 This brings us to one of the key objections to Laplace’s account. The notion of “equally possible” cases faces the charge of either being a category mistake (for ‘possibility’ does not come in degrees), or circular (for what is meant is really ‘equally probable’). The notion is finessed by the so-called ‘principle of indifference’, a coinage due to Keynes (although he was no friend of the principle): “if there is no known reason for predicating of our subject one rather than another of several alternatives, then relatively to such knowledge the assertions of each of these alternatives have an equal probability” (1921, 52–53). (The ‘principle of equal probability’ would be a better name.) Thus, it might be claimed, there is no circularity in the classical interpretation after all. However, this move may only postpone the problem, for there is still a threat of circularity, albeit at a lower level. We have two cases here: outcomes for which we have no evidence (“reason”) at all, and outcomes for which we have symmetrically balanced evidence. There is no circularity in the first case unless the notion of ‘evidence’ is itself probabilistic; but artificial examples aside, it is doubtful that the case ever arises. For example, we have a considerable fund of evidence on coin tossing from the results of our own experiments, the testimony of others, our knowledge of some of the relevant physics, and so on. In the second case, the threat of circularity is more apparent, for it seems that some sort of weighing of the evidence in favor of each outcome is required, and this seems to require a reference to probability. Indeed, the most obvious characterization of symmetrically balanced evidence is in terms of equality of conditional probabilities: given evidence \(E\) and possible outcomes \(O_1, O_2 , \ldots ,O_n\), the evidence is symmetrically balanced iff \(P(O_1\mid E) = P(O_2\mid E) = \ldots = P(O_n\mid E)\). Then it seems that probabilities reside at the base of the interpretation after all. Still, it would be an achievement if all probabilities could be reduced to cases of equal probability. See Zabell (2016) for further discussion of the classical interpretation and the principle of indifference.