Brassier and Toscano - Postface - Aleatory Rationalism (from Alain Badiou - Theoretical Writings)

POSTFACE Aleatory Rationalism Rimbaud employs a strange expression: ‘les révoltes logiques’, ‘logical revolts’. Philosophy is something like a ‘logical revolt’. Philosophy pits thought against injustice, against the defective state of the world and of life. Yet it pits thought against injustice in a movement which conserves and defends argument and reason, and which ultimately proposes a new logic. Mallarme´ states: ‘All thought begets a throw of the dice.’ It seems to me that this enigmatic formula also designates philosophy, because philosophy proposes to think the universal – that which is true for all thinking – yet it does so on the basis of a commitment in which chance always plays a role, a commitment which is also a risk or a wager. Alain Badiou, ‘Philosophy and the Desire of the Contemporary World’ This philosophy is in every respect a philosophy of the void: not only a philosophy that says the void that pre-exists the atoms that fall within it, but a philosophy that makes the philosophical void in order to give itself existence: a philosophy that instead of starting off from the famous ‘philosophical problems’ (‘why is there something rather than nothing?’) begins by evacuating every philosophical problem, and therefore by refusing to give itself any ‘object’ whatsoever (‘philosophy has no object’), in order to begin from nothing, and from this infinitesimal and aleatory variation of the nothing which is the deviation of the fall. Louis Althusser, ‘The Subterranean Current of the Materialism of the Encounter’ 1. In these pages, as elsewhere, Alain Badiou has steadfastly declared his allegiance to a tradition of philosophical rationalism among whose most illustrious representatives we can number Plato, Descartes, Spinoza, Leibniz and whose last and most problematic proponent is perhaps Hegel. Badiou is a

Theoretical Writings systematic thinker, profoundly at odds with the passion for the limit and the mistrust of pure thought that typified much twentieth-century philosophy, be it phenomenological, hermeneutic, deconstructionist or therapeutic. What’s more, he lays claim to the exalted standard of philosophical rigour represented by his rationalist predecessors while dispensing with venerable models of methodological discipline such as Kant’s transcendental critique, Hegel’s dialectic, Husserl’s phenomenological reduction, or Heidegger’s existential analytic. So what novel philosophical method underlies Badiou’s system? At first sight, none. Readers of Badiou well-versed in the grand tradition of German philosophy that begins with Kant and ends with Heidegger, in which methodological scrupulousness is the sine qua non for serious philosophizing, will find the conspicuous absence of anything like a methodological propaedeutic in a book as ambitious as Being and Event (1988) deeply troubling. Yet this is more than just a glaring oversight on Badiou’s part. For in his eyes, philosophy, like everything else, is a situation; it is neither unified nor perennial.1 The conviction that the philosopher is in a position to begin by defining and mobilizing a sui generis philosophical method assumes that a subject of philosophy is already given in a more or less absolute sense, whether as a normative model or in the latent recesses of a reflexive capacity available to all. Furthermore, it assumes that such a subject could articulate a method by appropriating its own intra-philosophical conditions; in other words, that method is something that I, as a subject of philosophy, always already possess, regardless of the discipline and training I may have to undergo in order to master it. Such a putative subject of philosophy would thus be autopositional or self-presupposing. It would strive to appropriate its own conditions as given within a philosophical situation which is already ‘naturally’ its own and which has the unique feature of being able to encompass and reflect all other situations. The counterpart of this auto-positional appropriation is thus the (chimerical) notion of something like a global or absolute situation, a reflexive Whole of philosophy. Following the terms laid out in meditations 8 and 9 of Badiou’s Being and Event, we could argue that the logic of such an appropriation is that of the re-presentation, or ‘state’ of the philosophical situation. Method, to adopt Badiou’s vocabulary, would thus be something like the state of philosophy. This intra-philosophical re-presentation of philosophy’s conditions harbours two spontaneous, or rather prejudicial, intuitions. First, an intuition about what needs to be philosophized. The authority of philosophical tradition is encoded in the re-presentation of the philosophical situation and serves to legitimate an intuition about those phenomena that will always require ‘philosophising’. To paraphrase Deleuze, the tradition and teleology of

Postface sophia converge in a kind of trans-historical ‘good sense’ about what requires thought. Favoured examples of these natural concerns of philosophy include the possibility of objective knowledge, the mystery of human selfconsciousness, the meaning of being, etc. Second, the auto-representation of philosophy mobilizes an intuition about what it is like to think philosophically (as opposed to scientifically or anthropologically or sociologically). Philosophy is transcendental critique, speculative dialectic, ontological questioning, deconstruction and so on. Thus, an intuition (rather than argument) about what needs to be philosophized is used to underwrite the characterization of the task of philosophy and the identification of the methodology best suited to that task. Accordingly, the intuition that cognitive judgement needs to be legitimated fuels the characterization of philosophical method as transcendental critique; the intuition that all consciousness is irreducibly intentional fuels the characterization of philosophical method as phenomenological reduction; the intuition that the meaning of being is at issue in human existence fuels the characterization of philosophical method as existential analytic of Dasein, and so on. Badiou rejects these philosophical intuitions together with the methodologies they subtend because he refuses the gesture of auto-position through which the subject of philosophy re-presents the philosophical situation and appropriates those intra-philosophical conditions deemed necessary for philosophizing. His philosophy does not begin with a gesture of auto-position but with an axiomatic decision entailing that philosophy be expropriated of its conditions, deprived of the appeal to intuition – whether natural or transcendental – and irrevocably sundered from its foundation.2 This decision is encapsulated in the axiom the One is not.3 It has a theorematic counterpart, which has its basis in the agonistic history of mathematical logic and its paradoxes: there is no Whole. The non-being of the One and the inexistence of the Whole are the indispensable correlates of the rationalist decision to identify mathematics with ontology.4 This is the decision that conditions Badiou’s entire philosophical enterprise. Rather than isolating and securing the kind of philosophical intuition that would provide the foundation for a method, this decision immediately deprives philosophy of its customary arsenal of intuitions about what needs to be philosophized and rules out the possibility of accessing a paradigmatic model of philosophical method. It thus ungrounds philosophy by evacuating it of all previously available founding intuitions about the propriety of its content and the appropriateness of its method. The simplicity of this axiomatic-theorematic conjunction (the One is not and there is no Whole) belies its devastating consequences for the usual premises that philosophy calls upon to shore up its ultimate sovereignty over the

