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The reference class problem is your problem too

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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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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Keywords

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