Continental Philosophy Review (2006) 39: 59–77
DOI: 10.1007/s11007-006-9014-5
c Springer 2006
Presentation as anti-phenomenon in Alain Badiou’s Being
and Event
RAY BRASSIER
Research Associate, Centre for Research in Modern European Philosophy, Middlesex
University, Bramley Road, London N14 4YZ, United Kingdom
(E-mail: r.brassier@mdx.ac.uk)
Abstract. In his magnum opus Being and Event, Alain Badiou identifies ontology with mathematics and uses a mathematical formalization of ontological discourse to generate an account
of extra-ontological ‘truth-events’. Informed by deconstructive critiques of the metaphysical
ontologies of presence, Badiou establishes an anti-phenomenological conception of ontological presentation. Presentation’s internal structure is that of an anti-phenomenon: presence’s
necessarily empty and insubstantial contrary. But the result is that Being and Event is riven
by a fundamental methodological idealism. Badiou cannot secure the connection he wishes
to establish between the formal discursive structure of mathematical ontology and extradiscursive reality. The decisive link between being and event, i.e. between Badiou’s purely
formal conception of ontological presentation and the extra-ontological reality of the event,
is precluded by the very structure of the concept of presentation which is central to Badiou’s
argument.
1. Introduction
In L’être et L’événement (Being and Event),1 Alain Badiou proposes to reconfigure the task of contemporary philosophy on the basis of the decision
that ontology is mathematics. “The science of being-qua-being exists since
the Greeks”, Badiou declares in his Introduction, “for such is the status and
meaning of mathematics, but only now do we possess the means to recognize this.” (EE 9) Since ontology is now a province of mathematical science, and since (contra Heidegger) being is neither inherently meaningful
nor the harbinger of truth, meditative rumination upon being is no part of
the philosophical remit. Moreover, since for Badiou epistemology can only
operate within the framework provided by mathematical ontology, and since
the mathematical science of being provides the paradigmatic mode of scientific access to reality, the implication seems to be (although Badiou never
explicitly says so) that epistemology can now be safely handed over to natural science (and to cognitive science in particular). Thus philosophy can
no longer be considered responsible for delineating the epistemic conditions supposedly guaranteeing our access to the world. For Badiou, neither
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ontology (whether metaphysical or post-Heideggerean) nor epistemology
(whether foundationalist or naturalized) lie at the heart of the philosophical
enterprise.
So far, so typically ‘postmodern’, cynics might object. Badiou would seem
to be merely proposing another variant on the well-worn theme of the destitution of philosophy, already familiar from figures such as Rorty and a host of
others. But such cynicism would be injudicious, for if Badiou enjoins philosophy to unburden itself of its traditional concern with ontology and epistemology, this is because he believes such a move to be the necessary prerequisite for
the deployment of a genuinely contemporary – or as he would have it ‘morethan-modern’2 – philosophical account of truth. Badiou’s primary concern is
with truth, no longer understood in terms of correspondence, coherence, or
aletheia, but re-conceptualised according to a logic of ‘subtraction’ which
springs truth from its basis in being and frees it from the grip of knowledge.
This is what allows Badiou to declare in the Introduction to Being and Event:
“We are at last the contemporaries of a beginning where the theory of truth
is concerned, now that the latter’s organic dependency on knowledge has
been undone. One then notices retroactively that what has enjoyed unrivalled
supremacy thus far is what I would call veridicality, and that, strange as it
may seem, ‘truth’ is a new word in Europe (and elsewhere)” (EE 9). Philosophy becomes the theory responsible for registering and conceptualizing the
irruptions of truths as breaks, caesuras, or ruptures in the order of being and
knowledge; ruptures which simultaneously reconfigure the order of reality
and the conditions structuring our access to reality. Badiou calls such ruptures
‘events’.
The whole impetus of Being and Event lies in Badiou’s attempt to generate an account of extra-ontological truth-events on the basis of an a priori
mathematical formalization of ontological discourse. Informed by deconstructive critiques of the metaphysical ontologies of presence, Badiou establishes
an anti-phenomenological conception of ontological presentation. Presentation’s internal structure is that of an anti-phenomenon which is presence’s
necessarily empty and insubstantial contrary: “Presentation is the exact contrary of presence” (EE 35). But the result is that Being and Event is riven
by a fundamental methodological idealism. Badiou cannot secure the connection he wishes to establish between the formal and discursive structure
of mathematical ontology and extra-discursive reality. The decisive link between being and event, i.e. between a purely formal concept of ontological
presentation and the extra-ontological reality of the event, is precluded by the
very structure of the concept of presentation which is central to Being and
Event.
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2. The a priority of ontological discourse
Badiou’s identification of ontology with axiomatic set-theory is a claim about
discourse, not about the world (EE 14). Accepting the Aristotelian definition of
ontology as the discourse on ‘being qua being’ (rather than qua ‘something’),
Badiou’s claim concerns the discursive intelligibility of being considered independently of any and every type of qualitative characteristic.3 Ontology
presents being as at once multiple and unitary: it is ‘counted-as-one’ and presented as a consistent multiplicity. Thus to be is to be multiple, but the intelligibility of being-multiple necessitates a distinction between consistent multiplicity insofar as multiplicity is counted-as-one, and inconsistent multiplicity
as that upon which counting operates, and which is retroactively posited as
being via the operation of the count. Anything that is must be counted-as-one,
but unity is not an intrinsic characteristic of being; it is merely the result of an
operation which produces consistent multiplicity from inconsistent multiplicity. Being qua being is neither one nor multiple; it is inconsistent multiplicity
(EE 32). Ontology is simply the discursive presentation of inconsistent multiplicity as such; which is to say, the presentation of inconsistent multiplicity
considered independently of any predicative characteristic other than its sheer
multiplicity (EE 36).
