Key Theories of Alain Badiou

Alain Badiou (b. 1937) was born in Rabat, Morocco. With a father an agrégé, like himself, in philosophy, and a mother agre´ge´e in French, Badiou is also a product of the E´ cole Normale Superieure (ENS) (rue d’Ulm). It was at the Ecole in the 1950s that he came under the influence of Louis Althusser. From Althusser, Badiou came to appreciate that philosophy has no object and is not a discourse about the whole, or totality, but is a specific discourse amongst others. Badiou’s other ‘masters’ (the term is Badiou’s) are: Jean-Paul Sartre, from whom he learnt the importance of existence as the domain of choice and decision-making, and Jacques Lacan who, in Badiou’s eyes, demonstrated that the subject is axiomatic (a product of truth, not of interpretation). In the 1960s at the E´ cole, Badiou was in fact a member of the famous Lacanian study group based around the journal, Cahiers pour l’Analyse, and published articles there on mathematical topics. He taught at the University of Paris VIII (Vincennes-Saint Denis) from 1969 until 1999, when he returned to ENS as the Chaire of the philosophy department. He continues to teach a popular seminar at the College International de Philosophie.


Always the political activist (influenced by his parents) much of Badiou’s life has been shaped by his dedication to the consequences of the May 1968 revolt in Paris. Not only the student revolt of May 1968, but also the Algerian war and the 1960s general strike in Belgium shaped Badiou’s political orientation. Arriving in Paris in 1956, Badiou experienced at first hand the violent methods used by the French police to quell the demonstrations against the war. Later, Badiou was sent to Belgium as a journalist to cover the strike and talk with miners and others, experiencing at first hand the plight of the workers. Since those days, he has refused to give up, like so many others, on the struggle to change society, and argues that the central maxim of philosophy is that equality should prevail. Just what Badiou means by equality is another matter.

Knowledge and Truth

Badiou’s central proposition is that knowledge does not give access to truth. Truth is a ‘hole’ in knowledge, even if being and knowledge go together. Truth here is the truth of the event as that which changes the basic parameters of how the world is known and understood. In addition, the approach Badiou uses to reveal his notions of being, truth and event are as much, or even more, mathematical than philosophical.

The collection of his essays, Infinite Thought (2003a), sets out, in schematic form, a number of the key themes of Badiou’s philosophical stance, a stance that re-joins Jean-Paul Sartre’s philosophie engagee: a philosophy of commitment, or more literally: a philosophy engaged with the world. For Badiou, the flaw in contemporary philosophy, in its tripartite orientations of Hermeneutics, Analytical and Postmodern philosophy, is that the ‘axioms’ it follows – truth is impossible; language is the site of philosophical thinking – are inadequate for dealing with philosophy’s historical mission to be concerned with the universal, revolt, logic and risk. A concern for truth is implicit within this mission. Without it, philosophy cannot meaningfully intervene in world affairs and so contribute to changing the world, a world ‘subordinated to the merchandising of money and information’ (Badiou 2003a: 48). In effect, Badiou is worried about the actual political impotence of contemporary philosophy in its three orientations, and, at the same time, about it failing in its mission to be universally transmissible (2003a: 51). Moreover, in light of the speed at which things happen in the contemporary world (also highlighted by Virilio), philosophy must act as a force for retardation: philosophical thought is leisurely; revolt today must as a consequence be leisurely.

In contrast to the human sciences, which are primarily concerned with statistical averages, philosophy is concerned with singularity. It is also concerned with rationality – not the rationality of the past, but with a revised rationality that is concerned with consolidating intellectual strength to counter fundamentalist passions. The violence of the contemporary world and, more broadly, what happens in it, means that philosophy must also be a philosophy of the event. Philosophy must be able to confront and intervene in world events as ‘the singularity of what happens’. Truth, as something new, is to be distinguished from knowledge, which is the knowledge of being. Justice and equality are not the result of true definitions, nor are they empirically demonstrable; they are rather part of thought itself – are a way of thinking.

The Multiple, the Event, Fidelity, Mathematics

In his overall trajectory, Badiou agrees with Lacanian psychoanalysis, which argues that truth and knowledge are quite distinct and that truth is founded on the void (Badiou 2003a: 86). However, Badiou’s view of this void is mathematical. The presentation of it can no longer be left to the province of intuition. Badiou’s fullest elaboration of the mathematics of set theory that underpins is given in his magnum opus, L’Etre et evenement (1988).

