Cladistics assumes as an axiom that classes are real (ie, acknowledges the approach called “realism”), which, together with the assumption that classes have originated in a dichotomously branching process from a single class, leads it to the conclusion that the class it calls clade, and thus also its particular object “a single Tree of Life”, is real.
Now, a problem with this conclusion is that it contradicts one of its own axioms, namely that classes are real (ie, realism itself), by defining the smallest classes as consisting of at least three classes (ie, one class cladistics calls “an ancestor class” and two classes it calls descendant classes), thus excluding single classes from a real existence, and thereby falsifying itself. The conclusion thus actually falsifies itself by falsifying one of its axioms.
A closer look on the class clade reveals that it actually is the realistic face of the interface between realism and nominalism, whose nominalistic face is Russell’s paradox. It means that the class clade actually is a practical paradox and thus can’t be found per definition. This fact may come as a surprise for cladists, but it can also be tested empirically by trying to find a clade out there (ie, in reality). Clades are, no doubt, very vivid in cladists’ minds, but real can they none the less never become (per definition). This fact does also actually falsify the whole fundament for cladistics, that is, both its axioms and its conclusion. It shows that cladistics actually doesn’t have a single right, ie, is totally wrong.
Cladists ought to have read William of Ockham more carefully when referring to his principle of parsimony (ie, Occam’s razor). The principle is indeed a fundamental guiding principle in discussions on reality, providing that we can distinguish discussion and reality. Otherwise, it guides into the world of paradoxical reasoning (for prime examples of this case, see Willi Hennig, Malte Ebach, Steve Farris and Gareth Nelson, among many, many others).
Cladistics is thus something as weird as the opposite to objective empirical science, that is, contradictory applied typology.
