Descartes Espiritual

download Descartes Espiritual

of 33

Transcript of Descartes Espiritual

  • 8/12/2019 Descartes Espiritual

    1/33

    Descartes's Geometry as Spiritual ExerciseAuthor(s): Matthew L. JonesSource: Critical Inquiry, Vol. 28, No. 1, Things (Autumn, 2001), pp. 40-71Published by: The University of Chicago PressStable URL: http://www.jstor.org/stable/1344260.

    Accessed: 07/01/2014 07:42

    Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at.

    http://www.jstor.org/page/info/about/policies/terms.jsp

    .JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

    content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

    of scholarship. For more information about JSTOR, please contact [email protected].

    .

    The University of Chicago Pressis collaborating with JSTOR to digitize, preserve and extend access to Critical

    Inquiry.

    http://www.jstor.org

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject to JSTOR Terms and Conditions

    http://www.jstor.org/action/showPublisher?publisherCode=ucpresshttp://www.jstor.org/stable/1344260?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/1344260?origin=JSTOR-pdfhttp://www.jstor.org/action/showPublisher?publisherCode=ucpress
  • 8/12/2019 Descartes Espiritual

    2/33

    Descartes's Geometry as Spiritual Exercise

    MatthewL.Jones

    IntroductionMost academics are familiar with a comforting fable, subject to minorvariations, about Rene Descartes and modern philosophy. Around 1640,Descartes philosophically crystallized a key transformation latent in Re-naissance views of humanity. He moved the foundation of knowledgefrom humans fully embedded within and suited to nature to inside eachindividual. Descartes made knowledge and truth rest upon the individualsubject and that subject's knowledge of his or her own capacities. Thismove permitted a profoundly new thoroughgoing skepticism, but ratherthan undermining universal knowledge by positing a uniformity of hu-man subjects, this move ultimately guaranteed intersubjective knowl-edge. Knowledge became subjective and objective. Not content merely tomake man himself the ground of knowledge, Descartes went further tomake the human mind alone the source for knowledge, a knowledgemodeled after pure mathematics. The new Cartesian subject ignored the

    Unless otherwise indicated, all translations are my own. I have benefited from RendDescartes, Rfgles utilesetclairespour la directionde l'esprit n la recherche e la viriti, trans. Jean-Luc Marion and Pierre Costabel (The Hague, 1977) and Regulae ad directionemngenii-Rulesfor the Directionsof the Natural Intelligence:A Bilingual Editionof the CartesianTreatise nMethod,trans. and ed. George Heffernan (Amsterdam, 1998).For helpful criticism and support, thanks to Mario Biagioli, Tom Conley, Arnold Da-vidson, Kathy Eden, Pierre Force, Peter Galison, Michael Gordin, David Kaiser, LisbetKoerner, Elizabeth H. Lee, audiences at Harvard, Cornell, and Columbia, and the editorsat CriticalInquiry.CriticalInquiry28 (Autumn 2000)? 2001 by The University of Chicago. 0093-1896/01/2801-0004$02.00. All rights reserved.

    40

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    3/33

    CriticalInquiry Autumn2001 41manifold contributions of the body, and Descartes assumed all real knowl-edge could come only from a reason common to all humans. The univer-sality of the knowing thing and the processes of knowing make thisCartesian subject a transcendental one. Above all, mathematics, with itsproof techniques, and formal thought, modeled on mathematics, exem-plify those things that can be intersubjectively known by individual butimportantly similar subjects.Versions of this fable appear in numerous analyses, some quite so-phisticated and textually based, some crude and dismissive. These ver-sions provide grounds for praising or dismissing Descartes and thephilosophical modernity he wrought.' Rather than surveying or evaluat-ing these appraisals, here I want merely to clarify and anchor historicallythe subject Descartes hoped his philosophy would help produce.2 Thisessay examines one set of exercises Descartes highlighted as propaedeuticto a better life and better knowledge: his famous, if little known, geome-try.Critics and supporters have too often stressed Descartes's dependenceon or reduction of knowledge to a mathematical model without inquiring

    1. My goal is not to undermine such appraisals but to offer a stronger historical basisfor them. To take two important critical exemplars from the serious literature: Femin-ist critics have stressed the historical conditions of gender and social status in the emer-gence of claims to universal knowledge based on universal mental processes. Structuralistand poststructuralist critics characterize the subject as essentially a product of linguisticpractices. For a survey of some of these approaches, see Susan Bordo and Mario Moussa,Rehabilitating the 'I', in FeministInterpretations f Rene'Descartes,ed. Bordo (UniversityPark, Penn., 1999), pp. 280-304. One can easily multiply examples to include those fromphenomenology (especially Husserl and Heidegger), cognitive science, and analytic philos-ophy. There are several important compendia of articles, often discussing and invoking Des-cartes. See, for example, WhoComesaftertheSubject? d. Eduardo Cadava, Peter Connor, andJean-Luc Nancy (New York, 1991), and Penser le sujet aujourd'hui,ed. Elisabeth Guibert-Sledziewski and Jean-Louis Viellard-Baron (Paris, 1988).

    2. Descartes used the term subject n the traditional Aristotelian manner. There arenumerous other historical corrections to the fable. See Stephen Gaukroger's introductionto Descartes:An IntellectualBiography Oxford, 1995), and John Schuster, Whatever ShouldWe Do with Cartesian Method?--Reclaiming Descartes for the History of Science, in Essayson thePhilosophy nd Scienceof Rene'Descartes,ed. Stephen Voss (New York, 1993), pp. 195-223. A key approach has been to underline Descartes's continuity with late scholasticism;for two recent examples, see Dennis Des Chene, Physiologia:NaturalPhilosophyn Late Aristote-lian and CartesianThought(Ithaca, N.Y., 1996), and Roger Ariew, Descartes nd theLast Scho-lastics (Ithaca, N.Y., 1999). Another key movement has been to undermine the view thatDescartes had no room for the senses. See, for example, Desmond M. Clarke, Descartes'sPhilosophyof Science (University Park, Penn., 1982), and Daniel Garber, DescartesEmbodied:Reading CartesianPhilosophy hroughCartesianScience(Cambridge, 2001).

    Matthew L. Jones ([email protected]) is assistant professor ofhistory at Columbia University. He is preparing a cultural history ofmathematics and natural philosophy as spiritual exercises in seventeenth-century France, especially in Descartes, Pascal, and Leibniz.

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    4/33

    42 MatthewL.Jones Descartes'sGeometrys SpiritualExerciseinto the rather odd mathematics he actually set forth as this model. Hisgeometry, neither Euclidean nor algebraic, has its own standards, its ownrigor, and its own limitations.3 These characteristics ought radically tomodify our view of Descartes's envisioned subject. Although the technicaldetails of his geometry might seem interesting and comprehensible onlyto historians of mathematics, the essential features grounding Descartes'sprogram can be made readily comprehensible. Descartes did far morethan theoretically (albeit implicitly) invoke the knowing subject in hisMeditations.To pursue his philosophy was nothing less than to cultivateand order one's self. He offered his revolutionary but peculiar mathemat-ics as a fundamental practice in this philosophy pursued as a way of life.Let us move, then, from abstraction about Descartes to the historicalquest for this way of life.In his earliest notebook, Descartes noted an ironic disjunction be-tween bodily health and spiritual or mental health. Vices I call maladiesof the soul, which are not so easily diagnosed as are maladies of the body.While we often have experienced good health of the body, we have neverhad any experience of good health of the mind. 4 Descartes's languageof spiritual malady harkens to Cicero's TusculanDisputations: Diseases ofthe soul are both more dangerous and more numerous than those ofthe body. 5For Cicero, philosophy offered succor for these diseases. As-suredly there is an art of healing the soul-I mean philosophy, whose aidmust be sought not, as in bodily diseases, outside ourselves, and we mustuse our own utmost endeavor, with all our resources and strength, to havethe power to be ourselves our own physicians (T,3.3.6, pp. 230-31). Thededicated pursuit of the spiritual exercises of a philosophy alone canovercome the sickness and delusion inculcated by institutions, tradition,and everyday commerce.6 Clear thinking and the nobility attendant upona healthy soul demanded work, exercise-askesis.Descartes's geometry was such a spiritual exercise, meant to counterinstability, to produce and secure oneself despite outside confusionthrough the production of real mathematics.' Descartes's famous quest tofind a superior philosophy took place within this therapeutic model. Cic-ero's account of philosophy's curative virtues and his vision of a self-

    3. My analysis of the geometry rests on a number of specialized studies, above all thework of Henk J. M. Bos, cited extensively below.4. Rene Descartes, Oeuvresde Descartes,ed. Charles Ernest Adam and Paul Tannery,2d ed., 12 vols. (Paris, 1971), 10:215; hereafter abbreviated AT5. Cicero, Tusculan isputations, rans. J. E. King (Cambridge, 1971), 3.3.5, pp. 228-29;hereafter abbreviated T6. For the theme of philosophy as a therapeutic for the soul in Hellenistic philosophy,see Andre-Jean Voelke, La Philosophie ommethirapiede l'dme:Etudesdephilosophiehellinistique(Paris, 1993).7. Spiritual exercises as a crucial category for understanding ancient Greek andRoman and particularly Hellenistic thought stems from the essential work of Pierre Hadot;see esp. Pierre Hadot, Exercicesspirituels tphilosophie ntique(Paris, 1981). Beyond the work

