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Avello Publishing Journal Vol. 1, No. 2011 Being a Sublime Event: a critique of Alain Badiou’s Magnum Opus

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Avello Publishing Journal Vol. 1, No. 1. 2011

Being a Sublime Event: A Critique of Alain Badiou’s Magnum Opus

Clayton Crockett, University of Central Arkansas

According to the theoretical physicist Lee Smolin, our human world is “incredibly big, slow and cold compared with the fundamental world” of particle physics as indicated by the Planck scale.1 Alain Badiou’s mathematical ontology is most fully developed in his book Being and Event, which represents a significant new philosophical understanding of the world, but perhaps his thought here is ultimately too “big, slow and cold” due to his overemphasis upon a static and axiomatic form of mathematics. In this article, I read Badiou’s mathematical ontology as an elaboration of the Kantian sublime, in which Badiou rigorously separates the mathematical sublime from the dynamical sublime in order to eliminate all vestiges of subjectivity from being. The result is a frozen ontology. On the other hand, the way that Badiou characterizes the event in Being and Event can be correlated with the dynamical sublime, so long as one recognizes that Badiou repudiates any transcendental subject who would be capable of synthesizing ontology or prescribing the conditions for an event. Badiou purges the subject from Being and Event, and this obscures the Theory of the Subject in his previous book. In some respects, Badiou is forced to compose his follow-up to Being and Event, Logics of Worlds, in order to restore the subjective aspect of existence and bridge the gap between the event-subject and the set theory ontology that precludes it. However, I will not discuss Theory of the Subject or Logics of Worlds explicitly here.2

This is a polemical project, and thus I am unfair to Badiou’s philosophy, however this does not mean that I do not take it seriously. In this article, I will show how Badiou’s mathematical ontology, that functions as both a condition of possibility and a condition of impossibility of an event, is eerily similar to a philosopher that Badiou despises, namely Kant.3 We could say that Badiou’s philosophy is quasi-Kantian insofar as it is obsessed with the conditions of possibility for an event to occur, a pure irruption of novelty beyond being. In order to think this chance, which is for Badiou also the possibility of becoming a subject and the political possibility of revolution, he is forced to formalize these conditions, even to the point of their exclusion of an event. Nonetheless, there is an event. Events happen; but, they are not common, ordinary or everyday events, which are saturated with the ideology of bourgeois capitalism. No, events must be dramatic and powerful. Events are makings and re-makings of history and of human beings who are subject to them. Being and Event represents the most extraordinary attempt to formulate and formalize the conditions of ontology within the resources of set theory, and to show where and how an event can happen, if it happens, even though we cannot entirely predict it.

Badiou struggles with and through this duality of ontology and event throughout his career. Being and Event is both his masterpiece and his most pronounced dualistic expression of these two terms. Logics of Worlds is written in certain ways for the same purpose as Kant wrote his third critique, the Critique of Judgment, to bridge the gap that Kant and Badiou had previously set up between pure and practical reason. If Being and Event is Badiou’s Critique of Pure Reason, then Badiou’s second critique was written first, and it is called Theory of the Subject. The subject mostly disappears in Being and Event, and but we should note that the subject as elaborated in Theory of the Subject is basically assimilated into the event in Being and Event, and presupposed in general for the entire book.

Before turning directly to Being and Event, I want to consider Badiou’s earlier work, The Concept of Model, and consider how a formal mathematical understanding of model drives Badiou’s work, even as he wants to use it as a basis from which to derive a revolutionary subject, which occurs in Theory of the Subject. The Concept of Model is based on a set of lectures Badiou gave in 1968 at the Ecole Normale Supérieure. Badiou was a student of Louis Althusser and a keen reader of Jacques Lacan, whose seminar he also attended. In this book, Badiou defines a mathematical understanding of model in a way that distinguishes it from a more general logical or philosophical understanding of model. Furthermore, Badiou wants to differentiate his conception of model from the pervasive notion of structure in French thought, as well as situate his understanding carefully with and against Althusser’s Marxist understanding of the relationship between science and ideology.

What is striking about the history of this book is that in the middle of Badiou’s lecture course the famous events of May 1968 broke out, interrupting them. Badiou was suddenly completely involved in supporting the students and workers in their protest against the Gaullist regime. Here is an incredible dramatization of the contrast between Badiou’s interest in philosophical-mathematical formalization and his deep engagement with radical Marxist and Maoist political struggle. The event occurs, unforeseen in the midst of his project of theoretical formalization, and Badiou immediately acts out of fidelity to the event of May ’68, thereby becoming a revolutionary subject. A good way to read Badiou’s later work is to see him wrestling with these the intersection of these two interests.

In the book The Concept of Model, Badiou sets out his theses concerning the notion of a mathematical model. He argues that we can isolate and separate a “concept of mathematical logic” from a more “descriptive notion of scientific activity”.4 When this specific mathematical concept of model is subsumed under a general philosophical category and thought in terms of the philosophy of science, it is ideological. But we can liberate this mathematical concept and deploy it in more practical, experimental and revolutionary ways. Badiou is suggesting that Althusser’s opposition between science and ideology is too broad and vague, and he wants to show where and how a specific scientific practice evades and resists bourgeois ideology.

