Conclusions
I have argued that the most recent versions of the causal theory are subject to serious limitations. The causal analysis of spatiotemporal coincidence considered in Section IV does not apply to space-times in which (1) fails. And current versions of the theory collapse altogether for typical cases of relativistic space-times which are closed in their temporal aspects. Second, I have pointed out that the program of recent causal theorists is based on a false dichotomy — open vs. closed times; for only a small subclass of relativisitic space-times can be said to be either open or closed in their temporal aspects, and the causal theory seems incapable of handling the cases which fall in between. Third, I have argued that the general theory of relativity does not provide motivation for the causal theory; on the contrary, general relativity promotes the view of spacetime as a substantial entity.
As a result, I do not see that the causal theorist has a convincing argument against the position which holds that in order to understand the subtle and complex temporal structures encompassed by relativity theory, one must accept space-time as an entity which cannot be analyzed away as an abstract mathematical construct used for representing the ‘physical’, i.e., causal, relations between events. And I cannot agree with van Fraassen (1970, p. 140) that
Philosophers were not long in appreciating this development [i.e., relativity theory], and the consequent construction of the causal theory of time and space-time must be considered one of the major contributions of twentieth-century philosophy of science.
For it seems to me that causal theorists have failed to appreciate this development and that the construction of the causal theory has served to obscure important and interesting facts about the temporal aspect of space-time.
Similar content being viewed by others
Bibliography
Carter, B., ‘Global Structure of the Kerr Family of Gravitational Fields’, Physical Review 174 (1968), 1559–1571.
Davidson, D., ‘The Individuation of Events’, in N. Rescher (ed.), Essays in Honor of Carl G. Hempel, D. Reidel, Dordrecht, Holland, 1969, p. 216.
Earman, J., ‘Space-Time, or How to Solve Philosophical Problems and Dissolve Philosophical Muddles Without Really Trying’, Journal of Philosophy 67 (1970), 259–277. (a)
Earman, J., ‘Who's Afraid of Absolute Space?’, Australasian Journal of Philosophy 48 (1970), 287–319. (b)
Fox, R., Kuper, C. G., and Lipson, S. G., ‘Faster-Than-Light-Group Velocities and Causality Violation’, Proceedings of the Royal Society (London) A 316 (1970), 515–524.
Grünbaum, A., Philosophical Problems of Space and Time, Alfred A. Knopf, New York, 1963.
Grünbaum, A., Modern Sciene and Zeno's Paradoxes, Wesleyan University Press, Middletown, 1968.
Hawking, S. W., ‘The Existence of Cosmic Time Functions’, Proceedings of the Royal Society (London) A 308 (1968), 433–435.
Kalnay, A. J., ‘Lorentz Invariant Localization for Elementary Systems’, Physical Review D 1 (1970), 1092–1104.
Kronheimer, E. H. and Penrose, R., ‘On the Structure of Causal Spaces’, Proceedings of the Cambridge Philosophical Society 63 (1967), 481–501.
Lacey, H. M., ‘The Causal Theory of Time, a Critique of Grünbaum's Version’, Philosophy of Science 35 (1968), 322–354.
Reichenbach, H., Space and Time, Dover, New York, 1958.
Reichenbach, H., The Direction of Time, University of California Press, Los Angeles, 1956.
Stein, H., ‘A Note on Time and Relativity Theory’, Journal of Philosophy 67 (1970), 289–294.
van Fraassen, B. C., An Introduction to the Philosophy of Time and Space, Random House, New York, 1970.
Wheeler, J. A., Geometrodynamics, W. A. Benjamin, New York, 1962.
Rights and permissions
About this article
Cite this article
Earman, J. Notes on the causal theory of time. Synthese 24, 74–86 (1972). https://doi.org/10.1007/BF00540142
Issue Date:
DOI: https://doi.org/10.1007/BF00540142