French philosophy in the twentieth century was marked above all by two projects.footnote1 For the sake of simplicity we might distinguish them with the labels of ‘subject’ and ‘science’. On the one hand, thinkers influenced by phenomenology and existentialism—Sartre, Fanon, de Beauvoir, Merleau-Ponty—embraced more or less radical notions of individual human freedom, and on that basis sought to formulate models of militant collective commitment that might engage with the forms of oppression or domination that constrain the subjects of a given situation. On the other hand, thinkers marked by new approaches in mathematics and logic, and by the emergence of new human sciences such as linguistics or anthropology, attempted to develop more adequate methods to analyse the fundamental ways in which a situation might be ‘structured in dominance’. In the 1960s in particular, many thinkers came to the conclusion that a concern for the subject or for individual freedom was itself one of the main mechanisms serving to obscure the deeper workings of impersonal and ‘inhuman’ structure, be it unconscious, ideological, economic, ontological, or otherwise.

It may be no exaggeration to say that, leaving aside obvious differences between them, the most significant French thinkers of the last third of the twentieth century—Deleuze, Foucault, Lacan, Derrida—all sought to develop forms of thinking that might integrate or at least accommodate aspects of both these projects; and that, conditioned by a broadly ‘scientific’ anti-humanism, might decentre but not simply exclude the role of an active subject. What is immediately distinctive about Alain Badiou’s contribution to this endeavour is the trenchant radicalism of his own peculiar subject-science synthesis. The basic elements of Badiou’s project are familiar: to renew quasi-Sartrean notions of project and commitment in terms compatible with the anti-humanist analysis of structures developed by Althusser and Lacan, and perhaps more importantly, with the scientific or ‘mathematizing’ formalism characteristic of the French epistemological tradition. But unlike any other major thinker of his generation—he was born in Rabat in 1937—Badiou formulates this synthesis in the uncompromising and unfashionable language of truth. Badiou’s chief concern has been to propose a notion of truth that holds equally true in both a ‘scientific’ and a ‘subjective’ sense. A truth must be universally and even ‘eternally’ true, while relying on nothing more, ultimately, than the militant determination of the subjects who affirm it.

This means that philosophy should concern itself with the consequences of truths that are both universal and exceptional. Philosophy thinks truths in the plural—truths that are produced in particular situations, that begin with a specific revolution or event, that are affirmed by a specific group of subjects, and upheld in the face of specific forms of reaction or denial. By ‘holding true’ to their consequences, the militant partisans of such truths enable them to persist, and to evade the existing norms of knowledge and authority that otherwise serve to differentiate, order and stabilize the elements of their situation. The discoveries of Galileo or Darwin, the principles defended by the French or Haitian revolutionaries, the innovations associated with Cézanne or Schoenberg—these are the sorts of sequences that Badiou has in mind: disruptive and transformative, divisive yet inclusive, as punctual in their occurrence as they are far-reaching in their implications.

Against the mainstream analytical tradition that conceives of truth in terms of judgement or cognition, against Kant as much as Aristotle, Badiou has always insisted (after Plato, Descartes, Hegel) that the material and active creation of truth is not reducible to any merely logical, linguistic or biological ‘capacity of cognitive judgement’.footnote2 Within a situation, a truth is the immanent production of a generic and egalitarian indifference to the differences that (previously) structured that situation. Perhaps the two most important general notions that underlie this philosophy of truth are fidelity and inconsistency. However varied the circumstances of its production, a truth always involves a fidelity to inconsistency. The semantic tension between these terms is only apparent. Fidelity: a principled commitment, variously maintained, to the infinite and universalizable implications of a disruptive event. Inconsistency: the presumption, variously occasioned, that such disruption touches on the very being of being. Inconsistency is the ontological basis, so to speak, of a determined wager on the infinitely revolutionary orientation and destiny of thought. Fidelity is the subjective discipline required to sustain this destiny and thus to affirm an ‘immortality’ that Badiou readily associates with the legacy of Saint Paul and Pascal. Inconsistency is what there is and fidelity is a response to what happens, but it is only by being faithful to the consequences of what happens that we can think the truth of what there is. In every case, ‘the truth of the situation is its inconsistency’, and ‘a truth does not draw its support from consistency but from inconsistency’.footnote3

To think the being of a situation as inconsistent rather than consistent is to think it as anarchic and literally unpresentable multiplicity. Badiou posits being as the proliferation of infinite multiplicity or difference, rather than as the orderly manifestation of stable and self-identical beings. For reasons explained in Being and Event (1988), the premise of Badiou’s ontology is that the innovative edge of modern thought, when confronted with the ancient alternative of either ‘one’ or ‘multiple’ as the most abstract and most fundamental quality of being, has decided in favour of the multiple. (This decision immediately implies, Badiou goes on to argue, that ontology itself should be identified with the only discipline capable of rigorously thinking multiplicity as such: post-Cantorian mathematics.) As far as the discourse of being is concerned, the multiple having priority over the one means that any figure of unity or identity, any conception of a being as a being, is itself secondary. Unity is the derivative result of a unifying or identifying operation performed upon a being that is itself without unity or identity, i.e. that in-consists.footnote4 Badiou admits that we can only ever experience or know what is presented to us as consistent or unified, but it can sometimes happen, in the wake of an ephemeral and exceptional event, that we have an opportunity to think, and hold true to, the inconsistency of what there is.