The error in cladistic reasoning

If we observe a dichotomously branching process, like an asexual propagation of cells, then we can classify this process in two different ways: (1) using an orthogonal system of classes as in the Linnean system, or (2) using a single class as in cladistics.

The difference between these kinds of classification is that an orthogonal system is internally consistent by avoiding the paradox of classification (ie, Russell's paradox), whereas a "single class" classification is inconsistent by encountering the paradox of classification (ie, Russell's paradox). It means that an orthogonal system is consistently consistent (ie, all possible classifications are consistent), whereas a single class classification is consistently inconsistent (ie, all possible classifications are inconsistent).

The cladistic idea (actually belief) that there is a single consistent "single class" classification to be found, which it calls "The True Tree of Life", is thus erroneous. A "single class" classification can in fact never reach consistency, because it requires that the class entity is inconsistent, which, in turn, would turn it inconsistent. Consistent inconsistency thus can't break even.

The error in cladistic reasoning resides in that it implicitly assumes as an axiom that the entities that are to be classified IS a class (for example cells) instead of IS CLASSIFIED as a class (for example cells). It thus rests on the erroneous axiom that classes are real, instead of being created by us. And, not unexpectedly, it leads to the erroneous conclusion that there is a single consistent "single class" classification to be found (which it calls "The True Tree of Life"). This hypothesized classification is thus actually a paradox that is inherent in classification (called Russell's paradox). This paradox can also be called "the impossibility of objective subjectivity". It tells us that subjectivity (ie, inconsistency) can never reach objectivity (ie, consistency), contrary to what cladistics claims, but does in this position instead encounter a paradox that we call Russell's paradox. Russell's paradox is thus actually the interface between subjectivity and objectivity - the impossibility of objective subjectivity.

This fact appears counter-intuitive to many of us, but it is just because we can't disclose subjectivity within subjectivity, since subjectivity "sees through" subjectivity. The fact thus appears more counter-intuitive the more subjective we are but less so the more objective we are. Our intuition thus depends on our preference for subjectivity (thinking in types) and objectivity (thinking in entities), respectively.