On the impossibility of cladistics (and other such "natural" classifications)

The problem with the approach in biological systematics called "cladistics", ie, classifying bifurcating processes into so-called "clades" and "paraphyletic groups", is that this classification is inconsistent (actually paradoxically contradictory, see Russell's paradox), because this inconsistency means that the classification in practice is an infinite recursion, that is, a self-contradiction.

Such classification (ie, cladification) can thus search for a consistent solution forever without finding one, since there simply is none to be found. The fundamental error with the classification is that it confuses the concepts category (ie, finite class) and entity in an erroneous belief (thus actually axiom) that categories are consistent entities. This confusion is an occupational injury among people that deal too much with categorization (like biological systematists specifically and scientists generically), and is, unfortunately, shared with more simple-minded people just over-simplifying matters.

Those of us that don't confuse these concepts thus has an obligation to emphasize the difference between them, ie, that a single entity is not a category and that a category is not a single entity, because they simply can't be (see Russell's paradox), to help the confused out of this devastating confusion and hinder non-confused from falling into it. Category and entity are actually orthogonal concepts, ie, diametrically opposed, whereof category belongs to our minds, and entity belongs to reality. Never will nor can these two concepts thus meet. The difference between them is and will always be a pain in the ass for all extremist categorizers, but it will remain forever.