infinite thought by alain badiou
TRANSCRIPT
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nfinite Thought
Truth and
the
Return to
hilosophy
L N
DIOU
Translated and
e ite
by
Oliver eltham and ustin
lemens
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ontinuum
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York Road
London,
SE
www.continuumbooks.com
15 Eas t 26th Stree t
New York
;\IY 10010
Editorial
material and
selection
Oliver Feltharn
a n d J u st i n
Clemens
Philosophy andDesire Philosophy and Film, Philosophy nd thewar against
terrorism
Alain Badiou
Philosophy
andArt,
and
The Definition of
Philosophy Seuil (from
Conditions
1992)
Philosophy
andthe Death
of Communism Editions de l Aube (from
D un
desastre obscur
1998
English language translations: Philosophy an d
Truth
Pli;
Philosophy
and Politices
RadicalPhilosophy; Philosophy and Psychoanalysis
( : )
Ana{ysis; all
other
English language translations
Continuum
Reprinted
2003
This paperback edition published 2004 by Continuum
All rights reserved. No
part
of this publication may be reproduced or
transmitted
in any form or by
any
means, electronic or
mechanical
including photocopying, recording or any information storage or retrieval
system,
without prior
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ritish
Library
Oatalcgufng-dn-Publicarlon Data
A catalogue record for this book is available from the British Library
ISB:\ 0-8264-6724-5 Hardback)
0-8264-7320-2
(Paperback)
Typeset
by BookEns
Ltd,
Royston, Herts.
Printed
and
bound
by in Great Britain by Th e Bath Press,
Bath
ont nts
An
introduction
to Alain Badiou s philosophy
I Phi losophy
an d
desire
2 Philosophy
a nd t ru th
3 Philosophy
an d
politics
Philosophy
an d
psychoanalysis
5 Philosophy
an d
ar t
6 Philosophy
an d cinema
7 Philosophy
an d
the
death of communism
8 Philosophy
an d
the
w ar
against
terrorism
9 Th e definition
of
philosophy
10
Ontology
an d
politics:
an
interview
with
Alain Badiou
Index of
names
v
39
58
69
79
9
109
6
4
65
169
95
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n introduction to l in
adiou sphilosophy
Alain Badiou is on e
of
France s foremost living philosophers.
Ye t
recognition
of th e force
an d
originality
of
his work in th e
English-speaking
world
ha s
been
slow to come
perhaps
because it is difficult to assimilate his work within the
established categories
of
contemporary French philosophy .
However such
recognition
is now
gathering mo men tu m. N o
fewer than six translations of his major works tw o
collections
of
his essays
an d
on e
monograph
on his work
a re c ur re nt ly in press. Th e first English-language con
ference devoted to his work was held in
Ma y
2002
at
Cardiff a critical introduction to his w or k h as a pp ea re d
an d three
translations
of
his w or ks Ethics eleuze an d
Manifesto for
Philosophy - a r e a l re a dy
on th e
shelves.f
Th e pre se nt volume aims to provide a brief accessible
introduction
to
th e
diversity
an d
power
of Ba d
iou s
thought
c ol le ct in g a series
of
conference papers an d essays.
Th e
opening text sets
the
scene giving a
polemical
overview of
th e state
of
philosophy in relation to the
contemporary
world. Th e second chapter gives a general overview v ia t he
categories
of
ethics
and truth of Badiou s model of
fundamental change in t he d om ai ns
of
art love politics
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Infinite Thought
an d science - philosophy s four conditions . Th e following
chapters present
specific applications of his
central
concep
tion of philosophy as an exercise of thought
conditioned
by
such
changes in ar t
Chapters
5 an d 6 on
poetry
an d
cinema), love Chapter 4 on psychoana lysis) , politics
Chapter
3)
an d
science. Since Badiou s
work
in relat ion
to science is mainly found in the huge tome L Etre et
I eoenement
Being and Event) we chose to sketch the
latter s
argument
in the introduction. Chapters 7
an d
8 exemplify
a return to on e
of
philosophy s classical roles:
the
analytical
denunciation of ideology, Badiou attacking first the
w ar
on
terrorism
an d
then
th e
d eath of communism . The
penultimate
chapter
sets
ou t
Badiou s doctrine on philoso
ph y in relation to its condi tions,
an d
th en the collection
closes
with
an interview with Badiou in which he explains
an d
reconsiders some of his positions.
In
o u r in tr o du ction we identify
on e
of
t he m an ne rs
in
w hic h B adi ou s philosophy differs from t he c ont e mpora ry
French philosophy known as poststructuralism: its treat
ment of
t he que st ion
of
th e
subject . We
t hen e ngage
in a
long, at times difficult, bu t necessary exegesis of
Ba d
iou s set
theory
ontology;
nece ssary since it grounds his entire
doctrine,
a nd n ot
particularly long in relat ion to its matter;
Being and Event comprises
over
500 pages in t he F re nc h
edit ion . At eve ry point we have attempted to render
th e
technical
detai ls in as
clear
a fashion as possible, yet
without
undue
distortion.
the prospective reader wishes to skip over the more
abstruse discussions offered in
th e
introduction, he or she
should feel absolutely free to do so - for Badiou is still his
ow n
best exegete.
He
effectively tries to speak to those
wh o
do no t spend their lives in professional institutions, b ut a ct
an d
think
in ways that usually exceed or ar e beneath notice.
As Badiou
himself
puts it: Philosophy privi leges no
l a nguage, not even t he o ne it is w r it t en i n.
An introduction to Alain Badiou s philosophy
Badiou s question
Badiou is neither a po stst ru ct ur al ist n or a n a na lyt ic
philosopher, an d for
on e
major reason:
there
is a quest ion
which
drives his
thought,
especially in his magnum opus,
L Etre et l eoenement.
T hi s q ue st io n
is foreign to
both
poststructuralism
an d
analytic phi losophy - in fact no t only
foreign, bu t unwelcome. is this
question
that governs
the
peculiarity of B ad io u s t ra j ec t or y an d th e
attendant
difficulties of his
thought.
In
th e introduction to L Etre et l ivenement
Badiou
seizes
upon an e xc ha ng e b et we en Jacques-Alain Miller
an d
J ac qu es L ac an d ur in g
the
famous Seminar
XI.4
Miller,
without blinking, asks
L aca n, the
grand theorist of
the
barred subject,
What
is your ontology? 5 Fo r
Badiou
this is
a crucial moment, for it reveals a fundamental difficulty
one that many argue Lacan never solved, even with his
loopy 1970s recourses to knot theory. Th e difficulty is t ha t o f
reconciling a modern doctrine
of
th e subject (such as that
of
psychoanalysis)
with
an ontology. Hence
Badiou s
guiding
question: How can a modern doctrine the subject be reconciled
with an ontology
Bu t
what
exactly does Badiou understand by a
modern
doctrine
of
th e subject ? Badiou takes it as g iven that in th e
contemporary
w or ld t he
subject ca n no
longer
be theorized
as
the
self-identical
substance that
underlies
change,
no r as
th e product
of
reflection,
no r
as
the correlate
of
an object.
This set
of
negative definit ions is all very famil iar to a reader
of
poststructuralism.
Surely one
could
object
that
post
s t ruct ura li sm has
developed a modern
doctrine
of th e
subject?
Th e pr obl em w it h pos ts tr uc tura li sm
is
that exactly
the
same set of negative definitions serves to delimit its implicit
ontology
whether of desire or difference): t her e a r e no self
identical
substances,
there are no stable products
of
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Infinite
Thou ht
reflection, an d since
there are no s table
objects
there
can be
no correlates of such objects.
Thus
in
poststrucruralism
there
is no distinction
between
the
general
field of ontology and a
theory of the subject; there
is
no tension between the being
of
the subject and being in general.
Where Bad iou
sees an essential
question
for
modern
philosophy,
then, poststructuralism
sees
nothing. For many
this lack
of
distinction
between the being
of
the
subject
and
the
being
of
everything
else
would appear
to be a virtue;
the
privilege
of the
rational animal is finally
removed
in
favour
of a less anthropocentric
ontology.
