Lonergan uses three devices to help him describe the new relationship between philosophy and theology: the moving viewpoint, sublation, and the two vectors of human development.
The first device is predominant in Insight. It is exemplified within elementary arithmetic when new rules have to be found to handle negative numbers, fractions and surds: these rules are able to handle not only the old numbers but also the new. Again, it is exemplified in the shift from elementary arithmetic to algebra, and from Newton to Einstein: Einstein’s theories account for Newton’s laws as well as what those laws could not account for, so that the latter become a subset of the former (see Lonergan, CWL 17:410). The moving viewpoint is therefore not a logical device, for logic can only bring out the virtualities inherent in the initial set of premises, but the moving viewpoint is able to take into account emergent novelty, and it does so only by modifying the initial premises. Thus the shift from philosophy or the ‘purely humanist viewpoint’ to the viewpoint of faith and theology is a movement in the viewpoint: faith and theology go beyond philosophy without disturbing what is proper to philosophy.
The second device emerges in the post-Insight years: theology is an Aufhebung or sublation of philosophy. But Lonergan is quick to specify that Aufhebung here is to be taken in Rahner’s sense rather than Hegel’s. (This would have to be clarified with all the observations Lonergan makes about the difference between his own position and that of Hegel: Lonergan's position is intellectualist rather than conceptualist, non-necessitarian, etc.)
The third device emerges in the post-Method years. The first two devices indicate clearly that theology goes beyond while respecting the competence of philosophy (and here Lonergan is far clearer than Caputo). The third device, however, without denying such sublation, exemplifies the intricate and intimate relationship between philosophy and theology better than the first two – for in the concrete we are often at the vectorial intersection between faith and reason, between what is received and what is personally appropriated.