Mark and Lack, Infinitesimal Subversion

49 Pages·2012·1.065 MB·English

by  Badiou, Alain

CHAPTERN INE
AlaiBna diou
Marakn dL acOkn:Z ero1
[510E]p istemborleoaagkwysa f yr oimd eolorgeiccaapl[te rurprsiee,i ] nw hich
evesrcyi ecnocmee tsom imei tosw nr eflectiinosnoa,fs ai rte xclutdheast
recaptiunrset'ist uotpieornatathlone ro ,t ioofTn r utahn,dp roceiendsst ead
accordtiot nhgce o nceopfat m echanoifsp mr oducwthioosnee,ff ecbtys ,
controanssete ,et koes x plain tthhterh oeuoogrfihy t s st ructure.
Whaotfa ne pistemoofllooggiyc ?
The represenotfta htidisio snc iwpiltihntiehn ne e twoorfik d eological
designparteosreisnt at sss o methfionrge tiogt nh ree aalsa, d iscotuhraste
presuptphopeso essi t[ipnogs oiftT riuortnah)t htehrat nh ceo nstruocfat ni on
objeThcitsi. sw haFtr eagber updtelcyl awrheehsne l ikeapn rso postioat ion
propnearm weh osree feroerdn ecen,o taittsih oTenr ,uo ert, h Fea lIsfteo .l lows
frotmh itsh alto giincc esscaonotrldyi ansam taensyl inkiends criapst ions
necesisnao rryd efroi rt t op asfsr oomn ei nvarinaabmlee- ofT-rtutheoe -
anothtehrul:so ghiecr bee comtehsse c ripitnfiudnrieatle nofet srhsu's ct ivil
sta[t'luiesnfin dsic ripdt'ueurtncaa iltdv eil avl e er.]i't
Ont hbea soifas l tlh oinsce a inn f adcetm onst-arsaJt aec qLuaecsaa nnd
JacquesM-iAllluaenirdn e rttoad koe-t haatss, o methwihnigcc hab ne k nown
undesre venraamle tsh,eT rufea lblesn eaittnhsa mewsh,i lneo netheless
preserivtcisin vsgit la tthurso tuhgieht eratiaotin tp set rhpaetbt,iu rahtlah us,s
ceaselreesgsilsyti etnrsei wan ngo nymnoaumse Thse. n ominmaolv emetnhte,
repetciotmipvuel tshiaoitnnt, h ceh aoifnp roposiutniroanvoseu,ldr si sbelief
int hTer uec'osm mopna tronmyamr,kn so thibnutgth lea cokv ewrh icthh is
movemegnlti wdietsh roeusti sotras nuccec ess.3
Tot hitsw ofporlodc (epsrse serovfta htTeir ounce o;n vocaantdmi aornk ­
inogfl acwke)w ,i olplp otshese t ratifiocfta hsteci ioenn stiigfinci fier.
1 TN: Fpiurbslti asshA eladBi and i'oMua,r qeutme a nquaep :r opdoesz r eoC'p,A 1 0.8
(win1t69e9r1 )05:-7 31T.r ansblyaZt aecdh LaurkyFe r asweirtR ha Byr assier.
2 CfG.o ttFlroebg' eO,nS enasneNd o mina'ti,un Rm eagdsii Pnnh ilosAonaplhyisciasl,
edH.e rbteF reigl andS elWlsia( lrNferYwio dr Akp:p letCoennt-u-rCyrof1t49s9),8, -5 012.
'Evedrelyca trieasv enteinnwc hei,cw hh amta ttsea rre ntohmeit naoa ft hweo rdiss, et­her
forteob ec onisdeedra sa p roeprn amea;ni dt nso minaittfuh mee,i r san yi,es i tthheTerr ue
ort hFea l'(s 19e.)' A[]ltl rusee ntehnacevet shs ea mneo minaatnuldm i,k eawliflsa elo snee s'
(29).
3 TN:Th e Frenrceha 'dLsm:eo uvemneonmti nlacalo, mpurlpeseitoionuts ied veep loie
/'impuaic srsotaienrnjcieare m alieps a tronuysmuedc ulV raciel,sam t a rqmueemd ea,nl sa
sequleindeecpeser oposidteci eoq nunsie, s qut'u nm anqsuuerq uoeil gllei ssasners e sinsit a11ce
succes.'
160A LAIN BADIOU
Ino uvri ebwo, tFrhe gied'eso lorgeipcraels eontfha itosiw onen n terprise
antdh ree capotftu hrriees p reseinntt ahlteei xoinoc fSo ing nilfiaecarkn, dt he
place-omfa-sltkah cpeku ,rp er oducetsisveent ch[ee5 ,1 1p)o sitpirooncaels s
throwuhgihc lho gaismc a,c hilnaec,nk ost hiidtno ge nso ptr oduce elsewhere.
Thel ogoiftc h Sei gniifisaem re4t aphyasr iepcrse:s eonftr aetpiroens enta­
tioanni, n tra-idperoolcoaegnsidpsc r aolg ression.
I TRIPLE ARTICULATIONO F THE LOGICAL PROCESS
Thet heoorfly o gpiecr tatiotn hsme o deosfp roducotfai d oinv isiinlo inn ear
writoirni gn scritphtdeii ocnh:o toofam s yt ructsueortfes dt atemwehnitcsh
havbee e'ni ntroidnuttcohefi edn 'a mle chanaisas nm( already prraowc essed)
material.
