Disjunction and Implicatures: Some Notes on Recent Developments

Uli Sauerland ZAS Berlin

July 2009, revised November 2009

Use of disjunction often allows us to draw additional inferences about the speakers belief: For example, (1) uttered by someone out of the blue would lead us to draw at least three additional inferences about the speaker. For one, we would infer that he didn’t see both Kyle and Ryan. Furthermore, we would infer that the speaker is neither certain that he saw Kyle nor that he is certain that he saw Ryan. What is certain is that he saw one of the two.

(1) I saw Kyle or Ryan in the crowd.

What are the mental mechanisms deriving such inferences? This question is central question of the recent discussion targeting scalar implicatures as examples with disjunction have been crucial in this debate. One of the leading questions in this debate is the following: Can the mechanism apply to constituents smaller than sentences? In work by Grice (1989) and work building on his intuitions, the computation of implicatures is tied to the act of speaking, the intentions of speakers, and the assumption that speakers’ act cooperatively. Therefore implicatures are assumed to be generally computed at the sentence level only, though this is not necessarily the only option even on a Gricean approach if speech acts can be embedded. Recent work has contrasted Grice’s position with

1 systems where implicature computation is not tied to speakers’ intentions, but a purely grammatical procedure. This grammatical procedure could in principle apply to any subconstituent of a sentence structure – it can be applied locally. Since scalar implicature computation is semantically at least very similar to the meaning of only, namely exhaustiﬁcation, work by Chierchia (2006), Fox (2007) and others has adopted the convention to mark constituents at which implicature computation applies with a silent operator abbreviated either as O (for only) or Exh (for Exhaustiﬁcation). In this paper, I adopt Exh. As far as I am aware of, while it is generally ac- knowledged that constraints govern the distribution of Exh, a proposal for the distribution of Exh is still forthcoming. At this point, what espe- cially Chierchia et al. (2009) and Chierchia et al. 2008 claim to have shown, though, is that Exh can occur in embedded positions and they therefore reject Grice’s connection of implicature to speaker intention. The phe- nomenon of Exh applying below the sentence level is also referred to as local implicature computation, as opposed to global computation at the sentence level. This paper discusses two potential arguments against a Gricean account of implicatures due to Chierchia et al. (2009) (see also Chierchia et al. 2008; the Hurford’s constraint data) and Fox (2007) (the Free choice data). The two classes of data are illustrated in (2) and (3) respectively.

(2) Hurford’s constraint datum (Gazdar, 1979): Mary read some or all of the books.

(3) Free choice datum (Kamp, 1973): You may eat the cake or the ice-cream.

Chierchia et al. (2008) claim that the account of these two classes of data requires local computation of implicatures. I take objection to this claim. In the following section I address Hurford’s constraint. I show that local implicature for each disjunct is in general not attested, but only global implicature computation. In particular, I argue that the another class of data

2 – the generalized xor data – have been mistakenly taken to argue for a local analysis of implicatures, while in fact the opposite is the case: only the global analysis can account for these data. The Hurford’s constraint data therefore constitute an exceptional case, and I propose to account for them as such. In the second section of this paper, I turn to the free choice data. I ﬁrst set out to clarify Fox (2007) argument: these data are actually not an argument in favor of a local account of scalar implicature, but rather the global analysis. However, Fox is correct to point out that the free choice data are problematic the Gricean picture of entirely post-semantic implicature computation. However, Fox’s argument depends entirely on the claim that free choice inferences are implicatures. On this issue, the current state of the art Chemla (2009) says that implicatures and free choice inferences have different properties with respect to embedding under universal quantiﬁers. Therefore, I conclude tentatively that Fox’s arguments do not threaten the global account. of implicatures.

1 Scalars under Disjunction

I want to situate the discussion of the data involving Hurford’s constraint in the context of the discussion of examples from Chierchia (2004) that were intensively discussed a few years ago (Sauerland, 2004b; Spector, 2005; van Rooij and Schulz, 2004). I want to call these data the Generalized Xor data for reasons that will become clear. I am to show that the generalized xor data require that the scalar implicatures of disjuncts cannot be locally computed in general. This conclusion then leads me to propose that the Hurford’s constraint data are cases of a repair strategy. Multiple disjunctions are a well known problem of the implicatures (Mc- Cawley, 1993; Simons, 1998). For expository purposes, consider an approach to the pragmatics of disjunction that assumes that disjunction is ambiguous between inclusive disjunction or and exclusive disjunction xor. Grice (1989) discusses and rejects this kind of approach, but it also fails in an instructive fashion with multiple disjunction like (A or B) or C. The salient attested interpretation of such an examples is that exactly one of A,

3 A A

A B, or C is satisfied as shown by the Venn diagram on the left in the following figure.C But,B this interpretationC cannotB be derived by the ambiguity-or- or approach. The figure below illustrates (A or B) xor C andC (A xorB B) xor C which result in unintuitive interpretations.

