Methodologies of "evolutionary systematics" (Simpson 1961, 1975; Mayr 1963, 1974 and later publications) and of "phylogenetic systematics" (= cladistics; since Hennig 1950, 1966) have been outlined by all their authors as vague combinations of ontological statements, pragmatism and
conventions. These methodologies have always obscured the facts that species are first of all time-limited entities; that lineages are difficult to define and to demarcate in practice; and that there is no way to capture the phylogenetic process in a static classification. Only static entities
of the phylogenetic tree (time-extended species and clades) can be inserted into the Natural System. It is inevitable to distinguish sharply between a synchronous classification of Recent taxa and a diachronic classification of (extinct and Recent) clades. "Phylosystematics" is defined here
as a methodology of classifying the organisms' diversity, based on ontological claims and on the assumption of ideal, sufficient-knowledge situations. It is shown that a number of non-contradictory theorems can be derived from first principles and well-defined conventions. The logical structure
of the theorems demonstrates that all of Hennig's terms and concepts form a coherent logical thought-framework (methodology).
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