 Can the significance of Dedekind’s methodology be brought out even further? Or can it be articulated more in different terms? One way to do the latter, already touched on above, is by highlighting the methodological values embodied in it: systematicity, generality, purity, etc. (Avigad 2006, also Haffner 2014, 2015, 2017). Another is by focusing on the kind of reasoning involved: “conceptual” or “structural” reasoning (Stein 1988, Ferreirós 1999), or in terminology often associated with Hilbert,  “axiomatic” reasoning (Sieg &amp; Schlimm 2005, 2017, Schlimm 2000, 2011, 2017). We might even want to talk about a novel “reasoning  style” in this connection, where “style”  is to be understood in an epistemological sense, not in an aesthetic, psychological, or sociological sense. Such a style brings with it, not just new theorems and proofs, but a distinctive kind of “understanding” of mathematical facts (Reck 2009, cf. also Tappenden 2005b, Müller-Stach 2017).