Theoretical Writings domain of thought. It is not just that philosophical thought no longer enjoys access to a fundamental arche´, principle, or universal overview (‘beings as a whole’) – that would be platitudinous – but that it must now abjure any intuition that continues to assume the integral unity of the phenomenon with which philosophy is supposed to begin, regardless of how it may be characterized. Philosophy cannot presuppose a unitary instance of thought, a unitary relation of intentionality, or a unitary phenomenon like ‘the world’. There is no such thing as what it is like to think. Philosophy, as a situation, can neither be founded on a unified subject nor reflected in a totality. It is this subtraction of philosophy from any authentic destination or secure and eminent placement within the system of thought that also separates the ‘decisionist’ predilection for the axiom from the theme of beginning or the origin, from all the instances of more or less laborious parthenogenesis that punctuate the history of philosophy. Philosophy has no starting point, no home, be it ego or Earth, praxis or contemplation. Decision as affirmed within the parameters of what we shall refer to as Badiou’s ‘aleatory rationalism’ is not grounded in some putative sovereignty since it is always a decision on an undecidable, on an event that philosophy itself does not and cannot give rise to. This has noteworthy consequences as far as the question of philosophical method is concerned. For Badiou, the methodological pomp and circumstance so beloved of German philosophers from Kant to Habermas is an otiose extravagance still wedded to a teleological and fundamentally organicist model of systemic integrity; one that continues to presuppose a transitivity between systematic consistency and systemic unity. On the contrary, the rigour and consistency of Badiou’s thought, from Theory of the Subject, through Being and Event, right up to the forthcoming Logics of Worlds, is not circumscribed in advance by a pre-delineated systemic unity linking philosophical subjectivity and reflexive totality. Hence the important amendments, revisions and retractions that Badiou has been willing to carry out, all the while reasserting his fundamental commitment to the basic axiomatic coordinates that have consistently shaped and oriented his thinking.5 For Badiou, the best guarantor of philosophical precision is not the sort of ostentatious architectonic splendour generated by the premise of systemic unity, but rather a bare axiomatic-theorematic mode of argumentation suited to the mobile constraints of systematic consistency. Badiou’s philosophy does not derive its cohesion from an underlying architectural blueprint but from a closely interconnected series of argumentative linkages between axioms and theorems; arguments sustained by the resources of mathematical thought as well as of poetic invention but devoid of any totalizing transcendental methodology.

Postface Purged of the intuitions that bolstered its claim to methodological autonomy and shored up its previous self-identifications, whether as transcendental epistemology or fundamental ontology, philosophy asserts its effective independence by renouncing its self-grounding pretensions and abrogating its traditional claims to the theory of being and the theory of knowledge, the better to identify itself as theory of truth. If mathematics, according Badiou, has always been the theory of being, it now seems that cognitive science (or even neurobiology) is in the process of hegemonizing the theory of knowledge. Here, as ever, the logic of subtraction provides the key to Badiou’s approach. It is a question of subtracting philosophy’s self-assertion from those modalities of definition that are a function of its statist representation as a discipline within the academy. Once under evental condition, philosophy need no longer conform to reactionary institutional interests bent on artificially perpetuating an arid and essentially anachronistic academic discourse. In asserting its own necessarily empty form as theory of truth, philosophy becomes free to engage with the most innovative manifestations of scientific, artistic and political thought. By emptying itself, philosophy identifies and formalizes its real conditions of possibility as extra-philosophical truths, without thereby re-appropriating them as ‘projections’ of a sui generis philosophical subject. 2. Far from relapsing into the kind of pre-critical metaphysical dogmatism that simply assumes a straightforward correspondence between thought and reality, Badiou radicalizes the critique of intellectual intuition – the cornerstone of Kantianism – by invalidating the authority of every form of philosophical intuition, whether transcendental, dialectical or formalphenomenological. This is why he refuses the premise of a fundamental transitivity between the philosophical and the pre-philosophical; the idea that philosophical insight is already latent in pre-philosophical experience and that the philosopher’s task consists in extracting the former from the latter in order to purify it. Though we might fruitfully seek instances of dialectical articulation or torsion in his work, this denial of intuition, presuppositions (objective or subjective), sensibility and everything that smacks of everyday perception and experience, makes Badiou’s philosophy – like his politics, we might add – a philosophy of separation. This separation is not to be understood as a simple abstraction; nor is mathematics the source of a new intuition, more securely grounded and powerful than that of philosophy. As Badiou asserts at the outset of Being and Event, mathematics, or ontology, is a discourse, and its privileged role in Badiou’s attempt to formulate a genuinely atheistic contemporary philosophy derives from the fact that it has succeeded in thinking (or ‘writing’) without the one: set theory thinks (or writes)

Theoretical Writings the multiple, but it does not have a concept of the multiple, an intuition of the multiple. Mathematics does not expropriate philosophy from its hold over ontology because of a privileged insight, or a superior method, but because of the deductive consistency and relentless inventiveness of its discourse. Thus, Badiou reinvents rationalism after Critique. But his is a rationalism purged of any intellectual intuition of the One or the Whole, be it Plato’s One-beyond-being, Descartes’s capture of the infinite in the One of God, Spinoza’s facies totius universi, Leibniz’s ideal of mathesis universalis or Hegel’s reflexive, self-articulating Whole. Rather than postulating the inexorable primacy of some figure of the One and the Whole, Badiou’s postCantorian rationalism asserts an untotalizable ontological dissemination and the aleatory emergence of a plurality of truths. For it is the decision to identify mathematics with ontology that functions as the precondition for the evental theory of truth, splitting the subject of philosophy from within by forcibly expropriating it of its (imaginary) grip on its own constitutive conditions. The conditions for the possibility of philosophy are no longer intra-philosophical. This claim is altogether more novel than its familiar Marxist ring may suggest. Badiou’s philosophy does not defer to the putatively extra-philosophical reality of history only to re-philosophize and re-idealize the latter by relentlessly dialecticizing its own relation to it. Philosophy purges itself of its imaginary self-sufficiency by subjecting itself to extra-philosophical conditions that are now themselves autonomous instances of thought with no need for a dialectical supplement ensuring their philosophical comprehension, mediation, or reflection. Instead, in identifying its evental conditions of real possibility, philosophy formalizes those conditions. That is why the challenge for philosophy is to mobilize an empty form, or to deploy a non-experiential arsenal of procedures whose substantive content must be filled out by extra-philosophical truths. But since all truths are extra-philosophical, and since a subject is nothing but the bearer of an evental truth, there is no autonomous subject of philosophy for Badiou. Thus systematic philosophy is rendered a-subjective and heteronomous. This heteronomy – the conviction that philosophical thought is always spurred from outside; that it is radically dependent upon the existence of a real, extra-philosophical instance, whether event or procedure – is one instance of Badiou’s basically materialist stance.6 Yet strange as it may seem, this expropriation of philosophy increases its potency. The transitivity of philosophy, its desperate suture to psychology, anthropology, politics, science, is what imposes extraneous limitations upon the potentially subversive capacities of philosophical reason. As far as philosophy and its conditions are concerned, sovereignty or ubiquity can only lead to impotence.7

Postface Philosophical thinking is thus internally fissured by the split between philosophy as empty or formal (metaontological) theory of truth and the substantive extra-philosophical truths that provide this empty philosophical form with the material it must seek to compossibilize. Whatever operational specificity philosophy possesses would seem to reside in this logic of compossibilization. Yet Badiou has yet to flesh it out beyond the rather vague indications provided in his Manifesto for Philosophy: ‘It is a question of producing concepts and rules of thought, which may in one instance remain devoid of any explicit mention of [specific] names and acts, while in another instance they may be intimately tied to them, but in such a way as to ensure that through these concepts and rules our era will be representable as the era wherein these instances of thought took place, which had never taken place before and which will henceforth be freely available to everyone, even those that are ignorant of them, because a philosophy has constructed for everyone the common shelter for this taking place.’8 Thus, if evental truths are now the material of philosophy, the task of compossibilization seems to consist in creating a conceptual space in which the ‘illegal’ inventions and truth procedures of ‘our time’ can demonstrate their shared fidelity to the disparate production of the generic and transmit the novelty of their formalizations. In other words, a ‘space’ (for want of a better word) in which subjects, always rare, can communicate in the absence of any pre-given horizon of consensus. Nevertheless, the vagueness of Badiou’s indications concerning compossibilization casts an ambiguous light on the status of his own philosophical project. For either Badiou’s philosophy merely provides one possible instance of compossibilization among others, in which case it becomes incumbent upon him to delineate a ‘novum organon’ for philosophy in the shape of a logic of compossibility for truths; or his principled disavowal of philosophical method entails that his philosophy is sui generis, and hence exemplifies the logic of compossibilization as a singular unrepeatable instance. But if Badiou’s philosophy is not only articulating an apparatus of capture for the truths of his own time and other times to come, but turns out to be the only instance of the compossibilization of truths which he thinks every philosophy should carry out, then surely this entails a severe limitation in its potency and rational transmissibility. In a move that seems suspiciously Hegelian, it’s almost as if it is only from the standpoint of Badiou’s doctrine that other philosophies can be recognized as what they were all along (despite their own pretension to ‘fill out’ truth or be the Truth of truth): ways of rendering compossible the truths arising from the generic procedures of their time. Moreover, the way in which Badiou’s own philosophy supposedly exemplifies the logic of compossibilization is not without inherent difficulties. For there is a stark disequilibrium in the constitutive conditions of Badiou’s