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    5/33

    CriticalInquiry Autumn2001 43selecting elite purifying themselves was disseminated widely in late Re-naissance and early modern Europe. Descartes had very likely encoun-tered Cicero's text at his Jesuit school; in any case his Jesuit pedagogywas predicated in part on this model of philosophy's ennobling, curativevirtues.8 The diagnostic then curative philosophical model received agreat boost from Pierre Charron's vastly influential Livres de la sagesse(1601). Charron calls man to himself, to examine, sound out and studyhimself, so that he might know himself and feel his faults and miserablecondition, and thus render himself capable of salutary and necessary rem-edies-the advice and teachings of wisdom. 9 But Descartes's early noteabove underlined his skepticism of the therapeutic capacity of (largelystoic) philosophy and contemporary accounts of wisdom-varying philos-ophies for living (see T, 3.3.5, pp. 230-31).1o However much he clearlydesired a therapy for the soul, Descartes could not see how to choose anyparticular one without a benchmark to use as a certain gauge of the soul'shealth. While he might second Charron's diagnoses of humanity's misery,Descartes at this early stage simply lacked any means to decide amongthe many treatments available in the early seventeenth century.Pages later in his notebook the first glimmers of a way forward ap-peared. He discussed a number of new mathematical discoveries involv-ing instruments and machines. Soon he applied these discoveries to thequestion of the soul's health. New forms of exercise, including geometri-cal exercise, could provide the means to come to a baseline of spiritualhealth.Descartes made the concreteness of these exercises clear. A few yearsafter writing his notebook, he advised studying the simplest and leastexalted arts, and especially those in which order prevails-such as thoseof artisans who weave and make carpet, or the feminine arts of embroi-dery, in which threads are interwoven in an infinitely varied pattern.The same held for arithmetic and games with numbers. It is astonishinghow the practice of all these things exercises the mind, so long as we donot borrow their discovery from others, but invent them ourselves (AT,10:404). Cicero had likewise maintained that intense personal endeavor

    of Hadot, see Michel Foucault, Le Soucide soi, vol. 3 of Histoirede la sexualiti, 3 vols. (Paris,1984), esp. pp. 51-85, and Arnold I. Davidson, Ethics as Ascetics: Foucault, the History ofEthics, and Ancient Thought, in Foucaultand the Writingof History,ed. Jan Goldstein (Ox-ford, 1994), pp. 63-80.8. See Regulae professoris humanitatis, Ratio atqueinstitutio tudiorum,ed. LadislausLukaics,vol. 5 of Monumentahistorica ocietatis esu(1591; Rome, 1965), p. 303.9. Pierre Charron, Livresde la sagesse(1601/1604; Paris, 1986), p. 369; my emphasis.10. And then how can we accept the notion that the soul cannot heal itself, seeingthat the soul has discovered the actual art of healing the body (T 3.3.5, pp. 230-31).11. See Dennis L. Sepper, Descartes'sImagination:Proportion, mages,and theActivityofThinking(Berkeley, 1996), p. 135 and his comments on the expansion of ingenium's powerthrough exercise, p. 140.

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    6/33

    44 MatthewL.Jones Descartes'sGeometrys SpiritualExercisewas necessary for health. Such study habituated one to experiencing clearand distinct order:

    We must therefore practise these easier tasks first, and above all me-thodically, so that by following accessible and familiar paths we maygrow accustomed,ust as if we were playing a game, to penetratingalways to the deeper truth of things. [AT,10:405; my emphasis]'2Descartes boldly announced, human discernment [sagacitas] consistsalmost entirely in the proper observance of such order (AT,10:404; CSM,1:35). Upon such discernment of order rested the ability to make the willcapable of clearly recognizing the intellect's guidance. And no activitydeveloped discernment better than mathematics:

    These rules are so useful in the pursuit of deeper wisdom that I haveno hesitation in saying that this part of our method was designednot just for the sake of mathematical problems; our intention was,rather, that the mathematical problems should be studied almost ex-clusively for the sake of the excellent practice which they give us inthe method. [AT 10:442; CSM, 1:59]Descartes's new geometry hardly offered a totalizing and algorithmicmeans for mechanically gaining knowledge of a mathematical world butrather gave exemplary practice in seeing and thinking clearly, in experi-encing with a healthy soul. Such effort, undertaken with one's greatestendeavor, could provide some standard for judging among philosophicaldoctrines and practices.But wait. What does all this historical detail have to do with the sub-stance of Descartes's mathematics? Descartes might have held mathemat-ics to be good for some exercise, but how possibly could that make itscontent, its essence, any different? After all, since Euclid had exemplifiedmathematical rigor, what could be more obvious than that mathematicsretains an unchanging core despite all its varied uses, its manifold repre-sentations, and the motivations for doing it?Few would now doubt the need to study rigorously the contingentconstitution of systems of thought, sets of epistemic practices, and theembedding of those constitutions within their cultural and social roles.In nearly every study of such systems, however, a cordoned-off core oflogic and rigorously argued philosophy remains. So, one ought rightly tocontend, however variable the cultural uses of philosophy and mathemat-ics, there remains an invariable, autonomous essence in each to be stud-ied in itself, an essence abstractable from those uses. My research takes as

    12. Descartes, ThePhilosophicalWritingsof Descartes,trans. Robert Stoothoff et al., 3vols. (Cambridge, 1984), 1:36; hereafter abbreviated CSM.

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    7/33

    CriticalInquiry Autumn2001 45its starting point precisely the historical contingency of how mathematics,logic, and natural philosophy were supposed to be rigorous, evident, co-herent, or certain during the seventeenth century in Western Europe.'After the criticisms of humanists, skeptics, and neoscholastics of the six-teenth century, the very definition and centrality of proof was contested.Simply put, Descartes rejected standard mathematical proof. And he washardly alone. No consensus existed around the objects of mathematics,its proof techniques, its proper institutional settings, its place in the hier-archy of disciplines, or its relationship to mathematical practitioners. 14Such contingency hardly implies sophomoric relativism. It means that thevery things that make a technical history of an object technical, system-atic, or rigorous are themselves historical. It means a plurality of pro-grams compete, each demanding serious, nonanachronistic technicalinquiry, none reducible to modern logic or proof, when the history oflogic and proof is precisely what ought to be explained.Descartes's account of mathematics called for changes in the objects fmathematics, so he limited proof processes, expanded kinds of allowablecurves, and added algebraic representation. Equally it altered the subjectsof mathematics. Recent historical attention to the self-fashioning of math-ematicians has paid too little attention to the variety of mathematicalpractices (and their metamathematical embedding) that were to helpeffect such fashioning. To assess correctly the contingent nature of mathe-matics demands examination of its practitioners' changing social embed-ding.'5 But equally, to evaluate its practitioners, one needs careful inquiry

    13. For metamathematical concerns in the seventeenth century, see Hermann Schii-ling, Die Geschichte er AxiomatischenMethode n 16. und beginnenden17. Jahrhundert(Hildes-heim, 1969), and Paolo Mancosu, ThePhilosophyof Mathematics nd MathematicalPractice nthe SeventeenthCentury New York, 1996).14. Recent studies of seventeenth- and eighteenth-century mathematical physics havecarefully detailed the specific mathematics of different thinkers. For examples, see MichaelS. Mahoney, Algebraicvs. Geometric Techniques in Newton's Determinations of PlanetaryOrbits, in Actionand Reaction:Proceedingsof a Symposiumo Commemoratehe TercentenaryfNewton's Principia, d. Paul Theerman and Adele E Seeff (Newark, 1993), pp. 183-205;Domenico Bertoloni Meli, Equivalenceand Priority:Newton versusLeibniz(Oxford, 1993); Mi-chel Blay,La Naissancede la mecanique nalytique:La Sciencedu mouvement u tournantdes XVIIeet XVIIIesidcles(Paris, 1992); and Douglas M. Jesseph, Squaringthe Circle:The WarbetweenHobbesand Wallis(Chicago, 1999), among others.15. See, for example, Mario Biagioli, The Social Status of Italian Mathematicians,1450-1600, Historyof Science27 (Mar. 1989): 41-95 and Galileo,Courtier:ThePracticeof Sci-ence in the Cultureof Absolutism(Chicago, 1993); Stephen Johnston, Mathematical Practi-tioners and Instruments in Elizabethan England, Annals of Science 48 (July 1991): 314-44;Robert S. Westman, The Astronomer's Role in the Sixteenth Century: A PreliminaryStudy, HistoryofScience 18 (June 1980): 105-47; J. A. Bennett, The Mechanics' Philosophyand the Mechanical Philosophy, Historyof Science24 (Mar. 1986): 1-28; Peter Dear, DisciplineandExperience:TheMathematicalWayn theScientificRevolution(Chicago, 1995); and Mahoney,The MathematicalCareerof Pierre de Fermat,1601-1665, 2d ed. (Princeton, N.J., 1994), pp.1-14, 20-25.

