DANIEL W. SMITH LOGIC AND EXISTENCE: Deleuze on the "Conditions of the Real"* Introduction Here is a philosophical problem that lies at the core of Deleuze's interest in the rationalists, and particularly Leibniz. By itself, thought has no means of distinguishing between the possible and the real: I can have a concept of 100 dollars in my mind, and while it may be important to me practically whether or not I actually have 100 dollars in my pocket, the existence of 100 dollars in reality changes nothing from the point of view of the concept, that is, from the viewpoint of pure thought. The position of the real is outside the concept, the existing thing is external to the concept. (This was Kant's argument against the ontological argument: existence is not a predicate; from the viewpoint of the concept, an existing God is no more perfect than a non-existing God.) Even though I know that unicorns do not exist, I can still form a concept or a representation of a unicorn, or defi ne the essence of a unicorn. For Deleuze, this is one of the fundamental problems of a theory of thought: How can thought leave this meager sphere of the possible in order to think the real, that is, to think existence itself, to think existing things. Pre-Kantians like Leibniz posed this problem in terms of the distinction between truths of essence ("A triangle has three sides") and truths of existence ("Caesar crossed the Rubicon"), while post-Kantians like Maimon posed the problem in terms of the distinction between the conditions of possible experience and the conditions of real experience. I would like to approach this logical problem from a semicinematic perspective. "Theoretically," Deleuze once mused, "Jean-Luc Godard would be capable of fi lming Kant's Critique or Spinoza's Ethics" (DI 141). In the 1990s, Godard did a multi-part fi lm entitled Histoire(s) du cinema; following Deleuze's suggestion, I am imagining Godard undertaking a similar project entitled Histoire(s) de la philosophie. I have no idea, of course, what Godard might have done in such a fi lm, but nonetheless I am presenting the fi rst part of this paper as a possible scenario for a single sequence of that multipart fi lm, which has as its title Logic and Existence, which I am borrowing from a well-known book by Jean Hyppolite.1 Here's the fi rst shot: a radiant sphere hovering in the middle of nowhere. Nothing is written on it, but we know it is the sphere of logic. The fi lm begins here for an obvious reason: if thought, on its own, is only capable of thinking the possible, it does so on the basis of what can be called logical principles. Classical logic famously identifi ed three such principles: the principle of identity (which says that "A is A," or "A thing is what it is"), and then two 362 smaller principles which seem to be specifi cations of the principle of identity: the principle of non-contradiction (which says that "A is not non-A," or "A thing is not what it is not") and the principle of the excluded middle (which says "either A or not-A," that is, between A or not-A, there is no middle term). Taken together, these three principles determine what is impossible, that is to say, what is unthinkable without contradiction: something that would not be what it is (which would contradict the principle of identity); something that would be what it is not (which would contradict the principle of noncontradiction); and something that would be both what it is and what it is not (which would contradict the principle of the excluded middle). This sphere of logic would seem to enclose us within the domain of the possible, or what classical philosophy called the domain of essences. But this opening shot sets up the problem with a visual image: Is there any way in which these three classical principles can be used to exit the sphere of logic and penetrate existence itself? The response to this question will take us through three scenes, which correspond to three broad sequences in the history of philosophy, three attempts to resolve this problem using one of these logical principles. Scene one focuses on the pre-Kantians, the rationalists; its star is Leibniz, since it was he who attempted to extend the principle of identity to the whole of existence. Scene two focuses on the post-Kantians, primarily the German Idealists; its story culminates in Hegel, since it was he who attempted to extend the principle of non-contradiction to the whole of existence. Scene three, fi nally, looks at that loosely related group of thinkers that often tend to be called, precisely, "existentialists," since it is they who attempted to extend the principle of the excluded middle to existence. The screenplay reaches its climax with Deleuze: at the end, it briefl y examines the reasons why Deleuze is at once fascinated with all three of these philosophical attempts to "think existence," but nonetheless thinks they fail, and why he ultimate charts out his own response to the problem. The ending, alas, is somewhat truncated, since the production went over budget, which meant that entire scenes wound up being consigned to the editing room fl oor. I. Leibniz and the Principle of Identity Scene one focuses on Leibniz, who would have been a perfect philosophical movie star, since he is a man of contradictions: he is somewhat reactionary, a defender of law and order, of the status quo, of "policing" in every sense of the term; he says malicious things about Spinoza; but at the same time he invents the calculus, and undertakes one of the most remarkable adventures of thought in the history of philosophy. The reason: Leibniz took the most basic principle of logic – the principle of identity – and attempted to make it penetrate existence in its entirety by formulating the reciprocal of the principle of identity, namely, the principle of suffi cient reason. Scene one briefl y shows how. 363 The classical formulation of the principle of identity is "A is A" ("blue is blue," "God is God," "a triangle is a triangle"). But such phrases, Leibniz writes, "seem to do nothing but repeat the same thing without telling us anything."2 The principle of identity is certain, but empty. Are we truly thinking when we say "A is A"? It's not clear. A more popular formulation of the principle of identity would be: "A thing is what it is."3 This formula goes further than the formula "A is A" because it shows us the region of Being governed by the principle of identity: identity consists in manifesting the identity between the thing and what the thing is, what classical philosophy termed the "essence" of a thing. But Leibniz then provides us with a more philosophical formulation of the principle of identity, which states that "Every analytic proposition is true." What is an analytic proposition? An analytic proposition is a proposition in which the subject and the predicate reciprocate with each other. The principle of identity is presented in the