NUMBER AS DETERMINING FORM OF GROUP 35
These explanations have thus had to do with social forma- tions which, to be sure, depended upon the number of the co-working elements, while at the same time our knowledge was insufficient so to formulate this dependence that we could draw from distinct numbers their sociological consequences. Meanwhile this latter is not absolutely excluded, if we turn our attention by preference to sufficiently simple structures. If we begin with the lower boundary of the numerical series, arithmetically defined magnitudes appear as unequivocal preconditions of characteristic sociological formations.
The numerically simplest formations which can at all be designated as social reciprocities appear to occur in the case of reactions between two elements. Yet there is a structure still simpler in external appearance, which belongs in sociological categories, namely, however paradoxical and essentially contra- dictory it seems, the isolated individual man. As a matter of fact, the processes which produce formations in the case of a duality of elements are often simpler than those necessary for the sociological characterization of the integer. In the case of these latter we have to do chiefly with two here pertinent
often remains no alternative but to think the situation as composed of two conditions ; the one more and the other less conspicuous. At all events we have to do in such a case as little with a composition as, for example, in the case of the so-called mixed feelings of friendship and love, or hate and contempt, or pleasure and pain. In these cases, at least in numberless instances, a quite unified condition of feeling exists, for which we merely have no immediate concept, and which we consequently, by means of the synthesis and reciprocal limitation of two other concepts, rather circumscribe than describe ; here, as in other instances, the proper unity of the exist- ing is not within our comprehension, but we must resolve it into a duality of elements, neither of which quite covers it, in order to think it as proceeding from the inter- weaving of the two. This is, however, merely a conceptual analysis, possible only after the fact, which does not trace the actual genetic process, the proper being of that unity. Where therefore the stereotyped concepts for social unities meeting and society, troop and army, clique and party, a few and a band, personal following and school, crowd and popular uprising, etc., etc. do not find an exact application, because the human material seems to be insufficient for the one, and more than enough for the other, there yet exists a sociological mold, precisely as unified and just as specifically corresponding to the numerical limitation as in those more definite cases. The fact merely is that the lack of a special concept for these innumerable shadings compels us to denote their qualities as a mixture of those forms which correspond to the numerically inferior and to the numerically higher structures.
