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.