Descartes Clear and Distinct Ideas

8/8/2019 Descartes Clear and Distinct Ideas

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Descartes's Early Doctrine of

Clear and Distinct deasStephenGaukroger

Philosophers inceArnauldhaveoften ound hedoctrine f clear nd

distinct deas, as it figures n works uch as the Meditations, istinctlyodd and implausible. My aim in this paper s to show that the originalversion f the doctrine, hich Descartesheld up to 1628, s very ifferentfrom he doctrine hat s defended n Meditations. shall argue that heearlier octrine s both more plausible nd more restricted hanthe atermetaphysical octrine. t s not doctrine hat erives rom onsiderationsaboutour cognitive elation o the xternal orld utonethat s concernedrather with he vidential uality f mages, otone which oncerns tselfso much with bsolute ertainty s with onviction, nd the mental magesit works with re not the highly bstract deas of the ater writings utvividpictorial epresentations. evertheless, t s this arlier octrine hatdevelops nto the ater doctrine f clear and distinct deas,and I believethat number f the severeproblems hat he ater doctrine was subjectto derive from he anomalousnature f its origins. shall not concernmyself ith he development nd transformation f the doctrine fter heabandonment f the Regulae n 1628. A study f the early version ndi-cates, however, hat the later one is a doomed attempt o convertgood but limited hetorical-psychological riterion f what constitutescompelling vidence nto a criterion which purports o guarantee urcognitive rasp gainst hyperbolic oubt. Moreover, hepictorial atureof the images to which the early doctrine s directed militates gainstthe view, ncouraged y Descarteshimself nd still widely ccepted bycommentators, hat he doctrine f clear and distinct deasderives romreflection ponmathematics. n fact, s I shall how, n so far s the arlydoctrine as a specific earing ponmathematics, t s actually n conflictwith t. But even f hetwo were n agreement, hesourceof the doctrinecertainly oes not lie in mathematics. he source, s I shall show, sultimately hetorical-psychological.

The Regulaead directionem ngenii,which were not published ntilafter escartes's death, were once generally hought ohave been com-posed n 1628.Therehave,however, lways beenthosewho have believed

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586 StephenGaukroger

that t east ome f hem were omposedarlier; ndfollowing eber'spioneering ork,' here s nowgoodreason o suppose hat he Regulaewere nfact omposed etween 619/20 nd 1626-28 nd that numberof tages f compositionre evident, ith ome f the Rules omprisingmaterial omposedt different imes. shallwork n theminimal ssump-tion hat Rules1 to 11datefrom round 620 with ualificationsotrelevant ere) nd thatRules12ff ate rom 626-28.2ctually, do not,strictly peaking,venneed odistinguishhese wo tages or hemainpurpose f my rgument; ut sincedoing o provides s with moreaccurate ccount f Descartes's ntellectual evelopmentnd since heminimal ssumptions nowrelatively ncontentious, ehavemore ogain han o osefrom ollowinghis hronology.

Intuitus nd the Doctrine f Clear nd Distinct deasin the EarlyRegulae

Our first oncern illbe with he earlyRules,dating rom round1620.Having stablishedhe nity fknowledgenRule1,Descartesetsout n Rule2 the reasonswe need method fwe are to succeedn ourinquiries;ndheholds p themathematicalciences s modelsn virtueof the certainty f their esults. ules 3 and 4 then et out the twooperationsnwhich hat method elies, amely,ntuition nddeduction.Rules5, 6, and 7 provide etails f how we are actually oproceed nthis basis, nd Rules 8 to 11elaborate n specific oints. he central

' Jean-PaulWeber, a Constitution u text des Regulae Paris, 1964).2 Following hegeneral hrust f Weber's ccount, nd adding revisions uggested n

John chuster, escartes nd the cientific evolution, 618-1634 Ph.D. diss.,PrincetonUniversity, 977),the schedule of composition hat am inclined o follow s one thatrecognizes wo composite ules 4 and 8) and three tages f composition. he first tageof composition s represented y what s now usually referred o as Rule 4B, i.e., thesecond part of Rule 4, where mathesis niversalis s discussed. This fragment, hichmay have nitially ormed art of the proposed Thesaurusmathematicus, robably atesfromMarch-November 619 nd n any ase before ule4A. The second tage f omposi-tion was 1619/20, he period fter he famous dream of 10 November. What seems tohavebeencomposed t this time were Rules 1 to 3, 4A, and 5 to 11, with he exceptionof parts of Rule 8. The Regulae were then abandoned nd taken up again in a ratherdifferent ein n 1626-28,when heremainder, eginning ith heremaining arts f Rule8, werecomposed.The three tages an be characterized riefly s follows: he fragmentfrom hefirst tage nvisages general orm fmathematics owhich articular mathemat-ical disciplines ould be subservient; he material rom he second tage ets out rules fmethod which go beyond pecificallymathematical oncerns, nd it draws on areas asdiverse s rhetoric, sychology, nd dialectic; nd the material rom he third tage saboveall concernedwith he mechanistic onstrual f cognition, lthough hefinalRulesreturn omore directlymethodological nd to mathematical oncerns. he whole enter-

prisewas finally bandoned n 1628.My concern n this paper s with material rom hesecondand third tages.


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Descartes's deas 587

topics here re the doctrines f ntuition intuitus) nd deduction, nd itis in these hat he novelty f Descartes's ccount resides.

