Alain Badiou’s work must be seen as an integrated whole, responding to the Left’s epochal 70s failure. His system, and understanding it, is now as essential to a new politics as was Marx’s.
If there’s a fundamental conviction shared by ancient philosophers, it’s that whatever thinking is, it’s vital for a good life. Socrates’s infamous tagline ‘The unexamined life is not worth living’ is an epitome of this attitude. Crucially, such ethics isn’t—or shouldn’t be—a merely personal concern for self-fashioning and self-aggrandisation along the lines of the current Instagram CBT Stoic revival, which effectively renders the earth-exterminating neoliberal order the chariot of necessity behind which all must run as fast as they can. No falling, weaklings, and cease your useless whining! Contra such popular images of philosophy’s use—which for the most part are indissociable from tyrannical demands to accommodate ourselves to the most violent aspects of the present—classical ethics was concerned with powers of virtuous action, infused with and directed by thought, and with linking these to a social and even cosmic destiny. The only real question was: how to develop effective modes of thought-action?
This is Alain Badiou’s question too. Yes, he is a contemporary French philosopher. Yes, he does also say things such as differends, differances and differenciations, as did J.-F Lyotard, Jacques Derrida and Gilles Deleuze. He also speaks, like Luce Irigaray, of this sex that is not one, and like Barbara Cassin of the sophistic effects of languages. But unlike all these figures, he maintains a rigorous commitment to universalism, to equality, to discipline and to organisation. Does this then put him in the nostalgic camp of the reactionaries still speaking of the necessity for order, for hierarchies, for the rule of law (or alternatively, the rule of the strongest), for a security state, for the superiority or at least the special benefits of Western Enlightenment? It does not. Indeed, against such ‘parliamentary-capitalist’ propaganda, Badiou continues to affirm the real and active possibilities today of what he calls ‘the communist hypothesis’.[1]
Yet Badiou also remains close to what is still condemned as ‘postmodern thought’ by public intellectuals as diverse as Jordan Peterson, Noam Chomsky and even a certain tranche of Arena commentators. Notorious for his Maoist activism in the 1960s and 70s, Badiou returned to hard-core philosophy in the 1980s, from which he emerged as the last great French philosopher of the twentieth century on the basis of a series of gargantuan treatises that included Being and Event (1988), Logics of Worlds (2006) and Immanence of Truths (2018), as well as sundry minor works, that revivified an almost unimaginably ambitious form of metaphysics for our own times. Drawing simultaneously from the most ancient and the most contemporary developments in such diverse fields as mathematics, logic, love and sexuality, the arts and politics, as well as his own lived experience of activist commitment, these works cut through the confusions and delusions of the present to offer a powerful and clarified vision of political action today.
Badiou’s background is similar to many luminaries of twentieth-century French philosophy—those whom Niilo Kauppi once sardonically named French Intellectual Nobility.[2] Like Louis Althusser and Albert Camus and Jacques Derrida, he was born in North Africa—in his case, in Morocco in 1937. His father Raymond was himself a notable intellectual, a mathematician trained at the notoriously elite École Normale Supérieure (ENS), who fought in the Resistance and following World War II became Mayor of Toulouse; his mother, Marguerite Rouxbédat, was also a graduate of the ENS in literature. Like his parents, Badiou trained at the ENS; his teachers, including Georges Canguilhem, were among the most eminent philosopher-academics of the French state.
In the closed yet cosmopolitan world of French academia, Badiou was part of an exclusive radical left-wing milieu. A student of Althusser, his compatriots included Étienne Balibar, Pierre Macherey and Jacques Rancière, all contributors in 1965 to the ground-breaking studies that made up Reading Capital.[3] Between 1965 and 1968 he worked on a TV show for which he interviewed some of the most influential philosophers of the day, including Michel Foucault, who later sourced Badiou for a job at the radical new university at Vincennes.[4] His academic articles of the mid-1960s drew at once on contemporaneous political philosophy, literature and mathematical logic, fusing formal criteria with barrel-rolling sentiment. Like any good post-Sartrean, Badiou also wrote plays and novels; his prose fictions even caught the eye of Sartre and de Beauvoir themselves.
But the key event of Badiou’s life turned out to be the events of May 68. Almost immediately breaking with Althusser and Althusserianism, Badiou became a French Maoist of the most committed kind. You can still taste the militantisme du jour in a text written in the full blaze of 1968, at once analysing and condemning the course of ‘the events’:
Thanks to an inversion that was far from paradoxical, when the idea of organization did finally come up, it was narrow, aristocratic, ‘vanguardist’ and military. It took no heed of the masses’ demand for organization and for an ideological structure. The uncertainty that is characteristic of the petty bourgeoisie could be seen in the quarrels between the infra-Bolshevism of mass spontaneity, and the hyper-Bolshevism of the intellectual avant-garde. Had it been absolutely preponderant, Mao Zedong’s theory of the need for a mass line could, it is true, have stopped this vacillation.[5]
In search of this mass line, Badiou, with his comrades Natacha Michel, Sylvain Lazarus and others, founded the L’Union des communistes de France (marxiste-léniniste) (UCFML) in 1969, a rival to the more famous Maoist groups that were the Parti communiste marxiste-léniniste français and the Gauche prolétarienne, and spent well over a decade dedicating himself to the struggle.[6] Unlike its Maoist fellow travellers, the UCFML was unambiguously committed to the Cultural Revolution, andplaced crucial emphasis upon the actions and achievements of the 1967 Shanghai Commune, which had expressly modelled itself upon the 1871 Paris Commune; this meant that rather than strictly following the directives of the Chinese revolutionaries, priority was accorded to the application of Maoist thought to the singularity of local French struggles.
