S-Article: Noys

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The Powers of the Negative: The Mathematics of Novelty

Benjamin Bishop

Sam Gillespie The Mathematics of Novelty: Badiou's Minimalist Metaphysics

Melbourne: re.press, 2008. ISBN 978-0-9803052-4-1 (paper). 175pp. $35.00 AUD $25.00 USD £16.00 GBP. Also available open access from www.re-press.org

How are we to distinguish mere change from actual novelty? To put this question in Lacanian terms, how are we to distinguish a permutation of the Symbolic qua structure from the emergence of novelty as the re-organisation of the coordinates of the Symbolic? It is this question that guides Sam Gillespie’s reconstruction of Badiou’s philosophy circa Being and Event (1988).1 Sam Gillespie’s death, in 2003, was an incalculable loss in all senses. This work has been brought to publication by his partner Michael Mottram, Chris Gillespie, and Sigi Jöttkandt. To do proper justice to this major contribution to thought I treat it in light of Badiou’s suggestion that the space of philosophy belongs to eternity. This involves at once recognizing the profound integrity of this work as it stands, and yet also outlining where the prescient problems it indicates have been addressed by Badiou and other thinkers.

Gillespie sets out to distinguish change from novelty through the by-now canonical contrast between Deleuze and Badiou. As Badiou admits, Deleuze might well be regarded as his “secret sharer”: they both begin from a thinking of multiplicity, they both defend the honor of philosophy against any reactionary slackening of thought, and they both insist that philosophy is defined in terms of its possible inventiveness against the pseudo-novelties of contemporary capitalism.2 In his reconstruction, however, Gillespie follows Badiou in arguing that despite these similarities they occupy fundamentally different orientations. Deleuze’s insistence on his philosophy as an endlessly inventive drawing out of the new through the virtual powers of difference, remains, for both Gillespie and Badiou, a playing out of difference dependent on the folding of the virtual past. Contra to Peter Hallward’s recent contention that Deleuze’s thinking is resolutely extra-worldly,3 in its insistence on subtracting itself from actuality, Gillespie argues that the fault of Deleuze’s thinking lies in its worldliness (and I would agree). Deleuze defines the virtual and the differentiating effects of novelty against and through the actualization and radicalization of tendencies in the world. What Deleuze lacks, and what therefore vitiates his thinking of novelty, is the capacity to begin from the void―the rupture that marks the inconsistency of Being, disrupts the world as it is, and which is the “strait gate” through which novelty enters the world.

As Gillespie states, and I can only concur, “One might regard Badiou’s project, then, as a means of reclaiming the powers of the negative away from the positivity and pure productiveness of Deleuze’s system” (Gillespie, 15). In fact we could go further and argue that Badiou provides the elements for a rehabilitation of the negative against the widespread tendency of contemporary theory to make recourse to a thinking of affirmation, a tendency that is not absent from Badiou as well.4 What Gillespie does, in a striking fashion and, more unusually, one deeply attentive to the mathematical dimension of Badiou’s thinking, is to stress Badiou’s own peculiar formalization of the negative. It is only from the void, as the point which inscribes the inconsistency of Being and is an axiomatic element of every set, that we can begin to distinguish the truly new.

Gillespie notes the privilege that Deleuze gives to philosophy as creating the conceptuality for innovation. In contrast, Badiou radically delegates the new to the four conditions of philosophy (art, science, politics, and love), in the moment of the event that ruptures with the world. The conclusion is that for Badiou “philosophy creates nothing as such” (Gillespie, 14). This is one of the senses of minimalism that inhabits Badiou’s philosophy, the minimal role of philosophy. The other, to which this work is devoted, is Badiou’s specification of ontology through mathematics in its most formal and minimal terms. What Gillespie probes sympathetically is this radically reduced role for philosophy, which seems to have nothing to really add, either in terms of defining the new or in terms of defining ontology. He recognizes the neuralgic point of Badiou’s subtractive vision: “Being and Event does little to theorize the relation between being and its actualization or individuation” (Gillespie, 14-15). What is fascinating is that Gillespie has already offered an analysis of this difficulty before Badiou’s own attempt to flesh out this question of relation in Logics of Worlds (2006),5 which deploys the operators of category theory to trace the emergence of the event in transcendental regimes of appearance.

