Hypothetical Frequencies as Approximations

Steeger, Jer. "Hypothetical Frequencies as Approximations." Erkenntnis (2022). https://doi.org/10.1007/s10670-022-00584-0

Hájek (Erkenntnis 70(2):211–235, 2009) argues that probabilities cannot be the limits of relative frequencies in counterfactual infinite sequences. I argue for a different understanding of these limits, drawing on Norton’s (Philos Sci 79(2):207–232, 2012) distinction between approximations (inexact descriptions of a target) and idealizations (separate models that bear analogies to the target). Then, I adapt Hájek’s arguments to this new context. These arguments provide excellent reasons not to use hypothetical frequencies as idealizations, but no reason not to use them as approximations.

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