Bertrand Russell demonstrated in 1901 that naive set theory leads to paradox.
This demonstration made Ernst Zermelo (1908) propose an axiomatization of set theory that avoids this paradox by replacing arbitrary set comprehension with weaker existence axioms, such as his axiom of separation (Aussonderung). Later modifications to this axiomatization proposed in the 1920s by Abraham Fraenkel, Thoralf Skolem, and by Zermelo himself resulted in the axiomatic set theory called ZFC. This theory was initially controversial, but became widely accepted once Zermelo's axiom of choice ceased to be controversial, and has since then remained the canonical axiomatic set theory down to the present day.
The German Nazi entomologist Willi Hennig did, however, ignore both Russell's demonstration, Zemelo et al's avoidance of this paradox and ZFC, when he in 1955 instead simply claimed that "only monophyletic groups [in effect Russell's paradox] appear to be natural groups". Hennig thus didn't consider the scientific discussion about Russell's paradox, which also confused biological systematists at the time since Darwin had presentated his theory "on the origin of species", but simply claimed that only this paradox appears to be natural groups. In spite of this Hennig's omission, his claim gave rise to the approach in biological systematics that today is called "cladistics", and which also today is searching for this paradox. This approach has thus totally missed the fact that naive set theory leads to paradox (as well as the scientific discussion about this fact).
The question now is thus: who in the world can explain to cladists that Hennig was ignorant about the discussion about monophyly (ie, Russell's paradox) when he made his claim that "only monophyletic groups [ie, Russell's paradox] appear to be natural groups". And, can cladists withdraw their claim at all (which is more of a belief than a claim)? Can cladists back off with their honor intact?
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