THIS PAST DECEMBER, French philosopher Alain Badiou gave a series of three talks in Southern California that collectively address one of the foremost questions of his vast body of work: How do we think the impossible? More urgently, how do we think the impossible at a time when what is “possible” is roughly delimited by the following: the self-perpetuating hegemony of global capitalism, the growing allure of the extreme right, the increasing trivialization of democratic politics, alarming economic disparity, and the notable apathy, even among the Left, about our conceptual dependence on stagnant liberal values? According to Badiou, these general features of the contemporary world are anything but postmodern and innovative. They are not, in a sense, novel or creative, but precisely laid out by Karl Marx in the 1860s, when the conservative reinstatement of state political and economic power quelled the continental revolutions of the 18th and 19th centuries. Communism prophesized late capital; we are now living its full historical unfolding.

Yet, the dramatic increase in global inequality due to capitalism’s all-encompassing reach seems to have been traversed, in recent years, by something else: the stirrings of revolution, the possibility of actual rupture with the state of things and localized historical change. Badiou is no stranger to these forms of events. He is one of our last living continental philosophers (some of his more celebrated contemporaries include Gilles Deleuze, Jacques Derrida, and Michel Foucault) to have fully witnessed the growth of Western Marxism and its revolutionary capacity in the events of May 1968 in Paris, in which Charles de Gaulle’s government was nearly brought to a halt due to worker and student riots. Following this pivotal moment, Badiou remained committed to the militant communism of the Far Left — including the ideas of Mao Tse-tung, about whom he has written extensively — even as the idea of revolutionary Marxism began to severely wane in popularity during the 1970s, ’80s, and ’90s. But now, given the visibility of recent events like the Arab Spring and the Occupy movement, it would seem that things may take a turn, both within the academy and far more importantly, outside of it, toward what we can call a resurgence of radical politics after years of dormancy.

A number of fellow philosophers remain committed to a Marxist framework — Étienne Balibar and Jacques Rancière come to mind — but Badiou’s philosophy is quite distinct. He is a rigorously, at times dizzyingly axiomatic thinker, and is uniquely faithful to the notion of Truth, which he draws from Plato, a somewhat unconventional choice of philosophical predecessor. For Badiou, truths begin as the immanent subtraction to what there is. And what there is falls under the rubric of what Badiou names “democratic materialism”: that there are only bodies and languages, sights of enjoyment and suffering (the body), and a semiotic system in which meaning is produced (language). But for Badiou, truths exempt themselves from what there is: they erupt in the form of what he names an “event” and initiate the new and the formerly impossible.

Truths occur in the realm of four generic procedures, according to Badiou: art, science, politics, and love. Following Plato, he draws an important distinction between what knowledge and consciousness can conceive as the “new,” or what we may think is a “truth,” and the idea of the New, of a Truth. Truths are not merely exceptional in Badiou’s thinking, but singular: a truth never repeats what was formerly possible, and thereby always constitutes a break with the rules and limits for what defines possibility in its particular moment. Truth procedures are also singular because they paradoxically reveal their generic character: a Truth is something that can be shared by anyone, rather than merely seized for identitarian interests. Politics in Badiou’s work, for instance, do not refer to the party, the state, or politicians and their maneuvers, but to an idea (Politics) to which ordinary people can collectively be faithful and carry out.

Armed with these general concepts, a reader of Badiou’s work could go in a few different directions: toward the more abstract and somewhat daunting large books that have appeared in translation in the last 10 years — Being and Event, Theory of the Subject, Logic of Worlds — or toward Badiou’s steady and short writings that respond directly to a contemporary world in crisis: his surprise hit in France, The Meaning of Sarkozy, a short piece in Le Monde on fanatical secularism, his prompt response to the protests in Taksim Square that concludes: “Long live the uprising of Turkish youth and their allies! Long live the creation of a new source of future politics!” Much continental philosophy of the last 50 to 60 years has been accused (and not without reason) of a certain obscurity and loftiness. But Badiou seems different, articulating passionate claims about the immediacy of politics in often crystalline terms. It’s no wonder that his popularity stateside appears to have grown exponentially beyond his initial appeal in his home country.

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In the first of his lectures (delivered at the Art Center College of Design in Pasadena), “Are we really in the Time of Revolts?” Badiou simply and schematically put our current century in perspective with the previous one. He maintained that since the French Revolution, history has played out as a number of social and political contradictions. Badiou drew from the Hegelian dialectic a concept that sees any synthesis or transcendence of terms as an overcoming of their inherently negative or antithetical relationship. But he is also deeply indebted to philosophical Maoism, which emphasizes the nature of division, conflict, and contradiction as the continuous and underlying state of the world. According to Badiou, our current world is defined by two contradictions: first, the division between capitalism and communism; and second, the scission of tradition and modernity. Each form proposes its own internal laws: capitalism commands individual freedom, organizes human relations under competition and private property, and maintains that equality is impossible. According to capitalism, any effort to realize equality will always be violent (Badiou cited the former USSR as a paradigmatic example of this notion). On the other hand, communism does not affirm private property, or competition, or even the state as natural givens.

