Abstract

This volume reflects a reawakened interest in the scientific writings of Descartes, at least partly inspired by recent research by historians and philosophers of science. The editor has gathered ten essays, all of which relate to what he believes is "perhaps Descartes' primary concern... the attempt to provide a philosophical foundation for mathematical physics". Three of the essays study Descartes' scientific writings, especially the Rules for the Direction of the Mind, with a view toward the later, metaphysical writings, which are understood by the authors as theoretical justification for the mathematical science of nature. Stephen Gaukroger recognizes that in the Rules Descartes yokes mathematics to physics, and attempts to explain why this project to establish a mathematical science of nature failed. The author maintains that in order to establish such a science, Descartes unites the objects of mathematics and physics by means of a two-fold reduction. First, the procedures of the two sciences are joined and assimilated to the general reasoning procedure, the method, advocated in Rule IV. Unfortunately, Gaukroger makes sweeping and unsubstantiated claims here. He imports Descartes' distinction between analysis and synthesis as modes of proof and applies it to the more technical uses in algebra and geometry, the "analysis" of the "geometricians" referred to in Rule IV. This hybrid notion he then identifies with the method announced in Rule IV; but Gaukroger interprets this method on the model of resolution and composition in the logical tradition. The second step of the reduction takes place when Descartes identifies the objects of the two sciences through his account of imagination in Rules XII and XIV. According to these passages, the imagination has a double function: since it is a corporeal organ, it receives and embodies real extended magnitudes; but since it is also the locus for images, it can represent "pure extended magnitudes," i.e., the objects of mathematics. Gaukroger acknowledges his debt to Jacob Klein for these insights. He fails to appreciate Klein's central point, however, that through his doctrine of imagination Descartes, either mistakenly or by conscious design, identifies a first intention with a second intention, and that this identification is at the heart of the modern conception of number. In conclusion Gaukroger attributes the demise of the mathematical project to Descartes' "essentialism". Metaphysical considerations, e.g., that the essence of body is extension, determine the scope of inquiry so narrowly that properly physical properties of bodies, such as hardness, are excluded from science. This claim is not only trivial, it is erroneous. In Rules VIII-XII Descartes sets limits upon human inquiry prior to and independently of any metaphysical considerations or claims about essence.