Mark Gawron
580 California St., Suite 400
San Francisco, CA, 94104
Unifying degree-based and mereological accounts of gradual change
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Abstract
Following Kennedy and Levin (2001), I will use the term predicate of gradual change to mean almost all accomplishments and all activities, excluding a class of cases describing abrupt transitions like those in (1), discussed in Rothstein (2004): One can separate work on the aspectual nature of gradual change into two broad classes, mereological and degree-based, exemplified in papers like Krifka (1989) and Hay et al. (1999). The degree-based work seeks to explain aspectual properties in terms of degree scales with the same structure as those of adjectives; the mereological work assumes a different, arguably more general, partial order structure, which is also taken to be play a role in the semantics of mass terms. This paper argues that both kinds of structure are necessary for verbs of gradual change and proposes a unified formulation, as well as a diagnostic for separating the cases. I will argue that for a class of problematic predicates lying in a boundary region, and for processes like deverbal adjective creation, a coercion operation mapping from one structure to the other is also necessary. A mereological account is most naturally motivated through the examples of incremental themes (Dowty 1991). The unifying property of these verbs was succinctly stated in Krifka (1989): If an incremental theme verb expresses a relation R and R holds in event e and Θ(e) is the incremental theme, then in any sub-event of e in which R holds a portion or part of Θ(e) stands in the relation R. Incremental theme predicates include eat, learn, write, mow, perform, and read. Degree achievements, in contrast, provide the point of departure for a degree based analysis (Hay et al. 1999, Zucchi 1998, Kennedy and McNally 1999, Kratzer 2000), because they offer a rich stock of cases in which telicity is determined with no reference at all to parts. For example, a suitcase closing (Filip 1999) does not progress by having more and more of the suitcase closed, but by having the suitcase more and more closed. Hay et al. (1999) (HKL) explicitly argue for extending a degree account to the class of incremental theme verbs, suggesting for example, that for a verb like eat, telicity is directly linked to the size or volume of the theme and Kennedy and Levin (2001) (KL) argue for extending it to all verbs of gradual change. They point out, correctly, that while a degree-based acount like theirs can be formulated to explain the aspectual properties Following KL, I shall assume that predicates of gradual change are quantizable properties of events. That is, I assume every degreeable verb α has a change function ∆ e for which it is sensible to write (2). Following HKL, I will refer to q as the difference argument. Mereological accounts may be unified with degree accounts by assuming change functions for them as well, with parts ordered by the part-whole relation as their range. Somewhat surprisingly, the HKL analysis is then completely compatible with a mereological account. The key to their analysis is the INCREASE operator, which requires a domain for which a notion of difference is coherent. I will show that what Krifka calls the Remainder Principle, often found among mereological axiomatizations (Krifka 1998), is sufficient to define differences: The Remainder Principle requires that for any two ordered elements, x < y, there exists a remainder r which does not overlap x and which can be summed with x to give y. In a word, r is the difference between x and y. For any partially ordered domain with differences, quantizing those difference arguments will allow the definition of INCREASE; the entire HKL account of telicity follows.
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