by Daniel Smith
A law of nature, as Hermann Weyl says, is necessarily expressed as a differential equation, and it is the calculus that establishes this link between mathematics and existence (Einstein's general relativity, for instance, made use of the tensor calculus). While axiomatics established the foundations of the calculus within mathematics, it is in the calculus itself that one must seek out the relation of mathematics with existence (problematics). This is no doubt the fundamental difference between Badiou and Deleuze. Badiou eliminates existence entirely from his ontology (there is no “being” of matter, life, sensibility …). In Deleuze, however, existence is fully a dimension of ontology as such: “force” is a determination of the being of matter (Leibniz); “vitalism” is a determination of the being of living things (Bergson); “intensity” is a determination of the being of the sensible (Kant); and so on. It is this genetic and problematic aspect of mathematics that remains inaccessible to set theoretical axiomatics.84
Badiou's neglect of the “problematic” dimension of Deleuze's thought results in numerous infelicities in his reading of Deleuze. In Deleuze: The Clamor of Being, Badiou's approach is guided by the presumption that “the starting point required by Deleuze's method is always a concrete case.”85 But this is a false presumption: for Deleuze, the starting point is always the problem, and “cases” are themselves derived from problems. The fundamental question is to determine which problems are interesting and remarkable, or to determine what is interesting or remarkable within the problem as such (group theory). If one starts with the case, it is in order to determine the problem to which it corresponds (“the creation of a concept always occurs as the function of a problem”) (ABC H). Paul Erdós famously assigned monetary values to mathematical problems, ranging from $10 to $3,000, depending not only on their degree of difficulty but also on their importance as problems, and he would pay out (often to graduate students) when the problem was solved.86 Similarly, Poincaré used to say that proving an uninteresting problem was worse than discovering a flaw in one's proof for a remarkable problem: the latter can be corrected, but the former will remain eternally trivial.87 The truth of a solution, in other words, is less important than the truth or “interest” of the problem being dealt with (a problem always has the solution it “deserves”).
Nor can one say—as Badiou frequently does—that Deleuze simply falls back on the “concrete” with the aim of producing phenomenological descriptions of the “figural.” Badiou goes so far as to claim that Deleuze's work “does not support the real rights of the abstract” and instead gives itself over to the “seductive scintillations of concrete analysis.” At best, Badiou thinks Deleuze draws “powerful metaphors (and yes, I do mean metaphors)” from mathematics and produces little more than “a metaphorizing phenomenology of pure change.”88 Not only does this imply a simplified view of the “concrete” (as Deleuze notes, “the true opposite of the concrete is not the abstract, it's the discrete … Lived experience is an absolutely abstract thing”),89 but also it entirely ignores Deleuze's development of a formal theory of problematics, and its complex mathematical sources. As Deleuze writes,
we must not see mathematical metaphors in all these expressions such as “singular and distinctive points” or “adjunct fields” … These are categories of the dialectical Idea, extensions of the differential calculus (mathesis universalis) … corresponding to the Idea in all its domains. (DR 190)
This avoidance, in turn, leads Badiou to make several misguided claims. In his book Bergsonism, for instance, Deleuze explicitly defines Bergsonian “intuition” as an elaborated method that consists in “the stating and creating of problems” (B 14). Badiou, to support his own theses, ignores this definition, and instead reinterprets intuition as a method that thinks beings as “merely local intensities of the One.”90 Similarly, Deleuze has suggested that
the intuitionist school (Brouwer, Heyting, Griss, Bouligand) is of great importance in mathematics, not because it asserted the irreducible rights of intuition, or even because it elaborated a very novel constructivism, but because it developed a conception of problems, and of a calculus of problems that intrinsically rivals axiomatics and proceeds by other rules (notably with regard to the excluded middle).91
But when Badiou links Deleuze to “the constructivist, and indeed intuitionist vision” of contemporary mathematics, he again ignores the link with problematics, and instead strangely construes the constructivist school as having pursued a purely “descriptive” task that starts from the sensible intuition of “already complex concretions.”92
