mind and Language 15:219–61. van der Sandt, R. (1992), ‘Presupposition projection as anaphora resolution’. Journal of Semantics 9:333–77. van der Wouden, Ton. (1997), Negative Contexts: Collocation, Polarity and Multiple Negation. Routledge. London. van Rooij, R. (1997), Attitudes and Changing Contexts. Ph.D. dissertation, Uni Stuttgart. van Rooij, R. (1998), The Specificity of Indefinites (Paper presented at Budapest workshop on indefinites). Unpublished MS, University of Amsterdam. van Rooij, R. (2001), ‘Exhaustivity in dynamic semantics; referential and

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Krifka, M. (2007), ‘Approximate interpretation of number words: a case for strategic communication’. In G. Bouma, I. Kra¨mer & J. Zwarts (eds.), Cognitive Foundations of interpretation. Koninklijke Nederlandse Akademie van Wetenschapen. Amsterdam. 111–26. Ladusaw, W. A. (1996), ‘Negation and polarity items’. In Shalom Lappin (ed.), The Handbook of Contemporary Semantic Theory. Blackwell. Oxford. 321–41. Lasersohn, P. (1999), ‘Semantic Halos’. Language 75:522–51. Levinson, S. (1983), Pragmatics. Cambridge University Press. Cambridge. Levinson, S. (2000), Presumptive Meanings. MIT Press. Cambridge, MA. Musolino, J. (2003), ‘The semantics and acquisition of number words: integrating linguistic and developmental perspectives’. Cognition 93:1–41. Papafragou, A. & J. Musolino (2003), ‘Scalar implicatures: experiments at the semantics/pragmatics interface’. Cognition 86:253–82. Partee, B. (1986), ‘Noun-phrase interpretation and type-shifting principles’. In J. Groenendijk, D. de Jong, and M. Stokhof (eds.), Studies in Discourse Representation Theory and the Theory of Generalized Quantifiers. Reidel. Dordrecht. 115–44. Perry, J. (2001), Reference and Reflexivity. CSLI Publications. Stanford, CA. Reinhart, T. (1997), ‘Quantifier scope. How labour is divided between QR and choice functions’. Linguistics and Philosophy 20.4:335–98. Rothschild, D. (2006), ‘Non-monotonic NPI-licensing, definite descriptions, and grammaticalized implicatures’. Proceedings of SALT 16 Tokyo. CLC Publication, Cornel (in press). Schlenker, P. (2006), Scopal independence: a note branching & island-escaping readings of indefinites & disjunctions. Journal of Semantics (in press).

Richard Breheny 139 descriptive pronouns’. Linguistics and Philosophy 24.5:621–57 van Rooij, R. & K. Schulz (2006), ‘Pragmatic meaning and nonmonotonic reasoning: the case of exhaustive interpretation’. Linguistics and Philosophy 29:205–50. Winter, Y. (1997), ‘Choice functions and the scopal semantics of indefinites’. Linguistics and Philosophy 20.4:399–468.

Winter, Y. (2001), ‘Plural predication and the strongest meaning hypothesis’. Journal of Semantics 18.4: 333–65. Winter, Y. (2004) ‘Functional quantification’. Research on Language and Computation 2:331–63. First version received: 29.11.2005 Accepted: 03.09.2007

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Journal of Semantics 25: 141–173 doi:10.1093/jos/ffm017 Advance Access publication February 28, 2008

An Epistemic Step for Anti-Presuppositions EMMANUEL CHEMLA Laboratoire de Sciences Cognitives et Psycholinguistique

Abstract (1) John believes that I have a. Alternative: b. Actual inference: c. Predicted inference:

a sister. John knows that I have a sister. The speaker does not have a sister. It is not common belief that the speaker has a sister.

According to Heim (1991), Percus (2006), and Sauerland (2006), this inference should follow from the comparison of (1) to (1a). However, such an analysis would only predict a very weak implicature: it is not common belief that the speaker has a sister. I propose to strengthen this prediction by two means. First, I rely on a precise understanding of the modern Stalnakerian view of presuppositions and common ground (Stalnaker 1998, 2002; von Fintel 2000; Schlenker 2006). Second, I argue that this inference depends on contextual factors. More precisely, I show that the Competence Assumption (see Spector 2003; van Rooij & Schulz 2004; Sauerland 2004) necessary to obtain secondary scalar implicatures should be supplemented with an Authority Assumption. I motivate this additional assumption on independent empirical grounds. Finally, I show how my proposal accounts for a wide variety of inferences with fine variations governed by (i) contextual differences and (ii) specific properties of the presupposition triggers involved.

1 INTRODUCTION An utterance of sentence (1) most commonly conveys the additional piece of information in (1b). Although this anti-presupposition looks very similar to classical cases of scalar implicatures, there is as yet no explicit derivation of this fact. (1) John believes that I have a sister. a. Alternative: John knows that I have a sister. b. Inference: I don’t have a sister. Let us assume the classical Stalnakerian view of presupposition and common ground (Stalnaker 1973, 1974) which states that a sentence with presupposition p is felicitous only in contexts where p is common belief (i.e. all participants to the conversation believe that p, all believe that all believe that p, and so on), or so the speaker thinks. If (1a) is an
The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected].

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Sentence (1) strongly suggests that the speaker does not have a sister:

142 An Epistemic Step for Anti-Presuppositions alternative to (1), the application of a Maximize Presupposition principle a` la Heim (1991), as given in (2), predicts the inference that the alternative sentence (1a) is not felicitous. In other words, it predicts that (1) implies that it is not common belief that the speaker has a sister. This prediction is much weaker than the intuitive inference: the speaker does not have a sister. (2) Maximize presupposition: Among a set of alternatives, use the felicitous sentence with the strongest presupposition.

1 This term is due to van Rooij & Schulz (2004); Sauerland (2004) uses the term Experthood Assumption.

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Soames (1982) and Horn (1989) noted that a similar puzzle arises with scalar implicatures: (3) John saw some of his students today. a. Alternative: John saw all of his students today. b. Predicted inference: It is not the case that the speaker believes that John saw all of his students today. c. Actual inference: The speaker believes that John did not see all of his students today. The comparison of (3) with (3a) and the application of the Maxim of Quantity—as given in (4), for instance—predicts that an utterance of (3) implicates (3b): it is not the case that the speaker believes that (3a) is true (written: :Bs[p], where p refers to the meaning of the alternative (3a) and Bs[. . .] is the operator true of the propositions that the speaker s believes to be true). This inference is weaker than the observed inference in (3c), that is Bs[:p]. (4) Maxim of quantity: Among a set of alternatives, use the most informative sentence you believe to be true. Spector (2003), van Rooij & Schulz (2004) and Sauerland (2004) argue that the inference in (3c) is not available in every context. Rather, this inference is the result of the epistemic step, that is the enrichment of the weaker inference (3b) via the following contextual assumption about the speaker: (5) Competence assumption:1 The speaker is opinionated about the truth of the alternative sentence p. Technically: Bs[p] _ Bs[:p].

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The purpose of this paper is to argue in favour of a similar solution to the puzzle exemplified in (1). More precisely, I argue that the Competence Assumption should be supplemented with an independently motivated Authority Assumption along the lines of (6). Importantly, the present proposal predicts a variety of inferences depending on fine contextual variations. (6)

Authority assumption: The speaker believes that she could convince her addressee that p is true by simply uttering a sentence presupposing p.

2 THEORETICAL SITUATION In this section, I first review the main facts about theories that use the maximize presupposition constraint and point out the minimal assumptions needed for this paper. Next, I show that a whole family of naive proposals inescapably fail to account for (1).

2.1 Background on maximize presupposition The purpose of this subsection is to introduce the minimal pieces of evidence in favour of the theoretical framework which will be assumed throughout the rest of the paper. In particular, I motivate the type of alternatives which are usually assumed to play a role in the application of the maximize presupposition principle and present a set of assumptions to which this paper is an amendment. 2.1.1 Initial motivation oddness of non-presuppositional sentences Consider the pairs of sentences given in (7) through (11). The (a) sentences are odd, and the (b) sentences are natural. Such examples were first discussed by Hawkins (1991) and analysed by Heim (1991), the underlying theory was subsequently developed in Magri (2006),

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In the first section below, I review the crucial parts of theories of maximize presupposition and show in more detail why naive solutions to the puzzle presented in (1) fail. The next section spells out the felicity conditions for presuppositional sentences delivered by a modern Stalnakerian view of presupposition as advocated by Stalnaker (1998, 2002), von Fintel (2000) and Schlenker (2006). These theoretical and technical considerations are the necessary preliminaries before I describe and motivate my own proposal. The last section reviews a range of facts that fit naturally with the present account. Technical details are confined to the Appendix.

144 An Epistemic Step for Anti-Presuppositions Percus (2006), Sauerland (2006) and Schlenker (2006). In a nutshell, these theories argue for an account of these contrasts in two steps: (i) the (a) sentences are in competition with the (b) sentences and (ii) sentences with stronger presuppositions are preferred, if felicitous. (7) Context: People have one father. a.
John has interviewed a father of the victim. b. John has interviewed the father of the victim.

(9) Context: People have two arms. a.
Mary broke all her arms. b. Mary broke both her arms. (10) Context: Mary has been cheating on John for years . . . a.
. . . and he believes it. b. . . . and he knows it. (11) Context: John, a teacher with a very bad hand writing, has just written an exercise on the blackboard. When he is finished he reads it aloud to make sure everyone can copy it down properly. A student may not hear it all very well and ask: a.
Can you read that word? b. Can you read that word again? (12) a.
I had tea and John had tea. b. I had tea and John had tea too. For the purpose of this paper, I rely on these examples to motivate the assumption that lexical scales (e.g. Æa, theæ, Æeach, theæ, Æall, bothæ,2 Æbelieve, knowæ, Æagain, Øæ, Ætoo, Øæ) generate competition between utterances; the competition involves the respective presuppositional content of these sentences. Note that in principle, the claim that the competition arises at a lexical level is not necessary and there is a principled way to test whether two sentences are alternatives of the relevant type on a case-by-case basis: in a context where the presupposition of the sentence with the stronger presupposition is 2

See Chemla (2007) for a potential worry about this scale.

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(8) Context: People have one father. a.
John has interviewed each father of the victim. b. John has interviewed the father of the victim.

Emmanuel Chemla 145

satisfied (i.e. common belief), the sentence with the weaker presupposition should be infelicitous. The focus of this work is the inferential pattern that should follow from such a paradigm without further assumptions. The general structure of the critical examples is given in (13).

A few remarks are in order. First, this account predicts inferences, these inferences have a presuppositional origin, but they are not presuppositions. Sauerland’s terminology ‘implicated presuppositions’ suggests that these inferences have a presuppositional essence and this is a position I am not willing to take. For this reason, I adopt Percus’ terminology ‘anti-presuppositions’. Note that it would be consistent with this terminology to refer to classical cases of scalar implicatures as ‘anti-assertions’. Second, I assume that any theory of presupposition should describe constraints on the use of a presuppositional sentence. This is independent from the type of mechanism assumed for presupposition projection or triggering; even if presuppositions ended up being a species of scalar implicature, for instance, this account would not be affected as long as the constraints on the use of presuppositional sentences remain the same. A significant proportion of this paper investigates the form that anti-presuppositions take under different Stalnakerian views on presupposition. Ultimately, this work argues in favour of a particular set of constraints for a presuppositional sentence to be felicitous and there is no reason why this result could not be extended to non-Stalnakerian frameworks (see, for instance, Thomason et al. [2006] for a discussion of constraints on presuppositions from the point of view of computer science). Finally, the characterization in (13) involves several approximations which are meant to simplify the application of these principles to the range of examples discussed in this paper. Percus (2006) investigates different formulations of the relevant principles and I refer to his work for a finer grained analysis. In particular, the format in (13) does not apply to more complicated cases where both the assertion and the

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(13) General structure of the critical examples a. Situation: A speaker utters a sentence S1. S1 has an alternative sentence S2, constructed via one of the lexical scales given above so that (i) the presupposition p2 of S2 is stronger than the presupposition p1 of S1 and (ii) their assertions are equivalent. b. Predicted inference: S2 is infelicitous, that is the constraints on its presupposition p2 are not met.

146 An Epistemic Step for Anti-Presuppositions presupposition vary between the utterance and its alternative.3 Of particular importance for the data investigated in this paper, the assumption in (13ii) seems to fail systematically for the scale Æbelieve, knowæ, so I will discuss this case in some detail.

(14) – Does Bill have a sister? – Yes. – Do you know that, or just believe it? What is the nature of this difference between believe and know, and is it encoded in the lexical content of these verbs? Not necessarily. In particular, one prediction of the proposal to be developed here is that sentences of the form ‘I believe that p’ convey, by means of antipresuppositions, that the speaker is somewhat uncertain about p (see example (35)). It seems to me that a pragmatic account of the difference between the two verbs would be desirable. Importantly, such a pragmatic difference between the two verbs would not play any role in the present analysis. In fact, whether or not there are additional differences between believe and know and whether or not these differences are semantic or pragmatic differences, the 3

Examples such as (i) have been recently discussed in the literature: a scalar term is embedded in the scope of a presupposition trigger. (i)

a. John knows that some of his advisors are crooks. b. John knows that all of his advisors are crooks.

Russell (2006) and Simons (2006) argue for a treatment of these cases which is very close to the view advocated here. Sharvit & Gajewski (2007) propose a treatment of these examples in terms of a local theory of implicatures a` la Chierchia (2004). This last type of grammatical approach would be more difficult to reconcile with contextual variations of the data.

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2.1.2 More on believe v. know Does the scale Æbelieve, knowæ ever lead to examples satisfying the constraints given in (13)? In particular, there might be differences between the assertions generated by believe and know. The goals of this section are, first, to argue that this difference between the two verbs is irrelevant for the present purpose (because it might not be at the level of their assertions), and second, to show that even if it was, it would just be an indication that the constraint in (13) should be relaxed and that doing so would not affect the core of the present proposal. There has been much discussion in the philosophy literature of the observation that know seems to convey that the subject’s belief is supported by adequate evidence, as suggested by example (14) (see Gettier [1963] for various possible versions of this difference and related puzzles, which are still debated).

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2.1.3 Summary Utterances of non-presuppositional sentences (e.g. (7a)) are infelicitous when a given presuppositional alternative sentence (e.g. (7b)) is felicitous. Consequently, a felicitous utterance of the first should trigger the inference that its presuppositional alternative is not felicitous. A proper theory of presupposition must postulate constraints on the use of presuppositional sentences; the inference is thus that some of these constraints are not fulfilled. In the present paper, I make explicit assumptions about constraints on the use of presuppositional sentences so that such a theory can account for the previously unnoticed range of different flavours that the predicted inference can have, depending on well-defined contextual variations.

2.2 Naive approaches, technical limitations I would now like to spell out exactly why example (1) is a puzzle for current theories of anti-presupposition. The main argument comes from the following quote from Sauerland (2006): ‘[anti-presuppositions] must have weak epistemic status in contrast to scalar implicatures and conventional presuppositions.’ In other words, it is claimed that inferences such as (1b) should never arise in such a strong form, contrary to the facts. In the second half of this section, I show that the technical structure of the theory does not allow for anti-presuppositions with such a strong epistemic status. Before getting into this technical overview, I explain why an intuitive comparison with classical cases of scalar implicatures remains incomplete.

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maximize presupposition principle does apply between believe- and know- sentences, as witnessed by the examples in (10). This might call for a modification of (13), but for the purpose of this paper, I will use this formulation at least as a working simplification, together with the counter-balancing approximation that believe and know only differ by their presupposition. Again, this is not a necessary step for our purpose. The reader might wonder why the scale Æbelieve, knowæ underlies most of the examples of this paper since it seems to involve unnecessary complications. One of the advantages of this scale is that the alleged content of the inference is easy to manipulate and to identify: it is fully expressed in the complement of the verb. To make sure that the data are not biased by peculiar properties of the Æbelieve, knowæ scale, examples involving the scale Æeach, theæ are presented in parallel without necessarily repeating the discussion (the empirical motivation for this scale is illustrated by (8)).

148 An Epistemic Step for Anti-Presuppositions

(15) Context: Someone just asked ‘Is the coffee machine working today?’ a. No, John broke it. b.
No, it is John who broke it. Let CðpÞ denote the constraint on the use of a sentence with presupposition p. The decision to utter a sentence which was in competition with a sentence with an additional presupposition p should allow the hearer to conclude that the speaker does not believe that p or that the speaker does not believe that the constraints on the use of presuppositional sentences were met (i.e. :Bs ½CðpÞ _ :Bs ½p). Importantly, it is reasonable to require that a speaker who uses a sentence with presupposition p believes that p and the predicted inference boils down to the claim that the speaker did not believe that the use of the presupposition p was felicitous: :Bs ½CðpÞ.4 In sum, whatever the constraint on the use of presuppositional sentences is, the inference one can draw from a sentence which has a sentence with presupposition p as an alternative is that the speaker does not assume this constraint to be satisfied. Since the constraint on the use of presuppositions is intricate, a rough comparison with scalar implicatures cannot settle the issue raised by (1). 4

The proof relies on particular assumptions on the structure of the speaker’s beliefs as spelled out in the Appendix. It basically goes as follows: if, then, assuming that Bs[Bs[p]] and Bs[p] are equivalent, we obtain that and by contraposition that. Thus, boils down to.

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2.2.1 Comparison with scalar implicatures incomplete At first sight, one could formulate the problem in the following terms: if a speaker utters the sentence (1a), she is committed to having a sister. Why would a cooperative speaker utter the less informative sentence (1) which does not convey this information? This formulation of the question is strongly reminiscent of cases of scalar implicatures and may receive a very similar answer: the least informative sentence is chosen because the speaker does not have the belief that the additional piece of information conveyed by the alternative is true (i.e. :Bs[p]). Unfortunately, another complication comes into play when the alternative triggers a presupposition because its use is restricted by independent principles. The very weak claim that presuppositions must obey particular conditions to be felicitous is not controversial in any respect, no matter what theory of presuppositions is assumed. Let us still back up this point with an example. The two sentences in (15) only differ by the amount of information they presuppose; the presuppositional version (15b) is infelicitous (we will come back to this example later).

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2.2.2 Naive contextual enrichment technical limitations As shown above, one cannot innocently rely on a rough comparison to classical cases of scalar implicatures to account for the fact in (1). The challenge now becomes more technical: if our hypotheses about presuppositions’ felicitousness are refined, can we explain the inference in (1b) as an enrichment of the bare prediction that the conditions of felicitousness were not met? In other words, we want to derive the inference that the speaker believes that p is false from the fact that presupposing p would have been infelicitous. One might argue that this enrichment looks very similar to the epistemic step and might be achieved thanks to contextual assumptions (e.g. the speaker could be assumed to be opinionated about the matter at hand). Following Stalnaker (1973, 1974), let us adopt the idea that a sentence with presupposition p is felicitous only in contexts where p is common belief—that is p is (part of the) common ground. What type of contextual assumptions should we recruit? Example (16) presents a range of attempts which are arguably inconclusive. The problematic parts are highlighted with question marks in the formulae in (16), and I very briefly explain the problems encountered below. The bottom line for each of these attempts is the following: the corresponding assumption is implausible or the outcome does not match our empirical observation (Bs[:p]). Example (16a) shows that trying to apply the competence assumption used in the case of standard scalar implicatures does not yield any fruitful enrichment: the predicted inference is too weak since it is true as soon as the speaker does not believe that the addressee believes that p. Example (16b) is an attempt to apply a generalization of this competence assumption: the speaker is opinionated as to whether p is common ground. The predicted inference remains too weak. Example (16c) is an attempt to generalize the competence assumption slightly differently: the speaker believes that p is common ground or that its negation is common ground. This assumption seems extremely speculative: under what conditions would a speaker believe that the common ground ‘is opinionated about p’ (i.e. the common ground settles whether p is true or false)? In any event, the prediction is now excessively strong: the inference is that the speaker believes that p is false, and not that :p is common ground. Example (16d) explores the minimal assumption that would be needed to obtain the advocated inference. Again, it is not clear why a speaker should assume for a proposition p that it is either common ground or false, there seems to be a much wider range of possibilities (e.g. the addressee does not believe the proposition).

