 The logical connection between scientific hypotheses and the evidence often requires the mediation of background information and auxiliary hypotheses. Let ‘\(b\)’ represent whatever background and auxiliary hypotheses are required to connect each hypothesis \(h_i\) among the competing hypotheses \(\{h_1, h_2 , \ldots \}\) to the evidence. Although the claims expressed by the auxiliary hypotheses within \(b\) may themselves be subject to empirical evaluation, they should be the kinds of claims that are not at issue in the evaluation of the alternative hypothesis in the collection \(\{h_1, h_2 , \ldots \}\). Rather, each of the alternative hypotheses under consideration draws on the same background and auxiliaries to logically connect to the evidential events. (If competing hypotheses \(h_i\) and \(h_j\) draw on distinct auxiliary hypotheses \(a_i\) and \(a_j\), respectively, in making logical contact with evidential claims, then the following treatment should be applied to the respective conjunctive hypotheses, \((h_{i}\cdot a_{i})\) and \((h_{j}\cdot a_{j})\), since these alternative conjunctive hypotheses will constitute the empirically distinct alternatives at issue.) 