August 2006


In reflecting on the debate between Deleuze and Badiou, my thoughts have turned to Hegel’s dialectic of quantum in The Science of Logic (cf. pgs. 202-313). In these passages it seems to me that Hegel all but anticipates the split between the respective ontologies of Deleuze and Badiou. This dialectic can be situated in terms of Hallward’s discussion of Badiou’s fundamental ontological decision in Badiou: A Subject to Truth. In a subsection to chapter 3, Hallward argues that the fundamental decision of any ontology begins with a decision as to what is first or more fundamental: numbers or things? The first orientation is, of course, that of Plato, where eidos constitutes true reality and the world of objects about us is composed of illusory and fleeting appearances from which thought must depart if it is to find truth, whereas the second is that of Aristotle where all thought begins with “primary substances” or individuals, and “things” such as numbers are merely constructions or abstractions of mind, not truly existing beings. In this second orientation, there is truth only insofar as it refers back to the buzzing world of objects.

Badiou’s own neoplatonic option, then, implies (at various stages of the argument) the destitution of the old categories ‘substance,’ ‘thing,’ ‘object,’ and ‘relation’; the ontological primacy of mathematical over physical reality; the distinction of mathematics from logic and the clear priority of the former over the latter. In this Platonic tradition, that mathematics is a form of thought means, first of all, that it ‘breaks with sensory immediacy,’ so as to move entirely within the pure sufficiency of the Ideal. Badiou refuses any cosmological-anthropological reconciliation, any comforting delusion that there is some deep connection (such as that proposed by Jung and his followers) between our ideas or images and the material world we inhabit… His ontology everywhere presumes the radical cut of symbolic representation from the nebulous cosmos of things and experiences that was first proposed by Descartes and subsequently given a particularly strident formulation by Lacan, who insists again and again that we ‘can only think of language as a network, a net over the entirety of things, over the totality of the real’ (S1, 399/262)… ‘Reality is at the outset marked by symbolic neantisation,’ and as Badiou confirms, every ‘truth is the undoing, or defection, of the object of which it is a truth. .’ In particular, ‘all scientific progress consists in making the object as such fade away,’ and replacing it with symbolic-mathematical constructions. (53)

Badiou’s point is very simple. The first step in science, according to this orientation, consists in no longer trusting in appearances. It is by turning away from appearances that scientific knowledge becomes possible. The most striking example of this is seen with regard to the shift from Ptolemy to Copernicus, where the appearance of how the sun and stars moves certain supports the geocentric hypothesis of Ptolemy, but where Copernicus’ break with appearances is what first sets us on the path of getting things right with regard to planetary motion. While I’m more than sympathetic to the jab taken at Jung here, I wonder if this is truly an accurate characterization of science. It is certainly true that there is no science without mathematization, but can science do away with the object in the way that Hallward and Badiou here propose? Can science proceed on the basis of mathematization alone? As I tried to argue in a previous post, Badiou’s ontology runs into problems when dealing with questions of the relationship between the pure order of being (multiplicity qua multiplicity) and actual situations. What Badiou lacks is any sort of explanatory principle that would allow us to understand why one situation arises rather than another situation from the infinite field of pure multiplicty belonging to ontology. The mathematical enthusiasts of Badiou have sternly lectured me for asking such an impudent question when mathematicians are only interested in studying the formal structure of numbers (is this use of mathematics a new rhetorical strategy?), but when Badiou argues that number is being and that it is of the essence of being to appear as a situation, then he has shifted from a discussion of purely formal, deductive, and possible fields explored with the sovereignity of thought by mathematicians, to a field of actuality that cannot be deduced. The question now becomes unavoidable, and it becomes clear that there is a difference between the materiality of a situation and the “materiality” of mathematics.

What is interesting here is that the debate between Badiou and Deleuze concerning quantitative and qualitative multiplicities closely mirrors Hegel’s dialectic of quantum. In treating the dialectic of quantum, Hegel distinguishes between extensive magnitudes and intensive magnitudes. In an articulation of this distinction that is almost identical to Deleuze-Bergson’s distinction between quantitative and qualitative multiplicities, the difference between extensive and intensive magnitudes lies in the fact that the former can be divided without changing in kind, whereas the latter cannot be divided without changing in kind. Thus, for instance, no matter how much I divide a bit of space (say my study), I still get more spatial units of measure such that this space is composed of those units of space; however, when dealing with intensive magnitudes such as boiling water, I cannot meaningfully suggest that this magnitude is composed of all the lower temperatures below it. Rather, an intensive magnitude such as boiling is a sort of indivisible and irreducible threshold at which things occur. Hegel goes on to argue that this distinction is, in fact, artificial and that we cannot properly think these two sorts of magnitudes apart:

…it is quite correct that there are no merely intensive and merely extensive magnitudes, any more than there are merely continuous and merely discrete ones; and hence, these two determinations of quantity are not independent species that confront one another. Any intensive magnitude is also extensive, and conversely. So, a certain degree of temperature, for instance, is an intensive magnitude, to which, as such, there corresponds a wholly simple sensation; and if we then go to the thermometer we find a certain expansion of the column of mercury corresponds to this degree of temperature, and this extensive magnitude changes together with the temperature taken as an intensive magnitude. It is the same in the domain of spirit, too; a more intense character exerts influence over a wider range than a less intense one. (The Encyclopaedia Logic, Geraets trans., 164-5)

It is not difficult to see that Badiou has sought to comprehend being purely in terms of extensive magnitudes, whereas Deleuze has sought to understand the world purely in terms of intensive magnitudes. For Deleuze, for instance, we must understand the manner in which a soap bubble individuates itself as resulting from an equalization of intensive magnitudes or surface tensions among the molecules composing the bubble. I understand an entity when I understand the intensities to which the actualized entity is a response or solution. These intensities are the dynamic factor driving system organization. Badiou, by contrast, is able to arrive at the idea that being is pure multiplicity without one because, when we focus on extensive magnitude alone we can endlessly divide any set (take the subsets of any set) without ever reaching a final set or ultimately primitive set. As such, being becomes pure dissemination without one. In Badiou’s case, it is interesting to note that in his most recent work, Logiques des mondes, he has been forced to extensively discuss intensity to account for the structure of worlds or situations. Unfortunately, Badiou’s concept of intensity pertains to the degree to which elements appear in a situation, rather than serving an energetic function presiding over the actualization of a new organization. For instance, in the situation comprising the United States it could be said that those elements called “leftist” are an intensity of a very low degree as there is very little in the way of a genuine leftist discourse or movement in the United States (even those who say they are on the left in the Democratic party are generally concervatives or supporters of the state… which have a very high degree of intensity by being more predominantly present in the U.S. situation). It’s clear that this concept of intensity is radically different than that advocated by Deleuze or Hegel.