The immedicaotnes equoeftn hciiesst hatth seo lree quiretmheatntht e
functiooftn himene gc hanmiussmt siatsth iuasltfy t imatelym suosbmtee thing
cuitna ne ffectfiavseh itohinen: s crip[teicornimstu usbrte em sec]h anically
separianttteowd do i sj[oidsonjiite nsct)l aswsheiscb,hy a, l lutsoit ohmnee cha­
nismmo sftr equeemnptlloyya ercdea ,l tlhecedl aosfds e rivsatbaltee maenndt s
thcel asnso -nod fe risvtaabtleem ents respectively.
The classdieficnailot fit ohaneb soclountseyi o sfat s eynsctaecmc,o rtdoi ng
whicahtl eaosntwe ell-feoxrpmreeds nsoibtoe dn e rivwaibtlhieitd n,e signates
precitshemilisyn imraelq uireImtiesnn ftr.a wcotuilbodetn a ntamtoocu onnts id­
erianm ge chantihsapmtr oduncoetsh iantag l- lp roducitnti hoiinsn stance
beijnugts htee ff ectiveo fdt ihvomisaseti eornoi nwa hlisco hni eos p erating.
Qnc losienrs pecittbi eocno,mc elset ahrat th ifisn adli visiimopnlt ihees
succesospievreao tfit ohnri enet rimceactheadn ibsemfsot:rh eec ya bn ea llo­
cat[etdto h cel aosfds e rivoarnb olne- dersitvaatbelmete hnsety sn)t,a mgumsst
bef ormetdh,es no rstiendnc,oed erivastyisotnieacsmla paobfsl ueb mitatliln g
oft hetmo i tpsr incoifdp ilvei s(iThoinjs.u smte antsh aetv esrpye cialized
machihnaaesn i np[uett nrienetw)oh icohn lsyp ecainfipdcr eviporuoscleys sed
materciaabnle is n troduced).
We mustth eredfiosrtei ntghumeie schh aniosfcm osn caitofenorn,ma at­
tinao,n dd eriiovna.t
Anyo ccluosfti hoaenu tonoofmt yhs ee comnedc han-irseml attoti hvee
thi-redn taliolssit nhvgee reys sein.cteeh.,pe r oductiveo ftf huleno cgtiicoanl,
4 By' loogfit ch Sei gniwfieem re;a n htehrseey stoefcm o ncetphtrso uwghhi cthh e
articuolfta htseiu obnj iescc otn ceiLvaecdk:, PPllaacceeh,So ultdueFrroe,r, e clSopsluirtet,i ng.
Thesceo ncehpatvbsee epnr odubcy)e adc qLuaecsaa nnwd e a cknowlade edfignei dteibtvtohe i m
eveansw ee ngaignte h per octehsacsti rcumstchreuiisbrtee h:sii tssh cer itpircoacle dure.
The thewseia sr dee fenhdeirnaegi mosn laytd elinetahtieim npgo ssiobfail loigotiftyc h e
Signitfihaewtro uledn vetlhoep scoirednaetnridi fi nwc h icthhe er asouftr heee p istemological
brewaoku lbdea rticulated.
MA RK AND LACK 161
proc5e Asnsdn. o thiinsmg o riem porttahnattnot ravtehrmesa ec hinoefr ies
logiintc h epirro poerrd er.
(aC)o cna tennTh:ae t aibosolpurtielmyar raywm ateroifta hlle o gical pro­
ces[s1 ]5i 2ss upplbiyae p da rtiscpuhleaorrfte e chnpircoadlu cwtriiotni:n g.
Thisc onsoifsa t ss toofc kg rmaaprhkissce, p araanbidln ed ecompofsoarbml­e,
inagfi ni(toear tm osdte,n umersaebatls ,ee w)te w iclaltl hl'e a lphabet'.
The firsmte chan'irsemc etihveemssae'r kfsr,o wmh icihtc ompofisneist e
seqcuee(snl injeuaxrt apowshiitcmihao yni sn clruedpee tiIttii sos neustp) t .o
produaclel fitnhisete eq ueonfct ehssi osr atn,sd o i itts h etsheaw tefi ndi nt he
outpouftt h miesc hanLiestmb .etS h pirso duct.
(bF)o rmaThteis oenco:mn edc hanoipsemr aotnSe ,ss oa st oe ffesctte,bp y
steapp ,ef ecrdti chyo,otn otemh aste parates withouts erqeumeanicnedse r those
thmea chi'naec cefprtotsmh' o tshea ittr ejeWcet wsi.lc la tllh osseeq uences
accepbtyte hdme a chi'nwee ll-feoxrpmreedsa snitdoh noest :h e'risl l-formed:6
Theo pera(ttoh'recs o mposn)'oe ftn htmiesc hanairstemh reu loffeo rsm a­
tinow,h icphr esccreirbtceao innfi guraasta icocnesp tcaobnlcea tentahtuiso,n s:
foerx amptlheme,a chiknneo wans' thpere diccaaltceuw liuteshq ualwiitlyl'
accetphstee queIn(cxex)as, n dn o-It(xx),b, uw ti rlelj tehcsete quexn(cxIe), .
Througahd angersoeumsa nltaixcit thyre,e jecstteadt emaernoetft se n
cal'lneodn -sense:
The seotfr uloeffs o rmactoinosnt itthsueyt netsa x.
