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Neo-classic

Neo-classic Alain Badiou’s Being and Event

Peter osborne

If anyone was in doubt about the continuing grip of French philosophy on the theoretical imagination of the anglophone humanities, the reception of the writings of Alain Badiou must surely have put paid to such reservations. The translation of his magnum opus, Being and Event, in spring 2006, brought to eleven the number of his books published in English in eight years – a period following swiftly on, not entirely contingently, from the deaths of Deleuze, Levinas and Lyotard (1995–1998), and coinciding with that of Derrida (2004).* However, it is not simply the number of translations that is remarkable (ʻremarkable, but not surprisingʼ, as Wittgenstein would say), but the fact that a philosophy such as this – for all its idiosyncratic philosophical charms – could so readily have assumed the role of ʻFrench philosophy of the dayʼ within the transnational market for theory.

Badiouʼs philosophy takes a forbiddingly systematic form; it is anti-historical, technically mathematical and broadly Maoist in political persuasion. It has no interest in (in fact, denies the philosophical relevance of) ʻmeaningʼ, and appears impervious to feminism. It takes a roguish self-satisfaction in its heterosexism.

Stylized individuality is a condition of branding, and ʻdifficultyʼ is a prerequisite of entry into this particular field, but there are more than market factors at work in Badiouʼs successful transition to international theorist. It is a gauge of a number of things: the desire still invested in the English-language reception of French philosophy; the theoretical heresies that a new generation of the so-called ʻoldʼ Left will overlook in exchange for political solidarity (Žižek, master of this field, is Badiouʼs mentor here); the strategic brilliance of two interventions – against Deleuze (The Clamour of Being, 1997; trans. 2000) and against the ʻdeliriumʼ of ethics (Ethics, 1994; trans. 2001);1 the inherent brilliance of Being and Event, for all its ultimate philosophical madness; and last, but by no means least, the rhetorical power of ʻthe (re)turn of philosophy itselfʼ – title of an essay of Badiouʼs from 1992.2 It is in the profoundly contradictory character of the return of philosophy in Badiou – at once avant-garde and breathtakingly traditional – that the historical meaning of his thought is to be found. [3] To anticipate my conclusion: Being and Event is a work – perhaps the great work – of philosophical neo-classicism. As such, at the level of philosophical form, it surpasses its ambivalent predecessor, Heideggerʼs Being and Time, in the rigour of its reactionary modernism. The modernity of Badiouʼs mathematics does not mitigate, but rather reinforces, the authoritarianism of his philosophical axiomatics and the mysticism of his conception of the event.

From philosophy to theory and back

It has been the fate of French philosophy within the anglophone humanities since the 1970s to represent contemporaneity in theory. Indeed, by a transcultural quirk of US hegemony, French philosophers are now beginning to become contemporary philosophers – that is to say, ʻphilosophersʼ in the strong, individualized sense of the word – even in France, via their English-language reception. The English ʻphilosopherʼ signifies differently when accompanied by the qualification ʻFrenchʼ. Yet while French philosophers have dominated theoretical developments in the anglophone humanities, it has largely been because of the power* Alain Badiou, Being and Event, trans. Oliver Feltham, Continuum, London and New York, 2005. xxxiii + 526 pp., £19.99 hb., 0 8264 5831

9. ^ Translation of Lʼêtre et lʼévénement, Editions du Seuil, 1988 (hereafter EE). Page references to the English translation appear in brackets in the main text. The first of Badiouʼs books to be translated was Manifesto for Philosophy (French edition, 1989), in 1999. 1999 was also the year of the first – and still the best – introductory critical essay on Being and Event in English, Jean-Jacques Lecercle, ʻCantor, Lacan, Mao, Beckett, même combat: The Philosophy of Alain Badiouʼ, Radical Philosophy 93, January/February 1999, pp. 6–13.fully post-philosophical character of their reception – post-philosophical in a delicately dialectical sense, whereby what is most philosophically productive has been manifest only in a non-philosophical setting.

There were several conditions of this situation, not the least being the philosophical problematicity of the disciplinary autonomy of philosophy. Recognition of this has been pretty much a criterion of philosophical modernity since Kant, and it comes in a variety of forms. Most significant in this context are, on the one hand, Derridaʼs modified extension of Heideggerʼs destruction of the history of ontology, whereby deconstruction came to occupy the space of Heideggerʼs postulation of a post-philosophical ʻthinkingʼ; and on the other, Althusserʼs introduction of the term ʻTheoryʼ (with a capital T) to designate what he had previously called ʻMarxist philosophyʼ – namely, ʻthe theory of theoretical practiceʼ, or the theory of ʻpractice in generalʼ – in order, as he put it shortly afterwards (while changing his mind and giving up the usage), to ʻreserve the term philosophy for ideological philosophiesʼ. [4]

In the Anglo-American context, there was a crossing and consequent de-specification of these two postphilosophical fields, and ʻTheoryʼ emerged as the name of the generic hybrid. The idea of Theory was adopted in a generalized non-Marxist form, in part precisely because this allowed for a sidestepping of the question of its complex relationship to philosophy. (The pragmatism of the native (post-)philosophical tradition had an enabling effect here too.) This was a nifty piece of footwork, in so far as it allowed for the investment of broad transdisciplinary fields by general-theoretical categories – be it the ʻtextualityʼ of a general semiotics, the ʻdiscoursesʼ of a Foucauldian historicism, or the topography of Lacanian metapsychology – uninhibited by their ties to philosophyʼs past. By the beginning of the 1990s, however, as political and institutional contexts changed, and Theory began to succumb to the reification and repetition of its commodification, the disavowal of its relations to philosophy became increasingly problematic. This was especially so once the far less equivocally philosophical work of Levinas and Deleuze was subjected to the same discursive conditions, under which it was (and still is) frequently travestied.