A A A

C B C B C B

correct (A or B) xor C (A xor B) xor C

One may attempt to attach this problemA by postulating a novel ternary exclusive disjunction operator that is deﬁned to make the correct prediction.

However, this is not a promisingC approachB because the problem illustrated by multiple disjunction generalizes as Chierchia (2004) (as well as Bern- hard Schwarz in unpublished work) discovered. One example demon- strating this from my own work (Sauerland, 2004b) is (4). In (4), the weak scalar term some in the scope of disjunction triggers an implicature of not all, but this could not be derived correctly on an lexical ambiguity analysis: Speciﬁcally, if postulated an ambiguity of some between at least some and some and not all in addition to the or/xor ambiguity of or, we would predict that (4) should be felicitous in the following scenarios: On the xor and some and not all-reading if Kai ate both the broccoli and all of the peas, and on the xor and at least some-reading, if Kai ate all of the peas and none of the broccoli.

(4) Kai had the broccoli or some of the peas last night.

The xor data argue for the global approach to implicatures. As far as I know, any published account of the xor-data is global, even though the relevant data are discussed in much of the literature advocating a local

4 approach to implicatures starting (Chierchia, 2004; Sharvit and Gajewski, 2008; Gajewski and Sharvit, 2009). While this is as far as I can see largely due to confusion in the literature, there is some motivation for this confusion: In unpublished work that preceded his 2004 paper (Chierchia, 2004), Gennaro Chierchia attempted a solution of the xor-data making use of a local implicature computation where implicatures are then not part of the sentence semantics, but projected. Specifically, Chierchia (2004) devel- oped an account for A or B or C and (4) that made use of local implicature computation and assumed that local implicatures do not contribute to the semantic meaning of a sentence. In the published paper, Chierchia still appeals to this intuition, for example when he writes implicatures are projected upwards and filtered out or adjusted. However, the published version of Chierchia’s work and all current work on the local approach has not ex- ecuted this intuition of Chierchia’s – and for good reasons, as I’ll show below –, but instead has adopted the semantic exh-operator. The exh-operator contributes an exhaustivized meaning to compositional semantics, rather than contributing subject to a implicature projection procedure. A first version of the exhaustification operator is given in (5). The subscript T of exh must denote a set of alternative propositions to S (the scope of exh). The content of T is determined jointly by context and by S itself.1 Exhaus- tification means that all the alternatives from T are false except for those entailed by S.

(5) Exhaustiﬁcation (preliminary version): 0 0 [[ExhT S]]= (S ∧ ∀ S ∈ A ((S 6→ S ) ∨ ¬ S)

In case of a disjunction A or B, Chierchia et al. (2009) and others assume T to equal the set containing A or B and A and B. Therefore ExhT (A ∨ B) is predicted to be equivalent to A xor B. Therefore, it is plain to see that local computation of implicatures as in ExhT(ExhT (A or B) or C) is equivalent to (A xor B) xor C, and therefore in general makes the wrong predictions for multiple disjunctions.

1For example, T may deﬁned as the set of scalar alternatives of S, i.e. those expressions derivable from S by replacement of scalar expressions with the alternatives. Or it may denote the subset of contextually relevant scalar alternatives.

5 The problem with multiple disjunctions on the localist approach stems from the fact that the exh-operator contributes to compositional meaning. As I pointed out above, if this assumption was abandoned it may be pos- sible to compute implicatures locally in the case of multiple disjunction. But, there would be a cost. Namely, there is another set of data that are generally taken to show that local implicatures can contribute to compositional semantics. Some of these facts have been ﬁrst discussed by Cohen (1971). Geurts (2009) provides a lucid summary. (6) illustrates implicatures drawn in the scope of negation (all from Chierchia et al. (2008)):

(6) a. Joe didn’t see Mary or Sue; he saw both. b. It is not just that you can write a reply. You must. c. I don’t expect that some students will do well, I expect that all students will.

