Ontology and World Politics

The contemporary discourse on world politics in IR theory oscillates between the two extremes of unproblematic presupposition and sceptical denial. On the one hand, the studies of global governance, norms, regimes and institutions take as a point of departure the existence of a worldwide dimension of politics, which is then specified in various ways. According to this logic, which is at work in e.g. idealist, liberal and constructivist theories, the referent domain of world politics exceeds the state-centric realm of ‘international relations’ and permits to incorporate into the discipline such formerly ignored problematics as gender, culture or identity as well as such formerly ignored actors as social movements, indigenous peoples and other minorities. In this manner, politics moves from the narrow confines of the international society of states to the widest possible, presumably universal domain of the world as a whole (see Lipschutz, 1992; Linklater, 1998; Albert, 1999; Wendt, 2003). On the other hand, realist approaches as well as critical orientations, from neo-Marxism to post-structuralism, maintain their scepticism about the very possibility of attaining such a universal dimension of politics or remain wary of the hegemonic aspirations at work in any attempt to practice politics on a ‘world’ level (Calhoun, 2002; Rasch, 2003; Odysseos and Petito, 2007; Mouffe, 2009; Dillon, 1995; Edkins, 2000; Edkins and Pin-Fat, 2005; Vaughan-Williams, 2009). While the debate between these two orientations has taken a myriad of forms throughout the history of the discipline (see Walker, 1993; Thies, 2002), what interests us is the status of the very idea of world politics, which oscillates between a presupposition that is so self-evident as not to merit a conceptual explication and a problematic phantasm, only accessible to thought in the form of a hegemonic pretension (cf. Walker, 2009: 20–28). We either do not need to know what world politics means, since it is ‘common knowledge’, or we cannot know it, since such knowledge is inaccessible, inconsistent or plain false. In this chapter we shall argue that this undecidable oscillation is due to the inconsistent concept of the world at work in the discourse on world politics in IR. We shall analyse three possibilities of conceptualizing the world and present the concept of the world as the void, which alone provides an ontological ground for overcoming the ambivalence of world politics in political and IR theory.

This constitutive ambivalence of world politics may be illustrated with the help of two influential monographs on the subject, Jens Bartelson’s Visions of World Community (2009) and R.B.J. Walker’s After the Globe, Before the World (2009). Both of these works offer highly sophisticated meta-theoretical interventions into the discourse on world politics that nonetheless persist in the oscillation between presupposing and denying its very existence. For Bartelson, the problematic status of the concept of the world community in the disciplinary discourse has to do with the differential logic of identity that has been constitutive of the discipline (Bartelson, 2009: 9–10). According to this logic, every identity is constituted by distinction from an ‘other’. Since a world community would lack such an other by definition, it is henceforth held to be impossible other than as a hegemonic imposture that claims for itself the universality it can never attain.

[As] long as we remain committed to this particularistic ontology, we will have a hard time making theoretical sense of any kind of human community over and above the plurality of particular communities presently embodied in the states system. As long as we regard the logic of identity as a predominant source of human belonging and identification, the formation of a community of all mankind will look highly unlikely because there are no human Others left that could provide it with a sense of sameness.

(ibid.: 42–43)

In his historical analysis of the visions of world community, from Dante to Kant, Bartelson demonstrates that this logic of identity is a relatively recent invention and can therefore be overcome by a return to an earlier understanding of world community as a wider cosmological context, in which a plurality of human communities are always already embedded.

[It] is not meaningful to distinguish categorically between communities of different scope, since all human communities derive from the same underlying and species-wide capacities. Human beings as well as the communities to which they happen to belong, are essentially embedded within a wider community of all mankind, within which the totality of human relations unfolds across time and space.

(ibid.: 11)

This emphasis on embeddedness directs Bartelson’s attention to the cosmological visions, within which the ideas of world politics and world community have been articulated since the Middle Ages. These visions escape the differential logic of identity by ‘positing a larger social whole within which all human communities are embedded as well as a vantage point over and above the plurality of individual communities, from which this larger social whole can be understood’ (ibid.: 20). Simply put, in order to break out of the pluralistic and particularistic logic of identity, it is sufficient to posit the world ‘as a universal and boundless phenomenon’ (ibid.: 43), within which all other communities as well as their individual members coexist. As a result of this move, the pluralistic logic of identity is brought back to its proper place within the overarching universality of the world community. Bartelson brilliantly demonstrates the way this logic of identity emerged as a result of a series of conceptual appropriations that he calls ‘nationalizations’, performed on the Medieval understanding of the world community as always already there, a ‘larger whole’ immanent to human existence as such (ibid.: 86–113, 167–170). While this appropriation has been remarkably successful both in theory and practice, it is possible to ‘restore the default settings of political thought’ (ibid.: 175) and reaffirm the world community no longer as an obscure telos of international politics, but as its very condition of possibility, something that is already here in the form of the presupposition , as long as human beings inhabit the same planet and share a common destiny. Yet, this reaffirmation ‘depends on its coherence and persuasiveness on the existence of a cosmological vantage point situated over and above the plurality of human communities and the multitude of individual human beings’ (ibid.: 181). In order to inspire resistance to all ‘forms of authority that keep mankind divided’ (ibid.: 181), the idea of the world community must be grounded in a cosmological concept of the world.

[The] relationship between cosmological beliefs and conceptions of human community is contextual in character, insofar as knowledge of the former helps us make sense of the latter and vice versa. One of the challenges posed by the idea of world community is that of constructing a cosmology common to all mankind, so that all human beings will eventually come to inhabit the same conceptual world.

(ibid.: 12)

In other words, our cosmologies of the world contextualize our conceptions of community and the other way round. Given the sheer diversity of cosmological visions of the worlds that Bartelson considers in his study, this argument cannot but appear paradoxical. If it is only in the context of a particular cosmology of the world that the concept of the world community can arise in the first place, it must logically be particular as well. We are thus back to the logic of identity, which, for all its historical contingency, ends up working even in the historical contexts where it was presumably absent. Having linked the concept of world community to the cosmological vision of the world, Bartelson must admit the historical plurality of ‘cosmological vantage points’ and is thus left with a myriad of particular figures of the ‘greater whole’, some of which admit of a world community more readily than others. While Bartelson does not identify with any particular historical cosmology and defers the question of the world community into the future when the ‘challenge of constructing a cosmology common to all mankind’ is successfully overcome, this deferral evidently does not resolve the question of what, if anything, could render this future cosmology more genuinely universal than its historical antecedents that, after all, also constructed worlds ‘common to all mankind’, which did not prevent the articulation of particularistic communities within them.

According to R.B.J. Walker’s After the Globe, Before the World , this is merely one of the aporias that await any discourse on world politics and make any invocation of a universal politics of the world highly dubious. Walker addresses the ways in which numerous attempts to move from international relations to world politics remain caught up in what they try to transcend, i.e. the ontopolitical tradition of modernity, which is itself already an attempt at resolving the antinomies, whose resolution we now associate with the idea of world politics (e.g. universalism/ particularism, nature/culture, individual/community, etc.) (Walker, 2009: 54–94). The ‘seduction’ and ‘temptation’ of world politics belong to the very tradition of the ‘international’ as its inherent transgression, something simultaneously desired and held impossible, or perhaps desired precisely and only as impossible (ibid.: 24, 83). For Walker, the question of world politics is always more difficult than it seems and the task of critical discourse is, in full accordance with Kant’s critical project, to guard its object against the illegitimate application of the powers of reason to it.

Thus, any inquiry directed by Walker’s approach is only bound to take us further away from the knowledge of what world politics is, while enhancing our knowledge of why this knowledge is impossible. Wherever we are, we are always ‘before’ the world, facing it as distant and inappropriable. Universalist claims are always ‘[enabled] within a particular array of boundaries, borders and limits’ and a ‘politics of the world’ that promises to do away with those remains ‘necessarily beyond reach’ (ibid.: 257–258). Thus, ‘anyone seeking to reimagine the possibilities of political life under contemporary conditions would be wise to resist ambitions expressed as a move from a politics of the international to a politics of the world, and to pay far greater attention to what goes on at the boundaries, borders and limits of a politics orchestrated within the international’ (ibid.: 2–3, see also 184–257). While there are numerous possibilities for political experimentation at these liminal sites, we would do well to remember that this experimentation always takes place on this side of the borderline. Thus, while Bartelson seeks to ‘deproblematize’ the question of world community, trying to rid it of logical paradoxes by enfolding the problematic of community into an explicitly cosmological context and thus making the world the a priori site of any community whatsoever, Walker hypertrophies this question, making it practically impossible to exit the condition of the international at all. World politics thereby appears to be endlessly oscillating between being presupposed as self-evident and unmasked as impossible.

It is easy to see that this perpetual debate cannot be restricted to the domain of ‘IR theory proper’, since it pertains to the conditions of possibility of the very disciplinary discourse of IR that necessarily remain inaccessible to this discourse (Foucault, 1989: 146–147). Nor may this debate be resolved within the domain of political science understood as the study of ‘domestic politics’, delimited from the international realm. As Bartelson (1995) has demonstrated, the disciplinary discourses of political science and international relations are constituted by the mutual exclusion of each other’s objects, whereby the positive delineation of political science is made possible by the delimitation of politics from the field of the international and its confinement inside the state, while the constitution of the discipline of international relations is enabled by bracketing off the conditions of possibility of the very objects, whose relations this discipline investigates. Thus, the two domains of knowledge are ‘united in a symmetrical relationship to each other: each discourse takes for granted exactly that which the other takes to be problematic’, the internal and external aspects of state sovereignty (Bartelson, 1995: 47). IR theory accords ontological priority to the state, which implies the givenness of internal sovereignty as the defining property of the antecedently present entity. Conversely, political science has external sovereignty as its unproblematic foundation, whereby the origins of the state are explained away with reference to exogenous dynamics of the ‘international’, the state emerging in the course of consolidation of power through perpetual warfare.

As long as the domains of political and IR theory remain constituted by what remains outside them, they can at best illuminate their own limits by pointing to each other’s blind spots. The overcoming of these limits requires a move to the level that precedes the very delimitation between inside and outside, external and internal, domestic and international, political science and IR. The question of world politics must be posed anew, no longer as the question of the possibility of the ‘domestication of the international’ in the form of the world state or the ‘internationalization of the domestic’ in the form of globalization, but rather as the question of a politics that precedes and exceeds this very distinction and has its locus and the source of its contents in the world as such. This question must therefore be relocated from the positive fields of knowledge, constituted by the prior division of the world into the domestic and the international, towards the ontological terrain, in which the being of the world as a domain of a possible politics may first be questioned.

