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2. Badious decision

Giving up leadership, then taking it back

Every truly contemporary philosophy must set out from the singular theses according

to which Althusser identifies philosophy.1

Alain Badiou,Metapolitics [1998]

In the 1970s Alain Badiou issued furious Maoist polemics against his former teacher. Only

decades later did he come to concede the lasting significance of Althussers philosophical

project for his own or at least the corrective theses ofLenin and Philosophy.2 In part this

softening of stance could be put down to an inevitable mellowing which comes with age and

achievement: the angry and scarcely read Maoist militant of the 1970s and early 1980s

transformed into a world renowned philosopher, overshadowing his mentor and becoming

possibly the continental traditions most respected living thinker. But the world had also

changed in the interim. Where in the 1970s targeting the limitations of Althussers quietist

programme could be seen as effecting a maximal scission in theoretical practice, the

postcommunist world of the 1990s and beyond would render such antagonism anachronistic.

The predominance of discourses of human rights, global governance, and perhaps more than

anything else the elevation of the master signifier of democracy to a position of

unimpeachable authority with, conversely, the assignment of communism, militancy,

revolution and the will to truth to describe all that went awry in the 20 th century has

inestimably reconfigured the terrain. Addressing the prerogatives of Althusserian

theoreticism in a 2007 interview, Badiou conceded the role of changing historical conditions

in its reappraisal.

Evidently the question of theoreticism does not have the same importance

today, but I would say that the relation between philosophy and politics today,

or the question (of the role) of theory has once again become very important

because the concrete situation has become very difficult and mixed. In those

years [69-] we had great hope, truly massive, in the situation.3


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From this vantage point of the present we can more easily recognise Badious underlying

proximity to his teacher.

I preface with these remarks because there is another reason why Badious philosophy

is infrequently considered in even qualified continuity with Althussers. The translation of

Badious books into English proceeding from his 1992 Manifesto for Philosophy, the 1997

critique of Deleuze, The Clamour of Being4, and his 1988 magnum opus, Being and Event,

and only recently working backwards to encompass the works of the 60s, 70s, and early

1980s, has certainly prejudiced interpretations in terms of an orientation towards comparisons

with more overly metaphysical rivals like Deleuze and Heidegger. Although the rectification

of this situation is underway thanks to the efforts of Bruno Bosteels and others in translating

earlier works such as Theory of the Subject, and in bringing to attention the renegotiation of

Althusserianism across Badious philosophical trajectory, it remains an underappreciated

angle. To what extent Althussers vanishing cause of structural causality persists in

Badious idea of the event, and how formative can be considered Althussers tendency to

privilege mathematics as the prototypical scientific practice in influencing Badious turn

towards mathematical ontology, is often clouded by the sharp distinction wherein Althusser

maintains history as being a process without a subject against Badious position which

could be put oppositely: there is history only insofar as there are events and subjects. In

isolating just this inversion, however, it is possible to lose sight of their overall conceptual

affinity, and moreover the political determinations contextualising their separation. The

matter at hand therefore demands a reconstruction of the implosion of the Althusserian

movement after 1968, up to which time two of Althussers prodigious students Jacques

Rancire and Alain Badiou remained constructive partners in the structuralist endeavour.

By tracing the genesis of Badious ideas to their Althusserian origin it is then possible to

follow how ideas found in Badious early works re-emerge in the mid to late 1980s after a

thoroughgoing purification from Althusserian doctrines. But precisely in regard to

uncertainty over the persistent question of intellectual authority in Badious philosophy

(whether construed as scientific or ontological) will this purification be put into question.

Although the large and ever-growing secondary literature on Badious philosophy has

traced his theoretical debts to Althusser, curiously little attention has been given to the

Badious rearticulation of the role for intellectual guidance of the masses. Not unsurprisingly

readings have fixated on the implication of politics occurring through sequences of

unexpected events as opposed to a piecemeal or teleological emergence across drawn outtimescales. Is political change a creeping process achieved through the steady building up of


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resources, or does it occur through spontaneous flashes that no amount of organization could

hope to engineer? Such is the binary to which Adrian Johnston has devoted a book-length

study of Badious conception of political transformation. Johnston examines in detail debates

surrounding Badious conception of the event: noting a dichotomy between those, like Peter

Hallward, who see Badious conception as lending itself to flash politics, and those, like

Bosteels, who place emphasis on the laborious, disciplined work of affirmation after the

event.5 Yet whichever way one looks at it neither perspective interrogates the question of

intellectual authority in Badious theory of the event in much depth. This, I suspect, is

because of the presumption that the events aleatory being automatically undermines the role

for mass guidance. Leninist readings of Badious philosophy such as Daniel Bensads have

understandably taken objection to the apparent anti-organizational conclusions that follow

from viewing the event as a political miracle bestowed upon militants.6Badious post-Maoist

formation of the LOrganisation Politique in the 1980s with its aim to practice politics

without a party organization of course only serves to reinforce to that impression. But the

source of contention only obliquely broached by this emphasis on the temporality of politics

is the part played by the intellectual. Or to put it as plainly as possible: just because the

militant sequence occurs after an event does this ipso facto imply a diminution of the role for

conceptually astute philosophers? If events are necessary for subject and if to some extent the

notion of the subject in Badious mature philosophy is transitive with that of the event, who

then is the subject? Who gets to decide an event really is an event? Whose enunciation of

what counts as an event is privileged? Given Badious repeated insistence that the purpose of

Being and Event (henceforth, B&E) is to establish a new conception of the subject, and

bearing in mind the highly complex formal discourse of subjectivity he establishes in the first

and second of his grand philosophy books, why not take Badiou on his word and think the

implications of his idea of the event through the question of the subject? If the hallmark of

Althussers conception of history as a process without a subject could be more accurately

appended with except the masses and their representative institution, the PCF what

determination is suitable for Badious conception of the subject?

To approach Badious philosophy from the right angle to address the above questions,

I will demonstrate the theoretical purpose played by the event in establishing a pre-reflective,

egalitarian political condition wherein vanguardist ambitions are immediately disqualified

from any role in deciding the right time, the right subjects, or the right issues for revolt or

revolution. By the same token, we will then see how the supernumerary, unpredictable eventis beholden to the subjects affirmation to seal its existence. The events duality as a both an


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undecideable happening and a result of a discourse of fidelity nonetheless maintains an

awkward relationship between the intellectual and mass politics. For Badiou claims the

subject of an event is not required to be one who actually took part in it: that is, the subject

can be perfectly exteriorto the facts on the groundas the French Maoists were to the actual

Chinese Cultural Revolution, and as many of the Maoists were to initial events of Paris 68.

More problematically still, in the mathematical artifice of B&E the delimitation of the

philosophers metaontological discourse to think the presentation of presentation, whilst

being circumscribed by an inability to produce any truths itself, is an ideal to which the

philosophical system will aspire but ultimately fail to maintain. The line between the

metaontologists impotent if omnipotent view from outside and the subjects active if

restricted view from the inside will hit the rocks by the crowning meditations on Paul

Cohens theory of forcing. Because from within the mathematical demonstration pursued in a

ground model of set theory the excess necessary for the objective event is repressed by the

constructive, transitive nature of the model. Thus, there is no irreducible fact of event to be

affirmed by an inhabitant inside this model. There is no impetus for an inhabitant subject of a

situation to force new truths out of a situation. The egalitarian event is lost. Either a uniquely

visionary subject within a situation can just see the possibility for forcing a new truth, or the

impetus for the initiation of the truth procedure needs to come from outside: from the

philosophical Subject who can prompt those with only their limited vision within any non-

ontological situation.

