(Paradoxico-) Critique of Badiou

Transcription

1 Draft Version Please do not quote or circulate (Paradoxico-) Critique of Badiou If the characteristic methods of 20 th century philosophy are themselves not to be portrayed as dead or refuted, they must indeed demonstrate their continued vitality. One precondition for moving ahead thus must be, as we have seen, that the contemporary representatives of critical thought must stop allowing themselves to be mischaracterized, or wrongly assimilated to weaker and less helpful positions such as constructivism and limitative conventionalism. One way that the critical positions can do this, I think, is by insisting once again on the centrality and significance of the problem of the origin and nature of language, and on its continued lack of positive solution, either by naturalistic science or any socialconventionalist account. This alone is, however, probably not sufficient to ensure a genuine conversation between Badiou and the legacies of Kantian critique; indeed, it may have even have the effect of sharpening the differences here. For even if we are clear that Badiou s attack on constructivism does not actually meet many of the critical positions available today, it is nevertheless indeed true that what I have called the methods of paradoxicocritical philosophy are universally committed to posing a question, with respect to mathematics or any other enterprise of using signs, that Badiou himself cannot, given his commitments, possibly raise. Specifically, for all of these approaches, there is always at least a question of how the sign signifies, how it is that the (finite) sign accomplishes the infinite dimension of meaning. This is, for instance, Wittgenstein s question about following a rule. In Derrida s language (for instance in Signature, event, Context, ) it is the question of iterability, of how the finite symbolic corpus of a language achieves the possibility of citation and graft in any of an openly infinite number of contexts. And it is the question that is, as we have seen, at the very center of Deleuze s analysis of sense. With respect to mathematics at least, Badiou cannot ask any of these questions, since all of his demonstrations depend on his method of simply reading the results of mathematics for instance of set theory or category theory straightforwardly, as if there were no interpretable gap between the sign and what it stands for, even when the signs of set theory or category theory are taken to stand for highly abstract political structures such as representation and the state.

2 Thus it may easily seem that here we have a case of genuine incommensurability, and no real possibility of a neutral discussion, since any such discussion, even to get off the ground, would have to make a decision as to whether to ascribe relative priority to mathematics or to language, and that this decision can hardly be neutral between the two broad approaches. Yet as we have seen above in detail, the paradoxico-critical orientation produces a doctrine of politics and change that does not exclude either a constitutive use of set-theoretical formalisms, or a determinative application of them to the problems of thinking the constitution of political communities and the possibilities of their change and becoming, or even a central consideration (for instance in Derridian or Deleuzian forms) on the basis of these formalisms of the transformative potential of the aleatory, discontinuous event. All of this suggests that there may indeed be a way to talk about the problems that are common to, for instance, Badiou and Derrida in a unitary way, and even to give reflection on mathematics a privileged place in doing so. In order to have this conversation, it would be important not to deny that mathematics has a kind of privilege in its universalism and lack of obvious cultural location, and at least to be open to the idea that mathematical structures do indeed have something very important to show us relevant to the questions of metaphysics and ontology that have defined western philosophy (as well as to the general questions of the formation and structure of political community and life). At the same time, it would be important not to foreclose, as Badiou does, the question of formal systems of symbolization, and especially how they operate in what is, after all (even if it is other things as well) the symbolic discourse of mathematics. An inquiry that examined mathematics systematically in this way, without denying its uniqueness but also without foreclosing its symbolic status and its close relationship (if not identity) to symbolic language might go some way to showing what kind of special place mathematics can have within a human life, or clarifying how it is that mathematical structure and order is related to language on one hand, and to the ontological structure of the world on the other. The most general locus of this kind of question might be put, once more, as that of an inquiry into the consequences of formalism as such. The question for this kind of philosophy is then how formalism (whether mathematical or linguistic ) enters a human life, and what it means to reflect on the formalisms we live by. Posing this question in a general way amounts to admitting that, while we do not yet know how mathematical structures are to be understood directly as determining and constraining both ontology and politics, we also do not yet know what kind of thing language is, and hence what it means to live a human life that is evidently taken up by its structure.