There is, however, a
price to be paid for lumping the
subject together
with
whatever
else is
usual ly recognized
in an
ontology.
Poststructuralism typically encounters a number
of
pro
blems in its theory of the subject.
Funnily
enough, these
problems
are quite clearly inherited From th e very
philosophical tradition
whose death poststructuralisrn
gleefully proclaims.
There
was enough lite left in the corpse
to pass
something
on
and wha t
it passed on were the two
fundamental
problems
in the thought
of the
subject.
The, first
;)roblem that
of
identity the
second, problem,
that o a g e ~ i Y the mind-body problem
derIves or
the
most
part from the former, an d the
free will
versus determinism
debate f rom the latter. Poststructuralists have concentrated
almost exclusively on a critique of the first problem, arguing
that
there
is no solution to the problem of the identity of the
subject because
the
subject has
no
substantial
identity:
the
illusion of an underlying
identity
is
produced
by
the
very
representational mechanism employed
by
the
subject in its
effort to
grasp
its
own
identity.
The same
line
of argument
is
also
applied
to the
identity ofany ent it y t hu s i nc ludi ng t he
subject within
the domain
of a general ontology.
Fo r
example,
in his introduction to a collection
of Philippe
Lacoue-Labarrh e s
essays, Derrida
identifies the
subject
with the
self- de
)constituting
rnovemen t
of
th e
text; the
4
n
introduction
to lain Badiou s philosopkv
subject is nothing
o th er t ha n
a
perpetual movement of
translation. This brings the subject within the
ambit o f
his
much-maligned bu t fateful early ontological claim:
There
is
no ou t sidc-
text. The
conseq uence
of
this
move,
of this
merger of the
subject
with
a
general ontology within
the
context
of
a
general critique
of
identity
an d
representation,
is the
emergence
of a pr ob lem with t he differentiation of
subjects.
How
can
one sub ject
be
differentiated
from
another without recourse
to
some
sort
of definable identity?
As for agency -
philosophy s
second fundamental
problem in the
thought
of the subject - the
consequence
of poststructuralisrri s almost exclusive concentration on
the
first
problem has
been
that the
critics of
poststructuralism
have h ad an easy pitch: all they have ha d to do is to accuse
the poststructuralists of robbi ng t he sub ject
of
agency: if
there is no self-identical subject, then what is the
ground
for
autonomous rational action? This is what lies behind the
infamous jibe that
poststructuralism
leads down a slippery
slope
to apoliticism.
When
poststructuralists do engage wi th the pr ob lem of
agency they
again
meet
with
difficulties, an d again precisely
because
they
merge t he ir t heory of
the
subject
with
their
general
ontology. Fo r
example, in his middl e per iod
Foucaul t a rgued
that
networks
of
disciplinary
power
no t
onl y r each i nt o th e mos t intimate
spaces
of the
subject,
bu t
actually produce what
we
call
subjects.
However,
Foucault
also
said
that
power produces
resistance.
His
problem then
became t ha t o f accounting
for
the source of such
resistance.
the sub ject - r ight down to its most
intimate
desires,
actions and thoughts - is constituted by power,
then
how
can
it be the source of
independent
resistance? Fo r such a
point
of
agency
to exist , Foucault needs some space which
has no t been completely
constituted
by
power,
or a
complex
doctrine on
the
relat ionship be tween resistance an d
independence. However, he has neither. his later work,
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Infinite Thought
he deals with this problem by assigning
agency
to those
subjects
who
resist power by means
of
an aesthetic
project
of
self-authoring. Again, the source
of
such privileged agency
why do some subj ects shape themselves a ga in st t he grain
an d
no t others? - is not explained.
What
does
Badiou
do
when
faced
with
these
two
fundamental problems
of
identity
an d
agency? First, Badiou
recognizes a d is ti nct io n b et we en t he g en era l domain of
ontology an d t he t he or y
of
th e subject. He does no t merge
th e one into
th e
other;
rather
the tension bet we en t he two
drives his investigations. Second, when it comes to the two
problems,
Badiou does the
exact
oppos ite to the posts true
turalists: he defers t he pr obl em of identity, leaving a direct
treatment of it for
t he unpubli s he d
companion
volume
to
Being and Event, whi le he
concentrates
on
t he p ro bl em
of
agency.9
F or B ad io u t he q ue st io n of
agencY is
no t
so
much
a
question
of
ho w a subject
ca n
initiate an action in an
autonomous manner but rather
ho w
a subject emerges
through an autonomous chain
of
actions within a changing
\ s i t u a ~ i o n < I ~ ~ ~ U ~ i t ~ , p o t
everyday
actions or decisions that
provIde eVIdence
of
agency for Badiou.
It
is
rather
those
extraordinary decisions
an d
actions
which
isolate lan actor
from their context , those act ions which show that a human
ca n
actually
be a free agent that
supports
new chains
of
actions
an d
reactions. .Q this reason, .not every
human
. b ~ i n g
is always a
subject;
yet
some
human
beings
ecome
subjects; those w ho a ct
InjiJeHlj tQ
a chance encounter with
an
evenilvhich disrupts the
;iluationAhey
find themselves
in.) -
A subject is born of a human being s decision that
something
they
have encountered which has happened in
their situation -
however
foreign a nd a bn or ma l - does in
fact belong to the situation
an d
thus cannot be overlooked.
Badiou
marks
the disruptive abnormality
of
such an event
by stating that whether it belongs to a situation or no t is,
6
An
introduction
to Alain Badiou s philosopky
strictly undecidable on the basis of.estahlished knowledge,
Moreover the subject, as
born of
a decision.ds not limited to
th e recognition
of t h e \ ~ : c \ l h ~ n c e
of
an
event,
bu t
extends
into a prolonged
investigation
pC the consequences
of
such
a q e , v ~ n t ~
0vestigation
is no t a passive, scholarly affair;
it entails
no t
o nl y t he active transformation
of
the
situation
i n ~ F l i c h t he e ve nt occurs bu t also the act ive transformation
of
the
human
being.
Thus
in Badiou s
p h i l o s o p h y b c ; f , i ~ g ( )
such thinK.as a s ll ? ject without such a p r ( l t ~ e s S of
subjectivization. - .
For example when two people
l l
in love, their meeting
- w hether th at
meeting
be
their
first
hours together
or
the
length
of
their entire courtship
- forms an
event
for them in
relation to which they change their lives. This certainly does
n ot m ea n that their lives are simply going to be the.,better,
for it; on t he c ont ra ry love ma y involve d e b t , ~ l i e ~ a t e d
friends,
an d r u ptu re with
one s family. The:
point
is
that
love
changes
their
relation to the world i ~ r ~ ~ o ~ ~ b l y : ' Th e
d ur at io n o f
the lovers relationship depends
upon
their
fidel ity to
that
event
an d
ho w
they c hange a cc or di ng to
what
they discover through their love. th e rea lm f
science
the most
obvious exal11ple of an event is
the
Copernican revolution,
the
e ~ l s ~ i I l g s u b j e c t ~ b e i n g those
scientists w ho w or ke d
within
its
wake
contributing to the
field we now
n am e m o de rn
physics .
Th e
consequence
of such a definit ion of the subject seems
to be
that
only
brilliant
scientists,
modern
masters, seasoned
militants
andcommitted lovers ar e adIriitte a into rhe fold. A
l i t t l e ~ n f a i ~ p e r h ; l p ~ ? Is Badiou s definition of th e subject
exclusive or elitist? On the on e side, you have
human
beings,
nothing much distinguishing them from animals in their
pursuit
of their interests,
an d
t hen , on th e
other
side, vou
a ~ c C the n e ;- er i te o r
fatttJful
~ ~ ~ t i s
has a dangerous ring,
an d
on e could be forgiven for
comparing it at first g lance to
Mormon
doctrine. However -
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infinite Thought
an d this is
crucial
-
there
is no
predestination
in
Badiou s
account. There
is
nothing o th er t ha n c hanc e e nc ount er s
between
particular
humans
an d
particular
e ve nt s; a rid
subjects
may
be
born
ou t of
such
encounters. There is no
higher or de r w hi ch
prescribes who will
encounter
an
event
an d
decide
to
ac t
in
relation
to it.
