, Volume 70, Issue 2, pp 211–235 | Cite as

Fifteen Arguments Against Hypothetical Frequentism

  • Alan HájekEmail author
Original article


This is the sequel to my “Fifteen Arguments Against Finite Frequentism” (Erkenntnis 1997), the second half of a long paper that attacks the two main forms of frequentism about probability. Hypothetical frequentism asserts:

The probability of an attribute A in a reference class B is p


the limit of the relative frequency of A’s among the B’s would be p if there were an infinite sequence of B’s.

I offer fifteen arguments against this analysis. I consider various frequentist responses, which I argue ultimately fail. I end with a positive proposal of my own, ‘hyper-hypothetical frequentism’, which I argue avoids several of the problems with hypothetical frequentism. It identifies probability with relative frequency in a hyperfinite sequence of trials. However, I argue that this account also fails, and that the prospects for frequentism are dim.


Relative Frequency Infinite Sequence Objective Probability Reference Class Fair Coin 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Bartha, P., & Hitchcock, C. (1999). The shooting-room paradox and conditionalizing on ‘measurably challenged’ sets. Synthese, 118, 403–437. doi: 10.1023/A:1005100407551.CrossRefGoogle Scholar
  2. Carnap, R. (1950). Logical foundations of probability. Chicago: University of Chicago Press.Google Scholar
  3. Church, A. (1940). On the concept of a random sequence. Bulletin of the American Mathematical Society, 46, 130–135. doi: 10.1090/S0002-9904-1940-07154-X.CrossRefGoogle Scholar
  4. Costantini, D., & Galavotti, M. (Eds.). (1997). Probability, dynamics and causalityessays in honor of R. C. Jeffrey, Dordrecht: Kluwer.Google Scholar
  5. de Finetti, B. (1972). Probability, induction and statistics. London: John Wiley & Sons.Google Scholar
  6. Elga, A. (2004). Infinitesimal chances and the laws of nature. Australasian Journal of Philosophy, 82, (March), 67–76. (Reprinted from Lewisian themes: The philosophy of David K. Lewis, by F. Jackson, G. Priest (Eds.), 2004, Oxford: Oxford University Press.)Google Scholar
  7. Hájek, A. (1997). ‘Mises Redux’—Redux: Fifteen arguments against finite frequentism, Erkenntnis 45, 209–227. (Reprinted from Costantini and Galavotti (1997). Reprint forthcoming in Philosophy of probability: Contemporary readings, by A. Eagle (Ed.), 2009, Routledge.)Google Scholar
  8. Hájek, A. (2003). What conditional probability could not be. Synthese, 137(3), 273–323. doi: 10.1023/B:SYNT.0000004904.91112.16.CrossRefGoogle Scholar
  9. Howson, C., & Urbach, P. (1993). Scientific reasoning: The Bayesian approach (2nd ed.). La Salle: Open Court.Google Scholar
  10. Jeffrey, R. (1992). Mises Redux. In Probability and the art of judgment. Cambridge: Cambridge University Press.Google Scholar
  11. Johnson, R. A. (1994). Miller & Freund’s probability & statistics for engineers (5th ed.). New Jersey: Prentice Hall.Google Scholar
  12. Kripke, S. A. (1980). Wittgenstein on rules and private language. Cambridge, MA: Harvard University Press.Google Scholar
  13. Lewis, D. (1973). Counterfactuals. Oxford/Cambridge, MA: Blackwell/Harvard University Press.Google Scholar
  14. Lewis, D. (1980). A subjectivist's guide to objective chance. In Richard C. Jeffrey (Ed.), Studies in inductive logic and probability (Vol. 2, pp. 263–293). Berkeley and Los Angeles: University of California Press. (Reprinted in Lewis (1986)).Google Scholar
  15. Lewis, D. (1986). Philosophical papers (Vol. 2). Oxford: Oxford University Press.Google Scholar
  16. Lewis, D. (1994). Humean supervenience debugged. Mind, 103, 473–490. doi: 10.1093/mind/103.412.473.CrossRefGoogle Scholar
  17. Lindstrom, T. (1989). An invitation to nonstandard analysis. In N. J. Cutland (Ed.), Nonstandard analysis and its applications (pp. 1–105). Cambridge: Cambridge University Press.Google Scholar
  18. McGee, V. (1994). Learning the impossible. In Ellery Eells & Brian Skyrms (Eds.), Probability and conditionals. Cambridge: Cambridge University Press.Google Scholar
  19. Reichenbach, H. (1949). The theory of probability. Berkeley: University of California Press.Google Scholar
  20. Seidenfeld, T., Schervish, M. J., & Kadane, J. B. (1998). Non-conglomerability for finite-valued, finitely additive probability. Sankhya Series A, 60(3), 476–491.Google Scholar
  21. Skyrms, B. (1980). Causal necessity. New Haven: Yale University Press.Google Scholar
  22. Stalnaker, R. (1968). A Theory of Conditionals. Studies in logical theory, American philosophical quarterly monograph series (Vol. 2). Oxford: Blackwell.Google Scholar
  23. van Fraassen, B. (1980). The scientific image. Oxford: Clarendon Press.CrossRefGoogle Scholar
  24. von Mises, R. (1957). Probability, statistics and truth, revised English edition. New York: Macmillan.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Philosophy Program, Research School of Social SciencesAustralian National UniversityCanberraAustralia

Personalised recommendations