form of a reciprocal proposition: there is a subject, A; then the verb "to be"; and then a predicate or attribute, A. The principle of identity states that, in the proposition "A is A," there is a reciprocity between the subject and the predicate, even though the distinction between subject and predicate remains. What Leibniz calls analysis is the operation that discovers a predicate in a notion taken as a subject: if I show that a given predicate is contained in a notion, then I have done an analysis. But Leibniz needs a second principle to make us think existing beings. The principle of identity posits the identity of the thing and what the thing is, even if the thing itself does not exist; existing things thus appear to lie outside the principle of identity. This second principle is what Leibniz calls the principle of suffi cient reason, the popular expression of which would be "everything has a reason." This is the great battle cry of rationalism – everything has to have a reason, there must be a reason for everything that takes place – which Leibniz, the greatest of the rationalists, will push to its limit. How can a principle as seemingly vague as "everything has a reason" make us think existing beings? That is what Leibniz explains in his metaphysical formulation of the principle of suffi cient reason: "all predication has a foundation in the nature of things" (FLB 42). This means that everything that is said of a thing is included, contained, or comprised in the concept of the thing. What is said or predicated of a thing? First of all, its essence, and at this level there is no difference between the principle of identity and the principle of suffi cient reason, which takes up and presumes everything acquired with the principle of identity. But what is said or predicated of a thing is not only the essence of the thing, it is also the totality of the affections and events – that is, all the differences – that happen to or are related to or belong to the thing in its existence.4 For example: Caesar crossed the Rubicon. Since this is a true proposition, Leibniz will say that the predicate "crossed the Rubicon" must be contained in the Caesar's notion or concept, and that we should be able to demonstrate that this is the case.5 This is an astonishing philosophical move, which would make for dramatic cinema, if thought itself could be fi lmed. The principle of identity gives us 364 a model of truth that is certain and absolute – "an analytical proposition is necessarily a true proposition" – but it does not appear to make us think anything. So Leibniz reverses the formulation of the principle of identity using the principle of reciprocity: "a true proposition is necessarily an analytic proposition." The principle of suffi cient reason, in other words, is the reciprocal of the principle of identity. Through this reversal, the identity principle forces us to think something, and it allows Leibniz to conquer a radically new domain, namely, the domain of existence. There are two things that might be said about Leibniz principle of suffi cient reason. The fi rst is that it seems absolutely crazy, it is hard to see how anyone could take it seriously. Ian Hacking once wrote that "Leibniz's claim that in every true proposition the predicate is contained in the subject is the most absurd theory of truth that has ever been advanced."6 It is easy to see why: Leibniz is claiming that, just as we can demonstrate that the predicate "three sides" is included in the subject "triangle," we should be able to demonstrate that the predicate "crossing the Rubicon" is contained in the concept of "Caesar." One can hardly imagine the conditions under which such a thing would be possible, unless we were God himself, with his infi nite understanding. But the second point is this: Leibniz's posing of the problem of suffi cient reason would mean nothing if he had not had the means to create the philosophical concepts that were necessary to explore the conditions of this problem (This is Deleuze's defi nition of philosophy: the creation of concepts in response to shifting problematics.) Here, we introduce a shot of Leibniz standing on a precipice, about to plunge into the labyrinth of the continuum, the maelstrom of the actual infi nite. He is calm, tranquil, and confi dent, however, because for every problem posed by his search for suffi cient reason he will create a concept adequate to it, even as he is falling into the abyss. Here are a few of those concepts – just enough to feel the power of Leibniz's thought. First, if everything I attribute with truth to a subject must be contained in the notion of the subject, then I am forced to include in the notion of the subject not only the thing I attribute to it with truth, but the totality of the world. Why is this the case? By virtue of a principle that is very different from the principle of suffi cient reason, namely, the principle of causality. The principle of suffi cient reason ("everything has a reason") is not the same thing as the principle of causality ("everything has a cause"). "Everything has a cause" means that A is caused by B, B is caused by C, and so on – an infi nite series of causes and effects. "Everything has a reason," by contrast, means that one has to give a reason for causality itself, namely, that the relation A maintains with B must in some manner be included or comprised in the notion of A.7 This is how the principle of suffi cient reason goes beyond the principle of causality: the principle of causality states the necessary cause of a thing but not its suffi cient reason.8 Thus, once Leibniz says that the event "crossing the Rubicon" is included in the notion of Caesar, he cannot stop himself: he is forced to include the totality of the world in Caesar's concept. This is because "crossing the Rubicon" has multiple causes and multiple effects, such as the establishment 365 of the Roman Empire; it stretches to infi nity backward and forward by the double play of causes and effects. We therefore cannot say that "crossing the Rubicon" is included in the notion of Caesar without saying that all the causes and effects of this event are also included in the notion of Caesar. This is the fi rst hallucinatory concept that follows from the principle of suffi cient reason: the concept of expression. Each of us, in our concept, expresses or contains the entirety of the world. A second concept immediately follows. For there is a danger here for Leibniz: if each concept of the subject expresses the totality of the world, this would seem to indicate that there is only a single subject, and that individuals are mere appearances of this universal subject (such as Spinoza's substance, or Hegel's absolute spirit), But Leibniz cannot follow such a path without repudiating himself, since his entire philosophy remains fi xed on the individual.9 To avoid this danger, Leibniz creates another new concept: each