There
is
o nl y c ha nc e .
Furthermore, there
is no s im pl e
distinction between
subjects
an d
humans. I I
Some humans
become
subjects, bu t only
some of the t im e, an d often
t he y b re ak t he ir
fidelity to an
event an d thus lose
their
subjecthood.
T hus , B adi ou
displaces the
problem of agency
from
the
level of the human to the level of
being. T hat
is, his
problem
is no
longer
t ha t o f
ho w
an
individual
subject initiates a
ne w
chain of actions, since for h im th e subject only e I l e r g ~ s in
the
course of such a
chain
of a ct ion s. His
problem
is
accounting
for
how
an existing
situation
- given that
being
for B ad io u, is
nothi ng ot he r than multiple
situations -
ca n
be
disrupted
an d
transformed
by such a
chain
of actions.
This displacement
of
the
problem of
agency
allows
Badiou
to
avoid
positing some mysterious
a utonomous a gent w it hi n
each
human
such
as free will .
H ow ev er , t he direct
an d
unavoidable consequence of
t he di spl ac ement
is that the
problem of
agency
becomes
the
ancient
philosophical
problem
of
h ow t he ne w
o cc ur s in b ei ng .
t
is no c oi nc id en ce that
Badiou s
q ue st io n - Wha; is
the
compatibility
of a s ub je ct
with
a
general
o nt ol og y? - l ea ds
directly
to this
venerable
philosophical
problem,
since it is
this
very problem which
also underlies
Badiou s early
work,
Theorie du sujet.r? In that
work,
Badiou s
so lut ion was to
develop
a
complex
poststructuralist remodelling of
the
Hegelian
dialectic.
L Etre et
l eoenement Badiou s
solution
is simply}o
, ~ s ~ ~ ~ t d ; ~ t
e ~ T e n t : happen , events
without
directly
assignal:Sle causes
which
disrupt
the
order
of
established situations.
decisions ar e
taken
by subjects
t
work
ou t
the consequences of s uc h e ve nt s,
new situations
8
n
introduction
to lain Badiou s philosophy
emerge
as a result
of
their
work.
Such
events d 9 , ~ ? t ) ( ) r . I ,
part o f w h at is , an d so
they
do no t fall under
th e
purview of
Badiou s general.ontology.
Thus the r 1 1 , ; ~ ~ ) ~ ~ _ ~ ~ ~ t w e . s . r : r : . . , t ~ e
being
of
subject an d th :
g e n : q l ~ : d ~ m a l Q }
. o , L B < l g l ~ ~ S .
ontology IS
a
contingent
relationship,
wInch
hmges oB._the
occurrence of
an eventand
the decision
of
a
subject
toactjn
fidelitv to
th a
t e ve nt .
WI;at,
then,
is this
general domain
of
Ba d
iou s ontology?
A1adem ontology: being
as multiple multiplicities
As
a lr ea dy m en ti on ed , t he re a re
tw o major
traditions
that
' ~ ~ i i o x
a
relation
to
ontology
in
l at e t we nt i et h-c ent ur y
philosophy: th e
analytic tradition
an d th e post-Heidegger
ea n
tradition. Th e analvtic
tradition either forecloses
ontology
in
favour
of epistem;lO
g
y r
reduces
ontology
to
a property of theories.P Th e
post-Heideggerean
tradition
p er pe tu al ly a nn ou nc es t he e nd
of
fundamental
ontology,
while
basing
this
pronouncement
on its
ow n f unda me nta l
ontology
of desire or difference.
Despite his rejection of
their
conclusions,
Badiou
does no t
simpfy
dismiss
the
claims of these
traditions.
O n
the contrary,
Badiou
t ak es his
starting
point
from
both
traditions:
th e
concept
of
situation
from vVittgenstein an d
t he i de a
of
th e
ontological difference from
Heidegger.
He
then
forges a
n ew o nt ol og y
within the
furnace
of
their
critiques of
ontology.
Heidegger
formulates
the
o nt ol og ic al d if fe re nc e as the
difference
between
Being
and.beings;
ha t is,
the
difference
between i f l d i ~ l d ~ - a l heings
an d the fact of
their
Being, that
they are. Fo r
Badiou the
term ' b e i n ~ s ) risks substantialization;
it is too close to
the t erm ' e n t i t y ~ existant
or
object .
Instead,
Badiou
proposes the term situation
which
he defines
as a
presented
multip)i ;it):::J.pr as
the
place of
taking
place
EE
32
Th e
term i situatioif
is
prior
to
an y distinction
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Infinite Thought
between substances and/or
relations
an d
socovershoth.
S itu ation s in clu de all those flows, properties aspects,
concatenations of events, disparate collective phenomena
bodies,
monstrous
an d virtual, that one
might
want to
e xami ne w it hin an ontology. Th e concept of situation is
also designed to
accommodate anything which
is
regardless
of its modality;
that
is, regardless of whether it is necessary, z
contingent possible, actual potential or virtual- a whim; .a (
supermarket a work of
art
a dream a playground f ight, a
fleet of t rucks, a mine, a s tock prediction a
game
of chess, or
a set of waves.
If Aristotle s fundamental ontological claim is
There
ar e
substances , t he n B ad io u s is
There
ar e s itua tions , or, in
other
words,
There
ar e multiple multiplicities . Th e key
difference
between Badiou s claim
and t ha t
of Aristotle is
that
for Aristotle
each substance
is a unity
that
belongs to a
totality - the
cosmos
-
which is itself a unit y.
Fo r Badiou
there is no uni fied totality
that
encompasses these multiple
multiplicities. Furthermore
there
is no basic or primordial
unity to these multiplicities.
It
is these two aspects of his ontology which, according to
Badiou,
guarantee
its modernity. fo r Badiou the task of
r.nodern. ontology is to b reak with classical ontology s
fundamental u D i t y D f ~ i n g both in t he l at te r s i n g ~ i : /
duaTitf\lIld irlirs totality-:f Leibniz expressed this bel ief of
classical ontology in die formula: What is no t a
being
is no t
a
being. H
However breaking with theclassical
unity
of being is no
simple task for ontology./fhe problem is
that
even if there is
no pr imordi al e quival ence bet we en unity
an d
being, for
B a di ou one must still recognize, following
Lacan that there is
~ q m e oneness - I I y a de l un; T h a t is, although unity is no t
primordli.i), there is some kind of effect of
unity-in
th e
R r ~ s e n t a t i o ~ o f l ~ e i n g . 1 5 Badiou s solut ion to this problem is
to argue thatsituations --:_presented multiplicities - do
have
An
introduction
to Alain Badiou s
philosophy
unity,
? , ~ t
s\Jcb unity is the result of an operation
termed
the
c q Y E . L k - o ~ T h i s
count is what
Badiou
terms the
situation s
structurii
A structure determines
what
belongs
an d
does
no t
belOlig to the situation by counting various multiplicities as
elements:\of
th e situation. An element is a basic
unit
of a
situation. A
structure thereby generates unity
at
th e
level
of
eacli)element of th e s i i l l ~ t i o n : } r : l ~ ? g e n . : r a t e s unity at the
level of the whole s i i u a t i ~ p y
unifyiIlgJhe
r n u l t i p l i 5 ~ i t y ( ) f
elements. This
a statiC
1
-definition of a situation: a
situation is a
p r e s ~ n t e d _ : 1 l u l i l 1 1 i < ; i t y .
. W h e r c ; ~ a : . ; we h :V e rio iCa::-ph ilosophers have often
thought of unity as the fundamental property of Being, for
B ad io u u ni ty is the
ifject J
gLj:ructuratiQu.. and not a
ground origin, or end. Th e consequence of th e u ni ty of
situations b ei ng t he
effect
of an
operation
is
that
a multiple
that
belongs to one
situation
ma y also
belong
to another
s it ua ti on : s it ua ti on s
do not
have mutually
exclusive
iden tities.