Leutsn otset raightthaaiwtfaa ,sGy o decle'lse btrhaetoerdie nmd ictahtee s,
finadli chot(otmhoyaft t h teh imredc hanciasnm)nf ootar', s trmoancgh'ib nee ,
effectuated witho-usti ntcrheee marareiae nl dwearuy7ns d ecisdtaatbel-e
5 The priviolpeegreadot fto hrio sc cluissi octnoh nec oefpm te anionrsg e n[sess e]tno,
whicbho tthh oer iginoaftt hiTeor nu (ed erivaabnidtl hiretje ye)c toifno onn -s(esnysnet ax­
formaotnir)e fbearc k.
6 Thatth dei vibseiw oint hout rmeemaantishn gaditev rae nniy n scriwphtaitosno( eiv.eer.
afi nisteeq ueonfsc ieg onfts h ael phatbheetr)e, aenax citsuptarsol c etdhuaret poenrtemo i ts
deteruminnabemi guwohuestlhtyehe rex presdsoieoosrdn o enso cto nfotrotm h reu loefts h e
syntax.
Focrl aslsoigciatclhs i,s sypnrtoapcectraitbncye m adteh oeb jecart e coufr dseimvoen stra­
tioonv etrh neu mboefrp arentihnte hseeex sp resCsfSi.to enp.Ch oelnKe l eeInne,t rotdou ction
Metamat(hAemmsatterNidocarsmtH :ho llPaunbdl isChoi.1n,9g 6 742a) n,pd assim.
7 A stromnaghc inies o nec apabolfpe a rtititohneii nnsgc ripotfr ieocnusr sive
arithmetic.
Note tthheaertxe i asw tesa bku ptef cerlto gimceaclhi asnmt:hP er oposiCtailocnuThalilus s .
systieismn deed:
-Consisitnee vnestre yn osfte h tee rm;
-Decid(afbolre weevlelr-yf eoxrpmreeds isctia bonen m, e chanikcnaolwwlnhy e tohrenr o t
iitds e rivable);
-Compl(eetveew reyl l-feoxrpmreeds issei iotndh eerri voarsb ulceth h attoa ddi tt ot he
axiowmosu lrde ndtehcrea lciunlocunss is)t;e nt
-Catego(raiolcfila tm lso dealrsie s omor.p hic)
The mereex istoeftn hcies Caplrceuslesunestv sep rraolb lfeomtrsh leo goiftc h Sei gnifier,
sieni ccto ntaniontsh- innoget v eanne mptpyl a-cteh awotu ladt tteoasl ta cIkna. lr li gotuhri,s
162A LAIN BADIOU
ment-st hvee rpyo ssiobiftl hiirtsey s purltep sousptehesex isotfae d nicceh ot­
omimceh casnmit hlaeta vreesm aniotn hdoeen er :w hsiucphpl tihdeees m on­
stramteicvhea nisimt rswa imwta ht ertihawele ,l l-feoxrpmreeds Osnilooynn s .
the conodfaip teirofsney cnttc aaxwn e s ummodne rivaatpioorni'ase .
The splsiitg niofyridnemgra ,r kbeydw haitlt a cckasbn,e e xhib[i1t)e5 d3
onliyni tdsi fferfernocamena utonomoorudtseh rai tis ndeed wchliocishse d,
tos aeyn,t idreecliyd (atbhlee ooftr hdfeeor r maotfsi yonnt agImnts h)si.es n se,
wec annmoati nttahiasntc isosric oonm pulistievreai tstih ioenn e viptraibclee
ofc losWuhraemt.u sbtes aid, iintssh tatethea exd i,s toefn icanenfa llible closed
mechanciosnmd ittihoeenx si stoefna mc eec hantihsamct a nb es aitdob e
unclosaanbtdlh ee,r eifnotreer lniamliltye d.
Thee xhiboifa st uiteo unpr restuhpeepx oisseotfsaef norceec losure.
Nowt,h eoreatnitciacli paastiiwdohena,nst e etdosb er emembeartte hdi s
poiintsth awth at fiwnedi nt hoeu tpouftt h sey ntamcetcihca niists hmse e otf
well-feoxrpmreeds wshiiocwnhesw ,i clalEl .l
(cD)e riivoTanht:te h imredc hanoipsemr aotnEea sn di,ng eneirssae lut,p
top roduce:
1. A perfdeiccth otboemtyw eTheens e(so dre rivable satnadnt oenm­ents)
These(sn on-dersitvaatbelmee nts).
2. A certtyapoieffn un ctiornelaalbt eitowne tehnet sweod ivihdaeldv es.
Thiss ecocnodn diitsci rounc Iifdai lc.h otwoamsty h oen lrye quiretmheennt
thcel assliocgaimlcea clh ani(stmhfseo rmaliozfaa rtiitohnm feoetrxi acm,p le)
woulbdef lawsliensacsloe,lft hemseec handiosi mnsd eseedp awrealtfleo- rmed
expreswsiitohnroseu mta inidnettroh dee rivaanbdtl hene o n-deriiv.aeb.l e,
inttoh es(eTas)n ndo n-th(eNsTe)s. 8
Anu ndecisdtaabtleems euncathst, h oen e consbtyrG uocdteielsod, b vi­
ouslnyo ta statemtehnawtto ulbde n eitphreorv a[bdlee tmraobnlneor]
systleamcn kost hinnorg ; diomtea srt kh neo thoifwn hgi cihta lirse taodmoyu ctho s atyh aiitts
evelna cking.
