Definition, Abstraction, Postulation, and Magic

Abstract

In recent work, Kit Fine proposes a new approach to the philosophy of mathematics, which he calls procedural postulationism: the postulates from which a mathematical theory is derived are imperatival, rather than indicative, in character. According to procedural postulationism, what is postulated in mathematics are not propositions true in a given mathematical domain, but rather procedures for the construction of that domain. Fine claims some very significant advantages for procedural postulationism over other approaches. This chapter raises some questions for the view and its promised advantages. One crucial set of questions concerns how exactly the commands of procedural postulationism are to be understood. And in particular, how literally are we to take talk of construction?