individual notion comprehends or includes the totality of the world, he says, but from a certain point of view. This marks the beginning of "perspectivist" philosophy, which would be taken up by later philosophers such as Nietzsche (who nonetheless understood the concept in a very different manner). Leibniz does not say that each individual expresses the totality of the world from its own point of view, as if everything were "relative" to the viewpoint of the subject, since in fact the exact opposite is the case: it is the subject that is constituted by the point of view. Point of view is the suffi cient reason of the subject: the individual notion is the point of view through which the individual expresses the totality of the world.10 But this propels Leibniz into yet another problem: for what then determines this point of view? Here again, Leibniz cannot stop. Each of us may express the totality of the world from a certain point of view, he tells us, but we necessarily express most of the world in an obscure and confused manner, as if it were a mere clamor, a background noise. This means that the totality of the world is really in the individual notion, but in the form of infi nitely small perceptions – another concept. These minute perceptions are like the "differentials" of consciousness, which are not given as such to conscious perception. If there is a small, reduced, fi nite portion of the world that I express clearly and distinctly, it is that portion of the world that affects my body. So Leibniz provides a deduction of the necessity of the body as that which occupies the point of view. I do not express clearly and distinctly the crossing of the Rubicon, for that concerns Caesar's body; but there are other things that concern my body – a certain relation to this room, this podium, this paper – which I do express clearly and distinctly. But he still can't stop, since each of these individuals must nonetheless express the same world. Why is this a problem? The principle of identity allows us to determine what is contradictory, that is, what is impossible. A square circle is a circle that is not a circle; it is impossible because it contravenes the principle of identity. But at the level of suffi cient reason, Caesar not crossing the Rubicon and Adam not sinning are neither contradictory nor impossible: 366 Caesar could have not crossed the Rubicon, and Adam could have not sinned, whereas a circle cannot be square. The diffi culty is: How can Leibniz at the same time hold that everything Adam did is contained for all time in his individual concept, and that Adam the non-sinner was nonetheless possible? No problem, says Leibniz, he simply invents an entirely new logical relation, which he calls incompossibility. At the level of existing things, it is not enough to say that a thing is possible in order to exist; it is also necessary to know with what it is compossible. Adam the non-sinner was possible in itself, but it was incompossible with rest of the actualized world. The conclusion Leibniz draws from this notion is perhaps his most famous doctrine, one which was caricatured by Voltaire in Candide and by the eighteenth-century in general: among the infi nity of incompossible worlds God had in his mind at the moment of creation, God made a calculation and chose the "Best" of all possible worlds to pass into existence, governed by a harmony that is pre-established by God. Thus, Leibniz says, when I want to demonstrate that the predicate "sinner" is contained in the concept of "Adam," when I perform the analysis, I pass from Adam the sinner to Eve the temptress, and from Eve the temptress to the evil serpent, and from the evil serpent to the apple, and so on. Moving forward, I show that there is a continuity between Adam's sin and the Incarnation and Redemption by Christ: there are series that are going to begin to fi t into each other across the differences of time and space. (This is the aim of Leibniz's Theodicy: to justify God's choice of this world, the "best" world, with all its interlocking series.) Such an analysis is infi nite because it has to pass through the entire series of elements that constitutes the world, which is actually infi nite; and it is an analysis because it demonstrates the inclusion of the predicate "sinner" in the individual notion "Adam." It is here that we end scene one, for we seem to have reached a blockage. It seems to go without saying that we, as fi nite beings, are incapable of undertaking an infi nite analysis: in order to situate ourselves in the domain of truths of existence, we have to wait for experience. Infi nite analysis is possible for God, to be sure, but this is hardly a satisfactory answer. We may be happy for God (close-up of God, smiling), but then we would wonder why Leibniz went to such trouble to present this whole story about suffi cient reason if it remains inaccessible to us as fi nite beings. This apparent blockage in Leibniz's thought will return at the end of our scenario, but what we have seen in scene one is the "delirious" creation of concepts one fi nds in Leibniz. Expression, point of view, minute perceptions, incompossibility: all these are concepts that are generated in Leibniz – created by him – as a result of his positing of the problem of suffi cient reason. This is why Deleuze says is it useless to pose objections to a philosopher: the more important thing, at least initially, is to extract the "problematic" generating their thought, and to follow it as far as one can. 367 II. Hegel and the Principle of Non-Contradiction But now scene two intervenes. It begins with a tracking shot that moves past a number of philosophical fi gures: Descartes, Leibniz (again, briefl y, in a fl ashback), then Kant and Fichte, and fi nally Hegel. Hegel is the culminating point of the second scene, which charts out the trajectory through which philosophy attempted to conquer existence, no longer through the principle of identity, as in Leibniz, but through the principle of contradiction. Scene two begins with Descartes, who is another good philosophical movie star: suave, debonair, long hair, goatee, he sleeps until noon every day, and likes working in bed, which I personally admire; Christina, the Queen of Sweden, the story goes, forces him to get up early; this gives him pneumonia, and he dies. Prior to dying, however, Descartes had attempted to think existence in his own manner, and his undertaking would have even greater repercussions in philosophy than Leibniz's. In the Meditations, Descartes claimed that, in order to doubt, I must be thinking; hence I am a thinking being. The question of doubt, it is true, does not bear on the existence of things, but rather on the knowledge I have of the existence of things. Insofar as I doubt, there is a knowledge that I cannot doubt, which is the knowledge of myself as a thinking being. But in this manner, Descartes was the fi rst thinker