Vivarium - Vol Xlvi, No 2, 2008

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VIVARIUM An International and Intellectual Journal forthePhilosophy LifeoftheMiddle and Renaissance Ages Aims& Scope Vivarium is an international ofphilosophy and journaldedicatedto thehistory thehistory of ideasfromtheearlyMiddleAgesto theearly-modern period.It takesa particular intheprofane interest sideofphilosohy anditsrelationship with otherareasof thought and learning fromtheseperiods.It is widelyrecognized as an unrivalled resource forthehistory oflogic,semantics and metaphysics. It studiesof ideas,textsand publishesphilosophical analysesas wellas historical theinstitutional ofmedievaland early-modern context and learning. It thought also welcomeseditionsof texts.It publishes a issue devotedto annually special a particular themeor philosopher. Editor L.W. Nauta(Groningen) EditorialBoard L.M. deRijk(Leiden), H.A.G.Braakhuis C.H. Kneepkens (Nijmegen), (Groningen), (Madison),E.P. Bos (Leiden)and D. Perler(Berlin). W.J.Courtenay AdvisoryCommittee T. Gregory (Rome),A. Zimmermann MA). J.E.Murdoch (Cologne), (Cambridge, Instructions forAuthors Contributions to thejournalshouldbe sentas an e-mailattachment andpaper versionto Lodi Nauta,Facultyof Philosophy, of Oude University Groningen, TheNetherlands A 52, 9712 GL Groningen, Boteringestraat ([email protected]). orcanbe obtainedfromtheeditor. stylesheetis availableatwww.brill.nl/viv Contributions mustbewritten inEnglish(UK orUS), French orGerman; they mustbe grammatically andstylistically correct. must Manuscripts be clearly typewritten withnumbered Use pages,doublespacingandwidemargins throughout. notendnotes. Titleandnameoftheauthorshouldappearon a separate footnotes, titlepage in orderto facilitate Each articleshouldbe anonymous peer-review. a 10-line which should state the conclusions abstract, accompanied by principal ofthepaperand2-6keywords, forindexing bothabstract andkeywords purposes; shouldbe in English. Authorsof acceptedcontributions receiveone setofproofsforproofreading. The publisher reserves therightto chargeauthorsforcorrections madeto the otherthancorrections oferrors thatoccurred in thetypesetting orconverproofs sionprocess. Authors receive1 complimentary article copyoftheissueinwhichtheir appears are sent to the first-named (in thecaseof multi-authored contributions, copies forprivate circulation. author)as wellas a PDF fileoftheircontribution Vivarium ISSN 0042-7543, onlineISSN 1568-5349)ispublished a year 3 times (print TheNetherlands, tel+31 (0)71 5353500, 2, 2321JCLeiden, byBrill,Plantijnstraat fax+31 (0)71 5317532.

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Vivarium 46 (2008)123-154

Signification and Truth of Semantics at the Crossroads

Epistemologa Ontology in Augustine's

Early Philosophical

and

Writings*

LaurentCesalli& Nadja Germann i.Br. Seminan Freiburg Philosophisches Abstract in Augustines of truthand signification Thisarticleis abouttheconception early of the shift In the first, Augusgradual part, semantic-linguistic philosophical writings. develthatAugustine Itreveals istreated theAcademics towards tines position closely. to is suited of Stoic elements a notion of which, epistemology, by integrating ops sign In thesecoftrueknowledge function asa transmitter expressions. through linguistic s andAugustine ofsignified structure ondpart,boththeontological (sensible) things areexamined. truths ofmathematical to theapparent solution Againhis tautologies incontrast thenatural thistime,however, outtobethekeystone; notionofsignturns bothparts In their of totheconventional complementarity, expressions. sign linguistic the overcomes with and showhowAugustine skepticism intensely (partially) struggles ofsignandsignification. hisconception ofthesensible worldthrough Keywords of andproportions, numbers ofsigns, semantics, theory skepticism, theory Augustine, of truth, theory judgment Introduction the"shoreof thebeatavita can be reachedonlyby Accordingto Augustine, This idea has a numberof of philosophy".1 "harbour the passingthrough *) Wewould readers for andseveral toKlausJacobi ourgratitude liketoexpress anonymous for andtoFriederike onearlier drafts ofthispaper, andcomments critical Schmiga, suggestions are ofthetext. Ourspecial redaction withthefinal assistance hervaluable however, thanks, thetext. shetooktocorrect forthetrouble K.Meredith towards directed Ziebart, l) SeeAurelius De beata vita , I, 1 [CCSL29,65.1sq.]. Augustinus, DOI:10.1 Brill 2008 163/156853408X297679 ©Koninklijke NV, Leiden,

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implications,the most importantof which consistsin the far-reaching identification of the path to happinesswiththe acquisitionof knowledge. Furthermore, justas thismetaphor speaksofonlya singleharbourand a single shore,we mustconcludethatthereis onlya singleapplicablemethod,namely theone truth. and a singlegoalin thesearchforwisdom,namely, philosophy, However,if man can attainhappinessonlythroughfinding(and attaining) theone truth,thentheintriguing questionarisesofwhatexactlythattruthis. The presentstudyfocuseson justthisquestion.Thisfocus,however, is determinedbycertainpeculiarities from the fact that as truth, expressed resulting s metaphor, can be attainedonlythrough byAugustine knowledge. threestandardobservations of all, mustbe made:first Here,thefollowing of thingsor mattersof fact knowledgeis notableforbeingat the interface the and mental acts (of (objects), cognitive knowingsubjects)thatreferto thoseobjects.Secondly,thesementalactshavespecificcontentsthatmustbe in sentencesin orderto be communicated to othersubjects.Thisis expressed if one wishesto determinethe truthor falsity of the also required,thirdly, in thus the of truth its epistemic acquired.Consequently question knowledge involvesat leasttwospheres:on theone hand,thelindimensionnecessarily betweenlinguisticsigns, sphere,includingthe relationship guistic-semantic theirsignification and truth;and on theotherhand,theontologicalsphere, theconnectionbetweenobjects,theirontologicalconstitution and embracing are reflected in thetwofolddivisionof our article. truth.Theseperspectives While thefirstpartaddressesthequestionof therelationship betweensign, thesecondsection and truthin itslinguistic-semantic dimension, signification the side of the matter to the fore.2 brings ontological discussestheproblemofknowledge and truthfrombothofthese Augustine as is perhapswell-known. However,as we shalltryto showwith perspectives, whichtogether conourstudy,theseperspectives twocomplements represent of As is from his s stitute notion truth. evident earlyphiloAugustinecomplex thisnotionis basedin extra-mental sophicalwritings, thingsand presupposes sensoryperceptionas thestarting pointfortheprocessof cognition.Nevertruthwhichcan be knownwithcertainty and is theless,it is an intelligible furthermore communicable. The keynotionwe willelucidatein thisconnectionis Augustinesconceptof signification , whichnot onlybridgesthegap

2)Thissubdivision toourrespective in thecomposition ofthis corresponds responsibilities Thefirst ofitsmain isthework while thesecond to ofLaurent Cesalli, body paper. part belongs NadjaGermann.

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aboutthose and knowledge betweenthesemioticleveloflinguistic expressions with theintelliontic the connects also but which to refers, language things which is based of , gibleside of things.This double function signification betweensignadata and signanatudistinction s fundamental uponAugustine talia*willbe broughtto lightand studiedin greaterdetail.On thisbasiswe shall argue thatAugustine,with respectto the acquisitionof knowledge is of knowledge, as wellas to thecommunicability throughsenseperception farlessskepticalthanis usuallyassumed.3 of his In orderto developthishithertounderacknowledged peculiarity to relevant the on theearliestof concentrate writings thoughtwe will,firstly, Contraacadémicos ourdiscussion, , whichappearsto leadto a skeptical namely, of knowledge.For according dead-endwithrespectto thesheerattainability man can to thistext,theonlytruths obtain,apartfromintrospective recogni, secondly,written tion, are logical-mathematical tautologies.De dialéctica afterContraacadémicos , willreveala solutionto theproblemofhowto shortly the mostrecentof our texts, communicateknowledge.De musica , thirdly, thecertaincognitionof intelligible evenprovidesan explanationconcerning itimpartsan at leastparto extra-mental inherent truths Furthermore, reality. a further tialescapefromConttaacadémicosapparentdead-end,by offering truths. mathematical of meansfortheinterpretion PointofView 1. Froma Linguistic-Semantic withan We wouldliketo openthe"linguistic-semantic" partofourdiscussion is of central that one anachronistic however, observation; importancefor and truth.When computer betweensignification graspingthe relationship are askedwhetheror not we will soon be able to workwithmanscientists made machinescapable of developingtheirown languages,the standard answeris the following:in orderto build computerscapableof developing be understood. theirownlanguages,thenatureofhumanlanguagemustfirst of human the nature have understood will we However, languageonce only between difference the of we areableto givea scientific qualitative description 3)Thatis,onphilosophical tohave seems theskepsis Foritisclearthatevenwhere grounds. leaves the means thehopeofcertain annihilated alone, always Augustine byhuman knowledge Contra Th. see certain of dooropenforanother Führer, Augustin knowledge, type (theological) undKommentar 2 und3,Einleitung Bücher velDeAcademicis, York, Académicos (Berlin-New 1997),31sqq.

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Thissomewhatsibylline answerto and genuineknowledge.4 mereinformation dimension. a primafacietechnicalquestionhas an obviouslyanthropological thisanswerappearsas a of thehistorianof philosophy, Fromtheperspective in thefirstbook of man Aristotle to the definition allusion givenby possible : Whatdifferentiates humanbeingsfromothersocially-organized ofhisPolitics bees- andherewe mightaddandfromcomputers animalssuchas,forexample, In brief,and etymologically the is theabilityto developlanguage.5 expressed: humanbeingis a "logical"animal.However,whatmoderncomputerscientistsexpressin theirownlanguageis byno meansa newidea. historical In the followingwe will considerone concreteand confirmed mere information and this between to difference genuine attempt analyze very of rhetoric, professor knowledge.This attemptwas made by recently-retired sometimebetweenthesummerof386 and EastersEve ofthefolAugustine, oftwosources: inthevicinity ofMilan.We willmakeuseprimarily year lowing De dialecticalWe académicos and his treatise s Contra Augustineearlydialogue wishto answerthequestion:"whatelementsof a conceptionof truthcan be oflinguistic as wellas in histheory foundinAugustinescritiqueofskepticism and signification?"7 signs willbe divided thelinguistic-semantic partofourinvestigation Accordingly, s positionregarding considerAugustine intotwosections.We willfirst skeptias itisexpressed andthenshifttohissemantictheory cismin Contraacadémicos in De dialéctica . Dead-End 1.1. A Philosophical Faithfulto his mainsource,CicerosLibriacademic i, Augustinediscussesthe centralskepticalthesesoftheso-calledmiddleand newAcademy.8 According 4)See,forexample, AModern andStuart Peter , Russell, Artificial Intelligence: Approach Norwig, Intheframe ofthispaper, 2nded.(Upper Saddle River, NJ,2003),chap.1.2.8("linguistics"). factual asfollows: a simple information andknowledge between thedifference weunderstand tothelevel ofvision") intheouter world isaffecting mysense belongs perception ("something would bedistinguished while ofmere information, byan"epistemic upgrade" knowledge genuine a tree"). I seeis,forexample, ("what 5)Aristotle, Politics , I,2, 1253a7-10. 6)TheContra thefollowing editions: Aurelius willbequoted from andDedialéctica académicos Contra académicos , ed.W.M.Green 1970),3-61[=CCSL29];Aurelius (Turnhout, Augustinus, B.D. Jackson ed.J.Pinborg, transi. Dedialéctica, 1975). (Dordrecht-Boston, Augustinus, 7)ForAugustines tofaith, seeEckard and of König, conceptionphilosophy itsrelationship Denken indenFrühschriften undphilosophisches Christlicher Glaube Philosophus. Augustinus 1970),22-26and131-136. (München, Augustins 8)Fortherelationship with oftheAcademics, seeFührer, theskepticism ofAugustine Augustin

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theskeptics positioncan be summedup as follows:sincenothto Augustine, withcertainty be known can judged with by our senses,nor anything ing which to baseassent.9 on have no we our reason, adequategrounds by certainty thatis, cognitionof truth,is Thisamountsto sayingthatcertainknowledge, is nothingotherthantherefutation s intention unachievable. Now,Augustine is thatknowledge In fact,hismainthesisin Contraacadémicos ofskepticism.10 the forrejecting The reason be can therefore is possibleand truth cognized.11 s own positionis linked,on theone hand,toAugustine skeptics philosophical incomto the on the other for truth motivated hand, and, intellectually quest ofskepticism and faith,as faithseemsindeedto presupposeassent. patibility for themerequestfortruthis insufficient However,accordingto Augustine, humanhappiness,whichwillonlybe achievedonce truthhas actuallybeen found.12 debatewhich reflects thehistorical académicos Thescenario depictedin Contra suchas Archesiofthemiddleand newAcademy, tookplacebetweenmembers such as Zeno and Chrysippus.13 laus and Carneades,and Stoicphilosophers, oftheso-calledStoiccriterion Whatwasat stakein thatdebatewas thevalidity inAugustines ownwords,is as follows: oftruth. Thiscriterion,

insein aswellasKurt Contra Académicos Flasch, 31-33, (cit.n.3 above), Einfiihrung Augustin. Denken 1994),36and55sq. (Darmstadt, 9)Augustine, Contra II,5,11. académicos, 10)Notethat onthe isambiguous: themiddle andnewAcademics towards position Augustine's in their because itdiscourages human toskepticism heishostile onehand, beings legitimate theAcademics hadanesoteric, believes ontheother hand, genuine Augustine questfortruth; a veilof authentic behind infact tried tohidetheir andthat Platonic doctrine philosophy they Contra académicos, II, 10,24andIII,17,38). (seeAugustine, skepticism n) Augustine, Contra académicos, II,9,23. 12)Augustine, Contra académicos, I,9,24-25. 13)SeeAugustine's inContra onthetopic considerations ownhistorical académicos, II,4, 10-6, in opposition be known stands thattruth cannot as thethesis oftheAcademics 15.Just with hisphilosophical oftheStoics toAugustine's soisthematerialism (neoview, incompatible access to ancient Greek main One should add here that orientation. Platonic) Augustine's aneclectic himself ofCicero wasprovided andHellenistic (106-43), bythewritings philosophy ThatAugustine haddirect forbothStoicsandAcademics. sympathy philosopher showing ofhis in theobvious Stoiccharacter is evidenced ofStoicphilosophy, however, knowledge of his mention Contra and De dialéctica Cresconium, I, 19, below, 24) 9-15) ( (see having p. in Pinborg, De dialéctica readsomelibriStoicorum (cit.n. 5 above). (seetheintroduction TheStoicTradition onAugustine, seeM. Colish, ofStoicphilosophy Fortheinfluence from 2 vols,(Leiden, Middle totheEarly 1985)vol.I, 329sq.andvol.II, 142-238, Ages, Antiquity esp.181-198.

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Asfortheir that truth couldnotbeperceived, tookthisfrom the opinion they apparendy famous definition oftheStoic, couldbeperceived that wasso Zeno,whosaidthattruth on themindfrom thesource ofitsorigin, thatitcouldnotoriginate from impressed whence itdidnotoriginate. Thiscanbestated more and in the briefly plainly following canbeperceived that cannot bepresent inwhat isnottrue.14 way:truth bythose signs - in the technical That which"is impressedon the mind"is a presentation oftheStoics,a phantasia,Now,a phantasiawhichexistsin sucha vocabulary that it can ariseonlyfromtheobjectit represents and no other,is one way whichcan serveas theadequateobjectofourassent.Sucha phantasiais then - a comprehensive calleda phantasiakataleptike For thatreapresentation.15 fromtheopeninglinesofthe son,italso qualifiesas "true".As can be inferred textjust quoted,the Academicsdevelopedtheirown skepticalpositionin reactionto theStoiccriterion oftruth.Therecannotbe sucha thingas a phantasiakataleptike oursensesnorourreasonare , saytheAcademics,sinceneither able to distinguish betweena comprehensive and a non-comprehensive presentation. Augustinenow mountsa twofoldcritiqueoftheAcademics,partlydeconstructive and partlyconstructive.16 Firstof all, on thenegativeside,he purto show the of the ports inconsistency Academics critiqueoftheStoiccriterion oftruth,as formulated byZeno; second,he intendsto showin a positiveway where certainknowledge , thatis, in whichdomainofhumanunderstanding, can be attained. In hisdeconstructive criticism oftheAcademics, pointstowards Augustine a dilemmafromwhichno skepticalphilosopher mayescapewithoutdamage: eitherZenos Criterionis valid- in whichcase howeverskepticism is abandoned- or it is not,in whichcase something can be known,eventhoughit

14)Aurelius theAcademics, transi. (NewYork, 1951),76-77 J.J.O'Meara Augustinus, Against Christian text: Contra académicos Writers, [=Ancient ,II,5,11 [CCSL29,24.10-16]. 12];Latin SeealsoContra académicos 'DasKriterium derWahrheit inAugustins ,III,9,18andTherese Fuhrer, Christianae 46 (1992),257-275, „Contra Académicos"', Vigiliae esp.258-262. 15)Onthenotion ofphantasia Phantasia ,seeF.H.Sandbach, ,inProblems kataleptike Kataleptike inStoicism A.Long(London, themain sources ofthat ,ed.Alexis 9-21;for 1971), doxographical - Diogenes notion Laertius andOpinions Eminent 46 and {TheLives , VII, 54), of Philosophers - see Cicero(Académica theProfessors , II, 77-78),Sextus , VII,247-252) Empiricus (Against Alexis A.Long, andDavidN.Sedley, The Hellenistic 2 vols.(Cambridge, vol.II, 1987, Philosophers, 243-254 (section 40)). 16)Fora detailed ofthat seeFuhrer, Contra Académicos (cit.n.8 above), analysis critique Augustin and303-307. 144-158

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withthefalse.17 And we mightadd heretheclassical maysharecharacteristics that no withoutassentto positioncan be refuted againstskepticism, argument is a thetruth.As a consequence,everyargumentagainstthe Stoic criterion one. self-refuting s critiqueis forourpurposesmoreinterThe constructive partofAugustine of theskepticsappearsalreadysomewhat esting.In it,Augustinescriticism theskeptics positionbeing,in fact,partially accepted.The crucomplicated, to whatextentAugustineis readyto go cial pointis of courseto determine oftheskepticsand atwhichpointhe is compelledto alongwiththeargument s leaveit behind.The answerto thatquestionis symptomatic of Augustine it overall. could be said that this position Simplyput, position philosophical a fundamental mistrust of thesenses.In fact,in Contraacadémicos expresses withregardto thesenses:theycanappearsto be a skepticalthinker Augustine theconstructive not provideus withcertainknowledge.18 Therefore, partof hiscritiqueofskepticism mustentailtheopeningup ofan epistemic spacefor certainknowledge whichis notgroundedin senseperception. Butwherecan such knowledgebe obtained?Augustinedistinguishes two realmsin which is thesubjeccertainknowledge, whichis to saytruth,is obtainable.The first domain that one and knows with that tive,introspective i.e., lives, certainty he lives;or thatone perceivessomething(withor withoutcertainty), and thatone is perceiving knowswithcertainty The other domain is something.19 ' - propositions thatoflogicaland mathematical oftheform ornotp truths as wellas arithmetical be false,says equationssuchas '2 + 3 = 5' can impossibly Augustine.20 In summary, s criticism ofskepticism in Contraacadémicos leads Augustine to a conceptionof truthas somethingthatcannotbe knownthroughthe senses,but onlythroughreason.21 AlthougharguingagainsttheAcademics, does not take on tel oftruth;rather, he disAugustine queltheStoiccriterion so to its field of from the sensible to the intellectual places, speak, application 17)Augustine, Contra académicos, III,9,21. 18)Theepistemological a corporalibus adincorporaba isa leitmotiv ofAugustine's program philoSeeforexemple Contra académicos , III, 11, 26,aswellasAugussophical writings. Augustine, De diversis sensibus Veritas tine, Ixxxiii, ), where q. 9 (Utrum corporeis quaestionibus percipi possit theanswer tothat isclearly question negative. 19)SeeAugustine, Contra académicos, III,9, 19. 20)SeeAugustine, Contra académicos , III,11,24andIII,13,29. 21)Hereonecannot - himself ofAnselm ofCanterbury a careful reader of helpbutthink - andhisdefinition oftruth assolamente ofCanterbury, De (seeAnselm Augustine perceptibilis veritate , 11).

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realm.Thatmoveis notwithoutconsequence:forthetwotypesoftruthwhich thepurelysubjectiveand thelogical-mathematical, Augustineacknowledges, non-communiThe former is essentially pay a highpricefortheircertainty. cableand thelatteris whatwe in moderntermswouldcall emptyand tautological.22Betweendesperatelyprivateand seeminglytautologicaltruths, however,therelies an entiredomain of human activityand knowledgeto which,it would seem,truthmustremainforeign:thedomainof language. entities, appearhereto be excluded Spokenwords,thosesensibly-perceptible This seemsto be the ineluctableconsequenceof as potentialtruth-bearers. as it unfoldsin Contraacadémicos s critiqueof skepticism , a pessiAugustine misticconclusionwhichleavesthereaderofthattextwiththeunsettling questionofwhyone shouldcontinueto discuss,write,readorteach- asAugustine ofcertainknowledgeto logical-mathematiobviouslydid.23The confinement truthsleadsto thequestionof theepistemicvalueof lincal or introspective can linguisticsignsbe the vehicleof trueknowledge? guisticexpressions: in De dialécticaoffers bothan answerto of s Augustine theory signification thatquestionand an elegantsolutionto theproblem.24 22)Forthesakeofclarity, thisstudy. wefallbackon thismodern terminology throughout truths as mathemacial arises whether thequestion theterminological however, ascpect, Beyond the wemean whith towhat inContra académicos them understands today correspond Augustine ofmathinthefact that therecognition ofthischoice Weseethejustification word 'tautology'. as a isnotpresented inContra académicos ascognizable truths ematical byAugustinewayoutof itdoesnot can be attained human of truth that it is a kind subjects, by skepticism: although - justastautologies itwould remain unclear donot.Otherwise, their increase why knowledge didnotreach inContra académicos hestill onseveral occasions insists ,that anycertain Augustine académicos , II,23and30aswellasIII,5 and43). (seeContra knowledge 23)Fortheimportance to ascompared oflanguage inAugustines ofcommunication conception MediTwoModels ofOccidental andAugustine. Aristotle seeIrène Rosier-Catach, Aristotle's, 2 vols.(NewDehli, andSignification inSigns evalSemantics', , ed.H.S.Gill,andG. Manetti, vol.II,41-62, 1999-2000), esp.41-42. 24)Itisa well-known value oflinoftheepistemic onthequestion that fact position Augustine's for in he denies in In time: the De over X, 389, 34), (written e.g. magistro changed signs guistic tolanwith asa skeptic usanything andappears toteach ofwords thecapacity respect example in396),where thenotion inDedoctrina Christiana willbenuanced Thisposition (written guage. trinitate In the De for a more finds oflinguistic , II, 31, 48). (see appreciation example positive sign De trinitate word nullius inner of the the XV, 10, , 19) {verbum (mental) linguae, finally,theory - 'linguistic' here ofthe"linguistic" notion a fully dematerialized shows only meaning having sign form ofmental wasanearly of the inner word that asweacknowledgeAugustine's insofar theory d'Ockham DePlaton à Guillaume intérieur. Lediscours seeClaude onthis Panaccio, aspect, language; howfarifatall istodetermine inthepresent 19.Ourpoint however, (Paris, 1999),108-1 study, totheskeptical analternative inDe dialéctica offers andsignification ofsigns theory Augustine's inContra académicos. which headopts attitude towards sensibly-transmitted knowledge

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as a WayOut 1.2. Linguistic Signification Dialecticholdsa predominant position,forAugustine, amongstthelanguagedisciIt is nota descriptive, but rathera reflexive relatedor trivialsciences.25 to in value of reason come for the nature and of the it, pline highestorder; relatedto spokenlanguage,but it is not light.Dialecticis indeedessentially "that which a science: sounds",saysAugustinein De diaprimarilyphonetic léctica , 5, "is not the concernof dialectics".26 However,withoutthatwhich sounds,withoutthewords,therecould be no dialectics,at leastnot in the of the sensein whichthatdisciplineis presented byAugustinein his treatise samename:thedialécticais thescientiabenedisputando1 and thereis no dismeansfor putewithoutwords.Thus thatwhichsoundsis an indispensable thetwonotionsofsignum andsignificatio Therefore, everydialectical cognition. in a role treatise. are the two central elements, They respecplay Augustines fromthat tivelya materialvehicleand a relation,whichallowthetransition to thatwhichdoes notsoundand is essenwhichsounds,and is notessential, tialto dialectics. Let us beginwithsignificatio . Whatlevelsand entitiesareinvolved,accordin to the semantic famous analysisoflanguage?The following ing Augustine, passagegivesa detailedanswerto thatquestion: Nowthat which themind, nottheears, from theword andwhich isheldwithin perceives themind itself iscalled a dicibile. Whena word isspoken notforitsownsakebutforthe itiscalled sakeofsignifying a dictio. Thething itself which isneither a word else, something inthemind, northeconception ofa word whether ornotithasa word itcanbe bywhich iscalled buta resintheproper sense ofthename. these four Therefore, signified, nothing aretobekept distinct: theverbum andtheres.2* , thedicibile , thedictio 25)SeeAurelius Deordine 89-137 , ed.W.M.Green (Turnhout, 1970), [=CCSL29]; Augustinus, ibid., II, 13,38. 26)Augustine, Dedialéctica, 5 [ed.Pinborg, 88.18]. 27)SeeAugustine, Dedialéctica , 1,1. 28)Augustine, Dedialéctica, Latin text For 5 [transi. 89-91]; [ed.Pinborg, 88.5-90.9]. Jackson, a detailed onthedistinction between dictio andres, seeHansRuef, verbum, dicibile, commentary über Semiotik undSprache. "DedialéczuAugustins Augustin Sprachtheoretische Analysen Schrifi " tica M. Ancient Rist, (Bern, 1981),82-115; John Augustine. Thought Baptized (Cambridge, DieSpur desZeichens. DasZeichen undseine inder Funktion 23-40; Meier-Oeser, 1994), Stephan desMittelalters undder Neuzeit York, (Berlin-New 1997),7-13;KlausKahnPhilosophie frühen derZeichen? über ert, (Amsterdam, 1999),9-11and35-45;Ch. Entmachtung Augustin Sprache of The toAugustine, ed.NorKirwan, Philosophy Augustines Language', Cambridge Companion manKretzmann andEleonore G. Manetti, Leteorie del 2001),186-204; Stump (Cambridge, nell'antichità classica (Milano, 1987),226-229. segno

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as its in thematerial,spokenword(verbum), The mindperceivessomething from itself is different A with a verbum content. coupled significate intelligible which in dicibile thencalleda dictio.Thatwhichis perceived thedictiois the , fromthe extraand mustbe distinguished is onlyintellectually perceptible mentalobject,namelythe res. Such intellectual perceptionof an intelligible contentin or froma materialobjectsuch as a wordis nothingotherthan thatsoundspresentsthemindwithsomeWheneversomething significano. that then to be soundingthingis at thesametimea signum cognized, thing a sign: tothemindsomething indicates sensed andwhich which is itself A signis something thesignitself.29 beyond The spokenwordas signis theobjectof a twofoldperceptionwithrespeccontents:on the one hand, the soundingword itselfis the tivelydifferent content,or object of sense perception;on the otherhand, the intelligible intellectual of the is the it dicibile , transmitted perceptionof the by object . animus or mind, in Contraacadémicos discussionofskepticism presJustas theAugustinián - namely,insistenceon the possibilityof human ents a Stoic component - so too mustAugustinián dialecticsbe considthetruth beingsdiscovering thetriadsemaiof whether The eredin thelightofitsStoicsources.30 question 29)Augustine, text Dedialéctica, 5 [transi. 86.10].lheconcep[ed.Pinborg, 87];Latin Jackson, - a viewthat a standard was not seems natural asa sign tionoftheverbum position today very arerather andStoictraditions, InthePeripatetic inthephilosophy ofantiquity. {semeia) signs assigns tospeak ofwords isnotthefirst orpremises, andifAugustine (Plato, indices, symptoms, asopposed datum asa signum theword himdidaswell), before Aristotle andtheStoics (verbum), itis ontheonehand, defined inAugustine a newly naturale tosignum ,acquires placeandvalue: in doctrina Christiana De will be which of into a fully developed theorysigns integrated general value ofthe theepistemic aslinguistic theverbum hand, (II,1,1-3);ontheother signconserves On that ofthesign(indication, traditional, premise). symptom, conception pre-Augustinian 1-34andthepartofthe DieSpurdesZeichens seeMeier-Oeser, (cit.n.28 above), question, - DerLehrer De in Aurelius Schulthess Peter , written Introduction Augustinus,magistro by oflinFuhrer annot. anded.byTherese 2002),26-41.Ontheconception introd., (Paderborn, du auxthéories introduction seeC. Chiesa, before Sémiosis-signes-symboles: Augustine, guistic signs Phro onSigns', 'St.Augustine etďAvistóte dePlaton 1991),aswellasR.A.Markus, (Berne, signe la et 2.1(1957),60-83,esp.60-65,andJ.Pépin, nesis 1976), (Villanova, Augustin dialectique esp.77-86. 30)Besides andSchulthess Ruef ofMeier-Oeser thestudies (cit.n.28above) (cit.n.28above), Stoic seeB.Mates, mentioned 1953),11-26. above, (cit.n.28above) (Berkeley, Logic

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semainoumenon and tynchanon noriy ,31in whichthesecondtermis thefamous in lekton stands the ofthedistinction madebyAugustine between , background verbum (or dictio ), dicibileand reshas beendiscussedat lengthin Augustinián studies.32 However,whatseemsto havegone unnoticedin previousresearch, is the similarity betweenthe Augustiniándefinition of sign and the Stoic notionofa presentation orphantasiaPHereis one ofthemaindoxographical sourcesforthatnotion:

31)Sextus theLogicians thelektor , II, 11.Astheconcerned reveals, Empiricus, Against passage thedicibile andtheir medieval enuntiabile anddictum tothose kinds of correspondents belong entities thatassume theroleofspecific, semantic correlates oflinguistic non-material, expresonthispoint, seeL. Cesalli, Leréalisme etontologie desproposisions; propositionnel. Sémantique tions chez DunsScot Richard etJean , Gauthier Jean Paris, 2007),34-36. Burley, Brinkley Wyclif( 32)Seeforexample Meier-Oeser 12sq.),whohimself, likeRuef(cit.n.28 (cit.n.28 above, 108sq.),doesnotseeintheStoiclekton theequivalent ofthedicibile above, Colish ,while (cit., n. 13above, vol.I, 329sq.),Manetti thetranslator ofDe (cit.n.28above, 227)andJackson, dialéctica ofthecontrary, seeB.D.Jackson, 'TheTheory ofSigns inSt.Augustines ,areconvinced De doctrina Revue desEtudes 15(1969),9-49,esp.47 sq.Themain christiana' Augustiniennes theaffinity between lekta anddicibilia area) that dicibilia aremental entities arguments against whereas lekta arenot,sincetheStoics conceived ofthought asbeing are material; b)thatlekta that which issignified, while toAugustine, that which are according linguistic expressions signify resandnotdicibilia' dicibilia entail thepossibility ofbeing saidandthus must beprior to c)that actual verbal whereas lekta areconsequences ofverbal Onthat see expressions expressions. point, G.Nuchelmans, Theories Ancient andMedieval oftheProposition. Concepts oftheBearer ofTruth andFalsity to assert the of (Amsterdam-London, 1973),116sq. Farfrom wanting identity lekton anddicibile fortheclaim that thetwoentities haveremarkable , wewishtoargue characincommon: teristics bothrepresent that which isneither a linguistic d)they e) signnora thing; both are linked mental themind thedicibile they essentially with activity: perceives (Augustine); themind andcontains thelekton Asforthearguments contra adduced above (Stoics). grasps observations canbemade:1.Thedicibile isnota thought butrather that (a-c),thefollowing which wegrasp a mental act- anintelligible content which, , must through justlikethelekton beimmaterial. 2.Thatlekta aresignified canbeunderstood asthefact that aretheimmedithey atecorrelate ofspoken words as dicibilia but that does not meanthat ourlinguistic are), (just donotultimately wesay'Dioniswalking, wedefinitely intend (when expressions signify things tosaysomething about a human andnotabout a lekton oflekton indeed ). 3. Thenotion being entails anactual useoflinguistic himself notes but,asMeier-Oeser (cit.n.28above, expressions, ofinternal ormental offers ananswer 12,n.58),theStoicnotion tothat speech objection. 33)Although - Jackson thecommentators ofAugustine's De dialéctica Ruef (cit.n.32 above), Meier-Oeser Schulthess (cit.n.28above), Kahnert (cit.n.28above), (cit.n.31above), (citn. Kirwan 30above), Markus Rist(cit. (cit.n.30above), (cit.n.31above), (cit.n.31above), Pépin - stress n.30above) andColish theStoic ofAugustines (cit.n.13above) semantics, background nonehaspointed outthat definition ofsign inDedialéctica shows similarities Augustines striking

