 Objection 4: The constraints on \(\sim\) are ill-motivated. This objection will vary with the constraints \(C(\sim)\) that are imposed on \(\sim\). One uncontroversial constraint is this: If \(A \sim B\), then \(c(A) = c(B)\). The further constraints imposed by Shimony (1988) and van Fraassen (1983) are more controversial (Joyce 1998: 594–6). Moreover, they limit the application of the result, since they involve assumptions about the form of the propositions in \(\mathcal{F}\). Thus, the calibration arguments do not show in general, of any finite algebra \(\mathcal{F}\), that a credence function on \(\mathcal{F}\) ought to be a probability function, since not every such algebra will contain propositions with the form required by the constraints \(C(\sim)\).