"Deduction" is a notoriously lippery erm n Descartes. DesmondClarkehas drawn ttention o contexts n which t s used to mean xplana-tion, roof, nduction, r ustification; nd on occasion t seems o do littlemore than describe he narration f an argument.3 n Rule 2 Descartesmakes claim bout deductionwhich t first makesone wonder ust howhe is using he term. He writes:

There re wo ways f rriving t a knowledge f hings, hrough xperiencendthrough eduction. oreover, emust ote hat while ur xperiences f hings

are often eceptive, hededuction r pure nference f one thing rom nothercan never e performed rongly y an intellect hich s in the east degreerational hough e may fail o make he nference f we do not ee it. Thosechains y which ialecticians ope oregulate uman eason eem ome to beof ittle sehere, hough do not deny hat hey re useful or ther urposes.In fact, one f the rrors o whichmen-men, say, notbrutes-are iable severdue to faulty nference. hey re due only o the fact hat men ake forgranted ertain oorly nderstood xperiences,r aydown ash r groundlessjudgements.4

It is not too difficult o see why Descartes hould want to maintain hatwe can never be mistaken bout deduction, orhe wants ntuition nddeduction o be the two trustworthy rocesses hatwe can use to lead usto genuine nowledge, nd as we shall ee,he makes he ameclaim boutintuition. ut to maintain hatwe can never make mistake n deductiveinference s nonetheless remarkable laim. n order o find ut preciselywhat he means, t s worth skingwhat precisely e is rejecting.What rethe "chains" by which the "dialecticians"hope to regulate nference?These are presumably he rules governing yllogistic, hose rules thatspecifywhich nference atterns re (formally) alid.The problem s todetermine hat t s that Descartesfinds bjectionablen such rules. Theclaim s certainly ot that hese rules re wrong nd that others must besubstituted or hem, hatnew chains"must eplace heoldones.Rather,the questionhinges n the role that one sees these rules s having, inceDescartes dmits hat heymay "be useful or ther urposes."What heis rejecting s their use as rules of reasoning, s something ne needs tobe familiar with n order o reason properly. f one looks at the ogicaltexts with whichwe know him to have been familiar, boveall those ofToletus and Fonseca, then we can identify heculprit with ome degreeof certainty: heJesuit ccount f "directions or hinking" directio nge-nii). The Jesuit ccount of logic which Descartes earned t La Fleche

I Desmond Clarke, Descartes'Philosophy f Science Manchester, 982), 63-74 and207-10.

4Oeuvres e Descartes, d. Adam and Tannery 2nd ed.; 11vols.; Paris, 1974-86), ,365 (hereafter AT").


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wasone nwhich ogicor dialecticwas construed bove ll as a psychologi-cal process which required egulation f t was to function roperly.5 nthe ight f this, ne thing hat we can take Descartes to be denying sthat mental rocesses equire xternal egulation, hat rules o guide ourthought re needed. This is made very lear n Rule 4:

[My]method annot o ofar stoteach s how o perform he ctual perationsof ntuition nddeduction,or hese re he implest f ll and quite asic. f ourintellect ere ot lready ble operform hem,t would ot omprehendny fthe rules f the method, owever asy they might e. As for other mentaloperations hich ialectic laims o direct ith he help f those lready men-tioned, hey re f nousehere, r rather hould e reckoned positive indrance,for othing anbe added othe lear ight freasonwhich oes not n ome waydim t.6

This is an important oint, or t is often mplicitly ssumed hat heprovision f such rules s ust what Descartes s trying o achieve n theRegulae.But this cannot be their im. Descartes'sview s that nferenceis something hichwe,as rational reatures, erform aturally nd cor-rectly.What hen o the rules for he direction four native ntelligence"

do that s different romwhat the old rules of dialecticdid? Well, thedifference eems o lie not so much n what the rules do as in what theyrely pon to do it. n Descartes'sview yllogistics elies n rules mposedfrom utside, whereas is rules re designed ocapture n internal rocesswhich perateswith criterion f ruth nd falsity hat s beyond uestion.This s that weaccept s true ll and only hatof whichwe have a "clearand distinct" erception. ut the elaboration f this principle s largelyconfined o the discussion f intuition," nd with oodreason, or t soon

becomesclear that deduction educes, n the imiting ase, to intuition.Towards the end of Rule 3 Descartestells us that "the self-evidenceand certainty f intuition s required not only for apprehending inglepropositions ut also for deduction, ince n the inference + 2 = 3+ 1,we must not only intuitively erceive hat plus2 make4 and that3 plus 1 make 4 but also that the original roposition ollows rom heother wo."Here the first wo perceptions re intuitions, hereas eeingthe connection etween hem s a deduction. ut the deduction eems nall important espects obe simply n intuition, lbeit n intuition hosecontent s a relation between other ntuitions. his clearly raises thequestion f the difference etween n intuition nd a deduction, nd soDescartes ets out why he believes t necessary o distinguish eductionfrom ntuition t all:

Hencewe are distinguishing ental ntuition rom ertain eductions n thegrounds hatwe are ware f movement r a sort f equencenthe atter ut

ISee StephenGaukroger, artesian ogic Oxford, 989), 46-47.6 AT, x, 372-73.


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not n theformer, nd also because mmediateelf-evidences not required ordeduction, s it is for ntuition; eductionn a sense gets ts certainty rommemory. t follows hat hose ropositionshat re mmediatelynferred romfirst rinciples anbesaidto be known n one respect hroughntuition, nd nanother especthrough eduction. ut he irst rincipleshemselvesreknownonly hroughntuition, nd the remote onclusionsnly hrough eduction.7

This s rather uzzling, ivenDescartes's xample. Memory n any genu-ine sensewouldseemto play no real role n the deduction rom + 2 =4 and 3 + 1 = 4 that 2 + 2 = 3 + 1.Why does he specify hat remoteconsequences re known only through eduction? ould it be that theconsequence n the example, which s far from eingremote, s knownnot by deduction ut by intuition? o: it is the example hat Descarteshimself ivesof a deduction, nd the only exampleat that. He seemsconcerned bove all to restrict ntuition o an absolutely nstantaneousact, so that f there s any temporal nterval f any kind, no matter owbrief, we are dealingwith deduction ather han ntuition. ut this s theonly difference; nd even this difference s undermined n Rule 7, whereDescartes laborates n the question f howto make ure hat deductionsare reliable:

