Graham Harman asks (very nicely) why I think he’s wrong to think that there are no units in Badiou unless they are counted as such. I don’t think he is wrong to think that, but I think I differ with him about what “counting” means in this context.

I believe - and I may have got this completely wrong - that Graham thinks that “counting” in Badiou means the conceptual discrimination of unitary entities within a kind of miasma of primal undifferentiated stuff; of course this won’t do if you want to say that objects (or indeed actants) are what there are, since it implies that there’s something that there is prior to there being objects that is wholly miasmic and un-objectlike, and that objects are a just patterns projected onto or discerned within this miasma.

I take Badiou to be saying, however, that anything that there is, is in the manner of an operational result that determines its unity. This seems to me to be not strongly inconsistent with the view that objects are what there are, although Badiou’s ontology also allows there to be things that are not particularly intuitively object-like (like transfinite cardinals, or generic subsets). It might be inconsistent with the view that there is something about the way objects are that subtracts itself from any united front they might present. The strongest challenge I see coming to Badiou from Graham, and the one that I find most enthralling, is that Graham seems to accord powers of subtraction to things that don’t “think”, and thereby releases not existence but novelty from its anthropocentric prison.

Anyway, here’s my account of what I make of the theme of the “count-as-one” in Badiou. Corrections are welcome…

“Oneness”, Badiou says, is an operational result: to be a unit is to be the result of an operation. What kind of operation? Badiou calls it the “count-as-one”. The count-as-one determines a consistent structure: to be a unit is to be structured as a unit, and to be a structure is to consist as one. This consistency is transitive: a structure contains no inconsistent elements, but is the consistent being-at-once of units with their own consistent structure.

This might lead to an infinite regress, but for the fact that the count-as-one also makes a one of an empty structure, the void, which is the consistent being-at-once of no units. Operating on nothing consistent, on pure inconsistent multiplicity (which is not what there is, but is being “itself”), the count-as-one determines this non-consistency as the consistency of nothing, and having got hold of this absolutely minimal consistency proceeds to elaborate a structure out of it.

Badiou never says what effects the operation of the count-as-one. Is it us? Is it things themselves? Both “us” and “things themselves”, insofar as they consist, are themselves operational results; both are “too late” to be in a position to count, to determine the oneness of things. Badiou is emphatic that “the subject” is a result, not an originating or determining agent. We are left with an operation without an operating agent, an operation that “just happens” insofar as units exist as its results.

It goes, if anything, like this: a structured situation is presented - bang. This situation contains all sorts of things: fruit bowls, irrational numbers, small kindnesses, earthworms, ontologists, methane, mp3s, Down’s syndrome, lube, pulsars, rhizomes, the Ukraine. (Some people are better at making these sorts of lists than others). It isn’t a cognitive artifact; in fact, it may be too diverse for any cognitive apparatus to encompass.

In particular, a situation may be so diverse that no predicate can determine it. This is a crucial point. When the count-as-one is described, as it rather frequently is, as assembling units like “the set of all pornographic images in which one or more participants is wearing a ‘saucy French maid’ costume”, this gives the misleading impression that counting-as-one means assembling diverse entities according to some rule that enables them to be grouped together.

This rule is assumed to be what Badiou means by “the law of the count” for each situation, such that situations are differentiated from each other by the rules that aggregate them - and this in turn suggests that it is ultimately human beings that structure situations by categorizing and enumerating the contents of the world, making sense of a perplexingly multifarious phenomenal manifold by organizing it into manageable, conceptually homogeneous units. This is a misunderstanding.

Sitatuations are structured from the “bottom up”, by being woven from the void, not from the “top down”, by straining a heterogeneous collection of pre-existing phenomena (or a river of molten ore) through a predicate. “Consistency” in this context does not mean having some property in common, or being conceptually harmonious. If that was what it meant, then there could be no “generic subset of the situation”, because such a subset is also a consistent multiplicity, a set counted as one, and yet it is also wholly conceptually erratic and irregular (from the standpoint, at least, of everything the situation previously afforded in the way of knowledge).

The “law of the count” just is the particular structuring operation that determines the consistency of a situation, but this operation should be understood as a particular unfolding of the axiom system governing presentation, a particular way of arriving - from nothing consistent - at the particular consistency this situation presents.

My guess, knowing too little of Heidegger to do more than guess, is that the count-as-one occupies in a similar position in Badiou’s ontology to the Es Gibt in Heidegger. It would be just as misguided to ask “who’s counting” the count-as-one as it would be to ask “who’s giving” the Es Gibt. The count-as-one simply describes the manner in which beings are presented; specifically, it describes the manner in which well-mannered beings are presented, their conditions of well-formedness and well-foundedness.

(Events, Badiou’s “immanent exceptions”, are ill-mannered beings, beings which have forgotten or forsaken their manners: they mis-present themselves, come on too strong, come off badly, fall to pieces and leave a bit of a mess - which description puts me in mind of one of my favourite lines from The Hitchhiker’s Guide to the Galaxy: “You go to pieces so fast, people get hit by the shrapnel”).

Badiou links together presentation, consistency, structure and oneness in order to insist that beings, whatever we might or might not think of them, are units in the regular embrace of an axiom system - “ancestral” beings neither more nor less than any other being in any other situation. The point is not so much that the world is not a flux of molten ore, out of which stable entities emerge or onto which human observers project patterns based on their pragmatic requirements or epistemological habits, as that even that which presents itself as a flux of molten ore thereby presents itself as one - undoubtedly a very internally complex and conceptually intractable one, but a one nevertheless - and that everything that is presented in its presentation is also presented as a one, even - at the limits of its consistency - the nothing-consistent that is registered by the void. Even the event, which dares to go out of doors without its foundation on, is not simply an erratic splurge of randomness, but is rather the “ultra-one” of a kind of excess of structure.

Various people, notably Peter Hallward and Levi Bryant, have complained that Badiou’s set-theoretic ontology doesn’t do justice to the relationality of the world, a complaint that slightly baffles me as it certainly does accommodate such beings as pre-orders, equivalence relations, topological spaces, groups, lattices, sheaves…but it’s true that they are all given as second-order effects of presentation, particular kinds of unitary structure that the operation of the count can unfold. If the primacy of relationality is your thing, then this subordination of relation to composition will presumably not please you; but I’m not sure that I understand the wider stakes of the argument, which seems to lie at the heart of the differend between Badiou and Deleuze.

I suppose the same question comes to bear on the difference between Badiou and Graham Harman: can the ontological cageyness of Graham’s objects, their evasiveness from and inaccessibility to each other, be adequately representated as a facet of a unitary structure? Or is the object fundamentally bifid (or perfidious), sinking back within itself even as it presents itself, harbouring its own “immanent exception” as the secret law of its being?