Cartesian Method and the Problem of Reduction

by Emily R. Grosholz

The Cartesian method, construed as a way of organizing domains of knowledge according to the "order of reasons," was a powerful reductive tool. Descartes made significant strides in mathematics, physics, and metaphysics by relating certain complex items and problems back to more simple elements that served as starting points for his inquiries. But his reductive method also impoverished these domains in important ways, for it tended to restrict geometry to the study of straight line segments, physics to the study of ambiguously constituted bits of matter in motion, and metaphysics to the study of the isolated, incorporeal knower. This book examines in detail the negative and positive impact of Descartes's method on his scientific and philosophical enterprises, exemplified by the Geometry , the Principles , the Treatise of Man , and the Meditations .

170 pages, Hardcover

First published March 14, 1991

Reviews

[K · Rating 4 out of 5]

This is a fascinating book that puts forth a very interesting, albeit controversial, reading of the Cartesian project. Grosholz's argument begins with an assertion of the unity of Cartesian method which seeks simple intuitive starting-points (simples) and subsequently attempts to reduce the whole of reality to those. In the case of geometry, the simples are straight lines, while in the case of physics the simples are Euclidean extension in terms of breadth, depth, and length. Subject-specific reductions allow for advances both in analytic geometry, as well as mechanics. Moreover, in an ingenious move, the physical world is geometricised, allowing Descartes to unify disparate disciplines.

However, the whole edifice is built on shaky grounds since the starting points of Descartes' philosophy are unable to support the relational structure that he eventually advances. For example, the crude simplicity of the foundations of Cartesian geometry excludes areas, curves, and infinitesimal magnitudes (although Descartes accepts these objects as complex constructions) thus hindering potential insights that were exploited by his contemporaries and successors, figures like Galileo, Leibniz, and Newton, and eventually led to the development of the calculus. Grosholz even hints that Descartes' difficulties in quantifying his physics were caused by his insistence on simple starting points and reduction. Another point by Grosholz is that while the unity of geometry and physics allows for the abandoment of the Aristotelian theory of elements, Descartes' novel unity of matter is incapable of fully supporting the mechanical interpretation of nature, and in particular, its specific applications such as the vortex theory of planetary motion.

The morale of the story, as Grosholz emphasises, is that Cartesian mathematics and natural philosophy (as well as Cartesian advances on physiological and cognitive domains) are far more pluralist than Descartes' foundational principles actually allow, and, consequently, reductive explanations, while theoretically powerful, are inadequate to fully explain the complexities of nature. Thus, while Grosholz deals with what would superficially appear as a historical inquiry on Cartesian science and metaphysics, the implications of her work are quite wide-ranging and surprisingly modern.