In the examples in (7) implicatures are drawn locally in other downward entailing environments (also from Chierchia et al. (2008)):

(7) a. If you take salad or dessert, you pay $20; but if you take both, there is a surcharge. b. Every professor who fails most students will receive no raise; every professor who fails all of the students will be ﬁred.

Crucially, the implicature is part of the content the downward entailing operator applies to in all of these case. If the localist approach would ﬁnd a solution for the multiple disjunction data along the lines of a separate projection mechanism for implicatures as sketched above, it would loose an account of these data. The global approach, on the other hand, can account for the xor data rather straightforwardly. I brieﬂy sketch the approach I proposed in Sauerland (2004b) (cf. Spector (2005)). It is based on the assumption that the logically strongest information is most cooperative at least in the contexts where scalar implicatures arise. It assumes like the local approach a notion of

6 scalar alternative, that informs the system as to which of the stronger alternatives it should consider. It furthermore assumes that discourse partic- ipants make a competence assumption about speakers: that speakers have deﬁnite opinion on every scalar alternative of a statement they make. The competence assumption divides scalar implicatures into two classes: those that can be derived without it, and those that can only be derived with it. The former I called [primary implicatures] and the later secondary implicatures. For illustration, consider the case of multiple disjuction (A or B) or C.2 I assume there that the alternatives to a disjunction A or B are not only the conjunction A and B but also the individual disjuncts A and B (see also Katzir (2007)). Then the set of scalar alternative to (A or B) or C is as shown in (8):

(8) A, B, C, A and B, A and C, B and C, (A and B) and C, A or B, A or C, B or C, (A or B) or C

The primary implicatures are derived from this set by preﬁxed each of them with the operator ‘the speaker is not certain that’ and testing whether this statement is compatible with the assertion the speaker just made. In this case, it is only incompatible for the assertion itself (A or B) or C. Hence, we arrive at the primary implicatures in (9), where ‘the speaker is not certain that’ is abbreviated as ¬ KS.

(9) ¬ KS A, ¬ KS B, ¬ KS C, ¬ KS (A and B), ¬ KS (A and C), ¬KS (B and C), ¬KS (A and B) and C, ¬ KS (A or B), ¬ KS (A or C), ¬KS (B or C)

Furthermore, secondary implicatures are derived by preﬁxed a scalar alternative with the operator ‘the speaker is certain that not’ (or alternatively by reasoning from the primary implicature ‘¬ KS ψ’ and the competence assumption ‘KS ψ or KS ¬ψ’ for a scalar alternative ψ). Naturally a secondary implicature will only be drawn if it is compatible with the assertion and the primary implicatures. The resulting secondary implicatures are the three below: 2Note that while this case is discussed in the 2004 paper, the exposition there is actually erroneous.

7 (10) KS ¬ (A and B), KS ¬ (A and C), KS ¬ (B and C), KS ¬ (A and B) and C

It is easy to verify that this derives the desired result by glancing back at the Venn diagrams at the beginning of this section. Hence, multiple disjunctions are a strong argument in favor of the global approach. What about cases such as (6) and (7). On important fact about these cases is that without adding a local implicature to the scope of the downward entailing operator, the sentences would all be contradictory. In an unpublished paper, Schwarz et al. (2008) test experimentally how frequently local implicatures are drawn in a downward entailing environment when this is not contraditory otherwise. They report that while for the positive case (11a), 64.7% of their subject draw an exclusivity implicature, only 6.8% do so in the downward entailing environment of (11b).

(11) a. Maria asked Bob to invite Fred or Sam to the barbecue. b. Maria asked Bob not to invite Fred or Sam to the barbecue.

This indicates that local implicatures of the type in (6) and (7) are only drawn when the sentence otherwise violates a pragmatic constraint or prior belief. I conclude therefore that this is best described as a kind of repair strategy of a metalinguistic nature following Horn (1985); Geurts (2009).3 In general, these can be represented by embedded speech act op- erators following Krifka (2001). With this background, consider now the Hurford’s constraint data. The argument in this case is based on the following constraint by Hurford (1974): A sentence that contains a disjunctive phrase of the form “S or S0” is in- felicitous if S entails S0 or S0 entails S. (12) gives some examples for the application of Hurford’s constraint:

3I am not considering in this paper a second class of examples with implicatures where the local implicatures may represent a strengthening of the global implicature since these are not directly linked to disjunction. See Sauerland (2004a); Russell (2006) and Geurts (2009) for discussion.

