The fundamental problem with cladistics (cladism) is that it rests on the inconsistent assumption that both single objects and holophyletic groups of objects (i.e., clades) exist at the same time. (An ancestor in a holophyletic group can of course not exist at the same time as its descendants, since an ancestor disappears in the same moment its descendants appear).
This fundamental problem has two main consequences:
1. that every logical reasoning resting in this assumption is inconsistent, that is, that its conclusion contradicts its assumption(s), and
2. that its “things” (i.e., clades, or holophyletic groups) can’t be found.
In summary: Being consistently inconsistent means contradicting oneself consistently, and “things” that neither exist nor have existed can of course not be found.
(This fundamental problem with cladistics (cladism) is actually the reason for the consistent Linnean system. Why should we complicate matters in biological systematics more than necessary? The Linnean system is the simplest way to avoid inconsistency).
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