Descartes’s matter theory, in the form it is presented in the second part of the Principles of Philosophy, has been criticized a number of times. His well-known account of material substance in terms of extension and extension alone proved to be very successful in the mechanical explanations employed and yet very problematic in its relation to the fundamental concepts of his physics. This is the case with his arguments in support of his defi nition of motion, with the consequences concerning a body at rest, and with his explanation of the individuation of bodies. Equally contested by his contemporaries (Cordemoy, Leibniz) and recent scholars (Garber, Grosholz), Descartes’s theory of matter is nevertheless very important for the foundation of his physics. As Stephen Gaukroger observes, “Part II of the Principles deals with the foundational principles of Descartes’ physical theory, which take the form of a synthesis of matter theory and mechanics” (Gaukroger 2003: 93).1 By Descartes’s theory of matter, I am referring here to his account that starts with the proof of the existence of bodies and goes through his discussion of the essence of matter up to the “proper” defi nition of motion.