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The Development of Scientific Method in the School of PaduaAuthor(s): John Herman Randall, Jr.Source: Journal of the History of Ideas, Vol. 1, No. 2 (Apr., 1940), pp. 177-206Published by: University of Pennsylvania PressStable URL: http://www.jstor.org/stable/2707332.

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THE DEVELOPMENT OF SCIENTIFIC METHODIN THE SCHOOL OF PADUABY JOHN HERMAN RANDALL, JR.The Aristotelian science which the thirteenth enturyhad soeagerly worked into its Christianphilosophyof life aimed at anunderstandingof nature divorced frompower over things. Butduringthesixteenth enturymore and more men began to hold thatscience shouldbe directed,notmerelyto understanding nd vision,but to a kind of understanding hatmight give power, action,andan improvement f thepracticalarts. A leading intellectual nter-prise of the timewas the search for a fruitfulmethod that couldservethisnewaimtowhichknowledgewas turning. Those thinkerswhose energieswere not wholly absorbed by the theological ssuesin termsof whichthe major battles were still beingfought, oncen-tratedon this problemof method as the paramountscientific askof the day.Ironically enough,whenthe fruitfulmethodwas finally discov-ered and proved in practice, t turned out to be the least novel ofall the elements that went into the formationof the new science.Afterexploringmany a blindalley,mencame to realize that one ofthegreatmedieval ntellectual raditionshad alreadymade an excel-lent beginningat just the kind of practical and useful knowledgetheynowwanted. In the thirteenth nd fourteenthentury chools,there had been workedout the idea of an experimentally roundedand mathematicallyformulatedscience of nature, and since thenmuchhad been done n theway of actual achievement. In Leonardo

thepenetrating,n the talian mathematicians nd physicistsof thesixteenth entury,n Copernicus,Kepler, and Galileo, sucha sciencehad indeed comeofage.Into this sciencethere enteredmanydifferenttrands, ach withits own history. And the powerfulstimulus mpartedduring thesixteenthcenturyby the recoveryof the techniquesof the Greekmathematicians s not to be minimized. But the conceptionof thenature of science,of its relation to the observationof fact,and ofthe methodbywhich t mightbe achievedand formulated, hatwashandedon to his successorsby Galileo,was not the workofthenewseekersafter a fruitfulmethod. It appears ratheras the culmina-tionof thecoioperativefforts ftengenerations f scientistsnquir-177

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178 JOHN HERMAN RANDALL, JR.ing into methodologicalproblems in the universitiesof northernItaly. For threecenturies henaturalphilosophersof the schoolofPadua, in fruitful ommercewiththephysiciansof its medical fac-ulty,devotedthemselves o criticizingnd expandingthisconceptionand method, nd to grounding t firmlyn the careful analysis ofexperience. It lefttheirhands witha refinementnd precisionofstatementwhich the seventeenth entury cientistswho used it didnot surpass in all theircarefulinvestigationof method.In contrastwith hiscumulative nd organizedelaborationofthetheory nd methodof science, hemanyhumanist eekers,revoltingfromthe scholasticismof the Scotists with theirtechnical termi-nist logic,seemtohave displayed all thecustomary gnoranceandfutilityof intellectualrevolutionaries, nd to have proposed newmethodsdistinguished hiefly ythenoveltyoftheir gnorance. Asmight be expected, these servants of the word for the most partsoughttheirnew method n language and in rhetoric, nd tried toerecta natural dialectic on the basis of Cicero and Quintilian.Others ikeBrunowerefascinatedbythesuggestionsofLully forauniversal language that mightreveal all truth. And still others,emphasizingtheplace of a knowledgeof nature in humanwisdom,urgedmentoclose theirbooksand observetheworld.The humanistsmightseek the method of a new science in therhetorician's rt ofpersuasion; a Vives or a Bacon, recognizingnousefulknowledge n the investigationsof the mathematicians ndastronomersof theirday,mightcounsel experience and ever moreexperience. Their combinedonslaughthelped to shakemen's faithin the complacentacademic traditionalismof the schools, alreadysorelydisturbedby thenew literaryand theologicalmovements; thardlycontributedmuchguidance to those already busily engagedupon scientific roblems. Both in its traditional nsightsand in itsnovel guesses the imaginationneeded the discipline of a criticalmethodbeforetherecould be any significant bservationof facts.The bodyofideas which n Galileo and Descartes dared to arrogateto itselfthename of natural science,and whichin Newton defini-tivelymade good thatproud claim,had otherand far deeper roots,stretching ack through nd beyondthe twelfth-centuryuropeanappropriationofancient earning.Historyhas fallen into error in acceptinguncritically he esti-mate thepioneerthinkers f the sixteenth nd seventeenth enturymade oftheirownturning wayfrom heheritageof thepast. Their


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SCIENTIFIC METHOD IN THE SCHOOL OF PADUA 179consciousness of freshdiscovery nd radical reorientation bscuredthe countless bonds of continuity,n materials, methods, nd evenachievements, nitingthemto theirpredecessors n the late middleages. In particularthefact thattheseventeenth entury cientists,in revoltagainst thehumanists' appeal to theauthority f thepast,preferred o put theirtrust n natural reason alone, and hencecared nothingforhistorical continuity, as sadly misled our judg-ment s to the fashion nwhich heir houghtwas generated. Takingthem t theirownword,we have assumedthatthatcooperativecriti-cism and reconstruction fa well-organized ystemofideas, shakenfromtime to time by fresh insights whichhave had to be workedinto the logical structure-that that process whichhas since theseventeenth entury een so characteristic ftheprocedureof scien-tific dvance, playedno part in its earlierstages.In thepresent generationmuch has been broughtto light abouttheorganizedscientific raditionsof the later middleages in whichthe sixteenth and seventeenthcentury pioneers carried on theirwork. But much moreremainsto be done. In particular,thefactthatseveral of the most nfluentialnvestigatorshave been Frenchhas focused attention on the activitiesof the Universityof Paris,while thefurther act thatmanyof themhave beenCatholic scholarshas madethemnotunduly ppreciativeofthe workofthefree-think-ing and anti-clerical talian schools. For its part, Italian scholar-shiphas been attractedbythespectacularhumanisticmovement ndbythepresumablymorenoveland original iteraryPlatonismoftheFlorentines. As a result,though t is clear that the thoughtof theItalian universities orms he mmediate ackground fthe sixteenth-centuryscientificmovementthat culminated in Galileo, its sub-stantial achievementhas as yetreceivedalmostno study.The basic idea of an experimentally rounded science of themathematicalstructureof nature appeared as soon as Europeansbegantoexplorethewisdom ofthe ancients. It developed within hegeneral frameworkfthefirst odyofancientmaterials to be assimi-lated, theAugustinianphilosophyof reason-itself the platonizedoutcome fHellenisticthought. It drewspecifically pontheArabicversions of Alexandrian science, though direct contact with thewholeofGreekmathematics, stronomy,nd mechanicswas the astto be established;Archimedeswas notknowntill the sixteenth en-tury. But the idea of such a science, and muchof its methodandconcepts,were in the possession of Europeans from the twelfthcentury n.


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180 JOHN HERMAN RANDALL, JR.Aristotle's logic, his theoryof science and method,was discov-ered n the Analyticsduringthe first alf ofthetwelfth entury;hisbasic concepts and principlesof natural science were learned from

thePhysics in the second half. The comingof Aristole introduceda body of materials too impressiveto be ignored. Thereafterforcenturies he Aristotelianphysical writingswere taken as thestart-ing-point or all natural science,howeverfarmenmight eventuallydepartfromthem; and theAristoteliantheoryof science,howevermenmight nterpret t,remained dominanttill the timeof Newton.From the beginning f the fourteenthentury, owever, hereset ina persistent nd searchingreconstructionf theAristoteliantradi-tion,which,whendirected o thePhysics, ed by gradual stages tothemechanical nd mathematical roblemsof theGalilean age, and whendirected to theLogic led to theprecise formulation f the methodand structureof science acclaimed by all the seventeenth-centuryscientists.There were twomaincriticalmovements uringthe ater middleages. The Ockhamitesbegan in Oxfordin the thirteenth entury,and whilepersistingtherefound a new strongholdduringthe nexthundredyearsintheFacultyof Artsat Paris. The Latin Averroistsbegan in Paris in the thirteenth entury, nd shiftedtheir seat toPadua early nthe fourteenth. Both set out byexpressing secularand anti-clerical pirit, nd by undertaking destructive riticism fThomismand Scotism, the thirteenth entury ynthesesof scienceand religion. But both soon advanced beyondmere criticism o theconstructive laboration of natural science: they became the twogreat scientific chools of the ater middle ages. The original workof the Ockhamitesbelongs to the fourteenth entury, hat of thePaduans, to the fifteenthnd sixteenth. The formerwas done indynamics,kinematics, nd thelogic of continuity nd intensity;thelatter, n methodology nd in the further evelopment f dynamics.Both turnedfrom heearlier religious syntheses o the purely natu-ral philosophy f Aristotlehimself;and bothdeveloped primarilybya constructiveriticism f theAristotelian exts and doctrines. TheOckhamiteswere at first he more progressive and modern ;theywere interested n the free development of the Aristotelianphysics, nd theirworks take the formof questions and problemssuggestedby Aristotle's analyses. The Averroists, though muchmoresecular and anti-clerical,were originallymore conservative ntheirattitude towardAristotle and his interpreterAverroes: their


