Abstract
This chapter focuses on the hole argument as an argument against substantivalism. It reviews some technical notions standardly presupposed in presentations of the argument. The core conclusion of the hole argument is that, under a substantivalist interpretation, any generally covariant theory such as general relativity (GR) is indeterministic. If relationalists deny that the manifolds in models of GR have a physical correlate, they owe us a positive alternative picture of what such models should be taken to represent. The substantivalist can claim, therefore, that, for all the hole argument has shown, GR is qualitatively or physically deterministic: given the past and the laws, all future physical facts might be fixed. Responses to the argument divide into those that accept the core conclusion and those that reject it. Responses rejecting the core conclusion can then be classified according to which key premise they reject.
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