All systematics which deserves the predicate “rational” is founded upon a concept or upon a proposition, by the aid of which a totality of specific diversities may be understood. That is to say: every system claiming to be rational gives us a clue by which we are able to apprehend either that there cannot exist more than a certain number of diversities of a certain nature, or that there can be an indefinite number of them which follow a certain law with regard to the character of their differences.
Solid geometry, which states that only five regular bodies are possible, and points out the geometrical nature of each of these bodies, is a model of what a rational system should be. The theory of conic sections is another. Take the general equation of the second degree with two unknowns, and study all the possible forms it can assume by a variation of its constants, and you will understand that only four different types of conic sections are possible—the circle, the ellipse, the hyperbola, and the parabola.
The system of chemical elements and compounds approaches the ideal type of a rational system in a high degree. In crystallography a similar end has been reached and systematics has here accounted for the limited number and fixed character of the possible forms of crystalline symmetry. Certain hypotheses about the possible forms of geometrical equilibrium among the ultimate elements of matter are the foundation of rational systematics in these cases.
It is not difficult to understand the general logical type of all rational systems, and logic indeed can discover it without appealing to concrete sciences or to geometry. Rational systematics is always possible whenever there exists any fundamental concept or proposition which carries with it a principle of division. The so-called “genus”, as will easily be perceived, then embraces all its “species” in such a manner that all peculiarities of the species are represented already in properties of the genus, only in a more general form, in a form which is still unspecified. The genus is both richer in content and richer in extent than are the species, though it must be added that its richness in content is, as it were, only latent: but it may come into actuality by itself and without any help from without.
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 special 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, but 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 honourable 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.
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.
Shall we ever be able to understand that? Or will organic systematics always remain empirical classification? We cannot answer this question. If we could, indeed, we should have what we desire! As simple relations of space are certainly not the central point of any problematic rational organic systematics even of the future, the question arises whether there could be found any principle of another type which could allow an inherent sort of evolution of latent diversities, as do all judgments about spatial symmetry. At the end of the second part of this book, we shall be able to say a few more words about this important point.
The concept of what is called a “type”, due almost wholly to Cuvier and Goethe, is the most important of all that classification has given to us. Hardly second in importance is the discovery of the “correlation of parts”, as a sort of connection which has the character of necessity without being immediately based upon causality. Rádl seems to be the only modern author who has laid some stress on this topic. The harmony which we have discovered in development is also part of this correlation. When, later on, we come to discuss analytically our well-established entelechy as the ultimate basis of individual organisation, we shall be able to gain more satisfactory ideas with respect to the meaning of the non-causal but necessary connection, embraced in the concepts of type and of correlation of parts.
The type is a sort of irreducible arrangement of different parts; the correlation deals with the degree and the quality of what may be called the actual make of the parts, in relation to one another: all ruminants, for instance, are cloven-footed; the so-called dental formulae are characteristic of whole groups of mammals. Of course all such statements are empirical and have their limits: but it is important that they are possible.1
It has been the chief result of comparative embryology to show that the type as such is more clearly expressed in developmental stages than it is in the adults, and that, therefore, the embryological stages of different groups may be very much more similar to each other than are the adults: that is the truth contained in the so-called “biogenetisches Grundgesetz”. But the specific differences of the species are not wanting in any case of ontogeny, in spite of such similarities in different groups during development, and a careful observer may even attribute a cell of a blastula to a particular species.
Recent years have created the beginnings of a systematics based on chemical differences of metabolism and its products: such differences in fact have been found to go hand-in-hand with diversities of the type in some cases (v. Bunge, Przibram, etc.).