to introduce into philosophy a formula that would later be developed extensively in German philosophy: the "I = I" or the "Self = Self" (Ich = Ich, Moi = Moi). Now although the "I = I" might appear to be simply a re-formulation of the principle of identity "A = A," in fact it has a completely different status. The identity A = A is the identity of the thing thought, and as such it is a hypothetical judgment. Its complete formulation would be: if there is A, A is A; if A exists, then A = A. But perhaps A does not exist, perhaps there is nothing. (This is why the principle of identity corresponds to the question, "Why is there something rather than nothing?") What Descartes showed was that the principle of identity is a purely hypothetical judgment: I can always doubt A, not only in its existence, but even in its concept. Thus, when Descartes says that there is one thing I cannot doubt, I = I, he did something radically new in philosophy: he discovered an identity that is no longer subject to this hypothetical condition: he discovered an unconditioned identity, or what came to be called a thetic or categorical judgment. This is the discovery of subjectivity: the position, or auto-position, of the subject, the I = I. Fichte would develop this thesis to its ultimate conclusion: one can only say "A is A" because A is thought, but what grounds the identity of what is thought is the reality of the thinking subject, the identity of the fi nite "I." Thus, the principle of identity, "A is A," founds its ground in the auto-position of the subject, the "I is I." In Descartes, the principle of identity left the sphere of logic for the fi rst time and took a fi rst baby step into the real, or into existence. A brief fl ashback to Leibniz, for this is precisely where his philosophy intervened. For although the I = I allowed Descartes to conquer a small island of existence, the Cartesian cogito is, as it were, enclosed in a citadel. Affi rming 368 something other than the thinking subject – such as the reality of something thought (mathematics) or the reality of something experienced (the sensible world) – will require an entire acrobatics, a series of complex reasonings on Descartes' part, all of which will appeal to the guarantee that God exists and is a truthful being. So although Descartes had obtained his little island of existence – the cogito – what Leibniz sought to attain was the adequation of thought with existence in its entirety, the real in its totality. What Descartes did not see was that the I = I does not simply refer to the little island of the cogito, posited in the certitude of itself, but rather expresses or comprehends the totality of the world as the set of its own predicates. Such is the signifi cance of the shift from Descartes' cogito to Leibniz's monad. But now scene two jumps ahead to Kant, famous for the regularity of his daily walks, and the bizarre garters he made to hold up his socks. Kant and the post-Kantians would take up Leibniz's project, but in a new manner, taking it in a different direction. The reason: after Leibniz, no one could affi rm that every true proposition is analytic. What had intervened was Kant's fundamental discovery of synthetic judgments. For Kant a judgment such as "The three angles of a triangle are equal to two right angles" is no longer an analytic judgment but a synthetic judgment, since its demonstration must pass through the concept of a square; the proposition is therefore a synthesis of two concepts. The results of this discovery were profound: Although Descartes had located the ground of the principle of identity in the "I = I," what Kant discovered was that the "I = I" is a synthetic identity, and no longer simply an analytic identity. It is here that perhaps the most famous episode in the attempt to reconcile logic and existence commences. The post-Kantian philosophers are precisely those philosophers who take Kant as their fantastic starting point, and who pursue the question: What is synthetic identity? What does the synthetic identity of the self consist of? The post-Kantian philosophers maintained that Kant had not adequately responded to the question he himself had posed. In order to give an account of synthetic identity, Kant had to invoke something other, something irreducible both to thought and to the Self: namely, sensibility, or the a priori forms of space and time. The post-Kantians, by contrast, wanted to ground synthetic identity in the Ego itself, and they therefore posited a new principle that was derived, no longer from the principle of identity, but from the principle of non-contradiction. For them, the Ego can not posit itself as identical to itself except by opposing itself to a non-Ego, to that which is outside the Ego. As Fichte would show, synthetic identity can be expressed in the formula: "The I is not the not-I." Here again, this is another astonishing philosophical formula – almost like a chemical formula – that marked a prodigious discovery in philosophy. It means that the "I" can be posited as identical to itself only by being opposed to a not-I, that is, through a negation of the not-I.11 This line of thought would fi nd its ultimate outcome in Hegel, who was the fi rst philosopher to think that, when he said "things do not contradict 369 themselves," he was saying something about things – that is, something about existence, and not merely about the possible. Not only was he saying something about things, he was saying something about how they are born and develop: they are born and develop by not contradicting each other. The Hegelian dialectic does not consist in denying the principle of non-contradiction, but rather in developing the principle of non-contradiction, in taking it to the letter. If the principle of analytic identity is the empty principle of essences, with which one can only think what Hegel calls abstract essentiality, the principle of non-contradiction is the principle through which thought and the real are engendered and develop simultaneously – to the point where Hegel can say that "the real is the concept and the concept is the real." III. The Existentialists and the Principle of the Excluded Middle This brings us to a truncated scene three, whose stars are a race of thinkers who sought to reconcile thought and existence, no longer at the level of the principle of identity (whether analytic or synthetic), or even at the level of the principle of non-contradiction (as in Hegel), but rather at the level of the principle of the excluded middle (A or not-A, but not both). This is the thought of the "either...or," and no longer the thought of contradiction; it is the mode of the alternative and no longer the negative. If thought can join existence in the excluded middle, it is because it implies that to think is to choose, that nature of my existence is determined by my choice. It is this means of conquering existence that came to be