150 An Epistemic Step for Anti-Presuppositions (16) Inconclusive attempts to account for the initial observation: a. :Bs[CG[p]] and (Bs[p] _ Bs[:p]) [ ((Bs[p] ^ :Bs[CG[p]]) _ Bs[:p])?? b. :Bs[CG[p]] and (Bs[CG[p]] _ Bs[:CG[p]]) [ Bs[:CG[p]]?? c. :Bs[CG[p]] and (Bs[CG[p]] _ Bs[CG[:p]])?? [ Bs[CG[:p]]?? d. :Bs[CG[p]] and (Bs[CG[p]] _ Bs[:p])?? [ Bs[:p]

3 FELICITY CONDITIONS OF PRESUPPOSITIONAL SENTENCES In the previous section, I argued that if the overall constraint to use a sentence with presupposition p is written CðpÞ, the predicted inference from an utterance of a sentence which has such a presuppositional sentence as an alternative is :Bs ½CðpÞ. Example (1) shows that, under certain circumstances, the inference is rather that Bs[:p]. At a very abstract level, this shows that if the latter is a contextual enrichment of the former, the relevant contexts ensures that: Bs[CG[p]] _ Bs[:p] (see (16d)). Interestingly, this suggests that a systematic investigation of the contexts where a strong inference seems to be drawn from a sentence with a presuppositional alternative could be a new source of information about the general constraints on presuppositions and, by the same token, about the very nature of presupposition. The focus of this paper is different: I will first try to establish a reasonable picture of what the constraints on the use of presuppositional sentences can be and then show that it accurately predicts inferences generated in various contexts.

3.1 What it takes for a presupposition to become common ground Stalnaker (1973, 1974) proposed that a sentence with presupposition p is only felicitous in contexts where p is part of the common ground (or

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To sum up, inferences such as (1) cannot be explained by elementary extensions of scalar implicature accounts. The correct explanation should rely on a proper understanding of the constraints on the use of a sentence with presupposition p; the classical view of presuppositions and common ground is not adequate. In the next section, these felicity conditions of presuppositional sentences are investigated in more detail following a modern Stalnakerian view of presupposition and common ground. The main appeal of the upcoming description of these conditions lies in the range of possible enrichments it accurately predicts for inferences similar to the one presented in (1), as will be illustrated in section 5.

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(17) Lemma (adapted from Schlenker 2006) If a speaker s and her addressee a both believe that p, if furthermore it is common ground that the speaker believes that both of them believe that p (i.e. CG[Bs[Bs[p] ^ Ba[p] ]]), then p is common belief. Arguably, if s uses a sentence with presupposition p, it becomes common belief that s expects everyone to accept p as true. On this assumption, the second condition in (17) is automatically satisfied when a sentence with presupposition p is uttered. The theorem in (18) puts together these results, spelling out the consequences of the utterance of a presuppositional sentence: (18) Theorem (adapted from Schlenker 2006)

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so the speaker believes). Stalnaker (1998) argues that this formulation is too strong, or at least it is inappropriate, because it does not tell whether the condition should be met before or after the utterance. A sentence with presupposition p is felicitous in contexts where an utterance of this sentence makes its presupposition become common belief. I refer to von Fintel (2000) for a thorough discussion of this claim; the key idea is that the common-ground constraint only holds at some point after the utterance of a presuppositional sentence. For the purpose of this paper, we need to spell out in more detail what condition must hold before an utterance of a presuppositional sentence. Stalnaker (2002) describes this timing version of the relation between presupposition and common ground; I rely here on Schlenker’s (2006) implementation of these ideas. In the remainder of this section, I review Schlenker’s analysis and extend it by bringing accommodation into the picture. The definitions, technical assumptions as well as the formal proofs of the results can be found in the Appendix. Some interesting differences with and improvements on Schlenker’s analysis (2006) are discussed in the Appendix. More generally, the main goal here is not to give a Gricean account of the maximize presupposition principle, as Schlenker (2006) aimed to do, but rather to describe the circumstances under which a sentence can make its own presupposition become common belief. The starting point of Schlenker (2006) is to elaborate what it takes for a proposition p to be common belief—assuming certain general hypothesis about the beliefs of the participants to a conversation. This leads to the lemma in (17). (The technical details are discussed in the Appendix.)

152 An Epistemic Step for Anti-Presuppositions If a speaker s and her addressee a both believe that p, if furthermore the speaker s utters a sentence S with presupposition p, then p becomes common belief. This theorem has to be enriched to allow for the possibility of accommodation: it is not necessary that an addressee believe that p is true prior to an utterance for p to become common belief right after this utterance. The straightforward technical result is given in (19):

This theorem (19) spells out the conditions under which an utterance of a sentence S makes its presupposition become common belief. These conditions are discussed in more detail in the next section.

3.2 Discussion of the constraints obtained The first hypothesis in (19)—s believes p—is unproblematic: a speaker who uses a sentence with presupposition p is committed to the truth of this presupposition. Noticeably, there might be cases like (20) where a speaker could break this rule but they are arguably deliberately distorted uses of presuppositions. (20) Context: John sees Mary at a party. He wants to discover whether his beautiful addressee is married, but he does not want to reveal that he would prefer her to be single. John may ask: Didn’t you come with your husband? Interestingly, assuming that speakers believe the presuppositions of the sentences they utter prior to their utterance, the set of conditions given in (19) provide necessary and sufficient conditions to ensure that the presupposition of a sentence S would become common belief after an utterance of S. The second condition in (19)—s utters a sentence S with presupposition p—represents the move to a modern Stalnakerian view of presupposition: it makes room for the possibility that the very utterance of a sentence contributes to its presupposition becoming common belief.

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(19) Theorem (introducing accommodation) If a speaker s believes that p, and if the speaker s utters a sentence S with presupposition p, and if furthermore s’s uttering this sentence S would cause a to accommodate and believe p, then p becomes common belief.

Emmanuel Chemla 153

(21) Context: There is a disagreement about the number 319; Mary is known to have very good mathematics skills. Someone just said that 319 is a prime number. a.
No, Mary knows that it’s not. b. No, it’s not. c. No, Mary believes that it’s not. The authority condition given in (19) and discussed above predicts this contrast: it is inappropriate to use a sentence if you are not an authority about its presupposition since the common-ground condition would not be met. Clearly, when there is an explicit disagreement between two people, none of them can claim to be an authority: it would require some arguments to make the other participant change her mind. Before moving on, a word of caution is in order: it is possible to use presuppositional sentences in situations of debate. For instance, ‘No, any first year student knows that it’s not’ is a perfectly plausible utterance in contexts like (21). This actually provides an additional

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The third condition in (19) introduces accommodation into Schlenker’s analysis and deserves more discussion—s’s uttering this sentence S would cause a to accommodate and believe p. This enrichment eliminates the problematic requirement that the addressee must believe the presupposition beforehand, which is what made Stalnaker’s original proposal fail to account for well-known cases of informative presuppositions. Intuitively, this condition describes a constraint on the relation between s and a with regard to p. In other words, it states that s is in a position to convince a that p by merely using a sentence which presupposes p, without any further effort (e.g. without providing rational arguments). I will refer to this condition by simply saying that ‘the speaker is an authority’ (relative to her addressee a and with regard to p). Finally, notice that this condition does not prevent the addressee from believing p before the assertion of S; in this case, s is trivially an authority about p since hearing a sentence which presupposes p should not make a revise her belief that p is true. This last condition can be fleshed out as follows. It is well known that in a conversation where there is a disagreement about p, it is inappropriate to use a sentence which presupposes p. This is exemplified in (21). In (21a), the second participant tries to convey that her addressee is wrong; it is inappropriate to do so with a sentence which presupposes something that the previous speaker denied. The example in (21b) shows that this constraint does not hold for assertion; (21c) shows that the non-presuppositional alternative to (21a) is also felicitous in this context.

154 An Epistemic Step for Anti-Presuppositions argument for my claim: such an utterance seems to deny that there could be a debate in the first place. If 319 turns out to be a prime number, having uttered a presuppositional version of a denial is much more embarrassing.5 Presumably, it is because presuppositional versions are much more aggressive, they deny the soundness of the discussion in the first place. In other words, my claim is that if the participants accept that there might be disagreement and debate, they should not use presuppositional sentences; if they do use presuppositional sentences, they make clear that they disagree that there could be a debate. Coming back into our main track, (22) rephrases (19) with the convenient terminology of speaker’s authority:

3.3 An additional constraint: non-crucial information In the previous section, I described the conditions under which an utterance of a presuppositional sentence can make its own presupposition become common belief. At first sight, this corresponds to the felicity conditions advocated by Stalnaker (1998). I suggest below that there might be an additional constraint, but, since it will turn out to be trivially satisfied in the relevant cases (see section 4), I keep this discussion short and informal. How do the conditions in (22) account for the contrast in (15)? Unfortunately, they do not. Intuitively, the deviance of (15b) is due to the fact that crucial pieces of information (e.g. the actual answer to an explicit question under discussion) cannot be conveyed by means of presupposition, and (22) does not require this. The modern Stalnakerian picture of presuppositions adopted here is a natural framework to capture this intuition. The previous section made extensive use of the idea that a presupposition p of a sentence S could unproblematically become common ground after an utterance of S. Nevertheless, this should not happen too late either. In other words, the presupposition of S can become common belief after an utterance of S, but it must become common belief before the sentence S achieves its illocutionary purposes.

5

Fortunately, 319 ¼ 11 3 29.

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(22) Theorem If a speaker s believes that p, and if the speaker s utters a sentence S with presupposition p, and if s is an authority, then p becomes common belief.

Emmanuel Chemla 155

Returning to the contrast in (15), the purpose of the utterance is to answer the question. By the time the presupposition that ‘somebody broke the coffee machine’ becomes common belief, the question is fully answered and the rest of the process is pointless.

3.4 General constraints on presuppositions

(23) Constraints on the use of presuppositional sentences: A sentence S with presupposition p can be felicitously uttered by a speaker s only if: a. s believes that p is true; b. s is an authority about p; c. p is not crucial for the current purpose of the conversation. This result was derived from a Stalnakerian view of presupposition, but it is of course compatible with other frameworks. For instance, Geurts (1999) and Abbott (2000) argue that pieces of information conveyed by means of presuppositions are ‘backgrounded’. Intuitively, background information should probably be (i) believed by the speaker (cf. condition (23a)), (ii) non-controversial (cf. condition (23b) and the discussion of example (21)) and (iii) non-crucial (cf. condition (23c)). It seems to me that the Stalnakerian approach focuses on condition (23b) while this alternative backgrounding view focuses on condition (23c), but this does not result in any problematic incompatibility. 4 THE PROPOSAL The initial puzzle involves situations of the following type: s utters a sentence S1, S1 has no presupposition but has an alternative sentence S2 which asserts what S1 asserts and additionally presupposes p. The maximize presupposition principle introduced in (2) states that S1 should not be uttered if S2 is felicitous. Therefore, the hearer should infer in this situation that it is not the case that the speaker believes that S2 is felicitous. According to the previous section, the predicted inference can be stated as: it is not the case that the speaker believes that the conditions in (23) are all met. The constraint in (23c) is automatically met in the relevant situations. Indeed, the speaker uttered S1 and thus decided not to

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Summarizing this section: a sentence with presupposition p is felicitous if p becomes common belief early on after the utterance of the sentence. The technical result (22) and the discussion in section 3.3 lead to the following reformulation of the general constraints on the use of presuppositional sentences:

156 An Epistemic Step for Anti-Presuppositions introduce p either by means of presupposition or by means of assertion: the speaker believes that p is not a crucial piece of information for the current purpose of the conversation. Thus, the predicted inference becomes: it is not the case that the speaker believes both that she believes that p and that she is an authority about p. Let Auths[p] stand for the proposition that s is an authority about p (where the addressee and the presuppositional sentence are left implicit). The inference can be written as: :Bs ½Bs ½p^Auths ½p Adopting a few straightforward assumptions about speakers’ beliefs (see Appendix), this is equivalent to: :Bs[p] _ :Bs[ Auths[p] ]. Example (24) summarizes this prediction:

This prediction is weaker than the inference described for (1), namely, the speaker believes that p is false. The claim is now that the stronger version of the inference arises only if the addressee believes that the two assumptions in (25) and (26) hold (in short, in contexts where these assumptions hold). (25) Competence assumption: The speaker s is opinionated about p. Technically: Bs[p] _ Bs[:p]. (26) Authority assumption: The speaker s believes in her authority about p. Technically: Bs[Authsp]. The contextual assumption (25) does not require much discussion, it is the exact same assumption needed to achieve the epistemic step in the case of classical scalar implicatures (see Spector 2003; van Rooij & Schulz 2004; Sauerland 2004). However, in cases of anti-presupposition, this assumption needs to be supplemented with the less standard assumption in (26) about the authority of s. Example (21) already provided independent evidence in favour of such an assumption. 5 FURTHER PREDICTIONS This section extends the proposed analysis to a range of further phenomena. As a methodological strategy, I often refer to the intuitive notions of Authority and Competence introduced in the foregoing,

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(24) Prediction of the maximize presupposition principle: Situation: a speaker s utters a sentence S1. S2 is an alternative sentence to S1; S2 asserts what S1 asserts, but additionally presupposes p. Predicted inference: :Bs[p] _ :Bs[ Auths[p] ].

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5.1 Believe in contexts 5.1.1 Undeniable competence and authority Let us start with the opening example (1) repeated here as (27). In this example, p refers to the proposition that the speaker has a sister; (28) is a parallel example involving the scale Æeach, theæ. (27) John believes that I have a sister. Inference: The speaker (believes that she) does not have a sister. (28) I bought a car for each of my brothers. Inference: The speaker (believes that she) has several brothers. It is fairly natural to expect people to be opinionated about their having a sister and the competence assumption is met in unmarked contexts where (27) is uttered. People also naturally consider themselves an authority as to whether they have a sister: we do not normally require any evidence to believe them in this matter. The authority assumption is satisfied too. As shown in (29), the application of the maximize presupposition principle combined with these two contextual assumptions now fully accounts for the inference in (27): Bs[:p]. (29) a. Applying the maximize presupposition principle: :Bs[p] _ :Bs[Auths p] b. With the authority assumption Bs[Auths p]: :Bs[p] c. With the competence assumption (Bs[p] _ Bs[:p]): :Bs[:p] Note that there is apparently an additional step here which might lead to the stronger conclusion that the speaker does not have a sister (:p rather than Bs[:p]). This could be accounted for by an additional

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and the relevant tests are discussed when necessary. Since the core of my proposal is a precise description of the interaction between inferences and contexts, I start with examples in a variety of different contexts. In each situation, the first examples involve the scale Æbelieve, knowæ, and parallel examples involving the scale Æeach, theæ are provided to ensure the generality of the empirical pattern. Then comes a series of less crucial examples involving slightly less standard cases of anti-presuppositions relying on too and again. These examples are interesting because the intuitive strength of the inference does not only depend on the contextual assumptions described above but also relies on intrinsic properties of these triggers. Finally, I discuss how anti-presuppositions interact with general projection properties of presupposition. Interestingly, many examples look like counter-examples if not handled with care.

158 An Epistemic Step for Anti-Presuppositions

(30) a. There is a leak. b. There is no leak. The summary of this digression is that an anti-presupposition might lead an addressee to form an opinion about a speaker’s beliefs; this is independent from the reliability attributed to this belief. 5.1.2 Authority with and without Competence (31) Context: During a trial, the judge summarizes the main facts: Mr. John Smith believed that Mrs. Mary Smith was cheating on him. Judges are supposed to refrain from subjective opinion, and in this sense, judges are highly reliable conversation partners. If the judge had said ‘Mr. John Smith knew that Mrs. Mary Smith was cheating on him’, everyone would certainly have accommodated that Mary was cheating on John. In other words, the authority assumption holds. Therefore, at least the inference obtained in (29b) goes through: :Bs[p]. Now we can investigate two variants of this example. First, imagine that this is the opening of the trial so that the judge is not supposed to have formed an opinion about the facts yet (i.e. the competence assumption does not hold). In this context, the sentence merely implicates that it is not the case that the judge believes that Mary was cheating on John: :Bs[p]. On a second version of this scenario, the sentence is uttered at a later stage in the trial where every piece of the investigation starts making sense and the judge should also start forming her own opinion about

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assumption of the form ‘Bs[:p] 0 :p’ which basically says that the speaker is reliable with regard to :p. This seems to be closely related to the authority assumption and one might think that the present proposal predicts this stronger version of the inference by default. However, even if the authority assumption entailed such a reliability assumption (which is not true strictly speaking, especially if potential rhetorical effects of presupposition are taken into consideration), it is important to note that the authority assumption applies to p while the Reliability Assumption applies to :p. This goes slightly off topic, but I would like to clarify this asymmetry between a proposition and its negation. Consider the example in (30). If your honest plumber tells you (30a), it is probably because she saw a leak. Unless she is a liar, there might very well be a leak. On the other hand, if she tells you (30b), it is probably because she did not find a leak, but this by itself does not mean that there is no leak and you might reserve your opinion.

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the case. One may now expect the competence assumption to hold (Bs[p] _ Bs[:p]) and the judge may be aware that one is very likely to infer from (31) that she believes that Mary was not cheating on John. Example (32) shows that the same range of judgments can be reproduced with the scale Æeach, theæ: the inference that Mrs. Smith had several accomplices comes in different flavours depending on whether the judge is expected to be opinionated. (32) Context: During a trial, the judge says: Did you check her mailbox? Mrs. Smith certainly exchanged e-mails with each of her accomplices.

(33) Mary is pregnant; John believes it too. In this case, it seems that the speaker uses the second clause as further evidence in favour of her claim that Mary is pregnant. In other words, she does not believe that she is an authority.6 This is exactly what the present proposal predicts as the computation in (34) shows. (34) a. Applying the maximize presupposition principle: :Bs[p] _ :Bs[Auths p] b. With the belief expressed by the speaker Bs[p]: :Bs[Auths p] The sentence in (35) provides a shorter version of the same type of example. Here again, there is an inference that the speaker is not an authority about Mary being pregnant. Interestingly, what might at first be seen as an essential difference between believe and know (i.e. roughly, the degree of confidence in the given belief) comes out as an anti-presupposition of believe. This is only a partial account since it only applies to first-person beliefs, but it opens a way to pragmatic accounts of this contrast.7 6 Note that this type of inference could trigger various interesting rhetorical effects. In particular, it could motivate under-uses of presuppositional phrases to increase the overall impression of objectivity of the speaker, who somehow avoids claiming her authority. 7 It might be that an utterance of the form ‘John believes that p’ naturally suggests that John uttered ‘I believe that p’, for instance, because our main access to other people’s beliefs is through their own words. Therefore, the inference that the belief expressed is somewhat uncertain would generalize to third-person belief reports.

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5.1.3 Competence without authority Contexts where the speaker is competent but not an authority were already discussed in (21): they arise naturally in situations of debate where every participant might be opinionated but none can consider herself as an authority. Let us look at a slightly different example:

160 An Epistemic Step for Anti-Presuppositions (35) I believe that Mary is pregnant.

(36) Context: Mary is a great linguist, she writes many excellent papers every year. Someone asks John how many papers she published this year. John replies: a. Mary published only one paper, I asked her to send each of them to me. . . b. Mary published only one paper, I asked her to send it to me. . .

