Scalar implicatures of embedded disjunction∗

Sentences with disjunction in the scope of a universal quantifier, Every A is P or Q, tend to give rise to distributive inferences that each of the disjuncts holds of at least one individual in the domain of the quantifier, Some A is P & Some A is Q. These inferences are standardly derived as an entailment of the meaning of the sentence together with the scalar implicature that it is not the case that either disjunct holds of every individual in the domain of the quantifier, ¬Every A is P & ¬Every A is Q (plain negated inferences). This derivation faces a challenge in that distributive inferences may obtain in the absence of plain negated inferences. We address this challenge by showing that on particular assumptions about alternatives a derivation of distributive inferences as scalar implicatures can be maintained without necessitating the absent plain negated inferences. These assumptions accord naturally with the grammatical approach to scalar implicatures. The paper concludes by presenting experimental data that suggest that plain negated inferences are not only unnecessary for deriving distributive inferences, but might in fact be unavailable. 1 Distributive inferences Disjunction in the scope of a universal quantifier tends to give rise to existential inferences pertaining to each of the disjuncts, specifically, that each of the disjuncts holds of at least one individual in the domain of the universal quantifier (henceforth, distributive inferences). This can make sense of the fact that a sentence like the following (1) Every brother of mine is married to a woman or a man. is perceived as infelicitous in a context in which all of the speaker’s brothers are married to a woman (and none are known by the speaker to be married to a man), that is, in a context in which distributive inferences of the sentence, given in (2), are false.1 ∗We would like to thank Yosef Grodzinsky, Roni Katzir and Benjamin Spector for helpful discussion and comments. Further acknowledgments to be added in the final version of the paper. 1If in the context the speaker is taken to be opinionated about the alternatives induced by a sentence that she utters and if the alternatives are taken to be relevant, an SI of the sentence based on the alternatives is generally computed. Although a subsequent cancellation of the SI may be possible, which may require a reanalysis of what is relevant in the context (see Mayol & Castroviejo 2013 on conditions on SI cancellation), the sentence is perceived to convey false information in the context if the SI is false (cf. Gazdar 1979, Horn 1984, Levinson 2000, among others).