Holes in Spacetime: Some Neglected Essentials

Abstract

The hole argument purports to show that all spacetime theories of a certain form are indeterministic, including General Relativity. The argument has sparked an industry of searching for a metaphysics of spacetime with the right modal implications to rescue determinism. In this paper, I first argue that certain prominent replies to the hole argument—namely, those that appeal to an essentialist doctrine about spacetime—fail to deliver the requisite modal implications. My argument involves showing that threats to determinism like the hole argument are more general than has heretofore been recognized. I then propose a novel essentialist doctrine about spacetime that successfully rescues determinism, what I call sufficiency metric essentialism. However, I ultimately argue that this doctrine is independently problematic, and teaches us that no essentialist doctrine about spacetime can succeed. I close by suggesting some lessons for future work on spacetime and the metaphysics of physics more broadly, and also drawing some morals for contemporary metaphysics, in particular about whether essence can be used to articulate a precise structuralist doctrine, and the relationship between essence and modality.