The image of Badiou Gillespie reveals is more uncompromising and disturbing than the one to which in the meantime we may have become safely inured. This is a Badiou whose thinking is predicated on the negative: “Negation is not a denial of the capacity of thought as much as it is the fundamental condition under which thought is enabled” (Gillespie, 28). Without this condition, we are left with a thinking of philosophy “that can only take recourse in a descriptive affirmation of what always already is” (Gillespie, 42). Although writing of Badiou in this instance, such a characterization could easily be extended to not only Deleuze, but also the work of Bruno Latour, Antonio Negri, and a substantial body of contemporary theory.6 Of course the difficulty comes in the exact specification of the nature of this void. Is it simply transcendent? This leaves the void as functionally indistinguishable from theological conceptions of God, especially those passing through negative theology. Instead, Gillespie identifies the void as a starting-point―the name of an internal impasse, of indeterminacy, that must be determined through the production of truths. Badiou’s thinking is not simply a worshipping of the void, a contemplation of the miraculous possibility of the event, but the attempt to think through the void, in order to stabilize a truth.

In this way, Badiou re-formulates exactly that concept of “determinate negation” that, according to Žižek, has been abandoned by recent theory.7 To do so, Gillespie argues, we must move beyond the event to examine the generic process by which the militant work of the subject renders “consistent” the inconsistency of the void. The difficulty that this raises is the relation between an event and the situation in which it appears. As Gillespie notes, Badiou’s supposition that the event comes from the edge of the void, coupled with the fact that every set contains a void element, would seem to imply an ontological identification and regularity of the possibility of events. In fact, Badiou stresses the rarity of events, and their disconnection from the formal relations of the situation. Given this disconnection, the obvious question becomes, how does a subject become engaged by an event? How does the generic subset emerge as a truth procedure in (and against) a situation? For Gillespie, as also for Simon Critchley,8 there remains something of a motivational deficit in this analysis. While we have a formal identification of events and their rarity, something is left lacking in the account: “a supplementary framework is needed to account for what it is that comes to grip or seize subjects as they encounter events” (Gillespie, 96). What is interesting is that Gillespie’s solution to this problem does not, unlike Simon Critchley’s, involve the playing-off of the pathos of finitude, everyday human suffering for example, against Badiou’s supposedly arid formalism.

Instead, in a gesture that is indebted to Badiou’s earlier Theory of the Subject (1982),9 and which foreshadows Badiou’s own recent return to that work in Logics of Worlds, Gillespie turns to Lacan’s account of anxiety as a possible answer. The importance of anxiety is that it is an affect which is certain. It also marks “a lack of lack,” which is to say a contact with the Real that cannot be denied. In this way, almost paradoxically, anxiety means that we lose our own individual relation to lack and are forced to confront, in the guise of the object (a), the empty ground of Being itself. In this way, we can complete the circuit from the claim that “[t]he ultimate ontological support of the world is nothing” (Gillespie, 139), to an experience of that “nothing.” For Gillespie anxiety is the bridge between Badiou’s radically subtractive, minimalist, and atheist ontology, and the subject as operator of the event.10 The tension here, not fully resolved in Gillespie’s account, is his claim that this affect of anxiety, sign of the emergence of the drive, does not need to assume “morbid or abject vicissitudes” (Gillespie, 117), as it often does in Žižek, for example.11 I am unsure of the certainty of the distinction Gillespie offers between a libidinal interest (subject to such vicissitudes) and an elementary relation―considering jouissance is involved in the latter, it is unclear quite how it avoids at least a minimal affective pathos, considering Lacan’s definition of jouissance as a paradoxical “pleasure in pain.”12

Leaving this aside, the supplementary function does not only cut one-way. If Lacan provides a minimal phenomenology of the subject, then Badiou raises the critical question of the forcing of this individual relation to anxiety towards a collective realization and instantiation of the generic. Again, one can only profoundly regret that this remains sketched out so rapidly, but it seems to suggest a re-articulation of Lacanian psychoanalysis with a collective politics through the concept of the subject.13 What is crucial here, and faithful to Badiou, is the passage through form. Anxiety signals the encounter with indiscernibility, and the necessity to give form to this “nothing” that eludes the speaking subject. In a way, we have the restoration of the category of “determinate negation” slightly displaced from its typical Hegelian coordinates, although much here, of course, depends on how exactly one reads Hegel. Whatever the difficulties that would be involved, which would no doubt be considerable, Gillespie has patiently worked towards negation as the condition of the possibility for a transformative philosophy.

This is what his whole project works towards, and Gillespie is not averse to asking the difficult questions that result. At the heart of the matter lies the difficulty in coordinating the new with the true. In Badiou’s case, this involves the praxis of forcing to instantiate the event, starting from the void. Hence, in Gillespie’s account, the event remains a less important category than those of the generic, forcing, and formalization, all these offer determinations of the negative and ways to persist with it.14 The problem we face is how to engage in this praxis in the face of the continuous “novelties” of capitalism. In the case of Deleuze, we find a worldly immersion that tries to radicalize the existent tendencies of capitalism―to transform capitalist deterritorialization to absolute deterritorialization.15 I have called this kind of thinking “accelerationism.” In Gillepsie’s account, Badiou offers a radically different solution: “to separate thought and action from conditions that have been set to it by the world, and its historical extension in the global market-place” (Gillespie, 145).