5.2 Other triggers In this section, I present empirical data involving presupposition triggers which might generate anti-presuppositions via null alternatives: again and too (see Amsili & Beyssade [2006] for related discussion). 5.2.1 Again Sentences with again are associated with alternative sentences without the particle (see example (11)). This accounts for the inference in (37b). (37) John will never go to Paris. a. Alternative: John will never go to Paris again. b. Inference: John has never been to Paris. (Adapted from Amsili & Beyssade 2006) At first sight, this inference goes through without any special assumptions about the context. This is an illusion: if the assumptions are explicitly blocked, the inference is blocked too. Imagine the following context: at a party your friend Mary meets a seductive stranger, John. John leaves the party early and Mary tells you how much 8

Examples of this kind involving the Æbelieve, knowæ scale are easier to construct, presumably because other people’s beliefs easily count as justification for the speaker’s own belief and this is what the target sentence ends up doing in these examples.

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Example (36a) is the usual counterpart example with the scale Æeach, theæ.8 As before, the second part of the sentence seems to be a justification for the first claim that Mary published only one paper: the speaker does not believe himself to be an authority for that matter. There are two ways to make this judgment clear. One way is to see that the second part of the sentence seems to be a reply to ‘How do you know that?’. Another way is to contrast (36a) with (36b). Example (36b) would achieve very different purposes: the speaker seems to assume that her addressee will accept that Mary published only one paper and the rest is a further comment on this.

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5.2.2 Too Part of the explanation for the strength of the antipresupposition associated with again-alternatives relied on the fact that again is not a content word. The presupposition trigger too might behave differently: (38) is similar to (37) while (39) is based on an example which should be more familiar. (38) John will never go to Paris. a. Alternative: ??John, too, will never go to Paris. b. Fragile inference: No one will ever go to Paris. 9

Note that a somewhat different way to exploit the ‘similarity’ is to say that the information conveyed in the alternative sentence might be just as relevant as the information conveyed in the utterance and to argue that, in general, relevance matters in the activation of alternatives.

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John seems to hate French people and how ugly he thinks the Eiffel Tower is. She concludes that (37). In this context, the inference (37b) does not go through because Mary might not have asked John whether he has ever been to Paris before and therefore she might not have any strong opinion about it. In fact, it is not hard to see that we find the whole range of inferences we described in the case of the scale Æknow, believeæ. Thus, the inference (37b) does require the contextual assumptions advocated here but interestingly, they seem to arise by default. This raises an interesting issue: what special features of this case make these assumptions jump into existence? This could be attributed to a particular property of again. Roughly, again is not a content word, it triggers a presupposition by picking up some content which is already expressed in the sentence and conveys that it already happened before. Therefore, the content of the presupposition of again is necessarily very similar to the actual assertion of the sentence. This is not true for know: the assertion is about someone’s beliefs whereas the presupposition may concern any facts in the actual world. Crucially, an assertion clearly implies a claim of competence and authority and this claim can naturally be generalized to the very similar presupposition that the alternative sentence with again would trigger.9 Importantly, classical cases of scalar implicatures also raise this issue: the competence assumption naturally jumps into existence in ‘out of the blue’ contexts. Again, a tentative explanation comes from the idea that an assertion is a claim of competence (and authority). Furthermore, it is ‘natural’ (to claim) to be an expert about a range of closely related facts so that any claim of competence and authority about p might by default be extended to a broader range of propositions, potentially including additional content of alternative sentences.

162 An Epistemic Step for Anti-Presuppositions (39) John is having dinner in New York. a. Alternative: ??John is having dinner in New York too. b. Fragile inference: John is the only one to have dinner in New York. (Adapted from Kripke 1990)

(40) Context: John and Mary, two naughty students, are called separately before the headmaster who is notoriously cruel. Afterwards, they want to know what happened to each other. Mary asks John: Did he beat you? a. Alternative: Did he beat you too? b. Inference: The headmaster did not beat Mary. (I owe this example to Bart Geurts, personal communication) 5.2.3 Summary of too and again I capitalized on properties of too and again to investigate and clarify how the present proposal applies to various other, sometimes quite delicate, cases. In general, presuppositions triggered by again are easier to accommodate than presuppositions triggered by too. Both of these particles have an anaphoric component but it seems that the content of the presupposition is easier to accommodate in the case of again. That presuppositions triggered by again are easier to accommodate than presuppositions triggered by too is certainly controversial (see van der Sandt & Huitink [2003], for

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The word too is not a content word, it is merely an anaphoric element. This anaphoric feature of the word has been used to explain why the presupposition it triggers is difficult to accommodate, as witness the deviance of (38a) and (39a) in contexts where there is no salient individual other than John (see Geurts & van der Sandt [2004] and Beaver & Zeevat [2004] for discussion). In other words, nobody can be an authority for these cases: it is not possible to convince anyone that the presupposition of (39a) is true simply by asserting (39a) since this presupposition is not retrievable from this sentence to begin with. Hence, (39a) is infelicitous and no inference like (39b) is predicted. The crucial element to explain why the inference does not go through in these cases is that it is not possible to accommodate the presupposition of the alternative sentence. Interestingly, there are special cases where it is possible to accommodate the presupposition of too. For instance, one might naturally accommodate from Mary saying (40a) that the headmaster beat her. Now, as predicted, the corresponding inference that the headmaster did not beat Mary does go through if she utters (40).

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instance). What is important for present purposes and should not be controversial is that in the examples provided the relative ease of accommodation of the alternative correlates with the strength of the associated anti-presupposition.

5.3 Other environments

5.3.1 Believe under negation The predicted inference in (41) is not borne out.10 The analysis of this example will remain incomplete, but I will argue that the problem faced here is orthogonal to the present proposal. (41) John does not believe that I have a sister. a. Alternative: John does not know that I have a sister. b. Predicted inference: I do not have a sister. c. Actual inference: I have a sister. The first important interfering factor is that believe is a neg-raising verb. In other words, the sentence in (41) normally means (42). Importantly, know is not a neg-raising verb and so the alternative (41a) cannot mean (42a), and the asserted content of (41) is thus stronger 10

Sauerland (2006) provides the following judgments for (i) and (ii).

(i) John doesn’t believe that 313 is prime. Inference: 313 is not prime. (ii) John doesn’t believe that Mary is cheating on him. Inference: Mary is cheating on John. These data would be somewhat contradictory: the anti-presupposition of (i) is claimed to be the negation of the content of the belief expressed, it is exactly the opposite for (ii). Rather than investing these particular examples in detail, I propose to analyse a more familiar example where, for instance, the contextual factors should be better understood at this point of the paper.

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The projection properties of anti-presuppositions simply follow from the projection properties of the presuppositional alternative sentences, no matter how presupposition projection is accounted for. This section first shows that when believe appears under negation, the present proposal seems to make incorrect predictions. I present an assortment of arguments which suggest that these apparent discrepancies arise from the interference of independent factors (e.g. neg-raising). The rest of the section shows that the predictions are correct when the interfering factors are out of the way. The relevant examples involve (i) negation with different scales: Æeach, theæ and Æevery, bothæ and (ii) the scale Æbelieve, knowæ in modal environments.

164 An Epistemic Step for Anti-Presuppositions than the assertion of its alternative.11 If the maximize presupposition principle compares sentences which differ only in their presuppositional content, sentences (41) and (41a) are not in immediate competition and this explains why the inference in (41b) is not an actual prediction of the present proposal.

(43) Jean ne croit pas que je suis linguiste. Jean ne believes not that I am-IND linguist. ‘Jean doesn’t believe that I’m a linguist.’ Inference: I am a linguist—the reading of believe is close to believe me (44) Jean ne croit pas que je sois linguiste. Jean ne believes not that I am-SUBJ linguist. ‘Jean doesn’t believe that I’m a linguist.’ Inference: I am not a linguist. 11

I implicitly assume here that neg-raising phenomena arise at the level of assertion. The minimal assumption needed to make the same point is that whatever principles drive these effects have precedence over the maximize presupposition principle.

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(42) John believes that I do not have a sister. a. Alternative: John knows that I do not have a sister. b. Predicted inference: I have a sister. c. Actual inference: I have a sister. Thus, the problematic inference (41b) can be ruled out, but we still want to account for the actual inference (41c). One line of investigation would be that, in general, alternatives should not be thought of as syntactic objects and one could investigate a more abstract mechanism which explains that (42a) is the relevant alternative to (41). Alternatively, one could think that the inference in (41c) is of a very different nature. For instance, it might be due to some interpretation under which believe would be close to believe me (when I tell him). Under this reading, (41) would mean something like ‘John does not believe me (when I tell him) that I have a sister’ or ‘I told him, but John does not believe me that I have a sister’. It would naturally follow from there that the speaker believes that she has a sister. One of the challenges for a proper formalization of such an approach would be to explain why this interpretation arises for (41) and not for (42) or for (1). Interestingly, this correlates well with the alternation of subjunctive and indicative moods in negative belief reports in Romance languages (see Quer [1998] and Egre´ [2004] for discussion):

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(45) Jean ne sait pas que je suis linguiste. Jean ne knows not that I am-IND linguist. ‘Jean doesn’t know that I’m a linguist.’

(47) Mary doesn’t know that I love her, but (at least) she doesn’t believe that I’m married. Inference: I am not married. This section started with the statement that (41) could be problematic. I mentioned a range of independent phenomena

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(46)
Jean ne sait pas que je sois linguiste. Jean ne knows not that I am-SUBJ linguist. ‘Jean doesn’t know that I’m a linguist.’ The facts of main importance are (i) the reading of believe which could be paraphrased as ‘believe me when I tell him’ appears when the indicative mood is used, example (43); (ii) the inference that ‘the belief’ is false does show up in French with subjunctive complements (i.e. also when the ‘believe me when I tell him’ reading vanishes), example (44). Here is a sketch of a theory. The subjunctive mood is the default mood (see Schlenker [2005] which provides an analysis of the French subjunctive via a competition with the indicative mood and with reference to the maximize presupposition principle). As such, the subjunctive mood may allow the competition between believe and know, while the indicative mood blocks it. In fact, the indicative mood may itself compete with the subjunctive mood and thus trigger the opposite inference. This description is quite far from being a complete account. In particular, it does not extend straightforwardly to languages like English which mainly lack the relevant mood distinctions. Nevertheless, this sketch of a theory is sufficient to claim that the present proposal would handle examples like (41) appropriately if other phenomena were better understood. I would like to add a last piece of data that argue accordingly. The predicted inference may emerge in English when the alleged alternative is suggested by previous linguistic material. The intuition here is that in (47), the first part of the sentence makes constructions of the form ‘Mary doesn’t know p’ salient so that if it is appropriate to use such a construction in the second part of the sentence, it should be done. In short: when the relevant alternatives are salient, scalar implicatures are more robust; (47) is an attempt to make the alternative salient by copying its structure in the first clause. This reinforcement seems to compete with the effects of the conflicting factors, so that the predicted implicature does emerge.

166 An Epistemic Step for Anti-Presuppositions (neg-raising, mood, salience of the alternative) which may explain this conflict. In the following section, I show that the proposal makes the right predictions when these issues are factored out. 5.3.2 Each and every under negation Let us consider as before that each and every are in competition with the and both, respectively. (Both universal quantifiers might very well be in competition with both the and both, but let us put this aside for simplicity.) For these scales, the alternatives for negative sentences are unproblematic and the inferences are maintained, as predicted. The relevant examples are in (48) and (49) for each and in (50) and (51) for every.

(49) I did not meet each of John’s friends. a. Alternative: I did not meet John’s friend. b. Inference: John does not have exactly one friend. (50) I met every friend of John’s. a. Alternative: I met both friends of John’s. b. Inference: John does not have exactly two friends. (51) I did not meet every friend of John’s. a. Alternative: I did not meet both friends of John’s. b. Inference: John does not have exactly two friends. 5.3.3 Believe under modals How do anti-presuppositions behave with regard to other environments? Examples in (52) show that embedding a believe-sentence in different modal contexts does not affect the anti-presupposition it triggers, just as it does not affect the presupposition of the corresponding alternatives (see examples in (53)). (52) a. John believes that I have a sister. Inference: The speaker does not have a sister. b. Perhaps, John believes that I have a sister. Inference: The speaker does not have a sister. c. For sure, John believes that I have a sister. Inference: The speaker does not have a sister. (53) a. John knows that I have a sister. Presupposition: The speaker has a sister. b. Perhaps, John knows that I have a sister. Presupposition: The speaker has a sister.

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(48) I met each friend of John’s. a. Alternative: I met John’s friend. b. Inference: John does not have exactly one friend.

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c. For sure, John knows that I have a sister. Presupposition: The speaker has a sister.

6 CONCLUSION Heim (1991) advocated a presuppositional counterpart to the maxim of quantity, the maximize presupposition principle. From then on, two different kinds of issues have been discussed in the literature. First, the consequences of this principle for the oddness of underpresupposing sentences have been widely investigated (see Amsili & Beyssade [2006] and Magri [2006] for recent discussions). Second, the independence of the principle from the maxim of quantity has been recently discussed by Percus (2006), Sauerland (2006) and Schlenker (2006). Although the ideas and data presented here strongly rely on this literature, the focus was somewhat different: what inferences does this principle predict? I argued that, so far, the predictions were too weak. As was proposed for the epistemic step (Spector 2003; van Rooij & Schulz 2004; Sauerland 2004), I showed how conversational inferences can be reinforced within the framework of the modern Stalnakerian view of presupposition and common ground. I reviewed a variety of empirical facts which support the particular contextual assumptions advocated. I also discussed how independent phenomena may interfere with the predictions. Although these issues were not settled, I argued that these conflicting phenomena could be factored out of the present analysis. In fact, the present interaction may provide new ways to investigate these phenomena (e.g. if issues having to do with mood interact with anti-presuppositions, a better understanding of anti-presuppositions might help understand better mood issues). Further investigations should explore anti-presuppositions generated by competition with a wider range of presupposition triggers (e.g. definite descriptions, wh- and it-clefts, gender and number features).

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5.3.4 Summary The present proposal naturally predicts the projection properties of anti-presuppositions as the mirror image of the projection properties of presuppositions: an anti-presupposition is the denial of the presupposition of some alternative sentence. Empirical discrepancies seem to arise if independent conflicting factors are neglected. I argue that these difficulties are orthogonal to the present proposal. These difficulties vanish if examples are constructed carefully, as exemplified in (48–53), where the problematic factors do not intervene.

168 An Epistemic Step for Anti-Presuppositions Ultimately, we should also address more complicated cases where both the assertion and the presupposition vary significantly between the utterance and its alternative, for instance, because of the presence of several scalar terms, possibly of different types (Æsome, allæ and Æbelieve, knowæ). This would take a much better understanding of the interaction between the maximize presupposition principle and the maxim of quantity (e.g. does one of these principles have priority over the other?) and is therefore left for future research. APPENDIX

Definitions and notations Let us start with the definition of the belief operators we are going to need: (54) Bx[. . .] designates the belief operator associated with the individual x. If p is a proposition, Bx[p] stands for x believes that p is true. (55) s and a are used as indexes for belief operators to refer respectively to the speaker and her addressees. They are also used to refer to the agents themselves. (56) The null operator T: It will be convenient to introduce the trivial, non-epistemic operator Twhich is true of a proposition p iff this proposition is true. Next, I introduce the tools to manipulate higher order belief operators (e.g. the speaker believes that the addressee believes that. . .). (57) Iterated self-beliefs: For all n > 0, Bnr ½p stands for the proposition which is true iff Bx. . .Bx[p] is true, where Bx occurs n times. (58) The set of higher order belief operators: B. B designates the set of operators obtained from any composition of belief operators associated with s or a. By convention, this set

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The goal of this appendix is to provide the formal implementation of ideas used in the text. A large part of these technical details were suggested in Stalnaker (2002) and spelled out in Schlenker (2006). The main contribution here is to introduce accommodation into the general picture. The resulting system deviates Schlenker’s so that it reveals some hidden assumptions (see (61)).

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includes the null operator T which can be obtained from the composition of zero belief operators. B ¼ T; Bs ; Ba ; Bs Bs ; Bs Ba ; Bs Bs Bs ; . . .: Technically, B can be defined as the minimal set of operators satisfying the following criteria: a. T 2 B b. "B 2 B; Bs B 2 B and Ba B 2 B (59) The set of strict higher order belief operators: B
. This set includes every strictly epistemic operators built from Bs and Ba: B
¼ BfT, that is the set of operators in B except T.

Assumptions about agents’ beliefs (61) Assumptions about agents’ beliefs: a. "x 2 s; a; "p; "B 2 B; BBx pBBx Bx p. b. "x 2 s; a; "p; "q; Bx ½p ^ qBx ½p ^ Bx ½q. Following Stalnaker (1998), Schlenker (2006) assumes that an agent’s beliefs can be represented by an epistemic accessibility relation between worlds. They require that this accessibility relation be transitive and euclidean and this guarantees positive and negative introspection. Simplifying a bit, (61a) imposes similar types of introspection properties. Interestingly, the universal quantification over the set of higher belief operators B also makes explicit that the properties of agents’ beliefs are very well known by the agents: agents have true beliefs about the structures of their beliefs. The second hypothesis (61b) is also satisfied by default in the epistemic worlds framework, it should be uncontroversial: as a first approximation, it is indeed equivalent for someone to believe that two propositions are true and to believe that each of these propositions is true.

Adaptation of Schlenker’s (2006) lemma Example (62) is the formal counterpart of (17). This is a straightforward adaptation of Schlenker’s (2006) example (5) together with the footnote 10 therein.

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(60) Common ground: CG[p] stands for p is part of the common ground, or equivalently: p is common belief. CG[p] is true iff "B 2 B
; B½p.

170 An Epistemic Step for Anti-Presuppositions (62) Lemma (adapted from Schlenker 2006) If (i) Bs[p]; (ii) Ba[p]; (iii) CG[BsBs[p]]) and (iv) CG[BsBa[p]], then CG[p]. Note that on the assumptions I make, (iii) entails (i). I keep them separate here because (i) has a different status: it must be true prior to the utterance (this is discussed above under (20)). Proof of (62). Let B be an operator in B
and show that, whatever operator it is, B[p] holds: 

If B ends with Bs:



If B contains no Bs operator:

B is of the form Bna with n > 0. Applying (61a) inductively, we obtain that for all m > 0, Bma ½p is equivalent to Ba[p]. Thus, B[p] is true according to (ii). 

If B ends with Ba and contains at least one Bs operator:

B is of the form B#Bs Bna with n > 0. Applying (61a) inductively, we obtain that B[p] is equivalent to B#BsBa[p]. Applying (61a) again (but with p ¼ Ba[p]), we obtain that B[p] is equivalent to B#BsBsBa[p]. Since B#Bs 6¼ T, (iv) shows that B[p] is true.

Adaptation of Schlenker’s (2006) theorem (section 2.3 therein) Theorem (63) is the technical counterpart of theorem (18) above. (63) Theorem (adapted from Schlenker 2006) If (i) Bs[p]; (ii) Ba[p] and (iii) s utter a sentence S with presupposition p, then p becomes common belief. Conditions (i) and (ii) are common to (62) and (63). Assuming that the utterance of a sentence with presupposition p makes it common belief that the speaker believes that both her and her addressee will come to believe that p; the hypothesis in (63iii) guarantees that (62iii) and (62iv) are about to be satisfied. So, the hypotheses of (62) are about to be satisfied and, therefore, so is its conclusion. This is what (63) states.

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B is of the form B# Bs (with B# 2 B) and B[p] is equivalent to B#Bs[p]. Applying (61a) twice, we obtain that it is equivalent to B#BsBsBs[p]. This is of the form B$BsBs[p] with B$ 6¼ T and thus is true according to (iii).

