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Rings, Holes and Substantivalism: On the Program of Leibniz Algebras

Published online by Cambridge University Press:  01 April 2022

Robert Rynasiewicz
Robert Rynasiewicz*
Affiliation:
Department of Philosophy, The Johns Hopkins University
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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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Type
Research Article
Information
Philosophy of Science , Volume 59 , Issue 4 , December 1992 , pp. 572 - 589
Copyright
Copyright © 1992 by the Philosophy of Science Association

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Footnotes

†

Send reprint requests to the author, Department of Philosophy, The Johns Hopkins University, 347 Gilman Hall, 3400 N. Charles Street, Baltimore, MD 21218-2690, USA.

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