 Recently another suggestion for how to get clearer about the nature of “Dedekind abstraction”  and, at the same time, avoid crude forms of psychologism has become prominent. Namely, instead of taking such abstraction to amount to a psychological process, it should be understood as a logical procedure (cf. Tait 1996, earlier Cassirer 1910).  Consider again the case of the natural numbers, where Dedekind is most explicit about this issue. What we are provided with by him is this: First, the language and logic to be used are specified, thus the kinds of assertions and arguments that can be made concerning the natural numbers; second, a particular simple infinity is constructed; third, this simple infinity is used to determine the truth values of all arithmetic sentences (by equating them with the truth values of corresponding sentences for the given simple infinity); and fourth, this determination is justified by showing that all simple infinities are isomorphic (so that, if a sentence holds for one of them, it holds for all).