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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.

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.

References

Alexander, H. G. (ed.) (1956), The Leibniz-Clarke Correspondence: Together with Extracts from Newton's Principia and Opticks. New York: Barnes and Noble.Google Scholar
Davidson, D. ([1979] 1984), “The Inscrutability of Reference”. Reprinted in Inquiries into Truth and Interpretation. (Originally published in Southwestern Journal of Philosophy 10: 7–19.) Oxford: Oxford University Press, pp. 227–241.CrossRefGoogle Scholar
Earman, J. (1977), “Leibnizian Space-Times and Leibnizian Algebras”, in R. E. Butts and J. Hintikka (eds.). Historical and Philosophical Dimensions of Logic, Methodology and Philosophy of Science. Dordrecht: Reidel, pp. 93–112.Google Scholar
Earman, J. (1978), “Perceptions and Relations in the Monadology”, Studia Leibnitiana 9: 212–230.Google Scholar
Earman, J. (1979), “Was Leibniz a Relationist?”, in French, P., Uehling, T., Jr, . and Wettstein, H. (eds.), Midwest Studies in Philosophy, vol. 4. Minneapolis: University of Minnesota Press, pp. 263–276.Google Scholar
Earman, J. (1986a), A Primer on Determinism. Dordrecht: Reidel.10.1007/978-94-010-9072-8CrossRefGoogle Scholar
Earman, J. (1986b), “Why Space is Not a Substance (At Least Not to First Degree)”, Pacific Philosophical Quarterly 67: 225–244.10.1111/j.1468-0114.1986.tb00275.xCrossRefGoogle Scholar
Earman, J. (1989a), “Leibniz and the Absolute vs. Relational Dispute” in N. Rescher (ed.), Leibnizian Inquiries: A Group of Essays. Lanham, MD: University Press of America, pp. 9–22.Google Scholar
Earman, J. (1989b), World Enough and Space-Time: Absolute versus Relational Theories of Space and Time. Cambridge, MA: MIT Press.Google Scholar
Earman, J. and Norton, J. (1987), “What Price Spacetime Substantivalism? The Hole Story”, British Journal for the Philosophy of Science 38: 515–525.10.1093/bjps/38.4.515CrossRefGoogle Scholar
Einstein, A. (1934), “On the Method of Theoretical Physics”, in The World As I See It. Translated by A. Harris. New York: Covici Friede, pp. 30–40.Google Scholar
Einstein, A. ([1917] 1961), Relativity: The Special and the General Theory. New York: Bonanza Books.Google Scholar
Geroch, R. (1972), “Einstein Algebras”, Communications in Mathematical Physics 26: 271–275.10.1007/BF01645521CrossRefGoogle Scholar
Gillman, L. and Jerison, M. (1960), Rings of Continuous Functions. New York: Van Nostrand Reinhold.10.1007/978-1-4615-7819-2CrossRefGoogle Scholar
Hacking, I. (1975), “The Identity of Indiscernibles”, Journal of Philosophy 72: 249–256.10.2307/2024896CrossRefGoogle Scholar
Hawking, S. W. and Ellis, G. F. R. (1973), The Large Scale Structure of Space-Time. Cambridge, England: Cambridge University Press.10.1017/CBO9780511524646CrossRefGoogle Scholar
Hewitt, E. (1948), “Rings of Real-Valued Continuous Functions. I”, Transactions of the American Mathematical Society 64: 45–99.10.1090/S0002-9947-1948-0026239-9CrossRefGoogle Scholar
Nomizu, K. (1956), Lie Groups and Differential Geometry. Japan: Gakujutsutosho.Google Scholar
Putnam, H. (1981), Reason, Truth and History. Cambridge, England: Cambridge University Press.10.1017/CBO9780511625398CrossRefGoogle Scholar
Quine, W. V. (1969), “Ontological Relativity”, in Ontological Relativity and Other Essays. New York: Columbia University Press, pp. 26–68.10.7312/quin92204-003CrossRefGoogle Scholar
Rynasiewicz, R. (forthcoming), “The Lessons of the Hole Argument”, British Journal for the Philosophy of Science.Google Scholar
Sachs, R. K. and Wu, H. (1977), General Relativity for Mathematicians. New York: Springer-Verlag.10.1007/978-1-4612-9903-5CrossRefGoogle Scholar
Stein, H. (1977), “Some Philosophical Prehistory of General Relativity”, in J. Earman, C. Glymour, and J. Stachel (eds.), Minnesota Studies in the Philosophy of Science. Vol. 8, Foundations of Space-Time Theories. Minneapolis: University of Minnesota Press, pp. 3–49.Google Scholar
Wald, R. M. (1984), General Relativity. Chicago: University of Chicago Press.CrossRefGoogle Scholar