Universal quantification as iterated conjunction

Dylan Bumford, New York University


I analyze distributive universal quantifiers like ‘each’ and ‘every’ in terms of iterated dynamic update. I argue that this minor adjustment to standard dynamic frameworks has at least two empirical advantages. First, because information flows forward through the universal computation, anaphoric elements can be interpreted “quantifier-internally” (Brasoveanu 2011). Second, because dynamic conjunction is just relation composition over input and output structures, the emerging representations are in a sort of disjunctive normal form that facilitates “functional” readings of indefinites. Following Solomon (2011), I suggest that these two phenomena are closely related, and argue that we should see them both as side effects of incremental update.