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 mech- anism apply to constituents smaller than sentences? In work by Grice (1989) and work building on his intuitions, the computation of implica- tures 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 sen- tence 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 im- plicature computation. In particular, I argue that the another class of data 2 – the generalized xor data – have been mistakenly taken to argue for a lo- cal 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 impli- cature computation. However, Fox’s argument depends entirely on the claim that free choice inferences are implicatures. On this issue, the cur- rent state of the art Chemla (2009) says that implicatures and free choice inferences have different properties with respect to embedding under uni- versal 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 gen- eralized 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 ap- proach 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 follow- ing 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 ex- clusive 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 confu- sion: 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 pro- jected 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 be- low –, 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 ^ 8 S 2 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.