 This survey perforce confines itself, in the main, to (neo-)logicist accounts of the natural numbers. But it is worth raising one more question about the extension of a neo-Fregean account in an attempt to cope with the real numbers. We shall call it the inclusion question. How is one to appreciate that the natural numbers qua reals are (in the non-punning sense of numerical identity) the natural numbers vouchsafed by logicism about the  naturals?[40]  This question is not answered by the neo-Fregean abstractionist account of the reals in Shapiro (2000). In that account, the various new abstracta are abstracted from quite varying equivalence relations, and no attempt is made to leave it open as a possibility that the natural number n is the integer n, is the rational number n, and is the real number n. (Although on p. 339 Shapiro writes that he proposes “to avoid the issue [of identity under inclusion] here”, his proposed treatment nevertheless answers the inclusion question negatively.) 