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.
Though Descartes is convinced that his physics is as simple as it gets, any Descartes student will be willing to attest to the fact that few concepts are harder to grasp than Descartes' concept of extension. His may well be a simple picture once you get past that crucial first step, but getting past that step is no easy task. (Actually, it is never a simple picture.)
The best way to get clear on the notion of extension is to try to get clear on what the notion does and does not include. We have already seen that extension does not amount to shape. Shape and extension are two different things. In fact, as you might recall from Part I, shape is a mode of extension. So what does the notion of extension include? Descartes tells us in II.1 that extension is just length, breadth, and depth. This makes sense if you think about the common use of the term "extended." What does it mean to be extended? It just means to spread from one point to another. A line is extended in one direction: it has length. A plane is extended in two directions: it has length and breadth. A body is extended in three dimensions: it has length, breadth, and depth.
The next step is to ask what it is about this picture that makes the common conception of rarefaction impossible. Why can a body not lose any length, breadth, or depth? It seems clear that if you take a seven inch by five inch by one inch board and cut off three inches of length from it, the original board is losing some of its extension. Why is this any different from the common conception of condensation that Descartes is so eager to attack? The answer is that in the case of the board, we all admit that in cutting off the three inches we are creating two separate bodies. The three inches by two inches by one inch that was lost from the original board do not just cease to be a part of body just because they cease to be a part of that original board. They now define a new body: a body that is three inches, by five inches, by one inch. If you cut off another chunk from this board, you would create yet another body. No matter how small you cut the pieces, even if you just took off some shavings, you would never separate the dimensions from body since to have dimensions is what it means to be body. (This is what Descartes means when he tells us in principle I.8 that the difference between quantity and substance is only conceptual. There is no such thing as three liters or twelve cubic feet, except insofar as there are bodies with this quantity of matter.)
On the naïve view of rarefaction and condensation, on the other hand, it seems as if extension can just float free of body. It seems as if body is one thing and extension is another, so that extension can be lost from body without the creation of another body. That is why Descartes needs to show that rarefaction does not involve losing extension at all. If you took a rarefied body and added together all of its matter, the quantity would be the same as in its condensed form. The only difference is that the parts of the matter are spread further from each other, separate by a different sort of matter.
This way of viewing extension provides a good enough level of understanding of body in order to tackle the next hurdle: the relationship between body and space.