In this brief, dense text, Badiou constructs the syntactic and semantic elements of his concept of a mathematical model, including rules of deduction, generalization and separation. Importantly, Badiou rejects the continuum hypothesis in this early work, claim that “a well-formed expression [should] be denumerable,” because “to speak of a model is to exclude the possibility of a formal language being continuous.”5 Badiou’s concept of model is specifically mathematical and not logical, because “an axiom if logical if it is valid for every structure, and mathematical otherwise.”6 The problem with logic, according to Badiou, is that it is too general and broad, and it diffuses the specific force of a mathematical logic by this ideological generalization. Not until Logics of Worlds (2006) does Badiou develop a positive satisfactory understanding of logic, because up until that point logic is too linguistic and ideological.7 In The Concept of Model, for a formal mathematical model to work it requires an exclusive specificity to become a weapon or a tool for practical and materialistic experimentation. A proper mathematical model allows for “the regions of mathematical science [to be] incorporated into the material apparatuses where this science is put to the test.”8 A materialist use of science puts a finite mathematical model into practice for a specific purpose. Badiou sums up his achievement towards the end of the book:

In other words, once clarified by dialectical materialism, the rigorous examination of the scientific concept of model permits us to trace a line of demarcation between two categorical (philosophical) uses of the concept: one is positive, and enslaves it to the (ideological) notion of science as representation of the real; the other is materialist, and, according to the theory of the history of sciences (a specific region of historical materialism) indirectly readies its effective integration into proletarian ideology.9

This materialist mathematical model becomes bifurcated in Badiou’s later work. On the one hand, the materialistic and exclusive model is more explicitly politicized into a materialist dialectic concerned with the composition of a proletarian subject in Theory of the Subject. On the other hand, the formalized mathematical model of The Concept of Model gets elaborated into the set theoretical ontology of Being and Event. Of course the language and formalization is much more extensive, but the crucial change in Badiou’s philosophy is the separating out of the subject from the realm of ontology and its identification with the event. In Being and Event, being as inconsistent multiplicity is set up in order to exclude the event, but also in a strange way to make it possible. The two concepts are constructed with the greatest possible tension. Within the context of Badiou’s ontology, though, the main advance of Being and Event beyond The Concept of Model comes with Badiou’s understanding of the empty set, or the void.

In Being and Event, Badiou claims that being qua being is mathematics, which is best expressed in terms of contemporary set theory. The postulates of set theory can be encapsulated in nine canonical axioms: extensionality, subsets, union, separation, replacement, the void, foundation, the infinite, and choice. These axioms, as Peter Hallward explains, “postulate, by clearly defined steps, the existence of an actually infinite multiplicity of distinct numerical elements.”10 Philosophy after Heidegger must grapple with and properly clarify this ontological situation using the tools of “the mathematio-logical revolution of Frege-Cantor.”11 The ontological situation can then be related to a modern, post-Cartesian understanding of the subject, and it is the task of philosophy to think this transition, which is the impossible passage from Being to Event.

So for Badiou, the fundamental insight is that “mathematics is ontology” (BE 4). Philosophy is oriented towards understanding ontology as pure mathematics, using the most sophisticated tools of mathematical formalization. This is why Badiou makes use of complicated mathematical equations and theorems throughout the course of the book. I don’t think that it is essential to be able to follow the equations and notations, however, in order to comprehend the basic ideas.

Being and Event proceeds according to a logic of axiomatic decisions. The first decision is to decide in favor of the multiple over against the One. If the one is not, or is derivative of the many, then there exists a primary multiplicity of being that cannot be directly thought. In order to think being, we have to present it in a situation, which means that we have to subtract from this fundamental multiplicity an element that will “count-as-one” in order to present it. In order for being to present itself in a situation, it must subtract from this multiplicity by means of a procedure known as counting, whereby a state of a situation “counts-as-one” a technically infinite state of affairs. The “count-as-one” is the condition according to which “the multiple can be recognized as multiple” (BE 29). Multiplicity as such characterizes mathematical ontology, but it cannot be presented directly.

The presentation allows for a stability, a structure, or a situation. A state is a later re-presentation of this original presentation: “the State always re-presents what has already been presented” (BE 106). Badiou claims that “there is no structure of being” (BE 26), but “the ontological situation [is] the presentation of presentation” (BE 27). What ultimately exists, the real as real or the thing in itself, is an inconsistent and unpresentable multiplicity. But we can present this multiplicity by means of the one, which does not exist, but functions to separate out an element of the multiple to allow us to think it.