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    8/33

    46 MatthewL.Jones Descartes'sGeometrys SpiritualExerciseinto technical content and practices, into the range of objects, tools, andallowed logic of their particular mathematics.What then is a spiritual exercise? Is it something like aerobics withcrystals? Spiritual exercises are sets of practices aiming for the cultivationof the self. Specifying a spiritual exercise means something like outlining(1) a set of practices; (2) a conception of the self, where the self need notbe exclusively a mind or an intellect; and (3) the people the exercises arefor, that is, the social field of the exercises' application, either explicit orimplicit. As a category, spiritual exercise demands a careful spelling outof intellectual detail and social framework.This study examines what seem at once the most esoteric and themost modern of Descartes's works, the Geometry f 1637, on its own terms,using his repetitive statements of its purpose, its contents, its foundation.He continually asserted that mathematics is an exercise, perhaps the bestthat we have. In taking this claim seriously, we can clarify Descartes's ge-ometry. Simultaneously we will escape the long tradition of equating thesubject Descartes aimed to create through his exercise with the so-calledCartesian and modern subjects. We will get at the subjects and objects ofDescartes's mathematics and early natural philosophy, as well as the prac-tices of language, of the body, and of the mind that constitute them.While a number of insightful scholars have rightly stressed the needto focus on Descartes's work as something practiced, they have largelyavoided his mathematics.16 His curious mathematics offers the key to un-derstanding how Descartes intended to have his philosophy practiced. Ifocus on the laborious nature of mathematics; it is exercise, hard exer-cise-a point obvious enough to mathematicians but too often absentfrom histories and philosophies of the subject. Only work using geometryas exemplar could produce the focused ingenium-the natural intelli-gence-that Descartes thought the very definition of cultivation.

    16. There is one exception, however: Toimitate Descartes' example, David Lachter-man rightly notes, one will need to practice and apply it, not memorize or passively receiveit (David Rapport Lachterman, TheEthicsof Geometry: Genealogyof Modernity New York,1989], p. 134). In a penetrating study of Descartes'sMeditations,Foucault insisted that recog-nizing the intelligibility of Descartes's choices rested on a double reading of his text asboth a systemand an exercise Foucault, My Body, This Paper, This Fire, Aesthetics,Methodand Epistemology, ol. 2 of Essential WorksofFoucault,1954-1984, ed. James D. Faubion [NewYork, 1998], p. 406); compare the considerably more historically grounded Gary Hatfield,The Senses and the Fleshless Eye: The Meditations as Cognitive Exercises, in EssaysonDescartes's Meditations, d. Amelie Oksenberg Rorty (Berkeley, 1986), pp. 45-79; for a nega-tive assessment of Hatfield, see Bradley Rubidge, Descartes's Meditationsand DevotionalMeditations, Journal of the History of Ideas 51 (Jan-Mar. 1990): 27-49; and for positive ri-postes, see Dear, Mersenne's Suggestion: Cartesian Meditation and the MathematicalModel of Knowledge in the Seventeenth Century, in Descartesand His Contemporaries,d.Roger Ariew and Marjorie Grene (Chicago, 1995), pp. 44-62; and Sepper, The Texture ofThought: Why Descartes's Meditiationes s Meditational, and Why It Matters, in Descartes'sNatural Philosophy,ed. Gaukroger, John Andrew Schuster, and John Sutton (New York,2000), pp. 736-50.

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    9/33

    CriticalInquiry Autumn2001 47EnvisioningtheAncients: TrueMathematics ndNoninstitutionalized hilosophy

    Descartes's early experiences of contemporary mathematics while inthe Jesuit school of La Flkche led him to conclude that mathematics wasgood only for clever tricks and mean trades. Subsequently he askedhimself how Plato'sAcademy refused to admit anyone ignorant of mathe-matics, this puerile and hollow science (AT 10:375; see CSM, 1:18). Theancients, he decided, must have had a mathematics altogether differentfrom the mathematics of our time (AT,10:376; see CSM, 1:18). Descartescaught glimpses of this true mathematics in the ancient mathematicians.Why only glimpses? In a remarkable piece of paranoid historical recon-struction, Descartes explained that the ancients fearedthat their method, being so easy and simple, would become cheap-ened if it were divulged, and so, to make us wonder, they put in itsplace steriletruthsdeductivelydemonstrated ith someingenuity,as the ef-fects of their art, rather than teaching us this art itself, which mighthave dispelled our admiration. [AT, 10:376-77, my emphasis; seeCSM, 1:19]

    The ancients' ruse of formal proof led Descartes's amazed contemporariesto memorize the ancients' sterile truths rather than to grasp the funda-mental relationships behind those truths.Descartes's friend, writer Guez de Balzac, made a similar point aboutCicero. Cicero's codified rhetoric for swaying the mob had been mistakenas his true rhetoric and dialectic and then fetishized.18 Balzac and Des-cartes's contemporaries had mistaken instantiations of technique for theessences of mathematics and rhetoric. These ancient techniques mightwell deceive, move, and direct, but neither dispel wonder nor producetrue orators and thinkers. Misapprehension of the ground of these tech-niques made their contemporaries the mob to be swayed, those needing

    17. For Jesuit mathematics pedagogy in France and at La Fleche, see Antonella Ro-mano, La Compagnie de Jesus et la revolution scientifique: Constitution et diffusion d'uneculture mathematique jesuite a la Renaissance (1540-1640) (Doctorat, Universite deParis-I, 1996), and the traditional source, Camille de Rochemonteix, Un Collegedef dsuitesaux XVIIPI t XVIIPsiecles:Le Collge Henri IV de La Flche, 4 vols. (Le Mans, 1889); see alsoGenevieve Rodis-Lewis, Descartes et les mathematiques au college, in LeDiscours t samithode:Colloque our le 350e anniversairedu Discours e la mithode, d. Nicolas Grimaldi andMarion (Paris, 1987), pp. 187-211.18. See Jean-Louis Guez de Balzac, Suite d'un entretien de vive voix, ou de la conver-sation des Romains, in Oeuvresdiverses,ed. Roger Zuber (1644; Paris, 1995), pp. 73-96,82-83. In his defense of Guez de Balzac's rhetoric, Descartes offered an historical accountof the loss of true rhetoric and the production of rules and sophismata to replace it. SeeAT, 1:9.

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    10/33

    48 MatthewL.Jones Descartes'sGeometrys SpiritualExerciseexternal discipline, when, presumably, they ought to have been the onesswaying the mob. They lost at once true mathematics and rhetoric andwith them knowledge, civility, and self-control.Descartes and Balzac connected institutionalization to this depen-dence on technique. Like many of their contemporaries, they envisionedthe ancients as successful, stable, and productive precisely because theywere honniteshommes-a sort of cultivated gentlemen-outside of stul-tifying institutions.19 Blaise Pascal captured this common seventeenth-century view well: One thinks of Aristotle and Plato only in the blackrobes of pedants, but they were honniteshommes,aughing along with theirfriends as they wrote their philosophy to regulate a hospital of mad-men. 20 Institutionalized supplementary technique for regulating othershad been mistaken for essential philosophical doctrine and consideredways of living.In contrast to moderns who fetishized final results, Descartes argued,the same light of mind that allowed [the ancients] to see that one mustprefer virtue to pleasure and honnetet6 to utility ... also gave them trueideas in philosophy and the method (AT,10:376; see CSM, 1:18).21 Des-cartes echoed Cicero's famous critique of Aristotle in phrase and intent:Whereas Aristotle is content to regard utilitasor advantage as the aim ofdeliberative oratory, it seems to me that our aim should be honestasandutilitas. 22Morality and utility characterized deep knowledge and trueskill. Descartes, Pascal, and Balzac, like many others in the early seven-teenth century, assimilated the ancients to their vision of honnitete .23nhonniteti, a genteel nonspecialization, proper manners, and truth makingoutside of formal institutions were intertwined with elements of tastemore broadly conceived.24

    19. See Emmanuel Bury, Le Sourire de Socrate ou, peut-on &trea a fois philosopheet honn&te homme? in Le Loisirlettr'l'~dge classique,ed. Marc Fumaroli, Philippe-JosephSalazar, and Bury (Geneva, 1996), pp. 197-212.20. Blaise Pascal, Pensies, in Oeuvres ompldtes e BlaisePascal, ed. Louis Lafuma (Paris,1963), no. 533, p. 578.21. Compare the Discours,AT, 6:7-8; see also Marion, Sur l'ontologie risede Descartes:Sciencecartesienne tsavoir aristotiliciendans les Regulae Paris, 1975), p. 151.22. Cicero, De inventione, in De inventione;De optimumgenereoratorum;Topica,trans.H. M. Hubbell (Cambridge, Mass., 1949), 2.51.156, p. 324; compare 2.55.166, p. 332 andpseudo-Cicero, Rhetorica d herennium, rans. Harry Caplan (Cambridge, Mass., 1954), 3.2.3,pp. 160-62; see also Quintilian, TheInstitutioOratoriaof Quintilian,trans. H. E. Butler, 4 vols.(New York, 1921), 3.8.22, 1:490, and Montaigne De l'utile et l'honneste, Essais, ed. Mau-rice Rat 2 vols. (Paris, 1962) 3.1, 2:205-21.23. On honniteti and Descartes's physical work, see Dear, A Mechanical Microcosm:Bodily Passions, Good Manners, and Cartesian Mechanism, in ScienceIncarnate:HistoricalEmbodiments f Natural Knowledge,ed. Christopher Lawrence and Steven Shapin (Chicago,1998), pp. 51-82, esp. pp. 62-63.24. Early in the century, the notion referred primarily to normative vision of judg-ment and taste among the nobility of the robe. Later, honnitetebecame an anticourtly, morearistocratic ideal. For honnitete,see Zuber, Die Theorie der Honnetete, in Frankreich nd