Yet it is necessary to wonder whether Badiou’s characterization of science is accurate. Can science proceed as pure mathematization, making no reference to intensive magnitudes? Perhaps this holds for astronomy, where we describe planetary motion without referring to intensive factors, but certainly disciplines such as quantum mechanics or chemistry would be all but impossible if we didn’t take into account intensive magnitudes. Moreover, I am not at all clear that this is an accurate picture of Lacanian psychoanalysis. Lacan certainly advocated the mathematization of psychoanalytic concepts, but it must never be forgotten that these concepts take their sense and orientation from the clinic. If it were not for variations in intensity, I could never locate, for instance, the objet a or a particularly significant signifier… These instances are accompanied by affect presented in the speech and behavior of the analysand (think of the Rat Man’s violent gestures and his famous facial expression portraying a “horror at an enjoyment of which he was unaware” that came to function as the ciphered key to his entire analysis), that cannot be strictly mathematized.

What I find interesting in reading the Deleuze-Badiou debate revolving around extensive and intensive multiplicities as mirroring Hegel’s dialectic of quantum is that the dialectic of quantum is the final moment of the broader dialectic of being in the “Logic of Being” portion of the Science of Logic. Those familiar with the Science of Logic will recall that this final moment resolves itself in the dialectic of measure, which then passes over into the the doctrine of essence, or relation and appearing. That is, by following the paths of Hegel (and I’m certainly not suggesting becoming Hegelian or that there is some inherent telos at work here in these debates), it might prove possible to productively think Deleuze and Badiou together, formulating an ontology of essence or appearing that goes beyond both of their positions. What this would be, I’m not exactly sure. At the very least, when offered alternatives such as that proposed by Hallward or Badiou between number and thing, I’m led to wonder why I should have to choose exclusively for one at all.

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Althusser famously argued that ideology isn’t simply a false consciousness or mistaken belief about the truth of our social relations, but rather that ideology is the means by which a social system reproduces its conditions of production. What Althusser saw so clearly was that social relations perpetually need to reproduce themselves if societies are to persist across time. In this regard, the biological organism ordinarily referred to as “human” is not sufficient to constitute a social system. As the example of the feral child demonstrates, there’s little resembling a person in a child raised outside a social network system. Rather, this organism must undergo a process of individuation that constitutes it as a social subject or an en-bodiment of social relations. (Incidentally, I also think this responds to Nick’s concerns about solipsism or communication, raised by Peter Hallward in Out of This World, over at the brilliant blog “The Accursed Share”. Insofar as individuation always occurs within a mileux or what Luhmann calls an “environment”, there can be no question of an inside unable to communicate with an outside. In Hegelian terms, that conception that treats the relation of the individuated individual to its mileux or environment as an external relation, is “abstract” and fails to see that the individual is only individuated in drawing a distinction between itself and an environment. Rather, the inside is itself constituted in relation to this outside, which includes other persons in its environment. This is the significance of Lacan’s understanding of the operations of alienation and separation and the constitution of the subject in the field of the Other, which is essentially a thesis about the structural coupling of a merely biological organism to a social world that precipitates a subject. As Bruce Fink expresses this point in The Lacanian Subject, a subject is a particular way of relating to or orientation towards the Other. Subjects are individuated in the mileux of the Other and forever retain the trace of this ongoing individuation in much the same way that the trees behind my home retain the trace of wind and weather patterns here in Texas. Moreover, fundamental fantasy can be seen as the particular strategy a subject has “emerged” for provoking certain perturbations/responses to the ideal Other the subject is structurally coupled to. This would explain why there is no such thing as “self-analysis” in psychoanalysis, and how analysis is a technique for transforming the structural coupling organizing a particular subject by creating a situation in which particular responses in the Other are not where the subject expects them to be. The analyst is that person who is there on the essential condition of not being there and who resembles a person without being one. It is for this reason that an analyst is able to assist in the precipitation of new subjectivities, as s/he doesn’t play the systemic game– the structural coupling –that organizes regular social interactions).

Regardless of what one might think about the particulars of Althusser’s theory of ideology, what is interesting here is that structures must perpetually reproduce themselves across time through mechanisms that bring human organisms to em-body these relations in a system of attitudes, postures, identities, and dispositions of action. Human organisms must be constituted as subjects, and apparently social relations only exist in and through the productive activity of interpellated subjects. In this regard, Althusser functions as a necessary corrective to structuralist conception of organization that tended to see structures as functioning of their own accord, forming some new third type of entity or being that is neither subject nor object, but which overdetermines both. As I argued in a previous post on Deleuze, it was this latter conception of structure that initially motivated Deleuze’s category of the virtual, for the concept of structure requires us to determine how, precisely, it’s possible for synchronous structural relations to exist in a world of actuality that unfolds diachronously.

However, the idea of structure reproducing itself in and through the actions of its elements (social subjects in Althusser’s case) promises the possibility of dispensing with the metaphysically idiosyncratic conception of the virtual, so as to think the world purely in terms of actuality. It is Luhmann who best describes this possibility:

One of the most important results of this encounter [of sociology with systems theory]… resides in the radical temporalization of the concept of element. The theory of self-producing, autopoietic systems can be transferred to the domain of action systems only if one begins with the fact that the elements composing the system can have no duration, and thus must be constantly reproduced by the system these elements comprise. This goes far beyond merely replacing defunct parts, and it is not adequately explained by referring to environmental relationships. It is not a matter of adaptation, nor is it a matter of metabolism; rather, it is a matter of a peculiar constraint on autonomy arising from the fact that the system would simply cease to exist in any, even the most favorable, environment if it did not equip the momentary elements that compose it with the capacity for connection, that is, with meaning, and thus reproduce them. (Social Systems, 11)

What counts as an element must be specified for each type of system analyzed. For instance, human beings are not elements of a social system. Rather, subjects are elements of a social systems. The social system constitutes human beings as subjects or elements of the social system. Put a bit differently, we can say that the social system uses human beings as the material by which to produce social subjects. In Badiou’s language, it is not human beings that are counted by the social system, but rather subjects. It is for this reason that it is said that humans are not elements of a social system. Ellison’s Invisible Man, for instance, might be seen as a novel about a man who experiences the split between how the social system counts him as a member and his status as a human being or individual, which isn’t counted at all.

