On The Origins of Vagueness in Natural Language

Abstract: Bert Lipman has famously argued that vague languages cannot be game-theoretically optimal. This creates a puzzle: if vagueness is of no use to language users, then why is it so prevalent in natural language? In this talk, we use signaling games (inspired by David Lewis' "Convention") to address this puzzle. In extant work involving signaling games, vagueness is modeled as a mixed (i.e., non-deterministic) signaling strategy. We argue that this modeling criterion is inadequate and instead propose modeling vagueness as the presence of a region in which signaling is (almost) absent, located between two regions of signaling. We show that on this understanding, vague languages can be optimal. We then introduce a new type of signaling game in which agents have to learn a signaling strategy from a limited sample of usage data of a previous generation. We observe that with various common learning algorithms, vagueness is created and remains stable for many generations. A natural conclusion to draw is that vagueness arises when speakers have to coordinate their signaling strategies on the basis of limited data in large state spaces.