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    11/33

    CriticalInquiry Autumn2001 49But Descartes and Balzac hardly thought the ancient gentlemen-philosophers reached their own ideal. That they took the trouble of writ-

    ing so many vast books about geometry, Descartes argued, showed thatthey did not have the true method for finding all the solutions (AT6:376). While the ancients had the seeds of true method, Descartes con-tended, they did not know it perfectly. Both Balzac and Descartes simi-larly argued that the ancients had the seeds of true rhetoric, but not truerhetoric itself.25The latter extended this account of the ancients' imper-fection to mathematics. His evidence? Their extravagant transports ofjoy and the sacrifices they offered to celebrate discoveries of little weightdemonstrateclearly how rude they were (AT, 10:376). This lack of self-control proved that some results came as surprises, gained not by me-thodic comprehension but rather miracle-like genius. Even if the luckyancients had the right informal social forms, they lacked the complemen-tary exercise necessary for eliminating imitation and surprise.Moderns needed better social forms and better exercises to renewand exceed the virtues of the ancients. Balzac spearheaded a movementto civilize the unruly texts of the Renaissance, to take the fruits of human-ism and strip them of the extravagance and pedantry exemplified inthe-to his mind--uncontrolled works of Montaigne or classical scholarslike Girolamo Cardano. Only then could humanism be properly deinsti-tutionalized and the true potential of ancient learning nourished. Thisreturn to the urbaniti of Rome's noninstitutionalized higher philosophyneeded new forms of writing and print, which Balzac tried to produce.26Descartes took Balzac's iconic attempt to write urbane political phi-losophy, ThePrince, as the physical model for layout of the DiscourseonMethod. In a number of letters to the great Dutch diplomat, musician,connoisseur, and poet Constantijn Huygens, Descartes gave detailed in-structions for the typographic layout, the typeface, the margins, the para-graph breaks, and even the sort of paper to be used.27 Its physical formNiederlainde, ol. 2 of Die Philosophiedes 17. Jahrhunderts,ed. Jean-Pierre Sch6binger (Basel,1993), pp. 156-66; Bury, Littiratureet politesse:L'Inventionde l'honnite homme,1580-1750(Paris, 1996); Domna C. Stanton, The Aristocratas Art:A Study of the Honnite Homme andthe Dandy in Seventeenth-andNineteenth-Century renchLiterature New York, 1980); MauriceMagendie, La Politessemondaineet les thioriesde l'honniteti,en Franceau XVIPsiecle,de 1600 a1660, 2 vols. (Paris, 1925); and Nannerl O. Keohane, Philosophy nd the Statein France:TheRenaissance o theEnlightenment Princeton, N.J., 1980), esp. pp. 283-88.25. See Balzac, letter to Boisrobert, 28 Sept. 1623, quoted in Bernard Beugnot, LaPrecellence du style moyen, in Histoirede la rhitoriquedans l'Europemoderne,1450-1950, ed.Fumaroli (Paris, 1999), p. 542.26. See Zuber, L'Urbanitefrangaise, Les Emerveillements ela raison:Classicismesittirai-resdu XVIPIsieclefrangais(Paris, 1997), pp. 151-61.27. See Henri-Jean Martin, Les Formes de publications au milieu du XVIIe siecle,Ordreet contestation u tempsdesclassiques,ed. Roger Duchene and Pierre Ronzeaud, 2 vols.(Paris, 1992), 2:209-24, and Jean-Pierre Cavaille, Descartes: Stratege de la destination,XVIPI iecle,no. 177 (Oct.-Dec. 1992): 551-59.

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    12/33

    50 MatthewL.Jones Descartes'sGeometrys SpiritualExerciseechoed its content's promises: new exercises proper for a noninstitutionalphilosophy of and for honniteshommesand perhaps femmes.Returning to the true mathematics hidden by the devious ancientsmeant the production of a better set of exercises producing knowledgeand civility. In debate around his Geometry,ne of three essays followinghis Discourseon Method,Descartes became enveloped in controversy withthe famous Toulousian mathematician and lawyer Pierre de Fermat. Des-cartes condemned Fermat's mathematics as wondrous and uncivil:

    Mr. Fermat is a Gascon; I am not. It's true that he has found numer-ous particularbeautiful things ... he is a man of great genius. But,as for me, I've always striven to consider things with extreme gener-ality, to the end of being able to infer rules that also have utility else-where. [AT 3:333; my emphasis]28Gascon was a well-targeted snub. It suggested provincialism, extrava-gance, amusement, and a quest for advancement: in sum, incivility anddisorder.29Descartes attacked how Fermat arrived at his results. Without

    industry and by chance, one can easily fall onto the path one must take toencounter it (AT 1:490). Fermat was doubly particular: he found prettytrinkets and he did so through genius-chancy genius. For Descartes,chance findings typified mathematics as then practiced. They were an in-ferior means toward a lower form of mathematical knowledge, one that,nonetheless, often produced results. The aleatory nature of such discov-ery produced wonder, dependence, and extravagance, not clarity, inde-pendence, and self-control.Fermat's mathematics was ironically inferior as mathematics ecause itfailed as a more general cultivating activity. Descartes's general geometricmethod, he claimed, offered true understanding, for an orderly construc-tive process produced all of its results.30 Every mathematical solutionneed not proceed by some new ingenuous technique dependent on indi-vidual instantiations of skill, expertise, and genius.31 For Descartes, realmathematical knowledge-cultivating knowledge-demanded chance

    28. As reported by Schooten to Christiaan Huygens. Compare Gaston Milhaud, Des-cartes avant (Paris, 1921), p. 160.29. Compare the similar attack on Descartes's friend Guez de Balzac as a Gascon,discussed in Jean Jehasse, Guezde Balzacet legenie romain,1597-1654 (Saint-Etienne, 1977),p. 117.30. See Henk J. M. Bos, Argumentson Motivation in the Rise and Decline of a Math-ematical Theory: The 'Construction of Equations,' 1637-ca. 1750, ArchiveforHistoryofExactSciences30 (Nov. 1984): 331-80, esp. p. 363. See also Gaukroger, The Nature of AbstractReasoning: Philosophical Aspects of Descartes's Workin Algebra, in TheCambridgeCompan-ion toDescartes, d. John Cottingham (Cambridge, Mass., 1992), pp. 91-114, esp. pp. 106-8.31. Nicely noted in Morris Kline, MathematicalThought rom Ancient to Modern Times(New York, 1972), p. 308.

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    13/33

    CriticalInquiry Autumn2001 51and genius be eliminated. He thusinsisted that mathematical prac-tices that made the assent to infer-ential steps-proofs-the essenceof mathematics be abandoned, al-though it required the temporaryuse and then transcendence ofsuch inferential steps. Descartesworked to sever, in his eyes, a truermathematics of cultivation from afalse one of mere calculation, pas-sive procedures, and deliberate de-ception.

    Descartes'sGeometry f 1637

    C

    D

    A

    FIG.1.-Example problem (my figure).The sixteenth and seventeenth centuries witnessed countless mathe-matical duels in which mathematicians tried to best one another withtheir ingenuity in solving particular problems.32A very simple exampleof a problem: Given a triangle ABC and a point D outside the triangle,one must construct a line through D dividing the triangle in two equalparts (fig. 1). All solutions must comprise a series of constructions ofcircles and lines produced by standard compasses and rulers. Usual solu-tions to such problems included no information about how to come tothe solution or how to go about solving another like it. 3Besting someonein a mathematical duel typically meant making others marvel at youringenuity in solving, not offering heuristic instruction. As the exampleabove indicates, Descartes criticized his rivals like Fermat, for findingnumerous particular ... things with genius rather than offering rulesuseful elsewhere in math or otherwise (AT 3:333; my emphasis).Descartes aimed to give a set of general tools offering a certainmethod for problem solving. The Geometry egan audaciously: Allprob-lems in Geometry can easily be reduced to such terms that there is noneed to know more than the lengths of certain straight lines to constructthem (AT,6:369). By assigning letters to line lengths, Descartes couldrepresent geometrical diagrams as algebraic formulas. His geometry32. Note, for example, those of Girolamo Cardano, Lodovico Ferrari, and NiccoloTartaglia. See Oystein Ore, Cardano,the GamblingScholar (Princeton, N.J., 1953), esp. pp.53-107; Mahoney, TheMathematicalCareerof Pierrede Fermat,1601-1665, pp. 6-7; and thereview of Arnaldo Masotti's LodovicoFerrarie Niccolo Tartaglia.Cartellidi SfidaMatematicabyAlex Keller, Renaissance Mathematical Duels, Historyof Science 14 (Sept. 1976): 208-9.33. See Bos, The Structure of Descartes's Giomitrie, n Descartes: l metodo i saggi, ed.Giulia Belgioioso et al. (Rome, 1990), pp. 349-69, esp. pp. 352-56.