What we have here is the thesis that elements of a system are perpetually being reproduced across time through the actions of those elements with respect to one another, which amounts to a dynamic stability. For example, in being counted under the class element “professor”, there is no intrinsic or enduring property that makes me a teacher. Rather, I am perpetually being constituted as professor by my own actions, the actions of my students with regard to me, the actions of the administration, other professors, and the actions of the community in which I teach. All of these processes must be perpetually renewed and repeated to constitute me as a particular type of element, just as the cells of a biological organism are perpetually producing themselves, producing other cells, and being produced by other cells. The structural relations defining identity are thus the results of ongoing activity that has its center and origin nowhere, but where identities can only be seen as an emergent result borne of certain relations. Consequently, we have a paradox in which elements are both constituted and constituting, where they are both products of a system and productive of system. In conceptualizing organization in this way, we are able to dispense with the unlateral determination of the actual by the virtual as thematized by Deleuze, replacing it with a model where events occuring among the elements can have an effect on structural organization (feedback loops). We also get a picture of how structural drift occurs over time, through systemic variations and with an “encounter” with the environment (allowing for a reconciliation of Badiou and Deleuze, where Deleuze’s thematization of the “encounter” in Difference and Repetition can be seen as serving a role analogous to that of Badiou’s event). It’s also worth noting that this account of emergent elements accords nicely with Badiou’s ontology of inconsistent multiplicities, and overcomes the descriptivism Hallward criticizes Badiou for in Logiques des mondes (in Badiou: A Subject to Truth, Hallward argues that Badiou’s use of category theory might describe social structures or organizations, but it doesn’t explain them or their mechanisms). Such an approach also explains why we never see perfect embodiments of structure, but always fuzzy variations approaching a statistical norm without encapsulating an absolute mechanistic determinism (a point sometimes ignored by structuralists in their heyday). Finally, we are able to see structural organization as a way of maintaining boundaries in a distinction between system and environment, by drawing a distinction between system and environment (a system, as articulated by Luhmann, perpetually reproduces a distinction between system and environment, or inside and outside, as a way of producing itself across time). As Luhmann puts it, “Systems must cope with the difference between identity and difference when they reproduce themselves as self-referential systems; in other words, reproduction is the management of this difference” (10). In short, one of the central questions of politics becomes that of how this management of identity and difference can be transformed. No longer is the question one of simply changing structure, but rather it becomes one of changing the relationship of structure (system) to its outside or environment (how structure reproduces the difference between identity and difference). What we would have here, then, would be an ontological vision that preserves Deleuze’s key intuitions without forcing us to commit to some of the more eccentric aspects of his ontology (it’s Bergsonism, ontological memory, the virtual, etc).

Eric, over at I Cite, has directed me to Thoburn’s Deleuze, Marx, and Politics as presenting a viable picture of Deleuze’s political thought. While I’ve drawn a good deal of inspiration from Deleuze as a thinker of complex dynamical systems or dynamic evolving stability, I’ve been less enthusiastic about his political thought, or even whether one can draw a coherent political project from his work with Guattari. It was this dissatisfaction that led me to thinkers such as Badiou and Ranciere. Simply put, unbridled creation and unlimited desiring-machines do not a politics make. While such may be appealing to the hipsters, there is little concrete that can be drawn from such premises. But perhaps I’m mistaken and have rashly rejected Deleuze’s work with Guattari out of sour grapes that they authorized an entire generation of cultural studies theorists to reject psychoanalysis in an uninformed and knee-jerk fashion. Over the next few weeks I plan to go through Thoburn’s work to see if this is the case.

Over at Acephalous, Scott has written a piece on why he doesn’t do theory. I have heard remarks like these from a number of quarters– though usually made by people from a certain reactionary contingent in English departments that resents having to be aware of theory (in contrast to these reactionaries, English departments deserve a good deal of credit for preserving what’s left of continental thought in the United States, where philosophy departments largely dropped the ball) –and find myself thoroughly perplexed whenever I hear them. From a Kantian or Luhmannian point of view, every person observes the world from the perspective of a particular frame and based on a particular set of distinctions. As the Anglo-American philosophers who trained me used to say, “all observation is theory laden”, and every judgment about a state of affairs in the world already presupposes a particular theory of how the world is. If I conclude that my partner is possessed because she is speaking in tongues, frothing at the mouth, and seeing things that I cannot see, my judgment presupposes a theory of the nature of the world, of the “ontological furniture” of reality (that it includes things such as demons, devils, souls that can be possessed, etc), and of how that reality is (that these spirits are concerned about human existence; there not being, as Epicurus famously pointed out, any a priori reason to believe the God(s) are concerned with the doings of humans at all). Such theory laden observation is unavoidable. When I view my partner behaving in this way, I conclude something quite different: that she is having a seizure, that perhaps she has a psychosis, etc. So what could it possibly mean to “not do theory”? Isn’t the claim that “one does not do theory” simply equivalent to arguing that one does not make the premises of their own theoretical universe explicit or meditate on their own theoretical assumptions about the world? How is it possible to read texts, analyze the world about us, etc., without implicitly employing a theoretical frame of some sort? In approaching any text, do I not already make an entire host of assumptions as to what a text is, what meaning is, what interpretation is, etc? I most often hear these sorts of remarks coming from those who advocate some sort of historicism. However, isn’t historicism an ontological theory of what makes things– texts, peoples, scientific disciplines –what they are? Doesn’t the historicist proceed on the theory that for anything that is or has taken place, for any situation, it’s being can be exhaustively explained by its historical context as an emergent product of that context? Deleuze and Badiou’s ontologies could thus be seen as militantly rejecting this [Foucaultian/Gadamerian] hypothesis.

Wouldn’t it be more accurate [and honest] to say “I don’t do a particular type of theory?” Approaching this question from the standpoint of the play of the signifier [the unconscious being structured like a language], I suspect that at the level of the unconscious the signifier “theory” is functioning a bit like it does for creationist fundamentalists in the American evolution debate, when it is declared that “Students should understand that evolution is a theory and not fact”. Whenever it is declared that one doesn’t do theory– usually by “hard nosed positivists”, historicists, or pragamatists –it seems to me that lurking in the background is the thesis that theory is somehow the “unproven” or undemonstrated, whereas the good historicist or positivist is just dealing with hard-nosed historical facts or sense-data. In short, the Quinean point that facts are functions of theories and theories are functions of facts (in endless feedback loops) is ignored, and the person rejects “mere theory” with an air of superiority (that I would call reflexive blindness).

Three questions then:

1) What is meant by theory when someone says “I don’t do theory”?

2) Is it possible to not do theory and what does such an activity look like?

3) What desire animates the desire not to do theory? Isn’t the desire to “not do theory” a figure of reaction? Isn’t it precisely theory that allows us to begin escaping the constraints of our historical and ideological situation?

Have at it!

