by Daniel Smith
Isn't it proper to desire to carry with it its own proper suspension, the death or the phantom of desire? To go toward the absolute other, isn't that the extreme tension of a desire that tries thereby to renounce its own proper momentum, its own movement of appropriation? … And since we do not determine ourselves before this desire, since no relation to self can be sure of preceding it, to wit, of preceding a relation to the other, … all reflection is caught in the genealogy of this genitive [i.e., “desire of …”].37
Thus, for Derrida, the possibility of openness or invention (e.g., the possibility of “an other justice,” “an other politics,” and so on)38 is necessarily linked to the transcendent Idea of the absolutely other. The “disruptions” Derrida introduces into thought are the movements of this formal structure of transcendence. One can see clearly how Derrida's notion of desire, in relation to, for example, the “infinite Idea of justice,” recapitulates the three moments of the transcendent theory of desire outlined by Deleuze:
1. the “call” to justice has as its object an “infinite” Idea that is unrealizable, and that transcends any determinable context;
2. what comes to fulfill the call to justice are “decisions” (e.g., by judges in a court of law), but these decisions as such cannot be determined to be just, so the call to justice is continually reborn; hence
3. the call to justice can never be fulfilled or satisfied, it is the experience of something that is fundamentally impossible.
Derrida seeks not only to disengage a formal structure of transcendence (différance), but to describe the desire or passion of that transcendence (defined as a double bind or experience of the impossible). For his part, Deleuze agrees with Derrida's analyses, and provides variations of his own, but they are always a prelude to eliminating transcendence and providing an immanent account of the same phenomenon: an immanent ontology (univocity), an immanent theory of Ideas (defined in terms of multiplicities and singularities), and an immanent theory of desire (defined as the prolongation or synthesis of singularities).
IMMANENCE, TRANSCENDENCE, AND ETHICS
No matter which formulation one considers, then, one finds Derrida and Deleuze following diverging philosophical trajectories, marked by these two vectors of transcendence and immanence. First, in the tradition of subjectivity, transcendence refers to what transcends the self (the other, the world)—or more profoundly, to the subject itself, as that which transcends the pure “flux of consciousness” or “flow of experience.” One can critique the status of the subject by appealing to the transcendence of the Other, or by appealing to the conditions of the immanent flux of experience that the subject itself transcends (theory of intensity). Second, with regard to the question of ontology, transcendence refers to that which is “beyond” or “otherwise than” Being—or, in its more contemporary form, to relations to the other that “interrupt” Being, or erupt or intervene within Being. Whereas Deleuze defines both Being and beings immanently in terms of a genetic principle of difference, Derrida defines différance transcendently as “originary” difference that is beyond both Being and beings. Finally, from the viewpoint of a Kantian (or neo-Kantian) epistemology, transcendence refers to those Ideas of objects that lie outside the immanent realm of possible experience. Deleuze attempts to formulate an immanent theory of Ideas and desire, while Derrida attempts to define a purely formal structure of transcendence and the passion of the double bind that it entails. In each of these areas, Deleuze's and Derrida's projects move in very different directions, despite so many surface similarities and affinities.
But this leads to an obvious final question: How should one assess this difference? Can one say that the trajectory of transcendence or immanence is “better” than the other? This is a difficult question, perhaps reducible, in the end, to what one might call philosophical “taste.” My own view is that the “philosophy of the future” (to use Nietzsche's phrase) needs to move in the direction of immanence, for at least two reasons. The most obvious reason is that the validity of a critique of transcendence above all stems from the theoretical interest to expose its fictional or illusory status—this has been a constant of philosophy from Hume through Kant to Nietzsche, its “demystificatory” role. But the more important reason has to do with practical philosophy, with ethics and politics. Kant, Levinas, and Derrida, along with many others, while perhaps denying transcendence a constitutive status, are none the less willing to assign it a practical role (regulative, imperative, communicative, and so on). For Deleuze, this is equally illegitimate, but it seems to have been a source of genuine perplexity to Deleuze. There is a curious passage in What is Philosophy? where Deleuze and Guattari more or less ask: What is it with immanence? It should be the natural acquisition and milieu of philosophy, yet such is not always the case. Moreover, the arguments brought to bear against immanence are almost always moral arguments. Without transcendence, we are warned, we will fall into a darkness of chaos, reduced to a pure subjectivism or relativism, living in a world without hope, with no vision of an alternate future. Indeed, the two philosophers who pushed the trajectory of immanence the furthest—Spinoza and Nietzsche—were condemned by both their contemporaries and their successors, less for being atheists than for being immoralists. The danger that was sensed to be lurking in both the Ethics and the Genealogy of Morals was precisely the danger of immanence.
