BADIOU

_ .....1IiIt . . original phtloeophcr wo~killg in

. Swl•• ' RI ~ . . ~ of postmodrm orthO<lox}'. Badi~HlrS work
. ' pn-ennial attftnpt to provtdc a sy...tcmanc theory of uuth.
P"'-nta, for the" 8nt tirm.' in Engli5h . a comprehcnsiH' o\'c~'''icw of
anbitioua systrm. ~ with Badiou's cont ro versi al assertIon. lha~
. tnaIhem.Itia. this vofumc. ;' out his theo~ of the e me rge nce err lr~ths
........ ~ betweee a 1Ubjfi1: md VI event. Also included I:> a
ntnct &om fonhi:omiDg work. on th<- login> of appcaranCf' and
01' oriel', ph ted heft' in mMK't' of its Frendl publication .
....' & ft' -r «.
oi.uch aDOIricaI figures as Spinoza. Kant and Hegel
_; ::~~ . . . ~. ~ . ;and radical politics, TMord kQJ
_ tMb .••.t lr" "cdwa
to oar oI lbr great thinkers of our time .
 Also available from Co ntinu um:

B eillg and Iioenr, Alain Badi ou

Theoretical
Infinite Though t : T ruth and the R etur n 0/ Ph ilosophy , Alain Bad iou
Think A gain: Atain B adiou and she Future of Philosophy ,
edited by Peter Hallward
Writings
A lain Badiou

Edited and t ranslated by Ray Brassier and AlbertoToscano

Co n linu um For Sam Gillespi e ( 1970--200 3), whose pioneeri ng work and ten a-
T he T ower Building 15 East 26th SUCCI
I I York Road N,,"'York
cious, pa ssiona te intellect remain an abid ing in spiration to bo th of us.
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, Ray Brossicr and Alberto T oscano 2004

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 Conte nts

List of Sou rces viii

Ed ito rs' Note IX
Au t h o r's Preface xiii

Section I . O n tology is Mathematics

L M athem atics and Philosoph y: The G rand Sty le and the L itt le St yle 3
2. Ph ilosoph y and M ath em atics; Infin ity and th e End of Rom an ticism 21
3. T he Question of Being T oday 39
4. Platoni sm and Ma the matical O nto logy 49
5. The Being of Number 59
6. One , Multiple, M ul tiplicities 67
7. Spiooee 's Clo sed Onto logy 81

S ection II . The S ubtraction of T rut h

8. T he Event as Trans-Being 97
9. On Subtraction 103
10. T ru th : Forcing and th e Unnameab le 119
I I. K ant 's Subtractive Ontology 135
12. E ight Theses on th e Universal 143
13. Politics as Truth Procedur e 153

S ection III. Logics of Appearance

14. Bein g and Appearance 163
15. Not es T oward a T hinkin g of Appearance 177
16. T he Transcen dental 189
17. H egel and th e Whole 22 1
18. Lan guage, Thou gh t, Poet ry 233

Notes 243
In d ex of Co ncepts 253
In d ex of Nam es 255
 List of Sources Editors' Note

'l\h thc matics and Ph ilosoph y: T he Grand Style and the L infc Style' is The p urpose of this volume is to d istil the essen tial lineam ents of Alain
translated from an unpu blished manusc ript; ' Philosop hy an d M athem atics: Badi ou 's phi losop hical doc trine. In spite of the p lural ' writings' in ou r title ,
In finity and the E nd of Roman ticism ' originally appeared as ' Phi losop h ic er thi s is no t a reader, an overview or a repr esen tative selection . Anyone alr ead y
marhem ariquc' in Conditions (Paris: Sc uil , 1992), pp. 157- 78; 'T he Question acq uainted with Badiou 's ' English ' wor ks, but not familiar with his entire
of Being Today' originally app eared as ' La question d e l'etrc uujc urd'hui' in outp ut, cou ld be forgiven fo r mistaking h im for a pole mica l essayis t - gifted ,
Cour t sraite d'omologie transitaire (Paris: SCUll, 1998), pp. 25-38; ' Platonism insightfu l, provocative, b ut by no mean s a th inker capab le of reca sting the
and Mathemati cal Ontology' origina lly appeared in Cour t traite d'ontoiogie existing param eters of phi losophica l d iscou rse. Those who have react ed scep-
tra nsimire, pp . 95-119; 'T he Being of N umbe r ' or iginally appeared in Court tically to zealous claims mad e on his behalf ma y feel legitim ately ent itled 10
trait e d'ama lcgie transitoir e, pp. 141-5 1; 'O n e, Mul tip le, Mu ltiplicities' ori- their sceptic ism on the bas is o f the evidence present ed by Badi ou 's extan t
gi na lly appeared as ' U n, mu ltipl e, multiplici ters), in multitudes 1 (2000) , pp . and forthcoming En glish pu b lication s (these be ing, in chrono logical orde r:
195-2 11; ' Sp inoza's Closed Ontology' ori ginally ap pea red as ' L'on tologie M anifesro f or Philosophy ; Deleuz e; Ethics; I II/ m ire Thought, Saint Paul, 011
fcr mec de Spi noza ' in Court trait e d'ontoiogie tr ansitoir e, p p. 73-93; 'T he B eckert; Handbook of Inaesthetics; 011 M etapolirics). Notwithstan ding the
Event as T rans- Being' is a revised and expand ed version of ' L'cycnem en t und eniable interest and ofte n strikin g origi nality of these works, witho ut an
comme trans-eire' in Court traitc d'omologie transitoire, p p. 55-9; 'O n Sub- ad equate grasp of Badi ou 's systematic doctri ne, they ca n easily be (and indeed
tra ction ' origin ally appea red as ' Co n ference sur la sousrracuoo' in Condif iolls, have been ) treated as works of po lem ical int erv ention , p edagogy, popularisa-
pp. 179-95; 'T ruth: Forcing and the Unnameable ' originally ap peared as tion , comment ary . . . in short, as works that might elic it ent hu siastic assent
'V eri te: forcagc ct inuomabl c' in Conditions, pp. 196-2 12; ' K an t's Su btractive or virulent rejecti on , bu t wh ich fail to comma nd th e patient , d iscip lined
O n tology' orig in ally ap pea red as ' L'ontologie soustrac ttve d e Kan t' in Court engagement solicited by an unp reced ent ed philosoph ical project. What do we
traite d'cntoiogie transitoire, pp . 153-64; ' Eight Theses on the U niv ersal' o ri- mean by an un pr ecedented ph ilosoph ical project? Quite sim p ly, th e one laid
g inally appeared as ' H uit theses sur I'univcrscl ' in Uniuersei, singulier, sujet, ou t in Bad iou 's Being and Eoent: ( 1988) - a book wh ich may yet tu rn ou t to
ed. I clica Sumic (Paris: K ime, 2000 ), pp . 11- 20 ; ' Politics as a Trut h Pr oce- have effec ted the most profoun d and far -r eachin g renewal of the pos sibilities
du re' origi na lly ap pea red in A brigi de met apolitiqnc (Paris: SCUll, 1998), pp. of philosophy since Heidegger's Being and Time, rega rdless of on e' s eve ntual
155-67; ' Being and App earan ce' origina lly appeared as ' L'etrc cr l'a pp araitrc' evaluation of the desirability or ultimate wor th of such a renewal. J ust as one
in Court trai ts d'ClI/tolllg;e transiroire, pp. 179-200 ; ' No tes Towar d a T h inking docs not have to be a Heideggerean to acknowledge the epoc h al importan ce
of A ppearance' is trans lated from an unpu b lished manuscript; 'The T ran s- of B eing and Tim e, on e does not have to accept Badiou 's start ling cla ims in
cendental' and ' Hegel and th e Wh ole ' ar e tr an slated from a draft man uscr ipt order to acknowledge th e astoni sh ing depth and scope of the proj ect in itiated
of Logiql/t'S des ntondes (Paris: Seuil , fo rt hcoming); ' La ng uage, T hought , in Being and Event , which is being exte nded and partially recast in th e forth-
Pocu-y' is tra nslate d from the aut hor's manuscript , a Portuguese lang uage coming The Logics of W orlds ( 200 5).
version has bee n pu b lished in Par a 11111<1 N ova Teoria do Sujeito: Conferi ncias Theoretical l\i'riti'lgs provid es a concentr ate of thi s p roject. Adrniucdly , it is
B rasilelras (R io d e j aneiro : Rclume-D umara, 1994), pp. 75-86. a book assembl ed from a wide variety of teXIS, so me published , some unpub-
lished : essays, book chapt ers, lectures, con ference papers, as well as two
x Theoret ical Wnt!ngs Editor s' Note

extra cts p reviewing The Login of Worlds. In spite of the heter ogen eity o f th e tinu um, and Keith An sell Pearson for pr ovidi ng us with th e init ial contact,
so urces, and the constrain ts these inevi tab ly imposed , we have deliberately We wou ld also like to exp ress o ur grat itude to those friend s wh o have con-
assembled the material in such a way as to articu late and exhi bit the fu nda- tribu ted , in one way or ano the r, to the conce p tion and prod ucti on of th is
mental structu re of Bad iou's system. Accordi ngly, Th eoretical tl'lri lillKs is volume, whether th rou gh ongo ing debate or ed itorial interven tions: Jason
divided into th ree distinct sections, each sect ion anchored in the preced ing Bark er. L orenzo C h iesa. John Co llins, Oliv er Feltham, Pet er Hallward, Ni na
ouc. Th us the book is exp licitly d esigned to be read in seq uential orde r . Each Power and Damian Vea l. M ost of all, our th ank s go 10 Alain Bad iou, whose
section unfolds the content and ramifications of a core component of Badicu ' s uns tin ting gene rosity an d con tinuo us su ppo rt for this ven tu re over th e past
doctrine. Sec tio n t, OmofoCJ' is M athematics, introduces the read er to the th ree yea rs have proved vital.
groundi ng ges tu re behind Badio u's p hilo sophical p roject, th e ident ification of
ontology with math emat ics. Section II , The Subtraction 0/ Truth , p uts R.B. , AT .
fo rward the lin k be tween th e fundamental conce pts of event. tru th and Londo n. Novcrnber 2003
su bject as they are articu lated onto th e on tological doctrine ou tlin ed in
Section L Sect ion III , Logics of A ppearance, outlines the recen t d evelopme n t
in Badiou of a theory of appearan ce that seeks to localize the truth -e ven t
within the speci fic cons istency, or transcendental logic. of what he calls a
wo rld. In con form ity with the ar ch itectoni c JUSt outl ined , eac h section begins
with direct treatm ents of the relevant featu re of Bad iou 's system (on rolcgy
and the axiom; subjectivity, su btra ction and th e even t; appearan ce, logi c,
wo rld), before goi ng on to elaborate on these: features th rough ( I) targeted
engagemen ts with key ph iloso phica l interlocu tors and/or ri vals (D eleuze on
th e Status of the multiple; Spinoza on axiomatic onlOlogy ; Kant on subtrac -
tio n and subjectivity; Hegel on totality and appearance ). and (2) brief exem-
plifications o f phi losop h y's engagement with its extra-p hiloso ph ical
conditions (emancipation and un iversality; the num erical schem atization of
po litics; the relation between language and poetry).
S ince we cons ide r Bad iou 's original materi al and our ar rangement thereof
10 ren der any fu rthe r p refatory remarks a h ind ran ce to th e reader's engage-
ment with th e work itse lf', we have chosen to confine ou r ow n remarks to a
postface, which will IT)' to gauge th e conseq uences and ex p licate the stakes of
Badiou 's p roject vis-a- vis the wider phi losophica l land scape. Were th e reader
to enco unte r int rac tab le d ifficu lt ies in navigatin g Badi ou 's co nceptual ap pa-
ratus, we strongly recomm end that he or she refers [Q what will un doub ted ly
remain the 'canonic al' com mentary on Badt ou 's thought, Pet er Hallward 's
Bad/Oil: A S llbjr!ct to T ruth (M inneapolis: Minnesota Un iversity Pr ess, 2003 ),
com p h::mc llling it if need s be with writi ngs from the b urgeo ning second ary
liter ature.
We have tried 10 keep ed ito rial inrcrve n rion s to a strict min imum, pr ovid -
ing biblicgruphica! refer ences or cla rifications wherever we deemed it neces-
sa ry. All no tes in sq uare bra cket s arc ours.
T he cd ltors wou ld like to thank Trista n Palmer , who first comm issioned
this pro ject, H ywcl Evans, Ver onica Mi ller and Sarah Do uglas at Con -
 Author's Preface

Philosop hical wor ks come in a pecu liar variety of form s. Uhimarely, however,
they all seem to fall somewhe re between two funda me ntal b ut opposing ten-
de ncies . At one ext rem e, we find the comp lete absenc e of writing an d the
espo usal of oral tra nsmi ssion and critical d ebate. T h is is th e path chosen by
Socrates, the venerab le incep to r. At the o the r extreme, we fin d the single
'great work', perpetually reworked in solitu de. This is basically the case with
Schope nha ucr and h is end lessly rev ised World as W ill ami Representa tion.
Between these two ex tremes, we find the classical alternation betw een p re-
cisely focused essays and vast synoptic trea tises. T his is the case with Kant,
Descartes and man y othe rs. But we also encounter the apho ristic approach,
much used by Nietzsche , or th e carefully orc hestrated success ion of works
dealing with p roblems in a clearly d iscerni b le seq uence, as in Bergson . Alter-
natively , we have an amassing of b rief bu t very dense texts, without an y
att empt at systematic overview , as is the case with Leibniz; or a d ispa rate
series of long , qua si-novelistic works (sometimes in vo lving pseudon yms), like
those produced by Kic rkcgaard and also to a certain extent by Jacques
Dcrrtda. We shou ld also no te the significant n umber of wor ks that have
acqu ired a myth ical status p recisely because the y were announced but neve r
finished: for example, Plato' s dialogue, Th e Philosopher; Pascal's Pensees, the
third volume of Marx's Capita l, pa rt two of Heidegger's Sein und Zeit, or Sar-
Ire's boo k on mo rality. It is also important to note how many ' books' of phil o-
sophy are in fact lecture not es, eithe r kept by the lecturer him self lind
subseq uent ly pu bli shed (th is is th e case for a ma jor po rt ion of Heidegger 's
work, bu t also fo r figu res like Jules La gncau , Merleau-P onty and othe rs), or
taken by students (this is the case fo r almos t all the works by Aristo tle that
have been hand ed down to us, bu t also for impo rtant parts of Hegel's work,
such as h is aestheti cs an d h is history of phil osop h y). Let's round off this b rief
sketch by rem ark ing that the phi losophical corpus seems to encom pass every
co ncei vable style of p resen tation: dramatic d ialogue (Plato, M alcb ranchc,
Sche lling ... ); novelist ic narrative (Rousseau, Hold erlin, N ietzsch e ); mat h-
ematical treat ises in the Eu clid ean manne r (Descartes, Spinoza ); auto-
 Theoret ical Wrltlngs Author's Preface

biograp hy (St. Au gu stine, Kie rkegaard .. .); expans ive treatises for me pu r- Wh at th ese essay s, which m y two fr iends have gathered and basicall y rein-
poses of wh ich the author has forged a new concep tual vocabulary (K an t, ven te d here, sho w - at lC2St in m y eyes - is that in o rder for the theor etical
F ichte, Hegel ...); poe ms (Pannenid es, Lucretius .. .); as well as m an y oth ers- triad o f being, truth, and su bject to hold , it is necessary to think th e triad
ba sica lly, anyt hing whatsoe ver thai can be classified as 'writing '. tha t follows from it - whi ch is 10 say th e triad of the mu lrip le (along with the
In other word s, it is impossible to prov ide a clea r- cut cri terion for what void), the event (along with its site) and th e ge neric (along with th e new
cou nts as a boo k of philosoph y. Co nside r the n th e case of th ese Theoretical forms of knowled ge wh ich it allows u s 10 for ce).
If/ ri l itlgJ; in what sense can th is presen t book really be said to be one of m y In other word s, what we have h er e is the theo re tical co re of m y phi loso-
books? Specificall y, one of my books of p hi losop hy? Is it not rather a book by phy , becau se th is book ex hibits, non-deductively, n ew technica l co ncept s th at
m y friends Ray Brassier an d Albert o T oscano? After all, the y gathered and allow us to tr anscribe the classical problematic (being, truth, su bject) into a
selected Ihe texts from severa l d ifferent books, which for th e mo st part were co ncep tu al assem b lage th at is not on ly modem, but perhaps even 'more-
nor stri ctly spea kin g ' works' but rather co llections of essays. They decided than-modem ' (given that th e adjective ' pos trnod ern' has been evacuated o f all
thai th ese texts merited the adjective 'theo retica l'. And th ey translated them con ten t). These co nce pts ar c: math em atical multiplicity, th e plurality of infi-
into English. so th at the en d res u lt can be said not to have existed anywhe re n ities, th e void as p roper nam e of being, th e even t as trans-be ing, fidelity , the
pri or to this publication . su bject of enq uiries, the generic and forci ng. These concep ts provid e us with
Basicall y, I wou ld like abo ve all to than k th ese two fr iend s, as wel l as the rad ically new term s req uired for a reform u lation of H eid eggcr's funda -
T ri stan Palm er fro m Co ntin uu m, who agree d to publish all this wor k. I me n tal qu estion: 'W hat is it 10 think ?'
would like to thank them because m el' have pro vided m e, along with other But one of th e aims of m y translato r friends is also 10 ex plain why m y co n-
read ers, wit h th e oppo rt un ity of reading a new, p reviously unp ublished book, cep tion of philosophy - an d hence m y answe r to the qu estion abou t th ink in g
appa rently autho red by someon e ca lled 'A lain Badiou ' - who is repu ted to be - requires that phi losophy remain under the combined guard of th e mathe-
none othe r than m yself. matica l cond ition as well as th e poetic co nd ition . Generally, th e co n-
What is the principal interest of th is new book? It is, I think, th at it p ro- tem po rary phi losop hi cs that pla ce th em sel ves un der th e auspices o f the poem
vides a new fonnulation of what can be cons idered to be the fundamental (e.g. in the wake of H eidegger ) diffe r essentially fro m th ose th at place th em -
co re of my philosophical doctri ne - o r ' theo ry', 10 adopt the term used in the selves u nder the auspices of th e ma thcme (e.g. th e various b ran ches of anal y-
title of this book . Rather than linger over exa m ples, de tails, ta nge ntial tical phi losophy). One of th e pec u liar characteristics of m y ow n p rojec t is th at
hypoth eses, the ed ito rs have co-ordinated th e sequence of fundamental con- it requires bo th th e reference to poe try and a basis in mathem atics. It does
ce pts in such a way as to con struct a fram ework for th eir articulation . They so, m oreover, th rou gh a combined critique o f th e way in wh ich H eidegger
try to show how, start ing from an onto logy whose paradigm is mathemat ical, uses poe try and the way ana lyti ca l phi losop hers use math em ati cal logic. I
I am able to propo se a new vision of wha t a trlllh is, along with a new vis ion be lieve th at th is double req uiremen t follows fro m th e fact th at at th e co re of
o f what it is to be th e Jubject of su ch a tru th. m y Ih ink ing lies a rat ional d enial of finitude, and th e co nvict ion that think-
This pairing of subject and truth goes back a long way. It is one o f th e o ldes t ing, ou r th inkin g, is essentially tied to th e in finite. But the in finite as form of
pairings in th e entire history o f ph iloso phy. Mo reo ver, th e idea that the roo t o f being is mathemat ica l, while th e in fin ite as resource for th e po wer of lan-
thi s pairing lies in a thi nking of pu re being , or being qua bei ng , is not exac tly guage is poe tic .
new either . But this is the whole po in t: Ra y Bra ssier and A lbe rto T oscano are For a long time, Ray Brassier and Albert o Toscano hoped th e titl e of this
co nv inced tha t th e way in whi ch I propose to link th e three term s being, tr uth , boo k wou ld be The S ulfur M uthet1le. Perhap s thi s is tOO esote r ic an expres-
and subject, is novel an d pe rsuasive; perhaps becau se th ere arc rigoro u sly sion . 8 Ul it encaps u late s what is essen tial 10 my th ink ing . T hought is a
exac ting conditions for th is lin kin g . In order for bei ng to be thi nkable, it has to 'm ath eme' insofar as th e p ure mu h ip le is on ly th inka ble th ro ugh math cm a-
be co nsidered on th e basis o f th e mathematical th eo ry of multipliciti es. In tical insc riptio n. But rhough r is a 's te llar mathem c' in so far as, like th e
o rde r for a tru th to co me forth, a hazardous su pple me nting o f being is sym bo l of th e srar in th e poe try of M allarmc, it co nstit ute s, beyond its own
required , a situa ted b ut incalculab le event . La stl y, in o rder for a subject 10 be em p iricallimits, a reserve of etern ity .
co nstit u ted, wha t m ust be d eployed in the situ ation o f th is sub ject is a m u lti- A .B
p licity tha t is ano nymous and ega lita rian, wh ich is to sa y, gen er ic. Paris, Sp ring 2003
 SECTION I

Ontology is Mathemat ics

 CHAPTER I

Mathematics and Philosophy

The Grand Style and the Little Style

In order to address th e relati on between mathematics and phil osophy, we

must first distinguish between the grand style and the little style.
The litt le style painstakingly construc ts mathemati cs as an objul for ph ilo-
sophical scrutiny. I call it 'the litt le style' because it ass igns mathem atics a
subservient role, as some thi ng whose on ly function seems to consist in
helpi ng to perpe tua te a well -defined area of ph ilosophical specialization, This
area o f specia lization goes by the nam e ' philosop hy of mathematics", whe re
th e genitive 'or is objective. The philoso phy of mathematics can in tu m be
insc ribed within an area of specialization that gOC1 by th e nam e 'epistemology
and hist ory of science'; an area pos sessi ng its own special ized bu reaucracy in
those acade mic comminees an d bod ies whose role it is to manage a perso nn el
comprising teac hers and researchers.
But in philosophy, specialization invariab ly gives rise to th e littl e st yle. In
Laca nian term s, we could say that it collapses the discou rse of the Master -
which is rooted in the master-sign ifier, the 5 1 that gives rise to a signifying
chain - onto the d isco urse of th e University, that perpetual commentary
which is well rep resen ted by the second moment of all speech, the 52 which
exists by making the M aster disappear thro ug h the usurpation of com me n -
tary.
The Hnl c sty le, whic h is characteristic of the ph ilosophy and epi stem ology
of math ema tics, str ives to d issolve the ontol ogical sovereign ty of mathe-
matics, its aris tocratic self-sufficiency, its unrivalled mastery, by con finin g its
dr amat ic, almost baffling existence 10 a stale com part me n t of academ ic
specialization.
The most tellin g feature of th e littl e style is th e manner in whi ch il exerts
its gr ip upo n its objec t th rou gh historicization and classification . We could
charac terize th is object as a neutered ma thematics, one which is the exclusive
preserve of the little sty le precisely beca use it has bee n created by ir.
Wh en the goal is to elimi nate a frighten ing master-sign ifier , classificatio n
and h isrc ricizaricn are the ha llma rks of a very liul e style.
4 Theore t ical Wri t ings t-tatremaucs and Philosophy 5

LeI me straigh ta way provide a genuinely worthy ins tance o f th e lill ie sty le; vers ion bu t only with th eir m odem co unte rpa rts known as Platonism, neo-
in o the r wo rd s, a great exam p le of th e lill ie sty le. I refer to the 'phi loso phical nominalism, and " eo-conceptu alism (th ough we sh all mostly om it th e prefix
re marks' thai co nclu de a tru ly remarkable work entitled Foundations of S et- 'noo -' since we sha ll h ave no opport un ity to d ea l with the o lder ve rsions).
Th eory, whose seco nd ed itio n, from wh ich I am q uoting h er e, dares from In additi on , w 1.' shall d eal wit h a fou rth attitude wh ich rega rd s th e who le
1973 . I ca ll ir grea t beca use , amo ng othe r things, it was written by th ree firs t- pro b lem of th e onto logica l status of un iversa ls in genera l an d of se ts in
rat e logicians and m athematicians : Abrah am F raenkcl , Yeh oshu a Bar -H illel particular as a met aph ysical pseud o-problem.I
and Azricl Le vy . This book's co ncl ud ing philoso phica l paragraph bald ly
states that: Clearly, the phi losophi cal inco rporation of mathem atics ca rried out by th e
little sty le amount s to a neo-classical ope ra tion pur e and sim ple. It assumes
Ou r first problem reg ards the ontological starus of SClS - not of this or th e that ma thema tics can be trea ted as a particular area of ph iloso phi cal co nce rn ;
othe r set, bu t se ts in general. S ince sets, as o rdi na rily und ers tood , arc wha t tha t thi s treatm ent necessaril y p roceeds th rough a co ns ide ration of logic and
ph ilosop he rs ca ll ll1li w rsals, o ur presen t prob lem is pa ri of the well-k nown langu age; th at it is en tirely com patible with read y-ma de philosophical cate-
and am p ly discussed problem o f th e ontological status 0/ ulliversals. 1 gories; and th at it lead s to a class ification of doc tr ines in ter ms of p roper
names.
L et us im m ed iately note th ree fea tures of th is bri ef parag ra ph, with which T here is an old tech nical term in phi losop hy for th is kind of neo-classicist
an y adept of th e little style would unhesitatingly conc ur . ap proach : scho lastici sm.
Firstl y, what is at stake is not what mathematics m ight enta il for ontology , Where ma th ematics is concerned, the little sty le amounts to a regional
bu t ra ther th e specific ontology of math em ati cs. In othe r wo rd s, mathematics scholasticism .
her e sim p ly represent s a particular in stance of a ready- mad e phi losop hical We find a perfect exam p le of thi s regional scho lasticism in an intervention
qu estion, ra th er tha n some th in g capable of cha llenging o r un derm in ing that by Pasca l Engel. P rofessor at the Sorbonne, in a boo k ca lled M athematical
qu estion, an d still less so me th ing capab le o f providi ng a paradoxical o r Object ivity.J In th e co urs e of a grammatica l eXCUr1US concerni ng th e sta tus of
dramatic so lutio n for it. statem en ts. Engel m anages to use no les s th an twen ty-five cla ssificatory
Second ly, what is th is read y-made ph ilosop hical q ues tion? It is act ually a syn tagm s. These are, in thei r order of ap pea rance in th is littl e jewel of scho-
ques tion conce rn in g logic, or th e ca paci ties of lan guage. In short, the lasticism: Platonism , on to logica l realism , nom in alism, ph enomenalism ,
ques tion of universals. O nl y by way of a p reliminary redu ct ion of ma them a- red uctionism, fictionalism , ins trumen talism, on to logical antireali sm , sem an tic
tica l problems to logical and linguistic problem s docs one become able to realism, seman tic an tirealism, intuiti onism , id ealism, verificationism, form-
shoe horn mathematics into the rea lm of philosop hica l quest ioning an d tran s- alism , co ns tructivism, agnos ticism, onrologjcal reduct ion ism, on to logical
fo rm it into a specialized objective region su bs umed by ph ilosoph y. T h is inflatio n ism. semantic atom ism, holi sm, logicism , onto logical neutralism.
pa rticu lar move is a fundamen tal hallm ark o f the lillie sty le. co nceptualism, empirical rea lism and co nce ptual Platoni sm. M oreo ver,
Third ly, th e p hilosoph ical problem is in no sense spa rked or provoked by rema rka ble th ou gh it is, Engel 's compulsive labelling in no way exha ust s the
th e ma th ematical prob lem; it has an indepen dent hist ory and, as the authors possi ble categorial perm uta tion s. These are p roba bly infinite, whi ch is why
rem in d us, feat u red prom in entl y in 'th e scho lastic debat es of th e m id dl e scholasticism is assu red of a bu sy fu tu re, even if, in con form ity with th e
ages' . It is a cla ssical problem , with regar d to which mathema tics re presen ts scholastic inj unction to inte llectual 's er ious ness', its wor k is invari ab ly
an opport unity for an upd ated , regional ad ju stm ent. carried ou t in team s.
Th is becom es ap par ent whe n we co nside r th e classi ficato ry zeal exhibi ted N evertheless, it is po ssible to sketch a b rief survey of m odem scholasticism
b y th e autho rs when they co me to outl ine the possibl e respon ses to th e in the com pany of F ra cn kcl, Bar-Hillel and Levy. Fi rst , the y propose defin i-
p ro b lem: lions for each of th e fundament al ap proac hes. T hen they ca utiously poi nt ou t
that, as we have alre ady seen with Engel, there are all sorts o f int er mediary
The th ree main tradi tional answe rs 10 th e p roblem of un iversals, stem m ing positio ns. F inall y, they designat e the pur est standard -bearers fo r eac h o f the
from medieval di scussions, are known as realism, nominalism, and concet nu- fou r position s.
atism, \'(' e shall no t dea l here wit h these lines of th ough t in th eir tr adi tional Lei'S ta ke a closer look.
 6 The oretical Writ ings t-tatr emaucs and Philosophy 7

F irst, th e d efinition s. In the follow ing pa ssage, the word 'set ' is to be one whether certai n ex isten tial sentences ca n be proved, or d isproved , or
un d erstood as d esign ating an y math em ati cal con figura tion that can be shown to be und ecidable, withi" a giw II lheory, th e other wheth er thi s
defined in rigo rou s language: theo ry as a whole sho uld be accepted,"

A P latonist is convi nced that correspo ndi ng to each well-defined (monad ic) Cam ap, th e th eoretician most rep resen tati ve of this clarificatory ap proach ,
co nd ition there exis ts, in ge ne ral, a set, or class, wh ich co m p rises all an d suggests that th e first prob lem , which d epe nd s on the reso urces of th e theory
on ly those en tities th at fu lfil th is co ndi tio n and wh ich is an enti ty in its in q uestion , is a pu rely technical one , and th at the seco nd p roblem boils
ow n right of an on tologica l status sim ilar to that of its membe rs. do wn to a practica l issue thai can on ly be decided according to various
A neo-naminalist declares himself un able (0 un derstan d wh at oth er peo ple criteria. which F raenkel et a!. sum ma rize as :
m ean when th ey arc talki n g about se ts un les s he is ab le to interp ret thei r
tal k as a fa;otl de parler. The on ly lan guage he professes h imself 10 [L )ikelihood of being cons isten t , ease of maneuverability, effectiveness in
unders tan d is a ca lculus o f ind ivid uals, cons tructed as a firs t-ord er deri vin g classical analysis, teachabiliry, perhaps pos session o f standard
th eory. mod els, etc.6
There are authors wh o are att racted neith er b y th e luscious jung le flo ra
of Platon ism nor by the ascetic dese rt landscape of neo- nominalism . It is by failing to di sti nguish between th ese: two questions that one en ds up
They prefer to live in the well-d esigned and perspicuous orcha rds o f neo- form ulatin g mean ingless metaphysical problem s such as; •Are th ere non-
conceptualism. They claim [0 unders tand what sets are, th ough th e den ume ra b le in finite sets?' - II question that can onl y lead to irresolvab le and
metaph or they p refe r is that o f const ructing (or invemi"g) rather than that ul tima tely steri le co ntro vers ies because it mi stakenly invokes existence in an
of singling out (or disCQtJed"g), whi ch is th e one cheris hed by th e Plato- absolute rather than mer ely th eory -relati ve sen se.
nis ts ... [Tlhey are not rea dy to accept axioms or theorems that would Clearly then. the littl e style encompasses all four of lh CSC' optio ns, an d
force them to admi t the ex istence of se ts wh ich are not co nstru ctively holds sway wheth er one adopts a realist, lingu istic, constructivist or purely
characteriza ble ." relativist stance vis-a-v is th e existence of mathematical en tities.
But this is beca use one has already p resu pposed that philoso ph y re lates to
T hu s th e Platonist ad mits th e existen ce of entities th at are ind ifferen t to math em atics through II critical examination of its objects , that it is th e mod e
the lim its o f language and transcend human con st ructive capacities; the of existence of th ese objects th at has to be interroga ted , and that th ere are
nom ina list on ly adm its th e existen ce of verifi ab le: indiv id ual s fu lfilling a ulti mate ly four ways of co nceiving of that existence: as intri ns ic; as nothin g
transpa ren t syntactic form ; an d th e co nceptua list dem ands that all existence but th e co rrelate o f a na me; as a m ental co ns truction; o r as a variable prag-
be subo rd inated to an effec tive con struct ion , wh ich is itself dependent upon matic co rrelate.
th e existence of enti ties that are either alre ady eviden t o r cons tructed. T he gran d style is entirely d ifferen t. It stipu lates th at m ath ematics
C hu rch o r Godel can be invoked as un comprom ising Plat on ists; H ilbert o r provi des a d irect illum ina tion o f ph ilosop hy, rath er tha n th e op posite , and
Bro uwer as uneq u ivocal conce ptua lists; and G oodman as a rabid nom inalist. that th is illu m in ation is ca rried ou t thro ugh a forced or even violent interven-
We have yet to ment ion the app roach whic h re mai n s rad icall y agn ostic, the tion at the core of these issues.
one tha t always comes in fourth place. Follow ing th esis I (' Sets have a re al I will now run th rough five m ajest ic exam ples of th e grand style:
exi stence as ideal en tities independent of the m ind '), thesis 2 (' Sets exist on ly D esca rte s, Spinosa , K ant , H egel and Leutr eamont .
as ind ividu al enti ties valida ting lingu istic expressions'), and th esis 3 (' Sets Firs t exam ple; D escart es, R egulae ad directianem iI/g el/ii, ' Ru les for the
exist as m en tal co nstructio ns'), come s th esis 4, the supern ume rary thesis: D irection of the M ind ', R ule II :
'T he quest ion abo ut the way in which sets ex ist has no m ean ing Ou tside a
given rhco rcuca t con text ': T h is furni sh es us with an evide nt ex planatio n of th e grea t su perio rity in
cert itude of A rithmet ic an d Geome try to other sciences. The forme r alone
Thc p revalent o pin ion s [i.e. Platon ism, nom in alism and conceptu alism ) arc d eal with an object so pu re and uncom plicated , th at the y need make no
ca used by a fu sion of, and con fusion betwee n , tWO different qu estions: the assump tions at all which experience ren ders uncer tain , b ut wh olly consist
8 r-tathemancs and Philosophy 9

in the rat ional deduction o f co nse q uences. T hey arc on that account mu ch In the ea rliest times to whi ch the h istory of human reaso n extends, mathe-
the easiest and dearest of all, and possess an object such as we req uire, fo r mat ics, among that wonderful peop le, the G reeks, had already entered
in th em it is scarce humanly pos sib le for an yone to crr except by inadve r- upon the su re path of scie nce . But it mu st not be sup pos ed that it \\'35 as
ten ce .... easy fo r m ath ematics as it was for logic - in which reaso n has to dea l with
But on e co nclus ion now eme rges ou t o f th ese cons id era tions, viz, no t itse lf alone - to ligh t upon, or ra ther cons truct for itself, th at ro yal road.
indeed , th at Arithmetic an d G eometry are the so le sciences to be stud ied, O n th e co ntrary , I bel ieve th at it long remain ed , es pecially among th e
b ut onl y th at in o ur search for th e di rec t road to wards truth we shou ld Egyp tians, in the groping stage, and th at th e tra nsformation m ust ha ve
bu sy ou rselves with no object abo ut whic h we cannot att ain a cert itude bee n due 10 a revolution b roug h t about b y th e hap py th ough t of a single
equ al to that of the demonstrations of Arithmetic and Geometry." ma n, the experi ments whi ch he devised m arking out the path upon wh ich
the science must en ter, and by followi n g wh ich , secu re prog ress
For Descartes, math ematics d early provides th e pa rad igm for ph ilosop hy, th ro ughout all ti me and in end less ex pans ion is in fallib ly secu red . ..
a paradigm of certainty . But it is im portant not 10 con fuse th e latter with a A new light Hash ed upon th e mind of th e firs t man (be he Thales or some
logical pa radigm . It is not p roo f th at lies behind th e paradi gm atic value o f ot her) who demo nstrated th e p roperti es of th e isosceles tri an gle. The true
ma thematics for th e phi losoph er . Rather, it is the abso lu te sim plicity and method, so he foun d , was not to inspect what he di scerned either in th e
cla rity of the ma thematical object. figu re, o r in the bare co ncept of it, an d from this, as it were, to rea d off its
Second example: Spinoza, appendix to Book On e of the Ethics, a text dear p roperties; but to b ring ou t what was necessari ly implied in th e concepts
to Lo uis Alth usser : th at he has himse lf formed a p rio ri and had pu t into the figu re in th e
co ns truction b y wh ich he p resen ted it to himse lf.9
So th ey m aintained it as certa in th at th e judgm ent s of the god s far surp ass
man 's gra sp . This alone , of co urse, would h ave caused th e truth to be T h us K an t thinks, firstl y, that mathem atics secured for itse lf from its very
hidden from the human ra ce to ete rn ity, if math em atics , wh ich is origin th e sure path of a science . Second ly, that th e cre ation of mathematics
con cerned not with ends, but on ly with th e esse nces and properties of is tantamount to an absolute his torical singu larity , a ' revolution ' - so mu eh
figures, had not shown m en ano ther stan dard of truth .... so that its eme rgence d eser ves to be singu larized : it was du e to th e felicito us
That is why we have such sayings as: ' So m an y heads, so man y att itudes', th ought of a single m an . Nothing co uld be further fro m a h istoricist or
'everyone finds his own jud gment m ore than eno ugh', an d 'th ere are as cul ruralist exp lanation. Thirdly, Kant thinks th at , once ope ned u p , the path
m any differences of b ra ins as of pa lates'. These prover bs show sufficien tly is in finite, in time as we ll as in space. This un iversalism is a con cr ete un ivers-
that men judge thi ngs acco rdi ng to th e d ispos it ion of th eir brain. an d alism becau se it is th e un iversalism of a tra jectory of th ough t that can alwa ys
imagine, ra th er than unders tand them. Fo r if men had underst ood th em , be retraced , irrespective of th e tim e o r the pla ce. And fou rth ly, K ant sees in
th e th in gs would at least co nvince them all, even if th ey d id not attract mathematics some thing that m arks th e perpetual rediscovery of its paradig-
th em all, as th e exam ple of mathem atics shows. ' matic fun ct ion , the ina ugu ra l co nception of a type of knowledge tha t is
neither em pi rica l (it is not what can be di scerned in the figu re), no r formal (it
It wou ld be no exagge ration to say th at , for Spmoza, mathematics governs docs nor co nsis t in th e pu re, static, identi fiable pro pert ies o f the co ncept).
the his to rlal d estin y of knowle dge, and hen ce th e econo my of freedom, o r T hus mat h ematics pave s th e way for th e critical representation of th inking,
beatitude . Withou t mathemat ics, humanity langu ish es in the night of su per- which consists in see in g knowledge as an instance o f non -em pirical p rodu c-
stitio n, which can be sum marized by the ma xim : th ere is some th ing we lion or cons truction, a sensib le cons t ruc tion th at is adeq uate to the cons ti-
can not think. T o whic h it is necessar y to add th at mathematics also teaches tu ting a p riori. In other wor d s, 'T hales' is th e pu tat ive name for a revolu tion
us so me th ing essential: th at whatever is thought truly is imm ed iate ly shared. that exte nds to the en rircry of philosophy - whieh is to say that Klint 's
Mathematics shows th at wh ate ver is un der stood is radically un d ivided . T o critica l project amounts to an exa m ina tion of the co ndi tion s of possib ility
know is to be absolutely and un iversall y conv ince d . th at un der lie Thales' con structio n.
T h ird example : Kam , Critique of Pure Reason, Preface to th e seco nd Fourth example: H egel , S cience of Logic, th e leng thy Rem ark th at follows
edi tion : the explica tio n of th e in fin ity o f th e q uantum :
10 Theoretcal Writings Mat hemat ICSand Pt'III0s0phy
"
[I) n a p hilosophical respect th e mathematical infini te is im portant because Lau rreamom, usin g th e post - Romantic name ' Maldo ror ', wants to bring
und er lying ir, in fact . is th e notion of th e ge nuine in fini te and it is far about a denatu ring of m an , a transmigration of his essence, a positive
superio r to th e o rdi nary so-called metaphYfital j"/illite on which arc based b<."'COm ing-monster. In o ther wo rds, he wants to ca rry out an ontological
the objections to th e mathematica l infinite. ... de regu lation of all th e ca tego ries of humanism . M athem at ics plays a crucial
It is worth wh ile: co nsidering more close ly the ma th em atica l conce pt o f the au xiliary ro le in th is ta sk. H ere is a passage fro m Boo k I I of M aldoror:
infinite together with the most noteworthy o f the att em p ts aimed at just i-
fying its usc: and eliminat ing th e di fficu lty with wh ich the method feels o rigo ro us math em at ics, J have not forgotten you since you r wise lessons,
itself burdened. T he considerat ion of these justifications and characteristics swee ter than honey, filt ered into m y heart like a refresh ing wave. lnsrin c-
of the mathematical infinite which I shall und ertake at some length in th is tivcly , from the cra dle, I had longed 10 d rink fro m you r so urce, o lder than
R emark will at th e same lim e th row th e best ligh t on th e natu re of th e true the sun, and I contin ue to tr ead the sacred sanc tuary o f your so lem n
Notion itself and show how th is latt er was vaguely present as a basis for temple, I, th e most faithful of your d evot ees. There was 3 vagu eness in m y
th ose procedures. 10 mi nd, somethi ng th ick as smo ke; b ut I managed to m ount th e ste ps wh ich
lead to you r altar, an d you drove away thi s dark veil. as th e wind b lows th e
The dec isive poi nt her e is th at, for H egel , ma th ematics and philosoph ical draught-board . You rep laced it with exces sive co ldness , co ns ummate
speculation sha re a fundamental concept: th e co nce pt of the infinite. M ore p rudence an d im placa ble logic.. . . Ari thmetic! A lgebra ! G eo metry! Awe-
pan icul arl y, th e des ti tu tion of the metaphysical co nce p t of infinity - in other ins pi ring tri nity! Luminous trian gle! H e wh o has not known you is a fool!
words, th e d estitu tion of classica l th eo logy - is ini tia lly undertaken th rough H e wou ld deserve th e ordea ls of th e gr eatest tortures; for therc is blind
th e de termination of th e m ath emati ca l co ncep t o f th e in finite. H egel d isda in in his ignora nt ind ifference . . . But you. concise mathem atics , by
obv iously has in m ind th e creation of th e d ifferen tial and in tegra l ca lcu lus th e rigoro us seq uence of you r un shakeable pro po sitions and the const ancy
during th e seve nteenth and eigh teen th ce n tu r ies. H e wan ts to show how the of you r iro n ru les, give to the d azzled eyes a po werfu l reflec tion of th at
true (i.c. d ialect ica l) co ncep tion of th e infinite makes its historica l appeara nce sup rem e tru th whose im pri nt can be seen in the o rde r of th e un iverse....
und er the auspices of mathematics. H is method is rem arkable: it con sists in You r modest pyra mi ds will last longe r than the pyram id s of Egy pt, those
exami ning th e contradic to ry labour o f th e Not ion in so far as th e lat ter can anthi lls raised by stup id ity and slavery . And at th e end of all th e cen tu ries
be see n to be at wo rk within the math ematica l tex t itself. The Notion is bo th you w ill stand on th e ruin s o f time, with you r cabba lisuc cip hers, your
acti ve and m anifest, it ru ins th e transce nden t th eo logi ca l co ncept o f th e lacon ic eq uations and your scu lpted lines , on th e aven ging right of th e
in finite, but it is not yet th e co nsc ious know led ge o f its own acti vity . U nli ke A lmighty, whereas th e stars will p lunge desp air ingly, like whi rlwinds in
th e m etaphysica l infinite, the m ath em atica l infinite is the same as th e good the etern ity of horrible and un ivers al nigh t, an d gri maci ng m an kind wi ll
in finite of th e d ialect ic. But it is lh e same on ly acco rding to th e d ifference thi nk of settling its accounts at th e Last Judgmen t. Thank you for the
whereby it does not yet kn ow itsel f as th e same . In this ins ta nce , as in Plato co un tless services you have do ne m e. Thank you for th e alien q ua lities
or in my own work, ph ilosop hy's role cons ists in infonning m ath em atics of with wh ich you en riched m y in tellect. Withou t you in m y struggle agai ns t
its ow n spec u lative grandeu r. In H egel , th is takes th e fonn o f a deta iled man I woul d perhaps have been d efeated. II
exam ination of wha t he refer s to as th e 'j ustifications an d characteristics ' of
the mathem atical concept of th e infin ite; an examination which , fo r h im, This is an arrest ing text. It d evelop s arou n d mat hem atics a kind of icy
co nsists in carryi ng ou t a m eticulous analysis of th e ideas of Euler and consecration , fai rly rem ini scent of th e d ialectical sign ificance o f the gre at
L agrange. T hro ugh th is an alysis, on e sees how the math em atical concep tion Mallanncan sym bo ls: the star, 'co ld from for getfuln ess and obsctesccoce';'!
of the in fini te, whic h for H egel is st ill ham pe red by 'the dl fficulry wit h wh ich the mirro r, ' froze n in [Irs] frame ' ;!) th e tomb, 'the so lid sep ulch rc whe rein all
the method feels itse lf bu rdened ' , harbours with in itself the affirma tive th ings harm fu l li c ' t~ and the 'hard lake haun ted be neath the icc by the tr ans-
reso urce of a ge n uinely absolu te concep tion o f quanti ty. parent glaciers of fligh ts never flown ' .15 All of whi ch seems 10 evo ke a glacial
It seems fitti ng that we shou ld conclude th is su rvey of the grand style with anti-h um an ism . But in La utreamom, th e 'excessive coldness' of mathem atics
a figu re who stra dd les the margin be tween philosophy an d th e poem: Isidore is co upled with a mo numenta l aspect , a so n of Masoni c sy mbolism of
D ucasse, aka th e Co mte de Lauireamon r. Li ke Rim baud an d Nietzsche, ercrnir y: the 'lum ino us tri angle' , th e 'co nstan cy o f iron rules' , th e pyramid _. .
 12 Theoret ical Wnt lngs r- te tbemaucs and Philosophy 13

J ust as N ietzsche wished 10 surpass Ch rist and announce the adven t of Soc ra tes: So o ur o verm an mu st be bo th ph ilosopher and so ld icr?
D ion ysu s by having Zarath ustra speak in the language of the G ospel s (' in G lauco n: Of co urse .
truth ' , ' I say unto you ', CIC. ) , Laurreamon r, by coupling Masonic csotcricism Socrates: Then a law m ust be passed - im med iately.
with Old T est amen t language, wants to d elineate th e monstrous beco mi ng to Glaucon: A law ? Why a law. in God's nam e? W hat law?
whic h an exh au sted , defiled m an kin d is d est ined . In thi s regar d , mathe- Soc ra tes: A law stip ulating th e teaching of hi gher arit hme tic, you dullard .
matics, wh ich is di vid ed in ro alge bra, arithmetic and geo me try - i.e. ' laco nic Hut we'll have trouble.
equations", 'ca bbalistic ciphers' and 'sc u lpted lin es' - renders an indispc n- Glaucon: Trouble? Why?
sab le service: it imposes on u s a kind of im placable ete rnity whic h d irectl y Soc ra tes : T ake a young fellow who want s to beco me ad mi ra l of th e fleet. or
challenges th e humanist conception of man . Mathematics is, in effect, 'o lde r mi nis te r, or president . or some th ing of tha t ilk. A youn g ho tsh ot straight
th an the sun' and will remain intact 'o n the ru ins of time' . Malh emalics is out of th e L SE o r Yale . D o you im agine he'll be ru shing to en rol at th e
th e d iscipl in e and th e severity, th e immutabili ty and th e ima ge of 'th at ins ti tute o f h igh er arithmetic? We'll have som e serious co nvi ncing to do ,
su p reme truth ' . This is only a sh ort Step away fro m saying that mathemat ics let me tell you .
inscribes bein g as such; a Ste p which. as you know. I have take n . But for Glauco n: I can 't imagine wh at we're goi ng to tell h im .
Lautreamom, ma th ematics is some thing even bett er : it is what furn ishes the Socrate s: The tru th . So me thi ng ha rsh. For exam p le: ' M y d ear fellow. if you
inte llect with 'alien qu ali ties ", This is an esse n tial po int: there is no intrinsic want to become m ini ster or admi ra l, firs t you have to srop being such an
harmon y between m ath ematics and the human intellec t. The exercise o f agreea ble young m an , a common yu ppie. Take numbers, for ins tance, do
mathematics. th e lessons - 's wee ter than honey' - th at it teac hes, is th e you know what numbe rs are? I'm no t ta lking about what you need to know
exe rcise of an alteration, an estrangem en t o f intellig en ce. And it is first and to ca rry out your petty little busin ess transactions, or co unt whatever it is
foremos t th rough this resource of strange ness that mathematica l et ernity you' re flogging on th e market ! I'm l3lking about num ber in so far as you
su bve rts ord inary thi nk in g. H er e we have the profound rea son why, witho ut co ntem plate it in its eternal essence through the shee r power of you r yuppie
mathem atics, without th e infecti on of co n ventiona l thinking by m ath ematics. intellect, which I p ro m ise to dc-yu pp ify! Number such as it ex ists in war. in
Maldoror wo uld not have p revailed in his fundamental struggle against the terrible reckoning o f weapons an d co rpses . But abo ve all, number as
humanist man. in his struggle to bring forth th e free m onst er beyond wha t brings about a co m plete upheaval in thinki ng. as what erases appro xi-
hum an ity of which m an is capable . mat ion and beco mi ng to make way fo r be ing as suc h, as well as its truth .'
O n all these points. from glacial ami-hum anis m to th c trans-hu m an ad vent Glaucon: After hearing your lillie speech , I th in k ou r yuppie friend will
o f truths. I th in k I m ay welt be Is idore Ducessc's one and on ly ge nuine ru n like he ll. sca red om o f his wits.
d isciple. Why then do I ca ll my self a Platonist rath er than a Ducassean o r a
son of Maldoror? T his is w hat I mean by th e gra nd sty le: arit hmetic as an ins tance of ste llar
Because P lato says exactly th e same thing. and warlike inhuman ity !
L ike Is idore Ducasse, Plat o claims that ma thematics und oes doxa and It should co me as no surp rise. then , tha t today we see mathematics being
defea ts th e so ph ist. Withom mathematics th ere cou ld ne ver arise, beyond attacked sys tem atica lly from all sides. J ust as po litics is being syste matically
existing h umanity. th ose philosop her-king s who represent th e overm an' s alle - att acked in the nam e of econom ic and state manageme nt ; or art sys tem atically
go rical name in the co nceptual city erected b y Plato . If the re is to be an y att acked in th e nam e of cu ltural re lativity; or love system atically attacked in
chance of seeing th ese ph iloso ph er-kings appear. the you ng mu st be taught tin' name of a pragm atics of sex. The littl e sty le of epis te mo logical specializa-
arithmetic, plan e geome try. so lid geo me try an d astronom y for at least te n lion is merely an unw illing pawn in th is anack. So we have no cho ice: if we
years. For Plato , what is admirable about mathem atics is not JUSt that, as is arc to defe nd ou rselves - 'we' who speak on behalf of p hilosoph y itsel f and of
well know n. it lieu its sights on pu re esse nc es, on the id ea as such. but also the sup plement ary step it can and m ust ta ke - we hav e to find th e n ew terms
tha t its utility ca n be exp licated in ter ms of th e only pragma t ics of any worth rcquircd for th e grand style.
fo r a man who has risen beyond man , wh ich is 10 say , in term s of war. Hut let us fir st rccapirul utc the teaching of our ad m ir ab le p redecessors.
Conside r lo r exam ple this passage from The R epublic, Book 7, 525c (wh ich I It is obvious th at for eac h of the m. the co nfro ntation with ma thematic s is
have taken Ihe libert)' to retran slate): an abso lu tely indi spe nsab le co ndition for philosop hy as such; a conditio n that
 14 Tbecreucat Wri tings r-ietreroeucs and Philosophy 15

is at once descriptively external and p resc rip tively immanent fo r philosop h y. 13stic aSIXCt of mathem atics. Similarly, for K ant . th e hisrorial d est in y of
This hold s even where mere are eno rmous d ivergen ces as 10 what co nst itu tes math em atics as cons tru ct ion of th e concep t in in tuition cons titutes a revol u-
the fundamental proj ect of p hi losophy. For Plat o, it consists in creatin g a lion that is entirely independen t of the destiny of logi c, whic h is al read y
new conception of politics. For Descartes. in enla rging the scope of absolute com plete and has sim ply bee n treadin g wate r since the time of its founder,
certainty to encom pass the essent ial ques tions of life. For Spinoza, in Aristotle. H egel examines the foundation of a conce pt , that of the infini te,
attaini ng the intellec tu al love of G od . For K ant, in knowing exa ctly whe re to an d dis regards the apparel of proo f. And altho ugh Lautr eam ont ce rt ainly
d raw th e line betwe en faith and know led ge. For H egel , in showing th e ,lpp reciates th e iron nece ssity of the d eductive p rocess and the cohe rence of
becom ing-subject of th e absolute. For Lautrearnom, in d isfigu ring and ove r- ligu res, what is most import ant for h im in ma th ema tics is its icy d iscipline
coming human ist man . But in each case, it is a q uestion of giving th anks 10 and power o f ete rnal survival. As for Spi noza , he sees sa lvation as resid ing in
' rigo ro us math em atics ' , II doesn 't matter whether phi losophy is co nceived of the onto logy that und erlies ma thematics , whic h is to sa y, in a conception of
as a rationalism tiro to tran scendence, as it is fro m Descart es to Lacan ; as a being sho rn of every appeal to meaning or pu rpose. and p rizing only the
vita list immanentism, as it is from Spinoza to Delcu ee, as pious criticism. as cohesiveness of consequen ces .
it is from K an t to Ricoeur; as a d ialect ic of th e absolute, as it is fro m H egel There is nOI a single mention o f language in all thi s.
to M ao Zedong; or an aestheticist crea tionis m, as it is from La u trea mo n r to LeI u s be blum and remark in passing that. in thi s regard, Wi ugenstci n,
N ietzsche. For the founder s of each of th ese lineages, it still remai n s th e case despi te th e cunn ing of his sterilized loquacity an d despite th e un den iable
that th e co ld radicali ry of ma th ema tics is th e necessary exer cise th rou gh for mal beau ty o f th e Tracuu ut - with out doub t on e of th e m asterpieces of
whic h is forged a th inking subject adeq uate to the tra n sform ations he w ill be ant i-p h iloso phy - must be co unted amo ng th e architects of th e little sty le,
forced to under go . whose p rinci p le h e sets ou t with his customary b ru ta lity. T hus, in proposi-
ExactJy the sa me hol ds in m y case. I have assigned ph iloso ph y th e tas k of tion 6.2 1 of the Traclatus, he dec lares: 'A pro posi tion of mathematics does
co ns tructing thought's embrace of its own ti m e, of refracting newborn tru ths not exp ress a th ough t.' J7 O r worse sti ll, in h is Remarks on the Foundations of
th ro ugh th e uniq ue pri sm of concepts. Ph ilosoph y mu st intensify an d ga th er M athema tics. we find this son of tri te pra gm atism , whic h is very fashionable
together. under th e aegi s o f system atic th inking, not just what its time nowadays:
im agines itself 10 be, but what irs time is - albeit unknowing ly - ca pable of.
And in order to d o th is, I too had to labo riously set down m y own lengthy I should like to ask somethi ng like: 'D oes every calc ula tion lead you to
' tha n k you' to rigorous mathem atics. som ething useful? In th at case, you have avo ided co n trad iction. And if it
L et me pu t it as bluntly as possible: if ther e is no grand sty le in th e way docs ne t lead you to an yth ing usefu l then wha t di ffer ence does it m ake if
p hilosop hy relates to mathem atics, the n th ere is no gran d style in phi loso ph y you ru n in to a con u adiction ?d 8
fu ll stop.
In 1973. Lacen, using a 'we' th at , for all its imperiousness, included bo th We can fo rgive Wittgenstei n. Bu t not those wh o shelter behi nd h is
psy ch oanalys ts and psychoan alysis, decla red: 'M ath em atical formalization is aesthetic cunning (whose entire im petu s is eth ica l. i.e . religious) the be tte r 10
our goal , our ide aL, 16 U sing th e sam e rh etoric, and a ' we' th at now incl ud es ado pt the littl e sty le once and for all and (vain ly) try to throw to th e mod em
bo th ph iloso phe rs and ph ilosoph y, I sa y; 'M ath ematics is our o bligation, our lions of ind ifference th ose de te rmi ned to rem ain faithfu l to the grand st yle .
al teration .' In any case , our maxim is: philosophy must .mte r into logic v ia mathematics,

... ' 10 / inca mathematics v ia logic.

