Space-Time and Isomorphism

Earman and Norton argue that manifold realism leads to inequivalence of Leibniz-shifted space-time models, with undesirable consequences such as indeterminism. I respond that intrinsic axiomatization of space-time geometry shows the variant models to be isomorphic with respect to the physically meaningful geometric predicates, and therefore certainly physically equivalent because no theory can characterize its models more closely than this. The contrary philosophical arguments involve confusions about identity and representation of space-time points, fostered by extrinsic coordinate formulations and irrelevant modal metaphysics. I conclude that neither the revived Einstein hole argument nor the original Leibniz indiscernibility argument have any force against manifold realism
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James Owen Weatherall (forthcoming). Regarding the ‘Hole Argument’. British Journal for the Philosophy of Science:axw012.
Hilary Greaves (2011). In Search of (Spacetime) Structuralism. Philosophical Perspectives 25 (1):189-204.

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