The Hole Argument Against Everything

Abstract

The Hole Argument was originally formulated by Einstein and it haunted him as he struggled to understand the meaning of spacetime coordinates in the context of the diffeomorphism invariance of general relativity. This argument has since been put to philosophical use by Earman and Norton (1987) to argue against a substantival conception of spacetime. In the present work I demonstrate how Earman and Norton’s Hole Argument can be extended to exclude everything and not merely substantival manifolds. These casualties of the hole demonstrate that the Hole Argument hinges essentially on our notion of determinism and not on the diffeomorphic freedom of general relativity. In order to prevent all things from falling into the Hole, I argue that we ought to restrict what we require of our deterministic theories. The central conviction which drives the arguments of this paper is that deterministic theories are not required to determine for future moments what they cannot determine for any present or past moments. The form of sophisticated determinism which I defend requires physical theories only to determine those facts for which they are a theory. Since general relativity is diffeomorphically invariant, spacetime point locations are not part the theory’s physical content and are therefore irrelevant for determinism. Since Earman and Norton’s original argument assumes that in substantival general relativity, one is required to determine spacetime point locations, their argument fails.