The move beyond the positive sciences of (inter)national politics entails that world politics may no longer be conceived in terms of the expansion of an already constituted domain of politics to a new, higher level or in terms of the articulation of new political content in the already constituted domain of the world. Both politics and the world must be problematized and redefined if the question of world politics is not to relapse into the familiar setting of (inter)national politics. The question of world politics is not merely a question of a possible passage ‘beyond’ the international that necessarily presupposes it as a point of departure but abandons the international even as a presupposition , its only legitimate starting point being the world itself. Thus, the ontological inquiry into world politics must proceed in three steps. First, we must elaborate the ontological concept of the world that may be a logically consistent ground of any possible politics. Second, we must define the notion of politics in general on the basis of this concept of the world as opposed to any distinctions drawn within this world. Only then, third, may we pose the question of world politics as a mode of politics that fully corresponds to its own concept. In the remainder of this chapter we shall take the first step by focusing on three possible concepts of the world.

Despite their diverging conclusions about the possibility of world politics and the world community, Bartelson and Walker appear to converge in the basic assumption about the sense of the ‘world’ in world politics. Bartelson’s world, which is already ‘behind’ us as an all-encompassing whole, within which we are embedded, and Walker’s world, which stands ‘before’ us as an unattainable universality, are indeed one and the same world, understood in the sense of the Whole , a cosmos, universe or totality, in short, everything . It is precisely this understanding of the world as the whole that accompanies the discourse on world politics from the very emergence of the IR discipline (see e.g. Morgenthau, 1948: Chapters 29, 30; Carr, 1981; Schmitt, 1976; Burton, 1972; Boulding, 1985). Whether or not one approaches world politics as already present or radically impossible, desirable or threatening, the world remains thought as the whole, the sum of all there is. Yet, what could possibly be wrong with this understanding of the world as the universal totality, which, after all, seems perfectly in accordance with common sense?

Let us posit the world as the whole, the sum of all beings. Such a totality must by definition count itself among its members, otherwise it would not be the sum of all beings, since it would remain outside itself. The world as the whole is thus endowed with a property of self-belonging. It should then be possible to divide it into two parts: the parts of the world that belong to themselves, such as the world itself, and the parts that do not, such as e.g. a set of five apples, which is not itself an apple. Let us then assemble the latter parts into a group of all parts that do not belong to themselves – a perfectly legitimate and even banal grouping, given that most multiplicities that we can think of are precisely not self-belonging. Yet, despite the banality of the predicate, this grouping turns out to be problematic as soon as we pose the question of whether it belongs to itself. If it does, it must count itself among its elements, which are defined by the property of not belonging to themselves. Yet, if it does not belong to itself, it must also count itself among its elements, which, after all, compose all the parts that do not belong to themselves. Whatever answer we choose, we end up with inconsistency, hence we must revise our original assumption and affirm that the world as the sum of all beings does not exist .

It is easy to recognize in this example a reformulation of Russell’s paradox, which has been foundational for the formulation of axiomatic set theory in the early twentieth century. Yet, how is set-theoretical logic relevant to the grand debates on world politics? After all, as twentieth century Continental thought from Heidegger to Foucault demonstrated, the universalist claims of logic and mathematics are highly problematic, both of these discourses being particular ‘regimes of truth’ among others. Yet, while the mode of thought inaugurated by set-theoretical logic might be particular, what is at stake in adjudicating its applicability to world politics is precisely what this particularity actually consists of. In Alain Badiou’s famous argument, set theory is in fact nothing other than ontology pure and simple, since it deals with being qua being and not any particular classes of beings, let alone their properties: being as such is nothing but pure multiplicity that can be adequately grasped by set-theoretical axioms precisely insofar as they subtract being from the positive properties of beings (Badiou, 2005a: 4–16).

Indeed, as long as we conceive of ontology in the rigorous Aristotelian sense as the study of being qua being rather than, in the currently widespread manner, as a fundamental worldview, social theory or even ideology (cf. Bosteels, 2010: 242), set theory offers the best paradigm of a theory of being as such as opposed to theories of particular beings or realms thereof. Sets are not a particular class of beings alongside others, e.g. human beings or social kinds, but rather the mode of presentation of all beings solely in their being (Badiou, 2005a: 23–30). For this reason, the axioms of set theory necessarily pertain to everything that is , including the entities of the international domain and the world as the result of their hypothetical totalization. To exclude these entities (be they states or persons, organizations or movements, etc.) from the field of application of set-theoretical axioms is simply to deprive them of being and reduce them to the status of simulacra , phenomenal apparitions without any ontological status. Yet, even if we were, if only for the sake of the argument, to assign the international domain to the status of a simulacrum, this would not help in removing the concept of the world from the zone of application of set-theoretical axioms. If the world is the whole, it must include not only the simulacra that are not but also all that there is , i.e. all entities to which set theory does apply. In short, as soon as we pose the problem of the world in ontological terms, the set-theoretical argument on the inexistence of the whole appears not merely applicable to the discourse on world politics but of direct and paramount relevance to it.

We may therefore conclude that concept of the world, understood in terms of cosmos, universe or totality, is ontologically inconsistent: the Whole has no being (Badiou, 2005a: 40–42; 2009b: 109–111). We must emphasize that this claim does not merely concern the antiquated pre-Galilean conceptions of the closed totality of the cosmic order, whose crisis was addressed by Alexandre Koyre (1957) in his seminal work From the Closed World to the Infinite Universe . Our argument works as much for the ‘closed world’ as for the ‘infinite universe’. The inexistence of the whole is an ontological principle that is irreducible to any particular cosmology and rather throws into disarray the entire cosmological enterprise. While Bartelson (2009: 10–13) equates cosmological accounts of world community with what he terms ‘social ontology’, in our argument ontology rather serves as a stumbling block for any cosmology whatsoever. The consequence of Russell’s paradox is the impossibility of totalizing being as such, not the being of any particular world, including our physical universe: ‘The question of the limits of the visible universe is but a secondary aspect of the inexistence of the Whole’ (Badiou, 2009b: 111). Thus, any cosmology is ontologically inconsistent, lacking any foundation in being.

Every multiple being enters into the composition of other multiples without this plural (the others) ever being able to fold back upon a singular (the Other). For if all multiples were elements of one Other, that would be the Whole. But since the concept of Universe inconsists, as vast as the multiple in which a singular multiple is inscribed may be, there exist others, not enveloped by the first, in which this multiple is also inscribed. In the end, there is no possible uniformity among the derivations of the thinkability of multiples, nor a place of the Other in which they could all be situated. The identifications and relations of multiples are always local.

(ibid.: 112)

As Jean-Luc Nancy has argued in his Sense of the World (1997), the only plausible cosmology can therefore only be strictly acosmic : ‘[T]here is no longer any world: no longer a mundus , a cosmos , a composed and complete order, from within which one might find a place, a dwelling and the elements of an orientation’ (ibid.: 4). And yet, this acosmism is not a matter of the deficiency of the contemporary or any other world but rather pertains to its very ‘worldhood’:

That there is not everything (or not the whole) does not define a lack or an ablation, since there was not any whole before the not-the-whole. It means rather that all that is (since there is really all there is) does not totalize itself, even though it is all there is.

(Nancy cited in Morin, 2012: 45)

For Nancy, the exhaustion of the myths of cosmos and mundus as universal totalities calls for the understanding of the world that does not presuppose the representation of its totality by the subject of cosmological reason:

We do not yet have a cosmology adequate to this noncosmos, which, moreover, is also not a chaos, for a chaos succeeds on or precedes a cosmos, while our acosmos is neither preceded nor followed by anything: on its own, it traces – all the way to the confines – the contour of the unlimited, the contour of the absolute limit that nothing else delimits. But it is a cosmology of this sort that we need, an acosmic cosmology that would no longer be caught by the look of the kosmotheoros , of that panoptic subject of the knowledge of the world, whose figure shed, in Kant’s work, for one last time, its last brief rays.

(Nancy, 1997: 48; see also 2007: 47)

Moreover, contrary to the contemporary cosmologies of the ‘infinite universe’ we must not confuse infinity with universality. In fact, the key philosophical accomplishment of set theory is precisely its ‘desublimation’ of the question of infinity, which is approached as a property of a ‘local’ set and not of beings ‘as a whole’ (Badiou, 2008a: 100, 106–112). According to Badiou (2005a: 142–143), classical metaphysics combined the Greek understanding of the finitude of being with the monotheistic affirmation of divine infinity. The infinite thus pertained not to being-qua-being but to that being that was beyond being (God). In contrast, set theory does not merely argue for the infinity of being or ‘nature’, which could easily be recomposed into the totalized figure of the infinite universe, but also ‘[proposes] the vertigo of an infinity of infinities distinguishable within their common opposition to the finite’ (Badiou, 2005a: 146). Set theory affirms an infinite proliferation of different infinite quantities, making it possible to distinguish between ‘larger’ and ‘smaller’ infinities.

Three features – the infinite’s indifferentiation, its post-Cantorian treatment as a simple number and the pluralization of its concept (there are an infinity of different infinities) have all combined to render the infinite banal, to terminate the pregnancy of finitude and to make possible the assumption that every situation (ourselves included) is infinite.

(Badiou, 2008a: 100, emphasis in original) ¹

Thus, the insistence on the infinity of the world has nothing to do with the conception of the world as the whole. Moreover, it is precisely because the world is infinite that it cannot be totalized into any figure of the whole without violating Georg Cantor’s theorem, foundational for set theory (see Badiou, 2005a: 142–160, 265–280). For any set whatsoever, it is possible to construct a set, whose elements are all the subsets of the original set, a so-called ‘power set’. We may easily intuit that this set would be quantitatively greater than the original set: e.g. the number of possible combinations of any three letters a, b and c is eight (a, b, c, ab, bc, ac, abc and finally the void set Ø, which is included as a ‘universal part’ of any set and which we shall discuss in detail below). Cantor’s theorem demonstrates that for infinite sets the size (or, in technical terms, cardinality) of this power set is also greater than that of the original set, and, moreover, it is inaccessibly greater. It is impossible to measure the excess of the set of parts over the original set, which remains open to choice – it is possible to posit any infinite cardinal greater than that of the original set as the ‘size’ of its power set (ibid.: 277–280).