To clarify, none of the above is said to smite Badiou. I have no intention here to add

to the burgeoning genre of anti-Badiou literature, with its accusations of Stalinism, or

comparisons between his politics and fascism because of their shared rejection of

democracy.7Quite the opposite, in your present authors opinion some kind of intellectual

guidance is unavoidable in all forms of politics. The argument rather serves as a genealogical

angle to make sense of Badious political break from Althusser and how he attempted totheoretically resolve this without lapsing into exaltations of democratic revolt. Addressing all

of the above points will involve, firstly, a discussion of Badious early work under the aegis

of Althusserianism. Secondly, how the events of 1968 led to the implosion of this project;

and particularly the singularity of Badious break from Althusser in comparison to Rancires

and also the political persuasion of the momentarily fashionable Maoist group, Gauche

Proltarienne. Thirdly, how Badious idea of the event departs from the vanishing cause of

Althussers epistemic break by posing the imperative of the subject to actualise itsconsequences. Fourth, and finally, how B&E strives towards resolving the issue of the


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authority of philosophers, but ultimately runs aground within the mathematical universe

deployed in Paul Cohens forcing technique.

We begin with those consensual years directly preceding 68, where Badiou seemed

poised to take the mantle of arch Althusserian with his sophisticated text, The Concept of

Model. For many of the same concerns will continue to surface in the metaontological edifice

ofB&Etwo decades later.

2.1 Early Work

Like other influential offspring of Althussers student cadre (such as Nicos Poulantzas) in

1966 Badiou wrote an extensive review of the high watermark texts of the periodFor Marx

and Reading Capital appraising them positively. The review essay, titled

(Re)commencement of dialectical materialism, isolates the question of change within

structural causality as the lynchin upon which the ulterior progress of dialectical materialism

depends.8 Remembering that for Althusser an epistemological break manifests itself

effectively in the complex, social whole through the rupture between science and ideology,

tracing a route from ideology to scientific disruption was for this milieu considered

dialectical materialisms highest calling.9 Alongside a number of other privileged

Althusserians Badiou was also invited to take part in the 1967/68 Philosophy Course for

Scientists. His distinctive contribution was to find the resources for distinguishing science

and ideology with respect to breakthroughs in 20th century mathematical model theory. In

this early work, Badious trademark identification with set theory is evident and there are also

hints towards category theory10 that will only re-emerge within the elaborate the post-B&E

system almost 40 years later in Logics of Worlds. This approach structures what could be

considered the arch-Althusserian text of the period, unrivalled in pushing Althusserian

formalism to its limits.

In more ways than one Badious contribution to the Philosophy Course lecture series his first fully-fledged theoretical text, The Concept of Model rests in almost total

agreement with the Bachelardian-Althusserian protocols. For not only does it pursue the

problematic through mathematics in a way shot through by the spirit of French scientific

rationalism (see 1.1), it also operates along the double semantic register of model

incidentally, already flagged up by Althusser in a footnote in Reading Capital11a word

signifying both a descriptive (ideological) notion of scientific activity, and a concept

(scientific) of mathematical logic.12

Badious thesis rests on the wager that through the use ofmathematical logic philosophy can perform the partisan role for the recovery of science that


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in the same lecture course Althusser insisted was philosophys duty; and it does thi s by

turning the mathematical, logical model against the ideological, empiricist conception.

Politically, this can be considered a contribution to class struggle in theory because of the

ideological influence of bourgeois technical, economic models in fostering a revisionist

Marxist deviation.13 Following Bachelard, however, Badiou does not wish to simply write off

modelling as a form of representation alien to science. Bachelards example of Bohrs model

of the atom portrayed as planetary orbits giving way to a more abstract statistical model

demonstrates the conservation of forms of models passing through the rupture from ideology

to science.14 So the easy optionrejecting models entirelyis off the table. The recovery of

science rather entails operating within modellings ideological terrain of representation,

drawing a line of demarcation within philosophy between the formal model (progressive) and

the vulgar epistemological model (reactionary).

Singling out Levi-Strauss conception for particular criticism, Badiou condemns

epistemological models for introducing a regulatory myth into epistemology. Presenting

epistemological models as a technical artifice that corresponds with an empirical given by

measure of their predictive success in experimentation permits the creation of models of

models, systems of systems, all conspiring to efface the reality of science being a production

of knowledge developing demonstrations and proofs internal to an historically specified

materiality.15 In other words, this conception obscures the development of science through

epistemological breaks. Logical models16 are superior for Badiou inasmuch as what appears

to be an analogous binary between empiricisms artifice-empirical couple in logics

syntactical-semantic dyad in fact reverses the relation. In logic semantics are the artifice,

whereas syntax is the given. Nonetheless, Carnapian logical positivism goes astray when it

represents mathematics formal syntax as the corresponding formal compartment of science,

and semantics as the application of this formalisation to a limited domain of empirical

objects, which it models. In Badious demonstration logical positivism is exposed as anillegitimate, ideologically determined concept of model because it fails to recognize how the

formal syntax (drawing on recursive algebra) and the semantic model (based in set theory)

adjoin one another in an experimental dialectic wherein models take part in generating the

syntactical systems of logic. As a consequence there is no pure, formal, or a priori

knowledge.17 Ray Brassier rightly notes that in a single stroke Badiou thereby rejects the

reduction of mathematics to both intuitionist a priori logic, and Quinean empirical

relativism, by suggesting that logic itself be conceived as doubly articulated betweensyntactic system and semantic structure.18 The rejection of the transcendental priority of


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logic, results in the position that the double articulation cannot be transplanted outside of

mathematics or duplicated in the relation between a supposedly formal theory and its

putatively material instantiation.19 New conceptual models come first, and their new

formalisations are retroactively cast: the formalisation procedure working on ideology to

affect a scientific rupture. In this way the lag between models and the revision of axioms

provides access to the historical origins of epistemological breaks. New mathematical models

cannot be derived from any one set of axioms, indicating a reciprocal dialectic. The

reconfiguration ofboth levels allows the dialectical materialist a view into the creative

genesis of new knowledge. Far from being simply an ideological notion, then, the model

delivers a fertile epistemological category; the model is the ordinance that, in the

historical process of a science, retrospectively assigns to the sciences previous practical

instances their experimental transformation by a definite formal apparatus. In sum, The

category of model thus designates the retroactive causality of formalism on its own scientific

history.20

Badious approach illuminates one approach for resolving historical epistemologys

unexplained procedure of how experimentation on ideology from within ideology can cause

an incommensurable scientific break. Because of the consistency theorem (every consistent

set of axioms admits a model), the theory of models necessitates a rupture within

formalization. An easily graspable example is Poincars attempt to construct a model of

Riemannian plane geometry out of a model based on the axioms of Euclidian geometry. If

the famous Euclidean axiom through two points passes one and only one straight line is

constructed in an inner model of a Euclidean sphere so that it becomes through two different,

non-diametrically opposed points in the sphere, there passes only one great circle one can

then deduce the non-existence of parallels axiom of Riemannian geometry. Reimannian

geometry is then assured by the Euclidean model. This model, though, proving the possibility

of both the retention and the negation of Euclids straight-line axiom, demonstrates the

independence of the axiom, resulting in a defeat for Euclidean geometry which was

necessary, and not a matter of circumstance... a matter of impossibility, and not impotence.21

Science breaks from ideology by releasing a truth, where the previous conception is proven

inconsistent.

Without a doubt Badious text represents the most sophisticated, technical application,

and nuancing of Althusserian dialectical materialism in its heyday. Where Althusser had only

talked about what must be done to identify the science/ideology rupture, Badiou locatedwithin mathematical practice the resources proving a revisable, experimental site of rupture


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between logical syntax and semantic models. Within the realm of logics formal inscriptions

he isolated a place free from ideology, yet around which ideology could cohere. Ideology is

not mere deception or foolishness; it has a rational basis and only experimentation on

ideology from within ideology can result in a dismembering of these axioms through the

scientific break.

IfThe Concept of Model appears to present a fertile ground for further research with

curiously few traces of succession, that is because, as Althusser observes in the Forward to

the book, the lecture series in which itwas delivered was interrupted by the events of May

1968. December that year, Althusser wrote that the somewhat theoreticist accents of this

text hearken back to a bygone conjuncture ... a project that was happily interrup ted.22

Recalling Althussers remarks inElements of Self-Criticism regarding the attempt to deduce a

speculative rationalist truth/error distinction between science and ideology where the class

struggle was almost entirely absent, the same problem could equally, if not more greatly, be

seen to haunt The Concept of Model, which despite perfunctory political incantations of

bourgeois epistemology, proletarian theory, and such like, is an entirely rationalist treatise

on the historical epistemology of scientific breaks within the mathematical sciences. This is

not to say that these insights could not be put to political labour in the form of critiques of the

supposed timeless axioms of neo-classical economics, and in other similar cases, but the

conception of the underlabouring role of politics to scientific truth is what 68 put into

question (even if it will remerge two decades later in Being and Eventin the desutured guise

of politics as handmaiden to an events political truth).

