The Logical Structure of Aristoxenus’s Theory of Music

Abstract

It has often been noted that Aristoxenus applied Aristotle’s philosophy of science to his theory of music, as Harmonics I-II presents principles and Harmonics III proofs of some theorems. This reading is rather superficial, however, since it relies on a vague notion of logic. In this paper the author shows: (i) that already in Harmonics I-II, Aristoxenus proves a number of theorems; (ii) that almost all proofs can be syllogistically reconstructed and do not involve inacceptable logical gaps; (iii) that the mathematical proofs are consistent with Aristoxenus’s program of an empirical theory of music; and (iv) that Aristoxenus’s Rhythmics contains a great number of theorems that are proved in a logically weaker sense as defined in Aristotle’s Topics.