 We have considered a number of different characterizations of the legitimate ways of measuring (in)accuracy and epistemic (dis)utility. Each has assumed that the measures of these quantities are numerically representable; that is, each assumes it makes sense to use real numbers to measure these quantities. Conor Mayo-Wilson and Greg Wheeler call this assumption into question (Mayo-Wilson &amp; Wheeler, ms.). They argue that, in order to represent a quantity numerically, you need to prove a representation theorem for it in measurement theory. And, if you wish to use that quantity as a measure of utility, or as a component of a measure of utility, you need to prove a representation theorem not only for the quantity itself, but for its use in expected utility calculations. They note that this was the purpose of the representation theorems of von Neumann &amp; Morgenstern as well as Savage and Jeffrey (see entry on  normative theories of rational choice: expected utility).  And they argue that the methods that these authors use are not available to the proponent of epistemic utility arguments. 