Regardless of what one thinks about the specific claims of Badiou’s ontology, his use of set theory, his account of the event and the subject, his programmatic tone, and so on, it is my view that Badiou is nonetheless of tremendous value insofar as he clearly formulates the central ontological thesis that so much thought in our age is grappling with in an unconscious or non-explicit fashion. This thesis is formulated in non-set theoretical terms in the first meditation of Being and Event. There Badiou observes that,

Since its Parmenidean organization, ontology has built the portico of its ruined temple out of the following experience: what presents itself is essentially multiple; what presents itself is essentially one. The reciprocity of the one and being is certainly the inaugural axiom of philosophy– Leibniz’s formulation is excellent; ‘What is not a being is not a being‘– yet it is also its impasse; an impasse in which the revoling doors of Plato’s Paremenides introduce us to the singular joy of never seeing the moment of conclusion arrive. For if being is one, then one must posit that what is not one, the multiple, is not. But this is unacceptable for thought, because what is present is multiple and one cannot see how there could be an access to being outside all presentation. If presentation is not, does it still make sense to designate what presents (itself) as being? On the other hand, if presentation is, then the multiple necessarily is. It follows that being is no longer reciprocal with the one and thus it is no longer necessary to consider as one what presents itself, inasmuch as it is. This conclusion is equally unacceptable to thought because presentation is only this multiple inasmuch as what it presents can be counted as one; and so on. (23)

This deadlock can be discerned everywhere in the history of philosophy, if only one has eyes to see it. It appears first in Parmenides, where the world of entities or beings disappears insofar as being is and non-being is not, leading necessarily to the conclusion that other beings must not be as we would then have to say what this being is not, thereby reintroducing non-being back into being. Further, it is found in every dialectic of the whole and its parts, whether we’re speaking of Plotinus, Spinoza and Whitehead, or the object as a whole composed of distinct qualitative parts, as discussed by Hegel in his account of perception and understanding in The Phenomenology of Spirit, or Husserl in his phenomenological analyses of how a being can both be composed of profiles and horizons and be one.

It would thus appear that treating being and the One as reciprocal and interdependent predicates necessarily leads to irresolvable aporia. Consequently, Badiou argues that we must make a decision to de-suture being from the One, thinking it instead as multiplicity qua multiplicity:

This decision can take no other form than the following: the one is not. It is not a question, however, of abandoning the principle Lacan assigned to the symbolic; that there is Oneness. Everything turns on mastering the gap between the presupposition (that must be rejected) of a being of the one and the thesis of its ‘there is’. What could there be, which is not? (23)

The consequence that follows from this is that being is to be conceived as pure multiplicity and that the one is to be seen as a result or an effect. As Badiou puts it,

What has to be declared is that the one, which is not, solely exists as operation. In other words: there is no one, only the count-as-one. The one being an operation, is never a presentation. It should be taken quite seriously that the ‘one’ is a number… Does this mean that being is not multiple either? Strictly speaking, yes, because being is only multiple inasmuch as it occurs in presentation.

In sum: the multiple is the regime of presentation; the one, in respect to presentation, is an operational result; being is what presents (itself). On this basis, being is neither one (because only presentation itself is pretinant to the count-as-one), nor multiple (because the multiple is solely the regime of presentation).

Let us fix the terminology: I term situation any presented multiplicity. Granted the effectiveness of the presentation, a situation is the place of taking-place, whatever the terms of the multiplicity in question. Every situation admits its own particular operator of the count-as-one. This is the most general definition of a structure; it is what prescribes, for a presented multiple, the regime of its count-as-one.

A structure allows number to occur within the presented multiple. Does this mean that the multiple, as a figure of presentation, is not ‘yet’ a number? One must not forget that every situation is structured. The multiple is retroactively legible therein as anterior to the one, insofar as the count-as-one is always a result. The fact that the one is an operation allows us to say that the domain of the operation is not one (for the one is not), and that therefore this domain is multiple; since, within presentation, what is not one is necessarily multiple. In other words, the count-as-one (the structure) installs the universal pertinence of the one/multiple couple for any situation. (24)

I quote this passage in full because it so nicely elaborates Badiou’s basic argument and the basic structure of his metaphysics. When speaking of being qua being we are invited to think pure multiplicity without any other predicates. This holds regardless of whether we are speaking about objects treated as unities or ones, systems, the universe, and so on. That is, it holds for the predicates of unity, wholeness, and identity.

