 Whitehead and Russell do carry out the step of the logicist program of deriving Peano’s Postulates based on the prior definitions of the notions of Natural number, 0, and successor, as Russell describes the project later, in (1919). This is in fact what is done in ∗120 “Inductive Cardinals” of PM, but is not described as such, either there or in introductory material. The results are not proved separately, but as they appear in a development of various results about natural numbers. Indeed some, such as ∗120·31, can only be seen to be versions of a Peano axiom with a bit of work.