Thus f, or xample, havefirst ound ut, y distinct ental perations, hatrelation xists etween hemagnitudes and B, then what etween and C,between andD, andfinally etween andE, that oes not ntail hat willseewhat he elation sbetween andE, nor an the ruths reviouslyearnedgiveme precise deaof t unless recall hem ll. To remedy his would unover hemmany imes, y continuous ovementf he magination,nsuchway hat t has an intuition f eachterm t the ame moment hat t passes nto the thers, nd this would o until learned opassfrom he first elationto the ast oquickly hat here as lmost o role eft ormemory nd seemedto have hewhole eforemeat the ame ime.8

In short, he more t approaches ntuition, hemore reliable eduction s.It is hard to avoid the conclusion hat deduction s ultimately odelledon intuition nd that n the imiting ase becomes ntuition.

Given this, the key notion s obviously hat of intuition intuitus).Intuition as two distinctive eatures: t is an instantaneous ct, and it

consists na clear nd distinct rasp f n idea. Asregards hefirst eature,it is striking ow Descartes s committed o instantaneousness rom isvery arliest writings: n the hydrostatics anuscripts ating from hebeginning f 1619,9 or xample, econstruesmotion n terms f nstanta-neous tendencies omotion; nd the mportance f nstantaneous cts orprocesses s something hathe will makemuchof n his ater writings. t

' AT, x, 370.8

AT, x, 387-88.' See in particular "Aquae comprimentis. ." AT, x, 67-74.


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this tage 1620), however,we have so little o go on that we can do nomore than note the fact that he seems committed o the idea of theinstant, ithout roviding he lightest int s to what he mportance finstantaneous rocesses onsists n. The notion f clear nd distinct deas,on the other hand, s something hose mportance orDescarteswe canunderstand, nd the origins f the doctrine an be reconstructed.

Descartes s certainly ot the first o employ he notion f clear anddistinct deas as a criterion or knowledge; he Stoics operated with asimilar riterion n their pistemology nd held that ur clear nd distinctcognitive mpressions rovideus with guarantee f the truth f theseimpressions. escartes may have been familiar with hisdoctrine, nd ifhe was, t would have been from ook 7 of DiogenesLaertius's ivesofEminent hilosophers, rom icero'sAcademica, r from he very riticaltreatment n SextusEmpiricus. ut think t unlikely hathe was simplytaking over the Stoic doctrine r even that he was influenced y thedoctrine n its pecifically toic form. or one thing, heStoic doctrine srestricted n its application n the first nstance o perceptual ognitiveimpressions other cognitive mpressions eriving heir guarantee romthese), whereas Descartes's paradigm case is that of a nonperceptualcognitive mpression ar excellence, amely, mathematics. t is crucial othe Stoic doctrine o take nto ccount heexternal ource of our mpres-sions,whereas n Descartes'sversion f the doctrine hequestion f thesource does not arise. Moreover, he Stoic doctrine, whereby we caninspect our cognitive mpressions o determine whether hey have theessentialproperties f clarity nd distinctness, as subjected o severecriticism y Sextus; nd Michael Frede has pointed ut that t was sovulnerable hat t is difficult o understand ow the Stoics could have

continued o defend t.10 t is therefore nlikely hat Descartes wouldsimply have taken over the doctrine without t least trying o remedydefects hat werepointed ut n the expositions f Stoic teaching. his isespecially he case since his own account, focusing n properties f theimage or idea, seems to rely on those very lementswhich were mostproblematic or he Stoics nd which heymade the greatest fforts ogobeyondby focusing n the external ource of our impressions. t is ex-tremely nlikely hat Descartes's ccountderives rom he explicitly pis-

temological ersion f he doctrine ffered ythe Stoics.Rather, t derivesfrom more general nd traditional ersion, ne which xplicitly ealswith ualities f deas, mpressions, r images n such a waythat t s nottheir ource hat s at issue but the quality f the mage tself, ust as it sfor Descartes.

In fact, escartes's ccount f clear nd distinct deashas some ratherstriking arallels with psychological heory f cognitive rasp that hewouldhave had some knowledge f from is studies t La Fleche.This

10MichaelFrede, Essays n Ancient hilosophyOxford, 987),152.


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theory, hough ristoteliann origin, s to be found ot nly n the toicversion ut lso n thewritings fQuintilian.t may t first eem eculiarthat Descartes houldderive is criterion rom workwhich s, withCicero'swritings, heclassic ccount f rhetorical nvention. ut thisaccountwasdrawn ponextensivelyn the sixteenth nd seventeenthcenturies,nd t s not t all surprisinghat escartes hould ave akenit as his tarting oint.

Rhetoric ook ver he raditional oncerns f ogic n a number fareas, specially n"invention,"hat s, he discoveryf hose rgumentsnecessaryoconvincenopponent,tarting romhared remises, f omecase that ne wants o establish. ristotle iscussed his uestion n abroadly cientificontext n the Topics, utby the ixteenth entury hemodels or uchconviction eredrawn rom hetoric, specially romQuintilian. uintilian evoted great ealof attention o discoveringargumentsikely o eadto convictionn areas uch s lawandpoliticaloratory; nd ndeed f conviction ere ne's aim, hen uch echniquesare more ikely o be of usethan n understanding f which yllogisticforms f rgument reformally alid. hisdoesnotmean hat he spousalof rhetoric arriedwith t a disregard or alid rguments, ut validitywasregarded erely s one ngredientn a good rgument. ow, his sa fair oint. lthough ristotle's yllogisticealswith robabilisticormsof argument nd holds hat rguments aybe validwithout eing or-mally alid, t sabove ll a theory f formally alid nferences;nd anunderstandingf formally alid nferencess not omething hat ne slikely ofind speciallysefuln rying oconvince recalcitrantpponentof ome ontentious onclusion.I1t s far rom lear hat ogic, nderstoodas a theory f the nature f formally alid nferences,s of anyuseby

itself n changingomeone'smind bout conclusionr that t s of nyuse n enabling s to understand hy omeone hanged heirmind s aresult f being onvinced yan argument.

