Hermodorus of Syracuse, a Sicilian disciple of Plato, is reported by Simplicius to have set out a classification of beings, which is of a piece with an argument for principle monism (in Ph. 247.30–248.18 > F 5 IP2; 256.28–257.4 = F 6 IP2). A similar classification appears in Sextus Empiricus’ Aduersus mathematicos X (262–75), where it is officially ascribed to some ‘Pythagoreans’ (Πυθαγορικοί) or ‘children of the Pythagoreans’ (Πυθαγορικῶν παῖδες), but seems ultimately based on Early Academic material. Virtually all commentators (...) have read these classifications conjointly. More radically, both have been taken to record Plato's oral teaching and to give essentially the same categorial scheme, which is regarded as the most developed instance of a so-called ‘Academic doctrine of the categories’. This article re-examines these texts and provides an alternative reading. Section 1 focusses on Hermodorus and defends three theses: (1) there was never such a thing as an ‘Academic doctrine of the categories’; (2) Hermodorus does not seem to recount what Plato said, but to propose an integrated interpretation and defence of aspects of his thought; (3) Hermodorus’ pronouncements about principles are incompatible with other testimonies on Plato's unwritten teaching, notably Aristotle's. Section 2 moves to Sextus and defends a fourth thesis: (4) despite their similarities, the classifications of Hermodorus and Sextus’ Pyrhagoreans are considerably different, though perhaps originated from the same debate. (shrink)