The reaction to this situation was a move away from ʻT/theoryʼ and a return to disciplinarity in the humanities, and with it the tradition virtues of both ʻoldʼ historicism and aesthetics. As a result, a dual pressure began to build up within the discursive space of Theory for a re-evaluation of the virtues of ʻphilosophyʼ. It is in this context that the hyper-philosophical approach of Badiouʼs Being and Event acquires its unique polemical force. Of the trio of post-Althusserians competing within the US academy for the honorary position of French philosopher of the day (the other two are Balibar and Rancière), Badiou is the one who most explicitly – indeed, massively – reinvests the field of Theory with the idea of philosophy. This time, though, (Badiouʼs Althusserian heritage notwithstanding) it is philosophy without Marxism – that is, without Marxʼs critique of philosophy – indeed, seemingly without any version of the critique of the self-sufficiency of philosophy which has hitherto been a condition of possibility of the continuation of European philosophy, ever since the critique of Hegel at the end of the 1830s. [5] The self-proclaimed ʻreturnʼ of philosophy in Being and Event is a return to a classical conception of philosophy, with a vengeance. This is its polemical force. It is Badiouʼs self-declared aspiration ʻto have done with finitudeʼ. [6] The story of Being and Eventʼs place in the history of philosophy is a Gothic tale of the doomed attempt of a philosophical classicism to take revenge on modern philosophy. Its result is a magnificent philosophical folly.

The strategic brilliance of Badiouʼs Deleuze lay, in essence, in its reduction of the terms of Deleuzeʼs thought to Badiouʼs, in the manner of a Heideggerian ʻviolent readingʼ, by emphasizing its classically philosophical character. Badiou was aided in this task by Deleuze himself: specifically, by the disciplinary conservatism of his final book with Guattari, What is Philosophy? (1991; trans. 1994), a text that tends to be read (erroneously, in my view) as a kind of methodological summation of Deleuzeʼs thought. The traditionalism of the demarcation of philosophy in What is Philosophy? became the point of entry for Badiouʼs appropriation and destruction of Deleuzeʼs thought. With What is Philosophy? Deleuze opened the door to Badiou and, after Deleuzeʼs death, Badiou moved in, exploiting to the full his projection of the two of them as ʻa sort of paradoxical tandemʼ. [7] In a way, this is where Badiou still resides in his philosophical reception in English – making-over his rivalʼs house – although he also has a political readership, egged on by Žižekʼs Pauline ʻnew Leninʼ. [8]

Heidegger – Dasein + mathematics = Badiou

Surprisingly, given his frequently expressed antipathy to Heideggerianism, [9] Badiouʼs conception of the contemporary philosophical problematic appears at first sight orthodoxly Heideggerian in its starting point: ʻAlong with Heidegger, it will be maintained that philosophy as such can only be re-assigned on the basis of the ontological questionʼ (2). Already, though, there is a difference. For by the ontological question Badiou does not mean ʻwhat is the meaning of Being?ʼ (Heideggerʼs version), but rather more simply ʻwhat is being qua being?ʼ Furthermore, Badiou takes this ʻwhat is?ʼ question to be answered by ontology as the ʻscience of being qua beingʼ – precisely that Greek metaphysical enterprise that Heidegger sought in Being and Time to replace with a fundamental ontology, which would no longer treat ʻbeing qua beingʼ on the model of particular beings/entities, as the special object of a metaphysical science. At the very outset, Being and Event thus polemically opposes itself to Heidegger on the very ground that they ostensibly share, and in a manner that seems to reproduce the precise structure of the object of Heideggerʼs critique.

Moreover, the philosophical basis of this opposition does not derive from a critique of the early Heideggerʼs version of the question of being, with its ground in the ontic peculiarity of Daseinʼs being-ontological. Rather, it derives from Badiouʼs independent pursuit of another possibility, another path for thought: a restoration of the rationalist traditionʼs grounding of philosophy in a thinking of mathematics. This path is opened up not by a philosophical event, but by a mathematical one: Cantorʼs set theory and specifically its treatment of infinity. Yet it cannot be discerned, and hence travelled, without the philosophical thought of being as ʻpure multiplicityʼ. This thought co-grounds the famous speculative thesis on which Badiouʼs system is built: namely, ʻontology is mathematicsʼ. It is because mathematics is the science of multiplicity, and being is pure multiplicity, that, according to Badiou, mathematics is the science of being. The syllogism is a simple one. (Mathematics is not a method or a model for philosophy here: mathematics is ontology.) This is a genuine co-grounding because, as we shall see, it requires Cantorian set theory to make the idea of mathematics as ontology work – to make the speculative thesis productive. There is thus a simple formula for Badiouʼs opening move: Heidegger – Dasein + (set-theoretical) mathematics = Badiou.

But what of the ontic peculiarity of Daseinʼs being-ontological, which is what allows – indeed, for Heidegger, dictates – philosophy to ask the ontological question in the first place? Badiou maintains a symptomatic silence. The issue is crucial since the competing fates of existential ontology and the new classical ontologies of Deleuze and Badiou depend upon it. The latter are polemically anti-phenomenological. But phenomenology is a stand-in for the real enemy here, which is existential ontology. The question is not that of the possibility, or otherwise, of phenomenology as such (a relatively easy target), but that of the unavoidability, or otherwise, of the existential. Badiou seems to believe that the reduction of ontology to mathematics cuts the Gordian knot of the ontically-ontological (ʻexistenceʼ, in Heideggerʼs sense). Yet while mathematics may be in a certain sense inhuman – a position to which defenders of Badiou tend to retreat at this point in the argument – philosophy as meta-ontology has a rather different discursive and historical status. Its inhumanity is no more, or less, than that of the (existential) inhumanity of the human itself. [10]

With regard to Heidegger, Badiou criticizes not the existential starting point and ground of his ontology, but the (conceptually independent) temporality of the ʻGreek returnʼ that is appended to it: ʻthe figure of being as endowment and gift, as presence and opening, and the figure of ontology as the offering of a trajectory of proximityʼ. (He rests on Derrida here.) Inverting Heideggerʼs terms, it is this, a poetic ontology ʻhaunted by the dissipation of Presence and the loss of originʼ that appears as ʻthe essence of metaphysicsʼ in the pejorative sense (9–10). In contrast, Badiou conceives his own project as thoroughly modern, ʻperhaps even “more-than-modern”ʼ. [11] Before we consider this paradoxical more-than-modernity, let us examine more closely the concept of philosophy in Being and Event.

