The World as Will and Idea: Complete One Volume Edition. Arthur Schopenhauer

be presented in perceptions, which are framed once for all, and are relatively few in number, but which yet encompass, contain, and represent all the innumerable objects of the actual world. This itself is sufficient to prove that the lower animals can never learn to speak or comprehend, although they have the organs of speech and ideas of perception in common with us. But because words represent this perfectly distinct class of ideas, whose subjective correlative is reason, they are without sense and meaning for the brutes. Thus language, like every other manifestation which we ascribe to reason, and like everything which distinguishes man from the brutes, is to be explained from this as its one simple source—conceptions, abstract ideas which cannot be presented in perception, but are general, and have no individual existence in space and time. Only in single cases do we pass from the conception to the perception, do we construct images as representatives of concepts in perception, to which, however, they are never adequate. These cases are fully discussed in the essay on the principle of sufficient reason, § 28, and therefore I shall not repeat my explanation here. It may be compared, however, with what is said by Hume in the twelfth of his “Philosophical Essays,” p. 244, and by Herder in the “Metacritik,” pt. i. p. 274 (an otherwise worthless book). The Platonic idea, the possibility of which depends upon the union of imagination and reason, is the principal subject of the third book of this work.

      Although concepts are fundamentally different from ideas of perception, they stand in a necessary relation to them, without which they would be nothing. This relation therefore constitutes the whole nature and existence of concepts. Reflection is the necessary copy or repetition of the originally presented world of perception, but it is a special kind of copy in an entirely different material. Thus concepts may quite properly be called ideas of ideas. The principle of sufficient reason has here also a special form. Now we have seen that the form under which the principle of sufficient reason appears in a class of ideas always constitutes and exhausts the whole nature of the class, so far as it consists of ideas, so that time is throughout succession, and nothing more; space is throughout position, and nothing more; matter is throughout causation, and nothing more. In the same way the whole nature of concepts, or the class of abstract ideas, consists simply in the relation which the principle of sufficient reason expresses in them; and as this is the relation to the ground of knowledge, the whole nature of the abstract idea is simply and solely its relation to another idea, which is its ground of knowledge. This, indeed, may, in the first instance, be a concept, an abstract idea, and this again may have only a similar abstract ground of knowledge; but the chain of grounds of knowledge does not extend ad infinitum; it must end at last in a concept which has its ground in knowledge of perception; for the whole world of reflection rests on the world of perception as its ground of knowledge. Hence the class of abstract ideas is in this respect distinguished from other classes; in the latter the principle of sufficient reason always demands merely a relation to another idea of the same class, but in the case of abstract ideas, it at last demands a relation to an idea of another class.

      Those concepts which, as has just been pointed out, are not immediately related to the world of perception, but only through the medium of one, or it may be several other concepts, have been called by preference abstracta, and those which have their ground immediately in the world of perception have been called concreta. But this last name is only loosely applicable to the concepts denoted by it, for they are always merely abstracta, and not ideas of perception. These names, which have originated in a very dim consciousness of the distinctions they imply, may yet, with this explanation, be retained. As examples of the first kind of concepts, i.e., abstracta in the fullest sense, we may take “relation,” “virtue,” “investigation,” “beginning,” and so on. As examples of the second kind, loosely called concreta, we may take such concepts as “man,” “stone,” “horse,” &c. If it were not a somewhat too pictorial and therefore absurd simile, we might very appropriately call the latter the ground floor, and the former the upper stories of the building of reflection.{13}

      It is not, as is commonly supposed, an essential characteristic of a concept that it should contain much under it, that is to say, that many ideas of perception, or it may be other abstract ideas, should stand to it in the relation of its ground of knowledge, i.e., be thought through it. This is merely a derived and secondary characteristic, and, as a matter of fact, does not always exist, though it must always exist potentially. This characteristic arises from the fact that a concept is an idea of an idea, i.e., its whole nature consists in its relation to another idea; but as it is not this idea itself, which is generally an idea of perception and therefore belongs to quite a different class, the latter may have temporal, spacial, and other determinations, and in general many relations which are not thought along with it in the concept. Thus we see that several ideas which are different in unessential particulars may be thought by means of one concept, i.e., may be brought under it. Yet this power of embracing several things is not an essential but merely an accidental characteristic of the concept. There may be concepts through which only one real object is thought, but which are nevertheless abstract and general, by no means capable of presentation individually and as perceptions. Such, for example, is the conception which any one may have of a particular town which he only knows from geography; although only this one town is thought under it, it might yet be applied to several towns differing in certain respects. We see then that a concept is not general because of being abstracted from several objects; but conversely, because generality, that is to say, non-determination of the particular, belongs to the concept as an abstract idea of the reason, different things can be thought by means of the same one.

      It follows from what has been said that every concept, just because it is abstract and incapable of presentation in perception, and is therefore not a completely determined idea, has what is called extension or sphere, even in the case in which only one real object exists that corresponds to it. Now we always find that the sphere of one concept has something in common with the sphere of other concepts. That is to say, part of what is thought under one concept is the same as what is thought under other concepts; and conversely, part of what is thought under these concepts is the same as what is thought under the first; although, if they are really different concepts, each of them, or at least one of them, contains something which the other does not contain; this is the relation in which every subject stands to its predicate. The recognition of this relation is called judgment. The representation of these spheres by means of figures in space, is an exceedingly happy idea. It first occurred to Gottfried Plouquet, who used squares for the purpose. Lambert, although later than him, used only lines, which he placed under each other. Euler carried out the idea completely with circles. Upon what this complete analogy between the relations of concepts, and those of figures in space, ultimately rests, I am unable to say. It is, however, a very fortunate circumstance for logic that all the relations of concepts, according to their possibility, i.e., a priori, may be made plain in perception by the use of such figures, in the following way:—

      (1.) The spheres of two concepts coincide: for example the concept of necessity and the concept of following from given grounds, in the same way the concepts of Ruminantia and Bisulca (ruminating and cloven-hoofed animals), also those of vertebrate and red-blooded animals (although there might be some doubt about this on account of the annelida): they are convertible concepts. Such concepts are represented by a single circle which stands for either of them.

      (2.) The sphere of one concept includes that of the other.

      (3.) A sphere includes two or more spheres which exclude each other and fill it.

      (4.) Two spheres include each a part of the other.

      (5.) Two spheres lie in a third, but do not fill it.

      This last case applies to all concepts whose spheres have nothing immediately in common, for there is always a third sphere, often a much wider one, which includes both.