Descartes' analysis of substance and principal attribute is probably the most important section of Part I. It is in defining this terminology that he lays the groundwork for his entire physics, by establishing the subject matter of that science. In defining physical substance entirely in terms of extension, Descartes is ensuring that the physical sciences can be conflated with the study of geometry. All properties of substance can be explained simply by appealing to the properties of geometric figures. It is in this discussion that we see Descartes at the height of his offensive attack on Scholastic philosophers.

Like the Scholastics, Descartes claims that substances are the most basic units of existence. Where he diverges is in claiming, first, that there are only three substances and, second, that substances and their essences have such a tight connection. According to the Scholastic view there were numerous substances, all composed of various combinations of the four elements. The essence of a substance was the property that made the substance the sort of substance that it was, but aside from that important role it was no different from other properties. The further properties of a substance did not have any connection to the essence. For example, according to the Scholastics the essence of man was his rationality. However, man could also have qualities such as "pale" and "tall" that had nothing to do with this essence. In addition, according to the Scholastics, substance could survive the loss of its essence, though naturally not as that same sort of substance. So, for instance, if a man lost his rationality he would cease to be a man, but he would not cease to be a substance. He would just be a different sort of substance. It is by strengthening the connection between essence and substance that Descartes is able to so reduce the number of substances in the world. If a substance cannot be conceived of without its essence, there are very few candidates for essence and, correspondingly, few for substance. The only things we cannot conceive of are the logically impossible.