GENERALIZED FREE CHOICE AND MISSING ALTERNATIVES MARIE-CHRISTINE MEYER The Hebrew University of Jerusalem appeared in Journal of Semantics, advanced online access, Nov 2015 Abstract In this paper I propose that there are unembedded disjunctions which receive a conjunctive interpretation via recursive implicature computation. This is unexpected: Since disjunction competes with conjunction, implicature computation will usually result in the negation of the conjunctive alternative. I argue that certain disjunctions do not compete with a conjunctive alternative, due to a constraint on the assertability of scalar alternatives. As a result, recursive implicature computation can strengthen matrix or into and in these cases. I discuss the prag- matic factors driving recursive implicature computation, as well as the scope of the proposed assertability condition on alternatives. 1 THEPUZZLE Asserting a disjunction A or B is a good way to narrow down the possibilities for what is the case to A and B without committing to the truth of either. The following exchange illustrates this: (1) X: He’s in France or in Spain. Y: You’re wrong. He’s not in France. X: I never said he was in France! X asserted A or B and Y tries to commit X to the truth of A – that seems wrong and X can rightly claim that she never asserted A. As the reader can check for herself, the same result is obtained when Y tries to commit X to the truth of B. Now compare this to the following case: (2) X: I have to go to the gym or else I’ll get lazy again. Y: You’re wrong. You don’t have to go to the gym. X: #I never said I had to go!1 X asserted A or else B and Y’s attempt to commit X to the truth of A is successful, as can be seen from the contradictory flavor of X’s denial in (2). Apparently, or else sentences commit the speaker to the truth of the first disjunct just like conjunctions do. 1 Note that here, as in all examples involving two occurrences of a modal element, we have to make sure the interpretation of have to stays constant across X’s and Y’s utterances. Otherwise, Y’s objection could be interpreted as targeting X’s grounds for stating the necessity (i.e., the modal base), as in the following exchange (where have to expresses circumstantial necessity): (i) X: Oh no, I have to pay taxes! Y: No you don’t. You can go to jail instead. X states that she has to pay taxes given that going to jail is not an option, whereas Y explicitly wants to include this possibility, which would obliterate the necessity of paying taxes (cf. Kratzer, 2012). 1 What about the second disjunct, B? As we will see shortly, B is actually interpreted as a condi- tional. If we spell this out, we see the same pattern: (3) X: I have to go to the gym or else I’ll get lazy again Y: You’re wrong. You won’t get lazy again (if you don’t go) X: #I never said I would get lazy (if I don’t go)! Asserting A or else B thus also commits X to B (understood as a conditional). The interpretation of or else disjunctions is illustrated again by the following examples. ‘⇒ f’ means that the hearer may conclude that f; this notation is intended to remain neutral as to the theoretical status of this inference – for example, it could be part of the assertion, a presupposition, or an implicature. (4) John must be rich or else he wouldn’t drive a Porsche a. ⇒ John must be rich b. ⇒ If he wasn’t rich he wouldn’t drive a Porsche (5) I have to do the homework or else my teacher will get upset a. ⇒ I have to do the homework b. ⇒ If I don’t do the homework my teacher will get upset These sentences constitute a new class of unembedded disjunctions which receive a conjunctive interpretation; with the exception of Klinedinst and Rothschild (2012), whose proposal will be discussed in more detail in section 4.2, no analysis has been offered in previous literature.2 Before delving into the details, it will be useful to give a schematic characterization of the construction in question. These sentences have the form in (6-a) and the interpretation in (6-b): (6) a. A or (else) WOLL b3 b. A & if not A’, WOLL b The construction poses two puzzles: How to account for the conditional interpretation of the sec- ond disjunct on the one hand, and how to derive the conjunctive interpretation of the disjunction as a whole on the other hand. My guiding hypothesis is that both properties are to be analyzed independently, and my proposal consequently consists of two independent ingredients. 