Thefirst uestion eems ather opertain otechniquesfpersuasion;and the im of rhetorical heoriess precisely ocapture nd elaborateupon those echniquesf persuasion hich re best fitted o differentkinds f situations. his does not prevent ogical onsiderationseingbrought obear, ut hesewillbe paramount nly n those aseswhere

deductive ertainty anbe achieved,nd such ases re not ikely obecommon.12 he second uestion-that fhow rgument anchange urbeliefs-is muchmoredifficult o deal with.The rhetorical radition,

" Aristotle s, of course, ware of the fact that different pproaches re needed ndifferent reas. As he tells us in the Nicomachean thics, it is equallyunreasonable oaccept merely robable onclusions rom mathematician nd to demand trict emon-stration rom n orator" 1094a25ff). ut what s at issue n the present ontext s whetherlogic, n practical ircumstances, an ever be necessary r sufficient oinduce onviction.

12

See the discussion n ch. 3 of A. Grafton nd L. Jardine, rom Humanism toHumanities London, 1986).


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drawing n Aristotelian nd occasionally toic psychology, ried o pro-vide some account of how our ideas might be compared n terms, orexample, f their vividness, nd it is not too hard to see how a notionsuch as "vividness" might operate as a rudimentary riterion or thereplacement f one belief by another. Although so far as I can tell)this topic was not pursued n any detail n antiquity, here re explicitseventeenth-century ccounts that show how the theory works. Male-branche's heory f the will soneexample.He tellsus that when acklingthe problem fhowwe are to resist lesser oodbywhichwe are tempted,in favor f greater ood,we must epresent hegreater ood to ourselvesas vividly s possible o that t becomesmore vivid n our mind han helessergood.The suggestion s that oncethe balance of vividness as beentipped,we will utomatically ssent o or wish for he greater ood.13 hisis a problem hat xercised escartes, nd Malebranche's ccount an beseenas a later development ithin artesian sychology. lthough t istreated n epistemological-psychologicalerms, ts ultimate ource ies nthe rhetorical-psychologicalheories fQuintilian, hoseworks escarteshad studied n detail at La Fleche.

The Roman rhetorical riters ookup elements rom hepsychologicaland poetic theories f their redecessors s well as from heir hetoricalworks. Paramount mong these earlier authors was Aristotle, nd inQuintilian's ritings ecan find lements otonly rom ristotle's heto-ric and Poetics ut also from heNicomachean thics nd the third ookof the De Anima. Quintilian s concerned-as were earlier writers nrhetoric, uch as Cicero and the author of the anonymous hetorica dherennium-with he qualitiesof the "image," with the search for ndpresentation f mages hatweredistinctive n their ividness nd particu-

larity. number f rhetorical nd psychological oncernsmeethere, ndit s a distinctive eature f Roman writers n rhetoric hat psychologicalcategories re used to provide basisfor hetorical nes.This s nowheremore true han n Quintilian's nstitutio ratoria.

The very possibility f this whole approach derives nitially romAristotle's efense f the emotions.Whereas lato banished heemotionsfrom he rational mind, Aristotle howed n the Rhetoric nd the Poeticsthe crucial role the emotions lay in judgment. n response o Plato's

doctrine hat art is mere mimesis, he elaborated he doctrine hat ntragedy, or xample,we are presented ot simplywith set of empiricalfalsehoods ut with n investigation f the causesof human behavior. yabstracting hese causes from particular ircumstances nd presentingthem n a universal ay, t spossible ocapture eatures f character ndintentions hich re normally bscured. he drama does this by movingthe audience to fear and pity. Now to defend his view fully, what is

13See the discussion n Charles J. McCracken, Malebranche nd British hilosophy(Oxford, 983),107-8.


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needed s a psychological heory f the emotions, nd more generally fjudgment, nd this Aristotle rovides n the third ook of the De Anima.An important art f this ccount akes heform f theory f he mage-making apacity f udgment, omething f which lato had a low opinionbut which Aristotle was concerned o defend.Aristotle ells us that theimagination phantasia) functions ather ike sense perception. t workswith mages hat enable the mind to think, and for his reason,unlessone perceived hings ne would not learn or understand nything, ndwhenone contemplates ne must t the ame time ontemplate n image[phantasma], or mages re like sense perceptions, xcept hat they rewithout matter" De Anima 432a7-10).