8 (12) a. #Mary saw a dog or an animal. b. #Mary saw an animal or a dog. c. #Every girl who saw an animal or a dog talked to Jack.

However, Gazdar (1979) noted a systematic exception to Hurford’s constraint: scalar terms can occur with their stronger scale-mates (Singh 2008 points out that there is an ordering restriction in such examples).

(13) a. Mary solved the ﬁrst problem or the second problem or both problems. b. Mary read some or all of the books.

In such examples, the literal meaning alone predicts that Hurford’s constraint should be violated because the first disjunct Mary solved the first problem or the second problem is entailed by the second one Mary solved both problems. Rather than complicating the statement of Hurford’s constraint, local implicatures provide a more elegant solution of the problem as Chier- chia et al. (2008, 2009) correctly point out. In representation (14), Hurford’s constraint is not violated, because the first disjunct is strengthened so as to not be entailed by the second disjunct since ExhT contributes the exclusivity implicature.

(14) Mary solved ExhT (the ﬁrst problem or the second problem) or both problems.

But, local implicatures cannot be generally computed in multiple disjunctions as we saw above in the discussion of the xor-data. While there have been no controlled experiments done on the generalized xor data, I doubt the the percentage of local implicatures in the general case will be much greater than in the case of a downward entailing environment. What then is the lesson to draw from the Hurford’s constraint date. Note ﬁrst, that in the case of these data, which we may represent abstractly as (A or B) or (A and B), the same problem as with the generalized xor data

9 doesn’t arise: While (A xor B) xor C generally isn’t equivalent to the intuitive meaning of (A or B) or C, (A xor B) xor (A and B) is equivalent to A or B because A xor B and A and B are disjoint. But, furthermore there is in this case as in the cases discussed in (6) and (7) a external factor, Hurford’s constraint, that forces the computation of local scalar implicatures. There- fore, I think the correct conclusion to draw from data such as (13) is that local implicature computation is a repair strategy that is derived by speech act embedding and is only available when otherwise a constraint such as Hurford’s is violated or the statement would contradict prior knowledge.

2 Free Choice Effects

Now let us turn to the second argument of Chierchia et al. (2008) as sup- porting local implicature computation; the argument based on the free choice data. The basic observation of free choice Kamp (1973) is that (15a) and (15b) are naturally understood as synonymous.4

(15) a. You may eat the cake or the ice-cream. b. You may eat the cake and you may eat the ice-cream but not both.

This effect can be described by attributing to (15a) the two free choice inferences as shown in (16):5

(16) You may/are allowed to eat the cake or the ice-cream. ; You may/are allow to eat the cake. ; You may/are allow to eat the ice-cream.

4The sentence also has a dispreferred second reading where it can be followed by I don’t know which and the free choice effect is absent. I assume with the literature on the topic that this is a case of ambiguity and don’t deal with this reading in the following. 5I put aside here the question whether this effect arises with indeﬁnites to and how general it is.

10 An important assumption of the argument by Chierchia et al. (2008) is that free choice inferences are implicatures. This argues against accounts of free choice inferences that derive them by changing the meaning of disjunction itself such as those of Zimmermann (2000) and Geurts (2005). The main argument to account for free-choice inferences as implicatures is that these inference disappear when the disjunction is embedded under negation (Kratzer and Shimoyama, 2002; Alonso-Ovalle, 2006). This is illustrated by (17), which does not mean that no one is allowed to eat the cake and the ice-cream, but has the stronger meaning that no one is allowed to eat either.

(17) No one is allowed to eat the cake or the ice-cream.

