by Daniel Smith
70.
See Lautman, Mathematics, Ideas, and the Physical Real, 97–8:
Riemannian spaces are devoid of any kind of homogeneity. Each is characterized by the form of the expression that defines the square of the distance between two infinitely proximate points … It follows that “two neighboring observers in a Riemannian space can locate the points in their immediate vicinity, but cannot locate their spaces in relation to each other without a new convention.” Each vicinity is like a shred of Euclidean space, but the linkage between one vicinity and the next is not defined and can be effected in an infinite number of ways. Riemannian space at its most general thus presents itself as an amorphous collection of pieces that are juxtaposed but not attached to each other.
71.
See DR 183, 181: A Riemannian multiplicity “is intrinsically defined, without external reference or recourse to a uniform space in which it would be submerged … It has no need whatsoever of unity to form a system.”
72.
Badiou, “One, Multiple, Multiplicities,” in Theoretical Writings, 78.
73.
See, in particular, DR 183, although the entirety of the fifth chapter is an elaboration of Deleuze's theory of multiplicities.
74.
See DR xxi: “We are well aware … that we have spoken of science in a manner which was not scientific.”
75.
See De Landa, Intensive Science and Virtual Philosophy, 15 (on attractors), and Chapters 2 and 3 (on symmetry-breaking cascades).
76.
De Landa, Intensive Science and Virtual Philosophy, 102.
77.
See DR 117: “In accordance with Heidegger's ontological intuition, difference must be articulation and connection in itself; it must relate different to different without any mediation whatsoever.”
78.
Badiou, Deleuze, 20. For Badiou's Neo-Platonic characterization of Deleuze, see 26: “It is as though the paradoxical or supereminent One immanently engenders a procession of beings whose univocal sense it distributes.”
79.
This conflation is stated most clearly in Badiou, Deleuze, 46: “the univocal sovereignty of the One.” For discussions of Badiou's reading of the doctrine of univocity, see Nathan Widder, “The Rights of Simulacra: Deleuze and the Univocity of Being,” in Continental Philosophy Review 34 (2001), 437–53, and Keith Ansell-Pearson, “The Simple Virtual: A Renewed Thinking of the One,” in Philosophy and the Adventure of the Virtual: Bergson and the Time of Life (London and New York: Routledge, 2002), 97–114.
80.
See, for instance, Badiou, “One, Multiple, Multiplicities,” in Theoretical Writings, 70: The One “may take the name of ‘All,’ or ‘Whole,’ ‘Substance,’ ‘Life,’ ‘the Body without Organs,’ or ‘Chaos.’”
81.
Ernst Mayr, “Is Biology an Autonomous Science?,” in Toward a New Philosophy of Biology: Observations of an Evolutionist (Cambridge, MA: Harvard University Press, 1988), 8–23.
82.
Badiou, “One, Multiple, Multiplicities,” in Theoretical Writings, 73.
83.
22 Apr 1980. See also 29 Apr 1980:
Everyone agrees on the irreducibility of differential signs to any mathematical reality, that is to say, to geometrical, arithmetical, and algebraic reality. The difference arises when some people think, as a consequence, that differential calculus is only a convention—a rather suspect one—and others, on the contrary, think that its artificial character in relation to mathematical reality allows it to be adequate to certain aspects of physical reality.
84.
See DR 178:
Modern mathematics leaves us in a state of antinomy, since the strict finite interpretation that it gives of the calculus nevertheless presupposes an axiom of infinity in the set theoretical foundation, even though this axiom finds no illustration in the calculus. What is still missing is the extra-propositional or sub-representative element expressed in the Idea by the differential, precisely in the form of a problem.
85.
Badiou, Deleuze, 14. See DR 192: “Representation and knowledge are modeled entirely upon propositions of consciousness which designate cases of solution, but those propositions by themselves give a completely inaccurate notion of the instance which engenders them as cases.”
86.
See Paul Hoffman, The Man Who Loved Only Numbers: The Story of Paul Erdós and the Search for Mathematical Truth (New York: Hyperion, 1998), 17.
