Scalar Presupposition, Assertions and Cantonese “gau3…SFPassert”

Cantonese gau3 ‘enough’ can be used as an adverb expressing a meaning of addition (cf. e.g. Cheng 1997; Wu 1997; Shan 2008; Matthews & Yip 2011; Liu 2013; Mai & Tan 2014), which is treated on a par with Cantonese dou1 ‘also’ or English ‘too’ and ‘also’. However, (1) shows that gau3 ‘enough’ and dou1 ‘also’ may not be absolute equivalents (cf. Matthews & Yip 2011). (1) Nei5 heoi3-gwo3 Jat6bun2 sap6 ci3, you go-EXP Japan ten times ngo5 gau3/?dou1 heoi3-gwo3 Jat6bun2 ng5 ci3 lok3/laa1I enough/also go-EXP Japan five times SFP/SFP‘You have traveled Japan for ten times and I have traveled Japan too, but for five times.’ This paper examines the semantics of Cantonese adverb gau3 ‘enough’. Lee and Lai (2016) argue that Cantonese gau3 ‘enough’ is an additive adverb demonstrating the following two properties. (i) Its additive meaning is governed by the Leftness Condition which gau3 ‘enough’ associates with the NP or phrase to its left at the surface structure, and can be any item within the IP scope, with such a constituent not restricted to the subject NP. (ii) Its occurrence has to be licensed by an assertive sentence-final particle (SFPassert). The licensing relation between gau3 and SFPassert requires the predicate to give a downward movement in the quantity or degree scale, which marks the assertion of the sentence, as shown in (2). (2) Nei5 heoi3-gwo3 Jat6bun2 ng5 ci3 you go-EXP Japan five times ngo5 gau3 heoi3-gwo3 Jat6bun2 ??sap6-ci3 / ng5-ci3 lok3/laa1. I enough go-EXP Japan ten-times / five-times SFP/SFPIntended meaning: ‘You have been to Japan for five times and I have been there too for ??ten times/five times.’Along the line of Lee and Lai (2016), I will argue that as an additive adverb, the semantics of “gau3…SFPassert” needs to be captured by a two-fold semantics, contributed by (a) gau3 ‘enough’ and (b) “gau3…SFPassert” respectively. •For gau3, its semantics is on a par, though distinct, from other additives, which adds its associate to a presupposed set. Therefore, like other additives, gau3 does not contribute to the truth condition of the proposition, and the proposition still asserts its prejacent to be true. What gau3 triggers is an existential presupposition of a set of individuals, which can be determined contextually or in the discourse, with the associate added to such a set. •What makes gau3 distinct from other additives is its obligatory occurrence with the SFPassert which serves to license its presence. The presence of “gau3…SFPassert” will in turn trigger a scalar presupposition which requires a point for contrast, with both the contrasting point and the point denoted by the co-occurring of gau3 and SFPassert to be interpreted on the same scale. SFPassert then is required to assert that the point denoted marks a decrease in quantity or degree from the contrasting point in the scale. The twofold semantics of “gau3…SFPassert” naturally marks the distinction of gau3 from other additive particles, including Cantonese dou1 ‘also’. On the other hand, to account for the obligatory licensing of gau3 by SFPassert, I will cast the idea under the Questions under Discussion (QUD) framework (Roberts 1996). The question, or goal of discourse in Stalnaker (1979)’s analysis, serves to set up a partition on the context set at the point of utterance, with each cell the set of worlds in which one complete answer to the question is true (cf. Groenendijk & Stokhof 1984, Roberts 1996). I will argue that the occurrence of gau3 needs to be licensed by an assertive sentence-final particle, as gau3 relies on the SFPassert to turn the proposition into an assertion. The proposition marked by “gau3…SFPassert” is uttered to provide a (partial or full) answer, with the first clause becoming the immediate question under discussion. The reference point given in the “gau3… SFPassert” proposition can be considered to give a focal presupposition that the last question or issue under discussion (QUD) denotes precisely that set of propositions which constitutes the focus semantic clause, and it is then answered by the interlocutor which has focus corresponds to the questioned item given by the speaker. As the speaker and the interlocutor can always add a question to QUD, which has not been explicitly raised, question accommodation is predicted. This can also explain why the scalar reading of gau3…SFPassert demonstrates flexibility towards scale selection.