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THEM ETHODO F DESCARTES A STUDYO FT HER EGULAE BY J. L. BECK OXFORD ATT HEC LARENDOPNR ES S 1952 OxfoUrndi vePrrseiAstyms e,Hn o usLeo,n dEo.nC4 . GLASGONWE WY ORKT ORONTMOE LBOURNWEE LLINGTON BOMBYA CALCUTTMAA DRAKSA RACHCIA PET OWNI BADAN GeofCfurmebye rPluebgliest,hot e hUren iversity PRINTEIDN G REABTR ITA!N PREFACE 'Thmea gnifipcheinlto swooprhclkio cniaentl h see ventceeenntwtuahrds yu neo sto mucthoi ts abc eeinntgou fgr eyn iusc-nec' aeprsaa tss sde'za 'Ulo'ierspb roimnta, is lep rinceipsadtlel 'appbliieqnu-etarois t bse ianc ge ntiunrw yh itchhCe a rtesian ruloefms e thwoedra et tenotbisveerlvye d.' R.G .C OLLINGWOOD Tol ootkh rotuhgceha taloofagl uieb roarer vyet,nos can oneo'wsnb ookshmeulsrvtee isn,fot rhmcee el ancchoonlic victtihoiainttas n i neviptaaorbfttl hepe r iocfge r eatness, inp hilosaosip noh tihcfieaerllo dfsl itaecrhaireyv ement, that postesrhiotupyla dty h deo ubttfurli bouftt aek iunpgo n itstehtleaf os fke xplatiotn hirene gos ftt h weo rwlhdat th e greraetam lelayno tnt, h per esumdpotuibottnlh egasrtse at nesisns peculatiivspe e rmfeacattntledeyv r,ens no rmally, compatwiibtalhc e e rtmauidnd le-ohbesacdueardni adt y markienda btioel xiptryoe nsessc ellefaT rhleywr.ie el vle n befo unbdr asvpeirwr hiaots ss ulmerese sv eretnhtteai sakl ly ofe xplawihnatithn eges mei npehnitl osooupghhehtratsvo e meanDte.s cairsot,fce osu risnne ow, a eyx emfrpotmt his posthufomromou fst ribaub tieb;l ioogfbr oaopakhnsyd artiocnCl aerst esian phiitlsoreseloqfpua hic yro enw ould sidervaoblluYeme eti. wt a Dse scawrhtole isk epnheidl o sophciocmamle nttaotr hiteer so ubwlaetdefo rusn di n pitrcsh erainvdce ormsp atrote hcdel esaprr wiantgoe ftr h e origtienxDatel.s phiiatsse s erttoti hcoeon nst Dreasrcya,r tes inso pte rfeccltelaaynr td h ree awdielrItl h,i angkr,te hea t hei nso tth eea soifep shti lostooup nhdeerrssa tntadhn adt,, forb ettfoerwr o,r smea,no yf t hCea rtewsriiatnri engs quidreet aeixlpelda nfoartt ihsoetn u doefpn hti losophy. Onew eabku ti nvinecxicbulfosere a newb oookn Cartepshiialno sloiipehnsty h fier mb eltiheafat st, h is voluimfaser fr omb eitnhgfie r sstoi, wt i clelr tnaoibtne l y thlea sitnt, h leo nsge roifew so rwkhsi dcahi wmi,t nho litjtulset ifitcoia nttieotrnhp,ter h eotu ogfDh ets cartes. Thep urpoofts hesi tsu idqsyu iltiem iIta emad t.t empt intgos eclto wanna ccoouftn htme e thoofDd e scawrittehs partirceufelraetrnoh c ieesa rwloyrt kh,Re e guladier eacdt io neimn geTnhieri e.a sfoormn ysc hooifct ehc eo mparatively unknoRweng ualaste hfo en dametnetoxafmtl y c ommentary vi PREFACE arseu fficieexnptllayii nmn yei dn trodcuhcatpoDtreeysr . caritpsee sr freicgtihlnhty ic so ntetnhttaihtroe en ma ela ning ofa g retahti nmkuesbrte s ougahntfod u nidn h iosw n writiMnygp su.r phoesrewe i blelfu lfililfIeh da vneo t cloutdheieds sbuuehtsa vhee lpmeyrd e adteour nsd erstand