Badiou’s fundamental theses are also oriented towards mathematics in another, more general way. Going back to Plato, Badiou observes that Plato relates mathematics favourably to philosophy because it breaks with doxa (opinion). Even if mathematics here means geometry and arithmetic, and refers to a set of objects, it is more insightful than the Romantic conception, as found in Hegel, which evaluates mathematics in terms of the way it presents its main concept, namely, the infinite. Because of this, Hegel sees mathematics as philosophy’s rival. He thus had to prove that the Romantic, philosophical concept of the infinite was superior to the mathematical one. So, whereas Plato sees mathematics as an ally of philosophy, Hegel sees the need to assert the superiority of the philosophical concept of the infinite over that of mathematics because the latter has no concept. In the Romantic view, then, mathematics must rely upon philosophy to provide the concepts of what it is doing; in itself, it is conceptually blind.

Romanticism separates philosophy from mathematics because, effectively, it could claim that philosophy ultimately dealt with the same thing (the infinite) as mathematics, but dealt with it more profoundly. To Romantic philosophy, mathematics would be naıve, while, in Badiou’s view, it is necessary to break with Romanticism so that mathematics can claim its rights as a type of thinking. Badiou thus works, as he says to ‘re-entangle’ mathematics and philosophy primarily for the reasons given above concerning the ontological status of infinite multiplicities. Not only does Badiou want to turn the tables on Romantic philosophy a` la Hegel and ‘re-entangle’ mathematics and philosophy, he wants to suggest, on the question of Being, that mathematics might have priority, that ‘mathematics is ontology’ (Badiou 2004: 38, emphasis added).

As Badiou sees Deleuze as the other philosopher for whom multiplicities are fundamental, he proposed to Deleuze that set theory maybe a better way of getting at notions like: ‘fold’, ‘interval’, ‘enlacement’, ‘serration’, ‘fractal’ or ‘chaos’ (Badiou 2000: 46). However, the author of The Fold was not persuaded, thus indicating a certain allegiance to the Romantic tradition. Badiou’s philosophical difference with Deleuze centres on the latter’s privileging, without argument, a set of key terms that then form the basis of a ‘norm’: movement, life, time, affirmation, multiplicity, difference.

Trained as a mathematician, Badiou realises that being, as a ‘multiple multiplicity’ (without unity), can only be presented as a kind of unity by mathematics – or, more bluntly, can only be presented at all by mathematics. The latter thus becomes the site of the elaboration of Badiou’s ontology. Consequently, mathematics has a higher mission than to be the handmaiden of applied science. It, and not traditional philosophy, truly addresses being because the absolute de-substantialisation of being, that much of post-modern thought has striven for, is essentially mathematical. And the mode of mathematics that Badiou considers to be fundamental in the task of presenting being as a kind of unity, is set theory. Mathematics also addresses the void – for the primordial opposition of unity and void (or One (Being) and Nothingness (which also has a being) cannot be sidestepped). However, to avoid the elemental unity simply sliding back into the unity of the time-honoured One, the ‘unity’ of the non-unity of multiplicities must be composed of further multiplicities, so that a single concept of multiplicity is avoided.

Set theory becomes appropriate for engaging with the multiple because there is no ‘set of all sets’; therefore no element in the theory implies an initial a priori global unity. Moreover, there is no definition of a set in set theory, but rather a relation of belonging ‘as well as a series of variables and logical operators, and nine axioms stating how they may be used together’ (Badiou 2003a: 15).

The void, or nothingness, is the other dimension upon which Badiou’s thought is focused. Here, the question concerns the status of the void in relation to being. Is there a being of nothingness, for instance? Can nothingness, for the mathematician, count for ‘something’? The answer is that both nothing and something constitute a situation (multiple of the multiple), but are not presented in it. In set theory, the void corresponds to the ‘null set’, the empty set that must be posited in order that sets in general can be presented. It is the ‘primitive name of being’ (Badiou 2004: 57) Against Heidegger, Badiou proposes that mathematics becomes the thinking of being qua being, not philosophy.

