approaches including cluster analysis (It is important to notice that empiricism is not the same as empirical study, but a certain ideal of doing empirical studies. With the exception of the logical approaches they all are based on empirical studies, but are basing their studies on different philosophical principles). (3) Historical and hermeneutical approaches including Ereshefsky's "historical classification" and (4) Pragmatic, functionalist and teleological approaches (not covered by Ereshefsky). In addition there are combined approaches (e.g., the so-called evolutionary taxonomy", which mixes historical and empiricist principles). Logical and rationalist approaches Logical division (top-down classification or downward classification) is an approach that divides a class into subclasses and then divide subclasses into their subclasses, and so on, which finally forms a tree of classes. The root of the tree is the original class, and the leaves of the tree are the final classes. Plato advocated a method based on dichotomy, which was rejected by Aristotle and replaced by the method of definitions based on genus, species, and specific difference. The method of facet analysis (cf., faceted classification) is primarily based on logical division. This approach tends to classify according to "essential" characteristics, a widely discussed and criticized concept (cf., essentialism). These methods may overall be related to the rationalist theory of knowledge. Empiricist approaches "Empiricism alone is not enough: a healthy advance in taxonomy depends on a sound theoretical foundation" (Mayr 1968, 548) Phenetics or Numerical taxonomy is by contrast bottom-up classification, where the starting point is a set of items or individuals, which are classified by putting those with shared characteristics as members of a narrow class and proceeding upward. Numerical taxonomy is an approach based solely on observable, measurable similarities and differences of the things to be classified. Classification is based on overall similarity: The elements that are most alike in most attributes are classified together. But it is based on statistics, and therefore does not fulfill the criteria of logical division (e.g. to produce classes, that are mutually exclusive and jointly coextensive with the class they divide). Some people will argue that this is not classification/taxonomy at all, but such an argument must consider the definitions of classification (see above). These methods may overall be related to the empiricist theory of knowledge. Historical and hermeneutical approaches Genealogical classification is classification of items according to their common heritage. This must also be done on the basis of some empirical