Set theory is that formulation of mathematical logic that allows us to think consistent and infinite multiplicities, and set theoretical ontology provides us a way to think being as being. Cantor’s set theory enables us to think consistent multiplicity as a set (BE 42), even though Cantor himself wanted to ground his set theory ontology in an absolute infinity that would be God. Badiou, an avowed atheist, discounts Cantor’s theological solution, and opts instead for the void, or the null set. The notion of the void provides the consistency of the thinking of being in mathematical terms, because it indicates the nothing that every multiple is a multiple of. If we choose not to name the void as one, the alternative is to name the void as multiple, which means that any presentation of being as a structured or consistent multiplicity has to separate itself from the void. The void is the means by which subtraction occurs, because it is a set to which no members belong. As Frederiek Depoortere explains, “what is named by ‘the void’ is unpresentable and inaccessible, while as named by ‘the void’, it is nevertheless presented and accessible.”12 The void is the subtractive suture to being (BE 67) that enables the count-as-one to present being as a consistent or thinkable multiple. The void is an empty set, the null set Ø, which is “the unpresentable point of being of any presentation” (BE 77).

The notion of the void is crucial for Badiou’s understanding of being, because the void allows for the excess of inclusion over belonging: “inclusion is in irremediable excess of belonging” (BE 85). The theorem of the point of excess means that for any subset of a set, there is always at least one member that is included in the set which does not belong to that set. This theorem pertains to what are called power sets. In the case of finite sets, a power set, or the set of parts or subsets that can be included in the elements of that set, can be calculated in exact quantitative terms. But for infinite sets, the calculation of a power set is not possible; “the quantity of a powerset is literally undecidable.”13 As Oliver Feltham notes, “for Badiou, there is thus an unassignable gap between presentation [belonging] and representation [inclusion]: there are incalculably more ways of re-presenting presented multiplicities than there are such multiples.”14 An evental multiplicity differs from an ordinary multiplicity precisely insofar as it includes elements that do not belong to it as a member of a particular set. Badiou puts it another way: “no multiple is capable of forming-a-one out of everything it includes” (BE 85). The fact that a set includes more parts than are capable of being represented prefigures an event but in it does so by inversion.

The distinction between belonging (to a set) and inclusion (as a part of a set, or a sub-multiple) emerges by means of the void. The void accounts for the fact that there is a sub-multiple that is a part which cannot be represented as belonging to a situation. As Badiou says, “there are always sub-multiples which, despite being included in a situation as compositions of multiplicities, cannot be counted in that situation as terms, and which therefore do not exist” (BE 97). This inexistence indicates the place of the void, which is necessary for the constitution of an evental site.

An evental site inaugurates a form of historicity. Historicity “is founded on singularity, on the ‘on-the-edge-of-the-void,’ on what belongs without being included” (BE 185). Although the event constitutes a certain break with being, it is in a way prefigured or conditioned already within being, because what becomes the event emerges out of the ontological excess of inclusion over belonging. In fact, the event is precisely the reversal of this excess, that is, a relation of belonging or self-belonging that exceeds inclusion in any situation. This means that Badiou is not ultimately a dualist in Being and Event, and furthermore the event is not an irruption of a mystical or transcendent reality. Badiou is interested in distinguishing the event from being, however, in order to be able to show how an event cannot simply be prescribed or predicted from within being. He states that the composition of the evental site “is only ever a condition of being for the event,” and “there is no event save relative to a historical situation, even if a historical situation does not necessarily produce events” (BE 179).

So rather than a strict dualism, an event emerges out of and is prefigured already by an inconsistent state of being. At the same time, an event is described as reversing this excess of inclusion over belonging. With mathematical ontology, we have an infinite or indefinite multiplicity, because there are always parts that are included within a set that cannot be presented as belonging within a set, but only delineated as a situation by an operation of subtraction. We count-as-one an indefinite multiplicity in order to present a situation, that is then represented as the state of a situation. With an event, however, belonging exceeds inclusion. That is, an event is characterized as a phenomenon where the relation of belonging or self-belonging takes precedence over its inclusion in any state or situation. Badiou says that “one cannot refer to a supposed inclusion of the event in order to conclude in its belonging” (BE 202). A multiple can only be recognized as an event by means of an intervention which is not included within the situation. “An intervention consists,” he claims, “in identifying that there has been some undecidability, and in deciding its belonging to the situation.” Rather than a simple reversal, it might be better to describe an event as a torsion or twisting of this relationship of inclusion and belonging, using a term from Theory of the Subject. Here the excess of inclusion of parts over belonging of elements in a set gets twisted up in such a way that the excessive parts fuse into a kind of belonging that irrupts in a kind of chain reaction. An event is a bomb.

