Reflections on a Relational Theory of Space

Abstract

The modern discussion of the philosophy of space and time continues in the pattern set by the controversy between Leibniz and Newton. The positions in that controversy are usually identified by the labels ‘relational’ vs. ‘absolute’ and the opposition thus marked is generally taken to be between the conceptions of space as “a lattice of quantitative relations” and as “a unity which precedes and makes possible all relations that can be discovered in it.”¹ Both positions, so described, are difficult to understand. There is, moreover, associated with each of them a special difficulty that I want to focus on, for these special difficulties will suggest a point of view that may aid our understanding of the controversy and its contemporary continuations.

I shall cite Adolf Grünbaum, Geometry and Chronometry in Philosophical Perspective (1968) as GCPP and my bracketed chapter and page references will be to this book. I want to take this opportunity to thank Professor Grünbaum for lively correspendence over the years and for making available to me the rough draft of a portion of some recent material of his that will contain careful and detailed reworkings of his position on space and time. Part of this material appenred in Grünbaum (1970).