 The most important of these remaining postulates is the one saying that every natural number has a unique (immediate) successor. In order to prove this in full generality, Frege had of course to take into account the possibility that an arbitrarily given natural number might far exceed the size of any collection of physical objects in the universe. To what concept, then, could he turn (for a given natural number n), whose cardinality would be the successor of n? 