Every concept-determining study faces the problem of comprehending conceptually an object that was first comprehended non-conceptually, and therefore of putting a concept in the place of non-conceptual notions of an object. This problem finds a specially clear expression in the concept-determining judgment (the definition), which puts in immediate juxtaposition, in its subject some non-conceptual notion of an object, and in its predicate a conceptual notion of the same object. Accordingly, the study that is to determine the concepts of Anarchism and its species has for its problem to comprehend conceptually objects that are first comprehended in non-conceptual notions of Anarchism and its species; and therefore, to put concepts in the place of these non-conceptual notions. 3. But our study may specify its problem still more precisely, though at first only on the negative side. The problem is not to put concepts in the place of all notions that appear as non-conceptual notions of Anarchism and its species. Any concept can comprehend conceptually only one object, not another object together with this. The concept of health cannot be at the same time the concept of life, nor the concept of the horse that of the mammal. But in the non-conceptual notions that appear as notions of Anarchism and its species there are comprehended very different objects. To be sure, the object of all these notions is on the one hand a genus that is formed by the common qualities of certain teachings, and on the other hand the species of this genus, which are formed by the addition of sundry peculiarities to these common qualities. But still these notions have in view very different groups of teachings with their common and special qualities, some perhaps only the teachings of Kropotkin and Most, others only the teachings of Stirner, Tucker, and Mackay, others again the teachings of both sets of authors. If one proposed to put concepts in the place of all the non-conceptual notions which appear as notions of Anarchism and its species, these concepts would have to comprehend at once the common and special qualities of quite different groups of teachings, of which groups one might embrace only the teachings of Kropotkin and Most, another only those of Stirner, Tucker, and Mackay, a third both. But this is impossible: the concepts of Anarchism and its species can comprehend only the common and special qualities of a single group of teachings; therefore our study cannot put concepts in the place of all the notions that appear as notions of Anarchism and its species.