A self-sufficient circulation

Being and Event is a systematic work in that it proceeds more or less deductively from its founding propositions – ʻbeing is pure multiplicityʼ and ʻmathematics is the science of multiplicityʼ – to derive a series of fundamental categories of Being (Parts I–III), Event (IV and V), Knowledge and Truth (and, one might add, Politics) (VI and VII), ending up with the Subject (VIII). This fourfold structure underlies Badiouʼs own more diffuse division of his thirty-six ʻmeditationsʼ into eight parts. In fact, it harbours an even more elemental, tripartite structure, Being–Event–Subject, in so far as the parts on Knowledge and Truth, whilst important, have a largely transitional structural function. Philosophy may have been ʻre-assignedʼ on the basis of the ontological question, but it is nonetheless towards the ʻtheory of the subjectʼ (ch. 35 – interestingly, one of the few appearances of the word ʻtheoryʼ) that Being and Event drives. [12]

Progress is ʻmore or lessʼ deductive in the conventional way of a system, with the steady introduction of supplementary premisses (explicit and implicit) moving the process forward according to a pattern that, while immanently ʻderivedʼ, is nonetheless structurally prefigured – the covert aim being logically to redeem, and thereby cover over, the prefiguration, or teleological projection. In this case, both the axiomatic and teleological moments stand out as philosophically decisive, while the demonstrations themselves take the form of a devilish logico-mathematical game, in which Badiou pits himself against a range of self-imposed tasks. The tasks are formidable and the detail of their execution is breathtaking in its ingenuity, even when accompanied by a growing sense of the philosophical redundancy of much of the mathematics, as elementary hermeneutical structures (the selective nature of interpretation, for example) are mathematically redescribed (ʻthe operator of connectionʼ), as the result of tortuous processes of derivation. (See Meditation 23, ʻFidelity, Connectionʼ.) This is in many ways an Alice-in-Wonderland world, in which nothing non-axiomatic can be accepted until it has been deduced, mathematically recoded, as part of the system. In fact, this is an ethical imperative for Being and Event, in which deduction is ʻthe means via which, at each and every moment, ontological fidelity to the extrinsic eventness of ontology is realizedʼ (242).

Yet Badiouʼs categories, the philosophical consequence of the thought that ontology is mathematics, whilst the result of a prodigious and highly abstract formal procedure, are in no way merely formal:

The categories that this book deploys, from the pure multiple to the subject, constitute the general order of a thought which is such that it can be practiced across the entirety of the contemporary system of reference. These categories are available for the service of scientific procedures just as they are for those of politics or art. They attempt to organize an abstract vision of the requirements of the epoch. (4)Badiouʼs categories thus appear to function much like the categories of Theory – that is, transdisciplinarily – although they have been derived quite differently, and aspire to a more lofty fundamental status. (Conceptformation in the field of Theory itself has been, historically, extremely eclectic, but generally involves some process of generalization and re-theorization of concepts from empirical disciplines, rather than deductive derivation, and the status of the result is usually ultimately pragmatic.) Precisely what the status of Badiouʼs more fundamental philosophical concepts is, however, is by no means easy to grasp. Everything hinges on, first, how Badiou arrives at the thesis that ʻontology is mathematicsʼ, and second, how we understand the operation of mathematics (qua ontology) both upon and within philosophy itself. For despite the Heideggerian starting point, Badiou insists that ʻphilosophy is not centred on ontology – which exists as a separate and exact disciplineʼ (mathematics), but rather ʻcirculatesʼ between ontology (= mathematics) and its other conditions, or more broadly ʻthroughout the referentialʼ (3, 19).

Despite appearances, Badiou is insistent that his philosophy has no ʻfoundational ambitionʼ. The reason for this is that it recognizes that it has ʻconditionsʼ. This is a rare historical and material moment in Badiouʼs thought. Philosophy thus cannot be absolutely self-grounding; self-grounding is not the basis of its self-sufficiency. Rather, what philosophy does ʻis propose a conceptual framework in which the contemporary compossibility of these conditions can be graspedʼ (4). The way it does this is ʻby designating amongst its … conditions, as a singular discursive situation, ontology itself in the form of pure mathematicsʼ. This designation is described as ʻdeliveringʼ philosophy (délivre EE, 10 – ʻsetting freeʼ would perhaps be better) and thereby ultimately ʻordainingʼ or preparing it (lʼordonée) for ʻthe care of truthsʼ. (The Pascal epigraph to Meditation 21 – the starting point of Balibarʼs essay on Badiou in RP 115 – reads: ʻThe history of the Church should, properly speaking, be called the history of truthʼ. [13] ) The role of philosophy here is thus a complex, if not a contradictory one. For it appears to act prior to its own constitution. Philosophy (i) designates one of its own conditions, as a consequence of which (ii) it is set free, allowing it (iii) to ʻproposeʼ a conceptual framework in which the contemporary compossibility of its other conditions can be grasped. Whether these other conditions are also ʻdesignatedʼ, or have some kind of more brute factuality, qua conditions, is at this stage unclear. But it is the first move which is of greatest critical interest: philosophyʼs designation of one particular condition (ontology in the form of pure mathematics) grounds the possibility of its grasping the compossibility of its conditions as a whole. Even if the other conditions are designated, one designation is qualitatively different from the rest. But how does philosophy do this? How does philosophy arrive at the conclusion that ʻmathematics is ontologyʼ? And what, according to Badiou, are philosophyʼs other conditions? It is at this point that the historical judgements set out at the start of Being and Event reveal themselves to be no mere introductory contextualization (as might be thought), but the argumentative basis of a project that otherwise presents itself in a far ʻpurerʼ form. Badiou offers varying overlapping descriptions of philosophyʼs current conditions in the introduction to Being and Event and elsewhere (principally in Manifesto for Philosophy). But in Being and Event these are initially grouped into three ʻassumptions about the current global state of philosophyʼ, which can be summarized as follows.

1. ^ ʻHeidegger is the last universally recognizable philosopher.ʼ 2. Mathematics and logic have conserved ʻthe figure of scientific rationalityʼ as a paradigm for thought. 3. ʻA post-Cartesian doctrine of the subject is unfoldingʼ, which has non-philosophical origins and complications.

These three assumptions give rise to the following prescriptions and specifications:1. Philosophy can only continue on the basis of the ontological question. (Otherwise, presumably, it would not be connected to ʻthe last universally recognizable philosopherʼ, and hence its philosophical status would be in doubt.)2. It is post-Cantorian mathematics (= set theory) that is the scientifically rational paradigm for thought.3. The places of practical unfolding of the postCartesian doctrine of the subject are psychoanalysis, contemporary art and politics.