3 A very good question for this future inquiry into the significance of formalism as such and in its entry into a human life would be: how does thought get a grip on infinity? 1 Since Plato (although he would not have seen it this way) we can put the problem of participation, or of the instantiation of universals, as a problem of the way an infinitary structure enters into finite, human life. And one of the greatest innovations of Badiou s project is indeed that it is the first to take account of the implications for this problem of the radical change brought about, in mathematics at least, by Cantor s theorization of multiple infinite sets. Of course, the critical projects that follow on the linguistic turn have their own multiple ways of posing the problem of the relationship between finitude and infinity, and it would be wildly inaccurate to see them simply as committed to limitative philosophies of finitude or indeed to denying the relevance of the problems and issues posed by the issue of infinity and its modes of existence or realization. Indeed, as I have suggested, the problem of how a finite corpus of signs (such as could plausibly be learned or understood by a finite human being) comes to be capable of an essentially infinite set of meanings might be put as one of the central problems of deconstruction itself. As we have already seen, despite the brilliantly insightful way Badiou himself applies formalism to the problems he confronts, from the perspective of this broader taxonomy, Badiou s treatment of the positions that most closely neighbor his own cannot, in general, be considered even barely adequate. For insofar as Badiou treats alternative critical positions at all, he massively and uniformly assimilates them to the constructivist orientation, which he devotes much of the formal apparatus of Being and Event to refuting. This refutation is the key element of his claim to provide an argument against the real-world liberal politics of democratic consensus, in which the state through its control of language legislates on existence and there is no possibility of an event, in Badiou s sense, ever taking place. This very strongly suggests the claim (though Badiou never makes it explicitly, in any case) that all of the thinkers that we have here treated as representatives of the paradoxico-critical orientation (including Lacan, Miller, Deleuze, Derrida, Agamben, Miller, Quine and Wittgenstein) are in fact constructivists, and thus that their critical positions ultimately simply provide support for the liberal politics of consensus itself. But as we have seen, this claim is certainly false. For all of these thinkers, the unity of the structure of language as such provides the basis for a non-constructivist critical position that demonstrates the fundamentally unsettling implications of this structure for the orthodoxies of contemporary belief. Moreover, there is reason to think that this omission or suppression affects in a fundamental way Badiou s argument against the orthodox political orientation of democratic materialism itself. In Logics of Worlds, Badiou again affirms the twofold link he sees between the constructivist position and both the 1 I owe this formulation to Bill Martin.

4 existing critical positions stemming from the linguistic turn, on one hand, and the orthodoxy of contemporary belief, on the other. Thus, the world of contemporary democratic materialism is identified as being, most probably, an atonic one in which there are no points, and so in which no faithful subjective formalism can serve as the agent of a truth. 2 As there are no truths, but only a managed life that is like a business that would rationally distribute the meagre enjoyments that it s capable of, there is also no place for any fundamental decision to occur, and all binary differences, up to the sexual difference itself, are deconstructed (note the term, which Badiou does not hesitate to use in reference to a movement that aims for a quasi-continuous multiple of constructions of gender ) in favor of a desire for generalized atony. 3 This is the world in which, as since there are no truths, there are only bodies and languages; it is rigorously opposed to Badiou s materialist dialectic, which, as we have seen, affirms in addition the existence of Truths beyond any language or any situated culture. Again, however, the philosophical positions that Badiou sees as dominant in contemporary academic life are, due to their continuing allegiance to the linguistic turn, opposed to this assertion and consigned to the side of democratic materialism: We can clearly see the opposition between the materialist dialectic and the two academic traditions that today lay claim to supremecy: phenomenology and analytic philosophy. These two currents both require a constituent assertion about the originariness of language. And both concur in seeing, whether in rhetoric or logic or in any case in the intentional forms of the control of syntagms the schema of this originariness. The materialist dialectic undermines this schema, replacing it with the pre-linguistic operations which ground the consistency of appearing. As a consequence, logic, formal logic included, not to mention rhetoric, all appear for what they are: derivative constructions, whose detailed study is a matter for anthropology. 4 Here, in a striking formulation of his ongoing assimilation of all positions descending from the linguistic turn to constructivism, Badiou assumes that any such position must, in reflecting on the implications of language, first demand its originariness and formulate the implications of its structure involving, exclusively, a regulative control of sytagms. By contrast, as we have seen, the paradoxico-critical orientation sees in the problematic ubiquity of language a fundamental aporia of origin and a multiplication of paradoxes of reflexivity that formally contest and disrupt any attempt to control the forms of language from outside. The constant and uniform basis for these insights is a continued fidelity 2 LofW, p LofW, p LofW, p. 174.