Onec ousladty h atthp ee rfecotfti hoPenr oposiCtailocnupalrluo sv itdheiesn tra-logical,
differerneetfriefanolttr h ree la'tiimvpee rfoefoc tthiseoyrns 't ems.
8 Iti sa ne ntidreifelfryeq nuets ttiodo ent ermwihneet hoernr o tth eerxei fsotersv ery
wello-rfmeedx presas mieocnh anical p(reoffeccetdtiuhvraweeto) u ladl lowt oku nso w' in
advan(ciew.'ie t.h hoauvti tnocg a roruytt h dee rivawthieotnoh)ren r oi tt d eirsi vable.
The existoefsn ucceah p roceddeufirnete hsde e cidoafab s iylstiWetemky .n o(wC hurch,
Kleetnheas)tu fficiesnttrlolyno gg imceaclh anairsgeme sn eruanldleyc idable.
Wes hounlodct o nftushdeee cidoafabs iylswititetytmhh eex istoernn ocne- exiosfat ence
statesmuecnthth ante itihtneo rir t nse gatairdoeen r ivThaeb plreo.b loeftm h eex istoefan nc e
undecisdtaabtleeim sneo nattp robloefdm e cidiatbybu,iat lp robloefcm o mpleteness.
A sysmtaeybm ed ecidaanbydle eit n comptlheettrheee:e n x iisnit (t u ndecisdtaabtleem)e nts
concerwnhiincight p oisss ible itnao d v'adnetccheir,do eau'ng h acptruoacle dtuhrateth, e y are
neitdheerri vnaobrrle ef utTahbcelo en.v ehroswee,vi ensro t,t r uaeni: m pormteatnat- mathematical
theorteitmeh sue n decidraebsiu(llCithtsuy r tcoth h)ie n complerteesnu(elGiistdsse Ilaf)( .s uffi­
cientlyf osrtmrsaoylns tgie)usm n decitdhaebinlit ees ,i tihnecro nsoiris ntceonmtp lete.
MA RK AND LACK 163
unprov(awbhliweco hu lbdem eaningOlnet shcseo) n.t ,rt ahhreey aorfGto del's
procoofn siinst thdsee monstrtahtasituo canhs tateimnsen opttr ovaIbitls e .
therefore clteoao rnloeyf t htaews hosa ilgvneesd.
An undecsitdaatbeilmnseeo nttth ree maionfdac e urt ,a s btuatt ewmheincth
iss ucthh ante itihtne orir t nse gatiisdo enr ivSaubclahes .t ateimsce enrtt ainly
irreufta(brleefu t=a ptrioooonftf h nee gatBiuoitnit )es .x pliucniptrloyvTh aebrlee .
iisn deaed di viwsiitohnro eumta ibnedtweerde enr ivaanbndlo en -derivable state­
ment-bsu bto tGho deslt'ast eamneidnt ntse gateinoudnp i nt hsea mdei vision.
Everytdheipnegnh desru ep oans pecsiyanlt aocpteircaa tnodtr h set ruc­
turweh icihgt o vertnhosep: e raotfno erg at[i1o15n .4
Wec anntohte retfaokGreoe d etlh'eso rteomm e atnh aetv edriyc hotomy
leavare esm ainodrte hrae,tv edruya liimtpyl aid eiss jtohiintrted r omn,te h at
woulbded e-cenrterleatdto ti hvreeu lteh aitn teronradleelraysc t he romft he
paiThri.s( commorne)a doiftn hgte h eorieasmm e taphyismipcoIarlnrt e.a lity,
thper oblem pteotr htpeaa irntsi scturluacrct ounrdailt ionso nit mhpeo sed
thilrodg imceaclh aniosvmea,rn da boviets se parative- tfhuiinssc tion
summeudpa boivneo ucro ndi2t.i on .
Whaitrs e quiirases fd o lliontw hsae:l phatbheetnre,ee tdosb ea no perator
(icta nb en egat[isoynm boalsi 1zoe rda nyo thetrhi:en tuimteiavneio nfg
-
negatiisao nno bstahcelrseeu )c thh aitfa s tatementt oob neeld oinvgiss ion
(tE T ort E NT)t,h etnh set atement boyab ptpaliytnioein dttg h oep erator
(i-.)ew9.i bleli nt hoet hdeirv is(-i tEo NnT o r- tE T ).
Whaitos r igiantia slslhuyee r en oittsh c eu atss ucbhu,at f unctrieolna ting
thsee parhaatlevdThe es G.o delliiamndi ote nso bte aorn t hdei chotaosm y
sucRha.t hiectro ,n cetrhnuesn ity-of-cororfte hsdepi osnjdpoeainrncttes .
Godel's statelmetethn etbr eaes f iugnncitfirieeosln:aa ttlhi asoten n edasc h
statetmoei ntntse gat(it.o n.- t..Th) eries n oe ffectdiivceh ottohmacytu ts
throauglohlft horseel ations.
Mechanims of
derivatoin �Mechanism of for mation
NT T
._.Sets
undecidable -t-··-· --···t·· eIxlplr-efsosrimoends c(omneccahtaennoiafst mi on)
proposition
"'�
t'... ....-.t'.
