Hyperloops Do Not Threaten the Notion of an Effective Procedure

  • Tim Button
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5635)

Abstract

This paper develops my (forthcoming) criticisms of the philosophical significance of a certain sort of infinitary computational process, a hyperloop. I start by considering whether hyperloops suggest that “effectively computable” is vague (in some sense). I then consider and criticise two arguments by Hogarth, who maintains that hyperloops undermine the very idea of effective computability. I conclude that hyperloops, on their own, cannot threaten the notion of an effective procedure.

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References

  1. Benacerraf, P.: Tasks, Super-Tasks, and the Modern Eleatics. Journal of Philosophy 59, 765–784 (1962)CrossRefGoogle Scholar
  2. Button, T.: SAD Computers and two versions of the Church-Turing Thesis. British Journal for the Philosophy of Science (forthcoming)Google Scholar
  3. Davies, E.B.: Building Infinite Machines. British Journal for the Philosophy of Science 52, 671–682 (2001)MathSciNetCrossRefMATHGoogle Scholar
  4. Dummett, M.: Hume’s Atomism about Events: a response to Ulrich Meyer. Philosophy 80, 141–144 (2005)CrossRefGoogle Scholar
  5. Earman, J., Norton, J.D.: Forever is a Day: Supertasks in Pitowsky and Malament-Hogarth Spacetimes. Philosophy of Science 60, 22–42 (1993)MathSciNetCrossRefGoogle Scholar
  6. Etesi, G., Németi, I.: Non-Turing Computations via Malament-Hogarth space-times. International Journal of Theoretical Physics 41, 341–370 (2002)MathSciNetCrossRefMATHGoogle Scholar
  7. Hamkins, J.D., Lewis, A.: Infinite Time Turing Machines. Journal of Symbolic Logic 65, 567–604 (2000)MathSciNetCrossRefMATHGoogle Scholar
  8. Hogarth, M.: Does General Relativity Allow an Observer to View an Eternity in a Finite Time? Foundations of Physics Letters 5, 173–181 (1992)MathSciNetCrossRefGoogle Scholar
  9. Hogarth, M.: Non-Turing Computers and Non-Turing Computability. In: Proceedings of the Philosophy of Science Association 1994, vol. 1, pp. 126–138 (1994)Google Scholar
  10. Hogarth, M.: Deciding Arithmetic using SAD computers. British Journal for the Philosophy of Science 55, 681–691 (2004)MathSciNetCrossRefMATHGoogle Scholar
  11. Hogarth, M.: Non-Turing Computers are the New Non-Euclidean Geometries. International Journal of Unconventional Computing 5, 277–291 (2009a)Google Scholar
  12. Hogarth, M.: A New Problem for Rule Following. Natural Computing (2009b)Google Scholar
  13. Lakatos, I.: Proofs and Refutations. Cambridge University Press, Cambridge (1976)CrossRefMATHGoogle Scholar
  14. Németi, I., Dávid, G.: Relativistic Computers and the Turing Barrier. Journal of Applied Mathematics and Computation 178, 118–142 (2006)MathSciNetCrossRefMATHGoogle Scholar
  15. Smith, P.: An Introduction to Gödel’s Theorems. Cambridge University Press, Cambridge (2007)CrossRefMATHGoogle Scholar
  16. Shapiro, S.: Computability, Proof, and Open-Texture. In: Olszewski, A., Wolenski, J., Janusz, R. (eds.) Church’s Thesis After 70 Years, pp. 420–455. Ontos Verlag (2006)Google Scholar
  17. Thomson, J.: Tasks and Supertasks. Analysis 15, 1–10 (1954)CrossRefGoogle Scholar
  18. Welch, P.D.: The Extent of Computation in Malament-Hogarth Spacetimes. British Journal for the Philosophy of Science 59, 659–674 (2008)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Tim Button
    • 1
  1. 1.Cambridge UniversityUK

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