 Let us see how the frequentist interpretations fare according to our criteria of adequacy. Finite relative frequencies of course satisfy finite additivity. In a finite reference class, only finitely many events can occur, so only finitely many events can have positive relative frequency. In that case, countable additivity is satisfied somewhat trivially: all but finitely many terms in the infinite sum will be 0. Limiting relative frequencies violate countable additivity (de Finetti 1972, §5.22). Indeed, the domain of definition of limiting relative frequency is not even a field, let alone a sigma field (de Finetti 1972, §5.8). So such relative frequencies do not provide an admissible interpretation of Kolmogorov’s axioms. Finite frequentism has no trouble meeting the ascertainability criterion, as finite relative frequencies are in principle easily determined. The same cannot be said of limiting relative frequencies. On the contrary, any finite sequence of trials (which, after all, is all we ever see) puts literally no constraint on the limit of an infinite sequence; still less does an actual finite sequence put any constraint on the limit of an infinite hypothetical sequence, however fast and loose we play with the notion of ‘in principle’ in the ascertainability criterion.