Another contradiction arises from the schism between tradition and modernity that roughly begins after the Enlightenment. Sedimented identities from the past are typically contained within the notion of tradition — religious, familial, ideological — placing the truth of the present in the past. In this way, tradition opposes innovation; its purpose is to repeat and transmit itself. Modernity wants to further itself as well, but as novelty rather than as pure repetition. Badiou claimed that in the 19th century, tradition aligned with capital (the interests of the bourgeoisie) and modernity with communism (the novel ideas of Marx and Engels). However, in the following era, we find these conflicts creating new and terrifying torsions among themselves: the fascist state, which sought to further genocidal identitarianism within capitalism, and the Stalinist state, whose only claim to novelty was a monstrous version of itself.

Which brings us to our current, and most complex set of entanglements. What is going on now, Badiou suggested, is a particular determination that there is no other kind of modernity than the one that capitalism provides. This is the dominant configuration of the Western world — we don’t have an anti-capitalist modernity that is clear to all. Instead, efforts to enact “strong” change (Badiou cited all recent uprisings, from Occupy to the ongoing situation in Egypt) end up internally fractured by the division between the traditional and the modern. We therefore must propose a rupture between capitalism and modernity, a kind of strong future rather than (to cite Badiou’s own pun on a different vision of human development) “no future.”

It is at this point that many may (and indeed have) taken issue with Badiou’s thought: How can relentless abstraction, and an intimate engagement with ideality, produce a concrete and practical vision of the “new” in the future? Isn’t retrospection really the only affirmation of what is a truth, and what is not? And didn’t Hegel and Mao both teach us that moving past existing contradictions requires something of the suspicious and mystical order of “purification” and, indeed, destruction?

I think that while Badiou’s philosophical writings can be dense, and often difficult to parse in practical terms, his lectures remain full of vibrant and extremely compelling claims. He argues for example that capitalism constructs our notion of what individual freedom is, and that a definition of freedom must affirm equality against capitalism itself, rather than in its service. Or the idea, crucial to the position of the Left today, that we need to elaborate critiques of old forms of political extremes (the fascist state, the communist state) that are different from capitalism’s own critiques of the same entities. Without forms of critique that don’t draw on the language of modern capital, we risk sliding into tautology, repeating capitalism’s subtle but all-encompassing grasp on the definition of our humanism.

In his book The Century, Badiou likens the 20th century — with its simultaneous movements of mass horror and intellectual inventiveness — to an image drawn from Russian poet Osip Mandelstam’s poem “The Age.” It is the image of a beast looking history squarely in the eye, producing terror through the acts of thinking and self-reflection itself. If this is the case for the recent past, what then, will the 21st century ultimately look like?

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Badiou’s second talk, at the University of California, Los Angeles (UCLA), followed up on this strange notion of necessary, but excessive and unbearable terror: the idea of the Real. The Real is crucial to one of Badiou’s main predecessors, Jacques Lacan’s, psychoanalytic thought. It is also an idea that many readers find to be missing in Badiou’s work. But in his lecture, “What is the Real?” Badiou considered the Real as the main current for thinking the impossible, and in some ways, for conceiving the space of emancipatory politics.

In Lacanian theory, the real designates what is excessive, unbearable, but also fundamental to subjectivity. The real resists all symbolization, and it is therefore to be distinguished from reality itself, to which it bears no relationship. In order to “touch” or experience the real we would have to surrender the comfortable distance that symbolization (or language) offers us. Nevertheless, Lacan increasingly suggested that mathematical formalization, or what he calls the “matheme,” bore an opening to the real. While it initially appears counterintuitive to claim that, of all things, mathematics, the discipline of proofs and certainty, can unlock this point of the unconceivable, it is worth remembering (as Badiou faithfully maintains) that math is pure presentation. It does not partake in the gap in which language and signification by necessity must ground themselves (a word stand as a placeholder for what is ultimately absent: the thing that it names, but numbers do not designate anything but themselves). Furthermore, mathematics’ seeming finiteness (countable numbers, ordering, rules) belies its extraordinary relationship to infinity (numbers are infinite, so is the void that grounds them): the closest thing we may have (outside of theology) to the “impossible.” For Badiou, infinity as a condition of numbers, and their ultimate possibility, offers a kind of truth of the real.