Badiou’s writings from this time are, not surprisingly, dominated by the question of revolutionary action. Entirely in line with the essence of ‘Marxist-Leninist’ praxis, Badiou holds that no effective politics is possible without a proper analysis of the situation in which one is intervening, and that no proper analysis is possible without drawing on—as did Lenin and Mao themselves—key concepts from the resolutely abstruse idealist philosophy of G. W. F. Hegel (of which more below).[7] As Mao says in The Little Red Book,
If there is to be revolution, there must be a revolutionary party. Without a revolutionary party, without a party built on the Marxist-Leninist revolutionary theory and in the Marxist-Leninist revolutionary style, it is impossible to lead the working class and the broad masses of the people in defeating imperialism and its running dogs.
To parody a well-known proposition from Immanuel Kant’s Critique of Pure Reason: politics without thought is blind; thought without politics is empty.
Badiou’s 1970s texts are dense yet incisive: to reread them today is to be struck by their clarity, intelligence and doctrinal archaisms:
Is the statist practice of the organization of everyone the condensation of the socialist experience, or is it the cultural revolutions that constitute the supreme political forms of class struggle, aiming at the dissolution of the state? Maoism cuts through this point: It is very much proletarian and revolutionary politics that remains the key to phenomena along the entire socialist transition. The state should be evaluated from the class struggle of the proletariat and not the reverse.[8]
But the major philosophical outcome of Badiou’s Red Years came in the form of their decline, defeat and dissipation. Externally speaking, by the decade’s end Mao was dead, the Cultural Revolution had failed, Capitalist Roaders were back with a vengeance and the great planetary wave of anticolonial revolutions of the postwar period was clearly subsiding. If French Maoism wasn’t doing that well either, it was just as clear that a new period of reaction was in full force globally, and that perhaps the time had come to take stock of the situation again—to re-uptake the struggle at the level of thought.
In 1982, Badiou published his first (self-nominated) ‘big book’, Theory of the Subject, under the state ascendancy of the abhorred Mitterand, for Badiou the emblem of political reaction and restoration. Whatever the genius of this weighty tome—it runs to over 360 pages in the English translation—a miasma of confusion reigns over the whole. It emerges from a time and place that is the very centre of epochal defeat for the red Left. Badiou’s preface is bitter and disjointed: he confesses, memorably, that ‘it is no doubt more instructive to write with respect to what one does not want to be at any price than under the suspicious image of what one wishes to become’[9]—shades of the venerable Alasdair MacIntyre.[10] What follows is at once brilliant and bewildered. The book attempts to rethink the possibilities for politics in an era of reaction by reconstructing the philosophico-practical grounds of what a properly political subject might be today, while evading both the Scylla of Sartre’s nihilating subject and the Charybdis of the decentred, disciplined (post)structuralist subject. The book contains extraordinary commentary on Hegel, of course, but also boutades concerning the Church Fathers, the hermetic French symbolist Stéphane Mallarmé, the differences in the theory of the subject in Aeschylus and Sophocles, enigmatic glosses on algebra and topology and much much more, bristling with paradoxes and seething with a mordant melancholic esprit.
Yet nothing in the book, however dazzling its insights and style, would likely induce anyone to a political conversion or a philosophical revelation. You might appreciate Mallarmé’s sonnets in a more refined fashion; you might even think again about the political and poetical significance of Friedrich Hölderlin’s interpretation of Sophocles’s Antigone; but you probably wouldn’t be convinced of the inner truth and greatness of French Maoism, or that Badiou was a thinker of the same stature as his better-known postmodern compatriots.
But to explain this requires—my apologies!—a brief detour through the arcana of the twentieth-century French academic uptake of Hegel’s thought. Whereas much of Europe, including Italy, Great Britain, Germany and Russia, had enjoyed a Hegelian flourishing in the nineteenth century—even the young Bertrand Russell had flirted with a form of Hegelianism—France had resolutely rejected any truck with the fellow, preferring, for a number of reasons, the grandiose social science positivism of its own Auguste Comte et al. If European Hegelianism was itself split between revolutionary and reactionary branches, the strong line of the former came through Marx, not least because of his confrontations with such left-wing Young Hegelians as Ludwig Feuerbach and Bruno Bauer.
It took the Russian Revolution to change this situation. Not only did the success of the Revolution encourage the post-First World War French Left to subscribe to the Revolution’s intellectual as well as its practical commitments—indeed, the French Communist Party was established in late 1920 in support of Lenin’s Comintern (Hõ Chí Minh was one of its founding members)—the consequent apparition of learned Russian émigrés in Paris supercharged a new academic interest in Hegel’s work. The most important of these were the two Alexandres, Koyré and Kojève (formerly Kozhevnikov), who, alongside locals such as Jean Wahl, started to lecture and publish on Hegel. Kojève in particular gave a series of lectures in the 1930s that subsequently appeared as Introduction to the Reading of Hegel, electrifying an entire generation of French intellectuals including André Breton, Georges Bataille, Jacques Lacan and many others.[11] Kojève—who later joined the Resistance as well as acting as an important bureaucrat decisive in the formation of the European Union (he received the Legion of Honour from Valery Giscard d’Estaing)[12]—made a unique intervention in presenting Hegel’s Phenomenology of Spirit (1807) as an anthropological dialectic of desire founded on a struggle for recognition by figures who would crystallise into master and slave. Indeed, History is nothing other than the intricacies of this struggle: the master, who wins the struggle by facing off against death—‘the Absolute Master’—is thereby condemned by his superiority to a life of enjoyment, while the loser, the slave, comes to know the difficulty of enforced labour that will nonetheless, in turn, transform not only the world but the slave himself into the egalitarian harbinger of a (quasi-)socialist finale.
