Representation and inconsistent multiplicity : Cantorʼs roots in Alain Badiou and Cornelius Castoriadis.

Philosophy attributes to mathematics the exclusive capacity of constructing pure knowledge – i.e. the thinking (of ideas) – reserving for itself the modes of its representation. In the first part of the article, we briefly trace the reverberations of representation stemming from mathematics in the thought from Descartes, Kant to Heidegger, and investigate how they unfold and influence the contemporary philosophies of Alain Badiou and Cornelius Castoriadis. Although the two share a common ontological root in Cantor’s naïve set theory, this aspect of their thought remains relatively unrelated. In the second part, we closely examine the respective usage of the notion of representation and its transmutation to a mathematical concept of inconsistent multiplicity, consequently arguing for a rare, but particularly important point of convergence of the two thinkers. It is this contradictory inconsistent multiplicity that represents an abstract concept for thinking Magmas (Castoriadis) or the Absolute (Badiou) – both conceiving it as the place in which Truth(s) are either ex-nihilo created or eternally residing.