In my wo rk this translat es into: m athem atics is th e science of bei ng qua
being. Lo gic perta ins to the co here nce of ap pea ra nce . And if the study of
N one of the parti san s of th e grand style ever be lieved that th e phi losophica l appearan ce also mob ilizes ce rtai n areas of mathem atics, th is is sim p ly
id entificati on o f math ema tics had 10 proceed by way of a logicizing or beca use, followi ng an in sigh t formalized by H egel but wh ich actuall y goes
lin gui st ic red uction . Suffice it to 53)' that for D escartes , it is th e int ui tive back to Plato , it is of th e esse nce of being to appea r. This is wh at maintain s
clarity of ideas that foun ds th e mathematical parad igm , nOI th e automatic th e form o f all ap pea ring within a mathem anzable transcendental o rder. Bu t
characte r of th e deducti ve p roce ss, which is m er ely the uni nterest ing , scho- he re, once agai n , transcendental logic, whi ch is a part of m ath ema tics tied to
16 Theore tical Wri tings t-tat hemancs and Philosophy 17

conte m porary sheaf theo ry, holds sway over form al or linguis tic Jogic, which ph ilosophy from ph enomenological religiosity; 10 re-found the meta ph ysical
is ultimately no more than a superficial tra ns latio n of the former . Iriad o f be ing , event and subject; to take a stand again st poetic prop hesying;
Reiter ating the ' we' I used ea rlier, I will say : M ath em atics leaches us abo ut ro identify gen eric m u ltiplicities as th e on to logical form of the true; to assign
wh at must be said concern ing what is; not about wha t it is permiJfib/~ to say a p lace to La can ian forma lism; and , mo re recen tly, to articulate the logic of
con cern ing wha t we rhi" k there is. appearing .
Le t'S say that, as far as w e're concern ed , mathem atics is always mo re or
less equivalent to the b ulldozer with wh ich we remo ve the ru bble mat
preven ts us from constructing new edifices in the open air.
M atbemattcs provides ph ilosop hy wi th a weapon , a fearso me mach ine of T he p ri ncipal di fficulty p robably resid es in th e assumption th at mathema -
though t, a ca tap ult aimed at the bastio ns of ignorance, supers tition and tical com pe ten ce requ ires yea rs of initiati on. Whence th e tem ptation, for the
men tal servitud e. It is not a docile grammat ical reg ion . For Plato, mathe- philosoph ical de magogue, either to ignore mat hem atics altoge the r or act as if
matics is what allows us to break free from the sop h ist ical dictators hip of the most pr imitive rud imen ts arc eno ugh in orde r to un derstand what is
linguistic immed iacy. For La utreamont, it is wh at releases us from the going on th ere. In th is regard , Ka nt set a very bad exam p le b y encou rag ing
morib und figu re of the huma n . Fo r Sp ino za, it is what breaks with su pe rs ti- generations of philosoph ers to believe th at th ey cou ld grasp the essence of
tion . But you have read their texts. Som e today would have us believ e th at mathematical judgeme nt th rough a single exam p le like 7 + 5 ,. 12. Th is is a
mathematics itself is relative, prejudiced an d inconsistent, need lessly arist o- bit like someo ne saying that on e can grasp the relation between p hilosoph y
cratic, or alterna tely, subservient to tech nology. You shou ld be awa re that and poetry by recit ing:
th is p ropagand a is trying to undermine wh at has always been most implac-
abl y opposed to spiritu alist approxima tion and gaud y scepticism, th e sickly H umpty Dumpty sat on the wall ,
allies of flambo yant nihilism . For the truth is that mathematics does not Hu mpty Dumpty had a great faJl.
understa nd th e meaning of the claim ' 1 ca nno t know' . The ma themalica l All the king's horses and all the king 's men
realm does not ackno wledge the existence of sp iritualist categories such as Co uldn' t put H um pt y together again!
those of the unthinka ble an d the un th ough t, supposedly exceedi ng the
meagre reso ur ces of human reason ; or of those scep tical catego ries whic h Afte r all, th is is JUSt a b unc h of verses, JUSt as 7 + 5 .. 12 is JUSt a bun ch of
clai m we cannot fever provide a definitive solu tion to a p rob lem or a definitive nu mbers .
answer to a serious q ues tion. It is strikin g that , whether one considers a phi losophical tex t written in the
The other sciences an: not so reliable in th is regard . Q uentin M dllassoux linle sty le or one wri tten in th e grand style, no justi fication wha tsoever seems
has conv inci n gly argued tha t p hysics provides no bulwark aga inst sp iri tualist 10 be req uired for quoting poetry, but no-one wou ld ever d ream of quoting a
(wh ich is to say obscurantist) speculation, and biology - th at wild em piricism piece of ma thematical reasoning . No-one see ms to consider it acceptab le to
di sgu ised as science - even less so. Only in math ematics can one un eq uivo- dispe nse with Hold cnin o r Rim bau d or Pessoa in favou r o f H um p ty
cally main tain th at if though t ca n form ulat e a problem , it can and will serve D um pty, or to d itch Wagner for Ju lio Iglesias. But as soo n as it is II question
it, regard less of how long it takes. Fo r it is also in mathem atics th at the uf mathe matics, the rea der eit her sim ply loses interest o r immediately assoc i-
maxim ' Keep going!', the o nly maxim requi red in eth ics, has the greatest ates it with the little style, wh ich is to say, with episte mo logy, th e histo ry of
weight. How else ar e we to expl ain the fact that the so lu tion to a pro blem science, specialization .
formu lated by F ermat more than three cen tu ries ago can be d iscover ed T his was not Phuo's point of view, nor that of an y of the great philoso-
today? Or that todny's mathem atician s are still actively eng aged in proving or phers. Plato very often qu otes poe try, but he also quotes theorems, ones
disp roving conjec tures first p roposed by the G reeks more th an two thou sand Which are p robably deemed relatively eas y by today's standard s, bUI were
years ago? T here can be no doubt that ma the matics conceived in the grand certain ly dema ndi ng wh en Plato was writing : th us, in the M e,/O for insta nce,
style is wa rlike, po lemical, fearsome. And it is by donning the con tem po rary the construct ion of th e sq uare whose su rface is double that of a given sq uare.
matheme like a coot of armou r that 1 have undcnaken, alone at firs t, to undo I claim the righ t 10 q uote in stances o f mathema tica l reason ing, provided
the disastrous co nseq uences of ph ilosophy's ' lingu istic tur n '; to dem arcat e the)' arc ap propriate to the p hiloso phical theses in the context of which they
18 Tbeorencal Wri t ings r-tathemaucs and Philosophy 19

ar e being inscribe d , and th e knowledge req uired for understanding them has not a fixed and irreversible acqu rstucn. T he historicity of mathematics is
alread y been made available 10 the reader . Gi ve us an example, I hear you noth ing b ut the labour of the in finite, its ongoing and unpred ictab le
say. But I'm nOI going to give you an exam ple: of an exam p le, beca use I 've rc- cxposition . A revolut ion, whether French or Bolshevik. cannot exh aust th e
alread y provided hu ndred s of real exam p les, int egra ted int o th e movement of fonnal concept of emancipatio n, even though it presents its rea l; simi larly,
though t. So I will men tion two o f these mo vements inst ead : th e prese ntation inc ma thema tical ava tars o f th e thou ght of th e infin ite do not exhaust th e
of D edek ind 's doctrine of nu m ber in Chapter 4 of Nwnber and N llmbers,l 9 ~ pccu l 3ti ve concep t of infinite though t. The confro ntation with mathematics
and the conside ration of the point of excess in M editation 7 of B eing and must constan tly be reconst ituted because the idea o f th e in finite on ly mani-
Evew. 20 Consult them, read them, using the reminders, cross- references and fests itself th rough the mo ving surface of its mathematical reconfigu ration s.
th e glossary I have p rovided in each book . And an yone who still cla ims not T his is all the more essent ial given that our id eas of the finite, and hence o r
to un dersta nd shou ld write to me telling me exactly wha t it is they don ' t the phil osophical virtualities latent in finitude, becom e retroac tively d isplaced
un derstand - otherwise, I fear, we' re simp ly dea ling with excuses for th e and rein vigorated th rough th ose crises. revo lu tions and changes of heart that
reader 's laziness. Ph ilosophers are able 10 u nderstand a fragm ent b y Anaxi- affect th e ma th ema tical schem a of the infin ite. The latt er is a mo ving front. a
man der, an elegy by Rilke, a sem inar o n th e real by Lacan , but not th e struggle as silent as it is relentl ess, where noth ing - no more th ere than else-
2.500·year-o ld proof that th ere are an infin ity of prime numbers . This is an where - ann ou nces the advent of perpetual peace .
una ccep table, anti-philosophical state of affairs ; one wh ich on ly serves the Wh at d o th e following notion s have in common as regards th eir sub tlest
interests of th e partisans of the little style. consequences for thinking: the infin ity o f prime numbers as concei ved by the
I have spoken of bulldoze rs and rubble. Wh ich cont em po rary ru ins do I Greeks. the fact that a fun ction tend s towa rd infin ity, th e infinitely sma ll in
h ave in mind? 1 think H egel saw it befo re anyone else: ultimately, mathe- non-stan dard ana lysis. regular o r singu lar infinite cardinals, the existence of a
maries p ropo ses a new concep t of th e infinite. And on th e basis of th is numbe r-object in a topos, th e way in wh ich an ope rator grasps and projects
concept. it allows for an imma nen tizatio n of the infin ite, separating it from an un tctalizab le collectio n o f algebraic structur es omo a fam ily of sets - no t
th e On e of theology. H egel also saw that the algebraists of h is time, like 10 ment ion hu nd reds o f other theor et ical formulation s. concepts, model s and
Euler and Lagran ge, had not q uite grasped th is: it is on ly with Baron Ca uchy determin ations? Probab ly someth ing th at has to d o with the fact that the
th at the th orn y issue of the lim it of a series is finally settled , and not un til infinite is th e inti mate law of th ough t. its nat u rally anti-natu ral med ium . But
Ca ntor th at ligh t is finally th rown on th e augu st q uestion of the actual in anoth er regard, th ey have noth ing at all in commo n. N othing that wou ld
in fin ite. H egel th ought th is con fus ion was due to the fact tha t th e 'true' allow one merely to reit erate and maintai n a simplified , allusive relation with
concep t of the infinite belon ged to speculation, 50 that mathematics was ma the matics. This is because. in th e word s of my late friend G illes Chatelcr,
merely Irs un consciou s bea rer, its unwitti ng midwife . The truth is that the lIle mathema tical elaboration of though t is not of th e orde r o f a mere linear
mathema tical revolution - th e rendering exp licit of what had always been unfold ing o r straigh tforward logical consequence. It comp rises decisive but
im plicit within mathematics since the tim e o f th e Greeks, wh ich is to say, the previously un known gest ures." One mu st begin again, beca use mathematics
thorou gh -going ration alizat ion of the infini te - was yet to come, and in a is always beginning again and transforming its abstract panoply o f concep ts.
sen se will always be yet to co me, since we still do not know how to effect a O nc has to begin study in g. wri ting and understanding again that wh ich is in
reason ab le ' forcing' of th e kind of infini ty proper to the continuum . Neve r- fact the hard est th ing in th e world to u nderstand and whose abstraction is
theless, we do know wh y mathematics rad ically sub verts bo th emp iricist thc most inso lent, beca use thc ph ilosop hical struggle against th e alliance of
mod erat ion an d elegan t scep ticism: math emati cs teaches us tha t there is no finitude and ob scu rantism will onl y be rekindled through th is recommence-
reason wha tsoeve r to confine th inking within the am bi t of finitude . Wi th mcnt .
ma thematics we know that , as Hegel woul d have said, th e infin ite is nearb y. T h is is why Mallu rm e was wrong on at least one poin t. Lik e evcry great
Yet someo ne mig ht ob ject: 'Well th en, since we already know the resul t, I'K>Ct, M:al1ar mc was engaged in a tacit ri valr y with ma thematics. He was
wh y not just be satisfied with it and leave it at that ? Wh y continue with the Irying to show that a densely imagistic poe tic line, when art iculated with in
arid labou r of familia riz ing ourselves with new axioms, un precede n ted the bare cadences of thinking, comprises as much if not more truth than the
proofs, difficu lt concepts an d inconceivably abstra ct th eories?' Because the cxtre-lingu isrlc inscr iption of the mathcme. This is why he could wri te, in :I
infinite, such as mat hem atics renders it ame nable to th e ph iloso phical will , is sketch for lgirur:
20 Theoretical Writings

Infinity is born of cha nce, which you have d enied . You , expi red mathem a-
tician s - 1, absolute pro jection . Shou ld end in In finity ,22
CHAPTER 2
T he idea is clear: Mallurmc accuses mathematicians of denying chance and
thereby of fixing the infini te in the heredi ta ry rigi di ty of calculation . In
Igitur, th at rig idity is symbolized by th e fami ly. Whence the poetic, ann- Philosophy and Mathematics
math emarlcnl operatio n wh ich , M allar me believes, binds infinit y to cha nce Infinity and the End of Romanticism
and is symbolized by the d ice-th row. On ce the dice h ave been cast , an d
regard less of th e resul ts, ' in fin ity escapes the family,.n This is why th e math-
ematici ans expire, and the ab stract conception of the infi nite along with
them, in favour of tha t impersonal absolute now represent ed by the hero.
But wh at M allarme has failed to see is how the o perations through which \'>;that docs th e tide 'ph ilosophy and mathematics' imply about the relation
mathemati cs h as reconfigu red the conceptio n of the infin ite are consta ntly between these two disciplines? Does it indicate a difference? An influence? A
affirming chance th rough th e cont ingency of th eir reco mmcnce me m . II is up boundary? Or perhaps an indifference? For me it im plies none of these. I
to philosophy to gath er togeth er or con join th e poe t ic affir mat ion o f infinity unders tand it as impl ying an identification of the mod alities according to
drawn metaphor ically from chance, and th e ma thematical construction of the wh ich mat hematics, ever since it s Greek inception, has been a condit ion for
infin ite, d raw n formally from an axioma tic int u ition . As a resu lt, the in junc- philosop hy; an identification of the figur es th at have h istorically ent an gled
tion to mathematical bea uty intersec ts with the injunction to poetic truth. mathematics in the determination of the space proper to ph iloso phy.
And vice versa. From a purely descriptive perspective , three of these modalities or figur es
T h ere is a very bri ef poem by Alvar o De Campos, one of the heter on ym s can be distingui shed :
used by Fe rnand o Pcssoa. De C am pos is a scientist and engineer and his
poem succi nctly summarizes everyth ing I ha ve been saying. You shou ld be O per ating from the perspective of p hilo sophy, th e first modalit y sees in
ab le to memorize it right away. Here it is: mathema tic s an approximation , or preliminary peda gogy, for question s
that are otherwise the provin ce of ph ilosop hy. O ne ackn owledges in
Newton 's binomial is as beautiful as the Vcnus de M ilo . mat hematics a certa in aptitude for thin king 'firs t pri nciple s' , or for
T he truth is few people notice iL2 4 knowled ge of being and truth ; an aptitude that becomes full y realized in
ph ilosophy. We will call thi s th e ontological modality of the relation
Style - grand sty le - sim ply consis ts in noti cing it . bet ween phi losophy and mathematics.
- T he second modality is th e one that tr eats math em atics as a regional
discipline, an ar ea of cog nition in gene ral. Philosophy then sets O U I to
examine wh at grou nds this region al ch aracter o f mathematics. It will
both classify mat hematics with in a table of fo rm s of knowled ge, and
reflect on the guaran tees (of truth or correc tness) for the discipline that
has been so classified. We will call th is the epistemolog ical modality.
- Finally, the th ird mod ality posits that mathematics is ent irely discon -
ncct cd from the questions, o r qu estioning, p rop er to ph ilosophy.
Accordi ng to th is vision of thi ngs , math ematics is a register of lang uage
games, a formal type, or a singu lar gra mmar. In an y case, mat hem atics
docs not t hillk an ything . In its most rad ical fo rm , th is o rien tation
subsu mes mathematics within a generalized techn ics that carries out an
un thinking manip ulation of being , a levelling of bei ng as pur e sta nding-
 23
" Theoreti cal W r itIngs Philosoph y and r-tatbemanc s

reserve. We will call this modality the , ri/;cal modality , because it philosoph ical text continued to be intrin sica lly co nd itioned by m ath em atics
accomplish es a cr itical d isjunct ion between th e realm proper to mathe- III vario us ways.
maries on the one hand, and th at of th inking as wh at is at slake in ph ilo- T he positivist and cmpiricist approaches , which have been highly influe n-
so phy o n the other . tial during the last tw o centuri es , merel y invert the Rom anti c spec u lative
gesture. The clai m th at science cons titu tes the one and on ly para di gm for
The qu esti on I would like: 10 ask is th e following; how do things stan d th e pos iti..-ity of knowledge can be made on ly from with in the com pleted
today as far as the aniculation o f th ese: three mod ali ties is co nce rned? H ow disentanglemen t of philosophy and the sciences. The anti-philosophical
arc we: to situate philosophy's m athematical co nd ition from th e pe rspective of \'crdi et returned by the various forms of positivism oven u ms th e anti-
philosophy? And the thesis I wish to uphold takes the fonn of a ges ture: scientific verd ict returned by the vari ous forms of Romantic ph iloso ph y, but
whereby mathematics is to be re-em angled in to philosophy's innermost st ruc- fails 10 in terrogate its initial premise. It is stri king tha t Heidegger and
ture; a st ructure from whic h it has , in actuality, bee n excluded. I What is Cam ap disagree about everythi ng, except th e id ea that it is incumbent upon
requi re d today is a new co nditioning of ph iloso ph y by mathematics, a co n di- us to in ha bi t and activ ate the end of metaphysics. This is because for both
tioni ng whic h we are do ub ly lat e in putti ng in to place: both late with respect Hcidegge r and Camap, the name 'm etaphysics' d esig nates th e C lassical era
to what mathem atics itself indicates, and late with respect to th e m inimal of philosop hy, th e era in whic h mathem ati cs and phi loso phy were still reci-
requiremen ts necessary for th e con tinuation of ph ilosop hy. W hat is u lti- procally entang led in a general representat ion of the opera tions of thought.
ma tely at stake here can be form u lated in terms of the followi ng question , Carna p wants to purify th e scien tific ope rat ion , wh ile H eidegger wishes to
wh ich weighs upon us and threatens to exhaust us: ca n we be de livered, oppose to science - in wh ich he perceives th e nihili st manifestation of
ji llollj' de livered, fro m our su bjection to Romanticism? meta phys ics - a pa th of th ink ing modelled on poe try . In th is sense, bo th
remain heirs to th e Romanti c ges tu re of d isen tanglem en t, albeit in differ ent
regis ters .
J. T HE DISJ UN C T IO N O F MATHEM ATICS A S This perspective sheds ligh t on th e way in which vario us form s of positi -
PH ILOS OP H I CA LLY CONS T I TU T IVE OF vism and empiricism - as we ll as that refined fo rm of so ph istry represented
ROMA NTIC ISM by Wingenstei n - re mai n inca pable of identifying math em atics aJ a type of
tJri"ki,w, even at a time when any attempt to characterize ir as so mething
Up 10 and including Kant, ma thematics and philoso phy were reciprocally else (as a gam e. a grammar, etc.) constitutes an affront to th e available
en tan gled, to the exten t th at Kant himself (followi ng D escartes. Leibniz, eviden ce as well as to th e sen sibility of every mathematician. Essentially,
Spinoza, and many oth ers) Still sees in the m ythic name of Thales a co mmon both logical positivism and Anglo- American lingui stic so phistry claim - but
origin for math em atics and know ledge in general. For all th ese philosophers, without th e Rom an tic force that wou ld acoompany a lucid awareness of
it is absolutely clea r that math ematics alone allowed the inaugural break thei r claim - that science is a techn iq ue for which mathematics p rovides
wi th superstition and ignorance. Mathem atics is fo r th em th at sin gu lar the grammar , or that ma thematics is a gam e and th e only im portant thing
form of thinkin g which has interrupted the S()f)ereigtlty of myth. We owe is to ide n tify its rule. W hatcver th e case ma y be , mathematics docs not
LO it th e first fo rm of sel f-s u fficien t think in g. ind ependent of any sacred thin k. T he on ly ma jor d iffer ence between th e Romantic founders of what I
postu re of enu nci at ion ; in oili er word s, th e firs t form of enti rely secul arized Would ca ll th e seco nd modern era (the first bei ng the C lassical one) and th e
th ink ing. posit ivists o r mod ern soph ists , is tha t th e forme r preser ve th e ideal of
But th e p hi losophy of Rom an ticism - and H egel is decisive in this regard - thinking (in art , or phi losoph y), whi le th e latt er on ly ad mi t forms of know-
carried out an almost complete disentanglem ent of philosop hy and rnath c- ledge.
m arie s. It shaped the co nviction that p hiloso ph y can and mu st deploy a A sign ifican t asp ec t of the issue is th at, for a gr eat sophist like Win gen -
thinking th at docs not at an y m oment internalize m ath em atics as cond ition st ein, it is po int less [Q etlter into mathematics. Wittgenstein , more casual in
for that deploym ent. I maintain that thi s di sentanglem en t ca n be iden tified as th is respect than H egel , p roposes merely to 'b rush u p agains t' mathematics,
th e Romantic spec ulative gestu re par exc elle nce; to the po int that it re tro- to cast an eye upo n it from afa r, th e way an artis t m igh t gaze upon some
actively d et ermined th e C lassical age of ph iloso phy as one in wh ich th e chess players:
 24 Theo re tical Wrltmgs Philosop hy and r-tathema ucs 2S

The ph ilosop her mu st twist and turn about so as [Q pa ss by th e m ath cm a- Jigmatic Sta tus, whet hcr it be with regard to ce rt ainty or with regard to
tical problems, and not run up agains t one - wh ich wou ld have to be truth .
solved be fore he co uld go further. We will here call ' Rom an tic' an y d isposition of th inki ng which determin es
H is labour in phil osophy is as it were an idleness in math ematics. th e infini te within th e Open, or as horizonal co rrelate for a histo ricit y of
I t is not that a new build ing has to be erec ted, or that a new b ridge has to finitude. T oday in parti cu lar, what essentially subsists of Rom an ticism is th e
be bu ilt, but th at th e geography as it now is, has to be d cscribed .f theme of fin itu de. T o re-imricatc mathem atics and philosophy is also , and
perhaps above all, to hav e done with finitude, wh ich is the p rin cipal contem -
But the tr oubl e is that mathem atic s, which is an exem plary discipline of pora ry resid ue of the Rom antic specu lat ive gestu re.
tho ugh t, does not lend itself to any kin d of d escription and is not represen-
ta ble in terms of th e ca rtograp h ic met aphor o f a co un try to which on e co uld
pay a qu ick visit. And in any case , it is impossible to be lazy in mathematics. 2. ROMAN TICISM CON T INUES TO B E T HE S ITE FOR
It is possibly th e on ly kind of thin king in whic h the sligh tes t lap se in co ncen- OUR THINKIN G TO DA Y, A ND T HIS CON TIN UA TION
tration entails the di sappearance, pure and sim p le, of what is be ing though t REN DERS THE T HE ME OF THE DEA T H OF GO D
about. Whence th e fact that W itt gen st ein is cont inuo usly spea king of som e- IN EFFECTUAL
thi ng other th an math ematics. H e speaks o f the impression he has of it fro m
afar and, more profound ly, of its symp to matic role in his ow n itinera ry. But The q uest ion of ma th em atics, and of its localization by ph ilosop hy, has th e
thi s descriptive and sym ptom atolo gical tr eat m en t takes it for granted that singular me rit of providi ng us with a profound in sight into the nature of ou r
philosop hy can keep mathematics at a distan ce. T his is exact ly thc sta ndard own time. Beyond th e claim s - no t so m uch heroic as em p ty - about an ' irr e-
effect th at th e Romantic ges tu re o f di sentang lem ent seeks to achieve. ducible modernity', a ' novelty still needi ng to be though t' , th e persist en ce of
Wha t is the crucial presupposition for the ges ture whereby H egel and h is the disju nction betwe en mathematics and phi losop hy seems to indicate th at
successors managed to effect th is lon g-lastin g di sjunction betwe en mathe- Romantici sm's his to rici st co re co ntin ues to fun ction as th e fundamental
matics on the one hand and philosophica l d iscou rse on the other? In my horiz on for ou r think ing . The Rom an tic gesture still holds sway ove r us
op in ion , this presupposition is tha t of historicism, which is to say, the tem per- insofar as the in finite contin ues to fun ction as a horizon al correlativ e and
alizuticn o f the concep t. II was th e newfound cert ain ty tha t infinite or true opening for th e histori city of finitude. Our m ode rni ty is Rom an tic to the
being could only be app rehend ed through it s own tem porality th at led th e exten t that it rem ains caught up in th e tempora l iden tification of the concept.
Rom antics to depose m ath ematics from its localization as a co nd ition for As a result, ma the matics is here rep resented as a condi tion for p hilosophy
philosophy. T hus the idea l and arem poral characte r of m ath em atical thin king only fro m the stand poin t of a rad ical d isjunctive gesture, whi ch persists in
figu red as the central ar gument in this deposit ion . Romantic spec u lation Oppos ing the historical life of thought and th e concep t to the em p ty and
opposes tim e and life as tem poral ecstesis to th e abstract and em pty etern ity formal eternity of mathem at ics.
of math ematics . If time is th e ' existence of the conce p t', th en mathematics is Basicall y, if one cons ide rs the status ascri bed to poetr y and mathematics by
unw orthy of that concep t. Plato, one see s how , eve r since Romanticism , they have swap ped p laces as
It could also be said that G erman Rom ant ic philosophy, whic h produced - cond ition s. Plat o wanted to banis h poe ts and on ly allow geomet ers access to
the ph iloso p hical m eans an d th e techn iq ues o f thought required for histori- philosophy. Today, it is the poe m that lies at th e heart o f th c philosophical
cism, es ta blished th e idea th at the ge nu ine in fini te on ly m an ifest s itself as a d ispos ition an d the mathem e that is excluded from it . In our time, it is
horizonal structu re f or the hist oricity of th e finitude of existence, But bot h th e mathe m atics which , altho ugh acknow ledg ed in its scient ific (i.e. tec hn ical)
rep resen ta tion o f the limi t as a horizon an d the theme of fini tude arc ent irely aspect, is left to lang uish in a con dition of ex ile and neglect by philosophcrs.
foreign to mat he ma tics, whose own conce p t of th e limit is tha t of a present- Mat hematics has bee n redu ced to a gram mati cal she ll wherein sophists can
poi nt and whose thi nk ing requ ires th e p resu ppo sit ion of the infin ity of its pu rsue their linguistic exerci ses, or 10 a morose ar ea of specialization for
site. For historici sm , of wh ich Roman ticism is th e philoso ph eme, math e- cobwebbed epistemo log ists. Meanwh ile, the aura of the poe m - seem ingly
mat ics, whi ch links the infinite to th e bounded power of the Jetter and whose since Nietz sche, but act uall y sinc e H egel - glows eve r brig hter. Noth ing
ver y ac ts rep ea l an y invocation of time, could no longer be accorded a para- illum inates contempora ry philosop hy 's fu ndamental ami-Platon ism more
26 Theoretical Wr itings Philosophy and Mathematics 27

vivid ly than its paten t reversal of th e Platonic system of cond itions for phil o-a Descartes was more of an ath eist than we are, because ete rni ty was not
sophy. somcthing he lacked. Little by little, a genera lized historicism is smotheri ng
BUI if this is the case, then th e question that concerns us here has nothing us bencalh a d isgusting venee r of sanctification.
to do with postmodc rni sm. For th e modem epoch comprises two periods, the When it comes 10 the effectiveness, if no t th e pr oclamatio n of the death of
C lassical and th e Rom antic, and ou r qu estion regard s post-romanticism . How God, the contempo rary quandary in which we find ourselves is a function of
can we get out of Rom anticism witho ut lapsing into a neoclassical reaction ? the fact tha t ph ilosoph y's neglect of math em atical th inkin g d elivers the
This is the real pr ob lem , one whose gen uine pertinence becomes apparen t infin ite, thro ugh the med ium of h istory, ove r to a new avatar of the One.
once we start to see how, behind th e th em e of 'the end of th e avant -gard es', Onl y by rela ting the infinite back 10 a neu tral banality, by insc ribi ng
the postmodc rn merely dissimulates a classical-romant ic cclccricisrn. If we etern ity in the math cmc alone, b y sim ultaneo usly abandon ing historicism an d
wish fo r a more precise formula tion of th is parti cular problem, an cxarntna- finitude , docs it become possible to think with in a rad ically dcconsecrated
[ion of the link be twee n phil osoph y and mathematics is the on ly valid path I realm. Hencefort h, the finite, wh ich conti n ues 10 be in th rall to an eth ical
know of. It is the on ly standpo int from whi ch one ha s a ch ance of cu ttin g aura and to be grasped in the pa thos of mortal- being, mu st only be conceived
straigh t to th e heart of the matter, which is no thi ng othe r tha n the critiq ue of of as a tr ut h' s di fferential incis ion with in the banal fabric of in finity.
finitude. The con tempo rary prerequisite for a desecration of thou ght - whic h, it is
T ha t th is critiq ue is u rgen tly req uired is confirmed by th e spectacle - also all tOO apparent, remains to be accompli shed - resides in a comp lete d isman-
very Romant ic - o f the increasing collu sion between phi losophy (o r wha t tling of the h istoricist schema. T he infini te must be su bmitted 10 th e
passes for ph ilosoph y) and religion s of all kinds, since the colla ps e of Marxist math cme's simp le and transpa ren t d eductive chains, su btracted from all
po litics. Can we reall y be surp rised at so-a nd -so's rabbinical Judaism , or so- jurisdiction by th e One, strippe d of its hcrizon al function as the corr elate of
and -so's con version to Is lam, or another 's thin ly veiled Ch ristian d evotion. finitude and released from th e metaph or of the Open.
given that everythin g we hear boil s down to this: that we are 'consigned to And it is at thi s point, in which thou ght is subjected to extreme tension, th at
finitude' and arc 'eutmially marta!' ? Wh en it comes to crushing the infam y math ematics summo ns us. O ur imperative consists in forging a new modality
of su perstition, it has always been necessary to invoke th e solid secular for the ent anglemen t of mathematics and phi losoph y, a modality thr ou gh
etern ity of the scienc es. But how can th is be d on e wilhin ph ilosophy if the which the Romantic gesture th at con tinues to govern us will be termi nated .
disentanglement of mathema tics an d philosophy leaves beh in d P resence and Mathematics has shown that it has th e resou rces to deploy a perfectly
the Sacred as the on ly th ings th at make ou r be ing -m ortal beara ble? precise concep tion of th e infinite as ind ifferent mult ipli city . This 'ind ifferen-
T he tr u th is that th is di sen tanglem ent defuses th e Nic tzschea n proc lama- riarion' of the in fin ite, its pos t- Can tc rian treatm ent as mere num ber , the
tion o f th e death of God. We do not possess the wh erewithal to be atheists so plur aliza tion of its concept (th ere are an infinity of different infinit ies) - all
long as the theme of finitude governs ou r thi nking. this has rende red th e infinite bana l; it h as term inated th e pregnan t latency of
In the deployme nt of the Romantic figu re, th e infinite, whi ch becomes the finitude and allowed us to realize that every situation (ourselves incl uded) is
O pen as site for the temporalization of finitud e, remains beho lden to th e One infinite. And it is thi s evcn tal capacity proper to math ema tical thought that
because it rem ains beholden to h istory. As long as finitud e remains the finally enjoins us to link it to the ph ilosoph ical p roposition .
ult imat e determi nati on of existence, God ab ides. He abides as that whose It is in thi s sense that I have in voked a ' P latonism of the multiple' as a
d isapp earance con tin ues to hold sway over us, in the form of the abandon- progra mme for ph ilosop hy tod ay.
ment, the d erel iction, or the leaving-behind of Being. The usc of the term ' P latonism' is a provocat ion, o r bann er, th rough wh ich
T here is a very tenaciou s and profound link betwee n the d isentanglement It) proclaim the closure of the Romantic gestu re and th e necessity of declarin g

of ma thema tics an d philosop h y an d th e preservation, in the inverted or once mo re: ' M ay no -one who is not a geome try enter here' - once it has been
diver ted form of fin itu de, of a non -a pp ropriabl e or unn am eable horizon of acknowledged tha t the non-geom eter remains in thrall to the tenets of
immo rtal d ivini ty. 'O nly a God can save us' , H eidegger cour ageo usly Romanuc disjunction and the pa tho s of finitud e.
proclaim s, bu t once ma thematics h as been deposed, even tho se witho ut his T he usc of the term 'multiple' indicates tha t th e infinite must be under-
cou rage conti nue to ma intain II taci t God th rough the lack of being engen- Stood as indifferent mu ltip lici ty, as the pu re material of bei ng.
d ered by ou r co-extensiveness with time. The conjunction of th ese tWO terms procl aims ther the death of God can be
 28 Theorencal W ritings PhIlosophyand r-ta hen aucs 29

r..nd ered ope ra tive witho ut privation , th at th e infin ite ca n be un tcthered fro m si\'c (dial/oial , which is not how you charact erize intellection . This d iscu r-
the One, that histo ricism is terminated , and tha t etern ity can be regained s i \"t.~ n ess lies midway betwee n (metax uJ o pinion Ldoxa J and int ellect (nousl . }
within ti me without the need fo r consecration .
In order 10 inau gura te such a programme, we w ill have to loo k back toward In exam in ing what is of significance fo r us in this text - i.e. th e relation of
th e history of the qu esti on. J sha ll p unctuate th is his tory at th e t w o ex trem i- conjuncr ion fd is jun etl0n between mathem atics and ph iloso phy - I will
ties of its arch: :1It one extreme stan ds Plato, who exiles the poe m and proceed by delineating the four fun da mental characteristics th at structure the
promotes th e malhcmc; while at th e OthCT stand s Hegel, who invents th e matrix for every co nce ivab le rela tion between th ese tWO d ispo sit ions of
Romantic ges tu re in philosoph y and is the th inker o f th e abasemen t of thought.
math ematics.
I. For Plato, math em at ics is a condi tio n for th inking or th eorizing in general
because it co nsti tu tes a break with doxa or opi nion . This much is fam ilia r.
But wh at need s to be emphas ized is th at math em ati cs is the only point of
3. PLATO CA RR IES O UT A PH IL OS OPH ICA L rupture w ith doxa thac is give n as exist ing, or constitute d, The ex iste nce of
DEPLOYMENT OF MATHEMATICS AT T HE FRONTIER m ath ematics is ult imat el y wh at constitutes its absolute singu larity . Ever y-
B E T WEEN T HOUGHT A N D T HE FREEDOM OF thing else that exists rem ains prisoner to opinion , but not ma th ematics.
THOUG HT So the effective. historical, independent existence of m athem atics
provi des a paradi gm for th e pom'bilily of b reaking with opin ion .
Plat o is ob viously th e one who d eployed a fundam ental entanglemen t of Of cou rse, th ere is d ialecti cal con vers ion, wh ich for Plato is a supe rior
mathematics and ph ilosop hy in all its ramifications. H e prod uced a ma trix form of b reaking with doxo. But no one can say whether di alect ical
for cond itioning in which th e th ree modalities of the mathematics/philosophy convers ion, whi ch is the essence of th e ph ilosophica l d isposition , exists. It
relation w ith wh ich I bega n are alread y im plicitl y contained. is held up as a proposal o r project. ra th er tha n as so me thi ng act ua lly
We wiII use Boo k 6 of T he R epublic as ou r poi nt of reference. This text is existi ng. D ialectics is a programme, o r initiat ion. wh ile mathematics is an
ca no nica l for our qu estion because it co n ta ins an account o f th e relati ons existin g, avai lab le procedure. D ialecti cal co nversion is th e (eventual)
between m athem atics and th e d ialectic. poin t at which th e Platoni c tex t touches the rea l. But th e on ly po in t o f
Let us examine th e followi ng passage from it. Socrates asks G teuccn, his extern al suppo rt for th e b reak with doxa - in th e fo rm of something that
interlocu to r. if h e has un derst ood h im co rrec tly . In order to ch eck, he in vites already exist s - is co ns titu ted by math ema tics an d mathematics alone.
him to provide a synopsis of th e p reced ing d iscu ssion . H aving reitera ted, as H aving sa id thi s, th e singu larity o f mathematics co nstantly and un fai-
is cus tomary, that this is all very d ifficult , th at he is not sure whether he ha s ling ly p rovokes opin ion, wh ich is th e reign of th e doxa. Whence th e
prope rly unders tood, an d so on, G lauco n ca rries on an d his synopsis mee ts cons tant broadsides agai n st th e 'abstract' or ' inh um an ' na tu re of mathe-
with Socrates ' app rova l: mati cs. Wh enever one seeks a rea l, existing basis for a thi nking that
breaks with every form of opi nio n , one can always reso rt to m athem atics.
The theorizin g concern ing be ing and the in telligible wh ich is su stained by U lti mately , th is singu larity proper to m ath ematics is con sens ual, because
th e science (i pin i mil of th e d ialec tic is clea rer tha n tha t sus ta ined by what everyone recogn izes the re isn't - and cannot be - such a th ing as ma tb e-
arc known as th e scie nces l u chl/il . if is ce rta in ly the case tha t those who m:nical opinion (wh ich is no t to rule out the exi stence of opinion s, gene r-
theo rize acco rdin g to the se sciences, wh ich have hypotheses as th eir prin ci- ally un favou rab le, about mat hem atics - q uite the cont ra ry). M ath em at ics
pies, arc obl iged to p roceed di scur sively ra the r than em pirically. Bu t exh ib its - lind th erei n lies its 'a ristocra tic' aspec t - an irrem edi abl e
bec ause th eir intui tin g rem ains de penden t on th ese hypotheses an d has no disco n tinu ity with regard to every sort of immedia cy proper 10 uoso.
means of accessing the princip le, they do no t see m to you to po ssess the Con versely, it may legitimately be assumed tha t every negative opinion
in te llection of what they theorize, which nevertheless, in so far as it is iIlu- abo ut ma th ema tics co nstitutes , whether exp licitly or implicitl y, a defence
nunared b y th e principle, co ncerns th e imeJligibi lity o f th e en tity. It seem s of the rights o f opinion, a p lea fo r the immediate sove reignty of doxa.
10 me you ch aracte rize the proced ure of geometers and th eir ilk as di scur- Romanticism , I believe, is gu ilty of this sin . As historicism, it has no
 30 Theoretical Writings Philosophy and t-tatnemancs 31

ch oice but to rum the o pi nio ns o f an era int o the tru th of that era. auth o ritarian gesture) and the pri n ciple (that wh ich is at once originary, a
T emporalizarion submerges the concept in the immediacy of hisroricized beg inn ing, and illuminatingly authoritative, a co m m and ).
representar ione, The Rom an tic pro ject im plies th e ou sting of mathe- Ultima tely, dialectics o r ph ilosophy is the ligh t shed by a second break
manes, because one of its effects is 10 render philosophy homogeneous wi th on th e obscuri ty of th e first , whose point of co ntact with th e real is m ath e-
the hiJU)n"cal /H1Wer of opinion, Philosoph y as th e co ncep tu al captu re of ma tics. If we ca n succeed in illuminat ing the hypothesis by the principle,
' the spirit o f me tim es ' cannot encompass an arcmporal break with the then eve" in math ematics we shall en joy th ough t'S freedom o r mobility
regime o f established d isco u rses. with regard to its ow n b rea k wit h opi nion.
YCl it is precisely th is ab ility to effect a real break with m e circu lating Alt hough mathematics genuinely en capsulates th e di scon tinu ity with
immediacy of doxa th at Plato prizes in the mat hematical capacity. doxa, only ph ilosophy ca n allow th ough t to es tablis h itself in suc h a way
2. H aving note d what Plato ad m ires abo ut m ath emat ics, it is necessary to as to asse rt th e princip le of thi s d iscontinuity. Phi losop hy sus pe nds the
address me tw ists in his argume nt. Wh at Plato sets out to explain to us is violence of the m at hem atical break. It es tab lishes a pea ce of the d iscontin -
tha i, however rad ical it may seem, th e mathematical break with opin ion is uou s.
lim ited because it represent! e f orced b reak . ThOSt: who practise the m ath- 4. Conseq uen tly, m athem at ics is mttaxu: its topology , th e site of its think in g,
em atical sciences are 'fo rced' to proceed acco rd ing to th e in telligible, situates it in an intermediary position . This theme will prove hugely influ-
rather than according 10 th e sen sible or 10 dasa . They are forced - thi s en tial throughou t C lassical philosophy (wh ich maintain s th e Platonic
im plies th at their break with opi ni on is, to so me extent, involuntary. entanglemen t of ph iloso ph y and mathematics). M athema tics will alwa ys be
una pparent to itself, and abo ve all devoid o f freed om. sim ultaneo usly eminent (o n account of its readily avai lable capacity for
That m athematics is h ypothetical, m at it makes use of axioms il ca nnot breaki ng with th e immediacy of opi nions) and insufficient (on account of
legitim ate, is an outward sign of what co uld be ca lled its fo rced comman- th e co ns trictive ch aracter wh ich its own obscure violence imposes u pon it).
dee ring of th e inte lligi ble. The mathem atica l ru ptu re is carried o ut un de r Thus, m ath em atics w ill be a truth th at / ails to aclJievt the form o/wisdom.
th e co nstraint of ded ucti ve cha ins that are th em selves d ependent upo n a It seems at first glance - and this is u sually as far as th e analysis goes -
fixed point which is stipu late d in aut horitarian fashion. that m at hematics is meta xu becau se it breaks with opin ion wit hout
T her e is some thi ng implicitly violent about Plat o's concep tion of att ain in g the seren ity of th e principle. In this sense , ma th ematics is
ma th ematics, someth ing wh ich opposes it to the co ntemp lative seren ity of located between op inion and intellection , or between th e immed iacy of
th e dial ectic. M athemat ics does not gro un d th ink in g itself in th e sovereign doxa and th e unconditioned principle soug ht by the dialectic . M or e
freed om o f its p roper d isposition. Plato believes, o r experi men ts with the fundamenta lly pe rhaps, we will say that ma them atics amounts to an in -
possib ility, as do I, that eve ry break with opinion, every founding di sco n- between in th ink ing as such ; that it intimates a gap whi ch lies even
tinuity o f thought can and probably must reso rt to mathemal ics, b ut also beyo nd the break with op in ion . This gap is th e one between th e general
th at there is so methi ng o bscure an d violent in that recourse . req uirem en t of d iscontinuity and th e illumination of thi s requirement .
The phi losophica l local ization of mathematics co njoins (a) the penna- But eve ry elu cidation of d isco ntin uity serves to establish the id ea of a
nent paradigmatic availabi lity of a d iscontinu it y, (b) a gro und in g of contin uity . If mathematics is ani mated b y an obsc u re violence, it is
thought outside opi nio n, and (c) a forced o bsc uri ty tha t canno t be app ro- because th e onl y thi ng tha t makes it su perior to opinion is its di scont i-
priated o r illu m inated fro m with in mathem atics itself. nu ity. D ialecti cs, which grasp s th e in telligible as a wllo/e, rather tha n JUSt
3 . Since th e m ath em atical break , wh ich has the adva ntage of bein g the di scontinu ou s edge that separates the inte lligib le from th e sensible,
suppo rted by a historical rea l ('m athem aticians and m athem atica l sta te- Integ rates ma th emat ics into a h igher co ntin uity. T he position of m ath e-
mcnrs exist' ), also has the di sadvantage o f be ing obsc ure and forced , th e matics as meraxu rep resen ts , in a ce rt ain sense, the in-between fo r the
elu cidation of this brea k with op inion req uires a second break , For Plato, th inking of th e d iscontinuou s and th e contin uous. Mathema tics eme rges
th is seco nd b reak, wh ich traver ses the inelu ctable opaci ty of th e first. is at th e poi nt where wh at d emands 10 be th ought is, on th e o ne h and, th e
co ns titu ted by th e acces s to a p rinci p le, whose name is 'd ialectics' . In th e rela tion be tween that whi ch is violen tly di scontinuous within th o ugh t as
philosophica l apparatus proper to P lato , th is gives rise to an op pos ition such , and on th e oth er. th e sovereign freed om Ihal ill um ina tes and incor-
between th e hypothesis (th at whi ch is presupposed o r asswned in an pora tes th is very violence.
 Philoso ph y and r-tat hernauc s 33
32 Theoretical W ri tings

M at hematics is the in-b auxen of trut]: and the freedom of truth , It is me But in a ph ilosophical perspective the mathematical in finite is impo r~a~ t
truth that is sti ll boun d by un freedom , yet wh ich is required by the because un de rly ing it, in fact, is th e notion of th e genuine infin ite an d It IS
violent ges tu re th rough wh ich the immediate is repud iated . Mathematics far superio r to the ordinary so-called metaphysical infinite on which are
be long! 10 truth, but to a constrai ned form o f it. Above and beyond th is based th e objections to th e mathem atical in finite. . . .
cons trained figure of tru th stands its free figure which elucid ates d iscont i- I t is wort hwhile consid eri ng more closely th e ma thematical ~ncept ~f t~e
nu ity: ph ilosoph y. infinite together with the most noteworth y of th e attempts aimed at JUSti -
Fo r centu ries. th is pos itionin g of math ematics at th e precise point fying its usc and eliminating the d ifficulty with which the meth od .f~ls
where tru th and the freedom of truth enter int o relation proved to be of itSelf b urdened. T he conside ration o f th ese just ification s and cha racte.ns t l~s
determin ing h istorical impo rta nce as far the en ranglemc m o f mathematics of the ma thematical infinite wh ich I shall undertake at some length 10 th is
and philosophy is concerned. Remark will at the same time th row the be st ligh t on the natu re of the true
Mathematics is parad igmatic. beca use it canno t be subord ina ted to the Notion itself and show how th is latt er was vaguel y p resen t as a basis for
regime of opinion. But th e fact th at th is insu bordination ent ails an impos - those proced u res.•
sibility also means that mathematics is incapable of shedd ing ligh t on irs
The fou r ch ara cteristics we h igh lighted in Plato's text arc all basically
own parad igmatic status . That philosophy is obliged to grormd ma the-
present in Hegel's analytical programme.
ma tics always sign ifies it mu st name and th ink the 'para di gmatic' nature
of the parad igm, establish th e illumination of the con tin uo us at the The mathema tical concep t of the infin ite was h istorically d ecisive in th.e
I.
moment of d iscon tin uity, at th e point where all ma thematics has to offer break with th e ord inary metaphysical conce pt of th e infin ite. Since in hiS
is its b lind, stubborn ina bility 10 pro po se anyth ing oth er than th e in relli- doctrine every brea k is a sublation or overcom ing (A ufh ebung), H egel
gible, and th e break. mean s to tell us th at the math ematical concep t of th e infinite effective ly
F rom th is mo ment on, C lassical ph ilosophy will con tin ually oscillate sublarcs th e metaphy sical conce pt of the infini te, which is to say, the
between th e acknow ledge me nt of the salutar y fun ction of math ematics concep t of the infinite in dogmatic rheology.
with respect to the d estiny of truth (th is is the on tolog ical mod e of cond i- It is in any case entirely legitima te to conside r ' me taph ysics' as ind i-
tioni ng), and the ob ligation to ground th e essence of thai fu nction else- cating a zone of opinion or doxa with in phi losop hy itself, one which
where, which is to say, in ph ilosophy (th is is th e ep istemo logical mode). Hegel declare s to be untrue (since it docs not po ssess the tr ue concep t .o f
The centre of grav ity for th is oscillation can be captured in the fo llowing th e infin ite). As in Plato, math ematics consti tu tes a positivc break With
term s: ma them atic s is too violently true to be free, o r it is too violent ly the un true concept of dogmatic op inion. Mathema tics h as the efficacy
Irce (i.e. d isconti nu ous) to be abso lu tely true. proper to a sub lating-break with regard to th e q uestion of th e infin ite .
2. Nevertheless, this break is b lind ; it is not illum inated by its own opera-
tion. At the very beg inning of h is Remark H egel says thi s:
4. HEGEL DEPOSES MATHEMATICS BECA US E HE
IN ITIATES A R I VA LRY BETW EEN I T AND The math ematical infinite has 3 twofold Inte rest. On the one hand its
PHILOSO PHY WITH REGARD TO T HE S A M E int rod uction into mathematics has led to an expa nsion of the science
CON CEP T, T HAT OF T HE IN FI NI T E and to importa nt result s; bu t on th e oth er hand it is rem arkable that
ma the matics ha s nOI yet succeeded in justifying its usc of this infini te
Hegel discusses the relation between ph ilosophy and mathematics in a by the Notion . . ..5
deta iled and techn ically informed ma nn er in th e massive Remark tha t follows
th e accou nt of the infini ty of the qua n tum in The S cience 0/ Logic. Altho ugh It is fair to say that we re- cncourner here the Pla tonic them e: we recog-
Hegel's conceptual meth od ology is far removed from Plato's, we on ly have to nize in th is success, in th ese ' importa nt result s' , the force o r existe nce
look at a few extracts to see th at the mo vemen t of osci llat ion initiated by the proper to mathematics, the fully deployed availability of a break . Bu t thi s
G reeks (ma th ematics produces a break, but does not illuminate it) conti nues success is imm edia tely ba lanced b y the absence of justification , and h ence
to govern Hegel's text: by an essen tial ob scu ri ty.
 34 Theoretical Wr itings Philosophy and r-tatf-em auc s 35

