Split semantics for non-monotonic quantifiers in than-clauses

Linmin Zhang, NYU Shanghai


Comparatives containing non-monotonic quantifiers within than-clauses pose non-trivial challenges for compositional semantics (e.g., Balloon A is higher than exactly two of the others are, see, e.g., Schwarzschild 2008). Following Bumford (2017a)’s split treatment for definiteness (see also Brasoveanu 2013), this paper argues for a two-stage semantic derivation for these comparatives: a bottom-up (from local to global) composition followed by a delayed top-down (from global to local) evaluation. More specifically, I propose that the semantic contribution of both these embedded non-monotonic quantifiers and the embedding morpheme than is twofold: first, they each introduce a discourse referent (i.e., some individual or degree-related value) during the stage of bottom-up composition; then, they simultaneously impose tests of maximality (and cardinality) during the stage of top-down evaluation. The current account further suggests that basically, the semantics of comparatives is similar to that of cumulative-reading sentences (e.g., exactly three boys saw exactly five movies), both involving simultaneous restrictions but no scope-taking among cardinalities or degree-related values. I show that this has profound implications for theories of comparatives.