Mathematics and the Sciences

Abstract

The author presents Proclus’ philosophy of mathematics, and its relation to the other sciences. The first half of the chapter collects the main questions and problems concerning the philosophy of mathematics as raised by Plato and Aristotle and taken up again by Proclus; the sources Proclus took recourse to in his addressing these issues; and the texts composed by Proclus in which these issues are primarily addressed. The second part, in which Proclus’ position is presented, first discusses the nature of mathematical objects, and their relation to soul; the distinction and relation between the mathematical sciences (arithmetic, geometry, harmonics, astronomy); the mathematical methods and their relation to dialectic; and the relation between mathematics and metaphysics and physics. Finally, the author briefly addresses Proclus’ relation to the mathematics of his day.