[We] know, since Cantor, that infinities are multiple, that is to say, are of different cardinalities – more or less ‘large’ like the discrete and continuous infinities – and, above all, that these infinities constitute a multiplicity it is impossible to foreclose, since a set of all sets cannot be supposed without contradiction. It is possible to demonstrate that, whatever infinity is considered, an infinity of superior cardinality necessarily exists. One need only construct (something that is always possible) the set of the parts of this infinity. From this perspective, it becomes impossible to think a last infinity that no other could exceed.

(Meillassoux, 2011: 229)

The consequences of this theorem for any cosmological conception of the world are staggering. As soon as we posit the existence of the world as the whole, it is possible to construct a power set of this world, which will be immeasurably greater than it, leaving an excess that cannot be incorporated into it. The same procedure can then be applied to this power set and so on to infinity. There is thus no such thing as ‘the absolutely infinite Infinity, the infinity of all intrinsically thinkable infinities’ (Badiou, 2005a: 277, cf. 283–284). The world as the whole is never all there is : there always remains an excess that cannot be subsumed under this totality, which is thus forever resigned to being limited, partial and particular, irrespective of how it is defined. The challenge that any possible universalism must necessarily face and come to terms with is quite simply the inexistence of the universe (cf. Brassier and Toscano, 2003: 279).

This challenge is also valid and highly pertinent for the contemporary rethinking of the concept of the world in terms of the infinite flux of becoming, complex autopoiesis, self-differentiation, etc. A good example of the persistence of the theme of the whole in this discourse is provided by William Connolly’s brilliant World of Becoming (2011), which brings together the philosophies of Nietzsche, Whitehead, Bergson and Deleuze, as well as recent trends in complexity theory and neuroscience, to argue for an ‘immanent realist’ vision of the world, lacking in divine transcendence yet irreducible to mechanical materialism. While Connolly’s conception of the world of becoming resonates with a number of themes that we shall address in this book, what makes it problematic from the outset is the construction of this world as the whole, an infinitely complex and ever-changing whole but a totality nonetheless:

[Do] you know what the world is to me? A colossus of diverse energies, without beginning or end, with each flowing over, through and around others, generating new currents and eddies. A play of waves, forces, and perceptions on different scales of complexity, endurance and time, with some swelling as others subside, with perhaps long cycles of repetition but none that simply repeats those preceding. And those bursts of laughter, bouts of sensual heat, workers’ movements, consumption habits, hurricanes, geological formations, climate patterns, contending gods, electrical fields, spiritual upheavals, civilizational times, species change and planetary rotations – they, too, participate in this veritable monster of energies, making a difference before melting down, to be drawn again into new currents, and again.

And the monster itself? It never completes itself, always rolling out and rolling in, with no outside or end-times, like a Möbius strip or Möbius current, never simply repeating, eternally evolving, and dissipating. A monster that feeds on its own excretions, that knows no joy, existential resentment, weariness, or horror, even as it houses all these, and more.

(Connolly, 2011: 176–177)

For all its extreme diversity and pluralism, invoked throughout Connolly’s text (2011: 29–32, 74–75, 83–84, 135–136), his world is manifestly one , a ‘colossus’ or a ‘monster’, which ‘houses’ these diverse beings without being reducible to or ‘knowing’ any of them. Yet, if we understand this monstrous world as the whole, what does it mean for it to ‘never complete itself’? If the world is forever incomplete, then it could not be the whole and the inconsistency could be avoided simply by perpetually deferring its completion. Nonetheless, incompleteness here refers only to the lack of teleological fulfillment and the lack of telos as such (see ibid.: 17–21): the world as becoming never attains a final figure. Yet, this infinite flux does not entail the abandonment of the idea of the whole: after all, if the world has no ‘outside’, then it must ‘house’ not only the diverse beings listed by Connolly but all beings, since otherwise these ‘non-housed’ beings would form its outside. The colossus of becoming is precisely the Badiouan ‘Other’ into which all beings are folded. Yet, as we have argued, this Other is inconsistent, insofar as it is always possible to recombine its elements into a set of all its subsets that would be infinitely greater than the original set. In other words, there is always a colossus even more colossal , a monster infinitely more monstrous than the one posited by Connolly. The world of becoming thus ends up incomplete not only in the temporal or teleological sense, but also in the sense of its particularity, due to the ever-present excess that cannot be housed by this ‘monster’. Even the world of infinite flux and becoming, which rolls in and out of itself, is not all there is.

Thus, the problem with cosmological accounts of world politics is the very notion of the world as cosmos. The reason why theories of world politics inevitably reach an impasse in their quest for the world community, society or state is that they persist in approaching world politics in terms of aggregation, agglomeration or totalization: the world must be the entire ensemble of beings or world politics means nothing or, more exactly, becomes a mere synonym for international relations. In short, political universalism is envisioned in terms of the formation of a universal set , whose best example in contemporary IR theory is Alexander Wendt’s world state, envisioned as a global political totality, founded on the Weberian monopoly of legitimate violence and the Hegelian universal recognition (Wendt, 2003: 504–513). While Wendt posits the emergence of this totality as teleologically inevitable, set-theoretical ontology renders its very figure inconsistent: whatever set we posit as the universal, there will always be a power set that will exceed it, i.e. would not belong to this world state, thus making the latter always less than the whole. The world state must from the outset renounce its universality and be forced into coexistence with the excess of its own power set that, ironically, also receives the name of the ‘state’ (of the situation) in Badiou’s ontology: as soon as there is a world state, there are in fact two , the ‘world state’ as the whole and another state that is (infinitely) greater than it.

The thesis on the inexistence of the whole permits us to reconstruct the disciplinary history of IR, conventionally presented as a perennial debate between realism and idealism. Notwithstanding their internal theoretical and methodological diversity, these two paradigms may be grasped as two distinct solutions to the problem of the inconsistency of the totalizing concept of the world. On the one hand, insofar as the world as the whole is never all there is, we must approach every empirical claim to world politics or a world community as a hegemonic gesture of universalization that can never attain the universality that it attests to but is always haunted by the excess that cannot be subsumed under the whole and must be eradicated in acts of symbolic or physical violence. In other words, behind every invocation of world politics we find the reality of hegemony, domination and subjugation. This suspicion of universalism and the designs for world unity are constitutive of various forms of political realism, from Carl Schmitt’s (1976) assault on liberal depoliticization to E.H. Carr’s (1981) critique of utopianism, and continue to animate the contemporary sceptical discourse on world politics in critical or post-structuralist orientations. In this manner, the inexistence of the world as the whole is held to demonstrate the impossibility of world politics as such, leaving us with a critical task of exposing the falsity of all claims to universality and the consequent affirmation of the pluralistic space of the international as the only real domain of political action.

On the other hand, it is possible to respond to the inconsistency of the world as the whole by renouncing every empirical claim to world politics in order to secure the preservation of its ideal , which then becomes a presupposition whose ontological status is indeterminate. This strategy is unsurprisingly pursued by various strands of idealist approaches. If the world as the whole lacks being, it can only be maintained in discourse by being idealized as beyond or otherwise than being. Thus, the impossibility of the totalization of being leads to the relocation of the totality of the world beyond being , where everything can exist, but only as unreal . Thus, it becomes possible to posit the world community as that in which all particular communities are embedded, as Bartelson does, yet the actual manifestation of that in which we are all embedded must remain foreclosed, so as not to reveal its ‘non-whole’ status: as soon as the world community is no longer the background in which we are embedded, but comes to the foreground as the political subject, it will necessarily reveal its own particular and hegemonic status.

In this manner, the notion of world politics ends up diffracted into idealist and realist positions that derive incommensurable conclusions from the inconsistency of the whole, resigning IR theory to a never-ending debate that could never be resolved, since neither of the sides is actually incorrect. While idealism makes of the world as the whole an ontological presupposition that may never attain a phenomenal status, realism moves from unraveling every phenomenal invocation of world politics as a simulacrum to the assertion of its ontological non-being. Whereas idealism makes of the world an inapparent being (a spirit ), realism transforms it into an existence without being (a phantom ). Either way, world politics appears lacking either ontologically or ontically, which does not preclude a discourse about it but rather makes this discourse plethoric and interminable, just as the non-being of the unicorn does not prevent its frequent appearance in artistic, literary, medical, mythical or heraldic discourses. Thus, as long as we are committed to the concept of the world as the whole, the discourse on world politics, either in the mode of realist unmasking or idealist valorization, remains a discourse on something that does not exist.

Having demonstrated that the world cannot be consistently posited as the whole, let us now consider an alternative possibility. Accepting the argument of political realism that every universal set is merely the effect of the hegemonic universalization of the particular, we may drop universality as the criterion of the definition of the world and define the world as a limited totality with no pretence to universality, a something rather than everything .

Indeed, such a non-cosmological, ‘local’ concept of the world was dominant in the twentieth century phenomenology, particularly the early work of Martin Heidegger. In the first division of Being and Time (Heidegger, 1962: 92–93) Heidegger begins his analysis of being-in-the-world as the basic state of Dasein with the outline of four possible concepts of the world. The first concept is ontic and refers to the totality of beings objectively present-at-hand. The second concept is ontological and refers to the being of these entities, interpreted as the nature of ‘things in general’. Third, the world is understood in another ontic sense as the world of Dasein, ‘that “wherein” a factical Dasein as such can be said to “live”’, be it a public or a private or even domestic world (ibid.: 92). Finally, the world may be grasped ontologically and existentially in terms of ‘worldhood in general’. Heidegger dismisses the first two ‘objective’ concepts as derivative and epiphenomenal, and focuses his inquiry on the second couple, the ontic world of Dasein and its ontologico-existential worldhood. The world is thus approached as that ‘wherein’ Dasein lives, the environment in which it encounters other beings not as objectively present-at-hand but as ‘ready-to-hand’ (zuhanden ) for one’s dealings in the world.

