A widespread misunderstanding of space is the other obstacle to the proper conception of body. Just like the misunderstanding of rarefaction, the misunderstanding of space leads us to believe that dimensions can exist independent of body. We generally believe that space is something empty, a kind of nothingness that exists between bodies. This nothingness, though, obviously has dimensions. Between my can of soda and my plate of food, there are three inches of space. Between the floor and the ceiling there is ten feet of space. Thinking of space as a nothingness that has dimensions leads us to conclude that extension in itself does not amount to body. Instead, we think that only the sensible objects floating in space—the can of coke, the plate of food, the goal posts, the floor and ceiling—are bodies. In other words, we think that in order to be body something not only needs extension, but it also needs sensible qualities such as color, hardness, etc.
Descartes' conception of space sets us straight. On Descartes' view space is nothing but insensible body. Body is only extension and the space between my can of soda and my plate of food has dimension just as truly as the can and plate do. Descartes gives two arguments for this claim. The first argument, found in I.11, is simply a repetition of the argument for the claim that extension is the essence of body. Again, he asks us to try to conceive of body without color, hardness, or etc. There is no incoherence involved in any of these conceptions. Then, he asks us to conceive of body without extension. We find that it is impossible to do so. Extension, therefore, is the essence of body. Obviously, if it really is true that extension is sufficient for body, then anything extended must be body. Since space is extended, space, too, is body.
The second argument comes in principle I.16. The claim that space is "nothing," Descartes claims, is patently absurd. We all admit that space has extension, and nothingness can have no properties. Space, therefore, must be something. Now that we have already admitted that space is something, there is nothing preventing us from admitting that space is body. So space, on Descartes' view, is not an empty vaccuum, but rather it is a plenum, or something that is filled.
After taking care of the notion of space, Descartes next turns to the related notion of place. While "space" is a term that we use when referring to the size and shape of bodies, "place" is a term that we use when referring to the position of bodies. Place, Descartes tells us, refers to a body's size, shape, and position relative to other bodies. Place, therefore, is a relative property. No body is in any one absolute place or position. Rather, a body is in numerous different places corresponding to all the other bodies with which you could view it in relation. To illustrate this point, Descartes draws an analogy to a man on a ship. If the man remains at the wheel of the ship, then in one sense he remains at the same place: his position on the ship has not changed. However, since the ship itself is moving in relation to the two shores between which it is traveling, the man is changing his place in relation to these shores as well. Strictly speaking, though, we determine the place of a body by the common surface it shares with other bodies. So long as a body retains its position relative to this common surface, we do not say that it has changed its place, even if it does change its position relative to other bodies. The man on the ship, then, is not moving, strictly speaking, because he only shares a common surface with the ship, and his position with respect to the ship is not changing.
Descartes' conception of space as insensible body is counterintuitive. It is extremely tempting to believe that bodies are things and that space is not. A primary worry that might trouble someone presented with this position is the concern that as a consequence of calling space a thing, Descartes is committing himself to the view that two things can be in the same place at the same time. After all, sensible bodies seem to occupy, or be in, space. However, Descartes has a good response to this worry. To think that sensible bodies are in some vast thing called "space" is to completely misunderstand what space is. Space is the extension between sensible bodies. Sensible bodies are in space, only in the sense that a ship is in water. The ship and the water are both bodies standing in a relative position to one another. Similarly, sensible bodies and space are both bodies standing in a relative position to one another. We do not object that a ship cannot be in water on the grounds that two things would be in the same place at the same time, so we should not object in the case of space and sensible bodies either.
Though the concepts involved might be counterintuitive, the work that Descartes does in his analysis of space and place allows him to draw many important scientific conclusions. First, this analysis allows him to argue in Part III that the earth does not change its place, even while presenting a heliocentric model of planetary motion. In addition, it allows Descartes to conclude (as he does in II.20) that atoms are a logical impossibility. By "atom," Descartes means an indivisible particle of matter. The reason that atoms are impossible is that all pieces of matter, no matter how small, have to be extended. Anything extended, in turn, must be divisible. Therefore, there can be no indivisible atoms.