A relational theory of physical space

Abstract

Our problem is to build a relational theory of space, i.e., one according to which space is a sort of network of relations among things. We take the notions of concrete thing and of action of one thing upon another as undefined, or rather as defined in another context. We define the notion of interposition between things in terms of the previous notions. We then define the separation between two things as the set of things interposed between them. The collection of things equipped with the separation function is called thething space—a representation of ordinary space sufficient for philosophical purposes but not for physics. The next step is to define a topology for the thing space: This is done with the help of the separation function. The set of things together with this topology is called thephysical space. We then define the family of balls lying between any two things and postulate that it satisfies Huntington's axioms for solid geometry. By adding a few more natural assumptions we render physical space a three-dimensional manifold, which is what current physical theories require. We abstain from any metrical considerations, not only because these would require building space-time, but also because our problem was not to describe space but to explain how it comes about. Nevertheless our construction of space involves the notions of event and of event composition, and the latter allows one to define a time order of events, which in turn is required to define the notion of action of one thing upon another. The upshot is a full-fledged relational and objectivistic theory of space based on the assumption that the physical world is constituted by changing things.