Heidegger proceeds to elaborate this concept of the world in terms of a referential totality of Dasein’s ‘involvements’ with other beings, where Dasein is absorbed in all kinds of assignments that involve various kinds of ‘equipment’ (Heidegger, 1962: 95–107). In its world, Dasein encounters other beings, which are disclosed to it in terms of practical functions that can be assigned to them and for which they are available. The paradigm of Heidegger’s world is thus the workshop, characterized by a ‘circumspective absorption in references and assignments constitutive for the readiness-to-hand of a totality of equipment’ (ibid.: 107, cf. Harman, 2002: 15–48; Malpas, 2006: 182–189). Thus, the world is always already there for Dasein as the referential totality of its involvements and the discovery of any concrete entity in the world is only possible on the basis of our pre-understanding of the world, in which we always already find ourselves. Similarly, before the world can be ‘known’ ontically in terms of the beings within it and ontologically in terms of the being of those beings, Dasein must first understand, however tentatively and indefinitely, its factical being-in-the-world as its basic or essential state, which grounds any possible knowledge of the world’s beings as present-at-hand (ibid.: 106). In this act of understanding is disclosed the structure of relations that define assignments and involvements of Dasein’s practical activity, which Heidegger terms the significance of the world (ibid.: 120).

The ‘wherein’ of an act of understanding, which assigns or refers itself, is that for which one lets entities be encountered in the kind of Being that belongs to involvements, and this wherein is the phenomenon of the world. And the structure of that to which Dasein assigns itself is what makes up the worldhood of the world.

(ibid.: 119, emphasis omitted)

Thus, Heidegger’s concept of the world in Being and Time is that of a limited relational totality, an ordered environment in which Dasein orients itself, sets itself tasks and acts on them. To this ontic concept of the world corresponds the ontological concept of worldhood ‘as such’, defined as the relational structure of significance, within which Dasein always already finds itself.

Alain Badiou’s phenomenology, presented in his Logics of Worlds (Badiou, 2009b) offers a similar concept of the world as a limited totality. Nonetheless, in contrast to Heidegger (1962: 121), for whom the world is necessarily disclosed to Dasein and to Dasein alone, Badiou’s phenomenology is avowedly ‘objective’, neutralizing any intentional or ‘lived’ dimension of the worlds he analyses, making the existence of worlds entirely independent from human existence (Badiou, 2009a: 38–39, 118–119). This accounts for a different relationship between ontology and phenomenology in Badiou’s work. For Heidegger ontology was itself necessarily phenomenological in its method, since its condition of possibility was Dasein’s pre-understanding of being, on whose basis the meaning of being is to be interpreted (Heidegger, 1962: 29–35, 49–63). In contrast, Badiou posits a rigorous disjunction between ontology and phenomenology while making both entirely independent of the existential analytic of Dasein, which is of little interest to him (Badiou, 2009b: 118). While ontology deals with being in the set-theoretical sense of pure or inconsistent multiplicity, the phenomenology of Logics of Worlds focuses on the localization of being as ‘being-there’, appearance in a determinate and ordered situation. It is this situation, structured as a network of identities and differences, that Badiou terms the world.

In more technical terms, the world is defined as a set that contains a transcendental and the transcendental indexing of all its elements (ibid.: 598). The transcendental refers to the order-structure that assigns the beings of the world various degrees of intensity of appearance. Contrary to the more familiar concept of the transcendental in Kant’s philosophy, Badiou’s transcendental organization of the world is a strictly immanent and objective process that accounts for the logical cohesion of appearance, which is not determined by the ontological composition of the situation – a key point we shall return to below (ibid.: 101, 121–122, 241–242). For this reason, there may be as many transcendentals as there are worlds. As an order-structure, the transcendental is a subset of the situation that performs logical operations of assigning the minimum of appearance in the world, the possibility of conjoining the degrees of appearance of any two values and the possibility of synthesizing the values of appearance of any number of elements in an ‘envelope ’ (ibid.: 102–103, 159–165). These operations permit the assignment of identity-functions to the beings that appear in the world or the ‘indexing’ of them on the transcendental. Transcendental indexing is a function that makes a transcendental degree of appearance (from the minimum to the maximum) correspond to a pair of elements of the set that appears in the world. For instance, if the identity-function of two elements a and b is the maximum, this means that they appear in the world in question to the same degree. On the basis of these operations Badiou builds up an elaborate phenomenology, in which any situation whatsoever, from a protest demonstration to a country house on an autumn evening, can be analysed as a world, structured by a particular transcendental order.

It is crucial to emphasize that Badiou’s notion of phenomenology is entirely distinct from, if not diametrically opposite to, the phenomenological tradition of the twentieth century in its various versions. As an objective phenomenology, the description of worlds must neutralize not their ‘real existence’ but precisely the intentional or lived dimension that, from Husserl onwards, has been the focus of the phenomenological method. ‘In doing so, we grasp the equivalence between appearing and logic through a pure description, a description without a subject’ (ibid.: 38). While this understanding of phenomenology at first glance appears scandalous from any conventional perspective, it is at the very least legitimate by the classic definition of phenomenology developed by Heidegger (1962: 49–62; 1988: 15–22): the apophantic disclosure of phenomena in the logos, ‘letting that which shows itself be seen from itself in the very way that it shows itself from itself’ (Heidegger, 1962: 58). Heidegger’s phenomenological ontology and Badiou’s objective phenomenology both disclose phenomena , i.e. beings that appear in worlds. What divides them is only the logos that they rely on in this disclosure, i.e. the hermeneutic discourse of the existential analytic of Dasein for Heidegger and the logical discourse of category and topos theory for Badiou. While it is certainly possible to debate which mode of logos is better at its apophantic task, what is important for our purposes is simply to establish the possibility of an objective phenomenology of worlds that has dispensed with the transcendental subject in favour of the idea of the transcendental as the immanent organization of the world.

Badiou’s conception of the world yields two important consequences. First, on the basis of the principle of the inexistence of the whole, we may conclude that there is always more than one world (Badiou, 2009b: 114–115). Moreover, the number of worlds can only be infinite: if there were a finite number of worlds, they could easily be agglomerated into the whole. Second, every one of these worlds is itself infinite . It is impossible to delimit a world either from below through the dissemination of its elements or from above through their totalization (ibid.: 306–310, 331–335). In the first case, the result of the dissemination of the elements of the world into ever-smaller elements would still be a component of the world in question: the world does not have anything ‘beneath’ it in the sense of a primal matter that escapes appearance. ‘If you disseminate an ontological component of a world by examining the elements of its elements, the result of this dissemination is still a component of the same world’ (ibid.: 307). In the second case, the totalization of all the possible subsets of the world into its power-set remains an entity of the same world. Since according to the theorem of the point of excess this power-set will be more numerous than the original set, ² it is impossible to prescribe a maximal number of elements in the world, which logically forbids the finitude of the world (ibid.: 309).

[Cantor] secularized the infinite by means of a literalization whose boldness – an unheard-of transfixion of the religious veil of meaning – orients us within a thinking still to come that can be encapsulated in a single phrase: insofar as a number is its real, every situation is essentially infinite.

(Badiou, 2008a: 225) ³

Thus, we have moved from the assumption of one world as the whole to the infinity of particular worlds that are themselves infinite. It is thus possible to analyse any situation whatsoever as a world, endowed with a particular transcendental. Instead of Connolly’s image of one ‘monstrous’ world of infinite flux and complexity, we end up with an image of an infinity of infinite worlds, which nonetheless need not be a priori posited as extremely complex or in perpetual flux. A world of presidential elections in a given country is certainly infinite, yet its transcendental order is relatively simple and stable, there being nothing particularly monstrous about it, aside, perhaps, from individual candidates. As soon as we abandon the identification of the world with the whole, Connolly’s dramatization of flux and becoming loses its urgency: evidently, some worlds are more complex and dynamic than others. Of course, this does not mean that these worlds all exist in isolation from each other. For example, the world of a protest demonstration or a refugee camp possesses a specific transcendental order and may be analysed as a world in its own right but also belongs to the wider worlds of e.g. municipal elections or immigration policy, which in turn both belong to a still wider world of regional politics and so on. Every world may belong to other worlds – the only world that it cannot belong to is the whole, which does not exist. Moreover, every world must belong to some other world, since the only thing that does not belong to anything else must be the whole, to which everything in turn would belong (Badiou, 2005: 45; 2009b: 112). Every world is a world of worlds but there is no such thing as the world of all worlds.

[The] unity of a world is nothing other than its diversity, and its diversity is, in turn, a diversity of worlds. A world is a multiplicity of worlds and its unity is the sharing out and the mutual exposure in this world of all its worlds.

(Nancy, 2007: 109)

This particularistic concept of the world can be fruitfully applied in political science and IR in the study of such limited totalities as the ‘worlds’ of local elections, G8 summits, universities, global trade, development aid, border policing or refugee camps. Each of those worlds is characterized by a specific transcendental order that can be reconstituted through a Heideggerian, Badiouan or other phenomenology but is at the same time part of a wider world and decomposable into smaller worlds that are also liable to phenomenological analysis. The politics of these worlds would then be derived from the transcendental, by which the world in question is governed. The study of politics in different worlds may then take the form of a Foucauldian ‘analytics of government’, the immanent reconstitution of positive dispositifs of governmental rationalities in such distinct worlds as diplomacy, humanitarian aid, counter-intelligence, which may overlap with, feed into or remain separate from one another, but never constitute anything like the whole (Foucault, 1991, 2008, 2007; Dean, 1999; Larner and Walters, 2004; Walters, 2006; Li, 2007; de Larrinaga and Doucet, 2010; Parker, 2012). ⁴

Yet, this understanding of the world and its politics cannot but be disappointing for any attempt to rethink world politics in its more familiar universalist sense, since ‘world politics’ here would simply mean a politics that unfolds within a particular world and what counts for politics in different worlds need not be the same thing. The very question of political universality appears to be foreclosed by the plurality of worlds with particular orders above or between which no authority exists. There is only an infinity of particular worlds with particular regimes of politics – an image that immediately brings to mind the pluralistic realm of the international. Is not world politics then strictly synonymous to international relations and the world simply identical to the international domain that it was intended to transcend (Walker, 2009: 21–22)? This is indeed the position of the diverse group of the critics of cosmopolitan universalism who affirm the pluralism of the international as the sole possible universal (see e.g. Jackson, 2003; Connolly, 1995; Mouffe, 2009), whereby the world is nothing but a plurality of worlds and world politics consists in maintaining this plurality against any hegemonic totalization.

