Jeff Malpas on differences between Aristotelian and Cartesian spaces.
Whereas Aristotle treats topos as tied to the bounding inner surface of a container, Descartes takes “l’éspace” to be identical with the area or volume enclosed within the container and “le lieu” [location] to be just a matter of the container’s position, with both notions tied to the concept of an extended body. From the idea of space as tied to a particular body, it is easy to arrive at a more generalized notion of space as the extended realm within which all bodies can be contained. Albert Einstein talks in just this way of the development of the modern idea of space: the idea of an “independent (absolute) space, unlimited in extent, in which all material objects are contained” is arrived at by “natural extension” from the concept of the particular space that exists within any particular enclosing body.
This Cartesian view of space is continuous with the Aristotelian in that
it derives from a concept of space (and of place) that is tied to containment. But the Cartesian view is much more dependent on ideas deriving
from the Greek atomists and Stoics than from Aristotle. Indeed, the Cartesian view of space is clearly descended from the idea of kenon or void that was especially important in providing the basis for a notion of space as undifferentiated and unlimited extension in writers from Philoponous to
Giordano Bruno. The Cartesian view is also indebted to Platonic ideas of
space. Plato’s view of space—the view presented in the famous discussion
of chora in the Timaeus — is explicitly criticized by Aristotle in the Physics. Aristotle takes it to be a view that reduces space or place to matter understood as pure extension. The Platonic account of the Chora is notoriously obscure, but it involves a concept of the Chora—or Receptacle—as opening up a space into which qualities can be received so that particular things can come into being. The Receptacle is thus the “Nurse of Becoming.” The concept of space or place that is involved in this account—of space as the receptive and nurturing opening or “womb” in which things come to be—is one that is amenable to a more geometrical or mathematical account than the Aristotelian. And this is not surprising since Aristotle’s concern, at least in the Physics, is with place as it plays a role in change, especially motion, which he defines “in its most general and primary sense” as change of place, while Plato is interested in the role of chora in generation, viewing the process of generation as itself governed by geometrical principles and forms. The space or place that is the chora is indeed a space of pure, featureless extension. For this reason, the Platonic account of space or place in the Timaeus can be seen as an ancestor to modern conceptions of space in a way that the Aristotelian notion cannot. Thus, although, in Introduction to Metaphysics, Heidegger claims (perhaps somewhat ambiguously, given the difficulty in establishing exactly how either place or “topos” should be understood) that “The Greeks have no word for ‘space’ . . . for they do not experience the spatial according to extensio but instead according to place (topos), [p. 69]” still he writes elsewhere that “Platonic philosophy — that is, the interpretation of Being as idea — prepared the transfiguration of place (topos) and of chora, the essence of which we have barely grasped, into ‘space’ as defined by extension. [P. 70]”