Most of Being and Event involves the elaboration of Badiou’s fundamental ontology, which is developed as contrast to or background of an event, which occurs apart from any prescribed conditions of possibility. According to Badiou, “with the event we have the first concept external to the field of mathematical ontology” (BE 184). As Bruno Bosteels writes,

ontologically speaking, self-belonging is even the only feature – condemned in set theory – that describes the event. On the other, though, it is tied to the situation by way of the evental site whose elements it mobilizes and consequently raises from minimal to maximal existence. And of the evental site, perhaps symptomatically, there is no matheme.15

So the event is distinguished from ontology by its excess of belonging over inclusion, but being and event do not constitute a dualism. If this is the case, then why does Badiou privilege the term event to such an extent? Because he wants to make the subject emerge out of an event, rather than dependent on any kind of pre-determined structure of being. The excess of inclusion over belonging, or parts over elements, sets up a knot or ontological impasse that constitutes what Bosteels calls “the closest site where an event, as a contingent and unforeseeable supplement to the situation, raises the void of being in a kind of insurrection, and opens a possible space of subjective fidelity.”16 A subject becomes subjectivized out of fidelity to an event rather than existing already at the level of being. At the conclusion of Being and Event, Badiou claims that his break with Lacan consists in dispensing with the necessary presupposition “that there were always some subjects” (BE 434).

Why does Badiou want to establish being on a mathematical basis that does not presuppose subjectivity? I suggest mainly because he wants to avoid the subjectivism that plagues modern philosophy and epistemology with its attendant relativism. As Quentin Meillassoux puts it, insofar as metaphysics accepts the situation of thought and being as one of correlation to consciousness, it ends in contemporary skepticism, which is “a religious end of metaphysics.”17 Here thinking becomes fideism, because there is no alternative to the finitude of reason due to the finitude of the reasoner. Mathematics is infinite rather than finite, so it represents a viable avenue to truth than avoids the subjective dead end.

Meillassoux sets up his alternative to strong correlationism by showing how this correlationationism is a consequence of Kantian philosophy. Meillassoux returns to Hume in order to propose a solution, which involves a radicalization of contingency. Building upon Badiou, and expressed as a consequence of Cantor, Meillassoux claims that “what the set-theoretical axiomatic demonstrates is at the very least a fundamental uncertainty regarding the totalizability of the possible.”18 This means that we cannot extend aleatory or chance reasoning beyond the objects given in experience to encompass “the very laws that govern our universe.”19 Meillassoux avoids Kantian correlationism by claiming that the very laws of reason and being are themselves contingent but stable, and “it is precisely this super-immensity of the chaotic virtual that allows the impeccable stability of the visible world.”20 Some metaphysicians might feel that this is a high price to pay to overcome the subjectivism and fideism implied by correlationism, but it is a strikingly original theory.

Like Meillassoux, Badiou has anti-theological reasons to privilege mathematics. For him, mathematics fully consummates the death of God, because it develops a secular understanding of the infinite. The fact that Badiou privileges the void rather than the One means that “God is dead at the heart of presentation.”21 This is why Badiou claims, against Cantor, that set theory precludes the absolute infinite that Cantor wants to posit as God.22 Infinite multiplicity disjoined from the tyranny of the One allows mathematics to adequately express being. Badiou criticizes Romanticism in its 19th and 20th century forms, which includes Heidegger and post-Heideggerianism, because Romanticism embraces subjective finitude and valorizes only a poetic expression of thought. According to Badiou, “Romantic philosophy localizes the infinite in the temporalization of the concept as a historical envelopment of finitude.”23 Badiou opposes the “pathos of finitude” with the “banality” of mathematics because mathematical infinity properly understood prompts no religious feeling on the level of the subject. He wants to avoid and eliminate the pathos of the sublime precisely by recourse to mathematical plurality that creates a situation of indifferent infinity.

Badiou’s complex reading of set theory in Being and Event is intimidating to non-mathematicians, but his philosophical use of trans-finite number theory represents a fascinating appropriation of Kant’s notion of the mathematical sublime that is purged of any pathos of feeling. Meillassoux helps us understand the stakes of Badiou’s mathematic ontology because he deploys mathematics against the implications of Kantianism, and it is interesting that Being and Event lacks a chapter on Kant, since it includes chapters on many other significant modern philosophers. My reading of Badiou’s mathematical ontology, paradoxically, is that it is a radical interpretation of the Kantian mathematical sublime. That is, Badiou is adamantly opposed to the subjective qualities of pathos that are engendered by the Kantian sublime, but his understanding of a mathematical infinity that cannot be synthesized into a One reproduces the structure of Kant’s mathematical sublime, stripped of any subjective faculties.

In the Critique of Judgment, Kant contrasts the mathematical with the dynamical sublime after elaborating a critical conception of beauty. The judgment of beauty consists of a free play or accord between the faculties of imagination and understanding when contemplating a beautiful object. The subject forms a judgment of taste based upon a feeling of purposiveness stimulated by the object, and this judgment lacks objective scientific content. At the same time, a judgment of taste is universally applicable, and can be ascribed to any rational being.

