When did Rembrandt get old? If you keep removing single grains of sand from a heap when is it no longer a heap? These questions and the many others like them will eventually lead us to the problem of vagueness. Timothy Williamson traces the history of the problem from discussions of the heap paradox in classical Greece to modern formal approaches, such as fuzzy logic. He shows the problems with views which have taken the position that standard logic and formal semantics do not apply to vague languages and defends the controversial realist view that vagueness is a kind of ignorance - there really is a grain of sand whose removal turns a heap into a non-heap, but we cannot know which one it is.