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SCIENTIFIC METHOD IN THE SCHOOL OF PADUA 181worksare characteristicallyommentaries n the texts. From 1400on, however,theyknew and taught all the OckhamitedeparturesfromAristotelian doctrine:Paul of Venice (*1429) is remarkablyup-to-date, nd his Summa Naturalis contains an exposition of allthe ideas of the dynamicsof the Paris Ockhamites nd the Oxfordlogicians. The works of these fourteenth-centuryhinkers wereprinted n many editionsso soon as the press reached Italy, all ofthemby 1490; and in the sixteenthcentury t was primarily theItalians who advanced by successive stages to the formulations fGalileo.About1400, herefore,he nterestnthedevelopment fscientificideas shiftsfromOckhamiteParis to thePadua Averroists. Fromthe time of Paul of Venice to Cremonini (*1631) the Aristotelianphysics and a nascent Galilean physicswere in definite nd con-scious opposition at Padua, and this critical conflict ontributedgreatly to theworkingout of the latter. Paul of Venice had beensentby his order to Oxford in 1390,where he remained for threeyears; he then taught fortwo morein Paris at thetime of the lastgreat Ockhamite,Pierre d'Ailly. He thusknewall the Ockhamitedevelopments t firsthand, and explained themfullythoughcriti-cally inhis encyclopedicwritings.His successor at Padua, Cajetan ofThiene (*1465), was themostradical scientificallyf theAverroists, nd themostsympathetic otheParis teachingson dynamics. He initiateda great controversyover the Calculations of Suisseth (Swineshead), in which all theargumentsfor a mathematical s against a qualitativephysicsareexamined, o that the documentsof this controversy,n many edi-tions,wereamongthefirstworksprinted n Italy in the1480's. ThefundamentalDe latitudinibusformarum f Nicholas of Oresme, nwhichthe ruleforuniformlyccelerated motionfirst ppears, cameout in 1482,with a discussion by Blasius de Parma de Pelicanis;Albert of Saxony's Tractatus de proportionibus, rguing for aquantitativetreatment fqualities (already reported n theSummaNaturalis of Paul ofVenice) also appeared inthesameyear; in 1496it was reprintedwiththeDe intensione t remissioneformarum fWalterBurleigh, defenseof the ogicofqualitativechange opposedtothespiritofOresme, nd witha fullreplytoBurleigh nbehalf ofquantitative nalysis bythephysicianJacopo da Forli. Amongthemost nteresting fall thesedocuments,ndicativeofa livelyconcernwithwhat was to becomethe fundamental cientificuestion, s the


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182 JOHN HERMAN RANDALL, JR.Tractatus de proportioni us of a Milanese physician, JohannesMarlianus (Pavia, 1482), whichbringsexperimentalproof to bearon the quantitativeside, describesthe rolling of balls down an in-clined plane tomeasuretheirvelocity nd acceleration, nd narratesexperimentswithpendulums.The questionwhether he operationof causes was to be formu-lated mathematically r qualitatively whether he first accidentof substance was to be taken as quantityor not-which happens tobe also theway in whichKepler expressedhis view thata cause is amathematical aw) was thusvigorously ebated at Padua toward theend of the fifteenthentury, nd thenotion of cause as a mathe-maticallyformulatedformal cause won many adherents. In thenext century here brokeout anothergreat controversy mong thePaduans as to whetherthe cause of natural motion was to besought n a formor in a force, hatis, in a definiteway ofbehavingor in something hat acted in a definiteway. Galileo joined thosewho identified cause witha force ; but since he also definedforcein termsof its way of acting,his divergencewas not great.And towards the endof the samecentury hereoccurred notherdis-pute,as towhether inal auses had anyplace innaturalphilosophy.The outcomeofthese successivedebateswas to delimitthe concep-tionofcause, and tomake theGalilean position nevitable. Theyarehere mentioned o suggestcertain other strands n thedevelopmentof Italian Aristotelianismwhichthis studydoes not presumeto setforth n detail,and which n particular illuminatethe change froma qualitativeto a mathematical reatment f natural operations.It has becomea recentfashiontoview thewhole Renaissance,and indeedthevery birth ofmodernscience tself, s philosophi-cally a turning rom heAristotleof the Schools to Platonism; andItalian thought f thefifteenthentury as beenrepresented s domi-nated bythatturning. But itmustnot be forgottenhat thevigor-ous intellectual ife of the Italian universitiesremained oyal to theAristotelian radition. Now inmost countries he fifteenthenturysaw theteaching nd refinementftheearlierphilosophies,Scotism,Thomism, nd Ockhamism,with ittlebasicallynew. But in north-ern Italy, at Padua, Bologna, and Pavia, and to a lesser extentatSiena, Pisa, and thebrilliantnewuniversity f Ferrara, Aristoteli-anismwas still a livingand growingbodyofideas. What Paris hadbeen in thethirteenthentury,what Oxford and Paris togetherhadbeen in thefourteenth,adua became in the fifteenth:he center n


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SCIENTIFIC METHOD IN THE SCHOOL OF PADUA 183which deas fromall Europe were combined nto an organized andcumulative body of knowledge. A succession of great teacherscarried thatknowledge o thepointwhere nthe nextcenturytcouldfind ruitfulmarriage withthe newinterest n themathematical ci-ences. In the Italian schools alone the emerging cience of naturedid notmean a sharp breakwithreigning heological nterests. Tothem t came ratheras the natural outcomeof a sustainedand co-operativecriticism fAristotelian deas. If inthesixteenth enturythe moreoriginalmindswere led to a formalbreakwith thePaduanteaching,wemustnotforget hatevenGalileo occupieda chairtherefrom 1592 to 1610, and that in method and philosophyif not inphysicshe remained typicalPaduan Aristotelian.That Italian Aristotelianismwas thus able to lead theEuropeanschools in the fifteenthnd sixteenth enturieswas due to severalcircumstances,not the least of whichwas the settled commercialprosperity heItalian citieshad now achieved. They had long en-joyed and taught n theiruniversities thoroughlyecular and anti-clerical philosophyexpressive of the new cultureof a this-worldlyand commercial ociety. By 1400that niceblend ofAristoteliansci-ence and Christian faithwhich Thomas and Duns Scotus had con-structedhad, in Italy at least, retreated nto the monastic orders.At Padua, Bologna, and Pavia therereigned n Aristotelianism hatmade little attemptto accommodate tselfto theologicalinterests.And it is no accident thatwhiletheChurch-controlledcience oftheNorthdrove all thosewhofelt thenewcurrents nto open rebellionagainst science tself, he anti-clerical cience of the talian universi-ties couldprogresssteadily n self-criticismo theachievement f aGalileo.

Fundamental also was the close alliance betweenthe study ofAristotleand the studyof medicine. At Paris theFaculty of The-ologycrowned heSorbonne; at Padua theFaculty ofArts led onlyto that ofMedicine, nd Aristotlewas there aught s a preparation,not for an ecclesiasticalcareer,butforthestudyofmedicine,with aconsequent trong mphasisonhis physicalwritings, isnaturalhis-tory,and his scientificmethodology. A physician's Aristotle isbound to differ roma theologian's. The teacherswroteno theo-logical works,no commentaries n the Sentences. They normallyheldmedical degreesthemselves;they applied Aristotle to medicalproblems, and to questions of methodarising in medical science;they nterpretedhimin thelightof thebest medicalwritersof theGreek and Arabic traditions.


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184 JOHN HERMAN RANDALL, JR.Finally, the libertyof teachingand speculation guaranteed byVenice,the eading talian anti-papaland anti-clerical tate,after tsacquisitionofPadua in 1404,attractedthe bestmindsfrom ll over

Italy,especiallythe philosophicalSoutherners. Padua remainedtothedaysof Galileo the eadingscientificchoolofEurope, thestrong-hold oftheAristotelianqualitativephysics, nd the trainereven ofthosewhowere to breakwith t. Cusanus,Purbach,Regiomontanus,Copernicus, s well as the talians, all studiedat Padua.If the conceptsof a mathematicalphysicswere arrived at by alongcriticism fAristotelian deas, the new method, the ogicandmethodology akenover and expressed by Galileo and destined tobecomethe scientificmethod of the seventeenth enturyphysicists,as contrastedwith he manynoisy proposals ofthe sixteenth enturybuccinators down to Francis Bacon, was even more clearly theresultof a fruitful riticalreconstructionf theAristoteliantheoryof science,undertaken t Padua in particular,and fertilizedby themethodologicaldiscussions of the commentatorson the medicalwriters. For threehundredyears,afterPietrod Abano brought heproblemsto thefore,the Paduan medical teacherswere drivenbytheirtexts,especiallyGalen, to a carefulanalysis of scientific ro-cedure. The greatcommentatorsnGalen,Jacopo da Forli (*1413),who ncidentallywrotewidelyon themethods f theParis physicists,and Hugo of Siena (*1439), graduallybuiltup a detailed theoryofscientificmethodwhich heAristotelian cholars,themselvesholdersofmedicaldegrees, ncorporated ntotheir versionof the nature ofscience. It is possible to trace step by step in rather beautifulfashion the gradual elaborationof the Aristotelian method, n thelight of the medical tradition,fromits first discussion in Pietrod Abano to its completedstatement n the logical controversiesofZabarella, in which t reaches the formfamiliar n Galileo and theseventeenth-centurycientists.This discussionofmethodwas carriedon in terms of thegeneralformal tructure f scienceand its relationto the subject-matternwhich t is to be discovered nd exemplified.As suchit is applicableequally to all fourof the Aristoteliankinds of cause; and hence itdoesnot nsist, nymorethan the extensivediscussionsof theseven-teenthcentury, hat the principles of natural science be strictlymathematicaln character nd that ts formalstructure e stated inmathematical erms. This mathematicalemphasis is an importantelement n Galilean science. It too has a long and gradual develop-