Emmanuel Chemla 171

Introducing accommodation Finally, theorem (64) is the formal counterpart of (19). It extends the previous result (63) by introducing the possibility of accommodation. (64) Theorem If (i) Bs[p]; (ii) s’s utterance of a sentence S with presupposition p implies Ba[p] and (iii) s utters this sentence S, then p becomes common belief.

Acknowledgements I am very grateful to Paul Egre´, Kai von Fintel, Danny Fox, Bart Geurts, Irene Heim, Nathan Klinedinst, Giorgio Magri, Philippe Schlenker and Benjamin Spector for their thorough comments and help. Special thanks to Philippe Schlenker for discussions which first motivated this work. I am also grateful to David Beaver and two anonymous reviewers of Journal of Semantics. This work strongly benefited from their comments which included very involved discussions of various pieces of data and very constructive suggestions.

EMMANUEL CHEMLA Laboratoire de Sciences Cognitives et Psycholinguistique Ecole Normale Supe´rieure 29 rue d’Ulm 75230 Paris Cedex 5 France e-mail: [email protected]

REFERENCES Abbott, Barbara (2000), ‘Presuppositions as nonassertions’. Journal of Pragmatics 32:1419–37. Amsili, Pascal & Claire Beyssade (2006), ‘Compulsory presupposition in discourse’. In C. Sidner, J. Harpur, A. Benz, and P. Ku¨hnlein (eds.), Proceedings of the 2nd

Workshop on Constraints in Discourse. NUI. Maynooth, Ireland. 5–10. Beaver, David & Henk Zeevat (2004), ‘Accommodation’. In G. Ramchand and C. Reiss (eds.), Oxford Handbook of Linguistic Interfaces. Oxford University Press. Oxford, (http://montague.

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The main contribution of this theorem is that Ba[p] may now become true after the utterance of S (by means of accommodation). As before, we conclude that at some point after an utterance of S, all the hypotheses of the lemma (62) are satisfied and therefore, so is its conclusion.

172 An Epistemic Step for Anti-Presuppositions of the Projection Problem. Unpublished MS, Princeton University. Magri, Giorgio (2006), Sketch of a Theory of Oddness. Unpublished MS, MIT. Percus, Orin (2006), ‘Antipresuppositions’. In A. Ueyama (ed.), Theoretical and Empirical Studies of Reference and Anaphora: Toward the Establishment of Generative Grammar as an Empirical Science. Report of the Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science. 52–73. Quer, Josep (1998), Mood at the Interface. Holland Academic Graphics. The Hague. van Rooij, Robert & Katrin Schulz (2004), ‘Exhaustive interpretation of complex sentences’. Journal of Logic, Language, and Information 13:491–519. Russell, Benjamin (2006), ‘Against grammatical computation of scalar implicatures’. Journal of Semantics 23:361–82. van der Sandt, Rob & Janneke Huitink (2003), ‘Again’. In P. Dekker and R. van Rooy (eds.), Proceedings of the 14th Amsterdam Colloquium. ILLC. Amsterdam. 181–6. Sauerland, Uli (2004), ‘Scalar implicatures in complex sentences’. Linguistics and Philosophy 27:367–91. Sauerland, Uli (2006), Implicated Presuppositions. Unpublished MS, ZAS, Berlin. Schlenker, Philippe (2005), ‘The lazy Frenchman’s approach to the subjunctive’. In T. Geerts, I. van Ginneken, and H. Jacobs (eds.), Romance Languages and Linguistic Theory 2003. Selected Papers from Going Romance 2003, Nijmegen, Nederlands 20–22 November. Benjamins. Netherlands 269–309. Schlenker, Philippe (2006), Maximize Presupposition and Gricean Reasoning. Unpublished MS, UCLA. Los

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stanford.edu/;dib/Publications/ accommodation.pdf). Chemla, Emmanuel (2007), ‘French both: a gap in the theory of antipresupposition’. Snippets 15:4–5. Chierchia, Gennaro (2004), ‘Scalar implicatures, polarity phenomena, and the syntax/pragmatics interface’. In A. Belletti (ed.), Structures and Beyond. Oxford University Press. Oxford. 39–103. Egre´, Paul (2004), Attitudes propositionnelles et paradoxes e´piste´miques. Ph.D., Universite´ Paris 1 and IHPST. Paris, France. von Fintel, Kai (2000), What Is Presupposition Accommodation? Unpublished MS, MIT. Cambridge, MA (http://web.mit.edu/fintel/ www/accomm.pdf). Last accessed: 14 January, 2008. Gettier, Edmund (1963), ‘Is justified true belief knowledge?’ Analysis 23:121–3. Geurts, Bart (1999), ‘Specifics’. In B. Geurts, M. Krifka, and R. van der Sandt (eds.), Focus and Presupposition in Multi-Speaker Discourse. ESSLLI 99. Utrecht. 99–129. Geurts, Bart & Rob van der Sandt (2004), ‘Interpreting focus’. Theoretical Linguistics 30:1–44. Hawkins, John A. (1991), ‘On (in)definite articles: implicatures and (un)grammaticality prediction’. Journal of Linguistics 27:405–42. Heim, Irene (1991), ‘Artikel und Definitheit’. In A. von Stechow and D. Wunderlich (eds.), Semantik: Ein internationales Handbuch der zeitgeno¨ssischen Forschung. De Gruyter. Berlin. 487–535. Horn, Larry R. (1989), A Natural History of Negation. University of Chicago Press. Chicago. Kripke, Saul (1990), Presupposition and Anaphora: Remarks on the Formulation

Emmanuel Chemla 173 Semantics, volume 17 of Current Research in the Semantics/Pragmatics Interface. Elsevier. 229–254. Stalnaker, Robert (1973), ‘Presuppositions’. Journal of Philosophical Logic 2:447–57. Stalnaker, Robert (1974), ‘Pragmatic presuppositions’. In Milton Munitz and Peter Unger (eds.), Semantics and Philosophy. New York University Press. New York. 197–213. Stalnaker, Robert (1998), ‘On the representation of context’. Journal of Logic, Language and Information 7:3–19. Stalnaker, Robert (2002), ‘Common ground’. Linguistics and Philosophy 25:701–21. Thomason, Richard H., Matthew Stone & David DeVault (2006), ‘Enlightened update: a computational architecture for presupposition and other pragmatic phenomena’. Paper presented at the OSU Workshop on Presupposition Accommodation. www.pragmatics.osu. edu/links/events/enlightened-update. pdf. First version received: 09.01.2007 Second version received: 18.06.2007 Accepted: 16.08.2007

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Angeles, CA. and Institut Jean-Nicod, Paris, France. (http://www.linguistics. ucla.edu/people/schlenker/MaxPres. pdf). Last accessed: 14 January, 2008. Sharvit, Yael & Jon Gajewski (2007), On the Calculation of Local Implicatures. Talk given at Journe´es de Se´mantique et Mode´lisation, Paris. Simons, Mandy (2006), Notes on Embedded Implicatures. Unpublished MS, Carnegie Mellon. University. Pittsburgh, PA (http://semanticsarchive. net/Archive/GIxMTUxO/embedded _implicatures_simons.pdf). Last accessed: 14 January, 2008. Soames, Scott (1982), ‘How presuppositions are inherited: a solution to the projection problem’. Linguistic Inquiry 13:483–545. Spector, Benjamin (2003), ‘Scalar implicatures: exhaustivity and Gricean reasoning’. In Maria Aloni et al. (eds.), Proceedings of the ESSLLI 2003 Student Session, Vienna, Austria. Revised version in Spector (2007). Spector, Benjamin (2007), Scalar implicatures: Exhaustivity and Gricean reasoning? In Aloni, M., Dekker, P., and Butler, A., (eds.) Questions in Dynamic

Journal of Semantics 25: 175–220 doi:10.1093/jos/ffm013 Advance Access publication October 16, 2007

What with? The Anatomy of a (Proto)-Role JEAN-PIERRE KOENIG, GAIL MAUNER AND BRETON BIENVENUE University at Buffalo, The State University of New York KATHY CONKLIN University of Nottingham

This paper describes a comprehensive survey of English verbs that semantically allow or require an Instrument role. It sheds light on the nature of Instrument roles and instrumentality by examining the distribution in semantic space of those verbs. We show first that verbs that semantically require instruments are typically semantically more complex than predicted by current theories of the structural complexity of verb meanings. We also show that verbs that require or allow instruments constrain the end states of situations they describe more than they constrain the agent’s initial activity. Our survey further suggests that the causal role played by the instrument is more varied than suggested by previous studies and requires the introduction of a new subtype of causal relation, which we dub helping. Finally, our survey demonstrates that verbs that semantically require an instrument cluster together more closely in semantic space and constrain the instrument’s (causal) role and properties more than verbs that merely allow the presence of an instrument.

An important goal of lexical semantics—in contrast to lexicography—is to map out the space of possible stem meanings: its informational boundaries and its organization, its geography, so to speak. Since Vendler (1967), it has become well-established that the space of verb meanings can be divided up into four quadrants: states, processes, changes of state, and causal situations, where the cause and effect can be either states or processes (see Carter 1976; Dowty 1979; Bach 1986; Van Valin & Lapolla 1997; Rappaport Hovav & Levin 1998, among others). The semantic information that defines membership in the four quadrants forms the backbone of the meaning of verbs or what Rappaport Hovav and Levin (1998) call the structural aspects of verb meaning. Much less is known about the organization of these quadrants or the micro-geography of this space. To put it differently, it is much less clear ‘where (. . .) the richness of the lexicon (is) to be introduced (. . .)?’ (Carter 1976). Ó The Author 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected].

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Abstract

176 What with?

(1) a. cause(s1, s2) ^ Pred(s1, A, I) ^ Pred(s2, I, P) ^ cause(s2, s3) ^ Pred(s3, P) b. cause(s1, s3) ^ Pred(s1, A,. . .) ^ Pred(s3, P,. . .) If, as we suggest in section 3, this analysis is, for the most part, correct, and if, as we argue in section 1 and elsewhere (Koenig et al. 1

Throughout the paper, we capitalize roles such as Agent, Patient and Instrument when they denote participant role names as convenient labels that do not commit us to a particular analysis of those roles (e.g. as traditional semantic roles, Fillmore 1968, or as proto-roles, Dowty 1991).

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Levin (1993) made initial strides in mapping the micro-geography of the space of verb meanings when describing narrower, semantically coherent, verb classes. But Levin’s classification was based on shared valence alternations. As such, it does not necessarily reflect a purely semantic organization of this space. Furthermore, although extensive, it was not meant to be complete with respect to any portion of the four quadrants. Similarly, FrameNet (Fillmore et al. 2003) provides insight into how very broad classes of verb meanings are fleshed out within quite narrow semantic fields or frames (e.g., the risk frame). But FrameNet does not systematically explore any quadrant of the space of possible verb meanings. The same can be said of suggestions of Carter or Rappaport Hovav and Levin about how idiosyncratic aspects of verb meaning are integrated into the structural aspects of verb meaning. This paper addresses more directly Carter’s question of how the informationally rich or idiosyncratic component and the structural component of verb meanings interact through a comprehensive study of a subclass of the causal situation quadrant. It analyses the meaning of all verbs typically known by adult, college educated, native English speakers that describe situations where, informally, an agent uses an instrument to affect a patient. We had several reasons for concentrating on verbs whose denotations must or may include an instrument to study the micro-geography of the space of verb meanings. First, if we follow Croft (1991), Talmy (2000) and others, we can describe most or all of those situations as follows: an agent of some sort acts on the instrument and the result of this action directly or indirectly causes a change of state in a patient or theme. To help the discussion, the formula in (1a) informally represents the relevant portion of the meaning of sentences that include instrument phrases for these authors. (Pred is a syntactic variable standing for various predicate names. We use A in the metalanguage formulae to denote the Agent in s1, I for the Instrument in s1, s2 and s3 and P for the Patient in s2 and s3. See section 2 for details.)1

Jean-Pierre Koenig et al. 177

Question 1. How structurally complex are the meanings of verbs whose denotations require or allow instruments? Put more specifically, what we intend to answer here is whether situations that include an instrument should be analysed as a sequence of three subsituations and whether, additionally, these subsituations are causally related, that is whether they can be analysed, as much of the previous literature assumes, as involving an agent acting on an instrument and changing its state or location and, then, the instrument acting

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2003), instruments are semantic arguments of some verbs, then the meanings of these verbs are structurally more complex than that of other verbs. They involve a sequence of three subsituations. They may not correspond to possible meanings in approaches such as Rappaport Hovav and Levin (1998) (and, possibly, Carter 1976) which hypothesize an upper bound on the structural complexity of verb meanings. Specifically, these authors hypothesize that verb meanings can include at most one causal relation, and therefore at most two subsituations [see the simplified formula in (1b)]. Thus, studying in detail the meanings of verbs that describe situations that may or must include instruments not only illuminates the micro-geography of that portion of meaning space, it may shed light on the boundaries of verbal meanings and bear on current hypotheses regarding those boundaries. Second, Instrument roles differ from most other participant roles in that they come in two categories. They are sometimes semantically required by the meaning of the verb (e.g. cut); and they are sometimes not semantically required, but merely permitted (e.g. eat). Koenig et al. (2003) argue, expanding on Dowty (1982), that this leads to a difference in the lexical status of the Instrument role. They are part of the meaning of the first, but not the second category of verbs. The question that arises is whether this difference in lexical status affects the geography of the meanings of the two categories of verbs. In other words, are there ways in which the meanings of verbs that require instruments are systematically different from the meanings of verbs that merely allow instruments? Finally, the cluster of semantic properties that define the Instrument participant role is less clear than that of other roles. There is widespread agreement on what cluster of properties define various Agent and Patient roles. But such is not the case for Instruments. A comprehensive survey of verbs whose denotations may or must include instruments might, therefore, clarify the nature of the Instrument role. More specifically, our survey of verbs whose denotations may or must include an instrument is intended to answer four questions.

178 What with? on a patient/theme and changing its state or location. Answering this question will help determine whether or not verb meanings that semantically require instruments are structurally more complex than other verb meanings. Question 2. What part of the structural meaning of verbs that allow or require instruments is fleshed out by individual verbs?

Question 3.

Are instruments always causes?

This question is concerned with whether instruments are always causes of a change of location/state in the patient, as numerous previous authors have claimed (Fillmore 1968; Jackendoff 1990; Croft 1991; Talmy 2000). We will show that the causal efficacy of the eventuality in which the instrument and patient participate [the eventuality s2 in formula (1a)] is not always the same across verbs. Variations in the instrument’s causal role,2 are therefore another way in which individual verb meanings specify the common structural part of the meaning of verbs. Question 4. Is the micro-geography of the meaning space of verbs that require instruments qualitatively different from that of verbs that allow instruments? The second and third questions examine the micro-geography of verbs whose meanings describe situations that allow or require the

2 As we discuss in detail in section 3, talking of the instrument’s causal role is loose talk on our part whose sole purpose is to facilitate comparison with previous approaches. Whenever we mention the instrument’s causal role, readers should keep in mind that we are actually referring to the causal efficacy of s2.

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This question is concerned with the portion of the structure of meaning that is delineated by individual verb meanings. Informally put, what aspects of the formula in (1a) do individual verbs (or verb classes) provide more information about? We are, in particular, interested in whether the meanings of individual verbs specify more the action an agent performs on an instrument or the results of that action. We will demonstrate that verb meanings are skewed in their informational load. Verbs in English that require or allow an instrument lexically encode quite detailed information about the instrument’s action and the effect the instrument has on the patient, s2 and s3 in formula (1a), but do not, typically, include much information about the action the agent performs on the instrument itself, that is s1 in formula (1a).

Jean-Pierre Koenig et al. 179

presence of an instrument. The fourth question examines whether that micro-geography varies between verbs whose denotations must or may include instruments. In particular, we are interested in whether there are differences in the kind of role the instrument plays in the described situation between verbs whose denotations require or allow an instrument. In other words, this question deals with whether the kinds of formulae in (1) would differ across the two classes of verbs and whether verbs whose denotations require an instrument are more similar to each other (occupy a smaller portion of semantic space) than verbs whose denotations only allow an instrument.

To elucidate the semantic space of verbs that describe situations that may or must include instruments, we conducted two surveys of over 5000 English verbs. The first survey, reported in Koenig et al. (2003), is quantitative and serves as a preliminary to the second, qualitative, survey on which this paper focuses. The aim of the first survey was to select verbs that describe situations which must or can include an instrument. It employed trained linguists as raters. These raters answered, for each verb they knew (approximately 4200 verbs), the questions in (2). (2)

a. Does one of the verb’s senses describe situations in which one participant must or can use another participant to perform an action (e.g. does Marc cut the chicken require or allow Marc to have used something)? b. Does one of the verb’s senses describe situations in which one participant must or can perform the action described by the verb with something (e.g. does Marc cut the chicken require or allow Marc to cut it with something)?

To examine the micro-geography of verb meanings describing situations that require or allow the presence of an instrument, we must first decide which verbs have a denotation that requires or allows the presence of an instrument. To avoid arbitrary selection of verbs (or, worse, unconscious cherry picking), an independent selection criterion is needed. Syntactic tests can help us here. Dowty (1989) calls semantic roles that are linguistically relevant L-thematic roles if the (second-order) properties that define those roles are criterial for the application of morphosyntactic constraints. Much work on the syntactic realization of

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1 SELECTING VERBS WHOSE DENOTATIONS MUST OR MAY CONTAIN AN INSTRUMENT

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semantic arguments shows that it has a strong semantic basis (Pinker 1989; Jackendoff 1990; Van Valin 1993; Goldberg 1995; Levin & Rappaport Hovav 1995; Wechsler 1995; Davis & Koenig 2000; Koenig & Davis 2001, among others). If this is correct, we can use the ability of a verb to co-occur with certain phrases traditionally thought to target instruments as proxies for a semantically based selection of verbs. Note that the set of verbs passing these syntactic tests is not guaranteed to form a natural semantic class. Even if the morphosyntactic constructions have a strong semantic basis, the induced verb class might simply be the union of natural semantic classes or form a radial category, as, for example, Dowty (1991) proposed for the proto-Agent and proto-Patient roles. Unfortunately, we know of no better way of selecting verbs. These tests are certainly better than arbitrarily selecting verbs whose denotations include an entity playing a particular role. It avoids any circularity and the issue of the semantic coherence of the selected verbs can be explicitly addressed once analysis is completed. Another advantage of using morphosyntactic criteria to select verbs is that we can explicitly discuss the status of the L-thematic role of Instrument, for which there is much less consensus than for the Agent and Patient L-thematic roles. The logic of this first, quantitative, survey reported in detail in Koenig et al. (2003) was as follows. In the context of Agent and Patient (proto)-roles, linking rules to subject and object positions of active verbs are often used as the primary set of constraints to define these roles. The corresponding constraint in the case of instruments in English would be the rule that associates instruments with the object of the preposition with. Another constraint relevant to the selection of our verbs associates instruments with the object of the active form of the verb use. For the most part, these two constraints select the same argument position of the same set of verbs. As Lakoff (1968) argues, in most cases, a sentence of the form X V-ed Y with Z can be paraphrased as X used Y to V. In short, the object of with and the direct object of use target very similar, if not identical, L-thematic roles and either morphosyntactic constraint is a likely candidate for the selection of the relevant class of verbs. We surveyed the English verbal lexicon using both constraints. If raters answered for a particular verb Yes, it must to both questions in (2), we classified the verb as requiring an Instrument role (hereafter a [+I] verb). If they answered for a particular verb Yes, it can to both questions, we classified the verb as allowing, but not requiring an Instrument role (hereafter a [6I] verb). Selecting verbs that pass both tests provides us with an operational way of eliminating (possibly) non-instrumental, so-called comitative, uses of the

Jean-Pierre Koenig et al. 181

preposition with illustrated in (3) and (possibly) non-instrumental usages of use, illustrated in (4).3 (3)

a. b. c. d.