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inthepsyche, Apresentation isa happening that occurs both andthat which displaying itself what hasoccurred it.Forexample, when vision we lookuponsomething caused white, by isanaffect; ofthis affect wecansaythat inthepsyche theactofseeing andbecause through isa white that itimplies there mine].34 [italics object The similarity appearsevenmoreclearlyifwe comparetheabove-quotedpasof thedefinition sagefromAetiuswiththeother,moredetailedformulation christian#. ofsignthatAugustinegivesin De doctrina cometomind, besides the which ofitself makes someother Fora signisa thing thing that itpresents tothesenses.35 impression betweendefinientes Do we have here a mere similarity , the Augustinián orarethedefinienda ofa presentation, ofsignandtheStoicdefinition definition We wishto suggestthatthereis morethana terminologithemselves similar? of objects.The Stoic but certainly cal resemblance, nothinglikean identity as the .36So the sort of is not the same signum thing Augustinián phantasia motivahave been the to be raised as to what could has philosophical question intohis definition of signan elementof the tionforAugustineto integrate astowhat thiscouldmean thequestion . Asa consequence, with theStoicnotion ofphantasia in the literature. Schulhas not been addressed of truth s for conception philosophical Augustine between theStoicinferential thedifference forexample thess 32-38)stresses (cit.n.28 above, notion ofsign ofaninference) andtheAugustinián istheantecedent ofsign(a semeion notion the Henotes however anditssignificate. a linguistic asa relation between (p.38),that expression inDe inAugustine's definitions ispresent notion oftheinferential given sign" "epistemic-logical a type ofphantasia Christiana. Ruef andDe doctrina dialéctica 108)mentions (cit.n.28above, on while which is an 5 the , chapter impression) commenting expressible (namely phantasia logike tothedicibile andnot tosuggest a Stoiccorrespondent ofDedialéctica , buthedoessoinorder ofsign. inconnection with definition Augustine's 34)Aetius, Phantasia Sandbach, 10];greek (cit.n. 17above), Piatita, IV,12[transi. Katalēptikē vol. 4 I. von vols. ed. veterum text'Stoicorum 2,21 Armin, , 1903-1924), (Teubner, fragmenta (n.54)]. 35)Aurelius Dedoctrina Christiana ,ed.andtransi, (Oxford, 1995), byR.P.H.Green Augustinus, CCSL ed.J.Martin 1-167 57.Latintext: [= 32];ibid.II, 1,1 [CCSL32, 1962), (Turnhout, 32.5-7]. 36)Asa matter viaa spetothesenses canbepresented that a signum isa corporeal offact, thing which a corporeal isrepresented that isprecisely while a phantasia (thecorcies, thing through which the that is be the to the would element , corporeal thing phantaston signum responding between a phantasia andthatof arecausalrelations there thephantasia causes ). Furthermore, andthat a signum arenosuchrelations between there isa phantasia a phantasia which , while isnatural. andrepresentation isconventional which a signum language signifies:

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- thiselement Stoicdefinition ofphantasia ofthetwo beingthecombination momentsofreflexivity and transitivity ofsomething (sûf-ostentatio) (ostentado was to else). In short,we believethatAugustinesreasonforthisintegration - in ensuretheepistemicvalueofwords- thatis of linguistic, sensiblesigns orderto tempertheratherskepticaloutcomeof the Contraacadémicos?1 But whyand howcan thenotionofphantasiahelpto achievethisgoal? As to the firstquestion,the centralroleplayedby thephantasiain Stoic offers a plausibleanswer.It is thepivotalnotionin theexplanaepistemology tionof knowledgeand itsfoundationin senseperception.38 Aboveall, as we haveseen(p. 5 sq.), theStoiccriterion oftruthis nothingotherthana peculiar kindof presentation, theso calledcomprehensive orphantasia presentation In . kataleptike linkinghisconceptionofthesignto theStoicnotionofpresen- they to providelinguistic tation,Augustine areat displayshisintention signs - withan essentialepistemicvalue. stakein theDe dialéctica - a briefcomAs to thesecondquestion- howis thisgoal to be achieved? parisonis requiredbetweentheroleplayedbythespeciesofa signin Augustines analysisofsignification and theroleplayedbythephantasiaofa thing in theStoics analysisofsenseperception.When I seea tree,forexample,my mindis affected (orphantasia)suchthatI knowthatthere bya presentation is, in the externalworld,a materialobjectwhichhas caused mypresentation,namelythe treeI am now seeing:perceptionis a sense-basedcausal inferencethat informsme about the actual presenceof an object in the externalworld.When I understand thespokenword'arbor- thatis, when thiswordsuccessfully functions as a signforme- mymindis affected bya 4 of the word arbor such I that know that this word refers to a kindof species naturalthing,namelya plant composedof a trunk,branchesand leaves: is a sense-basedepistemicinferencethatdoes not informme signification about the presenceof anythingin the externalworld beyondthe sound "arbor"itself,39 but rathergives me access to a kind of mentalcontent ť throughwhichI know to what kind of thingsthe word arbor refers.In treesin the externalworldare the reswe speak Augustiniánterminology: 37)Seeabove, p.7 sq. 38)Seeforexample The andOpinions Laertius, ,VII,49. Diogenes Lifes ofEminent Philosophers 39)There isofcourse thecaseofmaterial vs.use),where thesounding (mention supposition word isatthesametime andsignificate ofverbum anddictio inDe (seethedifference signifier isa rather case.Thecrucial dialecticay isthat onecanusesuccessfully 5),butthis particular point thesign'arbor without there while itisimpossible normal condiaround, (under anytree being toseea tree, when there isnotree Inshort, around. isnotrepresenting. tions) signifying

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ť aboutwhenwe correctly use thesignumarbor and theyarealso thethings we see,whenwe see trees.Whereasthatwhichthesignumťarbor showsto mymindbeyonditselfis not a treein theexternalworld,but thedicibileI 4 can graspfromtheword arbor: "Now thatwhichthe mind,not theears, perceivesin the word and whichis held withinthe mind itselfis called a ' dicibile saysAugustinein De dialectical To sum up: Augustinereachesthegoal of ensuringtheepistemicvalueof ofsenseperceplinguistic signsbytakingthebasicStoicexplanation-pattern tion(self-ostentatio /ostentatio ofsomething else)and makingitworkon two different levels.Whatwe gainthrough is notinforontologically signification mationabouttheexistence ofthematerial causeofa presentation we have,but ratherknowledgeofsomeabstractor formalcriteria the bywhichto identify we are about: is the to obtain way things speaking signification intelligible fromAugusverysignificantly knowledgefroma sensibleobject.Thisdiffers tinescontinually reaffirmed thevalueofsenseperception pessimism regarding forcognitionof truth:if truthis to be knowable,thenthe contentof that thelevelofsenseperception. what Thisis precisely knowledgemusttranscend thesignumas definedin De dialéctica and De doctrina Christiana is designedto do. In termsoftheexamplegivenabove(seeinga tree/usingsuccessfully the in theexternal word'arbor)theconclusion"thereis something worldcausing I presently have"is mereinformation, theimpression whilethecontent"that is a plantcomposedout of a trunk, whichis causingmyactualimpression branchesand leaves"is genuineknowledge(see p. 3 sq. above). Thatis whytherealso can be linguistic truth-bearers, namely, propositions, is and whyargumentation possible, whydialectics,thedisciplinadisciplinaIf all of theaboveis true,thenAugustine s definition of rum,is meaningful. a as well as his of can be seen as consepositive conception signification sign in Contraacadémicos ofskepticism . At theend of this quenceofhis criticism Cicero-inspired dialogue,thecognitionoftruthis confinedto thetwosterile the twofold realmsof subjectiveintrospection and tautology, nevertheless

40)Augustin, In De dialéctica , 5 [transi. 89-91];Latintext[ed.Pinborg, 88.5-90.9]. Jackson, thedicibile canbeseenasanearly form oftheverbum nullius ofverbum cordis that sense, linguae withFreges Sinndescribed as ofthelater De trinitat alsosomesimilarities e,XVandpresents ofthesignificate), see "eine ArtdesGegebenseins desBezeichneten" (awayof"being-givenness" undphilosophische Kritik 100 G. Frege, 'ÜberSinnundBedeutung', Zeitschrift fürPhilosophie (1892),25-50, esp.26.

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natureof the linguisticsign- whichon the one hand is perceptible by the - now content themindwithan intelligible sensesand on theotherpresents a third,intermediate domainin which ofdelineating opensup thepossibility thedomainoflinguistic truthcan be cognized,namely, expressions. Results 1.3. Interim ofthegeneralskepdead-end . DespiteAugustine s rejection (1) A philosophical thediscussionof the ticalclaimthatnothingcan be knownwithcertainty, leads to a conclusionthatis itself Academics'doctrinein Contraacadémicos partially skeptical:iftruthcan be known,thennot throughthesenses.The of thisphilosophicalconclusionbecomesapparentifwe 'dead-end'character observethe examplesprovidedof the sortof truthswhichare knowable introspective, privatetruthson the one hand,and analyticalor tautological - providedone is notcontentto reducephilosophy truths on theother either to solipsismor mereformalism. as a way out of skepticism. (2) Thesignification of linguistic expressions what a does when it as a sign, functions correctly sign , Signification, linguistic as definedbyAugustinein De dialéctica , makespossiblea semanticconception of truthforlinguisticexpressions. Accordingto Augustine,a signis a - se ipsumsensuiostendit - and that that can be the senses perceivedby thing nevertheless transmits an intellectual . In knowledge aliquidanimoostendit otherwords,thesignificatio bridgesthegap betweenwhatis perceivedbythe sensesand whatis perceived Thisis achieved bythemind,i.e.,theintelligible. of the elements from the Stoic definition of by integration phantasiaintothe definition ofsign,thusproviding valuein spite linguistic signswithepistemic oftheirmaterial, sensibleside:thesignificatio makesa signum . outofa verbum scientists would makes Contemporary computer say: significatio genuine knowledgeout ofmereinformation. Thewayoutofskepticism offered (3) Theneedforontological by foundation. thesignification oflinguistic is not to set the sufficient, however, expressions semanticconceptionoftruthuponan entirely stablefoundation. Augustinián describedas knowledgeof truth,thefactthat For,in orderto be legitimately as sensible ofthethingsto signs objectsprovideus withintelligible knowledge whichtheyconventionally stillrequiresthefulfillment ofa further conrefer, the dition.That is, the ressignified in must themselves by participate signa truth.Onlywithan examination oftheontologicaltruthofsignifiable objects and theirperceivability will the linguistic-semantic of the relation aspect betweensignification and truthreceivean entirely stablefoundation.

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2. Why Thingsare SemanticallyTrue advancestheopinionthatwhatexists,is true:"for In hisSoliloquies , Augustine thatseemsto me to be truewhichis".41His reasonfindsnothingobjectionable thatis,to res,overall,ontictruth.It is in thisview,and thusascribesto reality, thistruthof realitythatfoundsthe truthof linguistic expressions, precisely as discussed referto things(res).42 sincelinguisticexpressions Furthermore, aresigns(signa)and as sucharepartof a triadic above,linguistic expressions From and the thingsignified. theirinterpreter relationbetweenthemselves, on the one between thisit followsthatone mustdistinguish sharply signs thereare hand and thingson theother.43 However,accordingto Augustine, Butifthisis thecase,one must also thingswhichareat thesametimesigns.44 and thus possessbeyondtheirontic concludethattheyhave signification one. So thereis thegeneralquestion a semantic dimensiona further, namely to in which stand the relation of truth,and themoreparticular questhings as wellas how,and tionofwhatthingsthatareat thesametimesignssignify, In short,then,it is thisconnectionbetweenthings, withwhattruth-value. willbe pursuedin thispartofthestudy. that and truth signification one quickly on reality, In occupyingoneselfwithAugustinesreflections to numa notablecharacteristic, encounters namelythecentralroleattributed on the remarks ber.In thefirstplace arehiswell-known meaningof general numberforthe existenceof the sensibleworld,as forexamplein De libero arbitrioII, 16, 42: "They[sc. the skyand the earthetc.,NG] have forms

41)Aurelius libri duo, ed.W.Hörmann 1986),3-98[=CSEL (Wien, Soliloquiorum Augustinus, Latin text [CSEL89,56.14sq.]. II,5,8 [mytranslation]; 89];ibid., 42)Cf.De dialéctica forthe reisignum"; estuniuscuiusque , 5 [ed.Pinborg, 86.7]:"Verbum in cf. addition in the truth of a the truth of of foundation reality, Augusproposition (objective) videtur utcognitori estquoditasehabet , II, 5,8 [CSEL89,55.18]:"Verum tine, Soliloquia (...)"• 43)Cf.De dialéctica animo sealiquid estquod(...) praeter , 5 [ed.Pinborg, 86.8]:"Signum vellatet" velintelligitur 86.7 which "sentitur while theresisthat ostendit", [ibid. sq.]. 44)Cf.Augustine, uelrerum "Omnis doctrina Christiana Dedoctrina , I,2,2 [CCSL32,7.1-14]: nuncresappelaui, autem sedrespersignadiscuntur. estuelsignorům, quaenonad Proprie cetera estlignum sicuti (...). adhibentur, lapispecusatquehuiusmodi aliquid significandum derebus omnis resedamsignum II, 1,1 [ibid., est";ibid., 32.1-3]: "Quoniam (...) nonautem siquid nonetiam nisiquodsunt, nequisineisadtenderet, commonens cumscriberem, praemisi Die SpurdesRichens se significant aliudpraeter (cit.n. 28 above), (...)". Cf.Meier-Oeser, 23-26and29.

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Taketheseaway,and nothingwillbe left",45 or in becausetheyhavenumbers. De musicaW, 17, 57: "Butifyoutakethese[sc.thenumbers, NG] awayfrom the earth,it will be nothing".46 Especiallyin the latterwriting,however, expressions. Augustinegoes clearlybeyondthesegeneraland also traditional Therehe develops,with respectto things,a complextheoryof signsand whichconsistsof two complementary knowledge, parts:on the partof the a model of and and on thepartofthe perception knowledge, knowingsubject of an as well as semantic ofthestrucobject knowledge ontological grounding The basisis in bothcasesthesameprinciple:number. tureofreality.47 In viewof bothof thesecharacteristics and the above-mentioned central of of this the our will be as follows. The invesstudy, procedure question part will with an examination of s of number tigation begin Augustineconception and musicon thebasisofDe ordineand De musica . Followingthis,thefocus willturn,first to hisnumerological modelofperception and knowledge, and secondto his ontologicalas wellas semanticfoundingof realityon thebasis ofnumber.Lastly, somemaincharacteristics oftheconnection betweenthings, will and truth be set out. signification 2.1. Augustine's Conception ofNumberand Music In thesecondbook of De ordine , Augustinediscussesin detailthemeaning and roleofnumberin therealmofthescientific Therehe outlines disciplines. in an idealwaythedevelopment of thesevenliberalarts,and describestheir 45)Aurelius TheProblem anded.M. Pontifex , transi, (NewYork, Augustinus, ofFreeChoice Aurelius De libero arbitrio , ed.W.M.Green 1955),123.Latintext: (Turnhout, Augustinus, II, 16,42 [CCSL29,265.25sq.]. 1970),211-321[=CCSL29];ibid., 46)Aurelius Demusica liber ed.andtransi. Martin V7, (Stockholm, 2002); Jacobsson Augustinus, text: Aurelius De musica. Bücher i undvi.Vom ibid., VI,17,57,[ibid., 113].Latin Augustinus, ästhetischen Urteil zurmetaphysischen ed.Frank Hentschel Erkenntnis, 2002),172.52. (Hamburg, Forfurther aswellasliterature cf.C. Horn, derZahlen, Revue examples Augustins Philosophie desEtudes 40 389. 389-415, (1994), Augustiniennes esp. 47)ForDemusica cf.A.Keller, Aurelius unddieMusik. zu "Demusica" Augustinus Untersuchungen imKontext seines inAugustinus, De 1993);F.Hentschel, Schrifitums (Würzburg, 'Einleitung', musica. Bücher i undvi.(cit.n.46 above), thephilosophical relevance of p.vii-xxviii. Though - mainly this text haslongbeenrecognized andthough ithasformed theobject ofseveral studies - itsimplications from anaesthetic withrespect toAugustines ofsigns and perspective theory aregenerally Hentschel s "Einleitung" where heemphacf.,forexample, signification neglected, sizestheepistemological aswellas theological ofourtext, butdoesnotdrawa implications connection toAugustine s concept ofsignification. EveninKeller s thorough this is study aspect absent.

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" functions.While he identifies the task of the Triviumas recte respective thatof the Quadrivium48 as "beatecontemplar i".49The docere' he identifies subjectofthelatteris things(res),and itsgoalconsistsin leadingone fromthe beautyofsensiblethings,throughtheirformand measure,to theunderlying number: Thence she[sc.reason, intotherealm ofthevisible heaven and,surveying NG]advanced thatnothing other andearth, sensed thanbeauty waspleasing toher,andwithin that andwithin thoseforms, andwithin thosemeasures, numbers forms, measures, beauty, [..J.50 thecoreof thetrivialarts,mathematics (number),is Justas logicrepresents thatofthequadrivial.51 Whatthisconceptionimpliesfortheroleofnumber, is thatit is to be graspedas themeansforlayingbarethefixedand universal structure of the universe,beyondthe characteristics or conventionsof the worldof appearance.Of significance forthetopicof thisstudyis theactual in theQuadrivium,namely,beauty.This a objectregarded"mathematically" as detail insofar s conceptof beautyimpliesan agreenoteworthy Augustine mentwithmathematical laws.52 Thischaracteristic nevertheless provesto be a 48)Augustine inBoethius, which wasbrought time doesnotusethisterm, De upforthefirst arithmetic theterm itself onp. 11.64]. a>I, 1,64-130[CCSL94A,11-14; 49)Augustine a threefold functional division ofthose "inwhich fields therationabile develops inparagraph characterized as"actsrelating tosomegoal", 35.lhe first, maybebest appears" asethics, notbelonging tothesciences onwhich described intends tofocus inthe Augustine theother whereas twoarethe"theoretical" cf.Augustine, De ordine, sciences, II, 12, following, Theidentification of"recte with docere" theTrivium and"beate contem35 [CCSL29,127.1-6]. with the as here becomes clear the of Quadrivium plará suggested against background paraas a fielddealing is introduced withtheimposition ofverbal 35-42.TheTrivium graphs cf.ibid.[ibid., andthetranslation ofsignifications, Thetransition tothe 127.12-15]. expression ispresented asthedesire ofratio tocontemplate thedivine arts, however, beatitudes, quadrivial cf.ibid., 129.1sq.]. II, 14,39 [ibid., 50)Augustine, Deordine Latin text , II, 15,42 [my translation]; [CCSL29,130.1-4]. 51)Noone- soAugustine - should hisconviction toa point strive fortheknowledge sharpens inthese ofthesoulintheTrivium contained i.e.theself-knowledge andtheknowledge of arts, intheQuadrivium, thisdouble Godastheorigin ofallthings without science ofdialectics and cf.Augustine, Deordine, this distincmathematics, II,18,47[CCSL29,132.2-133.6]. Notably, tionconcerning thetwoapproaches toknowledge tothetwofold task ofphilosophy, corresponds cf.ibid.[ibid., "Cuius[sc.philosophiae est,una 133.12-14]: NG]duplex disciplinae, quaestio deanima, altera dedeo.Prima utnosmet utoriginem nostram". efficit, altera, ipsosnouerimus, 52)Cf.,forthis, Aurelius unddieMusik 275sq.,whoalso Keller, (cit.n.47 above), Augustinus theconnection andnumber; forAugustine's notion ofbeauty, cf. stresses between beauty

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betweenthings, necessaryconditionforhis conceptionof the relationship as will now be and demonstrated signification truth, throughtheexampleof De musica . Music, as one of the quadrivialarts,concernsall acousticphenomena. thestatusof thisobject:It is Augustinepermitsno doubtto ariseregarding notsubjectto thelimitations and particularities ofarbitrary as is, appearances forinstance,language,butfollowsuniversally-valid laws.Withrespectto the oftheobjectofhisinvestigation, at theendofthefirst universality Augustine, that the and laws of music book, emphasizes regularities applyto motion In thisway,he givesone to understandthatthe rules (motus ) in general.53 in musicapplyto everything uncovered and corruption, subjectto generation thusto realityin general.54 Withregardto thenotionof res, thisconcepthas consequences.'Res',accordingto this,meanseverything far-reaching appropriateas objectoftheQuadrivium,thatis,all natural'entitiescreatedbythe is correct, we mayfurther conclude One, or God.55And,ifthisinterpretation thatall natural'things, be theydiscrete or continuous, or spatially temporally structure of motion.56 With respect moved,are drivenby themathematical

A. Schmitt, 'ZahlundSchönheit inAugustins De musica , vi',Würzburger Jahrbücher fiirdie NeueFolge16 (1990),221-237, hereinparticular W.Beier224-237; Altertumswissenschaft. numerosa. ZuAugustins desSchönen undWeisheit 38 waltes, , Wissenschaft Aequalitas Begriff (1975),140-157. 53)Cf.,forexample, Demusica "Cumigitur ad , I, 13,28 [ed.Hentschel, 64.27-31]: Augustine, scientia estbenemodulandi, nonpossit huius, ipsamrationem disciplinae siquidem negari omnes motus (...)". pertinere 54)Thisinterpretation is further corroborated remarks inDe ordine where his byAugustines even than the one here. that the concept appears farther-reaching developed Byemphasizing detected arevalidnotonlyforarithmetic, andmusic, butastronomy as regularities geometry, well(thefourth ofthequadrivial healsoincludes thesupra-lunar motions oftheheavenly arts), bodies. alltheother those oftheplanets arethe"most and motions, constant", "fixed", Beyond "ultimate". Nonetheless are controlled thesameforce, dimensio and they byexactly namely numerus , cf.De ordine , II, 15,42 [CCSL29,130.9-14]. 55)Cf.,inthis definition ofresinDedialéctica 86.7sq.], connection, , 5 [ed.Pinborg, Augustines toabove, referred "Resestquidquid velsentitur, velintelligitur, p.16,n.43;therelevant passage: vellatet". Iftheinterpretation hereiscorrect, the"latent" cannot beGod,as presented things in a medieval in his n. "Sciuntur 125 notes, V, 2): suggested quoted byPinborg gloss p. (Chapter sentiuntur enimcorporalia, latet [sic,NG;onemight instead] expect spiritalia, intelliguntur vero materia". ipsedeusetinformis 56)With thischaracterization, werefer tothefamous definition ofthequadrivial establisharts, local movement and local rest as the multitudo, , see, ing magnitudo respective subject-matters, forthis, Dearithmetica, Boethius, I, 1,4 [CCSL94A,10.39-1 1.43].

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to the underlying mathematical we alreadyhave seen that laws,moreover, is convinced of their and Augustine rationality reliability: Butthat oneandtwoshould notbethree, andthat twoshould notbetwice asmuch asone, noneofthedeadwasable,noneoftheliving isable,nofuture manwillbeabletobring about.57 Theselawsofmathematics, aresubjectto no change, accordingto Augustine, but remaineverstableand are intelligible.58 With thesecharacteristics, i.e. and rationality, to the however, stability theypartakeofa feature prerequisite Withrespectto thequestionpursued acquisitionofknowledgeand certainty. it is crucial to notice here, that,accordingto our author,thesemathematical laws inhereto natural'things.For thismeansthatthereis in the sensible, - can extra-mental worldan intelligible which- whenperceptible structure provideone with certainknowledge.Hence, the questionsarise,first,of whether s conceptofperception and knowledgecontainsan explaAugustine nationforhow man can extracttheselaws fromsense-data,and, second, whetherthisknowledgeconsistsofmorethana tautological, emptytruth. 2.2. Augustines ModelofPerception and Knowledge In ordernow to shiftto Augustine s modelofperception and knowledge, we mustfirstrecallhis conceptionof thosekindsof objectswhichare able to transmit As demonstrated in thefirst knowledge. partofthisstudy, Augustine is convincedthatitis possibleformanto attainknowledge. to him, According 57)Augustine, De musica text 138.58,VI,12,35 [transi. 77];Latin [ed.Hentschel, Jacobsson, 'ZahlundSchönheit' Schmitt, 62]. Cf.,in thisconnection, (cit.n. 52 above),224 sq., whodiscusses notion ofnumber andemphasizes itsbothrational anddynamic Augustine's character. 58)Forthemathematical lawsandproportions, cf.Augustine, Demusica ,1,11,19[ed.Hentschel, utquasnobis certas monstraverint 48.34sq.]:"(•••) numéros, I, 12, (. . .)";ibid., fixasque leges "Recte istos tres numerus eiquippe tribui23 [ibid., 56.123-126]: igitur quaternarius sequitur, turistaproportione collatio. eoiamassuesce valeat, Quaequantum quodiliaunitas cognoscere, in rebus ordinatis hac una effici for similar such as thevisofthe notions, (...) (...)"; potest numbers andthelexoriusaequalitatis, cf.Augustine, Demusica, 1,11,18[ibid., 46.8]:"Namque istavisnumero inest "Unde(...), nisiaequalitatis VI, 10,27 [ibid., (...)"; ibid., 124.49-54]: iure dominanti "Cur(...), nisi(...) aequalitatis ( . . .)";ibid.[ibid., 126.61-64]: lege( . . .)".With to character of the stable and self-identical cf. der number, Horn, respect Augustins Philosophie Zahlen(cit.n.46above), toDelibero 389,396sq.(referring, here, arbitrio, II,7,15- II,8,20). thisaspect, cf.alsoDe ordine, aswellas Contra II, 19,50 [CCSL29,134.24-27], Regarding académicos n.20). III,11,24,andIII,13,29(seeabove, p.7 with

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boththeobjectsofknowledgeand thesignificata oflinguistic are expressions res.59 This meansthatmotionis generally suitedto functionas an objectof In since it is a order to explainhow men can cognize knowledge, thing. as the mathematical structure of motion, and number motion, ultimately in De musicabetweendifferent typesof numbers, Augustinedifferentiates with numeri at the level of the physicalworld,and probeginning corporales iudiciales at the level of the to numeri human intellect. Thosekindsof ceeding in theprocess next to the numeri are of numbers which, , importance corporales of perception,Augustinecalls numerioccursores^ numerirecordabiles and numeri sensuales , all ofwhichbelongto thehumansoul.60 in thisconnectionarenumerioccursores Of essentialsignificance , sincethey standat theinterface of sensiblephenomenaon thepartof theextra-mental on thepartoftheperceiving worldand sensory perception subject.Augustine devotesa greatdeal of space in De musicato explaininghow thesenumbers function.As analysisof the passagein questionshows,the purposeof his is to pointout thefactthatsenseperception extensive is an active, explication mentalprocess,and thatthismentalactnecessarily containsa "quasi-rational" Thisreveals,however, thatAugustineconceivesof bothreality component.61 59)EveninDe magistro maintains hismost the , where Augustine pessimistic position regarding of for he does not the expressions deny possibility significance linguistic transmitting knowledge, ofcognition assuch, De magistro cf.,forexample, , ed.K.-D.Daur(Turnhout, 1970),157-203 "Etidmaxime tibinitor X,34sq.[CCSL29,193.153-194.171]: [=CCSL29];ibid., persuadere discere cumremipsam uerbis alienis didici, (...), nosnihil (...), pereasigna, (...). Nonenim, sedoculis meis(. . .)";cf.,inthisconnection, DieSpur¿ies Zeichens credidi, Meier-Oeser, (cit. n.28above), with tothequotation inquestion, 13-20, ibid.,17-19. regard 60)There isyetonelastspecies ofnumbers, numeri inthehierarchy between progressons, falling numeri recordabiles andnumeri sensuales. toAugustine, form thebasisforthe they According ofsonus On numeri andtheir cf.Augustine, De function, (ormotus). production progressons musica Forfurther discussion andliterature with to ,VI,3,4 [ed.Hentschel, 74.2-76.25]. regard thesixdifferent ofnumbers, cf.Keller, Aurelius unddieMusik (cit.n. 47 species Augustinus 257-262; Hentschel, above), (cit.n.47above), 'Einleitung' p.xix-xxvi. 61)Perception, toAugustine's means thebehaviour ofthesoultowards according explanation, Ifthese received stimuli. stimuli aremathematically harmoniproportionate, they correspond toitsownmathematically ruled thenumeri Inthiscase,thesoulperoccursores. numbers, cally ceives with with otherwise thesoul's "reaction" areinboth pleasure, pain.Theratio underlying casestherational lawsofmathematics, which iswhy itsactivity ischaracterized as"quasi-rational"intheabove ForAugustine's cf.especially De musica , VI,5,9 interpretation. explanation, cf.ibid.,VI, 5, 10,[ibid., sive [ed.Hentschel, 88.31-90.77]; 90.58-62]: "(...) hasactiones, faciles sivedifficiles nonearnlatere, ethoc convenientiam, inconvenientiam, propter propter totum dicitur". 'ZahlundSchönheit' est,quodsentire Cf.,inthisconnection, Schmitt, (cit. n.52above), theactive roleofthesoulinthispart ofthepercep225sq.,whoalsoemphasizes tion-process.

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and humanperception structured: (and finally: knowledge)as isomorphically the laws of mathematics at this Hence, already {numerus). by very pointwe can assumethatthisisomorphism providesthe meansby whichAugustine willexplainthecognizability ofextra-mental things. Thisinterpretation findsadditionalconfirmation in a further characteristic, in sensuales . The roleofthistypeofnumber arising connectionto thenumeri is, accordingto Augustine,to judge whetheror not a perceivedmotionis i.e. structured lawsdescribedin proportionate, accordingto themathematical thefirst bookofDe musica : ... a fifth kind[sc.ofnumbers, inthenatural exists of NG]. . .,a kindwhich judgement when wearedelighted ofrhythms oroffended when a mistake perception, bytheequality ismade inthem. ForI donotdespise that oursense would nothave beenable your opinion toperform this without somerhythms init.62 hidden having are a measurewhichthesoul Accordingto thispassage,thenumerisensuales nature. Sense meansto comparethe possessesby perception, consequently, motionof an extra-mental with this measure. Whereaspleasureis the thing effect ofan accordperceivedbythesoul betweenthenumerological structure of an extra-mental and its inborn results from dismeasure, thing rejection The natural consists in agreement. judgement, correspondingly, precisely this act of uncoveringthe relationshipbetweenthe "external"and respective 62)De musica text[ed.Hentschel, seealsoibid. ,VI,4, 5 [transi. 17];Latin 76.3-8]; Jacobsson, velabhorrendo naturali iureferre 78.14sq.]:"(.••) velannuendo senten[ibid., quasiquodam naturale illudiudicium tiam"; ibid., VI,7,18[ibid., 104.32]: "(.••) nectarnen (. . .)".Augustine alludes tothis offormulation inbookI,cf.,forexamkind (and,consequently, already concept) 10 28.18 "Natura id fieri omnibus dedit sensum 5, I, audiendi, [ibid., ple, sq.]: puto, quae quo istaiudicantur". thisbackground, reason for to these Against Augustine's initially referring numeri sensuales asnumeri iudiciales which helater reserved for intellectual (a term strictly judge- Horn,Augustins intherealm ofrational becomes clear. der ment, knowledge) Philosophie thenumeri Zahlen(cit.n.46 above), sensuales with thesensus a concept to 401,links interior in which often refers his in with the connection Augustine philosophical particularly writings, "innate" ofanimals toproduce orhoneycapacity beautifully-ordered things, e.g.,nids(birds) combs cf.De ordine cf.alsoAugustines that , II, 19,49 [CCSL29,134.6-9]; (bees), emphasize theiudicium naturale is"nonratione sednatura" , I,2,3;ed.Hentschel, {Demusica 72.37).Thus heclearly connects these "innate" numbers with therationes seminales ofDediversis quaestionibus - An Ixxxiii therational, with divine order oftheuniverse. , q. 46 (Deideis ), andconsequently identification ofthenumeri sensuales with thesensus interior ismoreover bySchmitt, suggested 'ZahlundSchönheit' underlines the"quasi rationale Akte 231,whosimilarly (cit.n.52above), intheprocess derSeele" ofperception, and233.Cf.alsoDelibero arbitrio ibid., 227-230, , II,3, 8,25-11, 4, 13,51[CCSL29,240.38-246.10].

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"internal"numbers.As thisjudgementis basedon number,it is also "quasirational"althoughthenumerisensuales themselves arestillassignedto theact ofperception and notto actualintellectual knowledge. The measurein reference to whichmenjudge "naturally", Augustineusucalls dimensio or mensura . this dimensio or mensura also necessarily ally Again this time on the side of the of To disimpliesrationality, object perception.63 cernagreement withmensura meansto uncoverthebeautyof thisobject.By however, 'beauty', Augustineunderstands nothingotherthanthe numeroto structure inherent a which obeysthe lexaequalitatisand is logical thing whichis to say,mathematical. Thusarisesmans rational, consequently strictly naturalgift,his iudiciumnaturale , the bridgebetweensensorily-perceptible thingsand intellectual knowledge.64 Theseobservations render visiblea decisivecharacteristic ofAugustine s comthatman,in orderto be able to perceiveat plextheory, namelyhisconviction all, mustpossessan "innate"or "natural"abilityfora "quasi-rational" judgement.This"quasi-rational" formstheindispensable conditionofthe judgement to differentiate fromdisproportionate motions,andhence ability proportionate to detectthenumerological structure inherent to things.65 modelof Augustines and thus an to numerological perception knowledge represents attempt provide a theory to explicate hisaforementioned conviction thatperception, it although relieson thesenses,is nevertheless a rationally-founded act. Let us pursueAugustinesepistemological modela litdefurther still.Since contains a moment of on the level of perception judgmentalready sensory perof motions,66 ception,namelya naturaljudgement'of theproportionedness 63)Forexample, De musica istosrationabiles , I, 11,18 [ed.Hentschel, 46.1-3]:"(•••) omnes id estquiad sesehabent numerorum motus, dimensionem"; ibid.,I, 11,19 [ibid., aliquam adcertum modum rationem, "(•••) illam 46.27-29]: quae(...) revocat formamque praescribit 641 Fortheconnection between number andrationality, cf.thequotations andreferences beauty, n. with 52. above, 17-19, p. 65)According tothis, hemoreover thetransistion from sensible toknowledge of places things their structure ona thoroughly rational basis.Fora similar cf.Schmitt, 'Zahlund conclusion, Schönheit' that duetoAugustine's ofnumeri 233;Schmitt (cit.n.52above), emphasizes concept iudiciales numbers which will later call numeri sensuales there is no absolute (those ), Augustine therealm ofrationality andthatofthesenses, "daja derSinnselbst schon eine gapbetween rationale insichenthält". still isprerational, itaccords toratio Komponente perception Though Tothiswemaynowaddthatalsobetween therealm ofsensory andreality (ibid.). perception there isnoabsolute virtue of their gapby isomorphy. 66)Thisexpression willhenceforth beusedinthesense ofaccordance with thelawsofmathematics'. himself sometimes falls backonthenotion ofproportio inthisconnection. Augustine

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numeri iudiciales to be functions of proveon thelevelofintellectual knowledge thepreceding naturaljudgements. aboutjudgements: Theyarejudgements ButI formypartbelieve that whenthisverse, which weputforth, issung, Deuscreator omnium itwith these andevaluate itwith some and ,we[. . .]enjoy others, judicial rhythms that wepassanother, more sentence with those more hidden onthis certain, rhythms pleawhich thesentence ofthose sure, is,sotospeak, judicial rhythms.67 or not Accordingto this,thetaskofthenumeriiudicialesis to decidewhether thenaturaljudgementpassedon a thingis adequateor not,whichis to say whetherthe observedproportionedness is ^//-proportioned.68 Althoughat thispointit stillremainsunclearwhatexactlyAugustinehas in mind,we can establishthathe linkstheperception ofthingsand naturaljudgementregardwithyeta further structure measure,one which(at ing theirmathematical leastmetaphysically) precedesnaturaljudgement. Withrespectto thesubjectofknowledge, namelythehumansoul,Augus- fromthesensorypertineis now able to explaintheprocessof knowledge ceptionof reality, throughthe "quasi-rational" agreementor disagreement withtheperceivedstructures inherentto reality, up to a rationaljudgement this structure and the natural regarding judgement.Howeverto whatextent theobjectofknowledge itself and thusreality and itsallegedly mathematical - is ontologically structure secured,remainsto be seen; as does thelocus of thatmeasureaccordingto whichthisstructure is judgedto be well-proportioned.In thisconnection,thequestionmustalso be dealtwithof whether thisstructure possessesanyfurther signification. Foundation and theSignification 2.3. TheOntological ofReality ofItsStructure The clearestreference to thatmeasurewhichunderlies ofthesecjudgements - the numeriiudiciales - occursin De musicaVI, 11, 29, where ond order 67)Augustine, Demusica text ,VI,9,23[transi. 57];Latin [ed.Hentschel, 116.15-21]; Jacobsson, "... etaliudest - 120.54]: seealsoibid., 118.48 recte ansecus utrum VI,9,24 [ibid., aestimare, istadelectent, quodfitratiocinando". 68)Obviously, thissecond order reflects thedefinition ofmusic judgement presented byAugustineinbookI ("Musica estscientia bene Demusica 6.10;my modulandi", , I,2,2;ed.Hentschel, itscharacterization as "bene"; foraninterpretation ofthemeaning ofthis emphasis), namely cf.thefollowing section. theepitet cf.alsoKeller, bene, "well-proportionedness", Regarding Aurelius unddieMusik 253;cf.,incontrast, Hentschel, (cit.n.47above), Augustinus 'Einleitung xiii Our which tends more (cit.n.47 above), p. sq. interpretation,willbepresented shortly, towards Keller s view.

