consequence because upon them is based the real aim of knowledge, prediction. The former are those which have brought the very "reality" of the concepts into ill repute, while the latter show that the formation and the mutual reaction of the concepts practically constitute the entire content of all science. It is of the greatest importance, therefore, to distinguish between the two kinds of concept combinations, and the study of this differentiation forms the content of that most general of all the sciences which we have characterized as logic, or, better, the science of concepts.

7. Simple and Complex Concepts.

The formation of concepts consists, as we have seen, in the selection of those parts of different but similar experiences which coincide with one another and in the elimination of those that are different in kind. The results of such a procedure may vary greatly according to the number and the difference of the experiences placed in relation with one another. If, for example, we compare only a few experiences, and if, moreover, these experiences are very similar to one another, then the resulting concepts will contain very many parts that agree. But at the same time they will have the peculiarity of not being applicable to other experiences, since these are without some of the coinciding parts of that narrower circle. Thus, for example, the concept which a rustic chained to the soil all his life has of human work does not apply to the work of the city man. A concept will embrace a larger number of individual cases in proportion as it contains fewer different parts. And by systematically following out this thought we arrive at the conclusion that the concepts that are simple and have no different parts at all find the widest application or are the most general.

The elimination of the non-coinciding parts from the concept-forming experience is called abstraction. Obviously abstraction must be carried the farther the more numerous and the more varied the experiences from which the concepts are abstracted, and the simplest concepts are the most abstract.

By looking back over the ground just traversed, the less abstract ideas may also be regarded as the more complex in contradistinction to the simpler ones. Only we must guard against the error of literal interpretation and not suppose that the less simple concepts have really been compounded of the simpler ones. In point of origin they actually existed first, since the experience contains the ensemble of all the parts, those which have been retained as well as those which have been eliminated. It is only later, by a characteristic mental operation, after we have analyzed the more complex concept, that is, after we have disclosed the simpler concepts existing in it, that we can compound it again; in other words, execute its synthesis.

These relations bear a striking resemblance to the relations known from chemistry to exist between substances, namely, between elements and compounds. From the chaos of all objects of experimentation (chemistry purposely limits itself to ponderable bodies) the pure substances are sifted out—an operation corresponding to the formation of concepts. The pure substances prove to be either simple or compound, and the compounds are so constituted that they can each be reduced to a limited number of simple substances. The simple substances, or elements, retain this quality of simplicity only until they are recalled; that is, until it has been proved that they, too, can be resolved into still simpler elements. The same is true of the simple concepts. They can claim simplicity only until their complex nature is demonstrated.

With all these similarities we must be extremely careful never to forget the differences existing alongside the agreements. So hereafter we shall make no further use of the chemical simile. It was brought into requisition merely in order to acquaint the beginner the more readily with the entire method of investigation by means of a more familiar field of thought and study. It is quite certain, however, that side by side with the given similarities there are also radical differences. Moreover, the notion of simple and complex concepts or "ideas" had been elaborated by John Locke long before chemistry reached its present state of clearness concerning the concept of the elements.

Nevertheless since then the relation has been completely reversed. While the study of the chemical elements has in the meantime undergone great development, so that not only have the elements of all the substances coming under the observation of the chemist been discovered, but, inversely, many compound substances have been constructed from their elements, not even an approach to such a development is apparent in the study of concepts. On the contrary, the whole matter has remained at about the same point as that to which John Locke had brought it in the second half of the seventeenth century. This is due above all to the opinion of the most influential philosophers, that Aristotle's logic, or science of concepts, is absolutely true as well as exhaustive and complete, so that, at the utmost, what is left for later generations to do is only to make a change in the form in which the matter is presented. It is true that in more recent times the grave error of this view is beginning to be recognized. We realize that Aristotle's logic embraces but a very small part of the entire field, though in this part he displays the greatest genius. But beyond this general recognition no great step forward has been made. Not even a provisional table of the elementary concepts has been propounded and applied since Locke.

Hence in the following investigation we shall have to speak of the elements or the simpler parts of a complex concept only in the sense that these concept elements are simpler as compared with the complex concepts, but not in the sense that the simplest or truly elementary concepts have already been worked out. It must be left to later investigators to find these, and it may be expected that the reduction of some concepts until then considered elementary into still simpler ones will take place chiefly in times of great intellectual progress.

Complex concepts can, in the first place, be formed from experience, for in an empirical concept we meet with several conceptual component parts which can be separated from one another by a process of abstraction, but are always found together in the given experiences. For example, the concept horse has originated from a very frequent, similarly repeated experience. On analysis it is found to contain a vast number of other concepts, such as quadruped, vertebrate animal, warm-blooded, hairiness, and so on. Horse, then, is obviously a complex empirical concept.

On the other hand, we can combine as many simple concepts as we please, even if we did not find them combined in experience, for in reality there is nothing to hinder us from uniting all the concepts provided by memory into any combinations we please. In this way we obtain complex arbitrary concepts.

The task of science can now be even more sharply defined than before by the fact that it permits the construction of arbitrary concepts which in circumstances to be foreseen become empirical concepts. This is another expression for prediction, which we recognized as the characteristic of science. It goes deeper than the previous definition, because here the means for its realization are given.

8. The Conclusion.

First let us consider the scientific import of the complex empirical concepts. It consists in