It is not the events of 68 per se, nor just Badious turn against Althusser which is so

important for understanding subsequent developments in Badious philosophy. Rather, it is

Badious particular reaction to 68 and his particular turn against Althusserianism. For

unlike other rebel Althusserians Badiou always maintained a commitment to truth and a

highly formalistic philosophical approach. Despite the searing political disagreements of the

1970s, these loyalties, I argue, keep him closer to the original Althusserian projectof which

The Concept of Model is a tour de force exhibit. This violence in proximity is best put into

context historically, in contrast to the pathways of other dissident Maoists who formed the

Gauche Proltarienne (GP), and particularly in contrast to Rancires post-68 valorisation of

democratic revolt. An examination of the causes and consequences of the political maelstrom

that was May 68 is in order.

2.2 Implosions of 68


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Despite many commentators tiring celebration of 68 as a defeat of the idea of Marxist

revolution in favour of a world of single-issue NGO campaigning and resistance, they are

nonetheless right to isolate in 68 an historical fork in the road of continuing pertinence

today.23The legacy of 68 persists in defining the contours of contemporary politics: whether

that is within the pedestrian discourse of parliamentary campaigns (Nicholas Sarkozys

promising its erasure in the 2007 presidential campaign)24, or in the ideological and strategic

repetitions within contemporary protest movements.25 What makes the French May events of

68 so significant? To answer this question in the broadest theoretical light, one needs to set

the scene of the historical particularites of France under de Gaulles leadership, and the

Communist Partys integration with the status quo.

Formerly taking advantage of its role in the French resistance movement to cement its

revolutionary credentials, by 1968 the PCFs reputation was tarnished by their support for

Frances ruthless suppression of the Algerian independence struggle earlier in the decade.

Stalinist economism dominated the mindset of the PCF; at home their increasing reformism

had led to seamless assimilation within the democratic, parliamentary machine. In

combination with the Confdration gnrale du travail (CGT) they focused their energies on

limited pay and condition demands above revolutionary agitation. The state of the PCF

arguably provides a micropolitical exhibit of a more general macrosocio-political ossification

of French politics under de Gaulle, when the countrys bureaucratic and educational

structures were equally staid. In addition to the growing outrage accompanying the American

prosecution of the Vietnam War reaching a barbaric zenith in 68, all these factors helped

contribute to the considerable allure of Third Worldism and anticolonialism above that of

orthodox Soviet Marxism for young militants in the student movement. Significant student

and radical groups in the run up to 68 were the Union Nationale des tudiants de France

(UNEF), who had earned their radical credentials with steadfast opposition to the Algerian

war. The student group L'Union des Jeunesses Communistes Marxistes-Lninistes (UJC-

ML), counted Rancire, Victor Hugo, and Robert Linhart amongst its number.26 There were

also the Situationists and Socialisme ou Barbarie who positioned themselves outside of the

Marxist box. Then there were those who stayed within the PCF like Althusser, Balibar, and

Dominique LeCourt (the hardcore of the structural Marxist movement). Badiou, for his part,

was before 1968 a member of the Parti Socialiste Unifi (PSU), which had also opposed the

Algerian war.

Excepting the avant garde and anarchist factions, the Maoist affinity cutting acrossthese groups represented the main Marxist alternative to Soviet communism. Even as he was


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repeatedly forced to deny these leanings to retain his PCF membership, Althussers

theoretical intimations held out a seductive fusion of structural Marxisms aesthetic of

scientific certainty with the more voluntarist disposition associated with Maoism. So up until

68 Althussers programme was considered at least theoretically compatible with the swelling

discontent. At the same time, Althussers directly political writings on Student Problems,

dating back to 1963, jarred with the student movements concerns insofar as he advised their

further theoretical reflection on the science/ideology distinction, issuing a call for the

subordination of petit bourgeois student desires to the properly working class revolutionary

task. The position would soon backfire on Althussers prestige amongst the May radicals.

With voluntarist momentum behind their actions, the student groups initiation of the

May events upset traditional schemas whereby it should be the working class and their

representative institutions performing the leading role. It took a week after May 68 erupted

in street protests and barricades for the PCF and CGT to show any solidarity with the

university insurrections by calling a general strike, therewith bringing the Maoist groups

tardily in tow now they recognised working class struggle in the events. In tandem with the

escalation of strikes throughout factories across France pushing their demands much deeper

and also with a greater militancy than the PCF-CGT leadership, it left the traditional working

class institutions trailing behind on all fronts. Althussers strategy of patient reform on the

theoretical fringes of the PCF in preparation for it to regain a revolutionary disposition was

short-circuited by events on the ground. His quietism during this period was integral to the

implosion of Althusserianism. The disillusionment was not only personal; for the Maoists it

signalled the maladroit structuralist refounding of dialectical materialism, now associated

with order, losing its revolutionary kudos.

Jacques Rancires desertion from the Althusserian fold is emblematic of its

implosion. Part of the UJC-ML, which gave up on prising Althusser away from the PCF after

68 one faction went on to form the GP after its dissolution in 69 inAlthussers Lesson

(1974) Rancire indicts the entire programme as an attempt to preserve philosophy

Marxist philosophy in particular as the exclusive business of academically trained

specialists, implying that production is the business of the workers, whereas history is too

complex and affair for them, one they must entrust to the care of specialists from the Party

and from Theory.27Put into question by 68 was precisely the knowledge/power nexus; the

events marked the appearance of politics in a new form in the question of knowledge, its

power and its relationship to political power.28

As a sign of Althusserian complicity on theside of knowledge/power against the creative self-determination of the masses, Rancire


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notes that in the aftermath of the student revolts those university students who were card-

carrying members of the PCF were brandishing theoreticist texts as they called for the re -

establishment of order at the university.29 These insights serve to put into question the

politics of philosophers: its condition of possibility [...being] that it not put into question the

despotic figure of scientific power. Althusserianisms legacy is far worse than mere

quietism; rather, it bears the revisionist sign on the forehead of authoritarian leftism, which

is precisely the kinship between repression-by-science and repression-by-the proletariat.30

In this way, Rancire links Althussers revolutionary scientism back to

Zhadanovian/Lsyenokian proletarian science. In the UJC Rancire still detected traces of

the Althusserian imprint, but in the standpoint of the GP he perceived a positive new model

where intellectuals renounce their role in a division of labour and simply fight alongside the

masses against repressive state apparatuses.31 Those who stayed within the Althusserian

paradigm, whilst pushing a militant platform he disparages as ultra-left Platonists. All this

culminates in the lesson of 68 bearing a remarkably postmodernist overture. It is worth

quoting at length. 1968

was no doubt the birth of a new figure of subversion, but it was also quite

clearly the end of leftisms grand and totalizing discourse. The end, we might

say, of the opposition of small communist worlds to the big one In 1969, it

was still possible for leftists to encompass the anti-authoritarian uprising of

Frances youth and the proletarian struggles with their unifying discourse

[but] It is not just that these struggles which attack power in its varied and

sometimes contradictory manifestations, present us with a multiplicity that

makes achieving a synthesis more complicated. It is, more importantly, that

they are themselves a multiplication of the discourses of struggle Marxism

itself will continue to serve the ambiguous role it serves nowadays that of a

system of multiple identifications, of the place where discourses of revolt meet

and where the discourse of subversion is perennially being transformed into the

discourse of order.32

68 was a moment of dissimulation where the fracturing of the subjects of revolt into their

own self-presentation transforms Marxism into the role of an ideological police force,

attempting to re-present these disparate causes under subordination to the need for proletarianrevolution led by a vanguard party. No matter how far Althusser later withdrew from many


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of his positions, he would obviously never go this far. But interestingly, Althusser received

the publication of Rancires book not unfavourably and echoed some of its themes later in

the decade, denouncing extreme vanguard practice as reduplicating the bourgeois separation

of knowledge and power.33 In line with the GPs abrogation of this role, in the early 1970s

their members headed out to provincial factories in large numbers in order to agitate from

within the working class. At the same time as their corporeal political engagements required a

renunciation of aloof intellectualism, their theoretical work became curiously detached from

reality they believed revolution to be just around the corner. After the GP wound up in

1974, their anti-authoritarian disposition quickly led to dtournement of Marxist militancy in

general. Leading lights of the GP forged what became known as the new philosophy: a

melange of recycled cold war memes about the brutality of authoritarian ideology and of the

opposite need for a free world a turnaround earning them media praise from the likes of

Timemagazine, which featured their thought on a cover story announcing Marx is Dead.