The Roman rhetorical radition was especially oncerned with uchimages nd above all with he question f what features r qualities heymusthave f hey re to be employed ffectivelyn convincing n audience.Whether ne is an orator t court or an actor on stage, Quintilian ellsus, our aim s to engage heemotions f the udience, nd perhaps ogetit to behave n a particular way as a result. 4 To achieve his, n Quintil-ian's view, one must transform he psychological mage, the fantasma,into tsrhetorical ounterpart, he ikon. Kathy Eden has drawn ttentionto a very nteresting eature f this account, namely, hat Quintilian sconcerned bove ll with he vidential uality f mages. he orator eedsto exhibit ather han displayhis proofs. den sums up the situation sfollows:

Inthis iscussion .. the ld debt f Aristoteliansychologyo he undamentallylegal model f udgement nd action eemerges s a reciprocal elation. oinfluencehe utcome f legal udgement-the oal f he rator-Quintilian'sforensicmage elies n the ower f he sychologicalmagewhich, s far ackas Aristotle's e Anima, asdirectly ffected he udging ower f the oul.Conversely,operform ts office, he mage equires, ven t the psychologicalstage, he ividnessndpalpabilityharacteristicf eal videncen he aw ourt.In other ords, hepower f he mago o move he mind oa particularudge-ment elies n the ropertyt hareswith eal r demonstrativevidenceobearon the utcome f legal rial.'5

There re striking arallelsherewith Descartes'sdoctrine f clear nddistinct deas. Just s Aristotle nd Quintilian re concerned with thevividness nd particularity f the mages mployed y the orator, rama-tist, r awyer, o Descartes s concernedwith he clarity nd distinctnessof the mental mageshe refers o as "ideas." In both casesthere s somevariation n terminology-Quintilian alksofboth vividness nd particu-larity, nd vividness nd palpability nd Descartes of clarity nd dis-

14Quintilian, nstitutio ratoria, r. H. E. Butler, 4 vols.;Cambridge,Mass., 1985),

VI, ii, 27-35.15Kathy Eden,Poetic nd Legal Fiction n theAristotelian radition Princeton, 986).


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tinctness, larity nd vividness, larity nd simpleness, nd so on-butnothing inges n this. Now Descartes ertainly new Quintilian's exts:in the fifth ear of his studies t La Flechehe would have been requiredto study the Institutio n depth and may well have been required omemorize assages from t.16Among heGreek exts ewouldhave beenrequired o study was Aristotle's hetoric, ith ts detailed iscussion inchapter 3.11) of a kind of vividness ev&apyeaa)directed owards hesensesrather han the intellect. is familiarity ith rhetorical racticewould have been extensive, or the Jesuits had an intense nterest nrhetoric nd not only aught t n detail ut developed distinctive hetori-cal style which focused n the use of vivid mages.Central o the Jesuituse of images n both the teaching nd development f rhetoric wasPhilostratus's ikones, which offered xemplary xercises n the art ofrhetorical escription f imaginary) aintings17 hat depended pon theability, s it were, o paint a picture n language.Descartesretained ninterest n these rhetorical uestions hroughout he 1620s.18 here arethen number f possible hetorical ources orhis doctrine f clear anddistinct deas-Aristotle, Quintilian, hilostratus-and my aim is not totry oidentify particular writer r text s the ourceof his doctrine utrather o show he genre romwhich he doctrine erives nd nparticularto ndicate hat ts ources re rhetorical/psychological ather han piste-mological.However, am nclined o suspect, or easons hat willbecomeevident elow, hat doctrines istinctive o Quintilian layed key role.

The context f Descartes's ccount differs n one very mportant e-spectfrom hose f Aristotle nd Quintilian n that, or he atter, onvic-tion s conceived n discursive erms. n the case of Aristotle his s as trueof ogicas it is of rhetoric, rama, nd legal pleading. or Aristotle, he

dialectical yllogismwas designed o induce conviction n an opponent,the demonstrative yllogism oinduce onviction n a student, nd so on.The context f argumentation sdiscursive n the ense hat ne salwaysarguing with omeoneon the basis of shared premises; orunless therewere shared premises, he argument ould not begin. n the rhetorical,dramatic, nd legalcases the situation s evenmore traightforward, orhere what one is doing s directed owards n audience.For Quintilian"oratory" irtually akesover the wholequestion f nducing onviction,

16 In the fifth ear f study t La Flechethe moralwritings f Cicero, Caesar,Sallust,and others, nd the rhetorical ritings f Cicero and Quintilian ook up the major partof the curriculum. ee the Jesuit urriculum et out in the Ratio Studiorum, iven n G.Michael Pachtler Ratio Studiorium t Institutiones cholasticae . J. per Germanumdiu vigentes," Monumenta Germaniae aedogogia, X (Berlin, 1890), and the detaileddiscussion n Franqoisde Dainville, a Naissancede l'humanismemoderne Paris, 1940).

17See Marc Fumaroli, 'Age de l'eloquence Geneva, 1980).18Descartes showed a positive nd informed nterest n rhetorical ssues as late as

1628, n his open letter efending he rhetorical tyle f Guez de Balzac, on which eeThomasM. Carr Jr., escartes nd the Resilience f Rhetoric Carbondale,1990),ch. 2.


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and conviction s clearly irected t an audience. For Descartes, y con-trast, he central ask s to convince neself, nd only once one has donethis does one try o convince thers.

The question hat naturally riseshere s whether theory evoted oconsidering ow one convinces n audienceof something on groundsthat may not always dependon the truth f what one is arguing) ouldpossibly orm he basis for theory bout what characteristics f ideasenableus to recognize heir ruth, ven fwe wouldhavedifficulty onvinc-ingothers f that ruth. 9 he answer s that t could. What we must ocuson is the psychological ontent. sychological heory bout questions fjudgment as transmitted o the modem ra argely nthe form f rhetori-cal theory, specially hat of Quintilian. is treatise n oratory may wellhaveplayed critical ole n Descartes's hinking bout udging hetruthof theories n terms of the clear and distinct erception f ideas. OnQuintilian's ccount, nd here he followsAristotle, ivid llustration evi-dentia)of the facts goes beyond mere larity, ince he atter merely etsitself eseen,whereas heformer hrusts tself ponour attention."20 uthow do we achieve uch evidentia? he answer s given s follows:

If we wish o give ur words he ppearance f sincerity, e must ssimilateourselveso the motions f thosewho re genuinelyo affected,nd our elo-quencemust pring rom he ame eelinghatwedesire oproducen the mindof the udge.Willhe grieve hocan find o trace f grief n the wordswithwhich seek o movehim o grief? . It is utterly mpossible.ire lone ankindle, nd moisture lonecan wet,nor can one thing mpart ny colour oanother ave hatwhich t possessestself. ccordingly,he irst ssentials thatthose eelingshould revail ith s that wewish o prevail ith he udge, ndthat we should e moved urselves efore eattempt o move thers.2'

Quintilian hen goes on to ask how we generate heseemotions n our-selves, nd there ollows is account of the evidential uality f mages.The crucial point here s that unless one is already onvinced y one'sown mages, ne will not be in a position o use them o convince thers.So self-convictions a prerequisite or he conviction f others; nd self-conviction, ikethe conviction f one'saudience, epends n the qualitiesof the mage, mongst which must figure larity perspicuitas) nd viv-idness evidentia).

