Synthese 156 (3):563--585 (2007)

Authors
Alan Hajek
Australian National University
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.
Keywords Probability  Conditional probability  Reference class problem  Frequentist  Classical  Logical  Propensity  Subjectivist interpretations of probability  Kolmogorov  Popper
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DOI 10.1007/s11229-006-9138-5
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References found in this work BETA

The Logic of Scientific Discovery.Karl Raimund Popper - 1934 - London, England: Routledge.
Logical Foundations of Probability.Rudolf Carnap - 1950 - Chicago, IL, USA: Chicago University of Chicago Press.
Laws and Symmetry.Bas C. Van Fraassen - 1989 - Oxford, England: Oxford University Press.
A Treatise on Probability.John Maynard Keynes - 1921 - London, England: Dover Publications.
The Logic of Scientific Discovery.Karl Popper - 1959 - Studia Logica 9:262-265.

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Citations of this work BETA

Competence to Know.Lisa Miracchi - 2015 - Philosophical Studies 172 (1):29-56.
Deterministic Chance.Luke Glynn - 2010 - British Journal for the Philosophy of Science 61 (1):51–80.

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