I provide an overview of four current theories of scalar implicature: the pragmatic (or Gricean), the lexical, a combined pragmatic + lexical, and the grammatical theory. The empirical focus are global and local, but also intermediate implicatures. I argue that the grammatical theory is conceptually less well motivated than even the pragmatic + lexical theory, and that the grammatical theory therefore requires strong empirical support. I then focus on a novel empirical phenomenon – intermediate implicatures – which provides empirical support for the grammatical theory. I conclude that it seems necessary to adopt the grammatical theory.