Aristotle and Frege on Method in the Philosophy of Mathematics

Abstract

Aristotle discusses the philosophy of mathematics in the final books of the Metaphysics and approaches questions and problems in this subject from a metaphysical perspective. This way of undertaking the philosophy of mathematics is informed by his understanding of the nature and ends of science, according to which metaphysics is the broadest theoretical science concerned with being itself. We will motivate the further use of this approach by considering the problems Frege encounters as a result of his method of investigating the philosophy of mathematics, which begins from a more logico-mathematical perspective. These problems, broadly speaking, concern the degree to which Frege must take on metaphysical commitments despite wanting to show that mathematics deductively follows form logic; at the same time, these problems can also be explained and understood from an Aristotelian point of view which also offers a solution through the adoption of a more metaphysical method. Consequently, the philosophy of mathematics should be studied in a manner closer to Aristotle's and Frege's.