In response to Kushakov’s defense of Deleuze’s category of the virtual, I would like to clarify both what I reject in Deleuze’s account of the virtual and what I wish to preserve in the category of the virtual. At the outset, I should remark that I find Kushakov’s discussion of the virtual unrecognizable, and am certainly unable to agree with his claim that “the virtual [is] that which is simultaneously outside the category of being – that which cannot be brought into either infinite set – and upon which the possibility of being depends.” The problem is that this violates both the univocity and immanence claims of Deleuze’s ontology. Moreover, if we follow Deleuze’s equation of the virtual with Bergsonian memory as elaborated in Bergsonism, it is the virtual that truly is. As Deleuze there puts it,

We have…confused Being with being-present. Nevertheless, the present is not; rather, it is pure becoming, always outside itself. It is not; but it acts. Its proper element is not being but the active or useful. The past, on the other hand, has ceased to act or be useful. But it has not ceased to be. Useless and inactive, impassive, it IS, in the full sense of the word: it is identical with being in itself. (Bergsonism, 55)

Employing Deleuze’s sorting of time as developed in The Logic of Sense, it is thus not the case that the actual is sorted in two ways. Rather, the actual corresponds to chronos or the pure present which is not, and the virtual corresponds to aion or that which divides time into past and future. Deleuze had already developed this sorting of time when discussing the second and third syntheses of repetition (pure past and eternal return) as the dimension of the virtual. For instance, Deleuze’s discussion of Oedipus and Hamlet closely mirrors his discussion of aion in the 23rd series of The Logic of Sense. In any case, Deleuze-Bergson’s thesis is that this pure past is the condition for actualization. Or, put differently, aion is the condition of chronos. Or, yet again, the virtual is the condition of the actual. What I object to in Deleuze is thus two-fold: On the one hand, I reject his thesis about the inactivity or impassivity of the virtual (this is the driving point of Hallward’s entire critique which I discuss here). On the other, I reject Deleuze’s thesis that there is something like an ontological memory or pure past, detached from any subjects, that inheres in all being, in favor of a materialist position that sees the present as perpetually reproducing itself or rather which discerns being as composed entirely of actuality. This, of course, is a thesis that I am obligated to work out and develop.

While I reject Deleuze’s Bergsonian conception of the virtual in terms of an impassive, pure past where the entirety of the past co-exists both with itself and with the present, I do, nonetheless, believe that there is a virtuous conception of the virtual that responds to a very real problem. Deleuze taught that to understand a philosophy or a concept, we must seek to understand the problem to which it responds. It was this, primarily (and not buggary), that defined his “method” of reading philosophy. For Deleuze the question was always what unspoken problem animates this particular constellation of concepts, this particular configuration of thought? Similarly, we can ask what particular problem motivates Deleuze’s conceptualization of the virtual? To what problem does it respond? In order to answer this question a close reading of Difference and Repetition is required, and in particular chapters four and five. Indeed, I would say that the measure of any reading of Deleuze is found in what it has to say about chapters four and five of Difference and Repetition, and whether it attempts to reduce all of Deleuze to the first synthesis of repetition or habitus (a tendency so common in the secondary literature as to cause one to throw one’s hands up in despair, shaking one’s head in wonder at the fact that readers ignore Deleuze’s comments as to how habitus underlies the image of thought and the model of recognition).

I cannot provide such a reading here, but I will say that Deleuze’s account of the virtual is designed to account for the manner in which a discrete entity or being (an actuality) is the product or effect of a structure or system, whether this system be a social system, a lingustic system, a kinship system, a biological system, an ecosystem, etc., etc. Yes, yes, I know Deleuze ultimately comes to reject structuralism and level trenchant critiques against a number of structuralist thinkers. However, this was not always the case for Deleuze (cf. his early essay “How Do We Recognize Structuralism?” in Desert Island and Other Texts, where you will be treated to a neat summary of many of the themes of Difference and Repetition and The Logic of Sense), who recognized early the ontological challenges posed by structuralist thought. It was precisely his attempt to produce a philosophy proper to structuralism that eventually allowed him to break with structuralism, moving in a direction closer to chaos and complexity theory. Although it is seldom discussed, the emergence of structuralism in the social sciences also gave rise to new ontological questions that could no longer be summed up in a metaphysics where the principle kinds of things that are consist of only subjects and objects. Social structures are not in any one person’s mind, nor are they objects that we can observe in the world around us. Rather, they are some strange third thing that is neither subject nor object. And indeed, if we take Althusser’s claims about interpellation seriously (while adding bells and whistles), both subjects and objects are dependent on these structures. Setting aside Deleuze’s later critique of structuralism (his work during the sixties is staunchly structuralist), it can be said that Deleuze set out to theorize these structures.

Take the example of language. We say that langue is the condition of parole. Without language there is no speech. Thus, when I say to a friend “please leave me alone”, this enunciation isn’t possible with a prior shared system of language. There is a condition upon which this enunciation depends and that condition is language. Yet where is language? If language is as Saussure describes it (or as described by the linguist Labov, whom Deleuze and Guattari will come to endorse in A Thousand Plateaus), then language qua language is something that can’t be heard (as it’s composed of pure differences or phonemes such as b/p), it can’t be seen, it can’t be touched, it can’t be found in any particular object in the way that we might discern a quality such as red belonging to a ball. Moreover, language has the strange quality of being discontinuous in time. For instance, the entire world could cease to speak, yet the languages of the world would not cease to be. How is this possible? Now I only offer this as an example of how to conceive the problem Deleuze is responding to, and ask irate desiring-machines not to give me a lecture on how Deleuze and Guattari throw Saussure to the flames in their essay “The Postulates of Linguistics”. Yes, yes, I’m familiar with all of this, but that’s not the point. The point to focus on is the question of how a discrete being can nonetheless have a relational structure. (Incidentally, it will be noted that conservativism is almost invariably characterized by an inability to discern relations or instances of a relation in actual phenomena, treating discrete actuality as if it were all that is and ignoring the manner in which actualities embody systematicity and belong to broader organizational patterns). How is it possible for something to be a condition of beings (the beings in this instance consisting of speech-events), while not being discernible or measurable, or being located in any one particular person’s mind (an issue that becomes even more remarkable when we’re no longer dealing with social phenomena, but biological entities, weather patterns, ecosystems, etc)?

