Alain Badiou, Logics of Worlds: Being and Event II, trans. Alberto Toscano, New York and London: Continuum, 2009, 640 pp., $29.95 .

- John McSweeney (Milltown Institute)

In his magnum opus L’Être et l’événement (1988, trans. Being and Event [2005]), French philosopher Alain Badiou deployed post-Cantorian mathematical set theory to elaborate a novel ontology of the pure multiple capable of accounting for the complexity of a postmodern world, but equally capable of rejecting the postmodern erosion of politics before infinite differ-ence. (The pure multiple is conceived of, by Badiou, as a Zermelo-Fraenkel infinite set whose elements are themselves infinite sets, yet which, following Cantor, are countable.) Equally, he elaborated a powerful theory of the event, as an exceptional element of a situation from which the subject, act-ing in fidelity to it, can derive the truth of the situation. Although seminal for recent efforts to rethink the political within continental philosophy, this work, as Badiou himself recognized, remained a formal ontological analysis, which could identify the subjective function (“fidelity”), but could not ade-quately elaborate subjectivity as such. Furthermore, although suggestive of ways of thinking about concrete worlds, it did not yet describe a world at the level of appearance. Logiques des mondes (2006) – now translated as Logics of Worlds by Alberto Toscano, in a fine translation and timely publication – is Badiou’s eagerly-awaited follow-up to Being and Event, which sets out to address both these issues.
The earlier work’s notion of subjectivity as fidelity, rather than (for in-stance) as grounded in consciousness, allowed Badiou innovatively to pro-pose that political subjectivity is the subjectivity of a political movement rather than that of individuals, or, again, that, in cases of love, it is the cou-ple as couple who constitute its subject. Nevertheless, the reduction of sub-jectivity to an ungrounded decision for an event, and fidelity to it, risked the charge of decisionism. Now, in Logics of Worlds¸ Badiou provides a more complex framework within which to locate subjectivity. First, against criti-cisms that he limits what counts as an event rather arbitrarily, he proposes a four-fold typology of change. Alongside a decisive event, there are “modifi-cations” (change that does nothing to alter a world but is a moment of its re-production), “facts” (genuine but weak novelty), and (weak) “singularities” (intense quasi-events that have few consequences). Second, he further de-lineates the space of subjectivity, by suggesting two additional distinct pos-sible responses to an event: the “reactive subjectivity” that denies the event and the “obscure subjectivity” that assimilates the event in a manner that circumscribes its effects. Third, Badiou argues that subjective decision arises at specific “points” within a world, where its complexity becomes condensed to a binary either-or decision, for or against an event. Moreover, he allows that these decisions are embodied, although these bodies need not be organic bodies, but e.g. the various “bodies” developed by a revolution-ary force. Faithfulness to an event in a real sense thus involves becoming, point by point, the truth to which one is faithful, developing a physical im-petus toward change in a given world. Finally, he offers the insight that our capitalistic “democratic materialisms” induce “atonic” worlds, that is, worlds without decisive “points.” In response, he further broadens his sub-jective framework to allow for some importance to strictly pre-subjective action and analysis, which can bring the elided decisive “points” of our worlds to appearance. Thus, acts of resistance, protest, and critique, be-comes important as ways of forcing points of decision within a world.
Second, in the major focus of the work, Badiou deploys the sheaf the-ory and category theory associated with the mathematics of topology to con-struct an “objective” rather than a “subjective” phenomenology of appear-ance, against the post-Kantian tradition. The mathematics here is daunting, perhaps even more so than in the earlier work. Nevertheless, Badiou’s basic argument is relatively clear. Beginning from the idea that there is no one world (a “universe” that would explain the apparently different worlds we each occupy), he argues for a multiplicity of worlds each governed by a “logic of appearance.” Badiou offers multiple examples of such worlds, ranging from the manifold reality of a demonstration within a public space, to the peaceful surroundings of a house in the country on a summer’s event-ing. His point is that these are not simply different perspectives upon a sin-gle reality (e.g. mediated by different language-games), but that the “being-there” of pure multiples is characterized by a multiplicity of appearings of worlds. As Slavoj Žižek has put it, Badiou’s multiples have no “underlying” modes of being-there apart from their appearing in multiple worlds.
