  On this picture the general structure of the case for new axioms is this: First, for each interpretability degree one isolates the minimal points in the evidentness order and one organizes the entire degree under the degree of one statement being more evident than another. As one climbs the interpretability degrees the minimal points generally become less evident and so one seeks additional support. Second, one then examines the interconnections among the statements in the interpretability degree, in particular, among the statements which are low in the evidentness order. The hope is that a series of deep mathematical theorems will reveal structural connections that provides more and more evidential support for the statements. Should this be the case then the loss in evidence attached to the minimal points as one climbs the interpretability hierarchy would be compensated for by the gain in structural connections that are revealed as one ascends to richer domains of mathematics. 