The transition from beauty to sublime occurs when the object arouses discord or purposivelessness rather than purposiveness. The mathematical sublime occurs when a mind’s faculty of representation attempts to represent an infinite magnitude in a finite presentation, which outstrips the ability to comprehend what it apprehends. Imagination can apprehend to infinity, Kant declares, but when it leaves behind its fragile accord with understanding in the judgment of beauty, imagination threatens to burst the bounds of the finite representing subject, which is why reason must intervene and force a presentation. This presentation fails, which constitutes a breaking of imagination, but attests to the supreme power of reason in its ability to put an unruly imagination on trial. Kant says:

What happens is that our imagination strives to progress toward infinity, while our reason demands absolute totality as a real idea, and so the imagination, our power of estimating the magnitude of things in the world of sense, is inadequate to that idea. Yet this inadequacy itself is the arousal in us of the feeling that we have within us a supersensible power.24

Imagination outstrips the ability of understanding to comprehend its apprehension to infinity. So reason has to step in and force the situation by demanding the presentation of an infinite apprehension in a single finite image. This is similar to what Badiou calls the count-as-one, or the representation of a situation. The sublime apprehension or intuition is of an inconsistent multiplicity, and Kant specifically qualifies it as mathematical because it is a “logical estimation of magnitude.”25 Even if Kant is operating in much more straightforward linear terms compared to modern mathematics and magnitudes, as well as processes of understanding, he is getting at the same paradox as Badiou. The main difference is that for Kant, the sublime remains fundamentally aesthetic and romantic, because it is a product of the operation of a subject’s faculties.

When confronted with an object that induces a sublime judgment, Kant says that “the mind feels agitated;” it experiences “a rapid alternation of repulsion from, and attraction to, one and the same object.” Ultimately, “the thing is, as it were, an abyss in which the imagination is afraid to lose itself.”26 The agitation or vibration that unsettles the mind induces the pathos of finitude, that is, the finitude of a finite subject attempting to comprehend an infinite phenomenon. The subject experiences pain, purposivelessness and powerlessness in response to an object experienced as sublime, but she also experiences a powerful pleasure in reason’s ability to lift or elevate the subject above the object in contemplation, which is the essence of the dynamical sublime.

The dynamical sublime operates in a similar way to the mathematical sublime, but here the key issue is might or power, the imagination’s ability to reckon with the overwhelming force of nature, such as a waterfall, and reason’s ability to elevate the mind above such a conflict. Kant says that “when in an aesthetic judgment we consider nature as a might that has no dominance over us, then it is dynamically sublime.”27 The dynamical sublime consists of an elevation over nature or being that attests to reason’s superior might in a moral manner.

I am arguing three things:

1) Kant is already conflating the dynamical sublime with the mathematical sublime in his discussion of the mathematical sublime, because he is describing the power of an object to induce a discord within and among the faculties of the human subject and the power of reason to force imagination to admit its failure to present an infinite intuition. That is, in order for any experience to be determined as sublime, it must also be dynamical, even if it is also mathematical. So the mathematical sublime is a special case of the sublime in general, which is better characterized as dynamical, as concerned with the might and power of nature vs. the human mind.

2) Badiou strips out the mathematic sublime from its moorings in the dynamical sublime and its conflict of the mental faculties. His mathematical ontology is essentially a variety of the mathematical sublime purged of dynamic subjectivity. Kant cannot envision an ontological sublime phenomenon without relation to a subject. Badiou expresses precisely this thought in the language of set theory by characterizing being as an inconsistent multiplicity that cannot be represented in a situation without losing something that is included within it as a part. The Kantian abyss is here an operative void that subtracts a presented situation. The irreducible excess of inclusion over belonging repeats the irreconcilable conflict between imagination and understanding that Kant obscures in the Third Critique (and which also appears in the Critique of Pure Reason).28

3) In Being and Event, the event functions as a quasi-dynamical sublime, but this is more subtle and less apparent, because the subject emerges out of fidelity to an event. Badiou wants to reverse the priority of the Kantian transcendental subject, so the subject does not precede or prescribe either being or an event. At the same time, the dynamism of the event becomes or replaces the subject which was worked out in his previous book, Theory of the Subject.

The dynamical sublime works based on a model of elevation, and here is where the idea of the sublime leads directly to Hegel’s notion of sublation, with its conception of preserving at a higher level. Badiou, however, cuts off the mathematical sublime and radically purges it of any relationship to subjectivity. The elevation of the dynamical sublime is proscribed, but I am arguing that the dynamism of the dynamical sublime becomes horizontalized in and as the event in Being and Time. Here the event is ecstatic, or stands out from being in a way that retains the shadow of the dynamical sublime even though it is not a transcendental operation.

According to Kant, in the analytic of the sublime reason is forced to intervene to resolve the conflict between understanding and imagination, because imagination gets out of control and proceeds to infinity. Badiou wants to incorporate infinity into pure reason in an asubjective or neutral way, but he is Kantian in a sense, because he feels that it is necessary to break the romantic imagination with the discipline of formal-rational mathematical thought. The pathos-ridden subject elevates himself along with his presumption of nature, whereas the rigor of mathematical ontology as formulated by Badiou brings him back to earth and grounds him in a historical situation.