…[I]f an ontology is possible, that is, a presentation of presentation, then it is the situation of the pure multiple, of the multiple ‘in-itself’. To be more exact; ontology can be solely the theory of inconsistent multiplicities as such. ‘As such’ means that what is presented in the ontological situation is the multiple without any other predicate than its multiplicity. Ontology, insofar as it exists, must necessarily be the science of the multiple qua multiple. (28)

If these multiplicities must be conceived as inconsistent multiplicities, then this is because being, prior to the operation of the count-as-one, is without structure or any ordering operations. It is only through the operations of the count-as-one that being takes on structure and comes to consist of consistent multiplicities. Yet this pure multiplicity can only be grasped retroactively, for experience presents us with nothing but structured presentations– objects, things, happenings, persons, animals, and so on –that are “counted-as-one”. That is, multiplicity is thinkable without being presentable, and inconsistent multiplicity is not a phenomenological datum or a truth of experience, but an axiom of thought from which we begin. Just as Parmenides begins from the axiom that being is one and proceeds from there (and is followed in this by much of the philosophical tradition), Badiou asks us to begin from the premise that being is inconsistent multiplicity.

I am happy to follow Badiou in this axiom as I believe it is the central axiom of that episteme characterizing contemporary thought. Whether we are speaking of Heideggerian ontological difference, Derridean differance and dissemination, Deleuzian different/ciation, dynamic systems theory, Foucaultian archaeology and genealogy, or Lyotardian discourse analysis and differends, and so on, the thought of our time begins with the premise that being is difference or multiplicity, or that the one (whether in the form of wholes, substances, or entities) is an effect or result. The advantage of Badiou’s formulation is that it 1) clearly articulates the aporia that leads to this move in the most abstract and formal terms possible (we do not get caught up in the intricacies of careful deconstructive analysis of texts or in an analysis of lived experience; not that this is without merit), and 2) it indicates the problem posed to thought by this gesture: How is it possible to produce a consistent multiplicity out of inconsistent multiplicity? Or, put differently, “how does being one?”– here “to one” must be treated as a verb; one might even speaking of “one-ing”. Again, the advantage of Badiou is the sheer abstractness– I would call it concreteness –with which he poses this question.

My aim is not to follow Badiou in answering this question. He seems to give very little in the way of a satisfactory answer to this particular question as he is more intent on showing how being can be thought as pure inconsistent multiplicity via the resources of set theory, and clearing a space where that which is not-being-qua-being, or the event, might be articulated. While it is certainly true that his most recent work, Logiques des mondes, is designed to account for being-there or appearing (the “one-ing” of being), Badiou’s discussion of Dasein here strikes me as disappointing as it is primarily descriptive of consistent multiplicities, without giving us an account of how the operations that produce Dasein operate.

It is clear that the operations operating in the production of beings pertually withdraw from view, as we are always left with the result of these operations and are never before the operations themselves. It is in this sense that the world of situations presents us with a sort of transcendental illusion, in that we take the results or effects to be being itself, rather than discerning them as products of operations from pure multiplicity. As such, we continuously fall into various versions of substance metaphysics. But what are these curious operators that preside over the count-as-one? What is the operation by which one-ing takes place? Badiou appears to follow Lacan when he claims that one-ing is the work of the symbolic. This point seems confirmed in Logiques des mondes when Badiou declares that Il n’y a que des corps et des langages, there are only bodies and languages. Yet this solution strikes me as unacceptable as there are many consistent multiplicities that are not simply cultural or symbolic. Moreover, the operators of the count-as-one cannot be minds or subjects, as there are consistent multiplicities or beings that do not depend on minds. So what then are these mysterious operators? Can we conceive of operations without operators (as I think we should, lest we fall back into humanism)? And is the gulf between inconsistent multiplicity and consistent multiplicity too great to ever explain how it is possible for pure multiplicity to produce anything like an organized situation? Is it enough to restrict the predicates of being to pure multiplicity, or must we hypothesize additional predicates to account for one-ing? These are the questions I am asking. I am indebted to Badiou for having provided a clear framework for posing them. But I am not at all sure of the solutions that he proposes, which is precisely why I frolick so easily with Deleuze and others, without being very perturbed by their various disputes with Badiou.