Theoretical Writings system: almost all the conceptual details proper to the theory of philosophy’s evental conditioning are entirely dependent upon its mathematical condition. The ontological inconsistency of evental truth and the consequent characterization of philosophy as theory of truth is almost exclusively reliant upon the identification of set theory with ontology. In Being and Event, the impasse of the mathematical-ontological theory of presentation gives rise to a philosophical-metaontological account of how, via the decision that gives rise to a subject, that which is ontologically inconceivable or unpresentable – i.e. a set that belongs to itself, which is how Badiou defines an event (the ‘ultra-one’) – comes to supplement a situation by measuring the excess of representation over presentation.9 This is the theory of the generic set and of truth as subtraction. But the metaontological formalization of truths is only possible if the discourse of being qua being has been handed over to set theory, something which itself seems to be an evental decision. Does the theory of evental decision proposed in the course of Being and Event retroactively ground the decision with which the book begins, the decision that mathematics is ontology, that the One is not, and that there is no Whole? Does it do so in the manner of the Hegelian positing of a presupposition? If it does, its virtuous circularity may be incompatible with the expropriation of dialectical method and the abjuring of systemic unity which we have tried to suggest is intrinsic to Badiou’s system. For then the danger is that such virtuous circularity is won only at the cost of reintroducing the kind of dialectically coordinated systemic totality disavowed by Badiou’s own aleatory rationalism. But perhaps we are overstating the difficulty. For it could be that the theory of the event merely explains rather than grounds the book’s opening decision. In which case, conceptual consistency may be ensured without reintroducing systemic unity. Although we cannot hope to provide a satisfactory resolution of this issue within the confines of this Postface, our aim here as elsewhere throughout these remarks is simply to alert readers of Badiou to these sorts of difficulty. 3. As we now know, Badiou’s metaontological decision that ‘mathematics is ontology’ stipulates that beings always appear in situation. Consequently, ontology itself is a situation, the situation of post-Cantorian set theory, whose singular privilege according to Badiou is to be the only situation in which there is presentation without re-presentation, i.e. the presentation of presentation.10 This is to say that set theory effectuates a presentation of the multiple shorn of any predicative trait other than that of its pure multiplicity. Set theory is the theory of inconsistent multiples as such. This means that although set theory is a consistent presentation (since everything presented must consist, i.e. be counted-as-one, in the terminology of Being and Event),

Postface what is presented in set theory is nothing but pure inconsistency as such. For the originary set whose existence the theory declares, and from which all other sets are woven, is the empty set, which is simply the mark or inscription of the unpresentable, and is not to be mistaken for the presentation of the unpresentable (for Badiou the latter is impossible, on pain of mysticism). Thus set theory is the presentation of the multiple-without-oneness, which is to say, multiplicity-without-presence, for crucially, as Badiou emphasizes, ‘presence is the precise contrary of presentation.’11 That is why there can be no intuition or experience of being, only a coherent, formalizable discourse in which being itself is inscribed as pure inconsistent multiplicity. Once again, the austerely anti-phenomenological tenor of Badiou’s meontology (a theory of being as nothingness, an ontology of the void) cannot be overemphasized. As he puts it: ‘We will oppose the rigour of subtraction to the temptation of presence, and being will be said to be only insofar as it cannot be postulated on the basis of any presence or experience.’12 Consequently, the originary subtraction from presentation inscribed in settheoretical discourse, and hence the fundamental distinction between the consistency of presentation and the retroactively posited inconsistency of that which will have been presented (or ‘counted-as-one’) – i.e. the void qua inconsistent multiplicity – should not be conflated with some postHeideggerean version of the ontological difference. The notion of onticoontological difference is entirely foreign to Badiou. His is a meontological materialism wherein if being is nothing, this is not because it is more than anything, some sort of unconceptualisable excess, but simply because it is less than anything. L’e´tantite´ de l’e´tant – literally, ‘the entity-ness of the entity’ – is merely its inconsistent emptiness, an emptiness that cannot be reduced to the consistency of absence understood as the mere opposite of presence. Inconsistency, which is perfectly codifiable, is the originary, indiscernible ontological ‘stuff’ or ‘material’, rather than the entity’s adverbial coming-to-presence or the way in which it is spatio-temporally articulated. Meontological presentation operates quite independently of any notion of space and time, whether as a priori forms of intuition or ekstaticohorizonal phenomenalization. Badiou’s meontology is so radically indifferent to difference that it refuses not only qualitative and categorial differences but even Heidegger’s non-categorial but nevertheless categorical distinction between entities and their way of being. Consequently, the originary subtraction of the void’s multiple inconsistency cannot be equated with being’s withdrawal from presence in the bestowal of presencing: ‘[The] notion of ‘‘subtraction’’ is here opposed to the Heideggerean thesis of the withdrawal of being [. . .]. It is because it is foreclosed to presentation that being is, for man, bound to be sayable according to the imperative consequences of the

Theoretical Writings most stringent of all conceivable laws: the law of formalizable and demonstrative inference.’13 Yet if ontology is a situation, and if being is not available to intuition or experience, what pertinence can the concept of ‘being’ have outside of the ontological situation? If being is not given, whether in intuition or experience, and if the concept of ‘presentation’ is a purely formal concept generated from set theory and hence exclusively pertaining to the deductive consistency of set theoretical discourse, rather than to ‘experience’, then what relevance do the concepts of ‘being’ and ‘presentation’ have when considered apart from that discourse? Why are there situations other than the ontological one? What is the relation between the ontological situation and non-ontological situations? On what basis does Badiou distinguish between different kinds of situation, given that his ontology allows no differences in kind? The requirements of meontological univocity would seem to be perfectly satisfied by the mathematical situation alone. More precisely, Badiou’s refusal to specify the conceptual and procedural (as opposed to merely evental) parameters for the philosophical situation within which Being and Event operates threatens to ruin that univocity by introducing an equivocal dimension of analogy through philosophy’s metaontological re-presentation of ontology (set theory). Badiou’s recent work, culminating in the forthcoming Logics of Worlds (whose first chapter we have previewed in this collection), is an attempt to deal with these and related objections by supplanting the purely formal concept of ontological presentation in Being and Event with a more substantive concept of ontological appearance. Being appears precisely because there is no whole. Thus being is always localized or being-there (existence). Yet once again, difficulties arise because of Badiou’s reluctance to specify the philosophical situation in anything other than evental terms. Philosophy identifies the link between the pure unbinding of being qua being (as prescribed by set theory) and the bound character of being in situation (as delineated through the resources of category theory). Philosophy’s specificity would thereby seem to reside in its ability to identify the link between being and existence, and hence in effectuating the relation between the bound and the unbound – or the related and the non-related – by thinking the aleatory emergence of the subject of truth, such that the latter, in a position of ‘torsion’, undoes the related (knowable, classifiable) order (or language) of a situation. In this respect, the relation between bound and unbound, or related and non-related, is itself split: first, in terms of the ontological articulation of consistency and inconsistency; second, as the result of the suspension or disqualification of the system of relations that is constitutive of the situation which is transformed by the affirmation of an event. In other words,

