Abstract

Various ideals of purity are surveyed and discussed. These include the classical Aristotelian ideal, as well as certain neo-classical and contemporary ideals. The focus is on a type of purity ideal I call topical purity. This is purity which emphasizes a certain symmetry between the conceptual resources used to prove a theorem and those needed for the clarification of its content. The basic idea is that the resources of proof ought ideally to be restricted to those which determine its content.