In the lowest grade of eternal objects are to be placed those objects whose individual essences are simple. This is the grade of zero complexity. Next consider any set of such objects, finite or infinite as to the number of its members. For example, consider the set of three eternal objects _A, B, C_, of which none is complex. Let us write _R(A, B, C)_ for some definite possible relatedness of _A, B, C_. To take a simple example, _A, B, C_ may be three definite colours with the spatio-temporal relatedness to each other of three faces of a regular tetrahedron, anywhere at any time. Then _R(A, B, C)_ is another eternal object of the lowest complex grade. Analogously there are eternal objects of successively higher grades. In respect to any complex eternal object, _S(D1, D2, ... Dn)_, the eternal objects _D1, ... Dn_, whose individual essences are constitutive of the individual essence of _S(D1, ... Dn)_, are called the components of _S(D1, ... Dn)_. It is obvious that the grade of complexity to be ascribed to _S(D1, ... Dn)_ is to be taken as one above the highest grade of complexity to be found among its components. There is thus an analysis of the realm of possibility into simple eternal objects, and into various grades of complex eternal objects. A complex eternal object is an abstract situation. There is a double sense of ‘abstraction,’ in regard to the abstraction of _definite_ eternal objects, _i.e._, non-mathematical abstraction. There is abstraction from actuality, and abstraction from possibility. For example, _A_ and _R(A, B, C)_ are both abstractions from the realm of possibility. Note that _A_ must mean _A_ in all its possible relationships, and among them _R(A, B, C)_. Also _R(A, B, C)_ means _R(A, B, C)_ in all its relationships. But this meaning of _R(A, B, C)_ excludes other relationships into which _A_ can enter. Hence _A_ as in _R(A, B, C)_ is more abstract than _A simpliciter_. Thus as we pass from the grade of simple eternal objects to higher and higher grades of complexity, we are indulging in higher grades of abstraction from the realm of possibility. We can now conceive the successive stages of a definite progress towards some assigned mode of abstraction from the realm of possibility, involving a progress (in thought) through successive grades of increasing complexity. I will call any such route of progress ‘an abstractive hierarchy.’ Any abstractive hierarchy, finite or infinite, is based upon some definite group of simple eternal objects. This group will be called the ‘base’ of the hierarchy. Thus the base of an abstractive hierarchy is a set of objects of zero complexity. The formal definition of an abstractive hierarchy is as follows: An ‘abstractive hierarchy based upon _g_,’ where _g_ is a group of simple eternal objects, is a set of eternal objects which satisfy the following conditions, (i) the members of _g_ belong to it, and are the only simple eternal objects in the hierarchy,