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SCIENTIFIC METHOD IN THE SCHOOL OF PADUA 185mentat Padua in thefifteenthnidsixteenth enturies, s has beenalready ndicated;and thesediscussions nvolveboththe Oxford ogicof quantity nd the ssues it raised,and therecovery fGreekmathe-matical texts and techniques in the sixteenthcentury. But thisseems to be anotherpart of the story,best told in connectionwiththe particulartreatment f particularnatural questions. It wouldinvolve a different et of Aristotelian texts and problems,and awhollydifferent roup of passages; it seems best to present thedevelopment f methodological heory n its own terms, nd to post-pone thisother mportant trand.These menwere concernedwiththe discovery nd use of princi-ples in science. Like all thinkers rom he twelfth entury o New-ton, heyunderstood rincipium s Aristotleunderstood pxii,s thatfromwhich thingproceedsand has its origin n anyway whatever;specifically,n science a principium s thatwhich s in any way asource of understanding. The particular character of priorityand origin, f whichbothAristotleand the scientificheoryderivingfromhim distinguishedvarious kinds, depends upon the specificcharacterand contextof theproblemunderconsideration. The dis-tinctions etween he differentinds of orderand method, herefore,running hrough ll themenhereconsidered, re ipso factodistinc-tionsbetween1ifferent indsof priority, that s, betweendiffer-entmeaningsofprincipium.The questionof methodwas raised, and the terms n which t wasto be treatedfor threecenturieswere clearlyformulated, y Pietrod'Abano in his Conciliatordifferentiarumhilosophorum, t prae-cipuemedicorum, rittenn 1310. In discussing hequestionwhethermedicine s a science he points out that science is used in twosenses.

Sciencenthemost roperense sthatwhichnfershe onclusionhroughcauses which re proximatend immediate,ike thatsciencedefinednAnalytica osteriora,. I, c.2 [71b]; We thinkhatweknow thing n-qualifiedlysimpliciter)nd not in a sophisticalnd accidentalmanner,whenwethinkwe know hecause on account f whichpropter uam)thefact xists,hat t is thecauseofthatfact, ndthat t couldnot be other-wise ; andthis ind f ciencesgained rom demonstrationropteruid(demonstrationhereforer why) or whatGalencalled doctrinacom-positiva thecompositiveayofteaching).Theres a second ense f ci-ence hat s alsoproper,nd ndeed anbe saidtobe for smost roper; inceforusthenaturalway s toproceed romwhat smore nowablendcertain


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186 JOHN HERMAN RANDALL, JR.forustowhat smore nowablentheorder fnature: eethebeginningfthePhysica 184a]. When, n caseswhere ffectsnhere ntheir auses e-cordingoan essential rder fpriority,e arrive ytheopposite rder tthe auseweareseeking,hrough roximatend ogicallymmediate iddleterms; rwhenwe conclude n effectrommoregeneral auses, mittingcertainntermediateauses,weacquireknowledgey demonstrationuia(demonstrationhat)orwhats called doctrina esolutiva theresolutiveway of teaching).1

Pietro is heremaking his central distinction etweentwokindsofscienceand demonstrationntermsofthetheory f sciencedevel-oped in the PosteriorAnalytics. Science is defined s a demonstra-tiveknowledgeofthingsthrough heircauses; its instruments thedemonstrative yllogism,which establishes the relations betweencauses and theireffects.2The problemof forming uch syllogismsis theproblemofdiscovering auses and defining hem n such a waythattheycan serve as the middleterms ofdemonstrations.3Pietrois thus distinguishing etweentwo kinds of proof: that of effectsthrough auses, and thatofcauses through ffects.The transformation f thedemonstrative roof of causes into amethodof discovery s precisely the achievementof the Paduantheoryof science. That change of context s already suggested, nthe above passage, in Pietro's identification f the two kinds ofdemonstrationwith the various ways of teaching.or doctrina. and

1 Op. cit., Diff.3, Prop. 1; (ed. Venice 1496). The twoformsof demonstra-tion quia heredistinguished efer o An. Post. I, c. 13,whereAristotle s contrast-ing scientificnowledge f thewhereforeT' lOtTl) withscientificnowledge f thethat To o'tL). The first orm s illustrated y theproof,What does not twinkle snear,the planets do not twinkle, heyare therefore ear. This syllogismprovesnot the wherefore' ut only thethat'; sincetheyare not near because theydo nottwinkle, ut because theyare near theydo not twinkle. (An. Post. 78a.) Thecorresponding emonstrationropter quid, following he causal order rather thanour naturalway of discoveringhecause, makes thecause, nearness, themiddleterm:theplanets are near,hencetheydo nottwinkle. The otherformof demon-strationquia is the one where the middle term s more general than major orminor, nd does not exhibitthe proximatecause. Aristotle's llustration s, Whatcan breathe s an animal,no wall is an animal,therefore o wall can breathe.2An. Post. 71b.

3 In all our inquirieswe are askingwhether here s a middleterm or whatthe middleterm s: for themiddle s precisely hecause, and it is thecause we areseeking n all our inquiries. Thus, does the moon sufferclipse means, s thereoris therenot a cause producing clipse of themoon and whenwe have learntthatthere s, our nextquestion s,what then s thiscause? (An. Post. 90a)


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SCIENTIFIC METHOD IN THE SCHOOL OF PADUA 187oforder ordependence. These terms re drawnfromother sourcesthan Aristotle, and they bring with them an interest that ismethodological as well as purely logical. Pietro treats them atlength n Difference8. The Tegni (Techne) or art of medicine ofGalen commenceswith a prologue in which threedoctrinae or waysof teaching medical science are distinguished: by resolution, bycomposition, nd by definition.

In alltheways f eachingdoctrinae)which ollow definiterder herearethree rders fprocedure. One of thems thatwhich ollowshewayof conversionnd resolutiondissolutio) in it yousetup in yourmindthe hingtwhich ouareaiming,ndofwhich ouareseeking scientificknowledge,s theend tobe satisfied.Thenyouexaminewhat ies nearestto t, nd nearest othatwithout hich hething annot xist;norareyoufinishedill youarrive t the principlewhich atisfiest. . . . The secondfollows hewayofcomtposition,nd is thecontraryf thefirst ay. In ityoubeginwith he hingtwhich ouhave rrived ythewayofresolution,and then eturn o thevery hings esolved,ndputthem ogethergain(compone as) in their roper rder, ntilyouarrive t the ast of them.And thethird ollowshewayofanalysinghedefinition.4The first wo doctrinaehad been identified y theArabic commen-tator on Galen, Hali ('Ali ben 'Abbas, *994), with the two Aris-toteliankindsofdemonstration,hatwhichproceedsfromeffects ocauses, demonstrationquia (6rt), and that which proceeds fromcauses to effects, emonstrationpropter quid (6t6rt.' This divi-sion, however,was naturallyconfusedwiththethreefold istinctionmade by Averroes in the Prohemium to his commentary n Aris-totle's Phusica. into demonstrationimvliciter. r ofcause and beina.

4 GalieniprincipismedicorumMicrotegni umcommento ali, translatedfromtheArabic by ConstantinusAfricanus; no date or place of printing, ut prior to1479; Texts I, II, III, IV.5 Ibidem,Hali's commentn Text III: Demonstrationsre carriedout in thesetwo doctrinae;but demonstrationuare is effected y composition,nd demonstra-tion quia by resolution dissolutio). Cf. Conciliator,Diff. 8, Introd.: As Halisays,the compositiveway is effectedy demonstrationropterquid, the resolutiveby demonstrationuia; onlythesetwo kindsof demonstrationre to be assumed.The Aristotelian ourceof the distinctions givenas An. Post. II, 1 (89b); Pietroexplains it: It is written n the beginningof the second book of the PosteriorAnalytics: that the kinds of questionwe ask are as many as the kinds of thingwhich we know. For we knowonlywhat we have already asked about. And thekindsof questionwe ask are four: two simple,whether thing s, and what it is;and two composite, amely, hat (quia) it is, and whereforepropterquid) or why(quare) it is. (Conciliator,Diff.8, Prop. 3, ii.)