5 to (what we may see as) the logical event that was the origin of both the analytic tradition and structuralism, which in unrelentingly affirming the implications of the structural totality of language (or logic) as such, also removed it radically (witness the decisive polemics against psychologism and anthropologism that characterized the founding of the analytic tradition, as well as Husserl s phenomenology) from any anthropological or merely empirical derivation or account. We can begin to see what kind of difference this might make for contemporary political thought by returning to the two axioms of thought that Badiou distinguishes at the beginning of Logics of Worlds. The first of these is the axiom of the contemporary conviction: of democratic materialism: There are only bodies and languages. This orientation is thoroughly committed, Badiou suggests, to the pragmatism of desires and the obviousness of commerce, behind which lies philosophically the dogma of our finitude or of our carnal exposition to enjoyment, suffering and death. 5 Here, the life of the human is conceived as an overstreched animality a bio-materialism whose norm of the protection of all living bodies is to be guaranteed by bioethics, and contested by the strictly symmetrical (as Badiou suggests) position of an analysis of biopolitics in the style of Foucault. Moreover, the position thus defined is fundamentally democratic in that it is foundationally committed to a plurality of languages and to their juridical equality. This commitment yields an axiomatic devotion to the fundamentally plural and equal claim of all communities and cultures, colours and pigments, religions and clergies, uses and customs, disparate sexualities, public intimacies and the publicity of the intimate, to protection and recognition under the uniform law. 6 To this, Badiou opposes his own axiom, that of the materialist dialectic. According to this axiom, There are only bodies and languages, except that there are truths. 7 As Badiou emphasizes, the best way to understand the relationship of this axiom to the one it seeks to displace is to consider the syntax of the except: it is not that truths are the result of any kind of synthesis or supplementation to the democraticmaterialist world of plural bodies and languages; rather, they are excepted from subtracted from the totality of what there is. What there is in being everything that appears substantially in the world may indeed, Badiou allows, be limited to bodies and languages. However, by way of the fundamental and essential exception that a truth is, and which allows it to bring about the radical changes it can work in bodies and languages through the occurrence of events, there isn t only what there is. Thus, although the materialist dialectic agrees in a certain sense with democratic materialism in its restriction 5 LofW, p LofW, p LofW, p. 4.

6 of what is in being to bodies and languages this is, Badiou says, the common core of the materialism of both in another sense the materialist dialectic resists this consensual, orthodox perspective through its radical instance on truth, which breaks the continuity of the there is through the interpolation of a there is what there is not. 8 It is worth considering whether Badiou s language here is (even so much as) coherent, and hence whether (or on what basis, if not based on any difference in their existential claims) we can really distinguish between the sense in which the materialism of the materialist dialectic concurs, and the sense in which it breaks with, the materialism of democratic materialism. However, regardless of this, by comparing the formulation of the two axioms which Badiou thinks of as exhaustive of the presently available options, we may now locate very clearly the precise point at which the paradoxico-critical orientation is specifically excluded from Badiou s whole presentation. This is, unsurprisingly, the point of language, and what is absolutely decisive in this connection is that both of the axioms that Badiou states assume that language exists only in the plural. By contrast, as we have repeatedly and vividly seen in their detailed critical projects and results, the representatives of paradoxico-criticism uniformly operate by tracing the systematic, if paradoxical, implications of the fundamental assumption that there is a One of the structure of language or logic as such, a structure which is not exhausted by any specific, empirical language or any collection or plurality thereof, but bears its effects on the structuration of life through the fundamental effects of this totality. Whereas, therefore, Badiou treats the first axiom of democratic materialism as affirming a sovereignty of the Two (namely bodies and languages) which is to be opposed, according to his own orientation, by an affirmation of the Three (of bodies, languages, and truths), we may accordingly, on behalf of paradoxico-criticism, offer by contrast a third axiom that consists in the relentless affirmation of the implications of this One. We might indeed formulate this axiom as follows: There are bodies, and language exists as their exceptional, unifying pre-condition. Here, language is not affirmed as a plurality, either of language-games or of cultures; instead, it is the One of the universal presupposition of all intelligibility and all that is common, what first makes possible signification, and hence community, as such. The specific definition of the paradoxico-critical orientation is thus to be found in its relentless pursuit of this One, up to the radical and paradoxical consequences of the subsistence of language itself not, indeed, as any empirical or culturally located language but as the uniform, virtual and ideal, dimension of linguistic reality, the underlying ideological substrate which also founds the real of whatever takes place. This dimension is then intelligible, not as another 8 LofW, p. 5.