Badiou's emphasis on axiomatics also affects his readings of Deleuze's work in the history of philosophy. Badiou, for instance, complains that “Deleuze neglects the function of mathematics in Spinoza,” for whom “mathematics alone thinks being.”93 But this is not quite correct either: Deleuze explicitly criticizes Spinoza for allowing his mathematics to assume a purely axiomatic form. “In Spinoza,” Deleuze writes, “the use of the geometric method involves no ‘problems’ at all” (DR 323 n21). This is why, in his readings of Spinoza, Deleuze emphasizes the role of the scholia (which are the only elements of the Ethics that fall outside the axiomatic deductions, and develop the theme of “affections”) and the fifth book (which introduces problematic hiatuses and contractions into the deductive exposition itself).94 No doubt it is this emphasis on the problematic aspects of the Ethics that rendered Deleuze's Spinoza “unrecognizable” to Badiou, who focuses on the theorematic and axiomatic apparatus.95 Indeed, with regard to problematics, Deleuze suggests that Descartes actually went further than Spinoza, and that Descartes the geometer went further than Descartes the philosopher: the “Cartesian method” (the search for the clear and distinct) is a method for solving problems, whereas the analytic procedure presented in Descartes's Geometry is focused on the constitution of problems as such (“Cartesian coordinates” appear nowhere in the Geometry).96 In all these characterizations, one at times senses in Badiou the semi-patronizing attitude of the “royal” scientist, who sees Deleuze's thought mired in problematics and its inferior concepts, and lacking the robustness required for work in “severe mathematics” and its “delicate axiomatics.”
But perhaps the most striking omission in Badiou's work, especially given his political interests, is his neglect of Deleuze's political philosophy, since the latter is derived directly from these mathematical models. The central thesis of Capitalism and Schizophrenia (whose very title reflects the axiomatics–problematics distinction) is that capitalism itself functions on the basis of an axiomatic—not metaphorically, but literally.97 This is because capital as such is a problematic multiplicity: it can be converted into discrete quantities in our paychecks and loose change, but in itself the monetary mass is a continuous or intensive quantity that increases and decreases without any agency controlling it. Like the continuum, capital is not masterable by an axiom; or rather, it constantly requires the creation of new axioms (it is “like a power of the continuum, tied to the axiomatic but exceeding it”) (TP 466). In turn, capital produces other flows that follow these circuits of capital: flows of commodities, flows of population, flows of labor, flows of traffic, flows of knowledge, and so on—all of which have a necessarily “problematic” status from the viewpoint of the capitalist regime. The fundamental operation of the capitalist State, in Deleuze's reading, is to attempt to control these “deterritorialized” flows by axiomatizing them—but this axiomatization can never be complete, not only because of the inherent limits of any axiomatic, but also because new “problematics” are constantly in the process of being created. “The true axiomatic,” Deleuze says, “is social and not scientific.”98 To take one well-known example: for Deleuze “minorities” are, in themselves, non-denumerable multiplicities; they can be brought into the capitalist axiomatic by being denumerated, counted, given their identity cards, made a part of the majority (which is a denumerable multiplicity—that is, a multiplicity of discrete numerical elements); but there is also a power to mi
norities that comes from not entering into the axiomatic, a power that does not reduce minorities to a mere “tear” or “rupture” in the axiomatic, but assigns to them an objective and determinable ontological positivity of their own as problematic.99
The issue is not at all anarchy versus organization [writes Deleuze], nor even centralization versus decentralization, but a calculus or conception of problems of non-denumerable sets, against the axiomatic of denumerable sets. Such a calculus may have its own compositions, organizations, and even centralization; nevertheless, it proceeds not via the States or the axiomatic process but via a pure becoming of minorities.100
This brings us back again, finally, to the question of the event, which is where the Badiou–Deleuze differend appears in perhaps its starkest contrast. In effect, the respective ontologies of Deleuze and Badiou move in opposing directions: Deleuze's is a “bottom-up” ontology (from problematics to discretization-axiomatization), whereas Badiou's is a “top-down” ontology (elaborated exclusively from the viewpoint of axiomatics, denying the existence of problematics). From Deleuze's viewpoint, this denial of problematics constitutes the intractable limitation of Badiou's ontology, which consequently appears in two forms. On the one hand, for Badiou, Being is presented in purely discrete terms: what is “subtracted” from the “count-asone” rule that constitutes consistent sets (knowledge) is an inconsistent or “generic” multiplicity, the pure discrete multiple of Being, which in itself remains indiscernible, unpresented, and unnamable as such (the void); an event—that which is not “Being-as-Being”, if one occurs, intervenes “on the edge” of this void, and constitutes the condition of a truth-procedure. But this entire characterization revolves in the domain of the discrete; what is truly “unnamed” within it is the entire domain of problematics and its “repressed” notions, such as continuous