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188 JOHN HERMAN RANDALL, JR.in which as in mathematics he causes are firstboth for us and forthe order of nature; demonstration ropter quid, or of cause, inwhich, s in natural science,we startwithwhat is first n naturebutnotfirst orus; and demonstration fbeing,or of sign, n whichwe startwith effects o arrive at causes.6 The distinctionbetweenthetwoprocedures, hat from ffects o causes and that from ausesto effects, s thus Aristotelian. Averroes set the procedure ofmathematicsofffrom the a priori procedure of demonstration nphysics; fromGalen, and also fromthe rhetoricalmethod of Ciceroand Boethius,7 ame thetermsresolutiveand compositiveto desig-nate these twoprocedures.

For Pietro, this distinction fdoctrinaestillremained a distinc-tionbetween wokinds of science,of whichthefirst, r compositive,was alone science n the strictest ense; thesecondor resolutivewasscienceonlybecause of the weakness of the humanmind, whichin natural sciencehas to startwith experiencedeffects o discovertheircauses or reasons why (propter quid). There are really buttwo kinds of demonstration,or the a priorimethodofmathematicsand that of physicsare but two species of the one kind,demonstra-tionpropterquid.The physicianJacopo da Forli (*1413), whooccupied n turnthechairs of medicineand of natural philosophyat Padua, followedHali and Pietro in their distinction etweenthetwo doctrinae, om-positive and resolutive.8 He added, however, further nalysis of

6 Averroes says that thereare threekinds of demonstration:demonstrationsimpliciter,r causae et esse; demonstrationausae or propterquid; and demonstra-tionesse or significati . . Demonstration impliciter ccurs when cause and effectare equally known,whichhappens in mathematics, ut rarely occurs in naturalscience. Whence the Commentator Averroes] says in the beginning of thePhysics: 'If it happens thatwhat is knownto us is knownby nature, then thedemonstrationsn this sciencewill be of cause and being. If it happens that thethingsknownto us are not known by nature, and are not prior in being but pos-terior, hen thedemonstrationsn that sciencewill be of signs (signorum) and notdemonstrationsimpliciter. For in naturalsciencethe thingsknown to us are notthose thatare known impliciter,hat s, by nature; thecontrary btainsin mathe-matics. The things hatare known n the latter sciencesimpliciter, nd are causesprior n being, re known o us. ' (Conciliator,Diff.8, Introd.,Prop. IV.)

7 Likewise Ciceroand Boethius n theirTopics divided thepowerof definitioninto two parts: one dealingwith udgment,which s subdivided nto resolutive ndcompositive. (Conciliator,Diff.8, Introd.)8 By doctrinaHaly understands he manner,way,or path bywhich heteacherproceeds n teaching hepupil,either esolutive, ompositive r definitive. (Jacobide ForliviosuperTeqni Galeni,Padua, 1475; comm.Text I.)


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SCIENTIFIC METHOD IN THE SCHOOL OF PADUA 189the method of resolution which brings it closer to a procedure ofinvestigation.

Resolution s twofold, aturalor real, nd logical. Real resolution,houghtaken improperlyn many senses, s strictly he separationand division ofa thing nto ts component arts. Logical resolution s so called metaphori-cally. The metaphor s derived in this fashion: just as when somethingcomposite s resolved, he parts are separated fromeach other o that eachis left by itself n its simplebeing, o also when a logical resolutions made,a thingat first nderstood onfusedlys understooddistinctly, o that theparts and causes touching ts essenceare distinctly rasped. Thus if whenyou have a feveryou first rasp the conceptof fever,you understandthefever n generaland confusedly. You thenresolvehefever nto ts causes,sinceany fevercomes itherfrom heheatingofthehumoror ofthespiritsor ofthemembers; nd again theheatingof thehumor s either f the bloodor of the phlegm,etc.; until you arrive at the specific nd distinctcauseand knowledge f that fever.9This is a clear case of the method of medical diagnosis; Jacopoillustratesmostofhis distinctionswitha number fexamplesdrawnfrom medicine. The methodological sense of the traditional termsseemstohave crystallized nhis usage.'0Hugo of Siena (*1439), teacherof medicineat Padua, Ferrara,and Parma, is still more concernedwith methodology. Startingwith Galen,hedefines octrina s thesetting orth fwhat s demon-strable (manifestatiodemonstrabilis) it has twomodes,resolutionand composition, nd in a completescience ike physicsor medicineit is impossibleto use only one method; both are required,9 bid., comm.Text I.10 By theway of resolutionwe are to understanddemonstrationuia, that is,the knowledge f an effect roceeding o a knowledge f its causes; and conversely,bytheway of compositionwe are to understanddemonstrationropter quid. Thefirst s from the 'notion,' that is, from the knowledgeof the end, that is, of theeffect. This comes fromthe dissolution,' hat is, fromthe resolution f the effectinto its causes. The secondway comesfromthecomposition f what has been dis-covered, hat is, of the causes discoveredby resolution. For those thingsthat arediscoveredby resolution n demonstration uia are afterwardsput and joined to-gether n a demonstrationropterquid,untilwe arrive at the immediate ause, andconclude he effect. This exposition s approved bytheConciliator,Diff.8, and byGentilis, nd byothermoderns incethem. (Ibid., comm.Text I.)11 As all demonstrations either hrough cause or through n effect, octrina,which s the settingforthof what is demonstrable, an be carriedon only in oneof these two modes, that is, by resolutionor by composition. (Expositio UgonisSenensis super librosTegniGalieni, Venice,1498; comm.Text I.)


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190 JOHN HERMAN RANDALL, JR.because n theknowledgef causesweuse demonstrationuia, and inthe cientificnowledgefeffects euse demonstrationropteruid. It isthecommonpinionhatboth f theseproceduresre necessary,s wellas

the explanationf many efinitions.12A properscientificmethodwillbegin withthe effects,eek the cause,and then explain the effects romwhich t startedby that cause.In thediscoveryf themiddle erm r causeweproceed rom ffectocause. . . . Such a way of acquiringknowledgewe call resolutive, ecausein thatdiscovery e proceed romn effect,hich s commonly ore om-posite, o a cause which s simpler; nd becausebythis discoveryf the

causewe certifyhe effecthroughhecause,we say thatdemonstrationpro terquid and of cause s the foundationf resolutivenowledge....But I myselfee n thediscoveryf a science f effectshroughheir ausea doubleform f procedure,nd likewise n thediscoveryf a scientificknowledgef causesthroughheir ffects.The one procedures the dis-covery f themiddle erm r cause,the other s thesetting orth f itsconsequencesr effects.And theprocess fdiscoveryn thecase ofdemon-strationhroughauses s resolutive,hile hatofsetting orth heconse-quencesscompositive.n demonstrationhroughffectst s justtheotherway round.'3Thus Hugo refuses to separate the two procedures: in any scienceand in any demonstration, iscoveryor inventio and settingforththeconsequencesornotificatiooth enter s successivephases ofthemethodto be employed. Discovery and proof are both essentialmoments n all method.This notionof a double process in scientificmethodhad al-readybeen setforth yUrban theAverroist nhis large commentaryon the Physics in 1334. FollowingAverroes,he distinguishes hreemodes of demonstration:the demonstration impliciterof mathe-matics, nwhichthe principlesdo not have to be soughtafter; dem-onstrationof sign, proceedingfrom observedeffects, y which thephysicist earns the causes ofnatural things; and a thirdkind,demonstrationshich roceed rom auseswhich, hough hey re alwaysprior ndmoreknown uoadnaturamn,re often osteriornd less knownto us. Thisoccursnnatural cience,nwhich romhose hings rior orus,whosemodes reeffects,e investigateheir auses,which re posteriorand lessknown o us. And this s the wayof themethod fresolution.

12Ibid., comm. ext .13 Ibid., comm.Text I.


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SCIENTIFIC METHOD IN THE SCHOOL OF PADUA 191But after we have investigatedthe causes, we demonstrate he effectsthrough those causes; and this is the way of the method of composi-tion. Thus physical demonstrations ollow after mathematicaldemon-strations n certainty,because they are the most certain after those inmathematics.'4

Paul of Venice (*1429) examines still more closely this doubleprocedure in physical demonstrations, defending it against thecharge of being what Aristotle called a circular proof.Scientificknowledge f the cause dependson a knowledge f the effect,just as scientific nowledgeof the effect epends on a knowledgeof thecause, since we knowthe cause through he effect eforewe knowtheeffect

throughthe cause. This is the principal rule in all investigation,hat ascientific nowledge f natural effects emands a priorknowledgeof theircauses and principles.-This is not a circle,however:-In scientific ro-cedure there re threekindsofknowledge. The first s of theeffect ithoutany reasoning, alled quia, that it is. The secondis of the cause throughknowledgeof that effect; t is likewisecalled quia. The third is of theeffect hrough he cause; it is called propterquid. But the knowledgeofwhy (propterqtid) the effects, is not theknowledge hat (quia) it is aneffect. Therefore heknowledge ftheeffect oesnotdependon itself, utupon something lse.15The Commentator ecognizes a double procedure in natural science.The first s fromwhat is less known to nature to what is moreknown tonature, nd is from ffecto cause. The second s fromwhat s moreknownto natureto what is less knownto nature,and is from ause to effect....Natural sciencebeginsbothfrom hecausesand fromwhat s caused,but indifferentenses. It begins from hecauses inclusively, that s, byknow-ing them; but fromthe thingscaused exclusively, that is, by knowing

by means of them. . . There is thus a twofoldknowledge f everycause,theonekind by theprocedurequia and theotherby theprocedurepropterquid. The secondkind depends on the first,nd the first s the cause ofthe second; and thus theprocedurequita s also thecause of the procedurepropterquid.'6During the fifteenth entury attention was increasingly focusedon this double procedure involved in scientificmethod. It came14 Urbanus Averoystaphilosophus Summus . . commentorummniumAve-

roys super librumAristotelis de physico audito expositor,Venice, 1492; comm.Text II.15Summaphilosophiaenaturalismagistri auli Veneti,Venice,1503; I, cap. ix.16 Expositio Pauli Venetisuper octo librosPhysicorumAristotelis, ated 1409;Venice,1499; I, comm.Text 2.


