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: '.