Although can find no direct borrowings romQuintilian n Des-cartes's art, find t hard to believe hat omeone who knew his ext owelland who himself ffered uch a similar octrine wasnot nfluenced

19Note, for xample, heremark oMersenne n a letter f 25November 630: "I willtest, n the treatise n Dioptrics, whether am able to explain my houghts nd persuadeothers f a truth fter have persuaded myself f t-something am not sure of" (AT,i, 172).

20

Quintilian, p. cit., VIII, iii, 61.21 Ibid, VI, ii, 27-29.


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by t, or at least by his memory f t. t is a modelof elf-conviction longthe ines developed by Quintilian, suggest, hat s effectively he sameone taken up by Descartes n Rule 3, where we are told that what wemust eek ssomething e can clearly nd evidently ntuit clareet eviden-ter ossimus ntueri) nd that he mind hat s "clear and attentive" illbe able to achieve this. Although he early Rules draw their model ofknowledge lmost exclusively rommathematics, he point s that thedoctrine f clear and distinct deas is exhibited aradigmatically n thecaseof mathematics, ot that t s necessarily erived rom mathematics.It should not be surprising hat a conception ased on such a stronglypictorial modelof representation houldfind ts paradigmatic manifesta-tion n something s abstract s mathematics. n the earliest writing hatwehavefrom escartes, heCompendium usicae, larity f representa-tion sa focalpoint f the treatise. his amounts ofavoring hatpictorialform f representation n which differences an be detected t a glance;the representation f musical ntervals ot as a ratio of ntegers ut as apairing of lines' lengths by arithmetic roportion.22 oreover, n theCogitationes rivatae, which is roughly ontemporary ith the early

Rules,the mage-forming owerof the magination s made the basisforthe operations f reason, nd indeed ts power s extolled bove that ofreason:

Asimagination akes seoffigures o conceive fbodies, o ntellect akes seof certain ensible odies o figure piritual hings, uch s wind nd ight; ywhich, hilosophizing ore rofoundly, e can draw ur mind ycognition otheheights. t may eem emarkablehat here re moreweightyudgementsnthe writings f poets han f philosophers. he reason s that oetswritewith

more nthusiasm nd he orce f magination;here rewithin s, s nflintstone,sparks f the cienceswhich re educed hrough eason y philosophers utwhich re truck orth ypoets hroughmagination.23

The idea of this mage-forming owerbeing t the center f cognition sdominant n Descartes's thought t this period. Moreover, s a recentcommentator as pointed ut, at this time Descartesgenerally oes notusethe erm maginatio nd ts orrelates o ndicate imple perations utrather o denote ctive, xploratory, nvestigative rocesses: isualizinggeometrical onstructions, isualizing heend of apparently nfinite ro-cessesofdivision, pplyingmathematical onstructs ophysical roblems,synthesizing, hrough heact of istening, he discrete arts of a song.24

22 Cf. AT, x, 91-92.23 AT, x, 217.

24 DenisL. Sepper, Descartes nd the Eclipseof he magination, 618-1630," ournalof the History f Philosophy, 8 (1989),383-84.


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The Later Regulae and the Application fClear and Distinct deas to Mathematics

In the course of the 1620s Descartes developed a highly bstractconception f mathematics. he rhetorical-psychological onception fclear and distinct deas that we have ust looked at works n terms fpictorial r quasi-pictorial mages, nd as such t would eem nappropri-ate to the kind of mathematics hat Descarteswas pursuing t the timeof the later Regulae. But in Rules 16ff, escartes provides n accountof mathematics hat employs his conception.His aim is to show howmathematics s applicable o reality, nd this requires im to show how

mathematical perations an be represented n the magination, corpo-realbodywith two-dimensional urfacewhich s the ite of the represen-tation. n Rules 12-14Descartes had attempted o establish hat theexternal orld srepresented here ymeans f ines nd two-dimensionalfigures, nd in Rules 15ff e tries o show how mathematical perationscan also be represented n these terms n the magination, o that they"map onto" the representation f the world, o to speak. But he alsoattempts olegitimate hisrepresentation f mathematics n the magina-

tion; and in doing this, he invokes he clear and distinct ature f themathematical ntities nd operations erformed n the magination, nti-ties, nd operationswhich re pictorially epresented n two dimensions.The crucialpoint s that he egitimation f mathematics erives rom hepictorial orm hat ts operations ake in the imagination, ecause thislegitimation orks n terms f the doctrine f clear and distinct deas,which can only function n terms f notions which have a pictorial rquasi-pictorial ontent.

