Modality, exhaustivity, and scalar focus particles: Toward a modal analysis of 就 and 才

In this talk I present some preliminary thoughts on the semantics of the two scalar focus particles jiu 就 and cai 才. The novelty of the proposed analysis which contrasts it with previous literature is the claim that both particles are associated not only with scalar focus but also with goal-oriented or teleological modality, and it is the interaction between (a) scalar focus, (b) goal-oriented modality, and (c) the operator/agreement marker “dual” status of jiu and cai that altogether yield the intriguing syntactic and semantic patterns as exemplified in (1)-(2) below.

(1)a.[一個人]F就夠了。
b.張三就買了[一本書]F (，沒買其他東西)。
(2)a.[十個人]F才夠。
b.張三才買了[一本書]F (，沒買其他東西)。

I first argue that jiu signals the presence of a complex exhaustive intensional operator “O+HAVE-TO,” where O is the exhaustivity operator (≈ a covert ‘only’) that is familiar from the literature of scalar implicature since Fox (2007), and HAVE-TO stands for a teleological modal operator with universal quantificational force. In (1a), jiu is an agreement marker for a covert O+HAVE-TO that scopes above the F-marked phrase, and the main predicate (‘suffice’) provides the content for the teleologically accessible worlds that restrict O+HAVE-TO. A rough paraphrase of this sentence under this account is the following: ‘In order to reach a degree that is considered sufficient (= goal) in some contextually specified manner, there only has to be one person (= focus) for such goal to be achieved.’ This derives the meaning that ‘one person’ constitutes a sufficient condition. On the other hand, in (1b) jiu is the complex operator O+HAVE-TO itself (not an agreeing element), which takes the entire proposition as its nuclear scope. The restriction (a set of teleologically accessible worlds) is contextually supplied, e.g., to meet the speaker’s expectation about what ZS would buy. Thus, (1b) asserts the following: ‘In order to satisfy some contextually relevant goal, it only has to be considered that ZS bought one book.’ I then propose that jiu and cai minimally differs in the modal component: Cai signals the presence of O+CAN, where CAN is a teleological modal operator with existential quantificational force. Thus, (2a) is assigned the following interpretation: ‘In order to reach a degree that is considered sufficient in some contextually specified manner, there only can be 10 people for such goal to be achieved.’ This derives the meaning that ‘10 people’ constitutes a necessary condition. It will be shown that, despite the suggested difference of jiu and cai, the near-synonym of (1b) and (2b) in fact follows if the exhaustivity in these cases is relative to a covert, contextually specified goal.