7 being or object next to the plurality of bodies, but as the constant presupposition of all unity and unification of bodies into a community or social whole. As such, its relationship to bodies and their actions is precisely exceptional: as we have repeatedly seen (most directly in connection with Agamben), language is the place of the permanent state of exception in which signification and the linguistic function is always, paradoxically, outside itself in its reference to the totality in which it takes place, and inside itself in its capacity for self-reference, both at and beyond the boundary of sense that its own movement incessantly draws. II We have seen, as well, that the central issue at stake between Badiou and the variety of thinkers that can be grouped under the label of paradoxico-criticism is the significance of the paradoxes of totality and self-reference, which both see as essential. This difference determined by the initial difference of decisions when faced with these paradoxes, which imply the impossibility of uniting consistency and completeness in a single account or theoretical structure is indeed profound and elementary, and determines without exception all of the profound differences in method, structure, and outcome that we have seen in the last three sections. However, this is not to say that there is not profound and important agreement as well. Most importantly, both Badiou and the thinkers of paradoxico-criticism agree in an important and definitive way on the existence of the formal paradoxes of self-reference and their relevance for philosophical thought. This is already a very significant point of agreement, for it distinguishes the two positions decisively and irreversibly from the positions of onto-theology and constructivism, which do not recognize the general philosophical significance of the paradoxes, and so continue to attempt, in different ways, to combine completeness and consistency in a single, unified account of the totality of what is. This attempt even in some cases coexists with a formal recognition of the paradoxes themselves, as for instance in Russell s own essentially constructivist attempt to defuse the radical implications of the paradox he himself discovered through a regimenting theory of types. Furthermore, this agreement about the significance of the paradoxes between Badiou and paradoxicocriticism extends to an essential parallel in their understanding of what is for both one of the key resources of political thought about the structure and formation of languages and communities, their common recognition of an inherent structural excess that is always the result of representative or symbolic phenomena. This excess can be modeled, according to both orientations, by the relationship between a set and its power set, which displays all the arbitrary possibilities of re-grouping the initial set s members. As we have repeatedly seen, what paradoxico-criticism understands as the essentially syntactic excess of any signifying language over the totality of the signified is, for this orientation, both the original source of

8 the ideological effects inherent to signification as such and the key resource of criticism in its interrogation of the imaginary foundations of substantial (ideological) pictures of the unity of a society, community, or political whole. For Badiou, on the other hand, this excess is quite simply the excess of representation over presentation and essentially defines the structure of what he calls the state as such, what is always capable of mastering representation. On the existence of such an essential structural excess of what can be represented by linguistic means over what is simply present, however, Badiou and the paradoxico-critic can certainly agree. What are here seemingly simply minor inflectional differences about the interpretation a set theoretical structure will grow wider, however, as Badiou develops the subsequent implications of this excess within the structure determined by his initial decision to preserve consistency at all costs, and sacrifice the totality of the world or of being in which all problematic excess, according to the paradoxico-critic, must be considered to take place. The disjunction between paradoxico-criticism and Badiou s generic orientation is, then, real and profound, although it does not exclude, as well, some extensive and significant points of agreement. Summarizing what we have seen in considering the specific paradoxico-critical positions above, there is agreement on: the imperative to formally think the possibility of radical and discontinuous change under the heading of the event ; the conception of such an event as structurally disjoined from the ordinary order of things, and above all the attempt to theorize such change as necessarily passing through (though in very different ways!) the paradoxes of self-reference and totality. Both are deeply committed, in fact (we shall examine the common ground of this commitment in more detail in the next chapter) to finding points for the resistance and transformation of the existing structural orders of political totalities, both in the local sense of specific, situated communities and states, and in the more global sense of the entire structural order of global capitalism, along with the axiomatics of parliamentary democracy and multiculturalist conviction that underlie it and support its continued expansion. In this respect it can certainly be said, as Derrida reportedly said to Badiou, that the paradoxico-critic and the generic philosopher have, at any rate, the same enemies ; and it is important in the present context not to minimize the extent to which this commonality can indeed determine a common project that is at once radical, subversive, and grounded in the very consequences of formal thought itself. 9 On the other hand there is a profound and central structural disagreement, from which everything else that is at issue between Badiou and the paradoxico-critic proceeds, on the very ground of the ancient question of the One and the Many itself; this is the disagreement which we have repeatedly witnessed between the relentless affirmation of consistency, along with the sacrifice of the One of language and sense as such, and the 9 LofW, p. 546.

