Alexander of Aphrodisias was the greatest exponent of Aristotelianism after Aristotle, and his commentary on Metaphysics 1-5 is the most substantial commentary on the Metaphysics to have survived from antiquity. The commentary on book 1 has the further interest that over half of it is devoted to Aristotle's discussion of Plato. Aristotle's battery of objectives to the theory of Ideas is spelled out with fragmentary quotations and paraphrases from four of Aristotle's lost works, and we are given an extended account of Plato's 'unwritten doctrines' according to which the Ideas are numbers, namely the One and Indefinite Dyad. The deliberations for and against the theory of Ideas recorded by Alexander are more detailed than anything in Plato's dialogues and tell us more than any other source how they were conceived in Plato's most developed theory.