It is important to emphasize from the outset two fundamental ways in
which Badiou’s account of the ‘a priority’ of ontological discourse differs
from traditional metaphysical ontologies.
First, for Badiou, ontology itself is a situation, which is to say, a locally
circumscribed consistent multiplicity. For if presentation is necessarily multiple, and being is implicated in every presentation (EE 35), then there is no
single presentation of being capable of subsuming all others. Thus ontology
is not a universal or ‘all-encompassing’ situation. It is a determinate situation
alongside other determinate situations. But since, Badiou insists, all access
to being is via presentation, and presentation is always the presentation of
something, never of being itself (EE 35) (we shall see why below), ontology
distinguishes itself as that situation in which presentation as such is presented.
The privilege of the ontological situation consists in its providing the site for
“the apprehension of every possible access to being” (EE 36).
Second, the claim that ontology is mathematics is not a claim about the
concept of being. It is not the claim that being must be conceptualised as
multiple, and that the appropriate conceptual resources for thinking about
multiplicity are to be found in mathematics. For Badiou, ontology cannot be
coordinated around a ‘concept of being’ because the very idea of a ‘concept of
being’ is incompatible with the claim that being is inconsistent multiplicity.
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The injunction that the One is not and the thesis that being is inconsistent
multiplicity entail that ontological discourse operate without a concept of the
multiple (or ‘being’). Ontological discourse is coordinated around the prohibition of counting inconsistent multiplicity as one (as we shall see, what it
is counted as is nothing), which is to say that it is forbidden from defining
what it is that is consistently presented, or counted. To do so would entail
subordinating inconsistent multiplicity to the consistency of a single concept, reintroducing a categorical difference between being and its concept,
and thereby conceding the being of unity by acknowledging the existence
of a relation between distinct terms (since such a distinction presupposes
the ability to discriminate between individuated terms). Thus “it is necessary that the operational structure of ontology be able to discern the multiple
without having to make it one, and hence without relying on a definition of
the multiple” (EE 37). Set-theory satisfies this stricture by axiomatizing its
discursive presentation, prescribing rules for the manipulation of terms which
are compositionally, rather than conceptually defined. Any composition violating the rules is prohibited; everything permitted by the rules is prescribed
(EE 38). But at no point is what is presented explicitly (i.e. conceptually)
defined; it is merely compositionally specified via the rules prescribing the
legitimate deployment of the symbol of belonging. To be is to belong to a
set, everything that belongs is itself a set, and every set is defined in terms of
belonging, whose functioning is axiomatically specified. Thus the axiomatic
form of ontological discourse is necessary in order to obviate any variety of
conceptual definition which would re-objectify, and thereby unify inconsistent
multiplicity. Although philosophy provides a ‘metaontological’ gloss on this
axiomatic discourse through the use of such terms as ‘being’, ‘presentation’,
‘situation’, ‘multiple’, ‘consistency’, and ‘inconsistency’, it is imperative that
its conceptual schematization of the rules governing ontological discourse
not lapse into a re-presentation4 of ontological presentation by reintroducing
a concept of being or of the multiple: “For by putting being in the general
position of an object, its re-presentation would immediately undermine the
necessarily de-objectifying condition of ontological deployment” (EE 17/18).
As we shall see, the peculiarly delicate status of the relation between ontological and metaontological discourse is not adequately resolved by Badiou. We will argue that the equivocal status of metaontological discourse
vis-à-vis ontological discourse on one hand, and the world (or ‘reality’)
on the other, is the rock upon which Badiou’s philosophical edifice falters. Ultimately, we will suggest, a philosophy that chooses to relinquish
worldly plenitude in favour of subtractive ascesis must be prepared to take
the plunge into the black hole of subtraction. But in order to appreciate
the prohibitive consequences of the logic of subtraction, it is necessary
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to consider the peculiar structure of Badiou’s metaontological concept of
presentation.
3. The law of presentation
The inaugural declaration of Being and Event is that “the One is not” (EE 31).
Ontological presentation is devoid of unity. Or rather, unity is only the result
of an operation and “it is because the one is an operation, that it is never a presentation” (EE 32). Although presentation is necessarily structured, structure
is not an intrinsic aspect of being. The necessity of structure is a nomological
feature of discursive presentation, not an ontological characteristic of being
itself. “[T]here is no structure of being”, Badiou insists (EE 34). Thus it would
appear that Badiou is merely reiterating a familiar transcendental distinction
between the formal features of being as characterized relative to thought, or
‘for us’, and being as it is independently of thought, or ‘in itself’; which
would amount to the well-worn dualism of phenomenon and noumenon. But
this is not the case. For in fact, the split between counted consistency and
uncounted inconsistency, or structure and being, is an index of the underlying
identity between the inexistence of structure (i.e. counting) and the inexistence of inconsistency (i.e. being itself). To grasp this identity is to grasp
how the law of the count as condition for existence, which renders presentation possible by precluding the presentation of inconsistent multiplicity (i.e.
being itself), is ultimately indiscernible from the ontological inconsistency
whose presentation it forecloses. Thus the non-being (non-être) of the One,
the merely nomological status of structure, converges asymptotically with the
being-nothing (être-rien) of inconsistent multiplicity, whose necessary impossibility is retroactively attested to by the structure of the count. It is in this
sense that, for Badiou, ontology complies with the Parmenidean injunction
according to which “thinking and being are the same” (EE 49): the sense
in which theirs is an identity without relation. Thinking and being are both
nothing. Ontological discourse deploys their identity insofar as it operates
through the coincidence of structured consistency and de-structured inconsistency, without stipulating any relation between them as distinct terms. It
operates in complete disregard of any appeal to categorial distinctions between
different types of being. Accordingly, subtractive ontology is impervious to
attempts to hypostatize the difference between something called ‘thinking’
and something called ‘being’. But by the same token, it remains incapable
of acknowledging any distinction between discourse and world, thought and
reality, logical consequences and material causes.5 The law of presentation
is the guarantor of a literally vacuous isomorphy between thinking and being
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(all the more remarkable for being neither metaphysical nor transcendental);
but the price is a peculiar variety of discursive idealism wherein even the supplement of inconsistency invoked as a real interruption of the ideal order of
ontological discourse is itself merely an instance of unstructured thought: the
event as aleatory deciding of the undecidable, wherein thinking itself comes
to embody inconsistency.
