Rings, holes and substantivalism: On the program of Leibniz algebras

Philosophy of Science 59 (4):572-589 (1992)
Abstract
In a number of publications, John Earman has advocated a tertium quid to the usual dichotomy between substantivalism and relationism concerning the nature of spacetime. The idea is that the structure common to the members of an equivalence class of substantival models is captured by a Leibniz algebra which can then be taken to directly characterize the intrinsic reality only indirectly represented by the substantival models. An alleged virtue of this is that, while a substantival interpretation of spacetime theories falls prey to radical local indeterminism, the Leibniz algebras do not. I argue that the program of Leibniz algebras is subject to radical local indeterminism to the same extent as substantivalism. In fact, for the category of topological spaces of interest in spacetime physics, the program is equivalent to the original spacetime approach. Moreover, the motivation for the program--that isomorphic substantival models should be regarded as representing the same physical situation--is misguided
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DOI 10.1086/289696
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Emergent Spacetime and Empirical Coherence.Nick Huggett & Christian Wüthrich - 2013 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (3):276-285.
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On Einstein Algebras and Relativistic Spacetimes.Sarita Rosenstock, Thomas William Barrett & James Owen Weatherall - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52:309-316.
Determinism and Ontology.Gordon Belot - 1995 - International Studies in the Philosophy of Science 9 (1):85 – 101.

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