87.
See N 130: “Poincaré used to say that many mathematical theories are completely irrelevant, pointless. He didn't say they were wrong—that wouldn't have been so bad.”
88.
Badiou, Deleuze, 1, 98–9. See also 70, where Badiou links Deleuze with Plato's “metaphorical mathematics.” Badiou is referring to Deleuze's notorious distaste for metaphors, but there is no reason to think that distaste disappears here. The concept of the “fold,” for instance, is not a metaphor, but a literal topological transformation. Even the concept of the “rhizome,” whatever its metaphorical resonance, is directed primarily against the literal uses of “arborescent” schemas in mathematics and elsewhere (tree structures, branches and branchings, etc.).
89.
14 Mar 1978: “The abstract is lived experience. I would almost say that once you have reached lived experience, you reach the most fully living core of the abstract.” See also 21 Mar 1978: “You can live nothing but the abstract and nobody has lived anything else but the abstract.”
90.
Badiou, Deleuze, 36.
91.
TP 570 n61. See also TP 461:
When intuitionism opposed axiomatics, it was not only in the name of intuition, of construction and creation, but also in the name of a calculus of problems, a problematic conception of science that was not less abstract but implied an entirely different abstract machine, one working in the undecidable and the fugitive.
92.
Badiou, Briefings on Existence, 50. Badiou's claim that Deleuze's methodology relies on intuition is discussed in Deleuze, Chapter 3, esp. 31–40.
93.
Badiou, Briefings on Existence, 71.
94.
For the role of the scholia, see EPS 342–50 (appendix on the scholia); for the uniqueness of the fifth book of the Ethics, see ECC 149–50.
95.
Badiou, Deleuze, 1. See Badiou's essay on Spinoza, “Spinoza's Closed Ontology,” in Briefings on Existence, 73–87.
96.
See DR 161, 323 n21. See also Hersh's comments on Descartes in What is Mathematics, Really?, 112–13: “Euclidean certainty boldly advertised in the Method and shamelessly ditched in the Geometry.”
97.
See TP 455: “Our use of the word ‘axiomatic’ is far from a metaphor; we find literally the same theoretical problems that are posed by the models in an axiomatic repeated in relation to the State.” In part, this is a historical thesis: it is not by chance that Weierstrass's program of arithmetizing mathematics and Taylor's program of organizing work developed at the same time. See 22 Feb 1972:
The idea of a scientific task that no longer passes through codes but rather through an axiomatic first took place in mathematics toward the end of the nineteenth century, that is, with Weierstrass, who launches a static interpretation of the differential calculus, in which the operation of differentiation is no longer considered as a process, and who makes an axiomatic of differential relations. One finds this well formed only in the capitalism of the nineteenth century.
98.
See 22 Feb 1972:
The true axiomatic is social and not scientific … The scientific axiomatic is only one of the means by which the fluxes of science, the fluxes of knowledge, are guarded and taken up by the capitalist machine … All axiomatics are means of leading science to the capitalist market. All axiomatics are abstract Oedipal formations.
99.
In one text, Badiou seems to recognize the proble
matic–axiomatic distinction in his own manner:
Today, one starts rather from already complex concretions, and it is a question of folding or unfolding them according to their singularity, to find the principle of their deconstruction-reconstruction, without being concerned with the plane of the set or a decided foundation. Axiomatics is left behind in favor of a mobile apprehension of surprising complexities and correlations. Deleuze's rhizome wins out over Descartes’ tree. The heterogeneous lends itself to thought more than the homogeneous. (Briefings on Existence, 50)
But Badiou none the less seems to be moving in a Deleuzian direction when, in his more recent essay on “Being and Appearing,” he introduces a minimal theory of relation (through logic and topology), and even assigns the “event” a minimal ontological status: the event “is being itself, in its fearful and creative inconsistency, or its emptiness, which is the without-place of all place (see Briefings on Existence, 168).
100.
TP 471. And AO 255: “The theoretical opposition lies elsewhere: it is between, on the one hand, the decoded flows that enter into a class axiomatic on the full body of capital, and on the other hand, the decoded flows that free themselves from this axiomatic.”
