Scalar implicatures and the meaning of quantity wh-phrases under negation

Scalar implicatures and the meaning of quantity wh-phrases under negation Mandarin wh-phrases are known to have non-interrogative, existential uses in a restricted set of contexts (Huang 1982, Li 1992, Lin 1998, etc.). This paper focuses on the interpretation of the quantity wh-word ji 几 when it follows clausemate/sentential negation, e.g. (1a)-(1c).(1) a. 公交车上没几个人。 ‘(Only) a few people are on the bus.’ b. 没几个学生在写作业。 ‘(Only) a few students are doing assignments.’ c. 我和李四没说过几次话。 ‘I talked with Lisi (only) a few times.’ The traditional view that such ∃ wh-phrases behave on a par with NPIs (e.g. any) predicts that the examples in (1) should all have the [¬ > ∃] reading. However, this is not borne out: (1a) would be false if no one at all is on the bus. Likewise, (1b) is false if no student at all is doingassignments, and (1c) is false if I never talked to Lisi before. Meanwhile, in each example the quantity denoted by ji 几 appears to be rather small or insignificant, as indicated by the only component in the English translation. Importantly, such inference does not follow the [¬ > ∃] scope order, either. One may attempt to derive this “insignificant” ∃-inference via the reversed order, i.e. [∃ > ¬] (‘there is some quantity n such that n people are not on the bus’), where the wh-expression takes wide scope. This however cannot be correct, because there are infinitely many values of n that can make the proposition true. I argue the meanings of (1a-c) can be derived if we assume that the ∃-operator associated with ji scopes below negation (as the tradition has it) but the quantity variable n that ji introduces is interpreted against a specific domain, where specific is understood as contextually significant. (Suppose a bus can accommodate 30 people; then 8 individuals or more on the bus may be considered significant in this context.) That is, a ji-phrase is similar to a specific indefinite with a restricted domain of quantification. The assertoric content of (1a) can thus be given as (2). (2) ¬∃n[n ∈ a set of significant quantities & n people are on the bus] Further, I propose that the “insignificant” ∃-inference can be obtained as a scalar implicature (SI). Specifically, I follow the grammatical approach to SIs (Fox 2007, Chierchia et al. 2012, etc.) and assume that SIs can be compositionally derived through applying a covert alternative-sensitive exhaustification operator “O” (for ‘only’) to a sentence, defined as (3). (3) O(p) = p & all alternative propositions not entailed by p are false The complete LF of (1a) is therefore (4a). For (4a), the relevant alternative is the one shown in (4b), which differs minimally from the prejacent in the domain of quantities, i.e. one that consists of insignificant quantities. Exhaustification of O yields the strengthened meaning that can be paraphrased as (4c), in which the second clause corresponds to the “insignificant” ∃-inference. (4) a. O(¬∃n[n ∈ a set of significant quantities & n people are on the bus]) b. ¬∃n’[n’ ∈ a set of insignificant quantities & n’ people are on the bus] c. ‘There does not exist a significant quantity n such that n people are on the bus, though there exists an insignificant quantity n’ such that n’ people are on the bus.’ This analysis (which naturally extends to (1b) and (1c)) suggests that the application of O is obligatory in the interpretation of Mandarin Neg-Wh sentences, since otherwise we wouldn’t be able to derive the correct meaning. I further demonstrate a possible extension to other types of existential wh-phrases on the assumption that the operator O can interact with different kinds of contextual domains (of individuals, properties, etc.), and show how this proposal provides an SI-based compositional semantics for the data discussed by A. Huang (2013).