Descartes’s Mathematics

This chapter points out some issues about Cartesian geometry and Descartes’s program of solving geometrical problems by means of algebraic analysis. With this aim, it extends the corpus to Descartes’s mathematical correspondence and takes into account recent interpretations. The chapter first concentrates on Descartes’s methodological reflections on the algebraic resolution of geometrical problems like Pappus’s problem or Apollonius’s problem of the three circles, and compares Descartes’s classifications of mathematical problems of 1619 and 1637. It then addresses problems tackled by Descartes in his mathematical Correspondence that question the boundaries set in the Géométrie for the application of method. Finally, the method of indeterminate coefficients and its use in Descartes’s method of normals are briefly studied in order to underscore an Ariadne’s thread in Cartesian geometry: the elimination of equations. In conclusion, it is claimed that Cartesian geometry is neither the single Géométrie of 1637, nor a mere anticipation or deduction of this classic by Descartes, but the collection of somewhat different geometries, which are to be found in the mathematical Correspondence or the Latin editions of 1649 and 1659–61.

Descartes’s Metaphysics

This chapter defends the systematic nature of Descartes’s metaphysics by locating the source of many of his doctrines in one central, unifying principle. This principle, that the attributes of a substance are identical with the substance itself and with each other, underlies many of Descartes’s most important metaphysical doctrines. An appreciation of the principle resolves several interpretive puzzles pertaining to his metaphysics, provides Descartes with resources for answering objections, uncovers his reasons for holding doctrines that otherwise seem unmotivated, and reveals his commitment to views that he never explicitly affirms. It thus goes beyond the texts while also elucidating them in surprising ways.

Optics, First Philosophy, and Natural Philosophy in Hobbes and Descartes

This chapter concerns the contrasting approaches of Descartes and Hobbes to optics, first philosophy, and natural philosophy. In all three areas of inquiry both thinkers embraced the mechanistic “new philosophy”, according to which the phenomena of nature can be explained in terms of the motions and impacts of material bodies, yet they held radically different conceptions of what principles were essential to that philosophical program, the extent to which mechanism could be applied, and the role of God in both first philosophy and natural philosophy. Ultimately, even though they both aimed to offer an alternative to Aristotelianism, their differences were more significant than their similarities.

Gassendi as Critic of Descartes

Pierre Gassendi is best known today as a critic of Descartes. This chapter surveys Gassendi’s Objections to the Meditations, Descartes’s Reply, and Gassendi’s Counter-Objections in the Disquisitio Metaphysica. The central theme of this debate is methodology. Gassendi thinks that the methodology of the Meditations is hopeless: nobody can genuinely clear their mind of preconceived opinions, and if they did, they would not have discovered new foundations for the sciences, but instead be trapped in a state of suspended judgment. Gassendi’s critique is not entirely fair to Descartes, and Descartes’s reply fails to take seriously the main points of the critique.

Cartesianism and Feminism

Cartesianism constitutes a particular and crucial moment in the history of the relations between the aims of philosophy and feminist claims. This is explained by theoretical reasons (the new Cartesian science posits a human being that is fundamentally non-sexual and ungendered) and by practical reasons (the importance of the philosophical vocations for women and the feminist vocations for men that Cartesianism has permitted). Recent readings of Descartes (which see him either as a misogynist or as a philogynist) show that the theoretical connections between Cartesianism and feminism are strong: Cartesianism powerfully questions the relation of women to philosophy, both as subjects and as philosophical objects.

“Italy Did Not Want to Be Cartesian”

At the end of the eighteenth century, Appiano Buonafede (i.e. Agatopisto Cromaziano) had no doubt: Italy did not want to be Cartesian—just as it had not wanted to be Baconian—and this was “much better for Italy”. While Buonafede exaggerated, Cartesianism did not have an easy life in the peninsula. The first to experience this was Mersenne, who also on two occasions tried, with little luck, to promote its circulation among a Galilean circle in Florence and Rome by bringing Descartes’s books with him to Italy. And Galileo was not very welcoming, complaining about the indecipherable writings of the Minim. This chapter reconstructs the varied life of Cartesianism in Italy, starting from the discussions generated by the writings of the French philosopher.

Johannes Clauberg and the Search for the Initium Philosophiae

This chapter examines how the philosophy of Descartes contributed to Clauberg’s philosophical system. In this system it is metaphysics that imposes itself on the other sciences, as its contents impose themselves according to the order of knowledge. The core of Clauberg’s adherence to Cartesianism is thus linked to his conviction that Descartes’s philosophy is, above all, the discovery of the true “beginning” (initium) of philosophy, that is, the discovery of a principle that guarantees the primacy of metaphysics, established according to the order of knowledge. Clauberg aims to identify the first science, according to the order of knowledge of things (ordo cognitionis) as well as the order of teaching (ordo doctrinae), and consequently to establish the organization of all knowledge.

Robert Desgabets and the Supplement to Descartes’s Philosophy

This chapter is devoted to the distinctive form of Cartesianism in the work of the French Benedictine Robert Desgabets (1610–78). After a consideration of Desgabets’s defense of Descartes in controversies over the Eucharist that led to the first French condemnations of Cartesianism, there is a discussion of three “radical” doctrines in Desgabets. The first, the “creation doctrine”, involves an original development of Descartes’s doctrine of the creation of eternal truths; the second, “intentionality doctrine”, is taken by Desgabets to reveal the deficiencies of Descartes’s methodical doubt; and the third, the “union doctrine”, is directed against the claim in Descartes that we have purely intellectual thought. Finally, there is a brief evaluation of the claim in the literature that Desgabets’s system constitutes a kind of “Cartesian empiricism”.

Mersenne

Mersenne’s multidisciplinary interests marked the relationship of intellectual collaboration that linked him to Descartes, whose research and publications he solicited and promoted, though without ever becoming a “Cartesian”. Mersenne “molecularized” the Cartesian philosophy in terms of a series of specific issues, but the way in which the Minim triggered the debate generated criticism and polemics rather than adhesions to Cartesianism. Mersenne based his argumentations on philosophical and theological presuppositions that differed from those formulated by Descartes, particularly concerning the hypothetical status of science, the validity of logical-mathematical truths, the radicalization of divine omnipotence, and the argument of deceiving God. The unpublished theological manuscripts of the 1640s reveal, however, that after the 1641 Objections, the Minim was ready to accept crucial Cartesian metaphysical theses, but in his own peculiar way.

Descartes’s Mechanical but not Mechanistic Physics

Descartes is commonly characterized as the arch-mechanist who rejected the syllogistic demonstrations sought in Scholastic Aristotelian physics, and instead aimed at purely “mechanistic explanations” of natural phenomena. Typical accounts of physical phenomena found in his scientific works, such as that of the properties of salt, are thus interpreted as no more than structural explanations that posit one of many possible arrangements of variously shaped microscopic particles to account for the observed effects. By examining Descartes’s own statements about the different ways in which his physics is “mechanical”, and by placing these in the context of the Renaissance revival of the geometrical demonstrations found in the Aristotelian Questions of Mechanics, this chapter shows that, and in what way, Descartes aimed at mathematical and mechanical, but not mechanistic, demonstrations of physical phenomena like salt.