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Badiou and Deleuze on individuation, causality and infinite modes in Spinoza
Jon Roffe
Presented at the Melbourne School of Continental Philosophy
Research Day on Spinoza and the Infinite, December 2005.
All rights remain solely the property of the author.
1. Introduction
In lieu of an introduction, let me simply say that my subject here is Alain Badiou’s discussion of
Spinoza’s ontology in his masterpiece
L’être et l’événement.
He proposes a reading that
foregrounds a concept which is as central and celebrated to his philosophy as it is strictly
excluded by Spinoza: the void. In short, Badiou contents that for all Spinoza’s effort to offer an
ontology of total plenitude, the void returns in his philosophy under the (at first sight) unlikely
name of
infinite mode
.
What follows is organised into three moments. I will first give an exposition of Badiou’s intricate
critique of Spinoza. Next, I will challenge on a number of points Badiou’s exposition of Spinoza,
notably his treatment of infinite and finite.
1
It is my contention that Badiou only presents the
version of Spinoza amenable to his theoretical orientation, and that a more substantial account of
the issues opens up alternatives to the reintroduction of the concept of void in order to provide his
philosophy with consistency. Turning then to Deleuze, I will argue that he provides just such an
alternative, on the basis of his account of the relationship between modal essence and individual
existing modes.
2. Badiou’s reading of Spinoza
Badiou dedicates two quite detailed texts to Spinoza’s thought. The first, which the discussion
that follows will be based upon, is the tenth meditation of
L’être et l’événement
. The second,
dedicated to the notorious problem of the relationship between the attributes and the intellect that
is first alluded to in EID4 of the
Ethics
, is found in his 1998
Court Traité d’ontologie transitoire
,
entitled “L’ontologie implicite de Spinoza”. While the second is the stronger of the two pieces, it
relies at certain points on the argument made in the first; an examination of this text will have to
wait for another occasion. In both pieces, Badiou is concerned “to show that this foreclosure,” the
foreclosure of the void, “fails.” (BE 113) This failure, according to Badiou, can only be a good
thing, since it provides for a gap, a gap for the subject and for radical novelty in the form of
events. As such – and this is particularly clear in the text to be examined here – his goal is to see
in Spinoza a philosopher who fails in just the ways that his own philosophy succeeds. My concern
is less to undermine this attempt as a whole than to question the validity of the reading of Spinoza
that is used in its service.
The meditation on Spinoza in
L’être et l’événement
comes at the end of the second division of the
text, in which Badiou elaborates his concept of the
state of the situation
. Given that this
meditation begins with a paraphrase of
Ethics
, Book One, proposition 15 (“Whatever is, is in God
. . .”[
Quicquid est in Deo est
]) which reads: “all situations have the same state”, it will be worth
defining these two terms briefly.
Situation is Badiou’s first and most important ontological or meta-ontological concept. The
situation is defined as any result of an operation of counting-as-one, that is, as any consistent
multiple whatsoever produced through a unifying operation. We must consider this definition in its
proper generality: in order for anything to exist as a consistent whole, an operation of counting-
as-one must be presupposed. And every consistent whole as such is a situation. The scope of
the concept of situation is likewise completely universal: it pertains to every level, every modality,
every form of being, and every content thereof. This generality also guarantees the abstraction
proper to the concept: the count-as-one is the universal operator of consistency, but it imposes no
predication or form beyond the composition of consistency for a given multiple.
Let’s note an important supposition: if consistent multiplicity (or multiple-oneness, or what Badiou
also calls
presented multiplicity
) is the result of the count-as-one, then
inconsistent
multiplicity is
implicated prior to the activity of the count. It is, Badiou says, a retroactively legible consequent of
the count itself. Now, this inconsistency is in fact the source of a perennial and very real problem
that confronts any situation: consistent unified multiples are always threatened with the
inconsistency that their count-as-one presuppose. In fact, it is precisely this inconsistency as such
which cannot be counted-as-one. Inconsistency haunts the abstract form of the situation, and
challenges it with a particular kind of formal powerlessness. Badiou:
The consistency of the multiple amounts to the following: the void, which
is the name of inconsistency in the situation (under the law of the count-
as-one), cannot, in itself, be presented or fixed.