9 equally uncompromising affirmation of completeness, along with the constitutive paradoxes and contradictions of sense and meaning that it demonstrates. Without exaggeration, it is in fact possible to see this disagreement as fundamental to the question of the kind of response that is appropriate to the prevailing economic, political, and structural order of the day, which (as we have seen) the generic and paradoxico-critical orientations find common cause in opposing. Without deciding between the two orientations, we are nevertheless now in a position to trace these implications, and juxtapose them. As we have seen, one of the largest questions at issue between the generic and paradoxico-critical orientations is the question of the status of plurality itself. For Badiou s generic orientation, plurality is fundamental and irreducible, and any gathering of diverse individuals into a unity the production or formation of any One whatsoever is understood as the result of an operation (what he calls, in Being and Event, the count as one ) which is subsequent to the being of the many in itself. Paradoxicocriticism, on the other hand, affirms an originary One prior to any division or fracturing into the many, and constantly implied (even if only latently or virtually) in every use and instance of significative language as such. As we have seen, we can trace the implications of Badiou s fundamental decision in favor of plurality from the first moments of Being and Event all the way up to Logics of World s multiplicity of worlds and languages, which are, Badiou says, without common measure or commensurability. The paradoxicocritic will, by contrast, insist upon the problematics arising from the assumption (even if it is nowhere empirically verified) of a single language (or of language as such) and a single world, a totality of all that is, in which it takes place. What, then, are the implications of this disagreement for contemporary thought about the political change and its possibility? Here, it is possible and helpful to note a surprising fact about Badiou s position that, though it may otherwise escape our attention, becomes particularly clear when this position is contrasted with the paradoxico-critical orientation on the precise question of plurality that most deeply divides them. It is that, with respect to the overarching structure of the political order as such, Badiou is in fact very close to the spontaneous position of the relativist consensus that he would like most emphatically to oppose. The key point is that both affirm, as a fundamental starting point and by common contrast to the paradoxico-critical orientation, an essential plurality of communities or worlds, incapable of being subsumed to a single, common measure. This is, in the postmodernist jargon, the irreducible heterogeneity of identities and cultures, the diversity of contingent and conventionally instituted language-games, which yields as its only universal imperative the ethic of tolerance and inclusiveness

10 that functions here as a kind of ideological fixed point. Of course, Badiou will vehemently oppose this bland ethics on the basis of his own militant call for radical, transformative action in the name of the universal, which is, for him, equivalent to the faithful forcing of a Truth. Nevertheless, the structural commonality with respect to plurality itself makes for some interesting further homologies with respect to the role that both accord to language and meaning in the transformation of political realities, and raises doubts (once again) about the extent to which Badiou is indeed able accurately to portray the space of options open to genuinely critical political thought in our time. To begin with, as multiple commentators have noted, Badiou is by no means clear about the nature of the fundamental operations that for him function to structure a one out of a many themselves. In Being and Event, the operation of forming a One out of a Many, which is operative in the formation of any and every consistent set, as well as any object or phenomenon capable of being named, is termed the count as one; as noted, it is for Badiou always subsequent to the pure multiplicity, or many, that it counts. However, as to who performs this operation, where it is performed, or how, Being and Event is entirely silent. 10 The only information we gain about this operation at the point of its introduction is the claim that it is not essentially linguistic; this assertion will later be necessary, of course, in demonstrating that there are possible sets for instance the generic set that is essential to forcing that do not coincide with any linguistic predicate or set thereof. In Logics of Worlds, there are indications that the more elaborate apparatus of worlds and their transcendentals that there replaces the situations of Being and Event is intended, at least in part, to answer to worries about the capability of the earlier, simpler structure to portray the structures of the multiplicity of local situations in all of their vicissitudes. However, with respect to the more fundamental question of the actual operation that results in the imposition of structure (whether construed as that of a situation, formed from the count as one or as that of a structured world) the problem is, if anything, compounded. Here, recall, Badiou disjoins the realm of being, which is to be handled by means of set theory, from the transcendentally structured worlds of the realm of appearances, or phenomenology, which display a variety of specific logical structures comprehensible in terms of category theory. But we must here pose the question whether, for all of its rigorous and detailed formalism, Logics of Worlds actually succeeds in producing an improved understanding of those structures and relationships of objective appearing that are its central theoretical objects. These are, remember, not appearances-to-asubject or even appearances as structured or determined by conventional decision or by a contingent language community, but rather objective appearings to no one in particular, nevertheless rigidly 10 For some critical considerations about the count-as-one, see Johnston (2008).

11 disjoined from the ontological reality of things as they are in themselves. Although Badiou offers a detailed formalism of these degrees and relations, up to the variable intensities of appearance or existence within a world, he never answers the question of how we may establish in a neutral way what these intensities actually are. Along similar lines, the detailed theory of transcendentals shows in rigorous detail the formal connection to Heyting algebras and particular (generally non-classical) logics, but nothing in this elaborate theory seems to explain how the transcendentals and logics actually come to structure the worlds to which they apply, or to what they owe their force in governing these relations of appearing and intensities of existence to begin with. Indeed, the concept of world itself remains, despite its centrality to the whole project of Logics of Worlds, quite ill-defined; despite all the varied examples, we are never told in clear and non-circular terms, for instance, how to understand the unity of a world as such, or how to distinguish one from another. It may be that Badiou wishes to refrain from posing the quid juris question of the genesis of transcendental and the right of its application to a world, in that he fears that answering this question would inevitably lead back to one of the forms of idealism (subjectivist or linguistic) that he rejects. However, failing a good answer to the question of the force and maintenance of transcendental structures in determining appearances, it is very difficult to avoid the natural assumption that transcendentals are indeed structures of linguistic or conventional practice, established and held in place by the behavioral regularities of a specific cultural or language community. This assumption, of course, would lead directly back to the kind of culturalist relativism that Badiou wishes above all to avoid. However, it is not at all clear that he succeeds in forestalling it. This is not to say that Badiou s position is ultimately equivalent to the politics of a democratic, culturalist relativism that affirms a complete contingency of institution and irreducible plurality of language-games; but it nevertheless shows just how slender and potentially elusive is the theoretical passage on which Badiou stakes his entire claim to resist it. As we have recurrently seen and is witnessed in Badiou s own careful formulation of the difference between the democratic materialism of contemporary conviction and his own materialist dialectic, the sole point of difference here, on which everything else in Badiou s project (and hence, its entire ability to resist the politics of contemporary conviction) rests, is Badiou s unflinching and relentless affirmation of the exceptional being of (what he calls) Truths, and hence of the fundamental possibility of discontinuous and progressive change that they introduce. By contrast, paradoxico-criticism, which has little use for Truths in Badiou s sense, or for the faithful subject who orients himself toward their progressive realization, affirms from the beginning the existence of language as such and detects the essential possibility of discontinuity and change within any existing community and its structure at the fixed point of the paradoxical internal reflection of this structure into itself.