A lillie lat er , H egel wi ll Slate thai ' Success docs n01 justify by itse lf th e \lath ema tics for Plato means geom etry and arithmetic, th e objects of
sty le of procedure." The ex istence o f a mathematics of th e infinite has all hi
\\. Ie
h are figu res and numbers. That is why he is able to designate these
th e real force of a gen uine success. Nevertheless, one criterion stands ,,"('I<s of
thinking o r 'sciences', with the word uchni, understood as an
, "
higher than success: that o f 'the sty le of procedure' used to accom plish it. ."Clivit)' o f th ought whos e ob ject is d ~t~rmined in ad van ce . The break With
Only philosophy can elucidate th is style. But was not ' dialectics' in :pinion is localizable; the domain in which it is exercised singu lar"
Plato 's sense already a qu estion of style? Of the Style of thinkin g? Hegel does not un der stan d mathematics as the singular th.ou~t tha t
3. Thus JUS t as for Plato th e access to p rinci ple. which ca lls for the d ialec- pert ains to a spec ific domain of objects, but rathe r as the detenn~uo~ of a
tica l p roce du re, mu st sub late th e violent use of h ypotheses, simi larly for concept, and even, one could say, as the de termination of that whi ch IS the
H egel a co nce p t of th e genuine in finit e m ust sublate and groun d the Romantic co nce pt above all oth ers: th e infinite. .
math em at ical co ncept, which is endo wed on ly with its own success. The co nseq uences of thi s seem ingly innocuous di spl acem ent ar e incalcu l-
4. Lastly, as far as the concept of the infinite is concerned, mathem atics finds a blc. For P lat o , th e fact that m athematics res tricted itself to a realm of .
itse lf in an in termediary o r mediating po sition: it is meraxu. objects, that it dea lt in figu res and num be rs ra ther th an con stit uting a gen enc
O n th e one hand , m ath em atics is paradigmatic fo r thi s particular concept devo id of objects, d etermined m athem atics as a figu re of though t that
concept because it 'th ro ws th e best light on the nat ure of the true was always sin gu lar, as a particular realm o r procedure which di d no t need to
Not ion itself". rival th e overa rching ambition of philosophy .
But on the other, it is still neces sa ry to ' justify its use and eliminate But because H egel posits that the parad igmatic esse nce of mathematics is
di fficulties' - somethi ng that ma thematics is incapable of doing. The tied to one of th e central co ncep ts of ph ilosophy itse lf (i.e. th e concept of
philosop h er assumes his tra ditional role as a kin d of mech anic for the infin it~), he has no choice but to transform th e invariably sin ~la r
math em atics: mathematics works, b ut since it d oesn't know why it relation of entanglem~n t be tween phi losophy and mathem atics in to a rela tion
works, it n eeds to be taken apart an d checked . It 's alm ost ce rtain the of rivalry be for e the tribunal of T ru th. Moreover, since the true co nce p t of
eng ine will need replacin g . T his is because m athematics lies be tween the infin ite is th e ph ilosophical one, and thi s conce pt co ntains and gr ound s
th e met ap hysical or dogmatic concep t of th e infini te, wh ich modernity whatever is acceptable in its math ematical co un te rpart , ph ilosop hy ult imately
characterizes as a mere co nce p t of opinion, an d its true co nce pt, which proclaims the uselessness of the m ath ematical conce pt as far as thinki ng is
dialecti cs alone (in H egel 's sense ) is ca pab le of co nceiving . concerned.
It is ce rtain ly the case tha t the thi nk~rs o f th e C lassical era already co nsid -
But if th e four characte ristics th at singularized th e mathematicsjphilo- ered mathematics as a partially useles s activity, since it me rely dealt with
so phy pair in Plato tum up again in H egel, what has changed? Why docs objects that did not bave much 'worth' , suc h as figu res. But this d ep reciation,
the H egel ian text, wh ich provid es th e 't echnical ' fou ndation for the which opera te d ind irectly through an evaluation of the sin gu lar objects of
Rom an tic gestu re of di sen tanglement, effect a philosophical abaseme nt of math em atics , di d not call into qu estion the extern of th e mathematica l break .
mathematics, when th e P latonic text, on the co ntra ry, guaranteed its para. with op in ion. It merely indicat ed its loca l characte r , The uselessness attnb-
d igmatic value for cent ur ies? Why d oes thi s major Rem ark, wh ich is utcd to mathematics remained relative, since once thinking was estab lished
informed, at tentive and still learned (a learned nes s th at Nietzsche an d Withi n the n arrow realm of th e obj ect s in questi on, it rem ain ed absolutely
H eid egger wou ld late r di sp ense with) function as an abandoning of mathe - true that th e b reak with doxa enjoyed para d igm atic worth .
m at ics, rat her than as a new po sitive form of its em ang temc m with philo- H egel tu rn s this judgement of the ex trinsic uselessness of m athernauc s into
sophy? Wh y do we feci , or kno w, thn t after H egel 's assid uousness, ou r era's a judgem en t of its intrinsic u selessness. Once in structed by philosophy as to
Rom an tic d ive into the rcmpcralization o f the co ncept will aban don mathe- the true co nce pt of the infini te, we sec th at its mat hem at ical co nce p t is no
ma tics to th e specialists? mo re than a crude , d ispensabl e stage on the way to the former. T h is is th e
Well, wha t has changed is th at, fo r H egel, th e ce n tre o f gravity of m athe- price 10 be paid for th e rem poraliza non o f the co nce p t: everyth ing whi ch has
ma tics, and th e reason wh y it is deserving o f p hilosoph ical exam ina tion, must been sieved an d subleted is henceforth dead for thought. For Plato, by way
be re pre se nted as 0 concept, th e co nce p t of th e infini te, rather th an as a of co ntras t, ma them at ics and d ialectics arc two relations th at ca n be jux ta-
domain of objects. posed, albeit hierar chicalty, in an ete rnal configuration of bei ng"
 36 'tbeorenca t W riting s Philoso phy and r-tathemaucs 37

If Romantic philosophy after H egel was able [0 ca rry ou t a rad ica l di sen -, . mu ltiple , that of the lim it o rd ina l, wh ich pun ctuates the recapitu lation
bClOg -
nmg fcrnent of ma the m at ics fr om ph iloso phy, th is is becau se it proc laimed. f ur infin ity in a pu re, external 'd yin g'.
that ph ilosop hy dea lt with the same thing as mathematics. The Romantic u ; hiS is wh ere we find ourselves . O n one hand , the ethical pat.has .o f
gesture is bas ed on an idcn tificalion, not a d iffe re ntiation. In th e realm o f the . de wh ich o.....rat es under th e ban ner of death , presu p poses th e in finite
fin ltU .... ..- . '
co ncept of th e in finite, Hegel ian phi losop h y clai ms to co nstitu te a su perior th rau g h rempora
........ lizarion , and cannot dis pense With all th ose sacr ed, precar-
m ath ematics, wh ich is to say, a m ath ematics th at has sublate d, overta ken , or .
IOUS and defensive representa tions co ncern ing the pro m ise of a .God. who
left beh ind its own restrict ed math cm atici ty an d prod uced the ultimat e p hilo- . Id come to cauterize the ind iffer en t wound whi ch the world inflicts on
wOO . 'ffi
sophcme of its concept. the Roma n tic tr em b ling of th e Open . O n the othe r, an on to logy of indi crem
multiplicity th ai can withstand th e di sjunction and aba sem en t brou ght abo~t
by H egel ; one th at secu larizes and d isp er ses the infini te, grasps us human s In
5. THE R E- EN T AN G LEMEN T OF MATHEMATICS AND term s of th is di spersion , and adva nces th e prosp ect of a world eva cua ted of
PHILOSOPH Y AIMS AT A DIS S OL U TION OF THE every tu telary figu re of the O ne. . ..
ROMAN TIC CONCEP T OF FI NI T UDE A N D AT T HE The gap between th ese two options co nfigu res th e site of o ur IOlUal
ESTABLIS HMENT OF AN E VENTAL PH ILOS OPHY ques uon , wh ich con ce rned the possibi lity of an exi t from Romanticism. , a
O F T R UTH genui ne pos t- ro man ticism, the decomposition of th e th em e of finitude, and
the bracing acc ep tance of th e infinity of eve ry situation . The re- entanglement
In th e fina l analysis, we can say that what is at stake in th e co m ple te d isjune. of mathematics and ph ilosophy is th e opera tio n th at m ust be carried out ~y
tio n of phi loso phy and ma th ematics carri ed out by th e Rom an tic ges tu re is whoever wan ts to terminate th e power of m yths, whatever th ey m ay be . This
rhe localization 0/ the infin ite. includes th e m yth of errancy and th e La w, the m yth of th e immemo rial, and
Romantic phi losoph y localizes th e infinite in th e tcmporali zation of th e even _ for, as H egel would say , it is the sty le of p rocedure th at counts - the
co ncept as a h isto rial en velo pment of finitude. myth of the pain fu l absence of m yth . . .
Al the same time , in what is henceforth its ow n parallel bu t separate and In orde r for thought to ca rry OUt the decisive ruptu re with Rom an ricism
iso lated development , mathem atics localizes a plurality of infi nites in the (and th e q uestion is also po liti cal, because th er e have been historicist , and
in d ifference of th e pure mu ltiple. It has proc essed th e actual infinite via the hen ce Romantic. cleme nts in revolutionary po lit ics), we cannot do with~u t
banality o f ca rd ina l num ber. It has neu trali zed and com p lete ly deco nsecrated th e recourse _ which will perhaps once again be b lind , po ssibly stam ped With
the in finite, subtracting it fro m the meta phorica l register of the tend ency, the a cert ain constraint or vio lence - to the injunctions of ma th ematics . We
horizon. becoming. It has to m it from th e realm o f the O ne in order to disse- philoso phers. whose d ut y consists in th inki ng this time of ours beyond that
m inate it - whether as in finitely sma ll o r in fini tely large - in th e aura- free which ha s led to its devastation , must subject ourselves to th e co nd ition of
typol og y of multipliciti es. By initiating a thinking in which th e in finite is mathe matics.
irrevocably sepa ra ted from every instance of th e One, mathematics has, in its II is clea r thai the sta tement in terms o f which I p ro pos e to re-entangle
own dom ain , successfu lly cons ummated th e death of God. mathe matics and philoso ph y can no t be cha racterized by the cau tion proper
M ath em atics now treat s th e fini te as a special case whose co ncept is deri ved 10 th e epistemologica l modality. II is im perative to cu t stra igh t to th e on to-
from that of the infinite. T he in finit e is no longer that sacre d exce ption co- logical destin y of mathema tics. Thus th e st ate me nt will initiall y declare:
ordi narin g an excess over th e fini te, or a negation, a su blation of finitud e. For there is nothi ng but infinite m u ltiplicity, whi ch in turn present s infin ite
con te m po rary ma th emat ics, it is th e infin ite that adm its of a sim p le, positive mult iplicity, and the on e an d on ly halt ing po int in this presentation presents
d efiniti on , since it re presents th e ord inary form o f mu ltiplicitie s, whi le u is nOlhing. U jtimately, this halt ing po in t is th e void , nOI the O ne . G od is dead
th e finite tha t is ded uced from th e in finite by means of neg ation ur lim itation . at the heart o f p resen tation .
If one place s p hiloso p hy under th e co nd ition of such a m at hem atics , it But since mathematics pat ent ly has a cen tu ry's head start in the secu lariza-
becomes impossihle to m ainta in the discourse of the pa thos o f finitude. 'We' tion of the infini te, and sin ce th e on ly available conceptio n of m ult ip licity .as
arc Infinite, like every multiple- situation, and th e finite is a lacunal abstrac- infini tely weaving the void of its own inconsisten cy is wha t mathematics
tion. De at h itse lf me rely insc ribes us within th e natural form of infin ite since Cantor clai ms to be its own site. we shall also make the pro\'ocath'e and
 38 Theo retical Writ ings

the rape utic claim th at mathemat ics is ontology in the st ric t sense. which is to
say, th e infinite developmen t of wha t can be sai d of being q ua being.
F inall y, if th e traversal an d suspens ion of h isto ricism, indud ing H eideg- CHAPTER ]
gee's hist crial framewo rk, is ca rried out by sid ing wi th Canto r an d D edekind
aga ins t H egel as regard s th e d ialectic of finite an d infin ite, and if th e Slate.
rnen r 'ma the ma tics is ontology' toda y succeed s in putting ph iloso ph y un der The Que stion of BeingToday
co ndi tion, th e qu esti on th ai conce rns us beco mes th e following: what
happens to truth?
Will it consist in a d ialectic, as it di d for Plato and H egel? Will the re be
(b u t this ca n no longer be a matt er of ontology ) a higher , foundational, illu- 'There is no do ubt we arc inde bted to H eid cgger for havin g yoked phil oso ph y
m ina ling mode of int ellection, one th at will be app ro priate to the bruta lity of once more to th e question of be ing . We are also indebted to him for givin g a
such a break ? Is th er e so me thi n g that stlpp/eme",s th e m u ltip le ind ifference of name to th e era of th e fo rgetting o f thi s qu esti on , a fc rgertin g whose h ist ory,
being? These q uest ions be long to anoth er o rde r of enq ui ry, one that will fu el beginning with Plato, is the history of phil osophy as suc h.
the co ntinuation of p hilosophy by going be yond th e morose top ic of its 'end ', But wha t, in the final analysis, is the definin g ch aracteristic of m etaphysics,
in which it has been ens nared by th e exhaus ted Rom an ticism of finitude. T he which H eid egger co nceives as the h ist ory of th e withd ra wal of being? We
co re of such a ph ilosop hical p ropositi on , cond itioned by mod ern m arhe- know tha t the P laton ic gesture su bordinate s aletheio to th e idea : th e d clin ea-
m aries, is to ren der truths d epe nd ent on even tal localizations and sub tract no n of the Id ea as th e singular presence of the th inkable esta blishe s th e
th em from the so phistical tyrann y o f language. predominance of th e en tity ove r the initial or ina ugural m ovem ent of th e
Whatever th e case, it is incum bent on us to pu t an end to hist oricism and disclosure of bei ng . U nveiling and un concealment are thereby as sign ed th e
dismantle all those m yth s nou rish ed by th e tem pcraliza tio n of th e con cept . funct ion of fixing a p resence; but wh at is probably most im po rt an t is tha t
In doi ng so, reso rting to math ematics in it s co urageo us, so lita ry existen ce this fixation exposes th e bein g of th e en tity to th e power of a co u nt, a
will p rove neces sary, for in banishi ng every instan ce o f th e sacred and the ro unting-as-o ne. That through which ' wh at is' is wh at it is, is also that
void of every God, math em atics is nothin g but th e human h ist ory of et erni ty . th rough whi ch it is one . The pa radigm of the th inka ble is th e unificati on o f a
singu lar en tity through the power of th e one ; it is thi s paradigm , this norma-
rive powe r of the one, which erases bei ng's co m ing to itse lf or withdrawal
into itself as phusis. The them e of qu idd ity - the d eterm ination of the being
of th e entity th rough th e unity of its quid - is what sea ts being's entry in to a
Properly m et ap hysica l normative regis ter. In othe r wo rds, it is what des tin es
being to th e predomi nance of th e en ti ty.
Heidegger sums u p thi s m ovem en t in a series of notes entitled ' Sketches
for a H isto ry of Bein g as M etaphysics' :

T he p redomin ance of q uiddity brin gs forth th e predom inance of the entity

itsel f each tim e in what it is. The predom ina nce of th e en tity fixes be ing as
k(>;noll (the comm on) on the basis o f the hen (the one ). T h e di sti nct ive
feature of metaph ysics is decided . The one as unifyin g unity takes on a
normative funct ion fo r th e sub seq uen t d etermination of being. I

Thus it is becau se of the normative fu nction of the one in decid ing being
tha t bei ng is red uced to th e common, to em pty generalit y, and is forced to
endu re th e metaphysical p redomi nanc... o f the en u ry.
 40 Theoretical Wn tlngs The Quesuon o( BeingToday 41

\VIc can therefore defin e metaph ysics as the: comman dee ri ng of being by the . . d to su btra ct th inking from eve ry return of th e gods and firmly esrab-
one. T he mos t app ropriate syn thetic maxim for metaphysics is Leib niz's I n ~t C a . . . h h
. . within the certitude o f th e multiple? L ucretius IS c w o con ro ms
r
whi ch es tablishes the recip roc ity between bei ng and the one; 'That which it
• ~ " . . .
" • di rec t I" with that sub traction from the one constituted b y mconsrs-
not o"t. being is nOI a hei,W.' Ihlnk ID
, ",nfinit)', which nothing can en velop:
Conseq uently, th e sta rti ng point for m y speculative claim co uld be form u , "n
latcd as follow s: can one und o thi s bo nd between being an d th e one, br~ T herefo re th e nature of space and th e exten t of the d eep is so great I~at
wit h the one 's metaph ysical do m ina tion of being, without th ereby ens naring uncr brigh t Iighmings can traverse it in th eir cou rse , though th ey glid e
~ . \.
oneself in Hc idcg gcr 's desti na l apparatus. wit hout handing thi nking ove r to onwards th rou gh endless tracts of time ; no r can they by all th eir trav e 109
th e unfound ed promise of a saving rever sal? For in Hcidcgger himself the mtlke th eir journey an y the less 10 go: so w idel y sp reads th e gre at sto re of
characterization of metaph ysics as history of being is inseparable from a space in the un iver se all around w ithou t lim it in every d ir ecti on ."'
proclamation whose ultim ate exp ression , it has to be admitted, is th at 'only a
God can save us' . To in ven t a contem po ra ry fidelity to th at which has never bee n sub ject 10
Can th ink in g auain thi s deliverance - or has thinking in reality always the historial co nst ra int of onto-theology or the co m man d ing power of th e one
saved itsc lf, by whi ch I mean : deliver ed itself from th e normat ive po wer of _ such has been and remain s, m y aim .
the one - without it being nec essary to reso rt to p rophesyin g the ret u rn of The in itial d ecision then co nsists in holding that wh at is thinkable of being
the gods? takes the form of radical multiplicity, a multiplicity th at is not subo rdi n.atcd
In h is Introduction to M etaphy sics, H eidegger declares that 'a darken ing of 10 the powe r of the one , and wh ich , in BeirIg and Ev a n, I ca lled th e multiple-
th e world comes about on Eanh,.2 H e goes on to list th e es sen tial co m po- with ou t-ortene ss ,
n en ts of th is darkeni ng : 'th e flight of the gods, th e d estructi on of th e Earth. But in orde r to m aintain this pr incip le, it is necessary to abi de by some
the vu lgar ization of man, the preponderan ce of th e mediocre.? All these very com p lex requ irem ents.
th em es are co herent with the ide nt ificatio n of m etaphysics as the cxecerba-
non of th e no rm ati ve power of the on e. _ First of till, pure mu lt ipli city - the multiplicity deployin g the limitless
Yet although it is philosop hi cal thinking tha t depl oys the normati ve power resources of be ing in so far as it is sub trac ted from the po wer of th e one-
of th e one, phi losophy is also that whic h, throu gh an originary sun dering of can no t co ns ist in and of itself. Li ke Lu cretius, we m ust effective ly assume
its d ispos ition. has always con currently m obilized th e res istance to this th at the d ep loym ent of the mu lt iple is not co nstrained by th e imm ane nce
power, th e su btra ct ion fro m it. Acco rdingly, an d co unter ing H eidegger, we of a limit . For it is on ly too ob vious that such a co ns train t would co n firm
should declare: th e illum ination of th e wo rld has alway s accompanied its the power o f th e one as the foundation for th e multiple itse lf.
immemorial darkening. Thus th e flight of th e gods is also th e ben eficial event There fore, it is necessary to assume that multiplicity , envisaged as th e
o f m en 's tak ing-leave of them ; the destruction of the Earth is also th e co nver- expos u re of bei ng to the th inkabl e , is not avai lab le in the form of a
sion that renders it amen able to active th inki ng; th e vulga ri zat ion of man is consistent de lim ita tion. Or agai n: that ontology, if it exists, mu st be th e
also th e egal ita rian irruption of th e masses on to the stage of h istory; and the theo ry of Inconsistent m ult ip licities as such . This also en tails th at what
preponderance of the med iocre is also th e dense lustre o f what Mallanne is tho ugh t within on to logy is th e multiple shorn o f every pred icate
ca lled ' restraine d action' . other thnn irs mu ltiplicity .
Thus m y problem can be formulated as follows: what name can thi n king - More radi cally still, a genuinely sub tract ive science of bei ng qua being
give to its own im memo rial aucm pt to su btract bei ng from the gri p of th e m ust co rro borate th e powerlessn ess o f the one from withi n itself. A
one? Can we learn to recognize that, altho ugh there was Par m cnid cs, there merely external refu tal ion is insuffi cient evide nce fo r th e mu ltiple's
was also D cm oc ri tus, in whom, th rough di sseminat ion and recourse to th e without-o neness . It is the inco n sisten t compositio n of the multiple itself
void, the one is set as ide? Ca n we learn to mobilize th ose figures who so whic h points to th e undoing of the one.
obv iously exempt th emselves from H eid egger 's d cst inal appara rus? Fi gu res
such as th e magnificen t Lu cr et iu s, in whom th e power o f th e poe m, far fro m In th e Parmenides, Plat o gra sped this poi nt in all its patent difficulty b y
m aintain ing th e recou rse to th e Open in th e m idst of epochal di stress, tries exam ining the co nsequences of the following hypoth esis : the one is not . T his
 42 Theore t ical WrllJngs The Ooesuco of BeingToday 43

hypothesis is es pecially interesting as far as Hd dcggc.r's de termination of the _ F inally, a th ird conseq uence of th e su btractive commitm en t consist s in
d istinctive charact er of meta ph Ysics is con ce rned. What does Plato say ? Fint, exclud ing the poss ib ility of th ere be ing a defin ition of the multiple.
that if the one is not, it follows tha t me m ult ip iC" s immanent alreriry gi vQ, Heideggerea n analysis comes to ou r aid on th is poi n t: the genuinel y
rise to a process of limitless self-d ifferen tiation. This is expressed in the Socratic method of delineating the Id ea cons ists in grasping a definition .
striking form ula: rei aJ/a etera em;'. which cou ld be translated as: (he oth ers The method of d efinition is op posed to th e imperative of the poem
are Others, with a small '0 ' for the first othe r, and a capital '0 ', which I precisely to the extent th at it es ta blishes the normative powe r of th e one
wou ld call Lacanian , for [he second. Since the one is not , it follows that the withi n language itself. The entity will be thou gh t in its bei ng in so far as
other is O th er as ab solu tely pure multiplici ty, intrins ic se lf- di ssem ination. it is delineated or isolated thr ough the d ialectica l resource of de fin itio n.
T his is the hallm ark of Inconsistent mul ripliciry. Definition is the linguistic way of establish ing the p redo minance of the
Next , Plato shows that this inconsistency dissolves any supposed power of enti ty.
the one at its root , includ ing even the power of its withdrawal o r non-
existence: every ap pare nt ex position of the one imm ediatel y reduces it to an Yet by cla iming to access the mu ltiple-exposition of bei ng from th e
in finite m ultipli ci ty. I quote: perspective o f a d efinition, or d ialectically, by means of successive d elim ita-
tions, one is in fact already operati ng in th e ambit of the metaphysical pow er
For he who considers the matt er closely and with acu ity, then ladtint of the one.
oneness , since the om: is not, each one appears 3S limitless multi plicity.s The th inking o f th e m ultip je-with e u t-oneness, or of inconsistent m ultip li-
0 1)', can not the refore proceed by mean s of d efinition .
Wh3 1 can th is mean, if nor th at, su btract ed from th e one's metap hysical Ontology faces the difficult d ilemma of having to se t out th e th inkab le
gr ip , the multiple cannot be exposed to th e thi nkab le as a m ultip le com posed chara cter of the pur e m ultiple without be ing able to Slate un der what condi -
of ones? It is necessary to po sit that th e m u ltiple is on ly ever composed of tions a multiple ca n be reco gnized as such . Even this n egative requ iremen t
mu ltiples. E very m ultip le is a m u ltiple of m ult iples. cannot be exp licitly stated. O ne canno t, fo r exam p le, say that th inkin g is
And even if a m ultipic (an ent ity) is not a multiple of multip les, it wiD devoted to th e multip le and to nothing bu r the intrin sic m ult ip licity of the
nevert heless be necessary 10 p ush su btrac tion all the way. We sha ll refuse to multiple. Fo r th is thou gh t itself, becau se of its recour se to a del imi tin g norm,
conce de th at such a m ult iple is the one, or eve n com posed of ones . It will would al ready ent er into wha t Heidegger called the proc ess of the lim itat ion
the n , unavoidably, be a multiple of nothing . of being. And the one would th ereby be reinstated .
For su btraction also consists in th is: rathe r than conced ing tha i if there II Consequently, it is neither po ssible to define th e mu lti ple nor to exp lain
no multiple there is the one , we affirm tha i if there is no multiple, there is this absence of defini tion . The truth is that the th ink ing o f th e p ure multiple
nothing. In so doing, we obviously re-encoumer Lu cretius. L ucretiu s effec- must be such as to neve r mention the word 'multiple' anywh ere, wheth er it
tivel y exclu d es the poss ibility th at between the void and the multip le com- be in orde r to state what it d esignates, in acco rdance with th e on e; or to state,
po sitions of ato ms, the one migh t be attributed to some kind of third again in acco rda nce the one, what it is pow erless to designate,
principle: But what kind of th inking never defi nes what it th inks and never expo unds
it as an object? What do you call a th inking which , even in the writing that
T her efore bes ides void and bodies, no Ihird na tu re ca n be left self-existing binds it to the th inkable, refuses to ascri be any kind of na me 10 th e th in kable?
in the sum of th ings - neither one th at can ever at an y time come within The answe r is obvious ly ax iomat ic thinking . Axio ma tic thinking grasps the
ou r senses, no r one that any man can grasp by the reason ing of the mind .6 disposition of undefi ned term s. It never enco unte rs either a defin ition of its
terms or a serviceable explanation o f what th ey arc nc r. T he pr imordi al state-
T his is wba r governs L ucretius' cri tiq ue o f those cosmologies subo rd in ated ments of such an approach expound th e thinkable withou t them atizing it . No
10 a unitary principle, such as Heraclitu s' Fire. Lucretius clea rly sees that 10 dOUbt th e primitive term or terms arc inscribed. But if th ey are , it is not in
su btrac t ones elf from the fear of the gods req uires that benea th the mult ip le. the sense o f a naming wh ose referent wou ld need to be repr esen ted , but
th er e be nothi ng . And Ihal beyond the multiple, there be onl y the mu ltiple rather in th c sen se of being laid out in a seri es wherein the tcrm su bsIsrs only
once again . throUgh th e o rde red play of its founding connections.
 44 The or etxa! Wntlngs The Ouesnco of BeingToday 45

The most crucial requirement for a su btrac ti ve ontology is that its exp licit '11 ti<:s it to the commo np lace, to gene rality , which is th e root of its own
presentation take the form of the axiom, which p rescr ibes withou t naming , w temptation . And it is in this tear ing away that I perceive ·
meta Ph\'Sical
_
rather than th ai of th e dialectical definition. t's freedom with regard to its d estinal cons train t, what cou ld be called
thflugh "'-
It is on me basis of th is requirem ent that it becomes necessary to reinter. us metaph ysical lcnd ency.
p ret the famou s passage in the R epublic where Plate opposes mathematics to I \'f e could say th at once ontology embraces the axio mat ic approach or insti -

me dialectic. lutCS a th in king of pu re inco nsiste nt multiplicity, it has to aba ndon eve ry
Let us reread how Gl aucen, one of Socrates' interlocu tors, summarizes his a peal to p rin cip les. And conversely, th at every attempt to establish a p rin -
master 's th inking on th is point: :plC prev cots the multiple from being exhibited excl usiv ely in acco rda nce
with the immanence of its mu ltiplicity .
The th eorizing concern ing being and th e im dligible which is sustained by Thus we now possess five cond itio ns for any onto logy of pure mu ltipl icit y
the science [i pistim i) of the d ialecti c is clea rer than that sus tained by what as disconti nuation of th e power of the one; or for any on tology faithfu l to
arc know n as the sciences [lechml It is certainly th e case tha t those who what, in philosophy itself, ha s always stru gglcd against its own me taph ysical
theo rize according to these sciences, wh ich have hypothese s as th eir princi- lendency.
ples, are ob liged to p rocee d d iscu rsively rather th an empirically. But
beca use th eir intuiting remains depende n t on th ese hypotheses and h as no l . Ontology is th e th in kin g of inconsistent mul tiplicity, of mu ltiplicity cha r-
means of acce ssing the pri nciple, th ey do not seem to you to possess the acterized - witho ut immanent unification - solely in terms of the predicate
intellectio n of wha t they th eorize, which nevertheless, in SO far as it is illu- of its mu ltipl icity.
minated by th e principle, concerns th e intelligibility of th e ent ity. It seems 2. T he multiple is rad ically with out -onen ess, in th at it itself comp rises
to me you charact erize the procedure of geometers an d thei r ilk as di scu r- multip les alone . What th ere is expo ses itsel f to the thinkable in terms of
sivc (dian oial , wh ile you do not characterize intellection thus, in so far as mult iples of mu ltiples, in acco rd ance with the stri ct req uirement of the:
that d iscu rsiven ess is estab lished between lmelax u) opinion (doxaJ and ' there is'. In oth er word s, there: are only m ultiples of mu ltip les.
intellect (nous).' 3. Since there is no immanen t lim it ancho red in the o ne that could deter-
mine mu ltiplicity as such, th ere is no originary principle of finitud e. The
It is perfectly apparent that for Plato th e axiom is preci sely what is wro na multiple can therefore be th ought as in -fini te. Or even: infinity is ano ther
with math ematics. Wh y? Because the axiom remains external to th e think- name fo r multiplicity as such . And since it is also th e case that no
able. Geom eters are obliged to proceed discursively precisely beca use th ey do principle b inds the infini te to th e one , it is necessary to maintain that
not have access to the nonnative: power of th e one, whose name is prindp/e. there are an infinity of infin ites, an infinite d issem inati on of infinite multi-
What' s more, thi s constrain t con firms their exreriori ry relative to the pliciti es.
pri nci pal nonn of the th inkable. For Plato, once again, the axiom is the 4. Even in th e exce ptiona l case where it is poss ib le to th ink a multiple as not
bea rer of an obscu re violen ce, resulting from the fact that it does no t being a multiple of mul tiples, we will not concede the necessity of reintro-
con form to th e dialect ical and defin itional norm of the one. Altho ug h du cing the one. We will say it is a mu ltipl e of no thing. And just as with every
thought is cert ain ly p resent in ma them ati cs and in th e axiom, it is not yet as other mu lt ip le, thi s nothing will remain entirely devoid of consistency.
the freedom of thought, which the axio m subo rd ina tes to th e pa radig m or S. Every effective on tological presentation is necessarily axiomatic.
no rm of th e one .
On th is po int , my concl usion is obviously th e opposite of P lato 's . T he AI this point , en ligh tened by Cantor's refo und ing o f marhemarlcs, it
value of the: axiom cons ists p recisely in the fact that it remains sub tracted bcctlmcs possible to state: ontology is noth in g other tha n mathematics as
from the normat ive power of the on e. And unl ike Plato, I do not regard the: such. \\that 's more, this has been the case eve r since it s G reek origin; even if,
axiomat ic constraint as a sign that a un ifying, ground ing illumina tion is from the mom ent of its inception up un til now, as it struggled internally
lacking . Rather, I see in it the necessity of the subtractive gestu re as such, against the metaph ysical temp tation, math em atics on ly ma naged with dlffi-
th at is, of th e movemen t whe reby thought - albe it at the pri ce of the inex - eUh y, through pain ful effo rts and tran sforma tion s, to secure for itself th e free
p licit or of the impotence of no mina tions - tear s itse lf from everything that play of its ow n cond itions.
 46 Tbeoreucar Wri t ings The Question of BeingToday

\Vilh Cantor we move fro m a restrict ed ontology, in wh ich th e mu luple is rion of such a word . T his d emonstrat es how, in its essence, th e th ough t of
still tied to th e metaph ysical th eme of th e representation of objects, num tx:rs the pu re multiple requires no dialectical principl e, and how in th is regard
and figures, to a general ontology, in whic h th e corn ers to ne an d goa l o f all the freedom of th at thinking wh ich acco rds with bei ng resides in axio-
mathemati~ becomes though t's free ap preh ension of mu ltiplici ty as such , matic deci sion , not in th e intuition of a no rm .
an d the thmka b le is defin itively umeLhcrcd from th e restrict ed dimension of
m e object. \ \ort..-over , sin ce it was subseq uen tly established th at Canto r's ach ievem ent
We can now briefly elu cidate how pos t-Cantc rian m athematics beco mes in tav not so much in elaborating a particul ar th eo ry as in p ro vid ing th e very
a certain sense eq ual to its co nd ition s. s i~e for wh at is m ath ema tically th inkable (th e famo us ' para d ise' evoked by
Hilbert), it beco mes possible to state by way of retroa ct ive ge ne ra lizatio n
I . A set, in Canto r's sen se of the word , has no essence bes ides th at of being a that, ever since th e G reek origin of ontology, being has bee n persist entl y
multiplicit y; it is without exte rn al d etermination beca use mere is nothing to inscribed thro ugh th e d ep loymen t of pure m ath ematics. Co nsequen tly ,
restrict its ap pre hens ion with refere nce to so meth ing else; an d it is without th inking has been sub tracting itself from th e nonnative power of th e one ever
internal determ ination because what it gathers as multiple is indifferent. since ph iloso phy began . From Plat o to H u sserl and Wi nge nst~in , th e str iking
2. In the version of set-th eo ry established b y Zerrnelc and Fraenkel, th ere is incision which marhem atics carries out withi n phi loso phy shou ld be inter-
no other und efined primi tive term o r po ssible value for th e variables preted as a singu lar condi tio n: rhe co nd ition whe re by philosoph y experie nce s
beside s th at of sets. Thus every clem ent of a ser is itself a set. T h is is the a process whic h is not th at o f being's su bjugation at th e hands of rhe o ne .
rea lizati on of th e idea tha t every multi p le is a multi ple of m ulti ples, Thus un de r irs mathem at ical con dition , philosophy has always bee n the site
with out refere nce to un itie s of any kind. of a dis parate or d ivided project. It is true that phi loso phy exposes the
3 . Cantor fu lly ac kno w ledges not on ly the existence of infin ite sets, but the catego ry of truth to the unifying , m etaph ysical power of th e one. But it is
ex istence of an infinity of such sets . This is an absolutely open infini ty, also true th at p hilosophy in tu m also exposes th is power ro the subtract ive
scaled only by the point of impossibility and hen ce by th e real thaE defect ion of m athematics. Thus every singular philosophy is less an effectua-
renders it in con sist ent , whi ch amounts to the fact that there cann ot be • tion of metaph ysical desti n y than an attempt to subtract it self fro m the latter
set of all sets. This is some thi ng tha t was already acknowledged in L ucre- under the condition of mathem atics. The philosophical catego ry of truth
tius' a-cosmi srn. result s both fro m a normativity inherited from the Platoni c gesture and from
4 . Ther e does in fact ex ist a se t o f nothing, or a set possessin g no multiple as grasp ing th e mathem ati cal co nd ition that undoes th is norm. This is true eve n
an element . This is th e empty SC1 , wh ich is a pu re mark and out of wh ich in th e case of Pla tO h imself: th e gradual multipli cati on or mixi ng o f th e
it can be demonst rated th at all multip les of multip les arc woven. Thus the sup reme Ideas in th e S ophisr o r Philebw , like th e reductio ad absu,.dum of the
eq uivalence: o f bei ng and th e lett er is ach ieved once we have su btract ed th eme of the one in th e Parme nides, ind icate the ex tent to whic h th e choice
ou rselves from th e no rm ative power of th e one. Recall Lucretius' bct " 'een defin itio n and axio m, principle and deci sion , un ification and di sse-
powerfu l an ticipation of thi s po int in Book I, verses 9 10 an d following: minat ion, remains fluid an d indecisive.
Me re genera lly, if on tology or what is sayable of bei ng qua being is coex -
A small tra nsposition is sufficient for at om s to cre ate igneous or tcnsive with ma thematics, what are th e ta sks of ph ilosophy?
ligneo us bodies. Li kewise, in th e case of wo rds, a sligh t attcreno n in th e The first one probabl y consists in ph ilosoph y hum b ling itself, against its
lett ers allow s us to d ist in gui sh ligneou s from igneo us." Own latent wishes, before ma thernuucs by Ack nowledgin g that mathem atics is
in effect the th inking of pure being, of bein g qua be ing.
It is in thi s agency of th e leiter, to ta ke up L acan 's exp ress ion (an agency I say agai nst its own latent wishes, for in its actua l develop ment ph ilosoph y
h ere co nst it uted by the mark of th c void ), that the th ou ght of wh at let s has mani feSled a stubbo rn te nde ncy to yield 10 the soph istical injunct ion and
itse lf be m athem at icall y exhi bit ed as th e imm emo rial figu re of being to claim tha r al though an analysis of math em atics might be necessary to the
unfo lds wi th out-onenes s, wh ich is to say , without- metaphysics. vxistcnce o f phi loso ph)' , the fo rmer can not lay claim to the rank of ge nui ne
5. Wh at lies at the hea r t of th e presenta tion of set-theory is simp ly its bod y thin king. Ph ilosoph y is pa rtly responsible for th e reduction of mathema tics
of axioms. The word 'se t ' pla ys no part in th e th eory. Nor docs th e defini- to the status of mer e ca lcu lation o r technique. This is a ruinous image, to
48 Theoret ical Wr it ings

wh ich m ath ematics is reduced by curre n t opinion with th e ariSlOcra tic:

com plicity of mathematicia ns themselves, who ar c all too willing to accept
tha t, in any case, thc rabble w ill never be abl e ro und erstand thei r science. CHAPTER 4
II is therefo re incumbcm upo n philosophy to maintain - as it h as very
often attempted to, even as it obliterated tha t very attempt - that
mathematics thinks , Plat onism and Mat hematical Ontology

In the intr od uction to The Philosophy 0/ M athematics, a co llection of texts

edited by Bcna cc rraf and Putnam, we find th e fo llowing claim:

In gen eral, th e platonists will be those who con sider ma thematics as th e

discooery of tr uth s about structures whic h exis t indepen dently of the
activity or thought of mar hema ucian s. '

T his criterion of the exteri ority (or tra n scendenc e) of ma thematical struc-
tures (or objects ) resu lts in a d iagnosis of 'P latonism' for almost all works
belonging to the 'phi losoph y of science'. But thi s diagnosis is un dou bted ly
wrong. It is w rong because it presupposes th at the 'P lato nist' espo uses a
distinction between internal and extern al, knowing subject and known
'object' ; a di stinction whic h is utterly foreign to the gen uine Plat on ic Frame -
work. However firml y established this d istinction may be in contempora ry
epistemo logy, howev er fund am ental the theme of the obj ectivit y of the
object and the subjectivity of th e subjec t may be for it, on e ca nnot but
enti rely fail to gras p the tho ught- proce ss at wo rk in Plato on th e basis of such
Presuppositions.
First of all, it sho uld be noted th at th e ' independen t existe nce' of ma th e-
matical Structures is en tirely relative for Plato. What the metap hor of
anamnesis designa tes is precisely that th ought is never confro nted with
'Objectivities ' from which it is su pposed ly separated , T he Id ea is alwa ys
alread)' the re and wou ld rem ain unthinkable we re one not able to ' activate' it
in th ough t. Furthermor e, wh ere mathematical ideas in particu lar arc
conCerned , th e w hole aim of th e concrete de mo nstration provid ed in th e
.\1('1/<1 IS to es tablish their p resence even in the leas t ed ucated , most anon-
vm .
. ous nista ncc of thought - th at of the slave.
Pluto's funda ment al conce rn is 10 decla re th e imm anen t ide nti ty, th e
CO-belonging, of the know ing m ind and the known , their essen tial on to logical
COnHnensurab ility, If there is a sense in wh ich he rem ains hei r to Parm cn idcs,
who de clared 'it is the sam e to think and to be' , it is to be foun d in th is
50 Theoret ical W n tlngs Ptatomsm and Mathemat ical Ontolo gy 51

declaration . In so far as it touches on being , m athema tics intrin sically th inks. decisio/l tha t makes room for the undecidable and assumes that everything
By the same to ken , if m ath ema tics thinks, it accesses being intrinsically. Tbt relli, ll is ecnsistent ex ists.
th eme of a knowing subject who has to ' aim ' at an external object - a therne
wh ose origi ns lie in em piricism , even when th e pu tative object is idea l - ia In ordcr to gauge the polem ical charge of th is 'definition ' of Platon ism .
enti rely ill-sui ted to the p hi losophical usc to wh ich P lato put S the existence let us con trast it to the one proposed by F raenkel and Bar-H illel in T ile
of mathema tics. Fa/IIIJatio.1S of S et- Th eory :
M oreover. Plato is even less concerned with m ath em at ical
existing ' in themselves'. There arc two reasons for this: A Platollisl is convince d th at co rr espon ding to each well-defined (mon ad ic)
condition [which is to say, th e attribution of a predicate to a variable, in
I . ' Ideality' is the ge ne ra l n ame given to wha t is thinkabl e, and is in no wlrf the for m P(x)J there exists, in general , a set, or class, whi ch co m pri ses all
th e exclusive province of m ath ema tics. As the old Par m en ides points QUI and only those en tit ies th at fu lfil th is condition and wh ich is an entity in its
to the youn g Soc rates. in so far as we th ink m ud o r h air. we mUll own right of an ontological status sim ilar to th at of its m embers."
acknowledge th e idea of m ud an d th e idea of hair. In fact, ' Idea ' is the
nam e give n to what is thought , in so far as it is th ou gh t. T he Platonic: 1 do nOI bel ieve a Platonist can be co nvi nc ed of any thi ng of the so rt .
theme con sists precisely in rend er in g immanen ce an d tran scen den ce Plato himself continuously ta kes pains to show th at th e co rrelate of a well-
ind iscernible, in ta king up a position in a site of thi n king wherein thiI defined concept or proposit ion can be empty or inconsiste nt ; or that its
di stinction is in ope ra tive. A math em atical idea is neith er subjective ('the corres ponding 'ent ity' m ay n ecessitate ascribing an exor bitant ontologica l
acti vit y of th e m athem ati cian' ), nor ob jective (' ind epend ently existinl status to every th ing in voked in th e ini tia l expression . T hu s the co rrelat e o f
structu res'). In one and the same ges tu re, it b reaks with th e sensible an4 the Good , however lim pid th e d efin ition of it s not ion , however obvious its
posits the intelligi ble. In othe r words, it is an inst an ce of th inkin g. practical instan tiation , req u ires an exem ption from the status of Id ea (the
2 . It is not th e status of so-c alled m at hem ati cal 'objects' tha t Plato is intet'" Good is 'beyond' th e Id ea). The exp licit goal of the Parmenides is to
ested in, b ut the movement of thou gh t, because in the fina l analysil demonstrate how , in the case o f perfectl y clear stateme nts such as ' th e one
mathem atics is invoked on ly in ord er to be con trasted with d ialectics. But is' an d 'the one is not ', no matter what assu m ption we make about the
in the realm of th e thinkab le, every th ing is an Id ea . Thus it is pointless to corre late of th e one and th ose thi ngs that arc 'oth er tha n one', we co me up
loo k to 'objectivity' to provid e a basis for some sort of d iffe re nce betweee agains t a con trad iction . Which , afte r all, is the first exa m ple, albeit in a
kinds of th in king . O nl y the singu larity of th eir respective movemen tt purely ph iloso phical register , of an arg um ent proceed ing in terms of
(that of procee ding from hypoth eses o r of seeking ou t a p rinci ple) alloWS absolute undecid ab ility.
one to del imi t mathemat ical dianoia from d ialectical (or ph ilosop hical) Contrary to wha t F raenkcl and Bar-Hi llel declare, I mai ntain that th e
intellect ion . The separation of 'o bjects' is secondary an d always obscure. undecidab le con stitu tes a crucial cate go ry for Platon ism , and th at we can
It is an auxi liary catego rization ' in bei ng ' elaborated on the basis of c1uet never know in ad van ce wh eth er ther e will always exist a th inkable enti ty
provided by th ought . COrrespondi ng to a well-d efined exp ression. T he undecidable testifies to th e
Iacr that a Platonist has no con fide nce whatsoever in the clarity of lan guage
Fi nally, only one th ing is ce rtain : math em atics th ink s (m eanin g, in the When it comes to deci ding abou t existe nce . In thi s regar d , Ze rmclo's axiom is
language of Plato, that it cons titu tes a b rea k with perce ptual im mediacy) , Platonist bec ause it refu ses to allow the existe nce and co llection of th e
di alectics also thinks, and cons ide red in their protocol s, th ese rwo thought s 'cnuncs' valid ating a given ex p ression unl ess the y arc already given by an
d iffer. CX.iMing set. T hought requi res a cons tant and im m anent guaran tee of being.
On thi s basis, we can atte m p t to define Plato's in scrip tion of the merbema- T he undeci dab le is the reason behind the apor ctic style of th e dial ogues:
tica l cond ition for 'ph ilos ophizing' as follows: the aim is to reach th e po in t of th e unde cidab le pre cisel y in orde r to show
that though t m ust tak e a decision with regard 10 an even t of being , that
W e call Platonic the recogn ition of mathematics as a f orm of thinking tha t is tholJght is nOI primar ily a d escription or a cons truction b ut a break (with
intr onsitioe to perceptual and ling uistic ex perience, and tahich depends on JJ OPinion , wit h ex perien ce ), and hence a deci sion .
52 Theoretical W ri t ings Platon ism and Mat hemat ical Ontology 53

In this rega rd , it seems to me that GOOd. whom th e 'ph ilosophy of ma its existen ce, which is so me th ing othe r th an iu be ing . For as far as
maries ' co nt inues 10 class as a ' Platonist", di splays a superio r acumen. being is co ncerned , it is co rrobora ted onl y th rough its envelop ment in
Consider thi s passage from the famo us text ' Wh at is Cantor 's Co ntinu an insta nce of th ou gh t.
Prob lem ?' : T he crucial problem is that of truth . As soon as th ere is in ventive
thin king (as attested to by th e intelligibility of th e ax ioms), one can
However, the qu estion of the objective existence of th e objects of rna 'gi,'c meanin g to th e q uestion of th e truth or Ialsiry of proposit ion s'
rnarical intuition (w hich , inciden tall y, is an exact repli ca of th e qu estion that th is th ink ing legi timates. This meaningfulness derives precisel y
the obj ective exi stence o f th e outer wo rld) is not deci sive fo r the probl from the fact th at the thinkable, as Id ea, nece ssa ril y come s in to co ntact
under discu ssion here. The mere psychological fact of the existence of with bei ng , as well as from the fact th at ' tr u th' is on ly ever th e nam e of
intuition wh ich is sufficiently clear to pr odu ce the ax ioms of set-theory that thro ugh which thi nking and bein g co rrespo n d to one another in a
an open series of extensions of them suffices to give meaning to single process .
qu estion of th e truth or falsity of proposit ions like Cantor's continu The infinite and the finit e do not indicate a d istinction of an y mom cn -
h ypothesis. W hat, however, perha p s mo re th an anything else, just ifies lOU S importance for th in king. G OOel insists that 'acce ptance of (the)
accep tan ce of th is criterio n of truth in set-theo ry is th e fact th at con tin criterion of tru th ' results from th e fact that in tui tion (i.e. th e axioma -
appeals to mathemat ica l in tui tion are n ecessary not on ly for ob . . tizing d ecision) is con tin ually required bo th in order to d ecide
unambiguous an swers ro the Question s of transfin ite set-theory, but p roblems in finitary number th eory and to m ake d ecision s abo ut
for th e so lu tion of the prob lems of fin itary number th eo ry (of the type prob lem s concern ing transfinite sets. H en ce: th e m ovem ent of th ought,
Goldb ach 's co njectu re), whe re the m eaningful ness an d unam biguity of which is th e only thing that maners, does not differ essentially whether
conce pts en terin g into th em can ha rdl y be doubted. This follows from it deals with th e infinite or th e finite.
fact th at for every axioma tic system there are infinitely many undecida The u ndecidabl e is intrin sica lly tied to m ath em atics. Moreove r, it docs
p ropo sitions of thi s ty p~ . ) not so m uch constitute a ' lim it' - as is som et imes maintained - as a
perpe tual inciteme n t 10 th e exe rcise of inventive in tu ition. Since every
W hat arc the most im po rt ant feat ures o f th is ' Pla tonist" text ? appara tus of ma thematical th ou gh t, as sum m arized in a collection of
foundational axioms , com pri ses an element of undecidab ility, int uition
T he word ' int uition ' h er e sim ply refers ro a decision of inventi is never useless: mathematics must periodi call y be redecided .
tho ugh t with regard ro th e intelligibilit y of th e axioms . According
Godel's own fo rmu lation , it refers to th e ca pacity to 'prod uce F inally, I will characterize what is legi tima te to call a Platonic phi loso-
axioms of set -theory ', an d th e ex istence of such a capaci ty is purely phical orien tation vis-a-vis the modern mathem atical co ndi tion - and a
' fact ' , Note th at th e in tui tive function does not co nsist in grasp inl fortio ri, on to logy _ in term s o f three poi n ts.
'extern al' en tities , bu t instea d in vol ves clea rly d ecid in g as to a primarY
o r irred ucible pro position. The co m p rehensi ve inv ention of ax ioms
1. MA THEMA TI CS THINKS
co nfirm s th at th e mathematical propo sition is an in stance of thinkin'"
and is co nseq uently what expos es th e propo sition to tr u th , I have alread y de velope d thi s asser tion at som e length , b ut its im po rt ance is
The q uestion about the 'objective' exi ste nce of th ese suppos ed cbiece SUch rhat I would at least like 10 re itera te it her e. Let us recall , b y way of
is explici tly decla red to be second ary (it is 'no t decisive for the I:X3ln p lc, tha t \Xliugen stcin, who is not an ignoramu s in these ma u crs,
pro b lem under di scussion here'). Furtherm or e, it is in no way pec uliar declares that 'A proposit ion o f math em atics docs not ex p ress a th ou ght.'
to mathem atics, sin ce th e existence in q uestion is of th e same sort as (7'rUaa t fls, 6.2 1): 1 Here, with custo ma ry radicali ry, Wiugenstcin m erely
that of th e ex ternal wo rld , T o sec in math em atica l exi stence nominl re:.talcs a thesis that is cen tra l to eve ry variety of em p iricism , as well as to all
more, and no thing less, than in ex ist ence p lain and sim ple is aet ua.IJr SOphistry. I t is one which we will never have done refutin g,
very Platoruc : in each and every case, the th inka ble (wheth er it be' That ma the matics th inks means in particular that it regard s the d istinction
m ud , hair, a tr iangle, or com p lex num bers) can be int errogat ed u to between a kn owing subject and a known object as devoid of pertinen ce.
 S4 Tbeo-encar Wntlngs Ptatonem and Mathematical On tolog y SS

