 In order to come to terms with Suárez’s position, the first point to appreciate is that a nominalist of his day faced an immediate, inescapable problem. It is, in fact, the very problem mentioned by Suárez in the passage cited: Aristotelian science presupposes a conception of the organization of knowledge according to which a science must proceed via demonstrations, that is, deductions, or logically valid syllogisms, the premises of which are necessary, better known than their conclusions, and universal in scope (cf. Aristotle, APo. 71b16–25, 77b5–73a6; Met. 981a5–30, 1006a6–18, 1039b27–1040a7). If the premises are universal in scope, however, then that is presumably due to their featuring universals as terms. This is why, in part, Suárez is inclined to take the claims of realism about universals seriously. Like others of his time, he embraces an Aristotelian theory of demonstration and so must confront its evident commitment to realism.