Simple Matroids and Alfred North Whitehead's theory of dimension (1906)

Abstract

We give a correspondence between simple matroids and a reconstruction of Alfred North Whitehead's theory of dimension, as developed in "On Mathematical Concepts of the Material World" (1906). In brief, if a geometrical system in the generalized sense of Whitehead has finite ground set and is phi-maximal, then it is a simple matroid. Here "generalized" means that Whitehead's three-dimensional axiom is replaced by finite-dimensionality. Conversely, every simple matroid is a phi-maximal geometrical system in the generalized sense of Whitehead.