Thus, for illustration, we designate as a cube on the one hand any natural object in cubical form; on the other hand the simple form alone, which made the material contents into a “cube” in the former sense, constitutes of itself, independently and abstractly considered, an object for geometry. The significance of geometry appears in the fact that the formal relations which it determines hold good for all possible objects formed in space. In like manner it is the purpose of sociology to determine the forms and modes of the relations between men which, although constituted of entirely different contents, material, and interests, nevertheless take shape in formally similar social structures. If we could exhibit the totality of possible forms of social relationship in their gradations and variations we should have in such exhibit complete knowledge of “society” as such. We gain knowledge of the forms of socialization by bringing together inductively the manifestations of these forms which have had actual historical existence. In other words we have to collect and exhibit that element of form which these historical manifestations have in common, abstracted from the variety of material—economical, ethical, ecclesiastical, social, political, etc.—with respect to which they differ.
Now geometry has the advantage of finding within its field very simple figures to which the most complicated forms may be reduced. Truths respecting these simple figures are therefore very widely applicable. From relatively few fundamental truths all possible arrangements of form may be interpreted. In the case of social forms, on the contrary, an approximate reduction to simple elements has not been made. Social phenomena are too immeasurably complicated, and the methods of analysis are too incomplete. The consequence is that if sociological forms and names are used with precision they apply only within a relatively contracted circle of manifestations. Long and patient labor will be necessary before we can understand the concrete historical forms of socialization as the actual compounds of a few simple fundamental forms of human association.