Kojève’s interpretations, which were notoriously tendentious, sparked such excitement amongst the intelligentsia that much twentieth-century French philosophy can be considered an intensely ambivalent reaction to his work.[13] Even the strenuous objections of Althusser turned out to be fuel to the fire: Althusser famously assigned an ‘epistemological break’ to Marx’s Capital, whereby Marx separated himself brutally from the Hegelian legacy and thereby introduced a properly scientific approach to the field of the political. We will return to this division between ‘science’ and ‘ideology’ shortly, but suffice it to say here that the French were unable to leave Hegel alone even when explicitly repudiating him. One noteworthy symptom, as the linguist Jean-Claude Milner has pointed out, is that French academic writing shifted in the 1930s from the clarity that had governed from Descartes to Bergson, systematically contorting itself into properly ‘dialectical phraseology’—those rebarbative stylistic markers which continue to get lambasted today by such anti-‘postmoderns’ as Noam Chomsky.[14]
Yet this history is not a restrictedly academic one. Insofar as Marxism had emerged from Hegelianism, even the gritty details of socialist labour organising often got caught in the rift between the specificity of situations and history-as-totality, the actors at once energised and confounded by the cunning of reason which, according to one of Hegel’s most familiar gambits, undoes the best laid plans of mice and men at the same time as it projects society beyond itself. But whereas Hegel had been concerned with developing an abstruse idealist philosophy of absolute knowledge that was at once encyclopaedic and conceptual, Marx was, as the notorious Thesis 11 proclaims—and precisely in the context of a critique of Feuerbach, one of the most innovative and influential Young Hegelians—expressly concerned not to interpret the world, but to change it.
Still, Marx, and Marxism more generally, retained something decisive from Hegel. History remained the place of the taking-place of reason in the world. Such History, which is today often dismissed as oppressively ‘linear’, ‘rationalist’ or ‘Western’, nonetheless encrypted a number of crucial features which are hard for any putative historical thought to shake off without altogether abandoning its historical character. One of these was its emphasis on the irreversibility of events despite the overbearing determinations of repetition. Such ‘events’ were relatively rare historically, but were in fact the main routing-points of history as such. Whether it was Socrates getting out and about in the Athenian agora, Jesus getting himself crucified in the Middle East or Napoleon getting himself into hot water in icy Moscow, once such had happened, there was no going back. Any apparent return to an initial or former state would be merely a semblance, or a false return. Another crucial feature was the role played by antagonism: negation was the motor of history, and nothing could emerge that was not itself a negating response to a prior situation, nor could it prevent itself being negated in turn. Every apparent concord would hence be partial, mistaken, illusory or fugitive. Thirdly, and perhaps paradoxically, such irreversibility and antagonism did not prevent the possibility that eventually all antagonisms would themselves have to be fully expressed: that is, antagonism would irreversibly turn against itself. This is the question of totality, or alternatively, the End of History.
Whether or not Hegel had projected the end of history in the contemporaneous form of the Prussian state, and whether or not Marx preserved any formally homologous convictions, there was necessarily in both cases, due to the aforementioned operations of the dialectic, a non-negotiable conceptual commitment to a certain in-determination in human affairs. Let’s emphasise how this commitment, whatever the many different political and conceptual inflections it can receive—and has received—puts pressure on all our modes of action and understanding in the name of the future now developing indiscernibly at the heart of the present itself. Yet all action still has to be directed by a commitment—by definition in excess of our current knowledge—to the future-as-end, whether that be the triumph of the State Form Itself or the ultimate withering-away of the state following the successful proletarian revolution. These, then, are the fundamental operations of the notorious Hegelian dialectic, at least in the dominant forms that it enjoyed in twentieth-century France: the primacy of evental history; the centrality of contradiction as a driver of such events; and the claims of a temporalised totality as the endless end of History itself, the ultimate context for all becoming.
It is at this point that we can return to Badiou.
By 1982, then, it is not clear that another interpretation of Hegel—another metaphysics, however radical, however original, however Maoist—is able to compete with the mass of existing French interpretations of Hegel’s work. The ‘postmoderns’—Deleuze, Derrida, Foucault, Kristeva, Lacan, Lyotard—who were certainly all anti-Marxists in one way or another, had dealt with the legacy of Hegel in hallucinatory detail, decisively criticising the existence of the dialectic, its allegedly recuperative powers, its determinations of history, its disavowed violence, its self-effacing White and Western regionalism masquerading as a universalism. As Derrida, for example, had declared in ‘White Mythology’, riffing on Anatole France: ‘What is metaphysics? A white mythology which assembles and reflects Western culture: the white man takes his own mythology (that is, Indo-European mythology), his logos—that is the mythos of his idiom, for the universal form of that which it is still his inescapable desire to call Reason’.[15] In other words, Badiou’s Maoism was now coming off as a sclerotic Francophone political psychopathy, unsuited to the challenges of the present.[16]
Funnily enough, it is precisely due to a vicious self-critique of his own failures in Theory of the Subject that Badiou ends up becoming Badiou. The book presumes, rather than grounds, the existence and necessity of the very subject that is in question; this subject is ultimately entirely political; indeed, the political functions as an unjustified master-signifier throughout. Hegel remains the limit of thought, if in an anomalous, patently partisan way. An attempt to break through the impasse of the period, it had merely become an extension of the crisis in turn. A rethinking of philosophy was in order—one that genuinely transcended the assumptions Badiou could not hitherto escape.