How can this help us understand contemporary politics? It’s a bit of jump from abstract thinking to the realm of the political, but according to Badiou, if the real is generally what cannot be inscribed inside any kind of formalization, but is a necessary impossibility for form to exist, revolution acts a kind of “real” to the bare reality of the state. Revolution — a rupture with the “finitude” of the state — inaugurates infinity, albeit often terrifyingly and unexpectedly. The political real is thus much more than simply a form of non-meaning. It takes on the resonance of an “act” which subtracts itself from the laws of what is currently possible in any given state-based political situation or reality. For Badiou this act always means declaring equality — capitalism’s point of impossibility — an actual principle. The real is first and foremost an affirmation that “the impossible exists.”

Poetry showcases another opening to the real in Badiou’s thought, a violent struggle for it that he considers “prophetic.” The second half of Badiou’s talk focused on an elegy of sorts for Antonio Gramsci by the Italian poet and essayist Pier Paolo Pasolini entitled “The Ashes of Gramsci.” Buried in the Protestant cemetery in Rome, a resting place for all exiles, minorities, and general “heretics” to the Catholic state, Gramsci and his death represent for Pasolini an escape into the real. Because his death is so radically removed from all socially sanctioned forms of political life, Gramsci appears outside the state, though for Pasolini he cannot be forgotten, and he leaves traces that can only be thought through in poetic, rather than narrative language. This, for Badiou, is a kind of affirmation of the real.

The issue here is Pasolini’s overtly “tragic” grasp of the real. The poem is no doubt beautiful, poignant, and it pursues something that cannot be fully made clear in prose or description, something we could call “the real.” But there does seem to be an element in Badiou’s reading of Pasolini that gestures toward an obituary for the past: a century that strove for the real, whose own avant-garde managed to let it down.

While Badiou’s discussion of the poetic real in Pasolini seemed less congruent than his opening account of the real of mathematics, the message seems clear: radical thought should be uncompromising and ceaseless, driven toward an absolute, even if that means, as is the case for Pasolini’s vision of Gramsci, that one is exposed to failure. But it also need not be destructive and given to the endless movements of negation. Badiou’s most compelling assertion is that contrary to what we might want to believe, opening ourselves to the real can and should be “joyous.”

Badiou’s final talk, “Theater and Philosophy,” also delivered at UCLA, engaged with the most communal and therefore vital of art forms: drama. Having written a number of plays and commentary on theater since the 1960s, Badiou seems, in some ways, most at ease discussing theater and its relevance to philosophical thought. This final lecture focused on the distinction between Badiou’s preferred thinker, Plato, and everyone else’s favorite, Aristotle. While all of Plato’s writings are in the form of dialogues, a kind of theater, Aristotle inaugurates the chosen format for most philosophical work up until the present day: the academic treatise. But while Plato vehemently cautions against epic poetry and dramatic poetry (forms of theater) in The Republic, for instance, Aristotle maintains the quiet difference between theater and philosophy that should allow both to exist, albeit separately. Aristotelian theater purifies through catharsis, and therefore engages the audience in momentary terror and identification. For the audience, this movement facilitates a complete return from the limits of theatrical excess back to “normal” subjectivity (finally purged of its extreme desires and horrors). But philosophy is notably different: it is objective, and driven by reason.

In some ways, Badiou took us back to the origin of aesthetics in Western thought to consider what art can tell us about political life. Aristotle is at peace with theater, in a finally “indifferent” way. Plato’s version of theater is prone to corruption by dominant opinion, and is therefore dangerous. But it is also a movement and an action, the goal of which is to transform subjectivity. Plato is therefore suspicious of any therapeutic effect theater may have, since it is a movement of thinking, and not an act of representation that buries its own phantasms. Which is why, for Badiou, Plato’s theater is ultimately the “progressive possibility of the impossible.” Rather than a quiet reconciliation, it is the language of violent contradiction, of the engine of the dialectic itself. Like the ideas theater articulates in Plato’s work, theater is “luminous,” pleasurable, and active. And it reaches, most important, toward a truth.

Theater allows Badiou to consider a fundamental question put forth by the origins of philosophy: What is the ideal of existence? A good life or a true life? An acceptance of what exists, or a subjective will to change the world? Or, put another way, we can be at peace with the world as it is, and others as they are, or make a choice — necessarily discontinuous, of the order of rupture — for what must exist: namely the impossible.

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Badiou has become a bona fide celebrity in the philosophy world, enough so that his lectures begin to attract not just students and academics but quasi-leftists of all persuasions. While many could claim that renewed talk of revolutionary politics is at the end of the day merely armchair radicalism, democratizing philosophy is still crucial to not reproducing the Left’s death grip on its own cultural capital. For this reason alone, it worth considering Badiou’s continued efforts to make the idea of communism more than just a far-off dream with no definite contours. It points us in the direction of collective affirmation that can be at once political, aesthetic, deeply personal, and finally revolutionary.

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Ronjaunee Chatterjee is a doctoral candidate in the English Department at UCLA. She is finishing a dissertation on femininity and singularity in the 19th century.