This chapter investigates Boethius’ approach to the division of the sciences and his understanding of their relationship to philosophy as a whole. The questions are raised as to whether certain differences in approach discernible in texts spanning roughly two decades indicate development in his thinking, and whether his formal articulation of a quadrivium of mathematical sciences as subsidiary branches of philosophy implies or is intended to leave room for a trivium of linguistic arts. Finally, brief consideration is given to Cassiodorus’ understanding of the seven liberal arts vis-à-vis the Boethian taxonomy of philosophy, and its implications for instructional practice at Vivarium.