Badiou later referred to the new philosophers as enacting a Thermidorian reaction

against the subjective sequence of 68. His remarks are important because they shed light on

his alternative pathway from the event, which sought to reconcile the lessons of May with an

ongoing commitment to the revolutionary cause in which these energies were situated

avoiding its dissolution within the ex-post libertarian narrative. The Thermidorian

renegades, Badiou writes, separated activism from every principle and every situation, and

pretended that this activism was only ever connected with the Chinese or Soviet States.

Their disloyalty to the singular novelty of the forms and principles of activism from 1968-

1975 was based on making an irrational connection between these events and the worst

atrocities of state crimes in the socialist states. What is the relation between the Stalinist

camps of the 1930s and the blind and magnificent path that led thousands of young students

to the factories of France? Or between Stalinism and the multiform invention of new

practices of declaration, demonstration and organisation?34 Recalling the era Badiou

observes that amongst the fashionable milieu of the French ultra lefts leadership in the 1970s

in particular, Serge July, Jacques-Alain Miller, Jean-Claude Milner and Andr Glucksman

their abandonment of the revolutionary project and turn to the right was conditioned by

their questionable motivation for involvement in revolutionary politics in the first place.

Badiou cites the response to his inquiries as to why they all so suddenly quit: Because we

understood we were not going to take power. He sees this as the reason for their sudden

withdrawal the activities of the left: a blocked ambition the realization that it was goingto take a great deal of trouble and hard work in a situation that was not all that promising.35


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Badiou also blames the culture of the GP describing how there were a lot of young grand

bourgeoisin the GP, which made it reminiscent of the Russian anarchist movement Theirs

was an adventurist and fallacious style of action, but one that was exciting at the same time, a

politics that was also a fashion, its personal roots in actual fact not very deep.36

These observations help contextualise the difference between the GP and the Maoist

organization Badiou joined in 1970, L'Union des communistes de France marxiste-lniniste

(UCF-ML). The UCF-ML set itself in opposition to both the PCF and GP by arguing for the

need for a Leninist party organisation that would engage and build upon the spontaneity of

the masses. Opposing the communitarianism of the GP, it also argued for a strictly

universalist line in its engagement with immigrant workers.37So when Badiou described 68

as a genuine road-to-Damascus experience38 severing his connection with Althusserianism,

it by no means implied a swing to the kind of Maoism exemplified by the GP. Instead, the

theoretical paradox thenceforth required navigation between a scientific position that

fetishized concepts, and a praxical position that fetishized action and the immediate ideas of

its agents.39 Althusserianism on the one hand; the GPs anarcho-syndicalist sponteneism on

the other. In the Maoism of the UCF-ML Badiou and his comrades called for the

organization of the masses, but the organization of the masses dialectically implied the power

of disorganization. It was this original process of disorganization that unleashed, in an

incredible newness, the possibility of this organization.40 Let us see how these concerns

were reflected in his works of the 1970s and early 1980s.

2.3 Subject of the Break

Badious publications of the 1970s can be considered tributary to his first grand treatise of

1982, Theory of the Subject. Accordingly, in Theory of Contradiction (1975) the emphasis on

Maoist dialectics One splits into Two41 is pursued in order to redress the structuralist

foreclosure of the subject: that is, how can dialectical antagonisms in a situation be thought

without sliding into structural determinism?42In Maos maxim it is right to be rebel against

the reactionaries, Badiou writes, we find expressed the fact that Marxism, prior to being the

full-fledged science of social formation, is the distillate of what rebellion demands: that one

consider it right, that reason be rendered to it. The existence of a science of social formations

bears no interest for the masses unless it reflects and concentrates their real revolutionary

movement.43 The aim is thus to theoretically reflect a communist alternative to both the

PCFs economism on the right and to also counter the temptation of anarchism on the left the latter remaining stuck at the level of the glorious revolt against the repressive state, failing


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to create a lasting displacement of the social order. By following through Badious use of

formalism against deviations on both sides in order to think militant, subjectively induced

change, the break from Althusser can be put in better perspective. A measure of the

persistence of Althusserianism can then be registered against the more egregious ontological

anarchism indicative of the dominant Deleuzian inspired alternatives. Or, as Badiou puts it in

1982, we must quickly ground all this in the ordered soil of structures, unless we let

ourselves evaporate into the metaphysics of desire, that is, the substantial and nomadic

assumption of the outplace.44

For working through the paradoxes of order and change, Theory of the Subject

promulgates the provocatively anti-Althusserian gesture of Theory of Contradiction by

locating conceptual resources within Hegelian dialectics. In keeping with the Maoist splitting

of the dialectic Badiou bifurcates his structural (note, not structuralist) dialectic into two

dialectically conjoined, yet split, operations: one taking the place of the objective, the other

the force of the subjective. His investigation thereby aims at conceiving how a militant,

subjective intervention can apply sufficient force to reconfigure its previously objective place

(the strategy of the UCF-ML figured in ontology). And equally, lest two compact to one again

in the Stalinist party-state, how can the logic of places and the logic of forces be articulated

without fusion?45 If in this approach one can perceive something like Badious analysis of

how experimentation on model semantics can dismember their logical syntax (see 2.1)

indeed, Badiou pre-emptively counters the claim that this is a [dialectical] syntax of little

interest from the moment that the semantics of it [are] forced46it points to continuities with

the Althusserian epistemic break. Because as much as the analysis of structuralist objectivity

is inverted by Badiou to the place of the subjective, this is only accomplished through their

(structured) dialectic, touching upon the enduring rational kernel between Althussers

vanishing cause of structural causality and Badious later explicit formalisations inB&E.

Like Althusser, Badious structural dialectic differentiates the One and whole(analogously to the structuralist dialectical replacement of totality with whole). But unlike

Althusser, Badiou seeks to find the subjective channel for the absent cause of novel breaks.

Thus, the absent cause is always reintroduced into the whole of its effect. This is a major

theorem of the structural dialectic: in order for the causality of lack to exert itself, all terms

must be split.47 The difference, let us emphasize once more, therefore rests in Badious

inversion to a theory of the subject where political change is disentangled from its dependence

upon scientific analysis of objective conditions in order to act politically, in favour of a formal


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discourse of subjective intervention. Bosteels seizes the crux of Theory of the Subjects

dialectic of the subjective and the objective:

Between Althusser and Badiou, in fact, we might say that a decisive reversal of

perspective takes place whereby the absent cause, instead of providing us with

the master key to unlock the structural causality of overdetermination, becomes

synonymous with the transformative potential of an event. The economical

instance, which for Althusser serves as the principle example of a cause that

vanishes into the totality of its effects, thus continues to be present as it were

virtually in Badious doctrine of the event, except that the emphasis now shifts

away from the structural dimension towards the rarity of a subjective

intervention.48

Even as political economy is displaced by Badious emphasis on the application of subjective

force, his use of abstraction to think the correct line on the subjective level marks a form of

succession with the scientific Marxist and Althusserian traditions. Likewise, Badious

dialectics are configured so not to fall into the parlous teleological circularities to which

