by Daniel Smith
In Leibniz, then, the differential calculus refers to a domain that is both mathematical and psychological, a psycho-mathematical domain; there are differentials of consciousness just as there are differentials of a curve. Several important consequences follow from this. Space and time here cease to be pure a priori givens, as in Kant, but are determined genetically by the ensemble or nexus of these differential relations in the subject. Similarly, objects themselves cease to be empirical givens and become the product of these relations in conscious perception. Moreover, Descartes's principle of “clear and distinct” ideas is broken down into two irreducible values, which can never be reunited to constitute a “natural light”: conscious perceptions are necessarily clear but confused (not distinct), while unconscious perceptions (Ideas) are distinct but necessarily obscure (not clear).18 Indeed, Leibniz can be said to have developed one of the first theories of the unconscious, a theory that is very different from the one developed by Freud. The difference is that Freud conceived of the unconscious in a conflictual or oppositional relationship to consciousness, and not a differential relationship. In this sense, Freud was dependent on Kant, Hegel, and their successors, who explicitly oriented the unconscious in the direction of a conflict of will, and no longer a differential of perception. The theory of the unconscious proposed by Deleuze and Guattari in Anti-Oedipus is a differential and genetic unconscious, and thus thoroughly inspired by Leibniz.19
THE THEORY OF SINGULARITIES
There is a final problem that Deleuze points to in Leibniz's thought. On the surface, there would appear to be a contradiction between the principle of indiscernibles and the law of continuity. On the one hand, the principle of indiscernibles tells us that every difference is conceptual, that no two things have the same concept; to every thing there correspond determinate differences that are assignable in its concept. On the other hand, the principle of continuity tells us that things proceed via vanishing differences, infinitely small differences: that is, unassignable differences. Thus, Leibniz seems to be saying, at one and the same time, that every thing proceeds by an unassignable difference, and that every difference is assignable and must be assigned in the concept. The question is: Is it possible to reconcile the principle of indiscernibles with the law of continuity?
Deleuze's thesis is that the solution to this problem has to be posed in terms of the theory of singularities, which is an extension of the theory of differential equations. In logic, the notion of the “singular” has long been understood in relation to the “universal.” In mathematics, however, the singular is related to a very different set of notions: the singular is distinguished from or opposed to the regular; the singular is what escapes the regularity of the rule. More importantly, mathematics distinguishes between singular points that are remarkable and those that are ordinary. Geometrical figures, for instance, can be classified by the types of singular points that determine them. A square has four singular points, its four corners, and an infinity of ordinary points that compose each side of the square (the calculus of extrema). Simple curves, such as the arc of circle, are determined by a single singularity, which is either a maximum or a minimum, or both at once (the calculus of maxima and minima).20 The differential calculus deals with the more difficult case of complex curves. The singularities of a complex curve are the points in the neighborhood of which the differential relation changes sign (focal points, saddle points, knots, etc.); the curve increases, the curve decreases. These points of increase or decrease are the singular points of the curve; the ordinary points are what constitute the series between the two singularities. The theory of singularities provides Deleuze with his final, more technical definition of the law of continuity: the continuum is the prolongation of a singularity over an ordinary series of points until it reaches the neighborhood of the following singularity, at which point the differential relation changes sign, and either diverges from or converges with the next singularity. The continuum is thus inseparable from a theory or an activity of prolongation: there is a composition of the continuum because the continuum is a product.