Postface philosophy as a theoretical practice is defined by the manner in which it relates two subtractions: the ontological or axiomatic subtraction marked by the empty set and the evental subtraction which is the procedural substance of a truth-subject. Yet if philosophy is able to oversee these twin subtractions, is it not thereby accorded a function – first as meta-ontological, then as meta-procedural – every bit as totalizing, if not more so, than those figures of the Whole proposed by dialectics (whether idealist or materialist) and the Deleuzean ontology of the virtual? 4. What Badiou’s rationalism retains from the Kantian/Heideggerian critique of metaphysics is the fundamental distinction between truth and knowledge. However, contra both Kant and Heidegger, Badiou insists that truth’s extrapropositional character – its transcendence vis-à-vis knowledge – need not be consigned to non-conceptual intuition and the extra-conceptual and nonformalizable domains of morality or poetry. It can be precisely circumscribed using the resources of mathematical discourse. According to Badiou, truth’s unknowable or indiscernible character remains rationally conceivable because the distinction between the determinate possibilities of knowing and the indeterminate potency of thinking has been rendered ontologically specifiable through the work of the mathematician Paul Cohen. But Badiou’s ontology stipulates that the unknowable is never One; thus it is never an absolute, it is always situated, localized. Truth’s transcendence is only ever relative, never absolute; it is the transcendence from this situation through the unknowable of this situation. What is unknowable is only ever unknowable from within a situation, and the forcing of a truth (cf. ‘Truth: Forcing and the Unnameable’ in this collection) accounts for how what was unknowable within a given situation can be rendered knowable by transforming that situation’s cognitive dimensions from the inside. Truths are always plural and discontinuous, never unitary and homogeneous. By the same token, deductive consistency is discontinuously sequential rather than homogeneously arborescent, and hence no longer vitiated root and branch by the emergence of inconsistency (this is the upshot of what Badiou calls ‘the CantorGödel-Cohen sequence’). Upsurges of inconsistency petition new decisions and give rise to new deductive sequences. ‘Event’ is simply Badiou’s name for such upsurges. The axiomatic assertion of evental inconsistency – what Badiou calls ‘deciding the undecidable’ – is made in the absence of any pre-existing cognitive criteria for verifying that assertion. We affirm that something happened, even though we do not know how to prove or verify its occurrence. But the assertion itself will bring about the conditions for its own verification: in drawing the consequences of that assertion, we slowly transform the parameters of cognitive possibility governing the logic of the

Theoretical Writings situation in such a way as to render what was previously unthinkable thinkable (the situation’s generic truth) and what was previously unknowable knowable (‘forcing’ the generic supplement of the situation). It is the precise articulation of the deductive force of mathematics and a Real instance of rupture which defines the specificity of Badiou’s thought, setting it apart from the otherwise ambient concern with the themes of excess and exceptionality. Rather than leaving novelty to mutate dialectically into the structures of established fact or to remain ultimately indiscernible from states of affairs (an accusation levied at the concept of the virtual in Badiou’s Deleuze), the ontological apparatus set in motion by Badiou is intended to purify the event to the point where its incomprehensibility from the point of view of the knowledge or state of the situation is rendered exorbitant. Instead of discerning novelty in the interstices of any phenomenon, Badiou opts for conceding almost everything to the indifferent order of ontology – to the pervasive normalcy of things as they are – so as to ensure that the sundering of normalcy be in turn given its due. Evental novelty is not ubiquitous but rare, and the measure of its rarity is given by ontology’s almost boundless capacity for rendering all phenomena thinkable as more or less unexceptional. Indeed, one of Badiou’s most common polemical gambits, exhibited in his objections to Deleuze’s Riemann (in this volume’s ‘One, Multiple, Multiplicities’), consists precisely in seeing a kind of harmless banality where other thinkers think they perceive the outer limits of thought. But the event is precisely not what it is possible to think, at least not until its consequences have been drawn in a traversal of the situation and in the production of a truth, with all the consequences it entails. The event, as Real, is always in some sense impossible. And it is the great glory of mathematics that its history is marked by the decisions to force certain impossible entities into existence and intelligibility (be they imaginary numbers, infinitesimals, Mahlo cardinals or what have you). For Badiou, in complete contrast to classical rationalism or even the temporalized adventures of dialectics, everything is not thinkable here and now. Were it so, the capacity of being would be exhausted by the modality of the possible, and all novelty would have the status of an insignificant supplement, a simulacrum. Rather, what is unthinkable in situation now, rather than what is absolutely unthinkable, can become thinkable. As we have seen, for Badiou there can be no such thing as an other of thought tout court, an unthinkable sub specie aeternitatis. The productive and groundless character of truths and subjects entails the wager that ‘we will have been able to think what was previously unthinkable’. It also entails the purely adjectival character of rationality, the non-identity of reason as the principle for a possible, and thus implicitly actualized, space of possibilities. While we may axiomatically affirm the incompleteness of all situations, their

Postface lying at the edge of the void, and thus the ever-present chance that we may come to think and to be otherwise, there is no identity, even a negative one, for the impossible-Real that aleatory rationalism tries to situate through the resources of set-theoretical ontology (and specifically, the axiom of foundation and the theorem of the point of excess). In a sense, the whole point of the finely articulated apparatus of ontology is to reveal, through its paradoxes and points of undecidability, that the Real has a non-transcendental, situational specificity. Or rather, that precisely because it can only be subjectively attested in its effects, in the construction of a generic set, there is no such (one) thing as the Real, but rather nondenumerable instances of the determinate puncturing of different situations by the (empty, indifferent) truth of being. The multiplication of infinites ensures that there is no Real as absolutely Other, no unthinkable that would constitute the limit or transcendent object of a reason. Whence Badiou’s manifest indifference to the turn to the sublime (which he plausibly regards as founded on a completely impoverished notion of infinity and a rather miserable humanism) and his palpable and combative disdain for the pathos of finitude – both of which are, after all, intimately connected intellectual phenomena. Although foreclosed from the standpoint of the constituted knowledge or language of the situation, the Real affirmed by Badiou’s aleatory rationalism is not the counterpart of a thought marked by finitude, and it is not One, since it can only be retroactively attested, which is to say produced, for and through a determinate situation in the process of evental subjectivation. Thus, deductive fidelity offers a paradigm of rationality which is no longer about validating cognitive necessity but about wagering on the aleatory and unverifiable in a way that entails a process of conceptual invention and cognitive discovery that will transfigure the structures of intelligibility within a given situation. Far from hypostasizing ‘reason’ as some sort of faculty or disposition naturally inherent in the human intellect, far from seeking to bolster the allegedly normative authority of ‘rationality’, Badiou’s brand of rationalism subtracts ‘reason’ from the ambit of the psyche in a way that subverts the presumed fixity of cognitive structures and undermines the pseudotranscendental bounds of linguistic sense. This is a rationalism without ‘reason’, one that has been radically de-psychologized. ‘Rationality’ is a pseudo-normative category mired in logicism at best, psychologism at worst. Axiomatic-theorematic reasoning provides a model of ‘rationality’ whose resemblance or lack thereof vis-à-vis human cognitive processes is ultimately irrelevant. Moreover, this aleatory rationalism is devoid of constitutive interests or intrinsic ends that would conjoin the moral and the epistemological. It is ‘disinterested’ in the sense that it declares the possibility of a ‘formalised