Badiou says that the fundamental law of the subject is forcing (BE 410). Drawing on the work of Paul Cohen, Badiou claims that “despite being subtracted from the saying of being (mathematics), the subject is in possibility of being” (BE 410). The subject comes into being in accordance with the force of a sublime event by means of a generic extension that produces truth. The subject of truth “forces veracity at the point of the indiscernible” (BE 411). Truth is constituted by this forcing of the subject onto itself out of fidelity to an event.

The event surpasses ontology, which is Badiou’s name for what Kant calls understanding, although it conforms to Reason, which is Kant’s name for what Badiou calls philosophy. Imagination is incapable of thinking or producing the event. Events happen, however, at the sublime edge of the void where the abyss threatens to swallow formalized ontology. Badiou’s thought, however, like Kant’s, allows us to build a bridge across the gulf between pure mathematical-ontological and practical-historical reason. Kant’s problem is that the abyss of the sublime threatens the entire edifice of his Critique of Pure Reason, because understanding comes to ruin and Kant, taking the standpoint of Reason, blames imagination for not being able to do what understanding is supposed to do in the analytic of taste and what understanding clearly does in the Transcendental Deduction at the heart of the First Critique. Badiou wants nothing to do with Kant or with the Kantian sublime, but his thought in Being and Event repeats it in an uncanny way. Just as in Kant’s judgments of beauty, there are “certain statements which cannot be demonstrated in ontology, and whose veracity in the situation cannot be established” because they are not objective in Kantian terms (BE 428). At the same time, by what Kant calls a subjective universality, these statements “are veridical in the generic extension,” or by analogy in terms of the Critique of Judgment (BE 428). At the “point where language fails, and where the Idea is interrupted,” or understanding wavers, where imagination spins out of control, the Subject is brought face to face with the sublime event which it is. “What it opens upon is an un-measure in which to measure itself; because the void, originally, was summoned” (BE 430).

Kant’s reading of the sublime is from the standpoint of a subject, which is why the sublime carries what Badiou calls “a pathos of finitude” in an essay included in his Theoretical Writings. On the other hand, Badiou’s method of subtraction offers an alternative interpretation of the sublime. According to Badiou, “the madness of subtration constitutes an act….the act of a truth,” but this is a truth of mathematical being devoid of any subjectivity.29 Badiou emphasizes subtraction as opposed to sublimation or sublation, but I am interpreting each of these concepts (subtraction/Badiou, sublimation/Freud and sublation/Hegel) as varieties of the Kantian sublime.

Badiou subtracts the mathematical sublime from the dynamical sublime, with its pathos of finitude, but more radically, from any association with a subject’s faculties of representation. Cut free from a subject, mathematical subtraction, the core of Kant’s mathematical sublime, which indicates the excessiveness of infinity in relation to finite representation, becomes the basis for the elaboration of a fundamental ontology based on infinite multiplicity. The one is the one who synthesizes, or subjectivizes the multiple, or what Kant calls the manifold. But Badiou reverses this relationship with his idea of subtraction: subject emerges as an effect of subtraction from the multiple/being, the count-as-one. And the event occurs as the excess of belonging to a situation beyond what can be included in it, which is a (heterodox in relation to Kant) dynamically sublime event that precedes and produces a subject who can be faithful to it.

In another essay from his Theoretical Writings, Badiou discusses love and castration. He claims that for Lacan, love of truth is “purely and simply the love of castration.”30 Castration means that truth emerges from out of the void, which is an emptiness rather than a plenitude. Upon hear the word castration, most readers conjure up an emotional response, but Badiou wants to dispel any affect and think castration as subtraction without any pathos. He writes, “castration thereby manifests itself stripped of the horror that it inspires as a pure structural effect.”31 There is something extremely cold about Badiou’s thought, because he wants to reduce or eliminate the implications of pathos, horror or anxiety at the level of ontology and subjectivity. This procedure produces an austerity that empties conceptions such as castration, subtraction and the void of their romantic connotations, and it contrasts with the style of someone like Slavoj Zizek, whose work plays up these more affective aspects of reality.

The only way that philosophy can be adequate to being, and to confront truth, is to acknowledge truth as castration, as subtraction from an indeterminate and unmanageable multiplicity. Infinite multiplicity cannot be controlled and ruled by the One; the one or the count-as-one emerges out of infinity by means of the subtractive void. “Truth is bearable for thought,” Badiou claims, “only in so far as one attempts to grasp it in what drives its subtractive dimension, as opposed to seeking its plenitude or complete saying.”32 Infinite presentation is what Kant calls a manifold, and what Kant calls synthesis is actually for Badiou a subtraction, a count-as-one. The problem that Kant comes up against in the mathematical sublime is the fact that human understanding cannot conceptualize infinite multiplicity as infinite multiplicity, and this indicates a limitation of human thinking (although Kant is careful to blame imagination solely for this inadequacy). For Kant, and here is where the dynamical sublime comes in, the inability to process a mathematical magnitude in terms of its infinite multiplicity attests to a power of human reason to discipline imagination and elevate human thinking about nature. For Badiou, the power of human reason is split between the speculative power of mathematical reasoning, which is able to think being as being but unable to represent it without reducing or subtracting from it, and the practical dynamic ability of a subject to become herself by means of fidelity to an event.

