  Aristotle’s term ousia is usually translated as “substance”. What exactly Aristotle meant by the term is a thorny matter, much debated in the literature. His account of substance in the Categories holds individual things, which he terms “proper substances”, to be paradigmatic of substance. On this account, substance is best understood by analogy with a grammatical subject—it takes a predicate, and is not predicable of anything further. Thus, while animal is predicable of horse, and horse of Bucephalus, Bucephalus stands by himself, impredicable of, and hence, numerically different from anything else. Much of Aristotle’s account in the Metaphysics—written years later—seems to accord with this. However, Metaphysics (1017b10–26) complicates the story. Aristotle there describes four uses of the term. He concludes by reducing these to two broad senses—(1) substance as hypokeimenon, the ultimate substratum, which is not predicated of anything further; and (2) substance as form— that which makes each thing the kind of thing that it is. Indications within the text suggest that, by the time that he was giving the lectures that are collected in the Metaphysics, Aristotle regarded not individual things but the matter of which these individual things are formed as the ultimate subject of predication. On this conception, there is some sense in which Bucephalus is himself predicable of matter. Thus, while the substance of the Categories serves as a principle of individuation, the substance of the Metaphysics is more complicated, serving both to individuate Bucephalus and Seabiscuit and to capture the connection or sameness that holds between them.