Althussers epistemology took exception. HegelsLogic is materialist for Badiou only insofar

as it posits no simple contradiction in alienation so that the end would be contained in the

beginning, or vice versa.49 He locates the dialectical split (scission) in a fundamental operation

repeated throughout the Logic, which is glossed over and hidden by virtue of its sheer

ubiquity. This is how Badiou rescues a materialist dialectic from Hegel; the materialist

dialectic periodizes, while the other one makes circles.50 Infinitely recursive, hence properly

periodizing dialectics (permitting no teleology), follow from the positing of the something and

the something-other. The two terms represent not the simple contradiction/union of opposites

but rather a gap between being and being-placed similar to Heideggers demarcation of theontological and the ontic.51 The syntax and semantics are laid out with deceptive simplicity:

Apure being

Apbeing-placed

A = (AAp)operation of scission

From this hidden Hegelian operation where One splits into Two according to the placement of

pure being, Badiou demonstrates the possibility of deriving an unexpectedly complex

differentiation of the pathways for change and its impediments. Novelty is forged whenplaced-being acts to determine being itself Ap(A). Badiou puts this in contrast to the


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dialectical relapse (Ap(Ap) = P) of PCF revisionism, in which the communist project of

abolishing the space in which a proletariat can exist is replaced by a static opposition between

bourgeoisie and proletariat, each sustaining one another. This too is the principle of

structuralism in all its forms.52

But yet again the parallel with Althusser asserts itself: for where in high

Althusserianism the epistemic break of science from ideology was thought with respect to

sciences release of new truths against ideology as repetition, the same wager which will

continue to underwrite the ontology ofB&E mandates that every rightness and every

justice are, in principle, novelties; and that everything that repeats itself is invariably unjust

and inexact.53 The event issues from the qualitative concentration of subjective force to

reconfigure the status quo in a genuinely new formation. With the concentration of force

necessary for destroying the existing structures of the old order and discharging novelty

criteria for periodization [...are] required in terms of divergence, between the opposition

place/force and the opposition objective/subjective, for the clear arrangement of the paths of

the subject.54 What is this if it is not a reinvention of structural formalism with its attention

fixed on the subjective side of the equation?

The previous section argued that Badious idea of the event in many regards stays

more loyal to the original programme of Althusserian structural Marxism than Althusser

himself did in his aleatory materialist writings of the 1980s. There is no better demonstration

of this than their respective reflections on Epicurus and the privileged term in the schema of

void, atom and clinamen. For whereas Althusser in Underground Current attempts to push

his aleatory paradigm to its limit by locating the source of all change in the void conjoint to

his own ambitions to empty out (void) philosophy Badiou stays much closer to early

Althusserian project by isolating the necessity of contingency in the structural dialectic

between the terms. Badiou singularly stresses that the void cannot be constitutive of the

chance ordering of a world since it is in absolute difference to atoms. The difference is so

strong between void and atoms that nothing happens. Rather, both the void enabling the

atomic rain, and the clinamen which provides a deviation necessary for anything to assemble

into a world, represent vanishing terms. The clinamen is the absent cause whose effect is the

retroactive effacement of the cause because after the collision of the atoms the clinamen no

longer has anything to do with what happens and it is in vain that you would search the world

for an atom marked by the stigmata of deviation. All atoms are identical, the one affected by

the clinamen no longer bears any trace of it.55

Hence, Chance is a key concept in anystructural dialectic... For us, it is true that history is the fortune of the event, never to be


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confused with politics, which is forced subjective rationality. It is fully in keeping with

Marxism to say that history is the chance of political necessity.56 In contrast, by laying the

stress on chance without his corresponding earlier criteria for differentiating events from non-

events Althussers later writings abdicate thinking the rationality necessary to realise lasting

change by instead placing responsibility at the feet of the voids self sufficient production of

the new.

Although writing before Althusser, and long before Althussers aleatory materialist

writings would be published, Badiou could be directly rejoining Althusser when he writes In

the structural dialectic, the qualitative difference in which force emerges is not a nothingness.

It is a disappearance whose effect is the Whole from which it has disappeared.57 Neither the

void nor the clinamen are productive of change, because identifying them as subject seeks to

do away with the force needed to act upon chance events. In a remark that is crucially

important to cite for redressing misreadings of Badious later theory of the event as a miracle

summoned out of an omnipotent ontological void, Badiou derides the fixation on the clinamen

as the source of change (rather than a mere pre-condition) in consideration of the implication

that this requires an outplace that verges on the m iraculous, in opposition both to the

monotonous fall of atoms, of which the void is the cause, and to the laws that will govern,

subsequent to the clinamen, the composition of the Whole.58 No more need be said regarding

the persistence of the Althusserian idea of the absent cause of change in Badious theory of

the subject. A few more words are nevertheless still necessary on Badious references to

mathematics in the text, which prefigure the ontologisation of mathematics in B&Eto think a

new conception of the subject.

Badious attempted reconciliation of the ontological predominance of the Two with

the materialist, monist thesis that only matter exists is the site of the theoretical encounter

where the anticipation of the function mathematics will be asked to perform in his later works

can be found. Like Althusser, Badiou presents materialism as an ontological quarrel

exceeding the 19thcentury lineage of Marx, Engels and Darwin in turning the world on its

feet after the idealism of Hegel and Berkeley. In his reckoning, materialism is an axiomatic

position stretching back to Lucretius: There is the One is the monist thesis about being, for

which matter in reality is only the signifier. Every materialism posits the primitive unicity

of being, with the implication that its intimate constitution requires only one name. Matter is

this name.59 Drawing upon the Marxist inversion of Hegelian idealism to materialism as a

demonstration of the inadequacy of the reductionist materialist procedure insofar as itdenies thoughts role in renouncing its distinction from matter Badiou seeks to show the


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limits of what he calls the soothing vulgarity of yester-years materialisms.60 As Salanskis

also frames the materialist paradox: what the materialist calls matter must mean something

more determinate than being, in order for its annexation of the beings that ideality lays

claim to make sense.61Thus implied is the question of the status of mathematical objects in

the doctrine of materialism.

We posit that materialism exists in the recognition of two theses, one of which

names being and the other its order an order whose being lies in a vanishing

nominal overhaul:

- The thesis of identity: being is exclusively matter- The thesis of primacy: matter precedes thought, and not the other way

around.62

These theses are, of course, precisely Althussers from Lenin and Philosophy. The key point

that matter precedes thought does not, however, mean according ontological pre -eminence

to matter:

Primacy here does not mean ontological hierarchy, or pre-eminence, since

there exists only matter. It is nothing like the Platonist superiority of the

intelligible, subject to inversion. Primacy means that, in the process of

knowledge that founds the thesis of identity, the eclipse of thought stands under

the law of being, and not under that of thought itself.

The two theses of materialism give structure to the metaphorical

division of the process of knowledge. Therein lies the real efficacy of their

opposition.63

The materialist Two is metaphorical. Thus he can say, whilst maintaining the monism of

materialism, that materialism is dialectical is an understatement. It is entirely traversed by

the dialecticity of the dialectic, its double occurrence as structure and as history.64 Badiou

continues to draw an analogy between the dialectic of asymptote and reflection and algebra

and topology. The fact that despite the best efforts of 20th century mathematicians algebra

and set theory have proved irreducible to one another is considered metaphorically equivalent

to the procedure of materialism in attempting to assert that only matter exists, therebyoccluding the paradoxical role of thought in the statement. The Two matter, thought;


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asymptote, reflection; algebra and topology are more than the sum of their parts, they

operate to form an enigmatic excess over one another. It is here that in Theory of the Subject

Badiou moves closest to his ontology inB&E, pivoting on the power-sets excess of inclusion

over belonging. Also anticipating another crucial idea for the later text within the same

problematic: It is well known that the notion of the set of all sets is inconsistent. Similarly,

the concept of an integral material totality is only a porous fantasy of materialism, its

dejection turned back into idealism.65 Badiou uses the formal irresolution of algebra and set

theory to demonstrate the necessity of a subject a demand B&Ewill answer to exacting

mathematical standards.