12 How, then, should we attempt to address this pivotal question of the existence of what Badiou calls Truths, which determines in a very profound sense Badiou s project, yet nevertheless does not seem, from a larger perspective, to be verified by any incontrovertible evidence, whether empirical or formal? Though it is, again, extremely difficult to find neutral terms in which it is possible even to pose this question from an unbiased perspective, we may perhaps gain some insight into it by considering what Badiou himself says in addressing it, in a section of Being and Event titled (appropriately enough) Do Truths Exist? The question, Badiou says, is equivalent to the question of the existence of generic procedures of fidelity, and has both a de facto and a de jure dimension. He then articulates the question into the four domains or procedures of love, art, science and politics; in the political dimension specifically, the question of the generic procedure is, he says, equivalent to the existence of a generic politics which is the same as what was called, for a long time, revolutionary politics but for which another word must be found today. 11 How, then, will we settle, even on Badiou s own terms, the question of the existence of such a politics, including (as it must) the progressive dimension of realization according to which it discontinuously realizes its Truths? Badiou repeatedly gives what he does not hesitate to call empirical examples of events, but the problem is obvious: how are we to judge that these examples, which are in the political cases at least virtually always in line with Badiou s specifically favored (leftist and revolutionary ) political orientation, are genuine events really directed toward an eternal and timeless Truth, and how distinguish them, in general, from the various sorts of pretenders, merely incremental or continuous (and hence not genuinely evental) inflections, and reactionary reentrenchments that Badiou s doctrine distinguishes on a purely formal level? At the present juncture, however, is clear that the focus of Badiou s argument is most of all not on this de facto question of the actual existence and identity of events, but at the de jure question of their possibility: As a de jure question, the existence of faithful generic procedures is a scientific question, a question of ontology, since it is not the sort of question that can be treated by a simple knowledge, and since the indiscernible occurs at the place of the being of the situation, qua being. It is mathematics which must judge whether it makes any sense to speak of an indiscernible part of any multiple. Of course, mathematics cannot think a procedure of truth, because mathematics eliminates the event. But it can decide whether it is compatible with ontology that there be truths. Decided on the level of fact by the entire history of humankind because there are truths the question of the being of truth has only been resolved at a de jure level quite recently (in 1963, 11 B&E, p. 340.

13 Cohen s discovery); without, moreover, the mathematicians knowing how to name what was happening there 12 Therefore it is, according to Badiou, on a formal level that the question of at least the possible being of truth is ultimately decided, and there it is indeed verified by Cohen s discovery of forcing. We shall turn to the question of this interpretation of the formalism, and the various other possibilities for understanding it, in the next section. What kind of difference, though, does this question of the being of Truth (in Badiou s sense) make to the question of how we should think of the fundamental possibilities of political change in our time, and in particular to the question of how best to resist (or perhaps, transform) the consensual political axiomatics of the day, which (as all relevant parties agree) are deeply tied to the structural reality of global capitalism in its varied contemporary forms? To a certain extent, a specific answer to this question must await the further examination of those implications which, common to Badiou s generic orientation and the paradoxico-critical one, can indeed claim to be rigorous and univocal outcomes of the formal thought of our time, as such; we defer this examination to the next chapter. For now, however, it is possible to suggest the following. Because of its fundamental affirmation of the plurality of worlds and inspired, if not always obviously formally grounded or justified, invocation of the imperative of a militancy of truth and the kind of direction it defines, Badiou s orientation is uniquely capable of thinking the possibility of discontinuous transformation, whereby a specific state or community constituted by a determinate structure of inclusions and exclusions that has determined its political life, up to a certain moment, is transformed into a substantially different one, a distinct state or community constituted by a distinct but still determinate structure. This is doubtless important, for it figures, and indeed offers to provide formal terms for the support of, the hope of all progressive social transformations and all localized revolutions. But because it disavows the thought of the totality at a fundamental level, Badiou s thought is, in general, less well suited to thinking the possibility of varieties of change or transformation that indeed promise to affect, or even disrupt, the unity and hegemony of global and total systems of organization, order, and control. This leads to the another large question about the success of the project of Logics of Worlds, this time a question that also bears on the success of Being and Event. This is the question of the extent to which the elaborate formal apparatus that Badiou develops in both books in fact supports the militant political doctrines of evental change and generic Truth that underlie his more polemic claims, both with respect to existing philosophical projects and the larger socio-political situation. For it is one thing to give a formal 12 B&E, p. 341.