T her e is a co-ordinated mo vement of th ough t, co- ex tensive with being" the regime o f th e thinkab le determi ned by th ose very same in tuitions
which mathematics en velops - a co-e xtensiveness tha t Plato called ' Idea', In and pro tocols.
this move ment, di scovery and invention are strictly ind isce rnible - just like Next , the Plat oni st's desi re is fo r maxima l extension in wh at can be
the idea an d its ideatum. I1lnted ex istence: the more existences, th e be tte r, The Platoni st
gI,.spouses audacity in th ough t. H e d isdains res trictions and pro hibid
I m on s
foisted upon him fro m ou tsid e (p an icu larly those o rigina tin g fro m
2. EVERY I N S T A N CE OF THO UGHT - AND A FORT/ORi
timoro us p hiloso phemes). So long as the being envelo ped by th ought
MA THEMATICS - R EQU IR ES DECI SION S (IN T U I TION S)
prc\'e nts thought fro m lapsin g into inco nsistency , one can and should
TAKEN FROM T H E POIN T OF T HE UN DEC IDA B L E ( T HE NON_
p roceed boldly in asser ting existences. Th is is how thou ght pursues a
DEDUCIBLE)
line of inten sification .
T he result o f this fC3lUTC is a maximal expansion o f the principle of choice .. _ Lastly , the Platonist acknowledges a criterion whenever it bec omes
far as th e thinkable is co nce rned: since decision is primary and con tinuously apparen t th at a choi ce is n ecessary as to th e d irecti on in wh ich mathe-
requ ired, it is pointl ess 10 try to reduce it to protocols of construc tion 01' maries will develop . This cr iterion is precisel y that of maximal ext en-
externally regulated proced ures. On me cont rary , th e constraints of constI1JCa sion in wh at can be co nsiste ntly thought. Thus the Platonist will admit
lion (often and confusingly referred to as ' intuitio nist ' co nstraints , which is th e ax iom of choice rather than its negation, because a un ivers e
inappropriate giv en th at th e ge n uine ad voca te of in tuition is the Pla tonist) endo wed with th e ax iom of choice is larg er an d denser in terms of
should be: subo rd inated to th e freedoms of thinking d ecision. Which is why. in telligib le relatio ns than a un iverse that refuses to admit it . Co nver-
as long as th e effects en gender ed in th ought are maximal, th e Platoni st sees sely , the P latonist wi ll have rese rvations about admitting th e con ti-
no reason to refrain fro m free ly wieldi ng th e pri nciple of excluded middle. nu um h ypothesis, and even more so the hypothesis of const ruetibiliry .
an d con seq uen tl y reso rt ing to proofs by reductio ad absurdum. For universes regulated in acco rdance with these hypotheses seem
narrow and con st raine d. The cons tructib le un iverse is particu lar ly
pen uri ou s: Rowbottom has shown that if one admits a particu lar type
3. T HE S OLE CR I T ER ION FOR MATHEMATICAL QUESTION S
of large card inals (R am sey cardinals), th e co nst ructible real nu mbers
OF EXIS TENCE IS T HE INTELLIG IBLE CONSIS T ENC Y OF
beco me denumerable. F or the Platoni st, a den um erable contin uum
W HAT IS THO UGHT
seems far tOO cons tr icti ve an intuition. The Platoni st's co nvict ion find s
Exi stence he re mu st be co nsid ered an intrinsic d etermination of effecti ve reassu ra nce in Rowbouom's th eorem , wh ich privile ges decided co nsis-
th ough t in SO far as thi s th ought envelops bei ng . Those cases where it does tenci es over co ntrolled co nstructio ns .
not en velo p be ing in variabl y reg ister an inco nsistency, whi ch it is important
not to con fuse with an undecidability. In math ematics , bei ng , th ought and II the n becomes apparen t that a 'sc t -theo retica l' decision with regard to
consistency are one and th e same th ing . mathe ma tics, i.e. an on to logica l rew orking of Cantor's id eas (which , as I have
Several importan t co nse quences follow fro m th ese feat ures, in terms of shown, helps elucidate the th ink ing of being as pur e multiplici ty), imposes a
wh ich it is po ssible to recogn ize th e mod em Platon ist , who is a Platon ist of Platonic orie ntation of the kin d JUSt desc ribed. M oreover, thi s is con firmed
multiple-being . by the ph iloso ph ical choices es poused by GOdcl, who is (with Cohe n) th e
greatest of Ca ntor 's heirs.
- Fi rst of all, as G ddel poi nts Out, when it co mes (0 th e so-called ' para- Set- theo ry is indee d the p rototypical instance of a th eo ry in whic h (axio-
dox es' o f th e actual infinite, the P laton ist 's attit ude is one of ind iffer- matic) decision prevails ove r (d efin itional) co nstr uct ion . Empiricist s, along
ence . Since the realm of int elligibility in stitute d by th e infin ite seem s With the twentieth -cen tu ry partisan s of the ' linguistic tum', hav e no t been
10 pose no specific p roblem - whether w ith regard 10 axiomatic intui- slow in ob jectin g th at th e th eo ry ca nnot even define o r elucidate its cen tra l
tion o r w ith regard 10 d em onstrarive p ro toco ls - th e reasons ad duced conce pt; that of the SCt. T o this accusation a Platon ist like GOde l will always
for wo rry ing abou t in te lligibili ty are always extrinsic, psycho logi cal, or retort that wha t coun ts is axiomatic intuition s, which co ns titu te a space of
em piricist, and den y mathematician s their sc lf-s ufficiency ois-a-ois to tru th, not th e logical definition of prim it ive relati ons.
 56 Theoretical Wrttlngs Platomsm and Mathematl(a! Ontology 57

Contrary to the Ari stotelian or ientation (po tentiality as a p rimary sing u lao.. tdcrcd as a 'restrict ed un ive rse ', reflects the un iversal value of th e sta te -
con~1
..u nion of su bstanc e) and th e L eibnizian orientation (logical possib ility as • menl , loca lizes it . . .
'cla im 10 being '), set- theory kn ows only actual m u ltipliciry . The idea thar "h i~ th eo rem of reflecti on tell s us that what ca n be sa id wi th regard to
ac tua lity is the effec tive form o f being , and th ai possibility or potentiality are " tes s' being ca n also always be said in a de terminate site. O r th at every
'luTU t . '> • •
fictions, is a p rofoundly Plat onic motif. Nothing is mo re sign ificant in this -ment prescribes the possibility of a localization. One will recogmze her e
state".
rega rd m an the se t- thec re rkal tr eatm en t of the concept o f fun ction. WbII the Platon ic them e of the intelligib le local ization of all rat ional prono unce-
seems to be a dy namic ope ra tor, often mani fested in terms of spatial _ i.e. mente - whi ch is the very th in g H eid egger criticizes as the Idea 's 'segmen ta-
physical - schem ata (if y '" j ex), one will say th at Y 'va ries' as a fu nction of tion' of being's 'uncon cea lm cnt' or natura l presencing.
the va riation s of x, erc.j, is, in th e set-th eo retica l framewo rk, treated stri ctly More fund am en tally, set-theo ry's Platon ic vocatio n en tails co nsequences
as an actual multip le: the muhiple-being of the funct ion is th e graph , whieb
, " "
for three of th e con stitutive categories in any phi loso phi cal ontology: differ-
is to say a set whose elem ents are ordered pairs of th e (x, y) rype, and
allus ion to dy nam ics o r 'va riation ' is elim inated .
an, ence, the pri mi tive name of be ing , and th e un decidab le.
For Plato, d ifference is governed by th e Idea of th e Other. But acco rdi n g
Sim ilar ly, th e concep t of lim it, imbued as it is with th e experie nce of to th e way thi s idea is presen ted in th e Sop hist , it necessa ril y implies an intel-
becoming, of tend ing -toward, o f asym p to tic movement, is reduced to the ligible localiza tion of d iffere nce. It is to th e ex tent th at an id ea ' particip ates '
im m anen t characterizat ion of a typ e of m u lti p licity. T h us in orde r to be idtQoo in the Othe r, that it can be said to be d ifferent from another. Thus th ere is a
ti fied , a limi t ord inal does not need to be rep resented as th at toward wh ich localizable evaluation of di ffere nce: that of th e p roper modali ty acco rdi ng to
th e succes sion of ordi nals of which it is th e lim it ' tend s', sim p ly because it ;' which an idea, even though it is ' the same as itself , particip ates in the O th er
that succession as such (the eleme n ts of that succession are what d efine it as a as other id ea. In set-th eo ry, th is poi nt is taken up th rough th e ax iom of
set). T he tra nsfinite ordi nal Xo, whic h comes 'after' the na tural wbole extensionality: if a set differs from ano ther, it is beca use there ex ists at lea st
nu m be rs, is nothing othe r th an th e set of all natural whole num be rs. one clement which belongs to one bu t not th e other . This 'at least one ' loca -
In each and every case, set- theo ry d emonstra tes its ind isp utable derivatioa lizes th e diffe rence and prohi b its p urely globa l diffe rences. There is always
fro m Platon ic geni us by th ink ing virtuality as actu ality: there is on ly cee one point of d ifferen ce (just as for Plato an id ea is no t othe r than another ' in
kind of being, the Idea (o r in th is instance, the set). Thus th ere is no actuali- itself, bu t on ly in so far as it parti cipat es in the O ther). This is a crucial
zation, because every actualization presu p poses the existence of more trait , parti cu larly because it underm in es th e appeal (whether Ari stotelian or
one regi ster of existence (at least two: potentialit y and act ). Deleuzean) to th e qu alitative and to global, natural difference. In th e
Furthermore, set- theo ry co n forms to the principl e o f exisremial maxim- Platon ic sty le favoured by th e SCI-th eo retica l approach, alteriry can alwa ys be
aliry. Ever since Cantor, its aim has bee n to go beyond all p revious limi ta. red uced to p unctual d iffere nces , and difference can alwa ys be speci fied in a
uons, all cr iteria for 'reaso nable' existence (criteria wh ich arc in its eyel Uniform, eleme n tary fashi on .
extrinsic). The admission of increa singly huge card inals (inaccessible, Mahlo, In set-theo ry, th e void , th e empty set, is th e primiti ve name of being. The
measu rable, co mpact, supe rco m pact, enormous, ctc.) is intrin sic to its nat um emi re hie ra rc hy is rooted in it. There is a certain sense in wh ich it alone ' is'.
genius. But so tOO is the admi ssion of infini tesima ls of all SOrt s, in acco rdance And the logic o f difference im plie s th at th e void is un iq ue. For it can not
with th e th eory of su rre al nu m bers. Furthermore, this ap p roac h deploys differ fro m ano the r, since it co ntai ns no clem ent (no loca l point) throu gh
more and m ore co mplex and saturated 'levels' of being; an ontological hier- Which this differenc e cou ld be verified. T h is co mb ination of primitive
arc hy (the cum u lative hi erarc hy) tha t, in con form ity with an int ui tion which naming through th e ab solute ly sim ple (or the in-different, wh ich is the sta tus
th is time is of Nco-platonic ins pi ration, is such th ur its (inco nsistent) or t.h e O ne in th e Pannenidesy and found ing un iqu eness is indubita b ly
'to tality' is always co ns istently reflected in one of its levels, in the following Platon ic: the existence of wha t th is prim itive name designates m ust be ax ic -
sense: if a statemen t is valid 'for the un iver se as a whole' (in oth er words, if ll1atically d ecid ed , just as _ and th is is the up sho t o f the apo rias in the Pe rmo-
th e qua ntifie rs are take n in an u nlimited sense, so that 'for every x' really II/di S _ it is poi ntle ss to try to deduce th e existen ce (o r non-existen ce) of the

docs mean 'for any set whatsoev er in th e universe as a who le' ), th en th ere One: it is necessary ro deci de , and th en assume th e co nseq uenc es.
ex ists a scr in whi ch th at statem en t is valid (the qu anti fiers thi s time being F inally, as we have known eve r since Co he n's th eo rem, the co ntin u um
taken as ' rcla nv ized' to th e SCt in qu esti on). ~'h ieh m ean s th at th is set, nrp(nhesis is intrin sically undecidable. Many believe this signals th e veri ta ble
58 TbeoreucarWntmgs

~n o f the: pro ject of set- theory, or po ints 10 th e ' fragme ntation ' of what was
Inten ded as a unified cons truction. I have: said enou gh by now 10 make: it
clear ~al my o wn poin t of view is diametrically op posed to th is verd ict: the CHAPTERS
undecidab ility o f the contin uum h ypothesis marks the effecti ve comp letion of
sct- theory as a Platon ic orien tation. It indi cat es th e poin t of ffight th e a .
lh . • POna,
c I mma~ en t ~ r rancy . wherein thou gh t is experienced as 3 ground l~ Th e Being of N umb er
confrontatlon
. with th e undec idab le, or - to usc GOOd 's vocabulary - as a
continuous recourse to intu ition, which is 10 say, to decision.
.An..tiqualitarlvc localization o f difference, uni q uen ess of existen ce th ro u gh a
prt rruuve nam ing, intrinsic exper ience of the und ecid abl e: these arc the
features .through whi ch set- theory can be grasped by phil osophy from W Euclid's defini tions show how in the G reek con ception of number, the be ing
perspective of a th eory of truth, over and abo ve a mere logic of fonns. of numbe r is entirely dependen t u pon the metaphysical apo rias of th e one.
Number, acco rd ing to Definition 2 of Book 7 of Eucli d , is 'a mu lripli city
composed of units' . And a unit, acco rdi ng to Definit ion I of th e same boo k,
is 'that on th e basis of wh ich each of the th ings th at exist is called one'. U l ti-
mately, the being of num ber is the mul tip le reduced to th e pur e combina-
torial legisla tion of the one.
The exhaustion and even tu al collapse o f th is conc eptio n of the being of
num ber in terms of th e procession of the one ushers th e th inki ng of be ing
into the mod ern era. T his collapse is d ue to a combination of three facto rs:
the appearance of the Arab zero, the infin itesima l calcu lus, and the crisis o f
the meta phy sical id eality of the one. The first facto r, zero, introd uces
neutra lity and emptiness at th e heart of the conce ption of number. The
second , the in fin ite, eith er goes beyond th e combinetc ria l and heads towa rd
topology, or appends th e num erical position of a limit on to mere success ion.
The thi rd , th e obsolescence of the one , necessitates an attem p t 10 th in k
numbe r dir ectl y as pu re mu ltiplicity or mul tiple-with out-oneness.
\I:'bat initially ensues from all thi s is a kind of anarch ic d issem ina tion of th e
ccncepr of number. The d isci plinary symagm known as ' num ber theo ry'
bears witn ess to this: u ltima tely, it comp rises vast amounts of pu re algeb ra,
as well as part icu larly soph isticated aspects of comp lex an alysis. Equally
symplOmatic is the heterogeneity in the introductory procedures used for th e
differen t kind s of class ical num ber: axioma tic for natural whole numbe rs,
Structural for the ord inals, algeb raic for negative as well as rati onal numbers,
'vpological for real num be rs, an d largely geome tri cal for complex num bers.
Laslly, this dissemi natio n can also be seen in the non-caregorial chara cter of
the form al systems used 10 captu re number. Because they admit non -classical
Olodels, these systems ope n u p the fertile path of non -standard ana lysis,
thcreby rend cring infinite (o r infinit esimal) numbers respectable once again.
T he difficu lty for ph iloso phy , whose aim is to reveal how the conception of
nUmber h ar bo u rs an active th ink ing of be ing, is th at toda y, unl ike in th e
 60 The Being of Number 61
Theoretical Wr itings

Greek era, ther~ no longe r seems [0 be a un ified defi n itio n o f nu mber. ~ :"so note th at it includes an infin ity of as yet unnam ed species o~ n um bers,
co ncep t cou ld sim u ltaneo us ly enco m pass the d iscret e natur e of th e who l ~' Iarl , infinitesimals or num bers loca ted bet ween tWO adjacen t and
p3rll"'~ , . . .
the density
.
merme n th e transfinite numbering of Cantor's ordinals? In what sense is it
.
of th e rationa ls. the swarmi ng o f the in finitesim als not es, ~
--
dlscon n...... ted
classes of reals as well as all so rts of IOfinlle nu mbers, besides
, . .
dln3ls an d ord ina ls. I speak of a macro-body because It IS not a set. That
~r . . 10· ·
po~sib le ~or ~ ~ philosopher to relat e all th ese back to a sing le co ncep t, all the . why I ca lled it a co nfigu ra tio n. It is a clas s in u s own nght . IS IS
• d .
wh ile mairnammg and intensify ing th e concept's cognitive power as wel l obvioUS, because it ccnrain s all th e o rd inals, wh ich alre ady 0 .not co~ stllu te
. . I . U
u s smgu ar Inven tiven ess? L et 's try to cla rify thi s co nfusion by startin g f ., Invoking once mo re an intrinsic cha racteristic of multiple -being , we
a s~ .
the ordinary usn of the word nu m be r. rom .....ill say that the co nce pt o f nu mber designa tes an in con sist ent mu ltipl icity -
What do we mean by 'n um ber'? W hat is en taile d by O Uf uses of the te rm but add that the spec ies of num bers ca rve out co nsiste n t numer ical sit un-
and the rep resent ations associated with those uses? tionS withi n thi s inco nsis tency , whic h con stitutes their being. Thus the
First of all, by 'number' we understand an instance of measure. At the body of re al num bers consi sts; it is a set . Bu t its iden tifica tion as body of
most elementary level , num ber serves 10 d isti nguish betwee n the less and the nu~bcrs co mes do WTI to its bei ng an inte rnal consiste ncy in the inconsis-
mo re, th e large and the small. 11 pro vides a d iscr ete distrib ution of da ta. tency of th e site of num ber; in other word s, a sub-body of the numer ica l
T hu s one o f th e p rincipal requir ements for any spec ies of n umber is that iI: macro-body.
provide a structure of order. We could therefore say that the appa ren t anarchy or concept-less m uhipfi-
Secondly, a number is a figu re o f calculation. We' coun t with n umbers. To ON of the species of nu mbers resu lted fro m the fact that , u p until now , the y
cou ~t mean s to ad d, su btra ct, m ultiply, divide' . Thus We' will require of . we're effecruated in their opera tions but not loca ted in th eir bei ng . The
spec ies of number tha t th ese operations be pra ct icable or well-defined within macro- body provides u s with th e inconsisten t generic site where in numeri cal
~ t . T~hn i cally, th is means tha t a spec ies of num ber mu st be' ca pable of bei.na; consistencies co-exist. H enceforth, it beco m es legitim ate to conceive of these
Iden tified algeb raica lly. The com ple ted su m m ary of th is iden tifica tion is the multiplicities as pertaini ng to a sing le co nce p t, that of N u m ber.
algeb raic body structu re, whe rein all operat ion s arc possible . T he being of N um ber as such , which is tha t aspec t of number which
T hirdly, number mu st be a figure of cons istency. T his mean s th at its IWO thinks being , is u lti ma tely given in the defin ition of the ma cr o-body as tncon-
charac teristics, o rder and ca lcu lation , mu st obey ru les of co m patibility. For sistcm site of being for th e co nsistency of numbe rs.
exam ple , we expec t th e add ition of two clearl y positive num bers to be bigger Thus, we will use the term ' N um be r' (cap italized) to refer to every enti ty
th an each of th ese num be rs, or th e d ivision of a pos iti ve number by • that belongs to the mac ro-body . And we will use th e term ' num be rs' (lower
num ber greater th an one to yie ld a result smaller m an th e Dumber with ease) to desi gnate the di versity of species , or th e immanen t consistencies
which we sta rted. These ar e th e ' lin gu istic' req uirem en ts for th e idea of whose site is fixed by th e in consistency of Number,
num ber, in so far as it expresses me reciprocity of order and ca lculation. What th en is th e definition of a Number?
T echnically, thi s w ill be expressed as follow s: th e adequate figu re in which a This defini tion is admirably sim ple: a Number is a set with two me m bers,
species o f number is inscribed is tha t o f th e o rdered body, an ordered pair, co mp rising an o rd inal and a part of th at ord inal, in that
If, in light of all thi s, we want a defini tion of number to subs ume all its orde r. Accordingly, we will d enot e a Number as (a , X ), whe re X is a part of
species, th is mean s it mu st dete rmine what I will ca ll th e 'o rd ered macro- Ihe ordinal a, o r X~ a.
body' wherei n all th e spec ies of n umber may be situ ated . II mig ht be objected th at this defini tion is circu lar, since it ma kes u se of
This is p recisely th e result o f the d efin ition put forward by the great math- ordInals, whic h we have declared to be number s, and wh ich therefore already
em atician Co nway, un der the parad oxical nam e of 's u rreal num bers' . figu re in the macro-body.
In the general framework of set- theo ry, this definition spec ifics a con- But in rcalil y it is possibl e to p rovide an initial defini tion of ord ina ls in a
figuration in whic h a to tal orde r is defin ed , an d in whic h addition, sub trac- Purdy st ructura l fashion , without reso rting to any numerical catego ry what-
tion , m ulti p lica tion and d ivision are un iversally pos sible. Note that this SOever, not even (d espite thei r nam e) 10 th e idea of order. Von Neumann
configu ration or macro-body of num bers incl udes th e ordi na ls, th e whole defines an o rdi na l as a transitive set all of whose mem be rs are also transitive.
naturals, the ring of pos itive an d negative wh oles, th e bod y o f rational s an d But tra nsitivity is an ontological prope rt y: it sim ply m eans th at all the
th e body of reals, along with all tb ctr known structu ral determinat ions. But cleme nts of a set are also parts of th al set, or th at given a ell. you also have
 62 Theoretical W rit ings The Being of Number 63

a~~ . T his maxi m al co rrela tion between belong ing (or elem ent ) and incl us' bOdy, lh e site fo r th e ontologica l identification of everything that falls under
(or pa rt) endows transitive SCIS w ith a specific son of ontological stabilj concept of nu mber ,
onc whi ch I regard as peculiar 10 natural being. I It is th is natu ral stab ility th~no: can then go on to sho w th at all th e familia r spec ies of n umber arc in
ordinals. this imm anent homogeneity, which makes of th em the prime r . nsistenci es ca rve d ou t fro m this site; natu ral whole nu m bers, relative
~ ro .
mate rial of Number. tcrs rati on al num bers an d rea l numbers arc all sub-species of the
W hat is strikin g about the definition of Number - th e ordered pai ring nurn uuu
rnacro-
" ~..ll' or numbers th at can be identified within th e ontologica l site of
an ord in al and a part of that ordinal - is the instance of th e pair. In order !'lum ber.
d efine Number, it is necessary [0 ins ta ll oneself in th e rea lm o f th e two., But aside fro m these historical examples, the re are many o th er strange and
Number is not a simple mark. T here is an essenti al duplicit y ( 0 Num~ as yet un identified or unnam eab le entities swarming un der the co ncept of
Why this duplicity?
Number.
Because Number is an ontological gestu re - to usc the vocabulary of Here are two examples:
l
Chii te let - an d th e double marking is a tra ce of thi s gesture. On me
han d , you have a sta ble, homogeneou s m ark : th e ordinal . On th e oth er . I. We are accustOmed to co nside ring finite negative num bers. But the idea of
m ark th at , in a ce rtai n sen se, ha s been tom from the former; an inder a negative o f the infinite is ce rta inly m ore un usual. Nevertheless, within
nate part that, on the whole, docs not conse rve any immanent stab ility .... th e macro- body of Numbers, there is no difficulty in defining the negative
can be d iscontinuous, di smembered, and devoid of any co ncept - be",_ of an ordi nal, whether fini te or infinite.
there is nothing more errant than the notion o f th e 'part ' of a se t.
Thus the n umerical movement is, in a certain sense, th e forced,
lanced, in ventive sam p ling of an incalculab le part of tha t wh ich , by i ~
un. 2. It can demonstrated that. within the macro- body which identifies the site
of N um ber, th e real numbers incl ude all th e Numbers whose matter is
the first in finite ordinal, i.e . w. and whose form is infin ite. \l'hat can we
possesses all th e attri butes of order and in ternal so lidity. say abo ut those Numbers wh ose materi al is an infin ite ordinal gr eater
This is wh y, as a philosopher, I have renamed the two ccm poneats cI than w? Well. we can say th at, generally speaking, th ese are Numbers that
Number. I ha ve called th e o rd ina l the mate rial o f N umber, in o rder to evolal we hav e yet to st udy and th at remain as yet unnamed. The)' make up an
that donation o f stab ility and of a powerful but alm ost ind iffer ent intemll infinitely infinite reserv oir of Numbers be longi ng to an open future in
architecture. And I h ave called the pan of th e ord ina l th e /o nn of tbt which th e on to logica l forms of numericality will be in vestigated, This
N um ber, not to evoke a harmon y o r essence bu t rather to designa te tbM: testifies to the fact that th ose numbers wit h which we are fam iliar me rel y
which , as in cert ain effects achieved by contem po ra ry art , is in ven tivdJ make up a tin y fraction of w hat bein g harbours un der the co nce p t of
extracted from a st ill legib le backdrop of matter , Or th at which, by cxtraetiol Number. In oth er word s, the on tological prescri pti on lat en t in th e
a sam ple of unforeseeab le, almost ligh tni ng-like d iscontinu ity from ma uer, conce pt of Numbe r infin itely exceeds th e actual h istorical de termination
allow s an unalter able material d ensity to be glimpsed as th ough through the of known and named numerica l co ns istencies. T he word 'N um be r'
gaps left by tha i extraction . harbours a grea te r share of be ing than anythi ng math ematics has hi the rto
T hu s a N umber is en tirely det ermined by the cou pling of an ordinal been able to circ umscribe o r ca ptu re through the toils of its con sistent
ma terial and a form carved o ut fro m th at m at er ial. It is th e du plicity cc nsri- cons tructions.
ru tcd by a dense figure of m u ltiple - being and a lawless gesture of carving out
that traverses th at den sity. In fact , in each of its segme n ts , even in those that seem m ini scule from the
\'\lhat is remarkab le is that this simp le starti ng poi nt allows one to establish point of view of ou r int ellect , the macro-b ody of N umbe rs is pop ulated by an
all the properti es of orde r an d calcu lation required from that wh ich is infin ite infini ty of N um be rs. In th is respect it probab ly provid es th e best
suppose d to provid e the ontological co rre late for th e word ' N um ber'. POssible ima ge for th e uni ver se as described by Leib niz in pa ragra ph 67 of
T hi s is do ne b y proving - here lies the technical aspe ct of the matte r _ th.t the Monadology : ' Each po rt ion of matter may be co nceived as a garden full of
the uni vers e of N umbers is co mpletely orde red. and that one can d efine a plan ts, an d as a po nd ful1 of fish . But every bra nch of each p lant , ever y
body- structu re within it, whi ch m ean s add ing, m u ltip lying, sub tracting an d member of eac h ani m al, and eve ry d ro p of th eir liqu id part s is itse lf likewise
dividing. One th ereby accomplishe s th e cons tructio n of an o rdered macro- a sim ilar garden or pond.' ) Eac h m in iscul e sectio n in th e ma cro -body of
 CHAPTER 6

One, Multiple, Multiplicities'

I. I thought that my Dd eu:;;e had mad e: its point perfectly clearly. But since it
seems I was mistak en and I am being asked to restate my argument, allow me
10 reiterate wh y I consid er th e wo rk of Gill es Deleuze to be of exce ptio nal
importance. Deleuze conceded no thing to th e h egemonic theme of the end o f
philosophy, whe the r in its pa thetic version, which ties it to the d estiny of
Being, or its b lan d one, whi ch binds it 10 th e logic of judgeme n t. Thus,
Dd euze was neith er hermeneu tic nor analytic - th is is alre ad y a lot. He: cour-
ageously SCt ou t to cons truct a modem meta ph ysics. for which he d evised an
altogether origina l genealogy, a genealogy in which ph ilosophy and the
history of philoso phy are indi scernible.
Deleuzc freq uented th e more incontestable cogn itive p roduction s of ou r
time, and o f some othe rs beside s, treat ing th em as so man y inaugural 'cases'
for his spec u lative will. In SO doing, he displayed a d egree of d iscernment
and acume n unparall eled amo ng his con temporari es, especi ally where prose,
cinema, certain aspects of science and po litical experimentation are
COncerned. For Deleu ze really was a progressive, a reserved rebel, an ironic
supporte r of the most radical movement s. That is why he also op posed the
II OutJt a llx philo$ophes and rem ained faith fu l to h is vision of Marxism, makin g

no COncessions 10 th e flaccid resto ration of morality an d 'd emocratic d ebate' .

These are rare vir tues indeed .
MOfCO\·er , D eleuze was the first 10 prope rly grasp that a contemporary
rnetaph ysia mu st consis t in a theory of mu ltiplici ties an d an emb race of
Singularit ies. He linked th is req uirem ent to the: necessity of critiqui ng th e:
thornier forms of tra nscenden ce. He saw that only by posit ing th e univocity
of heing can we have do ne with the perenn ially religiou s nature of the inter-
pretation of mean ing . He clearl y art icu lated the conviction th at the truth o f
uni\·ocal be ing can on ly be grasped by th inking irs even tal advent.
T his bold programme is one .....h ich I also espo use. Obviously, I do nOI
think Delcu zc successfu lly accomplished it; o r rath er, I be lieve he gave it an
inflection which led it in a direction op pos ite to the one I think it shou ld take.
Otherwise, I wou ld have rallied to his concep ts and orie ntations of thoug ht.
 68 Theore tical Wri tings 69

Or r qua rrel can be formulated in a nu mber of ways. We co u ld approach it th lies in add res sing itse lf to each and everyone's an im al disq u iet, to
streng .
by vay o f some novel q ues tions such as, for example: how is it tha t, for f sed dcsi res to everything th at makes us scu rry about bhndly on the
our a m u ,
Delcrze, politics is not an au tonomo us form of thought, a singular section of desolate su rface of the: earth. . .
chao. one that differs from art, science and phil osophy? This point alone secon d, and most importantly, my appraisal IS based on the faa th at no
bea r. witness to ou r di vergence, and mere is :I sense in which everyth ing can .interesting' ph iloso ph y (to use Delea ze's own normative vocabulary ), no
be Slid to follow fro m it. BUI th e sim p lest th ing is to start fro m what sepa- mattcr how ab ru pt ly co nce ptual and anti -e~~ i ricist, has eve ~ bc:e~ conten t
ra I C~US , at the point ofg reatest proximity : the requ irement s fo r a metaphysics . tv to ado p t inh erited categorica l op positi ons, and that 10 thi s respec t
simp C . , . Plato I
o f th: m u ltip le. For it is 011 th is issue that m y critics were m ost voca l in their d taEsl philosoph ies cannot lay clai m to any kind 0 smg u am y . ato insu -
prc ust s. O r rather , not so m uch vocal as mu ffled, given the way they choked tutCS sim ultaneous proceedi ngs against rnuluplc- becoming (in the Th eaete/lls)
on uc quasi-my stical thesis of the On e. It seems these critics read my funda, m d th U l
e immobile-One ·
(in th e Pan nenides); p roce ed ings whose radic •ality• has
me na l claims (abou t th e On e, asceticism or uni voc ity), but failed to exam ine ).cl to be outdo ne. The notion th at th ought shou ld always estab lish Itself
eithe th eir co mposition or th e speci fics of m y argument . bevond categorical oppos itio ns, th er eby del ineat ing an unp reced en ted
Bu arc th ese cri tics really preoccu pied with th e Ete rnal Return, or d ~gon3l , is co nstitutive of p hilosop hy itse lf. The wh ole q ues tion consi sts in
Relaion , or the Virtual , or the Fold? I am not so sure. F or it seem s that Lhcy Mowing what value to ascribe: to th e operators of th is diagonal tra jectory ,
bclie-e, unlike their M aster, that all th is can be debated in ha ughty ignoraJXe and in iden ti fyin g the unknown ~UTCC to whi ch they summon th ought.
of tJrir opponen t's doctrine . Thus we see them resort to th e setting up of In th is regard, to sta te of a philosophica l framework - as I d id in detail -
elabcate trials for m isrep rese n ta tion. But such tri als can on ly be su perfict.l thai the co ncep tua l d iagona l it inven ts beyond the ca tego rical opposi tion of
or ccorrecr, given th at th ey invoke what academics ha ve w ri tte n abow: the One and th e M u ltip le is subo rdina ted to a renewed in tui tio n of th e powe r
D eleize's wo rks on Spinoza o r Ni etzsche. Even if m y cri tics in ten ded to of th e One (as is manifestl y th e case for th e Stoics , for Spinoza, for
show - as th ey shou ld , in co nfo rm ity with th e doc tri ne of fr ee indi rect Nietzsche, for Bergson and for D eleuzc) is by no mean s a 'critique' wh ich
d iscorrse that th ey've inh er ited - th at my claims abo ut Deleu zc con form ed to one shou ld hasten to ' refu te' in o rder to m ain tain some so rt of o rth odoxy
the tteses of m y book Being and Eoem, it wou ld still be necessary, as D eleuae concerning th e di agonal in ven tion itself. All th ese ph iloso phies, throu gh
himstlf at least att empted, to encaps ulate th e singularity of th at work. We operatio ns of gre at com p lexity to whi ch it is importan t to do justi ce case by
wou ll th en have somethi ng a little b roader and a little better th an a defence case, maintain th at th e effective intuit ion of the One (wh ich ma y take the
an d ilu stration o f textual o rthodoxy. We wou ld be ge tti ng nea re r to the name of 'All ' or ' W ho le', ' Subs tan ce', ' L ife'. ' the Bod y w ithout Organs' o r
in hermt phi losop h ical tension th at characteri zes ou r tu m of th e centu ry. 'Ch aos') is th at o f its immanen t crea tive power, o r of th e eternal return of it s
Nohing co uld be m ore po intless th an to argue, for exa mple, that th e oppo- differenti ating power as such . Thus, in conformity wit h Spinoza's max im ,
sition between the One and the M ult ip le is '$Iatic ' and then , as though the Stakes o f philosophy cons ist in adequa te ly thi nking th e greatest possibl e
unveiing the latest theoretica l innovation, to try to co unter thi s with a third num ber of particu lar things (this is th e 'em p iricist' aspect in D eJcuze - the
concen - such as tha t of 'm ul tiplicities", for ins tance - wh ich is supposed to disjunctive syn th eses o r th e 'sm all circuit'), in order to adequately think
nouri h the uni m aginable 'wealth ' o f th e mo veme nt of thought , the expert- Subst an ce, or the One (wh ich is th e ' tr anscend en tal' aspect - R elation or the
cnce ,f imma nence, th e q ualit y of the vir tual , or the infinite spee d of intui- 'g reat circu it' ). It is to th e prec ise deg ree that such sta kes are p resen t that
tion . co nsider this vitalist te rro ri sm - whose hall owed version was p rov ided Ihcs c apparatuses of thought arc p hi losop hies. O the rwise, they would be no
by Ne ta sche, an d whose po lite bourgeo is ve rsion , as G uy Lardrcau rightly more th an mo re or less lively phe nome nologies, vain ly and indefinitely
not es,derives from Bergson - [Q be puerile. recomm en ced. W h ich is wha t , as far as I can sec, th e m ajorit y of th eir d isci-
F iu of 311, becau se it presuppo ses the conse nsu al nature o f th e ver y norrn pll:s int end to red uce th em to .
that rrcd s [Q be examin ed and es tablis hed , to wir, rh m mov em en t is supe rior Sin ce we ar c d eali ng with phi losophy (and I be lieve I was among the first,
to imn obiliry, life su perior 10 th e concept, time 10 space, affirma tion (0 if not (he first, to have treat ed D elcuzc as a philosoph er), on ly th ose wh o
nega tion, d iffer ence to iden tity, and so on . In th ese laten t 'ce rtainties", wh ich remai n trapped by th e subjecti ve co nstraint of allegia nce o r acad em icism
co m mnd th e pe rem ptory met ap horical style of Deleu ze's vitalist and anti- believe that in orde r to say something abo u t it repe tition is required. T ruly 10
ca regoical exegeses, th ere is a k.ind of speculative demagogy whose: en tire SPeak about 1lI ph ilosophy means evaluating ; within a SCt-Up that is itself
 Theore tcat Writings One, Mult iple.Mult lpliclt les 71

in ventive, o r co nsigned 10 its own power, th e d iagonal operators that a rnec.. us to th ink a muhipliciry. By taking th ing s expe rien tially 'i n the
allo W's . .
physical apparatus proposes to u s. Conseq uen tly, it is not a qu esti on 01 .ddle', eve ry figu re of tra nsce ndenc e is rejected. Ne vertheless, It IS easy to
l
knowing whether ' m ultiplicities' is a term th at en d ures beyo nd th e catego.. ro th at thi s 'm idd le' is reall y the elemen t o f th e categorical op pos ition itsel f.
rica l oppo sit ion between the One (as transcenden ce) an d the Multiple (II ~r a mul tiplicity is really th at which, in so far as it is grasped by the nu me r-
em pirical givenn ess). This is trivially obvious in the co ntext of Deleuze'. ~ l one , ....i ll be ca lled a set, and in so far as it rem ains 'open ' to its own
m etaph ysical pro ject . What needs [0 be evalua ted with regard to th e Promilc :wer - or grasped by th e vital One - will be ~II~~ an effective mu ltiplicit y.
harboured by th e co ncept o f m u ltip licity - whic h is oriented towards a vi qt Once it is concep tually reoon srructed, muhipliciry appea rs as suspe" ded
in tui tion o f th e One and a th ink ing fidel ity to 'po werfu l inorgan ic life' or the btrr::u Il tWO fo rms of the One: on th e one hand, th e form th at relat es to
im pe rsona l - is th e intr insic density of th is co ncept, and wheth er a thinkioe counting, numbe r, th e set; on the other, th e form that relat es to life, cr eation,
whose own movement comes from elsewhere is ca pable of susta in ing the differentiation. The norm for thi s ten sion, the real conce p tual opera to r at
philosophical announcement bo rne by the co ncept of m u ltip licity . work with in it, is borrowed fro m Bergson: multiplicity will be call ed 'd osed'
Now, in m y view the co ns truction of this co ncept is ma rked (and thi s indio- when grasped by the numerical one, and 'open' when grasped by th e vital
ca tes its overtly Bergsonian lineag e) by a prelim inary deconstruction of the One. Ever y multiplicity is the joint effectuation of th e closed and th e open,
con cep t of set. D cleuze's dida ctic of m ultiplicities is from beg inn ing to end a but its 'veri tab le' mu lt ip le-bein g lies on th e side of th e open, JUSt as for
po lemic again st sets, just as th e q ualitative co nte nt of th e intui tion of Bergson the au thentic being of time lies on th e side of q ual ita tive duration,
durat ion in Bergson is only identifiab le on the basis o f th e discre d it tha t m ust or th e essence of th e dice-throw is to be so ugh t in the single primord ial
attach to the purely spatial q uantitative value of chrono logical time (on thiI Th row, and nOI in th e numerica l result di sp layed by the immobile di ce.
crucial issue I cann ot reg ist er an y kind of caesura between D Ifference tutti Now, assigning th e set to the d osed , i.e. to numeri ca l uni ty, reveals a
Repetition and the more detailed phi losop hical tex ts to be foun d in the two limited concep tion of set. This is wh at lies be-hind th e sup pos ed ' su blation'
volumes on cinem a). of th e set by the d ifferentiati ng open ing of life . But after Cantor, the set -
On thi s basis, I'd like to sketch th e demonstration o f three theses: w hich is int u ited as a m ultiple of multiples wh ose only halting point is the
void, with in whi ch infinite and finit e are eq ui valent , and wh ich guarantees
a. What D eleuze ca lls 's et' - in co ntradistinc tion to whi ch he ideoti6cl that every m u lti plicity is immanent and homogeneou s - cannot be assigned
m ultiplicities - does noth in g b ut repeat th e traditional determinations of either to number or to th e d os ed .
extern al, or analytical , multipli ci ty, effecti vely ignoring the extraordinary I have devoted an entire book (N umber and 'lUmberJ)'l to show ing bow , far
immanent d ialectic wh ich this co nce pt has un derg one at the hands of from th e set be ing reducib le: to number, it is ra ther number - i.e. an innu-
mathematics ever since th e end of th e n in eteenth cen tury. From thiI merab le infinity of kind s of number (for th e mos t part yet to be stud ied) -
po in t o f view, th e experiential co nstructio n o f mu ltiplicities is anachro- which presupposes th e prior availab ility of th e on to logy of sets for th e app re-
n istic, beca use it is pre-Cantorian . hension of its conce pt. Number is but a sm all an d particular sect ion o f being-
b. A s for the densit y of the co ncep t of multiplicities, it remain s inferior - mulliple such as it is given to thought in th e set -theore tica l axiomatic, wh ich
even in its qualitative d etermination s - to th e concep t of Multipl e that is really ra tional ontology itself. O nl y th e unwillingnes s to accept thi s poi nt,
can be extracted fro m the contemporary history o f sets . and the obstin ate wish to m ain tain at all COStS and in the face o f all evidence,
c. T his lag (one o f whose sym p toms is an ' im po verished ' in terp retation of that eve ry set is a num ber , can explain the very strange text whic h D elcu ze
R iemann), ma kes it impossible [0 su btract mult iplici ties from th eir eq ui- devoted to my book B eillg and Event in Wh at is Philosophy P No clea rer
voca l absor p tion int o the On e, or to achi eve the uni vocal d etermina tion of demonstration cou ld be given o f th e manner in wh ich the insistence on usin g
a mult ip le-wilhout-oneness, such as I have developed in m y own lhe normative logic of th e clo sed and the open as an interpretive filter vis-a -
doctrine. vis a phi loso phy that takes Ca nto r as one of its cond itions on ly succ eeds in
generating co nfusion.
2. The specific mode whe reby 'm ult ip lici ty ' lies beyo nd th c cate go rica l oppo- For th e set is the exe m plary inst ance of something th at is th ink able only if
sition of th e O ne an d the Multip le is of an in tervallic type . By this I mean One d ispe nses en tire ly with th e oppositio n be tween the closed and th e open -
th at , for D eleuz e, on ly th e play in ~l;omi'lg of at least two d isjunct ive figures fOr the importa n t reason that it is only on the basis of the un d etermined
 72 Theoretical Wntmgs O ne. Multiple. MultipliCIt ies 73

concept of set mal th is oppo sition can be granted a sat isfactory mean ing. . which exhaus ts it univocally . U ltimat ely, the topological construc tion of
could even say that the set is th at neu tral-m ult iple which is !lOll , . th th
S 011 the basis of a set- theoretical ont ology demonstrates at e set,
subtracted from bo th ope nness and closure. b ut wh ich is also :::n as such, is in no way an image of th e d osed, since it is indi fferen t to
sustain ing th eir oppos ition . alit" of closed and open. M oreover, it also in d icates that when
lhe d u - . .
We know in fact that if we take any set , It is po ssible fo r us to d ech'ed in th is manner, th e though t of th e open manages to remain faithful
n umerous topologies relative to it. No w, what is a topology? It is p COO nnd ple of imma nen ce and u nivocity fro m wh ich the vitalist noti on of
10 a p . .
the fixation of a concept of the O pal (or of the closed ). But rathe r multiplicity inevitably d eviates - for. rega r.dless of how closed It I~, th e
puuiog it s trust in dynam ic in tuition. as th e vita list orientatio n does. with vit3liSt multiplicity is obliged to signa l eq u ivocally towa rd th e openmg o f
the para doxical consequences th at I registered in my Deteuee, topo ""hich it is a mode.
ope rates - as every approach faith fu l to a principle of immanence mu st -
determin ing the relational effects of thi s opening (o r clo sure). A concepe J, Someone migh t objec t that only th e dialectic of th e open and the dosed -
th e open is su bstan tially established once we possess a multip le such that such as provides th e basis for the conce pt of mu lti plici ty (o r mu ltipl icities) -
d well with in it by laking th e inte rsection of two clemen ts, or the union of can do justice to becomi ng , to singularities, to crea tions . to th e in exhaustib le
many elements as we wish (even an infinity of element s). In other words, diversity of sensation and life; that it is trul y outrageous to sec in it some sort
inters ection of two op ens is an open, an d any un ion whatsoever of of phenomen ological monoton y; th at the post-Canterian theory o f the pur e
remain s ope n. As for the closed, it is n ever an ything bu t the d ual of multiple is incapable of eq ualling th is d escriptive capacity; and that the latt er
open, its compleme nt o r reverse. Its relational prop erties are symmetric in fact harbour s identity 's categorical reven ge on difference.
those of th e open: th e un ion of two closed sets is closed , and th e in te l bclieve the op posite to be th e case, for at least th ree reasons:
of any n um ber whatsoe ver of closed sets remain s closed . The closed
dwells. acco rd in g to imman ent path s th at d iffer from th ose of the open . A. Mathematics has th is pecu liar trait : it is always richer in su rp rising deter-
It is from the po int o f view of th is 'dwelling' alone , of thi s persist ence min:n ions than any emp irical donation whatsoever. The recurr ent th em e
the 'th ere' of a mul tiple be ing.there in operationally maintaining its of the 'abstract pov erty ' o f ma th ematics when compared to the
im man enc e. that we can elucidate one of th e main properties of open burgeon ing richness of the 'co ncrete' is an expression of p ure doxo (and
wh ich Deleuze (wrongly) identifies with th eir 'absence of parts', and one which , incidenta lly, was enti rel y fo reign to Deleuze himsel f). In
fore with th eir qualitative, or in tensive, singu larity. This propeny is w t actual fact, ma th ema tics shows itself pe rfect ly capable both of providing
'poin ts' of an open are pa nially insepara te, or not ass ignable, beca use schema s adequa te to expe rience , and of fru st rating thi s experience by way
open is Ih~ neighbourhood of each of its po;nu. It is in th is wa y th at an open " of concep tual inventions th at no intu ition cou ld ever acce pt.
topologicall y provokes a so rt of coalescence of th at wh ich const itu tes it. Take a simp le exa mp le: the emp irical no tion of 'graz ing' - i.e. th e
That the open po in ts back to a 'd welling' is not at all pa radoxical (th ere . . notion of a supe rficial touch , o f a contact whic h is almost identi cal with a
strong intuition s in H eidegger abou t thi s qu estion). If open ing, in its vt:rf non-contact, or eve n of a timid caress - is certain ly conce ived through the
cons truc tion, effectua tes a locali zation withou t an outsid e (wh ich reiteratct notion of tangency, o f the infin ites imal ap proac h toward a point , a not ion
th e idea that th e open q ua neigh bour hood ' loca lizes' all of its po in ts). it is which , ever since the G reeks, requires an ascetic effort of th inking and is
because 'open ' is an intrinsic dctcrminmic n of the mult iple - in other words. oriented toward the conce pt of the derivative of a fun ction. Very rou ghl y,
because we arc indeed dealing with an immanent construction. T his not the one can say th at , given the curve that rep resents a fun cti on , if th is
case with D clcuze, since in h is th inking th e open is always open to someth inl function can be d eri ved for a value of its argume n t, there will be a
othe r than its own effectiveness, namely to the inorga nic power of wh ich it is tangcm LO the curve at the point repr esent ed by th is value. One can there-
a mobile actu alizat ion. For Deleuze, to redu ce the open to its intern al power fore argue that the joint notions of curvat u re an d con tact at a single po int
of localization wou ld be to turn it into a closed set. M oreover , it is beca use it llf this cu rvatu re intu itively circu late betwee n the conce pts of con tin uous
mu st be ope n 10 its own be ing that th e vitalist notion of the open is ulti- functio n (cu rve) and dc rivarive at a po int (tan gen t). I have chose n this
ma tely on ly thinkable as Virt uality. By way of con tras t, the set-theoretical or eXamp le because it is quite Deleuacan , as well as bei ng one with whic h
ontological open is en tire ly con tained in the act ua lity o f its own d etermine- Dcleuze himse lf was perfectly familiar. Curvatures. co ntact s, bifu rca tion s,
 Theore t ICal Wflt lngS 7S

lin es o f flight (a tang ent touch es the curve an d flees ), differcntia tion~ . urn 'S for his p hilosophical th ink ing . In d eed , I have even praised him
- all th ese are cons tan ts of D eleuze's descriptions. 1 ow co nsider ;:0this. But sho rt of allowin g th ese examples simply to be rep roc essed b y
d iscovery, in th e n ineteen th ce ntu ry, th at th ere exist co n tinuo us fun . " ypw-dialectic o f th e dosed and the open, th ey must be allowed to
the
that canno t be d eri ved at any poi"" T ry to im agine a conlin uous icr into con flict with th e vitalist doc tr ine of m ultipliciti es ,
such that it is im pos sib le for a straigh t line to ' touch' it at an y point enOn this point, the case of Riemann 'IS 0 f ' d era bl e sj"gru ftcance.
consr
Even bett er: We can d emonstra te th at the se fun ctions, whi ch Riemann fasci nates D eleuzc because he b rilli an tl y co m plexifies th e
sub tracted from every em pirical intu ition, and are therefore s . dementary in tui tion of space, p roviding D eleuze with a wa r machine
spea king un represen teble, are 'mo re numerous' th an those that against th e unilate rally extensive (or extended) conception p rope r to the
hith erto gov erned ma th ematical thi nki ng . This is just a pan icular e.- Canesian or eve n K antian no tio ns of space. In effect, R iemann speaks of
a genera l law: eve rywhe re where math ematics is close to experien ce 'multiply extended' spaces, of varieties of space, th ereby anticipating the
follows its ow n movem ent , it di scover s a ' path ological' case that a modern notion of fu nctional space, H e validates D eleuz e's arg um ent s
lutely challe nges th e in itial intui tion . Math ema tics then establishes about the layered cha racter of th e plane o f im manence an d the non-
thi s patholog y is the rul e, and th at what can be in tuited is only an panitivc conception of localizat ions. It is also true th at Riem ann gener-
tion: We there by discover th at as th e thi nki n g of being qua bei ng, alizes the co nce pt of space bey ond an y em pirica l in tuition in at least th ree
maucs never ceases to d istance itse lf fro m its start ing poi n t. which is 110 respects: he inv ites the consi dera tio n of n -dimensional spaces, rather th an
found in an available loca l bei ng o r a contin gen t efficacy . JUSt spaces with a maxi m um of th ree dimensions; he tri es to thi nk rela-
This means in particular th at, in th e case of th e 'rhizoma tic' multi tions of position, form , and neighbouring in dependently of an y m etrics,
ties tha t serve as D elcu ze's cases (packs, swarm s, roo ts, interlacings, and therefore ' q ualitatively', wit hou t reso rting to n umber; and he
the variegated co nfiguration s proper to set-theory p rovi d e an in imagines we can h ave not only elements or poi nts bu t functions as compo-
ably richer and more com p lex resource: th ey always allow one to nems of spaces - such th at space woul d be ' pop ulated' by variations
fu rth er tha n co u ld be imagined . For instance. th e constru ction of a rath er than entities. In doing so, Riemann opens up an immen se dom ain
subse t in a panially orde red SCt not onl y surpasses in violen ce, as a cue for 'geo metric' meth od, one which is still bei ng co ntinua lly explored to
tho ught. any empirica l rh izomatic schema what soe ver, bu t, by esta b . th is very d ay. D etea ze's vita list th ough t co ncu n with th is mu lti -
th e co nditions for 'neu tra lity' in a multiple that is both dispersive and dimensional geo metriza tion, th is doctrine o f loca l variations, th is q ualita-
o rd inared, it actually su bs umes th e ontology of th ese sche ma ta. TbiI tive loca lization of te rritories ,
why , in elabo ra ting an on tology of the multi p le, the first rul e is follow Yet it is perfectl y clear th at, in order to ach ieve th e p rog ram me th ey
conceptual m ath ematical cons tructions - wh ich we know can overflow had set out, Riemann 's awe-in sp iring anticip ation s dem anded a specu la-
all d irections, no matter what th e empirical case, once it is a qu estion tive framewo rk entirely sub tract ed fro m the co nstra ints of em pi rica l intui-
th e resources proper to th e m ultiple. This ru le, of cou rse, is Pla tonis t: mill tion. Furthe rmo re , what th e 'geo me try' in ques tion h ad to grasp was not
no one enter here who is not a geo meter . T o usc an other exa mp le: empi rically attestable co nfiguratio ns (wheth er b ifu rcating o r folded ) but
zo ne of expe rience co uld offer a ramification of th e conce pt of ex perience rather neu tra l multi ples , detached in their being from every spa tial or
as de nse as th e one pro vid ed by the co nce p t th at think s all th e kinds 01 tem poral con no tatio n _ nei ther closed nor open, but beyond figu re. freed
ca rdi nals: i.e . inaccessible, co m pact, ineffabl e, measura ble, en ormous. from any imme d iate opposition be tween th e q uan titative and the q ualita-
M ah lo card ina ls, Ram sey cardi nals, Row bon om cardinals, etc? So whCII rive. T hat is wh y these an ticipations co u ld on ly cons titu te th e body of
we hear someone speak in such an im po verish ed manner abo ut a tra jectory modern m athem atics as such once D cdekin d and Can tor had succ eeded in
of thought 'at infini te speed', we have to ask; what infinite are you refer- math ema tizi ng th e p urc m ult iple under th c aus p ices of th e not ion of 'se t' ,
ring to? W hat is thi s supposed uni ty o f th e infinite, now that we ha« th ereby wrenchi ng th e mult ip le free fro m every preliminary figu re of th e
learned not only that th ere exist an infin ity of differen t infinjtes , bu t m- One, SUbtra cting it from th ose resid ues of experience still provid ed by th e
ther e is an infini tely ramified and co mp lex hiera rch y of types o f jnfinjtY? PUtative 'ob ject s' of ma thematics (n um be rs and figu res). and ulti m ately
I recogn ize the fact th at D eleuze is in no way contem p tuous of ma th e" allowing it to become th e basis in terms of which one could define and
m aries , and tha t th e differen tial ca lcu lus and Riemannian spaces pro vided study th e most paradoxical mu lti-dimen sional con figu ra tions - inclu di ng
 Tbeo-erc at Wn tlflgs One. MultIple. MultlpllCrtJes 77

all th ose harboured un de r th e name of ' spaces' . By redu cing Riem . excess is u1lassignable. Inother wo rd s, no measure cou ld be prescribed
thiS . .
tho ugh t to the no tion of q ualitative multip liciti es and tu rn ing it into for this excess, since it is some th ing like an er ra nt excess o f th e sci W ith
em b lem for an anti-Ca rt esian parad igm , D clcu zc overloo ks the Ont o .....cr 10 itse lf. th at is to say, th er e is no n eed to look to the All, the
that underli es Rieman n 's inve ntion, an onto logy whi ch , in a stagg rcsps . . hi 1 '
great cosm ic anim al,. or to ch~os for I~ e principl e ~f th e pure mu tlP .e s
di spla y of incons istency , Deleuze undermines, subm itting it to the excCSS-o\'e r-its el f: th is ex c~s IS d ed ucibl e from an interna l ~on-cohes lo n
cid able, a lbeit normative, ahernarive be tween th e close d and the open. between th e two types of Im m anen ce. Furthermore, th ere IS no need to
Riemann in no way represen ts a passage from th e Multip le (as op look to th e virtual for th e p rinci p le of indete rminacy or und ecidability
to th e O ne) to m u ltip liciti es. Rather, he heralds th e passag e from that alTcctS every act uali sati on . Every multiple is indeed acwally hau nted
su bsists of th e em pirical power o f th e O ne (in the mod ali ty of an ex by an excess of powe r that nothi ng can give shape to, except for an always
cnce of mathem atical 'o bjects' ) to th e m ult ip le-with out-o n e, whi ch aleato ry decision wh ich is on ly giv en through its effects.
effec t can ind ifferently welcome num bers, points, fun ction s, figures, It is ce rt ain ly th e case th ai experience must , eac h and every time, re-
p laces , since it does not p rescribe tha t of wh ich it is co mposed. determine th is immanen t excess. For example , deciding what to do about
power of R iem ann' s th ought res id es entirely in its " tUlra !izatiorl of diffi th e excess of the power of th e State (in its po litica l sense) over sim p le
t rice. Deleuze's interpretati on, whi ch sees in it a mobile co m p lexifica . presentation (peo ple's th ought) is an essentia l componen t of every
of the idea of plan e, is not incorrec t, bu t it fails to gra sp the tru e m singular po litics: if you decide th at the excess is very weak , you p repare
phy sical d etermination s proper to the Riemann ian parad igm . an insurr ection; if you th ink th at it is very large, you sett le on th e idea of
B. D eleu ze ro u tinely argues th at multiplicities, un like sets, have 'no a 'long ma rch ", etc. But th ese singu lar de terminat ion s arc by no means
This is indeed what, in m y view, explains the fact that th e oppos i . with in the reach of ph ilosophical description, since th ey are inte rn al to
between se ts and multipl icities takes place under the aeg is of th e O ne. th e effectu ations of truths (po litical, anisti c, etc.). What is philosophical
course, I can see that it is a question of savi ng qualitative singulari ty is rather setting aside every kind of specu lative empiricism , and assignin g
the viral power that accompanies it, bUI I do no t bel ieve Deleuze's m th e form o f these determ inations to their gener ic foundation : the theory
arc adequate for such an aim . A s a matt er of fact, th e opposite is th e of th e pu re multiple. F rom th is stand po int, the 'c oncre te ' operators of th e
the immanent excess thai 'a nimates' a set, arid which makes it meh that vitalist type, wh ich finall y refer th e po sitivity o f the Open to an immanent
multiple is imemally ma rked by the undecidable, results di rectly f rom creation ism whose foun da tion is to be found in th e chaotic p rodigali ty of
f act that il possesses rlOI Drily tlemem sJ bUI also pa rts. th e One, are obstacles, not sup po rt s. The co ncrete is mo re abst ract than
The failure to d istingu ish bet ween elem ents (what the mu lti the abst ract.
presents, o r com poses) and parts (that wh ich is, for th e multiple, repre- C. The wea lth of th e em p irical is co rr ect ly tr eated by D clcuze as a wealth ill
sentcd by a sub-m u ltip le) consti tutes a great weakness in any theo ry cl problems . T hat th e relation o f the virtual to the actual ha s as its paradigm
m ulti p licities. T h e stateme n t according to which mu ltip licities hav e DO the relation be twee n the problem and its so lution (rather than between
parts alrea dy indiffer cn tiares the two types of imman en ce, th e 1w0 fun da- the possible and its real izati on) in my view represen ts one of th e stren gths
mental form s of being -in wh ich set- theory separates when it di slinguisheS of the D elcuzean meth od . But what shou ld fo llow fro m thi s is th e falsity
between (elemen tary) belong ing an d partitive (incl usion). Now, the of a maxi m th at D eleuze ne vertheles s practises and teaches: th at we can
relation between th ese two forms is the key 10 every th ink ing of the b.:gin from any conc rete case what soever, rather th an fro m th e 'im port an t'
multiple, and to ignore it is in evitably to withdraw phi losophy fro m one cases, or from the history of th e problem . If we consider the not ion of
of its most exacting co nte m po ra ry co nditions. Problem in its o riginal cont ext, mat h ematics, it beco me s immed iately
At th e en d of th e ni neteenth century, Cantor effectively demo ns tra ted apparent that th e cons idera tion of a case taken at random p recludes an y
that th e power of th e SC I co m p rising the pa rts of a given se t (i.e. tha i access to th os e p roblems that have power , that is to say , to th ose
wh ich sustains th e inclusive type of imm anc nce) was neces sarily superior problems wh ose so lu tion m atters to th e du al beco m ing o f thought and
to th e power of th e set itself (t. e. th aI wh ich susta ins the elem en tary type what it th ink s. G alois once said that the problem was co nstitute d b y
o f immanence). This mean s lh at the re is an ontological excess of rcpre- reading 'the un known ' into th e texts of one's p redecessors: it is ther e th at
scn mtion ove r presentat ion . Thiery years ago, Co hen d emon strated th at the deposit s of p roblem s were to be found .
 78 Theorerc al WritIn gs One . Multiple. t-lulnphcrnes 79

