Hypothetical Frequencies as Approximations

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 these limits, drawing on Norton’s (Philos Sci 79(2):207–232, 2012) distinction between approximations (inexact descriptions target) and idealizations (separate models bear analogies to target). Then, adapt Hájek’s arguments this new context. These provide excellent reasons not use hypothetical as idealizations, but no reason them approximations.