Alain Badiou: FrOlll Ontology Politics and Back Sean Bowden

27 Pages·2012·0.65 MB·English

BulletindelaSociiteAmericainedePhilosophiedeLangueFranfaise
Volume 15,Number2,Fall2005
Alain Badiou: FrOlll Ontology to Politics
and Back
Sean Bowden
AreviewessayoEAlainBadiou,BeingandEvent,trans.OliverFeltham(Londonand
NewYork: Continuum, 2005), and Alain Badiou, Metapolitics, trans.Jason Barker
(LondonandNewYork:Verso,2005).
A senseof expectationgreetsthesetwonewtranslationsofthework
of Alain Badiou. For, first of all, it is the magnum opus Being and
Event,l originally published in France in 1988, that provides the
theoreticalbasis forthoseBadiouianpropositionswhichhavealready
provoked both strong interest and uproar in the English speaking
philosophicalworld.Textssuchas,ManifestoforPhilosopf?y,2Deleuze:The
ClamorofBeing,3Ethics:AnEssqy onthe UnderstandingofEvi44 and Saint
PauL· The Foundations of Universalism,5 were all originally published in
Frenchafter1988and,despitetheirclarity,presupposeinmanyways
anunderstandingofthesingularlynovelontologyoutlinedinBeingand
Event. Its translation is thus not only a major contribution to our
contemporaryEnglish speakingphilosophicalscene;italso coincides
withanestablishedandindeedgrowinginterestinBadiou'sworkas a
whole.
Secondly,itisBadiou's"politics"whichhasthusfargenerated
themostattention,dueinnosmallmeasuretohisEthics,whichswims
against most of the currents in contemporary political thought:
liberalism, communitarianism, identity politics and the politics of
differenceandalterity,tonamebutafe~Metapolitief thus arrivesasa
welcomefollowuptotheEthicsandaclarificationofBadiou'spolirical
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commitments.Aswillbe seen,however,Metapoliticsalsopresupposes
andgainsdepthfrom apriorreadingof BeingandEvent.
Apartfromthesheerambitionofthesetwoworks,thenovelty
and scopeof whose claimswill causemuchinkto be spilt,whatwill
strike the reader (with the appropriate patience) is their systematic
coherence. Whatis revealedin these two texts is aunity of thought
that defies any criticism based on a piecemeal approach (such as is
often directed at foreign language philosophers, the publication of
whose translated texts do not follow the same chronology as their
originals). Indeed, theinternal consistencyof Badiou's philosophyis
of suchimportance as towarrantan examinationofit.Whatis here
proposed is thus a schematic overview of Being andEvent--of its
structure,itsmajorargumentsandsomepointsofentryintothetext
followedbyanoutlineofMetapolitics,showinghowitistobeunderstood
as,inBadiou'swords,the"politicalcondition"ofphilosophyrecorded
"inconformitywith the parameters of ontology" (.M72). As willbe
seenfrom thelittlethatcanbediscussedhere,thereis muchinthese
twoworks tokeepus engagedforsometime.Timeenough,perhaps,
forBadiou'ssecondmagnumopus-appropriatelytitledEireetevenement
tome11:Logiquesdesmondes(BeingandEvent11:TheLogics0/ Worlds) and
published in French at the start of 2006-to appear in English
translation.7
BeingandEvent
TheaimofBeingandEventistoestablishtwomajorclaims.Thefirstis
that "ontology = mathematics:' or more precisely, thatwhat can be
said of being-qua-beingcan onlybe said by settheory (BE 13). The
secondandrelatedclaimisthat,insofarasitispuncturedbyan"event"
(Cohen's "proof" of the un-measure of multiple being), being-qua
being can only be said by set theory "as a truth": a "truth" which
philosophy alone can affirm as such, but for which set theory can
nevertheless think the sayable being (BE 18). Badiou sets out to
demonstrate these two theses through aseries of thirty-seven
"meditations." Some of these meditations are "conceptual": they
develop andarrange the concepts andproblemswhichare necessary
forthetrajectoryofthoughtwhichBadiouproposes.Othermeditations
dealwith the mathematical discourse appropriate to establishing the
aboveclaims.Others,finally;taketheformofinterpretationsofcertain
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figures in the bistory of thoughtwho "anticipate" various facets of
Badiou's project. This reviewwillconfineitse~for the mostpart, to
the first two typesof meditation, for the simplereasonthatBadiou's
forays into the bistory of philosophy do not so much advance bis
argument as contextualize it, allowing us to read retrospectively the
bistoricaldevelopmentof,as hewrites, the "mathematicalregulation
ofthe ontologicalquestion" (BE435).