The solution, however, seems to result in aporia. On the one hand, to avoid complicity with the capitalist ontology of the new and philosophical description, philosophy must be detached or disconnected from the “world as I found it.” On the other hand, this detachment or disconnection seems to leave philosophy with little way to assess whether an event has really taken place. The very abstract formalization Badiou engages in means that when it comes to his analysis of actual events we are left unsure of how far his philosophy can add to, or explain, how these constitute real events. It is noteworthy that, in a recent review of Logics of Worlds, Peter Hallward has raised a similar problem. Despite Badiou’s attempt to fine-tune his theory, and to provide, precisely, more detail of the “mediation” between ontology and appearance, his examples, dazzling as they may be, are still left materially indeterminate.16 While Badiou may now have a “logic” to describe the world, this does not appear to have solved the problem raised by Gillespie. After all, the Paris Commune remains defeated and Alexander remains victorious at Gaugamela, and what has describing these events in terms of category theory added to our understanding? Can such description really prove an event has taken place when an event requires subtraction from worldly standards of verification?

Gillespie’s answer is quite radical, not least in its consequences for Badiou’s philosophy:

It is only by radically separating itself from the world―so radically, in fact, that the question of a philosophical application of thought onto the world becomes an afterthought of sorts―that philosophy becomes an imperative to try out through militant activity. (Gillespie, 148)

Badiou’s “philosophy” would therefore become an experimental practice. Unable to truly decide whether anything was an event due to its detachment from the world, this detachment becomes the condition of militant practice. We could argue that this is a torsion of Marx’s injunction that “[t]he philosophers have only interpreted the world, in various ways; the point is to change it.”17

The risk is, however, that Badiou’s philosophy is rendered merely horatory, which his own model of prescriptive affirmation risks reinforcing.18 We are constantly called to action and given the reinforcement of descriptions of past events, and the promise of future events, but little means to guide and assess the current possibility of events. Gillespie’s contention is that the result of Badiou’s work is to suggest that transformation is only possible by giving up reflection on the world (Marx’s “interpretation”). This is a resolutely extra-worldly orientation, and not entirely unsympathetic considering the current miseries, which seem to invite despair, hedonist avoidance, apathy, or clinging to survival. The difficulty, raised with most insistence by Peter Hallward, is that to give up on description and interpretation is to foreclose the ability to intervene in any meaningful fashion. From this point of view, Gillespie’s reading indicates the persistence of a certain strain of Maoist voluntarism evident in Badiou’s work of the 1970s, in which politics takes command at the expense of philosophy, or over other forms of articulating existent power relations (Gramscian “hegemony,” Foucault’s “power-relations,” etc.). It is difficult to be sure whether Gillespie endorses this conclusion, which would seem to entail the auto-dissolution of philosophy into militant praxis. This would seem to leave Badiou as an example of that “speculative leftism” that he critiques in Being and Event.19 Badiou obviously has in mind Guy Lardreau and Christian Jambet’s L’Ange (1976),20 and argues that such thinking absolutizes the event―detaching us from the world at the cost of posing a perpetual Manichean dualism between revolt and power.

In fact, Bruno Bosteels has recently insisted on exactly this problem in Badiou’s thinking. In his reading, this absolutization of the event is not only correlated with ultra-leftism, but also with Badiou’s category of “anti-philosophy.” What Bosteels insists on is that this is not merely an external threat, but one intrinsically staged within Badiou’s philosophy:

But I would say that antiphilosophy teaches us that the real danger, including for Badiou’s own philosophy, is not the religion of meaning but rather the radicalism of the pure event as absolute beginning, or the treatment of the event as some kind of archi-event, that is to say, in the end, the conflation of the event with the act.

For Bosteels, more so than for Peter Hallward, there are dialectical resources in Badiou’s philosophy that would allow the containment of this internal “threat.” It is difficult to properly assess Gillespie’s position, but it would seem to indicate the temptation of antiphilosophy―directed towards a militant politics of the act, which forgets philosophy. This is an almost quasi-Wittgensteinian position, considering Wittgenstein’s quasi-Maoist advice to his students to quit philosophy and enter the factory.

Gillespie’s recourse to Lacan’s concept of anxiety is the attempt to avoid the complete detachment of the subject from the “nothing” of the void. Whether we agree with this characterization, and I feel that this is still hostage to an overly negative conception of affect in the sense of failure or finitude, we see that what Gillespie is straining towards is a new thinking of “determinate negation.” In this way, Badiou poses an acute problem to thinking in a transformative way, posing sharply the problem abandoned by phenomenological and pragmatist currents, which remain largely content to leave the world as it is. Here I think a supplementary condition of the present is not only the operation of capital, but also the collapse or retreat of the forms of agency that provided resistance to it. In the lack of such subjective instantiations, it becomes difficult to ground a thinking of radical transformation without conceding to the world as it is. It is the great merit of Gillespie’s work to confront us once again with this question.

