 Why do most mathematicians and philosophers not follow Dedekind more closely in this respect? Here the following difficulties play a role (cf. Boolos 1990, Müller-Stach 2017, among others): How exactly should his notions of “abstraction” and “creation” be understood, if they can be made sense of at all? And why did Dedekind insist on their use in the first place, since we seem to be able to do without them as axiomatic set theory shows? A partial answer to the latter question is: For Dedekind, the real numbers should not be identified with the corresponding cuts because those cuts have “wrong properties”; namely, as sets they contain elements, something that seems “foreign” to the real numbers themselves. Similarly, the natural numbers should not be ascribed set-theoretic or other “foreign” properties; they too should be conceived of “purely arithmetically” (see again Dedekind 1876b, 1888b). Can anything further be said in this connection?