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    14/33

    52 MatthewL.Jones Descartes'sGeometrys SpiritualExercisegained a toolbox of algebra-this is why the book is so famous. Everyalgebraic manipulation corresponded to a geometric construction. Forexample, the addition of two symbols meant the addition of one line seg-ment to another. In Descartes's mathematics, geometric problems get ge-ometrical constructions as solutions.34 Algebra should serve only as atemporary means toward conceiving ever more clearly and distinctly therelations among geometric entities.35To illustrate the power of his approach, Descartes addressed a keyproblem from antiquity-the Pappus problem.36In its simplest form, theproblem is to find all the points that maintain distances from two linessuch that the distances equal a constant. Solving the problem for a smallnumber of lines was relatively easy. But the traditional limitation to stan-dard compass and line constructions blocked the solution of the problemfor a higher number of lines.So Descartes needed more tools. He added a wider variety of curve-drawing instruments and defended their use (for an example, see fig. 3).His new machines generated a wider set of curves that could be used insolving geometric problems. With these new machines, Descartes be-lieved that he could solve the famous Pappus problem for any number oflines, thereby far surpassing the ancients. More important, he could doso as part of his systematic method for solving geometric problems andnot because of some ingenious insight or expertise, as in mathematicalduels.37Descartes concluded (perhaps foolishly) that he had provided thetools for classifying and systematically solving all geometrical problems

    EA B

    D AFIG. 2.-Multiplica-tion, from La Giomitrie, p.298.

    34. See Bos, The Structure of Descartes's Giomitrieand On the Representation of Curves in Descartes's Giomi-trie, Archivefor Historyof Exact Sciences24 (Oct. 1981): 295-338. He defined multiplication as follows: Let AB be unity. Ifone wants to multiply BD by BC, then one only needs to joinC to A, and draw the parallel from C to E. Then BE is thedesired product (since AB:BD::BC:BE and AB is unity,AB.BE = 1.BE = BC.BD); see fig. 2. Similarly,he defined thesquare root geometrically.35. Not all commentators agree on this point, in largepart because Descartes was well aware that his algebra couldproduce nongeometric solutions. See chapter 5 of Peter A. Schouls, Descartes nd the Possibil-ityof Science(Ithaca, N.Y., 2000).36. The Pappus problem: Let there be n lines L,, n angles 4i and a segment a, and aproportion /13.From a point P,one draws lines di meeting each Li with angle (i; find thelocus of points P such that the distances of the lines di maintain a set of proportions: Forn>2, 2n-1 lines, (d,?d,):(d+,1 d2,,_a)::cx: and for 2n lines, (dld,):(d,~ d2,,)...cL:P. I takethis description from Bos, On the Representation of Curves in Descartes's Giomitrie,p. 299.37. The Pappus problem itself acted as a sort of machine, which produced an ex-tended family of smaller problems, each with its family of orderly solution curves producedby a machine easy to imagine. On this, see especially chapter 2 of Emily Grosholz, CartesianMethodand the Problemof Reduction(Oxford, 1991).

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    15/33

    CriticalInquiry Autumn2001 53admitting certain solution. No longerwould slavish imitation of the big booksof the ancients and those of their mod-ern day followers be needed.Considerably more than meretools for mathematical problem solv-ing, his new geometrical tools offeredessential exercise:

    I stop before explaining all this inmore detail, because I would takeaway ... the utility of cultivatingyour esprit in exercising yourselfwith them, which is ... the keything that one can take away fromthis science. [AT,6:374]38

    C:y .

    ... BG A

    ..--

    FIG.3.-Geometric machine andassociated curve, from La Giomitrie, p.320. The machine rotates GL about G;GL, attached at L, pushes the contrap-tion KBC along the line AK. The inter-sections at C of GL and the ruler NKmake up the curve.

    Descartes'sCompetition: Range of SpiritualExercisesFor Descartes, self-cultivation meant developing the ability to allowthe will to recognize and to accept freely the insights of reason, and notjust following the passions or memorized patterns of actions. It meantessentially recognizing the limits of reason and willing not to make judg-ments about things beyond reason's scope.39 From the Rulesfor theDirec-tion of the Natural Intelligence ingenium] of the 1620s to the Principles ofPhilosophyand the Passionsof the Soul of the 1640s, Descartes criticizedcontemporary philosophical practices as deleterious to this proper self-cultivation. In his 1647 introduction to the French version of the Prin-

    ciplesof Philosophy,he argued that to live without philosophizingis properly to have the eyes closed without ever trying to open them;... this study is more necessary to rule our manners and direct usin this life than is using our eyes to guide our steps. [AT 9:2:3-4]

    Far more than mere precepts or an academic discipline, philosophy wasan activity directing the everyday; it was a mode of civility where the disci-pline of manner stemmed not from taught external techniques but ratherarose from internalized principles discerned by oneself. In studyingthese principles, one will accustom oneself, little by little, to judge bettereverything one encounters, and thus become more Wise. In contrast,traditional philosophy embodied memorized external rule of the self. Inthis they [his principles] will have an effect contrary to that of common Phi-38. Compare Gaukroger, Descartes,p. 153.39. This latter point appears most prominently in the fourth meditation.

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    16/33

    54 MatthewL.Jones Descartes'sGeometrys SpiritualExerciselosophy, for one easily notices in those one calls Pedants, that it rendersthem less capable of reasoning than if they had never learned it. [AT 9:2:18]In his important study of the image of Socrates in seventeenth-century France, Emmanuel Bury argues the century had

    a vision of ancient philosophy that stressed consciousness of the exis-tential character that ancient philosophy took on, so close, in manyways, to the spiritual exercises of the Christian religion: it is verymuch a question of a choice of a life, and philosophy has no meaningunless it is, in the final analysis, moral.40Yet we must not conflate late sixteenth- and seventeenth-century spiritualexercises with their ancient antecedents. Nor is it enough to consider theearly modern variants as merely Christianized, given the rapid and radi-cal transformations in the practice and theory of different Christianitiesduring this period. Understood and articulated through other aspectsof Early Modern culture, the ancient exemplary spiritual exercises wereresources many advanced to respond to seventeenth-century concerns.Central to the fundamental religious upheavals of the sixteenth cen-tury was a greatly reinforced emphasis on the individual as the unit forthe instillation of religious discipline.41 In France these religious transfor-mations coincided and interacted with wide-ranging social transforma-tions, still remarkably little understood. Social historians have long sinceabandoned the vision of an incipient bourgeois class rooted in a noblessede robeovercoming traditional elites. Exact social parameters are far lessimportant, however, than the tremendous uncertainty about what consti-tuted nobility or elite status.42One correlation with instability in socialposition and codes of conduct was the massive effusion of cultural pro-jects offering competing visions of distinction and nobility.43These cul-

    40. Bury, Le Sourire de Socrate ou, peut-on etre a la fois philosophe et honnetehomme? p. 205.41. Such an emphasis is fundamental in John Bossy, Christianityn the West,1400-1700(Oxford, 1985). For the notion of social disciplining, see Gerhard Oestreich, Neostoicismand theEarlyModernState,trans. David McLintock, ed. Brigitta Oestreich and H. G. Koenigs-berger (Cambridge, Mass., 1982); for the use of social disciplining and confessionalizationin describing the Reformation and Counter Reformation, see the overview of Germanscholarship in R. Po-chia Hsia, SocialDiscipline n theReformation:CentralEurope,1550-1750(New York, 1989), esp. chap. 6.42. The vague English word gentlemenmight translate any number of historians' cate-gories for France's elites or any number of contemporaries' own categorizations: noblessederobe,noblessed'dpee,aboureur, ourgeois entilhomme, onnitehomme,and many others.43. For a survey of the recent social history of elites in this period, see Jean-MarieConstant, Absolutisme et ModernitY, n Histoiredes lites en Francedu XVIeau XXe iecle, ed.Guy Chaussinand-Nogaret (Paris, 1991), pp. 145-216, and the useful but older study byJohn Hearsey McMillan Salmon, Society n Crisis:France n the SixteenthCentury(New York,1975), pp. 92-113; for educated elites in the late sixteenth century, see George Huppert,