Immanence can be said to be the burning touchstone of all philosophy [writes Deleuze] because it takes upon itself all the dangers that philosophy must confront, all the condemnations, persecutions, and repudiations that it undergoes. This at least persuades us that the problem of immanence is not abstract or merely theoretical. At first sight, it is not easy to see why immanence is so dangerous, but it is. It swallows up sages and gods. (WP 45)
From this practical point of view, Spinoza poses the most interesting test case of the position of immanence. Heidegger himself wrote notoriously little on Spinoza, which is a surprising omission, since Spinoza's Ethics is a work of pure ontology that explicitly poses the problem of the ontological difference in terms of the difference between the infinite substance (Being) and its finite modes (beings). Derrida too has written little on Spinoza. By contrast, Deleuze's reformulation of ontology in Spinozistic terms allows him not only to push the Heideggerian heritage in an immanent direction (rather than Derrida's transcendent direction), but also to understand that ontology in explicitly ethical terms. Like Spinoza, Deleuze defines beings immanently in terms of their intensity or “degree of power,” a degree which is actualized at every moment in terms of the whole of one's “affections” (which are none the less in constant variation). The fundamental question of ethics is not “What must I do?” (the question of morality) but rather “What can I do?” Given my degree of power, what are my capabilities and capacities? How can I come into active possession of my power? How can I go to the limit of what I “can do”? The political question follows from this, since those in power have an obvious interest in separating us from our capacity to act. But this is what makes transcendence an eminently pragmatic and ethical issue. The ethical themes one finds in transcendent philosophies such as those of Levinas and Derrida—an absolute responsibility for the other that I can never assume, or an infinite call to justice that I can never satisfy—are, from the point of view of immanence, imperatives whose effect is to separate me from my capacity to act. From the viewpoint of immanence, in other words, transcendence represents my slavery and impotence reduced to its lowest point. This is why transcendence itself poses a precise and difficult ethical problem for a philosophy of immanence: If transcendence represents my impotence (power = 0), then under what conditions can I have actually been led to desire transcendence? What are the conditions that could have led, in Nietzsche's words, to “the inversion of the value-positing eye”? How could I actually reach the point where I desire my slavery and subjection as if it were my salvation? (In a similar way, immanence poses a precise and difficult problem for a philosophy of tr
anscendence: How can one bridge the interval that separates the transcendent from the immanent—for instance, the interval that separates the undeconstructability of justice from the deconstructability of the law?)
In short, the difference between the two philosophical trajectories of immanence and transcendence must be assessed and evaluated, not simply in the theoretical domain, but in the ethico-political domain. In part, this is because the speculative elimination of transcendence does not necessarily lead to its practical elimination, as one can see already in Kant. But more importantly, it is because it is at the ethical level that the difference between transcendence and immanence appears in its most acute and consequential form. On this score, it is perhaps the difference between Deleuze and Levinas that presents this contrast most starkly. For Levinas, ethics precedes ontology because it is derived from an element of transcendence (the Other) that is necessarily “otherwise” than Being (and hence privileges concepts like absolute responsibility and duty). For Deleuze, ethics is ontology because it is derived from the immanent relation of beings to Being at the level of their existence (and hence privileges concepts such as puissance [power or capacity] and affectivity). This is why Spinoza entitled his pure ontology an Ethics rather than an Ontology: his speculative propositions concerning the univocity of Being can only be judged practically at the level of the ethics they envelop or imply. Put summarily, for Levinas, ethics is derived from transcendence, while for Deleuze, transcendence is what prevents ethics. It seems to me that it is at this level—at the practical and not merely speculative level—that the relative merits of philosophies of immanence and transcendence need to be assessed and debated.
