 What happens in Was sind und was sollen die Zahlen?, in the context of Dedekind’s logicist reconstruction of the natural numbers, is that the adoption of set-theoretic techniques is raised to a new level of clarity and generality. Dedekind not only presents set-theoretic definitions of various mathematical notions, he also adds a systematic reflection on the means used thereby and he expands that use in certain respects. For those reasons, the essay constitutes an important step in the emergence of modern set theory. In addition, we already saw that Dedekind presents the notion of set, together with those of object and function, as basic. Here an object is anything for which it is determinate how to reason about it, including having appropriate criteria of identity (Tait 1996). Sets are objects about which we reason by considering their elements, and this is all that matters about them. In other words, sets are to be identified extensionally, as Dedekind is one of the first to emphasize. (Even as important a contributor to set theory as Bertrand Russell struggles with this point well into the twentieth century.) Dedekind is also among the first to consider, not just sets of numbers, but sets of other kinds of objects as well.