Marc shopped with his wife. Marc crossed the desert with his wife. # Marc used his wife to shop. # Marc used his wife to cross the desert.

(4)

a. Alice uses her house to conduct her official business. b. #Alice conducts her official business with her house.

3 See Schlesinger (1979) for a thorough discussion of the relationship between instrumental and comitative uses of with. We do not believe, though, that Schlesinger’s data show that the two uses do not form discrete categories. The graded nature of his participant’s answers to whether a particular use of with meant together or by means of merely shows that uses of with in particular sentences may be analysed as instances of the meanings together or by means of to varying degrees. It shows that (putatively) ambiguous with phrases can be more or less biased towards one meaning or another in particular contexts. It does not show that there is no distinction in meaning. 4 Most of these verbs denote various containment relations, such as sheathe, garage, paddock, soak and so forth. The container or enclosed region of space can be mentioned as the direct object of use, albeit awkwardly, but seems to resist mention as the object of with according to our raters.

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A potential drawback of using the conjunction of both tests to select the class of verbs whose Instrument role we want to investigate is that it may lead to a ‘non-natural’ or arbitrary selection of verbs. Several facts strongly mitigate this worry. First, note that many verbs are excluded by applying both tests rather than the use test alone (less than 50 verbs were excluded as a result of our decision to apply the tests conjunctively).4 Second, since the application of two tests narrows down the set of verbs, if anything, it only increases the semantic coherence or ‘naturalness’ of the semantic properties common to the verbs. Third, there are independent reasons for distinguishing comitative uses of with from instrumental uses. For example, only comitative uses of X V-ed . . . with Z can consistently be paraphrased as X and Z V-ed . . .. Excluding comitative uses of with is, thus, independently motivated. We do not think that our choice of the conjunction of two tests to select the relevant verbs impugns the semantic coherence of the resulting list of verbs. Rather, it stresses that the notion of Instrument role targeted by our first survey is indeed an L-thematic role. That role corresponds to the semantic properties shared by the fillers of the complements of a set of verbs that were selected on the basis of lexical or morphosyntactic constraints. It does not necessarily correspond to other, plausible ways, of grouping participants in situations which others might name instruments. We will return to this issue in section 3. Prior to rating, a few clear cases were discussed with our two raters. For example, the verb behead was discussed and raters agreed that,

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excluding fictional uses, if ‘somebody beheads somebody’ is true, ‘she beheads him with something’ and ‘she uses something to behead him’ are also true. In contrast, the verb eat does not license the same entailment. If ‘somebody ate something’ is true, ‘somebody ate something with something’ or ‘somebody used something to eat’ are not necessarily true. But verbs such as eat license a weaker entailment, namely if ‘somebody ate something’ is true, ‘somebody may have eaten something with something’ and ‘somebody may have used something to eat’ are true. We also alerted raters to a few facts concerning the syntactic expression of an Instrument role to make sure that the bases of their answers were semantic (entailment or other semantic relations) and not syntactic. First, we pointed out that a verb can receive a must answer to the with test, even if that verb does not usually occur with a with-PP (in fact, a corpus survey of a sample of such verbs discussed in Koenig et al. (2003) suggests that they rarely do, see also Burgess et al. 1998). Second, we alerted raters to the fact that verbs that incorporate either a theme or an instrument, for example butter, pass the use or with test only under limited conditions, as Jackendoff (1990) points out. Third, raters were given guidelines as to what constituted a word sense. In particular, in answering the two questions in (2), they needed to attend to the fact that some valence alternations (e.g. the transitive/ inchoative alternation of verbs such as break) affect meaning, while others do not (e.g. the passive alternation, pace, Pinker 1989). Specifically, if a verb describes a situation that does not require an instrument (as per the entailment tests) in one valence frame, but does in another, they had to ascertain whether the two valences exemplified the same verb sense. Although it was impractical to provide extensive training in distinguishing between word senses, particularly given extant disagreement on the issue in lexical semantics, raters were given enough training for our purposes. Overall, raters received extensive training in judging entailment relations between sentences that are syntactically related (see below for complications). But the training they received did not teach them the notion of instrument we wanted to investigate. They knew we were interested in determining which English verbs have a sense that requires or allows an instrument and they knew that what we meant by that is that the relevant verbs enter into the entailment patterns we just discussed. But they were not told what an instrument is, nor did we have expectations about how they would classify each verb they knew. After rating all verbs they knew, raters met to resolve differences in assessments due to either a failure to imagine a possible applicable situation or differences in how criteria were applied. It became clear

Jean-Pierre Koenig et al. 183

(5)

a. Ants cut the leaves I had left on the porch. b. The chef cut the chicken with a boning knife.

In this case, our sense is that the second alternative is correct (namely, that cutting by humans and cutting by animals are sufficiently different 5 We use the term lemma in its psycholinguistic sense of a lexical unit that includes semantic and syntactic information (in particular, valence information), but not word form information.

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from the raters’ reconciliation that they decided that objects would count as instrumental entities only if something other than body parts could play the same role. Thus, eat did not count as an obligatory instrument verb. Although one must use a body part to eat (the mouth), one cannot use anything but a body part in that function. In contrast, poke does count as an obligatory instrument verb. Although one can use a finger to poke, one can also use a stick. Similarly, scratch was counted as an obligatory instrument verb, because, although a car may be scratched using one’s fingernails, scratching is not exclusive to body parts. Our rationale in deciding that body parts can be considered instruments is that many actions that most of the time involve a non-body-part instrument can be performed with body parts. Somebody can cut butter with an elongated fingernail or, less rarely, brush her teeth with a finger. The fact that the kind of action performed does not seem to be different whether one used a knife or one’s fingernail or a toothbrush or one’s finger and the fact that body parts can very naturally be the complements of use and with in these cases support our body-part criterion. The results of this quantitative survey revealed that about 12% of verb stems were associated with at least one lemma that denoted a situation type that required an instrument participant.5 Additionally, 35% of verb stems were associated with at least one lemma that denoted a situation type that allowed an instrument participant. These percentages should be viewed with some caution, as they assume that raters correctly distinguished among verb senses and that the issue of verb sense can be resolved unanimously. For example, both our raters judged the verb cut to be an obligatory instrument verb. But as one reviewer pointed out, ants can cut leaves and they can presumably only use body parts to do so. To account for such uses of cut, we must (i) relax the raters’ claim that body parts only count as instruments when something other than a body part could have been used by the agent as instrument (since, presumably, ants cannot use anything but body parts to cut leaves), (ii) assume that the use of cut in (5a) exemplified a different word sense than the use in (5b) or (iii) simply assume raters were wrong in their classification of cut as a [+I] verb.

184 What with?

(6) a. The policeman shot the fugitive (with his gun). b. The policeman sipped his iced tea (with a straw). The presence of an entity serving as instrument in the described event is necessary irrespective of the presence of the with-PP in sentence (6a). In contrast, the presence of an instrument is dependent on there being a PP in sentence (6b). Thus, whereas the use of shot illustrated in sentence (6a) requires the presence of something that the policeman used to shoot the fugitive, the use of sip illustrated in sentence (6b) does not entail that something was used by the policeman to sip the tea. Nonetheless, the referent of the object of with plays the same participant role in both sentences (see section 3.1 for qualifications). In other words, the verbs shoot and sip both describe events which include the same participant roles, when they include a with instrument PP. But only shoot lexically requires the presence of an instrument. The contrast between obligatory instruments and non-obligatory instruments suggests that we need to (partly) dissociate the semantic type of a participant role from its obligatoriness and that we cannot define arguments as members of a predefined list of participant roles. Finally, if we assume with Dowty (1982) and Koenig et al. (2003) that obligatoriness is a necessary condition for inclusion in the meaning of verbs, this means that the Instrument role may be part of the meaning of verbs whose denotations require the presence of an instrument. In

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to suggest that we are dealing with a different sense). Unfortunately, we know of no reliable argument to distinguish between these possibilities. Worse, we do not think any such arguments are likely to be forthcoming, given how notoriously difficult it is to decide on how many senses a word has (see Cruse 2000 for some of the complexities involved). That said, we do not think that the percentages mentioned above would change in a way that would substantially affect the issues discussed in this paper. Errors would affect only relative membership in the [+I] or [6I] categories. Since every verb that was classified as [+I] or [6I] was then independently classified by our qualitative survey, nothing substantial depends on the status of particular verbs. The results of Koenig et al. show that the obligatory Instrument Lthematic role is a participant role category that is as widespread as many better-studied participant categories (certainly more widespread than Recipients, for instance, which are included in the denotation of about 5% of English verbs, A. Goldberg, personal communication). They also stress, contra a widely held view, that participant roles are not uniformly semantically obligatory or optional. Consider the following sentences:

Jean-Pierre Koenig et al. 185

fact, Koenig et al. provide psycholinguistic evidence that it is part of the meaning of those verbs. 2 SUBCATEGORIES OF INSTRUMENTS

A subsituation s1 in which an agent (with some intentionality) participates and an instrument may participate. A subsituation s2 in which the instrument, and possibly the patient, but not the agent participates. A subsituation s3 in which the patient, and possibly the instrument, but not the agent, participates. Subsituation s1 precedes s2. Subsituation s2 precedes s3.








6

Although our analysis of the meaning of verbs whose denotations may or must include an instrument is couched in terms of subsituations, it can be easily recast within theories that do not recognize the existence of situations as individuals, but only recognize time intervals.

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To answer the four questions that are the focus of this paper, we conducted a second, qualitative, survey of the English verbal lexicon. The results of this survey, the main empirical contribution of our paper, are discussed in this section. The relevance of these results to the four issues we raised in section 1 is discussed in section 3. For this more indepth survey of about 500 verbs that require an Instrument role and about 1400 that allow an Instrument role, we could not use raters with only cursory semantic training who were blind to the goals of the survey. We therefore used a different method. The first author went through all verbs that were categorized as either requiring or allowing an instrument participant by raters in our quantitative survey and grouped them into classes based on their semantic similarities. More precisely, the survey classified one lemma that may or must include an Instrument L-thematic role, as per the first survey. When we talk of verb V in this and the next sections, we will always be referring to one lemma of verb V. This classification was then cross-checked by the coauthors. The criterion used for semantic similarity was the possibility of describing the meaning of the relevant lemma of the verb in terms of subsituations that are causally or temporally related (subsituations are defined as parts of larger situations, see Krifka 1998).6 Previous analyses of the notion of instruments (see Fillmore 1968; Schlesinger 1988; Jackendoff 1990; Croft 1991; Talmy 2000, in particular) explicitly or implicitly assume that situation types that include an Instrument role can be subdivided into at least three subsituations.

186 What with?

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These authors also assumed that subsituation s1 causes subsituation s2 and that subsituation s2 causes s3. For example, situations of cutting would be analysed into three subsituations, the agent’s manipulation or operation of a cutting instrument, the instrument’s contact with the patient and the cut the patient undergoes. Our survey followed previous research on instruments in assuming that a significant portion of the properties that define Instrument L-thematic roles can be determined by analysing the subsituations that make up a verb’s denotation. But we do not presume that the relation between s1 and s2 and s2 and s3 is strictly causal. As we will show, several other relations may hold between s1 and s2 and s2 and s3. For example, the relation between s2 and s3 may be one of helping (as, when binoculars help one see better a bird in the sky). When we discuss the notion of causality we assume and the range of other possible relations between s1 and s2 and s2 and s3 in section 2.1. We also do not presume that all verbs whose denotation requires or allows an instrument must be subdivided into three subsituations. For verbs like hit, for example, only two subsituations may be involved. We will use the terms s1, s2 and s3 to refer to the afore mentioned subsituations. Verbs in each subclass we describe share this temporal subsituational structure. When a verb’s denotation can only be subdivided into two subsituations, we label them, by convention, s1 and s3. Subclasses were determined on the basis of the categories of the subsituations involved. Verbs in each subclass denote classes of situations of which the relevant formula is true. Many predicate labels and predicative structures are self-explanatory. For example, we use cause and CHANGE-OF-STATE in their usual meaning. New predicates will be discussed when they are introduced. We use a superscript + on the particular relation R relating the subsituations s1 and s2 or s2 and s3 (e.g. cause+) to indicate that there is a temporal gap (and, consequently, intermediary events) between the subsituations of which the two terms that are the arguments of R+ are true. We use A in the metalanguage formulae to denote the Agent in s1, I for the Instrument in s1, s2 and s3 and P for the Patient in s2 and s3. Since each formula represents the common part of the meaning of verbs in a semantic class, individual verbs’ meanings differ in many other respects. Predicates in our formulae, thus, often denote more general relations than the relations appropriate for individual members of the class. For example, we represent the situational predicate that characterizes s1 as ACT to denote a dyadic, dynamic predicate of which A is the Agent. Individual verbs (and in fact, individual senses for each verb) typically vary as to the exact nature of the relation involved. We use small caps rather than

Jean-Pierre Koenig et al. 187

2.1 Obligatory instrument classes We first considered the semantic subclasses into which verbs whose denotations require instrument participants can be classified. The vast majority of obligatory instrument verbs fall into a small number (15) of classes.7 Cut. Verbs in this class denote situations in which an Agent A causes contact between an entity I and an entity P, causes possible motion of I while in contact with P, and, as a result, incises or severs a portion of P. This category includes many verbs, such as, amputate, bone, cut, dissect, guillotine, hack, incise, knife, core, castrate, gore, cleave, sever and eviscerate. The formula for this class of verbs is given in (7). The predicate INCISED is a generic predicate that covers all incisions and cuts that an object can undergo, while the predicate CONTACT stands for any kind of contact relation between two objects, with or without force imparted from one object onto the other. Members of this class specify further the nature of the contact relation, the nature of the instrument and the kind of incision involved. (7)

cause(s1, s2) ^ ACT(s1, A, I) ^ CONTACT(s2, I, P) ^ cause(s2, s3) ^ INCISED(s3, P)

This class is large enough that one can easily recognize subclasses, according to the nature of the severing and the part of the entity that has been severed. In particular, one can distinguish at least the following subclasses. 7

It should be understood that when we cite members of an instrument class, we mean that (at least) one sense of these verbs (not necessarily, the most salient one) belongs to that class and that different senses of a verb may belong to different classes.

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lower case letters to indicate that a predicate name is a cover term for a class of relations specified by individual verbs. More generally, individual members of a semantic subclass may differ from other members of the same class by lexically specifying additional information about either the relations involved or the properties of the instrument or patient. For example, verbs in the Drug class such as drug, gas or immunize vary from each other not only in the nature of the change of state the instrument induces in the patient but also in the nature of the instrument itself. As we will see, some verbs may describe situations that may include more than one instrument, one instrument that is required and one instrument that is optional. Such verbs, then, belong to multiple semantic classes. Finally, for mnemonic purposes, we name each class by a representative member.

188 What with?










Whip. Verbs in this category describe situations in which an entity, the instrument, is in contact with another one, the patient. There are many verbs in this category, including beat, bat, club, whip or whack. Many of these verbs require the patient to be animate, so that contact occurs with one of the patient’s body parts. (This can then lead to the so-called possessor ascension alternation.) There are three main subclasses of this class: Hit: This subclass describes situations characterized by formula (8). It is unclear whether a change of state in the patient is assumed or mere impingement on the patient involved (see Davis 2001 for details); hence, the absence of a second causal predication in the formula in (8). Members of this class lexically specify the nature of the contact between the instrument and patient. Comb: For these verbs, the described situations include a change of state of the patient with which the instrument is in contact, as shown in (9). Aside from comb, this subclass includes verbs such as groom (a horse).8 Members of this class additionally specify the nature of the change of state the patient undergoes.9







8

How much of a change of state necessarily occurs for a situation to be felicitously described by the verb comb is a difficult issue which we do not discuss any further. 9 The similarities between formulae (7) and (9) raise the possibility of analysing the Cut class as a subtype of the Whip class on par with the Comb class. Because the action of the instrument (admittedly not represented in our formula!) typically involves more than contact in the case of the Cut class, we refrained from folding that class under the Whip class, despite their similarities.

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Incise: For this subclass, the severed portion of the entity is relatively superficial (it does not go through the entity), as the name of the class makes clear. Other verbs in this subclass are carve (a piece of wood), notch, plow, scratch or etch. Pierce: For this subclass, the continuity of the patient’s surface is broken and the severed portion, which is sometimes quite small, is the part of an entity that disappears as a result of puncturing the entity (typically through and through). Other verbs in this subclass are puncture, harpoon, knife, prick or lance. Sever: For this subclass, a significant portion of the entity— something that can be called a part—is cut away or disconnected. The definition of significant is of course a matter of world knowledge, but the following verbs give a good idea of what the term covers: amputate, bone, core, eviscerate, castrate, gore, hack, prune or mow. Shred: Verbs in this subclass denote situations in which an entity is put into several, typically many pieces. Aside from shred, it includes grind, dice, cube, scallop and mince.




Jean-Pierre Koenig et al. 189


Poke: For verbs such as poke, dent or prod, the patient must be compressed [see (10)]. The particular kind of contact involved between I and P must be more forceful here (remember that CONTACT is a cover term for different kinds of contact relations that individual verbs may entail between I and P). It resembles that of pierce, except that the patient’s surface is not broken. Members of this class additionally specify the exact nature of the compression a part of the Patient undergoes. (8) cause(s1, s3) ^

ACT(s1,

A, I) ^

CONTACT(s3,

I, P)10

CONTACT(s2,

I, P) ^ cause(s2, s3)

(10) cause(s1, s2) ^ ACT(s1, A, I) ^ ^ COMPRESSED(s3, P)

CONTACT(s2,

I, P) ^ cause(s2, s3)

Drug. Verbs in this class denote situations in which an agent inserts an entity I into another entity P, whose presence causes or is intended to cause the subsequent non-locational or non-configurational change of state of P. Aside from drug and other ‘medical’ verbs such as gas, anaesthesize, immunize, vaccinate or dope, this class includes a certain number of cooking verbs, such as flavor and season. The formula common to this class of verbs is given in (11). It says that there is a dynamic subsituation that involves the agent and the instrument which causes a subsituation in which the instrument (e.g. the drug) is located within the patient and that this latter subsituation causes a change of state in the patient. Individual verbs within this class differ from each other by further lexical semantic constraints they impose on the category or properties of the instrument as well as on the particular changes of state undergone by the patient. As we will discuss in detail in section 2.2, an additional instrument (e.g. a syringe) can optionally be used to administer the substance inducing the change of state for situations described by this class of verbs. The Instrument role, in this respect, differs from the Agent and Patient roles. While there can be more than one Instrument phrase for situations described by sentences whose verbs are members of the Drug class, there can only be one Agent or Patient phrase for these situations. (11) cause(s1, s2) ^ ACT(s1, A, I) ^ in (s2, I, P) ^ cause(s2, s3) ^ CHANGE-OF-STATE(s3, P) 10 As Paul Portner points out, it is somewhat odd to label the relation between the agent and instrument of hit as ACT when the instrument is the agent’s hands. Since ACT is a cover term for more specific relations, we choose to extend its usual interpretation rather than use a separate cover term to cover instances in which a body part is used. Nothing substantial hinges on this choice.