variation. Such is the substance of the critique Deleuze addresses to Badiou in What is Philosophy? “The theory of multiplicities,” he writes, “does not support the hypothesis of an ‘any multiplicity whatever’”: that is, a purely “generic” discrete multiplicity (WP 152). The discretization program found its point of “genesis” in problematics, and in any adequate mathematical ontology there must therefore be “at least two multiplicities, two types, from the outset”—namely, the continuous and the discrete, the non-metric and the metric, and so on. “This is not because dualism is better than unity,” continues Deleuze, “but because the multiplicity is precisely what happens between the two”: that is, in the movement of conversion that translates the continuous into the discrete, the non-metric into the metric, etc. It is precisely this movement of translation, and Deleuze's own formalization of problematic multiplicities, that we have attempted to sketch out above. On the other hand, for Badiou, the “truth” of Being is presented in a purely axiomatic form. As a result, the articulation or “thinking” of a inconsistent multiplicity—the operation of a “truth-procedure”—can only be subjective, since it is only by means of a purely subjective “decision” that an event can be affirmed, and the hitherto indistinguishable elements of the multiplicity can be named, thereby altering the “situation” through the declaration of an axiom. Badiou necessarily dissociates this process of subjectivation from ontology itself, since it is only the subject's “fidelity” to the event that allows the elements of the altered situation to achieve consistency. Hence the fundamental duality that Badiou posits between “Being” and “Event,” and the separation of the articulation of Being from the path of the subject or truth. For Deleuze, by contrast, the genesis of truth (and the genesis of axiomatics itself) must always be found in problematics: Being necessarily presents itself under a problematic form, and problems and their ideal events always are ontological, not subjective. The generation of truth, in other words, is derived from the constitution of problems, and a problem always has the truth it “deserves” in so far as it is completely constituted as a problem. The greatness of the calculus in mathematics is that it provided a precise symbolism with which it could express problems that, before its invention, could not even have been posed. If Badiou is forced to define truth in purely subjective terms, it is because he wrongly limits his ontology to axiomatics, and denies himself the real ontological ground of truth in problematics.
The path followed by Badiou in Being and Event, then, is almost the exact inverse of that followed by Deleuze in Difference and Repetition, and the two paths exemplify Deleuze's own distinction between an immanent and a transcendent ontology. For Deleuze, a purely “immanent” ontology is one in which there is nothing “outside” Being or “other” than Being, and he therefore grants full ontological status to both problematics and axiomatics. Since Badiou limits his ontology to axiomatics, he is forced to reintroduce an element of transcendence in the form of the event, which is “supplemental” to ontology, “supernumerary”: there can be no ontology of the event, since the event itself introduces a “rupture” into being, a “tear” in its fabric. In What is Philosophy?, this is exactly how Deleuze defines the “modern” way of saving transcendence: “it is now from within immanence that a breach is expected … something transcendent is reestablished on the horizon, in the regions of non-belonging,” or as Badiou would say, from the “edge of the void” (WP 46–7). Whereas an immanent ontology “never has a supplementary dimension to that which transpires upon it,” an ontology of transcendence “always has an additional dimension; it always implies a dimension supplementary to the dimensions of the given” (TP 266; SPP 128). In this sense, Badiou's is indeed an analogical and reflexive ontology that requires a mechanism of transcendence to “save” the event.101 Though Badiou is determined to expel God and the One from his philosophy, he winds up reassigning to the event, as if through the back door, many of the transcendent characteristics formerly assigned to the divine. In Plotinus, it is the One which is “beyond” Being; in Badiou, it is the event which is “not being-as-being,” that “interrupts” Being. In religious life, what is transformative is fidelity to God; in Badiou, it is fidelity to the event. In Christian theology, it is God who creates ex nihilo; in Badiou, it is the subject who proclaims the event and in a sense assumes those once divine powers (as Badiou declares triumphantly, “I conceptualize absolute beginnings!”).102 The primary aim of this paper has been to clarify, in a more adequate manner than Badiou did, the fundamental points of disagreement between the two philosophers. Deleuze, however, often insisted on the irreducibility of “taste” in philosophy, and if these analyses are correct, it would seem that Badiou's taste for discretization and axiomatization in mathematics concealed a deeper taste for a kind of transcendence-within-immanence, with its conceptualizations of total ruptures and absolute beginnings.