By n OI follow ing this logic o f the un kno wn, which fun cti ons like: a s ..uh Dcleuze th e convictio n (which I think is po litica l) that every
I shar e h " ." . .
selec tion principle for p roducti ve forms of thought , em pi rical predi . thi nking is a th inki ng of sin gula rities. But SID~ for Ddeuze act ual
-nUln e . . 4 and since
• nI lh V " l
beco mes something like an arbitrary and sterile burden . The: pro e-" " li tries are always pu re ly formal modalities, 0 y e rrru a
ulUP 10
ends up being replaced by verific atio" p ure: and simp le. Ph ilosophi m. nv d ispe nses sense, I ha ve argued that Delcuze ha s no way of
speak ing, ve rification is always possib le. In m y youth, I too beJong~ un"I\~ ~ingularity oth er than by classifying the dlfferem ways in wh ich
this school: afte r San re, and follow ing the example of me cafe waiter ~~~
. la "ty is no t on tologicaJly singular; in other word s. by ctess 'f" t ylDg lh e
skier, the lesb ian , and th e black man, I co uld irrefutabl y transform ' smg u nt mod(.'S of actualization.
.. After all, this was alread y t e cross bo me b y
. h
differen .
' concrete' datum wh at soev er into a philosopheme. M u ltip lici ' " tsm , whose th cory of 's ingu lar th ings' osc illa tes between a schematisrn
Splnoz l~
sus pended between the open and the closed , or between the virtual . "Iily (a thi ng is a set of modes producin g a single effec t) and a schema-
~ ~- . " "
the ac tua l, can serve th is end , JUSt as I was in the habit of using th e in
usm 0 f " . pression (a th ing bea rs witn ess to the in finite powe r of substance).
"
nalized face- to-face of th e in-itself and the for-i tself for me same pu Similarly, for Odeuze, sin gularity oscillates betwee n a classificatory phenom-
By way of co n trast, set- theore tica l multip les can neve r be subordi na ted enology of mod es of actualization (and virrualization), on th e one hand, and
th is end , since th eir being bound to a deli ca te axiomatic entails that ontology of th e virtual, on the other.
ru le can never be: d escriptive. In th is regard, we cou ld say that the anI mainta in th at th e 'link' between these IWO approaches is not compatible
of the m ultip le ~es all the richer in p roblems to the exten t with either univcciry or immanence. It is thi s in compatibility that furnish es
in capable of validating any description. it can onl y se rve as a re the clue as to why D ejeuze's tex ts swarm with analogies , which are required
id eal for p rescrip tions. in order to determine the descriptive Ideas for which singu larities provide
the cases.
4. W hat difference is th ere exactl y be tween saying th at a pack of wolves That these Id eas (F o ld , Rh izome. Dice-thro w, etc.) aim at configuration s
th e sub terranean net work of a tube r pla nt are cases of rh izom e, and SIi in becoming, at d iffer en tiat ions, co unter- movements, inter facings, erc.,
th at the y both partake in th e Idea of th e rh izom e? In what sense are we changes nothing. I have always maint ained ma t Dcl eu zian sing u larities
tak e the fact that bo th Spinoza an d Bartleby the scrivener can be co m belong to a regim e of actua lization or vir tualization, and not to one of ideal
to Ch rist ? If Fou cault 's work te stifies to th e Fold betwee n th e visible and idem iry. But the fact that on ly co nc re te beco m ing s provid e the descriptive
sayable, is th is in th e same way as the films of Straub or M ar guer ite D models for a schem a in no way preclud es the latt er fr om being an Idea 10
who se singularity is defin ed in sim ilar terms? D oes the term ' layered ' which th e models are isomo rp hic. Plato' s m yth ical Parmeni des already
nat e the same property in Riem ann spaces (wh ich belong to a scien tific p 'objected' to Socrates that there m ust indeed be an idea of hair , or of mud . It
of refere nce ) and in a philosophical plane of imm anence? If in my boot remains th e case th at in order 10 argue that the th inking of singularity
spo ke of a ce rta in m onot on y in D d euze's work (wh ich , in my mi nd. wa requires th e intui tio n of the virtua l - whic h. I am co nv inced, plays me role
kind of Bergsonian tri bute: the re is, all th ing s co ns idered, a single motive . of tra nscendence (o r takes th e place o f descriptive Id eas) - one is obliged to
int uition), it was also in order to avoid d irectly asking such blunt questi dep loy, with ever- re newed virt uosi ty, an analogical and classificatory vis ion
This is beca use our int erpreti ve field for th e innumerable analogies of th is singularity. This is why it is so important to hold stead fas tly to th e
populate Del cuze's case studies allow s us to relate th em back to un ivocity • rnuhiple as such - th e incon sistent co m pos ition of m ulriples-without-oneness
a donation of sense that is un iformly deployed on th e surface of ac tualizatiOOl - which ident ifies th e sin gu lari ty fro m withi". in its strict ac tuality, stre tc hi ng
- and driven, in a manner identical to the po wer of Spinczist su bstance, b1 thought towards th e point at wh ich th ere is no difference bet wee n difference
the ont ological determinat ion of th e O ne -Life . Wh en cha lleng ed by thost and identity . A poi nt where there is singu larity because both di fference and
who, on th e Contra ry, do not wish for an ontologica l postu latio n of thi s tYpe identity arc indi ffere nt to it.
and who regard as ironic the q uestion 'Could D cleu ze's aim have bee n that Let me sum up : th e at tempt to subvert th e ' vertical' tr an scendence of th e
o f intui ting th e One?' (but what else exactly co uld a self-p roc lai med disci ple: ?nc through th e pla y of th e d osed an d th e open, whic h d epl oys mu ltiplicity
of Spinoza be: conce rned with?), m y response is to ask th em what status thef In the mob ile in terval betw een a set (inertia) an d an effec tive multiplicit y
would give to th ese analogies , especially in light of the fact th at the M astel' ~Iine of flight). p roduces a 'horizo ntal' or virt ual transcendence whi ch ,
expres sly dec lared th at ana logy ough t to be p rohibited. InStead of grasp ing singu lari ty, ignores the intrinsic resource of th e multiple,
80 Theor et ical W ri tings

pr esupposes th e chaotic power of the O ne, and ana logizes the mod
actualization. Wh en all is said and done, we are left with what oou:
~cfined as a natural myst icism . In order to ha ve don e with tran scend~ CHAPTER 7
IS necessary to follow th e thread of th e multiple-without-oneness - .
vio us to an y pla y of the closed and me open, cancelling any abyss be:
the finit e and the infin ite, purely actua l, hau nted by th e int ernal excess of ' Spinoza's Closed Ontology
parts - who se univocal singularity is ooto logica lly nameab le only by a f
o f wri ting su btracted fro m the poetics of na tural langu age. The on ly
that can be attuned 10 th e power of be ing is the power of th e letter.
th us can we hope to resolve th e pr oblem tha t defines contemporary tho
what exac tly is a universa l singu larity? wnco a propo sition in thou gh t p resen ts itself, o utside ma themat ics. as
originally philosophical, it bears on the generality of the ' there is' . II th en
necessarily inve kes three p rimo rdia l o perations.
First, it is necessary ro cons truc t and legiti mate th e name or names for the
'there is' , which 1 do with the term ' pu re multip le' and Deleuze does with
the term 'life', Su ch names are alwa ys grasped acco rding ro a more or less
explicit choice beari ng on the kind of hinge, or disconnection, tha t obtains
between th e one and th e multiple.
Second , it is necessary to deploy the relation or relation s on the basis of
which one pr oposes to evaluate the consistency of th e ' there is',
Lastly _ and thi s makes u p the complex body of every phi losoph y of be ing
to the extern that it may be conside red as an implicit math em atics - it is
necessary to guarantee th at the formally int elli gible relation s 'grasp' or seize
whatever is p resupposed , o r founde d , in th e names for th e 'there is' .
Lei me offer two rypical yet contrasti ng examples: the first is
poettco-philcscphicat, the second pu rely mathem atical.

_ In Lu creti us' en terp rise , the ' th ere is' is presup ~ under tWO n ames :
'void' and 'atoms'. T he on ly relations arc those of collision and con nec-
tion . What guarantees th at the relations grasp the nominal consti tuen ts
of the 'there is' is an una ssign able eve nt: the dinamen, or swerv e, th rough
which the indifferent tra jectories of th e ato ms en ter imc relation s
against the backdrop of th e void, in such a way as to compose a worl d .
In the ma th ematical th eory of sets, whic h we have already said mark s
the fulfilme nt of mathematics as th e thinking of multiple-being, th e
"there is' is pr esupposed und er th e nam e of the void alone , in the
empty set. T h e on ly relat ion is tha t of be longi ng. Relation 's grasp o f
(he ' there is' is guara n teed by its forms o f efficacy, wh ich arc encod ed
in axioms, spe<::ifically in the ope ration al axioms of the th eory. T h is
grasp eng ende rs a un iverse, the cumu lati ve, tra nsfini te hierarch y of
Sets, on the basis of the void alone ,
82 Th eoretical Wnllngs Scoceas Closed Ontology 83

It may well be that there ar c only two mod els of such a grasp , and hence teet necessit ates p roposition s abo ut being that are in fact heterogeneous
the o pera tion of thought thro ugh wh ich the na mes of be ing ar e oo-o rdi (d /lIe explicit pro positiO/IS .
by the relation th ai makes th em consist : th e cven tal mod el , whic h is th-.:
Lu cret ius. and th e axio matic m od el. In the Ethics, as we po inted OUI above•. th e ' th ere .is' is na~ed ' ~" BUI
Spi noza, wh o excl ud es eve ry event by p rec lud ing exces s, chance and -,ruction of th is nam e - wha t Spi noza ca lls ItS defini t ion - IS ex tre-
tht CO n ~ '
su bjec t, op ts un eq uivocally for the axiomatic model. Fro m this po int of Illd)' comp lex.
th e more geometrico is crucial. It is not just a form of th ought; it is th e God is ','lIS absoluu i,ifj"ite' , a "being absolutely infinite' :' Le t us, at the
tra ce of an original decision of thi nking. note th e req u ireme nt of th e indetermi nate te rm ens, 'being', as th e
eutse ,
A pu rely technical exam ination o f the Et hics ca n serve 10 h ighli gh t e' for a clrrua l 'there is' whose p re-comp rehension rela tes b ack to an
powerful simplicity. T he 'the re is' is indexed to a single name: abso -
OIltological . than ili e
layer th at is. if not deeper. then at least more extensive
infinite Substan ce, or God. The on ly relation admiued is that of QI terl11 'GOO'. "l nfinite' is obviously the crucial term here , because it fu nctions
Relation's grasp of the name is of the orde r of an immanent efT~ tiaa. to determ ine the in de terminate; it practi cally functions as the ' there is' for
th e ' the re is' as such , since, as we kn ow from Book I, Pro pos ition 34: ' the 'there is' . ' Infinite ' is d efined as follow s (Book I, D efini tion 6): ' a
power is h is essence itself: l W hich m ean s no t on ly that, in th e wonk substance consistin g of an infinity of attrib utes , of whic h each one exp resses
Book I, Proposition 18, ' God is the immanent, not th e transitive. cause: of an eternal and in finite essence',' The importan t thing h ere is that th e abso-
things'.2 but also th at thi s co ns titutes h is iden tity, as co nceived through luteness of divine infini ty is not q ualitat ive, or it self indete rminate. It refers
ca usal relation 's grasp of substance. back to an effectively p lu ra l, and hence quantita tive. infinity. The index of
Thus it woul d see m th at we are confro n ted here with a who lly affi quanti ty, or of th e fact tha t th e ad jective infinitum p resupposes a denumer-
immanent and in tri nsic propos ition about be ing . Moreover, it would able infillitos . is that thi s j,ifj",'ros lets itse lf be thought acco rd ing to th e
that d ifference in particu lar. whi ch is cons titu tive o f th e on to logy of 'eechness' , the unrmu[lwdque. of its att ribu tes . II is thus ind ubita b ly
tiu s (there is th e void and ato ms ), is her e absolutely subord inated. that composed of non-decomposable un ities , i.e. the att ribu tes. But then of co urse
nom inal. In other words, it is a matter of ex p ression , and in no way the concept of the in finite is covered by th e law o f d ifference . Becau se: it is
rnises the de termination of th e 'there is' un d er th e aegis o f th e one . AI composed o f 'ea chnesses", the infinity of attrib utes can be app re hen d ed onl y
we co uld cite co un tless oth er passages, let us, by way of evidence, quote through a primo rdi al d ifference. This ent ai ls that every att ribu te must . in a
Sc ho lium to Book II . Propos ition 7: 'a mode of ext ension and th e idea of certain sense, di ffer absolu tely fro m every othe r. In other word s: th e infin ity
mod e arc one and the same th ing, bu t exp ressed in two ways [duOOw of God, which is what singu larizes h im as su bs tance and entails that he is th e
espresso I'.) name for the ' th ere is' , is on ly th ink able un der th e aegis of the multiple, It is
But obv ious ly th is sim plicity is mer ely appar en t. In fact , I will sho w: the expressive difference of the att ribu tes th at ren der s th is notion of the
lTlultiple intelligible.
F irst , that th e operat ion s that allow for th e naming o f th e ' the re is' But what is an nn ributc? H ere is D efin it ion 4, Book I : ' By attrib ute, I
inte rco nnec ted in a multiple, complex fash ion, and th at in th is in understand what th e intellect pe rce ives of a subs tance, as co nsti tu ting its
connec tion th e proof of d ifference is co nst antly requi red . ~nce.''' T he an rib ure is th e esse n tial id en tification of a su bstance by the
Se cond , th at causa lity is no t the un iqu e foundation al relation; th ere intclk"Ct, intetleaus. T his im plies tha t the existe ntial singulari z:u ion of God
at least three, th e other rwo being wha t 1 shall call 'coup ling' an' ultimately depen ds u pon the elu cidation o f (o r th e basic evidence for) what is
'inclusion' , lTleant by iutel lecua.
Third , that ben ea th the unit y of the ' th ere is' , Spi noza delineates tbI In th e letter of M arch 1663 to Si mo n de Vries, Spin oza takes pa ins to
nega tive o utline of a typ e of singularity wh ich is in every way exceP" ~cclare that the word ' uuribu tc' d ocs not by itself cons titute a naming of the
tional , whose forma l charac teristics arc th ose of a su bject, and wholll there i~' in any way essen tially d istinct fro m the nami ng of th e latt er by
Sp inoeisr name is intellcctus. Followin g Bernard Paut rer's persuasi'ft SUbStance, H avin g rei te rate d th e definition o f su bstance he ad ds: ' I under -
arg ume nts, 1 sha ll trans late im ettecna as ' in tellec t' . One has gras Stand the same by attrjbu te, excep t that it is called attrib ute in relation to
the co re of Spi noxist on to logy when one has unders tood how th is Int (reSPf'Cl ll) the in te llect, wh ich anrf b ures such and such a deflnire natu re to
84 Theoretical WrItings Splnozas Closed Ontology 85

subs tance.'? Thus th e attri bu te, as wel l as th e mu lti plicity of attri [tributes of subs tan ce. It is the exe mp lary instance - and even the on ly
through whic h d ivin e infinity is identified, is a function of th e intcllttt., the a f an immed iately infin ite mod e of the attribute thou gh t, The
the general arrange me nt of th e ' the re is', there exists - un der th e name ' ~c ~i:te infin ite mod es are described, without an y examp le of their cxis-
- a singular loca lizati on, th at of th e intellect , upo n whose po int of vit1lr 1J1lJ1l being given, in Book I, Propos ition 2 1: ' All th ings wh ich follow from
renee . .
operations depend s th o ugh t's ca paci ty for rat ional access to d ivine i absolute nat ure of an y of God 's att ributes have always had to exist an d be
and hence to the ' there is' as such. ~~nitc.'<l In J uly 1675, a certain ~chuller ~sks Spi~oza o~ behalf of T schirn-
It is th us necessar y 10 recognize that th e intellect occupies the positioo :I US to provide examp les of ' th in gs which arc Immed iately p roduced by
fold - to take up the central con cept in Dclcuze's philosophy. O r, usina ~" Spinoza respo nds by saying th at 'i n thought' , th e example is 'abso-
own term inology, that th e inte llect is an ope ra tor of torsion. It is I lutdy infimte - -mte 11e . 10
as an immanent production of God, but is also required to upho ld The very concep t of infinite mod e occ u pies a paradoxical pos ition in the
naming of th e 'there is' as God. For only the singular operations of the i cconom}' of Spmoza's onto logy. It is in fact imposs ible to decide as to the
lea give meaning to God's existen tial slngularizatio n as infinite substance. a istence of any of th ese mod es, since th ey are neith er ded ucible a pri ori . no r
I beli eve th is concep t of torsion is at once th e enigma and the key to gi,'en in finite exper ience. We could say that the concept o f an infin ite mod e
Spino ztst app roac h to being , just as the dinamen is th e enigma of L u is coherent but existen tially un decidable. Bu t th e existence of an un decidabl e
or th e contin uum hypothesis the eni gma of set- th eory. can only ever be decided th rou gh an act o f axiomat ic positing . This is d ead}'
T o th ink th is torsion mean s asking the following question: how does what one sees in the case of the infinit e inte llect when, in the let ter 10 Olden -
Spinozist d eterm in ation of the 'th ere is' po in t back to its in terna l fold, burg from November 1665, for example, Spinoza writes: ' I maintain (statuo)
inte llect? Or, more simp ly: how is it possible to think th e being of int thai there is also in Nat ure an infin ite pow er of thinking.'l l Thus the in finite
the ' there is intellect'. if rational access to th e th ought of being or the intellect has, if not a verifiable o r provabl e existence. at least a status, th e
is' itsel f de pends upon th e ope ratio ns of the in tellect? O r again: th e in status conferred upon it by a 'sta LUo' .
is operative. bu t what is the onto logical status of its operatio n? As statutorily posi ted, th e infin ite intellect provid es th e basis for a series of
We will refe r to eve ryth ing req uired in orde r to th ink th e being of in intimately interco nnec ted operations.
- the collect ion of ope rations respon sible for th e closure of Sp' First of all, it is what p rovides a measu re for th e powe r o f God , Fo r wha t
thi nki ng of bei ng - as Sp moza' s implicit on tology . T his ontology is God can (and therefore must) p rod uce as imm an ent power is precisely every -
which the th inking of a being of though t presu ppo ses as he terogeneous to thing tha t the infinit e int ellect can conceive, Hen ce P roposition 16 in Book I:
th inking of being. 'From the necessity of the d ivine natu re there mu st follow infini tely man y
T he guiding thread for the in vestigation of th is imp licit onto logy is S things in infin itely many modes, (i.e., eve ryth ing which can fall under an
za's ccns rrucncn an d variat ion of the intern al fold , and hence of th e infinite inte llect), , 12 T hc in fin ite intellect pr ovides th e mod al norm for th e
of inrelleaus . extent of modal po ssibility . AU the thi ngs th at it can intellect - 'omnia quae
The in itial starti ng po int is though t (cogilalio) as an attribute of God, sl4b intelleelll", i"ji"illlm cadere POSSUIfl'- are held to exist.
is what Spinoza calls 'absolute though t' . and which he d istingu ishes Clearly. no other infinite mode imaginable by us possesses such a capacity
in tel lect. T hus. in the Demon st ration for Book I, Propo sition 31 he wri fer measuring God's powe r. T his holds in particular for the other exa mp le of
' By inte llect (as is known th rou gh itself) we understa nd not ab solut e thou an immed iate infini te mod e given by Spinoza, movem ent and rest, whic h is
~uPPOscd to be the co rrela te of in fin ite int ellect on thc sid e of extension. For
b ut on ly a certa in mode o f th in king . which mod e d iffers from the oth
suc h as desi re, love, and the like.' " Although it is that on the basis of w
,, -
IS obvious tha t no general p resc rip tion about God's pow er follows from the
the attributive identi fication s of subs rance exist. the in tellect itself is clearlY Pure Concept of movemen t and rest.
mod e of th e attrib u te ' tho ugh t'. We will say tha t as attri bu te, thought is ~.' he reason for th is dissymmetry is dear, It de rives fro m the fact that .
absol ute exposition o f bei ng . and that the intellect is th e interna l fold of tho ldes LIS intrin sic de termination as infinitc mod e of th e attribute o f
exposition. the fold from whence exposition in general o riginates. ughr, infinite intellect presu pposes an entirely differen t determlnatlo n,
In its initia l figu re. the in tellect is obviously infini te. It is nccessa OTIc whic h is extrins ic. For the intellect. whose components are idea s, is
infini te beca use it provides the basi s for th e identification o f the infinitY equally wcu determined by u'ha l it intellects. o r by what th e idea is an idea
86 Theor et ical Wn tmgs Spmccas Closed O nto logy B7

of. I t is thus that thc att rib ute s of God, as well as th e affect ion s of thos e a . the body. ,l ~ T h is shows that, gene rally speaking, th ere is a uni on
bores, co mpose (without any restriction whatsoeve r) what th e infin ite in ",l~'cen the idea and its object, incl ud ing instances of un ion tha t straddle th e
Icc! gra sps, und er stan ds o r co m pre hends (comprehenditi , Ce rtainly, God ~1. non between attrib utes. It is th is un ion , the rad ical singu lar ity p roper
dls/une . . .
that in which th e intellect, as infini te mode, is situated. T hat follows f enn ions of th e intellect , wh ich 1 call cou pling.
to t he op . ,
th c on tologica l relat ion of cau sality. The intellect is an immanent effttt . ob\'iousl" necessary to add the p ro VISO that co up ling has a norm . An

i_
It IS
God . But th e intellect is also such that it comprehends God and his 'dell can be mo re or less 'well coupled ' to its object . A comple te co up ling is
butes; th ey are the co rrelates of th e ideas tha t co nstit ute it . For every 1 lied tr ut h . This is Stated as ea rly as Book I, Axiom 6: ' A true idea must
an ' id ea o f" , it is co rrelated with an idea tum; in other words, the id ea n. cs fCC' with irs ob ject (ideatllm) .'16 Agreemen t is th e no rm for coupling and
object. And in th is sen se the attrib utes o f God and the modes of th ese :~hal makes of it a tru th . J ust like the relation of co up ling, this norm of
butcs arc ob jects of th e infinite intellect . agrttmcrlt is extr insic an d not, like causa lity. strictly immanen t to at tributive
The noti on of there be ing an object for an idea is all the stronger in dttcrmination . In th e Exp lanation of Book II , D efin ition 4, Spinoza carefull y
Sp inoza explicitl y stares ilia ! th e object partly singularizes or identifies distinguishes agreement as in trinsic nono of truth, wh ich ultima tely refers
idea , pa rti cu larly with rega rd [0 what be ca lls its ' rea lity'. Thus in back to causality , from 'what is extrinsic, namely, th e agreement between th e
Sch olium to Book II , P ro position 13 he writes: 'W t: cannot den y th at ' idea and its object (idearum l' .17 In the lan er instan ce, agreement refers back
di tfe r among themsel ves, as th e objects themselv es do, and that one is to coupling, rather than to ca usality . What 's more, it is clear tha t, apart from
excellent than th e other, and contain s more reality, jus t as th e obiect of the infinite mode of intellect, in no oth er instance bes ides the id ea is it neces-
one is mort: excellent than th e object o f the oth er and con tains sary for th e terms composing an infinite mode to support a re lation of
rea lity.' ll coupling. It is ce rtainl y no t necessary for th e other infinite modes. wha teve r
C learly, thi s presupposes a second [undamental relation bes ides cau salily; they may be, to com p ly with th e norm of co up ling . ag reement, whose res ult
relation that on ly has m eaning for the in tellec t and which abso lutely s' is truth.
larizes it. For we know that for 5p inoza , who never resorts to empiri . Like th e relation of ca usa lity, the rela tion of co upling imp lies the exi ste nce
the relation betwee n th e idea and its ideatum, or the idea and the objea of an infinite regress. Thus e\'ery mode has a cause, which itself has a cause ,
th e idea , is en tirely d istinct from th e rela tio n of ca usal action. T his is im and so on. Similarly, every idea cou p led to its object m us t be th e object o f an
in Book ttl , Propo sition 2: 'The body cannot d etermine the mind idea th at is co up led to it. This is the famous th eme of th e idea of the id ea,
thinking, and th e mind can not determine the body to motion , to rest, or which in the Seholium 10 Book II , Proposition 2 1 is examined in te rms of
anythi ng else (if there is an ything e1se).'H No ca usa l relation between the mind as idea of th e body and the id ea of th e mind as id ea of th e id ea.
idea and its object is conceivable beca use the relation of causality is Th e text sub tly weaves togeth er on tolo gical iden tity and th e relation of
applicable fro m with in an attributive identificatio n, whereas - an d here COupling : ' (T jhe m ind and the body are one and the same individ ual. whi ch
the en tire: problem - th e objec t of an idea of th e intellec t may perfectly is COnceived now unde r th e attrib ute of tho ught , now under th e att ribu te of
be a mode of an an ributc other than though t. extension . 50 the idea of th e mi nd and th e mind itself are onc an d th e same
A part icu lar kind of relation is requir ed to strad d le the di sjun ction be n" thing, which is co nceived un de r one and th e same attribute, namely, th ou ght.
att ribu tes in th is way, one whi ch cannot be cau sality . 1 will call th is rela . ' " For the idea of the m ind , th at is, the idea of th e idea, is nothi ng but th e
coupling , An idea of th e in tellect is always coupled to an object, whic h m form or the idea in so far as thi s is con side re d as a mode of th inking without
that a mod e of though t is always coupled to anoth er mode, wh ich ma y bel relation to the object.' lll T he 'one and th e sam e thi n g' seems to oblit era te
either to extens ion, 10 thou ght , or to a d ifferent attribu te entirely . evcry differen ce underlyi ng the relation of co up ling . Ne vert heless, that is not
T he po wer of this relat ion is attested to b y th e fact that Spinoza does bow thi ngs stand . For all that identifies th e individual is the co up le, as
hesit at e to refer to it as a ' union ' . Th us, in th e D em onstration fo r Book II , grasped by the in te llect. As a resu lt , in so far as the id ea of the body is
Proposit ion 2 1, he wri tes: ' We have sho wn tha t th e m ind is un ited to COUPled to th e body by strad dlin g the att ributive di s junction , it rem ains
body from the fact that th e body is th e ob ject o f th e mi nd (sec P I2 and 13); ~ccc ssar il y di stinct from th e idea of tha t idea, wh ich is coupled to th e latt er
and so by th e same reason ing th e id ea of m ind m ust be united with its 0 Il'l a manner im manent to th e at rribu rc of thoug ht. In other wo rd s, an effect
objec t, that is, with the mind itself, in th e same way as th e m ind is unit of identi ty always und erlies every relation . It is th e same individ ual that is
88 Theo-encal Wr it ings Splnozas Closed Ontology 89

alterna te ly intctlcc ted as body and as mind, and th en it is th e same min d . either a proof o r an elucida tion for the co nce pt in qu esti on: 'the
offCfl OS • . . ,2 1 .
is intellecred twice . BUI th is identity-effect is only int elligi ble accord ing " , 'od is a part of th e infinite Intellect of God . In ac tu al fact, thi s
,
hu J1l:l 11 . , . . '
th e ca tegories of the intellec t, and th ese ar c precisel y th e ones that a n gi . h '0 unment ioncd re13110n of incl usion h as to do With what, 111 m y
hll cr · .. ..
in co up ling. . ton cons titu tes the greatest Im ped ime nt for Spinozist ontology: th e
OPIOIO ,
U lt ima tely, th e ac tive structu re of infin ite intellect is rad ically singu lar in lalian betwee n the infin ite and th e finite .
way that p ro ves to be exo rb itant relative [0 th e ge neral p rinci ples of Ont o rc That we rea lly arc deali ng with an instance of inclusion , with a conceptio n
gical naming. .tn Ie.,,
ems · of sets , is confirmed by th e converse th esis: JUSt as the finite inte llect
. pori of the in fin ite in te llect, sim ilarly, th e infinite inte llect is th e ga th -
II de pends upon the un decidability associated wi th th e infinite rnodc:l. ,"
cring toge th er, the co llectio n, of finite intellects. Thus, in th e Schol ium to
II measures the total powe r of God. Book V, Propos ition 40 Spinoza writes: '[O jur mind , in so far as it un der-
I t imposes anothe r relation beside causality : stands, is an eternal mode of thinking, wh ich is d etermined by anothe r
mines th e do ma ins o f identity. eternal mode of th in k.ing, and thi s aga in by another, and so on, to infirriry; SO
m
At each of its poi nts or ideas. not on ly does th e infini te in tellect wt togeth er , they all constitute God's eternal an d infinite in te llect. : As the
ruare an infini te recurrence in acco rdance wi th ca usal ity, but infinite su m of an infini te cha in of finite modes, th e infinite intellect can be
second one. in accordance with coupling. designated as the limiI point of th e finitudes it tot alizes. Conversely, the finit e
intellect co nstitutes a poi n t of composition fo r its infinite su m. In th is
As a matter of fact, infinite intellect by itse lf constitutes an exception 10 instance , causa lity is merel y an appa ren t order since it is inca pable of leading
famous Proposition 7 of Book I J: 'The order an d co nnection of id eas is us out of th e finite . For, as is established by Book I, Pro position 28, a finite
same as th e order and connection of thing s.' 11I For it is im possible mode onl y ever has ano ther fini te mode as its ca use . Genuine relati on is
co nceive of (or for the intellect to re p resent) a stru ct u re isomorph ic with inclusive,
of the intellect itself in any att ri bute o ther th an thought. Conseq uen tly, Elsewhere, Spinoza has no qu alms when it comes to seve rely criticizing th e
attri bu te of th ough t is not isomorphic with any of the other att ri butes , undisciplined usc o f the pan/wh ole relation . Bu t when it comes to th e intel-
even in terms of th e relation of causality alone. lect, and in order to justi fy th e u SC: of the sam e word to designate bo th
Turning no w to th e human o r finit e intellect , th ings become even human opera tions an d the opera tion s of th e internal fold of the attribute of
complica ted . thought, he is left with no other option . O nly in clus ion can pro vid e a globa l
T he m ajor d ifficulty is th e follow ing : is it poss ible to conceive of th e finiW: accoun t for th e beillg of th e finite intellect .
in tellect as a mod ifica tion or affectio n of th e infinite intellect? This is me If we now try to un cover what th e operatiolls of thi s intellect co ns ist in , we
concept ion of the fin ite intellect ap parently im p lied by th e relati on of ca~ immediately re-encounrer th e relat ion of co u pling. T he essentia l motif
ulity as a cons titut ive relation for th e imm anent det ermination of th e ' there COnsists in identifying th e human m ind th ro ug h its cou p ling with the body.
is' . Unfor tunately, that cannot be correct. For Book I, Proposit ion 22 estab- One th ereb y avo ids d irectly in voking th e th ird relation, the relat ion of in clu-
lishes th at , 'W hatever follows from some att rib ute of God in so far as it is sion, by remaining at the loca l level , as il were. T he hum an m in d is an idea,
modified by a modifica tion which, th rough th e sam e att rib ute, exists necesS'· hence a finite co mpone nt of that whose higher mod alit y is the infinite int el-
rily and is infini te, must also exist nece ssaril y and be in fini te.,20 T o put it lect. It is the idea of th e body .
concisely, eve ry thing that follows fro m an immedi at e in fini te mode such II The great advant age of th is pu rely local rrcatrncn r is tha t it accounts for
th e infin ite int ellect is in turn infinite. H en ce the finite intellect cannot be an cverythi ng tha t rem ains obs cure in fin ite thought. We sho uld recall th at there
effect of the infini te inte llect. Wh y then do th ey have the same nam e? exists a norm for the relat ion of co upling : ag ree men t. \'(fe should also note
In orde r to reso lve this p ro blem, Spinoza p ropose s - no t without sorne thai if the idea docs not agr ee with th e object with which it is co up led, it is
hesitati on - a third fund amental relation, follow ing those of causality and obscu re, or untrue . Everything obscu re in th ough t will be ge ne ra ted and
coupl ing , whic h we will ca ll ' inclus ion'. G ran ted , the finite in te llect is not lIP tl'leasur ed in terms of the norm of agreerner u. T h e key 10 this lies in Book II ,
effect of infinite intellect; neve rtheless, says Spi noza , it is a P Url o f it. This is ProP<>sition 24: 'T he human m in d doc s nOI involve adequate kn owledge of
whm th e Corollary to Book II , P roposition I I ma in tains, albei t Wilhoul the parts com pos in g th e human body.'" The same thin g is pu t even more
90 Tbeo-euc al WntJngs SPJnozaS Closed Ontology 91

bluntly in the Demonstration for Proposition 19 of the same Book: • ·deas, o r even to every thing tha t is in $0 far as it is, is tru e; an d th at
to aII I
human mind docs not know the human body.•2~ or .d.::aS that follow from true id eas are also tru e.
Note th e complexity of this ap proach : c n tologically the mind is an idea, the ! her wor ds: there is no true knowledge of th at sing ular body of wh ich
In m ~ . . .
idea of the body. But this docs not mean that it knows its ob ject. For ind is the idea . But the fini te intellect necessarily has a true Idea of
~rml . .
rclarion of co upling bet ween the ide a and its o bject ad m its of d egrees; it " common 10 all bodies, and co nseq uen tly of wha t IS not singular, as
what I
be more or less subject to the norm of agreement. All the more so if it is as it is able to co uple with it.
com p lex idea , related to th e body's m ultiple co mposition. ~oe have true ideas because th e finite in tellect possesses ideas that arc
U ltimately, it is by appealing to the thi rd relation , th e relation of incl ed to non~si ngu la r objects, in othe r words, to common objects.
cou p l
th at th e onto logy of th e finite intellect is able to accoun t for all me th Ultimatel y, veri dical reaso n is woven out of common notions.
broached in Book V: since we are a part of the infinite intellec t, we ex We are fami liar with Spinoza's in cessant polem ics agains t un iversa ls and
ence ourselves as eternal. Moreover, it is by appealing to the second rell homon yms dc\·oi d of being . Ther e is a sense in which h is doc trin e on ly ad mi ts
of co u pling th at the m oor)' of the o peration s of this finite intellect is able the existen ce of singulari ties as immanent effects of the divine ' there is' . O n
illum inate th e th emes of Books III and IV: we do not immed iately havc the other ha nd , the on ly adm issible proof for the loca l operation of true idea s
adequate idea of what our own in tellect actually is. rests entirely on co m mo n notions, on th e gene ric properties of sin gulari ties.
The relation between these two re lations is cenainly nor straightfa Th e true is gene ric , even wh en bei ng is th e power of sin gulari ties.
In fact , th e diffi cu lty can be form ulated as fo llows: if th e finit e intellcc:l Spinoza docs not hes ita te to in sist that ' those notions whic h are ca lled
defined as an id eal co upling with th e body, yet one which is without common ... arc th e found ations o f our deduct ive capacity, .27 M ore dec isively
edge of its object , how do we account for th e possibility of true i still, in the D em onstra tion for Book II , Pro po sition 44, Co rollary 2, he
Although the rel at ion of incl usion exp lains it, the latt er is writes: '[T ]he founda tions of reason V ondall/ellla raciol/isl ar e notions (b y
global metaphor. W hat is th e local ope ration of tru th s? P38) wh ich ex plain th ose thi ngs whi ch are com mon to all, and wh ich
The pro b lem is not th at of know ing how we can have true ideas in (by P37) do not exp lain th e essence of any sin gu lar thin g. O n that accou n t,
extrin sic sense gov erned by th e no nn of agreement, for we ex perience they mu st be conceived witho ut an y relation to time, bu t un d er a ce rt ain
fact that we do. The true idea is its own verification, even in th ose ins species of eternit),.,28
wh ere it is val idated thro ugh co up ling, ag reement . This famous th eme is The object ion acco rdi ng to whi ch the third kind o f knowledge would have
ou t in th e Sc holium to Book II , Proposition 43: ' [H )ow can a ma n know to be essentially d ist inct from reason , pro vid ing us with a ' lateral' (or purely
he has an idea th at ag rees with its object (ideatum] ? I have just shown, intui tive) access to singularities th em sel ves, does not stand up. T he debat e is
th an su fficien tly , that thi s ar ises solely from his having an id ea whi ch too old and too co m p lex ro be b roached here . We will confine o urselve s to
ag ree with its object [ideaw m) - or that tru th is its own sran dard.'25 At noting tha t the Preface 10 Boo k V identifies , in an en tirely general fashion.
ju ncture, Spi noza w ishes to unify th e opera tional app roac h that the 'power of m ind ' wit h ' reaso n ': 'de sola melitis, seu raiionis pote", ja rJga m' ,
co up ling with the prope rly ontologi ca l app roach that uses in clusion. 11111 ' I shall treat onl y o f th e power o f th e mind, or o f reaso n .' zq An d also th at if
m ueh is clear fro m the con tin uation of th e argumen t: 'Ad d to thi s that the th ird kind of kn ow ledge is tru ly an 'intu itive science [scienria imuirwal' ,lO
m ind, in so far as it perceiv es things truly, is part of th e infin ite intellect iUst as ' the eyes of the m ind .. . are the demonstrations rhemsetves'," th en an
God .' 26 Thus, th e existence of true id eas is guarant eed at th e global levd b 'intUition' carried out thro ugh these eyes must co nsist of an 'imm ed iate'
the fin ite inte llect's inclusion in the infin ite in tel lect, and at th e local level, b grasp of th e proo fs, an ins tantaneo us ver ification of the ded uctive lin k
th e self-eviden t expo sition of th e agreeme nt of a cou pling. between common not ion s. But th is docs not rel ease us from th e pu re univers-
T he real p roblem is: H ow? H ow does the fini te intellect come to have trUCI ality Wherein the true ideas of the infinite in tellect reside.
id eas, given that it does not even have knowl edg e o f the body-object, rI Il\us we find ours elves back at the pu re ax ioma tic o f eternity from whence
whi ch it is th e idea? ~·e ini ually set OU t. For if th e rea lm of m e thi nkable is ga uged - for a fini te
T he so lution to rhi s prob lem , whi ch is st rictly operational since it is noC Intellect _ th rou gh 'th at wh ich is common to all' , th en the latte r actually
ex istential, is set o ut in Propo sitions 38 to 40 of Book I L These Propositions ~efers to the arrangeme nt o f the ' there is', wh ich is to say, to (he att ri bu tive
establish m at every idea referring back 10 a prope rty co mmo n to all bodieft Identificat ion o f d ivine infin ity.
 92 Theoretical Wnt mgs Scmceas Close d Ontology 93

This circular closu re of Spinozist ontology - a closure mediate d by being as mathema tically con ceived . All tru th is gen er ic. Alt er nately . what
st ructu res of the intellect - is enacted th rou gh a com p lex sc hem a,
need s to be recapit u lated .
,,,
. h·,nka blc of be in g is ma themati cal.

