Two Paths to Infinite Thought: Alain Badiou and Jacques Derrida on the Question of the Whole

This essay defends an idea that is no longer fashionable: that there is a whole. The motivation for a defense of this notion has nothing to do with intellectual conservatism or a penchant for Hegel. Rather, what we hope to establish is a second path into what Alain Badiou has called the ‘Cantorian Revolution’. In order to open this path we undertake a three-fold task. First, we deconstruct Badiou’s onto-logical project by isolating the suppressed significance of Ernst Zermelo. This point allows us to recover a Cantorian possibility for addressing the infinite as an inconsistent whole. Second, we turn to work by the logician Graham Priest in order to remove the absurdity of discussing true contradictions. Finally, we return to Jacques Derrida’s early work on Husserl in order to chart a phenomenological path to an affirmation of an inconsistent whole. We close, then, with the implications for contemporary philosophy.