I know, a third post tonight but I write so little these days that I have to get it down when I do. So a couple of weeks ago I was having a nice discussion with some good peeps on facebook and one of the participants said they don’t like Badiou because they think he’s exclusionary. Whatever the failings of Badiou the man might be, I don’t think this is a criticism that can really work for his ontology and political theory, i.e., he might not carry it through consistently, but the resources are there in the ontology to compellingly address this criticism. This requires a little discussion of history and mathematics.
Some History
Late 20th century Continental political theory was marked by the critical dissolution of all universal categories. The task of both postmodernism and deconstruction was to show the fraught nature of all cultural universals. This was generally done in one of two ways. One either showed that what claimed to be universal was secretly a veiled particularity hiding an unjust hegemonic exercise of power (what a mouthful!). For example, one would show that talk of human (a universal) rights that purported to apply to all humans beings was, in fact, a particularity. Through careful discourse or textual analysis, one would show that “human” really signifies “white, male, hetero, property owners” and that, therefore, “rights” don’t apply to all but are constructed to benefit the interests of that particularity.
Another strategy was to show the aporetic nature of all universals and categorizations. For example, you might show how the general category in fact relies on the borderline case whose identity cannot be decided in terms of whether or not it belongs or does not belong. This, for example, is what Derrida demonstrates in his brilliant essay “Parergon” in The Truth in Painting (my favorite Derrida, strangely). There he shows how the frame is the condition for the possibility of the artwork, while also being its condition of impossibility. Why? Because we can’t decide whether the frame belongs to the artwork or doesn’t. However, more substantially, Derrida shows that aesthetic theory itself is a frame for art whose status with respect to art is undecidable. In my view, Derridean deconstruction can be thought as the disciplined application of Goedel’s incompleteness theorems coupled with Freudo-Lacanian psychoanalytic theories of the symptom to case after case. The upshot of showing, in case after case, this constitutive incompleteness and undecidability is that classificatory terms– universals of a sort –are dissolved and no longer have their claim to authority. Everything becomes a platypus and Plato and Aristotle lose their shit.
Under this project, the political danger to be overcome– it seems –is the destructive effects of categorizations and their hierarchies. And in the aftermath of World War II, in all the wars surrounding nationalism, in the face of colonial horrors, in resistances to civil rights movements, why not? Dissolving categories and demonstrating their internal contamination went a long way towards ameliorating the horrors arising out of “identity”. No longer would identity categories be able to hold sway.
read on!
However, this absolutely necessary politics left us in a lurch. Having abandoned all “universals” or categories, having placed all of them, as it were, on “equal footing”, what next? We were left with an infinity of differences, yet can all of these differences peacefully co-exist in a happy happy daisy chain of harmony? Somehow strife and conflict seemed to persist in the world. What’s worse, we now found ourselves in a situation where to denounce anything advocated by a culture– female circumcision and foot binding, exile of homosexuals, etc –was seen as a form of violence and intolerance. In other words, we were left without a decision procedure.
A Little Math
It is here that I think Badiou’s discussion of sets is so important. Twentieth century Continental political thought is dominated by a critique of class logics. No, I’m not talking about Karl! When you hear “class” you shouldn’t think “Marx”, but should instead think Russell and Whitehead. In particular, you should think the Russell and Whitehead of Principia Mathematica. In mathematics and logic, a class is fundamentally different than a set.
Here’s the lowdown. Classes are defined intensionally (yes, the “s” is intentional). Roughly, the intenSion of a concept is the sense that defines that concept. Take a class like “ducks”. The class of ducks is composed of all ducks that exist past, present, and future. But what defines membership in that class? A shared collection of features that define the essence of “duckness”. That shared collection of features is the “intension” of the class. It is the conditions for membership in that category. 20th century Continental political theory occupied itself with contesting the soundness of intensions/essences pertaining to membership in a class: “white”, “female”, “human”, etc. It showed either that these essences/intensions were artificial and constructed, not natural, or that they couldn’t be coherently thought. In this regard, they again and again showed something like Russell’s paradox and Goedel’s incompleteness theorems at work in our attempts to think human beings in terms of class. And why not? Given that beings such as ourselves are self-reflexive and self-referential, it comes as no surprise that any attempt to pin us down in terms of essences, classes, or intentions is doomed from the start because we’re slippery critters and not just when wet.