Th e operation of th e count-for-oms is not pe rf orme d by
some agent
separate
to the multipl ic ity
of the
situation: in
classical or even relativist ontologies one ca n discern such
an
agent going
under
t he names of God History or Discourse.
Th e
distinction between a situation
a n d j t s structuring
count-for-one
only holds, strictly speaking,within ontology;
t he s it ua ti on is nothing other than
this
o l ? ~ r : t i o n o f
counting-for-one .16 a situation is a
counting-far-one
then Badiou
also has a
dynamic
definition
of
a situation.
Once
he has
both
a dynami as welLis
a ~ ~ . i l l . 1 i c . d a ~ ~ { t l o n ( ) f
a
situation -
the
operation of counting-for-one, an d unified
presented multiplicity - he is able to join his doctrine of
multiplicity to a reworking of H ei degger s ontologi ca l
difference.
Badiou states
that
the ontological difference.stands between
a situation an d the being of
that
situation; as for
Heidegger
this disjointing, in thought of situations from their being
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Infinite Though
allows ontology to unfold.
Unlike Heidegger,
however, the
being
of
a situation is not something
that
only
a poetic
saying can approach: it is, quite simply and
banal ly , the
situation before or rather,
without
the effect
of
the count
for-one; it is
the situation
as a non-uni fied or inconsistent
multiplicity.
After
or with
the
effect
of the count-for-one.sa
situation is a unified or consistent multiplicity.
. In order to understand this distinction) between an
i D r ~ ~ t i ~ t ~ i ; t iI(tiplicity . and a consistent rnultiplicjjy,
consider the si tuation
of
a footbal l team.
The par ticular
team we ~ a v e in.
mind
is a : ~ i r l s h a ~ } , ~ ; ~ , , ; e t
of
unruly players
each
havmg
the ir own
position,
~ r n g t h s
and
weaknesses;
all
of
whom are united, however undisciplined and chaotic
their play, by their belonging to the
team The
Cats . ?
Conside r then the same team from the point of view
of
its
being: it is a
disparate
multiplicity
ofhuman
bodies, each its
own
multiplicity of bones, muscles, nerves, arteries, bile
and
testosterone, each of these sub-e lements in turn a multi
plicity of cells
and
so on, whi ch ,
at
the b ~ r ~ level of their
brute
existence, have
nothing
to do
with that
unity
termed
The Cats . That is, at the level
of
the being of each element
of
the
team
there
is nothing
which
inherently
determines
that it is
an
element of
this
football t eam. Thus. at the
indifferent level
of
being,
the si tuation termed
h ~ Cats is
an
inconsistent and non-unified multiplicity. Granted, the
proper name Cats does have a certain
interpellative
power
in
the Althusscr ian
sense,
but
it
neither
resides
at
nor
generates the
level
of
being for
Badiou the word
neither
murders nor creates the thing, it merely assigns the
thing
a
multiplicity
- a certain
identity.
In
order to understand how Badiou might equat e these
inconsistent multiplicities with being, consider stripping
something
of
all
of
its
properties
to the extent
that
even its
identity
and
uni ty are removed.
Fo r many
philosophers,
parading their commitment to desubstantialization, there
12
n
introduction
to lain Badiou s phdosopkv
would
be nothing left
after
such an operation.
However,
for
Badiou,
what
would be left would simply be
the
being
of
that
something ,
and such being
could only bl
described
as
a n l n c o n s i s . t ~ n t m u l t i p i i c i ~ ~ Not
even
- t ~ r m i e ~ s ~ ~ t t ~ r
would be a c e e p t a D r e , ~ - s i n c e
matter
would have been one
of
the general propert ies we stripped away from
our
some
thing , Badiou s inconsistent multiplicity is therefore
not
to.
be equated with Aristotelian p rime matter ; its actual
status is, moreover, undecidable . Precisely because a
situation provokes the question
What
was there
before
)all
situations?
bu t
provides no possible access to this before
that
is not irremediably compromised by post-situational
terminology
and
operations, it is impossible to speak oLin
anYdixect
way,
With
the
thought of:inconsistent
m ulh:
phci t
Y. 1. it.l.lOU
gh
t t h e r e f o r e t o u c t ~ ~ . s ~ ~ ~ li
Il1i s;
wha-r
Badiou calls, following Lacan, its real J
-_ _. ~ , . ; . f . _
It
is
at
this
point that
we
turn
to a discussion
of Bad
iou s
use
of s e J J h e x ~ by
means
of
which
he gives all this rather
loose metaphysical t alk a solid
and
precise basis.
f V J ~ y set
theory?
Since Aristotle ,
ontology
has been a privi leged sub
discipline
of
philosophy; otherwise known as
the
discourse
on being. Badiou puts forward a radical thesis: if being is
inconsistent multiplicity, then the only
suitable
discourse for
talking
about
it is no longer philosophy but mathematics.
For Badiou, mathematics
is
ontology ,: Mathematicians, un
beknownst to themselves,
do nothing other than
continually
speak
of
or write being. This thesis enables Badiou to
reformulate the classical language
of
ontology being,
relations, qualities in
mathematical
terms: more specifi
cally, those of set
theory
because it is one
of
the foundational
disciplines
of contemporary
mathematics;
any mathematical
proposition
can
be rewritten in the language
of
set theory.
13
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Infinite Thought
In 1 Eire el I'eoenement,
Badiou
sets forth two
doctrines
to
support his adoption of set theory.
The
first,
the doctrine
on
inconsistent multiplicity, is explained in t he p revious
section. The second is
the doctrine
on
the
void.
Together,
these doctrines serve to bridge the gap between set theory,
with its infinity of sets,
and
Badiou's multiplicities of
situations.
Take
the
first doctrine. If the
being of
situations is
inconsistent multiplicity,
what
is required of the language of
such
being?
Simply
that this
language must present
multi
plicity as inconsistent,
that
is, as non-unified. To fulfil
such
a
requirement a
number
of conditions must be me t. First, in
order
to present multipl icity without unity, the multiples
presented
in this
language
cannot be multiples
of individual
things of
any
kind, since this wou ld be to smugg le back in
precisely
what
is in question the being
of
the One.
Consequently,
these multiples
must
also be composed of
multiples themselves composed of multiples, and so OIL
Second,
ontology
cannot
present
its multiples as belonging
to a universe, to
one
all-inclusive
total mult iple
- for that
would be to smuggle back the
One a t
a globallcvel. As such,
ontology s multiples must be boundless; they
cannot
have an
upper limit. The
third condit ion
is that ontology cannot
determine a
single
concept of multiplicity, for that would
also unify its multiplicities and, by so doing , uni fy being .
Set
theory
is
the
formal theory of non-unified
multi
plicities. It eets each of the three conditions outlined
above . First, a set is a
multiple
of multiples called
elements.
However , t he re is no fundamental difference between
elements
and
sets, since every element of a set is itself a
set. Second,
there
is no set of sets; that is,
there
is no ultimate
set
which
includes all the different types of set found in set
theory.
Such
a set
would have
to thereby
include
itself,
which
is expressly forbidden, on pain of paradox, by one of
set
theory's
axioms, that of foundation.
In
set
theory there
An
introduction
to Alain
Badiou s
ihilosophy
is an infinity of infinite types of infinite sets. As for the third
condition,
there is neither definition nor
concept
of a set in
set theory. What there is in its p lace is a fundamental relation
- 'belonging' as well as a series of
variables
and logical
operators,
and
nine
axioms
stat ing how
they may be used
together.
Sets emerge from operations
which
follow these
rules.
The
second doctrine,
which
Badiou
uses to
bridge
the gap
between set theory's infinity of sets and
particular
non
ontological situations, isNs doctrine on 'the void > Like the
doctrine of inconsistent multiplicity.x it is also a doctrine
about
the
nature
of
situations.
Badiou argues
that, in every
situation, there is a beirlg of the 'nothing'.