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the divineorderas the last instancein reference to Augustinecharacterizes whichtheadequacyofproportions be determined: may Butwhat issuperior inwhich that thehighest, eternal unshakeable, except unchangeable, where there isnotime, because there is nochange, andfrom which the exists, equality times arecreated andsetinorder inimitation andmodified ofeternity, while thecelestial rotation returns tothesameplaceandrecalls thecelestial bodies tothesameplaceand the and months and and lustra and the other orbits ofthestars years through days obeys thelawsofequality andunity andorder?69 The principleofall thingsand theirstructures formsthesumma consequently with God.70This has far-reaching conse, which is identifiable aequalitas for our it be concluded from this that the existence First, quences topic. may of thingsand theirstructures is ontologically foundedin thesummaaequalitas7l Beyondthisit becomesevidentthatthecompositionofthesestructures is actuallya mathematical one: everything thatexistsfollowsthelegesaequalitatisetunitatis.Henceitcan,in principle, be recognized bythelikewisemathhuman ratio in its proportionality.72 While the ematically-structured 69)Augustine, Demusica text ,VI,11,29 [transi. 67];Latin [ed.Hentschel, 128.8-15]. Jacobsson, Fora detailed oftheroleofordo inDe musica cf.Keller, Aurelius unddie analysis Augustinus Musik and241-246. 227-235 (cit.n.47above), 70)Inaddition tothequotation inthetext, Demusica cf.,for ,VI,8,20[ed.Hentschel, example, certe decet credere auctorem omnis 108.15sq.]:"(•••) deum, convenientiae quem atqueconandibid.,VI, 12,36 [ibid.,140.82-88]: "D. Nihilmihiomnino estde istorum cordiae", securius. M.Undeergocredendum estanimae estetincomtribui, aequalitate quodaeternum nisiabunoaeterno etincommutabili deo?(...) Illud(...) manifestum esteum(...) mutabile, seseintus addeummovet, utverum incommutabile . Cf. also De contra (. .)". intelligat genesi ed.J.-P. ManichaeoSy 1841),col.173-220[= PL 34];ibid.,I, 16,26 [PL34, Migne(Paris, nisiubisumma etsummus etsum186.1-3]: "(•••)• Necaliuminvenies, mensura, numerus, musordoest,idestDeum(...)". 71)Thatthelexaequalitatis forms theprinciple towhich wascreated according everything by De musica 56 God,is confirmed , VI, 17, Hentschel, [ed. 168.11-170.19]: by "Quamobrem fateri abunoprincipio illiacsimilem divitiis bonitatis (...) debet quisquís peraequalem speciem eius(...) omnia facta esseatquecondita inquantumcumque sunt". sunt, quaecumque 72)Foranexplicit foundation ofthenumbers with which thesoulmeasures allitsother numeri andmotions, the numeri cf. De musica 34-36 , , VI, 12, [ed. namely spiritualesAugustine, autem memoria nonsolum carnales motus dequibus Hentschel, 134.1-140.90]: animi, "Excipit iamdiximus, sedetiam dequibus breviter dicam. (...). Aequalitatem [se.cērsupra spirituales, tametmanentem, nisialicubi notaesset; NG]illam animus, (...) nusquam profecto appeteret estanimae estet (...). Ubiergocenses? (...) Undeergocredendum tribui, quodaeternum nisiabunoaeterno etincommutabili deo?". incommutabile,

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connectionbetweenthe foregoing model of knowledgeand the now ontoin can this thequestionregarding reality waybe established, logically-founded the inherent to remains thesignification of structures things open. In thisrespect, a centralroleis playedbya notionwhichrecursfrequently s writings and whichformsa well-known sub-classof throughout Augustine In De musica the most referhissignanaturalisnamely,vestigia.70 > important of encesto thisnotionarefoundat theend ofbook one and at thebeginning of numbook six. In bothcasesAugustinevoicestheopinionthat"vestiges to objectsof perception, eitherto our sensesor immediately bers",inherent The background of or "unchangeable truth".74 lead one towardsthe"interior" thisdescription formstheprogrampursuedbyAugustinein thisbook: He ones.75If one wishesto proceedfrom"physicalnumbers"to "immaterial" with his of and model intention into connection this conception reality brings conclusionsmaybe drawn.Thosemathematical thefollowing ofknowledge, - discreteand conwhichmenareable to recognizein all motions structures - are precisely the vestigia inherentin things. tinuous,spatialand temporal Since thesevestigesconcern"physicalnumbers",theysignify corresponding "immaterial numbers".

73)Forthevestigia Christiana naturalia assigna , II, 1,2 [CCSL32, , cf.,aboveall,De doctrina alia sunt alia data. Naturalia sunt, naturalia, 32.12-33.18]: quaesineuoluntate "Signorům igitur estfumus ex se sicuti se aliud ullo faciunt, praeteraliquid cognosci atque appetitu significant animantis adhocgenus transeuntis ( . . .)".For (...). Sedetuestigium pertinet ignem. significans De signis theimpact ofthisdistinction Bacon, , e.g.I, 3, ed.K.M. cf.,forexample, Roger ordinata suntnaturalia, autem 1978),82:"Signorům (NewYork, quaedam quaedam Fredeborg ex essentia sua et non ex intentione autem Naturalia abanima adsignificandum. dicuntur, quia animae rationem recipiunt". signi 74)Cf.De musica cum(...) musica , I, 8, 28 [ed.Hentschel, (...) 64.34-39]: "Quamobrem adipsa utcommodius eadem nonne prius persequi, oportet vestigia quaedam posuerit, vestigia "Satis diu(...) investigiis ibid.,VI, 1, 1 [ibid., 66.1-11]: (...) ducamur?"; (...) penetralia a sensibus carnis sumus. numerorum (...) quibusdam (...) putavimus (...) morati gradibus amore adhaerescerent veritatis NG]".In [sc.homines, (...) incommutabilis (...) duceratione Delibero arbitrio cf.Deordine furthermore, , II,16, addition, , II,15,43 [CCSL29,130.17-21]; 163 42, [CCSL29,265.15-17]. 75)Forthispurpose, 68.1sq.]:"Quamobrem cf.De musica ,VI,2,2 [ed.Hentschel, (...), uta reference tonumbers, direct transeamus adincorporea ibid., VI,12,34 (...)"; with corporeis certam et numeris nonreperiebamus illam, 134.4-9]: [ibid., quaminsensibilibus "Aequalitatem et tarnen adumbratam sed manentem, nusquam profecto praetereuntem agnoscebamus, locorum ettemporum, alicubi noninspatiis notaesset; hocautem nisialicubi animus, appeteret seeibid., foradditional evidence etistapraetereunt"; 136.27 namillatument, VI,12,35 [ibid., VI,12,36 [ibid., 140.75-79]. sq.];ibid.,

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What does this mean forthe seekerof knowledge?He makes,as just withthehelpofhisnumeri sensuales described, , the"quasi-rational" judgement thatthethingswhichhe perceivesare proportionate. He thencontinues,by meansofthenumeri iudiciales whichleads , withtheactual,rational judgement himto therecognition thattheyarewell-proportioned, whichis tosaythatone and thesamelawis thebasisofall proportions: thelexaequalitatis. Insightinto thelexaeqtialitatis thathe haveknowledge of its necessarily implies,however, fundamental the summa or unitas J6 The inherent principle, vestiges aequalitas in thingstherefore revealthe determining principleof theirmathematical whichis at oncetheontologicalfoundation ofreality.77 structure, At thispointthequestionarisesof therelationship betweentheonticand thesemanticdimensions ofa thing.The vestigesofnumbersarticulate themto on the level of the ontic of selves,according Augustine, composition things: or sensiblenumbers,in short,thebeautyand hence theyformthe"physical" the mathematical structure of things.Theirsignification refersaccordingly their "immaterial" numbers the realmof the lex through corresponding aequalitatis to the principleon whichtheyare based, thatis the summa - i.e. itsessentialmathematThusthecomposition ofa thing aequalitasitself. - performs ical structure a taskanalogousto thesemanticfunction of a sign. In viewoftheAugustinián of it could be here conception signs, objectedthat thesameepistemological problemnow ariseson the "semanticlevel"of the which we know s reflections on language;for alreadyfromAugustine things him to be of knowlmay capable providing althoughlinguistic signsaccording In short,thecertainty edge,theyareyetsubjectto theproblemofambiguity. oftheknowledgetheyprovideis questionable.78 76)Fortherelevant inthisconnection, cf.above, n.69.Fora short quotation p.25with survey ofthepath"vonderErkenntnis zurewigen cf.Hentschel, Gleichheit", Rhythmen körperlicher leaves theontological outof who,however, (cit.n.47 above), 'Einleitung' p. xix-xxvi, aspect consideration. 77)Inthis cf.theprecisely inverse ofcoming intobeing connection, process through cosmologicalnumbers inDe musica asdescribed "īstacerte , VI,17,58 [ed.Hentschel, 172.67-174.79]: sensus ministerio numeramus omnia, numéros, (...), locales (...) nisipraecedentiquaecarnalis busintimis etinsilentio inmotu, necaccipere illospossunt nec numeris, temporalibus quisunt habere. Illositidem intervallis etmodificai Vitalis motus serviens temporum agiles praecedit domino rerum nontemporalia habens intervalla numerorum sedtemomnium, suorum, digesta etintellectuals numeri beatarum animarum poraministrante potentia, supra quamrationales dei( . . .) usqueadterrena etinferna iuratransmittunt". Theproatquesanctarum, ipsam legem cessofknowledge thus tobethenoetic reditus ofthiscosmologica! emanation. proves 78)Forfurther details inthisregard, cf.partI ofthisstudy.

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of natAn answerto thisobjectionis providedbythecentralcharacteristic relation to therealmofsignadata, thereis a determinate uralsigns':in contrast thesignsin quesbetweenthe naturalsign and itssignification^ Regarding is precisely theiressentheirsignificatum tionhere,whichareall naturalthings, the naturalsign, and- insofaras theircarrier, tia, or essentialconstitution, - is eo ipsoontologically the ontoDue to thispeculiarity, founded.80 exists coincide. logicaltruthofthethingand thesemantictruthofthe"sign-thing" describedhereapply However,itshouldbe keptin mindthattheconnections createdbyGod.81Artificiallythatis to thereality to naturalthings, exclusively , fall, producedthingssuch as song or dance in the fieldof the ars musica of data into the to this , in necessarily signa conception, category according sideis notperseor naturallylinkedto theonticwhichthesemiotic-semantic betweenthenatural ontological.Finally,ifone regardsthesign-relationship and theprincipleto whichtheyrefer, namelythesummaaequal"sign-things" itasor unitas, thisrelationprovesto be twofold:in one direction,leading awayfromunityand towardsthosethingsbroughtforthout of ontologically in theotherdirection, it throughthelexaequalitatis', pointingsemanticallywhichorderedthem, numerorum via the vis from away things, epistemically and towardstheunitywhichis theirfoundational principle thatwhichmakes In conclusion to thispartofthepresof the truth. certain knowledge possible shallnow be fromour examination ent study,a fewspecialpointsresulting highlighted. Results 2.4. Interim . As has been and truth (1) On thefunctionofnumberin therelationofthings of shownon the basis of De musica, numbercorrespondsto the structure and in forth createdreality.It is boththeformative reality, power bringing 79)Fora comparative DieSpurdes cf.Meier-Oeser, dataandsigna ofsigna naturalia, analysis whoholds, Meier-Oeser Zeichens ibid., 26,"daßdiealsnatürli23-26;against (cit.n.28above), Natur Zeichen ihrer bereits Sachenicht chesZeichen ist",one eigenen aufgrund fungierende - precisely their consideration here under the'things' that itis- atleastregarding couldobject assign. that functions nature' very 80)Fortheontological - Cf.,incontrast, therelation cf.p. 25 withn.69 above. foundation, seeabove, which is or the data and between p. 12with arbitrary contingent, thing signified signa of such as the naturalia other kinds of to n.36.Furthermore, vestigeananimal signa contrary animal iscontingent whose occurrence by),boththeoccurpassed having (upontherespective isnecessary. inquestion here ofthevestiges rence andsignification 81)Cf.ouranalysis andDeordine inDe musica oftherespective above, p. 19. passages

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strucwhichleads humanreason,by meansof its corresponding the rař/0 In of the his use of to certain truth. ture, unparalleled Pythagoknowledge whatis, seen reanand Platonicnumber-theory, Augustinethusformulates of knowlas a whole,a detailed"mathematical" theoryof theisomorphism and reality.82 edge (2) On thestatusof things.In thisconnectionit should be stressedthat Augustine,despitehis generaldepreciationof the physical,sensibleworld, leavesno doubtthatthingsarethestarting pointin theknowledge-process.83 are a means towards our actualepistemic they only Admittedly, goal,thetruth. of vestigia and areas suchfitforuse,84and Nevertheless theyarethecarriers therefore recommended to all who striveforjoy in the presenceof eternal truth.85 If theinterpretation in reference tothings. (3) On themeaningof'significare' hereis correct, all createdor "natural"thingspossesssignification. presented are "natural whose immanent mathematical structure orbeautyis They signs", The a vestigeoftheirfoundational force of this "trace" is the principle. driving lexaequalitatis connectedto the"One" byvirtueofthe , whichis inseparably of which number thesignificatum ofall conception groundsit. Consequently naturalthingsis notonlyundoubtedly butalsoone and thesame,that certain, Truth. is,theone,ontological

82)Foranevaluation ofAugustine's useofPythagorean number cf.theclosely-related theory, assessment ofHentschel, derZahlund (cit.n.47 above), 'Einleitung' p. ix:"DieBedeutung zahlhafter Strukturen fürdenPythagoreismus istbekannt, aberinkeinem anderen Werk wird derWegvonzahlhaften Strukturen dessinnlich Wahrnehmbaren bishinzurErkenntnis des Göttlichen sofolgerichtig undbiszumZielbeschritten wieinDe musica . 83)Keller arrives ata similar Aurelius unddieMusik 279: result, (cit.n.A7above), Augustinus "Erkenntnis meint vonSinnesempfindung inGanggebrachte [. . .] eineimZusammenhang derdenkenden Seele[. . .]".With tothispeculiarity, wemust that respect Besinnung emphasize in De musica does not fall back on the of Contra académicos but rather , , Augustine, skepticism continues thetendency inDedialéctica cf.section 1.2.ofthispaper. ; forthis, present 84)Augustine - thewell-known himself here ofuti ofhisfrui, cf.Demusica , speaks complement "Sedqualis tibihomo illosnuméros, VI,14,45 [ed.Hentschel, videtur, 154.40-50]: quiomneš decorpore tantum refert, (...) adsalutem (...) nonadsuperfluam quisunt corporis omnesque velperniciosam sedadnecessariam velimprobationem utitur curiositatem, ( . . .)?"; probationem "Hisetenim, in tabula ibid., VI,14,46 [ibid., sunt, 156.73-75]: quoniam temporales tamquam carebimus". fructibus, (...) beneutendo 85)Cf.,forexample, De musica ,VI,15,49 [ed.Hentschel, 160.12-15]: "(•••) quanto ergotunc inunum deum etperspicuam intenti utdictum adfaciem' veritatem, est,'facie numero, magis nullainquietudine sentiemus etgaudebimus?". quibus corpora, agimus

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/Vivarium 46 (2008)123-154 L. Cesalli, N. Germann

. Insofaras can be semantically (4) On thequestionofwhether wrong, things these are and or "natural" is about created only thingsin the things speech inaccurately, providedone quadrivialsenseoftheword , theycannotsignify deceivesmen,which does not assumea geniusmalignas,who intentionally of thingshas as a did not. Howeverthischaracteristic Augustinecertainly will be their that not always true,but also that meaning consequence, only as theyare":"quaecumquesunt,in "are,whattheyare,insofar theynecessarily sunt".86 quantumcumque 3. Conclusion s conLet us returnto our starting point,namely,thequestionofAugustine The his notion of the role and of of truth key playedby signification. ception is betweenlanguage,perceptionand reality, close connectionhe establishes in what of our in theresultsof thetwo parts reflected inquiry.Accordingly, followswe willrecallour mainresultsin orderto emphasizetheircorrespondenceand complementarity. so called,"linguistic-semantic" As we hope to haveshownin thefirst, part of our study,Augustinedefendsdifferent positionsin the Contraacadémicos restricts . The critiqueof skepticismin Contraacadémicos and De dialéctica to the to of truth to sense, namely sphereof thingsimperceptible knowledge realm oflinthe entire truths. Thus puresubjectiveand logico-mathematical trueknowledge.In De dialécguisticsignsappearsincapableof transmitting this rather shifts from ticahowever, negativepositionto a positive Augustine thegapbetweenthesensible ofsignas a linkbridging one: bothhisdefinition and his epistemicconceptionof signification and intelligible, open a new avenueforcognitionofthetruthvia linguistic expressions. Althoughlinguistic theactualoftrueknowledge, as transmitters areable to function expressions of a further the fulfillment of this ization condition, yet requires possibility areontothatthosethingsto whichtheyareconventionally referring namely, true. logically De musicaprovidesa solutionboth to thisproblemand to the seeming truthsas discussedon thebasisof Contraacadémidead-endofmathematical on musicthatAugustinedevelopsan elaboratecosmocos. It is in thistreatise structure anditsconstitutive which model ontologically groundsreality logical charthe same structure As God. in one ultimateprinciple, precisely namely, 86)De musica 170.18sq.],asquoted above, ,VI,17,56[ed.Hentschel, p.25,n.71.

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thismodelensures theprocessofhumanperception and knowledge, acterizes of reality, or moreprecisely still:of itsstructure. thecognizability However, in the"ontological" due toAugustine s peculiarnotionofres,ourinvestigation an additionalaspectto the partofthestudywentyeta littlefurther, bringing fore:As someres, namelynatural'things,accordingto him,arealso signs,we was. It turnedout thatthose raisedthe questionof whattheirsignification the structure, byvirtueoftheirinherent "sign-things" signify, numero-logical one Truth,whichis at thesametimethefoundingprincipleof reality. Morethe over,and in contrastto the semanticlevel of linguisticexpressions, of"sign-things" is essentially inherent to thoseres.Consequently signification itunambiguously refers to itssignificatum , leavingno roomfordeceptionand thusforskepticism. With respectto the relationof signification and truth,theseresultshave severalconsequences:as thestudyofAugustine s earlyphilosophical writings has shown,onlythecombinationof thesemanticwiththeontologicalview ofhisnotionoftruth:theveryexistence promisesan adequateunderstanding of humanscienceis submittedto thethreeconditionsof therebeing(1) an structure ofobjectivereality(thetruthofthings),and (2) theposintelligible of thatintelligible structure with sibility cognizingand (3) communicating satisfactory accuracy(thetruthofsigns).Whatwe havehereis a symmetrical is describedin termsof linguisticand model,withinwhichepistemology the model involvesa linguistic-semantic side and metaphysical components: an ontologicalone, theaccuracyof humanknowledgebeingfoundedon the betweenwordsas signsofthings,and thingsas signsof isomorphism existing theirontologicaltruth. s philosophicalconceptionof truthinvolvesa theory Moreover, Augustine of intentional objectsof a peculiarkind:generally speaking,mentalacts of and understanding can be directedtowardsextra-mental perceiving things. Whenthisis thecase,thecontents ofthosementalactsareintentional objects. The peculiarity of theintentional objectsinvolvedin Augustinesepistemology,however(see forexamplethe dicibilein De dialécticaand the numeri in De musicò),is thefactthattheycan eo ipsoqualifyas truein virtue iudiciales oftheontologicaltruthofthethingstowardswhichtheyaredirected.In that sense,thoseintentional objectscan be describedas "alethic".Consequently, the ontologicaltruthof thingsis the conditionof therebeinga linguisticsemantictruth.87 At thecoreof theseboth realmsof truthis the notionof 87)Fortheroleplayed inmedieval andmodern theories ofintentionality, see byAugustine D. Perler, Theorien derIntentionalität imMittelalter where the a.M.,2002),403-405, (Frankfurt

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items( verbay which,in bothfields,connectssensoryperceivable signification with contents that are either ornaturally linked res) intelligible conventionally withtheseitems. due to Finallyand as we haveseen,Augustinefocuseson thingsprimarily theirusefulness' in leadingtheseekerof truthfromthesensoryworldto its truth{resas signa).However,althoughAugustines foundational, intelligible owninterest is directedtowardsthecognitionofintelligible objects,hismodel of perception and knowledgenecessarily sense as the presupposes perception of the of For the seeker of point starting process cognition. knowledge,in orderat all to detectthestructure inherent to things, mustin a first stagefocus on extra-mental besides the semantic dimension of thisposiHence, reality. tion(theverystructure ofworldlythingsis a vestigium), Augustinesconcentrationon the metaphysical structureof thingsmay have influencedhis in theirreflections successors on theconstitution ofthingsas thingsand in an in interest the nature as a increasing physicalentity.88

author shows howFranz refers Brentano toAristotle, Thomas andAugustine asprevious Aquinas thinkers whodefended the"mental ofobjects; in-existence" fortheroleofthenotion ofintentio inAugustine's of ocular vision mental M. and see '"Quamvidendo theory language, Sirridge, intus inDeTrinitate dicimus": andSaying inLanguage andCognition XV',Medieval , Seeing Analyses ed.S.Ebbesen, andR.Friedman andL.Cesalli, and 317-330 1999), Tntentionality (Copenhagen, Influence onBurley andWyclifs Vivarium Semantics', , Truth-Making: Augustines Propositional Vol.45,No.2.(2007), 283-297. 88)Cf.for theso-called ofnature" inthe12th Thisconcept hasbeen example "discovery century. coined Lathéologie audouzième siècle ithas (Paris, 1957), byM.-D.Chenu, esp.21-30.Recently, a renewed scientific cf.A. Speer, Die entdeckte Natur. zu interest, provoked Untersuchungen einer scientia naturalis im 12. the Meanwhile, (Leiden, 1995). Jahrhundert Begründungsversuchen hasbeenraised thescientific interest inthethings asthings whether canbetraced back question inthehistory toearlier ofphilosophy, cf.N. Germann, De temporum ratione. Quaperiods drivium undGotteserkenntnis amBeispiel Abbos von undHermanns vonReichenau (LeidenFleury C. Burnett, before Translations from Arabic Boston, 2006),esp.304-309; 'Physics Physics. Early inMss.British ofTexts Nature additional GalbaE IV', 22719andCotton Library Concerning Medioevo 27(2002),53-109.

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»-IG l0 (ê)'í»v BRILL

VIVA RIUM www.brill.nl/viv

Vivarium 46(2008)155-174

Über das Verhältnis

und individueller

materieller

Gegenstände

allgemeiner und mathematischer Thomas

nach

von Aquin

AndrejKrause Universität Seminar furPhilosophie, Halle-Wittenberg Abstract ofabstraction. Thisarticle examines oneaspectofThomasAquinas'understanding It toAquinas, showsinwhichway,according universal material and individual objects material objectsarethestarting pointformathematical objects.It comestotheconmathematical clusionthatforAquinastherearenotonlyuniversal objects(circle, mathematical that Universal mathecircle, line),butalsoindividual (this line). objects matical are of universal material and mathematiindividual objects objects properties calobjectsareproperties ofindividual material One typeofabstractio objects. formae leadsfrom material to universal mathematical a secondtype individual objects objects, fromuniversal material mathematical anda thirdtype objectsto universal objects, fromindividual material to individual mathematical the objects objects.Therefore, abstractio is of concept formae ambiguous. Keywords individual material universal material individual mathematical objects, objects, objects, abstractio universal mathematical objects, formae 1teiltThomasvon In seinerSchrift: De Trinitate SuperBoetium Aquindie theoretischePhilosophiein Naturphilosophie, Mathematikund Metaphysik ein. !) DieseSchrift wirdimfolgenden mit"InDe Trin." undnachSancti Thomae de abgekürzt De inOpera Boetium Trinitate Omnia tomus L (Roma-Paris, , , EditioLeonina, Aquino, Super wobeiinKlammern dieSeitenzahl dieser Eine wird. 1992)zitiert, jeweils Ausgabe angegeben ältere kritische istSancti Thomae deAquino, librum Boethii De Trinitate , Ausgabe Expositio super ed.Bruno Decker derDatierung, derMotivation undderStruktur (Leiden, 1955).ZurFrage dieser Schrift C. Hall,TheTrinity. AnAnalysis vgl.Douglas ofSt.Thomas Expositio ofthe Aquinas' ©Koninklijke Brill 2008 DOI:10.1 163/156853407X246090 NV, Leiden,

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Die Gegenstände dieserWissenschaften sollenjeweilsdurchdreiTätigkeiten desVerstandes erfaßtwerden,durchdie abstractio universalis a particularsdie abstractio formaeund die separatio.Die thomasische Einteilungder theoretischenPhilosophieund die damitverbundene Abstraktionslehre ist ein oft behandeltesThema.2Der vorliegende Aufsatzsoll einenbesonderenAspekt dieserLehreuntersuchen, dervon derbisherigen Literatur zu Thomasnicht diskutiert wurde.Er will verdeutlichen, inwiefern die Unterscheidung von und individuellen materiellen die für die Naturallgemeinen Gegenständen, vonallgemeinen undindiviist,zu einerUnterscheidung philosophierelevant duellenmathematischen fuhren kann.Diese Fragewurdebisher Gegenständen auch nichtvon den Arbeiten, die spezielldie mathematische Abstraktion des Thomasbehandeln,erörtert.3 Der Aufsatzbestehtaus dreiTeilen.Im erstenerfolgen einigewenigetermiohnedie die späterenAusführungen nichtvernologischeVorbemerkungen, standenwerdenkönnen.Im zweitenTeil wirddie fürdie Naturphilosophie De Trinitate Schriften desThomas York-Köln, (Leiden-New 1992),38-47.Andere ofBoethius vonAquin werden wiefolgt zitiert: Sth= Summa inOpera Omnia , Editio Leonina, theologiae, tomus IV-XII(Roma, De enteetess.= De ente etessentia Omnia 1888ÍF.), , in Opera , Editio XLIII(Roma, tomus Leonina, 1976). 2)Vgl.etwaL.-B.Geiger, Abstraction et séparation S. Thomas', Revue dessciences d'après etthéologiques 31 (1947),3-40(dazukritisch: 'Washeißt J.A.Aertsen, philosophiques MetaphysikbeiThomas vonAquin?', Miscellanea Mediaevalia 22/1(1994),217-239), Armand Maurer, St.Thomas The Division andMethods VandVIofhisCommenQuestions Aquinas. oftheSciences. onthe De Trinitate L.Oeing-Hanhoff, 'Wesen und XVIII-XXX, (Toronto, 1963), tary ofBoethius Formen derAbstraktion nachThomas vonAquin,Philosophisches 71 (1963),14-37, Jahrbuch undMethode dertheoretischen nachThomas von Neumann, Siegfried Gegenstand Wissenschaften derExpositio librum Boethii De Trinitate v. a. (Münster, 97-119, 1965), Aquin aufgrund super F.Wippel, Themes in Thomas D. C, 1984),69-104, John Metaphysical Aquinas (Washington, F.VanSteenberghen, 'Lastructure delaphilosophie selon S.Thomas Revue théorique d'Aquin', deLouvain C. Lafleur, 83(1985),536-558, ettripartition 'Abstraction, philosophique séparation delaphilosophie éléments del'arrière-fond farabien etartien deThomas théorétique. Quelques Boetium De trinitate, deThéologie etPhilosophie 5,article 3',Recherches d'Aquin, Super question médiévales Walter 67(2000),248-271, beiThomas von EineEinfuhrung Patt, Metaphysik Aquin. (London, 2004),19-47. 3)Vgl.J.F.Whittaker, "The Position ofMathematics intheHierarchy ofSpeculative Science', TheThomist E. Winance, 3 (1941),467-506, 'Notesurl'abstraction selonsaint mathématique Revue deLouvain T.C.Anderson, 53(1955),482-510, Thomas', Matphilosophique 'Intelligibel terandtheObjects ofMathematics inAquinas', TheNewScholasticism 43 (1969),555-576, 'Aristotle andAquinas ontheFreedom oftheMathematician', TheThomist ders., 36 (1972), A. Maurer, 'Thomists andThomas on theFoundation ofMathematics', 231-255, Aquinas Review 47 (1993),43-61. ofMetaphysics

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zwischenallgemeinenund individuellen materielrelevante Unterscheidung Im Teil wird zu den len Gegenständen dritten warum untersucht, expliziert. mathematischen Gegenständennach Thomas sowohl allgemeineals auch individuelle Gegenstände gehörenmüssenund in welcherWeisedie im zweitenTeildesAufsatzes von allgemeinen und individargelegte Unterscheidung duellenmateriellen für die von Gegenständen Unterscheidung allgemeinen mathematischen undindividuellen Gegenständen wichtigist.In diesemZusamwird sich unter anderem daß derBegriff derabstractio herausstellen, menhang ist. formaemehrdeutig I. Terminologische Vorbemerkungen4 Thomasunterscheidet theoretische und praktische Philosophie.Die theoretischePhilosophiesoll sich andersals die praktischePhilosophieDingen sie sollsich zuwenden,die nichtdurchdieTätigkeitdes Menschenentstehen, also beispielsweise wederfurdie menschlichen noch fiirdie Handlungen durchdie künstlerischen Werke interessieren. Tätigkeiten hervorgebrachten Innerhalbder Gruppe der Dinge, die von der theoretischen Philosophie betrachtet derGruppederDinge,die nichtdurchdie werden,also innerhalb werdendreiGruppenunterschieden, die Tätigkeitdes Menschenentstehen, in derEinteilung dertheoretischen MathemaPhilosophie Naturphilosophie, tikund Metaphysik sollen.Die GliederdieserGruppenhängen entsprechen starkvon der Materieab. Thomasnenntzwarauch eine jeweilsverschieden vonderBewegung, erberücksichtigt dieseAbhängigkeit bei der Abhängigkeit der theoretischen so daß sie eigentlichen Einteilung Philosophiejedochnicht, hiervernachlässigt werdenkann.Die GliederdererstenGruppesollenvonder MateriegemäßdemSeinundgemäßdemBegriff esseetintellectum) (secundum die zweiten Glieder der dem Sein,nichtabergemäß abhängen, Gruppegemäß demBegriff, unddie Gliederderdritten GruppewedergemäßdemSeinnoch Hierbeisolleinbeliebiges x genaudanndemBegriff nach gemäßdemBegriff. von derMaterieabhängen,wennin derDefinitionvon x ausgesagt wird,daß x materiell nachvonderMaterieabhänist,undgenaudannnichtdemBegriff in gen,wennnicht der Definitionvon x ausgesagtwird,daß x materiellist, wobei letzteres nichtohne weiteresimpliziert, daß in der Definitionvon x x daß nicht materiell ist. So wird, ausgesagt folgtdaraus,daß etwa in der Definitiondes Menschennichtausgesagtwird,daß der Menschkahlköpfig 4)Vgl.zumFolgenden InDeTrin. art.(137f.). q. 5 a. 1corp.

