Monotonicity Revisited: Mass Nouns and Comparisons of Purity

Abstract

Abstract Comparatives with more plus mass noun, like John has more milk than Bill, are naturally analyzed as referencing measure functions, functions like volume or weight that map individuals to degrees. Although such measure functions vary with context as well as the choice of mass noun, there are well known grammatical limitations on this variation. In particular, Schwarzschild (2006) proposes that only monotonic measure functions can enter into the interpretation of comparatives with more plus mass noun. While this Monotonicity Constraint has strong empirical support, Bale & Barner (2009) have drawn attention to data that seemingly contradict it. For example, There is more gold in the ring than in the bracelet can be evaluated based on whether the ring is made from purer gold than the bracelet. This seems to suggest that comparatives with more plus mass noun can reference purity, yet purity is non-monotonic ( Schwarzschild 2006; Wellwood 2015). Building on Solt (2018) and Bale & Schwarz (2020), we show here that comparisons of purity can be credited to monotonic proportional measure functions, thereby reconciling Bale & Barner (2009)’s observation with the Monotonicity Constraint. We provide independent support for this proposal, establishing that reference to the relevant monotonic proportional measure functions, but not to purity, yields meanings that accurately track speakers’ truth value judgments. Our analysis commits us to the assumption that the main clause and the comparative clause can invoke different measure functions. We propose that this is made possible by Skolemization and binding. Specifically, we posit covert expressions denoting measure functions which contain variables bound by different expressions in the two clauses.