It is precisely these ontological problems that Deleuze seeks to articulate with his account of the virtual. That is, how are we simultaneously able to think the continuous and the discontinuous together? The key passage occurs in chapter four of Difference and Repetition, “Ideas and the Synthesis of Difference”:

We opposed the virtual and the real: although it could not have been more precise before now, this terminology must be corrected. The virtual is opposed not to the real but to the actual. The virtual is fully real in so far as it is virtual. Exactly what Proust said of states of resonance must be said of the virtual: ‘Real without being actual, ideal without being abstract’; and symbolic without being fictional. Indeed, the virtual must be defined as strictly a part of the object– as thought the object had one part of itself in the virtual into which it plunged as though into an objective dimension. Accounts of the differential calculus often liken the differential to a ‘portion of the difference’. Or, following Lagrange’s method, the question is asked which part of the mathematical object presents the relation in question and must be considered derived. The reality of the virtual consists in differential elements and relations along with the singular points which correspond to them. The reality of the virtual is structure. We must avoid giving the elements and relations which form a structure an actuality which they do not have, and withdrawing from them a reality which they have. We have seen that a double process of reciprocal determination and complete determination defined that reality: far from being determined, the virtual is completely determined. When it is claimed that works of art are immersed in a virtuality, what is being invoked is not some confused determination but the completely determined structure formed by its genetic differential elements, its ‘virtual’ or ’embryonic’ elements. The elements, varieties of relations and singular points coexist in the work or the object, in the virtual part of the work or object, without it being possible to designate a point of view privileged over others, a centre which would unify the other centres. How, then, can we speak simultaneously of both complete determination and only a part of the object? The determination must be a complete determination of the object, yet form a part of it. Following suggestions made by Descartes in his Replies to Arnaud, we must carefully distinguish the object in so far as it is complete and the object insofar as it is whole. What is complete is only the ideal part of the object, which participates with other parts of objects in the Idea (other relations, other singular points), but never constitutes an integral whole as such. What the complete determination lacks is the whole set of relations belonging to actual existence. An object may be ens, or rather (non)ens omni modo determinatum, without being entirely determined or actually existing. (DR, 208-9)

The virtual is thus that half of the object that presides over its being or actuality. What the virtual explains is how a discrete (“unconnected”) actuality, entity, or being, can nonetheless belong to one and the same relational structure or system. Thus, for instance, my remark to my friend– “leave me alone” –is a discrete actuality, a unique speech-event isolated from other speech-events, but belongs to the system of the English language. Similarly, the specific color of my eyes are discrete in the order of being or distinct from other entities (other parts of my own body, other human bodies, animal bodies, etc), but nonetheless are actualizations of my genetic structure. Deleuze’s account of (indi)different/ciation in chapters four and five of Difference and Repetition is thus designed to account for how we move from this virtual domain of ideal relations and singularities characterizing a system, to unique actualized entities. Moreover, we can see why Deleuze would find Bergson’s account of the pure past attractive in developing an ontology of structures and systems as they relate to discrete actualities, insofar as the relations composing a system or structure are simultaneous with one another, yet time experienced at the level of actuality is experienced as perpetually passing. The pure past is one way to explain how organization, system, structure can persist in time despite the fact that actualities are constantly moving about and reorganizing themselves.

I take it that Deleuze’s account of the virtual as structure or system is the “virtuous” conception of the virtual, and the one that has been so quickly latched on to by thinkers such as Negri and Hardt. That is, I take it that describing the virtual as the “relational side” of the object is a productive idea. Nonetheless, I am uncomfortable with Deleuze’s proposal of an impassive ontological memory or pure past that insists in all actuality. I am also bothered by Deleuze’s claim that the actual contributes nothing to the virtual, but rather that all actualization moves from the virtual to the actual. This seems to leave little hope for any sort of concrete change produced at the level of actuality, insofar as we have a pure past, a past that has never been present, overdetermining all actualities without the actualities themselves contributing anything to being. It seems to me that this is the Deleuze, the Deleuze of the ontology of the pure past, that most Deleuzians themselves ignore, treating Deleuze instead as a sort of complexity theorist.

What if, however, we could account for the relational dimension of beings coupled with their discreteness without having to evoke something like a pure past? What if we could account for this relational dimension of all discrete entities sheerly in terms of actuality? In Social Systems, Luhmann has proposed that systems are entirely composed of events that cease to exist the moment they occur. That is, there is no substance in which systems inhere. As a result, the challenge of every system consists in the question of how it is able to perpetually reproduce itself from moment to moment. What are those events that generate connectivity to other events? Is there a way of conceiving being such that being reproduces itself at every moment in its relational organization, allowing us to dispense with strange ontologies that would require us to claim that the past IS? Could not organization, systematicity, be seen as an emergent property of elements, rather than as the result of another dimension called the virtual?

Since last week I’ve been largely out of commission cognitively due to health issues, but I’m slowly regaining the ability to think. During this time, I happened to come across a brief statement by Badiou, explaining why he considers himself a materialist. Here my remarks will be less than elegant, though I hope to localize a problem that seems to emerge with regard to Badiou’s ontology, and a place where it might become possible to think questioningly with Badiou (in tandem with Deleuze and what might motivate a Deleuzian ontology).

In an interview accompanying Badiou’s Ethics: An Essay on the Understanding of Evil, Hallward asks Badiou to clarify the relation between his mathematical ontology and the nature of material reality. Despite my great love of mathematics and my tendency to advocate some form of Platonic realism where the ontological status of mathematical entities is concerned, I think this question naturally emerges insofar as mathematical entities are often thought as idealities and possibilities, independent of the actuality characterizing the material world. Consequently, there seems to be something of a gulf or chasm between the infinite possibilities of the mathematical world and the actualities characterizing this world. In response, Badiou remarks that,

If we accept that there exists a situation in which what is at stake for thought as being-as-being [viz., ontology]– and for me, this is simply one situation of thought, among others –then I would say that this situation is the situation defined by mathematics. Mathematics, because if we abstract all presentative predicates little by little, we are left with the multiple, pure and simple. The “that which is presented” can be absolutely anything. Pure presentation as such, abstracting all reference to “that which” –which is to say, then, being-as-being, being as pure multiplicity –can be thought only through pure mathematics.

To the extent that we abstract the “that which is presented” in the diversity of situations, to consider the presentation of presentation itself– that is to say, in the end, pure multiplicity– then the real and the possible are rendered necessarily indistinct. What I call ontology is the generic form of presentation as such, considered independently of the question as to whether what is presented is real or possible… Are they real, do they exist somewhere, are they merely possible, are they linguistic products…? I think we have to abandon these questions simply because it is of the essence of ontology, as I conceive it, to be beneath the distinction of the real and the possible. What we will necessarily be left with is a science of the multiple in general, such that the question of knowing what is effectively presented in a particular situation remains suspended. A contrario, every time we examine something that is presented, from the strict point of view of its objective presentation, we will have a horizon of mathematicity, which is, in my opinion, the only thing that can be clear. In the final analysis, physics– that is to say, the theory of matter –is mathematical. (Ethics: An Essay on the Understanding of Evil, pgs. 127-128, italics mine)

