Abstract

This article is devoted to some of the dominant positions in the philosophy of mathematics, in Descartes and in Leibniz, and to their consequences drawn by these authors in mathematical analysis. I shall treat of Descartes’ epistemological conceptions of analysis and of the primacy of order, both of which are excellently exposited in the _Rules for the direction of the mind_ and of various mathematical devices which he developed later, from the time of the _Cogitationes privatae_ until the _Géométrie_.