E (well-formed
expressions)
9 Inc onforwmiitcthoy m mouns agweew, i lulst eh sey mb-otlod enotef uncttheio ofn
negattihorno ugthhoreue tm aionftd eherix sp osition.
164A LAINB ADIOU
Onem ighhto pteoe xpfeorlm T (thseeo tfd erivsatbaltee maelntlth se)
relatti. o.-nts.o; t hertwhisesy es,tw eomu lbdei nconsiBsuottne cena ttn.h en
goo nt os hotwh asto moeft herseel atwiioalnllsw aryesm aiinNn T :p recisely
thowshei ccho ncuenrdne cisdtaabtleem ents.
Whawte a rfea cweidt hhe riesa t earoifsn tgr ucrtautrhteeh raa nd ichot­
omyT.h ek etyo t hlei mit[aitlmiaiotntni ]foo llpoawrsa doxfircoatmlh fleay c t
thatths ee paramteicnhga niisfs omr cneodtt ob ep erfaencdtt h,u fso rcteod
presetrhcveoe n coefapr te verrseilblabete itwoetneh tnew hoa lvAesas r .e sult,
thliism itaftafirro onam,t testthiatnthsg ep apcreo dubcyet dhd ei vibseioanr s
thter aocfte h tee atrh acta us-eisdth ,o wrsa thtehrao tn e cainnndoetfi nitely
produtchseei gonft hlea twtietrhi ittn;h aitnc ertpalianct ehtser aiceseff aced;
thaast t romnegc han[i1sm5n 5e)ce ssaic toamtpeldse itvei siinro enj ecitti on
effecitnes a,c ohfi tpsa rotfsc ,e rtmaairnko sft hoel Wdh ol[eoT u.t ]
Theu ndeciidsna botlthe se u turaotfli aocbnku tt hfeor ecloofws huarites
lackthirnogtu hgfeha iltuopr reo duwciet,hw ihnai tds e rivabwlheo,lo eftt hhee
non-deraisnv eagbaltee d.
Thel imitmaetainotsnh: at th eerxei astst osm peo ibnte,t wetehpnea rTt s
andN T,a d istwaihntocuect o ncoenpett h:adt e lineiantt hesesp ,a ocfen on­
thesaes st,a tewmheonstne e gatciaonnn boeti nscrwiibtehdti hnse p aocfe
thesaenswd,h icihst h erefore toutn hrsiepsla actee.d Godeilns'o st tthheeo rem
siotfes eparaftaiioln'busuro tefi , tg sr eaetffiecsatc y.•o
Ift,h eretfhoterh ee,o roef'milsm itarteisofunrl'ott m h ceo nditoifio mnpse r­
fectaisosni gtnote hdde i chotmoemcihca nwiesm mu,sr te confi[gerumraeen ri]
thceo ncoeftp thl ea tstoae srt oi ncorptohroacstoeen ditWieo nwsi.l l then say:
Logiisact riaprltyi cuslyastt(eecdmo ncatesnyanttdiaeoxrn,i, v atthiaotn )
produact eesr midniavli siinlo inn eianrs crisputctihho ang ti,v aes nu itable
syntawgesm h,o ublead b le:
1. Toa lloicttao ot neoe f t htew oh alv(eTosrN T);
2. Toc onstars uycntt aogbmt aimneecdh anifcraotlmhl fieyr bsytt haed ditoifo n
af unctor (cgaelnnleeergdaa ltlsiyuo cnth)h ,ai ttfh fier siitsn o ndei vistihoen ,
secownidbl eli nt hoet her.
Condit(i1io)sin d ealslayt"i sbfiyce lda ssical m(esctehhtae nooirrsy m s
thfeo rmaliozfaa rtiitohnm Tehtesi ecc)o.in ssd a tisofinelbdyyw eamke cha­
nisma sst:r omnegc hanciustamsl t low oe ll.
10 Wew ialbls tfarionam n ayt tetmodp etc ipthhseetr a otfut shh ei atus ibnettwueietni on­
isma ndf ormaliinGs iidme lt'hse orOentm h.pi osi snetoe,u arp penodnSi mxu ylalnd'esm onstra­
tioann,d o urc ritoiftq huceeo ncoefp til tiamtion.
1 1 'ldcnblelyc'a aulsteh oiuitgs th r uteh aetv ewreyl l-feoxrpmreedsi sesii otnih neT r o r
NTt.h ee xisteonfac ne' effec(trievceu'ar lsgiovrei,pt rhomciectd)hu arwtoe u ld uastl oldo ewt er­
mineI nto whoiftch he stew oc lasisftea sli lsssh owtnob ei mpossiinmb alnieyn staThnicsie tssh _e
prohlcomft hede cldanbifltsiyhtseyt( ecnmfo .t8 e} .
MA RK AND LACK 165
11 NULLITY OF THE THING - IDENTITYO F MA RKS
Thisd escriopftt hileoo ng imceaclh anailslmou wss q tuoe sttihcoeon n struc­
tioonft hceo ncoefsp utt urteh diiosn m aainnad,l louwsts op recidseetleyr ­
minteh mee ta-thfeunocrteiotofitn chz ee ro.
Leutsd ecloaurtreh esetsho eua tts et:
1. The concepidte nohtfoi ltodyns l fyom ra rks. Logirce cnoeutvroeas rne y h as
self-idtehnitenivgcew,anh l e 'nt hiinusgn 'd ersitnto hosede nosfe tohbej ect
ofs ciendtiisficco urse.