known, broadly, as "existentialism." It is a line of thought has its own cast of characters: it begins with Pascal (a Catholic), and would be continued in Kierkegaard (a product of the Reformation), Sartre (an atheist), and is taken up in a modifi ed form in Badiou (the militant activist). What was at stake in Pascal's wager, for instance, was not the existence or nonexistence of a transcendent God, but rather the immanent modes of existence of those who must choose between his existence or non-existence. The result is a complex typology of different modes of existence: there are the devout, for whom there is no question of choosing; skeptics, who do not know how or are unable to choose; the creatures of evil, who are free to choose, but whose fi rst choice places them in a situation where they can no longer repeat their choice, like Goethe's Mephistopheles; and fi nally, the men of belief or grace who, conscious of choice, make an "authentic" choice that is capable of being repeated in a steadfast spiritual determination.12 Kierkegaard drew out the necessary conse quences of this line of thinking: decision or choice covers as great an area as thought itself. But this also means, secondly, that there are choices that I make only on the condition of saying, "I have no choice," like the woman who gives herself to a man on the condition of saying she is simply submitting to his choice, and not making a choice of her own – this is what Sartre called "bad faith." When Sartre wrote, after the World War II, "We have never been more free than under 370 the Occupation," he was speaking precisely of those shameful choices one makes on the condition of saying, "I had no choice!" In other words, in the end, we choose between choice and non-choice – the non-choice itself being itself a choice, since it is the form of choice that one appeals to when one believes that one has no choice. More recently, Alain Badiou has explicitly placed himself in the lineage of Pascal and Sartre when he locates the condition of the subject in its choice to maintain its fi delity to an event, thereby elevating the militant activist to the highest mode of existence (and no longer the person of belief). In all these cases, one can see that there is a genuine displacement of the principle of the excluded middle: choice is no longer between two terms (A or not-A), but between two modes of existence; and ultimately, it is a choice between choice and non-choice. In this way, the principle of excluded middle – the last of our three logical principles – is itself now made to bear upon existence itself, but in a fundamentally new manner. IV. Deleuze and the Principle of Difference We arrive now at the climax of the fi lm, or perhaps it's anti-climax. Unlike Leibniz or Descartes, Deleuze does not seem to lend himself to movie stardom: he read, he wrote, and he taught (when he was not ill), and outwardly, that sums up most of his life; the real drama took place in his thinking. So our fi nal image is a shot of Deleuze sitting at a desk, writing – and we hold the shot for several minutes, to give a sense of the passing of time, à la Tarkovsky. Where does Deleuze fi t into this story of Logic and Existence that we have just screened? In a sense, the answer is: nowhere. He writes about all three of these options, he is fascinated by them, and he is interested in the exact same problem: How can thought think existence? One of Deleuze's early lecture courses from 1956 has recently surfaced, and in it we can see Deleuze working through these same three traditions (in a different manner than I have done here), twelve years before he would fi nally publish his own "solution" to the problem, so to speak, in Difference and Repetition (1968).13 For Deleuze, the fulfi llment of this project of Logic and Existence, which animated much of modern philosophy, can only occur through the substitution of the a principle of difference for the principle of identity (in all its variations: identity, contradiction, the excluded middle). The fi nal scene can do little more than provide a sketch of the way in which Deleuze approaches the project of Logic and Existence in his own manner. The story we have just examined – a particular sequence in the history of modern thought – can be said to oscillate between two poles: God and the Self, infi nite substance and fi nite subject. Pre-Kantian thought found its principle in the analytic identity of the divine substance, while post-Kantian thought found its principle in the synthetic identity of the fi nite subject. For Deleuze, this supposed transformation no longer has any sense: God or Self, analytic identity or synthetic identity – it is one and the same thing, since the identity of the one 371 fi nds its condition in the identity of the other. As Deleuze writes in Difference and Repetition, "the oneness and identity of the divine substance are in truth the only guarantee of a unique and identical self, and God is retained so long as the self is preserved" (DR 58). Nietzsche had already seen that the death of God becomes effective only with the death of the self, and both Foucault and Klossowski would develop this theme in their works. As a result, the movement from the "A is A" to the "I is I" in post-Kantian philosophy – the move from God to the Self – did little more than to seal the form of what Deleuze calls "common sense," which is the form under which identity has been preserved in philosophical thought: subjectively, it is the same self that perceives, knows, imagines, and remembers; it is the same self that breathes, sleeps, walks, and eats; and objectively, it is the same object that is seen, remembered, imagined, and conceived by this self; and as I move from one object to another, it is in the same world that I perceive, breathe, and walk in (LS 78). This is why Kant could present the "object = x" or the object in general as the objective correlate of the "I think" or the subjective unity of consciousness. Even Kierkegaard dreamed of a God and a self rediscovered in a theatre of faith. Taken together, these can be seen to constitute the two poles of what Deleuze calls the dogmatic image of thought: the subjective identity of the self and its faculties, and the objective identity of the thing (and of the world) to which these faculties refer. This seals the alliance between the self, the world, and God as the three great terminal points of metaphysics: difference – or the diverse – is related to the form of a subject's identity, the form of an object's or a world's permanence, with God being the supreme principle of identities. More important than what happens before or after Kant, then, is what happens within Kant, in the fi rst Critique, when he criticizes the Self, the World and God as transcendent illusions, and thus invokes a mysterious coherence that excludes the coherence of the Self, the coherence of the world, and the coherence God (as well