 The basic discussion of the logical calculus could cease here if we had no other end in view for this calculus than the formalization of logical inference. But we cannot be satisfied with this application of symbolic logic. Not only do we want to be able to develop individual theories from their principles in a purely formal way, but we also want to investigate the foundations of the mathematical theories themselves and examine how they are related to logic and how far they can be built up from purely logical operations and concept formations; and for this purpose the logical calculus is to serve us as a tool. (1917/18: 188)