Imperfect Perception and Vagueness Giri Parameswaran∗& Timothy Lambie-Hansony March 27, 2016 VERY PRELIMINARY & INCOMPLETE Abstract This paper investigates the epistemic approach to vagueness that the source of vagueness is the speaker's inability to perfectly perceive the world. We study a standard communication game and show that imperfect perception is insucient to render vague communication about the world as perceived by the sender. However, if the receiver interprets the sender's message as a true statement about the world, rather than merely how it appears to the sender, then language becomes vague. We show that this vagueness is characterized by probability distributions that describe the degree to which a statement is likely to be true. Hence, we provide micro-foundations for truth- degree functions as an equilibrium consequence of the sender's perception technology and the optimal, non-vague language in the perceived world thereby unifying the epistemic and truth-degree approaches to vagueness. ∗Department of Economics, Haverford College, Haverford, PA 19041. Email:
[email protected] yDepartment of Economics, Haverford College, Haverford, PA 19041. Email:
[email protected] 1 1 Introduction Language is vague when the receiver cannot be certain of which `states' the sender of a message seeks to invoke. For example, although we routinely describe people or things as tall, heavy, fast, and so on, we would, in most cases, struggle to identify the boundary between tall and short, or between fast and slow. Indeed, vagueness is often associated with a `blurring of the boundaries' between the meanings of words. Many theories seek to explain the nature and source of vagueness.