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(9) cause(s1, s2) ^ ACT(s1, A, I) ^ ^ CHANGE-OF-STATE(s3, P)

190 What with?

(12) cause(s1, s2) ^ ACT(s1, A, I) ^ in(s2, I, P) ^ cause(s2, s3) ^ CHANGE-OF-CONFIGURATION(s3, P) (13) Jim loaded the truck with boxes with a forklift Putt. Verbs in this category describe situations in which an agent causes an entity P to move via forceful contact with another moving entity I [see the formula in (14)]. Other verbs in this category are bunt, rake (the lawn), shoot (billiards), sweep (a chimney), tee off or boot.11 Often, the motion of P is part of a more encompassing social activity so that the decomposition we give is but one part of the meaning expressed by the verb, as the verb golf (and rake to some extent) illustrates. Members of this class specify further the nature of the contact between the instrument and patient and the force that is imparted to the latter. (14) cause(s1, s2) ^ ACT(s1, A, I) ^ forceful-contact(s2, I, P) ^ cause(s2, s3) ^ MOVE(s3, P) Fasten. Verbs in this subclass describe situations in which an agent causes an entity P to be attached to another entity through a connection between the instrument I, the patient P and a third entity T [see the formula in (15)]. Of course, the constant ATTACHED would have to be analysed further, possibly in terms of the notion of joint motion 11 It might be possible for some (including one reviewer) to use the verb rake (e.g. the lawn) without anything being moved or rearranged. We find such uses marginal, at best.

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Fill. Verbs in this subcategory differ subtly from the Drug class in that, in this case, the change of state is that of the spatial configuration of the patient P (becoming full, etc.). Several verbs from the so-called load valence alternation belong to this class, for example, load and fill. For many verbs, including load, but not fill, the conceptual decomposition with which we semantically characterize the class is only one construal of the described event, the one typically encoded by the with-PP of the load alternation (see Anderson (1971) and Pinker (1989), among others, for discussion of the semantic differences between the two valence alternates of verbs in this class). The decompositional formula is given in (12). Typically, members of this class specify further the particular change of configuration that the patient undergoes. Like members of the Drug class, verbs in the Fill class can also combine with a semantically optional instrument, as sentence (13) shows. When they do, these verbs also belong to the Scoop class whose members describe situations in which an instrument which serves as a container of sorts is used to enable the motion of an entity.

Jean-Pierre Koenig et al. 191

(motion of one entity leads to motion of the other). But this finergrained analysis is not relevant to our present inquiry. There are two subclasses of this category of Instrument roles, depending on whether P and T are two distinct objects or two distinct subparts of an object. Members of this class further specify how the instrument and the patient are connected (consider, e.g., the difference between bracket, bolt and pin). (15) cause(s1, s2) ^ ACT(s1, A, I) ^ (s2, s3) ^ ATTACHED(s3, P, T)

CONNECTED(s2,

I, P, T) ^ cause




(16) cause(s1, s2) ^ ACT(s1, A, I) ^ CONNECTED(s2, I, x, y) ^ partof(x, P) ^ part-of(y, P) ^ x 6¼ y ^ cause(s2, s3) ^ ATTACHED(s3, x, y) Paint. Verbs in this category describe situations in which an entity (e.g., paint) laying on another entity P causes P to change state [see (17)]. Other verbs in this class are dress, oil, perfume, sugar, varnish and ice. The main difference between this category and the Drug category is the nature of s2, the location of the instrument on the patient, rather than in it. Some verbs in this category also seem to belong to the Drug category, such as stain (v. dye) (and some uses of gas). Properties of the patient seem to partially determine which of these verbs best describe the situation being discussed. Finally, members of the class specify which change of state is undergone by the patient as well as the properties of the instrument. (17) cause(s1, s2) ^ ACT(s1, A, I) ^ on(s2, I, P) ^ cause(s2, s3) ^ CHANGE-OF-STATE(s3, P) Ski. This class includes verbs which describe situations in which an agent uses an entity to help his or her motion. Other verbs in this class include canoe, bicycle, skate, drive or toboggan. Most verbs in this class only marginally pass the use and with tests because they are eponymous with the most typical instrument and because of the lack of range in 12

Deciding on membership in the two subclasses may depend on how one construes the patient for some uses of zip. Consider actions of zipping a lining into a raincoat where it may not be entirely clear whether the lining is a part of the raincoat.

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Buckle. Other verbs in this subclass are bolt, bracket, chain, handcuff, pin, rivet, screw, solder, velcro and weld. Button. Verbs in this subclass describe situations in which the ‘attachment’ is between two subparts of P [see the formula in (16)]. Verbs in this subclass include button, harness, snap and zip.12




192 What with?

(18) cause(s1, s2) ^ ACT(s1, A, I) ^ cause+(s2, s3) ^ MOVEmanner(s3, A)

PRED2(s2,

I, A) ^ part-

Cover. Verbs in this category describe situations in which the instrument is on or over another entity in such a way that it typically obscures the view of the object for observers in sight of the object. Verbs in this subcategory include carpet, hood, shroud, robe, mask, veil, among others. Verbs differ as to what part or portion of the patient is covered by the instrument, as the contrast between cover and blindfold illustrates. It might be possible to analyse the difference in terms of the notion of active-zone as defined in Langacker (1984). Each verb selects the relevant portion of the participant in the described action. In the same way that only teeth are relevant to the agent of bite, only the eyes of the patient are relevant to blindfold. We decided not to include obfuscate from view as a component of the metalanguage paraphrase of this subcategory, as the formula in (19) indicates [another, less plausible, decomposition for this class of verbs would be (20)]. That is, the effect achieved by the ultimate cause is not the one shown in (21). Rather, to obfuscate from view is a background condition that determines what counts as being on or over the object whose visibility is at issue, or between the center of perspective and that object. Certain verbs that describe an action by the agent that result in the instrument being on or near the patient also explicitly add the idea of an intentional obfuscation from view as part of their meaning. The word camouflage is a typical example of this further requirement. (AT is in small caps in (21) because the exact kind of location relation may vary in this case, and not necessarily be one of covering.) (19) cause(s1, s3) ^

ACT(s1,

A, I) ^ cover(s3, I, P)

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possible instruments. The indeterminate semantic part of this class is the nature of the instrument I itself (and its consequent exact role in partly causing the motion). Note that the causal role of the instrument is weaker here. It is only one of the causes of the motion: gravity, wind or some other force is needed. Our use of the predicate part-cause is meant to represent this weaker causal role of the instrument. The agent is also the patient for this class of verbs. The formula in (18) thus mentions the variable A twice. These verbs further specify how the agent moves (represented in the formula in (18) by the predicate MOVEmanner which denotes the class of manner of motion events). As mentioned above, + indicates that there is a temporal gap (and, consequently, intermediary causal events) between the subsituations of which the two terms that are the arguments of part-cause+ are true.

Jean-Pierre Koenig et al. 193

(20) cause(s1, s2) ^ covered(s3, P)

ACT(s1,

A, I) ^ on(s2, I, P) ^ cause(s2, s3) ^

(21) cause(s1, s2) ^ ACT(s1, A, I) ^ obscure(s3, I, P)

AT(s2,

I, P) ^ cause(s2, s3) ^

(22) Bob garnished his souffle´ with dill. (23) cause(s1, s2) ^ ACT(s1, A, I) ^ MORE-ORNATE(s3, P)

AT(s2,

I, P) ^ cause(s2, s3) ^

Scoop. Aside from scoop, verbs in this class include spoon, pump, milk, sponge, ladle, shovel, and siphon. They describe situations in which the ultimate cause uses an instrument to move another entity [see (24)]. (24) cause(s1, s2) ^ ACT(s1, A, I) ^ in(s2, P, I) ^ enable(s2, s3) ^ go-to(s3, P, Z) We use the predicate go-to to denote changes of location. For all verbs, the instrument plays a role in initiating the move by coming to include the entity that moves P. But verbs also require this inclusion to further enable (in the sense of Talmy 1988, 2000; Jackendoff 1990) the motion of P to another location (by contrast to verbs like garage). Talmy analyses the relation of enablement (or enabling causation) as the removal of a restraint that allows a change of location or state. For example, in sentence (25), the plug’s loosening allows gravity to move the water. A relation of enablement, thus, requires three situations to hold, the application of force to a patient [gravity in (25)], the presence of a situation that hinders the application of that force, and, finally, the disappearance of that obstacle. When one ladles or syphons liquid, an agent (indirectly) applies force to the liquid to move it, the application of that force would be hindered if the liquid was not held in place by the ladle or channelled by the syphon, and the instrument’s inclusion of

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Garnish. This class, exemplified in sentence (22), is similar to the Cover class. Verbs in this class include applique´, embellish, embroider, festoon, garland, garnish, smock. These verbs describe situations in which an entity A causes I to be in a certain stative locational configuration relation that makes P be more ornate [see (23)]. In the formula in (23), we use the predicate AT as a cover term for a set of possible static locational relations, such as those expressed in English by around, at, near, and on, as the particular relation varies with members of the class. (Additional instruments can be involved for some verbs, for example, the tools or utensils used to embed or attach I in formula (23) for verbs such as embroider or festoon.)

194 What with? the liquid removes that obstacle. It is in that sense that, for verbs in the Scoop class, s2 enables s3 rather than strictly cause it.13 (25) The plug’s coming loose let the water flow from the tank.

(26) cause(s1, s2) ^ ACT(s1, A, I) ^ mark(s2, I, M, P) ^ cause(s2, s3) ^ REPRESENT(s3, M, T) Notify. Verbs in this class describe situations in which producing a linguistic expression causes (or intends to cause) a change of state in another entity. In the formula in (27), the predicate expression is meant to apply to all sequences of linguistic expressions, while the predicate produce is interpreted as applying to any verb of creation. (27) cause(s1, s3) ^ produce+(s1, A, I) ^ CHANGE-OF-STATE(s3, P) ^ expression(I) The linguistic expression serves as the instrument I and the entity undergoing the change of state is the patient P. The change of state can 13 For the verbs pump and, in some uses, milk, the instrument’s causal role is stronger and s2 may indeed cause s3. 14 The notion of representation involved is intended to be quite broad and to cover the meaningless marks one leaves when one doodles or scribbles aimlessly. But even in these limiting cases, we would claim that the marks are representational in that they are defined negatively as abnormally meaningless. To use Fillmore’s (1982) terminology, such uses of the verbs doodle or scribble are defined relative to a frame in which marks represent something.

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Doodle. Verbs in this class describe situations in which putting marks M on the patient P using the instrument I makes M symbolize or represent something T, however, imperfectly [see (26)]. In the formula in (26), the predicate mark stands for an event in which an object leaves some marks on an another object; the predicate REPRESENT is used for any kind of symbolic or non-symbolic relation between marks on an object and what they represent for an implicit viewer.14 One could describe this class at another grain size by saying that the contact of the instrument with the patient causes the symbolization, but that description would not represent what we consider to be an important semantic requirement, namely that the contact leaves marks on the patient. So, while a finer-grained analysis of the subsituational structure of the denotata of verbs in this class might also mention the contact between the instrument and some object, what is critical for our purposes is that the result of the contact, namely the marks, serve as the cause of the symbolization. Verbs in this category include doodle, draw, ink, inscribe, dot, pencil, sketch, scribble, transcribe, write, underline, underscore, typewrite, type, print, and sign. Verbs such as engrave, etch, or inscribe may belong to both the Doodle and the Incise classes.

Jean-Pierre Koenig et al. 195

(28) a. Marla notified Bill of his demotion with a nasty post-it on his door. b. John defamed the military with his incendiary comments. c. He expressed his frustration with his inappropriate remarks on the rise of alcohol consumption. d. We primed the participants with two semantic associates. e. He was preaching abstinence with his sermon on the careful son. Roast. Verbs in this class describe situations in which a source of heat changes the state of the patient from a raw to a cooked state or from a cold to a hot state [see (29), where the predicate name COOKED/HOT is shorthand for the disjunction of these alternatives)]. (29) cause(s1, s2) ^ ACT(s1, A, I) ^ hot(s2, I) ^ cause(s2, s3) ^ COOKED/HOT(s3, P) This category includes verbs such as roast, cremate, steam, grill, barbecue, sear, braise, distill,15 fricassee, parboil, scallop,16 and scorch. Because the 15 16

Distillation requires a subsequent controlled cooling of the heated substance. This is a different sense of scallop than that used in the Shred subclass of the Sever class.

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be a change of mental state, as in sentence (28a), where the change of state is Bill’s knowledge state. But in (28b), the military’s reputation is what is affected. Strictly speaking, the production of the linguistic expression does not cause P’s change of state in sentence (28a), but rather, P’s understanding of the expression. We therefore included a superscript + to indicate that there may be a temporal gap between the subsituation that consists of the production of the linguistic expression and the change of state the patient undergoes. Verbs in this category are not very numerous (see sentences (28a)-(28e) for further examples). They include defame, express, libel, notify, preach, prime, salute. The prepositions through, via, and by can sometimes introduce instruments for this class of verbs. Note that when the patient P is in a mental state or has a belief [ frustration in (28c) or abstinence in (28e)], the changes of state consists in the mental state or belief being ‘visible’, not necessarily in it being recognized or understood by an audience. When the patient P is an audience, on the other hand [Bill in (28a), the military in (28b), or the participants in (28d)], the resulting state is the audience’s new mental state. Finally, as Paul Portner pointed out to us, in the case of verbs such as notify, produce involves not only a change in the patient’s belief but also a particular way for this change to occur (the patient must change his/her belief as a consequence of his/her recognition of the agent’s intention, see Grice 1957; Searle 1969).

196 What with? instrument is sometimes also a container for food, the instrument is often also what Koenig et al. (2003) call a participant location and can be expressed as a locative PP, as sentence (30) illustrates. (30) Jack bakes his pizzas in a wood-burning oven. For several verbs in this class, there is also contact between the instrument and the patient, although the contact may be with a more diffuse version of a substance (e.g., steam). Some verbs in this class (like there were in the Drug and Fill classes) can additionally take an optional instrument, as exemplified in sentence (31) ( J. Bohnemeyer, personal communication).17 Phone and Manicure.





Phone. This subclass describes situations in which a certain effect is achieved through the use of a particular artifact, but where the exact role of the instrument in achieving the effect is not necessarily very clear to the naive metaphysicists that language users are, to borrow Bach’s (1986) term [see (32)]. The class includes verbs such as (tele)phone, telegraph, photograph, radio, brake, mimeograph, scan, call, filtrate, gauge, machine, manufacture, televise and tool. Manicure. This subclass is similar to the previous subclass, but for the fact that the Phone subclass identifies an actual class of instruments, whereas the Manicure subclass identifies a process. Here, either native speakers do not know anything about the instrument involved but for its existence or there are several possible classes of entities involved so that there is no common set of properties these instruments would have. Some verbs in this subclass are electrocute, counterfeit, refrigerate, (de)oxidize, pasteurize, copy, manicure, magnetize, time, mummify, plumb, electroplate, reinforce, forge, and hoist.

(32) cause+(s1, s3) ^

ACT(s1,

A, I) ^

PRED1(s3,

P)

Verbs in this class— particularly verbs in the Manicure subclass— seem to focus more on the nature of the effect and do not specify what role the instrument plays in achieving the ultimate effect. There is also a temporal gap between the initial action on the instrument and the change of state of the Patient, as indicated by + in the formula in (32). Because there is no common category of the s3 subsituation across 17 Two of the native speakers we polled do not think the yeast in sentence (31) passes the with or use tests. But four other we polled accept sentences such as He used yeast to bake the cake. We surmise that it is hard for some speakers to think of the inclusion of ingredients in the dough as playing a causal role in the event (see section 2.2).

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(31) Floyd baked the cake with yeast.

Jean-Pierre Koenig et al. 197

members of this semantic class, we use the variable over predicate names PRED1 to stand for any situation category that has the patient as its argument. This class is overall quite sizeable. There are about 60 verbs in the Phone and Manicure subclasses.

2.2 Optional instrument subclasses

Charm or break. This class includes many verbs, for example, attenuate, beautify, break, charm, compel, dehydrate, defeat, defend, demonstrate, donate, gamble, lighten, madden, mock, obliterate, oppress, revive, and many, many other verbs.18 Many of these verbs denote induced changes of psychological states. The objects of with or of use in this case are often the result nominals of acts performed by the ultimate effector of the causal chain [e.g., remarks in sentence (33a) or jokes in sentence (33c)]. In other cases, the object of with or use seems to be a salient object in the acts that ultimately result in the effect. The sword in sentence (33b) is a salient object in the acts which attempt to prevent Joe’s defeat. What exactly Julie did with the sword is not lexically specified and can be variously specified in different contexts. In both cases, the role of the instrument can be represented in the same way as it was in the case of the Phone and Manicure class [see (34)]. In contrast to instruments for most of the verbs in the Phone and Manicure class, situation types described by verbs in this class do not constrain the intrinsic properties of the objects/acts that can serve as instruments very much. Whereas the range of object types which can be used to phone somebody is quite limited, the range of objects one can use to defend somebody is quite large; a hardened baguette might do in some cases! (33) a. Julie charmed us with her witty remarks. b. Julie defended Joe with her sword. c. He maddened us with his sexist jokes. 18

We assume that even words such as defend involve a change of state, although the causal relation between s2 and s3 must be conceived as a Prevent type of causation rather than prototypical causation (see Talmy 1985 and Jackendoff 1990 for details on causation parameters).

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We now turn to the subclasses of verbs which denote situations which do not require, but merely allow the presence of instruments (our [6I] verbs). As will be shown, the nature of the subevents s2 and s3 are often non-specific and, importantly, much less clear than it is for subclasses of obligatory instrument verbs. Furthermore, the role of subsituation s2 in the overall situation varies more across optional instrument subclasses than it does across obligatory instrument subclasses.

198 What with? (34) cause+(s1, s3) ^

ACT(s1,

A, I) ^

PRED1(s3,

P)

Convert. Verbs in this class describe situations in which a machine, understood broadly, is used by a human to induce some change of state or perform some action [see (35)]. (35) cause+(s1, s3) ^

ACT(s1,

A, I) ^ machine(I) ^

PRED1(s3,

P)

The class includes calculate, condense, convert, decode, design, harvest, inspect, pilot, purify, record, test, and many other verbs.

What characterizes instruments in this class is that they are typically artifacts whose purpose is to effect the change of state or perform the action. But the exact causal role or causal force of the instrument is not exactly determined. Take sentence (36c). The radio transmitter plays a causal role in the plane’s motion, but speakers may not know the exact role it plays. It is also unclear that the radio transmitter is the figure of the proximate cause, as Talmy (2000) claims. (Talmy defines the proximate cause as the causal event of the last member of a sequence of causal relations, our s2.) Presumably, what causes the plane to move is the mechanical motion of some of the planes’ parts set in motion by the waves the transmitter sent. In what sense would the transmitter be part of the proximate causal event? Similar arguments can be presented for most verbs in this class. As speakers, we understand these sentences, provided that we know that the instrument is a machine that can be used in creating the desired effect; we are not required to understand how the machines achieve this effect. Finally, note that in some cases, the machine is only one of the causal factors involved, as in sentence (37) below. The instrument in such cases can be said to help create the effect (see section 3 for the definition of the concept of helping). (37) He harvested the field with his old tractor. Eat. Verbs in this class are numerous. Below are some examples that illustrate the diversity of this class of verbs. (38) a. b. c. d. e.

Jean doesn’t know how to eat with chopsticks. Jill drank her soda with a straw. Ryan watched the bird with his new binoculars. Alicia lectures with overheads rather than with handouts. Joan hunted the turkey with a bow and arrows.

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(36) a. He converted the temperature with the conversion program. b. She designed her home with CAD. c. She piloted a model plane with a radio transmitter.

Jean-Pierre Koenig et al. 199

f. He plays volleyball with gloves. g. Susan always practices the piano with a metronome. h. Max repaired the faulty switch with a screwdriver.