In order not overstate the role mathematics plays in Theory of the Subject it is worth

observing that unlike inB&Eit is accorded no privileged ontological role; drawing on Lacan

it remains simply a precise tool of political formalisation. In its most provocative and

memorable formulation: Precision put into the razor of the Marxist barber, mathematics is

that unalterable blade with which one ends up bleeding the pigs to death. 66 The next section

will examine the consequences of the ontologisation of mathematics for Badious politics in

the context of his changing conceptions of the temporality and relevant forms of political

organization. Approaching the crux of this chapter, both the decision to equate ontology with

the forbidding formal discipline of mathematics, and the complex philosophical demarcation

of ontological and non-ontological situations will sharpen the question of the subject and to

what extent the existence of a subject requires a theorist of subjectivity (a Subject of subjects)

to provide impetus for change?

2.4 On the Subject of Being and Event

Badious 1988 magnum opus takes to newly baroque heights his formalisms of the subjective

procedures of order and change. But let us begin by reflecting upon the conjoined political

and philosophical shifts separating the text from its predecessor. Significant in this respect is

the fact that Badiou justifies his mathematical turn in a way departing from the politically

determined discourse of Theory of the Subject. On the corresponding level of his personal

political commitments this move coincided with the formation of the post-Leninist and post-

Maoist LOrganisation Politique a group established with former UCF-ML comrades in

1985 to pursue politics without a party. In no unclear terms the gap between philosophy and

politics formerly fused to at least some degree by intellectuals operating within political

parties, including even the more experimental UCF-MLwas widened both at the theoreticaland praxical level. So whereas in Theory of the Subjectevery subject was considered political


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(including, it is safe to assume, the philosophical), now discrete practices in the new lingo,

the four truth procedures: scientific, artistic, political, and amorous significantly exclude

philosophy as a truth bearing discourse.67 The ascription of philosophy qua philosophy as a

discourse subservient to the demands of these truth procedures should thus be seen to reflect a

subtly changing sense of the political role of philosophers. For by circumscribing philosophy

to a metaontological station in thinking the subjective procedures of truth creating practices

themselves dependent upon, and constitutive of, truths released by events Badiou at once

appears to limit philosophys scope but at the same time grants it an ability to make global

judgements on the conditions and forms of change.

Whilst this gesture appears to mark an even sharper discontinuity within the

Althusserian tradition than the Maoist formalisms of subjectivity from the 1970s and early

80s, many commentators on Badious early period that it in fact argue continues to resonate

with Althusserian themes. Luke Zachary Fraser, for one, identifies the way non-philosophical

truth procedures create splits in the regime of knowledge as the Badiouian successor to the

Althusserian epistemological break. And also as a mark of continuity from the 1970s period,

Bosteels describes how the dialectical rapport between truth and knowledge is precisely the

place of inscription of most of Badious debts to Maoism.68 But to gauge a more accurate

register of the continuity and discontinuity of this turn viz. Althusserianism, it is informative

to compare Badious mid-1980s change of direction to both the pre and post corrections of

theoreticism, which split Althussers corpus at 1967. Relevant for our present discussion is

how Althussers post-67 swing towards conceiving philosophy as class struggle in theory

compacted philosophys reflections on different practices to a singularly political register; but

by so doing continued to stress the political necessity of theoretical work. In this sense

Badious new conception of the subjects of different practices marks a return to the pre-67

high Althusserian programme of thinking finite, discrete practices conditioning one anothers

development through epistemological breaks. Yet in another sense, inasmuch as Badiousdeliberately excludes philosophy as a truth procedure, he also affirms Althussers post-67

correction of theoreticism from Lenin and Philosophy onwards, whereby philosophy was

posited as having no object of its own. If there is no strict homology with any one period of

Althusserianism, then, it nevertheless establishes Badious continuing negotiation of different

tendencies within the overall problematic. Accordingly, even if the prioritization of the

subjective in Theory of the Subject is further radicalised by Being and Events total

subtraction from any objective ground history, economics, etc. in favour of ametaontological theory of subjectivity (the faithful forcing of truths out inconsistencies


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manifest at particular sites) it will still have a hard time defending the claim that this

conceptualisation of subjectivity does not in fact continue to endow the philosopher with some

sort of conceptual knowledge to judge, and indeed, effect, political truth procedures.

The take home point from this comparison with Althusser is that Badious 1988

desuturing of philosophy from politics is intimately tied to rethinking of the role of

philosophers with respect to actual political practice. As such, one should turn to the

reconception of the subject to understand the philosophical-political reciprocity at work here.

Within the justificatory preamble to B&E the fact that Badiou lists no overt political

conditions should not be taken to naively imply that this is a lack without symptomatic

significance. Two of these conditions are:

1. A third epoch of science. Not demonstrative mathematics, nor the mathematization ofphysics, but a split, through which the very nature of the base of mathematical

rationality reveals itself, as does the character of the decision of thought which

establishes it.69

2. A second epoch of the subject. A subject not as a founding centre of thought as in theCartesian tradition; one which can only be thought in terms of its role in processes

with rigorous conditions.

Or, in short, conditions which combined pose the question: given pure mathematics being the

science of the being, how is a subject possible? A question asked in order to correct Theory

of the Subjects politically determined presupposition that there was some

subjectivization.70 The subject will thenceforth be proved through an ontological decision to

affirm mathematical rigour against Heideggerian romanticism a gesture appearing to mark

an extension of the Althusserian project by promulgating the spirit of French scientific

rationalism.71 However, in order that conceiving the subject through this intellectually

aristocratic practice not lend itself to elevated notions of Platonic philosopher kings whose

mathematical abilities endow them with unique qualifications for understanding existence,

order and the subjects for change the concept of the event, as a fully extra-ontological,

subjectively-named happening, works to disqualify any mathematical premonitions within

concrete situations, restricting its gaze only to the most abstract ontological reflections. As

Badiou would put it explicitly a decade after the book was published: While philosophy is all

about identifying what ontology is in an endlessly reviewed process, it is also the general

theory of the eventand it is no doubt a special theory too... Philosophy is the theory of what

is strictly impossible for mathematics.72

The event serves, within Badious subtractiveontology, precisely to philosophically sever the claim of philosophers to predict, organise, and


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delimit the right revolutionary moment within non-ontological situations, as the former

structuralists of the PCF were alleged to foolhardily wished during 68. The event is perfectly

egalitarian with respect to intellectual authority insofar as when it breaks out it provides a

happening that comes seemingly from nowhere it is a pure chance supplement to the

manifold situation for which it is an event.73 No vanguard party or small cadre or

professional activists, nor the state, NGOS or thinktanks, could predict its explosion within a

situation. Political discipline is rather shifted to the procedures taking place after the fact of

the emergence of aleatory inconsistencies in the regime of presentation. Only once the event

disrupts the seeming stability and completeness of an order of knowledge lies the possibility

for a subject.

But as we will see, the net result retains a disavowed role for the philosopher as what

could be described as the Subject of subjects in making judgements on what counts as a true

eventan imperative that troubled Badiou enough to claim one of the loose ends ofB&Ewas

philosophically distinguish[ing] [an] event from an important fact or from a becoming.74 By

the later meditations, too, the intellectual intrusions of the philosopher metaontologist into

non-philosophical truth procedures will deepen when Cohens forcing technique is used to

prove the freedom of subjective intervention to extend the situation. This is because within

Cohens constructible ground model of set theory, the excess of inclusion over belonging is

reduced to a minimum by the models cardinal transitivity. The structural conditions to

provide the possibility of an event are lost; and therewith the egalitarian, pre-reflective

happening providing an impetus for change within any non-ontological situation for non-

philosophical subjects. The upshot, I hope to demonstrate, is that true change requires the

philosophical metaontologist to suggest the possibility of transformation.

Rather than launch straight into the complex and technical architecture of Badious

treatise to deduce the above points, let us, however, start by paying attention to the

Introduction in order to sharpen our appreciation of why the category of the event determines

the choice to identify mathematics with ontology and, in particular, privileging of set theory.

2.5 Mathematics = ontology

Badiou emphasizes that establishing the philosophical decision identifying mathematics with

ontology is in no way the books goal; instead this book founds a doctrine [...that] institutes

the subject, not as support or origin, but as a fragment of the process of a truth.75 Yet

curiously few readings of the book seemed to have paid much attention to Badious professedintention to establish a new theory of the subject. In an edited collection of essays by all the


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leading lights of continental philosophy, none address Badious theory of the subject per se.