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192 JOHN HERMAN RANDALL, JR.to be knownby theAverroistic erm regress ; the dependenceofall strictdemonstration n theprior nvestigation nd establishmentof theappropriateprincipleswas strongly mphasized,and thede-tails of thatestablishmentwerecarefully xamined. The outstand-ing natural philosopherof the middle of the century,Cajetan ofThiene (*1465), repeats Paul's treatment.'7The fullest ccountof theseproblems s to be found n the com-mentary fAgostinoNifoon thePhysics (1506). Afterexplainingthe three kinds of demonstration n Averroes's prohemium, ndassigningto natural philosophy he two procedures, the one fromthe effect o the discoveryof the cause, the otherfromthe causediscovered to the effect, 18Nifo takes up at once the questionwhether his is a circularproof,and cites Philoponus, Themistius,and Averroesin defenseof sucha regressus.

Recentwritersrecentiores) aintainhat here re four inds fknowl-edge. Thefirst ind s oftheeffecthroughhe enses, robservation;hesecond s thediscoveryinventio) fthecausethroughheeffect,hichscalled demonstrationf sign; thethird s knowledgef the samecausethroughn examinationnegotiatio)ythe ntellect,romwhich here irstcomes uch n increased nowledgef thecausethat t is fit o serve s themiddle erm f a demonstrationimpliciter;he fourths a knowledgefthat ameeffect ropter uid,throughhatcauseknowno certainlys tobe a middle erm.Since the second knowledgeof the effectdifferswidely fromitsinitialobservation, his is no circle,but rathera regress. Nifothenasks, what is this examinationor negotiatioby the intellect?It is clearly neither a demonstrationnor a definition, or is itinduction.

This negotiatios compositionnddivision.For when hecause tselfhas been discovered,he ntellectomposesnd dividesuntil t knows hecause n theformf a middle erm. For thoughauseand middle erm ethe ame hing,hey iffern their ormratio). For it is calledthecausein as much s the effectroceeds romt,whethert be better nownhanthe effectr not. But it is a middle ermn as much s it is a definition.Fromeffecto cause s thus heprocedurefdiscoveringhecause; nego-tiatio s directedoward hecause as a middle erm nd a definition. ut17 Gaietani de Thienis,Recollecte super octo libros PhysicorumAristotelis,Venice,1496; Lib. I, Quest.v.18Augustini Niphi philosophi suessani expositio . . . de Physico auditu,Venice,1552; I, com.Text 4.


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SCIENTIFIC METHOD IN THE SCHOOL OF PADUA 193sincea definitions discoveredonly through ompositionnd division, t isthroughthem that the cause is discovered n the form of a middle term,fromwhichwe can then proceed to theeffect.'9

Nifo later added a further recognitio in which he suggestsanother view of what he calls demonstrative regress.It is customary o treat at lengththe regress in physical demonstra-tions; I say physical, because there is no regress n mathematics. Inthis difficultyhe most recent writers (iuniores) conceive threekinds ofknowledge n the demonstrative egress. The first s knowledgethat theeffect s (quia), i.e., that the proposition ignifying he effects true; andthis knowledge comes from the senses. For instance,that man has thecapacityforscienceis knownby sense. The secondkind of knowledge sof the reason why (propter quid) what is observedby sense is so. Thuswe considerthe reason whyman has the capacityfor science,and not thebrute; and we say,because he has a rationalsoul. Therefore f the effect,or ofthe proposition ignifyingheeffect,here re twokinds ofknowledge:the one, that it is true,and this is clear to sense; the other,why it is so,and this is knownto us through he discovery f the cause. Of the cause,or of the propositions ignifyinghe cause,there s but one kind ofknowl-

edge,and thisis discovery inventio),which s nothing lse than that it isthe cause, or that the propositions ignifying he cause are true. Hencethese writersconceivethat through his knowledgewhich s the discoveryofthe cause, or thatthe propositionswhich ignify hecause are true,thereis learned the reason why the effect s so, or why the conclusionwhichsignifies he effects true. Thus in the regress n physicaldemonstrationthere re threekinds of knowledge, f whichtwoare of the effectwhilethethird s the discovery f the cause. When the last is related to the effect,it is the reasonwhy the effects so; butwhen t is relatedto the cause, it isthe factthat t is the cause. And thisdiscoverys made through he effect.It is significant hatNifo cites his examples from the History ofAnimals, themost empiricalof theAristotelian writings.

From this it is clear that there s no need of any negotiatio o rendergreater our knowledgeof the cause, as we formerly eld; for the mereknowledge hat it is the cause is thereasonwhythe effects so. Yet whenI morediligently onsider he wordsofAristotle, nd the commentaries fAlexander and Themistius, f Philoponus and Simplicius, t seems to methat in the regressmade in physical demonstrationshe firstprocess, bywhich the discoveryof the cause is put into syllogisticform, s a merehypothetical coniecturalis)syllogism,incethrought thediscovery f the

'9 Ibidem.


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194 JOHN HERMAN RANDALL, JR.cause s syllogizedna merely onjectural ashion. Butthe econd rocess,bywhichs syllogizedhereasonwhy he ffects so throughhediscoveredcause,sdemonstrationropter uid-not that tmakes sknow tmpliciter,butconditionallyex conditione),rovidedhat hatreally s thecause, rprovided hatthepropositionsre truethat representt to be the cause,and that nothingelse can be the cause. . . . But you object that in thatcase thescience f nature s nota science t all. We must ay that thescience f nature s nota science impliciter,ikemathematics. et it isa science ropteruid,because hediscoveryf thecause,gained hrougha conjecturalyllogism,s the reasonwhy he effects so. . . Thatsome-thing s a causecan never e so certain,s that n effectxists;for heex-istence f an effects known o the senses. Thatit is the causeremainsconjectural,ven fthat onjecturalxistences better nownhan he ffectitselfntheorder fknowledgeropteruid. For ifthediscoveryf thecause s assumed,hereasonwhy he ffects so is alwaysknown.Hence ntheMeteors ristotlerants hathe is notsettingorthhetruecausesofnatural ffects,utonlynsofar s waspossible orhim, ndinconjecturalorhypotheticalashion.20

Here, then, at the beginning of the sixteenth century we findplainly set forth a formulation of the structure of a science ofhypothesis and demonstration, with the dependence of its firstprin-ciples upon empirical investigation. This was the one element inthe Aristotelian theory of science that had remained obscure. ThePosterior Analytics had seemed to say that while the principles andcauses in terms of which a given subject-matter might be understoodwere to be discovered through sense-experience, they were seen tobe true by vovs, y sheer intellectual vision. The scholastic theo-logians, like Thomas and Duns Scotus, had been led by their Augus-tinian Platonism to emphasize this power of intellectus to recognizethe truth of principles. It is significant that at no time do thePaduan medical Aristotelians attribute any such perceptive powerto intellect. The method bywhich principles are arrived at is ratherthe guarantee of their validity; they are dependent on thatmethod, and it is the cause of their explanatory power. Nifohas merely made explicit what is implicit in the long previousdiscussion.

Each of the major logicians of the century added his I t to therounding out of this conception. Achillini and Zimara both sharpenthe distinction between mathematics, demonstrated a priori, and ascience of nature which is demonstrated a vosteriort. even in the20 Ibid., comm.Text 4, Recognitio.


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SCIENTIFIC METHOD IN THE SCHOOL OF PADUA 195secondpart of tsprocedure, rom auses to effects, r propter quid.Zimara makes a new distinction etween order,concernedwith theteaching and exposition of the subject-matter, nd method, con-cernedwiththe discovery and demonstration f its principles andproperties. The order of exposition,Achilliniholds, should followthe order of nature. Though, as a Hellenist, SimonPorta, pupil ofPomponazzi and Achillini,brushes aside thetraditional ong discus-sions of method,he still accepts the double method of naturalscience, ollowingAlexander as the best nterpreter. Natural thingscan be consideredeither as they have been made and generated,oras they re; in the atter nvestigationwe mustproceed by dividing,from effects. He admits the regress as theprocedure to be fol-lowedin physics: first here s the way ofdiscovery, y which aloneprinciples re learned from he nvestigation fexperience; thentheway of science and judgmentby which we explain that experience.Pomponazzi' s commentary on the Physics remains unpub-lished;21 in his printedworks his treatmentof method s psycho-logical ratherthan ogical. His wholeargumentfromthenecessityof sense-images n all knowing eads himto emphasizethe intimateunionoftheparticularand theuniversal, nd thenecessitynot onlyofstartingwiththeformer utalso ofreturningoitby a reditus.Like most of the later Paduans, he followsAlexander rather thanThomas and Averroes in maintaining hat the intellectmust knowparticulars directly,n order to abstract universals fromthem.

