Pictured above is a pile of sand. One grain of sand doesn't constitute a pile, nor do two grains...so how many grains does it take to make a pile? The task of designing a theory of meaning for vague predicates like "pile" has proved to be surprisingly difficult. (Image courtesy of Ian Comley.)
The objective of the graduate-level course is to give people a sense of what "accounting for vagueness" is all about, why it's hard, and why it's important. This will involve surveying some prominent accounts of vagueness.