Nonetheless, the universalization of the international as the ‘world of all worlds’ merely throws us back into logical inconsistency. Since, as we have seen, the domain of the international cannot be the whole, it must be a particular world among others. The international does not lose any of this particularity by virtue of being a huge world that envelops the entire planet, especially as it does so in a specific and selective manner, including some entities while excluding others (non-state communities, postcolonial populations, global social movements, the environment, etc). We do not even need recourse to set-theoretical reasoning to demonstrate that the international is not the whole, since empirical examples of exclusion from this realm abound. Nonetheless, the focus on these empirical examples may ultimately be misleading, since it would orient the critical discourse on world politics towards advocating a politics of inclusion as the pathway from particularistic international politics to a genuine world politics. Yet, it is precisely this desire to include everything that leads us back to the inconsistent figure of the universal set and the problem of the hegemonic universalization of the particular: even if we were to concede the utterly utopian possibility of the transformation of the international that would overcome every exclusion, what this whole could never include is the excess of the set of its parts over its original elements.

While the idea of this excessive ‘power-set’ might appear too abstract, it is in fact of supreme relevance for the problem of the world. In Badiou’s ontology the operation of inclusion (grouping into subsets) is constitutive of what he terms the state of the situation , its ‘metastructure’ that re-presents its elements by, literally, counting them once more as parts (2005a: 81–111). Badiou’s use of the term ‘state’ to designate this operation accentuates its analogy with the political order, which is maintained by ordering the pure multiplicity of elements into distinct groups characterized by particular identities. Indeed, the simplest way to grasp the operation of the meta-structure is to conceive of it as the bureaucratic apparatus of the state, which is not concerned with individuals per se as pure elements but only as representatives of groups, be they grouped by class, gender, race, professional occupation, sexual preference or what not. ‘This [statist] coercion consists in not being held to be someone who belongs to society but as someone who is included within society. The State is fundamentally indifferent to belonging yet it is constantly concerned with inclusion’ (Badiou, 2005a: 107–108). Thus, while the originary structure of the situation is constituted by the pure belonging of its individual and disconnected elements, the state of the situation is constituted by ordering the possible combinations between these elements: ‘The State is not founded upon the social bond, which it would express, but rather upon un-binding which it prohibits’ (ibid.: 109).

And yet, although the operation of metastructural representation is meant to protect the situation from its unbinding, it actually threatens this very unbinding by introducing into the situation the excess of parts over elements. According to the theorem of the point of excess, there always exists at least one ‘excrescent’ element of the power-set that does not belong to the original set. It is easy to see that one such excrescent element is the state of the situation itself, which did not belong to the original situation, just as the bureaucratic apparatus of the state is structurally separate from the society and ‘represents’ nothing within it. Thus, in the case of the hypothetical universalization of the international there would be at least one element that would escape this universalization, while at the same time making it possible, i.e. the world state itself as a meta-structure of representation, which by definition exceeds the whole that it brings into being. Yet, we must also recall that with respect to worlds as infinite sets the Cohen-Easton theorem establishes that the excess of the power-set is strictly immeasurable and errant, capable of taking any (infinite) value. Thus, the universalization of the international into a hypothetical whole would not merely result in the paradoxical exteriority of the resultant world state to the totality that comprises it but in the literally limitless proliferation of excessive recombinations of elements that immeasurably exceed their originally infinite number. The inclusive politics of the universalization of the international opens up Pandora’s box, out of which come all kinds of monstrous combinations that cannot be subsumed under the inclusive order and mock its every claim to universality.

Thus, not only is the international not identical to the universal; as a particular world it is also not universalizable . The idea of the international as an actual or potential world of all worlds arises out of an illusory identification of totality and infinity. Since every world is a world of worlds, the international world may of course contain an infinite multiplicity of worlds, but the only thing that this or any other world cannot contain is everything . For this reason, the ethico-political drive for the greater inclusiveness of the international, advanced in various ways by feminist, postcolonial or poststructuralist theories, may certainly make the international a ‘better place’ but will not attain world politics. As Walker demonstrates admirably, one will never reach the universality of the world if one begins from the international (Walker, 2009: 26–31). There is no passage from any particular world, however diverse and inclusive, towards universality. Yet, while this claim leads Walker to a profound scepticism about world politics as such, the impossibility of passing from the international to the world is only a problem as long as we continue to envision the universality of world politics as necessarily mediated by particularity. If the world of the international is a particular world among others and, as Walker argues at length, its particular transcendental is historically contingent, the impossibility of arriving at the universality of world politics from the particularism of the international simply entails the need for another starting point for conceptualizing the universality of world politics. Since presupposing the world as the whole leads us to inconsistency and starting from particular worlds leads us nowhere, this new starting point is obtained by abandoning every totalizing conception of the world and asserting its universality without recourse to any mediation by the particular. It is this solution that we address in the following section.

While at first glance the particularistic conception of worlds merely confirms the impasse of the discourse of world politics due to the inaccessibility of the universal, it actually guides us towards a solution to our problem by raising the question of the conditions of the appearance of this infinity of worlds. Simply put, where are all these worlds? Just as we commonly speak of all the birds, books, athletes or mountains in the world, we may speak of the infinity of worlds as existing ‘in the world’. But what is this world in which the infinity of positive, transcendentally regulated worlds comes to appearance? If this ‘world of all worlds’ were itself a positive world, it would have to be a self-belonging universal set, which we have dismissed as logically inconsistent. And yet, it is barely possible to give up on the existence of such a world.

The problem is well illustrated by the ambiguity of Badiou’s own political maxim that prescribes resistance to all forms of exclusion, inequality and domination: ‘There is only one world!’ (Badiou, 2008b: 53–70). Since this statement so patently contradicts the claims in the Logics of Worlds about the infinity of worlds, misunderstandings may easily arise. Might Badiou mean that among the infinite number of worlds there is something like a ‘political world’, which is indeed ‘one’? This solution would evidently contradict Badiou’s preference for describing highly circumscribed and concrete worlds, including political ones, e.g. the world of a protest demonstration (Badiou, 2009b: 199–216), of a battle (ibid.: 277–288) or of revolutionary struggle (ibid.: 493–503). Of course, since every world is a world of worlds, it might be possible to isolate something like a world of ‘politics as such’ that would envelop the more specific worlds above, yet the result would be a trivial agglomeration whose advantages remain elusive. Thus, Badiou’s ‘one world’ cannot refer to any positive world, however general and loosely structured, but only to that in which an infinity of worlds comes to appear. Yet, what could this ‘in which’ possibly be?

From ancient Greek atomism onwards, this problem has been resolved by asserting that whatever exists positively does so in the empty space, vacuum or void, in short – Nothing (see Gregory, 1981; Badiou, 2009c: 56–64). Indeed, this answer appears to be the last remaining logical possibility: if we have excluded the possibility of the world being everything and we are not satisfied with a particularistic understanding of the world as something , then the world can only be nothing . Yet, everything depends on how we understand this ‘nothing’. As we shall argue in more detail in Chapter 2 , as long as it is understood in the merely negative sense of privation, lack or absence, we remain within the political ontology of the international, for which there are only particular worlds and nothing beyond them. Bartelson invokes this negative sense of the void in his criticism of contemporary cosmopolitanism, which lacks a positive vision of world community and only exhibits an ‘ontological void’ (Bartelson, 2009: 28). However, it is also possible to understand the claim about the nothingness of the world as a pure affirmation: there is a world, in which an infinity of infinite worlds appears, and this World, which we shall henceforth capitalize to distinguish it from worlds as limited particularistic totalities, is nothing but the void .

Let us elucidate this concept of the World by revisiting Heidegger’s work after Being and Time , in which there is a gradual shift away from the understanding of the world as a practical context of Dasein’s activity towards an ontological concept of the world as the clearing of being (cf. Malpas, 2006: 186–189). In his 1929–30 course of lectures, The Fundamental Concepts on Metaphysics , Heidegger defines the world as the ‘manifestness of beings as such as a whole’ (Heidegger, 1995: 284). What is at stake in this definition is not the whole of beings (the impossible universal set) but rather the disclosure of beings as beings (ibid.: 274–275, 279–280). The phenomenology of particular worlds in Being and Time as well as the analysis of the concept of the world in the history of philosophy in On the Essence of Ground (Heidegger, 1998: 97–134) are now reinscribed within a wider and more ambitious inquiry into the sense of the world that proceeds through the comparison between humanity and animality, between the ‘world-forming’ (weltbildend ) character of Dasein and the ‘poor in the world’ (weltarm ) status of the animal.

While ‘world-formation’ belongs to the essence of Dasein, in its everyday practices human beings inevitably fail to distinguish the world from the beings within it. For Heidegger, ‘[ordinary] understanding cannot see the world for beings. In relation to the individual trees and the way they are gathered together the forest is something else. It is that out of which the many trees belong to a forest’ (Heidegger, 1995: 347). The World is thus neither a being nor an aggregation of all beings but rather the opening or ‘projection’ (ibid.: 362), in which beings (and positive worlds as ordered realms of beings) become disclosed in the first place:

In the occurrence of projection world is formed, i.e. in projecting something erupts and irrupts towards possibilities, thereby irrupting into what is actual as such, so as to experience itself as having irrupted as an actual being in the midst of what can now be manifest as beings. It is a being of a properly primordial kind, which has irrupted to that way of being that we call Dasein, and to that being which we say exists , i.e. ex-sists, is an exiting from itself in the essence of its being, yet without abandoning itself (ibid.: 365).

Thus, the world is formed as an opening, which tears Dasein away from its actual preoccupations and throws it into the potentiality of existence, whereby the being of the beings around Dasein may be disclosed for the first time. Particular worlds of the kind analysed in Being and Time , which provide a practical context of Dasein’s everyday activity, are thus conditioned by the prior opening of the World, which tears Dasein away from its absorption in everydayness. This argument recalls Heidegger’s earlier claim in Being and Time about the withdrawal of the being of entities that are ready-to-hand (zuhanden ) from our access: these beings that Heidegger unites under the rubric of ‘equipment’, determined by their references and assignments, only become accessible as ‘present-at-hand’ (vorhanden ) when they break down, are lost, missing or standing in the way of our concerns (Heidegger, 1962: 102–107). It is precisely in this breakdown in the referential contexts that define a particular world that this world is ‘lit up’ or ‘announces itself’ as such (ibid.: 105).

This ‘announcement of the world’ is in the later works presented not merely as a result of conspicuous, obtrusive and obstinate presence of broken tools but as an effect of a ‘fundamental attunement’ or mood (Stimmung ), which in Being and Time has been addressed in terms of anxiety (Heidegger, 1962: 228–234). In the Fundamental Concepts of Metaphysics this world-disclosing mood is described as profound boredom and is addressed in the first 200 pages of the text, preceding the more specific engagement with the question of the world. In his phenomenology of boredom Heidegger moves progressively from the most familiar form of boredom as being-bored-by -something (a determinate object or situation) through the more general being-bored-with- something that arises from within Dasein and has no determinate object to the most ‘profound’ boredom, which is precisely the attunement through which the world is disclosed (Heidegger, 1995: 82–88, 113–125, 136–143). This profound form of boredom is characterized by the intensification of the two ‘structural moments’ that define boredom as such: being left empty and being held in limbo .