It is the second and third of these three conditions, taken together, that will subsequently be presented, in Manifesto for Philosophy, as the ʻfourʼ conditions of philosophy, where they are further reduced to: the matheme, the poem, political intervention, and love. (Badiou may reject Heideggerʼs poetic ontology, but he accepts his anachronistic Romantic reduction of art to poetry.) The philosophically important condition – the one that secures the general compossibility of the other conditions – is missing from Manifesto for Philosophy. This is the ʻsingular discursive situationʼ of ʻontology itself in the form of pure mathematicsʼ – the belonging together of the first two assumptions (above). Addressing the classical ontological question anew (having rejected Heideggerʼs approach as poetic), in the historical-intellectual context of post-Cantorian mathematics, leads to the sudden flash of insight that mathematics is ontology. In Badiouʼs words, ʻmathematics is ontologyʼ is ʻa meta-ontological or philosophical thesis necessitated by the current cumulative state of mathematics (after Cantor, Gödel and Cohen) and philosophy (after Heidegger)ʼ (15, emphasis added). This is the bedrock of Badiouʼs philosophy. Philosophy, which had thought it was – or, in any case, should be – ontology, finds itself ʻoriginally separated from ontologyʼ (13). Meanwhile, mathematics, although it turns out (unknowingly) to be – and hence always to have been – ontology, is nonetheless so discursively, not immanently, that is, only from the meta-ontological standpoint of philosophy. Mathematics, qua ontology, is ʻcommanded by philosophical rules, and not by those of contemporary mathematicsʼ (13). To put it another way: philosophy transcodes mathematics into ontology. So although philosophy is not ontology, it nonetheless still governs the ontological meaning of mathematics (it is philosophy as meta-ontology that asks the ontological question), and in this way remains the ʻqueen of the sciencesʼ. This is the paradoxical result of its history, which delimits the domain of ontology without itself ever having been able to answer the ontological question.

Furthermore, and crucially for Being and Event, philosophy is also concerned with the supposedly non-ontological and specifically modern topic of ʻwhatis-not-being-qua-beingʼ (15). On Badiouʼs account, this topic was introduced into philosophy, historically, by the third item on the original list of philosophyʼs current conditions: the post-Cartesian doctrine of the subject. For, it is by circulating between this supposedly non-philosophical condition (although one can actually find it in Kant) [14] and the unifying condition of the thesis that ontology is mathematics that philosophy produces the category of ʻwhat-is-not-being-qua-beingʼ. ʻWhat-is-not-being-qua-beingʼ (the event) is the negative ontological register of a non-ontological condition that becomes thinkable via the post-Cartesian subject. It is the mark of the distinctively post-Cartesian, and hence truly ʻmodernʼ, status of Badiouʼs philosophy, despite its (Heideggerian) assignation ʻon the basis of the ontological questionʼ.

Beneath its meta-ontological status, philosophy thus finds that it has its own quasi-ontological discourse after all. It is this quasi-ontological category of ʻwhat-is-not-being-qua-beingʼ that furnishes Being and Event with its project: namely, to give a philosophical elaboration of the concept of the subject by locating it, formally, via the philosophical rule over mathematics, in relation to a derivation of the categories of being (i.e. precisely what it is not). Hence the fourfold teleological structure of the book (above). In this respect, the text that Being and Event is rewriting/replacing is less Heideggerʼs Being and Time than Sartreʼs Being and Nothingness.

This is a strikingly original conception of philosophy, which, nonetheless, for all its originality, continues the pursuit of the mainstream of postwar French philosophy: namely, a theoretical anti-humanism or critique of the subject that is anti-Hegelian and post-Heideggerian in its basic historico-philosophical affiliations. Like all singular philosophical trajectories, Badiouʼs thought is heavily weighted towards its beginnings, its inaugural philosophical moves. And, as we have seen, although pronounced as ʻglobalʼ (à échelle mondiale – worldscale), these are highly specific. They carry with them three dubious philosophical assumptions:1. In the reformulation of Heideggerʼs ontological question and the designation of its appropriate (mathematical) form of address, there is the assumption that ontology has no immanent existentialphenomenological or semantic presuppositions.2. As consequence of its philosophical or metaontological treatment of ontology, there is the assumption that ʻontologyʼ is exhausted by an allinclusive opposition between ʻbeing-qua-beingʼ and ʻwhat-is-not-being-qua-beingʼ. (Here, not just despite, but even more by virtue of, Badiouʼs departure from Heidegger, the standard Hegelian criticisms of Heidegger would seem to apply.)3. With respect to philosophyʼs historical conditions, there is the assumption that there are only four historico-philosophically privileged partners, or, as they are also called, ʻgeneric proceduresʼ or ʻtruth proceduresʼ. One might ask, for example, as Žižek has asked, ʻwhat about the economic?ʼ Not in the quasi-disciplinary sense, to which Badiou restricts himself in specifying his conditions, but in the historical-ontological sense of the social conditions of biological reproduction. Is there really no ʻtruthʼ to be had there?

Badiouʼs lack of interest in this eminently materialist topic (oddly, he continues to insist on his ʻmaterialismʼ) corresponds to his neglect of philosophical critiques of the self-sufficiency of philosophy – a topic on which Marxʼs and Heideggerʼs thought converges. For while his image of philosophical thinking is the attractive one of a practice of circulation between its conditions, this practice is nonetheless conceived as fiercely selfsufficient in its taking up of philosophyʼs conditions into itself – including its ur-condition, mathematics as ontology, whereby, as he puts it, meta-ontologically, philosophy reorganizes the knowledge of mathematics by means of ʻthe imaging powers of languageʼ (xiv). Ontology may be mathematical, but philosophy (mathematicsʼ meta-ontological guide, without which its ontological status could never be known), remains fundamentally linguistic and conceptual in a manner that Badiou subsequently actively disavows. Philosophyʼs reorganization of mathematical thought must thus appear in the guise of axiomatic decision, as a philosophical, rather than just a mathematical, procedure.

