Aristotle’s On the Good and the “Categorial Reduction Argument”

Alexander of Aphrodisias reports a series of arguments from Aristotle’s Περὶ τἀγαθοῦ purportedly deployed by Plato to defend his doctrine of principles. One of these arguments, the so-called “categorial reduction argument”, underpins the postulation of the two first principles, the One and the Great and Small, through a bipartition of all beings into two categories, labeled ‘in themselves’ and ‘opposites’. I scrutinize this argument and compare it with other Early Academic bicategorial divisions and especially with the tripartite categorial distinction, itself apparently based on material of Early Academic provenance, included in Sextus Empiricus’ Adversus Physicos 2.262-275. I argue that the Περὶ τἀγαθοῦ account of the “categorial reduction argument” leaves open certain philosophical problems, and Sextus’ report is best interpreted, rather than as a more detailed version of that account (as a common view would have it), as an alternative formulation of it that incorporates a philosophical attempt to disentangle those problems.