He accordingly spends the 1980s rethinking all the materials already at his disposal—cutting-edge logic and mathematics, political activism, a love of the literary, the challenge of psychoanalysis and so on—which culminates in the vast treatise published in 1988 as Being and Event (526 pages in English, and for Badiou, the second of his ‘big books’).[17] What makes this book the single most important work of philosophy of the late twentieth century, an absolute conceptual masterpiece? Simply put, by its absorption of all the criticisms and defences of truth unleashed by the postmoderns and their enemies—and by its refusal to accept them, and its concomitant desire to reconstruct a philosophical justification of universal truth immune to these critiques. Note especially the key terms of the title, which in alluding both to Heidegger’s Being and Time (1927) and Sartre’s Being and Nothingness (1943) should give a sense of Badiou’s ambition.
Mathematics and physical science had re-entered philosophy in a new way in the late nineteenth century, above all through the work of Russell, who despite his early start as a Hegelian took up the new developments in mathematics and logic associated with such names as Georg Cantor and Gottlob Frege, fundamentally repudiating any Hegelian logic of negation-and-contradiction. Russell became one of the founders of so-called ‘analytic philosophy’ along with Ludwig Wittgenstein and others, whose inheritors are found in Oxford ordinary language philosophy and the Vienna Circle. This kind of philosophy tended to privilege a particular image of science—the so-called ‘hard sciences.’ In doing so, it—despite also undergoing a significant ‘linguistic turn’ in its inventions of concepts such as J. L. Austin’s ‘performative’ and H. P. Grice’s ‘implicature’—also repudiated what it derisively called ‘literary philosophy’.
But for Badiou to turn to maths for a philosophical guideway was a departure. The unreflective valorisation of the signifier ‘science’ was something French thought, including the postmoderns, particularly abominated. In this, they were in the wake of the Germans. As Theodor Adorno put it in an exemplary formulation:
Bourgeois society is universally situated under the law of exchange, of the like-for-like accounts that match and that leave no remainder. In its very essence exchange is something timeless; like ratio itself, like the operations of mathematics according to their pure form, they remove the aspect of time.[18]
Though they were only occasionally willing to admit it, the Frankfurt School could not help but draw on Martin Heidegger, whose famous neo-Romantic turn to the priority of poetry in the realm of thought, as well as his inveterate Nazism, itself depended on a deep historical reconstruction of the emergence of the deleterious regime of techno-science. A crucial part of this reconstruction was geared to showing that the modern epoch—that is, our epoch, of the forgetting of the forgetting of the question of the truth of Being—was particularly destitute insofar as it was under the planetary reign of technology, itself a consequence of the mathematisation of being accomplished precisely by figures such as Descartes himself. The late-eighteenth-century romantic turn in art and philosophy had repudiated this: Hegel had submitted the form of mathematical knowledge to the ‘properly philosophical idea’. History and poetry were truer than technology and science, a position still fundamentally held by many so-called ‘continental philosophers’ today.
So we have a tangle of strenuously antagonistic positions. Heidegger affirms that truth emerges from the events constituted by poetry rather than techno-science, re-examining the question of being using poetic-philological methods. The Marxist traditions—or more broadly, the traditions of political radicalism—are for politics over interpretation, demanding the subordination of thinking about the world to the categories, such as bourgeois and proletariat, of politics as such. The analytics simultaneously retain the hard sciences as an ideal image for thought, as they also turn their attention towards lemon-squeezing linguistic analysis. For their part, the poststructuralists, through close readings of the philosophical tradition, destabilise claims to truth through a critique of binary oppositions and a denial of any legitimacy to the category of totality. What does Badiou do in the midst of this carnivalesque uproar? He takes something from each of these tendencies, while inverting or diverting their inherited sense. His work can be seen as a careful synthesis and transcendence of the inherited thought traditions of modernity to create a new metaphysics, that, in establishing itself as a materialism, makes claims as essential reading for those who seek possibilities labelled as ‘political’ in the twenty-first century.
Central to this imperative is a pair of matching divisions: that of being—the world as it must be—and that of events. The field of beings—not Heideggerean Being, some mystery transcendent quality, but the full multiplicity of the world—can be inquired into through the investigations of mathematics, since mathematics is a rational form of truth that uncovers universal structures. Events are not mere occurrences and processes by which the world runs; this is the province of being. Events are happenings large and small—everything from the October Revolution to a few harsh words in a symposium or a village marketplace—which open up new possibilities in the world. Events escape determination—they do not, per se, exist—and thus offer the possibility of radically new things happening. If being is able to be thought by mathematics, events have a poetic structure—a term standing for art in general.
This doublet—maths-being and poetry-events—is supplemented by two other fields. Drawing from the postmodern turn, Badiou considers love as offering a model of how radical differences can encounter and sustain each other. And the traditions of revolution orient themselves towards mass political transformation that exceeds knowledge. Indeed, Badiou reconceives truth itself as just such a form of committed action, not just adequation or revelation.
