 The solution in PM is to guarantee that for each finite set of n individuals of type 0, there will be some object not in that set, which can be included in the set defining the successor. That such a new individual can be found is guaranteed by the Axiom of Infinity, which in effect asserts the existence of distinct individuals of any finite number. It is interesting to note the the “Axiom” of Infinity is not a primitive proposition of the logic of PM. Instead it is an additional hypothesis, to be used as an antecedent to mathematical assertions upon which it depends. The issue of whether the system of PM succeeds as logicism is thus not settled by noting that an Axiom of Infinity has to be assumed, but by determining whether that “Axiom” is derivable from logical principles alone.