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ist. wird,daß ernichtkahlköpfig ist,nicht,daß in dieserDefinitionausgesagt werden. In Definitionensollen geradewesentliche ausgesagt Eigenschaften Wenn also die Definitiondes Menschennicht aussagt,daß der Mensch ist.Der daß ernichtwesentlich ist,so istdamitgemeint, kahlköpfig kahlköpfig sein.Entsprechend Menschkönnteaberimmernochzufälligkahlköpfig gilt dann: Wenn die Definitionvon x nichtaussagt,daß x materiellist,so ist ist.x könntejedoch immer materiell damitgemeint,daß x nichtwesentlich die Abhängigkeit sein. Fernerscheintes angemessen, noch zufälligmateriell daß von der Materiegemäß dem Sein (secundumesse)so zu interpretieren, wenn Materie der von Sein dem daraus, etwasgenaudann gemäß abhängt, daß es existiert, GegendieseInterpretation folgt,daß auch Materieexistiert. könntesich ein Einwand erheben:Wäre es nichtmöglich,daß es etwas gibt,das nichtohne Materiesein kann, ohne daß dieses etwasvon der nichtmaterieller Materieabhängt,etwawennein bestimmter Gegenstand so daß einenmateriellen a- notwendigerweise Gegenstand b verursacht, Wäre a dann abervon b wenn b existiert? nur dann existiert, a tatsächlich b verurabhängigDiese Frageläßt sichbejahen:Wenn a notwendigerweise sacht,dannista von b abhängig,da a dannnichtohneb seinkann.Fernerist demAutorkeineÄußerungdes Thomasbekannt,in derein BeispielangegeSomitlassensichfolgende Einwandentspricht. benwird,das demgenannten auseinanderhalten: Definitionen Definition1: x istgenaudannGliedderGruppe1, wenngilt: auch Materie. dann existiert (1) Wennx existiert, (2) Die Definitionvon x sagtaus, daß x materiellist. Definition2: x istgenaudannGlied derGruppe2, wenngilt: auch Materie. dann existiert (1) Wennx existiert, (2) Die Definitionvon x sagtnichtaus, daß x materiellist. Definition3: x istgenaudannGliedderGruppe3, wenngilt: Materieexistiert. (1) Es ist nichtso, daß dann,wennx existiert, (2) Die Definitionvon x sagtnichtaus, daß x materiellist. daß manes mitDingenzu tunhat,die nichtdurch UnterderVoraussetzung, soll sich mit den Dingen der ersten die Tätigkeitdes Menschenentstehen, die auch Physikgenanntwird,mitden Gruppegeradedie Naturphilosophie, und mitden Dingenderletzten Mathematik die zweiten der Gruppe Dingen uniistdie abstractio Der befassen. die Naturphilosophie Gruppe Metaphysik

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versalis a particular die abstractio i, derMathematik formaeund derMetaphy" ' sik die separatiozugeordnet.Der Terminus abstractioselbstwurdevon Boethiusals Übersetzung des griechischen in die lateiWortes"aphairesis" nischephilosophische wobei "aphairesis" erstmalsvon Spracheeingeführt, in einemtechnischen Aristoteles Sinn gebrauchtwurde.5Inwiefern nun die in sich der Tradition des Aristoteles befindende dertheogenannte, Einteilung retischenPhilosophiein Naturphilosophie, Mathematikund Metaphysik heutenochbefriedigen Thomasselbstknüpft kann,sei einmaldahingestellt.6 mitseinerAbstraktionstheorie an Aristoteles wobei er die Probleme, die er an, unterdemTitelderAbstraktion zunächst vonAverroes übernimmt.7 behandelt,

II. Allgemeineund individuellematerielleGegenstände Nach Definition1 istx also genaudann GegenstandderNaturphilosophie, wenngilt,daßwennx existiert, auchMaterieexistiert, undwenndieDefinition von x aussagt,daß x materiell ist.Ein solcherGegenstandsoll beispielsweise derMenschsein.Zunächsteinmalfolgtaus seinerExistenzdie Existenzvon Materie,dennohneMateriegäbeeskeineMenschen.Ferner sagtdieDefinition des Menschenaus,daß derMenschmateriell ist,dennsie sagtaus,daß erein Sinnenwesen abersindmateriell. Die Naturphilosophie ist,Sinnenwesen ist, wie jedes Einteilungsglied der theoretischen eine Wissenschaft, Philosophie, scientia. Wissenschaften sollenallgemeine unddas könAussagenformulieren nensie nurdanntun,wennsie sichmitallgemeinen befassen.8 DemDingen nach ist nichtder individuelle Mensch,der MenschA oder der MenschB, derNaturphilosophie, sondernderallgemeine Mensch,derinA und Gegenstand B gewissermaßen enthalten muß: ist,so daß man Definition1 modifizieren 5)Vgl.P.Aubenque, 'Abstraktion Wörterbuch derPhilosophie I', inHistorisches , ed.Joachim Bd.1/A-C(Basel-Stuttgart, u.Josef deVries, derScholastik Ritter, 1971),42-44, Grundbegriffe desAbstraktionsproblems imMittelalter (Darmstadt, 1983),1.ZurGeschichte vgl.L. OeingAbstraktion Wörterbuch derPhilosophie Bd.1/ Hanhoff, III',inHistorisches , ed.Joachim Ritter, A-C(Basel-Stuttgart, derAbstraktionslehre desThomas stellt vorallem die 47-59.Neben 1971), desAlbertus mitderUnterscheidung vonvierAbstraktionsgraden einenHöhepunkt Magnus dieser dar.Vgl.Ulrich Die Erkenntnislehre desAlbertus Dähnert, Problemgeschichte Magnus andenStufen der'abstractio 'St.Albert andtheTheory of 1934),R.Z. Lauer, gemessen (Leipzig, Thomist 17(1954),69-83. Abstraction',^ 6)VanSteenberghen, 'Lastructure delaphilosophie hatdiesbezüglich théorique', beispielsweise erhebliche Zweifel. 7)Vgl.Oeing-Hanhoff, 'Abstraktion III',51. 8)Vgl.InDeTrin. q. 5 a. 2 ad4 (144).

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Definition 1': x istgenaudannGegenstand derNaturphilosophie, wenngilt: x Wenn dann existiert auch Materie. existiert, (1) (2) Die Definitionvon x sagtaus, daß x materiellist. (3) x istein allgemeiner Gegenstand. Aus (2) folgt:, daß x materiell ist,wenngleich (2), wie gesagt,nichtdamitidentischist,daß x materiell ist.Jedenfalls istjederGegenstandderNaturphilosomateriell. Inwiefern aber können materielle phie Gegenstände allgemeinsein? ThomashältzweierleiMaterienauseinander, materia und materia particularis universalis .9 , jene nennterauch materiasignata , dieseauch materiacommunis AusGründenderEinheitlichkeit seienimfolgenden dieTermini"individuelle Materie"fürmateria und "allgemeine Materie"furmateriauniverparticularis salisverwendet. Die materia ist das dermaterielsignata Individuationsprinzip len Gegenstände,10 so daß sich etwader MenschA und der MenschB, die individuellen ja materielleGegenständesind,aufgrundihrerverschiedenen Materieunterscheiden. Die individuelle Materiedes MenschenA istdessen Materie,etwadie Knochenvon A. Entsprechendes ganz bestimmte giltfür B. Zwar unterscheiden sich die beidenindividuellen Materienvoneinander, nursollendie individuelle MaterievonA, die individuelle Materievon B und die jeweiligenindividuellen Materiender anderenMenschenetwasgemeinsam haben,eine bestimmte etwavon allgemeineMaterie,die sichallerdings der allgemeinen Materieder Steineoder der Pferdeunterscheiden soll. Der individuelle Menschistmateriell der individuellen er Materie, hatbeigemäß bestimmte Knochen.Der allgemeineMenschistmateriell spielsweise gemäß derallgemeinen sondernallgemeineKnoMaterie,er hatkeinebestimmten, chen.Wendetsichdie Naturphilosophie einemindividuellen Menschenzu,so will sie etwasvon dessenallgemeiner aber auch etwasvon dessen Materie, Formwissen.Im Fall des Menschensoll die Zusammensetzung allgemeiner aus Materieund Formgeradedie Zusammensetzung aus Leib und Seelesein. So wiederindividuelle Menschzusammengesetzt istaus individueller Materie undindividueller Formbzw.individuellem Leib und individueller Seele,so ist derallgemeineMenschzusammengesetzt aus allgemeiner Materieund allgemeinerFormbzw.allgemeinem Leib und allgemeiner Seele.Die Naturphilointeressiert sich nach Thomas nur fur die sophie allgemeineMaterie(beim Menschen:furden allgemeinenLeib) und furdie allgemeineForm (beim 9)Vgl.InDeTrin. art.(143),ad2 (I43f.), SthI q. 85a. 1ad2. q. 5 a. 2 corp. 10)Vgl.InDeTrin. q. 5 a. 2 ad1 (143).

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Menschen:fürdie allgemeineSeele) einesindividuellen materiellen Gegenstandes.Sie soll,indemsievon den individuellen absieht,das Bestimmungen Dieses "HerausAllgemeineaus dem Individuellen gleichsamherausziehen. ziehen"nenntThomasabstractio a particulari.u universalis Die abstractio universalis a particulari istderwichtigste Fall derabstractio totius , bei deres um das Verhältnis von Ganzes und Teil geht.Bei der abstractio totiuswirddas Ganze ohne die Teile oder ein Teil (oder mehrereTeile) ohne das Ganze betrachtet. Zu dieserabstractio universalis a particulari gehörtdie abstractio ihr als man bei das als das Ganze insofern, {totum) Allgemeine logische auffassen kann,das aus den Besonderen,aus den Teilen,"herausgezogen" wird.12 Das Ergebnisdieses"Herausziehens" ist ein Gegenstand, der sowohl als auch materiell zwar er und ist materiell der ist, allgemein gemäß allgemeinen Materie.Die Naturphilosophie sieht Materie,nichtgemäßderindividuellen vonderindividuellen Materieab.13Damitsiehtsieauchvonderindividuellen Formab, denndieseergibtsichgewissermaßen aus derindividuellen Materie, da letztere, und nichtdie individuelleForm,das Individuationsprinzip der materiellen ist. Gegenstände Die GrenzenderAllgemeinheit derallgemeinen materiellen Gegenstände sollendurchihreDefinitionenbestimmtwerden.Wenn beispielsweise der Mensch eine Materie und eine Form hat,so allgemeine allgemeine allgemeine hat er doch keinebeliebige Materieund keinebeliebige Form,da er sichetwa von dem allgemeinen Steinoder dem allgemeinenPferdunterscheidet. Die des Menschen ist durch den bzw. die DefiAllgemeinheit allgemeinen Begriff nitiondes Menscheneingeschränkt. Der Menschistein vernunftbegabtes Sinnenwesen. Zwar muß man die Definitionsbestandteile und "vernunftbegabt" "Sinnenwesen" von den Teilen "Leib" und "Seele" unterscheiden, da etwa "Sinnenwesen" die Gattungangibtund "vernunftbegabt" denArtunterschied, aberweder"Leib" noch "Seele"die Gattungoder den Artunterschied angeund eristvernunftbegabt, erist ben;so istderMenschzwarein Sinnenwesen kein Leib er ist und auch keine Seele.14 Dennoch soll die Definition des jedoch Menschendie Grenzender Allgemeinheit der menschlichen Materieund Formangeben. n) Vgl.InDeTrin. art.(143),a.3 corp. art.(149).Einegeschichtsphilosophische q. 5 a.2 corp. zuInDeTrin. sichinLafleur, ettripartition . 'Abstraction, Untersuchung q. 5.a.3.findet séparation 12)Vgl.InDeTrin. art.(149).Vgl.auchPatt, beiThomas von 28. Aauin, q. 5 a.3 corp. Metaphysik 13)Vgl.In De Trin. intellectus communiter abstrait [sic]a materia q. 5 a. 2 ad2 (144):"unde . .,nonautem a materia communi inscientia naturali ." signata. 14)Vgl.De enteetess.c.II (372).

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univerdie durchdie abstractio materiellen Die allgemeinen Gegenstände, indivineben den keine sollen erkannt salisa particulari werden, Gegenstände sein. enthalten ihnen in sondern duellenmateriellen gleichsam Gegenständen, Positionals gemäßigter Üblicherweisewird diese universalientheoretische Realismusbezeichnet.Die thomasischenallgemeinenmateriellenGegenständesind keineIdeen im SinnePiatons,weil sie wegenihrerallgemeinen sind.Thomaslehntin In De Trin.die AnnahmederIdeen Materiemateriell er Menschist,keineplatoPiatonsab.15Somitistauch derMensch,insofern materieller nischeIdee, sondernein allgemeiner Gegenstand,der in jedem von derMateriegetrennt.16 Er ist nicht ist. einzelnenMenschen"enthalten" Nach Thomasgibtes also allgemeinematerielle (z. B. den allgeGegenstände meinenMenschen)und individuellematerielleGegenstände(z. B. diesen MenschenA). Die allgemeinenmateriellen Gegenständewerdendurchdie Sie exiabernichtgeschaffen. zwarerkannt, a particulari universalis abstractio nichtneben,sonderngleichsam, stierenauch ohnedieseabstractio , allerdings Natürlichwirft materiellen wie gesagt,in den individuellen Gegenständen. wo denn etwa PositionwichtigeFragenauf, dieseontologische die, genausich wenn es sich bei ihnen die allgemeinenmateriellen Gegenständebefinden, IdeenPiatonshandelnsoll?An welchemOrtbefindet nichtum die abstrakten er jeweilsgenauan den derallgemeineMensch?Existiert sichbeispielsweise Wenn Menschenexistieren? an denen die individuellen Raum-Zeit-Stellen, nein,wo dann?Wennja, wiekannes sein,daß einundderselbeGegenstand räumlich voneinander an mehreren, Mensch- sichgleichzeitig derallgemeine insofern daß dies man könnte Vielleicht Ortenbefindet? sagen, getrennten so daß sichein Menschgleichsamaufteilt, möglichist,als sichderallgemeine an einemvon x verTeil von ihmam Ort x und ein andererTeil gleichzeitig nichtim SinneThoDiese Antwortwärefreilich schiedenenOrt y befindet? ist, daß sich der allgemeineMensch mas, der vielmehrder Auffassung an x undybefinden sowohlanx alsauchanybefindet, vorausgesetzt vollständig Menschen.WaredannderallgemeineMenschan x und der sichindividuelle Würdensie ein und derselbeGegenstand? Menschan y tatsächlich allgemeine ihrerräumlichenKoordinaten(zu einem sich nichtzumindesthinsichtlich Ferner:Hört der allgemeineMensch gegebenenZeitpunkt)unterscheiden? Menschenmehrgibt?Diese wenn es keineindividuellen auf zu existieren, 15)Vgl.InDeTrin. art.(I42f.). q. 5 a. 2 corp. 16)InDe Trin. materiam insuiratione includunt art.(143): ..singularia signaq. 5 a. 2 corp. InDe Trin. communem..r materiam uero uniuersalia tam, q. 5 a. 3 corp.art.(149):"...inci Fußnote auch 13. a sensibilibus . . uniuersalia utponerent. inerrorem derunt separata..Vgl.

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Fragemüßtebejahtwerden,wennderallgemeineMenschnur"in"den individuellenMenschenexistiert. Andererseits dürfte es dannheutebeispielsweise keinallgemeines Mammutgeben,weil es kein individuelles Mammutmehr gibt.Wie wärenachThomasin diesemFallheutenocheinewissenschaftliche, alsoallgemeine MüßteernichtdochannehAussageüberMammutsmöglich? daß die materiellen zumindestinsofern ideell men, allgemeinen Gegenstände im SinnePiatonssind,als sie unabhängigvon ihrenwirklichen Exemplaren existieren können?Könntensie dannabernochmateriell sein? Wie dem auch sei,Thomasist derAuffassung, daß es sowohlallgemeine als auch individuelle materielle werGegenständegibt.Jetztsoll untersucht seien sie individuelloder den, in welcherWeise aus diesenGegenständen, sichdie mathematischen seinerAnsichtnach"herausallgemein, Gegenstände ziehen"lassen.

III. Allgemeineund individuellemathematische Gegenstände Auch die Mathematiksoll sich als Disziplinder theoretischen Philosophie ausschließlich mitsolchenDingenbefassen, die nichtdurchdieTätigkeitdes Menschenentstehen, ihreGegenständesollen nichtdurchden Menschen erschaffen werden.17 Darin stimmtThomasmitderklassischen Mathematik nicht überein,nach der die mathematischen Gegenstände gedanklichkonnicht erfundenbzw. erschaffen, sondernentdecktwerden.Diese struiert, Positionistalt,siefindetsichbereitsin PiatonsEuthydemos , wo vondenMeßRechnernund Sternkundigen daß sie "ihreFiguren künstlern, wird, gesagt und Zahlenreihen nichtmachen,sonderndiesesindschon,undsie findensie nurauf,wie sie sind."18 AuchAristoteles istaufdem GebietderMathematik Realist.19 Maurerbetont,daß die realistische von derMathematik Auffassung im gesamten13. Jahrhundert insbesondere auch bei Alberwurde, akzeptiert tus Magnus,RobertusKilwardbyund im allgemeinenbei den Magistern 17)ZurStellung derMathematik imthomasischen dertheoretischen System Philosophie vgl. "The Position ofMathematics', u.Patt, beiThomas von Whittaker, 43-47. Metaphysik Aquin, 18)Piaton, Sämtliche Werke 10vol.(Frank,290b,c,inPiaton ,ed.Karlheinz Hülser, Euthydemos furt amMain-Leipzig, vol.3,323. 1991), 19)Vgl.J.Annas, 'DieGegenstände derMathematik beiAristoteles, inMathematics andMetain ed.Andreas Graeser Annas Aristotle, dort 1987),131-147. physics (Bern-Stuttgart, bespricht insbesondere auchdenAbstraktionsbegrifF desAristoteles. Zumontologischen Status dermathematischen beiAristoteles Aristotle andMathematics. J.Cleary, Objekte vgl.auchJohn Aporetic Method inCosmology andMetaphysics York-Köln, (Leiden-New 1995),268-344.

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der Künstein Paris.20 Wir werdenallerdingssehen,daß nach Thomaseine besondereVerstandestätigkeit, die abstractio , dazu erforderlich ist,um forrnae die mathematischen zu erfassen, diese Gegenstände wenngleich Gegenstände nichtdurchdieseTätigkeitkonstruiert werden.21 Nach derin denVorbemerkungen Definition 2 istx genaudann genannten wenngilt: GegenstandderMathematik, dann existiert auch Materie. (1) Wennx existiert, (2) Die Definitionvon x sagtnichtaus, daß x materiellist. Die Bedingung(2) ist,wieeingangserwähnt, nichtohneweiteres damitgleichzusetzen,daß die Definitionvon x aussagt,daß x nichtmateriell ist,aus ihr alleinfolgtinsbesondere daß mathematische nichtmateriell nicht, Gegenstände sind.Thomasist gleichwohlderAnsicht,daß diese Gegenständein derTat nichtmateriell Formensein.Zwarsprichtergelesind,sie sollenquantitative daß die mathematischen davon, gentlich Gegenständemateriellgemäßder materiaintelligibilis nur sind, handeltes sichbei dieserMaterieumeineMaterieimübertragenen Sinn:Ein mathematischer istmateriell Gegenstand gemäß dermateria wenn er als "Stoff" oder "Mittel"innerhalb dann, intelligibilis gerade einesmathematischen Beweisesverwendet wird.22 Diese abgeleitete, imGrunde " von materia soll an dieserStelle äquivoke,bestenfalls analogeVerwendung nichtweiterinteressieren. Somitergibtsichfolgendemodifizierte Definition: Definition2': x istgenaudannGegenstandderMathematik, wenngilt: dann existiert auch Materie. (1) Wennx existiert, (2) x istnichtmateriell. 20)Vgl.Maurer, 'Thomists andThomas 60. Aquinas', 21)Anderson, Matter andtheObjects ofMathematics', diethomasische 'Intelligibel vergleicht derMathematik mitderaristotelischen. Erstellt sowohl Gemeinsamkeiten alsauch Philosophie Unterschiede heraus undbemerkt indiesem daßnach vieler KomZusammenhang, Auffassung mentatoren diemathematischen nachThomas eineArtZwischenstatus hätten: Gegenstände w.. . they areneither ofreason norrealbeings, butshare features ofboth" purely beings (vgl.559, Fußnote dierealistische Position desThomas 13).DieseInterpretation der gibt jedoch bezüglich mathematischen mißverständlich dennnachThomas haben diemathemawieder, Gegenstände tischen keinen wieauchimmer eines Produkts desmenschlichen Gegenstände gearteten Aspekt Geistes. Ebenso istAndersons daß nach Thomas die mathematischen Behauptung, Gegenstände to physical zumindest Quantitäten physikalischen korrespondieren (correspond quantities), andAquinas', sindQuantitäten mathematisch und 255).FürThomas unpräzise (vgl.Aristotle diesen sollen keine mathematischen sondern diemathematischen Gegenstände korresponieren> sollen dieseQuantitäten sein. Gegenstände 22)Vgl.InDeTrin. q. 5 a. 3 ad4 (150).

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Die mathematischen und in arithmeGegenständewerdenin geometrische tischeunterteilt, wobei der ursprüngliche der Geometrieder Gegenstand der die Einheitist.23ThoPunkt, ursprüngliche GegenstandderArithmetik mas kenntdie Arithmetik aus Boethius'De institutione arithmetica und die Geometrie ausEuklidsElementa Betrachten wir die geometriae.1A (abgeleiteten) Linie,Flächebzw.Figurund Körper.Nach Defigeometrischen Gegenstände nitionT existieren dieseGegenstände nurdann,wennMaterieexistiert, ohne daß sie selbstmateriell sind.Wie hatmandas zu verstehen? Nach Thomasist einesmatejedermathematische GegenstandeinAkzidenz,eineEigenschaft, riellenGegenstandes, der dann derjeweiligeTrägerdieserEigenschaft ist.25 Insofern die mathematischen im und die Gegenstände allgemeinen genannten im besonderen materieller geometrischen Gegenstände Eigenschaften Gegenständesind,existieren sie nurdann,wennMaterieexistiert. Auchwenndie mathematischen Gegenständenichtmateriellsind,so impliziertdoch ihre Existenzdie Existenzvon Materie,weilihreExistenzdie Existenzmaterieller und die Existenzmaterieller die ExiTrägerimpliziert Trägertrivialerweise stenzvon Materieimpliziert. Obwohl die mathematischen Gegenständean die Existenzmaterieller Trägergebundensind, geht die Materialitätihrer der Trägernichtauf sie über.Insbesonderefolgtaus der Nichtmaterialität mathematischen daß sie keine materiellen Teile materieller Gegenstände, sind. Gegenstände Die Gegenstände derNaturphilosophie werdenvermögeihrerjeweilsverschiedenenArtzugehörigkeit, ihrerjeweilsverschiedenen Definitionunterschieden. Die individuellen a usw.- sind Gegenstände derMenschA,dasPferd als individuelleGegenständefurdie Naturphilosophie nichtvon Interesse. LäßtsichEntsprechendes in BezugaufdieMathematik sagen?SinddieGegenstände der Mathematikalso allgemeineGegenstände?Der Mathematiker sollzwarebensowie derNaturphilosoph eineAbstraktion nursoll vollziehen, es bei der mathematischen Abstraktion um das "Herausziehen" bestimmter Formengehen,so daß diese Abstraktion abstractio der , Abstraktion formae Formgenanntwird.26 Die Form,die durchdie abstractio formaeabstrahiert,

23)Vgl.InDeTrin. art.Vgl.auch art., q. 5 a. 3 ad6 (151),SthI q. 1 a. 2 corp. q. 3 a. 5 corp. 'Notesurl'abstraction 488. Winance, mathématique', 24)Vgl.Maurer, "Ihomists andThomas 59. Aquinas', 25)Vgl.InDeTrin. enim materia sensibilis ad,lineam sicut q. 5 a. 3 ad2 (150):"non comparatur setmañs sicut subiectum inquoesse etsimiliter estdesuperficie etcorpore ." habet; pars, 26)Vgl.InDeTrin. art.(149). q. 5 a. 3 corp.

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" Formzusam, wird,ist nichtdie Form,die als individuelle herausgezogen" materiellen Materieeinenindividuellen men miteinerindividuellen Gegenstandbildet(etwadie Form- die Seele- des MenschenA), sie istauch nicht die als allgemeineFormzusammen die Formeinesmateriellen Gegenstandes, bilmateriellen Materieeinenallgemeinen miteinerallgemeinen Gegenstand det (etwadie Form- die Seele- des Menschenals Menschen),sondernsie ist die undzwarentweder Formdiesesmateriellen die quantitative Gegenstandes, Mathematik soll demnach die Form. Die arithmetische oder die geometrische erfasFormeinesmateriellen oderarithmetische Gegenstandes geometrische eine Zahl aus Kreis einer Münze27 oder sie einen aus sen,etwadann,wenn Sollendiese Formennun aber "herauszieht". Kollektion28 einerbestimmten sollen also die durchdie abstractio oder individuell sein, formae allgemein die Gegenständeder Mathematik, erfaßtenGegenstände, allgemeinsein,so der a particulari erfaßten universalis wie die durchdie abstractio Gegenstände Da die sein? sollen sie individuell oder sind, Naturphilosophie allgemein als solche eine und eine Disziplindertheoretischen Mathematik Philosophie sein soll, wirdsie sich letztlichum allgemeineAussagen,um Wissenschaft AussagenüberallgemeineGegenständebemühenmüssen.Insofernwerden von der Arten29, Gegenstände,mathematische allgemeinemathematische Thomas auch individuelle es nach erfaßt. abstractio Allerdingsgibt formae wiretwaseineReaktionauf einen mathematische Gegenstände.Betrachten vonderMaterieabsieht. EinwandgegenseineAnnahme,daß die Mathematik Der Einwandlautetwie folgt: betrachtet dieGeraden, Art.AberderMathematiker AlleGeraden sindvonderselben betrachten. nicht unddasQuadrat könnte erdasDreieck ersiezählt, andernfalls indem undderArt siesichderZahlnachunterscheiden insofern erdieLinien, Alsobetrachtet diederArtnach fur dieDinge, desUnterscheidens dasPrinzip Aber nachübereinstimmen. betrachtet.30 vomMathematiker dieMaterie . . . Alsowird istdieMaterie übereinstimmen, 27)Vgl.SthI q. 40a. 3 corp. art. 28)Vel.SthIq. 11a. 3 ad2. 29)Vgl.InDeTrin. SthI q. 7 a. 4 ad2,q. 85a. 1ad2. q. 5 a. 3 ad3 (150), "Omnes 30)InDe Trin. eiusdem Setmathematicus recte sunt linee a. 3 3 5 (145): speciei. q. arg. consietquadratum; numerando lineas rectas considérât eas,aliasnonconsideraret ergo triangulum hisque Setprincipium numero etconueniunt secundum dérât lineas differendi specie. quoddifferunt Eineetwas a mathematico materia consideratur . . Ergo estmateria. conueniunt secundum speciem Trinität. Eine Über die von in Thomas findet sich deutsche andere Auslegung Aquin, Übersetzung von De trinitate Inlibrum Boethii desBoethius. dergleichnamigen Übersetzung exposition Schrift HansLentz 1988),206. (Stuttgart,

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Es wirdalso so argumentiert: Alle Geradensindvon derselbenArt. Der Mathematiker zähltdieseGeraden. Also betrachtet derMathematiker GegenständeinnerhalbeinerArt. Man kannnurdann GegenständeinnerhalbeinerArtbetrachten, wenn man nichtvon derMaterieabsieht,die diese Gegenständeindividuiert. nichtvon der Materieab. (5) Also siehtderMathematiker (1) (2) (3) (4)

Bei diesemArgument sei einmalvorausgesetzt, daß die Aussage(1) wahrist. Das ist insofernnichtabwegig,als man individuelleGeradenzu einerArt zusammenfassen kann, indem man Geradenals bestimmtePunktmengen die definiert, gewissenAxiomengenügen.(2) wird vom Einwand damit daß manandernfalls Dreieckeund Quadratenichtunterscheiden begründet, könnte.Dies leuchtetein,da bei derDefinitionvon n-Eckendie Anzahlder Seitenzumindestimplizitrelevantist.Aus (1) und (2) folgt(3), aus (3) und Thomaskritisiert an dieser (4) folgt(5). SomitwärederEinwandberechtigt. (2) oder (3), die implizieren, Überlegungnun nichtetwadie Behauptungen daß es individuellemathematische Gegenständegibt,sonderndie Behaup31 Der erste Grund fürdie Unterscheidung dessen,was tung(4). eigentliche, zurselbenArtgehört,sei nichtdie Materie,sonderndie verschiedene Lageim Raum. Die Ursachefurdie zahlenmäßige Verschiedenheit ist,so Thomasan andererStelle,die räumliche Verschiedenheit.32 Diese Aussagenstehennuraufden erstenBlickimWiderspruch zurseiner wonachdie materia dermateriellen Ansicht, signatadas Individuationsprinzip , so wirdjetztdeutlich,soll gerade Gegenständeist,denndie materiasignata, ihrer räumlichen individuieren können.Da es sichbei den wegen Verteilung mathematischen Gegenständenum nichtmaterielle Gegenständehandelt, könnensie, so darfman Thomasinterpretieren, direktaufgrundihrerverschiedenen räumlichen ohneUmwegüberdie materia , Lage,gleichsam signata individuiert werden.DaherkannderMathematiker von derMaterieabsehen undindividuelle Geradenaufgrund ihrerverschiedenen Lageim Raumunterscheiden.33 zu den mathematischen sehrwohl Folglichgehören Gegenständen 31)Vgl.InDeTrin. q. 5 a. 3 ad3 (150). 32)Vgl.InDe Trin. lociconsideretur secundum suam q. 4 a. 4 corp.art.(132):"setsidiuersitas sicplanum estquoddiuersitas beiestcausadiuersitatis secundum numerum.n causam, 33)Vgl.auchInDeTrin. art.(129):"Inmathematicis enim non ratio q.4 a.3 corp. potest assignari diuersitatis harum duarum linearum nisi situm" propter

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individuelle die sichdannaufgrund ihrerLage im RaumunterGegenstände, scheidenlassen.Wenn man mitThomasannimmt,daß individuelle mathematischeGegenständeEigenschaften individueller materieller Gegenstände daß sich verschiedene sind,und wenn man fernervoraussetzt, individuelle materielle nicht an derselben Raumstelle befinden Gegenstände gleichzeitig auch dies tutThomas 34,dannkannmanmitihmderAuffassung sein,daß sich verschiedene individuellemathematische zu einem Gegenstände gegebenen Zeitpunktan verschiedenen Raumstellenbefinden.Wenn beispielsweisezweiMünzenzu einemZeitpunkt verschiedene Raumstellen einnehmen, dann nehmenauch die beidenKreise,die Eigenschaften dieserMünzensein Raumstellen ein. Zwarsindmathesollen,zu diesemZeitpunktverschiedene matischeGegenständenachDefinition2' nichtmateriell, sie könnenjedoch insofern im Raum sein,als sich ihremateriellen Trägerim Raum befinden. Getrenntvon ihrenTrägernsind die mathematischen Gegenständefreilich - überhauptnicht insofernunräumlich, als es siegetrennt gibt.35Folglich sind sie keine Formenim Sinne Piatons.Sie könnennur "an" materiellen siegetrennt von ihnenbetrachtet werden existieren, Gegenständen wenngleich können.36 Die beidenKreisehabenalso insofern eine verschiedene Lage im als sie eines sich im Raum befindenden Raum, materiellen jeweilsEigenschaft sind. Gegenstandes Haltenwirfest,daß es sowohlallgemeineals auch individuelle mathematischeGegenstände beide werden durch die abstractio gibt, formaeerfaßt.In welcherBeziehung, in welcherReihenfolge hinsichtlich derErkenntnis stehen dieseGegenständeim Prozeßderabstractio formaeiEs lassensichprinzipiell dreimöglicheFälleauseinanderhalten: Die abstractio formaeerfaßt mathematischen (a) zunächstdie individuellen Gegenständeund aus diesen die allgemeinen mathematischen Gegenstände oder (b) zunächstdie allgemeinenmathematischen Gegenständeund aus diesen die individuellen mathematischen Gegenstände oder 34)Vgl.InDeTrin. art.(128f.), a. 4 corp. art.(132). q. 4 a. 3 corp. 35)Vgl.InDe Trin. inerrorem utponerent mathemaq. 5 a. 3 corp.art.(149):".. . inciderunt tica.. . a sensibilibus nonsubsistunt separata..SthI q. 5 a. 3 ad4: ". . . mathematica separata secundum esse. . ." 36)Vgl.Maurer, 'Thomists andThomas hatklargesehen, 59.Thomas daßauchbei Aquinas', Aristoteles dieabstrahierten zwar abernicht alsgetrennt betrachtet werGegenstände getrennt, den.Vgl.Aubenque, Abstraktion P,43.