2. The conceopftt r uitsha ni deolodgeiscaiatglonb ro,t rhe capitaunlda ting
conceatlhiesn cgi enctoinficce opfts sel ecatniddo inv isIitdo ens.i gnates
globwahlalitysi ,t s,e dlaif fferenmteicahtaendi sm.
3. Thez erions o tth mea roklf a icnak sysbtuettmh s,ei g(n1 5t6h)aa tb breviates
thlea ocafkm arOkrr. a thieitrts :h i en dicawtiitohanis ,ni gniofyridnteghr a,t
theirasen i nscripprteisioentnn h tre e jedcitveidos fia onno tohredre r.
4· The logico-matshiegmnaiitfisise curat lu orneldty o i.t siIesitl n fdefinitely
stratified.
5. Inl ogail ca,ct kh aitns o ts iag nhifianesors igniifiitefs ror :e closed.
6. Thsei gniinfig eern eirnsao lat r ticutlola atctekhd r otuhgceho ncoefsp utt ure,
whospeu rchase tdheamtas nitdghsne si afiteiracs efyr tcaoinnd iAtnidot nh.e
construocftt hiacoton n diitnsio ottnh tea sokfp sychoanbauoltfyh siisst ori­
eam!a terioanllitysh ime:d eolsoigginciiassfiu eltr u red.
LikLea c'asan ccouonfGt osd 'estl heoraenmd stehmea notfii cmsp lication,
Jauceqsl-aAMiinl ldeirs'csu sosfFi roengasen "Bd oolaer aem biguiontu hsa t
thecyo mbisniem,u ltanaenodiu nsdliyts ltwyih,na cpter tationt sh eeffe ctive
construocfat l iooglnim ceachanwiistwmhh apter tationt sh (edi eological)
dicsourse twhhrioclhuo gghi crieapnrset sheecniotrn strutcott hieomnsse lves.
Consueetqnlwye,s houblewd a royf c omprehewnidtithnhigle no gical
procietssasen ltyfr ansloaftt hsieio gncn osn'cn teia_vgee nbcayci kn ttoh e lexi­
coonfs ubsumpThtiisno ont.i on, ientn hc(els opseecrdue elfraern)rt eilaalt ion,
litkhere e lantoetdio ofdn e notamtaisotknhss,e t rifcuntcltnyia eols seonftc hee
mappi[nr gesn vaotwi osr]k ilngosiicmdaeelc hanism.
Nothhienrgwe a rratnhtteis ot flobeej d Herteh teh iinnsgu lnloi: n scrip­
'
tiocnao nb jecitti.fy
Withtihnim se chanicaoln fiesn pdnasoc teh,bi untg revfeunrtcsiiobnlse
frosmy stteosm y stfermo,mm a rtko m ar-kn othbiunttgh mee chanical
dependeonfmc eicehsa niSsemmnsat.ii ctsse enltfei nrtslo o goincli yn saoraf s
iotp erbaettewse tewnol ogimcaot-hemastiigcnailofy ridnegar nsod,n c ondi-
12 Cf.J acquesM-iAlll'aeSirurn,te C u'p,A 1 .3.
166A LAIBNA DIOU
tiotnh atthf eun ctioofn sce osrprondbeentcweet ehnet sweoo rdearrtseh em­
sellvoecgsoi -tmhaemalt.i'c3a
Neitthheirnn ogor b ejchta vteh sel igchhtaenshctee ro ef acceadniyn g to
existbeenycotenh dee ixrc luwsiitohnto ruatc e.
Itflo lotwhsat thL ee ibnriezqiuainr oefms eenltf -yi,wd heincithsni etces­
sariyno rdteorp resetrrvueit sih n,t ra-(ltohgeiocraoelnt liiycn asalora)f si t
pertatiot nhsie d enotfim tayr kIstp. os tuloantt ehsbe,a soifas n inaugural
confideinntc hepe er maneonfcg er aphe[mgersias ep,]th hatth eerxei asnt s
'idenatpipclailc'oa ftt hiseoi ng niofyridntegori ts,oe nlef that preserves its
struc[t1 5u7 r]e .
Moroeveirit,ss cieansac w eh olteh atta ksees-ld ifenttyti ob ea p redi­
catoefm arkrsa thtehrao nft hoeb jeTchtir.su lcee ritnalhyo lfdostr h ose
facsto fw rigtp irnopteoMr a tehmatiBcutsi at. l shoo lfdostr h oisners icp­
tioonfes n geyrp ropteopr h yiscAss.B achaerldh asa dmriabdleym on­
strattheed ,op nrloypl eypr hyiscraull oefs ubtsuttiicoonn cearrntsi ficial
opreartso':hT ep ripnlcoeift hied etnyot fii nstruimtseh ntetr sup er ipnlcei
ofi dteinitnye veerxyp erimsecnite'an'Ilc4it e ts .h tee chniivncaarli aonfc e
traacneidsn strutmheasntut bst raalaclmt bsi gfuriottmyh seu bstiotfu tion
terms.
