I argued in Part I that Descartes' arguments based on the obscurity of substantial forms fail unless one presupposes his dualist metaphysics, but that his a priori argument against substantial forms is successful. In particular, I showed that it does not create a straw man if one reads it as targeting Suarez's doctrine of the substantial form and that, read this way, it reveals that, by this stage of his career, Descartes had a good grip on the strategy Suarez employed to argue for the existence of substantial forms. However, Descartes introduces this argument for polemical purposes after having re-acquainted himself with Scholastic philosophy in replying to the Objections to his Meditations. His own route to the rejection of substantial forms stemmed from scientific concerns, not from a critical engagement with Scholastic metaphysics. In Part II, I traced Descartes' arguments based on his identification of natural objects with machines, and on the superiority of mechanical explanations, back to developments in Aristotelian mechanics, and interpreted the nature of the scientific demonstrations he employs in the Discourse in this light. There, Descartes' scientific explanations take the form of demonstrations encountered in the newly founded science of mechanics. Mechanical demonstrations were considered mathematical in nature because they were based on the principles of geometry, and this is the sense in which Descartes takes his scientific explanations to be mathematical. Finally, I proposed a reading distinguishing Descartes' early theory of matter from his mature metaphysics.