A moment later Badiou reminds us of what ontology is, remarking that, “all of this simply confirms a very old and somewhat inevitable ontological programme: that ontology always gathers up what remains to thought once we abandon the predicative, particular determination of ‘that which is presented'” (129). Ontology, then, is what remains once we subtract all other predicates characterizing an existent or an entity. According to Badiou, all that remains after such an operation of subtraction occurs is pure multiplicity or multiplicity qua multiplicity sans any other predicates or qualities:

Now, the existent qua existent is absolutely unbound [I read this as “un-related”]. This is a fundamental characteristic of the pure manifold as it is thought in Set theory. There are only multiplicities and nothing else. None of them on their own is connected to another. In Set Theory even functions have to be thought as pure multiplicities or manifolds. This is why we identify them by their graph [I’m not sure what he’s getting at here with his reference to the graph of a function]. The “beingness” of the existent does not presuppose anything else than its immanent composition, that is, that it might be a manifold of manifolds. Strictly speaking, this excludes the possibility that there might be a being of the relation. When thought as such, and therefore purely generically, Being is subtracted from any connection. (Briefings on Existence: A Short Treatise on Transitory Ontology, “Being and Appearing”, 162. This essay can also be found in Theoretical Writings)

The key sentence in this passage is “manifold of manifolds”, which should be translated as “multiplicities of multiplicities”. In thinking Being as manifold of manifolds Badiou is effectively claiming that there are no ultimate or irreducible terms of which sets would be composed, but only endless multiplicities without ultimate identities, and that these manifolds are unrelated or unconnected to one another. As such, Badiou’s ontology is an ontology of infinite dissemination without One or an overarching unity at the level of either the whole or the part. Now I take it that the great merit of Badiou’s mathematical thesis is two-fold:

  1. Badiou’s ontology effectively allows us to escape any epistemological orientation in ontology, by sidestepping any questions of how it is possible for a subject to relate to being. That is, we need raise no questions of how a mind is able to know or represent being. This point might be obscure to those who have no background in philosophy of mathematics; however, ever since Frege and Husserl, questions of the psychology through which mathematics is known have been staunchly excluded from the thinking of the mathematical qua mathematical. Those unfamiliar with these arguments and the manner in which they trenchantly depose any psychologism would do well to refer to Frege’s Foundations of Arithmetic. This is why it’s so important to Badiou that ontology evade the distinction between actuality and possibility (as it must not be a matter of mind representing reality, but of a “common being” to possibility and actuality). It is also one reason that Badiou’s ontology diverges radically from Zizek’s Hegelian orientation. The consequences of this move are far reaching. In one fell swoop, Badiou is able to escape all questions revolving around the subject and anthropology. If mathematics truly is ontology, and if mathematics is independent of questions of knowledge, then all questions about differing subjective perspective on reality, different cultural perspectives on reality, etc., fall to the wayside as interesting psychological, anthropological, and sociological speculations, but speculations that are quite irrelevant to ontological researches. In short, ontology and philosophy no longer need concern themselves with cultural studies, linguistics, or the social sciences. This is what it means, for Badiou, to say that math inscribes the real.
  2. In a closely related vein, Badiou’s thesis allows us to depart, once and for all, from Heidegger’s endless preparations for properly posing the question of being. There is no need to engage in an elaborate hermeneutic of Dasein as that being that is “ontic-ontological” and who has a pre-ontological understanding of being, as the being of being is exhausted in its mathematicity.

To my thinking, these consequences cannot but come as a breath of fresh air to philosophy insofar as it has increasingly come to be dominated by cultural studies, rhetorical analysis, and pseudo-pious phenomenological discourses.

However, I wonder nonetheless whether Badiou hasn’t moved a bit too quickly. Badiou’s thesis regarding materialism seems to be that insofar as science always approaches matter mathematically, a mathematical ontology is necessarily a materialist ontology:

…it [the thesis that mathematics = ontology] is a fully materialist thesis, because everyone can see that the investigation of matter, the very concept of matter, is a concept whose history shows it to be at the edge of mathematicity… ‘Matter’ would simply be, immediately after being, the most general possible name of the presented (of ‘what is presented’). Being-as-being would be that point of indistinction between the possible and the real that only mathematics apprehends in the exploration of the general configuration of the purely multiple. Matter, in the sense in which it is at stake in physics, is matter as enveloping any particular presentation–and I am a materialist in the sense that I think that any presentation is material. (Ethics: An Essay on the Understanding of Evil, 130, italics mine)

What seems to be missing in Badiou’s account of materialism is precisely any discussion of this “concept at the edge of mathematicity”. I have highlighted these passages on how being-qua-being is the point of indistinction between the possible and the real to indicate that the moment we enter the realm of the material, we are no longer dealing with something merely possible, but rather with something actual. That is, something has been added to what we’re talking about, what we’re investigating, that isn’t strictly mathematical. Although mathematics is certainly an essential dimension of physics or any science (I would accept Kant’s thesis that mathematization is a necessary condition of scientificity), the object of any particular science is an object that cannot itself be mathematically deduced.

Doesn’t this edge of mathematicity, this element that is enveloped by mathematicity, itself have some claim to being? Hallward hits the nail on the head when he responds to Badiou’s elaboration of materialism, by remarking that, “It seems, however, that your most basic concept, the concept of a situation, oscillates somewhat between an essentially mathematical order and what appears to be a no less essentially eclectic order, combining heterogeneous elements of actuality” (129). The problem as I see it is that unlike being-qua-being, a situation (what Badiou now calls a “world”), does not straddle the distinction between the possible and the real. A situation is real, it is actual, it is this situation and no other.

It thus seems to me that for Badiou there is a tremendous gap between ontology as the “presentation of presentation” or pure multiplicity “without connection”, and the ordered situations of the world. One might respond by arguing that ontology is not in the business of explaining situations as it only studies pure multiplicities, not “consistent multiplicities”. However, Badiou himself says otherwise:

What links a being to the constraint of a local or situated exposure of its manifold-being is something we call this existent’s “appearing.” It is the existent’s being to appear insofar as Being as a whole does not exist. Every being is being-there. This is the essence of appearing. Appearing is the site, the “there” of the multiple-existent insofar as it is thought in its being. Appearing in no way depends on space or time, or more generally on a transcendental field. It does not depend on a Subject whose constitution would be presupposed. The manifold-being does not appear for a subject. Instead, it is more in line with the essence of the existent to appear. As soon as it falls short of being localized according to the whole, it has to assert its manifold-being from the point of view of a non-whole, that is, of another particular existent determining the being of the there of being-there [incidentally, Hegel already conceives appearing as appearing to another existent or Relation in the “Doctrine of Essence”, Science of Logic].

