Abstract
Despite the differences concerning the relative syntacticization of the relevant domain of restriction and focus effects in D-quantification and A-quantification, as suggested in Hajićová et al. (1998), what D-quantifiers like “most” and A-quantifiers like “always” have in common is that at some semantic level, they can be described as operators taking two set-type arguments and participating in tripartite structures. As mentioned in Chap. 2, Partee’s (1987, 1991) twofold classification of D- and A-quantification further distinguishes different roles played by syntax and focus in determining the mappings of these quantifiers to their tripartite structures. The distinction between A- and D-quantifiers thus represents different mechanisms of how surface syntax is mapped to semantic representation. In the case of D-quantification, syntax makes it visible which constituent is selected and mapped to the restrictor and the matrix: the determiner (D) as the operator, the common noun phrase (CNP), the restrictor and the verb phrase (VP), the matrix. Focus influences neither the selection nor the mapping of D-quantifiers and the insensitivity of D-quantifiers toward focus demonstrates their highly syntacticized nature, with focus failing to override the relevant syntactic partition. In contrast, A-quantification is less syntacticized, with grammatical relations or syntax not playing the determining role, except in some explicitly structured cases where there exists an explicit operator or marking to indicate a division into the restrictor and the matrix, e.g., if-clause. In simple clauses, it is obvious that a positional variability in focus will affect the partition of the tripartite structure. Focal mapping will be triggered, with the non-focused part selected to be the domain of quantification and the focus, mapped to the matrix. In other words, focus influences both the selection and mapping of A-quantifiers, with focal mapping overriding syntactic partition.
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- 1.
Throughout this book I have only taken contrastive focus into account, and it is represented in the form of phonologically stressed elements or syntactically contrasting items. It has been suggested that the presence of the copula hai ‘be’, a kind of established focus construction in Cantonese or Chinese (cf. M&Y; Liu and Xu 1998, among others), should be used. However, constructions of this type tend to be used for expressing identificational focus and as pointed out by Kiss (1998), identificational focus is characterized by the features of [presupposed], [identification] and [exhaustiveness]. Thus, identificational focus exhaustively identifies the elements of a presupposed set and as a consequence, the focused element is always interpreted in terms of exhaustiveness or exclusiveness. In order to avoid the confusion of whether the exclusive reading comes from the focus being an identificational one or comes from the focal mapping triggered, I have adhered to the prosodic or phonologically stressed focus, to make it clear that it is focal mapping which gives rise to the exclusive reading. This is particularly obvious in the case of -saai. As compared with the original mapping triggered by the lexical semantics of -saai, there is an additional exclusive reading on the focused constituent and this can only be coming from the focal mapping triggered, which represents a kind of mapping opposite to that triggered by the lexical semantics of -saai.
- 2.
One may question that whether -saai is a maximality operator, since assuming -saai as a maximality operator somehow can account for its “all” reading and its scalar reading when associating with gradable adjectival predicates. However, despite that both universal quantifiers and maximality operators can guarantee a maximal reading of its restrictive domain, assuming -saai as a maximality operator is in fact not plausible, for the following reasons. Analyzing -saai as a maximality operator would fail to explain a focus-background tripartite partition in some cases, since when the item selected by the Quantification Accessibility Hierarchy is in focus, what triggers would be focal mapping. If -saai were assumed to be a maximality operator, such a tripartite partition would not be possible. Moreover, an important underlying reason why we cannot assume -saai to be a maximality operator is that maximality operators are unary operators taking a sole argument, hence no tripartite structure partition. Unlike maximality operators, a universal quantifier is a dyadic operator, which matches situations denoted in the restrictive domain with those in the matrix. For references to maximality operators, readers are referred to Giannakidou and Cheng (2006), Cheng (2008) and Xiang (2008), etc.
- 3.
- 4.
The modal wui ‘will’ is added here and in subsequent sentences to ensure that when -maai associates with the focused subject, the scope taken is a TP scope. The association of -maai with the focused subject then has to be accounted for by an expansion of scope to TP, but not VP/vP-internal subject hypothesis.
- 5.
A preliminary version of the two-process approach to quantification has been discussed in Lee and Pan (2011). Lee and Pan discussed -saai only, but have brought up the issue whether quantification involves one step or two steps.
- 6.
Based on her analysis of St’át’imcets quantifiers, Matthewson proposes that the D combines with the NP predicate to create an entity-denoting element of type e first, and the created object is then taken as an argument by the Q-Det of type < e, << e, t>, t >> to yield a generalized quantifier of the desired type <<e, t>, t>. Matthewson’s proposal has later been counter-argued by Giannakidou (2004). We do not intend to compare the two analyses and Matthewson’s analysis of St’át’imcets is included here merely to show that previous analyses do recognize a parametric variation between the selection of NP and DP in D-quantification.
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Lee, P.Pl. (2012). The Role of Focus in Affixal Quantification – Does Quantification in Natural Language Involve One Process or Two?. In: Cantonese Particles and Affixal Quantification. Studies in Natural Language and Linguistic Theory, vol 87. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4387-8_5
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