(BE 93)
The inherence of that inconsistency particular to a consistent presented multiple is given a very
precise name by Badiou, which is the
void
.
2
Whereas inconsistency is a retroactive posit relative
to every count-as-one, the void is that
local
inconsistency “proper” to the situation in question.
The void belongs to every situation, and it is a void particular to the situation in question.
It is at this point that the concept of the state is put into play by Badiou. If we take the situation as
any set (as Badiou himself does), characterised by the primal relation of belonging
∈
(or
counting-as-one), then the state of the situation is indicated by the relation of inclusion,
⊂
. It is for
Badiou a second count of the original count-as-one itself, a resecuring of the structural oneness
of the situation. Thus the goal of this second count is to attempt to master the
revenant
of
inconsistency, ie., the void, by further securing the relation of belonging at a more precise level.
The second count counts-as-one all those elements counted-as-one in the formation of the
situation.
Here Badiou draws upon a connection between this second count and what he argues is its set-
theoretic counterpart, the power-set axiom, whereby every subset of the set in question is itself
counted-as-one. As Badiou points out in Meditation 7 of
L’être et l’événement
, the power of this
second count is vastly in excess of that of the first. This is of course one of Cantor’s famous
discoveries. Badiou also notes another important point which distinguishes the first count from the
second: in the first count, what is counted is members of the set, or multiples themselves. What
remains uncounted
directly
are the subsets or submultiples of the situation. Now these subsets
certainly belong to the situation (insofar as the multiples they belong to have been counted), but
they belong in an unregulated fashion. Furthermore, the void
qua
localised inconsistency, also
belongs to the situation, and in the same fashion. It is thus at this sub-level of the situation that
the threat of inconsistency remains, and which the second count-as-one takes as its regime.
In short the state of the situation is what guarantees that everything counted-as-one in a situation
is secured in its belonging by the excessive power of determination that the second count brings
about, thereby excluding the void from disrupting the consistency of the situation. Badiou writes:
The consistency of presentation thus requires that all structure be
doubled
by a metastructure which secures the former against any fixation
of the void.
(BE 93-4)
Now, Badiou transposes these terms into Spinoza’s thought in the following way: situation is the
name given to the attributes, and substance (God or nature) the name of the state. There are
thus an infinite number of situations, whose coherence or consistency are guaranteed or doubled
by the substance which they are comprehended by or included in. So, if we return to Badiou’s
opening paraphrase of Spinoza’s
Quicquid est in Deo est
, every situation has the same state, we
can see that this is strictly speaking true. According to Badiou, in composing an indissoluble
ontological unity between substance and attributes, Spinoza aims to foreclose any possibility of
the void returning to threaten the organization or structure of the attributes and the unity of
Deus
sive
Natura
. The force of Badiou’s argument rests on the insistence that, however magnificent the
effort to bring about this foreclosure, Spinoza’s philosophy still admits the void, under the name of
the infinite mode.
With these points in mind, we can turn to the substance of Badiou’s argument in meditation 10 of
L’être et l’événement
. Badiou begins with a more detailed account of the equation between
situation and substance than that which I offered earlier: “for Spinoza, the count-as-one of a
multiple, structure,
is causality
.” (BE 112) That is, the individuated elements of substance are in
the first instance presented as unified-by-cause. Of course it is the modes that he is referring to
here:
A composition of multiple individuals
(plura individua)
is actually one and
the same singular thing provided that these individuals contribute to one
unique action, that is, insofar as they simultaneously cause a unique
effect
(unius effectus causa).
(BE 112)
It seems clear that he is invoking the following proposition (EIP28) in the
Ethics
:
Every singular thing, or any thing which is finite and has a determinate
existence, can neither exist nor be determined to produce an effect
unless it is determined to exist and produce an effect by another cause,
which is also finite and has a determinate existence; and again, this
cause also can neither exist nor be determined to produce an effect
unless it is determined to exist and produce and effect by another, which
is also finite and has a determinate existence, and so on, to infinity.