The most ignificant spect f Descartes'shinking

bout mathematicsat this time s the very bstract way n which he conceives f numbers.To appreciate he mportance f his properly, t willbehelpful ocontrasthis conception f number riefly with that of Greek and Alexandrianarithmetic.25 ake the case of multiplication. n the construal f this

25What we must focus upon here s the relation etween rithmetic nd geometry.There was an especially lose relationship etween he two in antiquity, nd there reessentially woways n which his relation an be interpreted. n the first nterpretation,geometry asemployed n order oexpandthe resources f arithmetic, nd it was intro-duced n order o resolve he problem f ncommensurability y llowing ncommensurablemagnitudes oberepresented nproblematically. he result was what s sometimes eferredto as a "geometrical lgebra," way of dealing with rithmetical roblemswhich llowsone to go beyond he resources f arithmetic. lthough his view of the matter s thattraditionally ccepted despite he pioneering ork f Jacob Klein in the 1930s), t leastuntil the last twenty ears or so, it has been subjected o serious criticism nd nowlooks quite implausible. On the second interpretation, he geometrical rticulation farithmetical perations, arfrom ncreasing hegenerality nd abstractness f arithmetic,in fact iminishes t considerably. ndeed, here sa caseto be made that ncient rithmetic

is in fact form f metrical eometry. or more details ee Jacob Klein,GreekMathemati-cal Thought nd theOrigin fAlgebra Cambridge,Mass.,1968);MichaelMahoney, The


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operation nancientmathematics, emultiply ine engths y ine engths.If a, b, and c are line engths, or xample, X b is a rectangle avingsidesof ength and b, and a X b X c is a solid figure f sides a, b, andc. Even though we are dealing with abstract numbers, we are alwaysmultiplying umbers f something y numbers f something, nd conse-quently here s a dimensional hange n multiplication. his is indicatedby the fact hat we cannot multiply more than three numbers ogether,since he product sa solidwhich xhausts henumber f vailable dimen-sions.26

Thisextraordinarily onstrictive onception fnumbers as paralleledby an equally constrictive onception f arithmetic nd geometry, nwhich hepoint f the exercisewas to compute determinate umber rconstruct determinate igure espectively. or the mathematicians fantiquity t was only f such a determinate umber r figure ould beconstructed r computed hat one could be said to have solved the prob-lem. In the case of arithmetic, nly natural numbers were allowable assolutions; egative umbers, n particular, ere not, and were regardedas "impossible" numbers. owards the end of the Alexandrian eriod,most notably n Diophantus'sArithmetica, e begin o find search forproblems nd solutions oncerned with general magnitudes; ut theseprocedures evermakeup anything ore han uxiliary echniques orm-ing stage preliminary o the final ne,where determinate umbermustbe computed.27

In Rule 16 of the Regulae Descartes explicitly ets aside both theconstrictive onception f arithmetic hat imits t to computing etermi-nate numbers nd the constrictive onception f number hat, etainingthe ntuitive patial elements f geometry, onstrues multiplication s a

procedure n whichproducts re always utomatically f a higher imen-sion. The first e dispenseswith s follows:

It should e noted hatwhile rithmeticians logistae] aveusually esignatedeachmagnitude ya plurality f units r by somenumber, e are abstractinghere from umbers hemselves,ust as we abstracted bove Rule 14] fromgeometricaliguresnd from verythinglse.We do this not ust to avoid he

Beginnings f Algebraic Thought n the Seventeenth entury," n S. Gaukroger d.,Descartes: hilosophy, athematics nd Physics Atlantic Highlands,N.J., 1980), 141-55;A. Szabo,The Beginnings f GreekMathematics Dordrecht, 978); S. Unguru, On theNeed to Rewrite he History f GreekMathematics," rchivefor istory f Exact Sciences,25 (1975/76), 67-114.For some of the philosophical ationale ehind his onception fnumbers nd a defense f ancient rithmetic s a form f metrical eometry, ee StephenGaukroger, Aristotle n Intelligible Matter," hronesis, 5 (1980),187-97.

26 Thisconstraint s only ver verlooked nce n the whole f Greek nd Alexandrianmathematics, n Heron's Metrica I, 8), where two squares i.e., areas) are multipliedtogether, nd this maywell simply ave been an oversight. ne scholiast n Heron treats

it as such, nd there s no way n which Heron could have ustified he procedure.27 For details ee the exemplary ccount n Klein, op. cit.


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tedium f a long nd superfluous alculation, ut bove ll to make ure hatthose arts f he problem hich make p the ssential ifficultylways emaindistinct nd are not obscured yuseless umbers.f, for xample, heproblemis to find he hypotenusef right-angledriangle hose iven ides re 9 and12, he rithmetician ill ay hat t s 25 or 15.Butwe willwrite and b for9and 12, nd hall ind he ase obe a2+ b2. n this way he wo arts andb,which henumber uns ogether, re kept istinct.28

He continues y dealing with the question of dimensional hange inoperations uch as multiplication:

We should lso note hat hose roportionshat orm continuingequencereto be understood n terms f number f relations; thers ry o express heseproportionsnordinary lgebraic erms y means f everal ifferent imensionsand hapes. hefirst hey allthe oot, he econd he quare, he hird he ube,the fourth hebiquadratic,nd so on. These xpressions ave, confess,ongmisledme.... Allsuchnames hould e abandoned s they re iable ocauseconfusionn our hinking. or though magnitude ay e termed cube r abiquadratic,t should ever e represented o the maginationtherwisehan sa line r a surface.... What, bove ll, requires o be noted sthat he oot, hesquare, hecube, tc., re merelymagnitudesn continued roportion, hichalwaysmplies hefreely hosen nit hat wespoke f n the preceding ule.29In other words, he cube of a, for xample, s not designated 3 becauseit represents three-dimensional igure utbecause t s generated hrough

1 a a2a proportionalerieswith hree elations: = = -. Heconcludes:

a 2 a3

We who eek o develop vident nddistinct nowledgef hese hingsnsist nthese istinctions. rithmeticians,n the other and, re content o find heresult ought, ven f hey ave no grasp f how t follows rom hathas beengiven, ut nfact t s nthis ind fgrasp lone hat cience scientia]onsists.30

In these mportant evelopments escartes shows a very lear andexplicit wareness f the direction n which his algebrawasmoving.Heis now beginning o consider oth geometry nd arithmetic n terms f atheory f equations, hereby howing grasp of mathematical tructurewellbeyond hat of any of his contemporaries. he powerof algebra, s

Descartes onstrues t, s as a problem-solving echniquewhichhe denti-fieswith he ancient rt of analysis. t works y construing nknowns nterms f knowns, y providing symbolism or hem which nables hemto be slotted nto equations yingknowns nd unknowns ogether n asystematic ay.This procedure as immense dvantages ver, or xam-ple, the traditional eometrical roofs, nd Descartes believes hat an

28 AT, x, 455-56.29

AT, x, 456-57.30 AT, x, 458.