4. Structure, metastructure, re-presentation
The law of presentation is codified in the operation of the count, which is not,
because it cannot count itself as one. By absolving itself from its own count,
every count invites a “count of the count”, or what Badiou will usually refer
to as a ‘metastructure’ in an ontological context, and as ‘re-presentation’ in
all other situations. Although Badiou himself has an unfortunate tendency to
use them interchangeably, the distinction between these two intimately related
terms is decisive for his entire project. For while the ontological metastructure
provides the blueprint for non-ontological re-presentation, metastructure is
foreclosed to re-presentation (we shall return to this point in Section 7).
Badiou establishes the ontological necessity of the count of the count, or
metastructure, on the basis of the power-set axiom and the theorem of the
point of excess. The power-set axiom states that for every set α there is a
set β comprising all the subsets of α. β counts-as-one everything that is
included in α without belonging to α. The theorem of the point of excess
demonstrates that the power-set β is invariably greater than α by at least one
element. It is supplemented by the Cohen-Easton theorem, which shows that
the excess of inclusion over belonging is ultimately immeasurable.6 Since the
counting of elements (sets) unwittingly includes uncounted parts (subsets),
metastructure, or the count-of-the-count, is necessary because the consistency
of presentation is compromised by the latent inconsistency of that which is
included in it without belonging to it. The realm of inclusion implicit in
presentation provides a potential haven for the inconsistency which the law
of presentation prohibits. Thus “the consistency of presentation requires that
every structure be doubled by a metastructure” (EE 109) which counts-as-one
the inconsistency generated by the self-exemption of structuring. Ontological
presentation is articulated around this metastructural doubling necessitated
by the disjunction between belonging and inclusion. It is this reduplication of
structure which furnishes the model for ‘re-presentation’ in non-ontological
situations and the distinction between situation and state of the situation:
“every situation is structured twice. Which means: there is always at once
presentation and re-presentation” (EE 110).
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This “at once” must be taken quite literally: there is a perfect indivisibility
of structure and metastructure. But this indivisibility is precisely that of a
radical division, albeit one that is neither spatial nor temporal in character.7
Every presentation is split by this fissure between the count and the count-ofthe-count, which is to say, between belonging and inclusion (the latter being
only a variant of the former, rather than a second primitive relation), precisely
insofar as the count itself is nothing:
It comes to exactly the same thing whether one says that the operation of
the count is nothing insofar as it is the source of the one, but is not itself
counted, or whether one says that what is nothing is the pure multiple which
is operated upon by the count, since it is distinct ‘in itself’, which is to say
as un-counted, from itself as manifested by the count (EE 68)
Metastructure
is required in order to stave off the threat posed to presentation
.
by this underlying indiscernibility between the ‘non-being’ (non-être) of the
One and the ‘being-nothing’ (être-rien) of inconsistency. It is necessary in
order to preclude the presentation of nothing and “the ruin of the One” (EE
109). For the ‘being-nothing’ of inconsistent multiplicity not only designates
the gap between unified presentation and “that on the basis of which” there
is presentation; it is “the nothing proper to the situation, the empty and unsituatable point which avers that the situation is sutured to being, and that
what is presented roams in presentation as a subtraction from the count” (EE
68). What is presented is nothing, sheer inconsistency; but this inconsistency
is at once that of being and of structure.8 Ontological presentation grants us
an “unpresentable access” to inconsistency; to that which is not presented and
is nothing for it. This is ‘the void’ or being of the situation. It can never be
presented as a term of the situation, since it is the inconsistency latent in its
own structure. It is the name for that which in-consists within a situation; its
subtractive suture to being.9
5. The suture to the unpresentable
Let us examine the argument whereby Badiou seeks to establish thought’s
suture to the unpresentable. The axiom of separation stipulates that every assertion of existence concerning a set necessarily presupposes a pre-existing
set.10 Thus there must be an originary set whose existence provides the precondition for every subsequent set. This is the empty-set: the set to which
nothing belongs. Ontological discourse, which is the presentation of presentation, the presentation of counting-as-one qua belonging, affirms no existence, which is to say, no belonging prior to that to which nothing belongs. It
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affirms the being-nothing of belonging as that to which no belonging belongs.
Consequently, it is not belonging (consistency) whose existence is originally
declared, but non-belonging (inconsistency) as that which is already presupposed by every subsequent belonging. In fact, ontological discourse begins
with a negation of belonging, rather than an affirmation of non-belonging; a
negation whose very act is equivalent to an affirmation, or as Badiou puts it,
an “existence which does not exist” (EE 81). Thus the ontological axiomatic
accomplishes what Badiou refers to as ‘thought’s subtractive suture to being’ by declaring the existence of an inexistence. It asserts the being of the
un-presentable through a negation of presentation.
François Wahl11 raises a particularly interesting objection here: the argument that enjoins us to deduce the existence of non-belonging from the
negation of belonging merely reiterates the ontological argument. For even
if, as Badiou claims, the axiom of the empty-set affirms an inexistence rather
than an existence, since inexistence is no more of an ‘index of existence’
than was perfection in the classical version of the ontological argument, then
why should the inexistence of belonging enjoy any more right to existence
than any other inexistence – such as that of the One for instance?12 How
does the negation of belonging which establishes the existence of the void’s
‘being-nothing’ differ from the negation of unity through which Badiou asserts
the ‘non-being’ of the One?