The Set, Event and Being

In Etre et evenement (1988), Badiou addresses in detail the difference between ‘belonging’ (∈) and ‘inclusion’ (⊂) in relation to the void. A sub-set can belong to a set, but only the set itself can be included (see Badiou 1988: 95). Everything that is included belongs, but not everything that belongs to a set is included in it. Only the void is included in the void (Badiou 1988: 103). This evokes Agamben’s discussion of the exception in politics (Homo sacer), which belongs to politics but is not included (see entry on Agamben in this volume). The void is, Badiou concludes, the being of the multiple (Badiou 1988: 109). Singular multiples of a situation are presented in it, but are not represented. They belong to the situation, but are not included. Normal multiples are both represented and included. To change a situation radically, the aim is to have what belongs to it (singularity) included in it. As an example, we could say that early twentieth-century, avant-garde, music (Schoenberg) initially belonged to music, but was not included in it, whereas, latterly, this music is now included in music. The singular multiplicity is what Badiou calls an event, the key term in his philosophy (Badiou 1988: 195). In relation to this, ‘fidelity’, for Badiou, enables the discernment of singular multiples in a situation. It is the belief, if one likes, that at the beginning of the twentieth century Schoenberg’s music, as atonal, was music.

Being and the void become being and the event, and Badiou is concerned, theoretically and philosophically, with the gap between them – between something and nothing. This compares to the gap in Heidegger’s ontology between being and beings. Because he wants to avoid any hint of substantialisation, Badiou chooses the term, ‘situation’ to convey the nature of the multiple within which an event arises. Situation accommodates anything that is, regardless of its mode of being. A situation, then, is a ‘multiple multiplicity’. The aim is to arrive at the most elementary point of thought in relation to Being as de-substantialised, or de-essentialised. This point is that of the ‘multiple multiplicity’, which is even less substantial than ‘formlessness’ because matter as such has to be stripped away in order to get at the elemental point of thought: its ‘real’, as Badiou says, thus invoking Lacan.

An event challenges being (and therefore challenges mathematical and philosophical thought). And this challenge can occur at any time but not in just any place; an event will generally be located close to the edge of whatever qualifies as the ‘void’ or as what is indistinguishable in the situation. The material of an event is a site. As Badiou says: ‘an event is nothing other than a set, or a multiple, whose form is that of a site’ (Badiou 2004: 100). An event is also an unfounded multiple. It has no foundation outside itself (unlike being). Truth also has this quality. Again, unlike being, an event is not One. It has no determinable or perceptible unity. Truth is a multiplicity and is also something which disappears in its appearance.


A truth then can be of four types: scientific, artistic, political and amorous (Badiou 2004: 110). It is always a novelty, like the event. The axiom of truth is: ‘‘‘this took place, which I can neither calculate nor demonstrate’’’ (Badiou 2004: 112). It is in no sense an a priori, static thing, but is an act, something which brings something into being. Truth operates in a situation (as a multiplicity), within experience, not outside it. It is immanent in experience. Truth is not therefore given, nor is it a given point of departure, but has its origin in the very disappearance of givenness. And to this, Badiou adds: ‘I call ‘‘event’’ this originary disappearance supplementing the situation for the duration of a lightening flash’ (Badiou 2004: 122). Events can range from the French Revolution and atonal music to love. Love is an event because it is totally contingent; it cannot be anticipated or predicted. Genius, too, is an event and as such gives rise to truth.

To all this, Badiou adds the supplementary requirement of faith: an event (truth) entails faith that it has occurred in order that it be thought, for it is outside all regular and existing laws. Faith is the basis of a new way of being and acting in a situation. In relation to this, the subject is the bearer of faith, a bearer whose existence does not precede the event, but who is constituted – or is induced – by it. The subject is not psychological, reflexive nor transcendental. Thus, the subject in a love situation did not exist prior to the event of love. Such a subject has no ‘natural’ pre-existence (Badiou 2003b: 64). ‘The lovers enter as such into the composition of a subject of love, which exceeds both of them’ (Badiou 2003b: 64, Badiou’s emphasis).

Love, then, is one of the four domains of truth (science, politics and art, as well as love). These are four domains of subjectivation within which a genuine subject may appear because it is constituted by the domain itself. In each domain, the truth of the event gives rise to a subject, as we have seen already in the case of love: politics, giving rise to a revolution, gives rise to its subject; science, giving rise to totally new discoveries, similarly gives rise to its subject; art, in bringing forth that which is original and unanticipated, also gives rise to the subject of art. This notion subjectivation linked to the event may be contrasted with the abstract, formal, empty space for a subject supported byZˇ izˇek’s psychoanalytic approach. For Badiou, by contrast, nothing, the void, the empty space pre-exists a subject; it is not equivalent to a subject.

From another angle, truth and the event are mathematical following Cantor’s non-denumerable, transfinite numbers, which constitute the infinite. Thus truth is the realm of the infinite; it is not a finitude, as knowledge often proposes. Consequently, the event, too, participates in the infinite. With knowledge, a particular entity or phenomenal form is presented as truth. This cannot be; for truth as the infinite is universal not particular. Another implication drawn from this by Badiou is that truth has nothing to do with hermeneutics or interpretation. The latter is always concerned with finitude, never with the infinite. Meaning (finitude) and truth are thus at odds with each other, even in psychoanalysis, in relation to which Badiou still maintains his view that analysis is about truth more than it is about interpretation. As Marx, said, interpretation changes nothing.

