On the impossibility to define the indefinable

Biological systematics differs from all other kinds of “systematics” by a fundamental belief that there ought to be a “natural” systematization to be found. This belief is expressed already in Aristotle’s first known systematization of living organisms into inter-relative genera and species, passing over Andrea Cesalpino’s first attempts with a hierarchical system, via John Ray’s denial of rationalism for empiricism into Carl von Linné’s complete hierarchical system, further via Charles Darwin’s confusion of process and pattern into Willi Hennig’s up-side-down turning of process and pattern leading into today’s revival of the pre-scientific Parmenidian comprehension denying empiricism for an up-side-down rationalism.

The search for a “natural” systematization has thus led biological systematics from a one-sided and thus inconsistent comprehension of reality via a two-sided comprehension into its optimization, and then via the contrary two-sided comprehension back to the one-sided comprehension it started from. Biological systematics has thus completed the circle without finding the “natural” groups.

At this point, biological systematics ought to pose the question why the “natural” groups haven’t yet been found, instead of only continuing searching for them. If a complete set of “natural” groups had been possible to find, they ought to have been found by now. Biological systematics ought to pose the question whether there is a rational obstacle for the goal to be possible. It ought to pose the question of whether the goal is possible at all? Given that today’s biodiversity has originated according to a dichotomously branching principle (thus on several different levels, or inclusivities), can it then possibly be systemized into a single true systematization? Can several levels of dichotomies be summarized into a single true dichotomy on any single level? Is the goal “a natural systematization” rational?

I try to explain that this goal is self-contradictory and empirically wrong. It cannot be reached without self-contradiction, and, in theory, it is falsified by the fact that time is relative. Its problem is that it requires the concrete (i.e., reality) to be the same as our comprehension of it (i.e., the abstract), when concrete process equals abstract pattern, and vice versa. The concrete is simply diametrical, or orthogonal, to the abstract. This fact hinders a finding of a single “natural” systematization like a hard grip hinders the catching of a slippey soap. The soap will slip out of our hands as soon as we try to catch it in a firm grip. The soap is simply impossible to catch because it would mean that it’s not slippery, which it is. The definitions of words hinders us from finding a definition of a phenomenon that is indefinable, because it isn’t definable. Indefinable is not definable, like not slippery is not slippery (i.e., “not slippery” does not define “slippery”) . Negations cannot be defined, and a “natural” systematization is definitionally a negation, since differences are negations, and differences are more fundamental than similarities in systematization.

I thus claim that a “natural” systematization is impossible to reach by the relation between reality and conceptualization itself, and also empirically wrong (theoretically). It is, conceptually, as impossible to reach as defining the indefinable, and, existentially, as impossible to reach as fusing the concrete with the abstract. The search for it is a search for the carrot in front of the donkey’s eyes (or the treasure at the foot of the rainbow). Stupid is the word I would use for it. The Linnean system, on the contrary, adapts to the impossibility by incorporating it.