However, Wahl’s objection misrepresents Badiou’s argument. The logical
import of the axiom of the empty-set is neither that “non-belonging exists,”
nor that “the unpresentable” exists, nor even that “inexistence exists.” It does
not predicate existence of any concept, whether it be that of “non-belonging”
or “inexistence.” Its logical form is not that of a subject-predicate proposition.
Rather, the axiom asserts that “there exists a set β such that no set α belongs
to it”. The existential quantifier does not attribute a property to a concept. Its
import is that even in order to deny belonging, it is at least necessary to affirm
the existence of a mark of belonging. It is this “at least” that is singularized
by the assertion of the existential quantifier. And it is by negating this mark
of belonging that the axiom affirms the existence of a mark of non-belonging.
This is also why the being-nothing of the void cannot be formally conflated with the non-being of the One. The former is an assertion of negation,
while the latter is neither an assertion nor a negation since the unification of
multiplicity carried out through the operation of belonging has no ontological
status. Belonging is an operation, not an entity, an operation whose inexistence is converted into existence when it in turn is counted as belonging to
another set. It is this operation whose negation is asserted by the axiom of the
empty set, which is effectively the only belonging that exists. Set-theory begins by asserting the negation of belonging, a negation already presupposed
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by every subsequent operation of belonging through which multiplicity is
counted-as-one. Thus the inexistence of the void, the assertion of the negation of belonging, is both the precondition for the operation of the One qua
belonging, since all belonging presupposes the existence of (the name of)
non-belonging; and that which ensures that the existence of belonging per se
is never affirmed. Set-theory begins by declaring that non-belonging exists,
a non-belonging which authorizes all subsequent belonging, but the theory
neither asserts nor presupposes the existence of belonging.
The axiom of the empty-set asserts that the name of the unpresentable is
presented; or that there exists a name of inexistence. This nuance is crucial:
asserting the existence of a name in discourse is quite different from asserting
the existence of an extra-discursive concept. For it is through this nomination
that presentation is able to suture itself to the unpresentable without presenting
it. Thus, Badiou writes, “the inaugural advent” of the unpresentable consists
in “a pure act of nomination” (EE 72) which “since it is a-specific [. . .]
consumes itself, thereby indicating nothing but the unpresentable as such”
(EE 72). This nomination neither marks the return of the One, since it does
not make anything consist, nor does it index a multiplicity, since what it
presents is strictly nothing.
6. Presentation as anti-phenomenon
Presentation gives rise to an effect of unification, but is not itself unified
because it is split between the consistency of multiple-entities (presented in
terms of belonging) and its own inconsistent being, which is to say the nonbeing of the count insofar as it manifests a point of indiscernibility with the
being-nothing of the void. This indiscernibility is at once the guarantor of the
being of presentation (since the void of presentation is its suture to being)
and what threatens to subvert its law. The law of presentation requires that
this indiscernibility and the threat of structure’s own latent inconsistency be
forestalled through re-presentation insofar as it measures the gap between what
belongs to presentation and what it includes. Thus re-presentation reinstates
the law whereby the non-being of structure is separated from being-nothing.
More precisely, it ensures that their point of convergence remains asymptotic
by deferring it to the ‘future anterior’. The inconsistent being or void of
presentation (configured by the non-being of the count) “will have been”
presented through the re-presentation of everything which the count included
without presenting:
Consequently, since everything is counted, but since the one of the count,
being merely a result, implies as its ghostly remainder the fact that
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multiplicity does not originally have the form of the one, it is necessary to
acknowledge that, from within a situation, pure or inconsistent multiplicity
is at once excluded from the whole, and hence excluded from presentation
as such, but also included as what presentation itself or in itself ‘would be’,
were that which the law forbids as inconceivable to be conceivable: that
the one is not, and that the being of consistency is inconsistency (EE 66).
Thus presentation is internally fissured by the split between the consistency it
presents and the inconsistency of its own being (i.e. the inconsistency of
what it presents consistently). Every consistently presented situation harbours a latent reserve of inconsistency. But this inconsistency is only ever
a retroactive effect of the count; an insubstantial shadow cast by the structure
of substantiation. Consequently, the structuring operation whereby multiplicity is rendered consistent in presentation is also what prohibits the presentation
of being or inconsistency as such. Being is foreclosed to presentation (EE 35);
there is no conceivable ‘experience’ of presented being; it is ontologically intelligible precisely insofar as it remains “inconceivable for every presence
and every experience” (EE 35). Moreover, since “presentation is the exact
contrary of presence” (EE 35), and since every phenomenon is definable in
terms of presence to a subject of representation, or presence to consciousness,
then presentation is not a phenomenon. But this is not, as mystics and negative
theologians would have it, because being can only be presented as ‘absolutely
Other’: ineffable, un-presentable, inaccessible via the structures of rational
thought and therefore only approachable through some superior or initiatory
form of non-conceptual experience. This is the “Great Temptation” (EE 34)
to which philosophers invariably succumb if the denial of the being of unity
and the affirmation of being’s inconsistency is not qualified by the proviso
that there is no immediate, non-discursive access to being, and circumscribed
by the insistence that ontology is a determinate situation; one in which the
un-presentability of inconsistent multiplicity is rationally encoded in the compositional strictures of set-theoretical discourse. It is the axiomatic character
of ontological presentation which guarantees that inconsistent multiplicity is
inseparable from the operation of structuring. Consequently, the metaontological concept of presentation is that of an anti-phenomenon; a split noumenon
which vitiates every form of intellectual intuition insofar as it embodies the
unobjectifiable dehiscence whereby, in exempting itself from the consistency
which it renders possible, structure unleashes the very inconsistency it is
obliged to foreclose. The law of presentation conjoins the authorization of
consistency and the prohibition of inconsistency in an unpresentable caesura
wherein the deployment and subtraction of structure coincide. Thus the structure of presentation envelops a strictly ‘non-phenomenologizable’ scission
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which can only be inscribed in the formal ideography of set-theory. Ultimately,
only an insignificant letter, Ø, indexes the originary fissure whereby presentation deposes presence and binds itself to the mark of the unpresentable. Ø is the
initial incision that marks the hinge between consistency and inconsistency,
non-being and being-nothing.