Badiou’s use of mathematics has probably been the most controversial, but also the most radical of his proposals. He will even phrase it as a little equation: mathematics = ontology. What could this possibly mean? One key feature of so-called ‘pure’ mathematics is that it underlies modern science—all of it. There is no physics without maths: as Galileo himself once famously phrased it, ‘The book of the world is written in mathematical script’. Why this might be so is obviously a world-historical debate, but it is also the case that the mathematics that physics draws upon is only a tiny fragment of mathematical actuality; in other words, the powers and range of mathematics are wildly in excess of any possible empirical deployment. Badiou’s argument inverts the standard materialist and phenomenological treatments of the complex maths which began to emerge in the Renaissance, which treat them as abstractions nested within the real. Instead, he argues that such discoveries reveal fuller expanses of real possibility, of which the actual is simply a subset.
Take one of the most important developments in late-nineteenth-century mathematics—the invention of set theory by Cantor. In brief, Cantor showed that the infinity of the natural numbers (i.e., the integers 1, 2, 3… infinity) is ‘smaller than’ the infinity of the continuum (i.e., all the numbers between 0 and 1). Not only that: once one starts generating infinite numbers, one can continue to do so…infinitely. Moreover, infinite numbers don’t quite act as the finite numbers do: although it may seem that the set of squared integers (i.e., 1, 4, 9, …) must have far fewer numbers than the set of integers (i.e., 1, 2, 3, …), this turns out not to be the case; these two sets in fact equal each other. These astonishing demonstrations came at great personal cost—Cantor was in and out of asylums throughout his life—at the very moment they revolutionised modern mathematics.
For Badiou, this development shows that—contra Hegel, who had dedicated a massive effort in his Science of Logic to proving that the contemporaneous mathematical thinking of the infinite in regards to calculus was at once necessary yet defective in comparison to that of philosophy (the ‘bad’ v. the ‘good’ infinite)[19]—mathematics is a form of pure reason that unlike the laws of logic, which are also comparably pure, also makes claims about existence. In this case, maths proves not only that the infinite exists, but that infinite infinities exist, with no upper bound. It is with such mathematics that we can see how a consistent-yet-counterintuitive thought of existence can be rationally affirmed.
Moreover, this state of affairs ruins any consistent concept of ‘totality’. With different means in hand and ends in mind, Russell himself had already given a logical demonstration of this with his famous paradox, which is occasionally summarised as follows: does the set of all sets include itself? If it does, it doesn’t; if it doesn’t it does. The paradox shows the concept of ‘totality’ to be logically untenable; any attempt to totalise is therefore irrational; being irrational, it betrays its violent inequality. In sum, for Badiou, rather than criticising mathematics, philosophy must learn from, be conditioned by, mathematics.
Thus mathematics is ontological, albeit not only ontological. Yet however stunning its proofs regarding infinity, mathematics also thereby banalises and desacralises the infinite. Rather than God being infinite, as some medieval Catholic theologians held, everything that is is, so to speak. Or again, the finite ought to be considered a restriction of the infinities that precede it, rather than the basis of the infinite. Moreover, and precisely because of this, we can also say that what counts as contemporary techno-science is an ideology materially founded on the infinite reduction of our infinite possibilities for thought. However large the datasets, however supposedly powerful the algorithms that Artificial Intelligence now employs, they are exactly as far from infinite thought as Anthony Albanese or Barnaby Joyce; by contrast, for Badiou, any working mathematician is already necessarily thinking in a way that goes beyond the powers of any possible techno-scientific innovation. In other words, we already have true ideas that are literally in infinite excess of the reign of techno-science, upon which techno-science itself is reliant but which it covers-up (recouvrement, a technical term for Badiou); our task is to develop these ideas to combat the alienating extractions of the capitalist constriction of technology, which is essentially finitist falsehood.
To be clear: Badiou is not saying that nature and history can be simply expressed by the finding of their mathematical structures, which would be reductive scientism. Rather, the mathematics of fields, boundaries, sets and so on—a sustained inquiry too complex to summarise here—reveals the necessary structures of the real. Modern mathematics emerges as a historical event, but the infinities discovered must be regarded as real and not simply a product of inquiry. The process that other traditions represent as alienation or reification is post-scientific-revolution capitalism seizing on the technologies that pure mathematics make possible in order to reorder the world in its own violent and reductive image, while also working to hide the true powers of mathematics in plain sight. In the most basic mathematical terms, capitalism is obsessed with ensuring the finitude of ones, of identities, that it also seeks to proliferate and undermine. Whereas the relation between mathematics and ontology is for Badiou ‘invariant’—maths ‘speaks being’ in Babylon the same as in Boston—the apparent dominance of techno-science under capitalism is a specific historical moment.
Heidegger’s warning from the Right was that technological advance would fill the world with techniques directed to beings, entities, which would cause us to forget the question of Being and hence our capacity for authentic existence. Taken to America, such an approach became part of the New Left, and spread globally. It was then criticised in turn by the poststructuralists, who argued for the priority of irreducible difference and textuality. Badiou is also critical of Heidegger’s notion of Being, but not from the position of total indeterminacy of the poststructuralists. Instead, he sees claims to an indefinable absolute like ‘Being’ relying on mixed metaphorical modes that must be combated by subordinating the privilege of ‘bodies and languages’ to the concepts so strongly constructed by mathematics. The mathematical infinite is not a ‘jargon of authenticity’, for which Adorno once condemned Heidegger, but a rigorous, rationalist, open discourse that is at once more precise about existence—and more real.