ESSAY 18
Jacques Lacan
The Inverse Side of the Structure: Žižek on Deleuze on Lacan
I
n an interview in 1995, shortly before his death, Deleuze was asked by his interviewer, Didier Éribon, about his relationship with Jacques Lacan. In response, Deleuze told the following story:
Lacan noticed me when he devoted a session of his seminar to my book on Sacher-Masoch [1967]. I was told—although I never knew anything more than this—that he had devoted more than an hour to my book. And then he came to a conference at Lyon, where I was then teaching. He gave an absolutely unbelievable lecture … It was there that he uttered his famous formula, “Psychoanalysis can do everything except make an idiot seem intelligible.” After the conference, he came to our place for dinner. And since he went to bed very late, he stayed a long time. I remember: it was after midnight and he absolutely had to have a special whisky. It was truly a nightmare, that night.
My only great encounter with him was after the appearance of Anti-Oedipus [1972]. I'm sure he took it badly. He must have held it against us, Félix and me. But finally, a few months later, he summoned me—there's no other word for it. He wanted to see me. And so I went. He made me wait in his antechamber. It was filled with people, I didn't know if
they were patients, admirers, journalists … He made me wait a long time—a little too long, all the same—and then he finally received me. He rolled out a list of all his disciples, and said that they were all worthless [nuls] (the only person he said nothing bad about was Jacques-Alain Miller). It made me smile, because I recalled Binswanger telling the story of a similar scene: Freud saying bad things about Jones, Abraham, etc. And Binswanger was shrewd enough to assume that Freud would say the same thing about him when he wasn't there. So Lacan was speaking, and everyone was condemned, except Miller. And then he said to me, “What I need is someone like you” [C'est quelqu'un comme vous qu'il me faut.].1
This is a revealing anecdote, for at least two reasons. First, one might say that the disciple Lacan wound up “getting” was not Gilles Deleuze but Slavoj Žižek, among others, which puts Žižek's encounter with Deleuze in Organs Without Bodies in a revealing retrospective light.2 Second, and more importantly, Deleuze's personal encounter with Lacan took place after the publication of Anti-Oedipus in 1972. Anti-Oedipus presents, among other things, a famous critique (though not rejection) of psychoanalysis, which Deleuze and Guattari pursued, in part, by means of an engagement with Lacan's work. In this sense, one could say that Deleuze was indeed a Lacanian, but in the exact same manner that he was a Spinozist or a Leibnizian: he was neither a slavish follower nor a dogmatic reader of Lacan, but followed the internal trajectory of Lacan's thought to the point where he would push it to its “differential” limit (Deleuze's all-too-well-known image of philosophical “buggery,” which makes thinkers produce their own “monstrous” children). Despite Deleuze's initial worries about Lacan's reaction to Anti-Oedipus, Lacan obviously did not dismiss the book. On the contrary, not only was his reading of the book the apparent basis of his “summons” to Deleuze, but also he even seems to have been influenced by Anti-Oedipus in his own thinking. Žižek himself suggests that Lacan's later work (after Seminar XI in 1964) is marked by an increased interest in the theory of the drives and anti-Oedipal themes (OB 102, 176). Given the complex status of the drives that one finds elaborated in Anti-Oedipus (for instance, the thesis that the “drives are part of the infrastructure itself,” AO 63), one can assume that Lacan saw Deleuze neither as an antagonistic critic, nor even a potential bearer of orthodoxy (à la Miller), but rather a highly original fellow traveler.
