On the fundamental problem for Biological systematics

We (humans) invented concepts, and then started conceptualizing reality. The fundamental problem for this endeavor is that concepts (classification) is inherently orthogonal (see Russell's paradox), because it thereby lacks an unambiguous solution.This fact eventually led Biological systematics to Linné's consistent conceptualization of the biological diversity.

The German Nazi entomologist (ie, insect researcher) Willi Hennig did, however, take this endeavor one step further by starting to conceptualize conceptualization (later called Cladistics), as if conceptualization itself is the reality it conceptualizes instead of the reality. The problem with this step is simply that conceptualization isn't the reality it conceptualizes, but is instead in practice a paradox (see Russell's paradox). This step thus leads into barking up the wrong tree (or "jumping into crazy barrel", as we say in Sweden), or "screwing up matters", entering the back side of conceptualization where everything are up-side-down and contradictory.

Hennig did none the less get followers (called "cladists"), which took his step one step further by cutting off a return to the right "tree" (or "barrel") by boldly claiming (asserting) that this "tree" ("barrel") indeed IS the right "tree" ("barrel") and denying the right "tree" ("barrel"). It left the only way back to the right "tree" ("barrel") via a conceptualization of a conceptualization of a conceptualization of reality, which will take some time to find since it is a quite complicated track to follow. (Or by simply forgetting Cladistics).

The course of events above is actually just one more turn in Biological systematics' consistent tilting between the right "tree" (barrel"), also called "nominalism", and the wrong "tree" ("barrel"), also called "realism", due to its impossible fundamental aim to "find the true classification", which thus is a paradox. The discipline simply can't come to rest even concerning its fundamental approach, because there are always some biological systematists that don't understand this fundamental fact (ie, that the notion "a true classification" actually is a paradox). Instead, the discipline appears to remain a battle field for nominalism contra realism forever... (A "true classification" will it none the less never find).