" 1y conclusion is that th e mort geomarico is tr ue th ought itse lf as th inking

1. T h e path 10 th e identificatio n of the 'there is' un der the name 'God' . being, or of th e ' the re is'. Being can only be thought more geemetrico.
be accessed on ly thr ough a pre-comp rehension of difference, which ~n\'ersdY, all ma th ema tical thi nkin g is a th inking o f being w ithin a finite
turn provides the basis for the p ure ly extensive conceptio n of <ti }oCaliZ3tion . That is why, in effect , ' th e eyes of th e m ind are th e demons tra-
infinity. . s ....«nsclvcs'. With out mathematics , we are b lind .
uon u '
2. The pos sibility of the exte nsi ve co nception o f divine in fini ty p resu This concl usio n is, in m y opi nion , ind ubita ble . God has to be understood
- both for th e att ribu tes and for the measurem en t o f divine in finity _ as math em:Hicily itse lf. The name of the 'th ere is' is: matheme.
imcmal fold , an irreducible singularity, wh ich is me infinit e in te llect. Yet even within Spi ncea's tex t, the waY5 in wh ich thi s result is esta blished
3. The infinite intellect has all th e ch aract eri st ics , if not o f a su bject, that necessitate open ing up a space of th ought that is not regulated acco rdi ng to
least of th e su bjective modality or th e predi cati ve power associated the naming of th e ' th ere is' (th is is wh at I call th e ope ratio ns of closu re). The
its effect. As immedi at e in fin ite mode, it cannot be accessed through tams constitu ting th is space arc: indeterminacy, d iffe ren ce, subject, undecid-
usu al ways of es tablishing exist ence. T hu s it rem ains ex isten tiall y abilirv arypicality, co u pling, do ub ling , incl usion, genericity of th e true. An d
-' -,
cideble. The stru ct ure of the infinite intellect requires a relation a few othe rs as well.
than causa lity, whi ch was th e only kind of relati on p ropos ed at th e What is lacking is a foun ding ca tegory ca pable of accoun ting for this
This seco nd kind of relation is th at of co up ling . It has a no rm _ ecoverse or reverse of the mathem atica l, one th at would cons titute an excep-
m en t - which is th e gauge of tru th. L et us say that as an opc:ratioa tion 10 , or supplem en t for, th e ' the re is' . It is precisely at th is junctu re th at
tru th, th e ope ra tion of th e in te llect is aty p ical. U ltimately, co up ling . we need to introduce wha t, in th e wake of oth ers , I have ca lled 'the event ' .
nitizes ' every po in t of th e intellect, just as ca usa lity 'in fini tizes' Th e event is also what groun ds time , or rather - event by event - times. But
poi nt of th e 'th ere is' . We co uld say th at the intellect is intrinsicallJ Spinoza, who acco rd ing to h is ow n ex pression wished to thi nk 'withou t any
doub ling of the immanent p roduct ive po wer. relation to time ',n and who co nce ived freed om in te rm s of 'a cons tan t an d
U ndecida ble in term s of its exi stence; atypical in terms of its o,pe""' " eternal love of God? } wanted no part of it. \VIc co uld say he wis hed to thin k
eliciting a doubling effect - th ese arc th e trai ts wh ich , in m y eyes, id according to the pu re elevation of the mathcmc. In other wo rds, accord ing to
th e inte llect as a modalit y of the su bject-e ffect. the love of th e 'there is' : an ' in te llectual' love wh ich is on ly ever th e int ui tive
4. In o rde r to be loca lized , th e h um an or finite in tellect (m ind ) req uires shorth and for a proof, a glance from th e eye s of th e m ind .
tu rn a th ird rela tion, th at of inclu sion. J USt as the relation of cou YCI other th ou gh ts unfold with in the very doub lin g o f thi s exclusive
allows for a stradd ling of the di sjunction be twee n differen t auri bu thinking. These though ts will accept the math ematics of multi ple -bei ng . In
sim ilarly, th e relation of incl usion allows for a strad d ling of th e d isjutlO" this regard , they will be explicitl y Spincz ist. But the y will d raw th eir gen uine
rion between fin ite and infini te. T he intellect is th en ontologicaUy det impetu s from the im plicit, par adoxical Spinozism outl ined above, fro m th e
m ined as th e loca l poi nt of the infin ite intellect , wh ich is the recollectiad eVent al to rsion wherein, under the name ' intellect', the paradox of th e
of all these finite po ints. If one is willi ng ro grunt that the infini te inte llc:d Subject surges forth .
is th e int rin sic m oda lity of th e su bjec t- effect, it then beco me s possible II) T hese though ts will p ractise the elevation o f the mathc me, but, ta king
say th at the hum an inte llect is a localized effec t of the su bject. Or a stock or what exceeds o r ou tstrips it , they will no longer consent to giving it
di\,"n~' nam es.
subjec tive differ en tial. O r qu ite sim ply: a subjec t.
5. It is also possible to de fine the h uma n in tellec t in ter ms of co upling. AD i hal is why they will enjoy access to th e in fin ite wit hout bei n g encum-
im m cdla re consequ en ce of th is is that the on ly po in ts of tr uth are axio- bered by finit ude. O n this point, they will redi scover an inspiration that is
ftl Or l' PI · t than Spinozisr
.. .
m ane and general. The singu lar is su btracted from every loca l subjectiVC atorus
differen tial. In o the r words: the only capacity for truth tha t a subjccr.
hence th e hum an m ind , pos sesses is th at of a ma th em atics o f being, or
 SECTJONII

The Subtractio n of Trut h

 CHAPTERS

The Event asTrans-Being

If we assume that mathematics is the thinking of be in g q ua being, and if we

add mat th is thinking on ly comes int o effect when , at crucial jun ctu res in me
history of mathem atics, decisions abou t the exi sten ce of the infini te arc: at
stake, we will then ask: what is the field p roper to phil osoph y?
Of course, we know it is up to phi losophy to ident ify th e on tological
vocation of math ematics. Save for tho se rare mom ents of 'crisis' that we have
already mentioned , when the ma thema tician is struck by fear as he confron ts
tha I for which he is responsible (infinite multiples), mathem ati cs thinks
being, but is not the th inking of th e thought that it is. We cou ld even say
that in order to un fold historically as the th ink ing of being , and d ue !O th e
difficu lt separa tion fro m the meta ph ysical po wer of the One thi s en tails,
mathematics had to id entify itself as somethi ng enti rely d ifferent from
ontology. It is therefore up to philosophy to en unciate and valida te thi s
equation: mat hematics " ont ology. In so doin g , philo sophy unbu rd ens itself
of what appears !O be its highest respon sibi lity: it asserts that it is not up to it
to think being qua being.
Th is movemen t wh ereby philosophy, by iden tifying its cond itions , purges
itst:lf of wha t is not its responsibility, is one tha t span s th e enti re h istory of
philOSOphy. Ph ilosop hy freed, or discharged , itse lf from ph ysics, from
COSmology, from po litics, and from many other thing s. T oda y, it is important
~at it frees itself from on tology stricto sensu, Yet th is is a comp lex task, since
It implies a reflective and non -e pistemo logica l traversal of real mathematics.
In B( I/lX and Eve"" fo r exam ple, I simultaneously:

- " ud i ~"d the ontological efficacy of the axioms of set theory, via the cate-
gories of d ifference, void , excess , infini te, nature, decision , truth and
loub!l''C t;
- shOwed how and why on tological though t can effectuate itself witho ut
nceding to id en tify itself;
- examined , acco rd ing to my non -unified vision of the destin y of philo-
SOphy , the p hilosophi cal connect ions bet w een axiomatic in terp retations:
98 Theor etical Writ ings The Event asTrans-Being 99

Plato's Parmeuides on difference and the O ne , Aristotle on th e v . f heir own eleme nts be long to th e site. It is in fact clea r tha t there arc
co t
Hegel on the infin ite, Pascal on the decision, Rousseau on the beiDa non s whe re the cleme nts of thc clements of a m u ltip . le a1so bel
c ong to
anY case
trut hs, etc. rn ' ,~ nlultip le. T h e liver ce lls of a ca t, for exam ple , also belong to th e
tite gl \ en ., .. d
. . . of th e cat. Ce lls arc alive. This is why th e liver IS a so lid, integrate
\'lta!lIY • . . 1 .
In m y vie w, th is kind of work still rema ins ve ry largely open. T h e work .c part of th e tot ali ty that is the cat. Fhc liver IS not an events SIlC .
and org anl
Alben L au rman in the 19305 had alre ad y de m onstra ted that every signi .1 a cc ll can be cons ide red as a site , because th e m olecu les th at
Invcrse y, . '
and innovative fragm ent of real m athema tics ca n an d m ust , in so far II se it arc not 'organ ic' in the same sense as th e liver may be said to be
ecrncc. A chem ically de te rmi ned m olecule IS . no Ianger "a . ,. h
const itutes a living co ndition , elici t its own ont olog ica l iden tificat ion. I we m t c sense
un dertaken th is ta sk more recent ly both with respe ct to th e renewed CQn organic. cat can be said to be alive. . E yen if'itis
t It IS 0 jecuv c y a par t of the......,
' bi . " ca
tha t th e ...
tion of n um ber propo sed by Co nw ay and with rega rd to the theory of . lc ,gg"gate of molecules is not a vital co m ponent in th e sa me sense as
a ~ m p~ .
gories and T opoi. the fiver . We cou ld say that with th is agg regate we ha ve r~ac hed t.he mat e~tal
On th e oth er h and , th ere is th e vas t q uestion of th at wh ich su btracts i edge of th e car's vita lity. This is why such an agg regate WIll be said to be on
from onto logica l determination, th e q uestion of that whic h is /l ot being the edge of the void'; that is, on the edge of wh at separat es th e ca t, as .a
being . F or th e law of subtraction is im p lacable: if real on to logy is set OUl singular multiplc ·situation, from its pure ind isti nct being ~ wh ich is th e VOId
mathem atics by eluding th e norm o f th e O ne, it is also necessary, lest proper to life (and thc void proper to life, as death shows, IS m attcr). . .
allow th is nonn [Q re-establish itsel f at a global level, that ther e be a point T herefore, the abstract definition of a sire is th at it is a part of a situation
wh ich th e ontological (i.e. mathem at ica l) field is dct ot alized or cau gh t in all of whose elem en ts are on th e ed ge of thc void.
im passe. I have called th is point the event . Accordingl y, we co u ld also T he ontologica l ma terial, thc underlying multipli city, of an even t is a site
that, beyond th e iden tification of real ontology, wh ich mu st be cease thus defined.
ta ken up again, phi losoph y is also , first and fore most , thc genera l th eory Having said th is, we enco un ter a singular probl em , wh ich I believe estab-
the eve nt. T hat is, th e th eory of that which subtracts it self from onto lishes th e divi di ng linc between D eleu ze's doctrin e and m y own. The
subtraction. Or the theo ry of the im possib le p roper to math em atics. question is effectively the followin g: if wc gra m tha t th e event is what guar-
cou ld also say that , in so far as ma them atical th in king takes ch arge of anrecs that everyth ing is not m athc mat izable, m ust we or m us t we not
as such, the th eo ry of the event aims at the determ in ation of a trans-being, conclude that th e multi ple is intrins ica lly heterogcneo us? T o th ink that th e
What are the charac teristic traits of th e event, at least within the register event is a point of ru pture with respect to bcing does not exone rate us from
th e thi nki ng of be ing? What sub tracts the shee r ' what happens' fro m thinking th e being of the even t itself, of what I precisely call 'trans-bein g",
gene ral d eterminations of ' what is'? and of whic h I' ve just said that it is in every in stance a site. Beyond the
F irst of all, it is necessar y [Q po in t out that as far as its material acknowled gement that th c material of the even t is a site , does tran s-being
concerned, th e even t is not a mi ra cle. W hat 1 m ean is th at what co m poses require a th eory of th e m ultiple het erogeneou s to the one tha t accou nts for
event is al ways extracted fro m a situation, alwa ys related back [Q a sin being qua bcing ? In m y view, D eleuzc's position am oun ts to ans wer ing 'y es ' .
m ult ip licity, to its state, [Q th e language connec ted to it, etc . In fact, if . . In Order to th ink the cvc nta! fold , an ori ginari ly d up licitous theory of m ulti-
want to avoid lapsing into an obscu ranti st theory o f cre ation ex nihilo, '" plieitics is required , a theory that is heir to Bergson. Ext ensive and n umerica l
must accep t that an event is no th in g b ut a pa rt of a g iven situation, noth iPI multiplicities mu st bc di stinguishe d from int ensive or qu alita tive m ultip lici -
but e fragment of being, ties. An event is always th e gap betwee n tWO het er oge neou s multiplicitics.
I have called th is fragm ent th c cven ral site. T her e is an even t on ly in so fat What happe ns produces a fold between exte nsive segmen tation and th e imcn -
as th ere exists a site fo r it with in an effect ively d eplo yed situ ation (. sivc COn tin uum.
m ulti ple). . I, On the cont rary, argue that multiplici ty is axiom atically hom ogeneo us.
Needl ess to say , a site is not JUSt any fra gment of an effective m ult ip licity- r hereforc I mu st account for the being of the even t bo th as a ru ptur e of the
On e cou ld say that there is a sort of ' fragility' pecul iar to the site, whi cb law of segm ent ed mul tiplicities and as hom ogeneou s to this law. M y
di sposes it to be in so me sense 'wrested ' from th c situation. T his frag ility cad argument mu st pass through a de fection of the following axiom: an event is
be form ulated math ematically: thc elements of an evcmal site are such nOthing other than a set, or a mult ip le, whose fonn is that of a sitc. Hut th e
 100 Theoretical Writings The Event asTrans·Belng 101

arising o f th e: eve nt , as a supp lementation, su btracts one of the axioms or , '\" an even t is the advent of a situ ated multiple (there is a site of
Vlu f1l:l t<; • , .
mu ltiple, namely th e axiom of found atio n. ) and is in a position to be its own cleme nt . The exact meaning of
~ ~I . . . . .
Wh at docs the axiom of founda tion say? Thai in every mu lti ple, there it lation is th at an even t IS an unfounded mul tipl e. It IS this defection
this form u .
least one element th ai ' founds ' th is m ul tiple, in th e following sense: there foundation that turns it into a pure chance supp leme n t of th e mu ltiple-
an clemen t that has no element in common with the initial multiple. On of the, for which . ,It .IS an event, an dfrom wh lch j
IC It wrests " aa sit
Sl e f rom ', I...,..
situJlll OO
point , we can recall the examp le of th e cat . O ne will say tha t a cell ' f founded incl usion. . .
th e car as a living tmaliry, in the p reci se sense tha t th e cat, conceived in What happens - and , ina smuch as it happen s, goes beyond Its .m ultl ~le­
manner , is composed on ly of cells. It fo llows th at no d ement of the cdI bdn8 - is precisely th is: a fra gment of mu ltiplicity wr ested fro m all inclusion .
chem ical molecul e as such) is an clem ent of the C3t, since every elemeza In a flash, this fragment (a cert~i n modulation in a ~ymph~ny by Hay~ , a
th e living m u lti plicit y 'ca t' is a cell. rticular command in the Pans Co mmune , a Speci fic anxiety precedmg a
The on tological import of th is axio m is dear : th e d ecomposit ion of a :tclarat iOn of love, a unique in tu ition by Gauss or Galois) affirms its un -
plicir y always incl ud es a haiti/ill point. At a given moment, you will foundedness, its pu re cduent, wh ich is intransitive to th e place in whi ch ' it'
upon an element of the multip licity whose own compos ition no comes. The fragme nt th ereby also affirm s its belonging to itsel f. since th is
be long s to th is multiplicity. In other words: there is no in finite desceer coming can origin ate from nowhere else.
the cons tituen ts of a m ultiplicity . A mu ltiplici ty can cer tainly be (an d Consequently, it cannot be said that th e even t is O ne. Like every thi ng th at
ally is) infinite in extension (it possesses an infinity o f clements), bu t it it is the event is a multiplicity (its clem ents are those of the site, p lus itself).
, '
infinite 'genealogically', or in depth. The existence of such a haltin g Neverth eless, th is mu ltiplicity su rges up as such beyond every cou nt , It
stabilizes every mu ltip licit y upon itse lf, and guarantees th at in one poior fulminates the situation from whic h it ha s been wrested as a frag ment. T h is
least it encounters someth ing that is no longer itself. is what has pushed me to say that an eve ntal multiplicity, q ua tran s-being,
A crucial conseq uence of the axiom of foundation is that '10 multiple ~ can be declared 10 be an ' ult ra-O ne' .
an elemem of irself. In deed, it seems clear that no cat is an element of the We arc faced here with an extreme tension, balanced precariou sly between
which it is, no r are an y o f th e eat 's cells an elem ent of the cell whi ch the mult iple on the onc hand, and the metaphysical power of the O ne on th e
are, whi lst on the cont rary a cell can obviously be an element of the cat. other. It should be d ea r wh y th e general q uestion th at is th e object of my
That th is po in t deri ves from the axiom of foun dation can be dispute with Deleuze , which concerns th e status of the even t vis-a- vis an
dem on strated . Le t's su ppose th at a mul tiple is in fact an element of . ODtology of the multiple, and how to avoid reint roducing the po wer of the
(such that we have M eM, o r multiple 1\ \ ' be longs' to m ult iple: M ). Let's One at that point wh erein the law of th e multip le begins to falter , is the
conside r the set that has Ai as its on ly clement (th is set is called guiding qu estion of all cont emporary ph ilosophy. This qu estion is amici-
'sing leton' of M and is wr it ten {M D. I can affirm that th is set (th is sing Pated in Heidegger's shi ft from Sein to Ereignis, or - switch in g registers - in
is not fou nded . In actua l fact, its only elemen t is M , and since M is lacan, whe re it is entirely invested in the th ink ing of the ana lytical act as th e
elemen t o f M (our ini tial h ypothesis), it follow s th at all the elemen ts of eclipse of truth be twee n a supposed and a transmissible knowledge, between
cleme n ts are still clements. interpretatio n and the mathcm e. La can will find hi mself ob liged to say tha t
Thus if we accep t th e axiom of fou nd ation, we must exclude the po ssibililf thOUgh the O ne is not , the act nevertheless installs th e O ne . But it is also a
that a multiple may be a multip le of itsel f. decisive pr oble m fo r N ietzsche: if it is a qu estion of b reaking the h istory of
It is on this point tha t the even t departs from the laws of be ing. In effect. the w e nd in two , wh at, in the affirmative abso lute of life, is the th inkable
on event is composed of the clement s of a site, bu t also by the event itself, principle that wou ld command such a br eak? And it 's also the cen tra l
which belon gs to itself. ~roblem for \'Vin genst cin : how docs the act open u p ou r access to the
T here is noth ing Strange abou t Ibis d efinit ion. It is obv iou s, for example, mYStical clemc m ' _ i.e. , to the ethic al and the aesthe tic - if mea n ing is
that a reflection upo n the Fr ench Revo lut ion is an cleme nt of the revolu uOll alWayS capuvc 10 a p ropo sition, or alwa ys the prison er of grammar?
itself, or that th e ci rcums tances of an amo rous enco unter (of a love 'at lirtI . I? all these cases , the latent matrix of th e p roblem is the following: if by
sight') arc pa n o f thi s encoun ter - as is shown, from with in an instance ~ PhilOSophy' we mu st understand bo th th e jurisdiction of the O ne and the
love, by th e infin ite g loss of whic h th ey are the ob ject. COnditioned subtrac tion fro m th is ju risdiction. how can philoso ph y grasp
102 Thecreuc al Wn tlngs

what happens; what happens in thoug ht? Ph iloso ph y will always be div '
betwee n . on th e o ne hand , the recognition of th e even t as a supern um
adv ent of th e On e, and on th e o the r, th e though t of th e being of the ev~ CHAPTER 9
a sim p le exten sion of th e m ul tiple. Is truth wh at comes 10 being or
unfolds being? We rem ain divided. The whole point is to maintain, as r.
possi ble , an d under the most innovati ve con di tions of th ought, that, in On Subtraction'
case, truth itself is nami ng but a mu ltiplicit y. In the twofold sen se that
its oom ing (a truth elici ts th e adven t of a ty p ica l multi ple, a generic .
larit y) and its being (th ere is no Truth, th er e are on ly tru ths , disparate
untota lizablc) arc multiplicities.
This requ ires a radical inaugural gesture, which is the hallmark of Since I have bee n invited before you , for who m silence and speech are th e
philosop hy: to subtract the examination of tr u th s from the m ere form principal concerns , to honou r that wh ich subtracts itse lf fro m their ahema-
judgement. T his always mean s th e follow ing : 10 d ecide upon an ontolOlf don, it is 10 Mallanne I [Urn 10 mit igate my solitude.
mu lti plici ties. Consequentl y, (0 remain faith ful (0 L ucre tiu s, telling 0 T hus, by way of an epigraph for my address, J ha ve cho sen th is fra gme nt
that every instant is th e one in wh ich: from the fourt h scho lium o f lgitur:

From all sides the re opens u p an infin ite space I alone _ I alone _ am going to know th e void . You , you retu rn to your
When the atoms, inn ume rable and lim itless, amalgam .
Tum in every di rection in an ete rnal mo vem en t. I I proffer speec h, th e be tte r to re-immerse it in its own in anity.. . .
This, no doubt, constitutes an act - it is m y d uty to p roclaim it: this
Hopeful ly thi s clarifies why Deleuz e, d espi te his Stoic inflections, is, madness exists. You were righ t to man ifest it : do not th ink I am going to
2
myself, a faith fu l follower of Lu cretius . re-immerse you in th e void .

As far as the com pactness of your amalgam is concerned, I com e he re

duty-bound to declare that the madness of sub traction cons titu tes an act .
Ikn er, that it constitu tes th e paragon of th e act, the act of a truth, the one
through which I come to know the on ly thing one may eve r know in the
element of the real: the void of bei ng as such.
If speech is rcim mersed in ns inan ity by th e act of truth, don 't thi nk y ou
too will th ere by be rcim rnersed , you who retain the reason of the man ifest .
Rather, we will concur _ I th rough th e duty of speech, you through tha t of
rendering my speech manifest _ that th e folly of an act of tr u th exists.
Nothing can be gran ted exis tence - by which I mea n the existe nce that a
truth presupposes at its origi n _ with out und ergoi ng the tr ial of its su btraction .
It is nor easy to sub tract. Su b -traction , that which d raws under, is (00
Often mixed with ex-traction, th at which d raws from ou t of, that whic h
l1lincs and yields th e coal of know led ge .
Sublraction is p lu ral. The allegatio n of lack, of its effect , of its causa lity,
maSk1 ope rations all of which are irreducible to one anothe r.
These ope rations are four in number: the un decidable, the indiscernible,
the gener ic, and the u nnameab le. Four figu res d elineat ing the cross of being
 104 Tbeo-etxa! Wrrttngs On Sobtrac rco 105

when it surges fort h in th e trajectory as well as in th e obstacle of a trutb,. . that such an exp ression discerns the terms a . and a2 when th e value of
~'i llsa)
tru th 300 m which it wou ld still be too m ucb to say thai it is half.said . slat<:rnl-n t F(o .. o i) differs from th e value of th e statem en t F(~. 0 .).
•
as we sha ll sec, it is ra rel y-said, or even alm ost-not -said , tra versed as it it thef for eX:lm plc, a, is effective ly bigger th an Oz. th e exp ression 'x is bigger
th e incommensu ra ble un bi ndi n g be tween its own in finit y and the finitUde I - " discerns 0 \ and 0 2 since me statement ' 0 \ is bigge r than al tak es th e
the know ledge it pierces. thlUl ) 'true' whe reas th e state ment 'a2 is bigger th an aI ' takes the value ' false',
value .
LeI us begin with pu re formalism . You can sec then that an expression di sce rns two term s if p ut ting one m
Conside r a norm for the evaluation of Statements, in any given situatiaD. pl3cc of m e other and vice versa. i.c ., permuting th e terms in the expression ,
a lan guage. The most common of th ese norms is th e d istinction between chaflgCS th e value of th e sta tem ent.
verid ica l state men t and the erroneous statem ent. If th e lan guage in q Consequ ently, tWO term s are itldiJ'ernib/~ if, in the lan guage situation in
is rigo rously pa rtition ed , anoth er norm might be the di st inction ucstion, th er e exists no express ion to di scern them. T hus in a h ypo thetical
provab le and falsifiable sta teme n ts. Bu t for our p urposes, it is eno up ~guage red uced to the single exp ression 'x is bigger than y', if the two
there be such a norm. The undecidabl e statement will be th e one termS II, and a 2 are equal th en they are in discern ib le. For, in effect, th e
subtra cts itself fro m th at nonn. Co nsi d er a stat eme n t such that it CllDDOt expression 'a , is bigge r than a2' bea rs th e value 'false' , b ut so does th e
inscribed in any of th e classes within whi ch the norm of ~val uatiolt expression 'a 2 is bigger m an a,' .
suppose d to d ist ribute all possible utt erances. Thus tWO given ter ms arc said to be indi scernible with respe ct to a
The un decidable is thus th at wh ich subtra cts itself from a su p language situation if th ere is no two-place exp res sion of that language
exhaus tiv e class ification of statem en ts , rea lized accordin g to tb e marking th ei r d ifference th ro ugh th e fact m at permuting the te rms chan ges
ascribed to them b)' a no rm. I am unable to deci de an y assignab le value the value of th e resul tin g sta tem en t by inscrib in g th em in th e places
this state me nt, in sp ite of the fact that th e norm of assignation exists om, prescribed by the expression.
th e assumption of its com p lete efficacy. The und ecidabl e statem en t is s Th e indiscern ib le is what subtracts itsel f fro m the marking o f di fference as
valueless, and thi s is wh at con stitutes its pri ce, !.hrough which it co nt effected by evaluating th e effects of a permutation . Two terms arc indi scem-
th e laws o f clas sical eco nomy . ible when you pe rm ute th em in uain, These two te rms are two in num ber
GOOel's th eorem es tablishes th at in th e language situation known as only in the p ure p resentation of th eir bei ng . There is nothing in language to
order formalized arithme tic, whe rein the norm of evaluation is that of to OOw their duality with a differentiating valu e. They arc two, gra n ted , bur
pro vable, there exists at least on e statem ent that is undecidable in a not so that you cou ld re-mark th at th ey arc . Thus th e ind isce rnible su btracts
sense: neither it nor its negation ca n be proved . Thu s, formalized an diff erence as such from all rem arking, The ind iscernible subtra ct s th e two
does not fall un der th e aegis of a classica l economy of srareme nrs. (rom duality,
It has long bee n cust omary to rela te the undecidability of GOOd's. Al g~bra encoun tered th e qu estion of th e indi sce rn ible very eart y on, begin-
m cn t to th e fact tha t it lakes the for m o f the liar paradox , of a stat ning with the work of Lag ran ge,
declaring its own indemenstr abilhy - a statemen t su btracted from th~ Let us ado pt the ma thematical language o f pol ynom ial eq uations with
sim ply because it states th at it is n egati vely affec ted by it. We now know tt.- several variables and rational cc-e fficicrus. We w ill then fix the norm of
th is link bet ween undecidability an d paradox is co ntingen t. In 1971. J ~lu:iIlion as follows: if, whe n we subs titu te determi nate real n umbers for
Pari s an d L eo H arrington proved th e un decidabilit y o f a statem en t diet the variabk-s, the pol ynom ial cance ls itse lf ou t, we will say that the valu e is
th emse lves desc ribed not as a pa radox, but , I q uote, as 'a reasonably natudl ~" If lhl' POlynom ial does no t cancel itself out, we w ill say tha t the value is
th eo rem of a finite ccmbinaronat'. ' In thi s inst ance, subtrac tion is -.
,.
intrinsic opera tio n; it is not a conseq uence of th e statemen t's paradoxietl " Y Oder these co nd itions , a disurlling expressioll is obviously a po lynomial
structu re vis-a-vis the norm fro m whi ch it sub tra cts itsel f. 'lth two variables: p ex, y ), SUI it can e:lsily be proved, for example, that th e
Co ns ider now a language situation whe rein, as before, th er e exists a n()l1ll : 0 fl..tal numbers + 2 and -2 arc ind isce rnible. Fo r every polynomi al P{Xd'),
of evaluation for statemen ts. Take an y two given terms whatsoever, let'S s4 . e \'aluc of P( + 2, - 2) is the same as the value of th e po lynom ia l P(- 2, + 2):
.f the .
0\ and oz- Consider now ex p ressions o f th at lan gu age with pla ces for e tirst (When x takes me valu e + 2 and y _ 2) cancels itself ou t, the
terms. such as 'x is bigge r than y '; e.g. exp ressions of th e kind F(x. y ). SOcond (When x takes th e value - 2 and)' + 2) also can ce ls itse lf ou t. In othe r
 106 Tbecreucar Wrrtlngs On Subtracllon 107

word s. the p rinciple o f d ifferen tial evaluati on fails fo r eve ry pe nn u ta~ crUcially. th is means that for every expression F(x) there exist terms in the
the two n u mbers + 2 and -2 . eric set whi ch, when substi tu ted fo r :c, yield a statemen t with a certain
Consequent ly, we should not be surprised uiat it was unde r the imPet\le '''', c and that there arc other tcrms in th e samc set whic h, whcn substituted
\'11 u ,
the st ud y of permu tation groups th at Galois carne 10 configure the theo . "jc ld a statemen t with a different value. The generi c su bset is such
for ,l ,
space wherein the problem of resolvi ng equati on s by means of radic:ab n'Ciscly beca use, give n any expression F(x), it is subtracted from every
beca me int elligibl e. Galo is effectively Inve nted a calcu lus of the ind i ~Iection and cons truction authorized by that exp ression in the: un iverse U.
T h is point har bou rs cons iderable conceptual conseq uences wh ich will be The generic subset, we mi gh t say, contains a little b it of everythin g, so th at
out in th e ncar futu re by the contemporary mathematician and thinker no predicate ever collects together all its terms. The gene ric su bset is
Guitart in a forth coming book whic h, it shou ld be noted , makes use subtracted from p red ication by excess. T he kaleido scop ic character and p redi-
number of Lacan lan categories." a tive superabundance of the gcneric subset are such that noth ing d ependent
From the foregoing discussion we can retain th e following result: upon the power of a stateme n t and th e ide nti ty of its evalua tio n is capa ble of
the un decidab le is subtraction from a nonn, th e indiscernible is su circumscribing it. Language is inca pable of constructin g its contour o r th e
from a mark. character of its collection. The generic subs et is a p ure mu ltip le of th e:
Co nside r a langua ge situation where there always exists a norm of universe, one that is evas ive and cann ot be grasped through any variety o f
tion . And con sider now a fixed set of te rms or obj ects, let's say the set U. linguistic construct ion. I t indicat es that th e pow er of being proper to the
will call U a un iverse for the languagc situation. N ow let's take one of multiple exceeds the aspect of that po wer th at such construc tions arc capab le
objects, for instance al ' And let's take a single-place exp ression of of fixing acco rdi ng to th e unity of an evalua tion . More p recisely, th e generic
lan guage, for instance F(:c). If in the pl ace ma rked by x you put the is that insta nce of multiple- bein g whic h su btracts itse lf from the pow er of th e
you obtain a sta teme n t F(a l) to which th e no rm will ascribe a certain One in so far as the latter operates through language.
eit her true, false, or an y othe r value d etermined by a principl e of eva! It is easy to show that for every langu age endowed with a relation of
For example, let a2 be a fixed object in the un iverse U . Now, suppose equality and eq uipped with disjun ction - in othe r wo rd s, fo r almost eve ry
lan guage situation allows for th e exp ression 'x is bigger than a2" If .. language situation - a generic subset is necessari ly infini te.
act ually bigger than a 2' we obta in th e value ' true' for the statemen t 'a l i• . For let us su ppose th e o pposi te, that a gene ric subset is finit e.
than a2' - the statemen t in wh ich a 1 has come to occupy th e place ma rked bf Its terms will then mak e up a finite list , lee s say al> a2' and so on up
No w lee s imagine th at we take aU the term s in U wh ich are bigger ~ until a~ .
\,(/e thereby obtain a subset of U . It is th e subset made up of all those ConSider now the exp ress ion;x - al or x > a2' etc. , up to x - a~'. This is
a which, when substituted for x, give the value ' tru e' to the statement '. an expression of the type F(x) since the term s a 1> a2' etc., are fixed term s,

bigger than a2'. W e will say that th is su bset is const ructed in th e un ivetlt Which conseque n tly do not in dicate any 'emp ty' place. Moreover, it is
th rough the expression 'x is bigger than 0 2' . O.bVio us tha t the set made up of a l> a 2 . . . a~ is construc ted b y thi s exp ressio n,
Gen era lly, we sha ll say that a su bset of th e un iverse U is cons tructed by' ltnee only these term s can valida te an eq uality o f th e type 'X.l .." a/ when j
exp ress ion F(x) if that subset is mad e up excl usive ly of all th ose tcnDI lOcI from I to n. Accor d ingly, beca use it is constructib le, th is finite set
belo nging to U such th at, when put in th e p lace marked by x, th ey cannOt be gene ric.
th e stateme nt Pea ) a value fixed in ad vance - in o ther word s, all those t tan1 hus thc gene ric is that subtraction from the predi cative constructions of
such that the expression F(a ) is evalua ted in th e samc way. .Suage that the un iverse allows thro ugh its own infinity. The ge neric is
We will say that a su bset of the universe U is const ructible if th ere exist. Illtln13tely the superabu ndance of bei ng such as it is with d rawn from the
the langua ge an exp ress ion F(x) that construc ts it. ~rasp of langu age, once an excess o f d crermina rlon s engen ders an effec t of
T hus a gene ric subset of U is one th at jf nor cons tructible. No exp lhdetemll nacy.
F(x) in the language is evaluated in the same way by th e terms th at . In 196 3, Paul Co he n furnished p roof that even in verv robust langu ag
, Itu . ~

up a gen eric subset. I t is clear that a generic su bset is su btracted from III atlons, such as that o f SCt theory, the re exist universes in which gene ric
U!tip\" . . 5
ide ntification effected by means of a pred icate o f the language. No s' 1'1\ rcmes p resent th em selves . Since, as Lucan repeatedly asserted,
pred icatlve trait gathers together the term s that make up th e gene ric su athematics is the science of the real, we can be ass ured that th is singu lar
 108 Theoret ical Wntlngs On Subtrecnon 109

sub traction from the mark of on ene ss that language stamps upon the " .t tha t un iq ueness is dou bled seems to imply that one form of
,"",'-
j he
multiple is genu inely real. 0<'
. U l.' n~ ~
is.J the ruin of the other. It becomes imposs ible to su btract oneself
l
I have already said th e undecidable is a su bt rac tion from a norm of 1.1l1 q I " p, op er name if th is su btraction 's un iqu eness provide s th e basis for
frorn t ic
tic n and the indi sce rn ib le a subtraction from the remarking o f a d iffe ropt icty of a nam e.
We can ad d that the generic is in fin ite sub traction from the su bsumpti w' P ~ , ~ult there would seem to be no proper 0 f th
As a , "'.J , tne pr oper, w hircb iIS to
the multiple benea th the On e of the concep t. V no singularity of tha t wh ich sub tracts itself from all self-doub ling

F inally, consi de r a lan guage situation and its pri nciple s of evaluation. sa. ~ugh the nam e of its sing ularity.
again , consi der sing le p lace expressions of the kind F (x ). Am ong the thrBut this is on ly the case so Iong as t h e expression ion rh avmg
" no prop er
sib le values for statemen ts in this language situation - for instance the " " I)()ssib lc in the language situat ion in which one is ope ratin g. Alter-
the false, th e possi b le, or any other - let's establish one value once and n'""
nail 1)' , this is on ly th e case so lon g as the expression ' there is no cxpres-
·",
all, which we shall call th e nominatin g value . We shall the n say that sion F(.'\:) for wh ich th e unnameabl e term alone provides a nomi nati ng value'
exp ression F(x) "ames a term al belonging to that un iverse if tha t term it can itself be an express ion in the language. For only th is expressio n abo ut
only O1/e which, when su bstitu ted fo r x, gives to the stateme nt F (.:II) expression s can serve to na me th e un na meable, th ereby engendering the
nominating value. paradox.
For examp le, take two terms - .:II and a2 - as o ur un iverse. O ur I Yet it is generally not th e case that an expre ssion can refer to all possible
allows the express ion 'x is bigger than 022' , We will suppose th at th e expressions in a language. In this insta nce, the not-all preven ts th e depl oy-
natlng value is the tr ue value. If 021 is actually bigge r than a2' then the ment of the pu tative paradox. For if you state ' there is no express ion F(x)
si o n 'x is bigger than 022' nam es th e term al ' And ' 02 1 is bigger th an .:12" such that thi s or that' you arc in fact presu ppo sing, albe it negatively, that a ll
is the nom ina ting value, is effectively true, wh ile ' 022 is bigger th an a I" of the language can be inscribed in the unity of an exp ress ion. T h is in turn
is nor the nominating value, is false. Bu t the universe comprises on ly 021 would requ ire the langu age situation to be capab le of a high degree o f meta-
a2' Therefo re, al is the only term in the universe wh ich, when substi tuted linguistic reflexivity , whi ch could be sus tained on ly at the price of a paradox
x, yield s a stateme n t with the nominating value. even more da maging tha n the on e under conside ration.
The fact tha t an express ion names a term mean s that it is p rovi Moreover , in 1968 th e mathematician F urkhen p roved that it is possible to
sche ma for its p roper name. As always, th e 'p roper ' pr esuppo ses the suppose the existence of the unnameable witho ut contradi ction . F urkhen
T he named term is uniq ue becau se it gives to the exp ress ion th at names.. presents a fairly simp le language situa tion - someth ing like a fragment of the
the fixed nominating value . theory of the arithm etical successor, sup pleme nted wit h a small part of set
Acco rdi ngly, a term in the un iverse is 'unnam eab le' if it is the only MW theory - such that it allows for a model in which one term and one term only
thai nniuerse tha t is not named by any expression, remains nameless. Conseq uently, thi s is a model in which th e un nam eab le -
One shou ld be attentive here to the do ub ling o f the un ique. A tenD i.e., the SUbtractive reduplication of uniq ueness, o r the proper of the proper
named only in so far as it is the uniq ue term that con fers upo n an expr - well and truly exists.
the nom inating value. A term is unn am eable on ly in so far as it is th e uni Let us recapitu late. \'(Ie have the und ecidable as sub traction from the
term th at subtracts itself from th at un iqu eness. norms of evaluation, o r subtraction from the La w; th e ind iscern ible as
The unnameable is that which subtracts itself from the proper name and Sllblf'J ction from the mar king of difference, or su btraction from sex; the
alone in d oing so. Thus th e unn am eable is the proper of th e proper - generic as infin ite an d excessive sub traction from the concept, as p ure
singu lar th at it can no t eve n tolerate having a p roper nam e; so sing u lar in multiple or sub traction from the On e; an d, finally, th e unnameabl e as
singu larity as to be th e on ly one not to have a pro per name. ~b~ cucn - f ro m the proper name, or as a singula" " sub tracted f rom s mgu-
rity "
We find o urselves here on the verge of pa rado x. For if the uniqueness of larisaf
. Ion. Th esc arc th e an alyti cal figu res of being through w IC me Ianer
" " hi h ,"
un nameab le consists in not h aving a proper name, th en it seems th e uno
able falls under the name of ano nymi ty, which is prope r to it alone. Isn 't '
" InVoked whe never lang uage loses its grip.
What we mu st now do is move from the ana lytic of su btraction to its
one who has no name th e name of the unn ameable? The answer wou ld ~ialectic , and establish the lan er's topol ogical linkage. The fram e for thi s
to be yes, since the unnam eable is the on ly one to operate this su btract ion. Itlkagc is SCI OUI in th e ' gamma' d iagram belo w.
 110 Tbecrencal Writings On Subtraction
"'
. enesS o f what evades th e pr oper name in th e case of the un n ame-
the un:qu the posi tion of th e one with in th e su btrac t ive effect d iffers in each
, ble. \ ct

case· use it is sub tracted from the effect of the norm of evaluatio n, th e
Nom ination S :dablc statement falls ou tside the compass of wha t can be inscri bed ,
~ce "'hal defines th e poss ibilities of inscription is p recisely to be govern ed
ptt the norm. Thus GOOeI's statement is absent from th e domain o f the
b~'1Ible beCause neith er it nor its negation can be adm itt ed in to it. Ccnse-
P , . we could say that th e u ndec idable st ateme n t su pplem ents th e
quen t y, .. .. .
language siruat ion governed by th e no rm. I indicate this In th e d iagram by
the pluS sign appended to th e one.
Generic Th e unnam eable, on th e con trary , is embedded in th e intim ate depths of
Truth ffSCOta lion. It bears witness to the flesh of sing ularity and thu s provides th e
~int.like ground for the ent ire orde r in which term s are present ed ".This
radical underside of nam ing, th is folding of me p rope r back upon Itself,
Infinite designates that in being which underm ine s th e principl e o f th e one, such as it
Fideli ty Finite
has been esta blished by language in th e naming of the proper . T his weak-
ening of the one of lan guage by me po int -like ground of bcing is ind icated in
I should point out that only now do we enter fully int o the realm of the diagram by append ing the mi nu s sign to the one .
soph y, since everyth ing d iscussed so far is shared be tween ph ilosop by A$ for the indiscern ib le an d th e generic, th ey are coupled by th eir common
mathematics, an d hence be tween phil osophy and onto logy. presupposition of th e multiple. In discernib ility is said of at least two term s,
Speaking of onto logy, let it be said in passing that Lacan had no since it is a d ifference without a concept . And th e gen eric, as we h ave seen ,
about calling it a di sgrace - a disgrace of sense, or of the senses. A requires an infinite d issemi na tion of th e terms in th e universe, since it
di sgrace. I would add, a fami ly di sgra ce for ph ilosophy, net a fonn of provides the schema for a su bset that is sub tracted from all predicati ve uni ty.
housekeepin g but a di sgra ce for the phil osoph ical hou sehold. But for But here, once again, me type of mu ltiple differs in each case. The
'ontology' is jus t another nam e for mat hema tics - or. 10 be more criterion for the kind o f m ult iple imp lied in me ind isce rnible is cons titu ted
'mathem atics' is the name o f ontology as a language situation. I by the places mark ed out in a d iscerning expression. Since eve ry effective
evade the p lace where d isgra ce dw ells. Wh at we have here is 3 sub cractioD expression in a language situa tion is fini te, me mu ltiple of th e ind iscernib le is
onto logy as a whole from ph ilosophy, which is now simp ly the 1 necessarily finit e. The gene ric, on the con tra ry, requ ires the infini te.
situation in which tru ths - in the p lurality of th eir procedures - Th us the gam ma d iagram supe rimposes the logical figur es of sub trac tion
pronounceable as T ruth - in the singu lari ty of its inscri pti on. onto an Ont ological d istribu tion . T h ere is a quadripa rt ite d istribution of th e
But let 's return to th e gam ma diagram . one-more, the one-less, the finite, and th e infinite. A tr u th circulates within
It represent s th e trajectory of a tru th , regardle ss o f it s type . I mai ntain this eXhaustive qu ad ripartite Structu re, whi ch accoun ts for th e ways in whic h
there arc fou r types of truth: scientific, arti stic, political, and amo rous. being is given. S imilarly, the trajectory of a truth is traced by the comp lete
d iagram is p hilosophical in that it rend er s the four typ es o f truth cornpcssi logic of SUbtraction.
throug h a formal concep t of T ru th . Let us now follow this tra jectory.
Not ice how the four figures of su btraction arc distribu ted accord ing to In order for the process of a tr uth to begin, something must happen . As
regis ter o f p ure m ultip licity. T his also designa tes the latent being of ~\allarrnc wou ld PUI it, it is necessar y [hal we be no t in a p redicamen t where
acts. l10thing takes p lace bu t th e place. For the place as such (or structu re) gives
T he undecidable and the un nameable are coupled by their CO u~ Only repe tition, alo ng with the knowledg e whic h is known o r unknown
presupposi tion o f the one; a sing le statem en t in the case of the und eci " tthin It' , a know ledge th at always remains. 10. th e fini
tut u d e 0 f 'ItS ,ee, mg.
' I ca 11
112 Fheoreucal Wntings O n Subtraction 113

th e advent, the pure supp lement , the un foreseeable and disco n . free from any presu ppo sition othe r th an that of havin g to choo se, in
add ition: 'eve nt'. It is, to quote the po et once morc, that which is " chOice. absence (J r any dlsri
rsnn gu .rshi109 ma r k rn
· t h e present cd terms, t h e one
from th e cro up and th e f1 igh l' .6 A truth ari ses in its novelty - and every ,h< gh which the verification of th e conseq uences of the axiom will firs t
throu
is a novelty - becau se a hazardous supplement interru pts repetition.
['QCeed, . . .
tinct, a truth begins by surg ing forth. P Th is situation has freq uen tly been register ed 10 phi losophy, un der th e
But fro m the outset , th is su rging for th provid es th e basis for th e un 'freedom of indiffere nce ' . T his is a free dom that is not go verned by
able. Fo r the norm of evaluation tha i gove rn s the situ ation, or s :~:oticeablc difference, n freedom tha t faces up to th e ind iscerni ble. If
canno t be applied to th e statem ent ' th is event belongs to the situa tion' . lh~re is no value by wh ich to discrimina te wh at you have to choos e, it is you r
such a statemen t to be d ecida ble, th en clearly th e event wou ld al readJ freedom as such wh ich provides the norm, to th e po int whe re it effec tively
subjec t to the norm s of repetit ion, and cons equ ently wou ld not be becomes ind istingu ishab le from chance. T he indiscernib le is the sub tr action
Ever y stateme nt im plying the nam in g of the eve nt harbours an in that establi she s a poi nt of co incidence betwee n chance and freed om .
un decida b ility , And no assessment , 110 exh ibition, ca n com pensate for Descartes will make of thi s coincid ence God's p rerogative. H e even goe s so
insu fficienc y of th e norm . For hardl y has th e event surged form th an it far as to claim that , given th e axiom of d ivin e freedo m, th e choice of 4 rather
alrea dy d isappeared . It is noth ing but th e flash of a supp lem enta tion. than 5 as the ans wer to the sum 2 + 2 is th e cho ice be tween tw o ind isccrn -
empir ical ch aracte r is th at of an eclipse . T hat is why it will always be ibles. In this ins tance, the norm of ad dition is th at from wh ich God is axio-
sary to say that it too k p lace, th at it was given in the situ ation, and matically sub tracted . It is h is pu re choic e that will retroact ively constitute
un verifiab le statemen t, su btrac ted fr om the norm of evaluation , consti me norm, whi ch is to say act ively verify it or tu rn it into truth.
supp lem entatio n vis-a-v is th e realm of wh at language deci des: it is well Putting G od aside, I will ma intain that it is the ind iscernible th at co-
truly in this one- more th at undecidabili ty is pla yed out . ordinates the su bject as p ur e pw/ cw m in the process of ve rification. A su bject
A truth's first step is to wager on th is supplem ent. On e decides to is that which d isap pea rs bet ween two in dlscernibles, or that whic h is eclipse d
th e sta teme n t ' me event has taken place', wh ich co mes down to d ecidU. through the sub tract ion of a d iffere n ce without concept . This subject is that
undecidabl e. But of co urse, since the undecidable is su btracted from throw of the dice whi ch does not abolish chance b ut effectu ates it as verifica -
norm of evaluation , thi s d ecision is an axiom. It has no basis other thaD tion of the axio m that grou nd s it. W hat was d ecided at the po in t of the un de-
presuppo sed van ish ing of th e event. T hu s every tru th passes th roup cidable event will proceed th ro ugh this term, in wh ich the local ac t of a tru th
pure wager on what ha s being only in di sappearing. T he axiom of t:ndIl is represent ed _ witho ut reason or ma rked d iffer ence, and indi scern ib le fro m
wh ich always takes the fo rm 'this took place, wh ich I can neither its other. The subject, fragment of chance, crosses the di stance-less gap that
nor demonstrate ' - is sim ply the affirmat ive obverse of the su btr act ion of the subtraction of th e indisce rni b le in scri bes between two te rms. In this
undecidab le. regard the sub ject of a truth is in effect ge n uinely in -diffe rent: the ind iffer en t
It is in me wake o f th is su btraction that the infin ite procedure of veri 1o\·cr.1
th e true begi ns. It cons ists in exam in ing with in th e situation th e . Clearly, th e act of the subject is esse n tially finit e, as is th e pr esentati on of
qu cnces of th e ax iom . But this exam ination itself is not guided by any ~ ~discernibJcs in its bei ng. Neverthe less , the ve rifying trajecto ry goes on ,
lish ed law . Nothin g governs its trajecto ry, because th e ax iom that suppOrU mVCsting the Situation th rough success ive indiffere nces. L in le by litt le, what
has dec ided indepen dently of an y appea l to the no rm s of evaluation . T hLd takes shape behind these act s begins to d elinea te the contour o f a su bse t of
is a hazardou s tr ajecto ry, one without a concept. T he successi ve choices \~ Situat ion - or of the univ er se whe re in the cvcm al axiom verifies its
make up th e verification are devoid of any aim th at would be represen table e ~C(s This su bset IS clea rly infinite and remains beyond th e reach of
the object or sup port ed b y a princip le o f objectivi ty. ~rnpleti()n. Nevertheless, it is pos sible to sta te th at if it is co m ple ted, it will
But what is a pure cho ice, a choice witho ut a conce pt? O bviously, it it lOelUct b!
F a y be a generic subset.
cho ice fac ed with two ind iscernib le terms. If th ere is no exp ression to di u . Or hQW co u ld a series of pure cho ices enge nde r a subse t that co uld be
two te rms in a situation , one ma y be certain that m e choice wh er eby th e v o; lfie d by means of a p redicate ? T his could only be th e case if the trajectory
ficauon proceed s th rou gh one term rather th an the othe r has no basis in th a trUth was secretly gove rned by a concept or if the in discerniblcs whe rein
objective d ifference. be twee n them , It is th en a question of an absol ute ly e ~Ubject is di ssipated in its act wer e actu ally disce rned by a superio r in tel-
114 Theoret ical Wr itings On Scbtracnon 115

leer. This is wha t L cibniz though t, for whom the impossibi lity of i is followed by the h ypo thesis, wh ich fictivel y maintains a U nive rse
iblcs was a conseq uence of God 's computational intellect . But if there e\·eo~~lllcntcd by thi s gene ric su bset whose finite , loca l delineations arc
God to com p ute the situation, if the indiscernibles are genui nely i 5IJPP rrcd by the subjec t th rough the tr ial of the ind iscerni ble .
ible, the tr ajecto ry of truth cannot coinci de in the infinite with any SIJ~:at is it that obstructs such a hypoth esis? What limi ts the generic pow er
whatsoever. An d as a result, the verifi ed term s com pose - or rather. it f a truth proje cted through the fictio n of its com p letion, and hence of its
sup poses th eir infinite totalization, will haw com pose d - a generic s o , g wholly~said? I ma int ain that th is obstacle is no ne other than the
th e un iver se. Ind iscern ible in its act or as su bject, a truth is gene ric:
resu lt or being. II is sub tr acted from every recollection of the mult iple
"''lJonamcablc.
"
The anti cipal ing h ypothesis as to the gen eric being of a truth is obvio usly a
one of a designati on . !(Jrci'll of the sca rcel y ~ said . T h is forcing enacts th e fict ion of an all- saying from
Thus there arc two reason s, and no t just one , for maintaining that a the vantage of all infin ite and generic truth . But then there is a great tem ptation
is scarcel y-said . to exert this forcing on th e most inti mat e, most subtracted point of the situa-
T he first is that, since it is infinite in its bein g, a truth can be r cion, and to tr y to force th at which testifies to the situation's singu larity, tha t
on ly in the futu re perfect. It will h ave taken place as gene ric in fini which docs not even have a pr ope r nam e, the proper of the proper, wh ich is
taking-place, which is also its localized relapse into knowledge, is given anonymous bu t for whi ch 'anon ymous' is not even the adeq ua te name.
finit e act of a subject. There is an incomm ensu rabilit y be tween th e Let us say thai forcing, whi ch represents the infinitely gene ric character of
its act an d the infin ity of its being. T h is incommen su rabili ty is allO truth in the future perfect, encou nters its radi cal limit in the poss ibility that
relates th e verifying exposition of th e cven ral axiom to th e infinite b iu power of al l-saying in truth will result in a truth ult imately giving its own
of its com ple tion. or w hat relates th e indiscernible subtract ion, which name 10 the unn ameable.
the subject, to the gen eric subtraction , wherein is anticipated the The constraint thai the infinite, or th e sub tractive excess of the gener ic,
the su bjec t is a subjec t of, This is th e relation be tween th e almos t exerts on the weakne ss of th e one at the point of th e un nameable, may gi ve
the finit e, and me almost everythi ng , the infinite . Whe nce the fact that rise to the desire to nam e th e unname abl e, to app ropriate the pr op er of th e
truth is scarcely-said, since what is said about it is always tied to tile proper th rough naming.
order of verification. BUI it is in th is very desire. whi ch every tr u th pu ts on the agenda, tha t I
The second reason is intrinsic. Si nce a truth is a gen eric su bset perceive the figu re of evil as such. T o force a nam in g of the unnamea ble is to
un iverse, it docs not let itself be summarized by any predicate, il deny singularity as such; it is th e moment in which , in the name of a truth's
const ru cted by an y exp ression . T his is the n ub o f me matt er : there infinitely generic character, th e resistance of what is absolutely sin gular in
exp ression for truth. W hence the fact that it is sca rcely-said, since ul . $ingularity, of that sha re of being of the p roper wh ich is sub tracted from
the im po ssibility o f cons tr uc ting tr uth by mean s of an expression
down to the fact that what we k" ow of tru th is only know ledge - tha i
'"
. mlllg, appea rs as an obstacle to the depl oym ent of a truth seeking to ens ure
11$ dominion over the situa tion. The imperi alism of a truth - its worst desire

always finite , is arranged in the background of pure choices. - COnsists in invoking generic subtraction in order to force the sub tract ion of
The fact that a tr uth is sca rce ly-s aid articulates the relation betwcell the unnameabl e, so that it may van ish in th e ligh t of na ming .
ind isce rn ib le and the generic , wh ich is governed by an und ecidable axiOdL t We will call this a d isaster . Evil is the di saste r of a tr u th whe n th e desire to
Nevertheless, th e generic or subtractive pow er o f a truth can be solici orce the nami ng of the unnamea ble is un leashed in fict ion .
as such . The generic being of a tru th is never p resented, but we can I:
de is c~mmonly held that evil is the nega tio n of what is pr esent and th e
forma lly, that a truth will always have taken pla ce as a generic . li/,J 3101 what is affirme d , that il is murder and dea th , th at it is opposed to
Wh ence the possibility of a fictive d isposit ion of the effects of its ha a~~ I \o':O\II (j say instead that it is the d enial of a subtr ac tion . It is no t self-
taken-place . From the vanta ge poi n t of the subject , it is always poss iblf ~ matlon that evil affects, but rather always that wh ich is with d rawn and
hypothesize a uni verse wherein the Truth throu gh wh ich the su bject is Ih onYmous to the weakn ess of the on e. Ev il is not d isre spect for the name of
nncd will have com p leted its generic tota lizat ion. Wh at would th e
c other b h ' ,
" , Ut rat cr the will to name a t (m y pri ce.
q uenccs o f such a hypothesis be for th e un iver se in wh ich truth p I:tlu' 1.0tCQvc, ' H
' 'IS a Iso commo n 1y 1tc Id t b at tVI'I 'IS mendacit
" y, Ignora nce,
infinitely? T hu s the axiom , which decide s the undecidable on the basis rdctous Stup idit y. Bu t, alas, evil has the process of a tr uth as its rad ical
116 Theoret ical Writ ings On Subtract ion 117

condition. There is evil only in so far as there is an axiom of truth It ifv that this land d id not exist. But it docs ex ist , an d th is is wh at wears
po in t o f the undec idable, a tra jectory of truth at the poi nt of th e in . 1~t1 ~tJl." aut ho ritarian truth , for wh ich only what has bee n named th ro ugh
ible, an anticipation of th e being of truth at th e poi nt of the generic . ltOlI !bIn pow('t of th e gene ric ex ists. This erosion m ust be sus tained b y safe-
forc ing in tru th o f a nam ing at th e poi n t of th e unnam eable. die rding the pro pe r and th e nameless. L et us co nclude then by read ing
If th e forcin g of the un nam eab le su btract ion is a d isaster , it is "" 1 e·s poe m, whe re in eve rything I have sa id is dazz lingly ren dered :
,\ 1:u a "
affects th e situ ation as a whole by p ursuing withi n it singularity as 5
which the un nam eable is the emblem . In th is sense , th e d esire in L'ir t J"allloJriti SL trouble
supp ress the founh subtrac tive opera tion un leashes a capacity for des /-orsqllC, JOIlS rllli mot if, 0 11 dir
latent in every truth, in rhc p recise sense in wh ich M allarmc co uld write IN u midi que notre double
' Des truct ion was my Beatrice'." 1/Il;om ciell Ci: approjondir
Accordingly. the ethi cs of a truth co nsists entirely in exercising a
restrain t with regard to its powers. It is im po rta n t that the com b ined Que, sol de cent iris, SOli site
of th e un decidable, the ind iscerni b le. and the generic - or of th e eve:ac. l is savmt s'il a bien iri
su bject, and truth - sho uld ackn owledge as th e fundamental lim it N t pone pas de 110 m que d ie
trajec tory that un nameable whi ch Samuel Beckett chose as th e title for l/or de fa trompet te d'et' .
h is boo ks.
Samuel Becket! was ce rtain ly not un aware of the h idden ravages . Th e age of aurhoriry wears thi n
on th e sub traction of th e proper by the d esire for tru th . H e even saw in When, with out reason , it is stated
inel ucta ble violence of th ough t, when he has his U nna ma ble say this: '( Of this sou thl and which ou r twin
think . .. once a certain de gree of terror has bee n exceeded." But be' Unconsciousne ss has pe netrated
knew that the u ltima te guara ntee fo r the pos sibility o f a peace among
is roo ted in th e reserve o f non-sayin g; in th e lim it of th e voice vis-i -viI Tha t, soil of a h und red irises , its site,
which shows itse lf; in th at which is su btracted fro m th e absolute i Th e}' know if it was rea lly born :
to speak th e truth . This is also what he intended whe n in MoIJ,q It bears no nam e th at one cou ld cite,
reminded us th at '(tJo restore silence is the role o f objects, lO and Sounded by summer's gold en ho m . I :!
How Ir Is he congra tu lates himself on th e fact that 'the voice
o rdered I quot e that of our to tal life it states on ly three q uarters'. I I
Su b tra ctin g lies at the sou rce of eve ry truth. Bu t sub traction is also
in th e guise of th e unnameable, govern s an d sets a lim it to th e su
trajecto ry . There is on ly one m axim in th e eth ics of a truth; do not su
th e last su bt raction .
Wh ich is someth in g that Malle rm e, with whom I wish to concl ude,
with custo mary pre cision in his ' Prose (for d es Esseim es)' .
T her e is always the d an ger th at a tru th - however erran t and inco m pletl
may be - takes itse lf', in the wo rds of the poet , for an 'age of au thority'.
th en wan ts eve ry th ing to be tr ium phantly named in the Su m me r of r
no n . Bu t th e heart o f w hat is, th e 'so uthland ' (mid ,) o f our unconscio
of bei ng, docs not an d mu st not have a nam e. The site of th e true, whidt
subtracrivcly con stru cted - or, as th e poe t p uts it el sew here, the flower
co nto u r o f absence has separa ted from every garden - itself remai ns, ill
in timate d epth, su btracted from th e proper name . T he sky and th e
 CHAPTER 10