For Badiou, we can say that an inconsistent multiple of existing modes is counted-as-one through
the causal activity of an existing consistent multiple (Spinoza’s
res singulares
). Again, this seems
consonant with Spinoza’s text. However, Badiou claims, we are dealing here with a manifest case
of circularity. Every operation of the count-as-one (which brings about the existence or
presentation of singular things) relies upon the supposition of a prior singular thing which would
be its cause. Thus the unity of the singular thing in question is being supposed in its definition. In
Badiou’s words: “If in fact I can only determine the one of a singular thing insofar as the multiple
that it is produces a unique effect, then I must already dispose of a criterion of such unicity” (BE
112).
Badiou then notes that this circularity does not bother Spinoza at all, and this is because the
count-as-one of the multiplicity of existing modes which renders them consistent as a singular
thing is guaranteed by the state of the situation, that is, God. It is not just the case that singular
things are determined as such through causation, but that each thing which exists is caused to do
so by God. In Spinoza’s terms: “A thing which is determined to produce an effect has necessarily
been determined in this way by God; and one which has not been determined by God cannot
determine itself to produce an effect.” (EIP26) This is a textbook example of what Badiou means
by the second count-as-one, the state of the situation. Existing composite modes (singular things)
in a given attribute are guaranteed in their composition by the causal agency of substance, which
grasps them in their individuality.
Once more, it seems that little can be faulted at this point in Badiou’s argument. He identifies the
two orders of causation at work in Spinoza (it would be better to say the two modalities of
causation were this term not liable to confuse, since God is the immanent cause of everything):
on the one hand, the infinite network of cause and effect that characterises the world of existing
modes, and on the other, God-or-Nature as the sole causal agent.
It is at this point that Badiou intervenes, suggesting that we find here, through the real identity of
attributes (situations) and substance (state of the situation) “the philosophy
par excellence
which
forecloses the void
.” Given that the role of the state as we have seen is precisely to impose an
excessive meta-structuring (I am tempted to write ‘overcoding’ in the sense given to the term in
Deleuze and Guattari’s
Anti-Oedipus
, a term moreover which is precisely related to their account
of the State) of the situation in order to exclude the return of the inconsistent void, we can see
how Badiou can make this claim.
In a move reminiscent of a deconstructive reading, Badiou’s point (one I have noted a few times
already) is that Spinoza fails:
this foreclosure fails, and [. . .] the void, whose metastructural or divine
closure should ensure that it remains in-existent and unthinkable, is well
and truly named and placed by Spinoza under the concept of
infinite
mode
.
3
(BE 113)
More precisely, as we will see, it is the “notorious” point of intersection between “the infinite and
the finite” that the void re-emerges. Thus it is important, before turning to the question of infinite
modes directly, to insist on the role that finite modes play in Badiou’s analysis.
I quoted earlier EIP28, to the effect that every finite thing is caused by another finite thing, and so
on to infinity, and Badiou himself quotes the same text. He insists in fact that finitude is “an
essential predicate” of every singular thing, doubtless making reference to EIID7:
By singular thing I understand things that are finite and have a
determinate existence. And if a number of Individuals so concur in one
action that together they are all the cause of one effect, I consider them
all, to that extent, as one singular thing.
In sum, what individuates singular things, or unified finite modes, is that they have a singular
effect. But in what sense are finite things
finite
according to Badiou? Here we find a surprising
lacuna in his text: not once does he mention Spinoza’s own account of finitude, or even provide
an explicit definition of his own. The reader is left with two possible explanations. Either Badiou in
fact has Spinoza’s definition of finitude (EID2) in mind implicitly, or he is employing a different
definition that likewise remains implicit. To my mind, only the second of these is a viable option.
As I will show in the next section of the paper, Badiou’s account of finite modes overlooks their
essential character for Spinoza: their
limited
nature, rather than their denumerability. It is the latter
that defines finite for Badiou given his mathematical orientation, according to which finitude is
defined by the successor relationship between ordinals.