(39) help+(s1, s3) ^

PRED2(s1,

A, I) ^

PRED1(s3,

P)

Enter. This is a very small class; in fact, enter (and open in its ‘unlock’ sense), and one or two other verbs are the only examples we have uncovered. Key in sentence (41) is not the instrument of entering per se, but the instrument of an act which is the precondition of entering a room, that the door be open. Again, we will have more to say about the semantics of the predicate precondition in section 3. Because there are other subsituations between the agent’s act and the patient’s change of state, which are not constrained by the verb’s meaning, we again affix the superscript + on the predicate name precondition. (40) precondition+(s1, s3) ^ ACT(s1, A, I) ^ CHANGE-OF-STATE(s3, P) (41) Joe entered the room with a stolen key. Attach. Verbs in this class describe situations in which an agent causes two entities to be linked together. This class of optional instrument verbs is semantically identical to the obligatory instrument class Buckle, but for the fact that verbs in this class denote situations in which the presence of an external object to link the two entities is not required. Their common meaning can be described through the same formula, repeated below as (42) (T denotes an additional entity distinct from the agent, patient, and instrument). Verbs in this class include attach, couple, interlock, link, mount, and secure.

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They describe situations in which an agent uses an object to perform an action. For most of these verbs, the instrument helps the agent in performing the action, as shown in formula (39). Consider sentence (38a). The chopsticks do not really cause the food to move into the mouth. Similar arguments can be levied for most other verbs in this class and a fuller discussion of these verbs will be provided in section 3. The relation between the agent and the instrument or the effect on the patient vary tremendously among members of this class. Consequently, we use PRED2 to cover any dynamic relation between the agent and the instrument and PRED1 to cover any property or change in the patient. We also use the predicate help to indicate the ‘weak’ causal relation between the action of the agent on the instrument and the effect on the patient. We discuss in detail the semantics of this predicate in section 3.

200 What with? (42) cause(s1, s2) ^ act(s1, A, I) ^ CONNECTED(s2, I, P, T) ^ cause(s2, s3) ^ ATTACHED(s3, P, T) Trap. Verbs in this class describe situations in which an agent uses an instrument to prevent a patient from moving. But the agent does not have to use an instrument, as sentence (43) shows. Hence the inclusion of members of this semantic class in the class of optional instrument verbs. Verbs in this class are not numerous and include, in addition to restrict and trap, constrict, constrain, and contain.

(44) cause+(s1, s3) ^

ACT(s1,

A, I) ^ not(able(MOVE(s3, P)))

Administer. This class includes only a few members, the verbs administer and treat, as exemplified in sentences (46b) and (47). Verbs in this class describe situations in which an agent puts some medicine into somebody’s body and may or may not involve using an instrument to have the medicine penetrate the body [see (45)]. The contrast between sentences (46a) and (46b) demonstrates the optionality of the instrument. Because there are other subsituations between the agent’s act and the patient’s change of state, which are not constrained by the verb’s meaning, we again affix the superscript + on the predicate name cause. (45) cause+(s1, s3) ^

ACT(s1,

A, I) ^ in(s3, T, P) ^ medicine(T)

(46) a. The nurse administered the medicine orally. b. The nurse administered the medicine with a syringe. (47) The physician treated the sick patient with a course of antibiotics. Heat. This verb class describes situations in which the instrument, when present, plays the same role as that of situations described by verbs in the Roast class [compare the formulae in (48) and (29)]. But in contrast to verbs such as roast, some verbs, such as burn, defrost, freeze, heat and melt, do not require an instrument, as sentence (49) shows. The described situation still includes an event that causes s3, but there is no salient object which is manipulated by the agent to induce the effect in the situation described in sentence (49) and there is no entity that could be denoted as the object of with or use, which explains why our raters classified these verbs as [6I]. (48) cause(s1, s2) ^ ACT(s1, A, I) ^ hot/cold(s2, I) ^ cause(s2, s3) ^ COOKED/HOT/COLD(s3, P)

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(43) Pat restricted the intruder’s movement by threatening to break his legs.

Jean-Pierre Koenig et al. 201

(49) Pat heated her bathwater by letting the tub sit in the scorching Arizona sun for six hours.

(50) The US liberated Grenada with only 4000 men. (51) cause(s1, s2) ^ ACT(s1, A, I) ^ ACT(s2, I, P) ^ human(I) ^ cause(s2, s3) ^ CHANGE-OF-STATE(s3, P) Move. This class resembles the Putt class in describing caused-motion events, in which an agent acts on an instrument to cause a motion [compare the formulae in (14) and (52)]. Verbs in this class include deport, drop, elevate, gather, hurl, move, project, rotate, seat, and toss. (52) cause(s1, s2) ^ ACT(s1, I) ^ forceful-contact(s2, I, P) ^ cause(s2, s3) ^ MOVE(s3, P) Commute. This very small class (a couple of verbs at most) resembles the Ski class, except that even though most commutes involve some means of transportation, there is no semantic requirement that this be so. Runners might commute by running back and forth between their homes and offices. (53) cause(s1, s2) ^ ACT(s1, A, I) ^ PRED2(s2, I, A) ^ part-cause+(s2, s3) ^ MOVEmanner(s3, A) 19

The complement of with may be a machine. For example, with 1000 tanks or with one wellplaced bomb may be substituted for with only 4000 men in (50). But in such cases, the inanimate entity metonymically stands for the persons controlling the machine.

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Liberate. Verbs in this class denote situations in which humans are used as instruments [see the formula in (51) and sentence (50)]. The class is not that large and includes verbs such as invade, occupy, overpower, and support. Because the instrument is an animate entity, the relation between the agent and the instrument differs from that of other subclasses. The agent is ordering, persuading or simply controlling the actions of the instrument, and in many cases, the instrument could be substituted without much change in meaning as the subject of the verb. This class clearly refutes Fillmore’s (1968) claim that inanimacy is a necessary condition of instrumentality. The fact that most of the cited verbs belong to the field of military operations is not accidental. Instructions to soldiers are most likely to be followed so that, in some intuitive sense, the occurrence of s2, once the order has been given, is almost guaranteed. This ‘tight’ connection between agent and instrument makes the instrument resemble inanimate instruments which cannot escape their causal role.19

202 What with? Document. This class of verbs describes situations in which an agent composes some linguistic artefacts, but where the output can be either oral or written. It is only when the output is written that the use of an instrument becomes necessary and in this case, the formula representing the common meaning of members of the class is like that of the Doodle class (compare the formula in (54) to that in (26); M denotes the entity that serves as the mark). This class is small, and includes, aside from document, the words append, edit and outline. (54) cause(s1, s2) ^ ACT(s1, A, I) ^ mark(s2, I, M, P) ^ cause(s2, s3) ^ REPRESENT(s3, M, T)

As mentioned in section 1, our qualitative survey was meant to address four questions. Our discussion will address each question in turn. To help in this discussion, Tables 1 and 2 summarize the semantic properties of the subclasses of obligatory and optional instrument verbs, respectively. We included all aspects in which instrument subclasses may differ from each other: the categories of s1, s2, and s3, the kind of relation between s2 and s3 or s1 and s3, and the category of the Instrument. Some instrument subclasses do not readily decompose into three subsituations, so that the issue of the category of s2 is moot. In such cases, we left the relevant cell blank.

3.1 Question 1: What is the structural complexity of instrument verbs? In the introduction, we mentioned that situations that include an instrument may be more complex than other situations that include subsituations. To the extent that Instrument roles are part of the meaning of some 500 verbs, this complexity may exceed the bound on the structural complexity of possible verb meanings hypothesized in Rappaport Hovav & Levin (1998), that is it may violate the constraint that verb meanings include only one causal relation (or two subsituations).20 The first question we ask is whether, indeed, most verbs that require or allow instruments have meanings which involve three causally related subsituations. This question involves two different issues. The first is whether situations that include instruments can or 20

Strictly speaking, the issue only arises for verbs that are not eponymous with instrument names. For eponymous instrument verbs, Rappaport and Levin treat instruments as constants that do not lead to additional structural complexity.

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3 GENERAL DISCUSSION: WHAT IS AN INSTRUMENT?

Jean-Pierre Koenig et al. 203 Obligatory class s1 act act act act act act act act act act act act act act act produce+ act act

s3

contact

Causality

incised contact contact change-of-state contact compressed in change-of-state in change-of-configuration forceful-contact move connected attached on change-of-state pred2 movemanner cover at obscure at more-ornate in go-to mark represent change-of-state contact cooked/hot pred1

I

cause N/A cause cause cause cause cause cause cause part-cause+ N/A cause cause enable cause cause+ expression cause hot cause+

Table 1 Semantic category of s1, s2 and s3, the kind of causality involved and the semantic category of I for obligatory instrument classes

Optional class Charm/break Convert Eat Enter Attach Trap Administer Heat Liberate Movetr Commute Document

s1 act act pred2 act act act act act act act act act

s2

connected

contact act forceful-contact pred2 mark

s3 pred1 pred1 pred1 change-of-state attached not(able(move)) in cooked/hot/cold change-of-state move movemanner represent

Causality

I

+

cause cause+ help+ precondition+ cause cause+ cause+ cause cause cause part-cause+ cause

machine

medicine hot human

Table 2 Semantic category of s1, s2 and s3, the kind of causality involved and the semantic category of I for optional instrument classes

must be analysed as being composed of a sequence of three subsituations. The other concerns the nature of the relation between these subsituations (particularly, between s2 and s3). We answer the first question in this section and the second question in section 3.2.2.

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Cut Whip1 Whip2 Whip3 Drug Fill Putt Fasten Paint Ski Cover1 Cover2 Garnish Scoop Doodle Notify Roast Phone

s2

204 What with? The overwhelming majority of instrument subclasses we identified (as well as an even larger proportion of verbs requiring or allowing instruments) can indeed be analysed into the three subsituations we defined, our s1, s2 and s3. But to make the case that the meaning of verbs whose denotations require an instrument exceeds hypothesized bounds on event structure complexity, we must make the stronger claim that the meaning of these verbs must be analysed in terms of three causally related subsituations. Taking the verb cut as an example, our analysis summarized in formula (7) amounts to the following:

To the extent that entailments determine meaning, the entailments in (55) show that the three causally related subsituations are part of the meaning of the word cut. Is the presence of entailments such as those in (55) sufficient, then, to falsify the one-causal relation hypothesis put forth in Rappaport Hovav & Levin (1998)? Not necessarily. It is implicit in the hypothesis of Rappaport Hovav and Levin (or Carter), we believe, that the constraint applies to what one could call a ‘basic’ granularity level of semantic analysis. In other words, proponents of this hypothesis could object that the semantic analysis we propose, while correct, is more finegrained than the intended level of analysis for structural aspects of a word’s meaning. For example, the word look might be said to entail that the agent’s eyes focus on the object and that such focusing causes an image of that object to be on the agent’s retina. Even if these are true entailments for look, do we still want to say that the structural portion of the meaning of look involves two causally related subsituations? Most linguists would say No on the assumption that this level of granularity is not appropriate when assessing the structural complexity of a verb’s meaning. What we need, therefore, is independent evidence, in the form of grammatical or semantic constraints, that our analysis targets a semantically ‘basic’ level of granularity. Our analysis of situations that include instruments is not meant to suggest that the meaning of verbs whose denotations require an instrument be lexically decomposed. But the kind of evidence we need to answer the objection that our three subsituation analysis targets a non-‘basic’ level of granularity is similar to that used to argue for lexical decomposition. Unfortunately, traditional tests of lexical decomposition are of no great help here. The most reliable tests discussed in Dowty

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(55) Every situation that belongs to the class of cutting events entails that: (1) there is a situation s1 which is an act performed by an agent A on an instrument I; (2) there is a contact (with force) relation s2 between I and a patient P; (3) there is a (final) state of incision for P; (4) s1 caused s2, which in turn caused s3.

Jean-Pierre Koenig et al. 205

(1979) (internal scope of adverbs, re- and reversative un- prefixes) target the resultant state of so-called accomplishment stems. And, for some of our verbs, they do indeed show that there is final (reversible) state (our s3), as the possible internal reading of again in example (56) shows. (Recall that the internal reading of again in sentences such as (56) corresponds to interpretations in which what recurred is the attachment or altered physical state, not Bill’s or this particular KGB agent’s action; somebody else might have caused the original state.) (56) a. Bill fastened Marc’s seat belt again. b. A KGB agent poisoned Marc again.

21

As Roelant Ossewaarde pointed out to us, the two intermediary relations need not follow one another, as Example i illustrates: i.

Marc bakes with a wood oven and his mother’s cookbook.

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But there is no additional internal reading for sentence (56a) in which what happened is that the seat belt is connected to Marc again (the relevant s2, here), but Marc was not previously secured. In other words, the again test does not provide evidence that s2 is part of the meaning of fastened. The absence of such a reading may be because it is hard to imagine the seat belt being truly connected without Marc’s body being secured. We find it hard to tell whether there is an additional internal reading in which the poison is in Marc’s body again, but where it is somebody else who acted to poison Marc before (a Chinese agent, say) and the poison was not effective before (Marc did not change state). In any case, the complexity of situations that would correspond to this additional internal reading of again makes it difficult to put too much stock on the answer, either way. Fortunately, we know of two other pieces of evidence that suggest the linguistic relevance of our sequence of three subsituation analysis. The first piece of evidence in favour of our analysis comes from cases where more than one intermediary relation (more than one s2, so to speak) can be conceived of and targeted by a with-PP.21 Sometimes, one and the same verb can combine with two with-PPs, as (57) shows. The fact that both the objects of with can be the object of use demonstrates that both the mask and ether are instruments of anesthetized in (57a). (Similar arguments can be made for baked and filled in (57b), and (57c), respectively.) Putting a mask on the patient is one s2 and the drug’s later presence in the patient’s body is another s2 in sentence (57a). Similarly, the addition of yeast to the dough is one s2 and the wood oven’s transmission of heat to the dough is another s2 in

206 What with?

(57) a. The nurse anesthetized him (with a mask) (with more than ether). b. Marc bakes pizza (with a wood oven) (with yeast). c. Jim filled the truck (with boxes) (with a forklift). (58) a. The nurse used a mask to anesthetize him. b. The nurse used ether to anesthetize him. (59) a. The nurse used a mask to anesthetize him with ether. b. ??The nurse used ether to anesthetize him with a mask. It should be noted that, although both NP complements of with are instruments, there are constraints on multiple instrument PPs. First, when there are multiple instrument PPs, only one of the with-PPs can express the filler of an obligatory Instrument role. Second, speakers typically find the inclusion of both with-PPs awkward at best. Third, when one instrument is expressed as the object of use and one as the object of with, there is a strong preference for the instrument that corresponds to the subsituation that occurs first [the positioning of the mask precedes the delivery of the ether in (57a)] to be the object of use, as the contrast between (59a) and 59b) shows. (We thank Paul Portner for this last observation.) To understand the reason for the awkwardness of sentences that include two instrument with-PPs, we must first explain why there can be more than one instrument phrase for some speakers, as it runs counter to the assumption that there can be only one filler of a single semantic role (Dowty 1989; Carlson 1998). As Carlson argues, the uniqueness constraint is a constraint on eventualities, as fillers of roles individuate eventualities. Since each instrumental

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sentence (57b); the forklift helps move the box [one s2 for sentence (57c)], and the resulting location of the boxes in the truck is another s2 for sentence (57c). In terms of our analysis of situations that include instruments, the mask in (57a) causes the drug to be in the patient, which, in turn, causes the patient’s change of state. The wood oven in (57b) causes the pizzas to become heated and the yeast to be active which, in turn, helps raise the pizza dough (see below for a definition of the concept of helping). Finally, the action of the forklift in (57c) causes the boxes to move into the truck and the boxes’ location in the truck causes it to be full. The fact that the mask’s action is to cause the drug’s presence in the body, that is, s2 in our analysis of the Drug class, suggests that the granularity of our analysis is relevant to the analysis of multiple with phrases, and similarly for our other sentences containing multiple with PPs.

Jean-Pierre Koenig et al. 207

(60) a. Bill cut the bread with the knife. b. The knife cut the bread. (61) a. Bill ate the noodles with a spoon. b. *The spoon ate the noodles. Van Valin and LaPolla suggest that the difference between (60a) and (61a) is that the instrument plays a causal role in (60a), but not in (61a). More specifically, Van Valin and LaPolla assume that some situations that include an instrument can be analysed as a sequence of two causal relations, but that cut in the use illustrated in sentence (60b) only includes one causal relation in its denotation. They further hypothesize that only instruments that play a clear causal role can undergo the instrument subject valence alternation. What Van Valin and LaPolla have in mind are cases where the instrument causal role is clear and not a weaker kind of causal role, what we call helping in section 3.2.2 below. Expanding on their remarks, one can say that verbs like cut, as used in sentence (60a), fit the semantic template in (7) [repeated below as (62a)], but, when used as in sentence (60b), they fit the semantic template in (62b). In contrast, the spoon in (61a) does not cause the eating; it merely helps make it less messy (in our terminology). This is why, they argue, sentence (61b) is infelicitous.

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with-PP expresses the instrument of different subsituations of the situations described by the verb, there is indeed a single instrument per eventuality. The apparent possibility of more than one filler of the Instrument role is due to the possible presence of more than one intermediary situation in which an entity manipulated by the agent is used to ultimately induce a change of state (or a particular state) of the patient. In this context, we surmise that the awkwardness of two with-PPs is due to the need for speakers to subdivide the described situation more than they typically do to abide by the constraint discussed by Dowty and Carlson. The second piece of evidence that the three subsituation analysis targets a ‘basic’ level of granularity comes from the instrument subject valence alternation. Many scholars have noted that some, but not all, verbs that can combine with an instrumental with-phrase, have one valence alternate in which the instrument occurs as the subject of a transitive use of the verb (Fillmore 1968; Marantz 1984; DeLancey 1991; Levin 1993; Van Valin & Lapolla 1997, among others). The contrast between (60) and (61), adapted from Van Valin and LaPolla, illustrates this observation.

208 What with? (62) a. cause(s1, s2) ^ ACT(s1, A, I) ^ CONTACT(s2, I, P) ^ cause(s2, s3) ^ INCISED(s3, P) b. CONTACT(s2, I, P) ^ cause(s2, s3) ^ INCISED(s3, P)

(63) a. Jill broke the branch. b. The branch broke. We agree with Van Valin and LaPolla that the instrument subject valence alternation is a form of ‘anti-causativization’. But the clear causal role of the agent (its EFFECTOR role in Van Valin and La Polla’s terminology) is not a sufficient condition.22 Consider the verbs sweep and varnish from the Putt and Paint classes, respectively. (64) a. Joe swept the office with a broom. b. */??The broom swept the office. (65) a. Joe varnished the desk with polyurethane. b. */??Polyurethane varnished the desk. Although one might be reluctant to refer to the broom or the polyurethane as the cause of the office’s cleanliness or of the desk’s varnished look, both entities are part of a situation that causes the causal chain’s final effect, as our decompositional formulae show. Both entities thus play a causal role in the overall events. Similarly, contrast the verbs immunize and dope in sentences (66). (66) a. The booster shot finally immunized the cat. b. ??The heavy sedative doped him. Both immunize and dope involve the same causal chain, but dope entails, or at least strongly implies, intentionality, and thus, does not welcome an inanimate instrument as its subject. Sentences (64)–(66) show that the fact that the instrument plays a clear causal role is not a sufficient condition for its appearance as the 22 See Schlesinger (1988) for details on the various factors that affect the ability of an Instrument to be expressed as the subject of a verb.

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The relation between the two uses of cut in (60) is not unlike the causative/inchoative alternation one finds with verbs like break exemplified in (63) in that in both (60b) and (63b) the denotation of the verb includes one less causal relation than in its use in sentence (60a) and (63a) (see Levin & Rappaport Hovav 1995 for a different view). But since the situations described by (60a) include two causal relations, as we have argued, the situations described by (60b) are causal in a way that (63b) is not.