Theveryfirstmeditationsetsoutaconceptualproblemupon
wbichBadiou'sentireprojecthinges: thatoftherelationsbipbetween
the oneand the multiple. Itcanbe unpackedas follows. Onthe one
hand, anypresented concrete thingmustbe one: thisthingis always a
thinge Ontheotherhand,itisgenerallyheldthatpresentationitselfis
multiple: it is only ever a more or less confused manifold that is
synthesized (or "counted as one," as Badiou will say). Given this
situation,ifweaskwhetherbeingisoneormultiple,wefmdourselves
atanimpasse. For,if beingisone,thenthemultiplecannotbelButit
has justbeensaidthatpresentationitselfismultipleandtherecannot
beanyaccesstobeingoutsideofallpresentation.NoW;however,ifwe
affirm that being is multiple, we cannot simultaneously affirm that
being is equivalent to the one. And yet it is clear that there is a
presentationof thismultiple onlyif whatis presentedis one. Badiou
then states that such a deadlock can only be broken by adecision
wbichhedoesnothesitatetomakelTheone,hesays,isnot.Orrather,
theoneisaresult,apresentedmultiplicitywbichhasbeencountedforone.
Such a consistent multiplicityis called a situation, and every situation
musthaveacorrespondingstmcturewbichistheoperatorofthecount
as-one (BE23-24).
The general picture that ensues from this decision is the
following: everyidentifiable "thing" is in situation. Every being is a
consistent multiplicity, counted for one. What is not in situation,
therefore,canonlybequalifiedas no-thing.''Thereare"onlysituations
orconsistentone-multiples,andthesemustallbedownstreamfroma
structuringorcountingoperation(whateverthismayturnouttobe).
Indeed, forBadiou,evenontologyis astructuredsituation. Butnow;
ifitis agreed thatthe oneis onlyevera result,itfollows thatupstream
from any possible count-as-one there must be, and can only be,
inconsistentmultiplicity.Atthelimit,therefore,iftheoneisalwaysalready
aresult,inconsistentmultiplicity-thisno-thingwbichisoutsideofany
situation-mustbe presupposed as the very "stuff" thatis counted
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and henee the pure unqualified beingofanypossible being (BE 24
25).
NoW;sineebeingispresentedineverypresentation,andsinee
everythingthat"is"mustbein situation, this unqualifiedbeingeould
itselfonly''be''insofarasitiseountedforone.Sothen,whateouldthe
strueturebe-thatistosay;whateouldthe seieneebe-of thisbeing
quabeing?Inotherwords,whateouldontologybe?Itmustbeasituation
eapableofpresentingineonsistentmultiplicityasthatfromwhiehevery
"in-situation" thing is eomposed. It must "present presentation" in
general(BE27-28).Theonlywaythatontologyeandothis,following
Badiou,isbyshowinginitsverystrueturethatineonsistentmultiplicity
existsandthateverythingintheontologiealsituationiseomposedout
ofit,without,however,givingthis no-thinganyotherpredieatethan
itspuremultiplicity.WearenowleadtothestatementofBadiou'sfirst
thesis: the axioms of set theory fulfill this apriorieondition of any
possible ontology, sinee they both deelare that the no-thing-what
Badiouwilleallthe void--exists andgive onlyanimplicitdefinitionof
whattheyoperateon: thepuremultiple (BE28-30,52-59).
SohowdoestheZermelo-Fraenkel(ZF)axiomsystemfulfill
theaboveanalyzedpre-ontologiealrequirements?FirstoEall,itreduces
the"one"tothestatusofarelationship:thatofsimplebelonging,written
Inotherwords,everythingwillbe presented,notaeeordingto the
E•
one of a eoneept, but onlyaeeording to its relationof belonging or
=
eounting-for-one.'Something a'willthusonlybepresentedaeeording
toamultipleß,writtena ßor'aisanelementofß'.Seeondly,ZFhas
E
only one type of variable and henee does not distinguish between
"objeets"and"groupsofobjeets;'orbetween"elements"and"sets."
'Tobeanelement'isnotanintrinsiequalityinZF.Itisasimplerelation:
to-be-an-element-oEThus,bytheuniformityofitsvariables,thetheory
eanindieate,withoutdefinition,thatitdoesnotspeakoftheone,and
thatallthatitpresentsintheimplieitnessofits rules are multiples of
multiples: multiples belonging to or presented by other multiples.
Indeed, and thirdly,viathe "axiomof separation," ZF affirms thata
propertyorformulaoflanguagedoesnotdireedypresentanexisting
multiple.Rather,suchapresentationeouldonlyeverbea"separation"
or sub-set of an already presented multiplicity. A property only
determines a multiple under the supposition that there is already a
presented multiple (BE 43-48). Everything thus hinges on the
determination of aninitial multiple. Butas seen above, if the oneis
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only a "result," then there must be, upstream from any count,
inconsistent multiplicity, and it is this which is counted. It appears,
then,thatthisinconsistentmultiple-thevoid-mustbetheabsolutely
initialmultiple.
Buthowcanthevoidhaveitsexistenceassured,andinsucha
waythatontologycanweaveallofitscompositionsfromitalone?As
Badiou says, it is first of all by making this nothing be through the
assumptionof apurepropername: (2) (BE66-67).Thisisthetaskof
the axiom of the void: itpresents or "names" the void asthe setto
which no-thingbelongs. This not to say that the voidis thereby one.
Whatis namedis nottheoneof thevoid,butratherits uniqueness:its
"unicity."Inwhatsenseisthevoidunique?AnotheraxiomofZFteils
usthis.Thisisthe"axiomofextensionality" whichwillfixtherulefor
the difference or sameness of any two multiples whatsoever; thatis,
accordingto the elementswhich belongto each. Thevoid set, then,
having no elements-being the multiple of nothing-can have no
conceivable differentiating mark. But then, if no difference can be
attested,thismeansthatthereisaunicityofthevoid:therecannotbe
"several"voids; thevoidis unique and this is whatis signaledbythe
propername,(2) (BE 67-69).
Sohowarebeingstobewovenfromthisvoid?Whatiscrucial
tothisoperationiswhatisknownasthe"power-setaxiom"or"axiom
ofsubsets."Thisaxiomguaranteesthatifasetexists,anothersetalso
existsthatcountsasoneallthesubsetsofthisfirstset(BE62-63).Ithas
beenseenwhatbelongingmeans:anelement(amultiple) belongstoa
situation (aset) ifitis direcdypresentedand countedfor one bythis
situation.Whatthepowersetgatherstogetherareratherinclusionsofa
given situation. In otherwords, elements direcdy presented by a set
can be re-presented, thatis, grouped into subsets that are said to be
includedintheinitialset.Inclusioniswrittenc: ac ßora isasubset
(apart)ofß.8Thepowersetaxiomthussaysthatifasetaexists,there
alsoexiststhesetofallitssubsets:itspowerset,p(a) (BE81-84).NoW;
letitalsobesaidboththatthevoidisasubsetofanyset-itisuniversally
included-andthatthevoidpossessesasubset,whichisthevoiditself
(BE86).Indeed,itisimpossiblefortheemptysetnottobeuniversally
included. For, foilowing the axiom of extensionality, since the set(2)
has noelements,nothingis markedwhichcoulddenyitsinclusionin
any multiple. Whatis more, for this same reason, since the set (2) is
itself an existent-multiple (foilowingthe axiom of thevoid), (2) must
be a subsetofitself(BE 86-87).
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Thisispreciselythepointfromwhichtheaxiomsorlawsof
beingwillweavetheircompositionsfromthevoid.Theargumentisas
follows: sincethevoidadmitsatleastonesubset-itself-thepower
setaxiom canbeapplied.The setof subsets of thevoid,p(0),is the
settowhicheverythingincludedinthevoidbelongs.Thus,since0 is
included in 0, 0 belongs top(0). This new set,p(0), is thus "our
second existent-multiple in the 'genealogical' framework of the set
theoryaxiomatic.Itiswritten {0} and0 isitssoleelement":0 E {0}
(BE89).No~letus considerthesetofsubsetsof {0},thatisp({0}).
This set exists, since {0} exists. What, then, are the parts of {0}?
Thereis {0}itself,whichisthetotalpart,andthereis0,sincethevoid
isuniversallyincluded.Themultiplep({0})isthus amultiplewith/wo
elements, 0 and {0}. This is, in fact, woven from the void, "the
ontologicalschemaof theTwo,"whichcanbewritten {0,{0}} (BE
92,131-132).No~ sincethis set, {0,{0}},exists,wecanconsiderits
power setP({0,{0}}), which must also exist. Along with the void
which is universallyincluded, its parts are {0} and {0,{0}},... etc.
Thisprocess canobviouslyberepeatedindefinitelyanditisinfactin
this way that our counting numbers-our "natural" or "ordinal"
numbers-canbegenerated:
0=0
1={0} ={O}
2={0,{0}} ={0,1}
3= {0,{0},{0,{0}}} = {0,1,2}...
9
Itcanherebeseenthatatanypointinthechain,tobethenthsuccessor
ofthenameofthevoidistohavenelements.ThisiswhyBadioualso
callstheseordinals"number-nameordinals" (BE 139-140,153).
Whatisatstakehere,letusrecall,isanontology:the"lawsof
being."Soitshouldcomeasno surprisethat,from thisgenerationof
"natural"numbers,allwovenfromthevoidinaccordancewiththeZF
axioms,Badiouwillelaboratehisontologicalconceptof"Nature"asa
network of multiples which are interlockingand exhaustivewithout
remainder. In Badiou's formulation, a multiple a will be said to be
natural(alsocallednormal,ordinalandtransitive)ifeveryelementßof
thissetisalsoasubsetorpart(thatis,ifßE athenßca),andifevery
elementßof aisitself naturalinthisway (thatis,if'YE ßthen'Yc ß).
This doubling of belonging and inclusion guarantees that there is
nothing uncounted or unsecured in natural multiples which might
contradicttheirinternal consistencyand concatenation.Thus, justas
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Nature can never contradict itself, natural multiples remain
homogeneousindissemination.Everynaturalmultipleishereobviously
a"piece"of another(BE123-129).NoW;itisevidentthatthenatural
numbersgeneratedabove follow this formulacion. Fornotonlydoes
the element {0} have 0 as its unique element, since the void is a
universal part, this element 0 is also apart. Furthermore, since the
element0 doesnotpresentanyelement,nothingbelongstoitthatis
notapart. There is thus no obstacle to declaringit to be natural. As
such,thepowersetof {0}-p({0})ortheTwo: {0{0}}-isnatural,
and all of its elements are natural, etc. Thus, ordinal numbers both
formalize the conceptof naturalmultiples---of Nature-within set
theory ontology and are themselves existing natural multiples.
Furthermore,itcanbe saidthatthenameof thevoidis theultimate
naturalelementoratomwhichflunds the entireseries,inthe sensein
which the void is the "smallest" natural multiple. In other words, if
everynaturalmultipleisa"piece"of everyother,thevoidis theonly
naturalmultiple towhichnofurtherelementbelongs (BE 130-140).
Needless tosay;however,inBadiou'sset-theoreticalconcept
of Nature, there can be no possible formulation of Nature in itse!f.
Natureinitselfwouldbeamultiplewhichmakesaoneoutof allthe
ordinals.Butsince this multiplewoulditself have to be anordinalto
make a one out of all the ordinals that belong to it, it would also
belongtoitself. However, sinceno setcanbelongtoitself,Naturein
itselfcanhavenosayablebeing(BE140-141).Indeed,thatnoconsistent
setcanbelongtoitselfisafundamentalpresuppositionof settheory.
ZFcanevenbesaidtohaveariseninresponsetotheparadoxesinduced
byself-belongingsuchas those demonstratedbyRussell (BE40-43).
In fact, another of ZF's axioms, the "axiom of flundation," was
formulatedinorderto exclude self-belonging.This axiom says thata
setis founded ifit has at least one elementwhose elements are not
themselveselementsoftheinitialset,thatis,ifitcontainsanelement
whichhasnomembersincommonwiththeinitialset.Itisthusobvious
thatnosetfoundedinthiswaycanbelongtoitself (BE 185-187).
This last pointleads Badiou to examine a further problem,
evenif he does not setitup in quite this way. It has been seen that
there cannotbea setof allsetswhichwouldgovernthe totalcount.
Yetthis does notinanywaydispensewid1.thetaskof examiningthe
generaloperationof the count. For,because the oneis not, because
thecount-as-oneisonlyanoperation,somethingalwaysescapesthecount-
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as-oneandtherebythreatenstoruinconsistency.This"something"is
nothingotherthanthecountitse!f,andthisistrueofnaturalasmuchas
non-naturalsituations (BE93-94). Inotherwords,becausethe"one"
is only an operational result, if the count-as-one or structure is not
itself countedforone,itisimpossibletoverifythat'thereisOneness'
is also valid for the counting operation. "The consistency of
presentationthusrequiresthatallstructurebedoubkdbyametastructure
which secures the former against any fixation of the void," that is,
againstanyinconsistency(BE93-94).Thismetastructureofastructured
set-what Badiou also calls the state ofthe situation--is precisely the
powersetwhichcountsas oneallof theinitialset'sparts.Thepower
setcountsallofthepossibleinternalcon1positionsoftheelementsof
theinitialsetup toandincludingthe"totalpart": thecompositionof
elementsthatistheinitialset(BE 98).
This is allweil and good, butwhatif wewere dealingwith
infinitemultiples?Whatcouldthecountoftheinternalcompositions
ofaninfinitemultiplelooklike?Thisisarealandgeneralproblem,for
notonlyisNature(sincethemoderns) saidtobeinfinite,presentation
itsel~ even of finite multiples,is essentialfyinfinite. In otherwords, in
set-theoryontologythefiniteisitselfderivedfromtheinfinite,forthe
reasonthattheindefinitesuccessionoffinitenaturalmultiplesneedsthe
infinite in order to qualify it as the one-multiple that itis; thatis, in
ordertoform-oneoutofallofitstermsasfinite(BE,159-160).10This
ispreciselywhatthe"axiomofinfinity" declares:thereexistsaninfinite
limitordinal,written000, suchthatforalla,ifabelongs to000andifa is
notvoid,thena isafinite,naturalsuccessorordinal(BE154-159).And
whatis more, since the one is not, there cannotbe anyone-infinite
beingnamed00,butonlynumerousinfinitemultiples.Indeed,wecan
0
(andmust)generate,notonlyinfinitesuccessorordinalssuchthat00 E
0
Oll' for example, but alsoinfinite limitordinals such that 00, Oll'...00n'
0
000+1•••E OOOX)•••E OOCJ})CJ})'etc.(BE275-277).Iftheoneisnot,presentation
essentiaily concerns an infinite number of infinite multiples. The
questionthusremains:whatcouldthepowersetofaninfinitemultiple
looklike?
The more precise question that Badiou asks is in fact the
foilowing:isthepower-setp(ooJ-thatistosay,thecount-as-oneofall
possiblesub-setsoftheseriesoffinitenaturalnumbers,sufficientfor
a complete numerical description of the void-less geometrical
continuum--equivalenttoOll'thesmallestinfinitenaturalmultiplewhich
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BADIOU:FROMONTOLOGYTOPOLITICS
directly succeeds and counts-as-one (Oo? This is Cantor's famous
"continuumhypothesis"(BE295).Theimportanceofthishypothesis
isthat,if true,wewouldhavea"naturalmeasure"forthegeometrical
orphysicalcontinuum.Orinotherwords,wewouldhaveaquantitative
knowledge of being-qua-being. For, if the continuum could be
numericallymeasured, everymultiple couldbequantitativelysecured
therein.The"greatquestion"ofBadiou'sset-theoryontologyisthus:
isthereanessential"numerosity" ofbeing(BE265)?Theansweris,as
we shallsee: we possess anaturalmeasuringscale (the successionof
number-name ordinals), butitis impossible to determinewhere, on
this scale, the set of parts of is situated (BE 277-278). Or more
(00
precisely,foilowingtheworkofCohenandEaston,itappearsthatitis
deductivelyacceptabletopositthatp((OJis equalto or(O(Cl)~ ,or
(0347'
whatever otherinfinite cardinalwe should care to choose.11 InBther
words,theirwork"establishesthequasi-totalerrancyoftheexcessof
the state over the situation. Itis as though, between the structurein
whichtheimmediacyofbelongingisdelivered,andthemetastructure
which counts as one the parts and regulates the inclusions, a chasm
opens,whosefillingindependssolelyuponaconceptlesschoice"(BE
280).
This"un-measure"of thecontinuum,insofarasitthreatens
the countorconsistencyof thedeploymentofinconsistentbeing,is
whatBadioucallsthe"impasseofontology" (BE279,281).However,
itispreciselyinthis"un-measure"or"errancy" thatthedoubletaskof
Badiou's projectinBeingandEventfinds its pointof intersection. For
here,onthesideofbeing,itbecomesnecessarytothink"what-is-not
being-qua-being":tothinktheevent(alongwithitsconceptualcorrelates,
the subjectand truth). Whyis this thought"necessary"?Itis necessary
insofaras,facedwiththeimpasseofontologyandworkingwithinthe
shadow of the problem of the one and the multiple, these three
philosophicalconceptswillallowus onceagaintoairnatthethought
of inconsistent being qua "one"-being. Of course, because these
conceptsarephilosophical.,thethoughtofbeingqua"one"-beingcan
nolongerunfoldinstrictimmanencetoontologyanditsaxioms.The
thoughtof being-qua-being--of ontology-willratherbeconceived
of as an ongoingpracticalaffairor"truthprocedure" (BE284-285).
Andindeed,ifitisthecasethattheresolutionoftheimpasseofbeing
requires a"conceptless choice" tobemadeandthen"verified;'then
theconceptsofevent,subjectandtruthseemparticularlyweiladapted
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for thinkingthis task. Nevertheless,followingBadiou,thethoughtof
these three philosophicalconceptswillremain "homogeneous"with
the thoughtof beingingeneral,inasmuch as aparticularorientation
(thegenericorientation)withinset-theoryontologycanthir.Lkthesort
ofbeing-thatis,thesortofmultiples-which"correspond"tothese
notions.
So letus look at these concepts in more detail. First of all,
then,whatisanevent?Speakingconceptuall)T,aneventisanunpredictable
occurrence, something that comes to pass which disrupts the usual
wayinwhichthingsarecountedorgroupedtogether,therebyrevealing
the essentialinconsistencyof the situation.Theworkof Eastonand
Cohen-theabovementioned"proof"oftheun-measureofbeing
canthusbesaidtoconstitutesuchaneventindiehistoricaldevelopment
ofsettheoryafterCantor.Speakingontologically-thatis,fromwithin
thespacecircumscribedbytheaxioms of settheory-theeventisan
unfoundedmultiple(orrather,self-foundedmultiple:itbelongstoitself)
which supplements the situationfor whichitis an event. Itis a self
founding "supernumerary" something whose place cannot be
recognizedina situationeventhoughitcancome tobelongtoorbe
countedwithinthatsituation,givingthereby,aswillbeseen,the"truth"
ofsaidsituation(BE342).Beingself-foundingandviolatingtheaxiom
of foundation, the event can have no sayable being (BE 189-190).
Events in general would thus be completely foreign to ontology if
they did not, however, have a "site" within the situations for which
they are events: what Badiou calls the "evental site." This site is the
"foundational multiple": that multiple which is presented in a given
situation,butwhoseownelements arenotthemselvespresented (BE
175). It is easy to see why an event could only take place at such a
point.Foritisonlyatsuchapointthatsomethingmightappearwhich,
while not previously counted within the situation (remember: the
elements of a foundational multiple are not themselves presented),
needs tobecountedtherein, since,as foundational, this "something"
"detainsinitsmultiple-beingallthecommontraitsofthecollectivein
question" (BE17).Giventhesetwoaspectsoftheevent,Badiouthus
terms"eventofthesiteX amultiplesuchthatitiscomposedof,ontheonehand,
elementsofthesite,andontheotherhand,itselt...Theeventisaone-multiple
madeupof,ontheonehand,allthemultipleswhichbelongtoitssite,
andontheotherhand,the eventitself" (BE179).
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