Unlike a seventeenth-century philosophical system,

Badiou claims no self-evidence for his axioms. Rather, they are taken over from mathematics – the nine axioms of set theory, it is claimed, concentrate ʻthe greatest effort of thought ever accomplished to this day by humanityʼ. They ʻfoundʼ mathematics as ʻtheory of the pure multipleʼ (499). Within mathematics itself, these axioms are the result of ʻdecisionsʼ with a variety of functional justifications, and they are the object of ongoing and intensifying dispute. Within philosophy, however, they are treated as authoritative, as a consequence of the prior and fundamental decision to give mathematics sovereignty over ontology. The content of this decision is an identification of the concept of multiplicity at stake in the thesis that ʻbeing is pure multiplicityʼ with the concept of multiplicity at stake in mathematics, and in set theory in particular. Everything follows from this founding identification.

Using it, the Heideggerian distinction between being and beings (being qua being and the being of beings) can be re-presented as one between ʻinconsistentʼ pure multiplicity and ʻconsistentʼ impure multiplicity. The former can be shown to be properly called ʻthe voidʼ, since it cannot be counted ʻas oneʼ (ʻprior to the count the one is notʼ [52]); and the latter can be shown always to be situational (restricted, structural) because it can. Set theory can then be rolled out to expound the intricacies of the different ways in which different things can be counted. Or, rather, what there is can be determined by the structure of the count. Ontology is severed from all phenomenological relations to objects. But only because Badiou decided to so sever it, in advance. He then has the awkward task of restoring a connection between his set-theoretical mathematical entities, philosophically received ontological concepts (like nature and history) and the world – itself conveniently reduced, decisionistically, to the ʻfour conditionsʼ of philosophy (the matheme, the poem, politics and love).

The idea of the axiomatic decision re-presents the element of contingency inherent in all historical hermeneutics, logico-philosophically: that is, abstracted (or, as Badiou would say, subtracted) from its historical context – and hence from discursive justification – as the pure act of a philosophical subject. The authoritarianism of this philosophical axiomatics (philosophy by decree) is the political correlate of the mystery of the Badiouian ʻeventʼ.

Idealism of the encounter (or, structuralism + faith = event)

One of the main effects of the reduction of ontology to mathematics is the de-temporalization of being and non-being alike. This is Badiouʼs fundamental difference from – indeed, inversion of – Heideggerʼs early philosophy. It is covered over, to a great extent, by the word ʻeventʼ and the quasi-existential terminology – ʻsituationʼ, ʻdecisionʼ, ʻinterventionʼ, ʻfidelityʼ – that accompanies it. But, once grasped, it reveals the extent to which Being and Event is at heart a structuralist text. Time is reduced to two dimensions – synchrony and diachrony – and diachrony is no more than a serial ordering of synchronically defined situations. Situations are considered ʻhistoricalʼ in which there is ʻat least one evental siteʼ (ʻan absolutely singular multipleʼ), but there is no unity to these situations, no ʻevental situationʼ and hence no ʻHistoryʼ (176–80).

The everyday meaning of ʻeventʼ (something that brings about a change, mediating a ʻbeforeʼ and an ʻafterʼ in three-dimensional time) is both temporal and narrative. But while Badiouʼs ʻeventʼ is indeed a moment of change – fundamental change – the change that it represents is understood to have no relation to the situation in which it occurs. It is conceived not as a link in a narrative chain, but as absolute novelty, a pure beginning, which is literally ʻunnameableʼ in the language of the situation. This is both its grandeur and its pathos. Events do not occur within being. Events are subtracted from being. Events have situations as their ʻsitesʼ, since there must always be a specific situation in which an event occurs, in order that it surpass it. However, even though the event ʻbelongsʼ to that situation, it is not ʻincludedʼ in it. The event thus has the ʻbeing of non-beingʼ – not because it ʻtranscendsʼ being qua being, but rather precisely the opposite, because of its proximity to it. (Being qua being – inconsistency multiplicity/pure presentation – it should be remembered, is the void.)This is the central philosophical claim of Being and Event. The mathematical interpretation, and hence ontological demonstration, of the thesis of the non-being of the event is the hinge of the book. It joins ʻbeingʼ to ʻsubjectʼ. And it opens the way for the quasi-existential terminology that is the basis of Badiouʼs philosophico-political ʻmilitancyʼ. It is via this ʻmilitancyʼ that his thought communicates to whatever non-technical audience it can muster, through his shorter publications.

In brief, and without the formalization, Badiouʼs ʻmatheme of the eventʼ is a set-theoretical (= ontological), axiomatic translation, and hence philosophical transformation, of the intuitive notion that events exceed the situation to which they belong. It holds that an event is a multiple (everything is a multiple) composed of the elements of its site and also itself; that is, it is a set that belongs to itself, or what the logician Mirimanoff called an ʻextraordinaryʼ set. However, ʻextraordinaryʼ sets violate the ʻaxiom of foundationʼ, which Badiou had earlier made a ʻmetaontological thesis of ontologyʼ (190). (The axiom of foundation stipulates that any non-void set must possess at least one element whose intersection with the initial set is void; thereby prohibiting self-belonging, avoiding Russellʼs paradox, and ensuring regularity and order in the realm of the countable.) The event is thus excluded from being: ʻthe event is notʼ. As such, however, it has ʻthe being of non-beingʼ (what is not counted, and hence represented, within the situation), also described as ʻthe incandescent non-being of an existenceʼ (183). In presenting the excess of presentation over what is representable, the event is said to be on the ʻedgeʼ of being itself, or on the edge of the void. Yet, in being composed, in part, by the elements of its site, it still has a relation to the representable. It is thus not an instance of the void (being) itself – there can be no such ʻinstancesʼ – but of the void within a situation. It is said to impose itself ʻbetween the void and itselfʼ (182), although it would appear, rather, to stand between the void and the evental site, participating in but differing from each (a paradigm case of mediation, from a Hegelian point of view). [15]

