This text explores the role which the mathematical sciences played in Aristotle’s philosophical thought, in particular metaphysics and epistemology. It also thematizes the aporetic method by means of which Aristotle deals with philosophical questions about the foundations of mathematics. The first two chapters consider Plato’s mathematical cosmology in the light of Aristotle’s critical distinction between physics and mathematics. Subsequent chapters examine three basic aporiae about mathematical objects which Aristotle himself develops in his science of first philosophy. What emerges from this dialectical inquiry is a different conception of substance and of order in the universe, which gives priority to physics over mathematics as the cosmological science.