space an extended manifold of several dimensions, where the number of dimensions corresponds to the number of variable magnitudes needed to specify a location in the manifold; in particular, the three-dimensional manifold in which physical objects are situated and with respect to which their mutual positions and distances are defined.
Ancient Greek atomism defined space as the infinite void in which atoms move; but whether space is finite or infinite, and whether void spaces exist, have remained in question. Aristotle described the universe as a finite plenum and reduced space to the aggregate of all places of physical things. His view was preeminent until Renaissance Neoplatonism, the Copernican revolution, and the revival of atomism reintroduced infinite, homogeneous space as a fundamental cosmological assumption.
Further controversy concerned whether the space assumed by early modern astronomy should be thought of as an independently existing thing or as an abstraction from the spatial relations of physical bodies. Interest in the relativity of motion encouraged the latter view, but Newton pointed out that mechanics presupposes absolute distinctions among motions, and he concluded that absolute space must be postulated along with the basic laws of motion (Principia, 1687). Leibniz argued for the relational view from the identity of indiscernibles: the parts of space are indistinguishable from one another and therefore cannot be independently existing things. Relativistic physics has defused the original controversy by revealing both space and spatial relations as merely observer-dependent manifestations of the structure of spacetime.
Meanwhile, Kant shifted the metaphysical controversy to epistemological grounds by claiming that space, with its Euclidean structure, is neither a ‘thing-in-itself’ nor a relation of thingsin-themselves, but the a priori form of outer intuition. His view was challenged by the elaboration of non-Euclidean geometries in the nineteenth century, by Helmholtz’s arguments that both intuitive and physical space are known through empirical investigation, and finally by the use of non-Euclidean geometry in the theory of relativity. Precisely what geometrical presuppositions are inherent in human spatial perception, and what must be learned from experience, remain subjects of psychological investigation.
See also RELATIVITY, SPACE-TIME, TIME.
R.D.