In this way, the theory of singularities provides Deleuze with a model of individuation or determination: one can say of any determination in general (any “thing”) that it is a combination of the singular and the ordinary: that is, it is a “multiplicity” constituted by its singular and ordinary points. Just as mathematical curves are determined by their points of inflection (extrema, minima and maxima, etc.), so physical states of affairs can be said to be determined by singularities that mark a change of phase (boiling points, points of condensation, fusion, coagulation, crystallization) and a person's psychology by their “sensitive” points (points where a person “breaks down” in anger or tears; states of joy, sickness and health, fatigue and vitality, hope and anxiety). But such singularities, Deleuze insists, can none the less be considered apart from their actualization in a physical state of affairs or a psychological person (see LS 52). Deleuze here reaches a domain that is distinct from, and logically prior to, the three domains that Kant would later denounce as transcendental illusions or Ideas: the Self, the World, and God. Each of these Ideas has a determinate place in Leibniz's philosophy: God is the Being who, faced with the infinity of possible worlds, chose to actualize this World, a world that exists only in its individual monads or Selves, which express the world from their own point of view. But what this Leibnizian schema presupposes, Deleuze argues, is the determination of a “transcendental field” that is prior to God, World, and Self, a field populated by singularities that are a-theological, a-cosmic, and pre-individual. It implies a transcendental logic of singularities that is irreducible to the formal logic of predication. Here, for example, are three singularities of the individual “Adam,” expressed in an infinitive form: “to be the first man,” “to live in a garden of pleasure,” “to have a woman come out of one's rib.” And then a fourth singularity: “to sin.” We can prolong each of these four singular points over a series of ordinary points such that they all have common values in both directions; a continuity is established between them. But then add a fifth singularity: “to resist the temptation.” The lines of prolongation between this fifth singularity and the first three are no longer convergent: that is, they do not pass through common values; there is a bifurcation in the series at this singularity, and a discontinuity is introduced. Adam the non-sinner is thus incompossible with this world, because it implies a singularity that diverges with this world.
The theory of singularities plays a double role in Deleuze's work on Leibniz. On the one hand, it allows Deleuze to solve the riddle posed by the relation between indiscernibility and continuity within Leibniz's own philosophy. The world “in itself” is indeed governed by the law of continuity, since continuity is nothing other than the composition of singularities in so far as they are prolonged over the series of ordinaries that depend on them. But the world does not exist “in itself”; it exists only in the individuals that express it. And the real definition of the individual is: the accumulation or coincidence of a certain number of pre-individual singularities that are extracted from the curve of the world, each of them being discontinuous and unique, and hence governed by the principle of indiscernibles. Individuation, in other words, “does not move from a genus to smaller and smaller species, in accordance with a rule of differenciation; it goes from singularity to singularity, in accordance with the rule of convergence or prolongation that links the individual to such and such a world” (FLB 64). On the other hand, Deleuze is not content simply to provide a reading of Leibniz. “These impersonal and pre-individual nomadic singularities,” Deleuze writes, speaking in his own name, “are what constitute the real transcendental field” (LS 109). Difference and Repetition and Logic of Sense are Deleuze's attempt to define the nature of this transcendental field, freed from the limitations of Leibniz's theological presuppositions, and using his own conceptual vocabulary (multiplicity, singularity, virtuality, problematic, event, and so on). In Del
euze, the Ideas of God, World, and Self take on completely different demeanors than they do in Leibniz. God is no longer a Being who chooses the richest compossible world, but has now become a pure Process that makes all virtualities pass into existence, forming an infinite web of divergent and convergent series. The World is no longer a continuous curve defined by its pre-established harmony, but has become a chaotic universe in which divergent series trace endlessly bifurcating paths, giving rise to violent discords. And the Self, rather than being closed on the compossible world it expresses from within, is now torn open by the divergent series and incompossible ensembles that continually pull it outside itself (the monadic subject, as Deleuze puts it, becomes the nomadic subject).21