Theoretical Writings in-humanism’.14 It is rare, discontinuous and inherently subversive, inasmuch as it does not shore up the authority of cognitive norms, but rather disqualifies them. Where dogmatic rationalism asserts the sovereignty of ‘reason’ qua cognitive faculty harbouring the ends of our activity (whether manual or intellectual) and guaranteeing our orderly dwelling in a predictable categorized world, Badiou’s aleatory rationalism affirms the potency of thought as that which is defined precisely by the discontinuous invention of means for wagering on novelty and forcing the dysfunction of the categories that partition worlds into distinct domains that can be overseen, counted and controlled. This focus on the extra-philosophical procedures that allow subjects to avoid the structures of knowledge and produce generic truths outside the norms of possibility suggests that, despite the emphasis on axiomatic decision as an inaugural separation from any religious theme of origin or beginning, aleatory rationalism – the thinking of the event – is best understood in terms of the consequences of affirmation, consequences that, counter to traditional philosophical intuition, involve the invention of new extra-philosophical methods which in turn will inflect the practice of philosophy itself, much as Lenin’s theory of the party and Mallarmé’s experiments with syntax have left their mark on that space of compossibility constituted by Badiou’s thought. There is no sovereign subject of rationality, only rational subjects elicited by a decision on an event and caught up in the aleatory construction of singular universal truths. Consequently there is no thought outside of its dissemination in these procedures. What these procedures share, what renders them (retroactively) compossible is not their conformity to ‘reason’ but their production of generic sets, i.e. truths subtracted from the inevitably partial distributions of knowledge. Philosophy’s arduous task consists in coordinating these perforations of the orders of knowledge. ‘Thought’ – if we can speak of such a thing independently of situated procedures – is not defined as a faculty, but as the contingent and transversal product of such a coordination. 5. The mainstream of contemporary ‘Continental’ philosophy continues to operate within the bounds of the critical interregnum: the (broadly) antimetaphysical and post-rationalist problematic initiated by Kantian critique and radicalized by Heidegger’s fundamental ontology. We should not allow this post-Kantian consensus – conformity to which fuels the current détente among ‘Continental’ philosophers – to occlude the peculiar repartition of modesty and ambition carried out by Badiou’s philosophy. Confronted with the latter’s seemingly irrepressible confidence in the affirmative capacities of philosophical formalization, the Kantian reflex – now crucially and insidiously supplemented by the para-political and meta-aesthetic ideology of

Postface the unrepresentable (so well diagnosed by Jacques Rancière) – is to castigate what it identifies as a peculiarly anachronistic version of ‘fanaticism’. The recourse to set-theoretical ontology, mustering varieties of infinity as yet undreamt of by metaphysicians, seems to herald a baleful recrudescence of pre-critical dogmatism, a disastrous pretension, as Kant put it, ‘to SEE the infinite’. Perhaps it is time to consider whether the particular image of philosophy endorsed by Badiou may or may not prove reducible to a kind of ‘raving with reason’. To begin with, and in light of the demarcations rehearsed above, such fanaticism could not without further ado be ascribed to philosophy, strictly speaking. We have already noted that the secularization of the infinite requires that philosophy expropriate its putative capacity to think the latter. Thus, in abandoning the project of critique (or rather, in never taking it up), Badiou’s aleatory rationalism also abjures the putative pre-eminence of philosophy when it comes to delineating the very possibilities of thought. Far from constituting an instance of perilous philosophical hubris, the claim that ‘we can begin purely and simply with the infinite’ is a claim that rests on the inventions of mathematics. In other words, if the infinite can come first it is because philosophy has abdicated the autonomy of its intuition the better to defer to the cognitive innovations of mathematics and – in a way we shall not be able to investigate here – politics.15 If anything then, philosophy is immodestly heteronomous, since its hubris does not arise from its own capacities but from the capacities of thought in its heterogeneous instances of production and subjectivation. The plurality of thought, or rather of those procedures that produce truths, a plurality concomitant with the denial that there is a subject of or for philosophy, also entails the impossibility of carrying out an immanent delineation of the limits of cognitive or subjective possibility. Once immanence has been handed over to the actual and non-totalizable inconsistency of the set-theoretical multiple, and is therefore no longer immanence to a philosophical subject, the problematic of the limit (or even of what Badiou has sometimes referred to as ‘the unnameable’) is itself made relative to the situation under consideration. We have already mentioned that the subtraction of a unifying arche´ for thought makes the notion of an absolute limit vanish. Philosophy thus acknowledges the potency of thought, the fact that it has no absolute limit, by emptying itself of the appeal to an originary experience of thought. By disavowing traditional claims to privileged intuition and to a faculty of supra-disciplinary synthesis, Badiou’s philosophy precludes any attempt to impose a priori limits on non-philosophical thought procedures (whence the relentless affirmation that mathematics thinks, science thinks, politics thinks, love thinks). We could even say that for Badiou

Theoretical Writings philosophy evacuates transcendence by making nothing immanent to philosophy, and in particular by refusing to make thought, subjectivity and truth coextensive with philosophical practice. In this regard, Badiou’s philosophy cannot be seen as yet another in the sequence of hopeful subreptions or transgressions of the limits set by Kant or reset by Wittgenstein. Lest it be confused for some kind of scientia dei or mathesis universalis, for the mobile totalization promised by sundry varieties of dialectical thinking, or for the related realization of the latent content of philosophical practice in world-transforming praxis, it is imperative to reiterate once more the weight that must be accorded to the non-being of the One and the inexistence of the Whole. The sundering of the infinite (or, more precisely, of infinities) from capture in a unitary divinity, the absence of any pre-evental subject of cognition, and the mathematical affirmation that there is no (one) Universe, all clearly point toward the impossibility of reducing Badiou’s standpoint to that of any classical variant of metaphysical rationalism. This systematic thought is emphatically not a theory of everything. An examination of Badiou’s relation to dialectics, a constant in his intellectual trajectory, can prove illuminating in this regard. In a recent essay, Badiou writes, with reference to Hegel: ‘Not only, contrary to what Hamlet declares, is there nothing in the world which exceeds our philosophical capacity, but there is nothing in our philosophical capacity which could not come to be in the reality of the world.’16 This confidence in the powers of reason displayed by dialectical thinking leads Badiou to see in it the culmination as well as the collapse of classical rationalism. A culmination in the sense that any transcendent or transcendental check on the extension of rationality is removed; a collapse insofar as the hyper-rationalism of dialectics is fuelled by its hostility to the eminent role of mathematical infinity within classical rationalism (see ‘Philosophy and Mathematics: Infinity and the End of Romanticism’ in this volume). Though we are sympathetic to Bruno Bosteels’s claim that over and above the theorem concerning the inexistence of the Whole, Badiou’s recent onto-logical work on the theme of appearance could be seen to herald a qualified return of the kind of dialectical thinking so prominent in the earlier Theory of the Subject, it nevertheless remains the case that the mathematical expropriation of a sui generis philosophical intuition or subjectivity entails that there is no philosophical capacity per se that would stand as a potentially determinable reservoir for dialectical realization.17 The inconsistent is not the potential or the determinable and it is not ‘in thought’ as such. Rather than a capacity held by a totalizing reason, the modality of truth in Badiou is that of a retroactive possibility: only on the basis of a decision which no capacity guarantees and through the construction of a generic set that has no store of knowledge to refer to ‘will it have been

