"Universal mathematics" in Aristotle

pp. 289-331

in: Chikara Sasaki, Descartes's mathematical thought, Berlin, Springer, 2003

Abstract

In Mathematics in Aristotle, an anthology of Aristotle's passages on mathematics compiled with commentary by Thomas Little Heath and published posthumously in 1949, we encounter in the Chapter on Metaphysics a short section with the title " "Universal' Mathematics."¹ Jean-Luc Marion also refers to essentially the same passages as possible sources for Descartes's "mathesis universalis' in the annotations to his French translation of the Regulae ad directionem in-genii.² Whether or not Descartes knew these passages of Aristotle, we should examine those which Heath thought to refer to "universal mathematics.' The passages quoted by Heath can be classified into two groups: "universal mathematics' as a science and "universal propositions'. Let us begin with the first category.