Assuming for now that this argument is sufﬁcient to convince us that the free choice effect ought to be derived as an implicature, it provides another test where the global and the local can be compared. As Fox (2007) points out, the global approach fares badly on this comparison. This is very easy to see: If we use 3 (p or q) as abbreviation for “You are allowed to eat the cake or the ice-cream”, the primary implicatures predicted by the global approach as presented above are the following:

(18) a. ¬KS 3 p b. ¬KS 3 q c. ¬KS 3 (p and q) d. ¬KS 2 (p or q) e. ¬KS 2 p f. ¬KS 2 q g. ¬KS 2 (p and q)

Of these, (18a) and (18b) contradict the free choice inferences. Therefore, the global approach not only fails to predict the free choice inferences, but in fact predicts their negations. The local approach as presented above doesn’t do much better. We can apply exhaustiﬁcation in 3 (p or q) at two point; below and above 3. If

11 we apply it in both places, the result is ExhT (3 (p xor q)). If we assume that the scalar alternative to 3 is the necessity operator 2, we arrive at 3 (p xor q) and ¬ 2 (p xor q). While this does not contradict both free choice inferences, the result is too weak to derive the free choice inferences. The system Fox advocates is a hybrid of the local and global system presented above with some innovations of his own. It adopts from the local approach mainly the assumption that implicature computation is a grammatical process and contributes to truth conditions. Therefore implicature computation on Fox’s approach takes place before sentence pragmatics applies, and this avoids the conﬂict between primary implicatures and the free choice inference we observed in (18). In all other respects, Fox’s procedure is a global process for the reason just discussed. However, the global can also not be ExhT (3 (p or q)): This would predict just the implicatures ¬ 3 (p and q) and ¬ 2 (p or q), not the free choice inferences. Fox’s solution is to revise exhaustiﬁcation generalizing my proposal (Sauer- land, 2004b), which I summarized in the previous section. Fox adopts the assumption that the alternatives of a disjunction are not just conjunction, but also individual disjuncts. Since then the alternatives aren’t linearly or- dered, this has the consequence that potential implicatures can contradict each other. Indeed in the simplest case of disjunction, such a contradiction arises: If both alternatives to (19a) are negated, the resulting implicatures (19a) and (19b) contradict the assertion.

(19) John talked to Mary or Sue. a. John didn’t talk to Mary. b. John didn’t talk to Sue.

In my proposal, potential primary implicatures were ﬁltered such as to not contradict the assertion and potential secondary implicatures such as to not contradict either the assertion or the primary implicatures. While this address the case in (19) indirectly, the ﬁltering procedure would not directly say anything about a case like (19), where the individual implicatures don’t contradict the assertion, but taken together they do. Fox pro- poses a more general procedure that avoids problems arising from logical

12 relationships between conjunctions of potential implicatures and the assertion. He introduces the notion of innocent excludability as deﬁned in (20) to this end:

(20) q is innocently excludable given T and p iff. for any maximal subset S ⊂ T such that {¬φ | φ ∈ S} is consistent with p, q ∈ S

Innocently excludable alternatives are those that will not contradict the assertion when negated even in conjunction with other potential implicatures. The exhaustivity operator is then deﬁned as in (21) to negate exactly the innocently excludable alternatives:

(21) [[Exh]](T)(p)(w) ⇔ p(w) ∧ ∀q ∈ T(q is innocently excludable given T and p → q(w) = 0)

As an example, consider simple disjunction as in (19), abbreviated here as A ∨ B. The alternatives are shown in the graph in (22). There are two maximal subsets of the set of alternatives such that their negations are consistent with the assertion, and both are indicated in the graph. Only elements of their intersection are innocently excludable, i.e. only A ∧ B. In this way, the approach predicts the exclusivity implicature.

(22)

A ! B A " B

#x Bx $x Bx A " $x Bx A ! #x Bx A " #x Bx A ! $x Bx

#x Bx " %$x Bx

A ! (#x Bx " %$x Bx) A " (#x Bx " %$x Bx)

A ♢p !p

♢(p " q) !(p " q) ♢(p ! q) !(p ! q)

♢q !q Note that the approach doesn’t capture the primary, uncertainty implicatures such ¬ KSA and ¬ KSB for (22). So, it needs to be supplemented with a Gricean mechanism to derive these. ♢p " ¬♢q " ¬!(p ! q) !p " ¬♢" " ¬!(p ! q) Now consider Fox’s derivation of free choice effect using (23) as the paradig- matic example which I’ll abbreviate as 3 (p ∨ q). The result of exhaustiﬁ- cation(p ! q) at " the ¬ sentence(p " q) level" ¬! is(p computed! q) right below (23), where the arrows ♢ ♢ (p " q) " ¬ (p " q) indicate entailment relations. I did not include alternatives with 2 in the♢ ! graphic in (24) because these all are innocently excludable, and the impli- !(p " q) cature ¬ 2 (p ∨ q) results. From the alternatives!(p with! q) 3" ¬shown♢(p "in q) (24), the implicature ¬ 3 (p ∧ q) is derived.