Sincethe human oul grasps hesingular irsthroughhecogitativepower,nd then heuniversalhroughhe ntellect,ontemplatingt inthesamesingular hat s known hroughhesense-image,t trulymakes re-turn (reditumn),nd consequently conversion;incefrom hesingularknown hrough sense-imagehe same soul returnshroughhe ntellecttothe ame hing.22The two operationsof the intellecthe takes to be composition nddisjunction.BernardinusTomitanus (*1576), holder of the chair in logic atPadua foryears and teacherof Zabarella, carried thedevelopmenta step farther. He was almostwholly preoccupiedwithquestionsof method. In physicsbothdiscoveryand demonstrationproceed

21 A manuscript t Arezzo is describedby Fiorentino n his Studi e Ritratti,pp. 63-79, butnothing ouching n method s quoted.22De immortalitatenimae, ap. xii,3. cf. Apologia, , cap. 3.


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196 JOHN HERMAN RANDALL, JR.from igns,that s, fromparticulareffects;fromuniversals to par-ticulars s theway of explaining and stating what has been discov-eredin thecontraryway. He vigorouslydefendsthe regress asthemethod fnatural science; it is the combination fdemonstrationquia and propter quid. And for the first imedemonstration uiais formally dentifiedwith induction as the way of inquiry (in-quisitio). Withoutthe use of the method of induction,or of theregress, there could be no science of nature at all for thePeripatetic.Withthesame simplicity nd luciditywithwhichhe summedupthe collectivewisdomof thePaduan school on all theirotherprob-lems,Zabarella formulated he classic version of theirteaching onmethod, n the terms and with the distinctions ater so fruitfullyemployed and consciously expressed by Galileo. Out of this longand patient critique of the Aristotelian theory of science theredeveloped at last the methodthatwas to issue in freshtriumphsovernature. Logic Zabarella regards, following he Greeks,not asa science,butpurelyas an instrument.

The whole reatmentf ogic s about econdnotions; ut these re ourownwork, nd byourwill can either e or not be. Theyare thereforenot necessaryhings,utcontingent,nd hencedo not fall under cience,since cience s only fnecessaryhings.23Logic is a tool, soughtnot for its own sake but for its utility nfurtheringcience.

Logic s an instrumentalntellectualtateofmind habitus)or instru-mental iscipline,reated y philosophersromhepractice fphilosophy,which onstructsecond otionsn theconceptsfthings,ndmakes heminto nstrumentsywhich n all things he truemaybe known nd dis-tinguishedromhefalse.24In this sense it is like the other nstrumental iscipline, grammar.But logic is really twofold, one applied to things, nd already puttouse; theother eparate fromthings ; and the former s identicalwith cience tself. For thesciencesare nothingotherthan ogicalmethodsput to use. 25

For Zabarella, therefore, ogic and methodare interchangeableterms; and he criticizesthe logicians,who ought to treat method23 De Natura Logicae,L. I, G. iii.24 Ibid., I, C.xx.25 De Methodis, . I, c. i.


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SCIENTIFIC METHOD IN THE SCHOOL OF PADUA 197carefully, or eaving t rather to the physicians,who in turn neglectAristotle for their cherished Galen. Method is an intellectualinstrument roducing knowledge of the unknownfrom the known.. . .Method has the force of inference, and connects this withthat. 26 Method is therefore he same as the syllogism: the defi-nition of method does not differ rom the definition f the syllo-gism. The syllogism s, in fact, the common enus of all methodsand logical instruments.27 Since all necessary connection s causalin character, ll methodmust be eitherfromcause to effect r fromeffect o cause. There are hence only two possible methods,com-position and resolution.

For all scientificrogress rom heknown o theunknowns either romcauseto effectr from ffecto cause. The formers thedemonstrativemethod,he atter heresolutive; here s no other rocedure hich ener-atesa certain nowledgef things.For ifwe progressromomethingosomethinglse,of whichneithers the cause oftheother,here annot ebetween hem ny essential nd necessary onnection; ence no certainknowledgeanfollow romhatprogress. t is thus lear hat here an beno scientificmethod except the demonstrativend the resolutive. . . De-monstrativeethods a syllogismeneratingcience rom ropositionshatare necessary,mmediate,etter nown,nd thecausesof theconclusion.. . . Resolutivemethods a syllogismonsistingf necessaryropositions,which eadsfromhingshat reposteriorndeffectshat re better nowntothediscoveryfprior hingsndcauses.28

Zabarella makes the Averroistic distinction etween the resolu-tivemethod uitable for natural scienceand the analytic methodof mathematics. In the latter,both the principlesand the conse-quenceshave the same certainty nd are co6rdinate, o that whetherwe startwiththeone or the other s a merely echnical uestion. Innatural science,however,we must startwith effects bservedby thesenses.

Since becauseof theweakness f our mind nd powers heprinciplesfromwhich emonstrations to be madeareunknownous,and sincewecannot et outfromheunknown, e are ofnecessityorced oresort oakindofsecondaryrocedure, hich s theresolutivemethod hat eadstothediscoveryfprinciples,o thatonce hey re foundwe can demonstratethenatural ffectsromhem.Hence heresolutive ethods a subordinate

26 De Methodis, II, caps. ii, i.27 Ibid., L. III, iii.28 Ibid., III, xvii xviii.


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198 JOHN HERMAN RANDALL, JR.procedure, nd the servantof the demonstrative. . . The end of the de-monstrative ethods a perfect cience,which s knowledgef thingsthroughheircauses; but theend of theresolutivemethods discoveryrather han cience,ince y resolution e seek auses romheir ffectshatwe may fterwardsnow he ffectsrom heir auses, otthatwe mayrestin a knowledgefthe auses hemselves. . It is certain hat f n comingto anysciencewe were lreadynpossessionfa knowledgef all itsprin-ciples, esolution ould here e superfluous.29

There are two kinds of resolutive method,two ways of discovery,which differgreatly in their power.Theone s demonstrationrom ffects,hichn theperformancefitsfunctions exceedinglyfficacious;nd we employt for thediscoveryfthose hings hatare veryobscure nd hidden. The other s induction,which s a muchweaker orm fresolution,ndis employedor hediscov-eryofonlythose hingswhich re hardly nknown,ut needonlyto bemade little learer.

By induction we discover only those principles that are knownsecundum naturamr, that is, that are sensible, in that their instancesor singulars are perceived by sense. By demonstration a signo wecan discover those principles that are unknown secundum natu-ram', that is, the instances of which are not sensible, and hence canonly be inferred from their effects, ike first matter or the primemover. Zabarella is here following his teacher Tomitanus in mak-ing induction a form of the method of resolution. His distinctionbetween the two kinds of resolution in terms of the two kinds ofprinciple discovered is that between arriving at a formal and at anexplanatory principle; it is analogous to that made in the next cen-turybetween the laws ofmotion and the forces causing acceleration,between the mathematical principles of natural philosophy and theforces of inertia and gravitation-both of which Newton likewise'deduced fromphenomena.

Bythese ifferences,hen,nductions distinguishedrom emonstrationfrom ffects. or each s a resolutive ethodf going rom osteriorhingstoprinciples.Buttwokinds fprinciplerepresentedous. The onekindisknownnaturally i.e.,by ense], ndhence eedsno ogical nstrumentexceptnduction,ywhich lonesuchprinciplesanbemadeknown. Forall ourknowledgeakes ts origin rom ense,nor can we know nythingwith urminds nlesswehaveknowntfirstysense. Hence ll principles

29 Ibid., III, xviii.


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SCIENTIFIC METHOD IN THE SCHOOL OF PADUA 199of thiskind remadeknown o us by nduction,ndare thereforeot aidto be demonstratedr proved;for hose hings nly re said to be proved,strictly peaking,which re demonstratedhroughomethinglse. Butinductionoesnotprove thing hroughomethinglse; in a certainenseit reveals hat hing hroughtself.For theuniversals notdistinguishedfrom he particularn thething tself, ut onlyby reason. And since hething s better nown s a particular han s a universal,ecause t is saidtobesensible s particularnd not s universal,nductions thus processfrom he ame hing o the ame hing-fromhesame hing n that spectin which t s more bvious,o theknowingfthat ame hing n that spectin which t is more bscurend hidden. Therefore otonly re the prin-ciples fthings nown y nduction,ut also theprinciplesfscience rofknowing tself,which are said to be indemonstrable. . . The principlesofthe demonstrativeethod,hen, re discoveredy the resolutivemethod,some by induction lone,othersby demonstration signo.30

The originalityof Zabarella, and of the whole developmentofwhichhe is the culmination, s thus to set offa scientificexperi-ence from mere ordinaryobservation,the accidental or planlesscollectionof particular cases. The weakness of the logic of theSchoolmenhad lain precisely n theiracceptanceof firstprinciplesestablishedby mere commonobservation. In contrast,Zabarella,and withhim the whole new science, nsisted that experiencemustfirstbe analyzed carefully to discover the precise principle orcause of the observed effects, he universal structure nvolved inthem. Afterthis analytic way of discoveryhas been pursued,weare then n a positionto demonstratedeductivelyhow facts followfrom hisprincipleorcause: we can pursue theway of truth. Scien-tificmethod, hat is, proceeds from therigorousanalysis of a fewselected instances or illustrations to a general principle,and thengoes from hatprincipleback to the systematized nd orderedbodyof facts,to the science itself formally expressed. Zabarella callsthisthecombination fthe resolutiveand thecompositivemethods;and such were preciselythe procedureand the terms of Galileo.3'The presupposition f this method s of course thatthereexists anintelligiblestructure n the subject-matter nder examination, ofwhichthe particular cases observed by the senses are instances;Zabarella makes thisperfectly lain.30 Ibid., II, xix.

