 Dedekind’s answer to this last question is: Basic for logic are the notions of object (“Ding”), set (or system, “System”), and function (mapping, “Abbildung”).  These notions are fundamental for human thought, as he emphasizes especially for the notion of function. They are “logical”  in the sense of being applicable in all domains, indispensable for exact reasoning, and not reducible further. (This interpretation of Dedekind, and with it whether he should be understood as a logicist, is not uncontroversial. For the corresponding controversy, cf. Klev 2017, Reck 2019, and Ferreirós forthcoming, on the one hand, and Benis-Sinaceur 2008, 2015, 2017, on the other hand. We will come back to this issue in Section 3.) While not analyzable in terms of anything even more basic, the fundamental logical notions are nevertheless capable of being elucidated, thus of being understood better. Part of their elucidation consists in observing what can be done with them, including how arithmetic can be reconstructed in terms of them (also analysis etc.). For Dedekind that reconstruction starts with the consideration of infinite sets, like in the case of the real numbers, but now in a generalized, more explicit, and more systematic manner.