For this series of posts, I thought I would post in several installations a paper I wrote for a Badiou seminar I took this semester with John Protevi. Reading Being and Event was a real eye-opener for me. The depth and profundity of Badiou’s philosophy stunned me out of a dogmatic slumber. Prior to reading Being and Event, I had no appreciation for any ontology that wasn’t Heideggerian i.e. phenomenological in nature. The power of Badiou’s subtractive ontology is like a virus, infecting your mind.I think the exegetical style of the paper will be conducive for the blog format as I really didn’t attempt to do anything fancy with the text. I hope that people who are unfamiliar with Badiou’s work will give him a chance; I recommend starting with his Manifesto for Philosophy and then working your way up to Being and Event. Moreover, Peter Hallward’s book on Badiou was really helpful this semester; I highly recommend it. Anyway, I hope my readers will get something out of this, even if it is just an appreciation for an exotic style of thinking.
Operation of the Count
Badiou’s project in Being and Event starts with the fundamental decision that math is ontology. Moreover, math is thought in terms of the axiomatic set theory of Zermelo and Frankl. From within such a system, Badiou makes his central claim that the multiple is and the one is not. From this assertion, everything follows. Moreover, presentation – experience as such – is always the presentation of multiples, which are multiples of multiples, and so on ad infinitum. On the basis of this decision we can retroactively conclude that any “oneness” or unity in experience (such as seeing “a” coffee mug on the table) must always be the result of an operation. Badiou names this process the “count-as-one” operation. And because oneness is ruled to be a mere result in virtue of a metaontological decision, multiplicity is retroactively inferred to be that which is counted, the “stuff” structured in accordance with the counting operation. Moreover, what gets counted is inconsistent multiplicity and the result of the count upon this “material” of inconsistency is consistent multiplicity. A general motif for Badiou is order being counted out of the chaos and anonymity of the void. Accordingly, presentation is always structured in terms of this ordered consistency in virtue of the count. For Badiou, a structured presentation is a situation; presented multiplicity, by definition, is a situation.
However, it must be made clear that, strictly speaking, we cannot ontologically claim that what is counted (being itself) really is multiple because “being is neither one (because only presentation itself is pertinent to the count-as-one), nor multiple (because the multiple is solely the regime of the presentation)” (BE 24). It is only upon the logical realization that oneness is the result of an experiential operation that we are able to conclude multiplicity is prior to the count. Indeed, “The multiple is retroactively legible therein as anterior to the one, insofar as the count-as-one is always a result” (ibid.). Thus, we see that for Badiou, presentation (experience) is always structured; we never experience pure inconsistency except ontologically, that is, mathematically. Within the ontological discourse of being qua being, presentation itself is presented, and subsequently, counted-as-one. This count-of-the-count is the state of the situation, or metastructure. Accordingly, since ontology (presentation of presentation) is structured by the count, it itself is a situation. Nothing (literally) escapes the count-as-one operation.
Moreover, Badiou says that the connection between structured presentation (the resulting situation after the count) and the inconsistent multiplicity (“pure being”) is the void. “The void of a situation is the suture to its being [inconsistent multiplicity]” (BE 526). Consequently, the void is that which can be presented of the inconsistent multiplicity, which, it turns out, is literally nothing (since any “thingness” would be the result of the counting operation). The void is subtracted from the count in the sense that it is the “Non-one of any count-as-one” (ibid.). Although the void is not presented within the situation, it can nevertheless be presented (asserted) within ontological discourse as what avoids, or is subtracted from, the count, designated (marked) as “Ø”. Indeed, besides his declaration that the one is not, the Axiom of the Void is the only existential assertion Badiou infers from axiomatic set theory. From this null set, we can build everything. But because ontological discourse only applies to presented multiplicity, and presented multiplicity is always the result of a counting operation, we literally have nothing to say about that-which-is-presented (retroactively designated as pure multiplicity). Pure being (multiplicity) is thus based on nothing (the void) and our only recourse is to present this situation formally through ontological discourse i.e. formally present presentation itself.