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(c) sowohl die individuellenals auch die allgemeinenmathematischen aus gewissermaßen gleichzeitig Gegenständeunabhängigvoneinander, den gegebenenmateriellen Gegenständen. Kreises.Es könnte Ein Beispiel:Eine Münzehabedie Formeinesbestimmten Kreisund aus diesein,daß die abstractio formaezunächstden individuellen Kreiserfaßt, es könnteaberauch sein,daß sie zunächst semden allgemeinen Kreiserfaßt, und es Kreisund aus diesemden individuellen den allgemeinen Kreis könnteschließlichsein,daß sie beideKreise,sowohlden individuellen voneinander aus der derMünze als auch den allgemeinen Kreis,unabhängig Da es sich Münze erfaßt.WelcherderdreiFälleistnachThomaszutreffend? bei derMathematikum eineWissenschaft handelt,wirdes ihrletztlichum mathegehen,so daß die allgemeinen Aussagenüberallgemeine Gegenstände Ziel der abstractio sind. Außermatischen das formae Gegenstände eigentliche mathematischen demsollendie mathematischen Arten,d. h. die allgemeinen materiellen sonnicht nur aus den individuellen Gegenständen, Gegenstände, materiellen abstrahiert dernauchaus den allgemeinen werden, Gegenständen sondernauch von der allgemeinen indemnichtnurvon der individuellen, " .. a Materieabgesehenwird: Speciesautemmathematicae possuntabstrahi. Demnachgilt materiasensibilinonsolumindividuālused etiamcommuni"01 zweierlei: mathematischen werdenaus individuSatz 1: Die allgemeinen Gegenstände abstrahiert. ellenmateriellen Gegenständen mathematischen werdenaus allgemeinen Satz 2: Die allgemeinen Gegenstände materiellen abstrahiert. Gegenständen der Frage,in welcherBezieWegenSatz 1 istklar,daß Thomashinsichtlich die individuellen und mathematischen allgemeinen Gegenstände hung im Prozeßderabstractio denneineAbstrakformaestehen,Fall (a) favorisiert, tionallgemeiner mathematischer materiellen Gegenständeaus individuellen ist nur über individuelle mathematische Gegenständen Gegenstände möglich, so daß diese Abstraktion aus zwei Teilprozessenbesteht,einem ersten,in dem aus individuellen materiellen individuellemathematische Gegenständen werden,und einemzweiten,in demaus diesen Gegenstände "herausgezogen" 37)SthI q. 85a. 1 ad2. Vgl.Neumann, undMethode, 111:"Diemathematischen Gegenstand können sowohl vondersingulären wieallgemeinen Sinnesmaterie abstrahiert Gegenstände . . ."Vgl.auchWinance, werden 'Notesurl'abstraction 491. mathématique',

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individuellen mathematischen mathematische Gegenständen allgemeine Gegenstände"herausgezogen" werden. dieseszweitenTeilprozesses läßt sich fragen,ob Thomasdem Angesichts von Lorenzen38 zustimmen würde,gemäß dem bei der Abstraktionsbegriff Abstraktion im Grundenichtsanderesgeschieht, als daß in neuerWeisevon altenGegenständen erschaffen wird,jedochkeineneuenGegenstände geredet werden,wobei dieses"neueReden"dadurcherfolgen soll,daß man sichauf beschränktund Aussageformen, die sogenannteinvarianteAussageformen nichtinvariant als zurückweist. DemnachliegteinAbstraktisind, unzulässig onsprozeßgenau dann vor,wenn man lediglichbezüglicheinergewählten invariante HierbeiisteineAusÄquivalenzrelation Aussageformen akzeptiert. . dann invariant einer A(. .) genau sageform bezüglich gegebenen ÄquivalenzrelationR, wennfüralle x, y aus der BeziehungxRy folgt,daß die Aussage A(x) genau dann gilt,wenn die AussageA(y) gilt. Bei der Abstraktion beschränkt mansichalso aufdiejenigen sichnicht Aussagen,derenGültigkeit wenn man die relevante Konstante durcheinezu ihrgemäßR äquivaändert, lente Konstanteersetzt.Ein Beispielaus der Schulmathematik: Betrachtet werdendie Menge derpositivengemeinenBrücheund die Mengederpositivenrationalen Zahlen.Gehtmanvon dererstenaufdie zweiteMengeüber, wirdinsofern eineAbstraktion im SinneLorenzensvollzogen,als man dann nurAussagenzuläßt,derenGültigkeit sichbei Ersetzung einesBruchesdurch einendazu äquivalentenBruchnichtändert,man beschränkt sich also auf einer invariante Die bestimmte, bezüglich Äquivalenzrelation Aussageformen. wärein diesemFall die Relation,die Brüchegenaudann Äquivalenzrelation alsäquivalentansieht,wennderenZählerundNennerüberkreuz multipliziert das gleicheProduktergeben. KönnteThomasdiesemAbstraktionsverständnis furden zweitenTeilprozeß derobengeschilderten Abstraktion mathematischer allgemeiner Gegenstände - der Abstraktion aus individuellenmateriellenGegenständen allgemeiner mathematischer mathematischen Gegenständeaus individuellen Gegenständen- zustimmen? Dazu müßteereineÄquivalenzrelation angeben,durchdie die individuellen mathematischen zu MengenjeweilsuntereinGegenstände anderäquivalenter individueller mathematischer Gegenständezusammengefaßt werden.Von der Verschiedenheit der individuellenmathematischen Gegenständein diesenMengenmüßteabgesehenwerden.Die Menge aller Geradenkönnteeine solcheMengesein,die MengeallerKreiseeine andere. 38)Vgl. zum Folgenden Paul Lorenzen, Lehrbuch derkonstruktiven Wissenschaftstheorie (Mannheim-Wien-Zürich, 1987),161-169.

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Die Abstraktion würdedadurchgeschehen,daß man nur solcheAussageformenzuläßt,die bezüglichderÄquivalenzrelation invariant sind,also nur solcheAussagen,derenGültigkeit sichbei derErsetzungdes Ausdrucks, der fiireinebestimmte einzelneGeradesteht,durcheinenAusdruck, derfüreine anderebestimmteeinzelneGerade steht,ebensowenigändert,wie bei der einzelnenKreissteht, Ersetzungdes Ausdrucks,der fiireinen bestimmten durcheinenAusdruck,der fureinen anderenbestimmten einzelnenKreis steht.Man tutnurso,alsob manüberneueGegenstände, überdie allgemeine Geradeoder überden allgemeinenKreis,redet,obwohlman nurin neuer Weiseüberdie altenGegenstände, also überdie einzelnenGeradenund Kreise redet.VerbotensindsolcheSätzewie "Die Geradea hatkeinenAnfangsund keinenEndpunkt",solangedamitetwasanderesgesagtwirdals mitdem Satz "Die Geradeb hat keinenAnfangs-und keinenEndpunkt".Werdendiese beidenSätzeals tautologisch da sie ein und denselbenSachverhalt angesehen, den daß Geraden keinenAnfangs-und keinenEndSachverhalt, aussagen, sind sie punkthaben, zugelassen. Bei einerderartigen Abstraktionsverfahrens Anwendungdes geschilderten wärefreilich zu durch welche klären, einiges beispielsweise, Äquivalenzrelation genau die individuellenmathematischen Gegenständein bestimmte werden.Sehr Mengen,etwain die Mengeder Geraden,Kreiseusw.sortiert wahrscheinlich würdeThomasdas Lorenzensche Verständnis vonAbstraktion abernichtakzeptieren. Zwarvertritt auch er die Auffassung, daß durchdie Abstraktion keineneuen Gegenständegeschaffen nur werden, folgtdas für ihndaraus,daß sie schonin derextramentalen Weltsind,so daß mansie nur entdeckenmuß, währendes diese neuen Gegenständenach Lorenzennur scheinbar gibt,wirwürdennurso reden,als ob es sie gibt.Nach Thomaswerden wederdie individuellen noch die allgemeinenmathematischen Gegenständekonstruiert, vielmehrsind sie schonda und es kommtdaraufan, sie zu erfassen. Außerdemsoll es die Mathematikals vermögederAbstraktion Teil dertheoretischen mit Philosophie Dingenzu tunhaben,die nichtdurch dieTätigkeit desMenschenentstehen, dieseDinge könnenfolglich keineProduktedermenschlichen Redeweisesein. Nach Satz2 werdendie allgemeinen mathematischen aus den Gegenstände materiellen abstrahiert. Da das dieser allgemeinen Gegenständen Endergebnis Abstraktion wiederumdie in Satz 1 genanntenallgemeinen mathematischen der allgemeinenmathematischen Gegenständesind,liefertdie Abstraktion aus den individuellen materiellen überdie indiviGegenstände Gegenständen duellenmathematischen dasselbe Gegenstände Ergebniswie die Abstraktion derallgemeinen mathematischen ausdenallgemeinen materiellen Gegenstände

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wobeibei derletztenAbstraktion wird,daß die Gegenständen, angenommen materiellen aus den individuellen materiellen allgemeinen Gegenstände universalis a particularierfaßtwerden. Gegenständendurchdie abstractio Diese Zusammenhänge lassensichveranschaulichen: individueller materieller materieller Gegenstand individueller Gegenstand (MünzeA) (MünzeA) 1 individueller mathematischer derMünzeA) Gegenstand(Kreisform

I materieller allgemeiner Gegenstand Münze) (allgemeine

i mathematischer allgemeiner Gegenstand(allgemeineKreisform)

i mathematischer allgemeiner Kreisform) Gegenstand(allgemeine

Sowohl der linksals auch der rechtsdargestellte Ablaufliefertallgemeine mathematische Nun sich aber aus der Verschiedenheit Gegenstände. ergibt dieserAbläufe,daß der Begriff der abstractio ist,denn formaemehrdeutig das Abstrahieren mathematischer aus individuellen allgemeiner Gegenstände materiellen überindividuellemathematische Gegenständen Gegenständeist etwasanderesals das Abstrahieren mathematischer allgemeiner Gegenstände aus allgemeinen materiellen dieser Gegenständen, mögensichdie Ergebnisse auchnichtunterscheiden. Die Mehrdeutigkeit desBegriffs Abstraktionsvorgänge derabstractio resultiert weiter daß durch die abstractio daraus, formae formae nichtnurdie allgemeinen mathematischen Gegenständegewonnenwerden, sondernauch die individuellen mathematischen und zwaraus Gegenstände, den individuellen materiellen denn es ist offensichtlich, daß Gegenständen, etwader individuelleKreisnuraus einemindividuellen materiellen Gegenstandabstrahiert werdenkann.Thomassprichtzwarauch davon,daß man sichmehrere individuelle mathematische innerhalb einermatheGegenstände matischenArtvorstellen( ymaginari ) könne.39Dieses Vorstellenist jedoch nicht das Abstrahieren dieser Gegenständeaus individuellenmateriellen sondern der räumlichen Gegenständen, Ergebnisdes Berücksichtigens Lage dermathematischen Gegenstände. Es ergebensichalso dreiverschiedene Typenderabstractio formae: 39)Vgl.InDeTrin. q. 5 a. 3 ad3 (150).

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mathematischer aus individu(I) dieAbstraktion allgemeiner Gegenstände ellenmateriellen Gegenständen mathematischer aus allgemei(II) die Abstraktion allgemeiner Gegenstände nen materiellen Gegenständen individueller mathematischer (III) die Abstraktion Gegenständeaus individuellenmateriellen Gegenständen. Hierbeiist(III) einTeilprozeßvon (I). - seien sie individuell Thomaszufolgesind mathematische Gegenstände - Eigenschaften oder allgemein materieller Gegenstände,und zwarsind,so könnenwir sagen,individuellemathematische GegenständeEigenschaften individueller materieller und Gegenstände allgemeinemathematische GegenständeEigenschaften materieller allgemeiner Gegenstände.Wie ein individuellerKreis eine Eigenschaft eines individuellenmateriellen kreisrunden ist so der Kreis eine des ist, Gegenstandes allgemeine Eigenschaft allgemeinen materiellen kreisrunden Da allgemeine materielle Gegenstandes. Gegenstände vonderabstractio universalis a particulari erfaßtwerden,müßtederallgemeine materielle kreisrunde betrachtet werGegenstandvon derNaturphilosophie den. Ob ThomaswohldieseKonsequenzgezogenhätte? WendenwirunsnocheinmalderDefinition2' zu. Nach dieserDefinition istXgenaudannGegenstand derMathematik, wenngilt:(1) Wennx existiert, dannexistiert auchMaterie,und (2) x istnichtmateriell. Sowohldie allgemeinen als auch die individuellen mathematischen Gegenständeerfüllendiese denn wenn ein individueller mathematischer Definition, existiert, Gegenstand existiert aucheinindividueller materieller vondemderindividuGegenstand, elle mathematische ist,und wennein allgemeiGegenstandeine Eigenschaft ner mathematischer dann existiertein allgemeiner Gegenstandexistiert, materieller von dem derallgemeinemathematische Gegenstand, Gegenstand eine Eigenschaft ist.Außerdemsindwederdie individuellen noch die allgemeinenmathematischen Gegenständemateriell.Aber sollteThomas nicht auch derAnsichtsein,daß man die von derMateriegetrennten Substanzen, etwadie Engel,zählenkann?Sollteerdannnichtzulassen,daß ZahlenEigenschaften vonGegenständen seinkönnen,die nichtmateriell sind?Und könnte man nichtauch dann Engel zählen,wenn es nur Engel gäbe?Generellist die Annahme,daß mathematische materieller GegenständeEigenschaften Zahlenproblematisch. In dermodersind,schonfürnatürliche Gegenstände nenMengenlehre werdendieseZahlenalsbesondereMengenaufgefaßt, wobei dies in verschiedener Weise geschehenkann. Wenn Zahlen Mengen sind, dann sindsie zwarkeinemateriellen wäreForderung Gegenstände;insofern

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denn (2) der Definition2' erfüllt.Aber Forderung(1) wäre nichterfüllt, natürliche Zahlenlassensichauch so definieren, daß man lediglichdie leere Menge und eine "Nachfolgevorschrift" benötigt,um Mengenzu definieren, die dannjeweilsmiteinernatürlichen Zahl identifiziert werden.So kannman die Zahlen 0, 1, 2, 3, . . . etwaals 0, {0}, {{0}}, {{{0}}}, . . . oderals 0, {0}, wie es Zermelobzw.von Neu{0, {0}}, {0, {0}, {0, {0}}}, . . . definieren, manngetanhaben.40Fregebeispielsweise hat die natürliche Zahl n mitder aller n die Elemente so daß, wenn enthält, identifiziert,41 Menge Mengen, Zahlenals Eigenschaften betrachtet werdensollten,sie als Eigenschaften von also als Eigenschaften von Gegenständen, die wären,42 Mengenaufzufassen nichtmateriell sind.Diese so definierten Zahlenwärendemnachkeinemathematischen furThomas.Die Frage,ob es vielleicht andere,nicht Gegenstände aberdennochfurdie moderneMathematik brauchbare mengentheoretische, Definitionsversuche furdienatürlichen Zahlengibt,diegeeignet seinkönnten, der thomasischen Position,daß mathematische GegenständeEigenschaften materieller istein Gegenständesind,einenakzeptablenSinn abzugewinnen, ThemafureinenanderenAufsatz.

40)Vgl.Heinz-Dieter indieMengenlehre Ebbinghaus, Einfiihrung (Mannheim-Leipzig-WienZürich, 1994),77. 41)Vgl.Gottlob DieGrundlagen derArithmetik. Einebgisch mathematische Frege, Untersuchung über denBegriff derZahl,ed.Joachim Schulte 100. 2005), (Stuttgart, 42)Quineversucht indiesem Sinnefiirdieintuitive Anschaulichkeit vonFreges zu Fassung VanOrman undGegenstand 453. 1993), Quine,Word argumentieren. Vgl.Willard (Stuttgart,

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VIVA RI UM www.brill.nl/viv

ČÍ) BR1LL

Vivarium 46 (2008)175-191

Insolubilia Secundum

and the Fallacy Quid et Simpliciter

CatarinaDutilhNovaes University ofAmsterdam StephenRead UK University ofStAndrews, Abstract ThomasBradwardine makesmuchofthefactthathissolution totheinsolubles is in accordance withAristotle's of the in the Liar as that of secunfallacy diagnosis paradox dumquidetsimpliciter. PaulSpade,however, claimsthatthisinvocation ofAristotle by Bradwardine is purely in order to confer on his "honorary" speciousrespectability andgiveita spurious ofauthority. Ouranswer toSpadefollows Bradanalysis weight wardine s response totheproblem ofrevenge: of itself that itis anyproposition saying falsesaysmorethandoesBradwardine s proposition of it that it is and so false, saying follows fromthatotherproposition in of of what it and not only respect part says, . simpliciter Keywords insolubilia' Bradwardine, fallacy, Spade 1. Introduction It iswidelyrecognized thatthehistorical ofLiarparadoxesin the development laterMiddleAges,thenknownas Insolubili relatedto thefala, is intimately secundum et It is as not clear lacy yet quid simpliciter} entirely howexactlythe firstformulations of insolubilia(or logicalparadoxes)came about (the first such formulations are fromthe end of the 12th century),as the possible L.M.De Rijk, Modernorum P.V.Spade, 'Theorigins ofthemedieval (Assen, 1962-67); Logica Insolubilia-literaturt Studies inSpade, 33 (1973),292-309, and , Franciscan Lies, repr. Language intheLateMiddle inSophisms andLiars', in (London, 1988);C. Martin, Logic Ages 'Obligations Medieval andGrammar, ed.S. Read(Dordrecht, 1993). Logic ©Koninklijke Brill 2008 DOI:10.1163/004275408X31 NV, Leiden, 1258

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ancientsourcessimplydo notseemto offer enoughmaterialfora full-fledged realization oftheirdeeplyparadoxicalnature.Christopher Martin2 hasargued thatone ofthemainfactors in thedevelopment oftheinsolubilia convincingly in the Middle was the of the medievalkind genre Ages development typically oforaldisputation knownas obligationes. Indeed,fora successful performance in suchdisputations, itwasessentialto be ableto identify paradoxical proposithecasus, was oftenintendedto gentions,as thesetupforsuchdisputations, erate preciselythis kind of self-referential statement,and as grantinga defeat for the the Nevertheless, paradoxicalpropositionspelled respondent. seemsto be one of thebestcandidatesas fallacysecundum quid etsimpliciter themainancientsourceofinspiration fortheinsolubilialiterature. However,Paul VincentSpade has claimedin severalplaces that,while thehistoricalconnectionis patent,the conceptualconnectionbetweenthis fallacyand insolubiliais in factrathermeagre.3He saysthattheusesof this ofinsolubilia is conceptually fallacymadebyseveralauthorsin theirtreatment far from what in Aristotle had intended his own text;such uses, he very adds, are at best adaptationsof the originalconceptsdefiningthe fallacy secundum . Moreover, he considerslaterinvocations of this quid etsimpliciter in treatments of in in insolubilia Bradwardine s in solution , fallacy particular the 14thcentury, as purely"honorary";4 it was solelyout of respectforthe - indeed,a fallacyad verecundiam - thatBradwardine tradition invokedthis in connection with insolubilia not on and the basis of real fallacy conceptual kinship. In thispaper,we considerand rejectSpades assessment, withparticular to Bradwardine. We will that s in factfits Bradwardine solution respect argue into the structure the secundum neatly conceptual underlying fallacy quid et . s criticism stem from too narrow an of may Spade simpliciter understanding thisfallacy. we viewthisfallacyas a remarkably flexible By contrast, conceptual framework, to a of and but situations, variety phenomena applicable withoutlosingitscoherence. 2)Martin, andLiars'. 'Obligations 3)Spade, 'Theorigins ofthemedieval Medieval Liar : A CataInsolubilia-iiterature; Spade,The the ImoiubWiz-Literature in The 'Insolubilia', (Toronto, 1975); Spade, logue of Cambridge History Medieval A.Kenny eds.N. Kretzmann, andJ.Pinborg 1982), ofLater Philosophy, (Cambridge, inthemedieval 'Fiveearly theories Insolubilia-ìitetaxuré 25 (1987), , Vivarium 246-52); Spade, Insolubles ofPhilosophy 24-46;Spade, (Stanford 2005).K.Simmons, Encyclopedia Universality andthe Liar(Cambridge, dismissal ofsecundum 1993)§5.2.2,alsorejects Spade's quidetsimplicwith iter toPseudo-Sherwood's andOckham's treatments ofinsolubles. respect 4)Spade, n.46,repeated 'Fiveearly inSpade, Insolubles theories', §2.1.

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2. lhe Fallacysecundumquid et simpliciter is perhapsbestseenas a largeumbrella secundum The fallacy quidetsimpliciter ofphenomenacan be placed.Thebasicideais that underwhicha widevariety attributes onlyin a maybelongto a thingin an absolutesense,or bycontrast a termmaybe predicatedofa thingabsocertainrespector aspect;similarly, arises A in a certain or respect. fallacysecundum quid etsimpliciter lutely, only taken as in sense is a used in "an an when, particular argument, expression is not a Such passage alwaysunwarranted, thoughit wereused absolutely".5 to tryto identify but in manycasesit is, and thisis whyit is important patrelatedto thefactthattermscan applyabsoternsof sophisticalrefutations lutelyor only in certainrespectsto things.Aristotleclassifiedthe fallacy as a fallacyextradictionem secundum , thatis,a fallacythatis quid etsimpliciter usesoflanguage.However,on manyoccasions,it notdependenton particular of thiskindis indeed seemsthatwhatis at therootof a fallaciousargument in address texts factexplicitly A few medieval use of language. theparticular afterall,6and thisfallacy theissueas towhether maynotbe a fallacyindictione concludethat it is not, but this indicatesthat the doubt concerningthe was notuncommon. ofthisfallacy classification sevIn his Sophistical , Aristotle proceedsas usualbyproviding Refutations ofthisfallacy, eralexamplesofoccurrences else,the and,morethananything ofexamplessubstanexamplesarethecoreofhisdiscussion.The widevariety accountflexible is a and that this indeed tiatestheclaim umbrella, fallacy large ing fora wide varietyof phenomena.Let us take a look at some of these ElenchisI67al): De Sophisticis The first comesfromch. 5 (Aristotle, examples. then what isnotis.7 ofanopinion, Ifwhat isnotistheobject arenot Theproblemhere,Aristotle says,is that'to be X" and 'to be simpliciter while not to be the of In it is thesame. thiscase, really object opinion possible 5)Aristotle, inDavidRoss W.A. Pickard-Cambridge, Elenchis De Sophisticis I66b39,transi. Works vol. I. The Aristotle, (Oxford, 1928). (ed.), of 6)Dialéctica ofSherwood, IntroducModernorum Monacensis ), p.593;William (DeRijk, Logica Libro in Logicam tiones 1995),p. 200;SimonofFaversham, Quaestiones super (Hamburg, DunsScotus, etal.(Toronto, , ed.S. Ebbesen 1984)p. 157;John [sic]Elenchorum Quaestiones etal.(St.BonaveninOpera Elenchorum Lihrum Aristotelis, II,eds.R.Andrews Philosophica super NY- Washington ture, DC,2004). 7)Aristoteles Boethii: "Siquodnonest VI 1-3,ed.B. Dod (Leiden, Latinus 1975)translatio est,quoniam quodnonestest." p. 11. opinabile

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forexample),forto be theobjectofopinionis to be secun(a chimera, existing In thisfallaciousargument, dumquid, whileto be is to be simpliciter, then, adds is Aristotle inferred. from"tobeX" (secundum quid), "tobe" {simpliciter) i.e. that this confusionarises"becauseof the closenessof the expression, from'to be'" (l67a4-6),8and thisis an because"'tobe X* is butlittledifferent . closeto a fallacyin dictione exampleofa casethatseemsdangerously in thatit exposesthe mereoThe nextexampleis particularly significant is: The the facet of fallacy. example "Supposean Indianto be blackall logical with white but over, respectto histeeth;thenhe is bothwhiteand notwhite" (l67a8-9).9 The sameexampleis said to applyto an Ethiopian(latera recuron thisfallacy).The ideais thata black rentexamplein themedievalliterature man is whitesecundumquid, i.e. withrespectto a particularpartof him, moregenerally, beingblacksimpliciter, namelyhis teeth,whilenevertheless of thatapplyonlyto partsofan objectmaybe said to be attributes attributes in the to with theobjectsecundum (i.e. question), specificpart respect quid . to the objectsimpliciter of the wholewould be attributed whileattributes of these characteristic that a Buridansays Indeed,in the14thcentury, general is relatedto whatis predisecundum is "what is that quid predicated concepts thatthe thusimplying is to itswhole",10 as a part-in-mode catedsimpliciter is crucial. of these concepts reading mereological But forour presentpurposes,thetwo mostimportant examplesgivenby come in theextendeddiscussionin ch. 25 (180al 1-181^1) and are Aristotle trueand falseat and ofthemanwho sayssomething thoseoftheoath-breaker fortheforsources to be thesametime.Theseareindeedthought verylikely swearsto breakan mulationof the firstmedievalLiars.11The oath-breaker oath,and thenbreaksan(other?)oath.A problemwiththispassageis thatit seemsto allowfortwodistinctreadings:one accordingto whichtheoathin theverysameoath,and theotheraccordthatofbreaking questionis precisely this ing to whichthefirstoath is thathe willbreakan oath,not specifically and adds this second defends other oath but oath, reading, (Spade any very 8)Aristoteles esse différant etparum sintdictione eo quodpróxima autem "Videtur Latinus: etnonessequidetnonesse." quidetesse, p.11. 9)Aristoteles albusergoetnonalbus albusestdentibus; cumsitniger, "UtsitIndus, Latinus: 11. est." p. 10)J.Buridan, G. Klima(NewHaven, deDialéctica Summulae CT,2001),pp.554-5: , transi. velsimilestvelvere secundum estquoddictum manifestum "Unde simpliciter quidaddictum totum." sicut itudinarie (ed.Hubien). parsinmodoadsuum n) Cf.Spade, . InsolubiliaAiteiztxxie ofthemedieval "The origins

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Underthesecondreading, thatthisis howmostmedievaisreadthepassage).12 thisexampleis notexactlyanalogousto thetypicalLiarsentencein thatthere to oath 1 itself, as thereis withtheLiar:oath 1 does notrefer is no circularity butto anyotheroath.However,it is notimplausiblethatat leastsomemedieval authorsreadthispassageunderthe firstreading,namelythatthe oath madeis: 'I promiseto breakthisveryoath'. forourpurposesis thatfromthisAristoIn thispassage,whatis important tleconcludesthatbykeepingone oath (oath 1) but not keepingotheroaths (oath2 forexample,underthenon-self-referential reading),themanis notan secundum he is an r, oath-keeper quid withrespectto oath-keeper simplicite he would have to keepall hisoaths. oath1, butto be an oath-keeper simplicités not become obedient mandoes a disobedient merely by {simpliciter) Similarly, beingobedientonce,eventhoughhe maybe saidto havebeenobedientsecundumquid (180a35-¿2). This suggestsa quantificational readingof secundum to would statements and (affirmative) correspond simpliciter simpliciter. quid secundum statements while(affirmative) universal quid would quantification, this While existential to natural, very readingdoes quantification. correspond distinction not applyto all the caseswherethe secundumquid / simpliciter that cases of attributes in ch. Aristotle 25 holds;later applyto somepresents , butnotto eachofitsinstancessecundum quid (180b13-14): thingsimpliciter frombeingnot a thing,thoughgood absolutely, "Thereis nothingto prevent and or to a to a man, man, beinggood yetnotgood particular particular good nowor here."13 afterthe oath-keeper example,Aristotleasks whether"the Immediately sameman can at thesametimesaywhatis bothfalseand true"(180b2-3).14 answerto thisproblem,sayingthat"it is not He does not givea definitive easyto see in whichof the two connectionsthe word absolutelyis to be - withtrueor withfalse."15 rendered (180b3-4) (We shallsee laterthatBradwardinedoes havean answerto thisproblem.)But Aristotleadds thatit is thoughtrue possibleforsomething(a proposition)to be falseabsolutely, but not true in some particular i.e. for it to be true secundum respect, quid 12)Cf.Spade, Insolubles §1.3. ,3)Aristoteles aut "Nichil estbonum huicnonessebonům, Latinus: quodsimpliciter prohibet velnoninhocbonum." huicquidem bonum sednonnunc 50. p. 14)Aristoteles eundem simul etverum Latinus: "Similis autem ratio etdeeoquodestmentiri esse." p.50. 15)Aristoteles Latinus: "Sedquianonestfacile utromodoquisassignet simpliciter inspicere, essevelmentiri, difficile videtur." verum 50. p.

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. It is a tellingfactthatno mentionis madeoftheconverse, thatis, simpliciter thatsomething can be truesimpliciter whilebeingfalsesecundum quid, andwe shallsee laterthatBradwardine willindeedtreatthelattercase as impossible and theformer as possible(agreeingthuswithAristotle on theformer). The idea hereseemsto be thefollowing: takethetricky statements oftenmadeby politicians.While in mostcases thereis some truthto whattheysay,such statements areoverallfalse,i.e. falsesimpliciter , whilenevertheless beingtrue in somerespects, i.e. secundum quid. 3. Insolubilia-SolutionsBased on secundumquid a rangeoftextsdealingwithinsolubilia in thepre-Bradwardine Spadeaddresses He saysthathislistis notmeantto be exhaustive, butit is certainly period.16 of the insolubilia literature of this His list contains representative period. fifteen of which twelve connectionwiththe items, presenta director indirect . Manyof thesetextsareliteralcomments fallacysecundum quid etsimpliciter on theSophistici Elenchi . In , othersarecollectionsofquestionson theElenchi otherwords,theinsolubilia literature ofthisperiodis overwhelmingly evenif notunanimously markedbyitsconnectionwiththefallacysecundum quid et simpliciter. What seemsto makeSpade questiontheconceptualkinshipbetweenthis and solutionsto insolubilia is thefactthat"manyofourauthorsusethis fallacy had in mind."17 He adds that"the fallacyin waysquiteunlikewhatAristotle secundum et thus became a kind of authoritative framefallacy quid simpliciter workthatwasimposedsomewhatartificially on quitediverseattempts to solve theparadox."18 to supportthisaccusaSpadedoesnotreallygiveus arguments tionof artificiality; he is apparently convincedthatthedissimilarity between theoriginalconceptualframework of thefallacysecundum et quid simpliciter and itsusesin theinsolubilia literature is in factself-evident. whatneedsto be done to questionSpades claimis to showthat Therefore, thereis no suchdissimilarity, or in anycase notin a fundamental way.Medieval uses of thefallacyframework in particular, and of Aristotelian logicin are indeed characterized of concomigeneral, by thisintriguing relationship tantsimilarity and dissimilarity: whileessentially inspiredbytheoriginalAris16)Spade, 'Fiveearly theories'. 17)Spade, 'Fiveearly theories', p.32. 18)Spade, 'Fiveearly theories', p.33.

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wentbeyondtheseideas and totelianideas,themedievalauthorsinvariably to theoriginal Whether or not own twist. theyremainfaithful gavethemtheir that is byand largea matterofthedegreeofsimilarity framework Aristotelian one requiresin orderto passthejudgmentoffaithfulness. ourclaimthat,whilecertainly Now,in orderto substantiate goingbeyond theoriginalusesof thefallacysecundum , thereis neverthequid etsimpliciter betweenthisfallacyand themedieval lessconsiderable conceptualsimilarity insolubilia usesofit,we shallexaminethreedifferent waysin whichthefallacy Thevery in to treat Liarsentences. was order et used secundum quid simpliciter usesof thesamefallacyforthispurposeindicates factthattherearedifferent as we haveargued,and notthateachof thatit is indeeda flexible framework, fromAristotles a departure themis necessarily originalideas. In fact,in thepassagescommentedupon in theprevioussection,Aristotle theories. morethanfull-fledged is rather sketchy, puttingforward suggestions while false be secundum true He suggests thata proposition may simplicquid themedievalauthorswillthen iterbutdoesnotdevelopthispointanyfurther; and theywillalso investigate whyand with applythisidea to Liarsentences, . false is true secundum but what a Liar sentence to simpliciter respect quid Different answersto thesequestionsare thenproposed,and one cannotsay seemednotto had in mind",as Aristotle thattheyare"unlikewhatAristotle or in any havethatmuchin mindwithrespectto thisparticular suggestion, fromthetextalone. casenothingthatcan be gathered wayto applythisfallacyto theproblem,given Perhapsthemostintuitive withLiarsentencesis thattheyseemto be trueand thatwhatis problematic is to considerthepossibility falseat thesametime(whichis counterintuitive), secundum of attributions of truthand falsity combinations of different quid considersfourpossibiliSimonofFaversham to a proposition. and simpliciter it maybe and falsesimpliciter, ties:theLiarsentencemaybe truesimpliciter be secundum false secundum it true truesecundum and quidand quid' may quid the and . He dismisses or false secundum true falsesimpliciter, simpliciter quid to be truesimpliciter and falsesimfirst two:it is impossiblefora proposition if secundum and false secundum and it were true quid quid, itwouldbe pliciter, an ambiguousproposition(multiplex),whichit is not. He does not really on why but givescompellingarguments argueagainstthefourthpossibility, ' . It thethirdis thecase: dicofalsumis truesecundum quid and falsesimpliciter becauseit signifies otherthanthingsare;19but it is true is falsesimpliciter 19)Simon . . . quamsit Libro Elenchorum ofFaversham, ,p. 167:"aliud Quaestiones significai super inre".