31 For a typical statement f Galileo on the oint use of the rmetodoisolutivoand the metodocompositivo, ee his Opere,Ed. Nazionale, IV, 520. For a beauti-ful illustration, ee the accountof his firstdisciple,BenedettoCastelli, in Galileo,Opere,Ed. Naz., XVII, 160ff. See also Opere,VII, 75, and VIII, 212.


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200 JOHN HERMAN RANDALL, JR.Demonstrativenductionan be carried n n a necessaryubject-matter,and in thingshathavean essential onnection ith ach other.Hence tdoes not takeall theparticularsntoaccount,inceafter ertain f them

have beenexamined urmind traightwayotices he essential onnection,and thendisregardingheremainingarticulars roceedst oncetobringtogetherhe universal. For it knows hat t is necessaryhat the samerelationshould e embodiedntherest.32No clearer statement ould be made of the procedureof the seven-teenth-centurycientists.This double method, nd particularlythe analysis of instalnces,Zabarella considersmore fully n his little workDe Regressu.

The regresss betweenause and effect hen hey re convertiblendthe ffects better nownousthan he ause. Forsincewemust lways etout fromwhat s better nown o us,we first emonstraterom heknowneffectheunknownause, nd then eturnregredimur)rom he cause soknown othe ffecto bedemonstrated,hatwe mayknow hereasonwhy tis so.33Zabarella does not bring n nature, like Aristotle;for t is a logi-cal and not a metaphysical uestionhe is considering. Both dem-onstrations re made by us and for us ourselves,notfornature. 34In our way of discoverywe are following he order of knowledge,not that of things. Like Nifo, Zabarella findsfour stages in theprocedure that is the regress. First we observe the particulareffect. Secondly, we resolve the complexfact into its componentparts and conditions. Thirdly,we examinethis supposed or hypo-theticalcause by a mental consideration to clarify t and to findits essential elements. Finally,we demonstrate he effect rom hatcause.

When hefirsttage ftheprocedureas been ompleted,hichs fromeffecto cause,beforewe return rom he atter o theeffect,heremnustintervene thirdntermediaterocess labor) bywhichwe maybe led to adistinct nowledgef that cause which o farhas been known nlycon-32 De Regressu, c. 4. Cf. Galileo: The knowledgeof a single fact acquiredthrough he discovery f its causes prepares themind to ascertain and understand

otherfacts without eed of recourse o experiments,recisely s in thepresentcase,whereby argumentation lone the Authorproves withcertainty hat the maximumrangeoccurs when the elevation s 45?. He thusdemonstrates hat has never beenobservedn experience. (Opere,Ed. Naz., VIII, 296.)33 De Regressu,c. 1.34 Ibid., . 2.


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SCIENTIFIC METHOD IN THE SCHOOL OF PADUA 201fusedly. Some men [Nifo] knowing his to be necessaryhave called it anegotiatioof the intellect. We can call it a mental examination of thecause itself, r a mental consideration. For afterwe have hit upon thatcause,we begin to consider t, so thatwe may also understandwhat it is.-Zabarella thenproceedsto a further nalysis of this mental considera-tion. -But what this mental considerationmay be, and how it is accom-plished, have seen explained by nobody. For thoughsomesay that thisintermediate egotiatio f the intellectdoes play a part,stilltheyhave notshownhow it leads us to a distinctknowledge f thecause, and what is theprecise force of this negotiatio. . . There are, I judge, two thingsthathelp us to knowthe cause distinctly. One is theknowledge hatit is,whichprepares us to discoverwhat it is. For when we formsome hypothesisaboutthe matter in re aliquid praenoscimus)we are able to searchoutanddiscoversomething lse in it; wherewe formno hypothesis t all, we shallnever discoveranything. . . Hence when we findthat cause to be sug-gested,we are in a position o seekout and discoverwhat it is. The otherhelp, withoutwhich this firstwould not suffice,s the comparisonof thecause discoveredwith theeffecthroughwhich twas discovered, ot indeedwith the full knowledge hat this is the cause and that the effect, ut justcomparing histhingwiththat. Thus it comesabout thatwe are led gradu-ally to theknowledge f the conditions f thatthing; and whenone of theconditionshas been discoveredwe are helped to the discoveryof another,until we finallyknowthis to be the cause of that effect. The regressthusconsistsnecessarilyof threeparts. The first s a demonstrationthat(quod), by whichwe are led from confusedknowledge f the effecto aconfusedknowledgeof the cause. The second is this mental considera-tion, by whichfrom confusedknowledge f the cause we acquire a dis-tinctknowledgeof it. The third is demonstrationn the strictest ense(potissinma), ywhichwe are at length ed from hecause distinctly nownto the distinctknowledge ftheeffect.35These threephases mayindeedoccursimultaneously: hey are logi-callyratherthanpsychologically istinct. The end of theregressis a distinct cience ofeffects, hich s called sciencepropter quid.The theoryof science set forth n theAnalytics is a theory ofproof,nota theory fdiscovery. Here within heschool ofPaduanAristotelians, herehas beenworkedout whatwas so sorelyneeded,a logic of investigation nd inquiry. No longerare the firstprin-ciples of natural sciencetaken as indemonstrable nd self-evident:theyhave becomehypothesesrestingupon the facts theyserve toexplain. If Zabarella did notfollowup thesuggestionof Nifo thatall natural sciencetherefore emains conjectural and hvyothetical.

35 Ibid.,c. 5.


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202 JOHN HERMAN RANDALL, JR.it was because he believed that an examinationof particular in-stances would reveal an intelligible tructurepresent n them; andthis was precisely the faith that inspired seventeenth-centuryscience.

Principia essendi are not propositionsbut things,nor are they ofnecessity nownbeforehand. But often heyare unknown;and theycan bedemonstrated posteriori, houghnota priori. For if they themselves adpriorprinciples heywould not be principles.36But these principles of existence are no mere conveniences ofknowledge; they belong to their subject-matter, and are part of theintelligible tructure f the world.Propositionsaccepted in demonstrations romeffects,f we considerthem n themselves,re no less necessary, ess per se, or less essential, hanthe propositions f strict demonstration.But if we considerour minds,theyare not so clearlyknownby us to be necessary s the propositions fstrictdemonstration.Still we recognize certainkindofnecessityn them;if not so muchas is really there, t least so muchas sufficesorthat syllo-gismto deservethename and nature ofdemonstration.37

It is not surprising that Galileo should so often sound likeZabarella. For he arrived in Padua in 1592, while the echoes ofthe great controversies over method between Zabarella on the onehand and Francesco Piccolomini and his disciple Petrella on theother, fought in the 1580's, were still resounding-controversies ofwhich a witness has recorded:The schooloflogic at Padua was divided into twosects, hosewho were

partisansofZabarella,and thosewho werepartisansofPetrella,and a mul-titudeseemedto stand on either ide. Afterthismost exalted and famouscontroversy,o useful and fruitful o all studentsof logic,bothpublishedcommentariesn the PosteriorAnalytics;than whichcommentaries,houghthey re different,nd containdivergent eaching,n thecommonudgmentof learnedmennothing an be foundmoreexquisiteor moreclear.38In these two controversies, the points at issue were relativelyminor in comparison with the bulk of agreement on method. Picco-

lomini, an older man, holder of the first chair of natural philosophysince 1564. had come to Padua from Siena, bringing a certain36 De tribuspraecognitis, . iv.37 De speciebusdemonstrationis,. x.38 A. RiGcoboni,De gymnasiopatavino,Padua, 1598; IV, e. xi.