He
starts by
stating
that whatever is r ecognized as
'something',
or as
existing, in a
situation
is
counted-for-one
n that
situation
an d
vice versa. B y i ~ p l i c a t i o r i
what
is r/oilz'ing ,in a situation
must
go
uncounted. However,
it is
no t
as
though there
is
simply nothing in a
situation which
is uncounted - both the
~ o p e r a t i o n o f the count-lor-one
and
the inconsistent
multiple
which exists before the count are , by def in it ion, uncoun
table.
Moreover,
both a re necessary to the existence of a
situation orprt;.se rtat on;fprecise y
because
they constitute a
.situation as a situ;iTonthey-cannot be
p ~ e s e ~ t e d
within
the
situation itself . _ A ~ ~ s o < ; . s s ~ r y b i i t ~ . ~ g p : i ~ ~ ~ n I ~ 1 2 1 e they
constitute what Badiou terms the
'rultnlng'()r'fhe
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Infinite Thought
An
introduction
to Alain Badiou s
philosopf y
Set
theol)
A set is a unified multiplicity: its clements
ar c n ot
indefinite
an d dispersed; one is able to speak of a single, unified set.
B a di o u r e ad s
l1 E as
saying that multiple
l1 is
counted-for
one as an element of th e set or th e set is th e count-far
one of all those elements l1.
E ac h o f
those elements l1 could
the subset X
x
he set S
Sets ar e
made
up
of
elements. The elements of a set have no
distinguishing quality save t ha t o f
belonging
to it. This is wh y
t he y a re referred to simply as
variables
Y-
both w hen
t he y a re
elements
a nd w he n
t he y a rc
themselves considered
as sets. T he relation of belonging is th e basic relation of set
theory;
it
is written l1 E l1 belongs to or, l1 is
an
element
of th e set
There
is
another relation
in set theory, termed
inclusion, which is
based
entirely on
belonging.
Sets have
subsets , that ar e included in th e sets. A subset is a grouping
o f some o f
a set s elements.
Each of
a
subset s elements
must
belong to th e
initial
set. Take for e xa m pl e t he set 8 which
consists of th e elements l1, y.
ca n be written {, ~ y }
ha s
various
subsets like {o, an d
y}. Each subset
ca n
itself be given a n a me , i n de x ed to a n a rb i tr ar y m ar k. F or
example,
th e
latter
subset
y},
m ig ht b e
called
th e
subset
X. I t s i n cl u si on
in
8 is
written
X
8.
elements
particularities
of th e
situation
ar e
removed or
subtracted
from it. So, for Badiou, every
situation
is ultimately founded
on a void. This is
no t Heidegger s
Ab-grund no r s it some
theological creation ex nihilo.
The void
of a situation is
simply
what is no t there,
b ut
what is necessary for anything
to be
there.
When we turn to set
theory,
it turns out
it
makes
on e
initial
existential claim, that is, it begins by saying that just
on e
set ex is ts . This
particular
set is
subtracted
from th e
conditions
of
every
other set in set
theory:
that of
having
elements. This is th c null-set, a multiple of nothing o r o f th e
void.
20
O n th e sole basis
of
this
s ~ t
u s ~ n g operations
regulated by formal axioms, set t h e o r y \ : i I J f o l c l ~ an
infinity
of
further sets. S et t he or y t h us w ea ve s its sets
ou t
ofa void ,
o ut o f what,
in
a ny o th er situation,
is th e
subtractive suture
to
being o f t h at situation.
In
other words,
we
a l re a dy k no w
that
ontology
connects
to
other
situations
through being
th e
theory of inconsistent multiples. In each an d every non
ontological situation, its inconsistent multiplicity is a void.
Th e
only
possible
presentation
of a
void
in set
theory
is th e
null-set. Thus, t h e s ec on d wa y in which set theory
connects
to situations is
that
it constructs its inconsistent multiples
ou t
of
its presentation of t h e v oi d,
of
t he s u tu r e to
bcing o f
every
situation.v
So much for
th e
general connection between
situations
an d
set
theory s
infinite sets. There is al so a
connection
specific to
each
situation:
Badiou
holds
that
t he s tr uc tu re
of
each
s it ua ti on c an b e w ri tt en as a
type
of set. That is,
leaving
all
of a situation s properties aside an d
considering
o nly the
b as ic r el at io ns w hi ch h ol d
throughout
its multiplicity, on e
ca n
schematize
a situation in
ontology
as a set.
What, t he n, a re sets an d ho w
ar e
they
written?
16
17
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Infinite Thought
be counted and grouped an d
subdivided
in different
manners, resulting in different sets: there is no restriction
on th e n um b er o f
different
sets
they ca n
belong to As
noted
above, this is th e great flexibility of set
theory
once
on e
strips i denti t y a wa y f ro m m ul ti pl ic it y t he re is nothing to
prevent
a multiplicity
from
belonging to
an y
n um be r o f
other
multiplicities
nothing, that
is save its structure
certain types of sets only admit mul ti pl es w it h
certain
structures,
bu t
more
on that later).
If on e compares set theory to classical ontologies indeed
even to
that of
Deleuze, its modernity is
immediate.
It
makes no claims
concerning
th e nature
of
being, no r
c on ce rn in g t he adequation of its
categories
to be ing
It
makes no attempt to anchor its dis co ur se in necessity
through
an
appeal to some ground, w het her etymological,
natural
or historical It does no t
place
itself as
on e
linkage
within
a
larger
unified
machinery
such
as
evolution
or
complexity or chaos . there is a grand philosophical
claim
in
Badiou s
enterprise, it is not made
within th e
discourse of set
theory
itself
b ut
rather holds in th e
identification
of
set theory
as
ontology.
The
basis
of
set
theory is simply a set of axioms The necessity of these
ax io ms h as b ee n tested r at he r t ha n
declared
i nsofar as all
operations mad e on their
basis
must
h av e l og ic al ly
consistent
results
These
results
h av e b ee n
tested through a
century
of
work
within
set t he or y. N i ne a xi oms r e gu l at e t he
operations
an d
th e
existences
w h ic h w ea v e the
tissue
of
set
theory s universe
Fo r
Badiou
these axioms constitute a decision in thought, a
starting
point. The
axioms themselves
of
course are not
pure historical beginnings since they
ar e
the result of a series
of reformulations made over t he first few decades of set
theory: these reformulations were designed to prevent th e
occurrence of
logical inconsistency
within
th e domain
of
set
theory. Rather,
they
mark t h e b e gi n ni n g of
something
ne w
In introduction
to Alain Badiou s
philosophy
in scientific t hought i nas muc h as for
example,
it was no t
possible to conceive
of
two different types
of
infinity on e
larger
than
th e
other, before Cantor s pioneering
work
in set
theory.
Se t
theory
itself comes in a number of varieties: for
e xa mp le , t he re
a re f ou nd at io na l
an d
anti-foundational
types with v ar yi ng n um b er s a n d types of axioms Badiou s
ow n choice is to plump for th e orthodox version of Zermelo
Fraenkel se t
theory,
with its nine axioms. These are
generally called: Extensionality,
Separation,
Power-Set,
Union,
Empty
Set Infinity, F o un d at io n , R ep la ce m en t
an d Choice A n e xp la na ti on of all nine of these axioms
would exceed
th e
range
of
this
presentation, bu t
a quick
sketch
of five of t he n in e
axioms
s h ou ld s he d
some
light
on
ho w t h e u ni ve rs e of set
theory
unfolds
The
first concerns
identity
an d difference th e
axiom
of
extension:
every element
y
of
a set
is also
an
element
of
a
set an d th e inverse is true, then the sets
an d
ar e
indistinguishable an d therefore identical. Consequently, in
set
theory
ontology,
th e
regime
of
i dent it y a nd difference is
founded upon extension, no t quality. T hat is every
difference is localized in a point: for tw o sets to be different
at least
on e
element
of on e of th e
sets m us t n ot belong to
th e
other.
The
ne xt t hre e constructive axioms allow the construc
tion
of a ne w set on th e basis of
a n a lr ea dy
existing set The
axiom of separation
states:
I f
there
exists a set
a
then there
exists a subset
of
ll , all
of
whose elements
y
satisfy th e
formula F.
t
enables a set defined
bv
a formula to be
s e pa ra t ed out from an initial set If on e gives values to th e
variables
o ne could
then, for
example,
sep ara te o ut t he
subset of a ll g r ee n a pp le s
from
th e set of apples green
apples being
th e
formula in this example).
