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Cladistics is naive set theory, whereas Linnean systematics is axiomatic set theory.
It means that cladistics is contradictory, actually paradoxically contradictory as Bertrand Russell demonstrated already in 1901, whereas Linnean systematics is consistent.
It also means that cladistics is primitive, whereas Linnean systematics is derived.
The step from Linnean systematics to cladistics in biological systematics is thus a step from a derivation into a primitive. The emergence of cladistics in this discipline is thus a prime example of the danger of unrestricted simplification (ie, populism) - matters simply aren’t as simple as they can be simplified into.