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
1
1
Lee Smolin, Three Roads to Quantum Gravity (: Basic Books, 2001), p.63.
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
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.
2
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.
3
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 well4
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.
4
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
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.
5
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
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.
6
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 representation 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
7
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
12
8
Frederiek Depoortere, Badiou and Theology (London: Continuum, 2009), p.78 (italics in original).
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 submultiple) emerges by means of the void. The void accounts for the fact that there is a submultiple 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.
13
14
9
Oliver Feltham, Alain Badiou, Live Theory (London: Continuum, 2008), p. 95.
Ibid., p. 95.
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
10
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
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.
11
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 settheoretical axiomatic demonstrates is at the very least a fundamental uncertainty regarding the
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.
12
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 postHeideggerianism, 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
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.
13
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 nonmathematicians, 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
14
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
24
p.106.
25
15
Immanuel Kant, Critique of Judgment, trans. Werner Pluhar (Indianapolis: Hackett Publishing, 1987),
Ibid., p.107.
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
26
27
16
Ibid., p.115.
Ibid., p.119.
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
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).
17
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 pathosridden 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
18
(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
19
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
29
20
Alain Badiou, “On Subtraction,” in Theoretical Writings, p.105.
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 countas-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
30
original).
31
32
21
Alain Badiou, “Truth: Forcing and the Unnameable,” in Theoretical Writings, p.122 (italics in
Ibid., p.122.
Ibid., p.122.
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
22
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
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.
23
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 effectsseries.
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