Thusd etermtihnreeu dl,es eolff -iadlelnootwfnis ote yx cepatnitdoo nlse r­
atnesoe vocaotfwi hoanet v adietns,o etv einn ftohreom fr j ecetiWohna.it s
nostu bstitutabilsseo -mtfehoirrn-agid tiscueanlltflh yo uogfwh hti,ct hhl eo gi­
camle chanbiesanmr ots r aIcite s. p iosmsibtlote u rinit n taone vaenscean ce,
shimmeorcsiinlgl aatsFi roeng,e doheeps hawnhetna slml(aydit eioocglaically)
convotkheersne votkhetesh itnhgai tsn oste lf-idienon rtditecosra u lm mon
thzee rWoh.a its n ostu bstitutabilsfe or-efcsolerowd-i itthsaoepulptfe o arl
mark.
Yeath omonymporuesd iccaanit ned ebeecd o nstrwuictthelidon g ical
systtehmeser:xe i' scta locfiu dlein itniw thyi'cn ho ni-denitmsia tryk ed.
Ino rdteora v otihdse l ippoaflg aensg ulaegutesa , g rteoge i vtehn ea me
'equatlosi utcyah'h omonymporuesd iwchaitcwehe,w ildle nobtyeI (yx),
(rodinlayt,rh iwiosu lbder eaadsx :si i denttioyc.)a l
13 Web eliAelvoenC zhou rch tiois d eryniS tgehimtfa nwtiitSchy sn tianxt hlea sitn stance
(chf.i Isn trotdouM cattihoenmL aotg[iiPccrai ln cPertionncU:en tiovenr sPirteys1s ,9 566!5.:
'Thaesssei gnomfde enntost aatnivdoa nltsuo te hswe e lolr-mdfef ormulmaasyb em aduesa bstract
corresposnotd hetanhtc eetisrr,e atbmeelnottn otg hse orseynttai'x)c.a l
Semanbteiccosml eosg (isccaile onntliyfi c)iw htie stn hs ey notftah xde if febreetlwelcc1e1
syntaxes.
TN:F oarm oreex tentdreeda tomfte hnrete labteitownse yennta nadxs e mantics,s eeA lain
BadiThoeuC, o ncoeMfpo td( e91l6 9e!d.Z. a chLaurkyFe r aasneTdrz cuhiTehon, t ranZsa.c hary
LukFer a(sMeerl boruer.npe2r:e0 s0s7,) .
14 GastBoanc helI.:Aacrtdi,rv aittieo dnela apl hiysstcieoq nutee m(pPoarriPasUi:l 'n,e
159)1,5·
MARKA NDL ACK1 67
Wea rgeo itnogs hotwh atthc eu stohmoamroyn ydmiys simaur lealtae­s
tioonfp repspusoittihoaentx hibaigtasit,nhp ,er ioorfit thfyeor eclo[sdeud
for]c.lo s
Consifdoeerxr a mapfi lreso tr-dcearl c(uolnuiesnw hiicithis m opsbsliteo
quafynt oiveprr edeisct)ah:tpe er ditciavceo nasnottfe quaIli isit myp licitly
definbeywd a yo ft wo ax:i'o'm s
Ix(,x()T orteaflle xivity)
I(yx)::,:: :>[ A(::x::A:>) ( y])
Itm ight be tthhatothu aegx hitoo mfr eflexfiorvmiutlya wtietsht ihne
inrsicptoifot nhse calculouust po(uftti h nse y tnhteam cetcinhcia smth)e
fundamensteallf -iodfae nnlyte ittatytae lrBl u.tt h iiss tnhoceta sweh:aw te
havaeg reteocd a lls etlhfe- eoqfauv aalriitiaynsb o lteth s ee lf-iodfee vnetriyt y
marThke.b epsrto ooftf h iitssh tahtei qsu aalliltfoyow trsh ceo nstroufic ttsi on
negat-iI(oxn,:ix s)a well-foerxmperde sosfit ohnes ysteam l,e gible
exeprssion.
Yeitwt o ulbdew rontgoi magin-eI( xt,h(xaw)th ischho ublerd e aasd:X is
noetq u-aolri dent-tioic taslme alfrw)ki st htihsney stoerpm o,ts iiownist hin
thmee chantihsuemn ,t hinnkoanbl-lfse-e idoefn ttsihitegyan n,td h astu cah
(well-feoxrpmreedso)sr igoannt ihzseeu st uroifn gtu hnet hintkoat bhlee
calcuOlntu hsce.o ntyrf,a afrrr omma rkitnhugen thoug[h5t18,s ]it gfyhineni g
existoef-n I(cxe,p xr)e souspeipstf sun ctiownihitnogua m ta kri:it sn ecessary
thaotn e ubnela tebo contcheaxit,qv ueam ariks,' othtehrax'n t-hsea me
marpkl aceelds ew-hienor red feorrt hsitsa tetmobe enl to gicparloldyu ced.
Them erceo nvocationo-fxr 'ensvo oncl-afst-eiiiodtntey hn,set h immeorfii tnsg
self-diwffoeurlsidun ffigct,eoa nnihtihlseac trei pturaolf t ehexeni tsitreen ce
calcualnudps a,r ticoufel xaprrleys ssuicoahns- sI( x,ixn)w ,h icxh o ccsu r
twice.
The producotfti holeno giccoanlc epetqsu aolafin tdsy e lf-inequality
prepspuostehfseor ecloosfwu hraeits s c riptunroalnl-y-s ieednltfiThceal la.c k
oft heeq uiabslu iulpotnt haeb soalbusteoenft c hene o ni-dentical.