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secundum quid becausewhoeversaysthathe saysthingsareas he saystheyare falseandindeed andtheLiarsentencesaysthatitsayssomething speakstruly,20 false. itsayssomething to solveinsolubilia Anotheruse of thefallacysecundum quid etsimpliciter and concernedtheuse of oftheoriginalframework was in facta modification with respectto supposition. the conceptssecundumquid and simpliciter ' whichconsistedin knownas restriction thiswas thestrategy Broadlyspeaking, in term case self-reference: forexamof a of the restricting supposition given L in for virtueof 'false could not in L 'This sentence is : false, supposit ple, cast not all defenders of restrictio Bradwardine21 beinga partofL. As notedby itin termsofsecundum (Burleydid not),butsomedid,such quidetsimpliciter in F: 'egodico as Ockham22and Lambertof Lagny.23 Accordingto thelatter, F onl secundum for (thewhole) y quid',now,iffalsum falsum' falsumsupposits quid, sinceit saysof suppositsforF secundum quid, thenF is truesecundum itselfthatit is false,and indeedit is false(sincefalsumsuppositsforF secundumquid). However,Lambertinvokestheprincipleaccordingto whichthe partcannotsuppositforthewholeto claimthatfalsumcannotsuppositfor thatdoes notobtain,namelythatit F simpliciter, therefore, .Fsayssomething . The restrictio itis falsesimpliciter is false,and therefore approach,castin terms 24or not,was indeed et of secundum verypopularforquite quid simpliciter addressedagainstit byBradsometime,in anycase untilthesharpcriticism wardine. but Scotus Favershams, Finally,Scotus'solutionin somesensesresembles actus the between distinction a theoretical introduces namely sophistication, and actusexercitusa distinction widelyused in contextsother significatus

20)Simon sicut Libro ofFaversham, Elenchorum, Quaestiones p. 167:"quidicitsedicere super verum dicit." dicit, 21)T. Bradwardine, Texts andTranslations, Insolubilia Leuven, , ed.S. Read(DallasMedieval des inM.-L.Roure, 'La problématique textis found butunreliable 2008),§2.2.(Anearlier de del'édition destraités duXIV',suivie insolubles au XIIIesiècleetau début propositions du d'histoire doctrinale etlittéraire Archives W.Burleigh etTh.Bradwardine', W.Shyreswood, 205-326.) Moyen Age37 [1970], 22)SeeSimmons, andtheLiar , p.90. Universality 23)Lambert IlMentitore e ilMedioevo from hisLogica Extracts ofAuxerre. , inL. Pozzi, (Parma, Lambert of Lamberts edition a but unreliable 1 There is also 12-115. 1987), Logica'. complete pp. Lorica ofAuxerre, , ed.F.Alessio (Florence, 1971). 24)Indeed, inquite with fits ofsecundum themereological nicely interpretation quidetsimpliciter - seeSimmons, andtheLiar ofsupposition theideaofrestriction , §5.2.2. Universality

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- to accountforthequid withrespect as well25 literature thantheinsolubilia . to whicha Liarsentenceis truesecundum quid, whilebeingfalsesimpliciter ofScotus'solutionis to showthatthesecundum The interest quidetsimpliciter canbe combinedwithotherconcepts,in particular framework conceptsdetersimand/or/not secundum is said in which quid something miningtheaspects to Scotus,in thecaseof !egodicofalsum'theactussignificatus According pliciter. in thiscasetheactofsayinga falsehood, iswhatis signified bytheproposition, is whatis accomplished whiletheactusexercitus bythespeaker(itsperformaand indeedhe says Thespeakersaysthathe saysa falsehood, tivedimension).26 thisproposia trueactusexercitus.17 thushe performs a falsehood, Therefore, butitis false actus exercitus to the with i.e. tionis truesecundum , , respect quid is false.28 it that what of the it is a is, false', , because signifies sign simpliciter matter.Spade of Scotus solutionis stilla controversial The interpretation for distinction et of the secundum the quid simpliciter downplays importance as distinction / actus exercitus actus the and Scotus,29 interprets significatus more it But seems on self-reference".30 to somekindofrestriction "committed naturalto view the idea thatmorethan one act is involvedin assertinga propositionalongthelinesof Aristotles(dis)obedientman: ifhe obeysone quid in thesamewaythat specificcommand,he is merelyobedientsecundum is trueonlysecundum to a trueactusexercitus thatcorresponds a proposition / similar to theactusexercitus a distinction when Moreover, mentioning quid. it among classifies Bradwardine in his treatise,31 distinction actussignificatus 25)SeeG. Nuchelmans, inMedieval SemanActus Exercitus/ Actus 'TheDistinction Significatus ed.N. Kretzmann inMedieval inMeaning andInference 1988);I. (Dordrecht, tics', Philosophy, danslessophismes etactus actus exercitus entre 'Ladistinction Rosier, grammaticaux significatus andGrammar inMedieval in textes , duMs.BNlat.16618etautres Logic Sophisms apparentés', auXIIIesiècle etlasémantique comme acte.Surlagrammaire Laparole ed.Read;andI. Rosier, 1994),chap.5. (Paris, 26)Onecouldillustrate If contradictions. ofother with thisdistinction performative examples to is the actus else someone and asks'Isthere someone 'No', there?', replies significatus anybody somethere isindeed istoindicate that exercitus buttheactus there isn't there, anybody saythat - again actus exercitus. buta true a false actus there body significatus 27)"Etquidam circa actum dicendi secundum quid,quiavereexercet ponunt quodestverus Librum Elenchorum 53 falsam." orationem 514, Aristotelis, 14-15). Scotus, Quaestiones q. (p. super 28)"Quodautem falsa dicitur sitfalsitas quiaestsignum patet perhocquodoratio simpliciter, Scofalsi." etestsignum cumnihil Sedhaecesthuiusmodi falsi. dixerit, prius 'egodicofalsum', Elenchorum Librum Aristotelis, tus,Quaestiones q. 53(p.514,8-10). super 29)Hementions text inInsolubles inthemain ina footnote rather than itonly §2.3. 30)Spade, Insolubles §2.3. 31)Hedistinguishes Insolubilia : Bradwardine, dicere exercitum from dicere §5.8. conceptum

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thedistinguent es,i.e., thosethattryto solvetheLiarparadoxbysayingthatit should be distinguished, thatit is proneto morethanone reading.Bradwardinereproaches thedistinguentes fornotsolvingtheinsolubleaccordingto thefallacy secundum et quid simpliciter (eighthandlastopinionin Bradwardine Insolubilia ch. It is had Scotusin ) ( 5). unlikely, though,thatBradwardine mindin thispassage,as his description does notfitin wellwithScotus text; Scotushimselfrecognizesthatusingthe actusexercitus vs. actussignificatus distinction withrespectto Liarsentencesis nota theoryofhisown creation, - sinceScotus so Bradwardine to otherusesofthedistinction maybe referring obviouslyintendshis solutionto be relatedto the fallacysecundum quid et . simpliciter In sum,thefactthattheseauthorsall use theconceptssecundum quid et and yet presentquite different accountsof insolublesdoes not simpliciter to theoriginalsecundum mean,we takeit,thattheirsolutionsarenotfaithful framework. are all variations of Aristotle's They quid originalidea thatsome be true secundum while false . propositions may quid simpliciter 4. Bradwardineand theLiar Thomas Bradwardine was a RegentMasterin Artsat Oxfordin the early 1320s.It wasat thistimethathe composedhislogicalmasterpiece, De Insolu" bilibus Insolubiliamagistři Thome , as testified bytheMadridms.: Expliciunt de Bradwardyn de angliaregentis OxoniiP2 Afterfivechapterssurveying and other current of the that insolubles,primarily of dismissing eight diagnoses therestringentes terminorum no of (that termcan standforitselfor anything whichit is part),Bradwardine his own,apparently novel,diagnosis, presents setout lucidlyin a proofofhisThesis2 {secundaconclusio on the ), established basisoftwodefinitions and sixpostulates: Ifsomeproposition itself nottobetrue oritself tobefalse, itsignifies itself tobe signifies true andisfalse.33

32)Madrid, Bib.Nov.Univ. MS 105f.37rb; 'Ockham andsome MertoCent., J.A.Weisheipl, Medieval Studies 30(1968),163-213, theMSas"now lost". nians', p. 190describes Fortunately, itisstill tobefound intheHistorical oftheComplutense inCalleNoviciado Library University inMadrid. 33)Bradwardine, Insolubilia senonesseveram velseesse §6.4:"sialiquapropositio significet seesseveram etestfalsa." falsam, ipsasignificai

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it conin detailand at length.We can summarise is articulated His argument as follows: cisely SupposeA saysofitselfthatit is nottrueor thatit is false(and so nottrue, thatas Q, and supmore:abbreviate byPostulate1: Bivalence).It maysignify is one signifying 1 true Definition Then true. A is not ("A proposition by pose its trueor either that it not as are signifies, is, onlyas thingsare"),things not-Q.So if^4is nottruetheneithernot-QorA is true,in otherwords,if^4is thatA is nottrueand Q is nottrueand Q thenA is true.But byhypothesis, folwhatever So byPostulate2 ("Everyproposition whatA signifies. signifies A So is true. thatA itself A signifies lowsfromwhatit signifies"), (at signifies least)thatA is trueand thatv4is nottrue.Butthatconjunctionis impossible, mustfailto obtain.Hence,byDefinition1 again,A A signifies so something Bivalence is nottrue,and so by (Postulate1),A is false. a numberof stepsin theargumenthere,whereBradWeve runtogether wardineadducesPostulates 3-6, Definition2 and Thesis1. We'vealso applied of Postulate2, whichplaysan a strongdose of charityto theinterpretation essentialrolein theproof.Whatwe actuallyreadin themss.is: orabsolutely offact asa matter ormeans every signifies Every proposition or of fact a matter from it as which follows absolutely.34 thing theproofofThesis2, has to rewrite and accordingly Spadetakesthisliterally,35 and othersneeda makesareredundant claimingthatsomestepsBradwardine fromit" (the follows a [proposition] new principle,that"whatever signifies Princi'Bradwardine the Bradwardine 'Converse Principle',CBP), matching followsfromit."Spade ordenoteswhatever signifies ple',BP: "A [proposition] ButevenBP leadsto for Bradwardine.36 a is disaster that CBP to show on goes the about standard the consider For Z, whichsaysof Liar, reasoning paradox. itselfthatit is nottrue: sobyreductio , areasitsaysthey Thenthings L istrue. are,soL isnottrue; First, suppose L isnottrue. as areindeed then L isnottrue that (aswehavejustproved), But,secondly, things given L is true. Contradiction. so L saysthey are, 34)Bradwardine, utnuncvelsimsivedénotât Insolubilia §6.3:"Quelibet propositio significai vel istam ut nunc ad omne simpliciter." pliciter' quodsequitur 35)Spade,Insolubilia ofsignification s theory andBradwardine , p. 120. 'Insolubilia 36)Spade, ofsignification s theory andBradwardine , pp.128ff.

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is to block the second move here.By Bradwardinesdecisivecontribution Definition1, it is notenoughforL to be truethatL notbe true.Thingsmust as L saystheyare,and byThesis2, L also saysthatL is true.Buton be wholly mustprovethatif^4 oftheproofofThesis2,37Bradwardine Spades rewriting is nottruethenA is true,to applyBP (and concludeûiztA saysthatA is true). Butthatlastconditionalis all thatis neededforthesecondlegofthestandard thatL is not leg (acceptedbyBradwardine) proof- havingshownin thefirst L is true. thatconsequently true,to landin paradoxbyinferring 2 Whatwe needto do, then,is see howBradwardine actuallyusesPostulate 'if A is is not it in his proof.The conditionalto whichhe applies (see above) whatever elseA mightsay,whichwe trueand Q thenA is true. Q abbreviates areaboutto discoverincludesA s beingtrue.So all we haveis thejejuneconto ditional:'ifA is not trueand A is true(etc.),thenA is true'.Thatsuffices the concludethatA saysofitselfthatit is true;butit is notenoughto retrieve s solutionworks secondlegoftheproofofparadox.Thatis whyBradwardine as Spade claimsit does. and does notcollapsein theusualcontradiction, BP. What it uses is the morecautious Bradwardines proofdoes not use whateverfollowsfromwhatit signifies. signifies principle:everyproposition ofThesis2 in manyvariantsin later the demonstration Bradwardine repeats is the time this and principlehe uses.Sadly,he was uncharacchapters, every ofPostulate2, butcharity laxin hisstatement (is therean interpreteristically to hisactualproof(s) tationwhichdoesnotlandhimin paradox?)andattention but effective more cautious him the to of attribution principle. support 5. Bradwardine'sTheoryof Consequence followsfroma It speaksof"whatever closerexamination. Postulate2 warrants thatwhat mean? It claims What this ' does vel ut nunc simpliciter proposition This is an that in factalreadysignifiedby does so followis proposition. is closedunderconseextremely strongclosurecondition,thatsignification theclaimthatmuch makes nunc ut In fact, consequences including quence. true of the use allows nunc ut For merelycontingently consequence stronger. Then from ass is an that running. only Suppose,e.g., enthymematic premises. 'Everyman is running'we can infer'Everyman is an ass' ut nunc, bya syllogismin Barbara.The premiseis possibleand theconclusionimpossible.Yet

4Insolubilia 37)Spade, ofsignification andBradwardines , p. 122. theory

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Aristotle notedthattheimpossiblenevervalidlyfollowsfromthepossible thatis what possible'means.38 of thenotionof ut nuncconsequencecomesfroma treatise Thiscriticism The attributed to Bradwardine. on consequence(' Textusconsequentiarum) adduces,but is unmovedby,all thearguments editor,Niels Green-Pedersen, thattheworkis byBradshouldruleout thepossibility which,put together, wardine.The treatiseis a sustainedcritiqueof Ockhams SummaLogicae , s associationwithBurleys school,givessomeplauwhichgivenBradwardine to himin one ofthetwomss.in whichitsurvives. to itsattribution (It sibility is anonymousin theother.)But in thecourseof thatattackon Ockham,its " dismissesutnuncconsequenceas mistaken:Nihilestconseauthorrepeatedly 9 utnunc in Bradwardine s treatise on insolubles, quentiautnuncP In contrast, Bradwardine s is central and proof pervasive.Consider,e.g., consequence of Thesis1 (primaconclusio ) in ch. 6, whichhe will adduce timeand time again: affirmation or hasmany ordenotes whose extreme Every proposition supposita signifies andifonly denial forsomeofthem, one,forit.40 ' 'A is 2?, he says,wherethetermÄ has manysupTake sucha proposition, posita: toallitssupposita, areequivalent asa A andoneofthese', Thenthetwoterms, pointing ofthat ofthem addsdenial orexclusion oranything matter offact andneither (utnunc), 'A isÏÏ and'Oneofthese areequivalent: andsothese twopropositions kindtotheother, anaffirmation for oneofthesupposita ofA,andhence isffsignifies isB>;and'Oneofthese asa matter of A and'this A orthat, sotoodoes(AisB. Again, andsoon areequivalent A orthat areequivalent asa matter offact: "This andsoon, fact. Hencethese propositions isB' and'AisB' 41 38)An.Pr.I,32al9-20. 39)N.J.Green-Pedersen, onOckhams Doctrine ofconsequences: anedition , 'Bradwardine(P) 42 (1982),85-150,p.93§8. Grec etLatin Cahiers del'Institut duMoyen-Age 40)Bradwardine, multa habet Insolubilia cuiusextremum §6.4:"Quelibet supposita propositio et si sive dénotât affimationem vel unicum istorum, proisto." negationem proaliquo significai 41)Bradwardine, Insolubilia istiduotermini convertuntur utnunc: a etaliquod §6.5.1:"Tunc illorum omnibus suissuppositis, etneutrum additnegationem necexclusionem demonstratis a estb etaliquod nechuiusmodi isteduepropositiones convertuntur: istorum alium, super ergo est affirmatio etin estb,etperistam: istorum b, a, aliquod significatur proaliquo suppositoergo ista:a estb.Adidem istitermini convertuntur utnunc: a ethoca velilludetsicdesingulis. Ergo etistepropositiones convertuntur hoca velillud, etsicdesingulis estb,eta estb." utnunc:

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And similarproofsrunthroughsucceedingchapters. in thetwo betweenthedoctrines notesthisincompatibility Green-Pedersen ut nunc central how works,thoughwe thinkhe failsto appreciate consequence thattheirsupposedcommon . He suggests,therefore, is to the Insolubilia on consequenceis an authorchangedhismind.42 Perhaps,he says,thetreatise endorse to came later Bradwardine and consequenceutnunc. This earlywork fortheInsolubiliais an earlyworktoo.Weisheipl,notingthe is a non-starter, " as regentis of Bradwardine Oxonie' mentionedabove, Madrid description extendsit to 1326. But Ockthisperiodto 1321-4.Dolnikowski43 attributes hams SummaLogicaewaswritten Consequentiarum onlyin 1323,so theTextus and it can be no earlierthanthat.The twoworksare almostsimultaneous, Bradwardine. is thatthe Textus seemsveryunlikely Consequentiarumby ofutnuncconanswersthecriticism In fact,in theInsolubiliaBradwardine : Consequentiarum sequencefromthe Textus thatonlyan asswere be madea captious willbychance There supposing objection, a manisanass,and therefore a manissitting, bevalid: would inference this . . . then seated, hence soistheconclusion.44 ispossible, thepremise he says: Butthisis readilyanswered, theconcluoffact asa matter because offact, asa matter isvalid inference this that Itistrue A manis offact: asa matter areequivalent Forthese inthepremise. sionisunderstood for so on and or that andA manisthissitter sitting'.45 things sitting ruleappliesonlyto absoluteconsequence{conseIn fact,he says,Aristotle's shows. as thiscounterexample et quentiabona simpliciter),

42)Green-Pedersen, ofconsequences', Doctrine onOckhams ťBradwardine(?) p.88. 43)E.W.Dolnikowski, inFourteenthVision Time anda a View Bradwardine: Thomas ofEternity of 4. 1995), (Leiden, p. Thought Century 44)Bradwardine, forte instabit conclusioni "Huicautem cavillator, Insolubilia §6.5.3-4: suppoestbona:homoestsedens, asinus nensquodtantum sedeat, ergo (.. .) tuncistaconsequentia etconsequens." estpossibile, antecedens estasinus, homo ergo 45)Bradwardine, estbonautnunc, estquodistaconsequentia Insolubilia quia §ad6.5.4:"verum estsedens homo utnunc: convertuntur Istaenim inantecedente. utnunc intelligitur consequens sedentibus." velilludetsicdesingulis esthocsedens ethomo

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Bradwardine laysgreatstorebytheclaimthathis theoryis trulyAristotelian. Not onlydoes he dismissothertheories(namely,twoof fourversionsof the , thatthepartcannotstandforthewhole,and that theoryof therestringentes of thedistinguent in act fromitscompletion) theutterance es,distinguishing fornot assigninga fallacysecundum et to theinsolubles.He quid simpliciter claims that he is out Aristotle's true repeatedly spelling diagnosis.Thiscomes in ch. 7, in an extendedtreatment out mostforcefully of the problemof revenge. The term'revenge' was coinedbyR. Martin46 to describethepuzzlingsituationwherea theorist wantsto describethe Liar sentence(forexample)as ornottrue,orwhatever, whenthesentenceitselfappears false,ormeaningless, to sayjustthat,thatit is false,meaningless orwhatever. Ifthetheorist is right so to describetheLiar,and is speakingtruly, does it not follow that the why Liarsentenceitselfis true,and notfalse,meaningless orwhatever? Thisis thesituationBradwardine setsup in ch. 7. SupposeSocratesutters this: only A: Socrates a falsehood. utters - thatA is falsefolBradwardine wantsto saythatSocratesuttersa falsehood lowsfromThesis2, giventhatA signifies that it is false.But ifthe (ut nunc) diagnosisis truewhenBradwardine saysit,whywas it nottruewhenSocrates said it?Afterall, theirtwoutterances wereexactlythesame- samewordsin thesameorder. The answeris centralto Bradwardines solution:whatSocratessaysis selfbutwhatBradwardine comesto referential, saysis not. Finally,Bradwardine theeleventhobjection: Theeleventh isthis:from theresponse itfollows thatthefollowing objection justgiven, inference isvalid:Socrates utters thisfalsehood, 'Socrates utters a falsehood', so namely, Socrates utters a falsehood. Hencethere is herenofallacy secundum r, quidetsimplicite toAristotle's Elench. onthesolution ofthefallacy secundum 2,inthechapter contrary Soph. itisshown insolubles areparalogisms secundum ,where quidetsimpliciter byhimthat quid etsimpliciter. insuchinferences then there would notbeaninsoluble because it Moreover, isnota difficult isthedefinition ofinsoluble.47 yetthat paralogism, 46)R.L.Martin, Recent onTruth andtheLiarParadox (Oxford, 1984),p.4. Essays 47)Bradwardine, Insolubilia sic:existaresponsione istam conse§7.11:"Undécimo sequitur essebonam: Sortes dicithocfalsum dicitfalsum, dicit quentiam quodestSortes ergoSortes

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morethandoes the Bradwardine's replyto thisobjectionis thatA signifies it fallsunder A is For since is false. self-referential, that equiformjudgment himself Socrates true. it is that Indeed,suppose Thesis2 and so also signifies reasonsas follows,in hismind:he apprehends justtwopropositions: isapprehended B: Thisfalsehood bySocrates (intelligitur) to thisproposition: referring isapprehended C: A falsehood bySocrates If Socratesis temptedto inferC fromB, he will have committeda fallacy thatC is ForB entailsonlypartof C: C signifies secundum quid etsimpliciter. B but bothtrueand false(and apprehended onlythatC signifies bySocrates), is falseand apprehended quid but not by Socrates.So B entailsC secundum We nowseetheanswertoAristode's puzzle(180¿3-4) in §2 above. simpliciter. B in so faras it saysthatit is true from follows so C is B is truewhileC false, butnotin so faras itsaysthatit is false. discussionin ch. 11 of "merelyapparent Finally,considerBradwardine's to insolubles".Theymightappear be insolubles,but theirsolutiondoes not so theyare notrealinsolubles. turnon a fallacysecundum quid etsimpliciter, to,and argue: Forexample,supposenothingis referred to isreferred Nothing Sothisisnotreferred to, but to Socrates.Clearly,thepremisewas truewhenitwas uttered,48 referring was complete.So theconclusioncan never once theinference it was falsified conclusionis an the even be true, premisecan be. Bradwardine's though some Buridan to yearslater: insightwhichhas beenwidelyattributed 2° Aristotelem secundum falsum. quodestcontra quidetsimpliciter, Ergoibinonestfallacia eum ubi et secundum fallacie solutione de per apparet simpliciter, Elenchorum, quid capitulo consetuncintalibus Preterea secundum sintparalogismi quidetsimpliciter. quodinsolubilia diffinitione est de tarnen difficilis est ibi non insolubile nonesset quod paralogismi quia quentiis insolubilis." 48)Bradwardine, estfalsa, Insolubilia consequens §11.6:"Dicendum quia,quando quodminor verum fuerit licet inconsequente, falsificatur illius est,antecedens prodemonstrate consequentie anteprolationem consequentis."

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towhether itcanor orimpossible a proposition isnotsaidtobepossible Because according canbeorcannot beasissignified ofwhether cannot betrue, butonaccount byit.49 things 7. Conclusion Thus,as Bradwardine says,an insolubleis "a difficult paralogismsecundum some act on itselfwitha from the reflection of et resulting quid simpliciter A fallacysecundum occurswhen determination".50 privative quid etsimpliciter a fallaciousinference is madefroma premiseto a conclusionwherea property is wronglyattributedto somethingsimpliciter whereas,fromthe premise ofthisproperty to thethingcan be alone,onlythesecundum quid attribution in To solvetheinsolubleswhatwe needto do is blockthereasoning inferred. what is in effectthe problemof the secondleg of the standardargument, havingshownthatthepuzzlecaseis false,we mustshowwhyitdoes revenge: not followfromthat,thatit is true.The answeris thatit is truein part,but . onlyin part,and partialtruthis nottruthsimpliciter mustobtain- things it signifies For a propositionto be true,everything as itsaystheyare.Truthis a limitorpeakofsuccess;anyfalling mustbe wholly A proposition is trueifthingsareonlyas it saystheyare; offfromit is failure. ifthingsarenotso in anyrespect, it is false.Thisis why,accordingto Aristotle's undevelopedhunch,it is possiblefora propositionto be truesecundum (butnottheotherwayround);thishappenswhen quidwhilefalsesimpliciter at leastone ofthethingsit saysobtains,butnotall ofthem,whichmakesita propositiontruesecundumquid (withrespectto the particularthingthat A Liarsentenceis precisely a proposition ofthis obtains),butfalsesimpliciter. kind,and thecause of itsparadoxicalnatureis thefallaciousmovefromits it is onlyits truthsecundum to its truthsimpliciter, falsity quid thatcan be that it is false . thus Hence,Spades claimthat derived, simpliciter confirming withrespectto insolubilia arepurelyhonorary seems invocations ofthisfallacy fundamentally ungrounded.

49)Bradwardine, Insolubilia nondicitur velimpossibilis §11.6:"quiapropositio possibilis quia essevelsicimpossibile estessesicut velnonpotest essevera, sedquiasicpotest potest significatur Cf.Buridan, Summulae deDialéctica , tr.9 (.Sophismata Conclusion, ), ch.8,'Third peristam." 954-5. pp. 50)Bradwardine, estdifficilis Insolubilia secundum §2.1: "insolubile paralogismus quidetsimexreflexione alicuius actus secumdeterminatione pliciter supra privativa proveniens."

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Vivarium 46 (2008)192-221

Theory of materia prima in Marsilio Platonic Theology*

Ficino's

JamesG. Snyder TheCUNYGraduate Center Department ofPhilosophy, Abstract Thispaperis an examination ofthetheory ofmateria century primaofthefifteenth Platonist Marsilio Ficino.It limits itsdiscussion ofFicino's to theontological theory andepistemic status ofprimematter inhisPlatonic Ficinoholdsa "robust" Theology. of matter that makes two fundamental assertions: First, theory prime primematter exists of and it at least in Ficino's form, second, is, independent principle, intelligible. in of matter is this with framed a discussion of the theory prime paper divergence overthenature ofprimematter. philosophers amongScholastic Keywords Marsilio Platonism Ficino,matter, primematter, I in hisphilosophical thePlatonicTheology (1482), the Frequently masterpiece, RenaissancePlatonistMarsilioFicino (1433-99) speculatesabout the existenceof an utterly formless and passivemateriaprimathatfunctions as the of all material "indifferent Ficino asserts that receptacle" things.Although matter is devoid of all and his denial that the human prime quality, despite mindcanhaveanydirectand privileged ofit,he doesnot,forthese knowledge reasons,concludethatprimematteris nothing,or some fictiveabstraction thathas no realityapartfromthehumanmind,as Aristotle had likelymainFicinoheld in the PlatonicTheology tained.1To the contrary, whatmaybe *' I wishtothank Catherine Wilson andEmily Michael forcomments ondrafts ofthispaper. inMiamiatthe2007annual Anearlier version ofthispaper waspresented conference ofthe Renaissance ofAmerica. Society l) Aristotle, 7.3,1028b-1029a28. Metaphysics, Brill 2008 ©Koninklijke NV, Leiden,

DOI:10.1163/ 156853408X255909

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calleda "robust"theoryof primematter.On the robustview,primematter in a modeofexistencethatbelongsuniquelyto thosethingsthat participates fromnothing,and it existsin sucha waythatit arecreatedby God directly formsof all possessesin a confusedand tumultuousstatethe rudimentary materialthings.The existenceof primematter,accordingto Ficino,is not offorms, ofanything else,suchas theactuality dependentupon theexistence had previously as some philosophers or on form-matter argued. composites, The robustnessof primematteralso has epistemological implicationsfor infinite that the confusionof Ficino Ficino.In thePlatonicTheology , suggests if mindwill in even the human intelligible, primematteris,at least principle, orwithclarity and distinctness. neverknowit directly, of thebasicontologicaland epistemicstatus Thispaperis an examination . The conceptoccupiesa promiofprimematterin Ficinos PlatonicTheology nentand variedpositionin the largerargumentof the PlatonicTheology, servingat one and thesame timeas a premisein Ficinosargumentforthe of the of the materialism of the soul, as partof his refutation immortality " " the impiiduo Epicurusand Lucretius(amongothers),and as partof groundworkforhis vitalisticnaturalphilosophy.In this paper Ficinos theoryis theoriesof primematterthatwere framedwitha discussionof thedivergent in thethirteenth heldbyDominicanand FranciscanScholasticphilosophers The divergence concernedtheontologicaland episand fourteenth centuries. ThomasAquinas,who belongedto theDominitemicstatusofprimematter. can order,arguedthatprimematterdoes not existwithoutform,and is suchas on itsown.SeveralFranciscan philosophers, completely unintelligible a greater JohnDuns ScotusandWilliamofOckham,attributed degreeofrealFicinos to matter than did.2 theoryin thisway ity prime Aquinas Framing servestwo purposes:First,it opens up a way of approachingthe theoryof thegeneraltheoretical , and to determine primematterin thePlatonicTheology s existence the commitments on primematter and intelligibility. Approaching in this is because his and of matter theory, helpful theory prime way especially in hisphilosophy, haveremainedmostly thegeneralfunction thatitperforms use ofthe unnoticedand unexamined.3 Also,althoughFicinomakesfrequent 2)SeeThomas Lectura Deprincipiis Chs.I andII.AlsoseeJohn DunsScotus, naturae, Aquinas, 2. 12;andOpusOxoniense alsoa Franciscan, forthe , lib.II,d. 12,q. 1. Bonaventure, argued also ofprime matter. SeeInII. Sent however, .,d. 12,art.1,q. 1,2 and3. Bonaventure, reality helda doctrine ofseeds which Scotus andOckham denied. 3)While Ficino sviews ofprime andcorporeal matter haveremained forthemost unexampart tworecent articles havetouched onaspects ofit.SeeHiroshi ofSeeds and ined, Hirai, "Concepts

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, he nowherestraightforconceptof primematterin the PlatonicTheology of his theory reveals features Ficino of it. his view defends Instead, wardly the contexts across in and variousphilosophical eighteenbooksof elliptically whereFicino standson the the PlatonicTheology. Second,by determining to MedievalSchohis of status and matter, relationship ontological epistemic lasticismis complicated,if not clarified.Ficino scholarshave traditionally arguedthatThomasAquinasexercisedthe mostpowerfulinfluenceon the andithasbeenarguedandassumed ofFicinos philosophy, Scholasticelements Thomistic.4 thatFicinos theoryofprimematteris fundamentally Recognizing the beliefthatFicinowas a theories undermines of Scholastic the plurality of Whilea discussionofScholastictheories Thomistwhenitcomesto matter. on the does not exhaustFicinos philosophicalinheritance mattercertainly it in thiswayis a convenient issue,approaching pointof entryto examining elements on primematter. commitments Ficinos generaltheoretical Certainly Ficino argues of the Neoplatonictraditionof Plotinusare also significant. he departs withPlotinusthatprimematteris completely however, impassible; to and entitative a robust in fromPlotinus attributing reality primematter. oftheunderlying An examination conceptofprimematterthatis at playin Platonistin factpartedways revealsthattheFlorentine thePlatonicTheology of withThomasAquinas when it came to the existenceand intelligibility those in with primematter.In theend,Ficinos theorysharesmore common an entitative and theologianswho attributed realityto prime philosophers thatFicinogivesfor To thisend,thispaperexaminesthearguments matter. that in thePlatonicTheology s existence , and thetwodistinctions primematter to graspingthebasics thework,whicharerelevant Ficinomarksthroughout betweentheabsoluteand particular of his theory:First,Ficinodistinguishes where modesofexistence; and,second,betweenprimeand corporealmatter, the the latter in the absolutemode of existenceand theformerparticipates HisPhilosophy. Ficino: HisTheology, inMarsilio ; His ofMarsilio intheWork Nature Ficino," with M. Davies(Leiden, V.Rees, and,inthesamevol2002),257-284; , eds.M.Allen, Legacy in ofMatter Mirrors: TheConcept Divine GazesandBloody "Narcissus, Kodera, ume,Sergius corand Ficinos of with deals Neither 285-306. however, article, Ficino," theoryprime directly matter. poreal 4)Seetheintroduction in andThomism Platonism isSacred: TheSecular B. Collins, toArdis inItalian "Thomism Platonic Ficinos Marsilio 1974);PaulOskarKristeller, (Nijhoff, Theology inMedieval NC,1974),29-94;Kristeller, (Durham, Learning ofRenaissance Aspects Thought," andLetters inStudies inRenaissance 39; Ficino andHisCircle," "Marsilio 1956), (Roma, Thought ofMarsilio translations totherecent introduction Hankins' andJames andMichael J.B.Aliens Platonic Ficinos 2001),xi. (Cambridge, Theology

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particular. Finally,the paper concludeswithan explanationof the general functionthatmattertheoryperforms in Ficinos PlatonicTheology , and with on the and motivations thatground speculations philosophical theological Ficinos robusttheoryofprimematter. II The Aristotelian analysisof materialthingsinto theirform,matterand privationwas the dominantframework forconceptualizing materialthingsby Scholasticnaturalphilosophers, and it was notfullyreplaceduntilthedevelIt opmentof modernmechanistic philosophiesin theseventeenth century.5 was also theframework thatMarsilioFicinomostlyinherited fromtheScholasticsand thathe employedin his PlatonicTheology .6 On thisanalysisof materialthings,theformof a substanceis theprincipleof organization, the matterthesubjectin whichtheforminheres,and theprivationis theform thatthethinglacks.The matterofa giventhingis relative to theleveloforganizationthatis underconsideration, since a piece of bronze,whichis not withoutitsown formand matter, servesat thesametimeas thematterof a The mostfundamental statue,whichisyetanotherleveloforganization.7 matter,thatis,thematterthatis thoughtto be beneathall levelsoforganization, has traditionally beencalled"primematter"byphilosophers in boththePlatonicand Aristotelian traditions.8 Prime matter servesas the philosophical 5)Onalternative theories ofmatter intheMedieval seeAtomism anditsPlaceinMedieval period, ed. Robert Aurelien , (Leiden, 2007). Philosophy 6)Foranaccount ofFicino s basicontology, seeMichael s Theory "Ficino oftheFive J.B.Allen, Substances andtheNeoplatonists' Parmenides" andRenaissance Studies 12:1 Journal ofMedieval toFicino s Scholastic seeFicino s "Incipit 1982).Fordocuments (Spring, pertaining background, Tractatus and"Tractatus Marsilii" inPaulOskar Kristellers "Marsilio Ficino Physicus" Physicus andHisCircle," inStudies inRenaissance and Letters Vol. I 60-64 and , (Roma, 1956), Thought ofFicino 74-76.Fora discussion s Scholastic seeJames Plato andtheItalian education, Hankins, Renaissance PaulOskar ,Vol.I (Leiden, Marsilio Ficino andHisWork 1996),271-276; Kristeller, Five Hundred Years Florence andItsUniversity (Firenze, 1987),6-7;andJonathan Davies, After theEarly Renaissance (Leiden, 1998),21-22. During 7)SeeBookI ofAristotle's fora general account ofhisviews onform, matter andprivaPhysics tion. AtPhysics Aristotle howmatter isrelative tothelevel , II.2,194b9, oforganization explains that isunder consideration. 8)SeeRichard s Matter, andMotion: Theories inAntiquity andTheir Sorabji (LonSpace Sequel oftheory ofprime matter don,1988)fora discussion heldbythecommentators onAristotle; alsoseerelevant sections ofVolumes 2 (Physics) and3 (Metaphysics), ofRichard s The Sorabji

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ultimate and itwasthoughtto be conserved in theprocess subjectofall forms, ofsubstantial such as when one element is and change, corrupted a newone is generated. While therewas generalagreementamong Scholasticphilosophersthat materialsubstances haveas theirprinciples formand privation, there matter, was no generalconsensusabouttheprecisenatureofprimematteritself.The Thomistictheorywas not theonlytheoryof primematter.Thereexistedin thethirteenth and fourteenth centuries a plurality oftheories ofprimematter thatwereheld by variousScholasticphilosophersfromdiversetheological ordersand traditions. The different theoriesmadedivergent claimsaboutthe s existence and thedegreeto whichit is intelligible, ifat all. The primematter on the of that one attributed to prime disagreement depended degree reality matter:Is mattera thinand spectralentitythatis dependentupon thereality ofotherthingsforitsownqualifiedand partialexistence, or is it morerobust in its nature,such thatit mayexiston its own, and mayeven be known? ThomasAquinas held somethingalong the lines of the firstposition.He catearguedthatprimematteris a qualifiedentitythatexistsas a theoretical in the of material and as of actual form-matter gory metaphysics things, part he arguedthatprimematteris completely composites.Further, unintelligible on itsown.On theotherhand,philosophers who belongedto theFranciscan - such as Saint Bonaventure, tradition JohnDuns Scotus and Williamof Ockham- generally attributed a greater to primematter than degreeofreality ThomasAquinasdid. assertions aboutprimematter.9 First, Aquinasmadetwodistinctive Aquinas heldthatprimematterexistsonlypotentially on itsown,withoutform,but existsas an actuality onlyon accountofbeingpartofa form-matter composite.10He viewedprimematteras possessinga partialor incompleteexistence