Turning now to infinite modes. Badiou presents the core of his argument in a summary of what he
calls “Spinoza’s deductive procedure”, tying together propositions 21, 22 and 28 from Book I of
the
Ethics
. Taken together, he considers that they show a causal fork emerging which separates
infinite and finite. Proposition 21 claims that “everything which follows from the absolute nature of
any of God’s attributes [. . .] is infinite.” The next proposition, worth quoting at length, applies this
insight to modes:
Whatever follows from some attribute of God insofar as it is modified by a
modification which, through the same attribute, exists necessarily and is
infinite, must also exist necessarily and be infinite.
(EIP22)
Badiou glosses this as: “everything which follows from an infinite mode – in the sense of the
preceding proposition – is, in turn, infinite.”
Finally P28, which I have already cited, tells us that every singular thing (“or [
sive
] any thing which
is finite and has a determinate existence”) only exists and causes effects of its own if it in turn is
caused to exist by another pre-existing singular thing.
Now, Badiou argues that we confront two problems in the face of these allegedly existent infinite
modes. The first is that we cannot
experience
them. He insists, first of all, that according to
Spinoza all knowledge of finite modes comes from direct encounters with them. Their existence
cannot be deduced through Reason, since (as P28 tells us), they come about when caused to do
so by other existing modes – that is, there is nothing
necessary
about the existence of any
particular finite modes. Given, that is, that existing modes cannot be deduced directly from God’s
essence, being contingent on encounters with other existing modes, the only way we can gain
knowledge of them is through direct encounter. However, if infinite modes can only have a causal
relation with other infinite modes, such experience seems impossible, since we are finite beings
ourselves.
While I am saving my general criticisms for the next section of the paper, let me note here that
Badiou’s argument seems particularly ignorant of Spinoza’s epistemology at this point. The fact
that we cannot know infinite modes directly through encounters has nothing to do with its
ontological status and everything to do with the ontological status of human beings as beings of a
certain finite composition. The famous worm in the blood from Spinoza’s letter 15 to Oldenburg
can no more know the entire composition of the body which it is inhabiting than we can
know
the
infinite extended Individual that we are an intrinsic part of. On the other hand, there is a sense in
which we can conceive
4
of infinite modes, and that is through the common notions: all extended
bodies form adequate ideas of other extended bodies of a greater or lesser size when they
encounter each other, precisely insofar as they themselves are extended. As Spinoza claims:
“Those things which are common to all, and which are equally in the party and the in the whole,
can only be conceived adequately” (EIIP38) Further, we can recall P47 from the same book of the
Ethics
: “The human mind has an adequate knowledge of God’s eternal and infinite essence” on
the basis of the common notions.
The second, and to my mind more serious, problem that Badiou raises concerns the ontological
status of infinite modes: “The question is that of knowing in which sense these infinite modes
exist
.” (BE 117) Here Badiou notes the fact that Spinoza’s discussions of infinite modes are few
and far between, and when asked for concrete instances by Schüller in his letter of 1675 he only
mentions absolutely infinite understanding (under the attribute of thought), and the famous
facies
totius universi
, the figure of the entire universe (under the attribute of extension).
Furthermore, direct discussion of the topic in his key works is also sparse. On Badiou’s count, we
only find three moments in the text which address these modes directly or indirectly, and by and
large only repeat the examples given to Schüller: EIIP13L7 (concerning the entirety of extended
modality as a single Individual), EVP40S (which invokes the totality of the modes expressing the
attribute of thought as “the eternal and infinite understanding of God”) and EIP22 which I have
already mentioned (the proposition that argues that infinite causes lead to infinite effects).
According to Badiou, this scarcity of reference is keenly symptomatic. Infinite modes seem to sit
at the hinge between the infinity of substance, with its order of immediate efficient causality, and
the finitude of modes – they seem to hover between two determinations, between finite and
infinite, both a part of two causal chains and torn between them. Given that, in Badiou’s words,
“the immediate cause of a singular finite thing can only be a singular finite thing, and,
a contrario
,
a (supposed) infinite thing can only produce the infinite,” the name ‘infinite mode’ can only be
given to the void that emerges here in the causal chain:
It seems that the excess of the causal source re-emerges at the point at
which its intrinsic qualification, absolute infinity, cannot be represented on
the same axis as its finite effect.
(BE 116)
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