Postface possible’ to formulate the truth of a situation. Thus, while Badiou holds on to the dialectical refusal of any a priori constraint on thought, and to the subversive consequences of the realization of rationality, he abandons, in conformity with the motifs of expropriation and pluralization mentioned above, the notion that thought or philosophy can be unified or totalized as a capacity which would expand ‘its’ limits. Why not then simply dissolve philosophy into the multiplicity of discourses and practices, rescind its delirious pretension to sovereignty, dilute it into an ornamental meditation on the crimes and shortcomings of rationality? Why not simply welcome the age of sophistry? In a sense, Badiou’s opposition to these postmodern strategies is unjustified and indeed unjustifiable, at least from a transcendental as opposed to axiomatic standpoint. The commitment to the new, the exceptional and the generic is simply non-negotiable. As Badiou declares: ‘The new is the just.’ Equally, the Platonic injunction to separate truth from doxa, to cut through the dense and incoherent mass of opinions and the arbitrary norms that regulate the interactions of the polis is undoubtedly a primary requirement of Badiou’s philosophizing, but certainly not one that could be ‘legitimated’. For Badiou, to hold on to the category of truth, albeit in a guise that has been comprehensively recast, is to assert that philosophy’s task is always one of supporting or dis-inhibiting whatever subversions and separations occur in the different domains of thought. We may want to ask what renders such a conviction immune from Rortyan attempts to sap the confidence and foundations of philosophical practice. In a sense, nothing. The identification of philosophy with a kind of courage for truth, excess and separation is a subjective conviction with absolutely no guarantee either in the domain of representable objectivity or in the psychological structure of a cognizing subject. Yet closer examination of the sophist’s challenge reveals what is rationally objectionable about it. As Badiou has argued elsewhere (most prominently in the Manifesto for Philosophy), the inestimable worth of the sophist, from Protagoras to Lyotard, is his ability to alert the philosopher to the untenable nature of philosophical autocracy, to disabuse him of the futile and disastrous delusion of being the keeper of the Truth of truth. Moreover, the sophist’s nagging rejoinders open philosophy up to the multifariousness of cases, thus emphasizing the challenge inherent in the aim of reducing the equivocal phenomenology of common sense to the mathematical indifference of a rational ontology. All this militates toward Badiou’s call to spare the sophist, rather than to force his or her elimination. But to respond to the challenge of modern sophistry by expropriating philosophical intuition permits the truly contemporary philosopher to recognize that the sophistical schema only seems to be in favour of dissemination and

Theoretical Writings multiplicity. From the standpoint of an aleatory rationalism, it is essential to perceive how the sophist, while seeming to sing the praises of universal difference and exception and the inapplicability of any rational categorial schema, is still committed to the notion that the multiple can itself be characterized, that it can be given the quasi-transcendental lineaments of discourses, language games, embodiment, strategies, and so on. Though sophistry abandons the immanence of thought to philosophical intuitions of the kind still endorsed by critique and dialectics, it simply shifts the locus of unified transcendental legislation, to language in particular, thereby generating, beneath the gaudy apparel of discursive multiplicity, a new figure of the Whole and the One. Short of the resort to the unintuitable and the absolute alterity of some sublime instance, such postmodern thinking remains incapable, from Badiou’s perspective, of thinking the determinate emergence of an exception and its systematic yet aleatory disfigurement of an established situation. Situated excess is here pitted against the universal variability which, in its amorphous constitution, remains a profoundly conservative image of thought since it precludes the subtractive specificity of a truth – that which renders truth at once ‘illegitimate’ (it is irreducible to the language governing a situation, bereft of any proof or guarantee in the domain of knowledge) and rational (it proceeds through a strict, albeit decisionistic, logic of consequences). Most importantly, to affirm philosophy against sophistry is to reiterate the importance of localizing the practical break between thought (or truth) and language (or knowledge), something that can only be done, according to Badiou, so long as we are attentive to the rare instances in which a regime of discourse and intelligibility is suddenly beset by a dysfunction and transformed by a subject. Note here that one of the provocative consequences of such an approach is that for Badiou there is no difference in kind between opinion and knowledge, both being opposed by truth. This is not to say that there is any interest here in a critique of doxa, or in the establishment of a clear and distinct reservoir of knowledge to counter a common sense gone astray. Only real separations from doxa matter, those sequences in which the stability of a situation and its language are traversed, disqualified, and perhaps destroyed. In this regard, doxa is never the critical object either of philosophy or of a particular truth procedure, but rather the obstacle they circumvent and the material they transform. Needless to say, this means that Badiou’s philosophy abandons one of the main concerns common to critique, dialectics and sophistry, not to mention numerous manifestations of philosophical materialism: the account of the genesis of doxa or the sources of representation. Separation, rather than constitution, is the core of aleatory rationalism.

Postface 6. Badiou’s acosmism, with its undermining of totality, is adamantly not an intra-philosophical response to some sublime catastrophe of reason, predicated upon the dubious isomorphism of philosophical totality and political ‘totalitarianism’. It is the untamed infinities averred by mathematics and the boundless thought they announce which determine the attack on totality, not the thinker’s feigned humility or guilt at his or her inexcusable hubris. We could even say that just as Badiou eschews the faculty of reason only to intensify the possibilities of rationalism, so he focuses on the irruptions of the universal by postulating the inexistence of the Universe (or the Whole of all wholes). The obverse of this empowering evacuation or self-expropriation of philosophy, whose formalizing rationality is radically dependent on the contingency of events and truths over which it has no sway, is the refusal to provide any internal or immanent account for the genesis or possibility of philosophy itself (and the concomitant rejection of anything which is even distantly related to epistemology, including the discontinuous diagrams and narrations of Bachelard, Canguilhem or Foucault). According to Badiou, to display a concern with the genetic sources of philosophy would be once again to render extra-philosophical truth procedures (in science, politics, art, love) immanent to a more or less sovereign philosophical subject, one that would make a detour through their externality only in order, when all is said and done, to rediscover itself in the unfolding of its latent interiority. No such avenue is open to Badiou, who consequently seems to leave in abeyance the very question of the origin or beginning of philosophy, and, more broadly, the very problem of the genesis of the intellect as such. As Althusser once wrote: ‘There is no obligatory beginning in philosophy, philosophy does not begin with a beginning that would also be an origin. Philosophy jumps onto a moving train . . .’18 Thus, while Badiou’s philosophy is in great part preoccupied with generating a theory of the subject capable of thinking through the consequences of the truths of its time, it is bereft of a theory of (the emergence of) the philosophical subject. Indeed, it appears that one of the conditions for holding to the tenets of an aleatory rationalism is that of writing off as a dead end any reflection on philosophical subjectivation itself. This is of course a corollary of the definition of the event as undecidable and indiscernible from within the parameters of its situation. Aleatory rationalism is based precisely on the fact that there is no ‘reason’, in the sense of ratio or Grund, for events and the truths they give rise to. So while the type of philosophical subjectivity espoused by Badiou does seem to rest on the postulate which we could call that of ‘the justice of the new’ – on a kind of a priori and thus void fidelity to what happens insofar as it happens – the critical philosopher (or any of his