7. The metaontological exception
The question then is whether, given its anti-phenomenological structure, presentation obtains in any situation other than the ontological situation. In
this regard, it is crucial to note that only the ontological situation, i.e. the
set-theoretical axiomatic as presentation of presentation, is capable of remaining rigorously faithful to the injunction that the One is not:
In non-ontological (i.e. non-mathematical) situations, multiplicity is only
possible insofar as the law explicitly subordinates it to the law of the count
[. . .] ordinary situations, if one grasps them from their own immanent
standpoint, invert the axiom which inaugurates our entire procedure. They
state that the one is, and that pure multiplicity – i.e. inconsistency – is not.
This is entirely natural, since not being the presentation of presentation,
ordinary situations necessarily identify being with what is presentable, and
hence with the possibility of the one [. . .] Thus it is veridical [. . .] from a
standpoint internal to what a situation establishes as the form of knowledge,
that to be is to be unifiable. Leibniz’s thesis (“What is not one being, is not a
being”) governs the immanence of situations as their horizon of veridicality.
It is a thesis of the law (EE 65–66).
But if metaontology is clearly not the presentation of presentation, since its
discourse is entirely conceptual and since it has not sutured itself to the real of
presentation (the empty set); and if it is not subject to the horizon of veridicality governing ordinary situations, since it has suspended the Leibnizian thesis,
then what are its specific situational parameters? Where is Badiou speaking
from in these decisive opening Meditations of Being and Event? Clearly, it
is neither from the identity of thinking and being as effectuated in ontological discourse, nor from within a situation governed by knowledge and hence
subject to the law of the One. But then how are we to situate Badiou’s metaontological discourse, given that its stance is neither ontological stricto sensu,
nor that of ordinary knowledge? It is not ontological since the concepts it
mobilizes – ‘multiple, ‘structure’, ‘counting-as-one’, ‘situation’, ‘state’, and
most importantly ‘presentation’ – are transcendent vis-à-vis the immanent
resources of the set-theoretical axiomatic, whose defining characteristic is
precisely not to recognize itself as the science of being qua being, and hence
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not to objectify being by reflecting upon it.13 But neither is it an ordinary form
of knowledge, since it is not subordinated to the immanence of any particular
situation – not even that of ontology – and thus does not seem to be entirely
subject to the law of the One. Thus metaontological discourse seems to enjoy
a condition of transcendent exception vis-à-vis the immanence of ontological
and non-ontological situations.
Badiou maintains that it is the hallmark of philosophy to be conditioned by
extra-philosophical truths, which remain irreducible to the immanent norms
of knowledge, and which it must strive to ‘compossibilize.’14 But given that
philosophy itself is not a truth procedure, there can be no subject of philosophy strictly speaking for Badiou and thus he is at pains to explain how the
metaontological discourse which conditions his entire philosophy (and from
which he draws all the conceptual details for his theory of evental truth) is
able to exempt itself from the immanent conditions of knowledge governed
by the norm of the One.
The question can be put another way: Is the relation between ontology and
metaontology one of isomorphy or analogy? Badiou’s metaontological stance
in Being and Event perpetuates a dangerous equivocation between isomorphy
and analogy, between the literal localization of ontological discourse as presentation of presentation and the de-localization of a metaontological discourse which seems to straddle the ontic – i.e. the ordinary situations in
which the rule of the One ensures that being remains convertible with consistency – and the ontological – i.e. set-theory, in which what is presented is
presentation’s own latent inconsistency. The a-specificity of metaontological
discourse in Being and Event, the anomalous status of philosophical thought,
invites the impression that Badiou’s metaontological theses float between a representation of the mathematical presentation of being, and a presentation of
the imaginary re-presentations of ordinary knowledge, which remain in thrall
to the law of the One. Moreover, it is precisely the anti-phenomenological radicality of the concept of presentation which gives rise to the problem concerning the precise nature of the relations between the ontological situation, the
metaontological (i.e. philosophical) situation, and ordinary situations; which
is to say, between the set-theoretical axiomatic, subtractive metaontology, and
the supposedly ubiquitous law of the One.
A cursory glance at the overarching structure of the argument of Being
and Event reveals its complex character. On one hand, Badiou draws the
consequences of the decision that mathematics is ontology. It would seem that
this decision itself is ultimately ‘evental’ in nature. Thus it remains necessarily
unverifiable within the conceptual apparatus which draws its consequences.
But it is this apparatus which will explain how and why this unverifiability
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is not only possible but valid, albeit illegitimizable in terms of the norms of
knowledge.15 Badiou proceeds by identifying the situation in which there is
an authentic (albeit unexpected) ‘self-grounding’ of thought; the situation in
which thinking sutures itself to being. This suturing, which authenticates the
Parmenidean thesis according to which “thinking and being are the same”,
occurs within the set-theoretical axiomatic as presentation of presentation.
And it is on the basis of the latter that Badiou will explain the possibility
of evental decision in terms of a breakdown in the consistency of being; a
breakdown which will give rise to the decision that being is not-all and that
thought can find a foothold in ontological inconsistency.
