AbstractAn attempt has been made to establish axiomatically the principles of biological classification. It is shown that if phylogenetic classification is based on the notion of dichotomous origin of new taxa implied in Hennig's theory of cladism then the outcome must be a hierarchy in the form of a dichotomous dendrogram. Since the rules of traditional classification do not lead to this type of “phylogenetic tree” it is concluded that the conventions of ordinary systematics do not permit the erection of a “natural sy