The
power-set
axiom
states
that
all
of th e
subsets
o f an
initial set grouped
together
form another set termed th e
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Infinite Thought
power-set. Tak e for
e xa mp le t he
set { X}. It s
three
elements
can be g r ou p ed i n to
th e
following subsets: {}
{ ~ }
{X} {
{a
X}
an d
X} to
which
must be
added
both
what
is
termed th e maximal
subset
{ l ~
X}
and
by
virtue
of
a
rule explained later
th e null-set {0} Th e power-set
of
{
X} is thus:
{{o } { ~ } {X}
{
{ex
X} X} {ex
X}
{0}}
It is important to note that th e power-set of
an y
set is
always
demonstrably
larger
than th e
initial set.
T hi s m ea ns o ne ca n
always
generate larger
sets ou t
o f a n y
existing set.
Th e
axiom of union states that
all
of th e elements
8
of
th e
elements Y
of
an initial
set o themselves form another
set
termed
th e union-set. Th e
ne w
set is
t hu s t he u ni on
set of t he i ni ti al set o conventionally written ua. It shows
that sets
ar e homogeneously
multiple
when decomposed.
All
th e
axioms
listed so far
presume the
existence of
at
least
on e set bu t
they
do
no t
themselves establish
the
existence of
sets. The axiom of the null-set on th e
other
hand does. It
forms set
theory s
first ontological
commitment.
It states
that
there exi st s a n ul l- se t
an em pty
set to which
no
elements
belong - 0 This null-set is th e initial
point
of existence from
which
all
t he o th er
sets
of
set theory
ar e
unfolded using
th e
constructive axioms.
Fo r
example
from 0
by
th e
operations
prescribed
by th e
axiom
o f th e power-set
on e
ca n
demonstrate
the
existence of its power-set { }
an d then
by repeating the operation further sets
ca n
be unfolded such
as
{0 { } } an d {0 { } {0 {0}}} I t
is
just
such
unfolding
which
constitutes
the
infinity
of
sets.
Each
o f
t hes e ax io ms ha s
profound
consequences for
philosophical problems once one allows
that
set theory is
ontology.
In
order to use set theory to address philosophical
p ro bl em s B ad io u
makes a d is ti nc ti on b et we en o nt ol og y
proper that is t he f or ma l
language of
set t he or y
an d th e
discourse
of
meta-ontology
that
is a translation
of
set theory s
20
An introduction to Alain Badiou s philosophy
axioms
an d
theorems into philosophical terms.
Thus
for every
set-theoretical term there is
an
equivalent in
the
discourse of
philosophy. Fo r example a set is s pok en of in meta-ontology
as a multiplicity a situation or a
presentation .
One of th e
traditional
philosophical problems
to
which
set theory
responds
is t ha t o f t h e r e la ti on s hi p b e tw e en b ei ng
an d l a ng ua g e. A c co r di n g to Badiou this relationship is
concentrated
in t he w ay set theory ties th e existence of sets
t og et he r w it h t he ir
definitions. In
on e
of
th e
first
formula
tions of set theory
that
of
Gottlieb
Frege a set is
defined
as
t he extension of a c on ce pt . T hi s m ea ns that for
an y
well
formed formula in a first order logic which defines a
concept
a set of
elements
exists each
of which
satisfies
th e
forrnula.i? Th a t is t h er e c a n be no sets an d thus
nothing
in
existence for w hi ch t he re is no c on ce pt : e ve ry e xi st in g set
corresponds
to a
concept. Or
whenever
one has
a defined
concept one ca n d irectly d ed uce the
existence
of
a
corresponding multiple.
Thus the
r el a ti on sh ip b e tw e en
l a nguage a nd being
is
on e
of
exact correspondence.
However
Frege s
definition of sets -
and
by
implication
his articulation
of
th e
relationship
b e tw e en l a ng u ag e an d
being -
me t
with a problem. In 1902
Bertrand
Russell
discovered a well-formed formula to which no existent set
could correspond without
introducing
contradiction into
set
theory.s The
formula
is
t he
set
of
al l sets
w hi ch a re no t
members of themselves . Th e contradiction ensues w he n o ne
asks
whether
the
set
o f
elements which
satisfies this
formula
belongs to itself or not. I f it does belong to i ts el f
then
by
definition it d oe s not
an d
if i t does
no t
belong
to
itself
then
it does. This
contradiction
ruins th e consistency of th e
formal language
in which
th e
formula is
made.
Th e
consequence
of th e
paradox
is that it is
no t
true that for
every well-formed formula
a
corresponding multiple
exists.
In order to avoid Russell s
paradox
the axiom of
separation wa s
developed.
It proposes
another relationship
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Infinite Thought
b et we en t he existence
of multiples
an d well-formed for
mulas. Frege s definition
of
that relationship runs
as follows:
Va) [F a a
This proposition
reads: There e xi st s a set
such
that
every
term
a which satisfies t he f or mu la F is an element of that
set. Th e axiom of
s e pa rat i on o n
th e other hand looks like
this:
Va) Vy) [ y E a F y)) y E
t
reads:
f there
ex is ts a set
a then there
exists a
subset of
a
all
of w ho se e le me n ts y
satisfy t he f or mu la
F.
T he
essential difference
between
F r eg e s d e fi ni ti on an d
th e
axiom
of
separation
is
that th e f o rm e r d i re ct ly p ro p os es
an
existence while th e latter is
conditional upon
there
already
being a set in e xi st en ce , a. Th e axiom of
separation
says that
there
is a set
already
in existence,
then
on e
ca n
separate out
on e of its subsets,
whose
elements
validate
t h e f o rm u la F.
Sa y
for example that
th e
formula F is th e
property
rotten
an d on e
wants
to
make
th e judgement Some
apples are
rotten. Via
the axiom of separation,
from
th e
supposed
existence of
th e
set of all
a pp le s, o ne c o ul d s e pa rat e o u t th e
subset
of
rotten
apples.
T he relationship between being an d
language
implied by
t he a xi om of
separation
is therefore no t on e of an exact fit,
bu t rather
on e in
which language
causes
a
split or division
in e xi s te nc e EE,
53).
T he
conclusion Badiou
t hu s d ra ws
from set
theory
for th e traditional philosophical
problem
of
th e r elatio nshi p bet ween l an gu ag e
an d
being
is
that,
a l th o u gh l an g u ag e
bestows
identity
on
being,
being is in
excess
of
l a ng u a ge . T h is is quite clearly a materialist thesis
as befits Badiou s Marxist heritage. In meta-ontological
terms,
th e
axiom
of
separation
states that an undefined
existence
must always
be assumed in an y
definition
of a type
of
multiple. In short, th e very conditions
of
the inscription
of
22
An
introduction
to Alain Badiou s
philosoph
existence in language
require
that existence be in excess of
what the inscriptions define as existing.
So,
what
is
t h e g e ne ra l
result
of Badiou s adoption
of set
theory as
th e
language of being? Quite
simply
that it ha s
nothing
to
sa y about
beings themselves t hi s i s
t h e p r ov in c e
of other discourses such as p hys ics,
anthropology
an d
l i terature. This
is
o ne r ea so n w hy B ad io u
terms set
theory
a
subtractive
o nt ol og y: it s pe ak s of beings
without
reference to
their attributes
or their
identity; it is as if
th e
beings
ontology
speaks of have
ha d
all their qualities
subtracted
from them.
As a result, unlike
Plato an d
Aristotle s ontologies,
there
is
neither cosmos no r p h e no m en a , n e it h er c au se no r
substance.
S et t he or y o nt ol og y
does
n o t p ro po se
a
description
of
t he
furniture of the world ,
no r
does it concern itselfwith carving
reality at the joints . Its
ow n
ontological
c la im s im pl y
amounts to
s ay in g t he re
is a
multiplicity of
multiplicities.