Metaontologically speaking, it is important to see the extent to which presentation as experience plays a role in Badiou’s thinking. Indeed, he says “If the word ‘experience’ has any meaning, it is that of designating presentation as such” (BE 391). And because all presentation is presented multiplicity, and presented multiplicity is consistent (i.e. under the regime of the count), we can conclude that all experience as such falls under the counting operation. The pure infinite multiplicity of the world is always counted as multiplicity, that is, in terms of a structure or situation. Moreover, the count-as-one generates one-effects or “oneness” at all levels of human experience. Even within mathematical (ontological) discourse, where presentation itself is analyzed and broken down into its most abstract structure through set theoretic formulation, the structure of the count is continuously operative at multiple levels. Indeed, “given a situation whose structure delivers consistent one-multiples, there is always a metastructure – the state of the situation – which counts as one any composition of these consistent multiplicities” (BE 97). All situations are thus doubly structured according to the count. Moreover, as Badiou reminds us, it can be mathematically proven that the state of the situation is immeasurably larger than the situation. Technically speaking, the cardinality for the infinite set of the continuum of real numbers is immeasurably in excess of the first cardinality for the infinite set of integers (aleph-null). This idea of excess will be important when we introduce the second key term of Being and Event, for in the same way, the difference between being (in a situation) and the event is “errant and unassignable”.
That all situations are structured is especially important given our above discussion of the void. Because the void is the name of inconsistency in a situation and the count-as-one is always operative, we can never “get” at, or present, the void itself, only its mark Ø. That is, if we metaontologically examine the structure of presentation in its most abstract form in search of the foundational void, we will reach the structure itself, that is, the count-as-one operation, not the void. However, “In order for the void to be prohibited from presentation, it is necessary that structure be structured, that the ‘there is Oneness’ be valid for the count-as-one.” In other words, if we were to attempt a subtraction of the structure itself from the count in order to reach the void, by virtue of the count-as-one and the prohibition of the void’s presentation, the structure must in turn be counted-as-one. And if there is “Oneness” for the count-as-one, then we know that our access to the count is merely a result of an operation. Thus, the count itself escapes the count (BE 93). “The consistency of presentation thus requires that all structure be doubled by a metastructure which secures the former against any fixation of the void” (BE 94). Again, we can be assured that nothing escapes the count, otherwise, the void would contradict itself by being presented.
At this stage in our investigation, it would be natural to think that Badiou’s notion of the counting operation presupposes some sort of cognitive scaffolding wherein we understand presentation (experience) in terms of an organization of empirically given sense-data into a structured unity. After all, as we have seen above, Badiou does conceive of presentation in terms of an operation in which pure inconsistent multiplicity is organized, or “counted”, in terms of consistent multiplicity such that a structured situation results. Conceiving the counting operation in terms of classic sense-data theories would bring Badiou in line with a long history of philosophical reasoning wherein the subjectivity of experience is conceptualized in terms of an organization of raw sensory givens into a meaningful structure viewable by the mind’s eye in a theater of consciousness. This idea follows naturally from the Kantian notion of a transcendental function that synthesizes raw empirical input into a phenomenal realm constitutive of subjective experience.
However, if we were to conclude that Badiou falls into this traditional conception of subjectivity, and is subsequently open to the well known weaknesses of such theorization, we would be sorely mistaken. Indeed, Badiou is quite clear that his conception of subject “is not, in any manner, the organization of a sense of experience. It is not a transcendental function” (BE 391). The task of the next section then will be to explore the extent to which we can make sense of the count-as-one as an operation, which, nevertheless does not presuppose a cognitive scaffold of sensory organization or transcendental synthesis. The guiding question will be: how can we conceive of the subject without recourse to traditional conceptions of subjectivity? That is, how can we make sense of Badiou’s notion of subjectivity in terms that do not presuppose an interiority of consciousness wherein the external world is given to a subjective mind?
To be continued…