Alain Badiou is an anomaly. What he has attempted has all the allure of the obviously impossible. That's the fascination of the thing. Judge it retrograde or eminently contemporary, aberrant or a stroke of genius, but take it squarely for what it is: the painstaking effort on the part of an Althusserian Marxist, longtime Maoist, and unanalyzed disciple of Lacan to quit the confines that several generations of "limit-makers" have erected around philosophical practice.
Wittgenstein's fragmentary sophistics is merely a symptom. Revolutionary political theorizing, the various positivisms, and the vast textualization of the world all share the same restrictive modus operandi of suturing philosophy to some other, seemingly stronger, extrinsic body of thought. What's more, Jacques Derrida's interminable perambulations inside Western metaphysics involve a swap of one kind of system for another: the compelling demonstrative logic of systematic philosophy for the latent tissue of relations embedded in language. With the revelation of writing as the long-repressed factor--and its ultimate fetishization--the issue of demonstrability has curiously vanished from the horizon. Odd, wouldn't you say, in a century thoroughly dominated by mathematization? Badiou emerges right here, with a singular question: how do we advance, proceed, reinsert ourselves into a pattern of succession, the "plus-one" established by taking "one step more"?
In a word, Badiou has founded a philosophy. Take "founded" in the full philosophical sense. And that philosophy is rigorously systematic. Take "systematic" in the full philosophical sense. What does it require to reanimate a dead tradition? A single consolidating intuition permitting the kind of strategic move, in its elegance and simplicity, most often associated with a game of chess. It goes like this: ontology is mathematics. DON'T RECOIL. NOT YET. Some people don't know what ontology is, and even those who do, don't. (For confirmation, read the opening pages of Heidegger's Being and Time.) The word "Being" has always resonated with a mysterious attribution of some extra added value to "what simply is," and its science has remained philosophy's foremost red herring. By slipping mathematics into that eerie slot, Badiou snaps the file shut with assurance of ontology's thorough rationality. "What is" is pure multiplicity. As for what can be said about it, the mathematicians are still at work.
In his massive L'Etre et l'evenement (Being and the event), Badiou makes mathematical set theory the reader's guide to some 2,500 years of problems raised by ontology. From the axioms of set theory he not only recapitulates the history of philosophy but derives all the concepts of his system. DON'T RECOIL. NOT EVEN NOW: his prose is so tight and lucid that even in your relative mathematical illiteracy you'll be surprised to discover, like Plato's Meno, that you already knew how to draw the inferences. And in those inferences the stakes are revealed. What were the devastating criticisms forever leveled against systematic philosophy? That the system was invented and arbitrary, its propositions unverifiable. In Badiou's reformulation of philosophy as a contemporary systematics, only mathematics, the unassailable archetype of demonstrability, intelligibility, and transmissibility, can offer sufficient authority, sufficient legitimacy--not as a model but as the very armature of the system itself.
Badiou's philosophy, however, is not a philosophy of mathematics. For him there is no such thing. Nor is it about the world or consciousness or knowledge. He calls it a philosophy of time. Forget teleologies and historical determinisms, the Kantian a priori, Husserl's time consciousness, Bergson's duration. Think of it rather, to risk a neologism, as a neology. Set theory's closing chapter, the generic set, the set with no ascertainable identifying characteristic, the "set without qualities," provides Badiou with a unique and provocative prototype for theorizing the emergence of the new. …