Our aim here is not to denounce the putative ‘circularity’ of Badiou’s argument, which may well be perfectly virtuous. Nevertheless, it is important
to note that thought’s suture to being – or to ‘the real’ (sheer inconsistency),
since they are equivalent here – occurs within the set-theoretical axiomatic,
rather than within Badiou’s metaontological gloss on the latter; a gloss which
he interposes between ontology and the reader via the use of concepts such
as that of ‘presentation’. In other words, we have no assurances that thinking
has any purchase on being in situations other than the ontological situation.
More importantly, there seems to be no reason to assume that the concept
of ‘presentation’ indexes anything at all outside of ontological discourse, or
that presentation has any extra-discursive existence. Citing so-called empirical evidence, according to which “everyone can see that there is presentation,”
is out of the question. A Platonist as intransigeant as Badiou cannot appeal
to the doxas of common-sense as support for the existence of presentation.
Moreover, to resort to the authority of consciousness – whether empirical or
transcendental – would be to capitulate completely to the norm of the One insofar as its inviolability is encoded in the incorrigibility of phenomenological
intuition. Why then does Badiou speak of the ‘presentation’ of being-multiple
from the very opening of Being and Event? Of what variety of manifestation
is subtractive being capable, given that, as Badiou himself emphasizes “being does not present itself” [“l’être ne se présente pas”] (EE 35) and “it is
pointless to seek out anything in a situation that would bolster an intuition
of being-as-being” (EE 67)? If subtractive being is never given, what is the
link between the presentation of presentation and the so-called ordinary or
non-ontological regime of presentation? For despite the putative ‘a priority’
of ontological discourse as “condition for the apprehension of every possible
access to being”, it is far from clear whether the argument of Being and Event
proceeds a priori from the void of being to the multiplicity of presentation, or
on the contrary, and a posteriori, from the multiplicity of presentation to the
void of being. In other words, how is it that the unpresentable can give rise to
anything but subtractive – ontological – presentation?
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Ultimately, Being and Event establishes a necessary link between the void
of being and the ontological situation only at the cost of severing any intelligible connection between being and the multiplicity of presentation. The discrepancy between Badiou’s claims about the a priority of the ontological and
his surreptitious appeal to the a posteriori is revealed in the fundamental tension between certain of his more uncompromisingly anti-phenomenological
declarations, such as “there is no structure of being” (EE 34), and other more
equivocal claims, such as “presentation is never chaotic, even though its being
is that of inconsistent multiplicity” (EE 110). The multiplicity of presentation
implies that there must be presentational situations other than the ontological.
But since the set-theoretical axiomatic guarantees the consistency of presentation through the operation of counting-as-one, the aforementioned tension
obtains only insofar as presentation occurs in non-ontological contexts. What
then are we supposed to understand by the term ‘chaotic’ in non-ontological
situations? If Badiou means disordered, then the claim is at least empirically
contestable, if not downright false. But if ‘chaotic’ simply means ‘inconsistent’ then Badiou is merely reiterating an empty tautology: “what is consistently presented does not in-consist”. It is precisely the failure to clarify the
connection between ontological inconsistency and ontical consistency that
obliges Badiou to resort to hollow tautologies such as “consistency must be
consistent”. If unity is only ever the result of an inexistent operation, then what
non-tautological instance accounts for the necessary ubiquity of consistency?
8. The two regimes of presentation
The key to the nature of the articulation between the a priori and the a posteriori (or ontology and world) in Badiou lies in grasping the difference between
the two regimes of presentation, ontological and non-ontological. Both their
distinction and their relation are rooted in the difference between metastructure and re-presentation. Ontology as the site for “the apprehension of every
possible access to being” cannot be re-presented. Thus although the metastructural doubling of presentation provides the ontological paradigm for the
distinction between situation and state of the situation, and thereby for the
gap between presentation and re-presentation – the yawning chasm wherein
the possibility of the evental break with ontological consistency takes root – it
is precisely ontology as presentation of presentation, presentation of sheer inconsistent multiplicity, which precludes the possibility of interruption insofar
as it remains exempt from re-presentation:
“[O]ntology is obliged to [. . .] draw all the consequences of the gap between
belonging and inclusion while not being governed by this gap [. . .] Thus
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the state of the ontological situation is inseparable, i.e. non-existent [. . .]
Ontology’s consummate effectuation of the non-being of the one, implies
the inexistence of the state of the situation which it is, and infects inclusion
with the void, having already stipulated that belonging is woven solely
from the void. The unpresentable void here sutures the situation to the
inseparability of its state (EE 118).”
This is a particularly gnomic passage even by the standards of Being and
Event. But in fact it provides a decisive clue as to the underlying connection
between the ontological situation and non-ontological situations, i.e. between
subtractive discourse and presented reality. The ontological presentation of
presentation presents nothing; every consistent presentation is drawn from
the originary mark of unpresentable inconsistency. It is because ontology is
the “consummate effectuation” of the non-being of the One, the unique situation wherein consistency is only ever derived from inconsistency that it
only ever presents nothing, and can never encounter something – it can never
count the inclusion of anything other than the void. But recall that in nonontological situations, consistency prevails over inconsistency, the One is and
inconsistency is not: thus what is presented is convertible with unity. It is
precisely in such non-ontological situations that the immeasurable excess of
inconsistent inclusion over consistent belonging allows for singularities, i.e.
elements that are presented by the situation but none of whose elements are
re-presented by the state of the situation (EE 116). And it is such singularities that provide a point of leverage for the event (they can become “evental
sites”).16 The ontological situation only ever harbours the latent inconsistency
of the void; whereas non-ontological situations harbour the latent inconsistency of unity. It is the inconsistency latent in the units of ordinary presentation
that provides the resource for a transcendent break with the immanent form
of ontological presentation. The event is the transcendent intervention that
splits the immanent ontological disjunction between belonging and inclusion
into an undecidable duality or ‘two’, the better to transform the state of the
situation. This intervention is of course the operation of the subject, whose
transcendence the immanent objectivity of ontological discourse forecloses.