Furthermore,
set
theory
ontology
is
indifferent
to
th e
existence or non-existence of
particular
situations
such
as
t he
world or
you,
th e re ad er : B ad io u writes: w e
ar e
attempting
to think
multiple-presentation
regardless
o time
which
is founded hy intervention), an d s pa ce w hi ch is a
singular construction,
relative to
certain
types of
presenta
tion)
EE, 293 . What set theory
ontology
does, in li eu of
presenting what there is , is present th e
ontological
schemas
of an y
ontological claim;
that
is, it p re se nt s th e
structure
of
what an y situation says exists
ntological
schemas
o
different situations
Although
set
theory ontology
does
no t recognize the
infinite
differentiations
of concrete
situations,
it does
recognize
a
nu mbe r o f differences in th e
structure
of
situations. This
allows
it to
s c he rna t iz e d i ffe re n t concrete situations.
According to Badiou s meta-ontology,
t he re a re
three.basic
s tr uc tu re s w hi ch
ar e
found underpinning e ve ry e x is te nt
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nfinite Thought
situation.
To understand
the dif fe rent ia tion
of
these
structures
it is necessary to
return
to
the axiom
of
the
power-set and
its
meta-ontological equivalents.
The
axiom of the power-set
says that
there
is a set
of
all
the subsets ofan
initial
set, termed
the
power-set. In meta
ontological
terms,
the power-set
is
the state
of a
situation.
Thi s means that
every
multiple
already
counted a s - ~ m e ~ i ;
counted again
at
the
level
of
its
sub-multiples: the s ta te
is
thus
a
second count-for-one. Or , according
to
another of
Badiou s meta-ontological translations,
if a set
schematizes.a,
presentation,
then
its
power-set schematizes the representa
tion
of tha t presentation.v The state
is
made
up
of
all
the
possible
regroupings
of
the elements
of a
situation;
as
such
it
is
the
structure
which
underlies any
representational
or
grouping
mechanism
in
any situation.
\ e
should note
that
as
such
the term s ta te
includes
bu t is i n no way
reducible
to
the
position
of
a
government and
its
administration
in a
political
situation.
Badiou
distinguishes
three
types of
situation:(rtatural,
historical
and neutral.
What makes
them
different
at
a
structural level are
the
types of
multiple which
compose
t h e ~ There a re t hr ee
types
of
multiple:
normal
multiples,
:vhIch
ar; both
presented
by
the s i t u a ~ i o n ~ r : ? l e p r ~ s e n t e d
by
ItS
~ t a t e
(they
are
counted-for-one
twice ;
l,X crescentmultiples,
w h l ~ are o ~ l y represented
by
the
state;
and
singular
multiples,
which only oc cu r
at
the
level
of presentation,
and
which
escape
the
effect
of
the
second
count-for-one.
i
Natural s itua tions are def ined
as
having
no
singular
multiples
all of their multiples a re e ith er
normal or
excrescent, and each
normal
element
in
turn has
normal
elem:nts
E1 ,
146 . Neutral situations
ar e defined
as
having
a mIX of
singular,
normal
and excrescent multiples.?
Historical s ituations are defined
by
their
having
at least
one evental-sitc ;
a
sub-type of singular multiple.
In set
theory terms, a
singular multiple
is an
element
of a set, bu t
4
An introduction to Alain Badiou s
philoso hY
not one of
its subsets.
Since each of
a
set s
subsets is
made
entirely of elements that already
belong
to
the
ini t ia l s et .
the definition
of a
singular multiple
is
that,
first, it is
an
element
of
an initial
set,
and, second, some
of its
own
elements
in
turn
do
no t belong
to
the
initial
set.
It
is
these
foreign elements which ar e
responsible
for
the singulari tv
of
a
singular
multiple.
An
eoental-site
is
an extreme varietv
of
a
singular
multiple:
none
of
an evental-site s
e l e m e n t ~
also belong to
the
initial set.
Leaving l l ; ~ ~ a L s i t u a t i o n s
aside,
le t
us
turn
to
examples
of natural
and historical
situations.
Take,
for
an example of
a
natural situation, the
ecosystem
of a pond.
Ths m ~ I I t i p k s
which it presents
include
individual
fish, tadpoles, reeds
and
stones.
Each
of these elements is also
represented at the
level
of the s ta te of the
situation, which
~ a d i o u
also
q ua li fi es as
the
level of
the knowledges
of a
situation
- these
elements
are
known
elements
of
the situation.
Each element o f an
ecosystem is also
one of the
ecosystem s
subsets,
because each of their clements
also belong in
turn
to ecosystem;
for example
each fish s
eating and breeding
habits belong
to
the
e co sy st em as well as to
each
fish.
These
elements
a re thus normal
multiples.
one examines such
a
s i t ~ a t i ~ n
it
contains
no
singular
terms:
nothing
is
presented
which
not also
represented.
The test of
whether
a
situation
is
natural or not
is
whether
there
is
any element of the
situation
whose content is not also par t o f
the situation
- in
ecology,
every element
of a s ys te m, at
whatever
level of size
or
effect, is
interconnected.
Th e
situation
of
the
ecosystem
of
a
pond
is thus a
natural situation.
Take,
by contrast, as an example
of
a historical
situation,
a c ol le c ti on
of
possible
answers
to
the national is t concern of
what it is to beAustralian.
Some of the multiples presented
in
this
situation
would be
individual
stories
about bronzed
lifesavers,
Anzac
soldiers,
larrikins, whinging
poms,
wow
sers, convicts, explorers,
bushrangers and squatters. One
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Infinite Thought
would also find
Don
Bradman and the Eureka Stockade
belonging
to such a collection. In
the
twenty-first century,
this s itua tion s e lements would also comprise
individual
stories about the
Italian-Australians,
the Irish-Australians,
the Chinese-Australians, the Greek-Australians, the Turk
ish-Australians, and so on. At the level of the state
of
the
situation one
has submultiples such
as
hedonism, mateship,
equality understood
as samencss, the imperat ives fai r go
and she ll be
right
mate , anti-British sentiment, distrust
of
authority,
t he p rivi leging
of
know-how ov er th eory,
Protestantism, and Catholicism, etc.
From both socio-economic and cultural perspectives,
immigrant
groups
a re both p resen ted
and
re-presented.
Their contribution to what it is to be
Australian
is both
known
an d
knowable. For this reason we would argue
that
none of the
presen
ted immigrant multiples
are singular
multiples.
On
the other hand,
constitutively resistant
to
Anglo-Saxon
dreams
of assimilation, the mul tiple
abori
ginals forms
an
evcnral-site; its contents
remain unknown.
Of course, within other situations such as cultural, socio
logical and bureaucratic assessments of Australia,
abori
ginals
a re re-presen ted.
However, these spec ia lized
discourses
are n ot
in
the
position of
furnishing answers
to
the nationalist
question
What is it to be
Australian?
Th e
multiple
aboriginals forms
an
evental-sitc because the
sovereignty of Australia, the immigrant
nation ,
wzsfounded
upon the dispossession
of
indigenous peoples. Their relation
to this
particular
piece
of land
was
crucially
no t
recognized
at the very beginning
of
this entity termed Australia . Any
representation
of the con tent o f the multiple aboriginals
with
reference to what it is to be Australian,
would
thus
cau se t he uni ty of the si tuation to dissolve - in a sense, it
would entail the dissolution ustralia itself is this
constitutive irrepresentability
at the heart o f Australian
nation
alism that makes it a
historical
situation.
n introduction to lain Badiou s jJhilosoply
Badiou uses this division between natural and historical
situations to return
to his basic quest ion:
How
does
the
new
happen
in being? In
our
mythical, pollution-free pond,
though there may be
generation
after
generation
of new
baby fish,
nothing
really
changes:
barr ing another natural
catastrophe the ecosystem will remain in a state of home
ostasis.
In natura l
situations
Ecclesiastes
proverb
holds
true:
there
is nothing new
under the
sun. In historical
s ituations things are quite different. To return to
our
example of
Australian
nationalism, the
inherent
instability
of
the situation (it harbouring an unknowable evental-site in
its mids t) r ende rs it susceptible to wholesale pol it ical
transforma tion.