This is all very technical, but it is crucial to Badiou because it provides a mathematical (= ontological) explanation of the possibility of what otherwise appears from the standpoint of a de-temporalized being as inexplicable: namely, novelty. Mathematics has a transcendental function here. The argument seems to be that since there is a ʻplaceʼ for such an irruption within the set-theoretical count, this counters any possible accusations of arbitrariness or mysticism. However, this is not so clear, given that the demonstration is the result of a series of prior philosophical decisions (the mathematical restriction on the concept of being, de-temporalization, and the absolutization of novelty), which produced the ʻextraordinaryʼ status of the event in the first place. When the rationales of these philosophical decisions are taken into account, ʻphenomenologyʼ turns out to be harder to avoid than is supposed by the cheerleaders for axiomatics. On the other hand, belief – sheer belief – is nonetheless at the heart of Badiouʼs philosophy. And it is hard to eliminate its religious connotations. Indeed, in a kind of philosophical double bluff, Badiou courts them.The main difficulty for Badiouʼs conception of the event is that being absolutely new it is unknowable and unnameable. It can ʻonly be revealed in the retroaction of an interventional practiceʼ (178) which arises not out of knowledge, but out of faith: specifically, fidelity to the ʻtruthʼ of the event in question. In this respect, the event is the product of ʻpost-eventalʼ intervention and can only be sustained by it. The interventional practice in question is the ʻillegal choiceʼ of a name for the unnameable event. More broadly, fidelity takes the form of being true to the implications of the event, as worked out by the ʻoperator of connectionʼ, by organizing a fidelity to its meaning. This is a two-stage procedure. Badiou expounds this problematic from the point of view of ʻPascal/Choiceʼ. But the analogy is misleading, since the real problem here is not the same as that of Pascalʼs wager. It is the possibility and the consequences of political delusion. This is no small matter, especially given Badiouʼs personal political affiliations. It arises because Badiou separates truth from knowledge, absolutely. (A distinction between truth and knowledge is a condition of philosophy; their absolute separation, on the other hand, is the path to mysticism.) Yet the problem cannot even be thought from the standpoint of the separation, because fidelity to oneʼs chosen event can never be cognitively mistaken. It is a matter of pure belief. Belief not only that the world will actually render up ʻeventsʼ in Badiouʼs sense (his ontology only establishes their possibility), and that they will be ʻrevealedʼ to the retroactive agents of interventional practice, but also belief in these events themselves, irrespective of any cognitive or hermeneutical significance, manifestations of the truth of being. This is the religious dimension: the faith of ʻmilitancyʼ or what one might call Maoism without the self-criticism. (Faith in the event is militant because it speaks in the name of the unnameable, and hence against the established order, or what Badiou calls, with a rather wearing pun, ʻthe state of the situationʼ.) Being and Event provides the onto-theology for a religious conception of political practice. Badiouʼs only barrier to this slippage of politics back into religion is his linking of ʻbeing in truthʼ to the thought of ʻthe genericʼ. However, since this link is made via truthʼs indiscernibility, and a pure nomination of the indiscernible, one might be forgiven for thinking that it reproduces the structure of the problem, in a formal manner, rather than dealing with it. [16] Badiou embraces ʻthe randomness of the “militant” trajectoryʼ (337). Indeed, it is ʻrandomnessʼ alone that transcodes faith (fidelity to the encounter with the event) into ʻmaterialismʼ– which is understood here, as in late Althusser, in a restricted Democritian sense. No residue remains of Marxʼs sense of materialism – a materialism of practice – as a critique of the selfsufficiency of philosophy.

Space prohibits entering into the complexities of ʻthe genericʼ – a term taken from the mathematician P.J. Cohen and prized by Badiou as the ʻemblemʼ of his own thought (15) – save to note that, as a postdialectical (abstract and indeterminate) substitute for Aufhebung, it is the procedural path to the infinity of truth, and functions as the final transition to the theory of the subject. The generic is said to ʻfound the very being of any truthʼ, a truth being ʻthat which always makes a hole in knowledgeʼ (327), just as, for Lacan, a subject is a hole in being. For Badiou, subjectivization is ʻinterventional nomination from the standpoint of the situationʼ. Only a subject can ʻforceʼ a new situation to exist. The ʻentire beingʼ of the subject is ʻto encounter terms in a militant and aleatory trajectoryʼ. It is ʻsolely … the local effects of an evental fidelityʼ. As such, ontology can ʻthink its lawʼ but not ʻthe subject itselfʼ (393, 342, 395, 406, 411). This leads to a hallucinatory terminological crescendo as the whole apparatus of the book is condensed into a series of attempts to describe this law:

A subject is what deals with the generic indiscernibility of a truth, which it accomplishes amidst discernible finitude, by a nomination whose referent is suspended from the future anterior of a condition.

A subject is thus, by the grace of names, both the real of the procedure (the enquiring of the enquiries) and the hypothesis that its unfinishable result will introduce some newness into presentation. A subject emptily names the universe to-come which is obtained by the supplementation of the situation with an indiscernible truth. At the same time, the subject is the finite real, the local stage, of this supplementation. Nomination is solely empty inasmuch as it is full of what is sketched out by its own possibility. A subject is the self-mentioning of an empty language. (399–400)The ʻtheory of the subjectʼ really does seem to have reached the end of the road here.

For Badiou, the event, politics and the subject are all extremely rare (344, 392). Historically, different fields of activity are taken to be defined by the proper names associated with events to which new forms of subjectivization correspond: ʻSaint Paul for the Church, Lenin for the Party, Cantor for ontology, Schoenberg for musicʼ (393). Apart from the claim for Cantor, the canon is conventional. But the historical content of Badiouʼs philosophy is not itself philosophical (how could it be?). Rather, it involves a massive operation of philosophical re-presentation of the consequences of ʻdecisionsʼ taken elsewhere. Badiou is insistent that his thought is modern, ʻperhaps even “more-thanmodern”ʼ. However, it is in this ʻmoreʼ (which is also less than modern) that his neo-classicism resides.

