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The Hole Argument

Published online by Cambridge University Press:  28 February 2022

John Norton
John Norton*
Affiliation:
University of Pittsburgh
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Extract

The “hole argument” shows that spacetime substantivalism leads to a radical form of indeterminism in a broad class of spacetime theories. My purpose in this note is twofold. First I shall present a short and informal version of the argument in the form developed in Earman and Norton (1987). Second I will show how the argument can be extended to the case of “manifold plus further structure” substantivalism whenever that further structure admits certain common symmetries.

The hole argument depends on the possibility of displaying two models of some spacetime theory which agree everywhere but within a small neighborhood of the spacetime manifold. To illustrate how two such models are arrived at, I will describe the construction for the easy to visualize special case of a spatially homogeneous and isotropic expanding universe in general relativity. It will be clear how the construction can be extended to other spacetime theories.

Type
Part III. Natural Philosophy
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1988 , Issue 2: Volume Two: Symposia and Invited Papers 1988 , 1988 , pp. 56 - 64
Copyright
Copyright © 1989 by the Philosophy of Science Association

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References

Alexander, H.G. (1956) (ed.), The Leibniz -Clarke Correspondence. Manchester Univ. Press.Google Scholar
Earman, J. (1986), A Primer on Determinism. Dordrecht: Reidel.CrossRefGoogle Scholar
Earman, J. and Norton, J. (1987), “What Price Spacetime Substantivalism? The Hole Story”, British Journal for the Philosophy of Science 38:515–525.CrossRefGoogle Scholar
Einstein, A. (1914), “Die formale Grundlage der allgemeinen Relativitaetstheorie”, Preuss. Akad. der Wiss., Sitz. pp.1013-1085.Google Scholar
Norton, J. (1987), “Einstein, the Hole Argument and the Reality of Space”, in Measurement, Realism and Objectivity, Forge, J. (ed.). Dordrecht: Reidel, pp.153–188.CrossRefGoogle Scholar
Norton, J. (forthcoming), “Coordinates and Covariance: Einstein's View of Spacetime and the Modern View”, Foundations of Physics.Google Scholar
Stachel, J. (1980), “Einstein's Search for General Covariance”. Paper read at the Ninth International Conference on General Relativity and Gravitation, Jena. Published in Howard, D. and Stachel, J. (eds.), Einstein and the History of General Relativity: Einstein Studies, Volume 1. Boston: Birkhauser, 1989 forthcoming.Google Scholar