No dotuhbsett rucotfua rc ael culofuis dnetigteyn aelrliym pltihees
derivatoifto hnt eh e-s-il(xs, x): i••it sf althsatex sholudn obte e qutaoxl .
15 Ina seconodr dern lculiunsw ,h icohn e .:qauna ntoivfyep rr ediceaqtueaswl,oi utlyd
bed efinCeXdI Jiiicni· tolnyf,o nniwtiyt ht heL .eibnidzoicatnr ionfei ndiscernwihbilciehss ,
restrihcetretedo t heo rdeorfs igntsw:oi ndivivdauraila bflaelsl winigt heoxucte putiiJodanel rl
thes amep rediccaatneb ses ubstiteuvteerdy whseinrceet, heirnseo t hnigt om artkh ediirff erence.
ind assincoatlation:
l(x,"'y,)(, V a)l:Ja a((xJy).)
16 TN:11 lCca hiteextrh sa s' -l(xr,atxh)er't ha·n- -l(bxu,itxit )sc : l efarro tmh ceo ntext
thatth iissa m ispriAnstB .a diou remiatir fsk ast,lh atsx esh oubleud n eqtuoxa. lTh e negatiino n
thfeo rmuslhao utlhder eforeb ed ouble.
168A LAIBNA DIOU
Buats f aarsl acikcs o ncertnheids, t 'in'om enargkanso thbiuntg rteehjcet ion
of( oprr eseinntc)he oe t hdeiriv si(ohtna otf n on-thoefs etssht)ea tement
-I(xx,)w,h ichha bse epnr oduicdeedna tliblcyyt hsey ntamcetcinhcia sm.
Noa bseinsc evc ooknehdee rt hat wboeau nlydit nhbgu tth ael loctaot ion
oncel arsast htheartn oi tcso pmlem-eanctc ortdoti hnpego istirvuel eas of
mechan-iosfmw hatth imse chanriescvmee ifsr otmh pe roductofi ons
anot.h er
This alulsto orw esl ate,i dweiotlhoiognuifitclt atilrot anhc,eo ncoefip dte n­
tittoty h ceo npctoe ft ruth.
Nothtirnagn shpeirorefte hste h ionrig t cso ncept.
But stthaet emenit,s 'a''p7 tu rrueetlxhyp eddieeisngtn atoifao non p era­
tiocnoamlp lseixg,n isfiofe aasrsi, d enatniedtq yu aalriceto yn cerned:'8
IedniyttTh:e r elatiloongb itechat arotsw awrrdist iissnu gct hh iartte ceives
frotmh lea totneltryh omsaer ktshh aatv e beenb ytc heseri tginfiiecfydhi anign
asc apaobfbl eei snugb stiftoturht eemds eelvveersy wIhnte rruett.hh mi,es a ns
anmya rwkh atesvoewrho,s ien varrieacbolgen iisrt oiootinen d (tehxet ernal)
technoifgq ruaeep mhes.
Equya:lTh eirtee xias tssi gniofyridn(egar m echanoifsd me rtiiv)oa,n
whossee lecctoinvset raarsieun ctthsh atths et atemIxe(,nxat)ns -d I(x,axr)e
senttot wdoi fferdeinvitio sns.
Iff,r oamp erspteictvhe aitms o rset ritchtaoltfmy a themaltoigcoiancle,
wishecso ntsoit dhpeerr o ducmte cohiafsn ma-st3 h see otfd erivtahbelsee s,
oncea snya :t hmee chaniisss eumtp i ns ucahw ayt haipttr oduIcx(,exsa) n d
rjecet-sI( x,.x )
_But tthweios nesi cprtihoanvasel rebaedepynr oduicnte hdse a mdei vision
(htaotfw ell-feoxrrpmseesdi obnyas m )e cnhiasm(-as2 y nxt)Oa.n loyn t his
basiisisp t o sbslieg itvoae n ys entsoe rtehjee cotfoi nooenf t htew o tbhye
mechanoifds emr ivation.
Whaitns o etq ula-ttos-eiilosfn leyx cluhdeeroden c ondiotfhi aovni tnog
bep lacweidt hainna u tonomsoiugsn iofyridnegsr e;d imielnoytr agranized
'betnhet'ah oen weh icnhol ongheaarsp lafcoeir t .
Tom aintaatai lcnlo sitnts h,pi osi tnhtce,o rrelbaettiwotenhe en e-qtuoa­l
itsaenltdfh e wtoruubledet os atyr:u ittshh sey stoefcm o nstr[1a 95i]wn htisc h
differetnhtmeie actnhei asm,p- r3oductihnsegi ngle sItx(a,xtf)er moemn t
mechan-i2ws,hm icphr oduIc(,exxsa) n -d I(x,sxi)m ultsalnye.o u
The equal-taoss- ailtvsaeotlftif ro unct ohm edso wtn on om orteh aan
differencet,oa twhiatnhkdesrff ae[wcntp eaffrre etet ,]bi ertweseynn taanxd
17 TN:Th isi sr eaef rentcote h aer ti'cSluretew u'h,e rMei lwlreirt aeftseL,re ib'nTirzu:t h
isE.a ch tihisid negn ttioic tasle lf1' .(3C:p4A3 ).
18 TN:T heF renrceha 'dMs a"ilvsae reistpteu" rd,ee s aitgicnoonm mdo'dcueon m plexe
operastioginsrifi'feaueiy,,tlp oi/n'tiedree ltnl! ltgiiattee: '.