Estruturalismo na Filosofia da Matemática e a teoria das categorias: Um debate entre Steve Awodey e Geofrey Hellman

Abstract

For some years now there has been an interesting debate concerning the ability of category theory to provide an autonomous conceptual framework for a structuralist approach to the philosophy of mathematics. The starting point of the discussion can be referred to Steve Awodey's (1996) paper, in which he suggests that category theory is capable of providing an accurate and flexible notion of 'structure' for the purposes of a structuralist philosophy. Geofrey Hellman (2003), the main proponent of an alternative form of mathematical structuralism (modal structuralism), examined the possibility of such a suggestion and came to a partially negative conclusion. Two main replicas, resulting from diametrically opposed philosophical perspectives, were suggested by Steve Awodey (2004) and Colin Maclarty (2004). We will expose this debate, as well as examine and defend Awodey's position with our own arguments.