We are dealing here with some of the most remarkable properties of the so-called synthetic judgments *a priori* in the sense of Kant, and, indeed, it seems that rational systematics will only be possible where some concept of the categorical class or some proposition based upon such concept lies at the root of the matter or at least is connected with it in some way. In fact, all rational systems with regard to the relations of symmetry in natural bodies deal ultimately with space; or better, all systems in such fields are able to become rational only if they happen to turn into questions of spatial symmetry. All other genera and species, whether of natural bodies or of facts, can be related only on the basis of empirical abstraction, *i.e.* can never attain rationality: here, indeed, the genus is richer in extent and poorer in content than are the species. The genus is transformed into the species, not by any inherent development of latent properties, but by a mere process of addition of characteristic points. It is impossible to deduce the number or law or specifications of the species from the genus. Mere “classification,” if we may reserve the honorable name of systematics for the rational type, is possible here, a mere statement in the form of a catalogue, useful for orientation but for nothing more. We may classify all varieties of hats or of tables in the same way. BIOLOGICAL SYSTEMATICS At this point we return from our logical excursion to our proper subject of biology; for I am sorry to say biological systematics is at present of our second type of systematics throughout: it is classification pure and simple. We have a catalogue in our hands, but nothing more. Such a statement of fact conveys not a particle of censure, casts not the least reflection on the gifted men who created the classification of animals or plants. It is absolutely necessary to have such a catalogue, and indeed the catalogue of the organisms can be said to have been improved enormously during the advance of empirical and descriptive biological science. Any classification improves as it becomes more “natural,” as the different possible schemes of arrangement, the different reasons of division, agree better and better in their results; and, in fact, there has been a great advance of organic classification in this direction. The “natural” system has reached such perfection, that what is related from one point of view seems nearly related also from almost all points of view which are applicable, at least from those which touch the most important characteristics. There has been a real weighing of all the possible reasons of division, and that has led to a result which seems to be to some extent final. But, nevertheless, we do not understand the *raison d’être* of the system of organisms; we are not at all able to say that there must be these classes or orders or families and no others, and that they must be such as they are.