It is at this point that Deleuze's reading of Leibniz would end, and a reading of Deleuze's own philosophy would have to begin. Our aim here has been simply to follow Deleuze's deduction of a principle of difference, within Leibniz's own thought, from the simplest formulation of the principle of identity (A is A). An elaboration of Deleuze's own thought would have to move in the opposite direction, as it were, showing how Deleuze produces his own deduction of concepts starting from the principle of difference: the differential relation and its determinable elements, the resulting singularities that are extended in series (with their connective, convergent, and divergent syntheses), which thereby constitute a multiplicity, whose modal status is purely virtual (as opposed to constituting a set of “possibilities,” as in Leibniz), and so on. It would not be an exaggeration to say that almost all of Deleuze's fundamental metaphysical concepts (difference, singularity, multiplicity, virtuality) are derived from this Leibnizian matrix. Classical reason, says Deleuze, collapsed under the blow of divergences, discordances, and incompossibilities, and Leibniz's philosophy was one of the last attempts to reconstitute a classical reason. It did so by multiplying its principles, relegating divergences to so many possible worlds, making incompossibilities so many frontiers between worlds, and resolving the discords that appear in this world into the melodic lines of the pre-established harmony. But Leibniz's Baroque reconstitution could only be temporary. With the collapse of classical reason, the task of philosophy would be to think without principles, to start neither with the identity of God, nor the Self, nor the World, but rather a transcendental field of differences and singularities that conditions the construction of empirical selves and the actual world. This is the task that Deleuze adopts as his own: “We seek to determine an impersonal and pre-individual transcendental field that does not resemble the corresponding empirical fields” (LS 102). It is a thoroughly contemporary project, but one that allows Deleuze to reach back into the history of philosophy and make use of Leibniz's philosophy and Leibniz's concepts in the pursuit of his own philosophical aims.22
ESSAY 4
Hegel
Deleuze, Hegel, and the Post-Kantian Tradition
D
eleuze has often been characterized as an “anti-dialectical” and hence “anti-Hegelian” thinker. Evidence for these characterizations is not difficult to amass. In his well-known “Letter to Michel Cressole” (reprinted in Negotiations as “Letter to a Harsh Critic”), Deleuze, while discussing his post-war student days in the 1940s and 1950s, says explicitly that, at the time, “what I detested most was Hegelianism and the dialectic” (N 6). Nietzsche and Philosophy, which Deleuze published in 1962, is an avowedly anti-Hegelian tract; its final chapter bears the ominous title, “Against the Dialectic” (NP 147–94). Even as late as 1968, Deleuze writes that the themes of his magnum opus, Difference and Repetition, were in part attributable, as he states in its preface, “to a generalized anti-Hegelianism” (DR ix). This theme is echoed by Vincent Descombes, in his influential book Modern French Philosophy, who characterizes the entire generation of philosophers to which Deleuze belongs—which includes Jacques Derrida, Michel Foucault, Jean-François Lyotard, and Michel Serres—by their reaction against Hegel, and in particular against Alexandre Kojève's reading of Hegel.1 Foucault himself noted in his inaugural lecture at the Collège de France: “Whether through logic or epistemology, whether through Marx or Nietzsche, our entire epoch struggles to disengage itself from Hegel.”2
These characterizations have been repeated so often in the secondary literature that they have assumed an almost canonical status. They are the lens through which Deleuze's thought is inevitably read and interpreted, to the point where they have become clichés (in Deleuze's sense of this term) that prejudge the nature of his thought and pre-program its interpretation and reception. Such characterizations, however, are at best partial and at worst inaccurate. Deleuze is not an anti-dialectical thinker as such; one of the explicit aims of Difference and Repetition is to propose a new conception of dialectics, based on a principle of difference (and affirmation) rather than a model of contradiction (and negation).3 In this sense, Deleuze's early anti-Hegelianism is primarily polemical, and must be understood in the context of the revised theory of Ideas proposed in Difference and Repetition. In what follows, I would like to defend these claims, not by analyzing Deleuze's reading of Hegel as such, but rather by analyzing the context in which that reading should be understood. That context not only includes Deleuze's relation to the history of philosophy in general, but also and more particularly his relation to the post-Kantian tradition to which Hegel belongs. In his early work, when his anti-Hegelian polemics were strongest, Deleuze undertook a revisionary interpretation of the entire post-Kantian tradition—an interpretation in which the work of Salomon Maimon played a pivotal role. Deleuze's explicit critiques of Hegel, and his renewed concept of dialectics, should be understood in terms of the broader project Deleuze was pursuing in his work prior to the writing of Difference and Repetition.