So pointing to the fact of mathematics’ constitutive excess over the technologies that currently dominate us is a sign that the materials and ideas for a more radical resistance to domination are already here. For what we take to be ‘reality’ is only an infinitesimal part of the universe described by mathematics, and the former is always liable to being stringently transformed by mathematics which may appear to be not only currently inapplicable, but in fact flagrantly impossible. Consider the well-known example of the imaginary number i, the square root of -1—disdainfully named as such by none other than René Descartes himself—has crucial applications in the analysis of waveforms, and hence to an astonishing range of applied fields including quantum physics and computing. ‘Reality,’ in other words, is itself the outcome, not just of what’s possible, but also of what is (considered) impossible.
Yet not everything is mathematical; not everything can be thought mathematically; mathematics may be universal, but it cannot be total (as it itself proves); there are essential aspects of life where mathematics cannot go or proves useless. For Badiou, moreover, mathematics delivers a particularly stringent form of necessity. Either one conforms to its proofs or one abandons it altogether. But we also know that sometimes things happen—that is, happen beyond any capture by mathematics. This is what Badiou considers the realm of events, of occurrences that exceed or contradict what exists, even in the radically expanded ambit of the mathematical infinite.
Universal but never total: as Badiou also demonstrates in Being and Event, given that mathematics is self-determinedly incapable of thinking the peculiarities of contradictory yet real and affective experiences—that is, events, whether big or small—it needs to be supplemented by poetry, understood in the broadest sense as artistic invention. After all, across vast gulfs of time and culture, it is, as Marx himself notoriously maintained, still possible to be overwhelmed by Greek drama or Tang poetry. And postromantic thought, from the Schlegel brothers through Samuel Taylor Coleridge and Ralph Waldo Emerson to Heidegger, has been convinced that poetry is an absolutely crucial mode of thought. For poetry offers a form of thinking that exceeds what exists (as given mathematically); as such, it breaches the worlds we live in with the actuality of oddly captivating inexistents. Such inexistents themselves cannot be reduced to any received categories of identity; in fact, they show that all such categories—empirical, sociological, experiential, what have you—are incapable of grasping the paradoxes unveiled by art.
In this sense, poetry/art is not a separate ‘order’ simply because it can recombine parts of reality into things that do not exist—a blue lion, a talking star—but also because it can connect any conceivable possibility to any other conceivable possibility…to previously inconceivable possibilities. In that, art is always an event, even if written down, painted, and so on, in opening out what being could never produce of itself. In other words, having begun with what we can know of being by using mathematics, Badiou turns to what we can say of non-being by using poetry. For a poem can be enigmatic, affective, inconsistent, minor, thoughtful, unreasonable, all at once, and in being able to be so, it also presents versions of ungraspable-but-active paradoxes at the limits of thought. Poetry occupies the zone of the non-actual; it provides a hint of the unmathematisable. Poetry for Badiou can hence be considered as offering us models of how we can think about non-being, or more precisely what is neither simply being nor non-being, neither appearing nor vanishing: the event.
But if maths thinks ontology, and poetry events, Badiou also wants to affirm the claims of love and politics. Lovein all its forms—eros, agape, Buddhist maitri and so on—shows that new, unexpected connections are possible between persons despite the divisions that beset them, of background, identity, language and so on, and that something new, unexpected, can be forged in the world through a work of love. Love is a necessarily distinct third order, separate from being and the event: the reality of love cannot be reduced to, or filled out by, either of these in whatever combination. Love, moreover, is not linked by Badiou to any particular sentiment or affect; it does not designate a fusion of opposites, a particular or limited kind of sexual practice or a heteronormative ensemble. Rather, Badiou emphasises the creative struggle of differences that love exemplifies. Its existence proves that we can and will change our lives in previously unimaginable ways on the basis of unexpected events, and that in changing our own lives, we also struggle against the inertia or even hostility of the world itself. Crucial here is that, in order that there be some connection—however paradoxical—between the realm of being and the non-realm of events, some kind of subject has to construct it. What better image of such a subject than one (or two!) caught up the vicissitudes of eros, which sustains the difficult work of continuing to make new (real) connections between what is currently separated in the world?
Politics, the fourth field, is for Badiou the very opposite of what it is usually supposed to mean: the science of a necessary order. That is called economics. Politics is not immediately or directly an economic question of scarcity, of supply and demand, or of questions of authority and rights, of constitutions and their mechanisms. It is instead the discipline of the struggle towards equality, considered in its most radical forms. Equality is the infinite end that arises from the deep structural equality of humans in our form in the world; Communism is the general form of such equality, partially expressed in love (for Badiou, ‘love is the minimal form of communism’) but only fully expressable in the political register, of the many. Badiou thus takes up the challenges of a non-Hegelian, post-Marxist, quasi-Maoist thought of communism. For Badiou, communism is the core of any true politics, but this politics is to be separated from what political theory usually considers political. Rather, the struggle for equality can be the only criterion for a political ambition that neither supports the status quo (i.e., the hierarchies of order, good governance, social cohesion and so on) nor, anarchistically, considers the fomentation of radical chaos an end in itself.
