  The hole argument depends upon a gauge freedom in general relativity; that is, the presence of surplus mathematical structure in general relativity that has no correlate in physical reality. The hole argument provides a template for the analysis of gauge freedoms in physical theories. We learn from it that the identification of surplus mathematical structure cannot be achieved by any a priori or purely mathematical rule. Some physical grounds are needed. The hole argument provides two grounds that can be used: verifiability—changes in the candidate surplus structure make no difference to what can be verified in observation; determinism—the laws of the theory are unable to fix the candidate surplus structure.  