Appearing is an intrinsic determination of Being. The localization of the existent, which is its appearing, involves another particular being: its site or situation. This is why it can be seen immediately that appearing is as such what connects or reconnects an existent or its site. The essence of appearing is the relation. (Briefings on Existence, pg. 162)

I confess that I find these remarks exhilerating, though I am unable to understand Badiou’s thesis or the logical entailment necessitating that “because the whole is not, the existent must appear. ” It seems to me that there is a fundamental ontological axiom here that is currently the is a central theme of a good deal of contemporary theory (Deleuze’s thesis that the Whole is not giveable in Cinema 1 and that this is a condition for the given, Zizek’s thesis that the One is not, Lacan’s thesis that the world does not exist, etc. One of my central questions is that of how to understand the relation between the in-existence of the Whole (not simply that we cannot know the whole, but that the whole does not exist –and the givenness of the given. I am not sure why this question strikes me as so important, but there’s something there. Now, when Badiou glosses category theory in an earlier essay “Group, Category, Subject”, he largely describes my own ontological project:

In category theory, the initial data are particularly meager. We merely dispose of undifferentiated objects (in fact, simple letters deprived of any interiority) and of ‘arrows’ (or morphisms) ‘going’ from one object to another. Basically, the only material we have is oriented relations. A linkage (the arrow) has its source in one object and target in another. Granted, the aim is ultimately for the ‘objects’ to become mathematical structures and the ‘arrows’ the connection between these structures. But the purely logical initial grasping renders the determination of an object’s sense entirely extrinsic or positional. It all depends on what we can learn from the arrows going toward that object (whose object is the target), or of those coming from it (whose objects is the source). An object is but the marking of a network of actions, a cluster of connections. Relation precedes Being. This is why at this point of our inquiry we have established ourselves in logic, and not ontology. It is not a determined universe of thought we are formalizing, but the formal possibility of a universe” (Briefings on Existence, “Group, Category, Subject”, 144).

From my perspective, this is the place to begin ontologically, as I see no way that can account for the emergence of Relation on the basis of pure, unconnected multiplicity as described by Badiou. I am not certain why Badiou refers to this as a logic (generally I’m fuzzy on his conception of logic overall and why he is so hostile to placing math under logic), nor am I sure why he refers to this as the articulation of a possible universe, rather than a determined universe. However, when Badiou suggests that Relation precedes being, and proposes that we conceive entities as “networks of action”, “clusters of connections”, “bundles of relations”, I think this is the right direction to move in ontologically. It is this move towards conceiving beings as activities, as networks, as doings, that allows us to do away with substance ontology. This, then, is the central difficulty. One the one hand, Badiou wishes to claim that ontology is indifferent to the distinction between the possible and the real. Yet on the other hand, Badiou wishes to argue that it belongs to the essence of Being, that it is intrinsic to being, to appear. How can this be? How can we simultaneously affirm both of these theses without undermining the thesis that ontology is indifferent to the distinction between the possible and the real?

Could it be that this is the real source of Badiou’s hostility to Deleuze? It will be recalled that Deleuze defines his transcendental empiricism as that ontology that articulates the conditions of real being, and not all possible being. In developing this ontology Deleuze, following Bergson, advances a substantial critique of the category of possibility, arguing that the dialectic between the possible and the real is unable to give any account of how the real is realized insofar as the real in no way differs from the possible (Kant’s famous critique of the ontological proof for the existence of God, wherein he argues that “existence is not a real predicate”). That is, accounts of realization are unable to explain what the real contributes to being. It seems to me that Badiou finds himself in a very similar position and that for this reason it is difficult to identify his ontology as being genuinely materialist.

Following PEbird’s suggestion, it may be worthwhile to conceive the decision between set theory and category theory as a sort of parallax at the heart of ontology. As Zizek describes it,

The standard definition of parallax is: the apparent displacement of an object (the shift of its position against a background), caused by a change in observational position that provides a new line of sight. The philosophical twist to be added, of course, is that the observed difference is not simply “subjective,” due to the fact that the same object which exists “out there” is seen from two different stances, or points of view. It is rather that, as Hegel would have put it, subject and object are inherently ‘mediated,’ so that an ‘epistemological’ shift in the subjects point of view always reflects an ‘ontological’ shift in the object itself. Or– to put it in Lacanese –the subject’s gaze is always-already inscribed into the perceived object itself, in the guise of its ‘blind spot,’ that which is ‘in the object more than the object itself,’ the point from which the object returns the gaze. (PV, 17)

A parallax, then, is not a subjective point of view, not a relativism to a subject or observer, but rather a displacement or split ontologically inscribed in the object itself. This split, moreover, is absolute in the sense that it doesn’t allow for a higher resolution or reconciliation, but is rather irreducible. As Luhmann aphoristically puts it in “The Cognitive Program of Constructivism and the Reality That Remains Unknown”, “Cognition deals with an external world that remains unknown and, as a result, has to come to see that it cannot see what it cannot see” (Theories of Distinction, 129). And a bit more forcefully later, “Reality is what one does not perceive when one perceives it” (italics mine, 145). Luhmann, of course, was not familiar with Zizek’s concept of the parallax as it had not yet been invented, but the two are remarkably close here. A parallax revolves around that blind spot, that which I do not perceive, my gaze inscribed in the thing itself, that allows beings to appear as they do. If I adopt this point of view on the world– or an Whithead’s language, if I am a “superject” of this particular blind spot –another field becomes invisible to me (incidentally, this calls for a radically different reading of Hegel or new dialectics that has not yet been formally worked through or elaborated).

Like Holbein’s Ambassadors above, I can either see the men depicted in the painting or the skull floating in the foreground, but I cannot see both the figures in the foreground and the skull flying in the foreground at one and the same time. A parallax thus has the structure of a moebius strip. Topologically a moebius strip has only one side and one edge. However, in order to discover this, I require time. It is only by traversing the surface of the strip that I discover that what originally appeared to be on the other side was really on the same side. Zizek’s suggestion seems to be that a parallax is such that “front” and “back” turn out to be on one and the same side, but only when unfolded in the order of time or through a series of dialectical operations. As Zizek argues with regard to sexual difference, feminine sexuation is not the Other of the logic of the One found in masculine sexuation, but rather the the parallax of masculine sexuation or the One.

I am still trying to get my mind about the idea of the parallax and how exactly one goes about constructing one or perceiving a parallax at work. Despite this, PEbird’s suggestion that the opposition between category theory and set theory forms a parallax strikes me as fertile and perhaps productive in staving off a number of debates likely to emerge around ontologies implicitly organized around this opposition.