14 theory, even a rigorous and sophisticated one, of how we might think of what evental or punctual change actually is (even assuming that we can follow Badiou in all of the other aspects of his, often very imaginative, projections of formal structures into political categories); it is quite another actually to work toward changes of this sort in real, already-structured domains, or even to know in much detail how to go about doing so. Indeed, insofar as Badiou s theory of evental change in both books demands that the event, if it is to be truly transformative, amounts to the sudden, unpredictable advent to appearance of a kind of phenomenon that could not even possibly be discerned within the previously existing situation, it seems to deprive us even of the possibility of anticipating, even in vague outline, these possibilities of radical change or locating their likely sites of appearance until after the event. 13 Thus, it is not clear that Badiou s elaborate theory can actually play a significant role despite its strong rhetoric in supporting the kinds of change it ostensibly envisions. By contrast, as we have seen above, paradoxico-criticism, through its identification of inherent contradictions, incoherences, and weak points that are involved in the very structuring of any system of order as such, is much better suited at least to locate the points of the possibility of such global disruption, if indeed there be any such. Here, moreover, the yield of critical thought in its identification of such weak points of structure as such is not necessarily the replacement of one determinate structure with another, equally determinate one, but rather the identification and multiplication of the structurally necessary indeterminacy which the phenomena of the undecidable (in Derrida s sense) and the state of exception (in Agamben s sense) witness. This recognition provides, at the very least, a critical position from which it is possible to interrogate the legitimating claims of necessity that provide ideological as well as material support to various total systems of order, regimentation, and economy. For instance, as we saw in chapter 7 above, the formal and paradoxico-critical position that we may extract from the interlinked investigations of Wittgenstein and Turing into the axiomatic notions of computability and effectiveness provides a position from which it is possible to discern the weak points of uncomputability and ineffectiveness that must permanently accompany and structurally problematize, at 13 These problems with Badiou s theorization of political change have been noted by several commentators. Adrian Johnston makes this point a kind of crux of his perceptive and thorough book Badiou, Žižek, and Political Transformations: The Cadence of Change (Johnston 2009). Johnston there calls, in response to Badiou, for a kind of pre-evental discipline of change and even for a pre-evental forcing that would attempt to discern the systematic weak points at which it might be possible for political actors to intervene and produce fundamental transformations, even before the recognizable occurrence of anything like an event in Badiou s sense. For some closely related concerns, see (Hallward 2004b), pp