History does not determine our situations, and nor does the economy or technology; in fact, nothing totalises our situations; yet the resources are already here for us to enable a radical transformation of these situations. Our task is not to take command of nor to smash the state, but to follow a mass line of thinking beyond the constraints (e.g., divisions, identities, demands) of the present and not give way before the objections of what already exists. From within the communist tradition, this is Badiou’s challenge to Marx and to Marxists. His communism departs from Marxism strictu senso as an analytic control, not least insofar as the latter retains a commitment to totalisation (e.g., whether of labour and production or of accomplished state revolution). In an era which concluded with the collapse of China’s Cultural Revolution, the arrest of the ‘Gang of Four’ and the subsequent capitalist turn, forms of political reasoning that seek the determination of a situation are the exact opposite of what is required, which is an orientation to infinite possibility. Such politics must be a work of universal equality, of equalisation beyond history, the economy, the state, otherwise it will remain in fee to self-interest and tribal affiliations. Where Badiou differs from the poststructuralist affirmation of differences and disseminated subjects is precisely insofar as all such differences are in principle transformed in the course of a political process into the ‘same’—not a reduction to an identity, but the construction of a practice that is ‘for all’. This construction can never find a termination, as, being infinite, it is without end, but it operates immediately ‘as subjective universality’.[20]
Given Badiou’s injunction to think infinitely, it is now today possible to know we are indeed infinite—thanks in part to the advances of mathematics itself!—and, that affirmed, to enact hitherto undreamed-of forms of infinite equality in the present. Significantly, it is precisely here that Badiou sees himself as at once continuing a radical tradition of communism and also dispelling some illusions. Badiou’s emphasis is on continuing disciplined creative action. As he puts it in his Second Manifesto for Philosophy:
two things are already clear from the ongoing political experiences that have drawn the consequences of the previous century’s political history and have solid roots in the real of workers and the people: first, that it is possible to implement a politics that keeps its distance from the State, with neither power as stake nor parliamentarianism as its framework, and, second, that this politics proposes forms of organization that are far removed from the model of the part which dominated the entire twentieth century.[21]
Such a political double movement—non-statist and organisationally inventive—means that the stakes for political success are no longer set by the seizure of power, but by the ongoing egalitarian discipline of an organisation concerned to act according to the challenge of such events as the Paris or Shanghai Communes, October 1917 or the August Revolution. Badiou wholly rejects the idea that politics is about better or worse regimes, about meliorism or management. As he puts it at the beginning of Being and Event, we can no longer be satisfied in the current conjuncture by practices of critique, revolution or return. In terms of liberation, these can be seen as concluded. Neither can we be satisfied by theories that consider politics subject to necessity or determinism of any kind.
This is why a concept of the event is so critical to Badiou: events, however ambiguous, however minimal, offer a possibility of action that is not entirely subject to necessity, no matter how ambivalent its consequences may prove to be. Badiou is absolutely not offering a mere strategic playbook for radicals. His argument, drawn out of the late-twentieth-century collapse of existing politics, is that a rethinking of world and historical structures is absolutely essential. Not only must it be understood that Badiou’s four fields are not arbitrary, as is sometimes supposed, but necessary processes of thinking and acting in the world, so too must it be understood that sticking to inherited radical theories is absolutely defeating of radical possibility.
The key is not to substantialise the event. I noted above that Badiou takes poetry as a model for the event: this isn’t to make poetry a model for politics, but rather to underline that all events have this precarious, surprising, contradictory and vanishing nature. To remain faithful—a key term of Badiou’s—to what vanishing events have revealed is therefore to work in the world guided by such questions as: if this event that compels me was indeed real, what does that mean for this local struggle taking place now? Getting caught up in a truth-process, for Badiou, is an action of endless questioning of how one should act—which, as one continues, necessarily has effects in and on the world.
Yet Badiou insists he is still a materialist of some kind, or rather a proponent of a ‘materialist dialectic’ against what he see as the degraded ‘democratic materialism’ of our times. What sort of materialism can this be? After all, the great trajectory of philosophy and theory in the twentieth century has been to argue that the ideal philosophical categories are expressions of material, physical, present processes, from Husserl’s phenomenological building-up of complex mathematics as successive developments from a geometry grounded in the world to Sohn-Rethel’s development of Marx’s notion of the commodity as a ‘real abstraction’, in order to create a wider theory of conceptual abstraction as arising from real abstract relations.
Badiou’s answer to this is that the infinite is not an abstraction; rather, it is the finite that is an abstraction. As such, he sometimes prefers the term ‘subtraction’, given that truths subtract themselves from and are unable to be fully captured by the identity operations of whatever world in which they emerge. Nor does Badiou believe that conceptual abstractions arise from real abstract relations; after all, he thinks that what we call ‘reality’ is a restricted outcome of the more fundamental material processes that are truths. And the varied examples that he gives of such event-truths—whether of Cantor’s development of set theory, the activism of the Paris Commune, the extraordinary experiments of Mallarmé’s poetry or his analysis of the question of love—are all precisely directed to showing that such truths have a radical effect on the real itself.
As I’ve put it elsewhere, Badiou’s is a SLAP philosophy: Science, Love, Art and Politics are all necessary for there to be any philosophy at all.[22] They are the truths to which philosophy must attend. If they intersect with each other, affect each other, sometimes even rival or try to dominate each other, as they certainly do, this ontic aspect of truths does not prevent philosophy from acknowledging and attempting to capture their irreducibility to each other in a set of articulated Ideas. As I’ve tried to suggest above, such ideas are not something that just pops into your head. An idea is not just an opinion, not just an interesting observation, not just a predicate or master-signifier supposed to constitute reality. Rather, an idea is a new material organisation of what in-exists in the situation one inhabits, founding an in-principle infinite work that, in being finitely undertaken here and now, transforms that situation utterly. In his subsequent two great books—Logics of Worlds (2006) and Immanence of Truths (2018)[23]—Badiou takes these thoughts even further, drawing on recent discoveries in mathematical logic to do so.
Badiou often declares that even though we now know that the universe itself is finite and that all human endeavours will end in dust and ashes, to participate in a truth-process will never not be worthwhile. However weak, however transient, however compromised our situations are, philosophy enjoins humans to ‘live as Immortals’. The action-ideas given us by the truth-processes that are science, love, art and politics show us that it is possible. So why not give it a go? To rephrase slightly one of the great lines of the Internationale: we are nothing, let’s be infinite.