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    17/33

    CriticalInquiry Autumn2001 55tural projects were not some necessary superstructual reflections of somebase social relations; they were attempts to understand and to transformthose social relations along differing contested axes. As one historian hastermed it, a culture of separation saturated French elite culture.4 Whilenot reflecting accurately some actual social separation, this culture dis-played rather an often desperate, often highly theorized desire for disso-ciation and produced a wide array of different schemes that attempted todefine and justify divisions of society and hierarchy.45Each rested onsome different account of nobility-and many were nobilities of mind,morals, or the spirit and not in theory, of course, of land, a particulareducation, or a particular social position. So, early seventeenth-centuryFrench culture was awash in possibilities new and old for simultaneouslyreforming one's self and one's knowledge.46 These conflicting spiritualexercises offered different modes and ideals for cultivating the self: Igna-tius's SpiritualExercises and its various reformulations), Michel de Mon-taigne's Essays, the humanist ideal orator/citizen Charron's Livresde lasagesse,Jean Bodin'sMethodusadfacilemhistoriarumcognitionem,he alchem-ical romances of B6roalde de Verville, Eustachius a Sancto Paulo's Ex-ercices spirituelles, Pierre Gassendi's Epicureanism, Justus Lipsius'sNeostoicism, Cornelius Jansenius's Augustinianism, Seneca's De vita beata,Epictetus's Manual, to name but a few.47Les BourgeoisGentilshommes:n Essayon theDefinition of Elites in RenaissanceFrance(Chicago,1977); for elites and the transformation of manners, see Norbert Elias, The CourtSociety,trans. Edmund Jephcott (New York, 1983); Orest Ranum, Courtesy,Absolutism, and theRise of the French State, 1630-1660, Journal of ModernHistory52 (Sept. 1980): 426-51; andEllery Schalk, The Court as 'Civilizer' of the Nobility: Noble Attitudes and the Court inFrance in the Late Sixteenth and Early Seventeenth Centuries, in Princes,Patronage,and theNobility:TheCourtat theBeginning of the ModernAge, c. 1450-1650, ed. Ronald G. Asch andAdolf M. Birke (Oxford, 1991), pp. 245-63.44. Anna Maria Battista, Morale 'prive' et utilitarisme politique en France au XVIIesiecle, in Staatsrdson: tudienzur GeschichteinespolitischenBegriffs,ed. Roman Schur (Berlin,1975), p. 101.45. See ibid., and Huppert, LesBourgeoisGentilshommes;ompare Peter Burke, PopularCulture n EarlyModernEurope(New York, 1978), pp. 270-81. The sense of instability is wellillustrated by the proliferation of treatises desperately trying to identify unambiguous visualmarkers of social position, most famously, Charles Loyseau, A Treatiseof Ordersand PlainDignities, trans. and ed. Howell A. Lloyd (Cambridge, Mass., 1994).46. The term spiritualexerciseshad, of course, a dominant referent in Descartes's day:Ignatius of Loyola's SpiritualExercises,which itself drew on the ancient genre of spiritualexercises. For the most careful study of Descartes's relationship with the Ignatian exercises,one which casts great doubt on commentators seeking echoes of Ignatius in Descartes, seeMichel Hermans and Michel Klein, Ces Exercicesspirituelsque Descartes aurait pratiques,Archivesde Philosophie59 (Jul.-Sept. 1996): 427-40. For studies of such echoes, see, for ex-ample, the study of textual similarities in Walter John Stohrer, Descartes and IgnatiusLoyola: La Fleche and Manresa Revisited, Journal of the History of Philosophy 17 (Jan.1979): 11-27.47. For intimations on this, see John Stephenson Spink, FrenchFree-Thoughtrom Gas-sendito VoltaireLondon, 1960), esp. chap. 8, andJohn Cottingham, Philosophy nd theGoodLife:

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    18/33

    56 MatthewL.Jones Descartes'sGeometrys SpiritualExercisePartisans may have disputed the proper connected form of self-cultivation and knowledge production, but they did not question the exis-

    tence of such a connection itself.48Many of these stressed the digestionof historical exemplars while others stressed literary ones; such digestedexemplars, particularly of the Stoics, formed much of the ethics coursein Descartes's final year of schooling.49 A few, like Lipsius or Gassendi,focused on moralities grounded in natural philosophies.As Pierre Hadot has eloquently illustrated, for the ancient Epicure-ans and Stoics such as Marcus Aurelius, the careful study of the naturalworld mattered in large part for its importance as a spiritual exercise. Asis well known, natural philosophy uncovered in principle the naturalisticbasis for ethics. But, more strongly, working through that natural philoso-phy helped one to recognize both one's natural limits and abilities and acoherent moral end. So too in the Early Modern revivals of the ancientsects.These spiritual exercises were not a mere automatic reflection ofsome classes' aspirations, a cynical codification of their particular abilitiesas the good life. They were, however, attempts at defining criteria for a

    Reasonand the Passions n Greek,Cartesian,and Psychoanalytic thics(New York, 1998), chap. 3.For the uneasy coexistence of the ideals of pagan and Christian antiquities in the period,see Zuber, Guez de Balzac et les deux Antiquites, XVIe siecle, no. 131 (Apr.-Jun. 1981):135-48. Hadot has examined how physical thought figured in Marcus Aurelius's generalscheme of self-cultivation. Knowing the physical world allows one to concentrate fully onthat which can be changed, to achieve the state of apatheia. See Hadot, Exercicesspirituels,EExperience de la meditation, Magazinelitteraire,no. 342 (Apr. 1996): 73-76, and Hadot,Philosophy s a Wayof Life: SpiritualExercisesfromSocrates oFoucault,trans. Michael Chase, ed.Davidson (Oxford, 1995). Lisa Sarasohn recently has emphasized how Gassendi's physicalthought similarly figured within his Epicurean ethic of self-cultivation. See Lisa T. Sara-sohn, Gassendi'sEthics: Freedom n a Mechanistic Universe(Ithaca, N.Y., 1996). Compare, for

    Germany, Pamela H. Smith, The BusinessofAlchemy:Scienceand Culture n theHolyRomanEm-pire (Princeton, N.J., 1994), pp. 41-44, and for England, see Julie Robin Solomon, Objectivityin theMaking:FrancisBacon and the Politicsof Inquiry Baltimore, 1998), pp. 37-43. For the hu-manist tradition of history reading as moral instruction and the collapse of this in the lateRenaissance, see Timothy Hampton, Writingrom History:TheRhetoricofExemplarityn Renais-sance Literature Ithaca, N.Y., 1990). For differing accounts of the pedagogic role of logicaltreatises, see Wilhelm Risse, Die Logikder Neuzeit, 2 vols. (Stuttgart-Bad Cannstatt, 1964),vol. 1, chap. 6. For a fine account of artificial versus natural logic and their relations to com-templative versus active ideals, see Nicholas Jardine, Keeping Order in the School of Pa-dua: Jacopo Zabarellaand Francesco Piccolomini on the Offices of Philosophy, n MethodandOrder n RenaissancePhilosophyof Nature: The AristotleCommentaryTradition,ed. Daniel A. DiLiscia, Eckhard Kessler,and Charlotte Methuen (Aldershot, 1997), pp. 183-210, esp. p. 201.48. For example, in 1634, the famous correspondent Marin Mersenne weighed therespective values of mathematics versus natural philosophy as forms of self-cultivation. SeeMarin Mersenne, Questions nouyes,ou recreation essfavans (1634; Stuttgart-Bad Cannstatt,1972), pp. 76-88.49. See Rodis-Lewis, Descartes:His Lifeand Thought,trans. Jane Marie Todd (Ithaca,N.Y., 1998), pp. 15-16.

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    19/33

    CriticalInquiry Autumn2001 57kind of elite, an elite characterized by the careful development of particu-lar mental, spiritual, and moral virtues through technical exercise. Des-cartes produced his modern candidate for subjectivity in trying, like somany of his contemporaries, to effect a better seventeenth-century subjec-tivity, one suitable to the dislocations of his age. He rejected other formsof knowledge acquisition because they failed his criteria for proper culti-vation of the reason and the will.50

    Attention-Deflection isorder:RejectingFormsof CultivationIt is by now a commonplace that an exploding variety of new words,things, and approaches characterized and threatened Renaissance visionsof knowledge. Roughly, in Descartes's picture of the human faculties, theattention could be trained on the intellect, the imagination, or the mem-ory, but only one at a time. For the will to receive the guidance of theintellect, the attention must be focused on the intellect. Therefore, anyepistemic procedure keeping the attention away from the intellect fortoo long had to be rejected as noncultivating. Descartes wanted to over-come individual, disjointed fragments of knowledge but, like Montaigne,doubted whether contemporary intellectual tools could ever surpass them.For example, in an early notebook entry, Descartes complained that theart of memory was necessarily useless because it requires the whole space[chartam] hat ought to be occupied by better things and consists in anorder that is not right. The art'scollections of particulars not only failedas knowledge, but blocked it; they diverted attention away from the dis-cerning of order, a function of intellect, toward the recognition of dis-jointed particulars, a function of the memory. In contrast, the [right]50. This entire enterprise may seem altogether too vague, too inclusive. In callingsomething a spiritual exercise, I mean that:1) It comprises a set of practices, often including logic and mathematics, intendedultimately to lead one's self or soul toward some goal of self-cultivation. These practicesnecessarily involve the development of various faculties, including ingenium, ingenio, esprit,memory, wit, and so forth.2) In its more philosophical guises it would include2.1) an ontology,2.2) an account of the faculties to be improved,2.3) the appropriateness or inappropriateness of those faculties for gaining access tothe philosophy's ontology, an account of basis of the morality to be improved (which may ormay not be naturalistic, often depending on [2.1]).3) A specification of the social field at whom it is aimed, or whom end up pursuing it.Ignatius stressed the plasticity of the term: 'Spiritual Exercises' embraces every method ofexamination of conscience, of meditation, of vocal and mental prayer, and of other spiritualactivity.... Forjust as strolling, walking, and running are bodily exercises, so spiritual exer-cises are methods of preparing and disposing the soul to free itself of all inordinate attach-ments (quoted in Stohrer, Descartes and Ignatius Loyola, p. 25).