15 a fundamental level the coherence of any system (economic or political) constitutively devoted to these axioms. 14 Of course, the question of the local or global status of any specific political configuration or social whole is a difficult and delicate one, and it is not obvious either that all important political changes are not ultimately local in Badiou s sense of being essentially localized in a specific world among other actual or possible ones, or again that the implications of such situated changes cannot nevertheless, at least at times, be truly global in implying the fundamental and structural weaknesses of total systems of order as such. Again without resolving these questions, though, we can note that they extend to the massively complicated and difficult question of the reality and effectiveness of global capitalism itself, and to the prospects various systems enjoy of finding means or positions from which to resist, transform, or even replace it; we will take up this question in more depth in the next chapter This possibility of discerning the weak points of ineffectivity within regimes in which the effectiveness of techniques and technologies are uniformly presupposed appears to be closely linked to paradoxico-criticism s identification and critique of metaphysics, a critical category which Badiou does not employ. In the context of a perceptive discussion of Badiou, Jean-Luc Nancy raises the question of the privileged link between technics as the manipulation of nature and the metaphysical determination of man in terms of logos (for which, see chapter 1, above): Thus, ultimately, the name metaphysics, which subsequently arises as though by accident, is not really accidental at all. It has already been prepared through the complex of techniques that has produced nature as the object of a manipulation that is at once theoretical and practical Thus, there is a precondition that renders what Badiou calls conditions possible. This is a precondition which is at once and indissociably historical, technical and transcendental: by which I mean that it is necessary insofar as it is the reason for philosophy as metaphysics, and yet contingent because there is no sufficient reason for this reason. Politics, science, art and love all answer, within a mutual incommensurability, to the technical condition in the state of its metaphysical autonomization: each of them is structured by the unassignable character of its own principle and end, each of them is a technique or a technical configuration, or rather, each of them opens out onto an indefinite chain of technical transformations. (Nancy 2002), pp This role of metaphysics in pre-conditioning the (necessarily technical) procedures which Badiou calls the conditions of Truths is again connected, according to Nancy, with the logos: With the concept of the logos as such, which stretches from the order of discourse to that of verifying autonomy, a technique takes charge of the production of sense itself, rather than merely of subsistence or even super-sistence [sursistance]. This is the sense in which I am here characterizing metaphysics as a techno-logy: the sense of a breakout into a verifying autonomy of technics, or of denaturation. (p. 48) For more on these issues, and the opposition they tend to suggest between Nancy s position and Badiou s, see chapter 11, below. 15 In a highly suggestive, though brief, reading that bears multiple connections to the discussion here, Ray Brassier (2004) raises the question of the extent to which Badiou s conception of subjective action and fidelity indeed provides terms by which we can understand and criticize the systematic logic of the machine of global capital. Brassier suggests that Turing s demonstration of the necessary existence of uncomputable functions and procedures (see chapter 7, above) might provide for a kind of objective randomness that indexes the not-all-ness (pas-tout), the constitutive incompleteness whereby the Real punctures the consistency of the symbolic order (p. 57) and so provides an alternative to Badiou s subjective conception that is in fact better able to handle the constitutive contradictions and errant automation of global Capital. For more on this suggestion, with which the position of paradoxico-criticism can certainly agree, see chapter 11, below.

16 Having witnessed some of these differences in the specific oppositions of Badiou to various paradoxicocritical thinkers, above, we are now in a position to return to the formal schema of orientations in thought and consider in somewhat more detail the relationships between them. Here, again, is the schema: Language captures Truth Truth exceeds language Paradoxico-Critical: Completeness, inconsistency Generic: Consistency, incompleteness Criteriological/Constructivist Onto-Theological We can recapitulate, also, the definitions for each of the four orientations: Paradoxico-critical: Any position that, recognizing reflexivity and its paradoxes, nevertheless draws out the consequences of the being of the totality, and sees the effects of these paradoxes always as operative within the One of this totality. Generic: Any position that, recognizing reflexivity and its paradoxes, denies the being of the totality and sees these paradoxes as traversing an irreducible Many. Criteriological: Any position that attempts to delimit the totality consistently from a stable point outside of it. Onto-Theological: Any position that sees the totality as complete and consistent in itself, though beyond the grasp of finite cognition. All of these are positions that are essentially determined in relation to their thinking of the totality of what is or can be named. But thinking about totalities (even if we deny their existence) is always also thinking about limits; we have, then, four topological figures of the limit, and of the operations of thought at the limits.

17 Paradoxico-Critical: The thought of the limit is the inconsistent thought of in-closure: in thinking the limit, we are both within and without the totality we think. Generic: The consistent thought of the limit is always only possible from the perspective of a Truth, which is always essentially beyond any specific situation and cannot be fully stated while remaining within any such situation. Criteriological: The consistent thought of the limit is possible from an unproblematic theoretical position. Onto-Theological: The limit is consistent and coherent in itself, but cannot be conceived by finite thought, except as an infinite mystical excess. Correlative to these, we can discern four figures of infinity in its entry into human life: Paradoxico-Critical: The infinite enters human life at the point of the paradox of reflexivity, as the problematic presupposition of language, meanings and practices. Generic: The infinite is the inexhaustible resource of a Truth which calls forth the asymptotic progress of situations by means of its infinite, generic procedure. Criteriological: The infinite does not exist; all that exists is finite. Onto-Theological: The infinite is an absolute transcendent being, unreachable by human thought. Finally, and symmetrical to these (since as we have seen, the question of infinity is always closely connected with that of reflexivity) we have four figures of formal reflexivity: Paradoxico-Critical: The permanent structural possibility of reflexivity is the source of the effectiveness of essential paradoxes, which define the nature of meaning and signification as such. Generic: The actuality of reflexivity (as auto-nomination or as the appearance of the transcendental index of a world within that world itself) is the source of every possibility of real structural change. Criteriological: Reflexivity does not take place within the world. (This is, e.g., the position of Wittgenstein s Tractatus). Onto-Theological: Reflexivity takes place as the activity of a substance, for instance as reflection in consciousness or as the action of the subject.