Deriving the distributivity potential of adjectives via measurement theory

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 measurement-theoretic 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