 Theorem 4 (Joyce’s Main Theorem) Suppose \(\mathcal{F}\) is an algebra and \(\mathfrak{I} : \mathcal{C_F} \times \mathcal{W_F} \rightarrow [0, \infty]\) is a Joycean inaccuracy measure for the credence functions on \(\mathcal{F}\). Now suppose that \(c^*\) is a credence function in \(\mathcal{C_F}\) that violates Probabilism. Then there is a credence function \(c'\) in \(\mathcal{C_F}\) such that \(\mathfrak{I}(c', w) &lt; \mathfrak{I}(c^*, w)\) for all \(w\) in \(\mathcal{W_F}\). (In this situation, we say that \(c'\) accuracy dominates \(c^*\) relative to \(\mathfrak{I}\).)