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Perhaps the most important clear and distinct perception of all is the perception that extension is the essence of body. It is this perception that enables all of Descartes’s physics.
To say that the essence of body is extension is not just to say that extension is the most important property of body. Rather, it is to say that body simply is extension. What it is to be a body, is to be an extended thing. So long as there is extension, there is body, and so long as there is body there is extension.
Extension is just dimension. Bodies have extension in three directions—length, breadth, and depth. To be a body, then, is simply to have length, breadth, and depth. Bodies obviously have more properties than just length, breadth, and depth, though. For instance, they have a certain shape. These other properties, however, are simply determinate ways of being extended (also called modes of extension). A body can be extended as a square, as a circle, as a dodecahedron, or as any other conceivable shape. Size, too, is just a determinate way of being extended. A body can be extended five feet by twelve feet by two inches, or thirty centimeters by thirty centimeters by thirty centimeters, etc.
It is clear enough to see how size and shape are just determinate ways of being extended, but bodies also seem to have some other sorts of properties, such as color, sound, taste, smell, heat, and cold. How can these be determinate modes of extension? The answer is that they are not, and for this reason they are also not really properties of bodies. All properties of bodies must be deducible from extension, and these properties have nothing to do with extension.
These properties, therefore, do not actually belong to bodies, at least not in the way that we perceive them. (They might be said to exist in bodies insofar as they are only arrangements of the size, shape, and motion of particles with the power to create the sensation of these qualities in us. Alternatively, these qualities might just be said to exist in our own minds.)
By ridding body of all things but extension and its deducible properties, Descartes turns the study of physics into the study of geometry (the mathematics of extended bodies). The certainty of mathematics, therefore, can now be imported into the study of the natural world.