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algebraic emonstration eveals he teps nvolved n solving he problemin a completely ransparent ay. Indeed, t is the transparency f itsoperations, s much s its bstractness, hatDescartes inds f he greatestvalue in his new algebra.This "transparency" f algebraic perations swhatmarks hem ut as being ompletely ertain, nd what his ranspar-ency amounts o, in philosophical erms, s "clarity nd distinctness."Moreover, t brings with t all the connotations f pictorial vividnesswhich, haveargued, re such a crucial part of the doctrine f clear anddistinct deas as it figures n the early Regulae.Not only s the dea ofvalidation y means of pictorial ividness till ctive eight years ater nthe ater Regulae,but it is present n the most striking nd unexpectedcontext. aving established hehighly bstract, tructural eatures f hisnew lgebra-its concernwith magnitudes n general ather han particu-lar numbers nd shapes, hebasis for ts notation n series f continuedproportions ather han patial magery-Descartes roceeds nRule 18tovalidate t n terms f ntuitive bviousness, ermswhich re unashamedlyspatial and indeed pictorial. Having set out arithmetical perations nalgebraic erms, e continues:3"

From hese onsiderations t seasy osee how hese wo perationsreallweneedfor he purpose f discovering hatever agnitudes eare required odeduce rom thers nthe asis f ome elation. ncewehave nderstood heseoperations,henext hing o do s to explain ow opresent hem o the magina-tion for xamination,nd how to display hem isually, o later n wemayexplain heir sesor applications.f addition r subtractions to be used,weconceivehe ubjectn he orm f line, r n he orm f n extended agnitudein which ength lone s to be considered. or fwe add ine to ineb

a b

weaddthe ne to the ther n thefollowing ay,

a b

andthe esult sc.

c

And so on for ubtraction, ultiplication, nd division. he case of multi-plication llustrates he quite regressive ature f the representation farithmetical perations equired y Descartes'svalidating rocess.32

3' AT, x, 464.32 AT, x, 466.


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Again, fwe wish o multiply b byc,

C

we ought o conceive f b asa line, amely:

ab

in order o obtain or bc the following igure:

ab

c

There s clearly discrepancy erebetween he concern o represent

the operations f arithmetic lgebraically, n structural erms, nd theconcern o provide vindication f arithmetical rocesses n terms foperations o clearand vivid hat ne cannot ailbut assent o them. Theirony s that, aving aid this highpricefor indication, escartes lmostcertainly ealizedthat t would not succeed anyway; or n the uncom-pletedRules 19-21he extends is account o a set ofproblems-problemsthat must be set up in terms f several quations n several unknowns-that can be dealt with lgebraically ut which cannot be legitimated nthe way proposed; nd at this very point he abandons heRegulae.33

Conclusion

Descartesdoes not abandon the doctrine f clear and distinct deasafter 628.Rather, he transforms t from doctrine bout the evidential

33 The account f these ssues n ch. 6 of Schuster, p. cit., s an indispensable tartingpoint for further ork on these topics, lthough he sees the question n terms f an

ontological egitimation f mathematics, hereas see it n terms f an appeal to a notionof representation erived rom he rhetorical-psychological radition.


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value f mages nto ne abouthowwe are to guarantee heveridicalityofour ognition f he xternal orld gainst yperbolic oubt. he firstdoctrine s derived rom he rhetorico-legalradition, uitably illed utin terms erived romAristotelian sychology, hereas he second smetaphysicalndhasno such lassical recedent. hefirst elies n whatDescartes efers oas "the natural ight f reason," nd ndeed t s inmany espects onstitutivef he natural ight f eason,omething hich,like conscience on which t may havebeenmodelled,f onlyuncon-sciously),s an ultimate esort. he second elies n a divine uarantee,and-far from he riterion f clear nd distinct deasbeing omethinghuman eingshave forged orourselves-it ow becomes omethingwhichGodhasexplicitly rovided nd which e guarantees. iven hisdifference,nemight skwhat s the onnection etweenhe wo ersionsof he doctrine, nd ndeedwhether hey anbesaid obeversions f hesamedoctrine n anymore hanname.

There s in fact connection,nd t s a key ne:both octrines reconcernedbove ll elsewith he nature f elf-conviction.f he rgumentof thispaper s accepted, henwhatDescartess doing s moving roma rhetorical-psychologicalonception f conviction o a metaphysicalconception, move hat ccurs o earlier han 1628.Howwell-advisedthis movewasis not a question can dealwithhere.But t is worthremembering hat his move rom hetoric ometaphysicsesultedn: tbegan s a rhetorical-psychologicaloctrinenwhich he notion f clearand distinct dea was easyto recognize nd n which he problem ashow oexplain ow uch deas rose; nd t ended s a doctrine nwhichit was o difficult osay xactly hat clear nddistinct deawasthat tbecame laughing-stockn the econd alf f the eventeenthentury.

University f Sydney.

Descartes Clear and Distinct Ideas

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