(23) You may eat the cake or the ice-cream. ♢q " ¬♢p " ¬!(p ! q) !q " ¬♢p " ¬!(p ! q)

(24)

♢p

♢(p ! q) ♢(p " q)

♢q

Fox (2007) accounts for free choice by second order exhaustification (cf. Kratzer and Shimoyama 2002; Spector 2007). Second order exhaustification represents a recursive application♢p " ¬♢q of the Exh-Operator as shown in (25). Note that Fox assumes that for the primary exhaustification in the scope of the secondary exhaustification, the set of alternatives T is the same♢(p for! q) each " ¬♢ alternative(p " q) considered by the secondary♢(p exhaustification. " q) 6

6One consequence of this is that higher order exhaustification always lives on the partition of logical space introduced by♢q the " elements¬♢p of T. I.e. if two worlds occupy the same cell of this partition, no higher order exhaustification of will distinguish between the two worlds. This entails that if T is finite, at some level n of higher order exhaustification of level n, level n + 1 and any greater level will be equivalent.

14 ♢p !p

♢(p " q) !(p " q) ♢(p ! q) !(p ! q)

♢q !q

♢p " ¬♢q " ¬!(p ! q) !p " ¬♢" " ¬!(p ! q)

♢(p ! q) " ¬♢(p " q) " ¬!(p ! q) ♢(p " q) " ¬!(p " q) !(p " q) !(p ! q) " ¬♢(p " q)

♢q " ¬♢p " ¬!(p ! q) !q " ¬♢p " ¬!(p ! q)

(25) Exh(T0)(Exh(T)(You may eat the cake or the ice-cream)), where T0 = {Exh(T)(φ) | φ ∈ T} ♢p

♢(p ! q) ♢(p " q) The alternatives to be considered for second level in this case are shown in (26), where again the arrows indicate entailment. The result of second ♢q order exhaustification in this case differs from the of first order exhaustification because both 3 p ∧ ¬ 3 q and 3 q ∧ ¬ 3 p are innocently excludable.

(26)

♢p " ¬♢q

♢(p ! q) " ¬♢(p " q) ♢(p " q)

♢q " ¬♢p

Therefore, two new implicatures are predicted by second order exhausti- ﬁcation, namely ¬ (3 p ∧ ¬ 3 q) and ¬ (3 q ∧ ¬ 3 p). Given that the assertion states that 3 (p ∨ q), these two implicatures amount to exactly the desired free choice inferences: 3 p and 3 q. Note that Fox’s approach also provides an account for the generalized xor data discussed in the previous section. There we saw that other versions of a local approach don’t predict the right implicatures for the xor data. Fox’s system in this case essentially adopts the global solution of Sauer- land (2004b). Consider for example the case in (27):

(27) Kai had the broccoli or some of the peas.

Abbreviating this sentence to A ∨ ∃x Bx, (28) shows the alternatives Fox assumes for the examples, and computes which are innocently excludable. In this case, there are two different maximal sets that could be all negated

15 B

A ! B A " B

and still be consistent with the assertion. Therefore, only the alternatives included in both sets are innocently excludable. This predicts the implicatures ¬ (A ∧ ∃x Bx) and ¬ (∀x Bx) as desired.

(28)

#x Bx $x Bx A " $x Bx A ! #x Bx A " #x Bx A ! $x Bx

It is easy to verify that Fox’s approach also makes the correct prediction for the multiple disjunction case. Note though that Fox’s approach in this case applies exhaustiﬁcation glob- ally, and would indeed make wrong predictions if it was applied locally: Consider the representation#x Bx in (29)," %$ wherex Bx the second line uses the same abbreviations as we did previously.

A ! (#x Bx " %$x Bx) A " (#x Bx " %$x Bx) (29) ExhT (Kai had the broccoli or ExhU some of the peas) ExhT (Bx ∧ ExhU (∃x Bx))

A The alternative set U of the second Exh-operator in (29) consists of ∃x Bx and ∀x Bx. Therefore local exhaustiﬁcation yields ∃x Bx ∧ ¬ (∀x Bx). The alternative set of the higher exhaustiﬁcation operator is as shown in (30). Note that only A ∧ ∃x Bx ∧ ¬ (∀x Bx) is innocently excludable.