Theoretical Writings epigones) will look with suspicion upon a philosophy so determinedly and doctrinally committed to saying next to nothing about the conditions for its own exercise. Where the seemingly momentous sundering of philosophy from ontology is concerned, we are offered the account of a decision which, although strategically persuasive, cannot lay claim to any guarantee or justification besides that of the consequences it may harbour with regard to the intensification or purification of thought, as well as the latter’s capacity to separate instances of truth from the representational networks of doxa and knowledge. While philosophy’s self-expropriation for the sake of the event may turn it into a kind of metaontology (albeit one whose exact situation is difficult to pin down), there is no Archimedean point – whether faculty, subject or divine reason – from which to judge the validity or construct the consistency of the metaontological decision: mathesis is no longer universalis; all scientia is now without a deus. And yet one could argue that in spite of abdicating its powers of survey over thought, philosophy’s articulation of the unbound multiplicity of mathematics and the practical production of generic truths turns it into a supplementary instance, a transcendent apparatus for generating the aleatory univocity of being and event in the guise of a rare and formalized truth.19 This charge is perhaps exacerbated by Badiou’s refusal to countenance any account of the genesis of the philosophical subject itself. Ultimately, what we are faced with is a veritable division within contemporary philosophy’s materialist camp.20 The status of materialism in Badiou’s thought is not easy to adjudicate, and one would need to refer back to the lengthy treatment of it in Chapter IV of his Theory of the Subject in order to shed some real light on this issue. But in very broad and preliminary terms, we could say that Badiou’s materialism depends on: (1) a fidelity to the Lacanian notion of the Real as that which resists its symbolisation and capture in a thought of possibility; (2) a thinking of the event as immanent to the Real of a situation, that is, as being in a situation (presented) but not of a situation (represented); (3) a recasting of the praxiological tendency in materialism, through the thesis that the truth of an event can only be produced, and retroactively attested, via the construction of a generic set; (4) a repudiation of any figure of matter as (the) One or (the) Whole, in short, of any doctrine of monism (Badiou’s materialism is in this respect a variant on acosmism, and can be seen to derive from his strictly meontological use of the multiple); (5) a sharp and incontrovertible distinction, founded principally on point (1), which says that materialism is incompatible with naturalism, if by the latter we understand any attempt to account for the genesis of thought either in terms of some continuity with the natural sciences (neurophysiology, cognitive science, ethology) or in terms of a more metaphysical notion of natura naturans.

Postface Badiou thus wishes to argue both that thought is not some ineffable, angelic ‘stuff’ over and above situations and that it cannot be circumscribed (for instance, within the human nervous system) in such a way as to set the stage for its reduction, explanation or genesis. In a sense, the classical question of materialism is rescinded by Badiou to the extent that he does not permit of any operative distinction between the (material-) real and the ideal, displacing that traditional trope into the distinction between the real of the event and the knowledge, language or representation of the situation. The key difference between this aleatory rationalism – or what Badiou himself describes as his ‘materialism of grace’ – and a transcendental materialism of the Deleuzean variety is that while the latter wishes to set out the real conditions for the possibility of (the experience of) thought, the former leaves a fundamental heteronomy (which some might interpret as miraculous transcendence) in place. We could even hazard the statement that in a rather paradoxical manner, Badiou’s aleatory rationalism is a kind of historical materialism, in the precise, restricted sense that its claims regarding the real of the event as the basis of rare truths depends on a distinction – which Badiou maintains on set-theoretical grounds – between nature and history; a distinction which is profoundly inimical to any brand of naturalist materialism, whether of the ancient (Lucretius), modern (Spinoza) or post-Kantian variety (Deleuze and Guattari). Badiou’s is ultimately an anti-naturalist materialism. It rests on the provocative proposition that nature, far from being the arena of savage becomings, is a domain of perfectly adjusted representation, of seamless normality, and that the event-history is the only site of the upsurge of inconsistent immanence. But where does this leave not just materialism, but philosophy tout court? Badiou’s aim is to provide philosophy with the resources for formalizing – as opposed to substantializing – extra-philosophical novelty. His abiding conviction is that holding true to the independent rationality and subversive irruption of non-philosophical subjects means effecting a radical separation of thought, not only from the entire apparatus of critique, but also from the kind of naturalism proposed by most self-avowed materialists. However, by simply writing off the question of philosophical subjectivity as a hindrance to the reckoning with extra-philosophical truths, Badiou may well be depriving himself of the means for shedding light on the very logic of compossibility that specifies philosophy’s relation to its conditions, a logic that should also account for the manner in which Badiou’s own doctrine, far from being an arbitrary dogmatism, is conditioned, particularly by mathematics. Can Badiou retain his linking of rational ontology to the subjective contingency of truths without elucidating the way in which evental historicity and the atem-

Theoretical Writings poral theorems on being combine to generate philosophical discourse?21 Isn’t philosophical formalization, which relies on the unique capacity with which mathematical discourse is supposedly endowed – the capacity to inscribe the Real in transmissible symbolisms and chains of deductive inference – itself temporalized by events in mathematics and by its own practice of compossibility, thus demanding a much fuller, and perhaps more ‘critical’, account of philosophical subjectivity? When all is said and done, Badiou’s philosophy is simply a theory of truth, which is to say, of thought. But it is a theory which, while abounding in prescriptions about the style and ethos of philosophical practice, seems to be predicated on a deliberate refusal to formulate anything like a theory of philosophy or of philosophical subjectivity. Perhaps this refusal is the sine qua non for the revitalization of a senescent academic discipline. Alternately, the rejuvenation promised by Badiou’s philosophy may require a full and explicit account of how a subject comes to philosophy (and vice versa), in order to open the logic of compossibilization to theoretical practices whose possibilities extend beyond the co-ordinates of Badiou’s own relation to the extra-philosophical. R.B., A.T. London and Teheran, May 2004 NOTES 1 2 A situation is minimally defined by Badiou as ‘a multiple composed of an infinity of elements, each one of which is itself a multiple’. See the discussion in Peter Hallward’s Badiou (Minneapolis: Minnesota University Press, 2003), pp. 93–4. To forestall any possible confusion, it is important to note that, as a metaontological postulate, this notion of situatedness is not that of an existential subject-insituation or a Leibnizian-Nietzschean perspective on or from a world. Being-insituation is simply the ‘objective’ correlate of the inexistence of a Whole of all wholes, or Universe, and of the relative or local nature of ontological consistency. With this notion of expropriation, or rather self-expropriation, we have attempted in part to translate some of the key insights put forward by Oliver Feltham in his paper ‘Et l’être et l’événement et: la philosophie et ses nominations’ presented at the 2002 Badiou Workshop, which he co-organised with Bruno Besana at the University of Paris VIII-St. Denis. The proceedings of this workshop will be published under the title Alain Badiou. De l’ontologie à la politique (Paris: l’Harmattan, 2004). Feltham persuasively characterizes the relation between philosophy, mathematics and ontology in terms of a ‘hetero-expulsion’ of philosophy’s claim on ontology in favour of mathematics for the sake of a thinking of truth as praxis.