ESSAY 17
Alain Badiou
Mathematics and the Theory of Multiplicities: Deleuze and Badiou Revisited
D
eleuze once wrote that “encounters between independent thinkers always occur in a blind zone,” and this is certainly true of the encounter between Badiou and Deleuze.1 In 1988, Badiou published his book Being and Event, which attempted to develop an “ontology of the multiple” derived from the mathematical model of axiomatic set theory.2 Soon afterward, he tells us, he realized—no doubt correctly—that his primary philosophical rival in this regard was Deleuze, who similarly held that “philosophy is a theory of multiplicities,”3 but whose own concept of multiplicities was derived from different mathematical sources and entailed a different conception of ontology itself. In 1997, Badiou published a study of Deleuze entitled Deleuze: The Clamor of Being, in which he confronted his rival directly and attempted to set forth their fundamental differences. The study, Badiou tells us in its introduction, was occasioned by an exchange of letters he had with Deleuze between 1992 and 1994, which focused directly on the concept of “multiplicity” and the specific problem of “an immanent conceptualization of the multiple.”4 On the opening page of the book, Badiou notes that “Deleuze's preferences were for differential calculus and Riemannian manifolds … [whereas] I preferred algebra and sets”5—leading the reader to expect, in what follows, a comparison of Deleuze's and Badiou's notions of multiplicity based in part, at least, on these differing mathematical sources.
Yet as one reads the remainder of Deleuze: The Clamor of Being, one quickly discovers that Badiou in fact adopted a quite different strategy in approaching Deleuze. Despite the announced intention, the book does not contain a single discussion of Deleuze's theory of multiplicities; it avoids the topic entirely. Instead, Badiou immediately displaces his focus to the claim that Deleuze is not a philosopher of multiplicity at all, but rather a philosopher of the “One.” Nor does Badiou ever discuss the mathematical sources of Deleuze's theory of multiplicity. Instead, he puts forth a secondary claim that, in so far as Deleuze does have a theory of multiplicity, it is not derived from a mathematical model, as is Badiou's own, but rather from a model that Badiou terms variously as “organic,” “natural,” “animal,” or “vitalistic.”6
Critics have rightly ascertained the obvious aim of this double strategy of avoidance and displacement: since Badiou presents himself as an ontologist of the multiple, and claims that his ontology is purely mathematical, he wants to distance Deleuze as far as possible from both these concerns.7 To get at what is interesting in the Badiou–Deleuze encounter, however, these all-too-obvious strategies need to be set aside, since the real terms of the confrontation clearly lie elsewhere. Badiou's general philosophical (or meta-ontological) position turns on the equation that “ontology = mathematics,” since “mathematics alone thinks being.”8 The more precise equation, however, would be that “ontology = axiomatic set theory,” since for Badiou it is only in axiomatic set theory that mathematics adequately “thinks” itself and constitutes a condition of philosophy.9 Badiou's ontology thus follows a not uncommon reductionist strategy: physics is ultimately reducible to mathematics, and mathematics to axiomatic set theory. From a Deleuzian viewpoint, the fundamental limitation of Badiou's philosophy—but also its fundamental interest—lies in this identification of ontology with axiomatic set theory. Badiou's confrontation with Deleuze must consequently be staged directly on each of these fronts—axiomatics, set theory, and their corresponding ontology—since it is only here that their differences can be exposed in a direct and intrinsic manner.
From this viewpoint, two essential differences between Badiou and Deleuze immediately come to light. First, for Deleuze, the ontology of mathematics is not reducible to axiomatics, but must be understood much more broadly in terms of the complex tension between axiomatics and what he calls “problematics.”10 Deleuze assimilates axiomatics to “major” or “royal” science, which is linked to the social axiomatic of capitalism (and the State), and which constantly attempts to effect a reduction, or even repression, of the problematic pole of mathematics, itself wedded to a “minor” or “nomadic” conception of science. For this reason, second, the concept of multiplicity, even within mathematics itself, cannot simply be identified with the concept of a set; rather, mathematics is marked by a tension between extensive multiplicities or sets (the axiomatic pole) and virtual or differential multiplicities (the problematic pole), and the incessant translation of the latter into the former. Reformulated in this manner, the Badiou–Deleuze confrontation can be posed and explored in a way that is internal to both mathematics (axiomatics versus problematics) and the theory of multiplicities (extensive versus differential multiplicities).