The transcendence of the subject can be given a precise definition in contradistinction to the objective immanence of ontological discourse: whereas
the latter is the consistent presentation of the inconsistency latent in the void,
the subject is the consistent presentation of the inconsistency latent in unity
(it effectuates the generic).17
Ontological discourse precludes the possibility of the subject because it
can only draw the consequences of the gap between belonging and inclusion
up to the ‘point of impasse’ where their hiatus becomes strictly measureless
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and undergoes a phase-transition from immanence to transcendence.18 The
axiomatic consistency of ontological discourse encounters its own ‘impossibility’, i.e. its own extra-discursive ‘real,’ at the point at which the immanent
disjunction between structure and metastructure turns into the transcendent
excess of re-presentation over presentation. In other words, the ontological
a priori (discourse) intersects with the a posteriori (the world) at the point
where its effectuation of the inconsistency of consistency (the being-nothing
of non-being) flips over into an effectuation of the consistency of inconsistency (the non-being of being-nothing or subjective ‘truth’) through the
mediation of the event. Badiou generates the distinction between discursive
and extra-discursive presentation, presentation of presentation and presentation of ‘something’, by extrapolating from an immanent disjunction between
structure and metastructure in ontological discourse and converting it into
that measureless transcendence of re-presentation over presentation which he
claims characterizes non-ontolological situations.19 The result is that Badiou
can only delimit the sovereignty of symbolic law – the authority of ontological structure or the count – or acknowledge the domain of extra-discursive
reality by invoking a surplus of transcendence – uncalculable, unverifiable,
unobjectifiable and necessarily subjective – whose ontological schematization
fails to mask its inherent gratuitousness. Badiou bridges the gap between
ontological discourse and mundane reality by surreptitiously converting an
immanent hiatus in ontological presentation into a transcendent interruption
of ontological consistency. As a result, his philosophy simply stipulates an
isomorphy between discourse and reality, logical consequences and material
causes, thinking and being. Thinking is sufficient to change the world: such
is the ultimate distillation of Badiou’s idealism.
Ultimately, the role of subtractive ontology in Badiou’s philosophy is
merely auxiliary: it is essentially a de-mystificatory screen designed to prevent
us from becoming fascinated by the luxuriant plenitude of what there is, by the
actuality of the world as it is now, so that we may be prepared to seize the possibility of its radical transformation. Hence its essentially propaedeutic function
vis-à-vis the theory of the event. But Badiou’s problem is this: if ontology is a
discursive situation, if there is no non-discursive access to being, and if being
is neither a concept nor a datum of ‘experience’, then all that mediates between
ontolological presentation stricto sensu, in which neither ‘being’ nor ‘presentation’ play any conceptual role, and non-ontological presentation, is Badiou’s
own metaontological discourse. Its relationship to ontological discourse on
one hand, and non-ontological ‘reality’ on the other, consists in schematizing
the immanent disjunction between belonging and inclusion in the former so as
to convert it into a locus of radical transcendence in the latter. The goal of this
schematization is to synthesize the a priori regime of ontological presentation
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with the a posteriori regime of ordinary presentation. But ontology cannot be
the guarantor of “the apprehension of every possible access to being” if its
paradigm of presentation undermines the very possibility of access to being
outside the confines of the ontological situation. In fact, it is not ontology, but
metaontology that is the secret guarantor of the ubiquity of presentation for Badiou: it simply stipulates the impossibility of denying the existence of presentation in non-ontological situations. Nevertheless, the structure of presentation
is such as to render the idea of translating it from the ontological situation to ordinary situations absurd. There is only ontological presentation. Either Badiou
denies that ontology is a situation, in which case he is obliged to choose between mysticism, phenomenology, or metaphysics; or he accepts that the subtractive nature of presentation is such as to undermine all the non-ontological
consequences he wishes to draw from it; specifically, the theory of the event.
9. Consequences of subtraction
At this juncture, Badiou can respond in two ways: he can either choose to
correct the anti-phenomenological bias of the concept of presentation by
supplementing the subtractive ontology of being qua being with a doctrine of
appearance and of the ontical consistency of worlds20 – albeit at the risk of
lapsing back into some variant of the ontologies of Presence. Or he can accept the stringency of his concept of presentation and embrace the prohibitive
consequences of the logic of subtraction (The prospect of the forthcoming
Logiques des mondes [Logics of Worlds] suggests that he has – perhaps reasonably if disappointingly – opted for the former).
Rather than pursuing any sort of qualitative supplement to subtractive presentation, it is necessary to sharpen and deepen its disqualification of phenomenological donation (and of its dyadic structures such as temporalization/spatialization, continuity/discontinuity, quantity/quality, etc).
This sharpening and deepening entails three consequences:
First, if the sole real presupposition for subtractive ontology is that of the
existence of the name of the void, then this cannot be deduced by assuming
the consistency of multiplicity. As we have seen, to do so is to have implicit recourse to the authority of phenomenological donation. The legitimation of subtractive ontology should assume the following form: there is a decision which
allows one to assume a real presupposition and a real presupposition which
provides the basis for decision. The decision that being is nothing (primacy of
the subtractive signifier, Ø) should be determined by a real instance identified
independently of discourse. The real qua zero degree of immanence should determine its ideal nomination as void. The decision that ontology is mathematics
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can only be ratified via theory’s non-mathematical – i.e. non-discursive – suture to the real. Philosophy thereby abjures its metaontological role as transcendent mediator between science and reality, discourse and world.
