## Abstract

The reference class problem arises when we want to assign a probability to a proposition (or sentence, or event) *X*, which may be classified in various ways, yet its probability can change depending on how it is classified. The problem is usually regarded as one specifically for the frequentist interpretation of probability and is often considered fatal to it. I argue that versions of the classical, logical, propensity and subjectivist interpretations also fall prey to their own variants of the reference class problem. Other versions of these interpretations apparently evade the problem. But I contend that they are all “no-theory” theories of probability - accounts that leave quite obscure why probability should function as a guide to life, a suitable basis for rational inference and action. The reference class problem besets those theories that are genuinely informative and that plausibly constrain our inductive reasonings and decisions.

I distinguish a “metaphysical” and an “epistemological” reference class problem. I submit that we can dissolve the former problem by recognizing that probability is fundamentally a two-place notion: conditional probability is the proper primitive of probability theory. However, I concede that the epistemological problem remains.

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## References

Ayer A.J. (1963). Two notes on probability. In: Ayer A.J. (eds). The concept of a person and other essays. MacMillan, London, pp. 188–208

Bertrand, J. (1889).

*Calcul des Probabilités*(1st ed.). Gauthier-Villars.Carnap, R. (1950).

*Logical foundations of probability*. University of Chicago Press.Carnap R. (1963). Replies and systematic expositions. In: Schilpp P.A. (eds). The philosophy of Rudolf Carnap. Open Court, LaSalle, IL, pp. 966–998

Church A. (1940). On the concept of a random sequence. Bulletin of the American Mathematical Society 46, 130–135

de Finetti, B. (1937). Foresight: Its logical laws, its subjective sources, translated in Kyburg and Smokler (1964).

Fetzer, J. (1977). Reichenbach, reference classes, and single case ‘Probabilities’.

*Synthese, 34*, 185–217;*Errata, 37*, 113–114.Fetzer J. (1982). Probabilistic explanations. PSA 2, 194–207

Fine, T. (1973).

*Theories of probability*. Academic Press.Frieden, B. R. (1991).

*Probability, statistical optics, and data testing*. Springer-Verlag.Gaifman, H. (1988). A theory of higher order probabilities. In B. Skyrms, & W. L. Harper (Eds.),

*Causation, chance, and credence*. Kluwer.Giere, R. N. (1973). Objective single-case probabilities and the foundations of statistics. In P. Suppes et al. (Eds.),

*Logic, methodology and philosophy of science*IV (pp. 467–483). North Holland.Gillies D. (2000). Varieties of propensity. British Journal of Philosophy of Science 51, 807–835

Goldstein M. (1983). The prevision of a prevision. Journal of the American Statistical Association 77, 817–819

Hacking, I. (1965).

*Logic of statistical inference*. Cambridge University Press.Hájek, A. (1997). ‘Mises Redux’—Redux: Fifteen arguments against finite frequentism. In

*Erkenntnis*, Vol. 45 (pp. 209–227). Reprinted in*Probability, dynamics and causality*—Essays in Honor of R. C. Jeffrey, D. Costantini, & M. Galavotti (Eds.), Kluwer.Hájek, A. (2003a). Conditional probability is the very guide of life. In H. Kyburg Jr., & M. Thalos (Eds.),

*Probability is the very guide of life*:*The philosophical uses of chance*(pp. 183–203). Open Court. Abridged version in*Proceedings of the International Society for Bayesian Analysis*2002.Hájek A. (2003b). What conditional probability could not be. Synthese 137(3): 273–323

Hild, M. (in preparation a).

*An introduction to induction*.Hild, M. (in preparation b).

*Introduction to the concept of probability*: A reader.Jeffrey, R. (1992).

*Probability and the art of judgment*. Cambridge University Press.Jeffreys, H. (1939).

*Theory of probability*. Reprinted in Oxford Classics in the Physical Sciences series, Oxford University Press, 1998.Johnson W.E. (1932). Probability: The deductive and inductive problems. Mind 49, 409–423

Keynes, J. M. (1921).

*Treatise on probability*. London. Macmillan. Reprinted 1962, New York: Harper and Row.Laplace, P. S. (1814).

*Essai Philosophique sur les Probabilités*. Paris. Translated into English as*A philosophical essay on probabilities*, New York, 1952.Levi I. (1990). Chance. Philosophical Topics 18(2): 117–149

Lewis, D. (1980). A subjectivist’s guide to objective chance. In

*Philosophical papers Volume II*. Oxford University Press.Mellor D.H. (1971). The matter of chance. Cambridge University Press, Cambridge

Miller D.W. (1994). Critical rationalism: A restatement and defence. Open Court, La Salle, Illinois

Miller, D. W. (1996). Propensities and indeterminism. In A. O’Hear (Ed.),

*Karl Popper: Philosophy and problems*(pp. 121–147). Cambridge University Press.Peirce, C. S. (1867):

*Review of Venn*(1866), reprinted in*Writings of Charles S. Peirce*, Vol. 2, pp. 98–102.Popper K. (1959a). The propensity interpretation of probability. British Journal of Philosophy of Science 10, 25–42

Popper, K. (1959b).

*The logic of scientific discovery*. Basic Books.Reichenbach, H. (1949).

*The theory of probability*. University of California Press.Renyi, A. (1970).

*Foundations of probability*. Holden-Day, Inc.Roeper, P., & Leblanc, H. (1999).

*Probability theory and probability semantics*. Toronto Studies in Philosophy.Sober, E. (2000).

*Philosophy of biology*(2nd ed.). Westview Press.Spohn W. (1986). The representation of Popper measures. Topoi 5, 69–74

Strevens M. (1998). Inferring probabilities from symmetries. Noûs 32(2): 231–246

Strevens, M. (2003).

*Bigger than chaos*. Harvard University Press.van Fraassen B. (1984). Belief and the will. Journal of Philosophy 81, 235–256

van Fraassen B. (1989). Laws and symmetry. Clarendon Press, Oxford

van Fraassen B. (1995). Belief and the problem of Ulysses and the Sirens. Philosophical Studies 77, 7–37

Venn, J. (1876).

*The logic of chance*(2nd ed.). Macmillan and Co; originally published 1866.von Mises, R. (1957).

*Probability, statistics and truth*, revised English edition, New York.

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Hájek, A. The reference class problem is your problem too.
*Synthese* **156**, 563–585 (2007). https://doi.org/10.1007/s11229-006-9138-5

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DOI: https://doi.org/10.1007/s11229-006-9138-5

### Keywords

- Probability
- Conditional probability
- Reference class problem
- Frequentist
- Classical
- Logical
- Propensity
- Subjectivist interpretations of probability
- Kolmogorov
- Popper