Cladistics and Linnean systematics are merely the two possible classificatory solutions to "the problem of universals"

The "problem of universals" is an ancient problem in metaphysics about whether universals exist or not. This problem has two contradictory (orthogonal) solutions: Aristotelian essentialism and Plato's theory of forms, the former assuming that they do and the latter that they don't (at least not in the same reality as reality). Cladistics is consistent with the former and Linnean systematics is consistent with the latter, and they are mutually contradictory (ie, orthogonal). However, since classification of reality (for example into either clades or into genera, families, orders, etcetera) does not influence reality itself, Cladistics and Linnean systematics are merely the two possible (orthogonal) classificatory solutions to the problem of universals, Aristotelian essentialism and Plato's theory of forms, respectively.

This fact is, however, hidden behind the mutual contradiction between these two possible classificatory solutions by that it turns the difference between them into an existential problem for cladists and into an erroneous existential claim of cladistics to Linnean systematists. The mutual contradiction between them thus tilts the fact that they are merely the two possible (orthogonal) classificatory solutions to "the problem of universals" into a problem of cladistics' existential claim (ie, that universals exist). This claim was thus, as I have explained in recent posts on this blog, shown to be inconsistent by Betrand Russell in 1901 by what later became known as Russell's paradox (for those that hadn't understood this fact before, unlike Plato and many others).

It means that a biological systematist has to decide whether he/she believes that universals are real or not, ie, choose side between Aristotelian essentialism on the one hand and Plato's theory of forms/nominalism on the other, because the former leads to cladistic classification and the latter to Linnean systematics. However, if he/she chooses the former (ie, cladistic classification), then he/she has to be aware that it is inconsistent, ie, lacking consistent solution. None of them can thus reach the idea that cladistics calls "The Tree of Life".