Adrian Johnston, one of the most prolific commentators on Badious work, places the

treatises lex causae in legislation over the Parmenedian injunction to decide between the One

or the Many. Regardless of Badiousintentions, Ray Brassier, sees Badious accomplishment

almost entirely in terms of the way the opening meditations establish equality between

mathematics and ontology.76 Brassier even goes so far to airbrush out Badious

reconceptualisation of the subject, isolating only the way that the identification of axiomatic

set theory with the long sought for science of being qua being... affirms a fidelity to the

Cantor-event.77Apart from Peter Hallwards appropriately titledBadiou: A Subject to Truth,

most readers understate the centrality of rethinking the subject for the choice to identify the

discourse of Being with the elaboration of set theory across the 20th century in turn often

downplaying the freedom of philosophical metaontology to determine its own conditions and

its choice of an appropriate ontology. A few words therefore appear necessary on the

compulsions lying behind Badious equation of ontology with mathematics in light our

emphasis on how the decision marshals philosophy towards a new theory of the subject. This

involves situating the fidelity of Badiou to Albert Lautmans conception of how mathematics

serves ontological questions. And this, in turn, for the purpose of understanding Being and

Events use of Zermelo-Fraenkel set theory to establish: (1) a new theory of the subject, and

(2) the philosophical metaontologists separation from the truth procedures arising from non -

ontological situations.

Badious ontological Platonism asserts that Being is inconsistent multiplicity. In the

phenomenal world of particular things this multiplicity cannot be perceived or intuited: not

empirically, nor through any mystical apprehension. Philosophical questions are best

approached through the formal thought of mathematics, free from linguistic contamination or

empiricist temptations. The world we inhabit is a world of specific things, and if we want to

think Being in its multiplicity we have to subtract from all these to thinkpresentation as such:

that is, the presentational form of any-thing; and conversely, what presentation excludes as a

necessity i.e. Being, the inconsistent multiple which is not. With its very abstract rigour

mathematical discourse thinks presentation, and nothing more. Badious philosophical meta-

ontology78 (thinking the presentation of presentation) is thus not a thesis about the world

but about discourse.79 From where could Badiou have drawn inspiration for this idea? There

are few references provided by the text, but amongst the thin smattering Albert Lautmans (c.19081944) name recurs. Lautmans writings are nothing less than admirable and what I owe


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to them, Badiou admits, even in the very foundational intuitions for this book, is

immeasurable.80

Lautman was a French philosopher of mathematics with a working relationship with

the mathematician Jean Cavaills (c. 1903-1944), both killed in the same year by the Nazis

because of their involvement in the French resistance movement. Lautman can be considered

part of the movement of the French rationalist philosophy of science; he cited Bachelard and

emphasized the creative development of mathematics against Russells logicism. In The

Concept of Model one can already note an affinity with Lautman in Badious model theoretic

critique of logical positivism. By placing logic on the same level as other forms of

mathematics in the order of genesis of new structures within mathematics, Zamalea observes

how Lautman prefigures ... our conception of logic as it arises from model theory, in which a

logic is not only determined, but even defined ( la Lindstrm) by an adequate collection of

structures.81 With respect to the idea prevalent within logicism that a rich enough logical or

axiomatic essence could account for the entire existence of structures of mathematics,

Lautman counters that we always see a mode of structuration of a basic domain interpretable

in terms of existence for certain new entities, functions, transformations, numbers, that the

structure of a domain thus appears to perform.82 Yet as Badiou recalls in an interview with

Tzuchien Tho, at the time of writing the Concept of the Model Lautmans works were largely

unavailable; only with their publication in the 1970s did he gain any contact with the texts. 83

There should be no surprise, then, that Lautmans speculative contribution on the nature of

mathematics can more evidently be seen to inform Badious identification of mathematics as

ontology in the 1980s. Taking inspiration from a curiously unanthropomorphic reading of

Heidegger, Lautmans participatory Platonism conceives mathematics in relation to

philosophical metaphysics within a tripartite scheme. Dialectical questions whole/part,

continuity/discontinuity, etc. give rise to questions of the why, to which Ideas serve to

form connections to attempt to answer them. Mathematics then fills in these ideas with more

concrete, particular and precise ideas. The anteriority of dialectical questions to mathematical

development permits the posterior recovery of ideas from their mathematical exploration.

While the mathematical relations describe the connections that in fact exist

between distinct mathematical entities, the Ideas of dialectical relations are

not assertive of any connection whatsoever that in fact exists between

notions. Insofar as posed questions, they only constitute a problematicrelative to the possible situations of entities... the Ideas that constitute this


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problematic are characterized by an essential insufficiency, and it is yet once

again in this effort to complete understanding of the Idea, that more concrete

notions are seen to appear relative to the entity, that is, true mathematical

theories.84

Easily discernable are the similarities to Badious conception of mathematical Platonism

where all that we can know, and can ever know of being qua being, is set out, through the

meditation of a theory of pure multiplicity by the historical discursively of mathematics.85

This goes to explain why the Parmenedian dialectic of the One inaugurates the meditational

procession ofB&E. In another way, too, it clarifies the relationship of Badious philosophy to

the work of pure mathematicians, who he positions as working ontologists. In Badious view

there is no spontaneous philosophy of the mathematicians worth guarding in the same way

that Althusser insisted scientists need to be protected against the incursions of idealism. As he

would later carefully delineate the point: although mathematicians spontaneous philosophy

is Platonism, unlike his own Platonism it is an erroneous conception based on Aristotelian

tenets, whereby the ideal spectacle of its results follow from fictive activiation. 86

Platonism of this Gdelian kind he believes is a bit too dogmatic, and especially so when

contrasted against Lautmanian Platonism: that is, a Platonism of participation of the

sensible in the ideal, centred on the dialectic of ideas in the history of mathematics. 87

If mathematicians philosophy of their practice is not to be trusted, neither should their

spontaneous practice be credited with immediately releasing philosophical insight. On the

contrary, the trust working mathematicians place in solving specific problems is in principle

unproductive when it comes to any rigorous description of the generic essence of their

operations88 that is, to extracting the metaontological consequences of the ideas

mathematics works on with great exactitude. In this regard, a mathematician like Paul Cohen

would likely assume heroic stature for Badiou insofar as he renounced any philosophic

pretensions and gained his advances in the field of independence proofs by desuturing the

inhibitions of Gdelian Platonism from set theory to see how, in Cohens words, ideas which

at first seemed merely philosophical could actually be made into precise mathematics. 89

Similarly, Cohens scathing comments on those rare moments in history where philosophers

seek to insert themselves within mathematical practice to intra-mathematically clarify

philosophical questions would probably also gain Badious approval. In this vein, Cohen

describes Russell and Whiteheads Principia Mathematicaas totally unreadable, and in myopinion of very little interest.90 Mutatis mutandis, ideas and techniques that seem only


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mathematical (without any attempt to imbue them with ontological significance) can then be

transcribed backwards, la Lautman, to inform philosophical questions. It follows that

Badious focus on set theory as an ontological discourse is not reducible to simply following

the cutting edge practice or the philosophy of the unconscious ontologists; it is rather a site for

the extra-mathematical composition of the multiple conditions of an era. Badiou readily

admits that by the time of writing in 1988 set theory was no longer considered the most

fundamental or exciting field of mathematical development. His choice of set theoretic

ontology is instead a philosophical attempt to weld the post-Cantorian era of science with a

new idea of the subject.91 Although the imperative is for philosophy to stay broadly up to date

with the mathematical resources it draws upon, there is certainly room to manoeuvre

depending upon the philosophical questions at hand, which philosophers are free to determine

themselves. This observation provides an important corrective to the common beginners

misreading of Badiou which believes that just because set theory was considered foundational

for large parts of the 20th century, ergo Badious specification of it as the ontological

discourse must be transitive with its status within the mathematics community. Following this

misattribution, the existence of, and arguably superior rival for, the foundational prize within

contemporary mathematics category theory is then taken to expose the bad faith of the

irreducibly philosophical identification with set theory. But these objections are already

anticipated by Badious careful justifications for adopting set theory. Admittedly, Badious

own shift away from ontological theorising of the subject in later years exemplified by the

section on the typology of subjects in theLogics of Worlds, disjoint from the topological heart

of the Greater Logic has served to lend the impression that foundational (intra-

mathematical) considerations lie behind his allegiance to set theorys articulation of being qua

being. Occasionally, he has even seemed to slide towards this position when, for example, he

admits that I had to come to terms with Set Theorys rival theory regarding mathematical

foundations: category theory.92 But at least on the terrain ofB&Es justification of its use of

mathematics, following how developments in set theory lead towards a metaontology of the

subject is quite unambiguous: from the opening remarks of the Introduction to the way the

