 The second characteristic part of Dedekind’s methodology consists of persistently (and from early on, cf. Dedekind 1854) attempting to identify and clarify fundamental concepts, including the higher-level concepts just mentioned (continuity, infinity, generalized concepts  of integer and of prime number, also the new concepts of ideal, module, lattice, etc.). In this context, it is crucial for him to find “the right  definitions”; and this involves not just basic adequacy, but also desiderata such as: fruitfulness, generality, simplicity, and  “purity”, i.e., the elimination of “foreign”  aspects. (Geometric notions are foreign to the natural and real numbers, the definition of prime number must be at just the right level of generality, etc.). Moreover, once Dedekind has identified them, he studies the most important ones also in themselves, i.e., in terms of a separate part of the theory. This gives his approach a distinctive  “conceptual” character (cf. Stein 1988, Avigad 2006), and it points forward towards an axiomatic approach (Sieg &amp; Schlimm 2014, Schlimm 2017, also Haffner 2014, 2015, 2017)