as the coherence of language, which is capable of "denoting" everything else). If Deleuze can consider himself to be a "pure metaphysician," if he rejects the Heideggerian idea of "the end of metaphysics," it is because he believes it is possible to construct a metaphysics freed from the coordinates of the Self, the World, and God. "What is then revealed," he writes in Difference and Repetition, "is being, which is said of differences which are neither in substance nor in a subject" (DR 58). This is why Deleuze's metaphysics will focus on impersonal individuations that are no longer enclosed in a Self, and pre-individual singularities that are no longer enclosed in a God. This is the Dionysian world that Deleuze describes in Difference and Repetition, in which, as he puts it, "the divergence of affi rmed series forms a 'chaosmos' and no longer a world; the aleatory point that traverses them forms a counter-self and no longer a self; and disjunction posited as a synthesis exchanges its theological principle for a diabolical principle [...] the Grand Canyon of the World, the 'crack' of the self, and the dismembering of God."14 It is not that Deleuze denies subjects and objects have identities – it is 372 simply that these identities are secondary; they are the effect of more profound relations of difference. As Deleuze likes to say, just as there is no "pure" reason but only historically variable processes of "rationalization," so there is no universal or transcendental subject, but only diverse and historically variable forms of "subjectivation," and no object in general, but only variable forms of "objectivation," and so on. With this move, however, it becomes impossible for Deleuze to follow any of the paths we saw above, in our Godardian fi lm, since they each utilize a variant of the principle of identity to think existence, whereas in Deleuze the identities of the Self, the World, and God have been dissolved. But how then can one think the existence of a purely differential world? Clearly thought has to think difference directly, but Deleuze is fully aware of the paradox of such an enterprise: like Leibniz's project, it seems absurd. The image we began with – the sphere of logic – illustrated the problem that thought, one its own, can only think the possible, but it cannot think the real directly because the concept is blocked – and it is blocked precisely because the real is what is different from thought, it is difference itself. What is it that blocks the concept? For Aristotle, it was the accidents of matter; for Kant, it as the irreducibly spatio-temporal dimension of intuition – neither of which are conceptual. Deleuze himself states the problem clearly: "With the identical, we think with all our strength, but without producing the least thought: with the different, by contrast, do we not have the highest thought, but also that which cannot be thought?" (DR 226). This is the paradox that lies at the heart of Deleuze's project: difference is the highest thought, but also that which cannot be thought. This is why Deleuze's precursors adopted the strategy of utilizing the principles of thought itself – identity, non-contradiction, the excluded middle – and then attempted to think difference (or existence) through them. Deleuze in effect attempts the opposite strategy. For him, what blocks the concept is neither matter (Aristotle) nor sensibility (Kant). "What blocks the concept," he asks in Difference and Repetition, "if not the Idea? What remains outside the concept refers more profoundly to what is inside the Idea" (DR 220). The theory of Ideas takes us to the crux of the matter: what does it mean for Deleuze to say that difference can be grasped, not in a concept, but in an Idea? This is obviously a complex question, which the ending of our fi lm exemplifi es in three interrelated images. First, at the conclusion of the scene one, we saw that Leibniz's philosophy of suffi cient reason was blocked, since it seemed that an infi nite analysis of concepts could only be undertaken by God, with his infi nite understanding, leaving us fi nite human beings mired in obscurity and confusion. But this is where Leibniz overcame his explicit intentions (in the Nietzschean sense of "self-overcoming"), since he wound up providing us fi nite humans with an artifi ce capable of undertaking a well-founded approximation of what happens in God's understanding, and this artifi ce is the technique of the infi nitesimal calculus or differential analysis. We as humans can undertake an infi nite analysis thanks to the symbolism of the differential calculus. In the calculus, 373 the differential relation can be said to be a pure relation: it is a relation that persists even when its terms disappear, and it thus provides Deleuze with an example of what he calls the concept of difference-in-itself. Normally, we think of difference as a relation between two things that have a prior identity ("x is different from y"). With the notion of the differential relation, Deleuze takes the concept of difference to a properly transcendental level: the differential relation is not only external to its terms (Bertrand Russell's empiricist dictum), but it also determines its terms. In other words, difference here becomes constitutive of identity, that is, it becomes productive and genetic. This is what Deleuze means, in Difference and Repetition, when he says that relations such as identity, analogy, opposition, and resemblance are all secondary effects or results of prior relations of difference. Deleuze, in other words, approaches the problem of existence not through logic, which takes identity as its model, but through mathematics, which – in certain of its domains – developed a symbolism capable of thinking difference.15 If Plato found in Euclidean geometry a model of static and unchanging essences, Deleuze fi nds in the calculus a model of pure change (and thus a transformation in the corresponding theory of Ideas). The calculus is a symbolism for the exploration of existence. It is not by chance that the "mathematicization" of Nature, which lies at the heart of the so-called scientifi c revolution, took place through the calculus: "laws of nature" are expressed in the form of differential equations (although both Spinoza and Nietzsche railed against speaking of laws of Nature, since the "law" is strictly a social concept). This is why, in the nineteenth-century, philosophies of Nature – from Maimon to Novalis – usually took the form of explorations in the metaphysics of the calculus, and Deleuze is certainly a heritor of this tradition, although he prefers to speak of a dialectic of the calculus, rather than a metaphysics. Second, while it is true that the sensibility of the diverse is outside the concept (in Kant, intuitions are spatio-temporal; concepts are not), it is in Ideas that thought can think difference as the suffi cient reason of the diverse. Deleuze