Keny Chatain (MIT)
Cumulativity from homogeneity
Sentences with two plural-referring expressions, like (1a), display the cumulative reading in (1b). For simple sentences like (1b), this reading can just follow from stipulations for what it means for "wear(X)(Y)" to be true, when X and Y refer to two pluralities. Problematically, more complex cumulative sentences, where one of the arguments is a quantifier like every or less than 3, as in (2) and (3), cannot be explained by stipulations on the meaning of the predicate. Their cumulative reading must be derived compositionally, as a number of works have argued (Schein 1996, Landman 2000, Haslinger and Schmitt 2018, inter alia).(1)
a. The llamas are wearing the hats
b. Cumulative reading:
Every llama is wearing a hat
Every hat is worn by a llama
(2) The llamas are wearing every hat. (≠ for every hat x, "the llamas are wearing x" is true)
(3) The llamas are wearing less than 5 hats. (≠ for less than 5 hats x, "the llamas are wearing x" is true)
In this talk, I show that "most" of the complex cumulative readings follow if plural-referring expressions are interpreted as lowest-scope existentials. The underlying existential meaning is independently argued for in Bar-Lev's (2018) theory of homogeneity and other cases of homogeneity similarly provide independent motivation that these existential meanings are low-scoping. However, the low-scoping existential theory that I propose does not account for all inferences drawn from a cumulative sentence. The inferences not accounted for happen to be relevance-sensitive and polarity-sensitive. As such, they are the ideal target of a treatment in terms of exhaustification. I thus propose a mechanism for strengthening, different from the one proposed in Bar-Lev (2018) but suited to cumulativity. The resulting theory covers a large empirical ground, including the "essential separation" sentences of Schein and asymmetries in cumulative reading. Yet, I will highlight a missed prediction, the "mereological sum cumulativity" sentences (Schein, 1993), which proves problematic to other accounts as well.