The Hole Argument

Abstract

The “hole argument” shows that spacetime substantivalism leads to a radical form of indeterminism in a broad class of spacetime theories. My purpose in this note is twofold. First I shall present a short and informal version of the argument in the form developed in Earman and Norton (1987). Second I will show how the argument can be extended to the case of “manifold plus further structure” substantivalism whenever that further structure admits certain common symmetries.The hole argument depends on the possibility of displaying two models of some spacetime theory which agree everywhere but within a small neighborhood of the spacetime manifold. To illustrate how two such models are arrived at, I will describe the construction for the easy to visualize special case of a spatially homogeneous and isotropic expanding universe in general relativity. It will be clear how the construction can be extended to other spacetime theories.