If I were to try, on the basis of the above observations, to find the clearest description of a concept, to represent it graphically, I should compare it by no means to a geometrical figure. Rather, it reminds me of a photograph with vague and gradually vanishing outlines. At first glance, the photograph appears to be quite clear and distinct because our eyes are focused merely on the center, the picture proper. Presently, as we proceed to fix the outlines of the picture, we discover what was at first concealed from us; it is impossible to tell definitely where the picture proper ends and the mere background begins. Thus every concept in the empirical sciences has its central image and beside it a zone of transition gradually vanishing into nothingness. In some cases this zone is broader, in others narrower.

The existence of this transition or "twilight" zone is not to be removed by any definition, no matter how circumstantial, because there can be no definition except by means of more concepts. The ultimate reason for this lack of definiteness is found in the extreme complexity of phenomena, even those apparently quite simple. For this reason one or more qualities may be absent from some particular phenomenon,93 and yet one could not say definitely that on account of the absence of one of these the phenomenon is outside of the concept, or some other phenomenon is still within the concept notwithstanding the absence of some particular quality. It is utterly inadmissible to demand an absolute likeness of phenomena as a condition of being admitted as falling within a concept.

92 On this term, compare Paul Eltzbacher, "Uber Rechtsbegriffe," Berlin, 1899, pp. 16, 23, 33.

93 An example will make this clearer. How simple, harmonious, and comprehensible a concept does that of "finding" appear! Now Jhering ("Zivilrechtsfalle ohne Entscheidungen," p. 103) tells of the following case: A, B, and C are walking by the side of a brook. On the opposite bank, A sees a purse lying on the ground. He tells his companions and B whistles for C's dog, who goes to retrieve the purse. As he is on the point of swimming back with it, D, who is walking on the other side, sets his own dog on C's dog, and as a result picks up the purse. Who is the finder? The difficulty of answering lies in this that of the various essentials of the concept "finding," all of which we have in mind as a united whole and which are really united in the central point of the concept, one or the other is absent in the case of each of the four parties. What each of the four does, each time falls merely into the twilight zone of the concept.

Consequently, the average degree of indefiniteness increases as we ascend in the scale of sciences - ending with sociology94; in other words, it increases as abstractness and simplicity decrease while the concrete-ness and complexity of the subject-matter grow. In the lower mathematics, the twilight zone equals zero, while in the social sciences very many concepts, as for instance nearly all ethical ones, such as virtue or the good, etc., are hardly more, when you consider them closely, than adumbrations generated by feeling.

Nobody is better able than the lawyer to realize that concepts which at first appear very clear and definite so as to make us forget all possible difficulties in employing them turn out to be quite vague. Who, for instance, is likely to have doubts about the meaning of "human being"? Yet the law found itself compelled to delimitate this concept more closely, for instance by making rules providing the time when an embryo begins to be a human being, at what precise moment a man may be held to have died, whether an aborted foetus or a born monster is a human being; and then again doubts may arise as to what constitutes a monster, and so ad infinitum.

If a man is obliged to pay a hundred dollars, there seems certainly to be no doubt at all what he is obliged to do. Yet if he tenders a banknote for a hundred dollars and demands the change, is he entitled thereto? Or he may send ninety dollars by mail, and the addressee is required to pay the fee provided; did the addressee receive ninety dollars? A debtor, who is an intimate friend of his creditor, puts ninety dollars into the drawer of his absent creditor's desk and locks it; has he paid his debt? Again, the debtor notifies his creditor to call for his money - may he legally demand this of him? And if he may not, ordinarily, is the law different where the government, or a bank, is the debtor? All these questions ordinarily do not enter consciousness at all when we talk about "paying ninety dollars," because our consciousness is focused on the central feature of the concepts "paying ninety dollars," say for instance the image of two persons one of whom is handing over ninety dollars.95

94 See note 86 supra.

In all such and similar questions, juridical thinking will invariably arrive at a decision, but it can never be said in such cases that the process of arriving at a decision consists of subsumption of phenomena under a proper concept, or that the result was already comprised in the original content of the concept. On the contrary, when we called the concept into our consciousness, we never thought of these boundary cases, we thought only of the most typical cases. It is exclusively of the typical cases that one can say they were comprised in the original concept as we thought of it. For the rest, the original concept is merely a thread around which new phenomena, similar but not alike, are crystallized. The process by which the concept is applied to the boundary case is not one of analysis, of separating the component parts of the concept and seeing which of the parts covers the case, but one of synthesis, by connecting the original concept with a new phenomenon and extending the concept so as to cover the latter.

95 I have intentionally selected two examples dealing with relatively simple physical facts and concrete concepts, in which the zone of uncertainty is narrow. Now take concepts like merchant or document, and the sphere of uncertainty will become much broader.