 Apart from Frege, it is illuminating to compare Dedekind’s approach more with later set-theoretic ones. We noted in the last section that many of his innovations have been built into axiomatic set theory. Yet here too, several differences emerge if one looks more closely. To begin with, Dedekind does not start with an axiom of infinity as a fundamental principle; instead, he tries to prove the existence of infinite sets. This can be seen as another application of the methodological rule to prove everything “capable of proof”, as well as a crucial aspect of his logicism.  However, few set theorists today will want to go back to this aspect of Dedekind’s approach. (Dedekind’s argument in this connection is similar to an earlier one in Bolzano’s posthumously published work; cf. Ferreirós 1999, ch. 7, Klev 2019.) 