Deriving the distributivity potential of adjectives via measurement theory

Abstract

Abstract. The boxes are heavy can convey that each box is heavy (distributive), or that some individually light boxes qualify as heavy when lifted together (nondistributive; Schwarzschild 1996, Schwarzschild 2011). In contrast, the boxes are fragile generally requires each box to be fragile (distributive). Which adjectives behave like heavy or like fragile, and why? This paper proposes a measurementtheoretic account. For a gradable adjective to be understood nondistributively, I argue that a⊕b must exceed a and b along the scale associated with the adjective. That way, the contextual standard θ for what 'counts as' (adjective) in the context can be set in such a way that the composite object a⊕b surpasses the contextual standard θ while a and b individually fall short of it -a nondistributive understanding, in that the adjective is true of a⊕b together but not of a or b individually. This ordering is possible for heavy but not fragile, deriving their differences. More generally, researchers agree that an adjective's potential for distributivity depends on what we know about the property it describes. Making that idea more explanatory, this paper articulates which features of the property described by the adjective matter for distributivity and why.

Distributivity in Formal Semantics

“…These connections are also helpful in other areas. For example, Rothstein (2010) and Schwarzschild (2011) discuss distributivity in adjectives from a semantic point of view, while Scontras & Goodman (2017) and Glass (2018a) exploit the potential of pragmatic reasoning in determining whether a given adjectival predicate is interpreted as distributive. Other subfields in which distributivity has been studied include acquisition (e.g., Syrett & Musolino 2013, de Koster et al 2017, lexical semantics (e.g., Glass 2018b), and processing (e.g., Frazier et al 1999).…”

Revealing abstract semantic mechanisms through priming: The distributive/collective contrast

“…1 There is a question in plural semantics of whether or not all gradable adjectives give rise to the collective/distributive ambiguity. Some gradable adjectives have been traditionally considered to be "stubbornly-distributive" in that they do not seem to admit collective interpretations (Schwarzschild, 1996(Schwarzschild, , 2011Syrett, 2015;Glass, 2018). Recent evidence, however, has challenged this hypothesis (Scontras & Goodman, 2017).…”