Part II of the Principles begins with a proof that the physical world exists. Since there would be little use in studying physics if this were not the case, it seems like a good starting point for a physics treatise. Descartes' proof, predictably, rests on the guarantee of clear and distinct perception. As he established in Part I, we have a clear and distinct perception of something that has extension. If there were nothing out in the world matching this perception, then God would be a deceiver. And we all know by now that this cannot be the case. We can be certain, therefore, that something with extension, that is, physical substance (i.e body, or matter) exists.
Right after proving that physical body exists, Descartes takes a brief detour in principles II.2 and three, to talk about a particular type of matter that exists: our bodies. We can be sure that we have bodies, conjoined in a mysterious and intimate way to our minds, he tells us, because we have sensations such as pain. These sensations come to us unexpectedly, so they cannot simply be thought up by the mind. In addition, they clearly need to originate in something extended. Therefore, he concludes, our mind must be connected to a particular piece of matter. Sensory perceptions, he further tells us, are wholly intended only to act for the sake of this composite of mind and body. They are not supposed to supply the mind with fodder for intellectual ideas, but, rather, they are supposed to direct the human composite toward pleasure and away from pain. If they are used only for this purpose, they will cease to mislead us in our pursuit of truth.
Descartes now moves on to the real meat of his physics. He begins by restating that the only thing included in the nature of body is extension. This time, however, he runs though a few other candidates for properties that we might think are included in the nature of body: hardness, color, and weight. Once again, his argument rests on claims of conceivability. We can conceive of extension without hardness, without color, without anything at all, except without extension. Only extension, then, is really a necessary component of body.
Descartes then tries to account for the fact that no one else seems to think that the nature of body consists in extension. People are misled in this matter, he tells us, by preconceived opinions regarding the process of rarefaction and the notion of empty space. Descartes spends a lot of time and energy on the notion of empty space, and so that concept will be treated in the following section, but he corrects our view of rarefaction fairly quickly.
Most people, Descartes claims, have a very misleading view of rarefaction. They believe that when a body is rarefied it possesses more extension than it did when condensed. This leads people to believe that the substance of a body is something entirely separate from the extension. According to this view, extension can be added without adding new body. In reality, though, any extension is just body.
The correct view of rarefaction takes care of this problem. Rarefaction does not involve gaining or losing extension, it merely involves changing shape. Taking up more or less space does not amount to having more or less extension, it merely amounts to being a different shape. A rarefied body is just like a sponge filled with water. When a sponge is filled with water, the gaps between its parts are filled in with other bodies (i.e. water particles), and so it takes up more space. However, there is the same amount of spongy matter present when the sponge is filled with water, as when it is dry. The same is true of all bodies when rarefied. What can happen is that other bodies (particles of various sorts) can come between the parts of its matter, thereby causing the body to take up more space, without actually gaining any extension.