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    20/33

    58 MatthewL.Jones Descartes'sGeometrys SpiritualExerciseorder is that the images be formed from one another as interdependent(AT,10:230).51

    The pedagogic and reading practices associated with arts of memory,commonplace books, and encyclopedias promised to help discover suchinterconnection.52 But, too concerned with disconnected experiences andhistorical facts, these techniques necessarily prevented its discovery. Per-haps worse, narratives attempting to combine particulars generated notany interconnection but monstrous mixtures. Descartes gauged such nar-rative monsters as histories, not sciences. They always involved focusingthe attention on discrete elements in the imagination or memory, ratherthan focusing on the intellect's comprehension of fundamental unities ty-ing together apparently discrete elements.For Descartes, these epistemic failings led inevitably to moral ones.Deflection of attention yielded imitation, not introspection. Monstroushistories of disconnected facts misled those who rule their manners by theexamples they take from them. Ruling manners by imitation and not in-trospection allowed people to fall into the extravagances of the Paladinsof our romances and to conceive of designs that surpass their strength (AT6:7). Don Quixote's illusory windmills haunted the philosophical alterna-tives available to Descartes's contemporaries. Imitation and wonder madethem unable freely to consider, to choose, and to rule themselves.Descartes explained the range of disciplines he dismissed as history:By history I understand all that has been previously found and is con-tained in books. True knowledge meant, in contrast, the ability to resolveall questions by one's own industry, to become (here Descartes signifi-cantly uses the Stoic term) autarches, hat is, self-sufficient (AT,3:722-23).53Only self-sufficiency allows true inventiveness in reason and the morallife predicated upon it.54This expansive condemnation of history included mathematics. Inmathematics, as elsewhere, Descartes explained, imitating the ancients'works failed: Even though we know other people's demonstrations byheart, we shall never become mathematicians if we lack the aptitude, byvirtue of our ingenium,to solve any given problem (AT,10:367; see CSM,1:13). Empty mathematical facts would never eliminate wonder throughsystematic comprehension. Standard mathematical proof was a form ofimitation. Why?For Descartes, formal logical consequence, as in a syllogism or math-

    51. Translation from Sepper, Descartes'smagination, pp. 76-77.52. For humanist commonplace methodology, see, for example, Ann Blair, HumanistMethods in Natural Philosophy: The Commonplace Book, Journal of theHistoryof Ideas 53(Oct.-Dec. 1992): 541-51.53. Descartes made the same point in the Regulae; see AT, 10:367.54. Thus Descartes claims to break with imitatio,both textual and in life. CompareTerence Cave, The CornucopianText:Problemsof Writing n the FrenchRenaissance(Oxford,1979).

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    21/33

    CriticalInquiry Autumn2001 59ematical proof, rested on the possibility of surveying a formal deductionover time.55Considering a series of particular facts or observations in anenumeration demands the step-wise switching of attention as one reviewsthe series in memory or on paper; so, too, with the discrete steps of for-mal deductions:

    [When a deduction is complex and involved] we call it enumerationor induction, since the intellect cannot simultaneously grasp it as awhole, and its certainty in a sense depends on memory, which mustretain the judgments we have made on the individual parts of theenumeration if we are to derive a single conclusion from them takenas a whole. [AT,10:408; CSM, 1:37]If one knows A-B, B-C, C-D, D-E, then I do not on that accountsee what the relation is between A and E, nor can I grasp it precisely fromthose already known, unless I recall them all (AT,10:387-88; see CSM,1:25). The sequence in the proof offers good reasons to consentthat therelation between the first and the fifth is such. But in consenting we donot grasp the relation in anything like the way we grasp the more inter-mediate and immediately grasped relations. Descartes admitted that for-

    mal deductions could be perfectly certain invirtueof theform (AT, 10:406; CSM, 1:36).56Formal certaintyhardly made the result and its connection to the in-termediate steps at all evident.The discrete steps were just like a bunchof particular observations about the natural world. Both syllogistic causalphilosophy and mathematical demonstrations in their traditional forms,those products of the ancients' ruses, rested on memory. In slavishly imi-tating and assenting to proof, one allowed reason to amuse oneself andthereby one lost the habit of reasoning. In sum, one lost the foundationof regulating oneself in epistemic and moral matters.Descartes's ositiveConception f Knowledge

    Having rejected essentially all contemporary forms of knowledgeproduction, what resources did the young Descartes have left? In his ear-liest notebook, we find an antimemory, poetical view of knowledgeclosely associated with Descartes's first real achievements in geometrywith the help of machines and algebra.57He contrasted the laborious pro-

    55. See Andre Robinet, Aux sourcesde l'espritcartesien:L'AxeLa Ramee-Descartes: e laDialectique es 1555 aux Regulae Paris, 1996), pp. 191-96.56. See Marion'sannotations in Descartes, Rfglesutiles et clairespourla directionde l'espriten la recherche e la veriti, pp. 217-18.57. For this notebook and the vicissitudes of its transmission, see Henri Gaston Gou-hier, Les Premieres ensies de Descartes:Contributiona l'histoire e l'anti-renaissanceParis, 1958),

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    22/33

    60 MatthewL.Jones Descartes'sGeometrys SpiritualExercisecesses of reasoning in philosophy with the organic unity of wisdom andknowledge that poets divined.

    It seems amazing, what heavy thoughts are in the writings of thepoets, rather than the philosophers. The reason is that poets writethrough enthusiasm and the strength of the imagination; for thereare the sparks of knowledge within us, as in a flint: where philoso-phers extract them through reason, poets force them out throughthe imagination and they shine more brightly. [AT 10:217; seeCSM, 1:4]This poetic ideal, worthy of much further inquiry, promised knowledgeof a sharply aesthetic, intuitive character, illuminating the unity of its ob-jects and thereby appropriate for regulating oneself through attention onunities in the intellect.Descartes turned this poetic claim of his early notebook into an epi-stemic standard of unity and interconnection. He offered a new vision ofcause. This kind of cause eliminates the need for memory because oncethe cause is grasped one can easily reproduce its original justification.That knowledge of cause, however, is neither secured by those formalsteps, nor does it include an enumeration of them. Cause comprises,rather, knowledge of an organizing principle underlying the interdepen-dence of elements (see AT, 10:230).58Descartes claimed his new mathematics was a key exercise for culti-vation. A cultivating mathematics would give one experience in recogniz-ing the interdependence and evidence of the steps of a formal proof andmake those steps ultimately superfluous. Under this constraint, the seriesof proportions A-B, B-C, C-D, D-E of a formal proof would have to besomehow grasped all at once.

    What example did Descartes have of such a remarkable reduction ofdeductive knowledge? Thanks to his travels in Germany, he had a newproportional compass (fig. 4).59Descartes's compass begins with the twostraightedges YZ and YX (see AT 6:391-92). BC is fixed on YX. Otherstraightedges perpendicular to YZ and YX respectively are attached butcan move side to side along YZ and YX. As the compass is opened, BCpushes CD, which in turn pushes DE, which pushes EF, and so forth. Asit opens, the compass produces a series of similar triangles YBC, YDE,and Rodis-Lewis, Le Premier Registre de Descartes, Archivesde philosophie54, no. 3-4(1991): 353-77, 639-57.58. For discussion, see Sepper, Descartes'smagination, pp. 76-77; compare pp. 44-46.Compare also AT 10:204, 10:94.59. I skip completely over the difficult question of Descartes's encounters while inGermany. For a persuasive recent view, based on careful analysis of algebraic procedures,see Kenneth Manders, Descartes et Faulhaber, Bulletin Cartesien,Archivesde Philosophie58(Jul.-Sept. 1995): 1-12.

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    23/33

    CriticalInquiry Autumn2001 61

    Ir0o

    0so000o

    FIG.4.-Descartes's compass, from La Giomitrie,p. 318.

    YFG, and so on. This allows the infinite production of mean proportion-als, YB:YC::YC:YD:: YD:YE:: YE:YE Numerous problems in geometrycan be solved through finding such mean proportionals.With the compass in mind, we can grasp the ordering principle be-hind a sequence of continued relations. That is, we can grasp the relationbetween a first and last term (YB:YF) in something akin to our grasp ofan intermediate and more immediate relationship (YB:YC). We need notretain the individual proportions in memory to claim knowledge of anyof the particular relations because we can easily read them off the com-pass. The compass offered the crucial heuristic, a material propaedeutic,for Descartes' revised account of mathematics freed from memory andsubject to a criterion of graspable unity.60A simple mathematical instru-ment became the model and exemplar of the knowledge of Descartes'snew subject, the one supposedly so removed from the material.

    Evidenceand Deduction:An Aesthetics f DeductionRootedin a MathematicsDescartes distinguished the evidence of a proof from its formal cer-

    tainty. Formal demonstrations, like syllogisms or other logical forms of60. The equation b=a3 encodes both a curve and the progression 1:a::a:a2: a2:a3. Thisalgebraic progression encapsulates the constructive process of his compass. See Lachter-man, TheEthics of Geometry:A Genealogyof Modernity,pp. 165-66. Timothy Lenoir arguesthat, for Descartes, algebra served as a device for the easy storage and quick retrievalof information regarding geometrical constructions (Timothy Lenoir, Descartes and theGeometrization of Thought: The Methodological Background of Descartes's Geomitrie,HistoriaMathematica6 [Nov. 1979]: 363).

