Modality, Weights and Inconsistent Premise Sets

Abstract

This paper investigates two types of data that appear to motivate complicating the semantics for weak necessity modals. I argue that these data can be captured using the same conceptual resources within a conservative extension of the standard quantificational semantics. The resulting analysis illuminates previously puzzling and underappreciated semantic and pragmatic properties of weak and strong necessity modals, and clarifies the special role that expressions of weak necessity play in conversation, deliberation, and planning.