fantastic undertaking. But within certain limits even now traits of those socializations may be cited which exist between a limited number of persons, and which are characterized by this limitation. As transitions out of the most complete numerical indefiniteness to complete numerical definiteness, I mention certain cases in which the latter in principle is already of some sociological significance, but still without a determination of the same in particulars; namely:
1. The number works as a principle of division of the group; that is, there are portions of the same which are formed by enumeration, and are treated as relative unities. The special significance of separate numbers in this connection will be discussed later, and at this point I merely emphasize the principle. That a total group which feels itself in any way as one divides itself at all, and that it divides itself not merely from top to bottom, according to the ratio of the rulers and the ruled, but according to co-ordinated members, is one of the most tremendous advances of humanity; it is, to be sure, not yet the proper organic life instead of the mechanical coexistence of society, but, so to speak, the anatomical structure which constitutes the basis of the life-process. The division may proceed merely from the hereditary principle, or from associations formed by voluntary pledges, or from similarity of occupations, or from classification by local districts. To these principles there attaches itself the numerical variant which divides the mass of the existing men or families by a definite number, and so produces similar subdivision on the purely quantitative basis. The whole has toward each of these approximately the same relation which the subdivisions themselves bear toward their individuals. This principle is now so schematic, to be sure, that for its realization a more concrete one must be associated with it. The numerically equal divisions were composed of units in some way near to each other: relatives, friends, neighbors, or units which otherwise reinforced each other through likeness or unlikeness. The decisive factor is, however, that numerical equality constitutes the form-principle of the division—although it never decides alone, but merely plays a role varying from the