1 Alain Badiou, Being and Event, trans. and intro. Oliver Feltham (London and New York: Continuum, 2005).

2 See Alain Badiou, Deleuze: The Clamor of Being [1997], trans. Louise Burchill (Minneapolis and London: University of Minnesota Press, 2000).

3 Peter, Hallward, Out of this World: Deleuze and the Philosophy of Creation (London and New York: Verso, 2006).

4 For Badiou as “affirmationist” see, in particular, his “Third Sketch of a Manifeso of Affirmationist Art,” in Polemics, trans. and intro. Steve Corcoran (London and New York: Verso, 2006) 133-48.

5 Alain Badiou, Logics of Worlds, trans. Alberto Toscano (London and New York: Continuum, 2009).

6 I make this argument in my forthcoming work, The Persistence of the Negative: A Critique of Contemporary Continental Theory (Edinburgh: Edinburgh University Press, 2010).

7 Slavoj Žižek, In Defense of Lost Causes (London and New York: Verso, 2008) 337-380. See also Badiou’s comments on the contemporary “crisis of negation” in “‘We Need a Popular Discipline’: Contemporary Politics and the Crisis of the Negative,” Interview by Filippo Del Lucchese and Jason Smith, Critical Inquiry 34 (Summer 2008): 645-59, especially 652-53.

8 See Simon, Critchley, Infinitely Demanding: Ethics of Commitment, Politics of Resistance (London and New York: Verso, 2007).

9 Alain Badiou, Theory of the Subject, trans. Bruno Bosteels (London and New York: Continuum, 2009).

10 In comparison one could consult Ray Brassier’s Nihil Unbound: Enlightenment and Extinction (Basingstoke: Palgrave Macmillan, 2007), which also departs from the subtractive “nihilism” of Badiou’s thought but rather to pass outside the domain of the human subject altogether. Hence, for Brassier, the necessity is not so much for a psychological supplement to Badiou, but rather the dissolution of such a “folk psychology” in the name of a radicalized neurobiological reductionism, such as that of the Churchland’s.

11 Bruno Bosteels has made the most thorough critique of Žižek on these grounds, see “Badiou without Žižek,” Polygraph 17, “The Philosophy of Alain Badiou,” ed. Matthew Wilkins (2005): 221-44.

12 “What I call jouissance―in the sense in which the body experiences itself―is always in the nature of tension, in the nature of forcing, of a spending, even of an exploit. Unquestionably, there is jouissance at the level at which pain begins to appear, and we know that it is only at this level of pain that a whole dimension of the organism, which would otherwise remain veiled, can be experienced.” Lacan, quoted in Néstor A. Braunstein, “Desire and jouissance in the teachings of Lacan,” in The Cambridge Companion to Lacan, ed. Jean-Michel Rabaté (Cambridge: Cambridge University Press, 2003) 102-115, 103.

13 I have discussed this issue in my review of Yannis Stavrakakis, The Lacanian Left (Albany: SUNY Press, 2007) and Ian Parker’s Revolution in Psychology (London: Pluto, 2007), Historical Materialism 17.1 (2009): 183-90.

14 Zachary Fraser has also insisted on the importance of formalization, as against the usual fixation on the event, for the reading of Badiou. See Zachary Luke Fraser, “Introduction: The Category of Formalization: From Epistemological Break to Truth Procedure,” in Alain Badiou, The Concept of Model [1969] (Melbourne: re.press, 2007) xiii-lxv.

15 Gilles Deleuze and Félix Guattari, A Thousand Plateaus [1980], trans. Brian Massumi (London: Athlone, 1988) 88.

16 Peter Hallward, “Order and Event: On Badiou’s Logics of Worlds,” New Left Review 53 (September-October 2008): 97-122.

17 Karl Marx, “Theses on Feuerbach” [1845], Marxists Internet Archive 2002. <http://www.marxists.org/archive/marx/works/1845/theses/theses.htm> [accessed May 23, 2009].

18 See Alain Badiou, The Meaning of Sarkozy, trans. David Fernbach (London and New York: Verso, 2008).

19 Badiou, Being and Event, 210-11.

20 Guy Lardreau and Christian Jambet, L’Ange: Pour une cynégétique du semblant (Paris: Grasset, 1976).

21 Bruno Bosteels, “Radical Antiphilosophy,” Filozofski Vestnik, XXIX.2, “Radical Philosophy?,” ed. Peter Klepec (2008): 155-87, 177.


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