 First, we must make precise what we mean by actual and hypothetical calibration; then we can say which functions will count as measuring distance from these putative goals. We treat actual calibration first. Since we are talking of relative frequencies, we will need to assign to each proposition in \(\mathcal{F}\) its reference class: that is, the set of propositions that are relevantly similar to it. Thus, we require an equivalence relation \(\sim\) on \(\mathcal{F}\), where \(A \sim B\) iff \(A\) and \(B\) are relevantly similar. For instance, if our algebra of propositions contains Heads on first toss of coin, Heads on second toss of coin, and Six on first roll of die, we might plausibly say that the first two are relevantly similar, but neither first nor second is relevantly similar to the third. Proponents of calibration arguments do not claim to give an account of how the equivalence relation is determined. Nor do they claim that there is a single, objectively correct equivalence relation on a given algebra of propositions: this is the notorious problem of the reference class that haunts frequentist interpretations of objective probability. Rather they treat the equivalence relation as a component of the agent’s epistemic state, along with her credence function. Indeed, for van Fraassen, it is determined entirely by the credence function together with the form of the propositions in \(\mathcal{F}\) (van Fraassen 1983: 299). However, they do impose some rational constraints on \(\sim\) in order to establish their conclusion. We will not discuss these conditions in any detail. Rather we denote them \(C(\sim)\), and keep in mind that this is a placeholder for a full account of conditions on \(\sim\). Detailed accounts of these conditions have been given by van Fraassen (1983) and Shimony (1988). We say that a credence function \(c\), together with an equivalence relation \(\sim\), is perfectly calibrated or not relative to a way the world might be. We are now ready to give our first definitions; but we preface these with an example.