The first moment refers to Dasein’s ‘being delivered to beings’ telling refusal of themselves as a whole’ (ibid.: 137), whereby it finds itself in a state of indifference that envelops all beings, including Dasein itself. In this state beings around us evidently do not disappear but rather manifest themselves as such precisely in their indifference. The things we do in order to pass the time when bored, the diversions with which we try to entertain or amuse ourselves, fail to engage us, leaving us suspended in the withdrawal of beings. The second moment, being held in limbo, is closely related to this suspension. The beings that refuse themselves are nothing other than possibilities of Dasein’s existence that are left unexploited (ibid.: 141). What refuses itself to Dasein are the things it could have done, experienced or used, which now stand before it as wholly inaccessible. However, this withdrawal of concrete or specific possibilities impels Dasein towards a more extreme and originary possibility, the originary ‘making possible’ (ibid.: 143–144). In other words, the suspension of particular possibilities reveals what makes these possibilities possible in the first place and thus makes Dasein itself possible as the being whose essence is contained in its potentiality for being. Dasein is simultaneously entranced by the emptiness of the beings’ total indifference and impelled towards what Heidegger calls the ‘moment of vision’ (ibid.: 151–152, cf. Heidegger, 1962: 371–380), a resolute grasp of the authentic possibility of existence. It is thus the combination of the disclosure of the expanse of beings that refuse themselves and the experience of the extreme possibility of Dasein itself that constitutes the fundamental attunement in which the world formation takes place.

Yet, what exactly is revealed in this disclosure? As Giorgio Agamben (2004: 39–74) has argued in an incisive critique of this lecture course, Heidegger’s description of the world-disclosing attunement of Dasein is uncannily close to the phenomenology of animal life that Heidegger terms ‘poor-in-world’ (weltarm ). In Heidegger’s analysis, the animal is defined by captivation , its incapacity to suspend or deactivate its relation with its ‘disinhibiting ring’, i.e. its immediate environment that is never disclosed to the animal as such (Heidegger, 1995: 240–253). This condition of being delivered over to something that refuses itself is exactly the same as the first structural moment of ‘being left empty’. ‘In becoming bored, Dasein is delivered over to something that refuses itself, exactly as the animal, in its captivation, is exposed in something unrevealed’ (Agamben, 2004: 65). The sole difference between humanity and animality pertains to the second structural moment. While both animal and man can be left empty by beings that refuse themselves, no animal can ever be held in limbo. ‘What the animal is unable to do is suspend and deactivate its relationship with the ring of its specific disinhibitors. The animal environment is constituted in such a way that something like a pure possibility can never become manifest within it’ (Agamben, 2004: 68). In contrast, Dasein finds in this very manifestation the moment of its authentic existence as ‘world-forming’: ‘of all beings only the human being, called upon by the voice of being, experiences the wonder of all wonders: that beings are ’ (Heidegger, 1998: 234).

It is this difference that leads Agamben to a striking conclusion that remains only implicit in Heidegger’s text, since it runs contrary to the privilege his thought grants to Dasein. The passage from the world-poor animal to the world-forming man

does not open onto a further, wider and brighter space, achieved beyond the limits of the animal environment and unrelated to it; on the contrary, it is opened only by means of a suspension and a deactivation of the animal relation with the disinhibitor.

(Agamben, 2004: 68)

Just as the ‘voice of being’ is essentially silent (Heidegger, 1998: 236), ‘the jewel set at the centre of the human world and its Lichtung (clearing) is nothing but animal captivation’ (Agamben, 2004: 68). The opening of the World that is disclosed to Dasein does not mark a liberation from captivation but a deliverance to captivation: ‘whoever looks in the open sees only a closing, only a not-seeing’ (ibid.; see also Heidegger, 1977: 169–180). If the animal is open to a closedness that it could never access ‘as such’, the human being is able to do precisely that when it suspends its relation with the beings of the world – it is able to grasp the inaccessible as inaccessible: ‘Dasein is simply an animal that has learned to become bored. This awakening of the living being to its own being-captivated, this anxious and resolute opening to a not-open, is the human’ (ibid.: 70). Yet, this opening obviously does not amount to much or, in fact, to anything at all. The opening of the World as a result of the subtraction of the human being from its particular world in the mood of boredom opens Dasein to nothingness pure and simple:

From the beginning, being is traversed by the nothing: the Lichtung is also originarily Nichtung , because the world has become open for man only through the interruption and nihilation of the living being’s relationship with its disinhibitor. Being appears in the ‘clear night of the nothing’ only because man, in the experience of profound boredom, has risked himself in the suspension of his relationship with his environment as a living being.

(ibid.: 70)

In this manner, Heidegger’s explorations of the relation between humanity and animality in the 1929–30 course connect with his theorization of the metaphysical problem of the nothing in the lecture ‘What is Metaphysics?’, delivered during the same year. ⁵ In this lecture, Dasein is explicitly defined as ‘being held out into the nothing’ (Heidegger, 1977: 108) and this nothing is posited as the paradoxical ‘ground’, in which all beings come to appear: Ex nihilo omne ens qua ens fit [from the nothing all beings as beings come to be] (ibid.). While traditionally metaphysics tended to approach the nothing as the ‘counter-concept of being’, its pure and simple opposite, Heidegger demonstrates the way in which nothing, which is indeed not a being, nonetheless discloses the being of beings as such:

For human existence, the nothing makes possible the openedness of beings as such. The nothing does not merely serve as the counter-concept of beings; rather, it originally belongs to their essential unfolding as such. In the Being of beings the nihilation of the nothing occurs.

(ibid.: 104)

[The nothing] discloses these beings in their full but heretofore concealed strangeness as what is radically other – with respect to the nothing. In the clear night of the nothing of anxiety the original openness of beings as such arises: that they are beings – and not nothing. Only on the ground of the original revelation of the nothing can human existence approach and penetrate beings.

(ibid.: 103. Cf. Harman, 2002: 90–95)

The nothing is not a being, yet it nonetheless ‘prevails as being’, which ‘gives every being the warrant to be’ (Heidegger, 1998: 233).

As that which is altogether other than all beings, being is that which is not. But this nothing essentially prevails as being. We too quickly abdicate thinking when, in a facile explanation, we pass off the nothing as a mere nullity and equate it with the unreal. [Instead], we must experience in the nothing the pervasive expanse of that which gives every being the warrant to be. That is being itself. Without being, whose abyssal but yet to be unfolded essence dispenses the nothing to us in essential anxiety, all beings would remain in an absence of being.

(ibid.: 233)

In its everyday comportment Dasein usually loses itself among the beings ‘ready-to-hand’ in its particular world, much as the animal that is captivated inside its disinhibiting ring (see Heidegger, 1962: 203–224). For the inhabitant of a particular world, there are only the beings of this world and ‘beyond them there is nothing’, in the negative sense of mere absence (Heidegger, 1977: 85). Yet, in contrast to the animal, Dasein is capable of rising above the ‘superficies of existence’ in a fundamental attunement such as boredom in the Fundamental Concepts of Metaphysics or anxiety in Being and Time and What is Metaphysics? (ibid.: 104). However, this ‘rise above’ does not take us to another place, characterized by the rich diversity of beings and the plenitude of possibilities, but, on the contrary, entails our subtraction from all these beings and possibilities in our ‘world’, inhabiting our world as nothing, so that Dasein stands alone in the clearing of being as the ‘lieutenant of the Nothing’ (ibid.: 106).

This theme of the world as void culminates in Heidegger’s 1947 Letter on Humanism , in which he reinterprets the human as a ‘worldly’ being. Against the contrast between ‘worldly’ and ‘spiritual’ in everyday language, Heidegger understands Dasein’s worldliness in terms of its transcendence of any particular being or realm of being (i.e. a positive world) through being ‘placed freely into the clearing of Being, which alone is “world”’:

[For] us ‘world’ does not at all signify beings or any realm of beings but the openness of Being. Man stands out into the openness of Being. ‘World’ is the clearing of Being into which man stands out on the basis of his thrown essence. World is in a certain sense precisely ‘the beyond’ within existence and for it.

(ibid.: 252)

Thus, Heidegger’s conception of the world moves from the phenomenology of particular worlds as immanent practical contexts of Dasein’s activity to the affirmation of the World as the void or clearing, in which such worlds are disclosed to Dasein. It is important to emphasize that since the World as void is not a being, to posit the World as a clearing ‘beyond’ existence is not to engage in a quasi-theological move of positing a Supreme Being that transcends this world. The World does not designate a being, supreme or otherwise, but solely the opening, in which an infinity of infinite worlds may appear. The void is therefore the condition of possibility of any positive world whatsoever: it is that in which these worlds appear, but, in contrast to the two concepts of the world addressed above, it neither totalizes these worlds into the whole nor is mediated by them. Nonetheless, while avoiding the problems of these two concepts, the Heideggerian concept of the World raises other questions, particularly concerning the relation between the World as void and the positive worlds of the kind addressed in the previous section, e.g. the worlds of factory production, diplomacy, elections, development, migration or war. If these worlds simply come to appearance against the background of the void as ‘not nothing’, the World appears to be little more than a logical condition that can hardly ground any politics, reduced as it is to a neutral support of the infinite proliferation of positive worlds coexisting in the vacuum. In this manner, in an ironic reversal of Heidegger’s own intention, politics would be ‘deontologized’ and reduced to the positive principles governing autonomous worlds, between which no adjudication is possible, since what is beyond these positivities is purely and simply nothing (cf. Mandarini, 2009). Instead of universalism, we would end up with nihilism and relativism once again. In order to recover the universalist potential of the concept of the World as void we must elaborate its relation to the worlds it discloses. In other words, we must reassert the difference between the phenomenology of worlds and the ontology of the World in order to specify the way the latter affects the former. In the following section we shall pursue this question in an analysis of Alain Badiou’s ontology of the void.

