Vague reference and approximating judgments

"Mount Everest" is a vague name. That is (on the account here defended) there are many portions of reality all of which have equal claims to serve as its referent. We propose a new account of such vagueness in terms of a theory of what we shall call granular partitions. We distinguish different kinds of crisp and non-crisp granular partitions and we describe the relations between them, concentrating especially on spatial examples. In addition, we describe the practice whereby subjects use systems of reference grids as a means for tempering the vagueness of their judgments - for example when they say that Libya straddles the Equator or that the meeting will take place between 2 and 3pm. We then demonstrate how the theory of reference partitions can yield a natural account of this practice, which is referred to in the literature as 'approximation'.