Modernism + classicism = neo-classicism

It will be as well to start with Badiouʼs historical selfconsciousness. This is indeed that of a combination of the classical and the modern, although the combination is understood thematically, within the timeconsciousness of historicism, rather than as a matter of philosophical form; and Badiouʼs presentations of it are symptomatically inconsistent. In Being and Event, the classical philosophical problematic of being and truth is understood to come together with the distinctively modern problematic of the subject (inaugurated by Descartes, but moved decisively beyond him by Lacan), on the basis of the modernity of the mathematics of Cantor and Gödel and Cohen. Being and Eventʼs modernity is thus that of both ʻthe subjectʼ and set theory as a paradigm of rational thought. In Badiouʼs 2003 Preface to his Theoretical Writings, on the other hand, his work is understood ʻto allow us to transcribe the classical problematic (being, truth, subject) into a conceptual assemblage that is not only modern, but perhaps even more-than-modernʼ. Oddly, the subject is classicized here and Badiouʼs philosophy attains an autonomy from its own classical problematic via eight ʻnew technical conceptsʼ: mathematical multiplicity, the plurality of infinities, the void as proper name of being, the event as trans-being, fidelity, the subject of enquiries, the generic and forcing. [17]

This relative decline of the subject within Badiouʼs historical self-understanding corresponds to the shift of a greater part of the burden of philosophical modernity onto mathematics and its meta-ontological transcodings. Yet it is precisely the idea that philosophy is to be pursued, systematically, through a thinking of mathematics that is Badiouʼs philosophyʼs primary classical, rationalist and idealist trait – its return to Plato – however modern the maths. This is the ʻmoreʼ that is also less than modern, the carrier of the neoclassicism of Badiouʼs thought.[Those] who thrive on slogans, have always had the tactical advantage that they need only bring forth again, from a period of imprisonment, one single means … once cast aside as hopelessly antiquated, in order to launch it as an avant-garde achievement. [18]

This is particularly clear when we consider the broader polemical context of Badiouʼs thought: his expressed desire to ʻundoʼ the ʻdisastrous consequencesʼ of the twentieth-century linguistic turn, and more fundamentally, to turn away from Romanticism, very broadly conceived, by which Badiou means any temporalization of conceptuality. For Badiou, Romanticism is ʻany disposition of thinking which determines the infinite with the open, or as horizonal correlate for the historicity of finitudeʼ. It is the historical function of the philosophical understanding of Cantorʼs mathematics ʻto have doneʼ with this finitudeʼ. [19] This is Badiouʼs neo-classical delusion and his own historicism of ʻprogressʼ.

Just as Badiouʼs conception of philosophical modernity is historicist and inconsistent, so his conception of neo-classicism is similarly temporally naive, and comes in two separate versions. On the one hand, at a philosophical level, in Being and Event, neo-classicism is associated with a ʻconstructivistʼ orientation in thought (exemplified by Leibniz), which commands us to confine ourselves … to the continuity of an engendering of parts regulated by the previous language. A neo-classicist is not a reactionary, he is a partisan of sense.… The neo-classicist fulfils the precious function of the guardianship of sense on a global scale. He testifies that there must be sense. (292) This fits in with the role of mathematics in Badiouʼs thought in establishing continuity with classical philosophy. On the other hand, elsewhere, Badiou associates neo-classicism exclusively with scholasticism – ʻacademicizationʼ and ʻspecializationʼ – and, in mathematics, with ʻthe little styleʼ, to which he opposes his own ʻgrand styleʼ. [20] In neither case does he register the essential modernity of neo-classicism as a reaction against the modern within its own terms: a new beginning. Neo-classicism was (and is) a reactionary avant-garde – harbinger of the future of a past that is no more, if it ever was.Being and Event is a philosophical neo-classicism because it exhibits a classicism that is taken up into its modernity. Formulaically: modernism + classicism = neo-classicism. In fact, in historicist terms, since neoclassicism was a phenomenon of the 1920s, Badiouʼs neo-classicism is a neo-neo-classicism, a return to neo-classicism, or neo-classicism squared. Badiou is to contemporary European philosophy what the Picasso of the 1920s was to the art of that day. Musically, Badiou thinks he is Schoenberg, but he is actually Stravinsky.

It should be clear from these formulations that I understand neo-classicism, primarily, as a historical category of cultural form and only secondarily a stylistic or formal term. This is not the neo-classicism of conventional musical terminology – an objectivist reaction to the expressionism of late Romanticism (present in Badiouʼs ʻacademicizationʼ). As Adorno puts it, ʻexpressionism is objectivityʼ. Rather, it is Adornoʼs sense of neo-classicism as a historical regression to means and forms that no longer have any social objectivity, however formally ʻobjectivistʼ they may appear. In artistic terms, this means appeals to beauty, harmony, consonance, tonality – ʻa questionable orderlinessʼ that provides ʻa cloak of forced affirmationʼ. [21] Even when this forced affirmation is an affirmation of the new. We can see this in the compositional form of Being and Event.Badiou identifies three strands, thematically, within the overarching form of a series of ʻmeditationsʼ: the conceptual, the textual and the meta-ontological, or philosophical interpretations of the mathematical. However, this is a weak (possibly ironic) rhetorical gesture to the Cartesian tradition. It establishes little linkage to the specificity of Descartesʼ practice: there is no narrative of the philosophical subject here holding it all together, in fact, supposedly, no narrativity at all. The presentational form of the book is better viewed from the standpoint of its combination of systematicity with digressive textual historical-philosophical self-consciousness. This systematicity encloses both Badiouʼs conceptual and meta-ontological strands. While the historical-philosophical digressions on particular thinkers (Aristotle, Spinoza, Hegel, Mallarmé, Pascal, Hölderlin, Leibniz, Rousseau, Descartes/Lacan – to each modern philosopher, his or her own history of philosophy) interposes an intermittent modernism at the level of form:

neo-classicism practices the old custom of joining brokenly disparate models together. It is traditional music combed in the wrong direction. The surprises, however, fade away like little pink clouds; they are nothing but a volatile disturbance of the order within which they remain. [22]

Notes

1. ^ Reviewed by Keith Ansell-Pearson and Peter Dews in Radical Philosophy 103, September/October 2000, pp. 51–3, and Radical Philosophy 111, January/February 2002, pp. 33–7, respectively.

2. ^ Alain Badiou, Manifesto for Philosophy, trans. Norman Madarasz, SUNY Press, New York, 1999, pp. 113–40.

This was originally published in French in Conditions, Seuil, Paris, 1992.

3. ^ Lecercle remarks, ʻThere is no point in a historical treatment of Badiouʼs thought, which is explicitly antihistoricist.ʼ ʻCantor, Lacan, Maoʼ, RP 93, p. 7. But this is a non-sequitur, quite apart from its conflation of historical thinking with historicism, shared with Badiou (and inherited from structuralism). In other regards,

Lecercle is less concerned to maintain a strictly immanent approach to Badiouʼs thought. His example of an application of Badiouʼs system – to a reading of Mary Shelleyʼs Frankenstein – is happy to violate the terms of its self-understanding (as one must) by treating it hermeneutically, as a metanarrative. Ibid., pp. 10–11.

