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Plato's nephew Speusippus was already over 60 when he assumed the headship of the Academy on his uncle's death, and his reign was short (347–339). Aristotle is our principle source for the Old Academy (i.e. prior to 322), which is problematic, as Aristotle tends to be rather tendentious in the way he treats his contemporaries; but apart from Aristotle's evidence, we have very little to go on regarding Speusippus’ philosophy, as only two of his works, On Pythagorean Numbers and the Letter to Philip survive. The most original and influential aspect of Speusippus’ thought is his discussion of the nature of the first principles, in particular, his development of Plato's notions of the One and the indefinite Dyad (which Speusippus called the ‘One and Multiplicity’), and his attempt to explain how the totality of being came to be from these principles. Speusippus was innovative in his understanding of Platonic cosmology, as presented in the Timaeus, although his innovations, e.g. the notion of World‐Soul, did not make their mark until the Neopythagoreanism of the first two centuries A.D. Speusippus’ ideas on happiness and pleasure were already criticized by Plato in the Philebus, but he may have influenced the stoics on this point; while Aristotle, despite his barbed comments, probably learnt a lot from Speusippus’ logic, which included work on genera and species, and on ambiguity as the source of Sophist fallacies.

In this chapter, Dillon explores a number of questions regarding, firstly, the nature and structure of the Academy that Plato founded and bequeathed to his successors, and, secondly, the nature and doctrines he arrived at before his death. After examining the evidence, Dillon concludes that Plato purchased a private property, with its own garden, in the late 380s, located alongside a grove, or public park, which was outside the walls of Athens, and which was called the Academy after the hero for whom the park was named: Hekademos. Academic discussion in the last stage of Plato's career centres on the Theory of Forms as Form Numbers; in logic, the doctrine of diairesis or the logical divisions; and, in Ethics, the understanding of the virtues as means between extremes of ‘too much’ and ‘too little’; also important is the distinction made in the Laws between goods of the soul and external goods. Much of the physical or cosmological speculation of the Old Academy is focussed on the interpretation of the nest of problems presented by the Timaeus, which is not taken literally by Plato's successors; and on the attempt to reconcile this with Plato's oral teachings, i.e. the Unwritten doctrines.