302 THE PHILOSOPHY OF BIOLOGY 



number of elements, a very great number of different 

 things — things which consist of elements spatially 

 extended — can be obtained. 



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 |f* 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 multi- 

 plicity only when we associate with it the mental opera- 

 tions 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 



