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Forever is a Day: Supertasks in Pitowsky and Malament-Hogarth Spacetimes

Published online by Cambridge University Press:  01 April 2022

John Earman  and
John D. Norton
John D. Norton*
Affiliation:
Department of History and Philosophy of Science, University of Pittsburgh
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Abstract

The standard theory of computation excludes computations whose completion requires an infinite number of steps. Malament-Hogarth spacetimes admit observers whose pasts contain entire future-directed, timelike half-curves of infinite proper length. We investigate the physical properties of these spacetimes and ask whether they and other spacetimes allow the observer to know the outcome of a computation with infinitely many steps.

Type
Research Article
Information
Philosophy of Science , Volume 60 , Issue 1 , March 1993 , pp. 22 - 42
Copyright
Copyright © Philosophy of Science Association 1993

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Footnotes

†

We are grateful to David Malament and an anonymous referee for helpful suggestions on earlier drafts of this paper.

‡

Send reprint requests to the authors, Department of History and Philosophy of Science, 1017 Cathedral of Learning, University of Pittsburgh, Pittsburgh, PA 15260, USA.

References

Allais, V. and Koestsier, T. (1991), “On Some Paradoxes of the Infinite”, British Journal for the Philosophy of Science 42: 187–194.CrossRefGoogle Scholar
Barrow, J. D. and Tipler, F. J. (1986), The Anthropic Cosmological Principle. Oxford: Oxford University Press.Google Scholar
Benacerraf, P. (1962), “Tasks, Super-Tasks, and the Modern Eleatics”, Journal of Philosophy 59: 765–784.CrossRefGoogle Scholar
Benacerraf, P. and Putnam, H. (eds.) (1964), Philosophy of Mathematics. 2d ed. Cambridge, England: Cambridge University Press.Google Scholar
Chandrasekhar, S. and Hartle, J. B. (1982), “On Crossing the Cauchy Horizon of a Reissner-Nordström Black Hole”, Proceedings of the Royal Society (London) A: 301–315.Google Scholar
Chihara, C. S. (1965), “On the Possibility of Completing an Infinite Process”, Philosophical Review 74: 74–87.CrossRefGoogle Scholar
Earman, J. (1993), “The Cosmic Censorship Hypothesis”, to appear in Problems of Internal and External Worlds: Essays in Honor of Adolf Grünbaum. Pittsburgh: University of Pittsburgh Press. In press.Google Scholar
Earman, J. and Glymour, C. (1980), “The Gravitational Red Shift as a Test of Einstein's General Theory of Relativity: History and Analysis”, Studies in the History and Philosophy of Science 11: 175–214.CrossRefGoogle Scholar
Geroch, R. and Horowitz, G. T. (1979), “Global Structure of Spacetimes”, in Hawking, S. W. and Israel, W. (eds.), General Relativity. Cambridge, England: Cambridge University Press.Google Scholar
Grünbaum, A. (1968), Modern Science and Zeno's Paradoxes. London: Routledge & Kegan Paul.Google Scholar
Grünbaum, A. (1969), “Can an Infinitude of Operations be Performed in a Finite Time?” British Journal for the Philosophy of Science 20: 203–218.CrossRefGoogle Scholar
Hawking, S. W. and Ellis, G. F. R. (1973), The Large Scale Structure of Space-Time. Cambridge, England: Cambridge University Press.CrossRefGoogle Scholar
Hogarth, M. L. (1991), “Does General Relativity Allow an Observer to View an Eternity in a Finite Time?” Pre-print.CrossRefGoogle Scholar
Malament, D. (1988), Private communications.Google Scholar
Penrose, R. (1974), “Gravitational Collapse”, in De Witt-Morette, C. (ed.), Gravitational Radiation and Gravitational Collapse. Dordrecht: Reidel, pp. 82–91.Google Scholar
Pitowsky, I. (1990), “The Physical Church Thesis and Physical Computational Complexity”, Iyyun 39: 81–99.Google Scholar
Thomson, J. (1954–1955), “Tasks and Super-Tasks”, Analysis 15: 1–13.CrossRefGoogle Scholar
van Bendegem, J. P. (forthcoming), “Ross's Paradox is an Impossible Super-Task”, British Journal for the Philosophy of Science.Google Scholar
Wald, R. M. (1984), General Relativity. Chicago: University of Chicago Press.CrossRefGoogle Scholar