200-600 AD (London, from 2004)forselections Philosophy oftheCommentators Neoplatonic andthecommentators, onprime matter. philosophers, 9)Aquinas makes four basicassertions about inDeprincipiis matter naturae ,and actually prime inother discussions ofmatter. Inaddition tothetwoassertions examined also above, Aquinas for the of matter. Matter is one undifferentiated. matSecond, unity argues through being prime terwascreated from Prime matter isnotgenerated orcorrupted inthe byGoddirectly nothing. course ofnatural butisconserved. Fora general discussion ofThomas viewof change, Aquinas' seeJohn F.Wippel, TheMetaphysical From Finite to matter, Thought ofThomas Aquinas: Being Uncreated and Robert Thomas on Human 295-375; Passnau, 2000), Being (Washington, Aquinas APhilosophical Nature: la, 75-89(Cambridge, 2002),40-45. ofSumma Study theologiae 10)Sententia ,VII.2.1289-1292. super Metaphysicam

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of ofmaterialthings,thatis,on theexistence thatis parasiticon theactuality that to its Prime matter has no act actualform-matter pertains composites. ownessence,and in virtueofwhichitwouldcontinueto existin theabsence naturae ofsomething thatdoes,namely,form.In De principiis , Aquinasconofitself, that"matter existsincompletely cluded,therefore, needingsomething In SummacontraGentiles thesoul morein orderto exist."11 , whilecontrasting withprimematter, Aquinasstatesthat"primematterdoes not remainin act afterthe formsdeparture, exceptin relationto the act of anotherform," whereasthehumansoul does.12When a formis corrupted, then,theprime matterthatwas once its substratedoes not continueto existin actuality, replacesthe earlier accordingto Aquinas,unlessanotherformimmediately one. The qualifiedexistencethatprimematterenjoyson thisviewalso has Second,Aquinasassertedthatprime implications. epistemological significant matteris onlyknownindirectly byan analogydrawnwithsomeformmatter holds that any knowledgeof primematteris in itself composite.Aquinas inconceivable. Whatever accordperfectly knowledgeone has of something, a its which that to comes from definition of form, implied prime ing Aquinas, "cant be knownordefinedas such,butonly[known] matter, strictly speaking, by an analogy"with the matterthat belongsto the ordinaryobjectsof For instance,one reasonsthatjust as bronzeservesas the our experience.13 matterofa statue,so primematterservesas thematterforall levelsoforganization.Concludinghis discussionof primematterin the earlychaptersof

n) Thomas inSelected OnthePrinciples anded. , trans, Aquinas, ofNature, Writings Philosophical 68. McDermott (Oxford, 1993), Timothy 12)Thomas Summa Gentiles F.Anderson contra , Vol.2, trans. Dame, (Notre James Aquinas, 1956),264. 13)Thomas isfollowing OnthePrinciples Aristotle's 71.HereAquinas Aquinas, posiofNature, tionontheepistemic status ofthesubstrate foratPhysics Aristotle 1.7191a8-13. writes, argued "Theunderlying nature canbeknown Forasthebronze istothestatue, thewoodto byanalogy. thebed,orthematter andtheformless before form toanything which hasform, sois receiving theunderlying tosubstance, i.e.the'this' orexistent." nature R.P.HarAristotle, , trans. Physics inTheComplete dieandR.K.Gaye, Works Vol.I, Press, (Princeton 1984), University ofAristotle Thomas on Thomas' onI 326.In TheMetaphysical , Commentary Thought of Aquinas relying Sentences F.Wippel that I,q. 15,a.3,John (d.36,q.2,a.3) andSumma theologiae prime argues matter canalsobeknown ofdivine ideaforprime matter" that isnotdistinct from bya "kind thedivine ideaofthecomposite. Prime matter is known inthiswayinsofar as itis realized with theappropriate form. Asfarashuman areconcerned, mathowever, together beings prime tercanonly beknown andnotinitself. F.Wippel, The John byananalogy, Metaphysical Thought 325-327. ofThomas Aquinas,

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De principiis naturae thencan , Aquinassaysthat"[nļothingactuallyexistent be called primematter."14 PrimematterexistsforAquinas,therefore, in a or thin which is to saythatit is something thatfunctions sense, as qualified theultimatematerialsubstrate ofall things,butwhichdoes notsubsiston its own. Further, in spiteof our best efforts to bringit undersome rational matter must forever remain in obscurity, both to the finite account,prime humanintellect, and perhaps,byimplication, evento themindofGod. The Thomistictheoryof primematterwas controversial in thethirteenth and fourteenth centuries.15 Franciscan and philosophers theologians generally thanAquinasdid. arguedthatprimematterpossessesa morerobustexistence all itsownthatis notdependenton Theyclaimedthatprimematteris a reality the actualityof the form-matter and theyalso compositesforits existence, its ultimate Based on what was understood as arguedagainst unintelligibility. thedubioustheological and philosophical oftheThomistic view, implications suchas JohnDuns Scotusand Williamof Ockhamassigneda philosophers to primematter, greater degreeofentitative reality thereby viewingmatterin morerobustterms.16 TheThomistic threatened view,itwasgenerally thought, Gods omnipotence, sinceit impliedthatGod was impotentto createprime matter withoutform.ItwasalsothoughtthattheThomistic threatened theory Gods omniscience, sinceit impliedthatGod could notknowprimematter. BeforeAquinas,SaintBonaventure ofprime arguedthatthepurereceptivity mattercan be consideredin itselfthroughprivation, thatis,bystripping it of all formit is knownto be an "intelligible darkness"(tenebraintelligibilis ).17 Bonaventure statesthatprimematter"is able to be consideredby the soul Scotusarguesthat accordingto itsown essenceand as whollyunformed."18 matter in exists and not as the that prime actuality, just pure potentiality

14)Thomas OnthePrinciples 71. Aquinas, ofNature, 15)Intheseventeenth for that creation exnihilo isuninMilton, instance, John century, argues SeeChapter VIIofTheChristian Doctrine Milton forhisown"robust" ,where telligible. argues viewofmatter that shares somefeatures incommon with Ficino s view. In TheChristian DocMilton that matter isintrinsically trine, tocregenerally argues goodandwasatonetime prior ation anactual substance that wasconfused andformless. 16)SeeAllan "TheOckhmisit inTheConcept inGreek andMedieval Wolter, Critique," ofMatter McMullin F.Wippel, , ed.Ernán The MetaDame,1965),124-1 46;andJohn (Notre Philosophy , 312-313. physical Thought ofThomas Aquinas 17)Bonaventure, Commentarius inII librum Sententiarum , d.3,p.I,a. I,q. 2.AlsoseeChristoM.Cullen, Bonaventure (NewYork, 2006),45-46. pher 18)Quoted inChristopher M.Cullen, Bonaventure , 46.

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residesin actualform-matter Also,inasmuchas primematteris composites.19 an actuality, ScotusarguedthatGod can havean idea of it. The Dominican view,it was also arguedby Ockham,was also philosophically flawed,since therewas,in theend,no entity thatis actuallyserving as thesubstrate ofmaterialformsat all.20It was therefore that there has to be thought actually somethat is called its over thing "primematter," retaining identity time,and which functions as thesubstrate ofall materialthings. MarsilioFicinoaddresses boththeontologicalandepistemic statusofprime matterin thePlatonicTheology. It is arguedin thesectionsthatfollowthat Ficinos theorystandsin starkoppositionto theThomistictheoryas outlined above. Ficinomakescertainbasic assertionsabout primemattersexistence ofform,and he suggests thatitis in principle in itself, independent intelligible evenifthehumanmindcan come to knowit onlybyan analogywithordiof narymaterialthings,and by a comparisonof the levelsof thehierarchy in At least these two Ficino from therefore, being. respects, diverges Aquinas in hismostbasicunderstanding ofmatter, and insteadalignshimself withthe traditionof philosophers and theologiansthatassertedthe realityof prime matteris philosophically and theologically superior.This traditionincludes notonlytheFranciscanScholasticphilosophers, butalso Plato,Plotinus,the Hermes and pseudo-Egyptian sage Trismegistus, Augustine, amongothers. Ill Scholarshavetraditionally noteda strongThomisticpresencein theScholastic elementsof MarsilioFicinos philosophyand theology, especiallyin his PlatonicTheology as to on Platos dialogues,among , opposed his commentaries otherworks,whichreflect the Neoplatonismof Plotinusand Proclusmore

19)John DunsScotus, inMetaphysicam II,dist.12,quest1; Quaestiones 7,q.5;see OpusOxon. 2 ofRichard K. Cross, ThePhysics TheScientific Context especially Chapter ofDunsScotus: ofa Vision which contains a clear ofScotus' forthe (Oxford, 1998), Theological exposition arguments existence ofmatter, anditsnature; aswellasPeter "Scotus onMetaphysics," inTheCamKing, toDunsScotus Williams , ed.Timothy (NewYork, 2002),15-68. bridge Companion 20)William ofOckham, Summula naturalis inlibros 1.1-15; philosophiae Espositio Physicorum Aristotelis Brevis summa libri "TheOckhamist , 1.15.1-18.7; Cri, 1.3.Allan Wolter, Physicorum André ThePhysics 128-31. William Ockham 114Goddu, 95-107, (Leiden, tique," 1986), of of s Philosophy ofNature," inTheCambridge 118;and"Ockham toOckham , ed.Paul Companion Vincent 1999),147-149. Spade(NewYork,

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It haswrongly beenasserted prominently.21 byArdisB. Collinsthatthetheory ofprimematterthatFicinoheldin thePlatonicTheology is largely Thomistic. Otherinterpreters, such as Paul Oskar Kristeller, have assumedthatFicino helda versionofAquinas'theoryofmatter.In general,detecting a Thomistic flavorto aspectsof thisworkis certainly not withouta strongjustification. One neednotlookdeeplyin orderto findThomasAquinasin thepagesofthe PlatonicTheology , sinceFicinodeclaresthatAquinasis the "thesplendorof inthefinalbook.Elsewhere Christian hespeaksofhimaffectionately Theology" as "ourThomasAquinas."22 ThomasAquinashasalso beena significant partof Ficinos biography, at leastsincetheearlysixteenth TheSummacontra century. Gentiles is thoughtto havehad a roleto playin resolving a spiritual crisisthat afflicted Ficino in the 1450s. Ficinos earlysixteenth-century biographer, GiovanniCorsi,describesa periodin Ficinoslifein whichhe was afflicted withmelancholy in becausehad "strayed too farfromtheChristianthinkers" his pursuitof ancientpagan philosophy.23 Ficinowas givena copy of the in orderto SummacontraGentiles ofFlorence,Antoninus, bytheArchbishop modelfortheharmonization of pagan givetheyoungPlatonista successful philosophyand Christiandoctrine.Aquinas has been widelyviewedas an antidoteto Ficinosperceived paganismand heresy.24

21)There inthetwentieth ofMarsilio Ficinos weretwodominant interpretations philosophy there wasthesystematic ofPaulOskarKristeller, was First, and,there century. interpretation Yates andMichael themore creative theinterpretation ofFrances J.B.Allenthatemphasized elements ofFicino s thought. TheHermetic istoday thedominant andHermetic interpretation in"Paul B. Allen these two to Ficinos Michael discusses interpretation. J. approaches philosophy E Tenebris Ficino: Revocaverunt Reconsidered Oskar Kristeller andMarsilio ,"inKristeller (New Celenza hasargued thatKristeller washostile totheHermetic York, 2006),1-18.Christopher itinferior to"true" SeeChristopher "Paul andconsidered Celenza, philosophy. interpretation alsoinKristeller Oskar Kristeller andtheHermetic 74. Tradition," Reconsidered, 71-80, especially inthe G. Snyder's doctoral "Matter andMethod AlsoseeChapter OneofJames dissertation, ofMarsilio Platonic Center, Ficino," 2008),fora discussion (TheCUNYGraduate Theology when itcomes ofthese twointerpretations, toMarsilio Ficinos oftheshortcomings especially ofnature. philosophy 22)Marsilio Michael textedited Platonic Ficino, , Vol.6,trans. J.B. Allen, byJames Theology "Marsilio Ficino Hankins with William Bowen Mass,2002),138-139. Kristeller, (Cambridge, inRenaissance andLetters, Studies andHisCircle," 39,n.15. Thought 23)"TheLifeofMarsilio inThe Letters Ficino Ficino," ,Vol.3 (London, 1985),140. ofMarsilio 24)Zanobi thatFicino often toldhimthisstory anacquaintance ofFicino, claimed Acciaiuoli, OnFicino s "spiritual andCorsi s andAcciaiuoli s descriptions ofit, about St.Antoninus. crisis," Renaissance PlatointheItalian seeespecially Hankins, , Vol.I (Leiden, 1990),279-280, James

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Paul Oskar Kristeller arguedthatAquinas exercisedthe most powerful In thefirst ofhisphilosophy.25 on thedevelopment Scholasticinfluence chapa offers terof his seminalstudy,ThePhilosophy ofMarsilioFicino, Kristeller theThomisticthebriefexpositionofFicinos theoryofmatterthatresembles Kristeller explainsthatformoccupiesnearlythe oryin severalsalientrespects. that"matter is, wholerealmofbeingon itsownforFicino,and consequently and Further it."26 from so to speak,practically Aquinas aligning expelled Kristeller Ficinoon thequestionofmattersexistence, explainsthat"[m]atter ofitsown. It merelyhas,in respectto eachobject,theequal has no existence is nextto nothingand ofbeingand ofnotbeing.Matter,therefore, possibility does not standsmidwaybetweenBeingand Nothing."27 AlthoughKristeller nonsome in mind have he does in this mentionAquinasdirectly context, inherversionof theThomistictheorythathe believesFicino controversial Kristeller In a laterarticletitled"Thomismand ItalianThought," ited.28 argues his heart of the to thatwhen one "penetrate [Ficino s] [s] philosophy" very withThomasAquinas,one discovers, in searchof resemblances accordingto "Ficinoobviouslyknewhim thatamongScholasticphilosophers, Kristeller,

in diMarsilio "Perlabiografia Ficino," SeealsoP.O. Kristeller, andVol.II,454-459. reprinted Vol.I, 191-211. andLetters, inRenaissance Studies Thought 25)Michael as "alate forFicino a "feel" thatKristeller noted developed J.B. Allenhasaptly Renaisas an and Franciscan a tilt towards with scholastic early positions theological philosopher alone. in Platonic the immersion his near-total result of as a sance Theology While Neoplatonist" thesameisnottrue Franciscan held some Ficino that Kristeller positions, theological thought Thomas that Kristeller Inthisrespect, ofnature. forhismetaphysics Aquinas argued generally "PaulOskar SeeMichael onFicino. influence Scholastic wasthemostimportant J.B. Allen, Reconsidered inKristeller andMarsilio Kristeller , 9. Ficino," 26)PaulOskar Conant Ficino Marsilio ThePhilosophy , trans. (NewYork, Kristeller, Virginia of 1943).39. 27)PaulOskar Ficino The , 39. Kristeller, ofMarsilio Phibsophy 28)Itisperhaps ofany wasreally ofmatter thequestion that Kristeller didnotthink that likely lies elsewhere s of Ficino that the core Kristellers since to concern Ficino, philosophy argues deep Ernst Cas"Ficino s PlaceinIntellectual Ina 1945article, innatural than History," philosophy. ofnature, Aphilosophy ofNature. noindependent "wefind inFicino that comments sirer study - byCardano, oftheRenaissance onewaslater inthesenseinwhich bythinkers developed - wasunknown tonote iscorrect While Cassirer toFicino." Bruno Giordano Patrizzi, Telesio, inthePlatonic ofmatter , itisnotthecase isnoindependent thatthere Theology investigation iswhatCassirer which ofinthiswork, worth isnota natural thatthere speaking philosophy from the ascent in the souls as a saw natural Ficino step philosophynecessary generally implies. s PlaceinIntellectual "Ficino E. Cassirer, realms. totheimmaterial material Journal History," of theHistory ofIdeas6(4)(1945),489.

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ArdisB. Collinspossiblymakesthemost [Aquinas]betterthantheothers."29 ambitiouscase forFicinos Thomismin his book TheSecularis Sacred:Platonism and Thomism in MarsilioFicimsPlatonicTheology. ,30To makehiscase, Collinsin theappendixjuxtaposespassagesfromeachtextin orderto demonstrate"thatimportant sectionsof Ficinos workarecompletely dominatedby influence."31 with to Ficinos Specifically respect theoryof matter, Aquinas' ofprimematter"wouldcontradict CollinsarguesthatforFicinotheexistence itsnature."32 whenit comesto thewayin Collins*book has been influential whichscholarsviewFicinos philosophical debtto ThomasAquinas.33 It is undeniablethatThomismdid have a deep and lastingimpacton elements ofFicinos philosophy andtheology. as Kristeller However, significant a Scholastic inheritance is matter. Because Ficinos complicated recognized, in FicinoacceptedcertainThomisticphilosophical and doctrines, spiteofthe factthatFicinoperhapsknewAquinasbest,itdoesnotfollowfromthis,given That Ficinos generaleclecticism,thathe acceptedhis theoryof matter.34 to smooth over subtle it is all too differences said, easy yetsignificant among Scholasticphilosophers, and attribute most,ifnotall, Scholasticelementsof

29)PaulOskarKris Three Medieval teller, ofRenaissance Learning: Essays byPaulOskar Aspects andHisCircle," inStudies in "Marsilio Ficino Kristeller , 74.Alsosee,PaulOskarKristeller In this Kristeller also notes seven references to Renaissance and Letters 39. article, , John Thought Ficino s Opera omnia. DunsScotus throughout 30)Michael thatthere are"extensive from theSumma hasalsoargued J.B. Allen borrowings" Marsilio inMarsilio Ficino s Commentary onPlato's Philebus. Michael contra Gentiles J.B.Allen, andRenaissance Texts andStudies, Ficino: The Philebus 1975),23-24. (Medieval Commentary 31)Ardis inMarsilio Platonic TheSecular isSacred: Platonism andThomism Ficinos B. Collins, ,x. Theology 32)Ardis isSacred B.Collins, The Secular ,45. 33)Intheintroduction ofthePlatonic totherecent translations J.B.Allen, byMichael Theology the translation. In the to therecent aswellasinthetextual notes that introduction accompany Collins views onFiciofthePlatonic andHankins, translation ,Allen echoing Theology English bears theinfluence ofthesecond bookon nos Thomistic assert that thePlatonic debt, Theology state that"[occasionally Ficino tookpassages contra Gentiles creation oftheSumma , and,they in and he was interested sections almost verbatim from Thomas' clearly aligning argumentation, astheultimate scholastic ofthesaint whowasalready ofhiswork with that authority." emerging Marsilio Platonic Vol.1,xi. Ficino, Theology, 34)Kristeller indealing a general caution with Ficinos Scholastic heritage judiciously suggested he we tocall Renaissance when writes that "lest aretempted inhisEight the Italian Philosophers of Thomas that hecametosidewith Scotus him[Ficino] a Thomist, weshould remember against ofwhether is thequestion thewillortheintellect issues ononeofthecrucial them, dividing Italian Renaissance PaulOskar 39-40. Kristeller, 1964), (Stanford, ofthe superior." Eight Philosophers

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Ficinosthoughtto ThomasAquinas.The pre-eminent positionthatis today attributed to ThomasAquinasamongMedievalphilosophers is in facta postand even a Medieval, post-Renaissance development.35 Aquinasmay Although havebeenemerging as thepre-eminent Scholasticauthority in fifteenth centuryFlorence,Ficinodoes nothesitateto divergefromAquinason significant and theological in fact,in latefifteenth matters; philosophical century Italy,it has been arguedthatScotistmetaphysics was viewedas philosophicaland whenit theologically superiorto Thomisticmetaphysics, especially, ironically, cameto demonstrating theimmortality ofthesoul.36Whiletheattribution of a Scholasticdoctrinefoundin FicinosPlatonicTheology to Aquinasmayin therearespecialcases,suchas withhistheory ofprime manycasesbe justified, whereit is not. It will be arguedbelow,thatFicinoclearlydoes not matter, acceptAquinas'theoryof primematter,and opts insteadfora theorythat attributes a greater to primematter.BothKristeller and Coldegreeofreality linserroneously assumethatFicinoendorsedsomeversionof theThomistic does thisimplicitly theoryof matter;Kristeller byarguingthatFicinohelda version of the Thomistic whereas Collinsis explicitin hisassergeneric theory, tionthatFicinofollowThomason primematter. IV The previoussectionnotwithstanding, Ficinocan sounda lot likeAquinasin thePlatonicTheology whenhe discussesmatter.Ficinocan appearat timesto endorsebothof theassertions aboutprimematteroutlinedabove.He claims

35)Inhisrecent introduction toMedieval Marenbon writes that John philosophy, Aquinas' "unique andhisofficial doctrinal reflect status, Marenprominence, post-Medieval John developments." AnHistorical andPhilosophical bon,Medieval Introduction Philosophy: 2007),245. (Roudedge, 36)SeeJohn andtheMissing Monfasani, Ockhamists: "Aristotelians, Platonists, Philosophical inPre-Reformation Renaissance Monfasani has Liberty 46(2)(1993),247-276. Italy," Quarterly that Franciscan Scotists were inItaly attheendofthefifteenth andthebeginargued prominent "viamoderna ofthesixteenth centuries. Scotist theso-called as ning ,"wasviewed metaphysics, toThomistic theso-called "viaantiqua itcametoissues ,"when superior metaphysics, pertaining tothecreation oftheuniverse, aswellasinitscapacity torefute theAverroistic doctrine ofthe oftheintellect. Scotist waseven seenasproviding a support oftheimmortalunity metaphysics himself remained thepossibility of ityofthesoul,evenifDunsScotus agnostic concerning ofthesouls immortality. Renaissance Scotists on the that a anydemonstration argued, contrary, demonstration ofimmortality isindeed TheBishop ofPadua, Pietro whowrote Barozzi, possible. anedict theAverroistic in1489,wasa supporter ofScotist against position metaphysicians.

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ofall material as thesubstrate thatone and thesameprimematterfunctions and is matter that and, ungenerated uncorrupted, at a glance, prime things, existand thatit is completely eventhatprimematterdoes notindependently Ficinoexplainsearly s existence, on itsown.Concerningmatter unintelligible that"whatis last,thatis, corporeal in thefirstbook of thePlatonicTheology else It can neveract on anything has to be actedupon byeverything. matter, its action."37 of fornothingexistsbelowitwhichcouldbe thesubject ofitself, - as neitherexistsofitself Later,againin Book I, Ficinoexplainsthat"matter - nordoesitexistbecauseofthequaliand doesnotactofitself itis imperfect becauseof someformthatprecedes it exists Rather tiesthatit itselfprecedes. a qualifiedexistence In bothofthesepassages,Ficinoappearsto attribute it."38 likeAquinasdid. In thefirstpassage,he deniesthatmattercan do to matter, as theobjectofits sincenothingexistsbeneathitthatcouldfunction anything, on its doesnotexist own,butexists action;in thesecondhe claimsthatmatter ofform.Ficino in somelessersensethatis dependenton thepreviousexistence also claimsin severalplacesthatthingsare knownexclusively throughtheir is matter unknowable.39 formless that whichwouldseemto imply form, prime betweenAquinasand Ficino doctrinal of an overall assertion agreement Any is largely s ontologicaland epistemic status,however, on thequestionofmatter is not it those as such In above, apparentthat given misguided. quotations he does speak when and Ficinois evenspeakingabout primematterat all, he tendsto divergewidelyfromAquinasin his aboutprimematter, directly ofit.In thefirst mostbasicunderstanding passage,Ficinois actuallyspeaking materia matter aboutthenatureofcorporeal ), whichmustbe dis(; corporealis prima);and the secondpassagecan tinguishedfromprimematter(¡materia thatFicinomarksbetweenwhat a distinction in of be understood light only thatbelongto things.It is of existence modes the two to be takes he separate to primemata greater degreeofexistence arguedbelowthatFicinoattributes terthanAquinaswaseverwillingto,and he arguesthattheinfinite receptivity to God. Both of theseclaimsplace Ficinoin of primematteris intelligible to primemata greater who haveattributed ofphilosophers a tradition reality the even ter.This becomesevidentevenwhenone notesthat languageand

37)Marsilio Platonic ,Vol.1, 23. Ficino, Theology 38)Marsilio Platonic ,Vol.1,41. Ficino, Theology 39)Forinstance, most about thatwelearn inBookX,Chapter V,Ficino clearly objects explains theconditions from inisolation rational their about wethink when andmost principles reliably Platonic Marsilio ,Vol.3, 159. ofmatter." Ficino, Theology

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- suchas thatFicinousesto describematterin thePlatonicTheology imagery - is in itselfan indicationofsortsthat the"womb"and "seedbed"ofbecoming thereis a different conceptofmatteroperatingin FicinothaninAquinas.For whichis Ficino saysthatnature"isartmoldingmatterfromwithin," example, in in the bosom of matter is a form "hidden because way anygiven possible a more robust exisSuch attributes it is to before brought light."40 language It willbe arguedbelowthatanyperceivedresemblance tenceto primematter. that fromignoring severalkeydistinctions betweenAquinasand Ficinoresults matter and its existence. Ficinomakesin thePlatonicTheology regarding uses theconceptof primematterin theearly AlthoughFicinofrequently - especiallyin Book I wherehe arguesforthe booksof thePlatonicTheology - he givesarguments forits foror habitin nature ofan incorporeal necessity aremade in thecourseof existencein Book V, ChapterIV. Thesearguments In thischapterFicinofurnishes ofsoulovermatter. arguingforthegovernance fortheexistence ofprimematter. at leastthreearguments (1)

Naturamarsimitatur

beneathall of thatpersists First,Ficinoarguesthattheremustexista substrate theaccidentaland substantial changesthatoccurin naturebasedon an analart. between art and nature.Ficinostatesthatnatureimitates that he finds ogy Human craftsmen, Ficinoreasons,do not havethepowerto createanything bitofmatterthat fromscratch;rather, theytakesomepreexisting completely is at hand,and imprintin it a formthatthematteritselfdoes not possess.41

40)Marsilio aresimilarities between Marsilio Ficino Platonic Ficino, , Vol.2,57.There Theology tohave Bruno when itcomes tonatural Therobustness ofmatter andGiordano appears change. sview ofnatural Arobust matter holds the hadsignificant forFicino implications change. prime as ofallthings, to Ficino. Bruno also describes natural formless seeds according change coming indrawing Seeespecially the "from within" andhegoesfurther outthese matter, implications. De lacausa etuno. Second ofBruno's ,principio Dialogue 41)Marsilio Platonic s discussion ofthedifference Ficino, , Vol.2, 19.AlsoseeFicino Theology XIofthePlatonic . There Ficino between natural causes andGodinBookII,Chapter Theology matter of as essences of minds and that "God alone creates the bodies and many explains prime rational without anintermediary ora substrate." Platonic soulsaspossible ,Vol.1,167. Theology A natural orpower ina ontheother toFicino, "isa sort ofform limited cause, hand, according allitsforce certain oneparticular whatever itdoeswith anddoing result, waytoproducing doing itofnecessity." Platonic make a particular from the , Vol.1,165.Natural Theology thing agents materials that areathand, toFicino, andproduces itsdiverse effects from a combinaaccording tionofitsownlimited andthedisposition ofthematter that itispresent on. power, working

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Natureoperatesin muchthesameway,accordingto Ficino,withtheexceptionthatthematterthatit initially clotheswithformis completely formless. Naturedoes notpossessthecreativecausalityto bringtheverymaterialsubstrateof all thingsintoexistencefromnothing.Instead,it has thepowerto thatitfashions workwitha formless and pre-existing substrate intoa particuforms.In this larthisorthatwiththeguidanceofthemodelsoftheintelligible respect,Ficinos argumentresemblesPlatos storyabout the creationof the The Demiurgedoesnotcreatethe universe bytheDemiurgein the Timaeus.*2 it notcreatetheconfusedmatter of the forms and does themselves, archetypes of becomingin whichsensiblethingsbecome.The Demiand thereceptacle thatarepresentat handin the instead makes use of theserawmaterials urge In similarfashion,accordingto Ficino,nature construction of theuniverse.43 fromscratch.Natureworks,likePlatos Demiurge, does not createanything on what is alreadygiven,in thiscase, primematter.When the substantial changeof one elementintoanotheroccurs,naturedoes not createthenew that fromnothing,butfroma pre-existing materialsubstrate elemententirely is conservedthroughout thecourseofall changes.Fromtheseconsiderations, thecraftsman of theworld,has subject Ficinoconcludesthat"natureherself, allforms."44 thatis lackingallforms, butis equallyreadyto receive to ita matter (2)

Fromactuspurustopurapotentia

in Ficinos thatiswidespread Thesecondargument dependson an assumption - such levels of to which the sundryontological reality thought,according and haras matter, body,quality,rationalsoul,etc.- standin a proportional withone another.45 Each genus,accordingto Ficino,has monicrelationship thatexhibitorderand proportion; twoextremes and a seriesofintermediaries withGod standingon one end, in fact,all of realityforFicinois a hierarchy In on the other. this matter and formless chapterFicinomakeshiscase prime 42)Plato, Timaeus , 28c-30c. 43)OfTimaeus Plato's seeFrancis Cornford, 28c-30c, (London, 1937),37.Seealso, Cosmology ofthe Ficinos ofPlato's Timaeus anditsMyth "Marsilio Michael J.B. Allen, Interpretation in Honor Paul Oskar Kristeller in Studies of (Binghampton, festivum: Demiurge,"Supplementum NY,1984),399-401. 44)Marsilio Platonic ,Vol.2, 19. Ficino, Theology 45)Ficino inontology isevident inhisconsidthat there ismeasure andproportion s assumption There Ficino forms in the first book of the Platonic of eration ofthevarious Theology. grades of that exist at of forms of at least three different for the existence polar opposites grades argues thishypostasis.

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ofprimematterveryquickly,almostin passing.He explains fortheexistence that"[j]ustas God at thehighestlevelofthingsis pureact,"so theremust"be whichneedseveryat thelowestlevelwhichis purepotentiality, something thing,andwhichin itselfis withoutformyetcapableoftakingon all forms."46 on one pole The basicidea is thatwhenone findsthatthereexistssomething withineachindividualhypostaofbeing(or,forthatmatter, ofthehierarchy else,thatis thenegationofthe sis),thenone shouldexpectto findsomething on the otherend of the ontologicalspectrum.When it comes to the first, of s existence, then,Ficinoreasonsthattheexistence questionofprimematter in is a state of of that the existence purepotentialsomething pureactimplies on theotherhand,pure ity.Whilepureacthas nothingin it thatis potential, - eventhoughit existsin a mannerthatwillbe or primematter potentiality, in a statepoisedto and is therefore has below nothingofactuality, explained receivetheformsofall things.47 (3)

TheReciprocal oftheElements Interchange

oftheelementsin thischapFicinoturnsto thereciprocal Finally, interchange s existence. Ficinoclaimsthatbyexaminterto makehiscaseforprimematter changethatoccurswhenone elementbecomesanotherone ingthesubstantial hancmateriarn). Ficino can catcha glimpseof "thishiddenmatter"{latentem A case correct underof the elements as a turnsto thesubstantial study. change changeof somebit of earthintosomevolumeof standingof thesubstantial ofa formless and impassibleprime water,Ficinoargues,impliestheexistence Ficinoexamines all such transformations. matter thatis conserved throughout of substantial of two alternatives the possibility explanations change:first, eitherthe formof earthremains,in some attenuatedfashion,in the newly formed volumeofwater,or,second,whentheformofearthrecedes,itis comalternative cannotbe thecase, pletelyreplacedbytheformofwater.The first accordingto Ficino,sincetheformofearth,whichis dry,possessesa quality, it cannot to theformofwater,wetness.Therefore, whichis contrary dryness, be truethattheformofearthremainsat all in thenewlyformed water;on the theearthmustbe completely eliminated and replacedbytheformof contrary, 46)Marsilio III ofthePlatonic Platonic Vol.2, 19.Alsosee,BookX,Chapter Ficino, Theology, ifpure willpureactbefound, cannowhere There Ficino states that "nowhere potency Theology. exist." isarguing that thefact ofpure . . . Therefore matter must Ficino befound potency, simple notexist were itnotthecasethat where theemanation ofthelight ofGods creation would ends, Thevery ofpurepotency onpureact. existence depends pureactexisted. 47)Fora similar SeeChapter 16and17ofBookI ofThomas Summa contra Gentiles. view, Aquinas'

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is essentially water.The materialsubstrate wipedclean,so to speak,andwhere exists the formofwater.When theformof of earth once was now theform Ficinoexplains,theformofearth"vanishes intothechaos" waterapproaches, whichcontainsall thosepossibleformsthatare not at thepresentmoment The actual,and otherformsthatarepossibleandyetwillneverbe actualized.48 sincethere formofwater,however, cannotexistwithouta materialsubstrate, would be no foundationin whichtheformcould takehold.Thus,sincethe and because"nonewsubstrate formofwatercannotexistwithouta substrate, in the the course of substantial itself" change,thenitmustbe thecase presents thatthesameprimematter"whichwas thesubstancefortheformof earth Evenifone formis immediately nowreceives theformofwater."49 replacedby thesubstantial that Ficino thinks another, byconsidering changeofelements, or primematter, ofa materialsubstrate, thenecessary existence one discovers thatstandsbeneathand supportsall formsequally.50 But whydoes Ficino insistthat"no new substratepresentsitself"along in thiscase,water?Whycan itnot withtheappearanceofeachnewsubstance, Ficinomaintains is createdwitheach newsubstance? be thata newsubstrate witheach substantial thatthecreationof a new materialsubstrate changeis can infer from the first one for two reasons: First, argument, unacceptable would ascribeto nature outlinedabove,thatthecreationof a new substrate thepowerto createsomethingfromnothing,whichis wrong,accordingto If naturein factimitatesart, Ficino.Naturedoes not havecreativecausality. from does not create thennature something nothing,as artdoes not, but thatarepre-existing. makesuseofmaterials Second,wereitthecasethatprime withtheformofearth,thenthenaturalchangeofone matter was annihilated thingintoanotherwouldbe directedtowardsevil,accordingto Ficino.Somemustremainwhenone thingchangesintoanother.Ficino thing,therefore, behindthesecondpointin thefollowing the passage: explains reasoning and that small ofwater tonothing first reduced iswhether it[nature] Ourquestion portion If the it reduced water it some of the water. or whether then air, entirely preserved produced evil. Yetthat intention bedirected towards nature s intention would then tonothing, always which Andexistence since itisgoverned aimsatthegood, itself, byGodshighest goodness. 48)Marsilio Platonic ,Vol.2, 19. Ficino, Theology 49)Marsilio Platonic ,Vol.2, 19-21. Ficino, Theology 50)Thisargument Ina notetothetext ofthe thePythagorean isattributed toTimaeus byFicino. of to Plato's Ficino is here that Allen and Hankins Platonic 50D-51B , referring explain Theology Timaeus.

