This paper examines the philosophical background of phylogenetic systematics as proposed by Willi Hennig. Willi Hennig is found to espouse logical positivism and phenomenology. The concept of a semaphoront is phenomenological, and attributes to immediate sense data the same primacy as logical empiricism. The concept of a cladogram corresponds to a structure description sensu Carnap, and is rooted in Woodger's set-theoretical definition of hierarchy. Species figure in the cladogram as logical constructs, i.e. semaphoront complexes. This creates a tension between a set-theoretical concept of species where semaphoronts instantiate the membership criteria for their respective sets, and a historical conception of species where species as individuals are parts or components of the genealogical nexus. Hennig believed that the hierarchical system built on idealistic morphology could be re-interpreted as a genealogy on the basis of reciprocal illumination between the whole and its parts. The process of reciprocal illumination is based on the principle of congruence, which lies at the heart of the coherence theory of truth.