DELEUZE AND THE HISTORY OF PHILOSOPHY
Deleuze's early polemical reaction against Hegel must be contextualized, both sociologically and personally, in terms of the academic institutional milieu in which Deleuze was trained as a philosopher. (This French milieu has been analyzed by Pierre Bourdieu in works such as Homo Academicus and The State Nobility).4 When Deleuze was at the Sorbonne, doing philosophy meant doing the history of philosophy. In order to pass the agrégation examination in philosophy, which allowed one to teach in the French educational system, students were required to do close readings of classic texts in the history of philosophy. If they wanted to do “creative” work in this context, philosophy students necessarily had to do so in the context of interpretive readings of this type. François Châtelet, a fellow student at the Sorbonne, and later a colleague at Vincennes, recounts a story that illustrates the manner in which Deleuze, as a student, was able to negotiate the tension between the university's requirements and his own interpretive invention:
I preserve the memory of a reading by Gilles Deleuze, who had to treat I don't know what classic theme of Nicholas Malebranche's doctrine before one of our most profound and most meticulous historians of philosophy, and had constructed his demonstration, solid and supported with peremptory references, around the sole principle of the irreducibility of Adam's rib. At the expression of this adopted principle, the master turned pale, and obviously had to keep himself from intervening. As the exposition unfolded, the indignation was changed into incredulity, and then, by the end, into admiring surprise. And he justly concluded by making us all return the next week with our own analysis of the same theme.5
It is not by chance, therefore, that the works of Deleuze and Jacques Derrida are frequently indexed on readings in the history of philosophy. (Both thinkers persistently return to the history of philosophy, even after “experiments” such as Derrida's The Post Card or Deleuze and Guattari's A Thousand Plateaus.)6 Moreover, at the time, writing on certain figures often carried a certain political connotation; in seventeenth-century studies, for instance, Cartesians tended to be on the right, Spinozists on the left, and Leibnizians somewhere in the center.
There is also an idiosyncratic component to this question that is often overlooked. It
has been suggested that thought proceeds by way of the conflict of generations, the young rebelling against their elders. This seems particularly true with philosophers, whose initiation into philosophy can often be traced to a kind of theoretico-amorous admiration that at some point crystallizes around a particular teacher—what Michèle Le Dœuff has termed the “theoretico-erotic transference” (and which Plato simply called “eros”).7 In the Abécédaire, Deleuze has traced his own initiation into philosophy, at age fourteen, to his curious encounter with a teacher named Pierre Halwachs, whom he met on the beaches at Deauville (ABCE). Later, it was certain faculty at the Sorbonne, such as Ferdinand Alquié and Jean Hyppolite, who would occupy this role. What allows the student to overcome this initial transference, or the disciple to break with the master, Le Dœuff suggests, is precisely an institutional framework, which provides a third term beyond the dynamics of a dual relationship. In some well-known passages, Deleuze has evoked the effect these institutional constraints and related personal affiliations had on his philosophical formation:
I was taught by two professors, whom I liked and admired a lot: Alquié and Hyppolite … The former had long white hands and a stammer which might have been a legacy of his childhood, or there to hide a native accent, and which was harnessed to the service of Cartesian dualisms. The latter had a powerful face with unfinished features, and rhythmically beat out Hegelian triads with his fist, hanging his words on the beats. At the Liberation, we were still strangely stuck in the history of philosophy. We simply plunged into Hegel, Husserl and Heidegger; we threw ourselves like puppies into a scholasticism worse than that of the Middle Ages … After the Liberation, the history of philosophy tightened around us—without our realizing it—under the pretext of opening up a future of thought, which would also be the most ancient thought. The “Heidegger question” did not seem to me to be “Is he a bit of a Nazi?” (obviously, obviously) but “What was his role in this new injection of the history of philosophy?” … The history of philosophy has always been the agent of power in philosophy, and even in thought. It has played the role of a repressor: how can you think without having read Plato, Descartes, Kant, and Heidegger, and so-and-so's book about them? A formidable school of intimidation … So I began with the history of philosophy when it was still being prescribed. For my part, I could not see any way of extracting myself. I could not stand Descartes, the dualisms and the cogito, or Hegel, the triad and the operation of negation. (D 12–14)