Cumulativity from Homogeneity

Abstract

Since Schein (1996), cumulative readings of quantifiers have often motivated a departure from standard assumptions about composition. This dissertation proposes a new theory of these cumulative readings that connects them to the phenomenon of homogeneity. Specifically, taking inspiration from Bar-Lev (2018), I argue that predicates sometimes have weak existential meanings, which are revealed when placed under negation. The stronger meaning observed in positive sentences are the result of a procedure of exhaustification. By recognizing predicates' underlying weak meanings and their liability to strengthening, cumulative reading of quantifiers can be accounted for by maintaining relatively standard assumptions about composition. This analysis predicts a range of intricate cases, including Schein's famous video-game examples. It also predicts the truth-conditions of negative cumulative sentences and asymmetries in the availability of cumulative readings of quantifiers.