Summary
Given that the entire physical world is one giant plenum of physical substance on Descartes' view, how do individual bodies get individuated? The answer is through motion. Like space, motion is not separable from body. Motion, however, is not a kind of body. Rather, it is a mode, like shape. It, too, then, can be deduced from the property of extension.
Also as with space, the common conception of motion is dead wrong. The common conception of motion is of an action by which a body travels from one place to another. This definition makes it seem as if motion is something separate from body. Descartes, therefore, revises the definition of motion. Motion, he claims, is the transfer of a body from the vicinity of one group of bodies—contiguous and regarded as being at rest—to the vicinity of another group of bodies. (This makes perfect sense if we remember Descartes' definition of place. To be in a certain place just meant sharing surface contact with other bodies. To move, is just to change your position.) This definition makes it clear that motion is just a mode of body, rather than anything external to body. Rest too, then, is nothing but a mode of body.
Within the plenum, bodies are individuated through this motion. Bits of matter that move together away from one set of bodies, which are contiguous with it and considered at rest, count as one body. However, even within one body there are countless different motions taking place. To illustrate how this is possible, Descartes asks us to imagine a watch in the pocket of a man, who is himself on a ship. The wheels of the watch have one motion, the motion that individuates the watch, but they also share in the motion of the man walking aboard the ship, because they are in contact with him. Further, they also share motion with the ship, because the man is connected to the ship. Lastly, they share the motion of the earth, because the ship is in contact with the earth. The watch, the man, the ship, and the earth can be seen as comprising a single piece of matter, through their contiguity, or they can be seen as individuated bits of matter through their own individual motions.
Because space is filled, all motion must be in the form of a circle of bodies moving together. Whatever place A is going to reach when it moves, must first be vacated before A can get there. So in order for A to move, whatever is occupying that spot (say, B,) must move as well. Of course, for B to move another spot, now occupied by C, it must first be vacated, and for C to move D must vacate its spot, and so on. In other words, in order for any motion to take place several bodies must move simultaneously. In order for this simultaneous vacating not to go on ad infinitum, Descartes posits that motion takes place in a circle. Motion, then, is a continuous circuit.
From the fact that motion is a continuous circuit, Descartes concludes that there are an indefinite, or infinite, number of particles in the world. For any motion to take place, it is necessary that all imaginable particles shift their positions to some extent. There must, therefore, be an indefinite number of particles in the world. Descartes admits that this indefinite division is beyond the grasp of our finite minds, but he claims that we cannot doubt its existence.
Analysis
Descartes' account of motion is not much easier to understand than his account of space. Once again, though, going through the discussion step by step can shed some significant clarity. It is clear enough why Descartes defines motion as the transfer of body from one contiguous group of bodies to another. Since place is defined in relation to a contiguous group of bodies, a change in place should also be defined this way.
