THINGS

Fall 2001
Volume 28, Number 1

Most academics are familiar with a comforting fable, subject to minor variations, about René Descartes and modern philosophy. Around 1640, Descartes philosophically crystallized a key transformation latent in Renaissance views of humanity. He moved the foundation of knowledge from humans fully embedded within and suited to nature to inside each individual. Descartes made knowledge and truth rest upon the individual subject and that subject's knowledge of his or her own capacities. This move permitted a profoundly new thoroughgoing skepticism, but rather than undermining universal knowledge by positing a uniformity of human subjects, this move ultimately guaranteed intersubjective knowledge. Knowledge became subjective and objective. Not content merely to make man himself the ground of knowledge, Descartes went further to make the human mind alone the source for knowledge, a knowledge modeled after pure mathematics. The new Cartesian subject ignored the manifold contributions of the body, and Descartes assumed all real knowledge could come only from a reason common to all humans. The universality of the knowing thing and the processes of knowing make this Cartesian subject a transcendental one. Above all, mathematics, with its proof techniques, and formal thought, modeled on mathematics, exemplify those things that can be intersubjectively known by individual but importantly similar subjects.

See Also Stephen Toulmin : The Inwardness of Mental Life (Autumn 1979) Rudolf Arnheim: A Plea for Visual Thinking (Spring 1980) Lorraine Daston: Enlightenment Calculations (Autumn 1994) Mario Biagioli: Etiquette, Interdependence, and Sociability in Seventeenth-Century Science (Winter 1996)

Versions of this fable appear in numerous analyses, some quite sophisticated and textually based, some crude and dismissive. These versions provide grounds for praising or dismissing Descartes and the philosophical modernity he wrought.1 Rather than surveying or evaluating these appraisals, here I want merely to clarify and anchor historically the subject Descartes hoped his philosophy would help produce.2 This essay examines one set of exercises Descartes highlighted as propaedeutic to a better life and better knowledge: his famous, if little known, geometry. Critics and supporters have too often stressed Descartes's dependence on or reduction of knowledge to a mathematical model without inquiring into the rather odd mathematics he actually set forth as this model. His geometry, neither Euclidean nor algebraic, has its own standards, its own rigor, and its own limitations.3 These characteristics ought radically to modify our view of Descartes's envisioned subject. Although the technical details of his geometry might seem interesting and comprehensible only to historians of mathematics, the essential features grounding Descartes's program can be made readily comprehensible. Descartes did far more than theoretically (albeit implicitly) invoke the knowing subject in his Meditations. To pursue his philosophy was nothing less than to cultivate and order one's self. He offered his revolutionary but peculiar mathematics as a fundamental practice in this philosophy pursued as a way of life. Let us move, then, from abstraction about Descartes to the historical quest for this way of life.

1. My goal is not to undermine such appraisals but to offer a stronger historical basis for them. To take two important critical exemplars from the serious literature: Feminist critics have stressed the historical conditions of gender and social status in the emergence of claims to universal knowledge based on universal mental processes. Structuralist and poststructuralist critics characterize the subject as essentially a product of linguistic practices. For a survey of some of these approaches, see Susan Bordo and Mario Moussa, "Rehabilitating the 'I'," in Feminist Interpretations of René' Descartes, ed. Bordo (University Park, Penn., 1999), pp. 280-304. One can easily multiply examples to include those from phenomenology (especially Husserl and Heidegger), cognitive science, and analytic philosophy. There are several important compendia of articles, often discussing and invoking Descartes. See, for example, Who Comes after the Subject? ed. Eduardo Cadava, Peter Connor, and Jean-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 in the traditional Aristotelian manner. There are numerous other historical corrections to the fable. See Stephen Gaukroger's introduction to Descartes: An Intellectual Biography (Oxford, 1995), and John Schuster, "Whatever Should We Do With Cartesian Method?--Reclaiming Descartes for the History of Science," in Essays on the Philosophy and Science of René 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: Natural Philosophy in Late Aristotelian and Cartesian Thought (Ithaca, N.Y., 1996), and Roger Ariew, Descartes and the Last Scholastics (Ithaca, N.Y., 1999). Another key movement has been to undermine the view that Descartes had no room for the senses. See, for example, Desmond M. Clarke, Descartes's Philosophy of Science (University Park, Penn., 1982), and Daniel Garber, Descartes Embodied: Reading Cartesian Philosophy through Cartesian Science (Cambridge, 2001).

3. My analysis of the geometry rests on a number of specialized studies, above all the work of Henk J. M. Bos, cited extensively below.

Matthew L. Jones (mj340@columbia.edu) is assistant professor of history at Columbia University. He is preparing a cultural history of mathematics and natural philosophy as spiritual exercises in seventeenth-century France, especially in Descartes, Pascal, and Leibniz. p>