morceo mpltehtteee loxyftt hRee gualnadae,s a c orollary, thtee oxftt hDei scdoeul raMéts h odeI.tf h ien vestoifg ation thCea rtedsoicatonrf mi enteh hoadss o metciamrermsie e d beyotnhdle i moiftt hsRe e gulIha aev,te r iteofod l laosw closaespl oys sDiebslcea rotwenos r'dosef er x posiint ion thiwso rrku,l beyr ulIen.e vitablyh avpaerr oibsleenm s whiwcohu hladv cea lfolret dhd ei scuosfds oicotnre ixnes poundbeyDd e scarhtiemsse tianp htyrseiactails es. These doctrhianvbeees en no taendtd,h edne libelreaafsttie dley, int hbee ltiheaaftn d ye sersvterdio cfti unrceo mpleteness wiblelc ondobnyme ydp ursoufail ti miotbjeedc tive. Asfa ra sw apso ssIih balvqeeu, o tteedxfr tosmD escartes tos uppmoyri tn terprTehteahstaeiv boeen e.tn r anslated fromt hŒeu vrceosm pleèdtiebtsye,A d d aamn Tda nnery (trheefe reinncdeiscb aytt heaedb brevAiTa.fot liloonw ed byv olupmaeg,ae n,ld i nMeysfo )o.t nowtoeuhsla dv bee en shoritIfhe arnd o cth osteopn r iinnfut l all tlhi em portant passtargaenss ilnta htteee ixdtt s Iewtla fsI., faeslktti,on og mucohft hree adteoer x pehcitmt ol ooukpt hoer iginal worodfDs e scairntt hteews e vlovleu omtfeh sŒe u vreevse,n ifth ewseerc eo nvenaiveanitlYlea ytbi ltie si. m poritna nt sucahw ork tthhweah too lfet heev idsehnocuebl epd u t forwairnod r,d teoer n atbhlreee atdjoeu rd fogreh imsoefl f thceo rrecotfmn yei snst erpraenttdah taeitvo ind;ei nsc e ultimtahtteee loxyftD escaMryta eistm.h ereifospr rei maroinloeyfe xposaintidin otne rparneadtn acytr iiotni cism tr,ia esis tmsa ipnu rpotsode i,s enttahenesg sleeon ft ial Descarmteetsh'osd odloocgtiarcniadrnl ee s tiatwt iet hin hiosw na ssumpIttdi ooennsso .fot l ltohwa Irt e gahrids argumaesan bto cvrei ticism. Iit sIi, m aguinniev,e argsraetlehltdayh t e sotfDu edsy caritsea sne ssenptariotafp l h ilosospthuidJcioaehlsn . Lockwea sde finiotfte hlioysp inainodhn i,ns o toensa Méthodpeo ubri éetnu dliade orc tridneMre . d eCsa ratresest ill intereHsetw irniigt.neh s iJ so uronna7 l M arc1h6 78: PREFACE vii 'L'orqdur'eod no istu ivproeue rt udaiveeruc t illietsé ouvradgeMe rs.d eCsa rteetds ec, e uqxul ie osn cto mmen teozu e crsiultrad octersidtnec e o mmendc'earbp oarlrda lectduers eaM ethode. Pmaerdcietqsauun'lrtee r n e cit qu'nioluy sfa idte psr ogdrese eses s tuodnae psp rend d'une paràet v ilteefasru tqeus' coonm met d'eonre dtiundaiainrte lap hilosdoeeplsh cieoetql uele ' so'ni nsdt'rauiildtlel e au rs conduqiutfaielu t te npiorud re coulvavr eirrdi atnéts o ucte qurie galrpadh ei losTohpeah diveii.ssc'te ii nlslt rauncdt ive sounIdo .u gphetr htaoap dstd h atthi em medifoaltleolwy inpga ragorfat phhJe ourinsoa mli noLuosc.kh ea nso hesitianat divoinst ihpnehg i losonpohviiaccgaeal it nhset readoiftn hgfie r scto mmenetvaerwryr itotneC na rtesian methodotlhoCego ym,m enotauRi ermea rsquulreaM s é thode de MrD.e scaorfPt èerPseo, i spsuobnl,i isnIh6 e7Id. L ocke notehsa,r sbhulntyo itn