Descartes’s Reappraisal of Aristotelian Demonstrative Science

Lucian Petrescu

Ghent University

Abstract: 
The combination of the two forms of demonstration defined by Aristotle, demonstratio quia and demonstratio propter quid (apodeixis tou dioti and apodeixis tou hoti) is one of the most enduring ideas elaborated on by medieval philosophers. The idea that these two forms of demonstration are both valid and need to be combined with each other in scientific proofs is not to be found in either Aristotle or in the early Greek commentators. And yet, this medieval elaboration is not only left unchallenged by early modern authors—or by purist Renaissance figures, for that matter—but is instead cautioned and promoted. In spite of an extensive literature devoted to the subject, most of it concentrated on Galileo and the Padua school, much remains to be done in order to substantiate Randall’s suggestion of the reappraisal of Aristotle’s scientific method in the early modern period (Randall 1940). This paper revisits Descartes’s use of the two forms of Aristotelian demonstration. The Cartesian literature devoted to this topic has linked it with the question regarding the analytic or synthetic order of exposition and has focused on the extent to which the Meditations or the Principles follow one order or the other (see Brunschwicg, Rochot and Garber on Gueroult’s interpretation). I focus instead on the Essays of 1637 and I couple Descartes’s statements on the 'order' and 'method' of the Essays with his actual use of the two types of demonstration. I first argue that we can discern two consistent uses of Aristotelian demonstration in Descartes: (1) a 'minor scale' one, applied to the exposition of particular scientific demonstrations, where Descartes follows the combination between reasoning from effects to the principles governing the effects and back, applying the regressus model of proof; and (2) a 'large scale' use, through which Descartes presents his entire work as an exercise of coupling a demonstration propter quid with a demonstration quia. I take it to be both a rhetorical effort of persuasion for his Jesuit readers and an assumed effort of ridding physics of the probabilistic bent assigned to it by late scholasticism. The Essays are presented as an a posteriori demonstration, one half of an incomplete demonstration. I then analyze a passage from the Replies of 1641, in which Descartes makes clear the necessary connection between the two types of demonstration. I argue that for Descartes, in spite of a venerable tradition that regards the demonstration propter quid as superior to the demonstration quia, the a posteriori demonstration is necessary for assenting to the truths discovered through a priori reasoning. I support this reading by glancing at the aftermath of Descartes’s understanding of Aristotelian method in the first generation of Cartesians and at the role it played in constructing an image of Descartes as an arch-Aristotelian. Finally, I show that the relevant background for reading Descartes’s statements on Aristotelian method should be taken from Jesuit authors rather than from Italian Averroists like Zabarella (Reiss 2000).