I am reading Kant into Badiou in a provocative way, in order to show where and how Badiou’s project in Being and Event can be seen as post-Kantian in relation to the Kantian sublime even as he opposes and eliminates transcendental subjectivity. Where Badiou most radically departs from Kant is in his rejection of the privileged interiority of the faculties of the subject, which are obviously reintroduced in the dynamic sublime, which induces in the subject a profound awareness of her finitude. I think this radical purging of subjectivity is fascinating, at least in the efforts of a renewal of thinking beyond the limits of relativism and subjectivism as they have become instantiated in many theoretical expressions. By relegating the subject to an effect of the count-as-one, or representation, the subject is de-centered from the fundamental workings of being as being. At the same time, in his bracketing of subjectivity, Badiou freezes being in order for it to conform to his mathematical ontology.

To shift from the frozen ontology of his masterwork Being and Event to his follow-up Logics of Worlds as read through Theory of the Subject is a kind of recovery of subjectivity for ontology, although I do not have time to demonstrate this reading here.33 If subjectivity reappears at the level of ontology, then substance cannot be thought apart from subject, as Hegel asserts, and I would argue that this move renews the question of the dynamical sublime. What if we cannot completely separate the mathematical from the dynamical sublime, but have to think both, together? And what if we think ontology as the mathematical and the dynamical sublime together from a perspective radically de-void of subjectivism but not subjectivity understood broadly as the self-organization of complex self-adaptive systems? Such a reading would push Badiou in a more physical, if not meta-physical direction. If ontology is more dynamic and less static or frozen, then perhaps being must be thought not in terms of formal mathematics but in terms of energy transformation in post-Einsteinian terms. In his popular writings, the theoretical physicist Smolin argues that the lesson of Einstein today is that time and space are not background-dependent; they evolve. The interrelations and iterations of quantum loops or spin networks (Penrose) define space and time.34

We desire to fix space and time to a background (Newtonian metaphysics), just as we desire to formalize mathematical propositions as ontology (Badiou), just as we desire to find the basic building blocks of reality and name them (the standard model of sub-atomic particle physics). But what if what is really real about being is energy transformation, and what if we have not fully understood the implications of relativity theory? If this is the case, then perhaps the philosophy of Gilles Deleuze provides a better ontology than that of Badiou.35 We desperately need new ways of thinking about energy in both theoretical and practical ways, and the work of Alain Badiou helps philosophers get past some of the impasses of contemporary subjectivism, but ultimately his result in Being and Event at least is too frozen. We need to be able to think the sublimity of energy in mathematical and dynamical terms, beyond Kant but in a way that acknowledges the avenues for thinking that he opened up. Kant is relevant not merely as a foil or the caricature of his transcendental idealist subjectivity, but as part of what Deleuze calls an effect-series, from a Kant-effects series to an Einstein effects-series to a Badiou effects-series.


Badiou, Alain. Being and Event, trans. Oliver Feltham. London and New York: Continuum, 2006.

Badiou, Alain. The Concept of Model: An Introduction of the Materialist Epistemology of Mathematics, trans. Zachary Luke Fraser and Tzuchien Tho. Melbourne: Re-press, 2007.

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

Badiou, Alain. Theoretical Writings, ed. and trans. by Ray Brassier and Alberto Toscano. London and New York: Continuum, 2006.

Badiou, Alain. Theory of the Subject, trans. Bruno Bosteels. London and New York: Continuum, 2010.

Bosteels, Bruno. “Alain Badiou’s Theory of the Subject: The Recommencement of Dialectical Materialism.” In Lacan: The Silent Partners, ed. Slavoj Zizek (London and New York: Continuum, 2006

Bosteels, Bruno. “Thinking the Event: Alain Badiou’s Philosophy and the Task of Critical Theory.” In The History of Continental Philosophy, ed. Alan D. Schrift, (Chicago: University of Chicago Press, 2011), vol. 8.

Crockett, Clayton. Deleuze Beyond Badiou: Ontology, Multiplicity and the Event. New York Columbia University Press, forthcoming.

Crockett, Clayton. A Theology of the Sublime. London: Routledge, 2001.

Deleuze, Gilles. Kant’s Critical Philosophy: The Doctrine of the Faculties, trans. Hugh Tomlinson and Barbara Habberjam (Minneapolis: University of Minnesota Press, 1984.

Depoortere, Frederiek. Badiou and Theology. London and New York: Continuum, 2009.

Feltham, Oliver. Alain Badiou, Live Theory. London and New York: Continuum, 2008.

Hallward Peter. Badiou: A Subject to Truth. Minneapolis: University of Minnesota Press, 2003.

Kant, Immanuel. Critique of Judgment, trans. Werner Pluhar. Indianapolis: Hackett Publishing, 1987.

Meillassoux, Quentin. After Finitude: An Essay on the Necessity of Contingency, trans. Ray Brassier. London and New York: Continuum, 2008.