However , the existence of
an
evental-site in a
situation
does no t guarantee that change will occur. Fo r that
something extra
is required, a
supplement
as
Badiou
says,
which
is
an
v nt \ \
e
are
no t
talking
about any ordinary
event
here, like a birthday or
Australia
beating France in
rugby,
but r athe r
of a
totally disruptive occurrence
which
has no place in the scheme of things as they
currently
are.
Who will say what this event has been or will be for
Australian nationalism
was it the erection by Aboriginal
activists
of
a tent embassy opposite the National Parl iament
in 1972? The occurrence of an event is
completely
unprcdictable.27 There is no
meta-situation
- History
which would programme the
occurrence
ofevents in various
selected .situations,
;,
he
precariousness
of
historical
change
extends further:
no t only must
an
event
occur at
the evental-s ite
of a
situation,
bu t
someone
must
recognize and name that event
as a n event whose
implications concern
the
nature o f
the
entire
situation. Thus it is quite possible tha t an
event occur
in a situation
but that
nothing changes because nobody
recognizes
the
event s
importance
for
the
situation.
This
initial naming
of
the
event
as an event, this decision that it
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InJinite Thought
has transformational consequences for t he e nt ir et y
of
a
situation, is
what
Badiou terms
an
intervention . Th e
intervention is the first moment of a process
of
fundamental
change that
Badiou
terms a fidelity , or a
generic
truth
procedure .
A gener ic
truth
procedure is bas ical ly a praxis
consisting of a series
of
enquiries i nto t he s i tua ti on
made
by
militants
w ho a ct
in fidelity to
th e
event.
Th e
object
of
these
enqui ries is to work ou t ho w to t ra ns fo rm t he
situation
in
line with
what
is revealed by the event s belonging to th e
situation. Fo r e x amp le , w it hi n
t he s i tua ti on
of
ar t
in
th e
early twentieth century, certain artists
launched an enquiry
into the nature
of
sculpture once Picasso s cubist
paintings
ha d
been
recognized as
art .
Th e p ro ce du re m ad e up
s uc h e nq ui ri es is
termed
a
truth
procedure because It
unfolds a ne w multiple: th e
truth of
th e previous
situation.
Here
B ad io u draws up on -
an d
displaces - Hcidegger s
conception of truth
as
th e
presentation of
being.
Th e
ne w
entitv is a
truth
inasmuch as it presents th e
multiple being of
the
previous situation,
stripped
bare
of
an y predicates,
of
an v identitv.
Fo r
example,
take an
ar t
cri ti c in th e
e ar ly t w ent ie t h
century
wh o has
just
recognized
that
a
cubist painting
can,
indeed,
be
called art .
he was called upon to make a
predicative definition of
the
contemporary situation of
ar t
that
is,
if someone
asked hi m What is
an?
- he
would
have
found it impossible to respond - at tha t very moment, for
h ir n, t he d is ru pt iv e e ve nt we no w call cubism was
laying
ba re t he situation
of
ar t
as a
pure
multiplicity
of colours,
forms, materials, proper n a m e s , , > ~ i t l e s sl?aces with nofixed
contours : In
fact,
th e
common accusation that
contemporary
ar t
is ~ r a { u i t l i ~ , indeterminate,
an d
as such
could
be
anything
whatsoever with
a
label
slapped on it stuck in a
gallery; this
v e ry a c cu sa ti on
actually unknowingly strikes
upon
the
very
n at ur e o f
a
ne w
mul ti pl e: it is
anything
whatsoever
w it h r ega rd to established knowledge.
28
An
introduction
to Alain Badiou s
jilli osOpkJi
To
understand how a new multiple -
such
as
mo der n ar t
-
ca n
both exist,
an d
be stripped bare of any predicates (as
such being globally indescribable or
anything
whatsoever
we must
turn
back to Badiou s use
of
set theory.
Generic sets
and
processes
transformation
In order
to think
about
processes
of f unda ment al c hange
within his ontology Badiou
ha d
to work ou t how a multiple,
a set,
ca n
be new.
It
is
at
this
point
that
Badiou
introduces
the
c p \ t r , e ~ ~ i r \ c ~ ) 0 f h ~ s , , ; ~ v r k - what he calls t he
gene:ic
or
indis c:ertllbrhtv . ThIS at once an extremely difficult
concept,
bas;d
on the most innovative
mathematical
procedures, ye t also intuitively graspable. Badiou takes. this
concept from the work
of Paul
Cohen,
an
American
. 1963
mathematician w ho i nve nte d
th e
genenc set
Th e
first
point
to
work ou t
is
what th e
reference
point
could
be within
ontology
for such n o ~ t J t y . Especially since set
theory
ontology
appears to be a s ta tic , flat discourse, with
no
recpgnition of
th e .supposed universality of the situations
of time .and history :) Th e reference p o in t t ur ns ou t to be
/ l ~ n g u a g ~ .
In
set theory, on e c an h av e
models
of set theory
which
are
interpretations that flesh ou t th e bare bones
of
sets
an d
elements by giving values to the
variables
(such as y =
green apples in t he e xa mp le used above . A model
of
set
theory ha s its o wn l an gu ag e in which various formulas
express certain
properties
such as green .
Th e
model itself,
as a structured multiplicity, ca n be treated itse lf as a set.
Cohen t akes as his s t ar t ing point what he terms a grollIl51
model
of set theory.
Badiou
takes this
model
as the
schema
of
a historical situa tion. Each subset of this model satisfies a
property which
ca n be expressed in
the
language used in the
model. That is, every
multiple
found in
t he m od el
ca n be
discerned
using
th e
tools
of
language. A generic set, on the
o ther h and , is a subset that is new insofar as it cannot be
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Infinite Thought
discerned by that language. Fo r every property that
one
formulates,
even t he most general
such
as this
apple
and
this apple
and
this apple
the
generic set has
at
le st
one
clement
which
does no t share that
property. This
makes
sense intuitively:
when
someone tries to tell you about a
new
experience, whether it be
meeting
a person or s ee in g a work
of
ar t, t hey have a lot
of
trouble describing it accurately
and, every
time
you try to help them by suggesting
that
it
might
be a bi t like the
person
x or the filmy,
they
say No
no it s no t like that For every prope rty or concept you
come up
with
to describe this
new
thing, there is
something
in that
new
thing which does not qui te fit. This is all very
well bu t having a set which
one
can t
quite
describe
sounds a bit vague for set theory.
The
innovation
of Paul
Cohen s
work
lay in his d is co ve ry
of
a method of describing
such a multiple without betraying its
indiscernibiluyt
But what about
the
process
of
this
new mult iple
coming
into
being? How does a generic set provide the ontological
schema of processes
of radical
change in political scientific
artistic and
amorous
situations?
Badiou
holds that the
ground
model
schematizes an established historical
situation
before an event arrives. One can define a
concept
of a
generic
subset
within
such a
situation
bu t
one
cannot know
that
it e xi st s - p re ci se ly because it is one
of
those excrescent
multiples
noted above
(which
a re not
presented at
the
level
of
belonging to a
situation). The
generic subset is only
present
at the level
of
inclusion and, unlike all the other
subsets it cannot be known
via
its properties. To show that
a gcneric set
actually
exists
Cohen
d ev el op s a proccdurc
whereby one adds it to the existing ground model as a type
of
supplement, thereby
forming a new set.
Within
this
new
set the generic
multiple
will exist at the level of belonging,
or in meta-ontological terms, presentation. The new
supplemented set p ro vi de s
the
ontological schema
of
a
historical situation
which
has undergone wholesale change.
30
n
introdu tion
lain Badiou s philosopky
Fur thermore , Cohen developed a method
of
making
finite descriptions
of
this
new
supplemented set u si ng only
the resources of the initial set. Cohen termed this procedure
forcing and Badiou
adopts
it as an ontological model of
the
numerous practical enquiries that subjects who act in
f id el it y to
an
event
make
whil e t hey
arc
attempting to
bring about the change entailed by the event.
That
is
although,
say
an
activist working
towards
justice for the
indigenou