 There is a second path we can take, resulting in a second form of abstractionist structuralism.  It too has played a role in the recent structuralism debates; but, like the first, it can also be traced back further in time. Let us start again from a relevant higher-order concept, or from the axiom system that defines it, together with an arbitrarily chosen relational system falling under it (a set-theoretic system, say, possibly with urelements). The new suggestion is to proceed as follows: We “abstract away from the particular nature of its elements” so as to arrive at a novel, distinguished relational system that deserves to be called “the natural numbers” (cf. Dedekind 1888, especially as interpreted in Reck 2003). The intention is that the objects introduced by such abstraction only have structural properties, or better, only have these essentially. Also, together these objects form a system isomorphic to the one from which we started (unlike the equivalence class we just considered). Finally, it is the latter we now consider the relevant abstract structure. 