Our ordinary assertions are often imprecise, insofar as the way we represent things as being only approximates how things are in the actual world. The phenomenon of assertoric imprecision raises a challenge to standard accounts of both the norm of assertion and the connection between semantics and the objects of assertion. After clarifying these problems in detail, I develop a framework for resolving them. Specifically, I argue that the phenomenon of assertoric imprecision motivates a rejection of the widely held belief that a semantic theory for a language associates a single semantic value with each of the simple and complex
expressions of that language, relative to the contexts in which they occur. Instead, I propose that we adopt a framework I call semantic pluralism.