Les structures bourbakistes: objets ou concepts épistémiques ?

Abstract

Two currents of thought play an important role in the contemporary philosophy of mathematics. Although structuralism is not a new idea, it continues to unfold in multiple directions ranging from mathematical practice to its ontological dimension and to be the object of studies, for example as regards the modalities of its genesis. The classical conception of historical epistemology has been broadly enriched recently and is also at the heart of debates that renew the philosophy of science well beyond its classical themes. However, its use in mathematics requires specific analyses because notions such as rigor, experience or ontology have a different meaning and historical weight in mathematics than in the natural sciences. The purpose of this article will be to put some of these debates into perspective by focusing on one of the most significant phenomena of mathematics in the twentieth century—the structuralism of Bourbaki. It will focus in particular on the potentialities of historical epistemology in an attempt to show that its tools enable us to enhance our understanding of some of the issues of structuralism. We will focus on two key notions in the work of Rheinberger, Daston and Hacking, namely epistemic objects and concepts.