The primitive operation in set theory is that of membership. On the one hand, set theory in its ZF formulation leaves the concept of set itself undefined. Initially this might appear to be a point of minor interest. However, this point is crucial for the thinking of difference for if we could give a univocal definition of “set”, we would have reintroduced the One back into ontology, such that the One would precede difference. In leaving “set” undefined– if we were being cute Lacanians we could aphoristically say “The Set does not exist” –set theory insures that pure multiplicity without One serves as the ground of being. Being can thus be conceived as pure multiplicity without One, such that any identities we find among beings are the result of operations, but are not themselves primitive. As Badiou puts it,

if 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)

When we subtract all other predicates from being– for instance, Aristotle’s categories –we are left with the multiple alone. It is precisely set theory that is capable of thinking such pure multiplicities. If it proves necessary to separate being from the One so as to think it as pure multiples of multiples without One, then this is because the suture of being to the One leads to irresolvable paradoxes as can readily be seen in Plato’s dialogue Parmenides. Any unities we do find among beings are thus an effect or product of an operation, as the One is not and being consists only of multiples of multiples. Of course, this gives rise to a number of questions as to who or what operates these operations and how it is possible to move from pure multiplities to the various ones we find in the world about us.

Luhmann begins from the other side of the issue. Sadly Luhmann’s work is almost completely unknown in the English speaking world. Indeed, whenever I evoke his name I always feel a little bit silly as no one seems to know what I’m talking about. Nonetheless, it is my view that Luhmann has developed the most robust account of social systems or organizations currently available, and one that is fully compatable with a number of other trends already out there in social thought. Where Badiou begins with pure multiplicities, Luhmann begins from the perspective of constituted organizations. Where Badiou begins from the perspective of set theoretical membership as the primitive operation in ontology, Luhmann begins from the perspective of relation. That is, Badiou’s elements are ultimately unrelated, whereas Luhmann’s elements always only exist in relation. As Luhmann puts it,

Whether the unity of an element should be explained as emergence ‘from below’ or as constitution ‘from above’ seems to be a matter of theoretical dispute. We opt decisively for the latter. Elements are elements only for the system that employs them as units and they are such only through this system. This is formulated in the concept of autopoiesis. One of the most important consequences is that systems of a higher (emergent) order can possess less complexity than systems of a lower order because they determine the unity and number of the elements that compose them; thus in their own complexity they are indepdendent of their material substratum. This also means that the complexity that is necessary or sufficient to a system is not predetermined ‘materially,’ but rather can be determined anew for every level of system formation with regard to the relevant environment. Thus emergence is not simply an accumulation of complexity, but rather an interruption and new beginning in the constitution of complexity. Accordingly, we take the unity of an action to be not a psychological, but a sociological fact; it does not emerge through the decomposition of consciousness into the smallest unities that cannot be dissolved further, but rather through the social process of attribution. (Social Systems, 22-23)

For Luhmann, then, we are unable to think elements independent of their relations and systems in which they are constituted. Elements are only elements for a system. Take Althusser’s critique of humanism. If I am not mistaken, Althusser’s point is that humans are always humans for the particular ideological state apparatus that subjectivizes them or constitutes them as beings. There is no humanity that underlies all historical change, but only the autopoiesis that occurs in each and every historical situation, constituting subjects as this type of subject at this particular point in time. The beauty of Luhmann is that he gives an abstract formulation of the mechanisms by which social systems constitute these identities or subjects.

Now Luhmann is a functionalist in his account of the mechanisms by which these operations take place. Here we must take great care not to confuse Luhmann’s functionalism with some sort of utilitarianism, where needs and desires are pre-established and the social is teleologically driven to certain ends. Luhmann’s functionalism is neither a teleology, nor a utilitarianism, but would better be thought in mathematical terms as akin to mathematical functions, or as what category theory refers to as “arrows” presiding over morphisms and transformations. That is, functions describe the processes by which elements are constituted.

So far it thus appears that there’s a remarkable proximity between Luhmann and Badiou. Both are in agreement that there are no primative elements, but rather that elements are products or effects of operations, out of what is essentially chaos. As Luhmann puts it,

Every observation– this holds for second-order observations as well –uses a distinction to mark one side (but not the other). No procedure can get around that. Even negations presuppose the prior distinction and indication of what one wants to negate. One cannot start from an immediately given nondetermination– an unmarked space, a primordial entropy or chaos, an empty canvas or a white sheet of paper –without distinguishing this state from what is being done to it. Even when moving toward fictionality, away from the real world in which we exist, we need this distinction in order to indicate the ‘whence?’ and ‘where?’ This is how we construct reality. (Art as a Social System, 55)

(It’s interesting to note that Deleuze, in Francis Bacon: The Logic of Sensation, categorically denies that there’s such a thing as a blank canvas, but that there’s always a virtual painting in the canvas already, populated by the history of painting). Luhmann’s point is that organization emerges from this chaos. The principle difference between Luhmann and Badiou would be that where the former believes that we can say nothing about this chaos, Badiou argues that it is precisely this chaos– inconsistent multiplicities –that ontology studies. Where Luhmann focuses on the operations by which elements are constituted, Badiou focuses on this chaos of inconsistent multiplicities revealed by set theory. Similarly, both Badiou and Luhmann would agree that there are only situations (or in Logiques des Mondes’ terminology, “worlds”), and no global whole in which these situations inhere. For Luhmann this would be a logical consequence of the fact that worlds only emerge through drawing a distinction in which one space is unmarked (there’s always a blind spot or, following Zizek’s Luhmanianism, a frame), whereas for Badiou it follows as a consequence of the thesis that the One is not. There is thus a sense in which the two positions are complimentary.

However, we might wonder whether Badiou’s formalism and tendency (until Logiques des Mondes) to ignore the structure of situations, doesn’t cause problems elsewhere. As Luhman remarks, systems do not simply constitute their elements, they also regulate their elements. “Out of the relation among elements emerges the centrally important systems-theoretical concept of conditioning. Systems are not merely relations (in the plural!) among elements. The connections among relations must also somehow be regulated. This regulation employs the basic form of conditioning. That is to say, a determinate relation among elements is realized only under the condition that something else is or is not the case” (Social Systems, 23). In Althusserian terms, this would be the reproduction of the conditions of production, where the social system must perpetually reproduce itself by excluding other forms of relating among elements. The great service that Badiou has done, the tremendous power of his thought, lies in showing how formal ontology brings us to the point where we can see how an event is possible, or how there can be something other than the structuration of a situation. However, in ignoring the mechanisms by which situations regulate themselves, one wonders whether Badiou’s truth-procedures might not be a bit utopian in not attending to the sort of action necessary to transform the self-regulating mechanisms of social systems.

Where Luhmann is blinded to the possibility of events by virtue of seeing too much closure in systems (nothing seems to escape the constituting force of systems), Badiou, in focusing on pure multiplicities and formalism, seems blinded to the regulatory functions of systems in constituting their elements. I’m not sure where these wandering musings lead, but hopefully they get a bit further in framing a question.

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