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    24/33

    62 MatthewL.Jones Descartes'sGeometrys SpiritualExerciseproof, could, in his eyes, produce certainty. They did not, however, makethe connections one was proving evident.61 Descartes's radical move wasto demand that all real knowledge consist in the same sort of immediate,evidentcharacter as our knowledge of singular things around us cognizedclearly. In the Rulesfor the Directionof theNatural Intelligenceof the 1620s,Descartes formalized a new account of enumerative and deductive knowl-edge subject to the criterion of evidence. The new form of deductionextended evidence from single, simple intuitions of local things to knowl-edge of simple and complex unified systems. He privileged this form ofdeduction as necessary for allowing the will to see clearly the guidanceoffered by the intellect. Here I can give only a brief account of his deeplyproblematic but enticing vision.62He reduced all true knowledge to an ineffable intuition: two thingsare required for intuition: first, the proposition intuited must be clearand distinct; next, it must be understood all at once, and not bit by bit(AT 10:407; see CSM, 1:37). Descartes knew well that such instantaneous,intuitive grasp could hardly account for much complex knowledge. Buthe demanded more complex knowledge nevertheless retain the qualitiesof intuitions: The evidence and certainty of intuition are required notonly for apprehending single enunciations but equally for all routes (AT10:369; see CSM, 1:14-15).Anything more complex than immediate intuition, however, wouldnecessarily involve cognition over time using the memory, thereby mov-

    61. For the real conflicting demands of clarity versus demonstration as a standingproblem, see Leibniz' remarks on Ramus's and Mercator'ssacrificing of demonstrative rigorfor clarity of method, in Gottfried Wilhelm Freiherr von Leibniz, Projet et Essais pourarriver a quelque Certitude pour finir une bonne partie des disputes, et pour avancer l'artd'inventer, PhilosophischeSchriften, in SdmtlicheSchriftenund Briefe, ed. Berlin-Branden-burgischen Akademie der Wissenschaften, 7 ser. (Berlin, 1923-), ser. 6, vol. 4, pt. A, pp.968-69. Gaukroger has insightfully connected Descartes's epistemic standards to the Ro-man rhetorical tradition; see his Descartes's Early Doctrine of Clear and Distinct Ideas,TheGenealogy f Knowledge:AnalyticalEssays n theHistory of Philosophy nd Science(Aldershot,1997), pp. 131-52. For a fuller discussion of evidence in the philosophical, theological, andrhetorical traditions, see, for the foundational texts, Aristotle, Physics,1.1 (184a17-22) andPosterior nalytics,2.19 (99b15-100b17); Wesley Trimpi, Musesof One Mind: TheLiteraryAnal-ysis of Experienceand Its Continuity(Princeton, N.J., 1983), pp. 117-20; and Antonio P6rez-Ramos, FrancisBacon's dea of Scienceand theMaker'sKnowledgeTradition Oxford, 1988), pp.201-15. For a late scholastic account, see Eustachius a Sancto Paulo, Summaphilosophiaequadripartita:De rebusdialecticis,ethicis,physicis, t metaphysicisCambridge, 1640), pp. 135-36.62. The best account of deduction in Descartes is Doren A. Recker, MathematicalDemonstration and Deduction in Descartes's Early Methodological and Scientific Writings,Journal of theHistoryof Philosophy31 (Apr. 1993): 223-44; see also Frederick Van De Pitte,Intuition and Judgment in Descartes's Theory of Truth, Journal of theHistoryof Philosophy26 (July 1988): 453-70; Gaukroger, CartesianLogic:An Essayon Descartes'sConception f Influ-ence (Oxford, 1989); Yvon Belaval, Leibniz:Critiquede Descartes Paris, 1960); and DesmondM. Clarke, Descartes's Use of 'Demonstration' and 'Deduction,' in Rend Descartes:CriticalAssessments,d. Georges J. D. Moyal, 4 vols. (New York, 1991), 1: 237-47.

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    25/33

    CriticalInquiry Autumn2001 63ing one's attention away from the intellect. His proposed model of deduc-tion was to raise enumerations, including but by no means limited tomathematical and other traditionally deductive arguments, to certainknowledge of an evident character by bringing out the occulted orderorganizing them:

    So I will run through [all the particulars] several times in a continu-ous motion of the imagination, simultaneously intuiting one relationand passing on the next, until I have learned to pass from the firstto last so swiftly that no part is left to the memory, and I seem tointuit the whole thing at once. In this way our memory is relieved,the sluggishness of our intelligence redressed, and its capacity insome way enlarged. [AT,10:388; see CSM, 1:25]Descartes's vision of intuiting the whole thing at once rested onthere being a thing to be grasped at once, something guaranteeing theinterconnection of the objection and the continuous intuition of the ob-ject. His usual metaphor involved the chain: If we have seen the connec-tions between each link and its neighbor, this enables us to say that wehave seen how the last link is connected to the first (AT, 10:389; CSM,

    1:26; my emphasis). He limited knowledge to those things possessingsuch connections, like mathematics, as he understood it.His central example for his new deductions was the sequence of rela-tions described above. To understand fully the endpoint that A has inrelationship to E, we need to grasp not only the series of simple relationsbut the underlying order producing them. As we saw, the compass in thisexample offered the ordering principle, the how,behind these relations.Thus, the compass, properly abstracted, comprises the simultaneouslygrasped, clear, and distinct intuition produced by the sufficient enumera-tion of the relations. With this little example, one might experience whatit is like to have such an intuition, which, being basic, cannot be defined.

    Exercises:Evidence,Mathematics, nd TapestriesClear and distinct have long struck commentators as more aestheticthan epistemic and therefore useless as criteria for knowledge.63 Some-thing like this aesthetic quality attracted Descartes, for only an aesthetic

    criterion, drawn from poetry and rhetoric, could ensure the interconnec-tion central to real knowledge-the interconnected knowledge divinedby the poets. Aesthetichardly meant subjective in the pejorative sense. Exer-63. I use aesthetic n the modern sense and not the meaning of sensory impression ofthe seventeenth century. On this, see Paul Oskar Kristeller, The Modern System of theArts, RenaissanceThoughtand the Arts: CollectedEssays(Princeton, N.J., 1990), pp. 163-227.

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    26/33

    64 MatthewL.Jones Descartes'sGeometrys SpiritualExercisecise created the objectivehabit of recognizing the truly interconnected;developing the habit made Descartes's subject capable of intersubjectiveknowledge.He made this clear in his Rulesfor theDirectionof the Natural Intelli-gence. Natural intelligence (or,even worse, mind )poorly translates Des-cartes's term ingenium-a central, much disputed Renaissance term forartistic and poetical spark or genius. More specifically, the term could in-dicate the ability of an orator to imagine a situation so vividly, that, byspeaking, he could produce an evident picture in the listener's mind.64Developing this ability required intense practice.Descartes's ingeniumequally needed such concrete practice. In a veinfar removed from the image of the philosopher cogitating alone and with-out corporeal things, as I noted in the introduction, Descartes recom-mended studying the simplest and least exalted arts, and especiallythose in which order prevails. Such study habituated one to the affect ofexperiencing clear and distinct order. A proper form of geometry offeredthe best habituation. Mathematics provided exercise in recognizing howthings that are foundational for Descartes are indeed clear and distinct:the self, mind, extension, and God. It offered the practice that couldallow one to choose among philosophical therapeutics. Doing correct geo-metrical work mattered because it epitomized knowledge both certainand evident; it best could refine one's objectiveaste for and in truths. Thisaugust role for mathematics, however, set troublesome boundaries forcorrect geometrical work.

    Algebra:DevelopingMathematicalTasteand Threateningto SpoilItDescartes's account of exercise required a dangerous temporary useof artificial instruments to achieve this intuitive habituation. Like man-uals claiming to teach ostensibly natural manners, civility, or taste, suchartificial means always have something paradoxical about them. As witha primer on taste, Descartes's tools promised the supposedly naturalthrough the artificial. He attacked traditional formal reasoning becauseits forms promised natural knowledge through artificial means, but neversevered its attachment to the artificial.6564. See also Nicolas Caussin'sattempt to combinejudicium with highly personal ingen-ium in his rhetoric in Fumaroli, L'Age e l'loquence:Rhitorique t resiteraria, ela Renaissanceau seuildel'epoque lassique Paris, 1994), p. 288. Foringenium,see Martin Kemp, From Mime-sis to Fantasia:The Quattrocento Vocabulary of Creation, Inspiration, and Genius in theVisual Arts, Viator8 (1977): 347-98.65. Descartes's ambivalence toward algebra has divided commentators, with someseeing true modernity and algebraic liberation in the geometry, and others stressing thealgebra's secondary character. For the first, see Schouls, Descartes nd thePossibility f Science,

    This content downloaded from 194.117.18.21 on Tue, 7 Jan 2014 07:42:35 AMAll use subject toJSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
  • 8/12/2019 Descartes Espiritual

    27/33

    CriticalInquiry Autumn2001 65Nevertheless, Descartes recognized a need for arts to maximize ournatural but obscured capacities. In the Rules, Descartes explained that

    arts aided reasoning temporally by preparingone to intuit relations notimmediately grasped. The greater part of human labor consisted in thispreparation:Absolutely every cognition, which one has not acquired through thesimple and pure intuition of a unique thing, is acquired by the com-parison of two or multiple things among themselves. And certainlynearly all the industry of human reason consists in preparing thisoperation; for when it [the operation] is open and simple, there is noneed for any aid of an art, but the light of nature alone is necessary tointuit the truth, which is had by this. [AT,10:440; see CSM, 1:57]

    Once the complex nature has been grasped intuitively, that is, all at once,the art is no longer needed. Again the heuristic is of a string of propor-tions. Terms A and E are not immediately proportionate until C, B, andD are added to the picture.Descartes's early mathematical machines suggested that solutions toproblems in mathematics came from producing means connecting theobjects one wants to characterize, like the relations completely character-ized through his compass:

    In every question there ought to be given a mean between two ex-tremes, through which they are conjoined explicitly or implicitly: aswith the circle and parabola, by means of the conic section. [AT,10:229]66As we saw, Descartes's compass showed how a string of proportionals areintimately connected, as are their algebraic representations. The compassexemplified how to make enumerations, including deductions, for thedemand of sufficiency (see AT, 10:384-87).67 This necessarily demandeda movement from knowns to unknowns to fill the gaps sufficiently. Thismovement, in filling out a deduction, does not produce a being