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The difference between Linnean systematics and cladistics is that Linnean systematics implicitly assumes that we classify objects, ie, that objects but not classes are real, whereas cladistics instead implicitly assumes that we find classes, ie, that classes but not objects are real. (Both objects and classes can’t be real, because they are paradoxically contradictory, as Bertrand Russell demonstrated).
Linnean systematics is thus rational, whereas cladistics is irrational.