Abstract

This is a paper on a type of purity of proof I call topical purity. This is purity which, practically speaking, enforces 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. For some, this has been regarded as an epistemic ideal concerning the type of knowledge that proof ought to or at least might ideally provide. For others, including many working mathematicians, it has been largely a strategic or pragmatic ideal. Even these, however, see it (i.e. the ideal of purity) as serving generally epistemic ends.