The group of things, _a_, _b_, _c_, _d_--_x_, _y_, _z_, was an extensive manifoldness, since it was formed by juxtaposing in space the separate units of which it is composed. Yet it is an unitary thing, for it is a different thing from the group, _b_, _c_, _a_--_x_, _y_, _z_. It is also a multiplicity, for it can be transformed into every one of the 26! permutations, and broken up into the selections of some of the separate things of which it is composed, and of the permutations of the things taken in each of these selections. In a way these arrangements exist in the group _a_, _b_, _c_--_x_, _y_, _z_, and yet the group itself possesses no other actual extended existence than the group of things that it is. It is an _intensive multiplicity or manifoldness_ in that the potentiality of all the arrangements exists in it but not in the spatially extended condition. It is a multiplicity only when we associate with it the mental operations by which we conceive of its dissociation and rearrangement. By reason of these mental operations the intensive multiplicity of the group becomes the extensive multiplicity of its arrangements. This appears to be the only really philosophical way in which we can attempt to picture to ourselves the processes of individual and racial evolution. The “primitive” life-substance, or the undifferentiated ovum, each of them with its environment, was an intensive manifoldness, a multiplicity of distinct things or qualities which co-existed, and which were not separate each from other in that they occupied different compartments of space, but which interpenetrated each other. This notion of distinct things co-existing in time, yet occupying the same space, is not at all a difficult one. Our consciousness is such a multiplicity of states or qualities all in one. The idea of a group of figures has a very real existence for the sculptor, and he may visualise it with almost all the appearance of reality that the actual, material piece of statuary possesses. In his mind it is a real manifold existence, which nevertheless does not occupy the three-dimensional space which the marble fills. The musical notes C, F, A, C, heard in arpeggio, are things which possess real existence, but which are extended in time, and when we think of these separate sounds we lay them alongside each other in our mind in an empty, homogeneous medium which seems to be all that we think of as space. Yet the same notes heard simultaneously as a chord are not extended. They interpenetrate each other, but yet they are distinct things, since on hearing the chord we can recognise the notes composing it. As an arpeggio the notes are an extensive manifoldness, but as a chord they are an intensive manifoldness.