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isthepeculiar ofeternal from atsomepoint God,wouldbestolen gift bycauses things toGod.51 subsequent In thispassageFicinochangesthe examplefromthe substantialchangeof earthintowaterto waterchangingintoair.Ifitwerethecase,he reasons,that thewaterwerefirst reducedto nothing,thennaturewouldtendtowardsevil, sinceit would be robbingthingsof theveryexistencethatis Gods alone to thenaturaldesireof all things,includingnatureherself, give.Furthermore, to according Ficino,"is directedtowardsthegood,thatis, towardslife,existenceand so on, and nottheiropposites."52 Evenprimematter, whichis itself is describedby Ficino as being"desirousof the good, namelyof formless, form. . . becauseitis opento receiving thegood,and becauseitis necessary for a good world."53 Werenatureto reducesomethingto nothing,accordingto thenaturalappetitethatstrives Ficino,it would preventit frommanifesting forlife,existenceand thefulfillment of finalends. Ficinocontinues:"Since to God do not possessabsoluteexistence, but onlyqualified thingsinferior existence suchor suchexistence , theydo not havethepowerto abolish existencecompletely, but onlya particular mode of existence . . ." Moreover, Ficinoexplainsthat"Naturalagentscannotmakesomething out of nothing. Forto makesomething out ofsomething is easierthanto makeitout existing In additionto thenaturalappetitethataimsat thegood,Ficino ofnothing."54 in this argues passagethatnaturalagentsdo notpossessthecausalpotencyto createsomething fromnothing,muchless to reducesomethingto nothing. Naturecan onlymakea particular this,suchas water,changeintosomething elsethatis also a particular thisor that. Fromthesethreearguments Ficinoconcludesthattheremustexista formlessand impassible matter thatis withoutanyqualityor determination. prime Matteris notgenerated or corrupted in thenaturalcourseofthings,butpersistsas thesubstrate beneathall change.Ficinospeaksto theimpassibility and 51)Marsilio Platonic Ficino, ,Vol.2,21. Theology 52)Marsilio Platonic titled Naturalis" of Ficino, ,Vol.2,25.Seethechapter Theology "Appetitus Kristellers ThePhilosophy Ficino fora consideration ofthedoctrine of"appetitus ofMarsilio naturalis." s "Thomism inMedieval andItalian Also,seeKristeller Thought," Aspects ofRenaissance Learning. 53)Marsilio Platonic Vol.1,87. Ficino, Theology, 54)Marsilio Platonic s argument resembles anarguFicino, , Vol.2,21.Ficino Theology closely ment madebyJohn DunsScotus inLectura 11.12. Scotus fortheconservation ofmatter argues allnatural sinceagents do nothavethepower tocreate from throughout changes something Ifthere were foritsaction, that wasnoenduring mateis,ifthere nothing. nothing presupposed rialsubstrate, then theagent would becreating exnihilo. something

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of matterwhenhe writesthat"[m]attercannotbe changed incorruptibility fromwhatitis exceptbybeingchangedintonothing.Naturedoesnotpermit to be turnedintonothing.So matterdoes notpassaway.Much less anything willthatnaturalpowerwhichrulesovermatterpassaway."55 Thus,forFicino, thereis one "universal theindifferent of all formswhatsomatter, receptacle which "is to the universal craftsman of nature."56 ever," Primematter, subject Ficinoexplains,does notpossessanyqualityor determination, sinceifit did, he explains,itwouldnot"be fitto receiveanotherformcontrary to itsown," sincethepossessionof anyformwouldobtrudethepossibility of thepossessionofanyotherformthathas contrary qualities.57 Ficinodevotestheremainder of thechapterto fillingin thecontentofhis He arguesfortheunityofprimematter, thatis,that conceptofprimematter. thesameprimematterservesas theultimatesubstrate ofall materialthings.58 He also arguesthatprimematteris createdand not generated or corrupted. Finally,he explainsthatprimematterexistsin sucha waythatit is priorto extension.59 Primematteris thereceptacle of quality,thatis, to quantitative notonlytheformsand qualitiesthatarefoundin individualmaterialthings, butalso of theveryconditions, suchas quantitative thatmakethe extension, existenceof such thingspossible.Ficinoexplainsthat"thisprimematteris nevercorruptedbecauseit is thefoundationof all of corporealnature,and wereit destroyed, thewholeworldstructure wouldcollapse,"and thatprime matterdoes not require"anything elseas it seatbywhoseremovalperchance itwouldplungeintotheabyss"sinceit"isitself theprimefoundation ofall."60 V examinedin thepreviHowever,one shouldnoticethatthethreearguments ous sectionstatenothingabout primematterexistingin a mannerbeyond thatwhichAquinascountenanced. Thatis to say,everything thatFicinosays 55)Marsilio Platonic Ficino, ,Vol.2,27. Theology 56)Marsilio Platonic Ficino, ,Vol.2, 19. Theology 57)Marsilio Platonic Ficino, ,Vol.2, 19. Theology 58)SeeMarsilio Platonic "Youwitness onematter Ficino, , Vol.2,23.Ficino Theology explains: allforms inturn asitrises rarefaction andsinks condensation. Itis assuming through through because onematter suffices foroneuniverse; one,therefore, withbecause, firstly secondly being outform, itdoesnothaveanything ofwhich itcanbedivided intomany." bymeans internally 59)SeealsoFicino s definition inBookI,Chapter ofbody II ofthePlatonic Theology. 60)Marsilio Platonic Ficino, ,Vol.2,23. Theology

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in Book V, ChapterIV is consistent withtheviewthatprimematterexists as of a form-matter lacksanyindependent only part composite,and therefore subsistence on itsown.Therearetwofurther distinctions thatarerelevant to Ficinos theoryofprimematter.First,Ficinoarguesfora fullyunderstanding - the absoluteand theparticudistinction betweentwo modesof existence lar- thatbelongrespectively to thatwhichis createddirectly fromnothing, and thatwhichbecomesa particular thisor thatfroma pre-existing material substrate. betweenprimeand corporealmatter, such Second,he distinguishes thattheformer can existwithoutparticipating in a form-matter composite, whereasthelatercannot.61 Ficinoholdsthatprimematterpossesseswhathe termsthe "absolute"or "common"existence thatbelongsonlyto thosethingsthatarecreateddirectly and that come into beingwithouta substrate.Only God has the by God, causalpotencyto createtheabsolutemode of existence:"God alone creates theprimematterofbodies,"Ficinostates,"withoutan intermediary or a subAll otherfinitethingsthatarea particular strate."62 thisor that- thatis,those thingsthatpresupposeat least the existenceof the materialsubstrateand - havewhatFicinocallsthe"particular" extension modeofexisquantitative tence.Ficinoaddressesthisdistinction in thefollowing from BookV, passage XIII: Chapter Theexistence that comes after iscalled absolute existence. Forimmediately after nothing initssimplicity. comes existence . . Forsomething cannot become thisorthat or nothing suchunless itexists tobecoming thisorthat orsuch.Sothisorthat orsuchanexisprior tence doesnotfollow butcomes after andabsolute immediately uponnothing, simple existence. since itisGods alonetogivetoallcreatures thiscommon andabsoTherefore, luteexistence, butsince this existence comes after andbefore allmodes ofexisting, nothing then itwillbetheoffice ofGodalonetobring intoexistence from in something nothing order that what isgiven first toallthings, existence from thefirst itself, namely mayderive andthegifts that aresecond andthird from thecauses that follow.63 cause, Thispassageaddressesthepointmadein thefirst forprimematter s argument existence thatwasexaminedin SectionIV above.Primematteris amongthose 61)Thedistinction between andcorporeal orbetween andsecondary matmatter, prime primary iscommon inScholastic Asimilar distinction between anddesigter, philosophy. undesignated nated matter isalsofound inthephilosophy ofPlotinus. SeePlotinus, Enneads ,III.5.6,III.6.10. AlsoseeLloyd P.Gerson, Plotinus 15. (London, 1994),108-1 62)Marsilio Platonic Ficino, ,Vol.1,167. Theology 63)Marsilio Platonic Ficino, ,Vol.2,81. Theology

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fromnothing.OnlyGod hastheabilthingsthatcomeintoexistence directly to into existence from ity bringsomething nothing.Humanagents,andnature forthatmatter, do notpossessthepowerto createsuchexistence, lhe simple and absolutemode of existence, then,belongsto primematter, amongother in such a that it not does the of a formway things, dependupon actuality mattercompositeforitsexistence. Ficinoconsiders to therefore, primematter, be ontologically ofform.It exists,albeitnextto nothing, evenif independent theactuality offormis missingfromit. Ficinoalso marksthefamiliar Scholasticdistinction betweenthetwokinds - thatis, betweenprimeand corporealmatter.For Ficino,thetwo of matter to thetwomodesofexistence Prime gradesofmattercorrespond respectively. matteris the ultimatesubstratethatexistsin the absolutesensedescribed above. It is not nothing,but at thesame timeit standsnextto nothingon accountof beingbroughtinto existenceby the unique creativeact of God. Primematter, different fromcorporealmatter. In however, signifies something theorderof causes,primematterexistspriorto corporealmatteras it functionsas thesubstrate of quantitative extensionand of theprimary qualities. It is at theveryminimuma Corporealmatteris somethingquite different. whichFicinodefines as extension, compositeofprimematterand quantitative in the Platonic as a of matter and "body"early Theology composite prime extension.64 But corporealmatteralso has specificmagnitudes quantitative - thatis, thingsthatare a particularthisor that.Corporeal and qualities is thatkindofmatterthatis actuallyfoundin thematerial matter, therefore, in thematerial bodiesthatareexperienced world,whichpossesstheparticular mode of existencethatwas spokenof above. Corporealmatter,according to Ficino,is dependentfortheformofquantitative extension foritsexistence, whereasprimematteris not. Ficino explainsthat "[c]ommonmattercan existwithoutthis or that act of existence;but particularmattercannot existwithoutitsown particular act."65For Ficino,then,theexistenceof cormatter entails the existence ofprimematteras itssubstrate, whereasthe poreal 64)According toFicino, Platodefines as"made andofquantity. Itischaracbody upofmatter teristic ofmatter andextension andbeing onlytobeextended byspaceandaifected byaction; affected arepassive conditions. Butquantity isnothing buttheextension ofmatter; or,ifitis itissuchthat todivision even asitsubjects itisalways matter toanunendelse, anything subject ofexperiences onanyother andhasnoaffect matter thanitsown.Itfollow from ingsequence initself allthisthat isacted doesnotactbutsolely Marsilio Platonic TheolFicino, body upon." Vol.1,19. ogy, 65)Marsilio Platonic Ficino, ,Vol.2,67. Theology

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existenceof primematteralone does not entailthe existenceof corporeal matter.One should note thatthisdistinctionis similarto the distinction and qualifiedmatterin Plotinus.Plotinusarguesthatthe betweenunqualified to mattermakesit someformeris impassible,and thatany determination material substrate.66 fundamental from the most different thing in thisway:whenan moreor lessfunction Thesetwodistinctions together individualpersoncomesto be,suchas Plato,we do notsaythatPlatos father, Ariston,createdhumanityin an absolutesense,but onlythatAriston,who kindof matter, was himselffashionedin a particular "begotthisman,Plato, world finite and Nature kindofmatter." in a particular thingsin thematerial of corporealmatterwhen somethingis generatedor coravail themselves can rupted.They onlyworkon a matterthatis conditionedand preparedin a certainwaythatmakesitreadyto receivea form.Primematterstandsbeneath as itsultimate subject.OnlyGod can actwithcorporealmatterand functions between becausethe"distance Thisis thecase,Ficinoreasons, outanysubstrate. and all to no ratio at there is because is and existence existence, infinite, nothing exist."67 to or be this can exist than distance becauseno greater thought on Ficinos view of In fact,primematterperhapshas even morereality, thenaturalbody even and material of the all the than realm, qualities things, book of thePlatonicTheology in whichtheyinhere.In thefirst , in thecourse theprimacyof immaterial of establishing forms,Ficinoarguesthatmaterial whenthey areofsucha naturethattheyare"contaminated" formsthemselves and as a result"thissortofformis neiaredrawninto"thebosomofmatter," Ficinoreasonsthatthosethingsthatcannot therpurenortruenorperfect."68 cannotactuallyexiston theirown.The qualitiesor forms sustainthemselves, as muchas they"lie fallowin of materialthingsdo not sustainthemselves fortheir therefore and are else," "dependenton thatsomething" something in this in mind has The somethingelse thatFicino continuedsubsistence.69

^ Plotinus, ofthe matter isthemeeting that Enneads , 6.3.10.Plotinus ground prime explains altered ever itself andthatitdoesthiswithout thatitactslikea mirror, bythe being qualities, Plotinus iscompletely matter holds that itreflects. Plotinus that Thus, impassible. prime images not is of material matter is the that whatever then, strictly speaking things, proximate argues what itis from cannot bechanges "Matter concludes: else.Ficino butsomething matter, prime intonothtobeturned Nature doesnotpermit intonothing. anything bybeing changed except Vol. Platonic Marsilio 27. not So matter does 2, , Ficino, Theology passaway." ing. 67)Marsilio Platonic ,Vol.2,83. Ficino, Theology 68)Marsilio Platonic ,Vol.1, 29. Ficino, Theology 69)Marsilio Platonic ,Vol.1,31. Ficino, Theology

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Whilequalitiesdo notarisefromprimematteron their case is primematter. it has no since own, abilityon hisviewto actbyitsownpower,theyarenonein in sucha way extension thelesstaken bymatterand dividedbyquantitative theforms thattheycannotsubsistwithoutthematerialsubstrate. Therefore, ofmaterialthingsin a sensebecomematerial.In BookV, Ficinoreiterates his and that the forms of material are matter point, argues things dependentupon as a cause,since"fromMatters teemingwomb [they]aredeliveredin to the Here one findsFicinodepartingfromPlotinus. lightof day likea foetus."70 Ficinoascribesa robustand entitative realityto primematterthatgoes far the Plotinian of matter. Plotinusarguesthatprimematter beyondeven theory has no realclaim to beingat all, and is in realityveritablenon-Being,but Ficinodid not drawthisconclusion.71 Ficinoholdsthatmatterexistsand it roleto playin thestructure of thematerialworldthatis not has a significant as theemptyreceptacle ofbecoming. limitedto functioning theapparentresemblance betweenAquiSo how,then,is one to interpret nas and Ficinoon the questionof primemattersexistencethatwas noted thePlatonicTheology above?Simply,throughout , Ficinodoesnotalwaysspecifywhichtypeofmatterhe is speakingabout.Forthemostpart,primematter is called "primematter," or "commonmatter"by Ficino,althoughhe freto as calls it referred simply"matter"; corporealmatteris occasionally quently matter"and "specificmatter," as well as just matter," "secondary "particular "matter"plain and simple.Ficino holds thatprimematterexistswithout extension or anyqualityevenifcorporealmatterdoesnot.Prime quantitative in theexistence thatis presupposed of the mode ofexistence matterpossesses

70)Marsilio Platonic ,Vol.2,29. Ficino, Theology 71)Plotinus, toPlotinus inhisdiscussion oftheexistence doesnotrefer 10.6.7.Ficino Enneads, inhisdiscussion inBookI, Chapter III ofthe Plotinus ofmatter ofmatter. He doesmention not but is next to Ficino that matter is and Platonic explains prime nothing, nothing, Theology. the"disposition closest tomatter, dimension and from thisthat that Plotinus concluded namely state." andexists, however asa totally iscompletely insubstantial passive insignificantly, quality, matter. In thispassage, Ficino is notspeaking ofprime butcorporeal matter, Also, however, inthe ofqualities found toPlotinus withrespect tohisviewofthenature Ficino isreferring areinsubstantial, like"mere shadtoFicino, Plotinus heldthatthey material world. According streams ina rushing stream." Marsilio oflofty owsthat comeandgolikethereflections Ficino, of P.Gerson todescribe Plotinus usesa similar Platonic yVol.1,41.Lloyd theory image Theology asa succession Itisasifthenatural world "Asuccession isunderstood ofimages. matter: offorms isnotinpotency tothenextimage. Norareany ona movie screen werea film. Oneimage P.Gerson, Plotinus itself." actualizations ofthescreen , 112. Lloyd images

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materialthings.Ficinodoes nothold thattheabsoluteor common particular is dependentupon anyform-matter modeofexistence compositeforitsexisviewsformsas beingmorerealthanmatter.Furtence,evenifhe ultimately ther,unlikecorporealmatter,primematterdoes not requirethe material or anymaterialquality,foritsexistence. conditionsofquantitative extension, to primematterthatAquia gradeofexistence Ficinois attributing Therefore, werewrongto assertthat and Collins,therefore, nas did not.BothKristeller its matter"has no existenceof itsown,"or thatexistencewould "contradict from and instead Ficino In this nature."72 departs Aquinas, respect,then, thatassertedthebasicreality ofphilosophers withthetradition alignshimself ofprimematter. VI aboutthequestionoftheknowlFicinohaslessto sayin thePlatonicTheology edge of primematterthanhe does about its existence.He suggeststhathis own viewdivergesfromtheScholasticviewwhenhe mentionsthat"[s]ome thingsare evenapprehendedthroughthe idea of theiropposite,as eviland privationthroughthe idea of good and of habit,or,as some people think, have asserted While some philosophers matterthroughthe idea of form."73 thatprimematteris knownbyan analogywithform,Ficinoemploysalterna. To borrowa description methodsin thePlatonicTheology tiveepistemological with matteris not onlyknownthroughit relationship fromBonaventure, darkness."For form,but is, forFicino,graspedin itselfas an "intelligible beforehim,matteris graspedin a Ficino,as forAugustineand Bonaventure way throughour veryignoranceof it, whichamountsto a sortof learned thatsomething mustexistas thebasicmaterialsubignorancethatrecognizes strateof all things,butwhichmust,at thesametime,remainin darknessto our intellect.In theEnneads , Plotinusarguesthatone can knowmatterin a whichhe comparesto thebastard certainsense,as theeyeknowsdarkness, of at 52b of the Timaeusfortheexistence chainofreasoning thatPlatooffers thereceptacle ofbecoming.74

72)PaulOskar B. Collins, is ThePhilosophy Ficino TheSecular Kristeller, , 39;Ardis ofMarsilio Sacred ,45. 73)Marsilio Platonic Vol.1,173. Ficino, Theology, 74)Plotinus, Enneads , II.4.10.

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Ficinobroachesthequestionof theepistemological statusofprimematter in at leasttwofurther in the Platonic . First,Ficinoimpliesthat ways Theology one can considerthenatureofprimematterbyappealingto thevariousrelationsthatexistbetweenthesundrylevelsoftheontologicalhierarchy ofbeing. Ficino avails himself of the relations and that Specifically, proportions stand in orderto shedlightbelow,on primematter, betweenthevarioushypostases and quality;and upwards,on thesoul,mindand God. In corporealmatter, thiswayFicinobringsprimemattertogether withtheotherlevelsofthechain of beingintoa meaningful with one another,and fromthishe comparison drawsconclusionsaboutthenatureofeach.Ficinomakesuseofthiscomparain thePlatonicTheology tíomethodfrequently he argues , as when,forinstance, forthepurityof primematter.Ficinoarguesthattheorderof naturalbodies in such a waythatit descendsto primematterand ascendsto is structured theultimateform.Ficinoexplainsthatthe"closersomematterapproachesto thebetter, thetruer, thepurerthematterit is."Likewise,"The primematter, closera formis to ultimateform,themoreperfect it is as form."75 Ficinoalso thinksa meaningful comparisoncan be madebetweenmatterand soul,since bothstandat thebottommostrungoftheirrespective realms,thesensibleand theintelligible. As a result,theysharesomefeatures in common,accordingto Ficino,andwhatcanbe learnedaboutthenatureoftheone canalsobe applied to theother.Specifically Ficinohas in mindthewayin whichmaterialforms and ideasexistin each:justas primematterpossessestheformsofall thingsin so therationalsoulpossessestheideasin thesameway.Whileitis not potency, thecase,accordingto Ficinos view,thatone can cometo knowtheessenceof on thismethod,nonetheless, features of primematter primematterdirectly are revealedobliquelyby makinga comparative of the fundamental analysis levelsofontologyand theirconnections. Ficinoalso addressesthequestionof Gods knowledgeof primematterin thePlatonicTheology . He arguesthatGod can possessa certainknowledge of if in even human cannot come to know it the same matter, prime way. beings FicinoarguesthatGod understands infinite power thingsbecauseitsinfinite extendsthroughall things.All thingsareknownbyGod, Ficinoargues,irrespectiveof thewayin whichtheyexist,and thisincludesall thingsthatexist in actand in potency.In thenaturalworldthisincludestheinfinite receiving theprogression oftimeand thedivisionofwhatis continupowerofmatter, vision ous, amongotherthings.What exactlyFicinothinksthisintellectual 75)Marsilio Platonic Ficino, ,Vol.3, 133. Theology

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amountsto, however, remainsmostlyunclear,save forsome crypticsuggestions.In any case, Ficino arguesthatthisview is theologically superiorto alternative viewssinceitdoes notsuffer fromthe"impiouserrorofthosephilosopherswho thoughtthatGod seesonlywhatis finite."76 VII Ficino describesmatteras "kindling"withthe formsof all things,and he claimsthatin formless primematter"certainseedsof formslie hiddenand ferment."77 When he usesexpressions liketheseFicinois generally tryingto the and latent that he thinks to both capture crackling power belongs prime andcorporealmatter: theimperceptible sparksofall thingsthatkindlein matterawaitthefanning ofsoulin orderto issueforthfrompotencyintoact.The can in partbe explainedby the doctrineof meaningof thesedescriptions seminalprinciples:withinthe welterof primaryand corporealmatter,the seedsofall thingsferment andwaitfortherighttime,thatis,whentheproper materialconditionsexist,untiltheycome fullyintoexistenceas a particular thisor that.A discussionofnatures seedsin detail,however, goesbeyondthe - in which of this Suffice it to it is in such as these scope paper.78 say, passages Ficinospeaksaboutthepotencyand fecundity ofmatter thathe departsthe mostfromtheThomisticviewofmatter, and wherehisrobustviewofprime matteris mostevident. Thisfinalsectionwillconsidersomeofthelargeraimsandpurposesthatare behindFicinosfrequent speculationsabout matterin thePlatonicTheology. Ficinois notinterested in primematterforitsown sake;rather, he generally about the nature of matter in an effort to make his case forthe speculates of immaterial soulsand forms, and byextension, fortheimmortality primacy ofthesouland thesupremacy ofform.79 Ficinospendsmuchofthefirst book 76)Marsilio Platonic torejecting Ficino, theThomistic ,Vol.1,161.Inaddition view of Theology anditsclaims about theepistemological status ofprime matter, Ficino couldalso matter, prime haveinmindtheviews ofJohn whoargues thatthere must exist atomic indivisibles Wyclif, because Godcannot know that are infinite. See sAtomism," Michael, things "John Emily Wyclif inAtomism anditsPlaceinMedieval Philosophy. 77)Marsilio Platonic Ficino, ,Vol.2,63;andVol.1,87. Theology 78)SeeHiroshi ofSeedsandNature intheWork Hirai, ofMarsilio inMarFicino," "Concepts silioFicino: HisTheobgy, HisPhilosophyt HisLegacy , 257-284. 79)AlsoseeMarsilio Ficinos onPlato's In Chapter 28,Ficino commentary Sophist. explains: "Whatis calledanimate andliving andalivenotbecause ofthecorporeal bodyis animate mass. Otherwise would beliving. andlives some Therefore, anybody bodyisanimate through

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ofthePlatonicTheology a conceptofprimematterthatis devoid constructing ofanypowerto act,or to maintainunityforanyamountoftime.Whenmatterand bodyaredefinedin thesetermsitbecomesnecessary fortheorderliness of formand the motivepowerof soul to shapeand movematter, ifit is to becomeanything and remainone thingovertime.The overallaim ofFicinos is to demonstrate thatmaterialthingslack therefore, conceptofprimematter, and reality, and therefore to "separate[our]rationalsouls desire persistence frommatteritself," as he writesin thefinalsentenceof thePlatonicTheology , "so that,to the extentwe departfrommatter,we may therebyapproach God."80A consideration of the natureof primematteris necessary forthe souls ascentfromthematerialto theimmaterial realm.He explainsthatin order"toshowclearlyhowbestthemindsofmencan unlockthebarsofmorwitnesstheirown immortality and thusachievea stateofblessedness," tality, he willattemptto demonstrate "thatbesidestheinertmassofour bodies,to whichtheDemocriteans, and Epicureanslimittheirconsideration, Cyrenaics thereexistsan activequalityor power."81 If one does not come to a proper of thenatureofmatterand corporeality, Ficinosuggests, then understanding one is in dangerofbeingpersuadedbythearguments ofthematerialists, and ofbecomingan Epicurean.Thisis disastrous forFicino. - considered Not onlyareall materialthings in themselves as composites of extension and somequality passiveand inert,but primematter, quantitative theyalso lack any unity.The unityof materialbodies can only occur on accountofsomeforcethatis externalto matterand body.Ficinoarguesthat to theunityofanymaterial corporealmassis an impediment bodyon account of thedisparateand inertnatureof materialbodies.82 Thereis nothingabout thatholdsfastthedifferent corporeality partsofa materialbody,whichis by itsnaturedispersed.Certainly matter does notprovideanysuchstabilprime claimsaboutcorporeality. ity.Ficinogroundsthisconclusionon threefurther First,he arguesthatthereexistsdistancebetweenthe partsof matteron accountof quantitative extension.Second,he arguesthatmaterialbodiesdo thesoulitself. Sincethesouliseverywhere themover ofthe nature, incorporeal namely through andeverywhere itsmistress farmore andtherefore eminent than thebody, itis body deservedly tobe an incorporeal I havewritten substance... at length on these in my issues adjudged ."Marsilio Marsilii Ficini Commentario, inPlatonis trans. Ficino, [Platonic] Theology Sophistam, in Michael B. Icastes 242. Allen, 1989), J. (Berkeley, 80)Marsilio Platonic Ficino, ,Vol.6,219. Theology 81)Marsilio Platonic Ficino, ,Vol.I, 15. Theology 82)Seeespecially BookVI,Chapter VIIIofthePlatonic Theology.

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not endurewithfixity and stability. Insteadtheyare constantly changingin bothperceivedand unperceived he ways.Third, arguesthatall materialbodin a materialsubstrate, arealwayssubjectto opposing ies,in virtueofexisting such as heat and wetness and cold, qualities, dryness.FromthisFicinoconcludesthattheunityof a materialbody,be thatof a stoneor a person,does notcomefromanycorporealprincipleon itsown;in fact,beingextendedand assaultedby opposingqualitiesmakesthe unityof anymaterialbodycomand corporeality, Ficinoconpletelyimpossible.Giventhenatureof matter, cludesthat"theremustbe somethingin thebodybeyondthebody'snature whichunitesit,arrests the it,and containsit:unitestheseparated parts,arrests contains its own the disflux, mutually by unending simpleharmony body's A proper,thatis, Platonicconceptionofmaterialthings, cordantqualities."83 revealsthattheyarecompletely therefore, passive,inert,and lackingin unity, and therefore formand habit.84 theyareall in needofan incorporeal In addition,thediscussionof Book V, ChapterIV aimsat supporting the for the of the In soul. the immortality largerargument openinglinesof this Ficinostates:"Theimmortality ofthesoulis principally shownbythe chapter, factthatnaturesprimematter, whichis movedand formedby soul, must itselfbe perpetual."85 Ficinoclaimsthatsincematterbeginsonlybycreation and endsonlybyannihilation, and is therefore then perpetualin itsexistence, to and rulesovermatter, musta fortiori be persoul,whichimpartsvitality petual.As was arguedin SectionIV above,Ficinoheld thatmatteris never reducedto nothingthrough Ifmatteris perpetualin its anynaturalalteration. in thismanner, thensoul mustalso be immortal, Ficinoreasons.86 existence,

83)Marsilio Platonic Ficino, ,Vol.2, 171. Theology 84)G.W.Leibniz's useofPlatonism asa bulwark theriseofmaterialism resembles Ficiagainst no'sinthePlatonic SeeG. W.Leibniz, "OnNature inPhilosophical Itself," Theology. Essays, trans, anded.Roger Ariew andDanielGarber IN, 1989),155-167, (Indianapolis, especially Section 20 ofthe"Discourse onMetaphysics," 281159-160; 53;"TwoSectsofNaturalists," 284.On Leibniz's Platonic see Christia Leibnizs : Its Mercer, assumptions, Metaphysics Origins andDevelopment Mercer discusses ofFicino's (NewYork, 2001),173-205. aspects philosophy. 85)Marsilio Platonic Ficino, ,Vol.2, 17. Theology 86)Thetheory ofprime matter andtheimmortality ofthesoulcometogether inthepenultimate of Book where Ficino concludes as follows: "Matter cannot bechanged V, IV, paragraph Chapter from what itisexcept intonothing. Nature doesnotpermit tobe bybeing changed anything turned intonothing. Somatter doesnotpassaway. Muchlesswillthat natural which rules power over matter Matters ruler istheefficient which itform. Thatpower passaway. power gives give matter form which first setsitinmotion. Thesource ofmotion istherational soul. . ."Marsilio Platonic Ficino, ,Vol2,27. Theology

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It is finallyopen to speculationas to whyFicinoarguedfortheexistence of primematter, and did notadopta theorythatapproximated moreclosely theThomistictheory. It is reasonableto thinkthattherobustviewof matter appealedto Ficinoforat leasttworeasonsthatareconnectedwithhisbroader First,Ficinowas motivatedto hold a robustview philosophicalaspirations: forreasonsthatareassociatedwithhis theologyand naturalphilosophy. The robustness of matter, in Ficinosestimation, is a reflection of Gods wisdom. God governsall thingswiththegreatest ease,because"He is notdealingwith alienmaterials whichHe hasreceivedfromelsewhere, butwithhisownmaterialswhichHe makesHimself."87 God has designedthingssuchthatit does not affectthings"fromwithout,but movesthemfromwithin,"whichis thecase,accordingto Ficino,because"He is presentin theveryheartof all God does not workon thingsfromwithout,as humanhandsdo, things."88 butfromwithin,sinceprimematterhas beendisposed,bytheformless seeds and rudiments offorms, in sucha waythatitis mostreadyto haveform.89 The robustness of matteralso betteraccommodatesFicinos naturalphilosophy, whichincludeshisdoctrineofseminalreasonsand hisviewofnaturalchange. ForFicino,whena naturalchangeoccurs,itoccursas a resultofnatureworkingfromwithinthematterthatis at hand,eitherprimeor corporeal.Ficino statesthatnaturemoulds"matter fromwithin,as thoughthecarpenter were in thewood."90Thisis possiblebecausethereexisttherudiments and seedsof formin bothprimeand corporealmatter.91 The robustness ofmatteris consistentwithFicinos description ofthematteras a "womb,"and as "kindling" or in a stateof "ferment." Ficinoconceivesthattheformsof all thingsare not on matter as much as theyunfoldfromwithinthefoldsand recesses stamped of matteritselfaccordingto the rationalplan of divinemindand put into

87)Marsilio Platonic Ficino, ,Vol.1,199. Theology 88)Marsilio Platonic Vol.1,199. Ficino, Theology, 89)SeeMarsilio Platonic oftheformless seedsthat Ficino, , Vol.1,87fora discussion Theology arefound inprime matter. Fora discussion ofFicinos view ofnatural anditsrelationship change toprime seeChater 4 ofJames G. Snyder, "Matter andMethod inMarsilio Ficinos matter, Platonic Theologyr 90)Marsilio Platonic Ficino, ,Vol.1,253-255. Theology 91)Ficino that there arethree ofseeds: there arethe"formless" seeds First, generally argues grades inprime that reside inindividual there areseeds bitsofcorporeal matter; second, matter; third, there arespiritual that theorigination seeds oflifefrom brute andthespontanematter, explain ousbirth oforganisms where seeds aremissing. SeeMarsilio Platonic Ficino, , corporeal Theology Vol.1,87,257.

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actionbythemotiveforceofsoul.TheviewthatGod and natureaffect things a that Ficino hold fromwithinthe substanceof matter, therefore, required robusttheoryofmatter. The idea thatmatterhas somethingof realityin it, thatit possessesthe forFicino orrudiments offorms, seeds,vestiges mayhavealsobeenconfirmed That to have been conthe of itself. is Ficino say, may by history philosophy ofprimematter those that he vincedoftherobustness by philosophers thought Timaeusargued a pia philosophia: articulated Bya bastardchainofreasoning, fortheexistenceof thereceptacle of becomingat 52B of Platos Timaeus.In thePimander , HermesTrismegistus arguedthattheall ofnatureis contained, within the welter of the elements,and he describeslifeas brought latendy, thelivingthingsthatshe heldwithin."92 Plotinus forth"from[earth]herself ofbecomingwas a discussion thoughtthatPlatosdiscussionofthereceptacle ofprimematter. impassibilEchoingPlotinus,Ficinoassertsthefundamental as themeetinggroundofall qualities.ButunlikePlotinus, of matter ity prime and Ficinodoesnotclaimthatprimematteris veritably Augustine non-being. Bonaventure bothbelievedthatnatureis conditionedbyseminalreasons,and closerto his own time,FranciscanScholasticphilosophers held thatmatter can existindependent of form,and thatit can be known.Each of thesephielementsofwhatwouldbecomeFicinos theory ofprime losophersarticulated would have,in thislight, matter.If anything, theThomisticinterpretation fromtheviewof primematterof appearedpeculiarto Ficino,an aberration whomhe thoughtmadethecrucialturnfrommatethosepiousphilosophers rialto immaterial things.

92)Hermetica Brian , trans. (NewYork, 1992),3. Copenhaver

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