Meditations culminate in an interpretation of Paul Cohens forcing technique. That said, let

our own judgement on Badious success stand or fall with whether this new idea of the subject

maintains or undermines the understudy role Badiou claims to allot the philosopher in merely

drawing out the metaontological conclusions of extra-philosophical practices. So that no prior

knowledge of the text is assumed, this will involve a rather arduous, if unavoidable,


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exposition of the main sections of the book, before arriving at the crux of the argument with

the section dealing with Cohens forcing technique.

***

The axioms of Zermelo-Fraenkel (ZF) set theory provide the tripartite specifications of Being,

Event and Subjective Intervention for Badious mathematical ontology. These moments are

chronologically synchronous with the development of set theorys axioms and techniques

across the 20th century, from Zermelo to Paul Cohen. The axioms of Being are referenced to

the less contentious early 20th century axioms, in contrast to the more controversial additions

later on such as to the axiom of choice (forming ZFC), Gdels proof of the consistency of

constructability, and leading up to Cohens early 1960s method of forcing. Given the limited

space to present Being and Events dense metaontological reading of the development of set

theory, ahead of the exposition the table below summarises the three main movements of the

text and their relation to set theorys axioms, the mathematical ideas they embody, and their

philosophical interpretations divided in this way to reflect how Badious take on

mathematics reflects Lautmans. In the paragraphs which follow I rapidly abridge the main

moments of the books mathematical ontology in order to take us as quickly as possible to the

theory of the event and the subject, where the greatest attention will be fixed. Which is to say,

to take us rapidly to two crucial sections: the partitive excess of inclusion over belonging in

any structured presentation (the vanishing structural cause of the event thought through the

Cantor-Easton theorem), and the subjects role in forcing truth out of the situation (Cohens

theory of forcing).


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Architectural map ofBeing and EventMain movements and their ZF-C axioms,mathematical and philosophical Ideas

Axiom Mathematical Idea Philosophical Idea

Being{

Separation Sets existence is given.

The language separates

sets relations.

No direct access to Being.

Determines sets ontic existence.

Power-set The power-set p(a) of

any set (a) has more

parts; its cardinality is

greater.

Theorem of excess: there is at least

one element included in the state

that does not belong to any

situation.

Event{

Foundation Sets cannot belong to

themselves: ~(a a).

The event is non-ontolologial: its

self-belonging is prohibited by set

theory.

Intervention

(Subject) {Constructability All of set theory can be

rendered in a

constructible universe.

Axiom of foundation redundant;

axiom of choice more a theorem of

well ordering. All excess banished.

Constructability is the form of

knowledge.

Infinity There exist infinite sets. The actual infinite is decided.

Infinite sets necessary for axiom of

choice, for unnameable multiples.

Choice A function of an

element of any set can

be decided to represent

it.

Form of intervention. Arbitrary

choice of an unnameable element.

(N/A) Forcing to construct the

generic set: G. Creatinga generic extension of

the ground model,

where theorems about

the indiscernable can be

made verifiable or not.

Form of the generic . Theory of

the Subject to truth.

a. BeingThe absence of a definition of a set within the ZF axioms is the crucial starting point for

understanding Badious ontology since it immediately rules out any primordial definien of


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Being.93 Axiomatic set theory is rather structured presentation which prohibits the

presentation of Being so to not fall to pieces under the weight of its own inconsistencies

(large paradoxical sets, such as those exposed by Russells paradox). There is t herefore a

double move involved in Badious interpretation of Being within axiomatic set theory. On the

one hand, the axiom of separation, whereby all sets are constructed out of other sets,

prescribes a mathematical language foreclosing any direct access to Being, because every

existent is already assumed. Sets are simply given; the language of presentation (set theory)

merely separates out existents and structures their relations. On the other hand, in any

situation other than ontology the inconsistent multiple (the paradoxes the axiomatic is

designed to suppress) are equated with Being, because it is ruled out from presentation within

any structure. In a Heideggerian turn of phrase: the ontic givenness of consistent sets is taken

to imply an ontology of inconsistent Being. However, the operation by which structure

renders inconsistent Being invisible is retrospectively graspable by ontology; its outlawed

inconsistency may be a nothing within any situation, but for ontology it is not a non-being94

(Badiou opposes this distinction to structuralism, which conflates the two). The inability

within any structured situation to pre-emptively identity this nothing within the structure is

one of the primitive conditions for the event.

The imperceptible, inconsistent nothing within any situation Badiou terms the void,

and following set theorists inscription of the empty set he represents it with the symbol to

reinforce that this nothing is strictly unpresentable except as a lack. Ontology is only a theory

of the void, because if ontology presented the other terms in its presentation of presentation

it would put the void on the same level of structured presentation alongside every other

inscription; ontology would collapse to mere presentation of structure rather than delving

deeper into the unstructured Being of structure.95 The axiom of the powerset opens up a

distinction for ontology to grasp this non-presentable existence of the void. The axiom

prescribes the absolute excess of inclusion over belonging . Belonging is the count

forming the structure of the presentation of a situation, whereas inclusion operates as the

meta-structure, or the state of the situation the count of the multiples of the multiples (or,

sets of sets) forming a re-presentation greater than the initial multiples. In a play on words

designed to establish affinity with the Marxist revolutionary tradition, the power-set is

described as a representational state. Marxist thought relates the State directly to sub-

multiples rather than to terms of the situation By consequence, as a political programme,

the Marxist proposes the revolutionary suppression of the State; thus the end of representation

and the universality of simple presentation.96


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The excess of representational inclusion over presentational belonging a dialectic

which is knotted together97 lays the road to Badious new theory of the subject. It is a

significant point to reflect upon because it undermines some critical readings of Badious

theory in terms of a quasi-Kantian division between noumenon and phenomenon 98

(notwithstanding the fact that there is not a trace of phenomenology here). Albeit true that

Badiou maintains two levels in his inconsistent-Being/consistent-presentation ontology, with

only the latter perceptible for inhabitants of a situation, because the void is universally

included99 within meta-structure/re-presentation (the power-set) its presence as an empty set

(as a nothing {}) is implicated in the gap between sets belonging and included in a situation.

What could have been a potentially static juxtaposition of ontological inconsistent multiplicity

with structured, consistent presentation possesses a dialectical inflection from the initial

axioms of ZF onwards.

Badious distinction between nature and historical events clarifies the above point in

the assertionand this seems to be nothing more than an assumption based on a very classical

philosophical Idea of Nature100 that natural multiples are ordinals.101 These sets

transitivity from one to the other is premised on the maximal coincidence of belonging and

inclusion: there is no ordinal included which also does not also belong to another ordinal.

With the atomism implicated by the transitivity of ordinalsa halting point for the properties

of ordinals beneath which there is no more fundamental substratum the void is universally

included but has no dynamic to leave a mark in the gap between the meta-structure of

inclusion (the power-set) and the structure of belonging (presentational set). Nature is in static

equilibrium because of its ordinal numerary structure, hence leaves no room for events and

subjects. Badiou concludes that it is thus true that nature and number are substitutable.102

Naturalisation should not, however, be regarded as solely referring to the stability of the non-

human order; Badiou also sees the re-statification following an event as a process of

normalisation/naturalisation. Historical events are not demarked by the human as opposed to

the non-human; natural stability is the norm of human history too only the singular

interrup

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