(30) 16 B

A ! B A " B

#x Bx $x Bx A " $x Bx A ! #x Bx A " #x Bx A ! $x Bx

#x Bx " %$x Bx

A ! (#x Bx " %$x Bx) A " (#x Bx " %$x Bx)

Exhaustiﬁcation therefore results in the following interpretation.

(31) (A ∨ (∃x Bx ∧ ¬ (∀x Bx))) ∧ ¬ (A ∧ ∃x Bx ∧ ¬ (∀x Bx))

This is equivalent to the following disjunction where it is easy to see that the third disjunct, ∀x Bx ∧ A ∧ ¬ (∃x Bx), does not capture part of the intuitive interpretation of the generalized xor sentences.

(32) (A ∧ ¬ ∃x Bx) ∨ (∃x Bx ∧ ¬ (∀x Bx)) ∧ ¬ A) ∨ (∀x Bx ∧ A ∧ ¬ (∃x Bx))

To sum this chapter, I have shown that the free choice data represent a potential problem not for the global approach to implicatures, but for the assumption that implicatures and free choice inferences are all due to the same pragmatic mechanism. In fact, Fox’s account of implicatures is crucially global in the relevant sense. The argument against the Gricean account of implicatures Fox makes therefore is entirely dependent on the question whether free choice inferences should be accounted for in the same way as other implicatures or not. As noted above, approaches that build free choice inferences into the meaning of disjunction (Zimmermann, 2000; Geurts, 2005) do not account for free choice inferences as implicatures and in the case of free choice items we ﬁnd that the free choice

17 inferences are grammaticalized. The implicature account of free choice inferences rests on the observation by Kratzer and Shimoyama (2002) in (17) that free choice inferences do not arise when disjunction occurs in the scope of negation. However, there are other ways of accounting for this fact: it could be that the disjunction of Zimmermann or Geurts is a positive polarity item, while in downward entailing environments disjunction must receive the meaning of logical disjunction. At the time I was working on this paper, Chemla (2009) presented new experimental data casting further doubt on the assumption that free choice inferences are regular implicatures. Speciﬁcally, Chemla experimentally compares the strength as an inference of a universal implicature as in (33) with that of a universal free choice inference as in (34).

(33) a. Premise: Everyone passed most of his exams. b. Inference tested: No one passed them all.

(34) a. Premise: Everybody is allowed to give me the dissertation or the commentary. b. Inference tested: Everybody can choose which of the two he will give to the teacher.

As Chemla reports, there is a signiﬁcant difference. Namely, the universal implicature (33) is judged as less strong than the universal free choice inference in (34b) (see page 17 of Chemla’s paper). Chemla rightly notes that his result casts doubt on the link between scalar implicatures and free choice inferences. Note that Chemla’s result would be exactly predicted by the account sketched in the previous paragraph: The absence of a universal implicature in (33) argues further against the local approach to implicatures, but conﬁrms the global approach that only predicts the implicature that not everyone passed all of his exams for (33a). Furthermore a universal free choice is predicted if the free choice inference is part of the lexical meaning of disjunction.

18 3 Conclusion

In this paper, I considered some current work on the interaction of implicature computation and disjunction. In particular, I addressed data from Hurford’s constraint and data from free choice that Chierchia et al. (2008) discuss in their interesting paper. Speciﬁcally, they claim that these data provide support for a local approach to implicatures. The data from Hur- ford’s constraint, in particular, are taken to show that local implicature computation applies to each disjunct of a disjunction. I however show in Section 1 that in general an account that assume local implicature computation for each disjunct faces problem with the xor data, for instance multiple disjunction. In this cases, local implicatures are intuitively never available and therefore local implicature computation must be blocked. I have concluded therefore that the data involving Hurford’s constraint raised by Chierchia et al. (2008, 2009) are cases where we see a repair strategy at work, which may well be metalinguistic in the form of an embedded speech act. The second kind of criticism of the global approach I have addressed is that of Fox (2007) based on free choice inferences. As I have shown, Fox’s criticism does not actually directly adhere to the local/global distinction, but in fact his approach must crucially be global as well. Rather Fox’s argument targets the question whether implicature computation is entirely pragmatic, or at least partially semantic. While this is an interesting argument, I have shown that Fox’s assumption that free choice inferences are implicatures is at least worth further examination. If the assumption is dropped – and recent experimental data by Chemla (2009) suggest do- ing so – the global approach to implicatures can account for all the data straightforwardly.

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