This is also the way it functions, practically, in its cultural dissemination.

4. ^ Louis Althusser, ʻOn the Materialist Dialecticʼ (1963) – ʻRemarks on the Terminology Adoptedʼ (1965), For Marx, trans B. Brewster, New Left Books, London, 1969, p. 162.

5. ^ One could say that Althusserʼs own philosophy rapidly became a philosophy without Marxism too, in so far as his attempt to produce a Marxist philosophy was plagued by a split between its ʻMarxistʼ and its ʻphilosophicalʼ aspects – forever converting Marxʼs critique of philosophy (his materialism) back into philosophical categories, which consequently clashed with the rest of Marxʼs thought, all the way down to his final ʻaleatory materialismʼ of the encounter. See John Kraniauskas, ʻAlthusser after Althusserʼ, below, pp. 38–42.

6. ^ Alain Badiou, ʻPhilosophy and Mathematics: Infinity and the End of Romanticismʼ (1992), in Theoretical Writings, ed. Ray Brassier and Alberto Toscano, Continuum, London and New York, 2004, p. 25.

7. ^ Alain Badiou, Deleuze: The Clamor of Being, trans.

Louise Burchill, University of Minnesota Press, Minneapolis and London, 2000, p. 4.

8. ^ Slavoj Žižek, ʻLeninʼs Choiceʼ, Afterword to V. I. Lenin, Revolution at the Gates: A Selection of Writings from February to October 1917, edited by Slavoj Žižek,

Verso, London and New York, 2002, pp. 165–336. This political reading finds its philosophical correlate in the tendency to contrast the philosophy–science–art triad of Deleuze and Guattariʼs What is Philosophy? with Badiouʼs four ʻconditionsʼ of philosophy – science, art, politics and love – in order to imply that Badiouʼs philosophy is both ʻmore politicalʼ than Deleuzeʼs and has a greater range. However, the precise opposite might also be argued: namely, that Badiouʼs strictly exceptionalist conception of politics is a narrow variant of a classical conception that cannot grasp the fundamental ubiquity and complexity of the forms of power in capitalist societies, and consequentially fails to grasp their political processes in their most basic – that is, ontological – aspects.

It is precisely a similar narrowness in its conception of politics that characterizes the recently rechristened ʻoldʼ Left, albeit on the basis of radically different theoretical presuppositions.

9. ^ See, for example, the opening chapters of Manifesto for Philosophy.

10. ^ The question of the ontological status of mathematical reason is relevant to the critical meaning of Badiouʼs thought insofar as it is via mathematics that Badiou attempts to occupy the theological ideality of classical rationalism in a secular manner. On this model, mathematical truths are not merely eternal, but are unrelated to historical time. Mathematics has a (empirical) history as a discipline, but no immanent historicality. However, this question is subordinate to that of the ontological status of philosophical reason (in Badiouʼs terms, the ontological status of metaontology), into which mathematics is taken up. Appealing to the ʻeventnessʼ (that is, the non-being) of ontology itself (242) begs this latter question, which Badiou literally cannot think, since he has no ontology of social being.

11. ^ Alain Badiou, ʻAuthorʼs Prefaceʼ, Theoretical Writings, p. xv.

12. ^ ʻTheory of the subjectʼ is the title of an earlier book by Badiou, Théorie du sujet, Seuil, Paris, 1982. It was followed by Peut-penser la politique, Seuil, Paris, 1985 (Can Politics Be Thought?, Duke University Press, forthcoming), which contains initial versions of the concepts of event and intervention. Being and Event takes up the thought of these two previous texts in order to re-present it, systematically, on the basis of its ʻontological conditionsʼ (489), in the course of which it is, inevitably, modified. The telos driving the systematic structure of Being and Event thus comes from these earlier works.

13. ^ Étienne Balibar, ʻThe History of Truth: Alain Badiou in French Philosophyʼ, Radical Philosophy 115, September/October 2002, pp. 16–28.

14. ^ See Étienne Balibar, Barbara Cassin, Alain de Libera, ʻSubjectʼ, Radical Philosophy 138, July/August 2006, pp. 15–42, especially pp. 29–32. Kant simultaneously founds and ʻdecentresʼ the modern philosophical concept of the subject. As such, he is both the first truly ʻCartesianʼ and the first ʻpost-Cartesianʼ philosopher – hence his unparalleled, and continuing, centrality to contemporary philosophy.

15. ^ Badiou is less fastidious with linguistic/conceptual determinations than mathematical ones, despite his (formal) acknowledgement of ʻthe imaging power of languageʼ as the necessary medium of philosophy. Note the shift in the use of ʻexistenceʼ in his argument above, from a conventional ontological meaning – the axiom of foundation ʻforecloses extraordinary sets from all existenceʼ (190; EE, 210, trans. altered) – to a de-temporalized and generalized existential one, according to which it is precisely this foreclosure from ʻexistenceʼ (meaning ʻbeingʼ) that defines the singular ʻexistenceʼ of the event, in a manner not so dissimilar from the later Heideggerian Ereignis.

In this respect, Badiouʼs thought might be compared to a traditional metaphysical (= scientistic) version of the later Heidegger. Although generally absent from the text after his inaugural citation, Heidegger lurks in the shadows of Part V, ʻThe Event: Intervention and Fidelityʼ, in its final meditation, named ʻHölderlinʼ.

16. ^ Badiouʼs model for such fidelity is Saint Paul. Alain Badiou, Saint Paul: The Foundation of Universalism (1997), trans. Ray Brassier, Stanford University Press,

Stanford, 2004.

17. ^ Badiou, Theoretical Writings, p. xv.

18. ^ Theodor W. Adorno, Philosophy of Modern Music (1948), trans. Anne G. Mitchell and Wesley V. Blomster (1973), Sheed & Ward, London, 1987, p. 210.

19. ^ Badiou, ʻPhilosophy and Mathematics: Infinity and the End of Romanticismʼ, in Theoretical Writings, pp. 21–38, pp. 24–5.

20. ^ Badiou, ʻMathematics and Philosophyʼ, in ibid., pp. 3–20, p. 5.

21. ^ Adorno, Philosophy of Modern Music, pp. 48, 209.

22. ^ Ibid., p. 208.

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