SYSTEMATICS AND HISTORY
A. THE PRINCIPLES OF SYSTEMATICS
Rational Systematics
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 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.
In physics and chemistry no perfect rational systems have been established hitherto, but there are many systems approaching the ideal type in different departments of these sciences. The chemical type of the monohydric saturated alcohols, for instance, is given by the formula CnH2n+1OH, and in this formula we not only have an expression of the law of composition which all possible alcohols are to follow,—but, since we know empirically the law of quantitative relation between n and various physical properties, we also possess in our formula a general statement with respect to the totality of the properties of any primary alcohol that may be discovered or prepared in the future. But chemistry has still higher aims with regard to its systematics: all of you know that the so-called “periodic law of the elements” was the first step towards a principle that may some day give account of the relation of all the physical and chemical properties of any so-called element with its most important constant, the atomic weight, and it seems to be reserved for the present time to form a real fundamental system of the “elements” on the basis of the periodic law by the aid of the theory of electrons. Such a fundamental system of the elements would teach us that there can only be so many elements and no more, and only of such a kind. In crystallography a similar end has been reached already by means of certain hypothetic assumptions, and systematics has here accounted for the limited number and fixed character of the possible forms of crystalline symmetry.
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; or to express it somewhat differently, which would lead to contradictions, if division were to be tried in any but one particular manner. 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.
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.