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SCIENTIFIC METHOD IN THE SCHOOL OF PADUA 203Platonism with his Aristotelianism; but though he defends somePlatonic positions,on methodhe is as advanced as Zabarella, andas near to the ideas of the seventeenth-centurycientists. Heagrees on the central importance of resolution as theway of dis-covery. But against his demandthatmetaphysicsmust furnish hestarting-pointnd the frame of reference n all science, and thatthe scientistmust imitate the fixedstructureof nature,Zabarellamaintains the independenceand self-sufficiencyf natural science,and indeed of each particular subject-matter,making the end ofknowledge and inquiry a human thing,and directingthe sciencestowardhumangoals and aims. He defends heknowledgegivenbyinduction s perfect n its ownkind, the constitution f man beingwhat tis; it is nomere substitute orsomethinghatmightbe bettergained in a moreperfectway. And against Piccolominis Platonicconception f a natural order ofperfectionswhich sciencemustfol-low, he maintains a purely immanent onception of natural ends:theperfectfunctioning f each kind of thing n the universe is itsonly end,and each subject-matters tobe understood n termsofitsown principles. Indeed, in his criticismof Platonic notions ofteleologyZabarella wentfar along thepath theradical graduate ofPadua, Telesio, was following.Zabarella's version of theAristotelian ogic,though nterpretedand colored ntermsof each ofthe threegreattheoriesofknowledgeinherited nd reconstructed y theseventeenth-centuryhinkers,ndthoughreceiving n practicewide variationsof emphasison its sev-eral parts,remainedthe method nd ideal ofscienceforall naturalphilosophers Iuntil the fresh criticismsof Locke and Berkeley.For though the language is diverse, the whole great literatureonmethod hatfillsthe scientificwriting f the seventeenth entury sat bottom seriesoffootnotes o theOrganonof Aristotle. Indeed,the morefully he record of late medievaland Renaissance thoughtis studied, the clearer it becomes that the most daring departuresfromAristotelian sciencewere carried on withinthe Aristotelianframework, nd bymeans of a criticalreflection n theAristoteliantexts-however various the sources of theideas that fertilized hatcriticism. The father Iof modernscience, n fact,turns out to benoneotherthan theMaster of them that know.With Zabarella the Paduan school had reached its culminationand done itswork. His singlesuccessor,Cesare Cremonini *1631),went still farther n an appeal to experience. His Tractatus de


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204 JOHN HERMAN RANDALL., JR.paedia (1596) sounds like the solemnwarning of the great traditionof Aristotelian rational empiricism to the triumphantmathema-ticians.

Paedia is the power f udgingrightly bout the manner f teachingand learning, ounded n logic,with he opportunenterventionf experi-ence.... Its intrinsicfunetion s to understand,dispose, and constitutethegeneralmethod f all procedures.As Paedia is the mother nd nurse,so is method hedaughternd child. I add, with the nterventionfex-perience, ecause, hough ne be instructedy genius r by logic,unlesshe be also experiencedn thevery hing n which e s to udge,he will hereexercise o udgment. say opportune, r appropriate,ecause he amemanner f experiences not found verywhere.n mathematics,or theconfirmingfprinciplest is sufficiento employnduction asedon theobservationf what s in thematerials hencemathematicss abstracted;inthatfield hetruth f theprincipless immediatelyvident. But in thenatural ciences uch observations not so obvious way of gaining rin-ciples, or s thecollectionfprinciples y ts employmento easy. Thereis indeed equired laborious ttention,rocuredrom zealous pplicationtothings; nd evenwith t theprinciplesre arrived t notwithout eenthought.Moreover,his experiences necessary otonlyforthenaturalscientist,fhe s to arrive t firstrinciples;t is requisite or lmost verymanner fscience. For experiences likewise equirednmoralsnmuchthe samefashion,nd even n divinity,ince we do not ascendto thoseabstract auseswithout manifoldnd laborious ttentiono their ffects.39And so he counseled ever closer attentionto theway of discovery,to thecarefuland painstaking nalysis ofexperience, o themethodofresolution,withinwhichhe included as phases both nduction nddemonstration posteriort.

There was but one element acking in Zabarella's formulationof method: he did not insist that the principlesof natural sciencebe mathematical, nd indeed drew his illustrations argely fromAristotles biological subject-matter. Though he had studiedmathematics nderCatena and Barocius, and was accountedexpertin optics and in astronomy, hese studies failed to leave any funda-mental mpresson his thought. The gradual emergenceof mathe-matics ntothedominantposition t held in the seventeenth enturyis due to its cultivationby a small group of men working on theperipheryof themain intellectualmovements f the sixteenth en-turv. There is a conventionalview that this shift to mathematical

39Tractatus de paedia, c. ii; in Explanatio proemii librorumAristotelis dePhysicoauditu; Padua, 1596.


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SCIENTIFIC METHOD IN THE SCHOOL OF PADUA 205interests was powerfullyfurthered y the Renaissance revival ofPlatonism and its numbermysticism, erived from Proclus, fromthePythagoreantradition, nd from heCabala. In theGermaniesthishas somebasis in fact, nd Kepler may standas its consumma-tion. But it is difficulto find ny supportfor the view that attrib-utes the great achievementsof the Italians in mathematicsandmechanicsto the influence f Neoplatonism. On the one hand theItalian Platonists had almostno scientificnterest n mathematics,and their numbers led them t once to themazes of theology ndtheosophy. And on the other,with rare exceptions the Italianmathematicians ownthroughGalileo,when theypossessed a philo-sophical nterest t all,were notPlatonists butAristotelians n theirview of mathematics, f its relationsto physics, nd of the propermethod f naturalknowledge. What theyfound n theancientsandwhat theyworked upon themselveswas no mathematicalvision oftheworld,but effective echniquesand practical problemsof pro-cedure and discovery. What theyconstructed s new sciencesit remainedfor Descartes to interpret n the light of the traditionofAugustinianPlatonism.40

Indeed, the one contributionhe Humanists can fairlyclaim tohave made to the rise of modernsciencewas to send men to thestudyof the original ancientsources in mathematics. In reestab-lishingconnectionwiththe mathematics nd mechanicsof the Hel-lenisticAge, the appeal to the ancients ntroducedArchimedesandHero, as well as Apollonius,Pappus and Diophantus. The mathe-maticalmethodsof analysis and synthesis f Archimedes, fwhomTartaglia published the firstLatin edition in 1543, were the oneelementwhich neitherthe fourteenth-centuryckhamites nor thesixteenth-centuryaduans possessed. From them the mathema-ticianstooktheir tart, nd carriedtheday for thequantitativesideofthe Paduan discussion,to whichreferencehas been made above.With this mathematical mphasisadded to thelogical methodol-ogy of Zabarella, there stands completedthe new method forwhichmen had been so eagerly seeking. By the analysis of themathematicalrelations nvolvedin a typical effect or phenome-non we arrive at its formal structureor principle. From thatprinciplewe deducefurther onsequences,whichwe find llustratedand confirmedn experience. Science is a body of mathematical

40See E. W. Strong,Procedures and Metaphysics, Study in thePhilosophyof Mathematical-Physicalciencein the16thanzd 7thCenturies.


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206 JOHN HERMAN RANDALL, JR.demonstrations,heprinciplesof which are discovered by the reso-lutionof selected nstances n experience. This is the method alledby Euclid and Archimedes a combination of analysis andsynthesis, and by the Paduans and Galileo, resolution andcomposition. ' It is traditionaland Aristotelian n regardingthestructureof science as dialectical and deductive,and in seeing allverification nd demonstration s inclusion withina logical systemof deas. It has alteredthescheme ofthemedievalAristotelians nmakingtheprinciplesof demonstrationmathematical n character;and to the scholasticempiricismt has added the insistencethattheway of discovery s not mere observation and generalization,not

mereabstractionfrom ommon xperience, ut a careful and precisemathematical nalysis of a scientificxperience-what the medicaltraditionofPadua called resolution and whatArchimedescalledanalysis. And to that experiencedemonstrationmust return,na regress, forconfirmation,llustration,nd the guarantee of theexistence of the deduced consequences. But the returnto experi-ence is notforthesake of certainproof: forthroughout he seven-teenthcentury t is almost impossibleto findany natural scientistmaintaining hat a mere fact can prove any certaintruth.Columbia University

41 The precise formof thecombination f the metodoresolutivo nd themetodocompositivoGalileo most frequently mployedhe called the argomento ex sup-positione, ' and describedmostexplicitlyn his letterto Carcavi in 1637 (Opere,Ed. Naz., XVII, 90); it is clearly llustrated n his discussionof naturally acceler-ated motion n the Two New Sciences (Eng. tr.by Crew and De Salvio, 161). Thescientistbeginswith a hypothetical ssumption, mathematicalhypothesis hatdoes not come immediately rom the observation nd measurement f facts, butrather froman analysis of the mathematical elations nvolved in a given effect.The properties hat mustfollow are thendeductively emonstrated.Thirdly, asesor illustrations f thateffect re analysedto discoverhow far thoseproperties rereallyexemplifiedn them nd confirmedythem. The demonstration alileo callsthe compositivemethod ; the term resolutivemethod he applies both to theinitialmathematical nalysis of the problem, nd to theconfirmingnalysis of theexamples. See E. W. Strong,Procedures and Metaphysics,ch. 6; E. A. Burtt,Metaphysical oundationsofModernPhysical Science, p. 70 ff.; F. Wieser,Galileials Philosoph,pp. 51-68).

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