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resolution of the contradiction is very simple: The size of the circle demands the legal form naturally only in that relation in which the manifoldness of its elements is composed into a unity. The social unity is a graduated idea; the spirit and purpose of various circles demand various degrees in the closeness and strength of their unity; so that the social form of regulation which is demanded by a certain quantity of the circle, with respect to the degree of the unity which it is to achieve may still be the same with different quantities. The significance of the numerical conditions is thus not impaired if a greater circle, on account of its special tasks, may or must content itself without giving legal forms to its rules, just as in other cases is possible only to a smaller circle. Those undisciplined civic structures of Teutonic antiquity did not yet possess the cohesion of the elements which, existing in the case of great groups, is both cause and effect of their legal constitutions. Likewise in both the collective and the individual relationships between modern states there arise certain norms in the mere form of custom, because there is lacking here a unity of the parties necessary to be the vehicle of a legal order, and such a unity is in part supplied in a smaller, just as in a looser, circle by the immediate reactions of element with element. This, however, corresponds precisely with the function of custom as a form of regulation. Consequently the apparent exceptions really confirm the correlation which appeared between custom and law on the one side, and the quantities of the circles on the other side.

It is evident that the concepts "greater and smaller circle" are of a very crude scientific order, entirely indefinite and fluctuating, and properly applicable in general only in order to point out the dependence of the sociological form-character of a group upon its quantitative limitations. It cannot serve in any way to show more exactly the actual proportion which exists between the former and the latter. Nevertheless it is perhaps not in all cases impossible to make out this proportion more exactly. In the thus far observed formations and relationships any attempt to assign precise numerical values would evidently be, for any stage of our knowledge that can be foreseen, a completely

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 rôle varying from the

greatest to the least importance. This size is highly significant for the group. Nomadic stocks, for example, often have, in default of otherwise stable life-content, scarcely any other possibility of organizing themselves except in accordance with the number-principle. Its significance for a crowd upon the march controls even today the structure of armies. It persists naturally in the circumstance that often in the subdivision of a conquered or colonized or newly discovered land, where in the first instance there is a lack of real standards of organization, the principle of correlation, according to numerically equal divisions, has the first place; for example, the oldest constitution of Iceland is controlled in this way.

2. While we have up to this point been concerned with the numerical equality of different divisions, the number may be used further in order to characterize a single, and indeed leading, circle of persons from within a total group. For example, it was in many cases the custom to designate the administrative group of the craft-organizations by their number: In Frankfort the heads of the wool-weavers were known as "The Six;" among the bakers it was "The Eight;" in mediæval Barcelona the senate was called "The One Hundred," etc. It is extremely noteworthy how precisely the most eminent personalities are designated by that which is in itself least distinguishing, which is completely indifferent to every qualification, namely, mere number. The presumption behind this fact seems to me to be that with a number, say with six, not six individual, isolated elements, simply standing side by side, are meant, but a synthesis of these. Six is not I and I and I, etc., but a new concept, which is realized by the concurrence of these elements, and not pro rata in each of them for himself. In other connections we must designate the vital functional reciprocity of elements as their unity, which rises above their mere sum and in sociological antithesis with it. Here, however, in giving a name to a body of administrators, a committee, etc., by means of the mere sum, in reality that functional togetherness is in mind, and it is, as a name, possible only for the reason that the number in itself signifies a unity formed of unities. In the case cited, The Six are

not scattered through a homogeneous circle, but they signify a definite and firm articulation of the circle, through which six persons from its number are made eminent, and then they grow together to a guiding unity. The characterless impersonality of the naming by means of the number is just here highly characteristic; for it denotes more decisively than any less formal idea could that herewith no individuals, as persons, are meant, but that it is a purely social structure; the structure of the circle demands a definite quota of its units as a guiding body. In the purely numerical concept resides the pure objectivity of the formation, which is indifferent to everything personal in the separate member, and only demands that he shall be merely one of The Six. There is, perhaps, no more effective expression with which to emphasize, along with the social eminence of individuals, at the same time the complete irrelevance of everything which they stand for as persons outside of this function.

The unity of grouping which reveals itself in the composing of elements into a higher number is brought to light with special clearness by means of an apparent instance to the contrary. That senate of Barcelona which was called the One Hundred had at last in reality more, up to the number of two hundred, without on that account changing its name. The same phenomenon appears when the number operates, not as a distinguishing, but as a dividing, principle. Where the division of the population according to hundreds occurred, which we shall discuss later, there was never exact preservation of this precise number of members in the subdivision. This is expressly stated of the old German Hundreds. The number is in this case, therefore, immediately the synonym of the social member, which at first included, or was supposed to have included, precisely such a circle of individuals. This apparently insignificant fact shows the immense significance of numerical definiteness for the structure of the group. The number becomes indeed independent of its arithmetical content; it shows that the relation of the members to the whole is a umerical one; or, the number having become stable, represents this relation. There remains at the same time the idea of the subdivision, to consist of one hundred

elements, only that the empirical relations actualize this division with greater or less exactness. If it has been said of the German Hundreds that they were intended to express merely an indefinitely large number between the individual and the totality of members, this designates precisely the asserted sociological type. The life of the group demands a middle resort between the One and the All, a bearer of definite functions which neither the One nor the All can discharge, and the structure devoted to these tasks is thus named in accordance with its numerical composition. The functions do not give the name, because they are manifold and variable. What remains is merely the consolidation of an aliquot part of the totality into a unity. How great this part is in each case may be uncertain. The permanent numerical designation shows that the numerical relation in general was felt to be the essential thing. Therewith appears in the social realm an occurrence whose psychological form is elsewhere observed. The Russian types of coin are said to have been derived from an old system of weights, and it was of such sort that every higher type contained tenfold the amount of the lower. As a matter of fact, however, not merely the absolute but also the relative amount of metal in the coins often varied, but at the same time their values, after they were once brought into the numerical order, remained constant. While, therefore, the real proportions of metal value are shifting, the service which they have to render to commerce through the constancy of these nominal relations is marked by the fact that the historically first weight relations give permanent name and symbol for these later relations. In other ways, also, the number becomes the representative of the thing which it enumerates, and then the essential matter, namely, that the real affair in question is a relation between the whole and the part, is denoted by the fact that the numerical concept of the earlier relation covers all later changes. Thus the tax upon the miners in Spain in the sixteenth century was called the Quinto because it amounted to a fifth of the value, and it retained its name later when the proportion was quite different. In the same way the word "tithe" came to have, among the old Israelites and in many other places, the significance of

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