justthla'ytc,c e o mmenteasitr e rempdleti a ndtec hosiensu taiusl ujeesqt u elsloenpstl us capabdl'eesm barqruaeds isnesrt draunliserc seo mmence menettqs u eislpt l uasv antadgene elu epxsa vso qiurde e l es lirIeh .a'va et temtpokt eeedtp h cirsi tiicnmi isnwmdh en writmiyno gw nc ommenotnat rhmyee thoofDd e scartes. Tos omeex temyng tr eiantd ebtteodt nhweers ist oifn gs othmearybs e m easubrye dfrt ehqeu ewnictwyhh iIcr he fer tot heBmu.tt h epsaes srienfegr ernecperse osnelansy tm all propoorftt hioofrsnoe mw hoImh avlee armnoesdTt o.h ave hadt hper iviolfae tgtee ntdhilene gc toufrP erso fessors GilsaonnLd a poarttt ehS eo rboannndte h,o osfet hlea te ProfesJsooarc haitOm x forids,t oh avien curard eedb t whiicithsi m postsoie bsltei fomrao tnee soertl oaf c know ledtgooe t heTrohs a.v dei scutshtseee oxdftD escartes with J. thlea Ptreo fessAo.Sr m iwtahis ni tsaer lefv eloaftt hieo n corrweacytt or eaapd h ilosowprhiitIced aronl; o ptr etend toh avlee afurlnltty hl ee sbsuoItnf eaebllt eor ecogtnhiez.e ideTahlep. r inwtoerdok fsP rofesGsiolrssao nnLd a porte J. havper oviendv aluMarb.l Le.A. u stoifMn a gdaCloeln legkei ndllemyne th idse taniolteoedfPs r eosfs Joora chim's lectuTrheeg sr.e aptaerortfw haIth avlee aarbnotDu ets caritsde uste o t hien struacntwdir oint oifnt ghseg sree at schoalnapdrh si losoapnehdve erwnsh ,em ny i nterpretation diffefrrosmt heimryos b,l igdaotenisoo etnn dIm. u satl so VIII PREFACE exprmeygs rsa tittotu hWdeae r doefMn e rtaonntd o M r. W.H .W alosfhM ertwohnoh avree atdh romuygm ha nu scrTihpethy.a vter iteoid m prmoyvs et yalnehd a voeff ered manhye lpsfuulg gesIt hiaovnbese .eh ne lpbeydt heir encouraagnehdma evpnert o fiIth eodp,fre o,mt hecirri ti cisbmusfot,r m anoyft hseh ortcwohmiidcnheg,ss p tihteei r helspt,ri elmla iintn h wiosr Ika ,l oanmer eposnsible. L.JB.. MERTON COLLEGE,O XFORD 20 Febru1a95r1y CONTENTS I.THER EGU LAE §I.T heRe gulaanetd h Deis cours §2.T heT exotft hRee gulae 8 §3.T heP laonft hRee gulae II IIT.HEU NITYO FT HOUGHTA NDS CIENCE §r.K nowlaendMdge et hod §2.P erceapntIdim oang ination IIIT.HEF IELODF K NOWLEDGE §r.R eflection §2.T heI deoaftl h Sec ieanncMdea st hematics §3.T heC ertaoifMn attyh ematics 39 IVI.NTELLECTIUNATLU ITION §r.T heT wofoFludn ctoifto hInen tellect 47 §2.A ProbolfTe emr minology 48 §3.I ntelIlnetcutiutailo n 50 §4.S ornCeh aractoefIr nitsetliIlcnestc utiutailo n 55 V.THEO BJECOTF I NTELLECTIUNATLU ITION §r.T heS imploifIc nitteyl Ilnetcutiutailo n 65 §2.' SimNpalteu res' 66 §3.' SimPprloep ositions' 75 VIT.HEN ATUREO FI NFERENCE §r.I ntelIlnetcutiautnaDidleo dnu ction §2.T heN atuorfDe e duction §3.' NeceCsosnanreyx ions' VIIC.ARTESIDAEND UCTIOANN DT HES YLLOGISM §r.' ThPee rfeMcett hoofDd e monstration' IOO §2.C ritiocfti hSseym l logism I02 §3.I mplaincEdix tp licit VIIEIN.UMERATION §r.P roviSsuimomnaaorlfty h Mee thod III §2.E numeration II4 §3.T heR oloefM emory I20 §4.' CompElneutmee rations' 126 CONTENTS X IXD.EMOSNTRATION §z.' EumesriaIvtneid ou ctio' 134 §2.S ummaorfty hR eu loefDs e monstration 143 X.THEE SSENTIOAFLM SE THOD §z.T hReu loefMs e thod 147 §2.T hDee finiotfMi eotnh od 152 XIT.HER ULEOSF A NALYSAINSD S YNTHESIS §z.O rtlaenrTd h inking §2.T hReu loefA nalysis §3.T hMee thoofSd y nthesis XIIT.HES ECREOTF T HEM ETHOD §z.' ThSee corfte htMe e thod' §2.' AEnx ericnMi esteh od' XIITIH.ES CIECENO FO RDER §r.' MathVuelsgiasr is' §2.' MatheUsniisv ersalis' XIVT.HES OLUTIOOFNP ROBLEMS §1.T hMea them'aSthieclall' 203 §2.P erafencIdtm perPfercotb lems 206 §3.A not'hEexre irnMc eitsheo d' 210 XV.THEM ETHODI NM ATHEMATICS §r.S enasneId m aginianRt eiaosno ning 215 §2.' Entinaojtaam' 221 XVIT.HEM ETHODI NP HYSICS §1.M athemaantPdih cyss ics 230 §2.T hReo loefE xperience 239 XVITIH.EORAYN DP RACTICE §1.M athemaanttdhi Pecr sin cipPiah ilosophiae §2.T hDei optrique XVIITIH.EM ETHODI NP HILOSOPHY §r.L ogaincMd e thod §2.T hMee thoofAd n alaynsSdiy sn thesis §3.T hMee thiontd hM ee ditationes INDEOXF P ASSAGFERSO MT HER EGULAE INDEOXF N AMESA ND SUBJECTS 312 ...,1 I THE REGULAE §1.T hRee gulaaent dh Dei scours A EFWy eaarfstt ehdree aotfDh e scapretressir,su tmeonutr s wercei rcuilnta htleie nagrc nierdoc fFl reasna cntedh Leo w Counttrhaiametos ntghsmeta nusclreuifnptpt usb lwiassh ed at reaotnLi osgeBi aci.l tlh:fieert bs,it o groafDp ehsecra rtes, repotrhtast FathRearp ifonri, n sthaanscdae ti,hd a Dte scahratbdee sg au n Logwihci hcehh ande vfienri sbhuettdh ,aa fe tw fr agmeonftt hse treasttriieslmela iinnte hpdeo sseosfos nioeofh n i s dainswdcei rpel es enti'tElreudd .i.ta.vi iogno'sr eoauwrsac msha daem onhgispsta pers butth ewraens o thfoiunngbd e arintgi otflt' ehE er udintoyireo tn ', anythwihnigcc ho ubledl ookuepdoa nsa L ogiwci,tt hh sei ngle excepotfhi io'snR ufolrets h geu idaonftc heme i nidnt hsee arch aft·eTrr urtuhl'ue,ps o wnh icah m osetx celLloegnmitca yb e modelalnewddh icuhn doubctoendtalac yio nn sidpeorratobiflo en himse th1o d. Baigloleoesntt ogi hvieos p intihotanhtR e e gualraaefu e l ler anmdo rdee taeixlpeods oiftt hiCeoa nr temseitahtnoh da n thoaftt hDei scdoelu aMr ést hwohdiehc ehc onsitdobe ear s merseu mmaorfty hm ea imne thodoplroigniccaiva pille ews , whiDcehs cahritmeshsea eldxf p remsosrteehd ao nn c2Y ee.t, ont hweh otlheme,e thoofDd e scahrabtsee essnt udwiietdh, af enwo taebxlcee pitnti hoeenx sp,o soiftt hiDeoi ns cIotu rs. inso stu rprtihstaihtnsi ghs o uhladvh ea ppeCnleedr.s elier himsfreilefan,nd dd i scoifDp elsec atrowt heosCm,h anut letfhtre e sponosfip buiblliittshyhme ia nngu scorfti hpet s philosdoipndho aettr t,ma ucchih m porttoat nhRceee g ulae ofw hihcehh a tdh oer igiintn hawelr itoifDn egs caarntde s, waqsu iwtiel ltiohna gno dv etrht ea tsaokn syc hodleasri rous ofu nderttahekedi intgoi fwn hgah tec lecaornlsyi oddedr ed 1 l'AbBbaéi lLlaVie etd ,eM onsieur D(ePsa-r1Ci6as9r,it1 2.e )8s,2 . 