will argue that intensity (intensive magnitude) is the suffi cient reason of the sensible. Intensity is never given in the diversity of experience, since it cancels itself out when it is explicated, but thought can nonetheless think it in the form of an Idea. The phenomenon of lightning, for instance, is the result of a difference of potential in a cloud, a difference in charge, but the condition under which the lightning appears is the resolution of this charge, the cancellation of the difference. Deleuze will therefore draw a sharp distinction between diversity and difference: "Diversity is given, but difference is that by which the given is given, that by which the given is given as diverse. Difference is not the phenomenon but the noumenon closest to the phenomenon" (DR 222). Difference, in other words, is the suffi cient reason of the diverse, which is not given in a concept but in an Idea – and an Idea that can become actualized in various manners. This is Deleuze's response to Leibniz's problem of suffi cient reason: there is an Idea of sensibility, just as there is an Idea of matter, and thought itself is capable of penetrating this 374 Idea. Consider two further examples. The concept "mountain" might allow us to recognize Mt. Everest, but it says nothing about the fact that Everest is the ongoing actualization of a complex process, which includes the pressure of the India tectonic plate slamming into Asia, the folding of the earth's crust, the weathering and erosion of the Himalayan range, and so on. The concept "lion" might allow us to recognize an animal in front of us, but it says nothing about the lion's territories, the paths its takes, the times it hunts and rests. The latter are spatio-temporal dynamisms that cannot be derived from the concept, but are the actualization of a differential Idea. "There is nothing which does not lose its identity as this is constituted by concepts," Deleuze writes, "when the dynamic space and time of its actual constitution is discovered" (DR 218-219). Third, and perhaps more importantly, what is the condition under which thought is capable of thinking difference as the suffi cient reason of the sensible? Deleuze's response is that Ideas are always given to thought under the form of problems: if difference is that which cannot be thought, then thought is capable of thinking difference only under a problematic form, in other words, as something that provokes thought, which engenders thought, which problematizes thought (which is why, in the calculus, the differential exists in the problem, but must disappear in the solution.) This is Deleuze's great theme against what he calls the dogmatic image of thought: thinking is not the result of a prior disposition, but the result of forces that act upon thought from the outside, of encounters that do violence to us, that force us to think, and what engenders thinking is always an encounter with a problem. Who is it that in fact searches for the truth? The best model is found, not in Plato's model of friends in dialogue, but Proust's model of the jealous lover, who fi nds himself living within a problem, and constrained, involuntarily, to explore its conditions. Such is the paradoxical status that Deleuze assigns to metaphysics: metaphysics can indeed tell us what the ultimate components of reality are, but these components turn out to be problems, of which we can have no "knowledge" per se (they are "obscure"), although they provoke us to think. Being always presents itself to us under a problematic form. This paradox is similar to the one expressed in the doctrine of univocity: Being has a single, univocal sense – but this single sense is difference, that is, a disguising and displaced difference that is "neither in substance nor subject," and is "no less capable of dissolving and destroying individuals than constituting them temporality" (DR 38). So we conclude with three "images" – difference-in-itself as a pure relation; intensity as the suffi cient reason of sensibility; and the being of problems that provoke thought – which in fact can never be given in experience, but rather constitute the conditions of the real. And this, indeed, is the upshot of the scenario we have tried to present here under the rubric of Logic and Existence. The problem we began with was: How can thought think existence? How can thought get out of its concepts and logical principles and think the real? Our screenplay presented scenes from the three great trajectories in the 375 history of modern philosophy that attempted to resolve this problem, drawing their inspiration from one of the three principles of classical logic: identity (culminating in Leibniz, the pre-Kantian), non-contradiction (culminating in Hegel, the post-Kantian), and the excluded middle (culminating in the existentialists). But when thought uses the principles of logic, in its attempt to penetrate existence, it remains in its own element (identity): it is thought imposing its own principles on existence. Our concluding images – which point to a sequel – show how Deleuze's contribution was to have inverted the procedure, so to speak. For Deleuze, thought must think something that is contrary to the principles of thought, it must think difference, it must think that which is absolutely different from thought but which nonetheless gives itself to thought, and wrests thought from its natural stupor. This is no longer thought imposing itself upon existence, but existence forcing itself to be thought, forcing itself to be thought. There is thus an intelligibility to Being, there are Ideas in sensibility itself, but they always present themselves under a problematic form, as a difference that forces itself to be thought. In this sense, one could say that Deleuze remains a rationalist, but it is a modifi ed rationalism, a rejuvenated rationalism, a rationalism unbound – in short, perhaps, an empiricism. And the credits roll... Daniel W. Smith smith132@purdue.edu NOTES: * "This paper was originally presented at the conference "Deleuze and Rationalism," which took place on 16-17 March 2007 at the Centre for Research in Modern European Philosophy at Middlesex University, London." 1 Jean Hyppolite, Logic and Existence [1952], trans. Leonard Lawlor and Amit Sen (Albany: State University of New York Press, 1997). This book completes the project Hyppolite began with Genesis and Structure of Hegel's "Phenomenology of Spirit," trans. Samuel Cherniak and John Heckman (Evanston, IL: Northwestern University Press, 1979), and examines the relation between the phenomenology and the logic. Deleuze wrote an important review of the book in 1954, "Jean Hyppolite's Logic and Existence," which is included as appendix to the English translation (pp. 191-5). 2 Gottfried Wilhelm Leibniz, New Essays on Human Understanding, trans. and ed. Jonathan Bennett and Peter Remnant (Cambridge: Cambridge University Press, 1997), p. 361. 