 It might seem that the criterion of admissibility goes without saying. The word ‘interpretation’ is often used in such a way that ‘admissible interpretation’ is a pleonasm. Yet it turns out that the criterion is non-trivial, and indeed if taken seriously would rule out several of the leading interpretations of probability! As we will see, some of them fail to satisfy countable additivity; for others (certain propensity interpretations) the status of at least some of the axioms is unclear. Nevertheless, we regard them as genuine candidates. It should be remembered, moreover, that Kolmogorov’s is just one of many possible axiomatizations, and there is not universal agreement on which is ‘best’ (whatever that might mean). Indeed, Salmon’s preferred axiomatization differs from  Kolmogorov’s.[2]  Thus, there is no such thing as admissibility tout court, but rather admissibility with respect to this or that axiomatization. It would be unfortunate if, perhaps out of an overdeveloped regard for history, one felt obliged to reject any interpretation that did not obey the letter of Kolmogorov’s laws and that was thus ‘inadmissible’. In any case, if we found an inadmissible interpretation that did a wonderful job of meeting the criteria of ascertainability and applicability, then we should surely embrace it.