While Badiou restricts the term ‘world’ to the positive totalities regulated by a transcendental order, the void is the most important concept in his ontology and functions in the manner resonant with Heidegger’s clearing, yet also radicalizing his ontological insight. Ironically, while in ‘What is Metaphysics?’ Heidegger famously accused mathematics and other exact sciences of being incapable of treating the nothing (Heidegger, 1977: 94–95), Badiou’s use of the set-theoretical category of the void set to ground ontology demonstrates precisely the kind of engagement with the nothing that Heidegger sought.

In Logics of Worlds , Badiou departs from the void as the first determinable set. Since in a set-theoretical ontology one can only posit a set if one can determine its composition, it is possible to immediately determine a set that has no elements, i.e. the void set Ø. The thinkability of all other sets depends on their belonging to specific worlds. Yet, since the void set has no elements, it logically appears in any world whatsoever:

Since the void is the only immediate being, it follows that it figures in any world whatsoever. In its absence, no operation can have a starting point in being, that is to say, no operation can operate. Without the void, there is no world, if by ‘world’ we understand the closed place of an operation. Conversely, where something operates – that is, where there is world – the void can be attested.

(Badiou, 2009b: 114)

While for Heidegger every particular world must be disclosed in the void, for Badiou it is the void itself that appears in every positive world. Moreover, in contrast to Heidegger, for Badiou the void is not merely the clearing of being but literally its building block, so that whatever appears in the world ultimately depends on the void for its being . To recall, what appears in Heidegger’s clearing, i.e. beings and worlds as ‘realms of beings’, is not itself composed of the clearing but is disclosed against the background of the Nothing as precisely not nothing. The genitive in the phrase ‘clearing of being’ is both subjective and objective: the clearing both belongs to being (it is being’s own clearing) and what being itself is (it is being that is cleared ), which is why Heidegger’s ultimate answer to the question of what being is is ‘nothing’ (1998: 233). However, it does not follow from this that beings are also nothing, but rather that being as nothing ‘distinguishes itself from all beings’ (ibid.). In contrast, for Badiou beings are indeed ‘woven out of the void’ (Badiou, 2005a: 57, cf. Badiou, 2009b: 112–113). This certainly does not mean that everything is in fact made of nothing, but merely that in order to be grasped in the aspect of their being, beings must be subtracted from all positive predicates they are endowed with in particular worlds, just like Dasein is in the mood of profound boredom:

What ontology theorizes is the inconsistent multiple of any situation, that is, the multiple subtracted from any particular law, from any count-as-one, the a-structured multiple. The proper mode in which inconsistency wanders within the whole of a situation is the nothing, and the mode in which it unpresents itself is that of subtraction from the count, the non-one, the void.

(Badiou, 2005a: 58)

Insofar as the entirety of beings in any given world is subject to a transcendental ordering that makes it consistent, that which remains inconsistent can only be nothing. For this reason, ontology is equivalent to a theory of the void and, moreover, can only be a theory of the void, since if it asserted the existence of any other beings, it would reduce itself to phenomenology, i.e. the description of the transcendental orders of particular worlds. Ontology must therefore begin and end with the void, all of its terms being derived from the void alone (Badiou, 2005a: 57).

[The] absolutely primary theme of ontology is therefore the void – the Greek atomists, Democritus and his successors, clearly understood this – but it is also its final theme because in the last resort, all inconsistency is unpresentable, thus void. If there are ‘atoms’, they are not, as the materialists of antiquity believed, a second principle of being, the one after the void, but compositions of the void itself, ruled by the ideal laws of the multiple whose axiom system is laid out by ontology. Ontology, therefore, can only count the void as existent.

(ibid.: 58)

All the beings of every world are, in their being , compositions of the void. With the help of the axioms of set theory, it is possible to generate an infinite number of sets from the void alone, starting from the two, a coupling of the name of the void Ø and its singleton (a set whose only element is the void): [Ø, {Ø}], and so on to infinity. Thus, the World as void is not merely the ‘nothing’ against whose background beings emerge but rather the ontological condition of possibility of all the beings, which appear in all positive worlds. Insofar as the void figures in any world whatsoever, it is a ‘universal part’ (ibid.: 86–88), underlying the constitution and structuration of every particular world. It is easy to see that the universality of this ‘part’ satisfies the criteria of immediacy and non-totalizability that are necessary to avoid logical inconsistency: insofar as the World is nothing, it is the very opposite of the Whole, and insofar as it is the ground of all being, it is always already there, immediately, in any world whatsoever. Thus, the World is the universal that precedes and exceeds the constitution of anything particular, making possible the proliferation of the infinite number of worlds while proscribing their aggregation into the whole.

While the World is in every world, it is important to emphasize that there is no necessary relation between the World as void and the positivity of worlds – it would be absurd to suggest that the void of being could somehow prescribe positive forms of appearance (Badiou, 2009b: 118). If one could infer appearance from being, there would only be one positive world whose transcendental order would somehow ‘correspond’ to the void – that world would have to be the Whole and is therefore impossible. The positivity of worlds as regulated structures of appearance is thus not determined by the void of the World, which only conditions the being of the being of these worlds. It is nonetheless possible to make the opposite move of inferring being from appearance that would establish ‘an ontological halting point’ (ibid.: 195) to the infinite proliferation of intra-worldly appearances. In Badiou’s postulate of materialism, ‘every atom of appearance is real’ (ibid.: 218–220), so that whatever appears in the world must have an ontological correlate, a multiplicity composed of the void. This postulate excludes the possibility that appearance in any given world would be grounded in something virtual or that something that exists in the world would lack any being (ibid.: 219). Yet, while this postulate excludes the existence of purely virtual or chimerical beings, the transcendental of the world remains without any foundation in being and hence precisely virtual and chimerical. In Badiou’s own account (2011: 75), the transcendental ‘does not exist’, at least not in the same way as the beings that it orders. As a set of degrees of appearance, the transcendental is certainly as real as any other set, yet its operation on the beings of the world that endows the world with a positive order has no foundation in being. It is precisely this lack of being that accounts for the contingency of the order of every world: ontologically, no world is necessary, even if all that appears in it is real.

Thus, we end up with the tripartite scheme, in which the abyss between an infinity of positive worlds and the void of the World is bridged by the set-theoretical ontology of pure multiplicity: the World as void of being – beings composed of the void – beings positively ordered in worlds . What the World makes possible is, strictly speaking, not this or that world in particular but rather the proliferation of being as inconsistent multiplicity, which is then ordered in accordance with the transcendental of a given world, which itself has no foundation in being. In other words, the World as void brings forth the ontological material for the construction of worlds that ensures that whatever appears is real without prescribing how it should appear. Thus, while whatever appears in the world is necessarily grounded in real being, the mode of its appearance is absolutely contingent , having no ontological correlate. There is no ontological reason why any world should be what it is and even why any particular world should exist at all.

This scheme permits us to reappraise the theme of becoming that we have addressed above with respect to Connolly’s (2011) concept of the world. The idea of becoming may now be conceived on two distinct levels. On the one hand, becoming pertains to the emergence of the being of worlds out of the void of the World. While the World as void does not become, since there is nothing in it that could possibly change, all worlds are becoming from the World but only in the aspect of their sheer being: the World grants worlds their being but not their appearance. We may term this ‘ontological becoming’ or ‘becoming-being’. Contrary to Connolly’s idea of becoming as monstrous autopoietic flux, this mode of becoming is in fact quite ordinary and even tedious, since it consists in the infinite proliferation of infinite sets, distinguished solely by their extensionality: [a, b], [a, b, c], [b, c, d] and so on. On the other hand, becoming may pertain to the process of intra-worldly ordering and transformation, in which beings of the world are endowed with positive identities. We may term this ‘phenomenological becoming’ or ‘becoming-appearance’. Contrary to Connolly’s exultation of becoming as an ontogenetic force, this mode of becoming has no relation to ontology whatsoever, since the World does not prescribe even that there should be this or that world, let alone what positive form it would take. Thus, instead of defining the world in terms of becoming, we end up with the World which does not become by definition and an infinity of worlds whose becoming is ontologically grounded in the void yet remains ontically or phenomenally contingent.

Thus, the World and particular worlds remain disjointed and irreducible to each other in the manner of Heidegger’s ontological difference. The insistence on the difference between the World and worlds distinguishes our approach from the influential rethinking of the Heideggerian concept of the world by Jean-Luc Nancy. In the Sense of the World and the Creation of the World (1997, 2007), Nancy operates with two notions of the world that resonate with our concepts of the world as a particular ordered totality and as the void of being. On the one hand, Nancy defines the world in the early Heideggerian and late Badiouan manner as a limited ‘totality of meaning’, giving such examples as ‘Debussy’s world’, ‘the hospital world’ or ‘the fourth world’ (Nancy, 2007: 41). On the other hand, Nancy also claims that the world is ‘in a sense, nothing’ (Nancy, 1997: 159) or ‘the growth of/ from nothing’ (Nancy, 2007: 51), the ‘opening in which finite singularities dispose themselves’ (ibid.: 72). This world as void is the condition of possibility of the infinity of positive worlds, but is so neither as a foundation or an origin but simply by ‘weaving the co-appearance of existences’ (ibid.: 70).

However, Nancy then makes a striking move of identifying these two figures and thereby annulling the very idea of ontological difference: ‘the ontological difference is null. Being is: that the being exists’ (ibid.: 71). In other words, ‘the being is nothing more than being itself’ (Nancy, 2011: 59). Thus, the closed totality of the world ends up somehow identical to the opening of the World that makes it possible, so that ‘the sense of the world is this world here as the place of existence’ (Nancy, 1997: 56). With a clear allusion to Badiou’s Being and Event , Nancy claims that ‘there is neither being nor event, just existences with their comings and goings’ (Nancy, 2007: 73). In his attempt to purge Heidegger’s philosophy of every trace of heroism and decisionism, Nancy opts for the utter trivialization of the theme of transcendence: Dasein is indeed ‘held out in the nothing’, yet this nothing is not ‘beyond existence’ but rather the everyday dwelling place of any Dasein whatsoever, which itself is now entirely indistinct from the ‘inauthentic’ beings that Heidegger disparagingly referred to as the ‘They’ (das Man ) (Heidegger, 1962: 163–168; cf. Nancy, 2003: 50–52). The World is this world here and nothing else. ⁶ Nancy develops the theme of this identity in his reinterpretation of the idea of the creatio ex nihilo :

[The] world is created from nothing: this does not mean fabricated with nothing by a particularly ingenious producer. It means instead that it is not fabricated, produced by no producer and not even coming out of nothing (like a miraculous apparition), but in a quite strict manner and more challenging for thought: the nothing itself. In creation, a growth grows from nothing and this nothing takes care of itself, cultivates its growth. The ex nihilo is the genuine formulation of a radical materialism, that is to say, precisely, without roots.