3 Leibniz, New Essays, p. 408. 4 See Wilfred Sellers, "Méditations leibniziennes," in Leibniz: Metaphysics and Philosophy of Science, ed. R. S. Woolhouse (Oxford: Oxford University Press, 1981), p. 31. "If the nature of a substance is to account for its individuality, it must account for episodes [events], and not merely the capacities, powers, and dispositions – all, in principle, repeatable – which were traditionally connected with the natures of things." 5 Louis Couturat, "On Leibniz's Metaphysics," in Leibniz: A Collection of Critical Essays, ed. Harry G. Frankfurt (Garden City, N.Y. Anchor Books, 1972), pp. 19-45. "The principle of identity states: every identity (analytic) proposition is true. The 376 principle of reason affi rms, on the contrary: every true proposition is an identity (analytic)" (p. 22). 6 Ian Hacking, "What Mathematics Has Done to Some and Only Some Philosophers," in Proceedings of the British Academy 103 (2000), pp. 83-138: 105. 7 See Benson Mates, The Philosophy of Leibniz: Metaphysics and Language (Oxford: Oxford University Press, 1986), p. 157: "To discover the reason for the truth of the essential proposition 'A is B' is to analyze the concept A far enough to reveal the concept B as contained in it." 8 Leibniz, "On the Radical Origination of Things" [1697], in Leroy E. Loemker, ed., Philosophical Papers and Letters (Dordrecht, Holland: D. Reidel, 1956), p. 486: "However far you go back to earlier states, you will never fi nd in those states a full reason why there should be any world rather than none, and why it should be as it is." 9 Leibniz wrote a short text entitled "Refl ections on the Doctrine of a Single Universal Mind" [1702], in Loemker, ed., Philosophical Papers and Letters, pp. 554-560, in which he shows that, although there is indeed a universal mind (God), it does not in any way prevent substances from being individual. See Deleuze's commentary in his seminar of 15 April 1980. 10 See Leibniz, "Monadology" [1714], §57, in Loemker, ed., Philosophical Papers and Letters, p. 648: "Just as the same city viewed from different sides appears to be different and to be, as it were, multiplied in perspectives, so the infi nite multitude of simple substances, which seem to be so many different universes, are nevertheless only the perspective of a single universe according to the different points of view of each monad." 11 Deleuze, seminar of 17 May 1983. 12 Blaise Pascal, Pensées, trans. W. F. Trotter (New York: E. P. Dutton, 1958), § 418. Deleuze analyzes this Christian tradition in his two-volume Cinéma, where he draws a parallel between the philosophy of Pascal and Kierkegaard and the fi lms of Bresson and Dreyer; see MI 114-16 and TI 176-9. Bresson perhaps even offers a fi fth type of mode of existence in his great fi lm Au hasard, Balthazar: the donkey who possesses the innocence of one who cannot choose, but who nonetheless suffers the effects of the choices or non-choices of humans, which ultimately kill it – one of the most poignant scenes in the history of cinema (see MI 116). 13 Qu'est-ce que fonder ? [What is Grounding?], cours d'hypokhâgne, au Lycée Louis-leGrand, Paris, 1956-1957, available at webdeleuze.com. 14 Although this quote is from Logic of Sense (LS 176), it summarizes the essential themes of Difference and Repetition. 15 The (fatal) limitation of so-called "analytic metaphysics" is its reliance on a logicist, formalist, and set theoretical metaphysics inherited from the nineteenth-century. See, for instance, Ted Sider's stated assumption, in Four-Dimensionalism (Oxford: Oxford University Press, 2001), "that modern logic's quantifi cational apparatus mirrors the structure of reality" (p. xvi). Logique et existence : Deleuze à propos des « conditions du réel » Pour Deleuze, l'un des problèmes fondamentaux d'une théorie de la pensée est de savoir comment la pensée peut quitter la sphère du possible pour penser le réel, c'est-àdire pour penser l'existence elle-même ? La position du réel semble être hors du concept. Des pré-kantiens comme Leibniz approchaient ce problème par le biais de la distinction entre vérités d'essence et vérités d'existence, alors que des post-kantiens comme Maimon l'approchaient par la distinction entre les conditions de l'expérience possible et celles de l'expérience réelle. La logique classique défi nit la sphère du possible par 377 trois principes logiques – l'identité, la non-contradiction et le tiers-exclu – et la présente étude examine les trois grandes trajectoires qui, dans cette histoire de la philosophie, ont tenté d'utiliser l'un de ces trois principes classiques pour pénétrer l'existence ellemême : 1) Leibniz (et les pré-kantiens) cherchait à étendre le principe de d'identité à l'existence entière ; 2) Hegel (et les post-kantiens) cherchait à étendre le principe de non-contradiction à la totalité de l'expérience ; et 3) le groupe des penseurs appelés de manière assez large « existentialistes » cherchait à étendre le principe du tiers-exclu à la totalité de l'existence. La conclusion examine les raisons pour lesquelles Deleuze a été fasciné par chacune de ces tentatives philosophiques pour « penser l'existence », tout en pensant néanmoins qu'elles ont toutes échoué ; et pourquoi aussi il a fi ni par développer sa propre réponse au problème en faisant appel à un principe de différence. Logica e Esistenza: Le 'Conditioni del reale' in Deleuze Per Deleuze, uno dei problemi fondamentali per una teoria del pensiero è: come può il pensiero abbandonare la sfera del possibile per pensare il reale, ossia, pensare l'esistenza stessa? La posizione del reale sembra essere fuori dal concetto. Prekantiani come Leibniz affrontano questo problema in termini di distinzione fra verità dell'essenza e verità dell'esistenza, mentre post-kantiani come Maimon affrontano il problema in termini di distinzione fra condizioni dell'esperienza possibile e condizioni dell'esperienza reale. La logica classica ha defi nito la sfera del possibile secondo tre principi logici – identità, non-contraddizione, e il terzo escluso – e questo saggio analizza tre grandi 'parabole' della storia della fi losofi a che hanno tentato di usare uno di questi tre principi della logica per penetrare l'esistenza stessa: (1) Leibniz (e i prekantiani) hanno tentato di estendere il principio di identità a tutta l'esistenza; (2) Hegel (e i post-kantiani) hanno tentato di estendere il principio di non-contraddizione a tutta l'esistenza; (3) il gruppo di pensatori (solo approssimativamente legati fra loro) chiamati "esistenzialisti" ha tentato di estendere il principio del terzo escluso all'esistenza. La conclusione analizza sia le ragioni per le quali Deleuze era affascinato da ciascuno di questi tentativi fi losofi ci di "pensare l'esistenza" nonostante fosse convinto che esse avessero fallito, sia perché egli in conclusione tracci la propria risposta al problema facendo appello al principio della differenza.