101.
See Badiou, Deleuze, 91: “Deleuze always maintained that, in doing this, I fall back into transcendence and into the equivocity of analogy.”
102.
Badiou, Deleuze, 91. See also 64: “Truth must be thought as ‘interruption.’”
Essay 18: Jacques Lacan
The Inverse Side of the Structure: Žižek on Deleuze on Lacan
1.
“Le ‘Je me souviens’ de Gilles Deleuze” (interview with Didier Éribon) in Le Nouvel Observateur 1619 (16–22 Nov 1995), 50–1.
2.
Slavoj Žižek, Organs Without Bodies: Deleuze and Consequences (London: Routlege, 2003).
3.
F 42. Deleuze was speaking of Virilio's relation to Foucault.
4.
See Alain Badiou, Deleuze: The Clamor of Being, trans. Louise Burchill (Minneapolis: University of Minnesota Press, 2000), 3–4.
5.
LS 124. See also LS 96:
How are we to reconcile these two contradictory aspects [of sense]? On one hand, we have impassibility in relation to states of affairs and neutrality in relation to propositions; on the other hand, we have the power of genesis in relation to propositions and in relation to states of affairs themselves.
6.
N 170. Elie Sambar was the editor of the Revue des études palestiniennes.
7.
Eugene Holland's Deleuze and Guattari's Anti-Oedipus: Introduction to Schizoanalysis (New York: Routledge, 1999) is one of the few works that deals extensively with the Deleuze–Lacan relationship (see, for example, 89–91).
8.
Immanuel Kant, Critique of Judgment, trans. James Creed Meredith (Oxford: Oxford University Press, 1952), Introduction, §3, footnote 1, 16n1. See also TRM 309:
Anti-Oedipus had a Kantian ambition, we attempted a kind of Critique of Pure Reason at the level of the unconscious. Hence the determination of the synthesis belonging to the unconscious; the unfolding of history as the effectuation of these syntheses; and the denunciation of Oedipus as the “inevitable illusion” falsifying all historical production.
9.
Jacques Lacan, “Kant with Sade,” in October 51 (Winter 1989), 55–75. For Deleuze's use of Lacan's reading of Sade, see his “Humor, Irony, and the Law,” in M 81–90.
10.
AO 26–7. At one point, Deleuze and Guattari describe the project of Anti-Oedipus in explicitly Kantian terms:
In what he termed the critical revolution, Kant intended to discover criteria immanent to understanding so as to distinguish the legitimate and the illegitimate uses of the syntheses of consciousness. In the name of transcendental philosophy (immanence of criteria), he therefore denounced the transcendent use of the syntheses such as appeared in metaphysics. In a like fashion, we are compelled to say that psychoanalysis has its metaphysics—its name is Oedipus. And that a revolution—this time materialist—can proceed only by way of a critique of Oedipus, by denouncing the illegitimate use of the syntheses of the unconscious as found in Oedipal psychoanalysis, so as to rediscover a transcendental unconscious defined by the immanence of its criteria, and a corresponding practice that we shall call schizoanalysis. (75)
11.
ECC 7–22. See also AO 310:
Elisabeth Roudinesco has clearly seen that, in Lacan, the hypothesis of an unconscious-as-language does not closet the unconscious in a linguistic structure, but leads linguistics to the point of its auto-critique, by showing how the structural organization of signifiers still depends on a despotic Great Signifier acting as an archaism.
12.
In Logic of Sense, the distinction between surface and depth is paralleled in the difference between Lewis Carroll (surface) and Antonin Artaud (depth), but Deleuze's preference for Artaud and the dimension of depth (rather than surface) is already evident: “We would not give a page of Artaud for all of Carroll. Artaud is alone in having been an absolute depth in literature, and in having discovered a vital body and the prodigious language of this body” (LS 93).
13.