Trut h: Forcingand the Unnam eable'

When a ph ilosop her ma kes a claim about truth, is it not natura l - 'na tura l' in
a sense which ety mo logy uph old s th ro ugh tho roughgoing artifice - for him to
do 50 from th e bias of h is love? D oubtless , th e Platon ic ges ture - regist ered ,
acclaimed, then revi led throu gh th e cen turies - persists in d isce rn ing a
connotation of superior inte nsi ty in th e wise friend sh ip of philosaphia; es pe-
cially when it is in the shelte r of wisdom tha t we d iscov er tru th's enigm a
and, u a resu lt, at th e heart of sere ne fri endship that we encounter th e
r IClDptSt of love . As Lacan demonstrated in his stra nge app ro pria tion of a real
S)'fff/'Osium , it is th rou gh this transference (in eve ry sense of the word ) that
philosophy is ab le 10 proclaim itse lf ' love of tru th ',
Thus whe n Lacan insists th at the position of the psych oanalyst sure ly does
nol consist in loving tru th, the re can be no doub t thai he is m aintaini ng the
Stance he end ed up descri b ing as th at of an 'a m i-ph iloso p hy',
Yet in doing so, Lacan clea rly appoints himself educator for eve ry phi lo-
SOphy 10 com e. In m y view . only th os e wh o have had the co urage 10 work
through Laca n's anti- philosophy wit hou t faltering dese rv e to be ca lled
'contemporary phi loso phers'. There are nOI many of them, But il is as a
contempora ry philosopher tha t I will h ere endeavou r 10 elucidate what I
dec: lare to be a retu rn of tru th . Lei's say that I'm speaking h ere as a
PbJIosoPher~subjcct su ppos ed to know anti -philosophy'[ - and hence as a lover
OC truth supposed to know what little faith can be afforded to th e protestations
lnadein th e nam e of such a lo ve.
T:;an deli neates h is concept o f th e love of truth in the sem inar entitled
td. , R~tru of PSj'chocmaly sis, whic h has recent ly been publish ed in an
lt lOn I sh,] ] ·
that ' sim p ]y tak c as 11
. IS,
. W II. h Out en ten.ng .Into t h e controversies
.
I Invariab ly attend the in scription of the living w ord in to th e d ead tener.'
morn ,this sem inar. Le can m akes the radical claim th at since truth is pri-
lht dian,·
10 , k·Ind 0 f po wer ]essness or weakness; .If th ere IS . .
such a thing as
!hi " C of tru th, il can only be the love o f th is powerlessn ess, th e love of
Nt . . .eakness . It 's worth no tin g tha t in this claim L acan for once echoes
e~ll(;he, for wh om tru th is in a cert ai n reg ard th e im potent form of
 120 Theoretical Writings Truth: Forcingand the Unnameable 121

pow er , or th e nam e that th e powerle ss give to power in i he disj unc tion between transcen dence an d im ma nence. T ruth is not of
il. 1. the order of someth ing which stand s above the givcnness of ex perience; it
But Lacan immediately distances himself from th e D ionysian roeceds or in sists within experien ce as a singu lar figure of immanence.
For Laca n, th e weakn ess wh erein tru th d wells is not roo ted in reY~
,. ~c disjunction betwee n th e p red icab le and th e non -predicable. There
resentm ent . T hat which affects tru th with an insu rmo untable restri ctioa, existS no single p redicarive tra it capa ble of subsum ing an d tot alizing th e
obviously enough, castration . T ru th is th e veil th row n o ver th e im poQj componen ts of a truth . T h is is why we will say that a tru th is nondescrip t
of saying it all, of sa yin g all o f truth. It is both wha t ca n on ly be half: or generic.
and what d isgu ises thi s acu te powerlessness th at rest rict s the access to
- in an act of p retence, whereby it transforms itself in to a total .
,. Th e disjunction between the infinite and th e finit e. Co nce ived in its
being, as someth ing that can not be co m pleted , a tru th is an infinite mu lt i-
itself. T ru th is the' mask of irs own weakness. In which regard Lac.n plicity.
echoes H eidcggcr, fo r whom tru th is the VCI)' veili ng o f being in its .t. The disjunction between th e nameable and th e unnameable. A tru th 's
d rawa!. Except that Lacan d ist ances himself com p letely fro m th e patboe capacity for di ssem inating itse lf into judgem en ts with in th e field of
which H c:idegg er characterizes the becom ing- dis tress of me veil aDd knOwledge is b locked by an unnameable point , whose nam e is forced only
fo rgetting. For castration is stru ctural, it is srrucrure itse lf, so th at for at the cost of d isaster .
there can be no place for th e p ri mord ially un castrered, whi ch is whal lbe
Socratic th in kers and poets u ltimately are for H eldegg er . Th us a tru th find s itself qu adruply subtracted from the exposition of its
' 'Uhat th en, for Lacan, is th e love of truth, given this authoritative I being. It is neither a suprtm um. visib le in the glare of its self-s u fficiency, nor
struct u re? We mu st not shy awa y fro m the consequences: it is purdy r that which is circumscri bed by a p redica te of knowl ed ge, no r tha t whi ch
sim ply the low of castra tion. subsists in th e fami liarity of its finitude, nor that whose erudite fecund ity is
'X' e are so accu stomed to thinking of castra tion in term s of horror blessed with bound less po wer.
are as to nished to bear La can d iscussing it in terms of love. Neve To love truth is not only to love castration, but to love th e figures in wh ich
Lacan does not hesit at e. In the sem inar dat ed 14 Jan uary 1970 we read: its horror is d rawn and qua rte red : im ma nen ce , th e ge neric, the in finite, and
the unnameable.
The love of truth is th e love of th at weakness whose veil we have Let us cons ider the m one by one .
it is the love of Uta! wh ich is hid den by truth, and whi ch is called Tha t tru th , or at lea st Ofl r truth, is pu rely immanent was one of F reud's
do n." lUnplest yet mo st fun dam ental insigh ts . Freud was un co m prom ising in his
dcfttlcc of th is princi ple, especially against j ung. It wou ld be no exaggera tion
T hu s, un d er the guise of Ute love we bear towar d it , tru th affec ts cas ~o say th at one of Lucan 's p rima ry mot ivations was to mobilize thi s F reud ian
with a veil ing . Casrrauon thereby manifests itself stripped of the horror tnsight against th e scicn ristic and moralisti c objectivism of th e Chi cago
SChOOl.
it inspires as a p ure structural effect.
The phi losopher w ill refo rmulate th e mat te r as follows: tru th is d I. ..... ill use th e word 's itu ation' - the most anodyne wo rd imaginable - to
for th ough t, wh ich is to say, philosop hicall y lovable, only in so far a'
au cmprs 10 grasp it in what drives its subtraaiue d im ension, as opposed ". "hlgnate th e mu lti ple made up of circumstances, language, an d object s,
. SOme tr uth can be said to o perate. ' 'V'e will say that this operation is
rein
the
see king its plenitud e or com p lete saying . ;" , situation, and is neither its end, nor its norm, nor its destin y. S imi -
I r y th
So let us try to weigh tr uth in th e scales of its po wer and its powerles lh ' e experience of the an alyst dearly shows that a tru th works throu gh
its process and its lim it, its affirmative infini ty an d its essen tial subiracti irs:lSUbject - esp eciall y th rough h is sufferin g - in me situation of an alysis
eve n if this weighing , an d th e concom itan t desire to att ain a precise m ~ f. .T rUth comes in to being wit hin this situation th rough the success ive
of tru th 's indi spensable math emat ica l co nnection (not to mention , L Tallons that ma ke u p th e an alysis. M oreo ver, it is II m istake to th ink th at
"Ie e .
dem ands of brev ity), entails approximation. ill lh XIStencc of th is truth consuuncs a p re-g iven norm for what is obse rved
I shall co ns truct th e sc ales for th is weigh ing of tru th by m eans of a q thou e ~a lysis, or that it is a maucr o f di scovering or revealing the tr uth , as
ru p lc di sjunction : gh It Were some secret en tity buried , so to speak, in me deep exteric rity
122 Theoretical Wntlngs Truth: ForCingand the Unnameable 123

o f th e situation. T he whole poi nt is that ther e is no d epth, an d depth is • n the anal ysand is provided with th e painful oppon uni ty for encoun-
1'.j\ efC1
an oth er nam e - treasu red by th e he rm eneu ts - fo r transcend ence. . a truth, for crDssing a tru th along hi s pa th. H e em erges from th is
Wher e docs a truth co me from men, if its proces s is strictly irnmaneot ten;~nter either armed or disarm ed . Perhaps th is approach sheds some light
if it is not given as the secret dep th or inti mate essence of th e situation? : the mysteries o f what Lacan, no doubt th inking of th e real as im passe.
can it ad van ce wi thi n the situatio n if it has not alway s already been . lied 'the pass' .
withi n il? La can 's geniu s lay in seeing that. as with Co lum bus', til. csBut we now find ourse lves preci sely in th e domain of th e im passe. I said
answer is already contained in th e question . If a truth carmo r originate that a truth comes in to be ing at th e end of its p rocess only as a subset of th e
its being given, it mu st be because it has its origin in a di sappearance . I sitU3 tion.seL Yet th e situation regist ers an y n um be r of su bse ts. In d eed , this
'event' this originary di sap pearance supp lemen ting the situation for fO\'idcs The bro ad est po ssib le d efini tion of knowl ed ge: to name subs ets of
duration of a lightning flash; situated within it only in so far as nomine ~c situation . The fun cti on of the language of th e situa tion co ns ists in ga th -
subsists; and in sisting in truth precise ly in so far as it ca nnot be ~"'''d ering togeth er the clem ents of the situ ation acco rding to one or other predica -
presence. Obviously, th e event is the philosophical ana logue of (for ri ve trait , the re by cons titu ting th e extens ional co rre late for a con cept. A
what Freud called the primal scene. But since th e latter is endowed willa. subset - s uch as those of cats o r dogs in a perceptu al situation, o r o f hyster-
force of truth only through its abolition, and has no place oth er tba icaJ or obsessive traits and sym p toms in an analytical situation - is ca ptured
di sappea rance o f the havin g-ta ken - pl ace. it would be futile to ask, utiDI through concepts of th e language on th e basis of indi ces of recognition attri -
reali st ca tegories pro per to the situatio n . wh ether it is accurate or butable to all the term s or elem en ts that fall under thi s co nce pt. I call this
represents a fiction . This q uestion remain s gen u inely undecida ble, ill ("WDttptual and nominal swarm ing of forms of kn owled ge, th e ency clopedia
logical sense. Except that th e effect of truth cons ists in retroactively of the situ ation . The ency clope d ia is wha t class ifies subs ets. But it is also the
datin g th e fact that at th e po int of this undecidable th er e was th e di polymorphous in terweavi ng o f forms of knowledg e th at langu age co ntin ually
ance - acutely real and henceforth immanent to the situation - not elicits.
th e undecidable, bur of th e very questi on o f the undecida b le. Yet if a tru th is m erely a su bset of th e situation , how d ocs it distinguish
Su ch is the first sub tractive d ime ns ion of truth, whose im mane nce iuelf from a rubri c of know ledge ? T hi s q uestion is ph ilosoph icall y crucial. It
upon the un decidab ility of what that im ma nence retraces. is a matter of knowi ng whether the price of immanen ce ma y no t be purely
Wh at then is a truth th e [ruth of? There ca n be tru th only of the Ii and simply th e reduction of tru th to kn ow led ge; in o ther words, a d ecisive
whe rei n truth insists, because nothing transcenden t to the situ ation i. concession to all th e va riants of positivism. M ore profoundly, the q uestion is
to us. Truth is not a gua ran to r for th e appreh en sion of so mething whether immanen ce may not entail some son of neocl assica l regres sion that
dent to th e situ atio n. Sin ce a situation, grasped in its pure bei ng, is only "''OUld forsake the impet us given by Kan t, an d later retrieved by Heid egger,
a pa rticular m ul tiple, th is m ean s that a truth is only ever a sub- raul . to the crucial di sti nc tion bet ween truth and kn owled ge, wh ich is also th e
th at multi p le, a subse t of the set nam ed 's itua tio n'. Such is th e rigour ~ distinction between thou ght and cogn itio n. Simplifying somewha t, this
ont ological req uirement of immanen ce. Because a truth proc eeds wi neoclassical version of imma nence would basically end up cla im ing th at once
situatio n, what it bea rs witnes s to does not in an y way exc ee d th e si you have d iagnosed an ana lysan d's case, which is to say, recogn ized h im as
W e co uld say a truth is included in that which it is th e truth of. hYsterical or obsess ive or pho bic; once yo u have es tablishe d th e predicanve
L et me open a cautionary par enthesis at th is stage. Cautionary beCI trait inscr ibi ng h im in the ency cloped ia of the ana lytica l situ ation, th e real
have to ad mit that I am not , nor have ev er been , nor will probably ever Work has been done. It is then on ly a matter o f drawing consequences.
either an an alyst or an an alysand, or even a psych oanal yti c pat ient. I am
unanal yscd . Ca n the un analysed say so meth ing about an alysis? You will " Ilccause of the way in wh ich he env isaged his fidel ity to F reu d , La can care-
r1.cally rci ectcc th is nosol ogical vision of the ana lyt ical situation. T o th at
be the jud ge of th at. It seems to m e from what I have sai d so far :d, he took up the modern notion of a non-con ceptual ga p bet ween tru th
truth is at sta ke in an alysis. it is not so mu ch a truth of th e subject as a ond fonns of knowledge and p roject ed it onto the field of psychoa na lysis . N ot
of the ana lytical situation as such ; a tru th which, no doub t, th e anal I Iy did he di sti nguish between truth and knowledge, h e also showed that a
will hencefo rth have to cope wi th, but which it would be one-sided ~ sssemially unknown ; that it q ui te litera lly con stitut es a hDle in fo rm s
d escribe as be longi ng to h im or he r alon e. An alysis see ms to me a si ·Iedge.
 124 Tbecrencal Wnllngs Truth: ForCIng and the Llnnameable 125

In doing so - and this is in my opinion a point whose consequetlcta

As ..,
l~ ~
so often the case, m athematics bolsters Lacan's insigh t. At th e beg in -
yet to be fully grasped - Lacan declared that psychoanalysis was not. . of the 19605, the mathematician Paul Co he n showed how, for a given
of knowledge but a way of thinking. I c to 1ld enuify su b sets 0 f It
rungit was poSS ·bl ' posscssmg
' aII ·me Ch aracte nstrcs
"
L

Yet des pi te th e claims of th ose who would like to effect a theo ¢ dined
' ' abo ve. Co hen ca lls a subset that ha s been subtra cted from every
recu perati on of psychoan alysis - and they are indefatigable, rather aU rmination in term s of a fixed expression of th e langua ge a ge"eric subset.
someone who has figured O U t how to rum p ig- feed int o 3 communi on ~oerco\"l:r,
, he uses a demonstra tive p rocedure to pro ve th at th e h ypothes is
. ..
an d who like 10 ind ulge in del ectable speculatio ns about the rranscen...... dull generic su bsets e xis t IS co asrsrem .
the Big Other. Lacan h imself, on the who le, refused any co mp rom ise T went y yea rs earl ier, GOdei had p rovided a rigoro us definition for th e idea
the immanence of tr uth. of a subset named in knowledge. T hese are su bsets whose elemen ts validate a
He thereby had to fo rce OUf impasse and establish that, aI jixtd expression of the language. GOOd h ad ca lled the se cons tructible su bsets.
reducibl e to a dcpthless su bse t of th e situation, a truth of the si But Cohen ·s generic subsets are non-con structible. They are tOO ind et ermi-
none the less heterogeneous 10 all those subsets registered by forms 0( l\:iIte to corr espo nd to, o r be tot alized by, a single pre dicative exp ression.
ledge. Th ere can be no do ubt th at th e op pos ition between co ns tructible sets and
Th is is the funda mental meani ng o f the maxim conc ern ing 'half- generic sets p ro vid es a purely immanent ontological basis for the oppos ition
That a truth canner be entirely said means tha t its all, the subset between knowledg e and tru th. In th is regar d , Co hen's demonstration th at
co ns titutes with in th e situ ation, cannot be captu red by means of a p me existence of generic subsets is cons isten t am ou nts to a genuinel y m oder n
tra it th at wou ld turn it into a subsection o f the en cyclopedia. The r proof that tru th s can exist an d that the y are irred uci ble to an y ency clopedic
stake in the ana lysis o f such and such a woman cannot be assimi lated datum whatsoever , Co hen 's theorem mobilizes th e ontological radicaliry of
fact that she is, as th ey say, a hysteric. Ther e is no doubt th at mao,. fIl the math eme to co nsummate th e modernity inaugurated by the K an tian
co m ponents of th e tr u th operating in thi s situ ation possess th e dis . distinction between th ought and knowledge.
tr aits of wh at, in th e register of knowled ge, is ca lled h ysteria. But to .., Th at a truth is ge neric rather tha n co nstructible, as Lacan b rilliantly
not to do any thing ill truth , For the tru th in question necessari ly 0 intuited in h is m ax im about tru th 's half-saying, also impli es that a tr u th is
othe r co m ponents, wh ose traits arc not pertinent as far as the ency infinite - our th ird d isjunction.
conce p t o f hysteria is co ncern ed , and it is only in so far as these: """,,_ Th is point seems to rebut every ph iloso phy o f finitude, in sp ite of th e way
sub tra ct th e set fro m th e predicate of hysteria that a tru th, rather than a Laan inscribed fin itude at th e heart of desire th rough the th esis of the objet
of knowledge, proc eed s in its singularity. Thus how eve r con fid en t the Ptti, Q . The being tha t sustains d esire resides entirely in th is object, wh ich is
ne sts of hysteria and the con sequences d ra wn fro m it m ay be, not 0DlJ' also its cause. And since th e defini ng characteristic of the obj et petit a is th at
they not con sti tu te a sayin g of tr uth , they do not even con stit ute itS it is always a partial obj ect , its fini tude is con stitutive.
say ing, since the fact that they are ascribab le to know ledge entai ls that But the di alect ic of th e finite and the infi ni te is extr eme ly to rtu ous in
w",p/~tely mi ss the dimen sion o f truth. l.acan, and I d are say th e ph ilosopher 's eye here glim pses th e lim it , and
A truth is a subset of m e situa tion but one whose co m ponents cannOfI ~e the rea l, of what ps ychoanalysis is capable when co nceived as a form of
to talized by means of a predicate o f th e language, how ever sop his ticated thinking, which is ind eed how Laca n envisaged it.
predicate . T hu s a truth is an ind isti nct su bse t; so nondescript in th e Wf1 :nat a tru th is infin ite cons titut es an objection to th e ph ilosophica l rurni -
ga th er s toget he r its components th at no tra it share d by thc latter would natIOn on fin itude on ly if th at truth rem ain s imma nent, and hen ce only in so
ar as .
th e subset to be id entified by knowled ge. 'v It touches on th e real . If tr u th is tr an scendent , o r supra-real, it ca n
Obviously, it is because it is incl ud ed withi n th e situ ation in th e fonn t ry ....ell, unde r the namc 'God ' o r some ot her nam e _ such as 'th e Other' _
singu lar indet ermi nacy o f its co nce pt, an d becau se it is su btract ed ffOlll ~sign the entire desti ny o f the subject to finitude.
c1assificarory gra sp o f th e lan guage of the encyclopedia, that such a su ""hosaid that La can sid ed with the im manence o f tru th . But I added : 'on th e
:'I truth of th e situ ation as suc h, an immane n t product ion of irs pu re rnu \Iii I.t '. For, strictly speaking, he observes the constraint of im manence only
being, a truth o f its bei ng qua being - as op posed 10 a kn owledge of !hit ""hthin what co uld be called the primo rdial morivm ion of his thought. Els e-
that regiona l particulari ty of the situation . ere, we en co un ter significan t osci llations , arising from La can 's tendency to
 126 'r beoretc at Writings Truth: FOf"on g and the Unnameable 127

equivocate when it co mes to severing every link with th e her""",,,,... · _ c.g. the h ighly particul ar ti me pro per to ana lysis. What e\'er the
fin itude to whic h. alas. th e ma jorit y of con te m po rary ph iloso phiz ina it ~ll Stc norm gove rning its ext ension , such a time remain s irr em ed iabl y
· lfl !
marely rt..du cible. T oday, thi s herm eneutics of finitud e seems to be ill it1 . And so th e tru th that un folds within it does not attain the co m ple te
tc.
process of rein stalling II pious discourse, II religiosity whose litt le God filu sido n of its infini te bei ng. F reud 's gen ius was to grasp th is poi nt in
seem to constitute the minimum of transcendence compatible witll COmPO guisc of the III " 0 f ana IySIS,
. fin "n c diimensron " w hiICh a1ways 1cav es open, like
de mocratic convivialir y 10 which we arc told there is no longer any thc ing chasm, the truth th at slips into th e tim e inaugurated by analysis.
vable alte rnative. • ~~ nOWseem to find ourselves d ri ven back to cas tra tion. as to that whic h
There is no do u bt that we owe to Lacan, and specifically [0 his . tnI th \.cils. th ereby granti ng us pennission to love it.
insistence on th e d ist inction between th e logic of sense and the logic at For if a tru th re mai ns open onto the in finity of its being, how are we to
the conce pt ual ap para tu s req u ired to expose th e abject ion o f pio us . uge its power? T o say that tru th is half-said is to say tOO little. The
As for democra tic conviviality, we know it was not Lacan's forte. : latiO n bctw~ the finit ude proper to the time of its co m pos ition - a time
tha t it is net even II satisfactory ideal becomes mor e apparent every day f()l.lllded by th e even t of a di sappearan ce - and the infini ty of its be ing is a
we cons ide r those who lay claim 10 his legacy. relation without m easure . It is better to say instead that a tru th is litt le-said,
Nevertheless, the equivoca tion on Lacan's pa n persists. It is thi s or ecen that a tru th is almos t not spoken. Is it then legitim ate to spea k of a
tio n th ai lea ds h im to say in Or W orse ...' - to choose just one povo'cr of the true, a power required in orde r to found the co ncept of its
among man y - that Cante r's non-d en umerable transfinite cardinals C\'mrual powerlessness? In the seminar I quoted at the outset, La can plainly
'an object which J wou ld ha ve to cha racterize as mythic' . I would lUtts that ' it seems to'be am ong th e ana lysts , an d among them in parti cu lar,
th ai it is not possible to proceed very far in drawing th e co nseq uenca lhat, invoking certa in taboo words with which their di scourse is festooned,
infinity of th e true without in sisting th at non-denumerable cardina li one never noti ces what truth - whic h is to say. powerlessn ess - is'. /> I concu r .
not m yt hic. But in order to be nei th er like those festoon ed ana lyst s, nor sim ply jealo us of
T o ad van ce beyon d La can perhaps we must above all p ut our truIC the festooned , we sh all have to thi nk th e powerlessness of a truth. which
ma theme on this particular po int - wh ich is, of co urse , ano ther pruupposes tha t we first be ab le to co nce ive its powe r.
rem aining fai thful to th e mas te r. This entails first and foremost that we I conceive of th is po wer - perhaps alrea dy recognized by Freud in th e
fast to the affirmation , by way of mathemat ical proof, that every a ttgOry of 'working through' - in terms of th e concept of fo rcing, which I
infini te. take directly from Co hen's mathematical wor k. Forcing is the po in t at wh ich
Let us su ppos e th at a tr uth wer e finit e. As a fini te subset of th e si • truth . although inco mplete, autho rize s antici pations o f knowledge
is made up of the term s a" a1' and so on u p to a... where" fixes th e ' concerning not what is bu t what will have been if truth atta ins comp letion.
d imen sion of thi s tru th. In o ther word s, it is a truth com p rising " · Th is anticipatory d ime nsion req uires tha t tru th judgem en ts be form ulated
nents. It imme dia tely follows tha i th ere exis ts a p redi cate ap prop riate to III Ihe futu re perfect . Thus wh ile almos t noth ing can be said about wh at a
su bset, which , since it is inscribed in th e encyclopedia, falls under
pu rview o f knowledge. This is to say th at a finite subset co uld not be
::th is, Wh~ it comes to what happens 0" conditio" thaI that tm tlr will have
, th ere eXIStS a forcing whereby almost everything can be Stated.
It is necessarily co nstru cti ble. Consi de r th e predicate ' id entica l with As a result , a tr u th opera tes thro ugh th e retroaction of an alm ost nothing
and the a .. .
ide nti cal wit h 0 1' ••• or ide n tica l with an·, which is always availab lc ill nnc rparion of an almost everything .
language of a situation. The set made up of th e terms in q uest ion - l.e, ilial'h e crucial poi nt, whi ch Paul Co hen se tt led in the realm of on to logy, i.c. of
term s aJ> a1. and so on up 10 a.. - is exact ly circumscribed b y th is p r . c~el1l:ltics, is th e follow ing; you ce rtain ly can no t straightforwardly name th e
In other wo rds , this pred ica te con str ucts th is subset; it identifies it CUm ents of a generic subset, since th e laner is at once incomplete in its in fin ite
language, th ereby excluding thc possibility o f its be ing generic. idcxa~it ion an d sub tracted from eve ry predicate wh ich wo uld d irectl y
qucn tly, it is not a tru th . QED . ~ II 10 th e languagc. BUI you can maintain that if such and such an
The infin ity of a trulh immediately im p lies that it cannot be corn p Ill<! I unll hove bun in the supposedly com p lete generic subset. then such
Fo r th e su bse t that it co ns titu tes, and which is delineated o n th e basis al llthSUch a statem en t, ra tionally co nnectable to the element in q uestion , is, or
evental disa ppearance, ls co mposed th rough a succes sion th at inau Cr will have been, correct. Co hen d escri bes th is meth od _ a m ethod
 128 Theoretical Writings Truth: Forcmg and the Unnameable 129 ,I
,

constraining th e correctness o f starernents according to em amicipatory cc again, as th e un analysed , I need to sound a note of ca ution here and
bearing Oil the composition of a" infinite get/en", subut- as thai ofjorcirrg. OOrk thai I am not sure if it is ap pro p riate to ca ll th e act of th e analyst an
I say 'correct' or 'co rrectness' because Lacan superimposes the rdP'- !'<Iatio n . I would prefer to ca ll it a forcin g - despite th e word's scan da-
be tween the correct an d the true: onto th e opposi tion between know itll~ aut horitarian ring . For it is always a matter of intervening according to
truth . But it is necessary to see wh y the stateme n t caugh t up in \t)USI) .....nded h ypo thesis ofa truth taki ng its co urse in th e analytica l situation .
tbC sUS,,-
cannot , without serious confusion . be called true. For its value is d do not think it tOO forcefu l to register a hint of dou bt as to th e value of
only according to a co nd ition o f exis tence wh ich pe rtai ns to a generic . I relation in m an y of th e dead master's texts. This should not be too
and h en ce according to a cond ition of truth. It1I~sing wh en one recal ls that all so rts of h erm eneu ts , Steppi ng into th e
I usc th e: term oeridiaat 10 descri be th e value of a ' forced ' SUI s~ open ed up by th e faithful Paul Ricoe ur, have tri ed to make th e term
simu ltaneo usly indi cates the gap as we ll as th e connection with tru th. ~l('rprctation' bear th e bu rd en of the p utative link. between psychoa nalysis
extrapolating from Cohen's math eme [0 what it prescr ibes for the and the revamped forms of p ious di scourse . Le t me be b lunt: I do not
pber, we will say that a truth proceeds in situation, devoid of me bclicv(' analysis co ns ists in interp reta tion . It is ru led by truth , not meanin g.
either to say or to complete itself. In th is sense (rum is abso lutely But it certainly docs nOI co nsist in discooering tru th , since, tru th being
almo st not bei ng wha t it is. Nevertheless, with regard to any given s generic, we know it is vain 1'0 hope that if"'tou ld be uncover ed . The sa le
truth has th e po wer to antici pate the following cond itional judgement: rctJUIining hope is that ana lysis wou ld cons ist in forcing a knowled ge in to
or that component will have figure d in a sup posedly co m p lete truth, truth through th e risky game of anticipation, by mean s o f which a gen eric
statement in q uest ion w ill have bee n either verid ical or erroneoes, truth in the process of comi ng in to being d elivers in fragmentar y fashion a
power of a truth, de ployed in th e d imension of the future perfect, constructible kno wledge.
legi slating about what is verid ically saya b le, in antici pation of its own Having gau ged the power of tru th , m ust we say it exte nds to all th ose
renee. Obviously, what is veridica lly sayable is a matter of knowl~ statemen ts that circu late in th e situ ation in which it opera tes , with out excep-
th e category of the verid ical is a category of knowledge. Conseq tion - even if only on co ndi tio n of th e wager about its co mi ng in to being as a
w iII say that al though a truth is castrated with rega rd to its own . multiple? D oes truth, in spite (an d because) of its generic natu re, possess the
power, it is all-powerful with regard to possible form s of knowledge. POWer of naming all imaginable veridicalities?
of castra tio n does not fall be tween truth and knowledge. It separateS To respond affirmatively wou ld be to di sregard th e return o f cast ra tio n,
from itself, thereby re leasing truth's po wer of hypothetical an ' • aod of the love th at bin ds us to it through truth, in the terminal form o f an
withi n th e encyclopedic field of knowled ge. This powe r is tha t of fo . absolule ccs racte _ a te rm wh ich , although given in th e situation , is radicall y
I maintain that th e analyti cal experience is built on such a basiL subtracted fro m th e grip of veridical evaluation . T he re is a poi nt thai is
which , little by littl e, comes to be aruculated in th e cou rse of analysis • U11forccab1c, so to speak. I call thi s poi nt the unnam eable, wh ile in th e rea lm
on ly th at which weave! th e in terminable infinity of th e true in to. of PJ)'choanal ysis La can ca lled it enjoymen t.
meter ed tim e, bUI also - and es pec ially with regar d 10 the rare in t let us COnside r a situation in wh ich a truth p roceed s as the trace of a
of the analyst - the ant icipatory marking of what it will have been ""soil" vanished event; a siruauo n im manently supp lemen ted by the becom ing of its
say veridically, in so far as this o r th at sign, act, o r sign ifier will have OWn tru th. For a generic tru th is th e paradox o f a pu rel y in ternal an onym ous
sup posed as a compone nt of the truth . We know th at this an tici S\iPP1emeOl, an imma nent add itio n . Wh at is th e real for suc h a configuration?
mark ing depend s upo n th e futu re perfect tense of the cm pirical romp . ltl us rigo rou sly dis ting u ish between being and th e rea l. This d istin ct ion
of analysis, beyo nd wh ich any suppos ition as to tru th 's co m ple tion l~ ~Iread~' ope rative in Lacun's very first sem ina r, since on 30 June 1954 he
impossible, since th c situation has been termi nat ed an d with Ir th e fo ~I.rns th;lt the three fu nd amental passions _ love, ha le and ignora nce - ca n
a possible veridic aliry proper to th e judge men ts abou t that situation- tit inSCribed 'onl y in th e realm o f being, and nOI in th at o f the real' .7 Thus, if
testifies as 10 how an en unciated veridicaluy can be ca lled knowledge. ore 10\'e of tr u th is a passion, th is love is certain ly di rec ted towar d the being
tl'llth b .
knowled ge ill lrwh. As 10 wha t [his knowledge truly is, thi s kno A. r uut It faltc rs upo n encountering its real.
'forced ' by the tr eatm en t, th e analysand is our sole witness , 0 S far as the bei ng of trut h is concern ed, we have already acq ui red its
through a retroaction Ihat ba lances th e anucipaucn of forcing. ~t: il is that of a ge neric multiplicity subtrac ted fro m th e constructions
 130 Theoret ical W r it ings Truth: ForCing and the Unname able 131

of know ledge. T o love tr uth is to love th e ge neric as such and this is . th that wh ich is excluded fro m the po wers of truth? Is to
...io.k ill tru
in all love, we have here someth ing that goes astray. someth ing that _ .
ink It nO.
• also thereby to name it? And how co uld we ever name the
the order of language, so meth ing that is maintained in th e errancy th able?
excess through the power o f th e forcings it permits . ~'s response to this paradoxi cal appeal is never exp licitly spelled o ut.
Nevertheles s, th ere remains th e qu esti on of th e real upon which tbia 1..3 it comes to trans-phallic or seco ndary j ouiswIJu , one sees La can
errancy and the powe r that it founds come ro faher. «Then. to the tri an gle: o f the femini ne, th e infini te an d the unsayable, abou t
rUng
In thi s regard, I would say thai in th e realm determined by a situatioa rcso'ch Ute least that can be sa id is that it seems to hark back to a pre-
the generi c becoming of its tru th , what testifies 10 a real is a single . iu di era That fem in ine enjo yment ties th e infinite to the un sayable, and
f reu Ian .
point - one and on ly one - wh ere the power of truth is cut sho n . stical ecstasy p rovide s evid ence for this, is a th em e I would cha rac-
_
~~ .
co mes to this term, no anticipatory h ypo th esis abo ut th e gen eric su
allow judgement 10 be forced. It is a genuinc:l y u nforceab le term . No
, a radical tcst by the Ideal
. as cult ural. O ne feels that, even in Lacan, it has not yet been subm itted
.
of th e ma themc.
how advanced th e process of tru th , thi s term may never be p<acribool 10perhapS one of the sou rces of Lacan 's diffi culties resides in th e paradox o f
such a way th at it wou ld be cond itioned by this tru th . No matter bow the unnameable, a paradox wh ich I will formu late as follows: if the unnamc-
th e transfcrrna rive resou rces p roper to th e imma nent traci ng of th e abk is uniqu e wit hi n the domain of a tru th, is it not then nameab le p recisely
nam ing is approp riat e for th is term of th e situa tion. That is why on account of th is pro pe rty ? Fo r if wh at is not na med is ulri que, not being
un nameable. Un namea b le shou ld be under stood nOI in terms of th e named functions as its proper name. Ultimat ely, would n 't ' the unnameab le'
resources of knowled ge and th e encyclo pedia, bu t in the precise be the proper name for the real of a situation traversed by its truth?
which it remai ns out of reach for th e veridical antici pat ions f Wouldn't un sayable enjoym en t be th e name for th e real of the subject, once
tru th . It isnot un nameable ' in itself , wh ich wou ld be m,:~~:~
unnameable with rega rd to th e singu lar proce ss of a truth . The
he or she comes to grips with his or her tru th , or with a tru th withi n the
therapeutic situ ation ?
emerges only in me dom ain of truth . But then the unnameable is named in tru th ; it is forced, and truth
This sheds so me ligh t on why, in th e situation o f th e p sychoanalytic: soeesses a genuinely boundles s rese rvoir of power.
menr, wh ich is p recisely on e of the sites wherein one su pposes a uudl Here onc e again , m athematics comes to ou r aid. In 1968 , th e logician
at work, enjoymen t is at once what that tru th d eploys in te rms of the _ Furkhen proved th at the un iqueness of th e unnameab le is no objection to its
what remains forever sub tract ed from the veridical expanse of the existence. Furkhen created a mathematical situatio n in which the resources of
This is because , from the perspective of psychoana lytica l tru th , or the Ihe language, alo ng with its capac ities for naming, are dea rly defined, and in
of me situation of treatment, enj oyment is p recisel y the point of the which there exis ts one term, and one term on ly, which cannot receive a
ab le that co ns titu tes a stum bling block for th e forcings permined b1 name, which means th at it ca nno t be id entified by mean s of an ex pression of
truth. Ihe language.
II is imperative to insist th at th is term is unique. There can no t be Consequemly, in th e regist er of th e matheme, it is pe rfectly cons isten t to
more unna meables for a singu lar tru th . T he La canian maxi m, • maintain tha t one te rm and one term on ly in a give n situation rem ain s
oneness', is here fasten ed to th e irred ucible real, to wha t co uld be called unrorceable for a gener ic tru th . It is thus that , in th e situa tion sup plemen ted
'grain of th e real ' jam m ing th e machin ery of tru th , whose power consitCI by its trut h, the real of that supp lementation is attested to. No m atter how
being th e m ach inery of for cings and hence the m achiner y for p PoWerful a truth is, no matter how capable o f veridicality it p roves to be, th is
finite ve rid icalit ies from the van tage po in t of a truth tha t cannot be a ~wer comes to falter upo n a single term, whi ch at a str oke effects th e sw ing
plished. H ere , the jam m ing effected by the One-rea l is oppos ed to the .tom a\]' JX)\\"erfulness to po werlessness and di splaces o ur love of tru th fro m
Its ap
opened up by vcridicalir y. Peeraoc c, the love of the ge neric, ro its esse nce , th e love of the unna me-
~ble .
T his effe ct o f onenes s in the rea l, elicited by th e power of tru th, consti
tru th 's powerless obve rse. This is signa lled straigh t awa y by th e r NOt that the love of th e ge ne ric is noth in g. By itse lf, it is rad icall y d ist inct
difficulty th at arises when it co mes to thinking thi s effec t. How caP ~Ofn the love of opinions, wh ieh is th e passion o f igno ran ce; or from the
th ink tha t which su btract s itself from every verid ical nam ing? How (:III. lastrous des ire for co m p lete constructibil ity . But th e love of the unnam e-
132 Theoret ical Wri tings Tr uth~ Forci ng and th e Un nameable 133

able lies beyond eve n the ge neric. an d it alone allows the love of truth to th e veridical and to what can not be comp leted; to analysis
W ~h . .
maintained without disaster or dissoluti on coming 10 affect th e veridical 110 'nable all d intermi na b le. O r, as Sam uel Becken p uts II III the fina l word s
entirety . For where tr uth is conce rned, on ly by under going the ordeal lttfl1l k which is not called T ne Unnamable for nothing : ' you must go on, I
powerless ness do we di scover th e ethic req uired for assum ing its 1X'Wer.
of' bOO . ,,,
. go on I Will go on .
The circumstanc es in which we find ourselves in th is autumn of an' '
enjoi n m e to conclude, in an apparently incongruous m anner, with
Ilyich U lyanov , also known as Lenin . whose: statues it is f
nowadays to tear dow n .
Let u s note in pa ssing that, were a La can ian tempted to join in the
those now toppling statues, he or she would do we ll to reflect CIQ.
following paragraph fro m th e semina r dated 20 M arch 1973, which
thus:

Marx and L en in , F re ud and Lacan ar e not co upled in bein g. It i,

letter they fou nd in the Other that, as being s of knowledge, they
two by two, in a supposed Other. 8

T hus the wo uld -be Laca nian toppler of Len in 's statues has to cxplaia
Lacan identified h imse lf as Freud's Le nin .
Let'S add th at. at a time when many ana lysts are worried about
relation to the state, even if only in th e monumental gui se of the:
Revenue and th e Eu ro pean U nio n, th ey wou ld surely do bette r to
Lenin 's wri tings th an those o f the starue- tcpplers - supposing such
exist.
Lenin felt obliged to write: 'Theo ry is all-powerfu l because it is true.'
is not incorrect, since forcing subordi nates to itself in antici patory fitsb.iM
expanse o f th e situation through a po tentially infin ite netw ork of
judgements. But , on ce agai n , th is is on ly to say the half of it. It is
to add : 'Theo ry is powerless, because it is true.' This seco nd half of the
rnem 's co rrectness is sup po rt ed by th e fact that forci ng find s itse lf in
im passe of th e un nameable . But on its own, this seco n d half of COrT
no more capable of Slaving off disas ter th an the firs t.
T hus L eni n seems to ha ve adop ted a relation of love vis-a-vis cas
thai veils the latt er in that h alf of power whi ch it found s. By way of con
it is onl y too appa rent that th e starue-to pplcrs seem 10 have ado Pted
d irect love of pow erlessness wh ich does nothing b ut pave the way for '
no ns de void o f truth .
Is this os cillano n ine vita b le? I don 't think so. U nder the stern guaran tee
[he rnat hcme , we can ad vanc e in to that open expanse wherein th e love
[ruth is rela ted 10 cast ration from the twofold pe rspective of power
powe rlessnes s, of forcing and th e unnam eable. All thar is req ui red of US
 CHAPTER II

Kant's Subtractive Ontology

lfal first sight it appears that Kan t has no on tology, since he seems to declare
the very idea incon sistent , th is is because he is abo ve all the ph ilosoph er o f
relation, of the linkages between ph enom ena, and thi s cons titutive p rimacy of
relation forb ids all access co the being of th e thing as such. Are not Kant's
ftmous catego ries of experience a veritable concep tua l catalogue of every
conceivable kind of relation (inh erence, causa lit y, communi ty, limi tation ,
torality, etc.)? Is it not for Kant a q uestion of sho wing that the u ltim ate ba sis
for the bolmd character of representations cannot be sough t in th e being of
the represented and mu st be su peri mposed upo n it through th e constituting
synthetic power of the tran scendental sub ject? It m ight seem as if th e
Kantian solution to the problem of structu red rep resen tation am ounted to
identifying the p ure inconsisten t mu ltiple (o r bei ng qu a being, in my concep-
tion of ontology) with the ph enomenality of the phenomenon , and the
COUOting-as-one (in my voca bula ry , being qua given or be ing 'in situation')
"ith relation, whic h is itse lf set out on the basis of th e struct u ring acti vity of
the subject. The experience: of th e phenomenal manifold wo uld be rendered
COnsistent through th e powe r of counting-as-one ( i.e . th e uni versa l linkag es)
thaI the sub ject imposes upon experience.
BUI that is not the case . For in one of his most rad ical insi gh ts, Kan t firml y
distinguishes between bj" ditrg ( Vcrbindung), which is syn thes is of the
: ifold of pheno mena. and unity (Ei" heit) , whic h provides th e o riginary
Ih IS for bindi ng as such: ' Bind ing is rep resentation of th e syn the tic un ity of
the manifold. The repr esen tation of thi s un ity can no t th erefore ari se ou t of
r/ binding. O n th e Contrary, it is wha t, by ad d ing itself to the representation
~c mani fold, first makes possible the concep t of the b indi ng."
Tela ~re then it seems tha t, far from being resolved th rough the categories of
.. lion, the prob lem of how the incons istent ma nifold comes to be coun ted-
be"Qnc must ha\'c been d ecided in advance in orde r for relational syn thes is to
tion.~ sibJ e. Kant sees very clearly tha t th e consiste ncy o f muhiple-prcsema-
tl1tU ~s originary, and that th e relation s whereb y phenome na arise ou t of th at
tlPle-p rcsentatio n are me rely derivati ve realities of experie nce . The
136 Theoret ical W rit ings Kants Subtracnve On tology 137

questi on of th e qualitative uni t)' of experience puts re lation in its , ' "l'llthetic judgements arc possible, by whi ch he means those
prl On ~
which is seco ndary . It is first necessary to groun d th e fac t that 110"' a . cknow lcdged bin dings whic h he be lieves to be operative in
presents unifi ed multip licities; only the n is it pos sible to think the '\'erSllJ\y
uti! . mat a hematics or Newto n ian P hvsi ysrcs. AI·LUlOUgh iIt n. as as !Its POint
, 0f
phenomenal rel ati on s. .bUc1idlll ll" in what is probably an erroneo us ana 1ysrs ' 0 f t h e farm 0 f scrcn
sci unc '0

In othe r words, it is necessary to un de rstand th at th e SOurce of the departure the rigour of his proc ed u re lead s hi m to radical cond itions and
entS
experience (the synt hetic un ity of th e mani fold) cannot be th e same II stJ,rent lon . ,~ _ such as those 0 f umry
uni an d biIndim g. B ut ,L inc I'rrruung
.. <Tect 0 f
en
e1I1S .•
the one. The place of th e form er is in th e transcendental system of "'" , of departure ex tends into th e conseq uences, wh ich do not always
the pOInt . . .
T he latt er is nece ssaril y a specia l fun cti on , one wh ich Kant cert ainly deliver the fu ll extent of th eir significance .
to the understa nding, b ut whi ch is al read y p resu pposed in C'ategorial cklIrlY roach the 'there is oneness • 10 . terms 0 f ,meL is biIndimg ental'I S
' th ere IS
tioning' . K ant calls thi s su pre me fu nction of the understanding - the To'napp consequ ences for th e doc trine a f the one. Th ere 15 ' In
' K an t a d "rsunct
antc r of th e genera l uni ty of experience, an d henc e of 'the law of the
'originary apperception ' . If we set aside the subjective conn otatioc
notion of orig inary appe rception, wh ich is co nceived of by Kant as the
:t
certro of me fact th at th e supre me function of th e cou nti ng-as-one is invoked

suppo
bea!use an o riginary con sistency is ul tim at ely req uired in or der to
Y rt the binding acti vity of the categor ies. As a result , thi s 'one' will be
. .
cendent ai unity of self-consciousness'," and focus strictl y on its f conceived only for th e needs of binding, th e co ncept of consistency wil l be
we should have no d ifficu lty recogn izin g in it what I call th e limited to what is req ui red by the intrin sicall y rela tional n ature of the
one, which Kant ap plies [0 rep resentation in genera l, co nceived as • phc:nom enal mani fold , an d the fundamental structure of presentation will be
abst ract siruanon. O rigina ry app ercep tion is th e name for th e subordinated to the illu sory structu re of re presentation . T his trace, which
noth in g can enter into p resentation without havin g bee n submitted • reduces the origina ry p resentation of th e multi p le-as-one to the sta tus of
to the deter mination of its un ity; ' Syn thetic uni t)' o f the manifold necessary condition for the conce ption of representable bindings, resides in
uo ns, as gen erated a priori, is th us the ground of th e iden tity of a !he fact that , in K ant, the one-multiple is limited to the form of th e object.
itself, which precedes a priori all my determi nate tho ught, ,3 WbM: Ultimately, if Kan t is on ly ab le to think th e one -m ult ip le in ter ms of th e
boun dedness po ssible is not the bi nd as such , wh ich , from th is point narrow representa bility of the object, it is because th e movem ent of h is
in-exists , bu t the pu re faculty of bindi ng, whic h is not reducible to discourse subordina tes the qu estion of presen tat ive consistency to the rcsolu -
relation s since only the one can account for it; it is th e o rig inary law lion of the cr itica l problem, which is conceived of as an epistemological
cons iste ncy o f th e m u lti ple , the capaci ty for 'bringin g th e manifold of Problem. Kam ian ontology, which H cidegger characterizes so aptly, labours
representation s un der the uni ty of ap perception'." brneath the shade of its ince p tion in th e pure logic of cognition .
Thus Kant clearl y conceives of th e d istin ction betwee n th e co But the category of me ob ject is not pertinent w hen it comes to designatin g
one as guaran tor of co nsistency and origi na ry structure for all pre...... what exists in so far as me latter mani fest s itsel f in situation as the counted-
and bind ing , whic h characterizes all representable structures, in tennl 0IIt of the pure multiple. O nly from th e per specti ve of b inding does me
gap between p ur e origina ry apperce ption (th e function of un ity) obitet designate the one. T h e object is me aspec t of the ex ist ent th at is rcprc-
syste m of catego ries (th e fun ction o f sy nthetic binding) wit h in the ~table acco rding to th e illusion of the bind . The word 'object' is no mo re
dental activity of the un derst and in g. than an equivocal co mp romise be twee n tWO entire ly separate prcbl cmatics:
But K an t introd uces orig in ary apperception on ly as a p recond itioo ~t of the count ing-as-one of th e inco ns iste nt m u ltiple (the ap pear an ce o f
com p lete so lution 10 the p roblem of rela tion . It is the attemp t to eI l~g), and that of the connected , em pirical cha racter of existe nts, T he
orde r, wh ich is for him th e co rrelate of knowledge, that enjo ins him to lloti
<::a.J
on of Q btlen IS an cqutvocanon,
. . one t h at co rrcspo n d s to t h at a t her rypr- '
the one, \Vh at I mean is th is (wh ich ha s bee n co m pe llin gly indi cated ~Y K.ant ian equivoca tion, whic h ascr ibes bo th the su pre me fun ction of
Heid egger): wha t is always probl ematic in K an t is not so m uch th e Ii ty ~ originarr ap pe rce ption - and th e ca tcgorial fun ct ion of bindin g to the
radica liry of h is concl usions, in whic h regar d he excels in aud acity, but ngle te ' .
% c rm understanding'. . . .
the singu lar narr owness of th e m eans of access to th is radicality . In rru lltt.i n Kant write s that ' the transcendental un uy o f app erception IS that
prob lematic docs not ha ve its origi n in the question of th e po ssibili ~?_ thrOugh whic h all the manifold given in a.n intuit ion is .un it: d in the
p resentation in ge nera l. The primar y q ues tion for him is that of ''''9:'1 of an cbiecr'," he red uces th e one- m uluple to the object III such a
 138 KanIS Subtractrve Ontology 139

way as 10 allow th e same term to also designa te what is bo und in r . h is changeab le, with out fixity or permanence, has as its co rrelate rcpre-
lC
non by th ese bindings. Co rrela ted with o riginary ap pe rce ption as the \\'h
scP phen omena, w hirc h ' 3S rcp rcscn tancn
" s, [h ave ] th eir
" object, and can
ted
ava ilab le to it in th e manifo ld of presentations. th e object will also be seh'es in tum beco m e objects of othe r representauc e s' ." The tran scen-
lated with th e ca tego ries conceived as 'concepts of an ob ject in g ~I subjec t, as given in originary appercep tion - the su preme gu aranto r o f
means of which th e intu ition of an object is regarded as derermirud in :eah'C unity . (an~ hen ce of ,th e uni ty ~f th e , representati on of ~bjects),
of one of th e logical [ unctions of judgm ent '. to That what ex ists in ex lative to wh ich representat ion s of objects IS alone possible' , ' pu re,
also an object with in it is eviden ce of the 'do ub le register ' in which : riginary, unch angeable consciousness ' I I) - h as as its co rrelate an object
argumcm ope rates: at once ontological, in accordan ce with th e one ( 'which cannot itself be int uited by us'! ' because it is the form of objecti vity
no n of being (w hich is multi ple); and epistemological, in accordana: iI1 general, the 'transcenden ta l object = x',12 wh ich is di stinct fro m empirical
logica l form of judgement . But asid e from th e fact th at it is I U objeCtS, This object is DOt one am ong 'several ' o bjects because it is the
provide a basis for the bind o r rela tion - which H um c was finally ,nrera/ concept of consistePlcy f or all possible bound obj ectivity , the principle
cons ider a pu re fict ion , devoid of bei ng - the tr ouble wit h this equi !hat provides th at oneness on th e basis of whic h th er e are objects available
concerning th e object is th at it weakens th e rad ical di stinction, 1M binding. The tran scen den tal object is ' th ro ughout all our know ledge one
proposed by Kan t, between th e origin of th e one and th e ori gin of and the same = x'. u
For Kant ho lds to his conviction tha t the a priori con ditioos So on the one hand we have th e su bject of experience (immed iate
binding of phenomena must include, un der th e nam e of obiecr, the sclf.ronsciousness) with its m ultiple correlates, th e objects bound in repre-
cond ition of the one as th at whic h provid es stab ility for what is nu.w.... ttnlauon; and on th e oth er we have o rigi nary appercep tion (pu re, singu lar
th e field of representations. W hat other m eaning can we give to the consciousness) wit h its co rrelate, the object of objectivity, th e postu lated x
formulation: 'the conditio ns of the pouibility of ex perience in from which bound ooieas de rive thei r un ita ry form,
likew ise cond it ions of the possibility of the objects of expen'ena',1 But the featu re co mmo n both to orig ina ry apperception as transcendental
the word 'ob jec t' here exp licitl y serves as a pi vot between the """"1iII prot~subject and th is ,Y. as transcendental proto-object is that, as the primi-
th e con sistency of presenta tion (referrin g back to th e m u lti ple as such, Dve, invarian t forms required for th e po ssibil ity o f represen tation , th is
originary stru ct u re ), an d th e derivat ive co nd ition of the link bet ween subiect and th is obj ect remain absolutely un -prescatcd : they arc refe rred to ,
sentable 'ob jects' (referring back to empirica l m u ltip licity, or illusory Over and above all possible experience, on ly as th e void withdrawn fro m
tions)? being, for wh ich all we have arc nam es.
Granted , K an t is well aware th at what is left undetermined by the The subject of o riginary apperception is merel y a necessary ' nume rical
'the being of th e object', its object ivity, th e pure 'so meth ing in genenl unitt , an imm uta b le power of oneness, and is un knowabl e as suc h. Kan t's
tha t provides a basis for the bei ng of bi nding witho ut th at x itself ever entire critique of th e Ca rt esian cogito is based on the im pos sibihry of main-
p resented o r bo und. An d we also know th at x is th e pur e or in raining the tr anscende nta l su bject's absolu te power of oneness as an instance
m ult iple, and hence that th e object, in so far as it is the correlate cI ~ knOwledge, as the determination of a po int of the rea l. O riginary apperce p-
apparen t binding, is de void of being . Kant has an acute sense of th e tion is an exclusi\'e1y logica l form , an em pty necessity: 'beyond thi s logical
rive nature of ontology, of the void through whi ch the presentative si Olcaning of the '"I", we have no knowledg e of th e subject in itself, whi ch as
is con jo ined to its being. By th e sa me token, the exisrenr-co rrel... .... ~tf1l;tum unde rlies this " I", as it does all th oughts' ,14
originary appercept ion conceived as non-existent operation of th e co no . for the transcenden ta l object '" x, K an t exp licitl y declares tha t it ' is
rq,lh g to us - being as it is some thing th at h as to be d ist in ct from all our
Ln
as-one is not , strictly speaking, th e object, b ut ra th er the for m of the
in general - wh ich is to say , th at abso lu tely ind ete rm inate being from rescmal ions' ,I'
th e very fact th at there is an object originates. At the most in tense rq,- r;e s\Jb~rac~i\'e radicalir y of K an tian ontology culminat es in gro und ing
his ontological med itat ion , K ant comes to con ceive of the operation at lila ~ta tlon m th e relation between an em p ty logical sub ject and an object
liS noth IDg,
t
co un t as the correlatio n of two 'Voids,
K ant sp lits bo th te rms in the subjec t/o bject pairing , The em pirical su thel\.1,ore(l\'C'
Ii r 1r canuot accept H crtd eggcr
ce cce' s account of the differ
" en ces between
whi ch ex ists 'accord ing to the determinati on s of our Sta le in inn er se d f'St 3nd second ed ition s of th e Cri tique of Pure R eason. For H eidegger,
 140 Theoretcal Wr itings Kaots Subtra ctive On tolog y 141