1.1 Preview Before presenting the details of my analysis, I will provide a quick preview of the core idea. I claim that or else disjunctions are standard disjunctions: Their basic semantic meaning can be defined in terms of Boolean ∨. As is well known, this basic semantic meaning can be strengthened by scalar implicatures. Generally speaking, scalar implicature is the result of adding to the basic meaning of a sentence W the negation of an alternative S which could have been asserted instead 2 In an unpublished manuscript, Dever (2009) also mentions or else sentences, though his theoretical interest is in dynamic semantics and embedded epistemic modals. He does not attempt to offer a solution to the conjunctive inter- pretation of these disjunctions. 3 I follow Abusch (1985) in using WOLL as a cover term for the morphological variants will and would. In non-future uses like in conditionals, WOLL is interpreted as a universal modal operator, as shown below. 2 and expresses a stronger, equally relevant proposition. In the case of disjunction, the relevant alternative is of course the corresponding conjunction.4 The process is illustrated below: (7) Standard Disjunction: A or B a. Basic meaning: A ∨ B b. Competitor: fA and Bg c. Strengthened meaning: A ∨ B & ¬(A ∧ B) Different views exist as to the precise mechanism by which this strengthening is achieved — it may be a pragmatic process, as in (Neo-)Gricean theories, or due to a covert, only-like syntactic operator, as in grammatical theories of scalar implicature (e.g. Grice, 1975; Horn, 1972, 1984; Levinson, 2000; Chierchia, 2004, 2006; Fox, 2007). But there are disjunctions which seem to undergo a radically different kind of strengthening than that in (7); these are Free Choice disjunctions as in (8): (8) You may have ice-cream or cake a. Basic meaning: ◇(A ∨ B) ≡ ◇A ∨ ◇B b. Strengthened meaning: ◇A ∧ ◇B Kratzer and Shimoyama (2002)’s seminal insight was that the Free Choice effect in (8) can be derived if the strengthening mechanism can also lead to the negation of higher-order competitors, i.e., competitors which have already been strengthened themselves. This is illustrated below: (9) Competitors of (8): fYou may have ice-cream, you may have cakeg Strengthened meaning: You may have ice-cream but not cake, you may have cake but not ice-cream Formally: (10) Higher-order competitors of (8): f◇A ∧ ¬ ◇ B, ◇B ∧ ¬ ◇ Ag Negating these higher-order competitors (i.e., the strengthened rather than the basic meaning of the competitors) yields the quasi-conjunctive interpretation of (8):5 (11) You may have ice-cream or cake a. Basic meaning: ◇(A ∨ B) b. Higher-order strengthening: ◇(A ∨ B) & ¬(◇A ∧ ¬ ◇ B) & ¬(◇B ∧ ¬ ◇ A) ≡ ◇A ∧ ◇B Could this insight be used to account for the conjunctive interpretation of sentences like (12)? 4 For the sake of simplicity I leave out the single disjuncts here, though these are of course part of the full set of competitors (cf. Sauerland, 2004; Katzir, 2007). This simplification has no consequences here, as the single disjuncts could not both be consistently negated, and negating just one disjunct would lead to problems discussed under (12) below and will therefore not be allowed under any theory of implicature either. 5 I use the term quasi-conjunctive because, while the Free Choice meaning is a conjunction of modal claims (◇A ∧ ◇B), there is still one conjunctive competitor whose basic meaning may be excluded even under the Free Choice reading, viz., ◇(A ∧ B). Thus, while the Free Choice reading entails that both A and B are allowed by themselves, it may also entail that not both are possible at the same time (cf. Fox, 2007 and Chemla, 2009a for critical discussion). 3 (12) [John must be rich]A or [he wouldn’t drive a Porsche]B Meaning: A ∧ B And if (12) can indeed be derived by the same mechanism as Free Choice, wouldn’t this predict that any disjunction can receive a conjunctive meaning? As it turns out, this undesirable outcome is avoided because of competition: As we saw in (7), a disjunction competes with its conjunctive alternative, usually resulting in the negation of this conjunction to be added to the basic meaning. Generally, it should not be possible to strengthen the meaning of f if the result is equivalent to the meaning of one of f’s competitors. In the frame- work of Fox (2007), to which we will turn in more detail below, this is achieved by only allowing for higher-order strengthening after basic strengthening as in (7).6 For standard disjunction, this means that the negation of the conjunction will be added before any higher-order strengthening can take place. Re-introducing the conjunctive meaning through subsequent higher-order strength- ening a` la Kratzer & Shimoyama is thus ruled out by a simple consistency constraint.