In any early work, Judith Butler, for instance, characterizes Deleuze and Guattari's conception of desire as “an originary unrepressed libidinal diversity subject to the prohibitive laws of culture,” an a-historical or “pre-cultural ideal” à la Rousseau or Montesquieu, a “natural eros which has subsequently been denied by a restrictive culture,” arguing that Deleuze and Guattari promise “a liberation of that more original, bounteous desire.” See Judith Butler, Subjects of Desire (New York: Columbia University Press, 1999), 214–15, 206. Žižek, rightly, does not follow this interpretation.
14.
See Gilles Deleuze, “Desire and Pleasure,” in Foucault and his Interlocutors, ed. Arnold I. Davidson (Chicago: University of Chicago Press, 1997), 185–6, and TP 215.
15.
Deleuze, “Desire and Pleasure,” in Foucault and his Interlocutors, 186.
16.
Jacques Lacan, On Feminine Sexuality, the Limits of Love and Knowledge: The Seminar of Jacques Lacan, Book 20: Encore, ed. Jacques-Alain Miller, trans. Bruce Fink (New York: Norton, 1999), 62. I would like to thank Emily Zakin for this reference. Lacan was speaking of Jean-Luc Nancy and Philippe Lacoue-Labarthe, The Title of the Letter: A Reading of Lacan (1973), trans. François Raffoul and David Pettigrew (Albany: State University of New York Press, 1992).
Essay 19: Pierre Klossowski
Klossowski's Reading of Nietzsche: Impulses, Phantasms, Simulacra, Stereotypes
1.
This essay is a reading of Pierre Klossowski's Nietzsche and the Vicious Circle, trans. Daniel W. Smith (Chicago: University of Chicago Press, 1997), which is cited in the text as NVC.
2.
Cited in Johannes Gachnang, “De la conquête des images,” in Pierre Klossowski (Paris: Flammarion; Brussels: Ludion, 1996), 9 (“I am a ‘maniac,’ period, that's all!”).
3.
Pierre Klossowski, “Postface,” in Jean Decottignies, Klossowski (Paris: Henri Veyrier, 1985), 137.
4.
Friedrich Nietzsche, Will to Power, trans. Walter Kaufmann and R. J. Hollingdale (New York: Random House, 1967), §§492, 489–91.
5.
See Alain Arnaud, Pierre Klossowski (Paris: Seuil, 1990), 8–9, who cites Augustine, Meister Eckhardt, and Theresa of Ávila as precursors to Klossowski. Arnaud's book is one of the best general introductions to Klossowski's work.
6.
In English, the only treatment of Nietzsche's conception of the impulses comparable to Klossowski's is Graham Parkes's magisterial work, Composing the Soul: The Reaches of Nietzsche's Psychology (Chicago: University of Chicago Press, 1994).
7.
Friedrich Nietzsche, Will to Power, §259, 149.
8.
Cited in Park
es, Composing the Soul, 291–2.
9.
Nietzsche, Will to Power, §481, 267.
10.
Friedrich Nietzsche, Daybreak: Thoughts on the Prejudices of Morality, trans. R. J. Hollingdale (Cambridge: Cambridge University Press, 1982), §109, 65.
11.
Nietzsche, Will to Power, §387, 208: “The misunderstanding of passion and reason, as if the latter were an independent entity and not rather a system of relations between various passions and desires; and as if very passion did not possess its quantum of reason.”
12.
Friedrich Nietzsche, The Gay Science, trans. Walter Kaufmann (New York: Vintage, 1974), §307, 245–6.
13.
Deleuze's essay on Klossowski, “Klossowski, or Bodies-Language” (LS 280–301) emphasis Klossowski's relation to Kant:
The order of God includes the following elements: the identity of God as the ultimate foundation, the identity of the world as the surrounding milieu, the identity of the person as a well-founded agent, the identity of bodies as the base, and finally the identity of language as the power of denoting everything else. But this order of God is constructed against another order, and this order subsists in God, and consumes him … The order of the Antichrist is opposed point by point to the divine order. It is characterized by the death of God, the destruction of the world, the dissolution of the person, the disintegration of bodies, and a change in the function of language, which now expresses nothing but intensities. (292, 294)