Kant retrea ted 'fro m th e doctrine of th e tr anscendental ,'",,~... cend cntal su b jec t) and the void as name of bei ng (the object == x ).
According to Heidcggcr's exegesis, th e ' spontaneous i m~tus' of (tilt tr,ll~\~'
th illo ges tu re wou ld also posit th at th e object is nor the ca tego ry
vers ion posited th e imagination as th at ' th ird Iaculr y' (bes ide thOSe of !'l,I\1r3 'which th ought gains acces s 10 th e bei ng of rep resen tations. It would
biliry and und erst an ding) p rov iding a basis for th e reg ime of the dtfOUgb 'pt the d issolutio n of both obj ect and relation in pu re multiple
th ereby guaranteei ng th e pos sib ility of onto logical knowk dge. "" a::ion. with out the reby relapsing into H umean scep tici sm.
rep roaches K an t for failin g to go fu rt her in explo ring this 'UI1knowb ~ertheh.--Ss. K an t is an extremel y sc ru pulous and rigorous phi losopher.
the essence of man and fo r red ucing th e ima gination LO a m ere ' " ere is no doub t he saw h ow , "m wanung to groun d t h e uruvcrsa . I'Ity 0 r
th e un d ers tand ing. Kant, h e says, ' pe rce ived the unkn own and wu ~ s he W3S in fact open in g up an un th inkable aby ss between th e with-
retreat. It wa s no r just th at the tra nsc en d en ta l powe r o f imaginatiaQ rdJ~of th e tra nscendenta l o bject and th e absolute un ity of originary apper-
ten ed him, but ra ther th at in betwee n [the two ed itions] Pun: ~ . betw een the on tological site of binding and the fun ction of the o ne.
reaso n dre w h im increa singly under its spell'. 16 ~~~itatiOns an d retractions attested to by th e m ajor d ifferences between
In m y op in ion, Kant 's deci sion not to resort 10 the positivity cf !he IWO editions of the Critique of Pure Reason, whi ch ha ve a particu lar
facul ty (the imagination ), his reduction of th e problem of the ODe to bearing on the statu s of the transcende mal subject, do not , in m y opin ion ,
mere operation of the und erst and ing, te st ify to his critica l intransi stem from hesitat ions over the ro le of im agination . They arc th e p rice to be
his refu sal to conced e anyth ing to th e aesthet ic prestige of the on paid for th e proble ma u c relati on between the narro wn ess of th e prem ises
presence. T he 'p res tige of pure reason' ma y well be ano ther name (examination of th e for m of jud gment s) and th e extent of the conse quences
intransigence when faced with th e great te mptation. For Kant, tbia (the void as poin t o f being). It is clear th at the root of th is d ifficul ty lies in
wher e th e genuin e dang er lies: that of having to acknowledge, the notion of object - a to pic to which H eid eggc r devot es a dec isive exegesis.
perspective of th e transcen dental subject as well as fro m that of the Kant burdens hi msel f with a notion th at, pertinent th o ugh it may be for a
x , Ute crucial significance of Ute void. thereby illumina tin g - for the critical doct rine of b ind ing, sho uld be di sso lved by the operations o f
independently of all negative th eo logy - th e paths o f a su btra cti ve llntology.
Is thi s to say that K ant 's ent erp rise is entirely su ccessful? No, By the same token , faced with the abyss opened up in bei ng b y the dou ble
con tin ues to bea r th e trace of th e fact th at the origin of th e deductioD naming of th e void (acco rding to th e subject and according to the object),
th e theory of b ind ing . K ant effectively ascribes th e foundational Kant will take u p th e pro b lem again but from anoth er an gle, by asking
the retaiiou between two voids. H e does so, in the tina l analysis, beaaIC himself wher e and how these rwc voids can in tum be counted as one . T o
an em p ting to ground the ' th ere is' of objects, th e ob jecti vity of the 1llSw("T these questions, an enti rely d iffe rent framework will be neces sa ry,

which is the so le sup port for th e deployment of th e categoriai bindiDI which is to say, a situatio n o ther than th e epistemological one. What is essen-
manifold of re presentations. For K ant, th e object remain s the sok tialJ)· at stake in th e Cn',iquc of Pure Reason is th e d emonst rat ion th at both
th e one in rep resen tat ion. T he synth etic un ity of co nsciousn ess is tht Void of the sub ject and th e void o f th e ob ject be long to a single realm of
not on ly for knowledge of th e object , but beca use it ' is a condi tioa bring, which Kant will call th e supra -sensib le. From th is poi nt of view, far
which every int u ition m ust stand ill order to income an objeer f or • • &o.n being the instance of 'meta physical' regres sion it is sometim es regarded
othe rwise, in th e absence of thi s synth es is, the man ifold would not be ta, the Second C ritique co nst itu te s a necessary d ialectica l reworking of th e
in one consciousness' ." The subord ination of theo ry to the kno w ontOlogical impa sses of th e first. It s aim, in a di ffer ent situ ation (th at of
\·oIUnl . . . . . .. . .
univ ersal relations (its epi stemo logical in ten t) for ces th e powe r 01 aT) acucn), IS to co unt as one that whi ch , In th e cogrunve snu ano n,
'<m .
coun ting- as- one to ad m it re p rese n ta ble obj ects as its conseq uence and aiDed the enigm atic corr elate of t wo absences.
the void in con form ity with the general idea of the su bject/object re inN~\lcnhclc~s, in the registe r o f know ledge, K ant 's powerful on tological
tUllio · . . . .
whic h rem ain s the un qu estioned framework for ontolo gy as such . ll1t ns rema lO teth er ed to a starting J)OlOt restr icted to th e form of judge-
Kan tian Cri tique hes ita te s on th e th reshold of the ulti mate s[ep,
consist s in po siting rha r relati on is not, an d thai this non-being of
diff ers i" ki"d from the non -being o f the one, so th at it is impossi
,O
I
f ht
Ord (Which , it mu st be said, is the lowest degree of th inking), wh ile in the

rts lllt .
loca lization, they remain tied to a con ception o f the subject which
of the lauer a protoco l of constitutio n, wh erea s it can , at best, on ly be."
arrange an identi ta rian sy m metry betwee n th e void o f th e co un tinB
142 Theoretical Wri t ings

In sp ite of this, we can hold on to the notion th at the q uesti

SUbjL"Ct is that of idc n riry, and hen ce of the one, with th e prov isootJ.
su bject be understood , not as the empty centre of a tran scenden tal CHAPTER 12
rath er as th e operationa l un it}' of a mult iplicity of effectua tion s of .
Or as the multiple ways of bei"g self-identical,
Eight Theses o n t he Un iver sal

t. T HO UGH T IS TH E PROPER MED IUM OF THE

UN I V ERSA L

By 'thought' , I mean th e sub ject in so far as it is constituted th rou gh a

process rhar is transversal relative to the tota lity of available form s of know-
ledge. Or, as Lacan pU IS it, the subject in so far as il constitutes a hole in
knoWledge.

R EMAR K S;
t. That thought is the proper medi um of th e un iversal means th at noth ing
exists as uni versal if it takes the form of th e object or of o bjective legality.
The universal is essent ially 'anobicctiv c' . I t can be experienced onl y
rhrough the p rod uctio n (or reproduction ) of a trajectory of thought , an d
this trajectory cons titu tes (or reconsti tutes) a subjective disposit ion .
Here arc tWO typ ical examp les: the un iversality of a mat hematical
Proposition can on ly be experienced by in vent ing or effectively rep rodu -
cing its proof; the situated univer salit y of a po litical statement can on ly be
experienced through the militant practice that effectu ates it.
b. T hat thought , as su bject-tho ught, is constituted th rou gh a pr ocess mean s
that the uni versa l is in no wa y the resul t of a tra nscenden tal constitu tion,
Which Wou ld presuppose a constitu ting su bject . On th e con trary, th e
Opening up o f the possibi lity of a universal is the p recond itio n for th ere
being a sub ject-thou ght at the local level. T he subject is in variab ly
summoned as though t at a specific point of that procedure th rough which
the universal is constitu ted . T he un iversal is at once what d etermines its
cwn poin ts as subject-thoughts and the virt ua l reco llection of those
~ints. Thus the cen tral d ialectic at work in the un iversal is that of the
Ocal, as subject, and the globa l, as infini te procedu re. This dialectic is
<On .
StHm ive o f th ough t as such.
Con sequ ent ly, the u niversality of the p roposition ' the series of pri me
nl1llthers goes on forever ' resides bo th in the way it summo ns us to repeat
 144 Tteoreucat Wri tings 145

(or redi sco ver) in th ought a un iqu e proof for it, b ut also in tbe uni\'crsa lity o f universalit y. This d efinition is fatally ta utological. It
proc edu re th at . fro m the Greeks to th e p resent day, mo bililea ~. ~~sary co un terpart of a p rot ocol - usu ally a vio lent one - th at wan ts
th eory along with it s underlying ax iomat ic. T o put it anoth~ If Ille "ici ll: genui nely part icu lar particul arities (i.e. immanent particul ari ties )
un iversality of th e practical state me nt ' 3 cou ntry's illegal . 10 ~ . freezes the p red icat es of the la t te r int o self-sufficien t id cntitarian
wo rke rs musr have their rights recogn ized by th at country' ~_ bt"'usc I~
bioallons.
so ns of mili tant effectuations through which po lit ical sUbj t<JIl1 us it is necessary to maintain tha t every un iversal present s itsel f not as a
acti vely cons tituted, but also in th e global proce ss o f a politics, in 'fh riZ3tion of th e pa rticula r or of d ifference s, but as a singu larity that is
what it p rescribes co nce rni ng th e State and its decisions, rules and ft8Il1J; ted from iden tita rian predica tes; although obvious ly it proceeds via
c. That th e p rocess o f th e uni ver sal or truth - th ey are one and the lIl~redicatt."5. The subtractio n of particulari ties must be opposed to their
transversal relative to all availab le inst ances of knowledge means ~tion. But if a singu lari ty can lay claim to th e uni versal by sub traction.
un iversal is always an inca lculable em ergen ce, ra th er lhan a . is beClIuse the p lay o f iden tita rian predicates , or th e logi c of those forms of
stru cture. By the same token, I will say that a truth is in""OIiIlo ~'lcdge that desc ribe particularity, prec ludes any possibility o f foreseeing
knowledge. and even tha t it is essentially unknown. This is "'>do" or I."l)OCCiving it.
o f exp laini ng wha t I m ean when I charac terize truth as uncon Consequently, a u niv ersal singu larity is not of the order of bei ng , but of
I will ca ll particular whatever can be d iscerned in know ledge bJ tilt order of a sudd en eme rge nce. W hence th esis 3:
of descrip tive predicates. But J will call singular that wh ich.
identifiable as a proced ure at wo rk in a situation , is
subtrac ted from every p red icative d escription . Thus th e cu ltural J. EVERY UN I VER S A L O R IG INA TES IN AN E VEN T,
th is or th at population arc particular. But thai which, travenm, AN D THE EVEN T IS IN T R A N SI TI VE TO T HE
tra its and deact ivating every regist ered d escription, universally PARTICULA R IT Y O F T HE S ITUA TION
a th ought-subject, is singular. Whence th esis 2:
The correlation between uni versal and event is fundamen tal. Basically, it is
dear that the qu estion of po litica l universalism depend s entire ly on th e
2. EVER Y UNIVERSA L IS S INGUL A R, OR IS A regime of fidelity or infidelity ma in ta ined, no t to th is o r tha t doctrine, but to
S INGULA R I T Y the French Revolution, or th e Paris commune, or O cto be r 19 17, or the strug-
ales for national libe rat ion, or M ay 1968 . A ccntra ria, the negation of po litica l
lltIiversalism, th e negation of the very th em e of em ancipation, requ ires m ore
REM A RK S :
than mere reac tio nary propaga nda. It requ ires what co u ld be ca lled an
There is no possib le un iversal sublation of particu larity 8S suc:b. ~al rft}jn·on;rm. T hu s, for exam ple. Purer's attempt to sho w that th e
co mmon ly claim ed nowadays tha t th e on ly gen uinely uni versal p .~ Rt".'olution was entirely fut ile; or th e inn umerable arternpts to red uce
co nsists in res pec ting particularities. In m y opinio n , thi s thesis is . . ~ 1968 to a student stam ped e toward sexual liberation . Evem al revi-
ten t. This is d emonstrated by th e fact th at any att em p t to put it into ::;:urn targets (he co nn ection betwee n univ ers ality and singu larity. Nothing
invariably runs up again st part icu larities wh ich th e ad voca tes of is II ~Iace bu t the p lace, p rcd icariv c descr iption s are su fficien t, and wh ateve r
u nive rsality find int o lerab le. T he trut h is that in orde r to maintain Itta nl\lcrsally valuab le is strictly objective. l n fi ne, thi s am ou nt s to th e claim
respect for pa rticu larity is a uni ver sal value, it is necessa ry to haVC ~ whatever is univ ersally valuable resides in the mecha nisms and powe r of
d ist ingui shed between good pa rt icularities and bad ones. In othe r wor~ I tal. along with its statist g ua ra ntees.
neces sary to have esta blished a h iera rch y in the list of d escripti ve p r Ilr~. that case, the fate of the hu man ani mal is sealed by the relatio n betwee n
.....liCiti . . . .. . .
II will be cla imed , for exa mple, th at a cu ltural or religious parti F' ve narucuta ri tics and legislative generalities .
bad if it dOC": not incl ude within itself respect for o ther pa rt icularities- ~0,. '" cvcm to in itiate a singu lar proced ure of un iversa l!...catio n, and to
,~tUtc its sub ject through lh:u procedu re, is con tra ry to the pos itivist

l
this is obvious ly to sti pula te th at th c formal uni versa l al ready be incl
the particu larity. Ultima tel y, th e universality of respect for parti cu l ng of particulari ty and gene ra lit y.
146 T heore tical W ritings Eight Theses on the Urnversat 147

In this regard , th e case of sexual differen ce is significant . T he p • c cons titutively uncertain; every th ing that el icits a 'may be, maybe not ';
reJ118m~
particu lari ties identifying the positi ons 'm an' an d ' woman' within • thing whos e status can be end lessl y debated acco rd ing to th e ru le of
society can be conceived in an abstract fashion. A general principle ~"C~ecision, whic h is itself ency clopedic ; every thing about whi ch knowled ge
pos ited whereb y the rights, status, characteristics and hiera rchies ~ inS us not to decide. Nowadays, fo r insta nce, knowledge en join s us not to
with these posi tions sho uld be subject to egali tarian regulation by die ~de abo ut God: it is q uite acce p table to m ainta in that perhaps 'so meth ing'
This is all well and good, but it does not provide a ground for any ~tS' or pahaps it d oes not . We live in a society in whi ch no valence can be
universality as far as the predicative distribution of gend er roles is en 'bed to G od 's existen ce; a scclery th at lays claim to a vague sp irituality.
For this to be th e case, there has to be th e sudden ly emerging s°inaWo. :Iarlr . knowlcdg~ en joins u s not to decide about th e possible existence: of
an encounte r or dec lar at ion ; om: tha t cry stallizes a su bject whose 'afIOth~r pclirlcs': it is ta lked abou t, but nothing co mes of it. Another
Lion is p recisely its subtractive experienc e of sexual difference. Such . cPDlple: arc th ose workers who do not have proper papers but who ar c
comes abo ut through an amorous encounter in wh ich the re occurs I .-orting here, in France (or the United Kingdom. or th e U nited States . . .)
live synlhes is of sexuated positions. Thus th e amorous scene i. lilt ptrt of this coun try? D o th ey belong h er e? Yes, probably, sinc e th ey live and
gen uine scene in whi ch a uni versal singularity pertaining to th e 1Wo 'WOlt here. No , since th ey don't have th e necessary papers to show that th ey
sexes - and ultimately pertaining to difference as such - is prrx:I. ...... arc Frwch (or Bri tish. or Am~rican .. .), or livin g here legall y. The exp res-
is wh er e an undivided sub jec tive expe rience of absolute diffttalCle $ion 'illegal imm igrant' des ignates the un certain ty of vale nce, or th e non-
place . We all know that. wh ere th e in terp lay between the sexes is nlen~ of valence: it designates peo p le who ate living hen , but don't reall y
people are invariably fascinated by love sto ries; and this fuCa. bdong here, and hence people wh o can be: th rown out of th e co untry, people
directl y pro po rti onal to the vari ous specifi c obstacles through W'Iaa wbo can be: exposed to the non-valence of the valen ce: of th eir presence: here
formations try to thwart love . In th is in stance. it is perfectly c~ IS "-orkers .
attraction exe rt ed by the un iversal lies precisely in the fact thae it Basia lly, an even t is wha t decides about a zon e of ency clopedic indiscem-
itself (or tries to sub tract itself) as an asoci al singu larity from the ibility. Mor e p recisely, the re is an implicative form of th e type: E ..... d (E).
of knowl edge. which reads as: every real subiecu vauc n b rou ght abou t by an event, wh ich
Thus it is nec essary to maintain that th e universal emerges as a disapPears in its appearance, implies that E, whi ch is undecidable within th e
and th at all we have to begin with is a preca rious su pp lemen t .~tion, has bee n decided. This was th e case , fo r exam p le, when illegal
streng th resides in th ere being no available predicate capable of su immigrant workers occupied th e chu rch o f St . Bern ard in Pa ris: th ey
to knowledge PIIblicly declared th e ex istence and valence: o f wh at had bee n without
T he question then is: what m aterial instance, what un classifiable l'alettce, thereby decid ing tha t those wh o are here be long here and enjoin ing
presence, p rov ides the basis fo r the subjcct ivating procedu re wbote fleople to dr op the ex pressi on ' illegal im mig ran t' .
m ot if is a universa l? I will call c the e....en ta l statement. By virt ue of the logi cal rule of detach-
;"1, we sec th at the abolitio n of the event, wh ose en tire be ing co nsis ts in
saPJ>ea ring, leaves behi nd the evcnral state ment u, which is implied by the
4. A UN I VERSA L IN I TIA L L Y PRESENTS I T SELF A weu, as someth ing th ai is at once :
DEC ISIO N ABO UT A N UNDECIDA B LE
a real of the situ ation (since it was already there);
This poin t req uires careful elu cidation . but som eth ing wh ose valence undergoes radical change, since it was
I eall 'e ncy clo pedia' the general sys tem of pre dicarive knowledge undl"Cidablc but has bee n decided . It is something that had no valence
to a situation: i.c . what eve ryone know s about poli tic s, sexual difti but now doc s.
cu lture, art, tech nology, etc. T here are certain lh in gs, statem en ts,
no ns or d iscursive fragment s whose valence is not decidable in tertJll lir:l~ns~qUentIY, I will say th at th e ina ug ural ma teriali ty for any u niversal
encycloped ia. T heir valence is un ce rtain, floating, anonymous: theY , lanll' is th e evc ntal stateme n t. It fixes the presen t for the subject-
the margin s of th e encyc lopedia. They co m prise every th ing whOlC iht OUt of which th e uni ver sal is woven .
 '48 Theoretical Wn tmgs EIght Theses on the Universal
'4'
Su ch is th e case in an amorous enco unter, whose su bjective pr~ this poin t, p lat o's apo logia in the M ellO remains irrefutable. If a slave
in one form o r anothe r by the statem ent ' I lo ve you', even as tbt: ()rI. ' '- ing about the cveme t foundation of geo me try , he rem ain s incap-
..-n\\'S nou
stance of th e encounter is erased . Thus an undecidabl e disjuncti~ w-. of \'lIlidating the cons tr uction of the square of the surface that doubl es a
is decided and the inauguration of its subject is lied to the """'''''. ~ $<Quare. But if one provides h im with the basic da ta and he agrees to
the evemal sta te me nt. J1'~ ',-ale it he will also subjectivate th e const ruction un d er con sideration .
Note that every even ral statemen t has a declarat ive st ru cture, sub~e implicat ion th at inscribes this construction in the presen t inaugu-
whethe r the statement takes th e fonn of a proposition, a wodt. a 1b: b)' geometry's G reek emergence is universally valid .
tion or an axiom. The evemat statemen t is im plied by th e even t's ratSortt eol'lC might object: ' You' re making thi ngs too easy fo r you rself by
disa ppearing and d eclares tha t an undecid able has been decided or . \'Oking the au tho rity of mathema tical inference.' But th ey wou ld be wrong.
was witho ut valence now h as a valence. The constitu ted sub ject ill , universalizing procedure is implica tive. It verifies the consequences
E\'C11
the wake of thi s d eclaration, whi ch opens up a possible space thJt follow fro m th e evental state me nt to which the vani shed event is
un iversal . jnckxed. If the protocol of subjec ti vario n is ini tia ted und er the aegis of thi s
According ly, all th at is req u ired in orde r for the un iversal to $u tement, it becomes cap able o f inven ting and esta blish ing a set of univer-
d raw all th e consequences , with in th e situation, of the evc nta l Stat sail)' recognizable con seq uences.
The reactive denial that the even t took place, as exp ressed in the maxim
'nothing took place but the p lace', is probab ly the on ly way of un derminin g a
5. T HE UNIVERSA L H A S A N IMPLlCA TlVB universal singu larity. It refuses to recognize its con seq uences and cancels
STRUCTURE 'I\'hau~ver present is p roper to th e evenra l procedure .
Yet (Yen rhis refusa l canne r cancel the universality of im plicat ion as such .
O ne common objection to the idea of un iver salit y is that ev"," ' " Tau the Fren ch Revo luti on: if, from 1792 on, th is constitu tes a radical
exists or is re p resent ed relates bac k to particular cond itions and erem, as indicated by th e immanent decl ara tion whi ch states th at revolu tion
lions govern ed by disparate forces o r interest s. Thus, for instaaee, • such is now a po litical catego ry , then it is tru e that th e citizen can only be:
maintain it is impossible to attain a universa l grasp o f differen ce CDnStitutc:d in accordance with the d ialecti c of Vinue and T error. This impli-
th e: abyss between th e way th e laner is grasped, depending on ClItion is both undeniable and universall y transmissible - in th e writings of
occupies th e pos ition of 'man ' or the pos ition of 'woman ', Still otbe," Saint-Just, for instance. B UI obvi ously, if one thinks there was no Revolu -
th at th er e is no common de nominato r underl ying what various tion, then Virtue as a subjecti ve d isposition does DOt exist ei the r and all that
groups choose to call 'artistic activity '; or th at nor even a rna rtnlains is the T error as an ou tb urst of insa n ity in viting moral condemna tion.
p roposition is intrinsica lly uni ver sal, since its valid ity is entire ly ~et a 'Cfl if politics d isa ppea rs, the universality of the im plication th at pu ts it
upon the axiom s th ai su ppo rt it. Illto effecr rema ins.
What thi s hermeneutic perspecti valism ove rlooks is that every 'lbere is no need to invoke a conflict of int erpret at ions here. This is the
singularity is presented as th e network of conseq uences entailed nub of my sixth thesis:
cventa l d ecision . W hat is un iver sal always takes th e fonn (; _ 11:, w~
the evemel statemen t and It is a conseq uence , or a fidel ity. It goes
saying th at if someone refu ses thc decision abo ut 1:, or insistS, in 6. T HE UN IVERSA L I S UN I VOCA L
fashion, on reducing I: to its un decid able status, or maintains that whit
I.
taken on a valence sho u ld rema in without valence, then th e implicative ,L 110 far u-, subicc u vauo n occ u rs through th e con seq uences o f the even t,
\litre '
in no way en join s them to acce pt the valid ity of the conseq uence, 1UI. lin IS a un ivocal logic proper to the fideli ty thai constitu tes a un iver sal

thclc ss, eve n they will have to ad mit th e universality of th e form of ' &ularity.
titli
ere . h
iio n as such. In other wo rd s, even they will have !O ad mit that if the we ave to go back to the evcmat statemen t. Recall that th e statement
sub jecrivared on the basis of its statemen t, whatever cons eq uences ~~tes w.i thi n a situ ation as somet~ing. ~ndL'Cid3blc. There i~ agr~ment
be invent ed as a resu lt will be necessary . boul liS existe nce and Its undecidability. From an ontolog ical pomt of
ISO Tbeo-encaf W ntlngs Eight Theses 00 the Universal 151

view, it is one of the mult ipliciti es of which the sit uation is coml'Oled. EVE R Y UN I VERSA L S IN G ULA R IT Y R EM AIN S
a logical point of view, its valence is in te rm ediary or undecided. Wi-. 7. IN COMPLETABLE OR OPEN
th rough the even t does nOI have to do with th e being that is at stake
event, nor w ith the m eaning o f the even tal sta tem ent . It pe rta ins Is Ihesis req ui res by wa y of co m men ta ry con ce rns th e man ner in whic h
to the fact that, whe reas previously the evcntal state me n t had ~ ."
I'l" Ihlb'CC the locali za u.on 0 f a umversa
' I stngu
' Iarny,
' is be un d up W1Ul
IS '.• t h e
I
able , henceforth it will have been decided , o r decided as tr ue. Ibe s.u J Ih~ onlo log ical law of being-mu ltiple. O n th is parti cu lar issue, it is
previously the evcm al statem ent had been d evoid o f sign ificance. iltfin.lt~: 10 snow that there is an es sential complicity be tween the philoso -
possesses an exception al valence. This is wha t happened with the ~:bof finilu de, on the one hand, and relativism , o r th e negation of th e
immigrant workers. who demons tra ted their existence at the 51. ~\.ersal and the d iscrediting of th e notion of truth, on the othe r. Let me
ch urch. UlI1 . :.. terms of a single: maxim: The latent violence, th e presumptuOUS
put II .. .
In othe r words, wha t affects the statement, in so far as the latter iI ItfOPItce inhe re nt in th e currently prevalent co nc ep tion of hum an righ ts
up in an Implicative manner with the ev ental di sappearance , is of the !krh'($ from the fact th at th ese are actually th e rights of fin itud e and ulti -
the act, rather than of being or meani ng . It is pr ecisely the register of lIlItdy _ as th e insiste nt th eme of democratic euthanasia in dica tes - the
thai is uni vocal. It just so happened that th e state m en t was decided, rights of death. By wa y of co ntrast , the even tal concep tion of un iversa l singu-
d ecision rem ains subtracted from all interpretation. It relates to tbt larities, as J ean - Fr9.n ~o is Lyota rd rem ark ed in Th e Diffe rend, requ ires that
the no, not to th e eq uivoc al p lu ra lity of m ean ing. human rights be though t of as th e righ tS of th e in fin ite.
\Vhat we ar e talking abo ut here is a logical act , or ev en, as one
echoi ng Rimbaud, a logica l revolt . The event decides in favo ur of
or eminen t va lence of that w hich the previou s logic had co nfined to die 8. UNIVERSA LITY IS NO TH ING OTHER T HAN TH E
of the undecidabl e or of non -valence . But for th is to be possible, the FAITHFUL CON S T R UC TI ON OF AN INFIN I T E
act that modifies th e va lence of one of th e co m po nents of th e si G ENER IC M ULTIPLE
gradually begin to transform the logic of th e situ ation in its
Although th e bei ng- multip le of th e situation rema in s unalte red, the What do I mean by ge neric m ultiplicil Y? Q uile sim p ly, a su bse t of the sit ua-
its appearan ce - the system th at eval uat es and con nects all the mul . tion that is nOI determined by an y of th e pred icat es of encyclopedic kne w-
be long ing to th e situation - can un dergo a p ro found transfo rma tion. It ItdgCj that is to say, a mu lt iple suc h th ai to be long to it, to be one of its
trajectory of th is m utation tha t composes the ency cloped ia's univ clements, canno t be the resu lt of having an identi ty , of pos sessing any parti -
d iagonal . cular propert y. If the un iversa l is fo r everyon e, th is is in th e precise sens e
The th esis of th e equivoc iry of th e universal refers the u niversal . thai to be insc ribed wi thin it is not a matter of posses sing any particular
back to th ose generalities whose law holds swa y ov er particu lari ties. II detenninat ion. T h is is th e case with political ga th erings, whose universali ty
grasp th e logica l act that uni versall y and uni vocall y inaugurates a follows from thei r in difference to social, national, sexua l or gene ra tional
tion in the en tire structu re o f appearance. Origin; with the amo rous couple , wh ich is universal because it produces an
For every un iversal singularity can be defined as follows : it is me ~ivided truth abo ut the d iffer ence: between sexuated pos itions; with scien-
whi ch a sub ject- tho ught becomes bo und in s uc h a wa y as to ren der tific thoo!)" wh ich is un iversal to the ext ent th at it removes eve ry tra ce of its
capab le of inirlnring a p roc edu re which effect s a rad ica l modificatio n Provenance in its ela bo ration; or with arti stic co nfigurations whose sub jec ts
logi c of the situation, and hence of what appears in so far as it ap pears . ttt work5,' an d . .
III winch, as M allnnne. remarked , the parucu ' 1arny
' 0
fh
me
Obviously, th is mod ifica tion can never be fu lly acco m p lished . F :l:tor has been abolished, so mu ch so tha t in exemplary in aug ural co nfigura-
ini tial un ivocal act, wh ich is a lways loc alized, ina ugu ra tes a fidel ity. ~ li S' SUch as the Iliad and the Ody ssey , th e pro per nam e that underli es the m
in vention of consequences, tha t will prove to be as infi nit e as the si IUb.Ofner - ulti m ately refers ba ck to noth in g bUI th e vo id of any an d ev ery
J~t .
itse lf. Wh en ce thes is 7;
~us the universal arises accordi ng to the chance of an aleatory supple-
r. It leaves be hi nd it a sim ple d eta ch ed state me nt as a trace of th e di s-
152 Theoretical Writings

appearance of the even t th at foun ds it. It initiates its p rocedur e ill

uni vocal act th rough which th e valence of what was d evoid of valence
to be deci ded . It bind s to this act a su bject- though t that will inven t CHAPTERll
qu ences for it . 11 faithfully constru cts an infin ite generic mu ltip licity,
by its very opening , is what Thucyd ides declared his written history 01
Peloponncsian war - un like the laner 's historical particularity - WOUld Politics as a Truth Procedure
XCHl j.la. cs at t, 'someth ing fo r all lime ' .

When, and unde r what condi tions , can an event be said to be politi cal? What
is the 'what happens' in so far as it happens politically?
We will maintain that an even t is po litical, and mal me p roced ure it
engages exhibits a political truth, only under certain conditio ns. These cond i-
tions pertain to the ma teria l of th e even t, ( 0 the infinite, to its relation 10 th e
sate of the situation, and to th e numericality of the procedure.

I. An event is political if its mat erial is collective, or if the even t can only be
anri buted to a collective multiplicity. 'Collective' is not a n umeri cal
concept here . We say th at the event is ontologi cally collecti ve to the ext ent
thai it provides the vehicle fo r a virt ual summoning of all. 'Co llective'
means immed iately un iversal izing . The effecti veness of po liti cs relates to
the affirm ation according to which ' for every x, the re is thou ght '.
By 'though t' , I mean any tru th procedure considered subjectively .
'Though t' is the nam e of the su bject of a truth p rocedure. The use.o f the
term 'collective' is an acknow ledgem en t th at if thi s though t is political, it
belongs to all. It is not simply a qu estion of add ress, as it is in th e case of
ouie- types of truth. Of course, eve ry t ruth is addressed to all. But in the
case of polit ics, the univ ersality is intrinsic, and not sim ply a funct ion of
the address. In politi cs, th e possibi lity o f the tho ught that ident ifies a
Subject is at every mom ent available to all . Those that arc con stituted as
Subject of a po litics arc called the militants of the procedure. But
'militant' is a category without bo rders, a subjective determination
without identi ty, or wit hout concept. T hat the poli tical event is co llective
pr('Scribes that all are the virtua l militants of th e though t th at p roceed s on
the basis of the eve nt . In th is sense , politics is the single tr uth procedure
thai b not on ly generic in its result, b ut also in the loca l composition of
its subjl.'ct.
Only po litics is int rins ically req uired to d eclare that th e thought that it
is is the tho ug ht of all. T his d eclaration is its cons tit utive pr erequisite. All
that the mathematician requires, for instance, is at least one o the r mathe-
154 Theoretical Wr itings Pohncs asTr uth Procedure 155

m arician to recognize th e valid ity of his p roof. In o rder to assure i lberclor . e us re-presenta tion. M ore specifica
...- lly, the sta te of th e situation
th e thought tha t it is, love need onl y assume the two. T he artiSt u.l . r ~sent S co llective situ ations, whi lst in th e co llecti ve situ ations th em -
((" h'CS,
p "" singulan. tlCf;
. arc not re-presen tee _ oJ b dOth· · I
need s no one. Science, art and love 3 fC aristocra tic tru th Ptoecd,",,- U[ p resentee. n rs pcmt,
co ur se, th ey arc addressed 10 all an d unive rsalize th eir own s' st fer th e reader to m y B t.i''IJ and EfJflm , M ed itation 8.'
But th eir regime is not that of the collective. Politics i. i·....... (('A fundamenta l datum of on to logy is th at th e State of th e situation
withou t th e sta temen t that people, taken ind istinctly. arc capable 01 alwaYS exceed s the situa tion itse lf. There are alwa ys mo re parts th an
th ought th ai co nstitutes th e post-evental po litica l subject. This . deiJlenrs ; i.c. the representative mu ltiplicity is always of a higher power
clai ms th at a po litica l th ought is topologically co llective, meanina than th e presentative multiplicity. This questi on is reall y that of power .
cannot exist othe rwise than as th e th ought of aiL The power of the State is always supe rio r to that of the situ ation. The
That the cen tra l acti vity of po litics is the ga The,.ing is a local State, an d hence also th e eco nomy, whi ch is toda y th e norm o f th e State,
of its intrins ically co llective, and th erefore principally universal, are characterise d by a st ructu ra l effect of separation and superpower with
2. The effect of lhe collective character of the po litical event is that regard to what is sim p ly presented in the situation.
presents as such th e infinite character of situations. Politics ""'. . . . It has been mathematicall y demonstrated that thi s excess is not measur-
exhibits the infinity of th e situ ation. Every po litics of t:manci paboa able. There is no answer to th e ques tion abou t how mtlch th e power of the
finitud e. rejects 'bcing towards death". S ince a po litics includa State exceeds th e individu al. or how m uch th e power of representation
situation th e thought of all, it is engaged in rendering explicit tbc aeeeds that of sim p le presentation . The excess is errant. The sim plest
rive infin ity of situations . aperience of the relation to the State shows that one re lates to it without
Of co urse, every sit uation is on to logically infinite. But only ever being able to as sign a measure to its power. The representa tion of
summons th is in fini ty immediately, as su bjective universality. the: State by power. say public po wer, points on the one hand to its
Science, for example, is the ca pture of th e void and the infuUtc escess, and on th e other to the indeterm inacy or errancy o f this excess.
lett er. It has no co ncern for the subjective in finity of situa~ We know that when politics ex ists, it immediately gives rise to a sh ow
p resents th e sensible in the fini tud e of a work, and the infinite oaIy of power by th e State. This is obvio usly du e to the fact that politics is
venes in it to th e extent that th e artist destines the infinite to the collc:ctive, an d hence un iversally concerns th e par ts of the situa tion,
But politics treats th e infini te as such according to the principk til thereb y en croach ing upon th e domain from whi ch the sta le of the situa-
same. th e egalitarian p rinciple. This is its starting-point: th e si tion draws its existe nce. Politics summo ns th e power of the Slate.
open, neve r closed , and the possible affects its immanent IU 1-.{oroo\'er , it is th e only truth proc ed ure to d o so directl y. T he usual
infinity. We will say tha t th e numericality of the po litica l procectura: symptom of thi s sum mo ning is th e fact that politics invariably encounters
th e infinite as its first term ; whereas for 10vCJ,.th is firs t term is the OGII repression . But repres sion, wh ich is th e em p irical form of the erran t
science the void; and for art a finite num be r. T he infin ite co mes lnID SUperpower of the St at e, is not the essential po int.
in every tru th p roce du re, bu t on ly in po litics does it take th e tint T he real cha rac te ristic of th e political event and the truth procedure
T h is is because on ly in po litic s is th e deliberation about the po5sibk that it sets off is that a po litical event fixes th e errancy and assigns a
hence abo ut th e infin ity of th e situation ) constitu tive of thc process i measu re to the su perpower of th e State. It fixes the power o f the State.
3. La st ly, what is th e relation betwee n poli tics and the state of the sit Consequ en tly, th e po litica l event in te rrupts th e sub jective errancy of th e
and more particul arly between po litics an d the State, in both th e Power of the Stare. It con figu res the sta te of the situation. l t gives it a
gical and histo rical senses of th e term ? figure; it con figures its power; it me asures it.
The state of the situation is the operation wh ich , wit hi n th e sitUA E.mpiri cally, thi s means that whe never th er e is a genu inely po litica l
codifies its pa rt s o r su b-sets. The Stale is a so rt of metast ru ctu re tha t event , the Stat e reveals itse lf. It reveals its excess of power, its rep ressive
ctscs th e power of the co u nt over all the sub-sets of the situation- S dimension. But it also reveals a m easure for thi s usually invisible excess .
situation has a state. Every sit uation is th e p resent ation o f itself. of Por it is essen tial to th e nor m al fu nctio ni ng of th e Sta te that its power
co mposes it , o f wha t belongs to it. But it is also given as sta le of the rCtnain measure less, errant, un assignabl e. T he po litica l even t puts an en d
lion, that is. as th e inte rnal co nfigu ration of its parts o r sub-seU. to alllhis by assigning a visible measure to th e excessive power of th e Sta te.
 156 The o retical Writ ings Pohucs as Truth Procedure 157

Politics puts the State at a distance, in th e distance of its m poli tics, we have no m ean s of knowing any th ing other tha n : c is
~ .f r
toJ1l
resignation that characterizes a time without po litics feed s on the "" T his in determ ina te superiori ty m asks the aliena ting and
(0 .....
th e State is not at a dista nce, because the measur e of its POwer iii "",,"0, natu re of th e state of th e situation .
~SI\' C
People arc held hostage by its unassignable errancy. Politics i, ,cp litical even t prescribes a measu re for th e measurclessncs s of th e
ru ption of th is errancy. It exhibits a measure for Sl a t e power. fbew':ugh the sudden ly eme rge nt materiality of a unive rsa liz.able collec-
sense in whi ch politics is ' freedom '. The Sta te is in fact the Stile, ..bstitutes a fixed measure for th e errant c; one that almos t invariably
' :e. t SO'
enslavement of the pans of the situation, an enslavement wbose P' inS superi or to the power a of sim ple presentation, of course, bu t wh ich
precisely the erra ncy of superpo wer, irs measurelessness. F ~ longer en dowed with th e alie nating and repres sive powers of indetermi-
If no We will use the expression It(r:) to symbolize th e resu lt of the po litical
co nsists in putting the Sla te at a d istance th ro ugh th e COUectin
ment of a measure for its excess. And if th e excess measured, it is ""', 'ption d irected at the State.
the collective can measu re up to it. ~ mark II designates the po litica l fun ction. I I is exercised in several

We will call political prescription the posr-evema l esrabli $pICCS (though we sh all ~~t go in to th~ detai ls here) co rrelated with ~e
fixed measu re for th e power of th e State. pIIceS of a singu lar. ~ htl cs ('p laces ' . m th ~ ~~ defin ed ~y Sy l\'3l~
uurus), 2 This function IS th e trace left m th e: Situation by th e vanished po h-
We can now proceed to elabo rate th e nu me ricality o f th e politiall DcsI even t. What conce rns us h ere: is its p rinci pal efficacy, whi ch co nsi sts in
d ure . iDtefTUpting the indeterminacy of sta te power,
Why does every tru th p rocedure possess a numericality? Because The tint three terms of th e n umericality of th e po litical procedure, all of
dcterm ineucn of each truth's relation to th e d ifferent types of m which are infinit e, arc ultimately th e following:
singu larize it: the situeucn, th e state of the situation , th e even t,
su bjective opera tion. This relation is exp ressed by a number r I. The infinity of the: situ ation, which is summoned as such thro ugh th e
Cantorian o r infini te num bers ). Thus th e procedu re has an abs tract collective dimension of th e political event, whi ch is to say, thro ugh th e
fixed in some typ ical numbers which encode th e 'tra versa l' of the supposition of thought's ' for all' , We will re fer to it as 0".
tha t are on tologica lly cons titutive of thi s proc edure. Z. The infin ity of the sta te of the si tuatio n, which is summone-d for th e:
Let us give Lacan his du c: h e was the firs t to make a systematic purposes of rep ression and aliena tion because: it supposedly controls all the
numer icality, whethe r it be a questi on of ass igni ng the subject to ttrO collecti\'cs or sub-sets of th e situation. It is an infin ite cardina l n umber th at
gap between I and 2 (th e subject is wha t falls betwee n th e pri m ordial remains inde term in ate, th ough it is always su perior to th e in finite powe r of
icrs Sl and 52), o f th e syn th etic bearing of 3 Clhe Bor ro mean kno n ial the situation of whi ch it is th e state. We will therefore- wr ite : E > 0",
real, th e symbolic and th e ima gin ary ), or o f the funct ion of the l. The- fixing by po lit ica l p rescri ption, unde r an eve nta l and co llective co nd i-
feminine jouissance, tion, of a measure fo r state power. T h rough th is p resc ri ption, the er rancy
In the case of poli tics , we said that its first term, wh ich is linked of State powe r is interrup ted and it beco mes po ssible to u se mi litan t
collective charac te r of the po litica l event, is the in fini te of th e situatioa. watchwor ds to p racti se and calculate th e free di stance of po litica l thinking
the sim p le in fin ite, th e infinit e of presentation . T his infinite is de t frOlll the Sta te. We write this as It(r:), de sign ati ng a det erminate infinite
th e value o f its po wer is fixed . cardinal num ber.
We 3 150 said th at politics ne cessari ly sum mo ns th e state of th e si
an d th erefor e a second in finite. T h is seco n d infinite is in excess of the tornl etuS t ry larify the rundamenml opera tion
10 can lon 0of prcscnpuon
" b y gtvm
" g
its powe r is su per ior, bu t in gene ral we can no t know by how much. IJJt e: example s. The Bolsh evik in surrection of 1917 reveals a wea k St ate,
excess is mea sureless. We con the refo re say th at th e sccond te rm of q~.rrnined by war, wherea s rsarism was a parad igmatic in sta nce o f the
numericalit y is a seco nd infinite , the one of S tate power , and th at all WI itt,; l~sacr ed inde te rm inacy of the State's superpo wer. Ge nera lly speaking,
lirre:ct" .. . .
know about this infinite is tha t it is super io r to th e first , and that this fla ' tuna r-y forms o f poli tica l though t arc tied to a po st-cverual dctc rmi-
ence rem ains und eterm in ed . If we call 0" th e fixed infini te card inality ~~ of th e power o f the State as bei ng very weak or even inferio r 1'0 the
situation, and c the ca rdinality that me asu res th e power of th e State, tr of simp le collective represe ntation .
158 Theore tical Wntmgs POIttICS asIruth Procedure 159

By way of cont rast , the M.aoist choice of pro longed war an d the en . . "hich this power is enve loped. If th e politica l event allo ws for a cla rifica-
o f th e cities by the countrys ide prescribes 10 th e Sta te wha t is st ill an III \ fi.xation , an exh ibition o f th is power, th en the egalita r ian maxim is at
m easu re of its power and carefully calculates th e free d istan ce n.-.. 000; ~IIY pracli cab le.
power. T h is is the real reason why M ao' s question rem ains the ~ut whst is the figu re fo r thi s equality, th e figure for the p resc ription
how can red power exist in Ch ina? Or, how can th e weakest prevail ~br each and every sin gu larity is to be treated co llectively an d ldenu-
strongest in th e long run? \l(1hich is to say th at, for Mao. I( c) - the ~}' in political tho ught? Thi~ figu re i.s obvioU51~ th e I . T o fina lly co unt as
lion conce rni ng the power of State - remai ns largely s u ~rior to (J the .....hat is not even counted IS what IS at Stake 10 every ge nuinely po litical
o f th e situa tion such as it is summoned by th e political p rocedure . :Ughl, eve ry prescription th at summo ns th e co llecti ve as such. The I is the
This is to say that the first three components of num ericality - tbe llutnw cality of the same, and to produce th e same is tha t which an emanci-
in finitcs 0", c, I((e) - arc affec ted by each singu lar politica l seq umce patol'}' political procedur e is ca pable of. T he I di sfigures every non-egali-
not have any son of fixed determ inati on, save for that of th eir mutull (Irian claim.
lion s. Mo re speci fically, every poli tics proceeds to its own JXIIt To prod uce th e same, to co un t each one universa lly as one , it is necessary
prescription vis-a -vis the power of the State, so that it cs~tially 10 work fowl/y , in th e gap opened between po litics an d the State, a gap
creating the political function :n: in the wake of the ev ents ! u psurge. .-bose princip le resides in th e measu re 11(c). This is how a M aoist po litics
Whco th e political procedure exists , such that it manages a """'IlI ...as able to experimen t with an agrarian revo lution in th e liberated zon es
vis-a-vis th e State, then and only then can th e logic of the same, tba (~ beyon d th e reach of the reactiona ry armies ), o r a Bolsh evik poli tics
egalitarian maxim proper to evcry politics of emancipation, be set out. 1f1S able to effect a partial transfer of certa in state operations into the hands.

For th e egalitarian maxim is effectively incom patible with the 0( the soviets, at leas t in th ose ins tances wh ere the latter were capable of
state excess. The matrix of inequality consists precisely in th e im asuming th em . What is at wo rk in su ch situa tions is once agai n th e po liti cal
of measuring th e su perpower of th e stare. Today, for example, it is function 11, applied under th e co nd itions of th e prescriptive d istance it has
name of th e neces sity of th e libera l eco nom y - a necessity without iuc:1f created , but thi s ti me with the aim of producin g the same, o r producing
concept - tha t all egal ita rian po litics are deemed to be im possi lbt real in accordance with an egalitarian maxim. O ne will th erefore write:
de nounced as abs urd. But wh at cha racterizes th is blind po wer of -l:l(c» => I in orde r to designate this doub ling of th e po litica l fun ct ion wh ich
Capita l is p reci sel y the fact that it can not ~ eit he r m easured or fixed worts to prod uce equality un der the cond itio ns of freedom of though tf
po int. All we know is th at it prevails absolutely ove r the subjective Pl'lIctiee ope ned up by th e fixatio n of Slate power.
collectives, whatever they m ay be . Thus in order for a po litics to be We can now co m plete th e numer lcaliry of th e polit ical procedure. It is
p ractise an egalitarian m axim in the sequ enc e opened by an even t, it i' comPOSed of three infinnes: th at of the situa tjc n; th at of th e sta te of th e situ a-
lu te ly neces sary th at the state of th e situation be pu t at a di stance tion. which is ind ete rmina te; and that o f th e p rescr ip tion, which inte rru pts
strict determination of its powe r. the indeterminacy and allows for a di stance to be tak en vis-a-vis th e State.
Non-egalita ri an conscio us ness is a m ute consciousness , th e cap livc This num encatiry is com p leted by th e I . whi ch is part iall y engende red b y
err ancy, o f a po wer which it can no t m easu re. This is what cxp laiDl the pcluical fu nctio n under the cond itions o f th e distance from th c State ,
y,·h· h
arrogant and perem ptory charac te r of non-e galit ari an state men ts, even rc themselves derive from this function . H ere. th e I is th e figu re of
~ualit ;.· an d sameness.
they arc obviously incon sist ent and abject. For th e statements of
pc rary reaction ar c shored up enti rely by th e errancy o f state excess, i.e. ~e tturncricaliry is written as follows: 0 , 1:, n(c), :n:(It(c» ~ 1.
the un tramme lled violence o f ca pi ta list anar ch y. T his is wh y libera l I the ' at singularizes the po lit ical p roced ure is th e fact that it p roceed s from
ment s com bi ne certain ty abo ut pow er with to tal indecision abo ut its th Infinite to the I . It makes th e 1 of equa lity ari se as the univer sal truth of
quen ccs for people' s lives and the un iver sal affirm ation of collec tives. S~ COlk'<:live by carry ing out a prescripti ve ope ra tion upon the infinity of th e
Egalitarian logic can onl y begin when the St ate is co nfigu red , put is bf an Operation wh er eb y it co nstructs its own auto nomy , or d istance, and
d istance, measured . It is th e er ran cy of th e excess th3t im pedes egali a le to '~" rrcc tuatc -u s maxim
Co - Wit- h 10
i l h at d -rsrancc.
logic, not the excess itse lf. It is no t the sim p le power of th e sta te of the iIllo nVcrscl y, let u s not e in passing that, as I esta blishcd in ConditiO/lS,' the
tion th at prohibits egalita rian politics. It is th e obscu rity and m easu re! rous proc ed ure. whic h deploys th e truth of differe nce or scxuation
 160 Tbeoretcel WntJngs

(ra ther th an of th e co llective), proceeds from th e I LO th e infin ite th

medi ation of th e two. In th is sense - and I leave the reader to medj
th is - politi cs is love's n umerical inverse. In othe r words, love beau. SECTION III
po litics ends.
And since the term 'de mocracy' is today decisive, let me
providing m y own defin ition of it, one in which its idc nu ry with Logics of Ap pearance
be render ed legib le.
Democracy consists in the always singu lar adjustment of ff
equality. BUI what is the moment of freedom in po litics? It i.
wherein the Stat e is put at a distance, and hence the one wherein the
function n ope rates as the assignation of a measure to the errant I
of th e sta te of the situa tion. And what is eq uality, if Dot the
whereby, in the distan ce thus crea ted , the po litical fun ction is
again, this time so 35 to produce the I ? Thus, for a determinate
p rocedu re, th e political ad jus tme nt of freedom an d eq uality is
the adjustment of the last two terms of its numcricality . It is wri nca:
1t{n(&» ::::;. IJ· It sho uld go without saying that what we hav e beN
notation of democracy. Our two exam ples show that thi s notatioD
singular names : 'soviet s' d uri ng the Bolshevi k revolution , 'liberated
d ur ing th e M aoist p rocess. Bu t democ racy has h ad many other namtI:
past. It has some in the present {for example: 'gathering of th e Poli '
nizanon and of the collective of illegal imm igran t workers fro m the
and it will have others in the fu tu re. .-
D espite its rarity, politics - and hence de mocracy - has existed ,
will exist. And along side it, un der its dema ndi ng cond ition, m
which is what a philosophy d eclares, with its own effects in miDd,
worthy of the name ' po litics' , O r alternately, what a thought d eclarel
tho ught, and under whose condi tion it th inks what a thou gh t is.