Second, we should not accept Badiou’s intimation in Being and Event that
there are varieties of structure other than the counting-as-one of belonging, formalized in the set-theoretical axiomatic. It is necessary to insist that, far from
being a mere formalization or abstract model of the operation of unification,
belonging exhausts consistency. There are no other presentative operations
given prior to or independently of belonging. Were that to be the case, presentation would be a phenomenon. But if presentation is a subtractive noumenon,
an anti-phenomenon, all there is to consistency can be exhaustively articulated
by the mathematical theory of inconsistent multiplicity.
Third, the decision that ontology is mathematics annuls the distinction
between presentation of presentation and presentation of ‘something’. There is
only ontological presentation as literal regime of subtractive inscription. What
is presented is empty inconsistency. The caesura of subtractive presentation
requires transcendental supplementation via a ‘cut of the cut’, rather than
metaontological supplementation via the schematization of the ontological
impasse as event. Thus the transcendental supplementation of the logic of
subtraction dispenses with the event altogether. It is a question of isolating
and redirecting those components of Badiou’s thought which seem best suited
for the deployment of an exacting ontological nihilism.
Notes
1. Alain Badiou L’être et l’événement (Paris: Seuil, 1988), henceforth ‘EE’. An English
translation by Oliver Feltham is forthcoming from Continuum in 2006.
2. Cf. Alain Badiou, ‘Author’s Preface’ in Theoretical Writings, ed. Ray Brassier and Alberto
Toscano (London: Continuum, 2004), xv.
3. For an illuminating examination of the relation between Aristotle’s and Badiou’s characterizations of the task of ontology, cf. Jean-Toussaint Desanti ‘Some Remarks on the
Intrinsic Ontology of Alain Badiou’ in Think Again: Alain Badiou and the Future of
Philosophy, ed. Peter Hallward (London: Continuum, 2004), 59–66.
4. Cf. Section 4. I shall write ‘re-presentation’ whenever using the term in Badiou’s sense;
and ‘representation’ whenever using the term in its more familiar philosophical sense.
5. A point made by Peter Hallward in Badiou: A Subject to Truth (Minneapolis: University
of Minnesota Press, 2003), 276.
6. Cf. EE, Meditation 5, 95–107. This ‘greater than’ is to be understood in terms of the
concept of quantity, which is defined in terms of cardinality. Badiou establishes the concept
of cardinality and the immeasurability of the excess of inclusion over belonging with
reference to the Cohen-Easton theorem in EE, Meditation 26, 293–309.
7. For Badiou, ontology is necessarily indifferent to spatio-temporal categories: being qua
being has nothing to do with space and/or time – this is of a piece with his Platonism.
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8. “The nothing is as much that of structure, and hence of consistency, as that of pure
multiplicity, and hence of inconsistency” (EE 68).
9. The void only becomes discernible within a situation as a result of the dysfunctioning of
the count which gives rise to the ‘ultra-one’ of the event. Cf. EE, Meditations 17 and 18,
199–212.
10. Cf. EE, Meditation 3, 49–59.
11. See Wahl’s incisive paper ‘Présentation, Représentation, Apparaı̂tre’ [‘Presentation, Representation, Appearance’] in Alain Badiou. Penser le multiple, ed. Charles Ramond, (Paris:
L’Harmattan, 2002), 169–187. All subsequent references to Wahl’s article will be abbreviated to ‘PRA’.
12. Wahl, PRA, 177.
13. These metaontological concepts must be distinguished from the metaontological use of
the term ‘being’, which Badiou is careful not to reify into a concept. ‘Being’ is simply a
proper name – that of the empty set, Ø – for the unpresentable.
14. Cf. Badiou’s Manifeste pour la philosophie (Paris: Seuil, 1989). Manifesto for Philosophy,
trans. Norman Madarasz, (Albany: SUNY University Press, 1999).
15. For the distinction between truth and knowledge, cf. EE, Meditations 31 to 36, 361–
471, but also ‘On Subtraction’ and ‘Truth: Forcing and the Unnameable’ in Theoretical
Writings, ed. Ray Brassier and Alberto Toscano (London: Continuum, 2004), 103–117
and 119–133 respectively.
16. Cf. EE, Meditation 16, 193–198.
17. Cf. EE, Meditation 35, 429–447.
18. For Badiou’s account of the impasse of ontology, cf. EE, Meditation 26, 311–315. Badiou
seems to disavow the appeal to transcendence insofar as he aligns it with the ‘ontotheological’ orientation which he sees exemplified in the theory of ‘large cardinals’. A
large cardinal is one whose existence is not deducible from the axioms of set-theory and
hence requires the assertion of a supplementary axiom. Such an axiom is stronger than
the one which guarantees the existence of a limit-ordinal and the succession of transfinite
alephs. The theory of large cardinals fends off the measurelessness of ontological excess by
positing the existence of super-alephs that circumscribe it ‘from above’. But it is necessary
to distinguish between the assertion of the existence of transcendent objects, such as the
super-alephs, which do not acknowledge the impasse of ontology, since they do not force
a decision as to the value of the power-set of the smallest denumerable infinity, aleph-null;
and the assertion of unobjectifiable transcendence, which is precisely the transcendence
of decision, i.e. subjective intervention, vis-à-vis the immanent objective parameters of
ontological discourse. It is insofar as he endorses the latter option that Badiou can be
described as an advocate of radical transcendence.
19. This is the crux of the distinction between natural situations, which are characterized
by the maximal equilibrium between presentation and re-presentation and circumscribed
by aleph-null, smallest denumerable infinity; and historical situations, for which that
transitivity no longer obtains since they harbour singularities (evental sites) which are
potential loci for the singularization of excess. Cf. EE, Meditations 11–16, 141–198.
20. This is François Wahl’s recommendation. He argues that Badiou fails to establish a necessary link between the inconsistency of being and the consistency of presentation and
concludes that subtractive ontology remains insufficient. Thus Wahl concludes “the ontology of presentation and of beings, the ontology of the multiple determinations of being,
still remains to be done” (PRA 187).