Page:Science and the Modern World.djvu/248

 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