AAP 2026 CONFERENCE

What is empty space? Philosophers in the tradition stemming from Newton, through say Bertrand Russell down to, say, David Lewis, have thought of empty space as a manifold of things called points, and a region of space as empty if no material thing is located at any of the points in that region. These points possess locations and stand in spatial relations to one another; that is, they are things that possess properties and relations (rather than being properties or relations in themselves). There is a rival tradition (stemming from Leibniz) that dispenses with any such things as ‘points of space’ and countenances only material things and properties or relations among them. We will discuss a third option: a property theory of space. Spaces in general (including for instance ‘colour space’) are manifolds of properties; and location space is a manifold of locational properties. This way of thinking opens the possibility of a true void, a region consisting of locations that are not occupied by anything at all—not even by ‘points.’