THE PRINCIPLES OF SYSTEMATICS 245 



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 un- 

 specified. 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 