These two criteria allow us to assess the differences between Badiou and Deleuze in a way that avoids the red herrings of the “One” and “vitalism.” Although Badiou claims that “the Deleuzian didactic of multiplicities is, from start to finish, a polemic against sets,”11 in fact Deleuze nowhere litigates against sets, and indeed argues that the translation (or reduction) of differential multiplicities to extensive sets is not only inevitable ontologically, but necessary scientifically.12 What separates Badiou and Deleuze is rather the ontological status of events (in Badiou's sense). For Deleuze, mathematics is replete with events, to which he grants a full ontological status, even if their status is ungrounded and problematic; multiplicities in the Deleuzian sense are themselves constituted by events. In turn, axiomatics, by its very nature, necessarily selects against and eliminates events in its effort to introduce “rigor” into mathematics and to establish its foundations. It would be erroneous to characterize the problematic pole of mathematics as “merely” intuitive and operative, while “royal” axiomatics is conceptual and formalizable.
The fact is [writes Deleuze], that the two kinds of science have different modes of formalization … What we have are two formally different conceptions of science, and ontologically, a single field of interaction in which royal science [e.g., axiomatics] continually appropriates the contents of vague or nomad science [problematics], while nomad science continually cuts the contents of royal science loose. (TP 362, 367)
The task Deleuze takes upon himself, then, is to formalize the distinction between problematic and axiomati
c multiplicities in a purely intrinsic manner, and to mark the ontological and scientific transformations or conversions between the two.
Badiou, by contrast, in taking axiomatics as his ontological model, limits his ontology to the pole of mathematics that is constituted on the elimination of the events, and he therefore necessarily denies events any ontological status: “the event is forbidden, ontology rejects it.”13 As a consequence, he places himself in the paradoxical position of formulating a theory of the event on the basis of an axiomatic viewpoint that explicitly eliminates events. The event thus appears in Badiou's work under a double characterization. Negatively, so to speak, an event is undecidable or indiscernible from the ontological viewpoint of axiomatics; it is not presentable in the situation, but exists (if it can even be said to exist) on the “edge of the void” as a mark of the infinite excess of the inconsistent multiplicity over the consistent sets of the situation. Positively, then, it is only through a purely subjective “decision” that the hitherto indiscernible event can be affirmed, and made to intervene in the situation. Lacking any ontological status, the event in Badiou is instead linked to a rigorous conception of subjectivity, the subject being the sole instance capable of “naming” the event and maintaining a fidelity to it through the declaration of an axiom (such as “all men are equal,” in politics; or “I love you,” in love). In this sense, Badiou's philosophy of the event is, at its core, a philosophy of the “activist subject.”
Deleuze and Badiou thus follow opposing trajectories in their interpretations of mathematics. For Deleuze, problematics and axiomatics (minor and major science) together constitute a single ontological field of interaction, with the latter perpetually effecting a repression—or more accurately, an arithmetic conversion—of the former. Badiou, by contrast, grants an ontological status to axiomatics alone, and in doing so, he explicitly adopts the ontological viewpoint of “major” science, along with its repudiation and condemnation of “minor” science. As a result, not only does Badiou insist that Deleuze's concept of a virtual multiplicity “remains inferior to the concept of the Multiple that can be found in the contemporary history of sets,”14 but he goes so far as to claim “the virtual does not exist,”15 in effect denying the “problematic” pole of mathematics in its entirety. Interestingly, this contrast between Badiou and Deleuze finds a precise expression in a famous poetic formula. Badiou at times places his entire project under the sign of Lautréamont's poetic paean to “severe mathematics,” which Deleuze, for his part, cites critically:
