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Infinite ThoughtTruth and the Return toPhilosophy

ALAIN BADIOU

Translated and edited byOliver Feltham and Justin Clemens


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ContinuumThe Tower BuildingI I York RoadLondon, SE I 7 ~ www.continuumbooks.com

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Editorial material and selection Oliver Feltharn and Justin ClemensPhilosophy andDesire, Philosophy and Film, Philosophy and" thewar againstterrorism" Alain BadiouPhilosophy andArt, and The Definition of Philosophy Seuil (from Conditions,1992)Philosophy andthe Deathof Communism Editions de l'Aube (from D'undesastre obscur, 1998)English language translations: 'Philosophy and Truth' Pli; 'Philosophyand Politices' RadicalPhilosophy; 'Philosophy and Psychoanalysis' (!:')Ana{ysis; all other English language translations ContinuumReprinted 2003This paperback edition published 2004 by ContinuumAll rights reserved. No part of this publication may be reproduced ortransmitted in any form or by any means, electronic or mechanicalincluding photocopying, recording or any information storage or retrievalsystem, without prior permission in writing from the publishers.British Library Oatalcgufng-dn-Publicarlon DataA catalogue record for this book is available from the British LibraryISB:\" 0-8264-6724-5 (Hardback)

0-8264-7320-2 (Paperback)

Typeset by BookEns Ltd, Royston, Herts.Printed and bound by in Great Britain by The Bath Press, Bath

Contents

An introduction to Alain Badiou's philosophyI Phi losophy and desire2 Philosophy and t ru th3 Philosophy and politics4- Philosophy and psychoanalysis5 Philosophy and ar t6 Philosophy and cinema7 Philosophy and the 'death of communism'8 Philosophy and the 'war againstterrorism'

9 The definition of philosophy10 Ontology and politics: an interview with

Alain BadiouIndex of names

v

3958697991109126141165

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An introduction to AlainBadiou's philosophyAlain Badiou is one of France's foremost living philosophers.Yet recognition of the force and originality of his work in theEnglish-speaking world has been slow to come, perhapsbecause it is difficult to assimilate his work within theestablished categories of 'contemporary French philosophy'.However, such recognition is now gathering momentum. Nofewer than six translations of his major works, twocollections of his essays, and one monograph on his workare cur rent ly in press. ' Th e first English-language conference devoted to his work was held in May 2002 atC ardi ff, a c ri ti ca l introduction to his work has appea red,and three translations of his w or ks Ethics, Deleuze, andManifesto for Philosophy - are already on the shelves.f

Th e present volume aims to provide a b ri ef, a cc es si bl eintroduction to the diversity and power of Badiou's thought,c ol le ct in g a series of conference papers and essays. Th eopening text sets the s cen e, g iv in g a polemical overview ofth e state of philosophy in relation to the contemporaryworld. Th e second chapter gives a general overview, via thecategories of ethics and truth, of Badiou's model offundamental change in the domains of art, love, politics


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Infinite Thoughtand science - philosophy's four 'conditions' . The followingchapters present specific applications of his central conception of philosophy as an exercise of thought conditioned bysuch changes in ar t (Chapters 5 and 6 on poetry andcinema), love (Chapter 4 on psychoana lysis) , politics(Chapter 3) and science. Since Badiou's work in relat ionto science is mainly found in the huge tome L' E tre etI'eoenement (Being and Event) we chose to sketch the latter'sargument in the introduction. Chapters 7 and 8 exemplifya return to one of philosophy's classical roles: the analyticaldenunciation of ideology, Badiou attacking first the 'war onterrorism' and then the 'death of communism'. Thepenultimate chapter sets ou t Badiou's doctrine on philosophy in relation to its condi tions, and th en the collectioncloses with an interview with Badiou in which he explainsand reconsiders some of his positions.

In our introduction we identify one of the manners inwhich Badiou's philosophy differs from the contemporaryFrench philosophy known as poststructuralism: its treatment of the question of the subject . We then engage in along, at times difficult, bu t necessary exegesis of Badiou's settheory ontology; nece ssary since it grounds his entiredoctrine, and not particularly long in relat ion to its matter;Being and Event comprises over 500 pages in t he F renchedit ion . At eve ry point we have attempted to render thetechnical detai ls in as clear a fashion as possible, yet withoutundue distortion.I f the prospective reader wishes to skip over the moreabstruse discussions offered in the introduction, he or sheshould feel absolutely free to do so - for Badiou is still hisown best exegete. He effectively tries to speak to those whodo not spend their lives in professional institutions, but a ctand think in ways that usually exceed or are beneath notice.As Badiou himself puts it: 'Philosophy privi leges nolanguage, not even t he one it is writ ten in. '

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An introduction to Alain Badiou's philosophyBadiou's question

Badiou is neither a po stst ru ct ur al ist n or an ana lyt icphilosopher, and for one major reason: there is a quest ionwhich drives his thought, especially in his magnum opus,L'Etre et l'eoenement. Thi s que st ion is foreign to bothpoststructuralism and analytic phi losophy - in fact not onlyforeign, bu t unwelcome. I t is this question that governs thepeculiarity of Badiou' s t ra jectory an d the attendantdifficulties of his thought.

In the introduction to L'Etre et l'ivenement Badiou seizesupon an exchange between Jacques-Alain Miller andJacques Lacan dur ing the famous Seminar XI.4 Miller,without blinking, asks Laca n, the grand theorist of thebarred subject, 'What is your ontology?'5 For Badiou this isa crucial moment, for it reveals a fundamental difficulty one that many argue Lacan never solved, even with hisloopy 1970s recourses to knot theory. The difficulty is tha t ofreconciling a modern doctrine of the subject (such as that ofpsychoanalysis) with an ontology. Hence Badiou's guidingquestion: How can a modern doctrine of the subject be reconciledwith an ontology?

But what exactly does Badiou understand by a 'moderndoctrine of the subject'? Badiou takes it as g iven that in thecontemporary world the subject can no longer be theorizedas the self-identical substance that underlies change, nor asthe product of reflection, nor as the correlate of an object."This set of negative definit ions is all very famil iar to a readerof poststructuralism. Surely one could object that poststructuralism has developed a modern doctrine of thesubject?

The problem with poststructuralism is that exactly thesame set of negative definitions serves to delimit its implicitontology (whether of desire or difference): there are no selfidentical substances, there are no stable products of

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Infinite Thou/;htreflection, an d since there are no s table objects there can beno correlates of such objects. Thus in poststrucruralism thereis no distinction between the general field of ontology and atheory of the subject; there is no tension between the beingof the subject and being in general.

Where Bad iou sees an essential question for modernphilosophy, then, poststructuralism sees nothing. For manythis lack of distinction between the being of the subject andthe being of everything else would appear to be a virtue; theprivilege of the rational animal is finally removed in favourof a less anthropocentric ontology. There is, however, aprice to be paid for lumping the subject together withwhatever else is usual ly recognized in an ontology.Poststructuralism typically encounters a number of problems in its theory of the subject. Funnily enough, theseproblems are quite clearly inherited From th e veryphilosophical tradition whose 'death' poststructuralisrngleefully proclaims. There was enough lite left in the corpseto pass something on -- and wha t it passed on were the twofundamental problems in the thought of the subject.

The, first ;)roblem i that of identity; the second, problem,that o ( a g e ~ i Y " ' the mind-body problem derIves for' the mostpart from the former, an d the free will versus determinismdebate f rom the latter. Poststructuralists have concentratedalmost exclusively on a critique of the first problem, arguingthat there is no solution to the problem of the identity of thesubject because the subject has no substantial identity: theillusion of an underlying identity is produced by the veryrepresentational mechanism employed by the subject in itseffort to grasp its own identity. The same line of argument isalso applied to the identity ofany ent it y t hu s i nc ludi ng t hesubject within the domain of a general ontology. Fo rexample, in his introduction to a collection of PhilippeLacoue-Labarrhe's essays, Derrida identifies the subjectwith the self-(de )constituting rnovemen t of th e text; the

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An introduction to Alain Badiou's philosopkvsubject is nothing o th er t ha n a perpetual movement oftranslation." This brings the subject within the ambit o f hismuch-maligned bu t fateful early ontological claim: 'There isno ou t sidc- text.' The conseq uence of this move, of thismerger of the subject with a general ontology within thecontext of a general critique of identity an d representation,is the emergence of a pr ob lem with t he differentiation ofsubjects. How can one sub ject be differentiated fromanother without recourse to some sort of definable identity?As for agency - philosophy's second fundamental

problem in the thought of the subject - the consequenceof poststructuralisrri's almost exclusive concentration on thefirst problem has been that the critics of poststructuralismhave h ad an easy pitch: all they have ha d to do is to accusethe poststructuralists of robbi ng t he sub ject of agency: ifthere is no self-identical subject, then what is the ground forautonomous rational action? This is what lies behind theinfamous jibe that poststructuralism leads down a slipperyslope to apoliticism.

When poststructuralists do engage wi th the pr ob lem ofagency they again meet with difficulties, an d again preciselybecause they merge t he ir t heory of the subject with theirgeneral ontology. Fo r example, in his middl e per iodFoucaul t argued that networks of disciplinary power no tonl y r each i nt o th e mos t intimate spaces of the subject, bu tactually produce what we call subjects." However, Foucaultalso said that power produces resistance. His problem thenbecame t ha t o f accounting for the source of such resistance.I f the sub ject - r ight down to its most intimate desires,actions and thoughts - is constituted by power, then howcan it be the source of independent resistance? Fo r such apoint of agency to exist , Foucault needs some space whichhas no t been completely constituted by power, or a complexdoctrine on the relat ionship be tween resistance an dindependence. However, he has neither. In his later work,

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Infinite Thoughthe deals with this problem by assigning agency to thosesubjects who resist power by means of an aesthetic project ofself-authoring. Again, the source of such privileged agency why do some subj ects shape themselves aga inst the grainand not others? - is not explained.

What does Badiou do when faced with these twofundamental problems of identity and agency? First, Badiourecognizes a d is ti nct ion between the genera l domain ofontology and the theory of the subject. He does not mergethe one into the other; rather, the tension between the twodrives his investigations. Second, when it comes to the twoproblems, Badiou does the exact oppos ite to the posts trueturalists: he defers the problem of identity, leaving a directtreatment of it for the unpublished companion volume toBeing and Event, whi le he concentrates on the problem ofagency.9

For Bad iou, t he que st ion of agencY'is not so much aquestion of how a subject can initiate an action in anautonomous manner but rather how a subject emergesthrough 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 thatprovIde eVIdence of agency for Badiou. It is rather thoseextraordinary decisions and actions which isolate'lan actorfrom their context , those actions which show that a humancan actually be a free agent that supports new chains ofactions and reactions. .EQF this reason, .not every human

. b ~ i n g is always a subject;' yet some human beings becomesubjects; those who act InjiJeHlj)tQ a chance encounter withan 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 intheir situation - however foreign and abnormal - does infact belong to the situation and thus cannot be overlooked.Badiou marks the disruptive abnormality of such an eventby stating that whether it belongs to a situation or no t is,

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An introduction to Alain Badiou'sphilosopkystrictly undecidable on the basis of.estahlished knowledge,Moreover, the subject, as born of a decision.ds not limited tothe recognition of t h e ' \ ) ~ : ' c \ l ' h ~ n c e of an event, bu t extendsinto a prolonged investigation pC the consequences of sucha q e , v ~ n t .. T N 0vestigation is not a passive, scholarly affair;it entails not only the active transformation of the situationi n ~ F l i c h the event occurs but also the active transformationof 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 ofsubjectivization. - ' . '

For example, when two people [ i l l in love, their 'meeting'- whether that meeting be their first hours together, or thelength of their entire courtship - forms an event for them inrelation to which they change their lives. This certainly doesnot mean that their lives are simply going to be the.,better,for it; on the contrary, love may involve d e b t , ~ l i e ~ a t e dfriends, and rupture with one's family. The: point is that lovechanges their relation to the world i ~ r ~ ~ o ~ ~ b l y : ' Thedur at io n o f the lovers' relationship depends upon theirfidel ity to that event and how they change according towhat they discover through their love. In th e rea lm 9f'science the most obvious exal11ple of an event is theCopernican revolution, the e ~ l s ~ i I l g s u b j e c t ~ b e i n g thosescientists who worked within its wake contributing to thefield we now name 'modern physics'.

Th e consequence of such a definit ion of the subject seemsto be that only brilliant scientists, modern masters, seasonedmilitants andcommitted lovers are adIriitte'a into rhe fold. Al i t t l e ~ n f a i ~ , p e r h ; l p ' ~ ? Is Badiou's definition of the subjectexclusive or elitist? On the one side, you have human beings,nothing much distinguishing them from animals in theirpursuit of their interests, and t hen , on the other side, vou- 1 1 a ~ c C the ne;-er i te or fatttJful ~ ~ ~ ' t h i shas a dangerous ring, and one could be forgiven forcomparing it at first g lance to Mormon doctrine. However-

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infinite Thoughtand this is crucial - there is no predestination in Badiou'saccount. There is nothing o ther than chance encountersbetween particular humans and particular events; aridsubjects may be born ou t of such encounters. There is nohigher order which prescribes who will encounter an eventand decide to ac t in relation to it. There is only chance.Furthermore, there is no simple distinction between subjectsand humans. I I Some humans become subjects, bu t onlysome of the t ime, and often they break the ir fidelity to anevent and thus lose their subjecthood.

Thus, Badiou displaces the problem of agency from thelevel of the human to the level of being. That is, his problemis no longer tha t o fhow an individual subject initiates a newchain of actions, since for h im the subject only e I ! l e r g ~ s inthe course of such a chain of act ions. His problem isaccounting for how an existing situation - given that being,for Bad iou, is nothing other than multiple situations - canbe disrupted and transformed by such a chain of actions.This displacement of the problem of agency allows Badiouto avoid positing some mysterious autonomous agent withineach human such as ' free will'. However , the direct andunavoidable consequence of the displacement is that theproblem of agency becomes the ancient philosophicalproblem of how the new occurs in being.

I t is no coincidence that Badiou's quest ion - Wha; is thecompatibility of a sub ject with a general ontology? - leadsdirectly to this venerable philosophical problem, since it isthis very problem which also underlies Badiou's early work,Theorie du sujet.r? In that work, Badiou's so lut ion was todevelop a complex poststructuralist remodelling of theHegelian dialectic. In L'Etre et l'eoenement, Badiou's solutionis simply}o , ~ s ~ ~ ~ t ! d ; ~ t ' ' e ~ T e n t . : happen', events withoutdirectly assignal:Sle causes which disrupt the order ofestablished situations. If decisions are taken by subjects towork out the consequences of such events, new situations

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An introduction to Alain Badiou's philosophyemerge as a result of their work. Such events d 9 , ~ ? ! t ) ( ) r . I " ,part of 'what is', and so they do no t fall under the purview ofBadiou's general.ontology. Thus the r 1 1 , ; ~ ! ~ ) ~ ~ _ ~ ~ ~ t w e . s . r : r : . . , t ~ ebeing of ~ h subject and 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._theoccurrence of an eventand the decision of a subject toactjnfidelitv to tha t event .WI;at, then, is this 'general domain' of Badiou's ontology?

A1adem ontology: being as multiple multiplicitiesAs a lready mentioned, there are two major traditions that

' ~ ~ i i o x a relation to ontology in late twentieth-centuryphilosophy: the analytic tradition and the post-Heideggerean tradition. The analvtic tradition either foreclosesontology in favour of epistem;lOgy)or reduces ontology toa property of theories.P The post-Heideggerean traditionperpe tual ly announces the end of fundamental ontology,while basing this pronouncement on its own fundamentalontology of desire or difference.Despite his rejection of their conclusions, Badiou does no tsimpfy dismiss the claims of these traditions. On the contrary,Badiou takes his starting point from both traditions: th econcept of 'situation' from vVittgenstein and the idea of the'ontological difference' from Heidegger. He then forges anew ontology within the furnace of their critiques ofontology.Heidegger formulates the ontolog ical d if fe rence as thedifference between Being and.beings; (hat is, the differencebetween i f l d i ~ l d ~ - a l heings and the fact of their Being, thatthey are. For 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 definesas a 'presented multip)i(;it):::J.pr as the 'place of taking place'(EE, 32). Th e term i'situatioif is prior to any distinction

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Infinite Thoughtbetween substances and/or relations and .. socovershoth.Situations include all those flows, properties, aspects,concatenations of events, disparate collective phenomena,bodies, monstrous and virtual, that one might want toexamine within an ontology. The concept of 'situation' isalso designed to accommodate anything which is, regardlessof its modality; that is, regardless of whether it is necessary, zcontingent, possible, actual, potential, or virtual- a whim; .a ('supermarket, a work of art, a dream, a playground f ight, afleet of t rucks, a mine, a s tock prediction, a game of chess, ora set of waves.If Aristotle's fundamental ontological claim is 'There aresubstances', then Badiou's is 'There are s itua tions' , or, in

other words, 'There are multiple multiplicities'. The keydifference between Badiou's claim and t ha t of Aristotle isthat for Aristotle each substance is a unity that belongs to atotality - the cosmos - which is itself a unit y. For Badiou,there is no uni fied totality that encompasses these multiplemultiplicities. Furthermore, there is no basic or primordialunity to these multiplicities.It is these two aspects of his ontology which, according toBadiou, guarantee its modernity. fo r Badiou, the task ofr.nodern. ontology is to b reak with classical ontology's

fundamental u D i t y D f 9 ~ i n g both in the lat ter 's i n g ~ " , i : /duaTitf\lIld irlirs totality-:fLeibniz expressed this belief ofclassical ontology in die formula: 'What is not a being is nota being.'HHowever, breaking with theclassical unity of being is nosimple task for ontology./fhe problem is that even if there isno primordial equivalence between unity and being, forBadiou one must still recognize, following Lacan, that there is~ q m e oneness - 'I I y a de l'un;' That is, although unity is notprimordli.i), there is ." some kind of effect of unity-in the

R r ~ s e n t a t i o ~ o f l ~ e i n g . 1 5 Badiou's solution to this problem isto argue thatsituations --:_presented multiplicities - do have

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An introduction to Alain Badiou's philosophyunity, ! ? , ~ 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'sstructurii) A structure determines what belongs and does notbelOlig to the situation by counting various multiplicities aselements:\of the situation. An element is a basic unit of asituation. A structure thereby generates unity at the level ofeacli)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 thelevel 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 ( ) felements. This i : ~ ' 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 oftenthought of unity as the fundamental property of Being, forBadiou uni ty is the ifject"J gLj:ructuratiQu.. and not aground, origin, or end. The consequence of th e uni ty ofsituations being the effect of an operation is that a multiplethat belongs to one situation may also belong to anothers ituation: s ituations do not have mutually exclusiveiden tities.The operation of the count-for-oms is not performed bysome agent separate to the multipl ic ity of the situation: inclassical or even relativist ontologies one can discern such an

agent, going under the names of God, History, or Discourse.The distinction between a situation andjts structuringcount-for-one only holds, strictly speaking,within ontology;t he s it ua ti on is "nothing other "than this " o l ? ~ r 9 : t i o n o f'counting-for-one'.16 If 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 asituation - the operation of counting-for-one, and unifiedpresented multiplicity - he is able to join his doctrine ofmultiplicity to a reworking of Heidegger's ontologicaldifference.Badiou states that the ontological difference.stands betweena situation and 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, thebeing of a situation is not something that only a poeticsaying can approach: it is, quite simply and banal ly , thesituation 'before ' or rather, without the effect of the count for-one; it is the situation as a non-uni fied or inconsistentmultiplicity. 'After' or with the effect of the count-for-one.sasituation is a unified or consistent multiplicity. '. In order to understand this distinction) between ani . D r ~ ) ~ t i ~ t ~ i ; t 'm'iI(tiplicity . and a consistent rnultiplicjjy,consider the si tuation of a footbal l team. The par ticularteam we ~ a v e in. mind is a : ~ i r l s h a ~ } , ! ~ ; ~ , , ; e t of unruly playerseach havmg the ir own position, ~ r e n g t h s and weaknesses;all of w hom are united, however undisciplined and chaotictheir play, by their belonging to the team 'The Cats".'?Conside r then the same team from the point of view of itsbeing: it is a disparate multiplicity ofhuman bodies, each itsown multiplicity of bones, muscles, nerves, arteries, bile andtestosterone, each of these sub-e lements in turn a multiplicity of cells and so on, which , at the b ~ r ~ level of theirbrute existence, have nothing to do with that unity termed'The Cats'. That is, at the level of the being of each elementof the team there is nothing which inherently determinesthat it is an element of this football t eam. Thus. at theindifferent level of being, the si tuation termed T h Cats' isan inconsistent and non-unified multiplicity. Granted, theproper name 'Cats ' does have a certain interpellative powerin the Althusscr ian sense, but it neither resides at norgenerates the level of being for Badiou the word neithermurders nor creates the thing, it merely assigns the 'thing' a multiplicity - a certain identity.

In order to understand how Badiou might equat e theseinconsistent multiplicities with being, consider strippingsomething of all of its properties to the extent that even itsidentity and uni ty are removed. Fo r many philosophers,parading their commitment to desubstantialization, there

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An introduction to Alain Badiou's phdosopkvwould be nothing left after such an operation. However, forBadiou, what would be left would simply be the being ofthat 'something', and such being could only bl' described asa 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 ofthe general propert ies we stripped away from our 'something', Badiou's 'inconsistent multiplicity' is therefore not to.be equated with Aristotelian ' pr ime matter '; its 'actual"status is, moreover, 'undecidable'. Precisely because asituation provokes the question 'What was there before )allsituations?' bu t provides no possible access to this 'before'that is not irremediably compromised by post-situationalterminology and operations, it is impossible to speak oLinanYdixect way, With the thought of:inconsistent m'ulh:''phci tY.'1.,it.l.lOUgh t t h e r e f o r e t o u c t ~ ~ . s. ~ ~ ~ y n . liIl1i!.s; wha-rBadiou calls, following Lacan, its 'real' .J), , -_ _. ~ " , " . ' ; . ' f . _

It is at this point that we turn to a discussion of Badiou's'use of s e J J h e ( ) x ~ ) by means of which he gives all this ratherloose metaphysical t alk a solid and precise basis.f V J ~ y set theory?

Since Aristotle , ontology has been a privi leged subdiscipline of philosophy; otherwise known as the discourseon being. Badiou puts forward a radical thesis: if being isinconsistent multiplicity, then the only suitable discourse fortalking about it is no longer philosophy but mathematics.For Badiou, mathematics is ontology",: Mathematicians, unbeknownst to themselves, do nothing other than continuallyspeak of or write being. This thesis enables Badiou toreformulate the classical language of ontology being,relations, qualities in mathematical terms: more specifically, those of set theory because it is one of the foundationaldisciplines of contemporary mathematics; any mathematicalproposition can be rewritten in the language of set theory.

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Infinite ThoughtIn 1/Eire el I'eoenement, Badiou sets forth two doctrines to

support his adoption of set theory. The first, the doctrine oninconsistent multiplicity, is explained in t he p revioussection. 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 ofsituations.Take the first doctrine. If the being of situations isinconsistent multiplicity, what is required of the language of

such being? Simply that this language must present multiplicity as inconsistent, that is, as non-unified. To fulfil such arequirement a number of conditions must be me t. First, inorder to present multipl icity without unity, the multiplespresented in this language cannot be multiples of individualthings of any kind, since this wou ld be to smugg le back inprecisely what is in question the being of the One.Consequently, these multiples must also be composed ofmultiples themselves composed of multiples, and so OILSecond, ontology cannot present its multiples as belongingto a universe, to one all-inclusive total mult iple - for thatwould be to smuggle back the One a t a globallcvel. As such,ontology's multiples must be boundless; they cannot have anupper limit. The third condit ion is that ontology cannotdetermine a single concept of multiplicity, for that wouldalso unify its multiplicities and, by so doing , uni fy being .Set theory is the formal theory of non-unified multiplicities. It 'meets each of the three conditions outlinedabove . First, a set is a multiple of multiples called elements.However , t he re is no fundamental difference betweenelements and sets, since every element of a set is itself aset. Second, there is no set of sets; that is, there is no ultimateset which includes all the different types of set found in settheory. Such a set would have to thereby include itself,which is expressly forbidden, on pain of paradox, by one ofset theory's axioms, that of foundation.!" In set theory there

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An introduction to Alain Badiou's !ihilosophyis an infinity of infinite types of infinite sets. As for the thirdcondition, there is neither definition nor concept of a set inset theory. What there is in its p lace is a fundamental relation- 'belonging' as well as a series of variables and logicaloperators, and nine axioms stat ing how they may be usedtogether. Sets emerge from operations which follow theserules.The second doctrine, which Badiou uses to bridge the gap

between set theory's infinity of sets and particular nonontological situations, isNs doctrine on 'the void'>. Like thedoctrine of inconsistent multiplicity.x it is also a doctrineabout the nature of situations. Badiou argues that, in everysituation, there is a beirlg of the 'nothing'. He starts bystating that whatever is r ecognized as 'something', or asexisting, in a situation is counted-for-one in , that situationan d vice versa. B y " i ~ p l i c a t i o r i , what is r/oilz'ing",in a situationmust go uncounted. However, it is no t as though there issimply 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 multiplewhich exists before the count are , by def in it ion, uncountable. Moreover, both a re necessary to the existence of asituation 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 thesituation itself ." _ A ~ , ~ s o < ; . s s ~ r y b i i t ~ . ~ g p : i ~ ~ ~ n I ~ 1 2 1 e , theyconstitute what Badiou terms the 'rultnlng'()r'fhe"


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Infinite Thought An introduction to Alain Badiou's philosopf!ySet theol)'

A set is a unifiedmultiplicity: its clements ar c n ot indefiniteand dispersed; one is able to speak of a (single, unified) set.Badiou reads l1 E as saying that multiple l1 is 'counted-forone' as an element of the set ~ or the set is the 'count-farone' of all those elements l1. Each o f those elements l1 could

the subset XxCShe set S

Sets are made up of elements. The elements of a set have nodistinguishing quality save t ha t o f belonging to it. This is whythey are referred to simply as variables o: ~ Y- both whenthey are elements and when they arc themselves consideredas sets. The relation of belonging is the basic relation of settheory; it is written l1 E ~ l1 belongs to ~ or, l1 is an elementof the set ~ There is another relation in set theory, termedinclusion, which is based entirely on belonging. Sets have'subsets', that ar e included in the sets. A subset is a groupingof some of a set 's elements. Each of a subset's elements mustbelong to the initial set. Take for example the set 8 whichconsists of the elements l1, ~ y. I t can be written {, ~ , y } . I thas various subsets like {o, ~ and { ~ y}. Each subset canitself be given a name, indexed to an arbi tr ary mark. Forexample, the latter subset { ~ y}, might be called the subsetX. I ts inclusion in 8 is written X c 8.

elements

particularities of the situation ar e removed or subtractedfrom it. So, for Badiou, every situation is ultimately foundedon a void. This is no t Heidegger's Ab-grund, no r is it sometheological creation ex nihilo. The void of a situation issimply what is no t there, but what is necessary for anythingto be there.When we turn to set theory, it turns out it makes oneinitial existential claim, that is, it begins by saying that justone set exists . This particular set is subtracted from theconditions of every other set in set theory: that of havingelements. This is thc null-set, a multiple of nothing o r o f thevoid.20 On the sole basis of this s ~ t , u s ~ n g operationsregulated by formal axioms, set t h e o r y \ : i I ! J f o l c l ~ an infinity offurther sets. Set theory thus weaves its sets ou t ofa 'void',out o fwhat, in any other situation, is the subtractive sutureto being of that situation. In other words, we already knowthat ontology connects to other situations through being thetheory of inconsistent multiples. In each and every nonontological situation, its inconsistent multiplicity is a void.Th e only possible presentation of a 'void' in set theory is th enull-set. Thus, the second way in which set theory connectsto situations is that it constructs its inconsistent multiples ou tof its presentation of the void, of the suture to bcing of everysituation.v'

So much for th e general connection between situations andset theory's infinite sets. There is al so a connection specific toeach situation: Badiou holds that the s truc tu re of eachs itua tion can be wri tt en as a type of set. That is, leaving allof a situation's properties aside and considering only thebas ic relat ions which hold throughout its multiplicity, onecan schematize a situation in ontology as a set.

What, t hen, a re sets and how ar e they written?

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Infinite Thoughtbe counted and grouped and subdivided in differentmanners, resulting in different sets: there is no restrictionon the number of different sets they can belong to. As notedabove, this is the great flexibility of set theory once onestrips identi ty away f rom mul tipl ic ity there is nothing toprevent a multiplicity from belonging to any numbe r o fother multiplicities, nothing, that is, save its structure(certain types of sets only admit multiples with certainstructures, bu t more on that later).

If one compares set theory to classical ontologies, indeedeven to that of Deleuze, its modernity is immediate. Itmakes no claims concerning the nature of being, no rconcern ing the adequation of its categories to be ing. Itmakes no attempt to anchor its dis cour se in necessitythrough an appeal to some ground, whether etymological,natural or historical. It does no t place itself as one linkagewithin a larger unified machinery such as 'evolution' or'complexity' or 'chaos'. I f there is a grand philosophicalclaim in Badiou's enterprise, it is not made within thediscourse of set theory itself but rather holds in theidentification of set theory as ontology. The basis of settheory is simply a set of axioms. The necessity of theseax ioms has been tested rather than declared i nsofar as alloperations made on their basis must have log ical lyconsistent results. These results have been tested through acentury of work within set theory. Nine axioms regulate theoperations and the existences which weave the tissue of settheory's universe.

For Badiou these axioms constitute a decision in thought, astarting point. The axioms themselves, of course, are notpure historical beginnings since they are the result of a seriesof reformulations made over t he first few decades of settheory: these reformulations were designed to prevent theoccurrence of logical inconsistency within the domain of settheory. Rather, they mark the beginning of something new

18

",In introduction to Alain Badiou's philosophyin scientific thought inasmuch as, for example, it was notpossible to conceive of two different types of infinity, onelarger than the other, before Cantor's pioneering work in settheory.

Set theory itself comes in a number of varieties: forexamp le , t he re are foundat iona l and anti-foundationaltypes, with varying numbers and types of axioms. Badiou'sown choice is to plump for the orthodox version of ZermeloFraenkel set theory, with its nine axioms. These aregenerally called: Extensionality, Separation, Power-Set,Union, Empty Set, Infinity, Foundat ion, Replacementand Choice. An explana tion of all nine of these axiomswould exceed the range of this presentation, bu t a quicksketch of five of the n ine axioms should shed some light onhow the universe of set theory unfolds.

The first concerns identity and difference, the axiom ofextension: I f every element y of a set II is also an element of aset and the inverse is true, then the sets II an d areindistinguishable and therefore identical. Consequently, inset theory ontology, the regime of identity and difference isfounded upon extension, no t quality. That is, everydifference is localized in a point: for two sets to be different,at least one element of one of the sets must not belong to theother.

The next three 'construct ive ' axioms allow the construction of a new set on the basis of an a lready existing set. Theaxiom of separation states: 'I f there exists a set a, then thereexists a subset of ll , all of whose elements y satisfy theformula F. ' I t enables a set defined bv a formula to beIseparated out from an initial set. If one gives values to thevariables o ne could then, for example, separa te out t hesubset, ~ of all green apples from the set of apples, I I ('greenapples' being the formula in this example).

The power-set axiom states that all of the subsets o f aninitial set grouped together form another set termed the

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Infinite Thoughtpower-set. Take for examp le t he set {, ~ X}. It s threeelements can be grouped into the following subsets: {}, { ~ } ,{X}, {, ~ } {a, X}, and { ~ X}, to which must be added bothwhat is termed the 'maximal' subset { e l , ~ , X}, and, by virtueof 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 the power-set of any set is alwaysdemonstrably larger than the initial set. This means one canalways generate larger sets ou t o f any existing set.

Th e axiom of union states that all of the elements, 8, ofthe elements, 'Y, of an initial set, o; themselves form anotherset termed the union-set. Th e new set is thus the unionset of the ini ti al set o; conventionally written ua. It showsthat sets ar e homogeneously multiple when decomposed.

All the axioms listed so far presume the existence of at leastone set bu t they do not themselves establish the existence ofsets. The axiom of the null-set, on the other hand, does. Itforms set theory's first ontological commitment. It states thatthere exist s a nul l- se t, an empty set to which no elementsbelong - 0. This null-set is the initial point of existence fromwhich all t he o ther sets of set theory are unfolded using theconstructive axioms. For example, from 0, by the operationsprescribed by the axiom of th e power-set, one candemonstrate the existence of its power-set {0} ' and thenby repeating the operat ion, further sets can be unfolded suchas {0, {0} } and {0, {0} ' {0, {0}}} . I t is just suchunfolding which constitutes the infinity of sets.

Each of these axioms has profound consequences forphilosophical problems, once one allows that set theory isontology. In order to use set theory to address philosophicalproblems Badiou makes a dis tinc tion between ontologyproper, that is, the forma l language of set theory, and thediscourse ofmeta-ontology, that is, a translation of set theory's

20

An introduction to Alain Badiou's philosophyaxioms and theorems into philosophical terms. Thus for everyset-theoretical term, there is an equivalent in the discourse ofphilosophy. For example, a set is spoken of in meta-ontologyas a 'multiplicity', a 'situation' or a 'presentation'.

One of the traditional philosophical problems to whichset theory responds is tha t o f the relationship between beingand language. According to Badiou, this relationship isconcentrated in t he way set theory ties the existence of setstogether with the ir definitions. In one of the first formulations of set theory, that of Gottlieb Frege, a set is defined as'the extension of a concept '. Thi s means that for any wellformed formula in a first order logic which defines aconcept, a set of elements exists, each of which satisfies theforrnula.i? That is, there can be no sets, and thus nothing inexistence, for which there is no concept: every exist ing setcorresponds to a concept. Or , whenever one has a definedconce pt , one can d irectly d ed uce the existence of acorresponding multiple. Thus, the relationship betweenlanguage and being is one of exact correspondence.

However, Frege's definition of sets - and, by implication,his articulation of the relationship between language andbeing - met with a problem. In 1902, Bertrand Russelldiscovered a well-formed formula to which no existent setcould correspond without introducing contradiction into settheory.s'' The formula is 'the set of all sets which a re no tmembers of themselves'. Th e contradiction ensues when oneasks whether the set of elements which satisfies this formulabelongs to itself or not. I f it does belong to i tsel f then, bydefinition, it does not, and if i t does no t belong to itself, thenit does. This contradiction ruins the consistency of theformal language in which the formula is made. Th econsequence of the paradox is that it is no t true that forevery well-formed formula a corresponding multiple exists.

In order to avoid Russell's paradox, the axiom ofseparation was developed. It proposes another relationship

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Infinite Thoughtbetween t he existence of multiples and well-formed formulas. Frege's definition of that relationship runs as follows:

( 3 ~ ) (Va) [F(a) (a ~ ) This proposition reads: 'There exists a set such that everyterm a which satisfies t he formula F is an element of thatset.' Th e axiom of separat ion on th e other hand looks likethis:

(Va) ( 3 ~ ) (Vy) [( (y E a) & F(y)) (y E ~ ) ] .I t reads: ' I f there exists a set a, then there exists a subset ofa, all of whose elements y satisfy t he formu la F. ' Theessential difference between Frege's defini tion and theaxiom of separation is that the former direct ly proposes anexistence while the latter is conditional upon there alreadybeing a set in existence, a. Th e axiom of separation says thati f there is a set already in existence, then one can separate outone of its subsets, ~ whose elements validate the formula F.Say for example that the formula F is the property 'rotten'an d on e wants to make th e judgement 'Some apples arerot ten. ' V ia the axiom of separation, from the supposedexistence of the set of all app les, one could separate out th esubset of rotten apples.

The relationship between being and language implied byt he axiom of separation is therefore no t on e of an exact fit,bu t rather on e in which language causes 'a split or divisionin existence' (EE, 53). The conclusion Badiou t hu s d rawsfrom set theory for the traditional philosophical problem ofth e r elatio nshi p between l anguage and being is that,a l though language bestows identity on being, being is inexcess of language. This is quite clearly a materialist thesisas befits Badiou's Marxist heritage. In meta-ontologicalterms, the axiom of separation states that an undefinedexistence must always be assumed in any definition of a typeof multiple. In short, the very conditions of the inscription of

22

An introduction to Alain Badiou's philosophexistence in language require that existence be in excess ofwhat the inscriptions define as existing.

So, what is the general result of Badiou's adoption of settheory as the language of being? Quite simply that it hasnothing to say about beings themselves this is the provinceof other discourses such as phys ics, anthropology andl i terature. This is one reason why Bad iou terms set theory asubtractive ontology: it speaks of beings without reference totheir attributes or their identity; it is as if the beings ontologyspeaks of have had all their qualities subtracted from them.As a result, unlike Plato and Aristotle's ontologies, there isneither cosmos nor phenomena, neither cause no r substance.Set theory ontology does no t p ropose a description of ' thefurniture of the world', no r does it concern itselfwith 'carvingreality at the joints'. Its own ontological c la im s implyamounts to say ing there is a multiplicity of multiplicities.Furthermore, set theory ontology is indifferent to theexistence or non-existence of particular situations such as' the world' or 'you, th e re ad er' : B ad io u writes: 'we areattempting to think multiple-presentation regardless oj time(which is founded hy intervention), and space (which is asingular construction, relative to certain types of presentation)' (EE, 293). What set theory ontology does, in li eu ofpresenting 'what there is', is present the ontological schemasof any ontological claim; that is, it p re sents the structure ofwhat any situation says exists.

Ontological schemas of different situationsAlthough set theory ontology does no t recognize the infinitedifferentiations of concrete situations, it does recognize anumbe r o f differences in the structure of situations. Thisallows it to schernatize different concrete situations.According to Badiou's meta-ontology, the re a re three.basics truc tu res which are found underpinning every exis tent

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Infinite Thoughtsituation. To understand the dif fe rent ia tion of thesestructures it is necessary to return to the axiom of thepower-set and its meta-ontological equivalents.

The axiom of the power-set says that there is a set of allthe subsets ofan initial set, termed the power-set. In metaontological 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 isthus a second count-for-one. Or , according to another ofBadiou's meta-ontological translations, if a set schematizes.a,presentation, then its power-set schematizes the representation of tha t presentation.v' The state is made up of all thepossible regroupings of the elements of a situation; as such itis the structure which underlies any representational orgrouping mechanism in any situation. \ e should note thatas such the term 'st ate' includes bu t is in no way reducible tothe position of a government and its administration in apolitical situation.

Badiou distinguishes three types of situation:(rtatural,historical and neutral. What makes them different at astructural level are the types of multiple which composet 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 byItS ~ t a t e (they are counted-for-one twice); l,X"crescentmultiples,w h l c ~ are o ~ l y represented by the state; and singularmultiples, whic h only oc cu r at the level of presentation,and which escape the effect of the second count-for-one. iNatural s itua tions are def ined as having no singularmultiples all of their multiples a re e ith er n orm al orexcrescent, and each normal element in turn has normalelem:nts (E1!, 146). Neutral situations ar e defined as havinga mIX of singular, normal and excrescent multiples.?"Historical s ituations are defined by their having at leastone 'evental-sitc'; a sub-type of singular multiple." In settheory terms, a singular multiple is an element of a set, bu t

24

An introduction to Alain Badiou's philosoPhYnot one of its subsets. Since each of a set's subsets is madeentirely of elements that already belong to the ini t ia l set .the definition of a singular multiple is that, first, it is anelement of an initial set, and, second, some of its ownelements in turn do no t belong to the initial set. It is theseforeign elements which ar e responsible for the singulari tvof a singular multiple. An eoental-site is an extreme varietvof 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 saside, le t us turn to examples of natural and historicalsituations.

Take, for an example of a natural situation, the ecosystemof a pond. Ths m ~ I I t i p k s which it presents include individualfish, tadpoles,' reeds and stones. Each of these elements is alsorepresented at the level of the s ta te of the situation, which~ a d i o . u also quali fies as the level of the knowledges of asituation - these elements are known elements of the situation.Each element o f an ecosystem is also one of the ecosystem'ssubsets, because each of their clements also belong' in turn ,to t ~ ecosystem; for example each fish's eating and breedinghabits belong to the ecosystem as well as to each fish. Theseelements a re thus normal multiples. I f one examines such as i t ~ a t i ~ n , it contains no singular terms: nothing is presentedwhich IS not also represented. The test of whether a situationis natural or not is whether there is any element of thesituation whose content is not also par t o f the situation - inecology, every element of a system, at whatever level of sizeor effect, is interconnected. Th e situation of the ecosystem ofa pond is thus a natural situation.

Take, by contrast, as an example of a historical situation,a collection of possible answers to the national is t concern ofwhat it is to beAustralian. Some of the multiples presented inthis situation would be individual stories about bronzedlifesavers, Anzac soldiers, larrikins, whinging poms, wowsers, convicts, explorers, bushrangers and squatters. On e25


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Infinite Thoughtwould also find Don Bradman and the Eureka Stockadebelonging to such a collection. In the twenty-first century,this s itua tion 's e lements would also comprise individualstories about the Italian-Australians, the Irish-Australians,the Chinese-Australians, the Greek-Australians, the Turkish-Australians, and so on. At the level of the state of thesituation one has submultiples such as hedonism, mateship,equality understood as samencss, the imperat ives ' fa ir go!'and 'she'll be right mate!', anti-British sentiment, distrust ofauthority, t he p rivi leging of kn ow-ho w 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 bothknown an d knowable. For this reason we would argue thatnone of the presen ted 'immigrant' multiples are singularmultiples. On the other hand, constitutively resistant toAnglo-Saxon dreams of assimilation, the mul tiple 'aboriginals' forms an evcnral-site; its contents remain unknown.Of course, within other situations such as cultural, sociological and bureaucratic assessments of Australia, 'aboriginals' a re re-pres en ted. However, these spec ia lizeddiscourses are n ot in the position of furnishing answers tothe nationalist question 'What is it to be Australian?' Th emultiple 'aboriginals' forms an evental-sitc because thesovereignty of Australia, the 'immigrant nation', wzsfoundedupon the dispossession of indigenous peoples. Their relationto this particular piece of land was crucially no t recognizedat the very beginning of this entity termed 'Australia'. Anyrepresentation of the con tent o f the multiple 'aboriginals'with reference to what it is to be Australian, would thuscau se t he uni ty of the si tuation to dissolve - in a sense, itwould entail the dissolution of 'Australia' itself I t is thisconstitutive irrepresentability at the heart o f Australian nationalism that makes it a historical situation.

26

An introduction to Alain Badiou's jJhilosoplyBadiou uses this division between natural and historical

situations to return to his basic quest ion: How does the newhappen 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 naturalcatastrophe the ecosystem will remain in a state of homeostasis. In natura l situations Ecclesiastes' proverb holdstrue: there is nothing new under the sun. In historicals ituations things are quite different. To return to ourexample of Australian nationalism, the inherent instabilityof the situation (it harbouring an unknowable evental-site inits mids t) r ende rs it susceptible to wholesale pol it icaltransforma tion.

However , the existence of an evental-site in a situationdoes no t guarantee that change will occur. Fo r thatsomething extra is required, a 'supplement' as Badiou says,which is an event. \'\1e are no t talking about any ordinaryevent here, like a birthday or Australia beating France inrugby, but r athe r of a totally disruptive occurrence whichhas no place in the scheme of things as they currently are.Who will say what this event has been or will be forAustralian nationalism was it the erection by Aboriginalactivists of a tent embassy opposite the National Parl iamentin 1972? The occurrence of an event is completelyunprcdictable.27 There is no meta-situation - 'History' which would programme the occurrence ofevents in variousselected .situations, ..... ;, . ,

he precariousness of historical change extends further:no t only must an event occur at the evental-s ite of asituation, bu t someone must recognize and name that eventas a n event whose implications concern the nature o f theentire situation. Thus it is quite possible tha t an event occurin a situation but that nothing changes because nobodyrecognizes the event's importance for the situation. Thisinitial naming of the event as an event, this decision that it

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InJinite Thoughthas transformational consequences for the ent irety of asituation, is what Badiou terms an 'intervention'. Theintervention is the first moment of a process of fundamentalchange that Badiou terms a 'fidelity', or a 'generic truthprocedure'. A gener ic truth procedure is bas ical ly a praxisconsisting of a series of enquiries into the situation made bymilitants who act in fidelity to the event. The object of theseenqui ries is to work ou t how to t ransform the situation inline with what is revealed by the event's belonging to thesituation. For example, within the si tuation of ar t in theearly twentieth century, certain artists launched an enquiryinto the nature of sculpture once Picasso's cubist paintingshad been recognized as 'art'. The procedure made up ~ such enquiries is termed a 'truth procedure' because Itunfolds a new multiple: the ' t ru th' of the previous situation.Here Bad iou draws upon - and displaces - Hcidegger'sconception of truth as the presentation of being. The newentitv is a truth inasmuch as it presents the multiple-being ofthe previous situation, stripped bare of any predicates, ofanv identitv.

For example, take an ar t cri ti c in the ear ly twentiethcentury who has just recognized that a cubist painting can,indeed, be called 'art'. I f he was called upon to make apredicative definition of the contemporary situation of ar t that is, if someone asked him 'What is an?' - he would havefound it impossible to respond - at tha t very moment, forhirn, the disrupt ive event we now call 'cubism' was layingba 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 . ~ p d sl?aces with nofixedcontours.: In fact, the common accusation that contemporaryar 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 agallery; this very accusation actually unknowingly strikesupon the very nat ur e o f a new mul ti pl e: it is 'anythingwhatsoever' with regard to established knowledge.

28

An introduction to Alain Badiou's jilli/osOpkJiTo understand how a new multiple - such as 'modern art'- can both exist, and 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 andprocesses of transformation

In order to think about processes of fundamental changewithin his ontology Badiou had to work ou t how a multiple,a set, can be new. It is at this point that Badiou introducesthe c p \ t r , e ~ ~ i r \ c ~ ) 0 f h ~ s , , ; ~ v 9 r k - what he calls 'the gene:ic' or'indis"c:ertllbrhtv'. ThIS IS at once an extremely difficultconcept, bas;d on the most innovative mathematicalprocedures, yet also intuitively graspable. Badiou takes. thisconcept from the work of Paul Cohen, an American. , . , . 1963 28mathematician who invented the genenc set 111

The first point to work ou t is what the reference pointcould be within ontology for such n o ~ t J t y . Especially since settheory ontology appears to be a s ta tic , flat discourse, withno recpgnition of the .supposed universality of the situationsof'time' .and 'history':) The reference point turns ou t to be

/ l ~ n g u a g ~ . In set theory, one c an have 'models' of set theorywhich' are interpretations that flesh out the bare bones of setsand elements by giving values to the variables (such as y =green apples in the example used above). A model of settheory has its own language in which various formulasexpress certain properties such as 'green'. The model itself,as a structured multiplicity, can be treated itse lf as a set.Cohen t akes as his star t ing point what he terms a 'grollIl51model' of set theory. Badiou takes this model as the schemaof a historical situa'tion. Each subset of this model satisfies aproperty which can be expressed in the language used in themodel. That is, every multiple found in the model can bediscerned using the tools of language. A generic set, on theother hand, is a subset that is 'new' insofar as it cannot be

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Infinite Thoughtdiscerned by that language. Fo r every property that oneformulates, even t he most general such as 'this apple andthis apple and this apple . . . ', the generic set has at least oneclement which does no t share that property. This makessense intuitively: when someone tries to tell you about a newexperience, whether it be meeting a person or see ing a workof ar t, t hey have a lot of trouble describing it accuratelyand, every time you try to help them by suggesting that itmight be a bi t like the person x or the filmy, they say, 'No,no, it' s no t like t ha t! ' For every prope rty or concept youcome up with to describe this new thing, there is somethingin that new thing which does not qui te fit. This is all verywell, bu t having a set which one 'can't quite describe'sounds a bit vague for set theory. The innovation of PaulCohen's work lay in his discovery of a method of describingsuch a multiple without betraying its indiscernibiluyt''

But what about the process of this new mult iple cominginto being? How does a generic set provide the ontologicalschema of processes of radical change in political, scientific,artistic, and amorous situations? Badiou holds that theground model schematizes an established historical situationbefore an event arrives. One can define a concept of ageneric subset within such a situation bu t one cannot knowthat it exists- precisely because it is one of those 'excrescent'multiples noted above (which a re not presented at the levelof belonging to a situation). The generic subset is onlypresent at the level of inclusion, and, unlike all the othersubsets, it cannot be known via its properties. To show thata gcneric set actually exists, Cohen develops a proccdurcwhereby one adds it to the existing ground model as a typeof supplement, thereby forming a new set. Within this newset, the generic multiple will exist at the level of belonging,or in meta-ontological terms, presentation. The newsupplemented set p rovides the ontological schema of ahistorical situation which has undergone wholesale change.

30

An introduction to Alain Badiou's philosopkyFur thermore , Cohen developed a method of making

finite descriptions of this new supplemented set using onlythe resources of the initial set. Cohen termed this procedure'forcing' and Badiou adopts it as an ontological model of thenumerous practical enquiries that subjects who act infidel ity to an event make whil e t hey arc attempting tobring about the change entailed by the event. That is,although, say, an activist working towards justice for theindigenous peoples in Australia will not know what overallshape justice will take, they will be able to predict cer tain ofits features and some of their predictions may be verif iedearly on in the process of change. Fo r example, a particularexperiment in public health practices in indigenous communities may reveal i tsel f to be part of the movementtowards justice due to its sensitivity to issues of selfdetermination and cultural difference.

For Badiou, the actual work wh ich carries ou t thewholesale change of a histor ical s itua tion - in his te rms, thef ideli ty pract ised by subjects to an event consists of suchexperiments; finite enquiries into the nature of the event, usingan invented idiom to approximate what is discovered throughsuch enquiries. Historically, one can understand this conceptof fidelity as a remodelling of the Marxis t concept of praxis,subtracting the latter from the encompassing unities ofhistorical determinism, revolutionary theory and the Partyline. What results from suchsubtractions is a p raxi s made upof a hazardous series of bets, bets on the nature of the situationto come. Many o f these bets will fall wide of the mark, bu tthose that hi t the target will help construct the new situation.

Of course, Badiou recognizes that the number of shapes afidelity can take, especially in domains as d if fe rent as art,politics, science and love, is infinite; and further, that anumber of different fidelities may be developed in the samesituation to the same event - for example, both PierreBoulez an d John Cage developed their music in f ide li ty to


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Infinite Thoughtthe event of Schoenberg's invention of the twelve-tone series,bu t in very different directions. Yet Badiou's general claim isthat in each case of a fidel ity it is a matter of the new cominginto being, and in set theory onto logy the only way toschematizc that process is through Paul Cohen's concepts ofthe generic set and forcing. Thus, however particular - andindeed, however precarious a decolonization processwithin a colonialist pol it ical situation, at the level of thestructure of its mul tipl ic ity, it is a gener ic set. The relationthis process entertains with the established colonialistsituation is not one of pure exteriority (romanticism) norof subsumption (realism), bu t that of indiscernibiliiy. That is,none of the categories employed by colonialist discoursesserve to discern its nature.

Hence the indiscernibility of a gener ic t ruth proceduregrounds both its singularity and i ts sovereignty, insofar as itis subtracted from and thus independent of any knownentity in the situation, such as 'parliamentary democracy','mining interests', ' the proletariat ', or 'the native'.

But within the debates around post-colonialism, theromantics and the realists will always have one lastobjection to an argument such as ours: that there is anexception to the rule, s ince the categories of one colonialistdiscourse in particular seem to serve quite well fordiscerning the nature of a decolonization process, the latestcategories of European philosophy, those of Alain Badiou'sset theory ontology. However, this would be to miss thepoint entirely. Ontology does not discern the nature of anysituation, much less th at o f a particular fidelity. Ontologyonly speaks of the structure of multipl icity: it has nothing tosay about the qualities or identitv of anv concrete situation.For Badiou such would be the province of other discourses,practical or theoret ical . This is the first guard againstimperialism built into Badiou's philosophv - the indifferenceof ontology towards the concrete. .

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An introduction to Alain Badiou's p h i l o s o ! } f ~ vThe second guard lies in Badious refusal of any

t rans it iv ity between ontology and politics. As a goodmaterialist, .Iie r ecognize s the autonomy of materialprocesses and argues that the names philosophy comes upwith to reflect particular political transformations arenot andcannot be identical to those names that are thrown up by theactual process of transformation within a political situation.The task of philosophy is no t to predict nor determine theshape of justice, or of modern art , or even the form a unifiedfield theory might take. Philosophy's ta sk is to reflect andlearn from those transformations happening in contempor-ary historical situations; to the point where it develops whatBadiou terms a ~ p a c e of compossibility' for all contemporaryfidelities. The relationship behveefiphilosophy and politics- as with art, science and love - is thus one of conditioningor dependence. Philosophy is no longer sovereign. rt is as ifphi losophy has finally hea rd t ha t cry addressed to it fordecades , a cry voiced by so many artists, scientists, activistsand lovers whose activities it has deafly appropriated fromon high, t he cry 'SHUT UP AND LISTEN!!!'

And even if Badiou's conception of philosophy maintainsa strict separation between the practice of philosophy andthe diverse practices of art, politics, science and love, it docshave one practical consequence. Quite simply, if you wantto do po li ti cs, go become an activist, go decide what eventhas happened in your political situation. I f you want to dophilosophy, try to think the compossibility of contemporaryevents in each of the four domains of art, politics, scienceand love (and, of course, read all of Being and Event once it'spublished). Just don't confuse the two.

A note on notesFollowing Badiou's practice, we do no t reference texts hementions, t rusting the readers ' own curiosity to guide them.

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Infinite ThoughtAdmittedly, it is a rather abrupt gesture. It does not placethought under the sign of the demand for knowledge bu tsimply under t ha t o f desire.

Notes

I. Th e following tit les by Alain Badiou are current ly in press orforthcoming: Being and Eoent, trans. Oliver Feltham (London:Continuum Books, forthcoming); Theoretical 11/ritings, trans.an d ed. Alber to Toscano and Ray Brassier (London:Continuum Books, 2003); Handbook of Inaesthetics, t rans . A.Toscano (Stanford, CA: Stanford University Press, 2003); St.Paul: The Foundation of Universalism, trans. R. Brassie r(Stanford, CA: Stanford University Press, 20(3); On Beckett,ed. and trans. Nina Power and A. Tos cano w it h B runoBosteels (Manchester: CIinamen, 2(03); The Century/Le Siecle,t rans . A. Toscano with responses by A. Toscano and SlavojZizek (Paris/London: Seuil/Verso, 2003). Badiou's Abreg delvlitapolitique (Paris: Seuil, 1998), translated by Jason Barker,is forthcoming from Verso . See also Peter Hallward, Subject toTru th : An Introduction to the Philosophy of Alain Badiou(Minneapolis: C niversity of Minnesota Press, forthcoming)and P. Hallward (ed.), Think Again: Alain Badiou and the Futureof PhilosojJlry (London: Continuum Books, forthcoming).

2. See J. Barker, Alain Badiou: A Critical Introduction (London:Pluto Press, 2002); A. Badiou, Ethics: An Essay on theUnderstanding of F.vil, trans. Peter Hallward (London: Verso,2001); A. Badiou, Gilles Deleuze: The ClamorofBeing, trans.Louise Burchill (Minneapolis: University of Minnesota Press,2(00); A. Badiou, AfaniJesto for P h i l o s o p / ~ v , trans. NormanMadarasz (Albany, NY: SUNY Press, 1999).

3. A. Badiou, L'Etr et l'eoenement (Pa ri s: Edi ti on s elu Seui l,1988). All further references will appear as page num bel'S inbrackets in the body of the text.

4. Jacques Lacan was a French psychoanalyst f amous for his

::34

An introduction to Alain Badiou's j)hilosopkvfusion of Freud, Saussurean linguistics, structuralist anthropology, French psychiatry and mathemati cs into onecontinually evolving and powerful theory of the subject.Jacques-Aiain Miller subsequently became Lacan's son-inlaw, executor of his esta te, head of one of the largest Lacanianschools of psychoanalysis, an d one of Laran' s p remi ercomrnentators.

5. Ontology is thc philosophical discourse defined by Aristotle asthe science of being qu a being. Historically it has treated suchquestions as 'What is being?' and 'Why is t he re somethingrather than nothing?'

6. For a particularly dense and concent rated elaboration ofBadiou's theory of the subject see 'A finally objectless subject',in the a n t h o l o ~ y Who Comes After the Subject? ed. E. Cadava(London: Routledge, 1991'I.

7. Jacques Derrida, 'Desistance', in Philippe Lacoue-Labarthe,~ v p o g r a p / ~ y , Mimesis, Politics, Philosophy, ed. C. Fynsk (Cambridge,MA: Harvard University Press, 1989).

8. See, for instance, ]VI. Foucault, Power!Knowledge: SelectedInterrinos and Other Writings 1 9 7 2 ~ 1 9 7 7 , ed. C. Gordon, trans.C. Gordon et al. (New York: Pantheon, 1980).

9. A. Badiou, Logiques des mondes ( P a ~ i ~ : . " S e ~ i ~ ~ o r t h c o m i n g ) .Insofar as Badiou's concept of a , ~ e n e r i c multiple, whichmakes up the 'stuff of his faithful subjects, delivers a rigorousdefinition of s ingulari ty , one could argue that the classicalproblem of the id en ti ty o f subjects, or that of theirdifferentiation, is indirectly treated inasmuch as the genericmultiple is strictly differentiated from eve ry predicate, See'Generic scts and processes of transformation', pp. 29 33.

10. 'Fidelity', ' even t' , and ' si tuat ion' a re all technical terms ofBadiou;s .ontology and their meaning will he explained inwhat follows; however, the reader's intuitive sense of thesewords can be trusted to provide an initial approximation.

11. At this point we should note an important complication ofBadiou's theory of the subject; Badiou also terms 'subject' the

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Infinite 7 houghtactual individual theorems which make up modern physics.Similarly in the domain of ar t he terms 'subject' particularmusical works rather than their composers. This shift simplyreinforces his separation between the human as an individualanimal, and the human acting as subject, thatis asapoint ofrisk, invention and geclsion, . . . -

12. A. Badiou, Thiorie du suje! (Paris: Seuil, 1981).13. See Willard V. O. Quine, 'Ontological relat ivi ty ' , Il 1

Ontological Relatioity and Other ESSIlYf (New York: ColumbiaUniversity Press, 1969).

14. G. W. Leibniz, 'Letter to Arnauld April 30 1687', inPhilosophical Writings, trans. J. NT. Morris (London: Dent &Sons, 1934),72.

15. According to Badiou this was also Kant's problem in the firstcritique insofar as the l at te r d id no t grant immediate uni tyeither to the thing i tself or to the sensuous manifold, yetattempted to account for the apparent unity of experience.

16. See the interview included in this volume.17. We would like to thank ou r colleague Amelia Smith for this

example.18. This axiom was introduced in order to deal with a paradox

t ha t appea red early in the development of set theory.Russell's paradox emerges on the basis of sets being able tobe members of themselves. It is more familiar in the paradoxof the barber who shaves all t he men in the village who don'tshave themselves: who shaves t he b ar be r? We return to t hi sparadox below.19. Students of philosophy may be reminded of the status ofKant's Ding-an-sidi and of transcendental apperception in thefirst Critique.

20. In French, l'ensemble-uide. In Badiou's text this harmonizes ata terminological level with t he F rench for 'the void of asituation': le vide de la situation.

21. Th e doctrine on inconsistent multiplicity is prior, in the orderof argument, to t he doctr ine on the void of situations

36

An introduction to Alain Badiou'sphilosophbecause to accept that set theory's null-set presents thenothing of situations, one must al ready have accepted thatsets present the being of situations.

22. A first order logic consists of a series of signs: existential anduniversal quantifiers, variables, propert ies and logical connectors; disjunction, conjunction, implication, negation andequivalence. Propert ies are never found in the position ofvariables, that is, first order logic does not express propertiesof properties: that is the province of second order logic.

23. See B. Russell , 'Letter to Frege', in J. Van Heijenoort (ed.},From Frege to Codel: A Source Book in Mathematical Logic(Cambridge, MA: Harvard University Press, 1967), 124.

24. vVe should note that if this meta-ontological translation islegitima te, the superior size and complexity of the power-set,with regard to its initial set, has fundamental consequencesfor the classical philosophical problem of the relationshipbetween presentation and representation (and thus for anypractice based on the critique of representations), as it doesfo r the classical political problem of the relation between thestate and the people.

25. Due to the excess of inclusion over belonging - the superiorsize of a set 's power-set compared to i ts el f - every situationhas excrescent multiples.

26. 'Even tal -s ite' is a neologism that has been coined in order totranslate Badiou's site euenementiel. 'Event-site' is not appro priate, because it suggests that the site is defim:d by theoccurrence of an event, whereas in Badiou's conception, thereis no guarantee t ha t a n event will occur at a site ivinementiel,the sole guarantcc being that if an event does occur in thesituation it will do so at that particular point of the lattert ermed the evental-site.

27. This is precisely how Badiou breaks with historical dctcrrninIsms.28. The reference for the mathematicians is P. Cohen, Set Theoryand theContinuum Hypothesis (]\\ew York: W.A. Benjamin, 1966).


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Infinite Thought29. See Meditations 34 and 3.1 of L'Etre et I'eoenement for a full

explanation of Cohen's method.

38

CHAPTER 1Philosophy and desireThis philosophical investigation begins under the banner ofpoetry; thus recalling the ancient tie between poetry an dphilosophy.'

Rirnbaud employs a strange express ion: 'Ies revol teslogiques", 'logical revolts'. Philosophy is something like a'logical revolt' . Philosophy pits thought against injustice,against the defective state of the world an d oflife. Yet it pitsthought against injustice in a movement which conservesand defends argument and reason, and which ultimatelyproposes a new logic.

Mallarme states: 'All thought begets a throw of the dice.'It seems to me that this enigmatic formula also designatesphi losophy, because phi losophy proposes to think theuniversal - that which is true for all thinking - yet it doesso on the basis of a commitment in which chance alwaysplays a role, a commitment which is also a risk or a wager;

The four-dimensional desire i f philosoph);These two poetic formulas capture the desire of philosophy,for at base the desire of philosophy implies a dimension ofrevolt: there is no philosophy without the discontent of

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Infinite Thoughtthinking in its confrontation with the world as it is. Yet thedesire of philosophy also includes logic; that is, a belief in the"power of argument and reason. Furthermore, the d e s i r ~ _ ( ) . f .\philosophy involves unioersality: philosophy '-addresses all "" ' h u r : t . 1 < . t r } ~ i ! . 5 - 1 h . i p ~ i n g b e i n g s since it supposes that all humansthink. Finally, ph11osophy'takesns,kj:-'ITii'iiKiilg'i's'a!\vaysadCt:'lsl(lir"which supports independent points of view. Thedesire of philosophy thus has {(JUr dimensions: revolt, logic,universality and risk.I think that the contemporary world, our world, theworld that we strive to think and transform, exerts anintense pressure upon these {(JUr dimensions of the desire ofphilosophy; such that all four dimensions, faced by thewor ld , find themselves in a diff icult and dark passage inwhich the destiny and even the very existence of philosophyis at stake.

To beg in with, as far as the dimension of r evolt isconcerned, this world, ou r world, the 'vVestern' world (withas many inverted commas as you wan t), docs not engage inthought as revol t, and for two reasons. First, this wor ldalready decrees itself free, it presents itselfas 'the free world'- this is the very name it gives itself; an 'isle' of liberty on aplanet otherwise reduced to s lave ry or devastation, Yet, att he same time - and this is the second reason this world,our world, standardizes and commercializes the stakes ofsuch freedom. It submits them to monetary uniformity, andwith such success t ha t our world no longer has to revolt tobe free s ince it guarantees us freedom. However, it does no tguaran tee us the free use of this freedom, since such use is inreality already coded, orientated and channelled by theinfinite glitter of merchandise. This is why this world exertsan intense pressure against the very idea that thinking canbe insubordination or revolt.

Our world also exert s a strong pressure on -the. dimension,I 'of logic; essentially because the world is submitted to the

P h i l o s o p / ~ v and desireprofoundly illogical regime of communic.ation. Comn,-lUnicat ion t ransmi ts a universe made up of disconnected Images,remarks, statemen ts and commentar ie s whose acceptedprinc ip le is incoherence . Day after day communicationundoe s all rel ations and all pr inciples, in an untenablejuxtaposition that dissolves every relation bet.ween theel ement s it sweeps a long in its flow. And wha t IS perhapseven more distressing is that J;I)}I;S,s,C\o,rrrnu;nication presentsthe wor ld to us as a spectacle devoid of memory, a spectaclein wh ich new images and new remarks cover, erase andconsign to oblivion the very images and remarks that havejust been shown and said. The logic which is specifically

"'undone t f ~ e r e is the logic of time. It is these processes ofcommunication which exert pressure on the resoluteness ofthinking's fidelity to logic; proposing to thought in the latter 'splace a type of imaginary dissemination.As for the universal dimension of the desire of philosophy,our world is no longer suited to it because the world isessentially a specialized and fragmentary world; fragmentedin response to the demands of the innumerable ramificationsof the technical configuration of things, of the apparatuses ofproduction, of the distribution of salaries, of the diversity offunctions and skills. And the requirements of this specialization and this fragmentation make it difficult to perce ivewhat might be transversal or universal ; that is, what mightbe valid for all thinking.

Finally we have the dimension of risk. Our world does notfavour riskv commitments or risky decisions, because it is aworld in w'hich nobody has the means any more to submittheir existence to the per il s of chance. Existence requiresmore and more elaborate calculation. Life is d e v o t e ~calculating security, and this obsessiOii with calcul .. . a armean hv othcsi s th a

e s a t Irow e Ice, because in such a wQ!lQ.LOu lIluch fISk In a throw of the dice.

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Infinite ThoughtThe desire for philosophy thus encounters four, prj ncipalobstacles in the world. These are: the reign of m e r ( ~ h a n ' d i s e ,

the reign of communication, the need for technicalspecialization and the necessity for realistic calculations ofsecurity. How can philosophy take on this challenge? Isphilosophy eapable of such a challenge? Th e answer must besought in the state of contemporary philosophy.

The present state ~ f p h i l o s o p h . yWhat are the principal g lobal tendencies in contemporaryphilosophy if we cons ider it f rom a bird's eye point of view?I think it can be said that three principal orientations canbe dis tinguished in phi losophy today. These orientationscorrespond, in some measure, to three geographical loca-tions. I will first name and then describe them. The first canbe called the hermeneut ic orientation , which historicallygoes back to German romanticism. Th e best-known namesattached to this orientation are Heidegger an d Gadamcr,and its historical site ,V1s originally German. Then there isthe analytic orientation, originating with the Vienna Circle.Th e principal names connected to it are those of Wittgcnstein and Carnap. Despi te its Austrian origin, it nowdominates English and A mer ican a cademi c philosophy.Fina lly, we have what can be called the postmodernorientation, which in fact borrows from the other two. Itis without doubt the most ac tive in France, and includesthinkers as different as Jacques Dcr rida and Jean-Frans;oisLyotard. It is equally very act ive in Spain, Italy an d LatinAmerica.A hermeneutic orientation, an analytic orientation, and apos tmodern orientation: there are , of course, innumerableintersections, mixtures and networks of circulation betweenthe three, bu t together they form the most g lob al a nddescriptive geography possible of contemporary philosophy.

4-2

Philosophy and desireWhat then interests us is how each orientation designates oridentifies philosophy.

The hermeneutic orientation assigns philosophy the aimof deciphering the meaning of Being, the meaning of Being-in-the-world, and its central concept is t ha t o f interpretation.There are s ta tements, acts, writings, and configurationswhose meaning is obscure , latent, hidden or forgotten.Philosophy must be provided with a method of interpretation that will serve to clarify this obscurity, and bring forthfrom it an authentic meaning, a meaning which would be afigure of ou r destiny in relation to the destiny of being itself.Th e fundamental opposition for hermeneutic philosophy isthat of the closed and the open. In what is given, in theimmediate world, there is something dissimulated andclosed. Th e aim of interpretation is to undo this closureand open it up to meaning. From this point of view thevocation of philosophy is a 'vocation devoted to the open' .This vocation marks a combat between the world ofphilosophy a,mIthe world of technique since the latter isthe accomplishment of closed nihilism.

The analytic orientation holds t h f , , a j ! ? ~ f p h , i l ~ ) s ~ p h y tobe the strict demarcation of those utteranc:es which havemeaning and those which do not . Th e aim is to demarcatewhat can be said and what it is impossible or illegitimate tosay. Th e essential instrument of analytic philosophy is thelogical an d grammatical analysis of utterances, an dultimately of the entire language. This time the cen tr alconcept is not interpretat ion bu t the rule. The task ofphilosophy is to discover those rul es that ensure anagreement about meaning. The fundamental oppositionhere is between wha t can be regulated and wha t canno t beregulated, or what conforms to a recognized law assuring anagreement about meaning, and what eludes all explicit laws,thus falling into i llusion or discordance. For the analyticorientation, the aim of philosophy is therapeutic and

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Infinite Thoughtcritical. It is a question of curing us of the illusions and theaberrations oflanguage that divide us, by isolating what hasno meaning, an d by returning to rules which aretransparent to all.

F inal ly , t he postmodern orientation holds the aim ofphilosophy to be the deconstruction of the accepted facts ofou r modernity. In par ti cu la r, postrnodern philosophyproposes to dissolve the great constructions of the nineteenthcentury to which we remain captive - the idea of thehistorical subject, the idea of progress, the idea of revolution,t he idea of human it y and the ideal of science. It s aim is toshow that these great constructions a r e : ' ; ; ~ t d t l t e d , that welive in the multiple, that there are no great epics of historyor of thought; that there is an irreducible plurality ofregisters an d languages in thought as in action; registers sodiverse and heterogeneous that no great idea can totalize orreconcile them. At base, the objective of postmodernphilosophy is to deconstruct the idea of totality - to theextent that philosophy itself finds itself d e s t a b i l i z ~ ~ d . Consequently, the postmodern orientation activates what mightbe called mixed practices, de-totalized practices, or impurethinking practices. It situates thought on the outskirts , inareas that cannot be circumscribed. In particular, it installsphilosophical thought at the periphery of art, and proposesan untotaJizable mixture of t he conceptua l method ofphilosophy and the sense-orientated enterprise of art.

The common themes rif the three orientations ofphilosophyDo these three orientations - so summarily described - haveanything in common? Does anything allow us to say that,despite this diversity, features ca n be found which s ignal auni ty of contemporary philosophy? I would suggest thatthere are two principal features that the three orientations,hermeneutic, analytic and postmodern, have in common. I t

44

Philosophy and desireis these common fe atur es whi

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