2 Cffo.r,e xamtphlleee, tt toPe. Vr at(iAeTri. 5. 5 139-16)', Jveo udsi rparie mière menqtu,me o nd essne'piaon i énttéd 'ensetiogumntaeeM r é thoddaenl sed iscours oùj el ap ropoSseebe.e 'l opw.1, 7 2. 5479 B 2 THE REGULAE fragmeonftm su,cl he ismsp orttahnatcnhle ee twtheircsh wourleda acw hi dpeurb lic.X Oncea hna rybd lia Cmlee rsfoertl hiienrfik riasnntgfod r e mosotfw hawto ualtdt rmaocretea saiw liyd peurb alnidc thaudstd to hfaem eo hfi asl refaamdoyumsat se Trh.ee x ample oft hmiass tweoruh ladvj eu sthiificseh doi inlc eea vaisnigd e thien comapnlsdeo tmee wahraLitad t tienxI tnt. hD ei scours heh asda i'dII:fw riitnFe r enwchhi,ic tshh lea nguoafg e myo wcno unitnpr rye,f etroLe antcwiehn i,ic tshh oaftm y teacihitebs re sc,aI uh soept eh tahto wshemo a kues oeft heir naturreaalws iotnh poruetj uwdibileclb e e tjtuedrog efms y opintihoantnsh owsheob elioenvlieynt hwer itoiftn hges anci2eL nattsie.ntr' h,pe r efatcote hP er inchierp eiiat,e rated thsea mceo nviacstt oti hoteny poefr eadheehr asid nm ind: 'Ih avoeb serhveew dr'i,t' eoesnx, a mitnhinena gt uorfe mandyi ffemrienncittsh ,ta hte arrveee rfeyws od ull-witted ors loowfu ndersttahnatdhtie anyrgi e n capoafub nldee r standsionuognp di noiroe nvsea nc quiaritilhn hegi ghest scieintfch eeswy,e rbeu ttr aiinnte hdre i gwhaty T.h'e3r e cabne l itdtoluetb htaD ets catrhtoeustg hhtatht ae v erage intelmlainag nedhn,etw ouhladva ed dewdo,m4 aw napse r fectclayp aobfrl eea dainnudgn dersthainwsdo irnokngs philosaonptdhh ymi,es a nntoo tn ltyh Dei scbouuttrh se Meditatainodtn hePesr incipia IPnha i cleorstoapihni ae. meastuhrpiers a iseawmobritmthiayoys n e etmoh avbee en realTihzeeD di.s cfiorusrptsu ,b liisn1h 63e d(s7 o msei xty 1C ft.h per efaocfeC sl erswehliiacerhpre u bliisnhv eodlv .o f A T,e specially thteh iprrde fapc.6e 5,1 '.L beo Mn. C lersaesBl aiyeclrae'l ,hl iemdw, a pse rsonally morien terients htteeh de oloigmipclailco aftt hiCeoa nrst edsoicatnrH iend ei.d , howevleerno,dr s hotwh mea nusctroih pictsls o frsiee nMdasl.e bramnucshte certahianvsleey et nh emT.h eP èreP oishsaodcn e rtarienatldhy Re e guslaeee, hiCosm mentoauiR ree marsquuleras M éthoded eMr Desca(r1t6e7sp1 p)7.,3 an7d6 . 2A T.v i7.72+- Jo. J lnt haeu thloert'ttsote hrte r ans(lAaTti.ox( r P aIrIt1) 21,7- 32).T hes ame vieiwsfo undi nt hRee gulIaVe,', q uoedt ieaxmp ericeonmtpirao bcautmu r, saepivsisdiemaeim lulqsou sli,i ttoepreirnsau mn qunaamv arluonntsg,oe l iedti us clardieou bsv rieibsju usd icqauraqemu, pi e rpeitnsu coh osluinvste rs(aAtTix.'. 37121)-.2 5 4H ew riitnea ls e tttoPe èrr Vea tiaefe rw,m ontahftset rh peu blicoaftt hieo n Disco'ucrpeses:n snéeme 'so nste mbêltépr reo pàrm eest tdraenu snl ivorùje ',a i vouqluule e s femmêmmeess peunitsesqneudnertle cq huoe(s AeT'i. 5. o6 22-2s).S ee alwshoa Bta islaliyenstL aVi ei,i5 .0 a0n,td h ceh armsitnugbd yAy d amD,e scartes, Seasm itfémiinéisn Peasr,1i 39s7,.