descriptive physical science, where the correspondence used for scientific purposes is of this type. Such are the instances which occur in crystallography, where the symmetry of a physical object is studied by considering what group of rotations, or of internal reflections in one or in another plane, or of both combined, will bring any ideal crystal form to congruence with itself. All such operations as the rotations and reflections that leave the crystal form unaltered are, of course, operations which bring to light an essentially self-representative character in the crystal form, since by any one such operation the crystal form is made precisely to correspond with itself, while the operation can at once be followed by a new operation of the same type, which, again, leaves the form unaltered.
While, however, self-representative systems of ideal or of physical objects belonging to the later types play a great part in exact physical and in mathematical science, their study does not throw light upon the primal way in which the One and the Many, in the processes directly open to thought’s own internal observation, are genetically combined. For physical systems which permit these transformations of a whole into an exact image of itself are given as external “conjunctions,” such as crystal forms. We do not see them made. We find them. The ideal cases of the same type in pure mathematics have also a similar defect from the point of view of Bradley’s criticism. A system that is to be made self-representative through a “group of substitutions,” shows, therefore, the same diversities after we have operated upon it as before; and, furthermore, that congruence with itself which the system shows at the end of a self-representative operation of any type wherein all elements take the place of all, is not similar to what happens where, in our dealings with the universe, Thought and Reality, the Idea and its Other, Self and Not-Self, are brought into self-evident relations, and are at once contrasted with one another and unified in a single whole. Hence, we shall indeed continue to insist, in what follows, upon those self-representations wherein proper part