Postface 3 4 5 6 7 Although, as Badiou, following Lacan puts it, ‘there is oneness’, il y a de l’un – a crucial qualification pertaining to the distinction between the inconsistency of being qua being and the consistency of being qua appearance. We will have more to say about this below. We write ‘rationalist’ rather than ‘rational’ advisedly, since for Badiou the domain of the decision and the axiom lies outside of any simple dichotomy between the ‘rational’, understood as that which is always already vouchsafed by a standard image of adequate cognition, and the ‘irrational’, understood as the act welling up from some obscure source, be it demonic, vital or unconscious. The only time Badiou uses the adjective ‘rational’ in any philosophically consequential way is to qualify ontology. ‘Rational ontology’ identifies the sequence of attempts to wed ontology to mathematics, and thereby to subject philosophy to the cutting edge of mathematical invention. Bar a few, somewhat marginalized exceptions (Desanti, Cavaillès, Lautman), it is a sequence which was terminated in philosophy by Hegel and was continued, more or less implicitly, within the work of mathematicians such as Cantor and Cohen. The expression ‘rational ontology’ in no way indicates a reference to some quality or ideal which could go by the name of ‘rationality’. Or rather, the dissemination of ontology and the demotion of human cognition effectuated by rational ontology makes any unitary, nonevental, definition of rationality impossible. It is worth noting that Badiou’s one defence of rationality ‘as such’ comes in a plea for a philosophy that would be able to counter the idiotic fanaticisms and archaisms that mark the contemporary world. See ‘Philosophy and Desire’ (originally entitled ‘Philosophy and the Desire of the Contemporary World’), in Infinite Thought, edited by Oliver Feltham and Justin Clemens (London: Continuum, 2003), p. 55, where he writes: ‘Philosophy is required to make a pronouncement about contemporary rationality. We know that this rationality cannot be the repetition of classical rationalism, but we also know that we cannot do without it, if we do not want to find ourselves in a position of extreme intellectual weakness when faced with the threat of these reactive passions.’ Examples would include Being and Event’s critique of the notion of ‘destruction’, which is a fundamental category in Theory of the Subject; Logics of Worlds’ critique of the account of evental naming in Being and Event; Badiou’s own recent decision to retract the theory of the unnameable outlined in texts such as ‘On Subtraction’, ‘Truth: Forcing and the Unnameable’ and the Ethics; and last but not least, the completely revised theory of the event Badiou proposes in Logics of Worlds. In Meditation 3 of Being and Event and ‘Notes Toward a Thinking of Appearance’ (this volume), Badiou identifies Zermelo and his ‘axiom of separation’ as the source for such a materialism within the lineage of rational ontology. For a long treatment of the question of materialism in Badiou’s earlier work, see The´orie du sujet (Paris: Seuil, 1982), pp. 193–253, and Bruno Bosteels’s forthcoming Badiou and the Political (Duke University Press). Whence Badiou’s insistence, in the wake of his turn away from the dialectics of destruction espoused in Theory of the Subject, on the exemplary status of Mallarmé’s notion of action restreinte, restricted action. For the concept of suture see the Manifesto for Philosophy and Alberto Toscano, ‘To Have Done

Theoretical Writings 8 9 10 11 12 13 14 15 16 17 18 19 with the End of Philosophy’, Pli: The Warwick Journal of Philosophy 9 (2000), pp. 223–4. Manifeste pour la philosophie (Paris: Seuil, 1989), p. 69. Badiou characterizes Cantor’s theorem, in which the quantitative excess of the state of a situation (representation) over a situation (presentation) is shown to be undecidable, as ‘the impasse or the real point of ontology’. This theorem, along with the related Cohen-Easton theorem, which establishes ‘the complete errancy of excess’, will provide the basis for Badiou’s theory of the event. See L’eˆtre et l’e´ve´nement (Paris: Seuil, 1988), p. 559. L’eˆtre et l’e´ve´nement, Meditations 1–6, pp. 31–117, in particular pp. 35–6. L’eˆtre et l’e´ve´nement, p. 35. L’eˆtre et l’e´ve´nement, p. 35 L’eˆtre et l’e´ve´nement, p. 35. Alain Badiou, The Century (forthcoming). This point is made by Nina Power in ‘What is Generic Humanity? Badiou and Feuerbach’, Subject Matters: A Journal of Communication and the Self 2, forthcoming. ‘Metaphysics and the Critique of Metaphysics’, trans. Alberto Toscano, Pli: The Warwick Journal of Philosophy 10 (2000), pp. 189–90. This is not to say that there is no problem of capacity or potentiality in Badiou’s thought. However, it is a problem that arises in the context of his characterizations of the relationship between thought and ‘generic humanity’ rather than in his vision of philosophical activity per se. See Nina Power and Alberto Toscano, ‘‘‘Think, Pig!’’: An Introduction to Badiou’s Beckett’, in Alain Badiou, On Beckett, ed. Nina Power and Alberto Toscano (Manchester: Clinamen Press, 2003). Louis Althusser, ‘Le courant souterrain du matérialisme de la rencontre’, E´crits philosophiques et politiques, Tome I, ed. François Matheron (Paris: IMEC, 1995), p. 576. We have chosen to dub Badiou’s project an ‘aleatory rationalism’ precisely in order to foreground what, in the final analysis, distinguishes it from the tradition sketched by Althusser in that late fragment. Although focused on chance as the real basis for any production of truth, Badiou’s philosophy maintains the rationalist allegiance to mathematisation so as to circumscribe and separate the event and its consequences from the ordinary course of the world. As we have tried to suggest, Badiou invokes Cantor, Zermelo and Cohen (among others) in an attempt to overturn Althusser’s late verdict, to wit that all rationalism must be teleological, essentialist and committed to a notion of the origin. What prevents aleatory rationalism from being the mere acknowledgment (constat, a term emphasised by Althusser) of the deviations of matter, and turns it into an intervention, is the manner in which it articulates a rational, set-theoretical ontology and a theory of the subject, which is exactly what Badiou, in all his writings on Althusser, criticises his old mentor for failing to do. Without a theory of the subject, according to Badiou, materialism collapses into a description of material events and fails to grasp the difference between real novelty and mere change, or, more importantly, the difference between a truth and a catastrophe, be it political or topological. This is the crux of the rather elliptical verdict on Badiou’s Being and Event

Postface 20 21 voiced by Deleuze and Guattari in their What is Philosophy? (London: Verso, 1994), pp. 151–3, where they identify three interlinked instances of transcendence: (1) the evental site; (2) the nondescript multiplicity [multiplicite´ quelconque], which they juxtapose to their theory of the two multiplicities (intensive and extensive); (3) philosophy itself. They appear to argue that it is the first two that combine to make philosophy into an activity of survey: ‘philosophy thus seems to float in an empty transcendence, as the unconditioned concept that finds the totality of its generic conditions in the functions (science, poetry, politics, and love). Is this not the return, in the guise of the multiple, to an old conception of the higher philosophy?’ Although we are willing to concede the possibility that Badiou has reinvented a certain eminence for philosophy, Deleuze and Guattari’s verdict misses the crucial point: the generic procedures cannot be totalized and do not, as such, ‘fill out’ philosophy. They are not functions because they do not depend on ‘slowing down’ the infinite into a space of coordinates. Furthermore, the axiomatic character of the set-theoretical thinking of the multiple is based precisely on the possibility of eschewing any concept of it, whether unconditioned or not. This division has been amply and ably treated by Éric Alliez in De l’impossibilite´ de la phe´nome´nologie (Paris: Vrin, 1995). ‘Atemporal’ here refers to ontology in its ‘current state’. Although its situational character entails that mathematics is itself punctuated and transformed by its own events, and therefore endowed with a kind of historicity, the axioms and theorems that make up the discourse on being are not themselves temporally conditioned. In other words, according to Badiou, the periodisation of mathematical truths is just as historical as that of politics or art, but mathematical truths are eternal, as are those of politics and art.