(ii) the components of any complex eternal object in the hierarchy are also members of the hierarchy, and (iii) any set of eternal objects belonging to the hierarchy, whether all of the same grade or whether differing among themselves as to grade, are jointly among the components or derivative components of at least one eternal object which also belongs to the hierarchy. It is to be noticed that the components of an eternal object are necessarily of a lower grade of complexity than itself. Accordingly any member of such a hierarchy, which is of the first grade of complexity, can have as components only members of the group _g_; and any member of the second grade can have as components only members of the first grade, and members of _g_; and so on for the higher grades. The third condition to be satisfied by an abstractive hierarchy will be called the condition of connexity. Thus an abstractive hierarchy springs from its base; it includes every successive grade from its base either indefinitely onwards, or to its maximum grade; and it is ‘connected’ by the reappearance (in a higher grade) of any set of its members belonging to lower grades, in the function of a set of components or derivative components of at least one member of the hierarchy. An abstractive hierarchy is called ‘finite’ if it stops at a finite grade of complexity. It is called ‘infinite’ if it includes members belonging respectively to all degrees of complexity. It is to be noted that the base of an abstractive hierarchy may contain any number of members, finite or infinite. Further, the infinity of the number of the members of the base has nothing to do with the question as to whether the hierarchy be finite or infinite.