A Leibnizian Space

Abstract

Leibniz said that space and time are well-founded phenomena. Few readers can make much literal sense out of this idea, so I shall describe a small possible world in which it is true. I do not contend that Leibniz had my construction in mind, but I do follow Leibnizian guidelines. The first trick is to reverse the maxim that every monad mirrors the world from its own point of view. Points of view, and hence a space of points, can be constructed from a non-relational account of the perceptions of each monad. But we cannot fabricate space alone. We must build up laws of nature simultaneously. We must also employ a measure of the simplicity of the laws of nature. Moreover we require that, in a literal sense, the perception of each monad is a sum of its Petits perceptions. The identity of indiscernibles, in its application to space, is an automatic consequence of this construction. Although I shall examine only one possible world, there is a general recipe for such constructions, in which none of the above elements can be omitted. This is a striking illustration of the way in which the many different facets of Leibniz's metaphysics are necessarily inter-connected.