 The second component of Joyce’s account of epistemic disutility for credences is a set of mathematically-precise conditions that a measure of the gradational inaccuracy of a credence function at a given possible world must satisfy. A putative inaccuracy measure for credence functions over an algebra \(\mathcal{F}\) is a mathematical function \(\mathfrak{I}\) that takes a credence function \(c\) in \(\mathcal{C_F}\) and a possible world \(w\) in \(\mathcal{W_F}\) and returns a number \(\mathfrak{I}(c, w)\) in \([0, \infty]\) that measures the inaccuracy of \(c\) at \(w\). (The set \([0, \infty]\) contains all non-negative real numbers together with \(\infty\).) Here is an example, called the Brier score:   \[\mathfrak{B}(c, w) := \sum_{X \in \mathcal{F}} |v_w(X) - c(w)|^2\]   Thus, the Brier score measures the inaccuracy of a credence function at a world as follows: it takes each proposition to which the credence function assigns credences; it takes the difference between the credence that the credence function assigns to that proposition and the ideal or vindicated credence in that proposition at that world; it squares this difference; and it sums up the results. We shall not give all of Joyce’s conditions here, but just note that the Brier score just defined satisfies them all. Let us say that any putative inaccuracy measure \(\mathfrak{I}\) that satisfies these conditions is a Joycean inaccuracy measure. And let Joycean Inaccuracy be the claim that all legitimate inaccuracy measures are Joycean inaccuracy measures.