Now sets, sets are something different. Sets are not defined intensionally, but extensionally. What does that mean? That means that a set is simply whatever entities happen to belong to it (it’s extension). Big woop. Well yeah, it is a big fucking deal. Why? Because a set doesn’t require a shared essence, intension, or set of features in order for elements of the set to be members of that set. You can have a set composed of an umbrella, a grilled cheese sandwich, the Adventure Book in the film Up, the idea of a Harry Potter, the moon, and a tissue and its still a set. These entities share nothing in common but all the same belong to that set. In other words, shared identity is not the condition for the possibility of the being of a set. Sets are Sunday gumbo in Louisiana… For those of you in the know, Sunday gumbo is made of whatever happens to be on hand.
There’s another interesting feature of sets as well. Because sets are defined extensionally by the elements that belong to them, the ordering relations between elements is of no consequence to the being of the set. The set {x, y, z} is identical to the set {y, z, x} because both sets have exactly the same extension: elements y, x, and z. So what! Well think about it. In class logics– and now I am talking Marx and politics and not Russell and Whitehead –ordering relations matter. Owners dominate workers (O > W), Whites dominate people of color (W > C), men dominate women (M > W), members of the dominant religion dominate those of marginal religions and the secular (R > S). There’s an order in which relations between elements have to occur and those relations are treated as being natural. A set theoretical logic, by contrast, reveals the an-archy of elements or how they can occur in any number of relations without any of those ordering relations being natural or inevitable. Where class logics are Platonist in the sense of the Republic, set logics are Lucretian. That’s important. Things can be shuffled.
A New Type of Politics
The brilliance of Badiou is that he basically accepts all of postmodernism and deconstruction. He even formalizes it or shows its structural underpinnings. Badiou’s ontology basically says “yeah, everything’s different and there are no identities, all identities are ‘performed’ or constructed– what he calls the ‘count-as-one’ –and each attempt to form a one or identity is doomed to aporia.” All class logics fail, not just for Marxist reasons but for logico-mathematico reasons as well. It’s a feature, not a glitch. But still, Badiou continues, given an aporia or an undecidable, you have to decide. Nothing prevents a decision with respect to what’s undecidable (and notice how closely he parallels Derrida in The Politics of Friendship here!). And if we should decide, what should we decide?
It seems to me that Badiou says we should decide on behalf of sets. The basic question is, the question where we begin to move beyond the negative moment of the late 20th century where we were only shown how things fail, is “how is a set politics possible?” or “what would a set politics look like?” I don’t know that Badiou is successful in answering these questions, but I do think he’s posed the right sort of question. A set politics would be a politics that does not require shared identity, subsumption under a class-universal, to have membership in that collective. The basic question of set politics, then, is that of how to form a collective out of the incommensurable without resorting to a shared intension? This, incidentally, why Badiou’s politics cannot be exclusionary. It’s already premised on the idea that terms don’t have a shared intension defining membership in the collective.
A New Universal
Those of us who grew up in the traditions of postmodernism and deconstruction immediately twitch when we hear the term “universal” because we think of classes or categorizations that share the same intension. We can call this concept of universality “closed universals”. Closed universals are such that in order for a term to be a member of the class or universal it has to have qualities x, y, and z. Those terms that lack features x, y, and z or that only have one or two of these features, are treated as deficient and are either given a subordinate status or ought to be destroyed or exiled. Yeah, that’s bad. We don’t want that sort of universality.
Badiou’s universals, by contrast, are open universals. Open universals are not based on a shared set of features or an essence, but are instead based on the open-ended and endless project of gathering elements within the collective. Where open universals are “prior” in the sense that the identity is already established, open universals are posterior in the sense that with each new case we have to decide whether or not it is an element and how the other elements have to be reconfigured once this element is included. Let’s take the example of Badiou’s discussions of love. He’s pretty heteronormative. So we come across a queer couple, say a trans woman with a cis bi guy. Are they in love? Seems so. Then they must be counted. But is counting them the end of it? Nope. Now that we’ve encountered this new case, all the prior elements have to be rethought and reconfigured in light of this new instance. Suddenly the Two of the couple in love is no longer a sexed two in the Lacanian sense, but is something else. Everything must be rethought. The universal here is a work, a praxis, a yet to come, rather than a prior-ity that’s already there.