(Nancy, 2007: 51)

Thus, creatio ex nihilo means that the world is ‘all there’, that there is no other world or otherworldly supreme being behind it or, more precisely, what is behind it is the void from and of which the world grows (ibid.: 71–73). This world here as the positive totality of ‘something’ is nothing but the growth from and of nothing itself, while this nothing is in turn nothing but the opening of and for this growth of something. Since for Nancy the ontological difference is null, the positivity of the world and the void of the World ultimately merge into a single figure of creatio ex nihilo , which may be approached either as the positivity of the created world or the facticity of the process of creation from/of nothing. ‘This opening as nothing, which neither presents nor gives itself, is opened right at the same level of the finite singularities as their being together or their being-with and constitutes the disposition of the world’ (Nancy, 2007: 73). Since, contrary to Badiou, Nancy does not draw a distinction between being and appearance, the World (the being of something as nothing) and the world (the appearance of nothing as something) must remain indistinct.

Nancy is certainly correct in emphasizing that the World as void is nothing ‘otherworldly’ in the mythical or theological sense and can only be accessed in ‘this world here’ as the condition of its very emergence, the ‘universal part’ that is ontologically always already there in any world whatsoever. This is the reason why in this book we shall retain the term World for the void at the risk of terminological confusion: to assert that there are worlds and there is the World is to emphasize that we are talking almost about the same thing, with the caveat that the World is precisely not a thing, not a being or a realm of beings and for this reason can never coincide with what it makes possible, remaining in excess of every positive world, transcending it from within as its ‘universal part’.

It is this caveat that Nancy’s identification of the world and World obscures but which will be crucial for understanding the political significance of the concept of the World. As we shall demonstrate in detail in the following chapter, the possibility of world politics is conditioned by the disclosure of the World within positive worlds , which manifests the contingency of their transcendental orders and thereby opens these worlds to the possibility of transformation. It is evident that for this disclosure to be possible, the World and ‘this world here’ must be distinct. Moreover, the insistence on the identity of a given positive world and the World makes it difficult, if not outright impossible, to conceive of the possibility of the transformation of this world, the possibility that we conventionally associate with politics. If the World were simply this world here, without remainder or excess, how could one possibly confront what Nancy himself terms the ‘unworld’ (immonde ) of contemporary politics, the ‘global’ agglomeration of worlds into a ‘glomus’, a tumorous growth of inequality, injustice and domination, which is closed off from the void that makes it possible into a suffocating self-immanence (Nancy, 2007: 33–34)? If the ‘unworld’ can be transformed into a better world, this is only because it is non-identical with the World and this non-identity may be brought to appearance within the ‘unworld’ itself, illuminating its contingency and hence the potentiality of its transformation. It is only because the World is not this world here (or any other positive world) that this world here is not all there is and, as the famous slogan goes, ‘another world is possible’. The World is that which, ontologically belonging to but not necessarily appearing in every positive world, conditions the possibility of every world’s becoming-otherwise.

Let us now summarize the findings of this chapter and their implications for rethinking world politics. We began with the demonstration of the logical inconsistency of the understanding of the world as the whole, which is at work in much of the contemporary discourse of world politics, both affirmative and critical. We then proceeded to the particularistic conception of the world, in which the world is understood as a limited totality regulated by a transcendental order. Finally, we have presented the concept of the World as the void, in which an infinite number of infinite worlds are disclosed. Rather than attempt to attain the universal on the basis of the particular, we have posited the void as the immediate and non-totalizable universal that makes possible an infinite multiplicity of particular worlds without prescribing their positive ontic order. While the concept of the world as the Whole reduced world politics to hegemony and imperialism and the idea of the infinity of worlds as limited totalities resigned us to relativism and nihilism, the concept of the World as void at first glance appears to make the very concept of world politics a logical impossibility.

It is clear that any politics derived from the World cannot affirm any principle or value that would derive from the positive order of any particular world, be it tradition or law, identity or culture. No particular being or realm of beings could be the source of such principles, whose only ground must be being itself, understood as the void of its own clearing. Yet, how can the void, i.e. literally nothing, found a politics and what content could such a politics possibly affirm? Our analysis of the three concepts of the world leaves us with three possible responses to this question. First, it is possible to dismiss the concept of the World as void as nonsensical, abstruse or irrelevant and return to the familiar ritual of the affirmation of the world as the Whole and its denial in the particularistic pluralism of the international, whereby world politics continues to function as the impossible object, perpetually juggled by idealist and realist discourses without ever being grasped by either of them. Second, we may accept the concept of the World as the sole logically consistent construction of universality yet proceed to infer its irrelevance to politics due to its incapacity to ground any positive content. This solution, which we shall address in the following chapter in terms of nihilism , accepts the concept of the World and then denies the possibility of world politics precisely on the basis of this acceptance: since the World is void, world politics is impossible and there are only particular modes of politics in particular worlds. Finally, the third response consists in taking up the challenge of rethinking world politics on the basis of the concept of the World as void and ventures to derive universal principles of such politics from the disclosure of the World in particular worlds. As we have argued in the Introduction, what is at stake here is more than simply the relocation of the familiar concept of politics to a different level or domain, but rather the redefinition of politics as such on the basis of the World, which alone prevents the inquiry into world politics from a relapse into the aporias of (inter)national politics. Thus, in the following chapter we shall develop the formal concept of politics articulated on the basis of the relation between the World and worlds, while in Part II we shall address the universal principles, derived from the disclosure of the World, that form the content of politics and present a typology of forms of politics developed on the basis of these principles.

1 For a more detailed discussion of the set-theoretical notion of infinity, particularly in comparison with the Hegelian treatment of this theme, see Badiou (2008a: 106–112; 2005b: 161–170).

2 This theorem (see Badiou, 2005a: 84–86) demonstrates that there always exists at least one element of the power-set that is not an element of the initial set, i.e. there are more parts than there are elements. Its demonstration invokes Russell’s paradox of self-belonging: a set y of all elements of a that do not belong to themselves is shown to belong to the power-set of a , but not to a itself, since the latter option would then invite the paradox of self-belonging that contradicts our initial definition of y . This theorem finds further elaboration in Cantor’s theorem that demonstrates that the cardinality of the power-set always exceeds the cardinality of the original set and the Cohen-Easton theorem that demonstrates that for infinite sets, which primarily concern us here, this excess is immeasurable.

3 It is important to distinguish this logical argument about the infinity of worlds from the ontological argument about the infinity of sets . While all worlds are infinite, it is obvious that not all sets are infinite and that numerous finite multiplicities exist (the void set, singletons, etc.). In a transitional period between Being and Event and Logics of Worlds Badiou defines his assertion of the infinity of situations as a ‘modern axiom’, a ‘conviction’ rather than a ‘deduction’, that seeks to transcend the discourse of finitude dominant in twentieth-century philosophy (Badiou, 2005c: 182–183). Nonetheless, as long as the necessary infinity of situations is proclaimed on the ontological level, it remains problematic due to the abundance of evidence to the contrary. After the publication of Logics of Worlds it is possible to separate this ‘axiom’ from ontological arguments as a phenomenological deduction of the necessary infinity of worlds that says nothing about the infinity of sets. See more generally Hallward (2003: 66–71).

4 In a somewhat unkind endnote in Logics of Worlds , Badiou addresses the proximity between his phenomenology of worlds and Foucault’s archaeological analyses of epistemes and genealogical analyses of dispositifs only to argue, with a reference to an unpublished thesis by Cecile Winter, that ‘in Foucault there is no formal theory of the transcendental [and thus] empiricism prevails’ (Badiou, 2009b: 527). Notwithstanding this criticism, there is clearly a resonance between the objective phenomenology of worlds and Foucault’s analytics of government, insofar as both seek to reconstitute immanent ordering structures that condition the emergence of objects and subjects in a given world. What Foucault’s approach really lacks, in stark contrast with Badiou, is not so much a formal theory of the transcendental (Archaeology of Knowledge [Foucault, 1989] seems to contain at least prolegomena to such a theory) but an explicit ontology that would be a correlate to phenomenological analysis.

5 While the theme of the nothing becomes particularly prominent in Heidegger’s writings after Being and Time , it is certainly not absent from his magnum opus . We need only recall the discussion of conscience as the mode in which Dasein’s authentic potentiality for being is attested (1962: 312–347). Not only does the call of conscience say nothing, expressing itself ‘in the mode of keeping silent’ (ibid.: 318), but Dasein itself in the role of the ‘caller’ of conscience, ‘is definable in a “worldly” way by nothing at all, [as] the bare “that-it-is” in the “nothing” of the world, [the Self] thrown into the nothing’ (ibid.: 321–322). Moreover, in the discussion of Dasein’s guilt Heidegger invokes the double nothingness or nullity of Dasein. First, as a ‘thrown’ being Dasein always already finds itself delivered over to a certain field of possibilities that it has no power over; it exists as (and from) its own basis but this basis is itself negative and serves as a burden for Dasein. On the other hand, as a potential being that exists in the mode of projection Dasein chooses among these possibilities but in choosing one of them necessarily negates all the others. Thus, ‘[Dasein’s] being means, as thrown projection, being-the-basis of a nullity (and this being-the-basis is itself null)’ (ibid.: 331). Thus, Dasein is the ‘null basis for its null projection, standing in the possibility of its being’ (ibid.: 333). This theme of double nullity evidently resonates with the two structural moments of boredom in the Fundamental Concepts of Metaphysics , being left empty (the nullity of thrownness) and being held in limbo (the nullity of projection) that define the disclosure of the World.

6 In this reduction of the World to the world, Nancy arguably performs the inversion of the approach of Gilles Deleuze, which consists in the sublimation of ‘this world here’ (or any given world) to the status of the World or, in Deleuze’s terms, the virtual. Any particular created world, endowed with an immanent positive order, may be restored to the dynamic status of the process of creation through what Peter Hallward calls ‘despecification’ (Hallward, 2006: 161), the emptying out of its positive properties. The world is thus only perceived as the actual(ized) instance of the Virtual as the perpetual event of creation. Thus, while Nancy treats the World as our world, Deleuze treats our worlds as instances of the World. See more generally Badiou (2000: 43–53) and Hallward (2006: 27–53).