An Original Thought with Difficulties

Badiou’s philosophy is certainly original in its use of mathematics and the idea of truth and the event as separate from knowledge and being. In addition, the idea of subjectivation that Badiou works with, coupled with the notion of faith provides a refreshing counter to cynicism and nihilism. On the other hand, difficulties arise when it comes to evaluating events that have taken place and forms of subjectivation that have come into being. These would include: Nazism, Stalinism, and aspects of the Chinese Cultural Revolution, or even art as pure narcissism. These may well be events, but what is the truth they convey? Partly, at least, that it would have been better had they not taken place. In effect, Badiou spends so much time using sophisticated mathematical axioms demonstrating what an event is and how it is imbued with truth – always a term to capture attention – that what is happening – today, as well as in the past – very much takes second place. Thus another dimension to Badiou’s philosophy is required: a strategy for evaluating events and their related forms of subjectivation, in order that we can, as well as grasp the nature of an event, also stand against certain events. The extent to which such evaluation would also involve interpretation (not in the realm of truth for Badiou) remains an open question.


Fifty Key Contemporary Thinkers From Structuralism To Post-Humanismm Second Edition  John Lechte Routledge 2008

Badiou, Alain (2000), Deleuze: The Clamor of Being, trans. Louise Burchill, Minneapolis and London: University of Minnesota Press.
—— (2003a), Infinite Thought: Truth and the Return to Philosophy, trans. Oliver Feltham and Justin Clemens, London and New York: Continuum.
—— (2003b), L’E ´ thique: essai sur la conscience du mal, Caen, France: Nous.
—— (2004), Theoretical Writings, trans. Ray Brassier and Alberto Toscano, London and New York: Continuum.
—— (2005), Being and Event, trans. Oliver Feltham, London and New York: Continuum.

Badiou’s Major Writings
(2005a [1988]) Being and Event, trans. Oliver Feltham, London and New York: Continuum.
(2005b [1998]) Briefings on Existence: A Short Treatise on Transitory Ontology, trans. Norman Madarasz, Albany: State University of New York Press.
(2005c [1998]) Metapolitics, trans. Jason Baker, New York: Verso.
(2005d) Le Sie`cle, Paris: Seuil.
(2004a) Theoretical Writings, trans. Ray Brassier and Alberto Toscano, London and New York: Continuum.
(2004b [1998]) Handbook of Inaesthetics, trans. Alberto Toscano, Stanford: Stanford University Press.
(2003a) Infinite Thought: Truth and the Return to Philosophy, trans. Oliver Feltham and Justin Clemens, London and New York: Continuum.
(2003b [1997]) Saint Paul: The Foundation of Universalism, trans. Ray Brassier, Stanford: Stanford University Press.
(2003c [1995]) On Beckett, trans. Alberto Tascano, London: Clinaman Press.
(2003d) L’E ´ thique: essai sur la conscience du mal, Caen, France: Nous, in English as: Ethics: An Essay on the Understanding of Evil, trans. Peter Hallward, New York: Verso.
(2000 [1997]) Deleuze: The Clamor of Being, trans. Louise Burchill, Minneapolis
and London: University of Minnesota Press.
(1999 [1992]) Manifesto for Philosophy, trans. Norman Madarasz, Albany: SUNY Press.
(1992) Conditions, Paris: Seuil.
(1990) Le Nombre et les nombres, Paris: Seuil.
(1988) L’E ˆ tre et l’e´ve´nement, Paris: Seuil.
(1985) Peut-on Penser la politique? Paris: Seuil.
(1982) The´orie du sujet, Paris: Seuil.
(1976) with Franc¸ois Barme`s De l’ide´ologie, Paris: Maspero.
(1975) The´orie de la contradiction, Paris: Maspero.

Further Reading
Barker, Jason (2002), Alain Badiou: Strong Thought, London: Pluto Press.
Hallwood, Peter (2003), Badiou: A Subject to Truth, New York: Continuum.
Hallwood, Peter (2004), Think Again: Alain Badiou and the Future of Philosophy, London: Continuum.
Wilkens, Matthew, issue editor (2005), ‘The Philosophy of Alain Badiou’, Polygraph 17, Durham: Duke University.

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