 The core of the procedure just described is the following: Something is true for the natural numbers exactly when the corresponding statement holds for all simple infinities (i.e., is a semantic consequence of the Dedekind-Peano axioms). What, then, are the natural numbers? They are those mathematical objects whose properties are determined by all arithmetic truths; we “abstract away” from everything else in terms of a logical procedure. Moreover, this procedure can be spelled out, precisely and consistently, in terms of “structural abstraction principles”  (cf. Linnebo &amp; Pettigrew 2014, Reck 2018 for details). Along such lines, all that matters about mathematical objects, indeed all that is built into their identity and nature, is what the corresponding mathematical truths determine. Consequently, it is by specifying those truths that we “create”, or better  fully characterize, them. The resulting position seems clearly not psychologistic, and it might be called “logical  structuralism” (Reck 2003, Yap 2009a).