Badiou can support such a conception because he defines the being-there of each pure multiple as having a degree of intensity of appearing in each world within which it appears. Within his mathematical framework, intensity is a qual-ity of individual multiples rather than a relational quality, so that one can com-pare the relative intensities of multiples within a world without having to posit an interrelationship between them. (The logic of appearing is governed, Badiou argues, by the multiple having “maximal” intensity.) Thus, it becomes feasible to think multiples as having distinct intensities in multiple worlds, without these worlds becoming entangled and “bleeding into” one another. Moreover, deploy-ing the framework of modes of change, modes of subjectivity, embodied be-coming, and points, it becomes possible to think these worlds dynamically as sites of contested, multivalent change.
Although it addresses questions left open by Being and Event, Logics of Worlds is not simply an addendum to the earlier text, but a major work in its own right. It opens up significantly new terrain in political philosophy in the continental tradition, not least suggesting novel ways in which the im-possible (a critical philosophy that is not bound by the subjective post-Kantian tradition) may in fact be possible. Moreover, its novel style (com-bining abstract mathematical analysis and a proliferation of concrete exam-ples and autobiographical references) and intent (the conclusion is entitled “What is it to Live?”) are concerned with articulating nothing less than a passionate politics and ethics, grounded in the worlds within which we live today, and specifically those in which Badiou himself is immersed and im-merses himself. To echo the title of one of his earlier works, it is perhaps his most profound manifesto for philosophy, as well as a manifesto, to echo Gilles Deleuze, for “a life.”
At the same time, the work is not without its tensions. Although Badiou has contextualized subjective decision and fidelity in ways that significantly re-duce charges of decisionism, he is nonetheless insistent upon a sharp distinction between the subjective and the pre-subjective that proves difficult to maintain. The problem here is less decisionism as such than that of doing justice to the continuity of what Badiou terms pre-subjective and subjective experience, or what others might simply term subjective experience. For example, how might one prepare the ground for decision without some judgment about where “points” lie, or decide for an event without some subjective sense that a given occurrence is an event? Even if events cannot strictly be known (they exceed the existing order of a situation), this does not prevent subjective processes playing a role in deciding for an event.
A second difficulty is one long since highlighted by Badiou’s commentator Peter Hallward. Hallward has consistently argued that Badiou’s mathematical models abstract excessively from human reality, a significant casualty being the notion of relationality (as has been seen, above, in his logic of appearance). The point is well made, but a qualification might be added. It is arguable that Badiou’s deployment of mathematics is part of a “truth procedure” in fidelity to the Cantorian event of thought that inaugurates modern mathematics. The pur-pose of this deployment would, then, according to Badiou’s own logic, be to ex-ceed and disrupt our current ways of thinking. But as with any event, truths do not entirely displace existing knowledge but remain in a relation of disruption to them. In this light, less concern needs to be expressed over the adequacy of Badiou’s mathematics in modeling human reality, as it would not constitute such a model, but something approaching a corrective that reveals new possibilities within the situation. This, in turn, would raise questions about the status of Badiou’s ontology and logic of appearing, and whether he consistently refuses to construct an alternative order of knowledge in favor of generating a disruptive truth-procedure. Equally, it would place emphasis upon whether Badiou has suc-ceeded in identifying a real event of thought and not, say, merely a “weak singu-larity.” Of course, to defend Badiou’s mathematical approach in this way is to turn attention to the question of the performative subjectivity by which he con-structs his works and its consistency with the subjectivity delineated in them. This, in turn, suggests that, in spite of significant achievements in reorienting contemporary continental thought toward truth and objectivity, the principal per-sisting tensions in Badiou’s work circle about post-Kantian-sounding questions of subjectivity that resist reduction to his refiguring of subjectivity as fidelity.