Badiou’s ‘Being and Event’ and the Mathematics of Set Theory by Burhanuddin Baki (review)

One of the distinctive features of Alain Badiou’s philosophy is his equation of mathematics and ontology. Badiou’s claim in his massive Being and Event that ontology is mathematics is of course controversial. Fairly evaluating the claim’s sense and working through its details and consequences presents problems for many readers, however, since it involves at least some working knowledge of higher mathematics, specifically set theory. Although Badiou himself provides the careful reader of his tome with enough information to follow the various lines of thought explored therein, it is often not enough to appreciate the scope of the work. Burhanuddin Baki’s book is thus a welcome addition to the secondary literature on Badiou. Most of the existing literature adequately describes how Badiou uses mathematics qua ontology and provides basic, accessible overviews of the key set-theoretical concepts that structure his thought. Baki goes a step further; whereas most of Badiou’s key interpreters approach the mathematical conditioning of Badiou’s ontology from the perspective of philosophy, Baki reads Being and Event from the perspective of contemporary set theory. That is, Baki follows Badiou’s own suggestion that the ontologist must also be a mathematician. Unlike many readers, Baki has substantial background in mathematics, so he is well positioned to take up the role. What results is not another description of Badiou’s system but a critical reconstruction of it, done from the side of its mathematical conditioning. This is important since, as Baki himself notes, Badiou’s own use of set-theoretical axioms, concepts, and functions is not straightforward but idiosyncratic, often obscure, and on the whole somewhat limited. Baki’s reconstruction clarifies the decisions Badiou makes in the mathematics he deploys, providing extended technical discussions, crucial background information and context, and, when necessary, criticism of Badiou’s presentation. Over eight chapters, Baki deals with the major themes of Being and Event, largely by mirroring Badiou’s own organization. Thus, like Badiou himself, Baki’s discussion and focus lead up to and conclude with the theory of the event and the subject, with a strong emphasis on its mathematical conditioning. Although he does not really forge any new paths in or from Badiou’s ontology, Baki’s reconstruction is compelling and, perhaps more importantly, useful. His discussion opens up some of the more opaque aspects of the mathematical grounding of Badiou’s system, allowing readers not well versed in set theory or contemporary mathematics more generally to engage the latter at a deeper level. Chapter 7 on forcing and generic sets is especially helpful, since these most crucial elements of Badiou’s ontology and philosophy are among the most difficult to understand. Nevertheless, Baki’s book is not for the novice reader. The discussion is often technical and assumes a fair amount of knowledge of Being and Event and the set-theoretical apparatus woven through it. Pointing that out is not so much a criticism as an acknowledgement of the reality that attends focusing on and working through the mathematics that underpin Badiou’s system. Those who do have that knowledge, however, should appreciate Baki’s contribution.