[1] See, inter alia, the book of that name: Alain Badiou, The Communist Hypothesis, D. Macey and S. Corcoran (trans.), London and New York: Verso, 2010.
[2] Niilo Kauppi, French Intellectual Nobility: Institutional and Symbolic Transformations in the Post-Sartrian Era, Albany: State University of New York Press, 1996.
[3] Now published unexpurgated in English as Louis Althusser et al., Reading Capital: The Complete Edition, Ben Brewster and David Fernbach (trans.), London: Verso, 2016.
[4] The transcripts of Badiou’s TV interviews have been published in English as Badiou and the Philosophers: Interrogating 1960s French Philosophy, Giuseppe Bianco and Tzuchien Tho (trans.), London: Bloomsbury, 2013.
[5] Badiou, The Communist Hypothesis, pp 88-89.
[6] See the extraordinary reconstruction of Badiou’s day-to-day political struggles by Bryan Cooke and Robert Boncado in ‘“Long live the International Proletariat of France!”: Alain Badiou and the SONACOTRA Rent Strike 1975-1979’, Philosophy Today, 62(4), 2018, pp. 1139-1163 and their ‘1967: The Shanghai Commune, French Maoism & the Case of Alain Badiou’, Australia and New Zealand Journal of European Studies, 9(3), 2017, pp. 68-84.
[7] See the texts now published as The Red Years (London: Bloomsbury Academic, 2017). If you will permit some antipodean resentment: despite the blurb that these have been ‘hitherto unavailable in English’, the local Melbourne publisher re-press had previously made available The Rational Kernel of the Hegelian Dialectic (2011) as well as other texts by Badiou. It is perhaps also worth noting that one of the key Althusserian innovations was the denial that Marxism was indebted to Hegelianism: the break into science, for Marxism, came with the suppression of the residua of Hegeliana.
[8] Alain Badiou et al., The Rational Kernel of the Hegelian Dialectic: Translations, introductions and commentary on a text by Zhang Shiying, Tzuchien Tho (ed. and trans.), Melbourne: re-press, 2011, pp 64-65.
[9] Alain Badiou, Theory of the Subject, Bruno Bosteels (trans.), London and New York: Bloomsbury, 2009, p. xl.
[10] Alasdair C. MacIntyre, Against the Self-Images of the Age: Essays on Ideology and Philosophy, Notre Dame: University of Notre Dame Press, 1971.
[11] An English version is available as Alexandre Kojève, Introduction to the Reading of Hegel, Raymond Queneau and Allan Bloom (eds.), James H. Nichols (trans.), New York: Basic Books, 1969. French feminism, decolonialism, sociology and philosophy were shaped by Kojève’s influence on thinkers such as Beauvoir and Fanon, Aron and Merleau-Ponty.
[12] See Luis J. Pedrazuela (ed.), Alexandre Kojève: A Man of Influence, Lanham: Lexington Books, 2022 and Jeff Love, The Black Circle: A Life of Alexandre Kojève, New York: Columbia University Press, 2018.
[13] See, inter alia, Bruce Baugh, French Hegel: From Surrealism to Postmodernism, New York: Routledge, 2003, and Michael S. Roth, Knowing and History: Appropriations of Hegel in Twentieth Century France, Ithaca: Cornell University Press, 1988. And lest we forget, Judith Butler’s first book was on precisely this topic: Subjects of Desire: Hegelian Reflections in Twentieth-Century France, New York: Columbia University Press, 1987.
[14] See Alain Badiou and Jean-Claude Milner, Controverse: Dialogue sur la Politique et la Philosophie de Notre Temps, Paris: Seuil, 2012, p. 174.
[15] Jacques Derrida and F.C.T. Moore, ‘White Mythology: Metaphor in the Text of Philosophy’, New Literary History, 6(1), 1974, p. 11.
[16] For more detail on this, see my ‘Badiou, Hegel and the Thinking of Modernist Thought-Action’ in Arka Chattopadhyay and Arthur Rose (eds.), Understanding Badiou, Understanding Modernism, London: Bloomsbury, 2024, pp. 37-49.
[17] Alain Badiou, Being and Event, Oliver Feltham (trans.), London and New York: Continuum, 2005.
[18] Theodor W. Adorno, ‘The Meaning of Working Through the Past’. in Critical Models: Interventions and Catchwords, Lydia Goehr (intro.), Henry W. Pickford (trans), New York: Columbia University Press, 2005, p. 90.
[19] See G. W. F. Hegel, The Science of Logic, George di Giovanni (ed. and trans.), Cambridge: Cambridge University Press, 2010, passim, e.g., pp 108-125; 204-234.
[20] Alain Badiou, Metapolitics, Jason Barker (trans.), London: Verso, 2005, p. 143.
[21] Alain Badiou, Second Manifesto for Philosophy, Louise Burchill (trans.), Cambridge: Polity, 2011, pp. 122-123.
[22] See Justin Clemens, ‘Had We But Worlds Enough, And Time, This Absolute, Philosopher…’, Cosmos and History, 2(1-2), 2006, pp 277-310.
[23] Just for the record, Logics of Worlds (Alberto Toscano (trans.), London: Continuum, 2009), is 617 pages in English and Immanence of Truths (Susan Spitzer and Kenneth Reinhard trans., London: Bloomsbury, 2022) 612 pages.