Smolin, Lee. Three Roads to Quantum Gravity. New York: Basic Books, 2001.

1 Lee Smolin, Three Roads to Quantum Gravity (: Basic Books, 2001), p.63.

2 This article is a chapter from a larger book project on Deleuze and Badiou, that reads Badiou’s critique of Deleuze in Gilles Deleuze: The Clamor of Being and criticizes it, in order to open up my own interpretation of Deleuze. See Clayton Crockett, Deleuze Beyond Badiou: Ontology, Multiplicity and Event (New York: Columbia University Press, forthcoming). In chapter seven, I offer a reading of Logics of Worlds in conjunction of Theory of the Subject that claims that this reading is a better, more dynamic understanding of Badiou, but one that still has problems relative to my understanding of Deleuze.

3 In Logics of Worlds: Being and Event II, trans. Alberto Toscano (London: Continuum, 2009), Badiou says that “Kant is the one author for whom I cannot feel any kinship.” He is a philosophical sadist, “a paradoxical philosopher whose intentions repel, whose style disheartens, whose institutional and ideological effects are appalling, but from whom there simultaneously emanates a kind of sepulchral greatness” (pp.535-536). Gilles Deleuze was also ambivalent about Kant, calling him an “enemy,” and the “fog of the North.” See the Translators’ Introduction to Gilles Delezue, Kant’s Critical Philosophy: The Doctrine of the Faculties, trans. Hugh Tomlinson and Barbara Habberjam (Minneapolis: University of Minnesota Press, 1984), pp. xv-xvi. Deleuze engaged much more extensively and productively with Kant’s philosophy, however, while Badiou largely neglects it.

4 Alain Badiou, The Concept of Model: An Introduction of the Materialist Epistemology of Mathematics, trans. Zachary Luke Fraser and Tzuchien Tho (Melbourne: Re-press, 2007), p.9.

5 Ibid., p.33 (italics in original).

6 Ibid., p.35 (italics in original).

7 See Badiou’s discussion of the distinction between logic and mathematics in The Concept of Model and his later philosophy in the interview with Tzuchien Tho that follows the translated text of The Concept of Model, specifically ibid., p.85.

8 Ibid., p.43.

9 Ibid., p.48.

10 Peter Hallward, Badiou: A Subject to Truth (Minneapolis: University of Minnesota Press, 2003), p.83.

11 Alain Badiou, Being and Event, trans. Ray Brassier (New York: Continuum, 2006), p.2 (hereafter abbreviated BE in the text with page numbers in parentheses). Words or phrases in italics are italicized in the original text, not my emphasis.

12 Frederiek Depoortere, Badiou and Theology (London: Continuum, 2009), p.78 (italics in original).

13 Oliver Feltham, Alain Badiou, Live Theory (London: Continuum, 2008), p. 95.

14 Ibid., p. 95.

15 Bruno Bosteels, “Thinking the Event: Alain Badiou’s Philosophy and the Task of Critical Theory,” in The History of Continental Philosophy, ed. Alan D. Schrift, (Chicago: University of Chicago Press, 2011), vol. 8, p.

16 Bruno Bosteels, “Alain Badiou’s Theory of the Subject: The Recommencement of Dialectical Materialism,” in Lacan: The Silent Partners, ed. Slavoj Zizek (London: Continuum, 2006), p.150.

17 Quentin Meillassoux, After Finitude: An Essay on the Necessity of Contingency, trans. Ray Brassier (: Continuum, 2008), p.46.

18 Ibid., p.105.

19 Ibid., p.105.

20 Ibid., p.111.

21 Alain Badiou, “Philosophy and Mathematics: Infinity and the End of Romanticism,” in Theoretical Writings, ed. and trans. Ray Brassier and Alberto Toscano (: Continuum, 2006), p.39.

22 See Depootere, Badiou and Theology, p.120.

23 Badiou, “Philosophy and Mathematics,” p.38.

24 Immanuel Kant, Critique of Judgment, trans. Werner Pluhar (Indianapolis: Hackett Publishing, 1987), p.106.

25 Ibid., p.107.

26 Ibid., p.115.

27 Ibid., p.119.

28 See my interpretation of the Kantian sublime, including my reading of the Critique of Judgment into the Critique of Pure Reason, in Clayton Crockett, A Theology of the Sublime (London and New York: Routledge, 2001).

29 Alain Badiou, “On Subtraction,” in Theoretical Writings, p.105.

30 Alain Badiou, “Truth: Forcing and the Unnameable,” in Theoretical Writings, p.122 (italics in original).

31 Ibid., p.122.

32 Ibid., p.122.

33 See Crockett, Deleuze Beyond Badiou, chapter seven, for this interpretation of Badiou, which avoids many of the problems I raise here with regard to Being and Event.

34 See Smolin, Three Roads to Quantum Gravity, p.128.

35 See Crockett, Deleuze Beyond Badiou, chapter eight, for an energetics of being based on Deleuze’s thought.

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