Abstract
Four ordering systems have been used most frequently in taxonomy: (1) special purpose classifications, (2) downward classifications (identification schemes), (3) upward or grouping classifications (traditional), and (4) Hennigian phylogenetic systems. The special properties of these four systems are critically evaluated. Grouping classifications and phylogenetic systems have very different objectives: the former the documentation of similarity and closeness of relationship, the latter of phylogeny. Both are legitimate ordering systems.