Analysis

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.