Badiou’s Logics: Math, Metaphor, and (Almost) Everything

Mathematics plays a central role in the philosophical system of Alain Badiou. The aim of this essay is to situate this appeal to mathematics in the broader context of his work, including its literary and political elements. Alain Badiou’s appeal to mathematics is a process, a system that has been developing for close to half a century. Although there is an overarching mathematical theme, the system is too expansive and variable to admit a simple description. I focus here on a few questions that relate to the role of mathematics in his later work, as presented in the Logics of Worlds [9] and in some of the relevant but less formal initial meditations. I felt I had to let the text unfold or digress, following the multiple logics of its subject, toward extra-mathematical considerations—literary, artistic, political—from which Badiou’s work cannot be fully separated. In the first part [29] of this incomplete record of my attempts to understand the position and significance of mathematics in Badiou’s philosophy, questions arose about the choice of the formalization that acts as the mathematical framework of Being and Event [5]. At that stage of the evolution of Badiou’s work, ontology is identified with set theory, which in turn is presented in the ZFC axiomatization, although other choices are possible. The question of principles guiding this and other selections—of the axiomatic system and “foundational” backdrop or framework, mathematical and non-mathematical examples, terminology and style—is not the only one that could be discussed. Highlighting this particular set of problems also represents a choice, a decision (this time on my part); other questions necJournal of Humanistic Mathematics Vol 7, No 1, January 2017