[It is normal for classification approaches to be diverse].

It is asserted that the postmodern concept of science, unlike the classical ideal, presumes necessary existence of various classification approaches (schools) in taxonomy, each corresponding to a particular aspect of consideration of the "taxic reality". They are set up by diversity of initial epistemological and ontological backgrounds which fix in a certain way a) fragments of that reality allowable for investigation, and b) allowable methods of exploration of the fragments being fixed. It makes it possible to define a taxonomic school as a unity of the above backgrounds together with consideration aspect delimited by them. Two extreme positions of these backgrounds could be recognized in recent taxonomic thought. One of them follows the scholastic tradition of elaboration of a formal and, hence, universal classificatory method ("new typology", numerical phenetics, pattern cladistics). Another one asserts dependence of classificatory approach on the judgment of the nature of taxic reality (natural philosophy, evolutionary schools of taxonomy). Some arguments are put forward in favor of significant impact of evolutionary thinking onto the theory of modern taxonomy. This impact is manifested by the correspondence principle which makes classificatory algorithms (and hence resulting classifications) depending onto initial assumptions about causes of taxic diversity. It is asserted that criteria of "quality" of both classifications proper and classificatory methods can be correctly formulated within the framework of a particular consideration aspect only. For any group of organisms, several particular classifications are rightful to exist, each corresponding to a particular consideration aspect. These classifications could not be arranged along the "better-worse" scale, as they reflect different fragments of the taxic reality. Their mutual interpretation depends on degree of compatibility of background assumptions and of the tasks being resolved. Extensionally, classifications are compatible as much as they coincide by context and hierarchical structure of included taxa. Intentionally, typological classifications are compatible if included taxa are comparable by their diagnoses, while phylogenetic classifications are compatible if the included taxa are ascribed monophyletic status. A brief consideration is given to the "new phylogenetics" (= "genophyletics") as to a classificatory approach aimed at elaboration of parsimonious phylogenetic hypotheses based on molecular biology data and employing numerical methods of cladistic analysis. This approach is shown to borrows some phenetic ideas and revives scholastic principle of unified classificatory basis. It is supposed that, in a time, biological classification would get escaping from plethora of positivistic ideas (including those being developed by nowaday cladistics) and would assimilate (revive) more actively holistic worldview.