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subject of the verb. Is it a necessary condition? The answer is yes . . . except for verbs of the Whip1 and Cover1 classes (if formula (19) is correct), as Fillmore (1971) and DeLancey (2001) noted (an issue we turn to momentarily). Thus, the use of hit in (67b) does not describe a causal situation that results in a change of state, but mere forceful contact between the stick and the fence. (67) a. Marc hit the fence with a stick. b. The stick hit the fence.

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Although not every verb we analyzed as involving three related subsituations may combine with two distinct kinds of instrument withPPs or take part in the instrument subject valence alternation, many do across many of our obligatory instrument classes. This suggests that the level of granularity of our analysis is not too fine-grained to qualify as an analysis of their structural meaning. As our discussion of the instrument subject valence alternation suggests, not all verbs’ meanings that require the presence of an instrument can be analysed into three subsituations. In particular, the Hit subclass of the Whip class (what we call Whip1 in Table 1) and the Cover1 class do not seem to be analysable as a sequence of three subsituations. Hitting, touching or whacking do not seem to involve a necessary change of state on the part of the entity being more or less forcefully put into contact with the instrument. As formula (8) shows, it involves at least one causal relation. This is why they can participate in the instrument subject valence alternation. But the strong causal role of the instrument does not seem to be a necessary condition for this. We take the distinct (necessary) condition for participation in this morphosyntactic process to support our semantic analysis of these two classes. One possible conclusion to draw from the fact that members of the Whip1 and Cover1 classes behave differently from members of other instrument subclasses is, as one reviewer pointed out, that verbs like hit and poke might not describe situations that involve an instrument at all and the object of with, when a with-PP co-occurs with such verbs, might be a THEME rather than play an Instrument role (as, e.g. DeLancey 2001 claims). After all, as we mentioned earlier, our morphosyntactically based selection of verbs is no guarantee of semantic coherence. It seems unlikely to us that a displaced theme would be the semantic role borne by the object of use (our second morphosyntactic criterion used in selecting verbs whose denotations require or allow instruments). But there is little we can say, in general, were one to object that our instrument subclasses do not form a single semantic category and that some of them do not truly include an Instrument role. Such an

210 What with?

3.2 Questions 2–3: Where is the richness of the lexicon? 3.2.1 Question 2: What part of the meaning is further specified by individual verbs? Our qualitative survey shows that the semantic space of verbs whose denotations require or allow the presence of an instrument is not randomly distributed. The 500 or so verbs that require an L-thematic Instrument role fell into 15 semantically coherent classes and the 1400 or so verbs that allow an L-thematic Instrument role fell into 12 (less semantically coherent) classes. But not all aspects of verb meaning seem equally relevant for grouping verbs into instrument subclasses. For example, for the most part, the category of s1 is weakly determined and irrelevant to the grouping of verbs. Most of the time, it is very general, some action involving the agent and the instrument. Nothing more specific can be said about that action. The action on the instrument involved in parents medicating a child with pills and a dentist anesthetizing somebody have little to do with each other. The same is true of the actions involved in guillotining a prisoner and cutting bread. Both involve some action on the agent’s part on the instrument. But the actions involved have very little to do with each other. In fact, the way in which the Agent manipulates the instrument might vary significantly among the class of situations that are described by a single verb; just consider the various ways of drugging somebody. The agent might pick up a needle and insert it in somebody’s vein; or the agent might put pills on the counter that somebody picks up, or might even simply tell somebody to obtain and ingest pills. The categories of s2 and s3 are more specific than the category of s1, as Tables 1 and 2 make clear. Most changes that the patient undergoes

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objection would be based on the intuition that a subset of our instrument subclasses can be grouped together to define a ‘core’ notion of instrument, to the exclusion of some other subset of instrument subclasses. Our qualitative survey has isolated semantically coherent subclasses of verbs that require or allow an L-thematic Instrument role (through our with and use tests). It does not, by itself, determine whether or not the union of all the classes or of a subset of them is also semantically coherent. To conclude our answer to the first question we raised, the semantic complexity of verbs whose denotations must include an instrument suggests the need to expand the range of meaning templates that form the backbone of the meaning of verbs and requires expanding our view of the boundaries of the complexity of verb meanings to include the possibility, in restricted cases, of sequences of three subsituations.

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23

The pre-linguistic nature of this bias suggests we ought to find similar informational skewing in verbs describing situations that require instruments in other languages, an issue we leave to another paper.

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are specified among members of a subclass: changes of location, being incised, more ornate, and so forth. When the change the patient undergoes varies across members of an instrument subclass, it is at least consistent across a single verb’s denotatum. All situations of drugging involve some chemical change in the patient. Similarly, the category of s2 is typically specified (some location or change of location of the instrument, some contact between the instrument and the patient, etc.). Why is it that verb meanings seem to care more about the properties of s2 and s3 than those of s1? Our hypothesis is that this difference in informational specificity is a consequence of the fact that s2 and s3 are effects (typically end states), whereas s1 is only a cause. More precisely, we interpret this difference in informational load as the lexical (type frequency) reflex of the discourse tendency (token frequency) observed by Lakusta & Landau (2005) to mention goals/end states more than source/beginning states. They observed that when children and adults are asked to describe films of events, they tend to use more prepositional phrases that describe the goal of the path of motion or the end state of a change-of-state verb than prepositional phrases that describe the source of the path of motion or the beginning state of an (induced) change of state verb. We surmise that this end-point bias might, over time, lead speakers to make more fine-grained distinctions in event categories on the basis of the effects of causal events than on the basis of causes. In other words, increased attention to results leads to more discrimination about the results and, ultimately, more informational load carried by the portion of the verb’s meaning that characterizes the result. This typefrequency reflex of a token-frequency difference is similar to what Slobin (2004) claims for verbs of manner of motion. To simplify, Slobin claims that the fact that English expresses the manner component of the conceptualization of motion as a main verb rather than as an optional adjunct, as in Spanish, leads to more use of manner of motion verbs (increased token frequency) and this, in turn, leads to more fine-grained distinctions in the English verbal lexicon (increased type frequency). The sources of the differences in token frequency are quite distinct. In the case of manner of motion, verb differences in token frequencies stem from differences in the constructional means available in the two languages (see Talmy 2000). In the case of the end-state bias, differences in token frequencies are most probably due, as Lakusta and Landau argue, to a conceptual, pre-linguistic bias.23 But in both cases, increase in

212 What with? use seems to have led to more fine-grained distinctions being made in a corner of semantic space: in the case of motion events, it has led to more fine-grained distinctions in the manner component of the conceptual structure of motion events; in the case of instrument verbs, it has led to more fine-grained distinctions in the result states of the sequence of situations that make up events that include instruments.

24 In two cases, namely the Whip and Cover classes, the situation is different. For these two classes, there is a contact relation between the instrument and the patient or a cover relation between the instrument and the patient, respectively. For some members of this class, there are further effects of the contact or cover relations, some change of state that the contact induces or some obscuring of the patient from view, respectively. But for other members of these classes, no clear further effect can be recognized. For those verbs, it does not seem possible to ascribe a causal relation between s2 and s3, as there is no s2. 25 As mentioned earlier, previous literature discusses the issue in terms of the instrument’s causal role. Strictly speaking, causes are eventualities and fillers of Instrument roles can only be metonymically referred to as the cause of an event or a change of state, just as in sentence (i) the bullet can only metonymically be said to be the cause of the president’s death. i. A bullet killed the president. Not all entities can stand for a causal event/proposition and determining which entities can metonymically stand for a causal event is a difficult problem we do not discuss in this paper. We therefore cast our discussion exclusively in terms of whether s2 caused s3.

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3.2.2 Question 3: Is the relation between the subsituations always causal? Our survey of the semantic subclasses of verbs whose denotations may or must include instruments shows that verbs vary in the kind of relation that holds between the situation that includes the instrument, but not the agent (our s2) and the final effect on the patient (our s3). Most of the time, it is pretty straightforward that s2 caused s3. In some of the formulae we use to characterize the various instrument subclasses, the instrument is only mentioned in the predication that involves the agent and therefore, there seems to be no causal relation between s2 and s3. But, in most cases, the absence of an s2 is not due to the fact that there is no causal eventuality in which the instrument, but not the agent, participates. Rather, it is due to an artefact of our summary formulae. Consider a verb such as phone. It is hard to pinpoint the particular situation type that involves the phone, but not the caller, that (partially) causes the verbal connection between the agent and patient (our s2). Mention of s2 is, thus, left out of the formula. In those cases, s2 caused s3, but our analytical regimen does not represent it.24 But, even in cases where the formulae include three distinct subsituations it is not always true that s2 caused s3, despite the seeming consensus that instruments play a causal role in the event they take part in [and are, thus, similar to (proto)-Agents] (see Fillmore 1968; Jackendoff 1990; Croft 1991; Talmy 2000).25 In this subsection, we consider in more detail the relations that can hold between s2 and s3, as

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it serves to illuminate a further dimension of variation between verb meanings that are otherwise quite similar. Consider the following sentences. (68) a. b. c. d. e. f. g.

John watches birds all day with his binoculars. Bill cooks his steaks with butter. Floyd baked the cake with yeast. Bill entered Joan’s room with a duplicate key. Joe scooped the ice-cream with a wooden spoon. Connie skied down the slope with her new skis. Alisa walks her cat with a leash.
















s2 can be the true cause of the final change of state s3 (i.e. the contact and motion of knives or other similar objects do cause the severance in the Cut class). We used the relation name cause in this case. s2 can be the cause of a precondition of the change of state s3. This is the case for the key’s location and motion in the keyhole in sentence (68d). We used the relation name precondition in this case. s2 can be one of a joint set of causes of the change of state s3. This is the case for the skis’ contact with the snow in sentence (68f ), which does not by itself cause motion-in-a-skiing manner, but is only one of its causes. We used the relation name part-cause in this case. s2 can enable a change of location s3. This is the case with the spoon containing the ice-cream in (68e). We used the relation name enable in this case. s2 can cause the event/action to lead to a better resulting state or to be performed better. We used the relation name help in this case.

In all but the first case, s2 did not strictly speaking cause s3. But s2 is a cause or one of the causes in all cases. The last case is the most interesting as it does not strictly speaking involve causing an event or a subevent of a complex event (either a precondition or an arbitrary subpart of the event described by the sentence). For instance, the binoculars’ location in front of John’s eyes in sentence (68a) does not cause the event of watching (or even the seeing, as John might have

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For many of these sentences, speakers that we informally polled were reluctant to say that the relevant s2 caused the effect, that the butter’s being hot caused the change of state from raw to cooked, or that the leash’s hold on the cat caused its motion. For all these cases, we introduced additional relation names in our formulae, part-cause, enable, precondition and help. An inspection of our various instrument classes reveals that s2 can play one of the following roles.

214 What with? seen the birds without binoculars). But it caused that event to be performed better. Similarly, the butter being hot does not cause the steak to be cooked, but it makes the cooking easier or makes the resulting state of the meat better than if no butter had been used. (These dimensions are, of course, determined pragmatically; they depend on what we believe the virtues of butter, yeast or lenses are.) Rather, s2’s efficacy involves what one could call helping. The binoculars’ position help John see better. Viewed this way, we can define the concept of helping as involving the following:

Paul Portner (personal communication) pointed out to us that our analysis of helping that is involved in the meaning of sentences such as (68b) is only valid to the extent that causality is not analyzed as a relation between event tokens (maybe, by analysing it along the lines of a relation between facts, as defined in Kratzer 2002). The addition of the butter did cause the particular event of the steak being cooked in a particular way, at least if we analyze causality as involving counterfactuals of a certain kind (following Goodman 1955 and Lewis 1973). If the butter had not been added, that particular event-token would not have occurred, although a similar cooking event, with a possibly less tasty outcome, would have occurred. We believe the issue raised in the case of our definition of helping is a general issue for eventive theories of causality, that is, for the view that eventualities are causes of other eventualities (see Hobbs 2005, among others). Imagine Jeri just bought new shoes that lessen the burden of running on her knees, allow her to push harder, and run faster. It would be misleading to say that the shoes caused Jeri to run, but not that the shoes caused Jeri to run faster. Similarly, imagine Marc’s leg goes numb at times and when that happens, he has a ‘heavy’ foot; he presses more on the accelerator and drives faster or above the speed limit. It would be misleading to say that the numbness in his leg caused the car to move, but not to say that the numbness caused the car to go faster or too fast. Finally, imagine that Roberto, a budding artist, begins a painting of the area around his house, something his wife asked him to do and he had set out to do on that day at that time. Because of nagging injuries, he had to take some potent painkillers that made him

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Definition 1 An eventuality e1 helps the occurrence of token e2 of the event category C iff (i) there is an ordering of tokens of C along a pragmatically defined scale (ease of performance, how good the resulting state is, fewer unwelcome ‘side effects’); (ii) e1 caused the token e2 of C to be higher on that ordering than it would otherwise have been.

Jean-Pierre Koenig et al. 215

see things differently. His painting this day is, as a result, less realistic than usual. It would be misleading to say in this situation that his being medicated caused the landscape to be painted, although not that it caused it to be painted less realistically. These examples make clear that whether an eventuality c caused another eventuality e depends on the category or description of e (and, similarly, on the category or description of c), something not unexpected, given the normative aspect of causality (see Goodman 1955). It is, therefore, reasonable to relate situations that involve what we call helping to a suitably general relation of causality, whatever the correct analysis of this notion ultimately turns out to be.

A final, interesting result of our survey is that the micro-geography of the meanings of verbs whose denotations require an instrument differs from that of verbs whose denotations merely allow an instrument in several distinct ways. First, although the semantic space of verbs that allow an Instrument is not randomly distributed, it is less tightly organized (insofar as the ways in which instruments affect verb meaning are considered) than that of verbs that semantically require an instrument. This is easily seen when comparing Tables 1 and 2. The category of s3, that is the effect the instrument has on the patient, varies widely across members of an optional instrument subclass. Just consider the very large Eat subclass, for example, which includes verbs as diverse as auction, check, discover, eat, look and scavenge. There is no common result state category we can assign to all these verbs. Verbs in the Cut class are characterized by the common result state of the patient being incised. Similarly, verbs in the Paint class share the result state that some substance has been put on the surface of the patient. But this is not the case for the large class of verbs in the optional instrument Eat class. What this means is that verbs in this latter class are less similar to each other than verbs in the obligatory instrument Cut or Paint classes. To speak somewhat metaphorically, the space of meanings occupied by members of the Eat class is less densely populated or scattered over a larger portion of semantic space than verbs in the Cut or Paint classes. Second, tokens of situations described by verbs whose denotations merely allow an instrument are also more scattered in semantic space. In general, optional instrument verbs are less informative and allow more variation across the situations to which they can felicitously apply. For example, many more optional than obligatory instrument verbs do not include an easily identifiable s2 (marked in Tables 1 and 2 by an

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3.3 Question 4: Are there differences in micro-geography?

216 What with?

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empty cell). In other words, the causal role of s2 or the effect the agent has on the instrument (since s2 is, in many cases, both the effect of s1 and the cause of s3) is not particularly clear. In this case, obligatory and optional instrument subclasses differ in degrees of specificity. Individual verbs that require instruments constrain the way the agent affects the instrument (and, thereby, the way the instrument affects the patient). Individual verbs that merely allow the presence of an instrument are often much less constraining. Third, for several subclasses of optional instrument verbs, there is a significant temporal gap between the action of the agent on the instrument and the effect on the patient, as indicated by a superscript + on the causal predicate in Tables 1 and 2. Counting classes rather than verbs for simplicity, three out of 14 obligatory instrument classes and seven out of 12 optional instrument classes involve a gap between the action of the agent on the instrument and the effect on the patient. In other words, for many more optional verbs, the action of the agent on the instrument is not directly causally related to the action of the instrument on the agent. The fact that when instruments, by hypothesis, are part of the meaning of the verb, the event structure that includes the instrument is causally more constrained is reminiscent of the work we cited regarding the complexity of verb meanings. Being included in the meaning of verbs seems to, on average, reduce the temporal range and complexity of the event. Situation types that require the involvement of an instrument are less causally complex than situation types that merely allow an instrument’s involvement. Finally, our inspection of verbs whose denotations require the presence of an instrument shows that they are more constraining about the properties of instruments that must occur in the described situations than verbs whose denotations merely allow the presence of an instrument. The contrast between the verbs behead and kill is fairly typical of the difference we found between the two classes of verbs. The range of instruments that can be used to perform a beheading is much more limited. The instrument must have a sharp enough edge and the forceful contact of that sharp edge must be the cause of the severance for beheading actions. None of these constraints apply to situations of killing. The fact that only verbs whose denotations require an instrument are eponymous with the instrument name is an extreme example of the general tendency of verbs that semantically require instruments to put more constraints on the appropriate instruments of the described actions. In summary, the inclusion of an instrument in verb meanings goes hand in hand with a finer and sharper partitioning of semantic space.

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Compared to verbs in an optional instrument class, verbs in an obligatory Instrument class have the following two properties: 1. Situation types denoted by verbs differ less from each other (the role played by the instrument in the events is closer across verbs or the instruments themselves are more similar across verbs). 2. Situation tokens denoted by single verbs are more constrained.

4 CONCLUSION Much work on the lexical semantics of verbs over the past quarter century has focused on the general organization of the space of verb meanings. In this paper, we extended this work in two distinct ways through the semantic analysis of verbs whose denotation allows or requires an instrument. The first issue we addressed is whether the range of structural templates for verb meanings that have been proposed in Carter (1976), Dowty (1979), Rappaport Hovav & Levin (1998) and Van Valin & Lapolla (1997) needs to be augmented to account for verbs that include an Instrument role in their denotations. Our answer is that, indeed, an additional subkind of causal situations should be recognized among the possible structural templates for verb meanings, a template that model sequences of three causally related situations (in the broad sense of causality discussed in section 3.2.2). Second, our paper began to complement research on the structural aspect of verb meanings by considering what, other than the common event structural meaning, makes up a verb meaning. Three major conclusions emerged from our survey. First, not all portions of a verb’s structural meaning seem as likely to be elaborated. More specifically, the space of verb meanings we examined exhibits a type-frequency reflex of the token-frequency bias towards goals and result states observed by Lakusta and Landau (2005). Individual verbs are more likely to encode fine-grained distinctions about result states than initial states. Second, verbs that encode a sequence of three subsituations seem to vary more than other verbs in the exact nature of the causal relation involved between those subsituations; in particular, a weaker notion of causation, what we call helping seems to be required in some cases. Third, semantic distance between individual verb meanings seems to vary more when the relevant

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Determining the cause of this sharper and more fine-grained delineation is beyond the scope of this paper. At this point, any proposed explanation for differences in the micro-geography of verb meanings that require or allow an instrument would be sheer speculation on the phylogeny of verb meaning.

218 What with? piece of information (the presence of an instrument in the described situations) is not part of the verbs’ lexical meaning. Our study of the micro-geography of verb meanings is, of course, preliminary, as we focused on a small, understudied portion of the causal quadrant of that space. But it suggests that there may be some ‘structure’ and information of general linguistic relevance to each quadrant. Once we leave structural aspects of verb meaning, it is not just all idiosyncratic information. Acknowledgements

JEAN-PIERRE KOENIG, University at Buffalo, The State University of New York e-mail: [email protected]

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This research was supported (in part) by research grant number 1 R01 MH60133-01 from the National Institute of Mental Health, National Institutes of Health and by grants from the Center for Cognitive Science at the University at Buffalo. We gratefully acknowledge Tom Graves, Cori Grimm, Amanda Haimson, Anne Joergensen, Leana Longley, Eugene Lubliner and Alissa Melinger for their work on the English verbal lexicon project and Juergen Bonhemeyer, Karin Michelson, Roelant Ossewaarde, Chris Phipps and three anonymous reviewers for comments on previous versions of this paper. We owe a particular debt to Paul Portner for his tireless efforts. Our paper would not be what it is without him.

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