 Nagel’s two-term relation account has been modified by weaker conditions of analogy and a role for conventions, requiring it to be satisfied not necessarily by the two original theories, \(T_1\) and \(T_2\), which are respectively new and old and more and less general, but by the modified theories \(T'_1\) and \(T'_2\). Explanatory reduction is strictly a four-term relation in which \(T'_1\) is “strongly analogous” to \(T_1\) and corrects, with the insight that the more fundamental theory can offer, the older theory, \(T_2\), changing it to \(T'_2\). Nagel’s account also requires that bridge laws be synthetic identities, in the sense that they be factual, empirically discoverable and testable; in weaker accounts, admissible bridge laws may include elements of convention (Schaffner 1967; Sarkar 1998). The difficulty lay especially with the task of specifying or giving a non-contextual, transitive account of the relations between \(T\) and \(T'\) (Wimsatt 1976).