From quite early in his career, Descartes lists shape as one of the three genuine “modes” of extension or ways of being extended, the other two being size and motion. This austere ontology of body is in sharp contrast to the Aristotelian Scholastic model of the explanation of natural phenomena that appeals to an elaborate scheme of forms and qualities. As a proponent of mechanistic scientific explanations, Descartes held instead that all natural phenomena can be explained entirely in terms of the arrangements of corpuscles, or extended microbodies, characterized solely in terms of size, shape, and motion.

Although motion plays a central role in Descartes’ natural philosophy, shape is no less important to his scheme of scientific explanation. This is because the way that motion is characterized seems to presuppose that body has a determinate extension or shape. According to the “proper” characterization of motion Descartes introduces in the Principles, it consists in “the transfer of one piece of matter, or one body, from the vicinity of the other bodies which are in immediate contact with it, and which are regarded as being at rest, to the vicinity of other bodies” (AT VIIIA 53, CSM I 233). Yet this account presupposes the individuation of bodies from one another, which in turn seems to presuppose that a body, insofar as it is delineated from the bodies that surround it, has at any particular moment a determinate extension or shape. Further evidence for the explanatory importance of the mode of shape can be found in Descartes’ insistence in his early work, the Rules, that shape plays a central role in all cases of sense perception: “Sense perception occurs in the same way in which wax takes on an impression from a seal. It should not be thought that I have a mere analogy in mind here” (AT X 412–13, CSM I 40–41).

As obvious as the idea that shape is a modification of extension might seem, there are deep interpretative and philosophical difficulties with Descartes’ claim. The principle interpretative difficulty is that it is not clear what he means by “shape,” a difficulty that is exacerbated by the fact that he never offers an explicit explanation.