Is cladistics inconsistent or not?

Biological systematics has lately (during the last 50 years or so) experienced a fundamental rift between proponents for a new approach called cladistics and traditional Linnean systematics (in the context of evolution called evolutionary taxonomy). The rift is rooted in Darwin's illustration of the origin of biodiversity as "the origin of species", since cladistists claim that they base their classification only on the bifurcating phylogenetic relationships between biological species, whereas Linnean systematists (ie, evolutionary taxonomists) assert that cladistics is inconsistent. Well is cladistics inconsistent or not?

The rift concerns classification of a bifurcating process, and classification of the entities (eg, biological species) in bifurcating processes has a tendency to distort our minds.

There are only two principally different kinds of classification of bifurcating processes: (1) a flat classification conflating entity with class (in this case represented by continuity), also called pattern and process, by using mutually exclusive classes (ie, clades and paraphyletic groups) and then categorizing these classes separately (ie, cladistics), and (2) an orthogonal system of classification keeping entity and class consistently apart by using (categories of) categories of classes (eg, evolutionary taxonomy).

The former (1) is simpler to understand, but also paradoxically contradictory in present (ie, between before and after in continuity) and thus lacking a consistent solution, whereas the latter (2) is more difficult to understand, but consistent and thus having several consistent solutions. The (only) principal difference between these two possible options is thus that the former (1) lacks consistent solution, whereas the latter (2) has several consistent solutions.

The fact that puzzles us, and thus drives the distortion of our minds, is that there is no single unambiguous ("true" or "natural") classification of a single such process. Frustration over this fact was probably resposible for cladists' radical move to simply assert (actually define) that there indeed is a single unambiguous ("true" or "natural") classification to be found, in the form of what they first called "monophyletic groups" but later became known as "clades", but which consistently ought to be called "holophyletic groups". This assertion is thus wrong. There is no such unambiguous classification "to be found". Classifications are actually not found at all, they are produced.

So, why isn't there a single unambiguous ("natural") classification of a single such process ("to be found")? Well, this question has millions of possible answers, but the mere attempt to explain it is actually irrational. An answer can only point to how the idea of such classification is inconsistent (actually paradoxically contradictory), like Bertrand Russell did in Russell's paradox, and to that it is falsified by the fact that time is relative to space, not explain why it is. The reason that such classification is lacking is a fact and as such inexplicable. Facts can't be explained; only directed processes can. It just allows us to draw conclusions about what it says about reality. The most fundamental of these conclusions is that reality is not rational, that is, that reality is irrational. The only alternative to this conclusion is to deny facts, that is, to BE irrational (like cladists do and are). Also the answer to why a single unambiguous ("true" or "natural") classification is lacking is thus lacking.

This fact explains the problems non-cladists had (and have) to respond to cladists' erroneous assertion (which Ashlock and Mayr, among many others, experienced and experience). If cladists choose (or don't understand better) to ignore facts and be irrational, then there is nothing the rest of us can do about it. There is no possibility to force anyone to accept facts and be rational. The option to ignore facts and be irrational can't be closed. That's why I'm just trying to explain that cladistics is irrational, so that cladists will have a harder time to lull others into the belief that it is rational (and thus that rationality is irrational). My only aim is, as a Swedish leader for the left wing party once expressed it, that: "there must be some kind of order also in the left wing party [ie, biological systematics]".

Classification of entities in a bifurcating process thus has a tendency to distort our minds, but I resist allowing it distort them to the degree of turning irrational into rational and vice versa, that is, turning biological systematics from a science into a belief, even if the fact that there isn't any unambiguous classification of a single bifurcating process is frustrating. Being irrational is extremely confusing, and biological systematics can probably not compete with all other beliefs anyway, especially since it evidently lacks a God. Instead, I struggle to retain biological systematics among the rational sciences by advocating evolutionary taxonomy for classification in the context of evolution. But, as I explained above, I can't hinder anyone from denying facts and being irrational. The gate to denial of facts and irrationality can't be closed.

Cladistics does thus not base its classification only on the bifurcating phylogenetic relationships between biological species, but on any contradictory belief in a bifurcating relationship between biological species. It actually tries to categorize a contradictory classification (ie, into clades and paraphyletic groups) of any bifurcating process, which actually is a generic phenomenon and therefore conflated with a category. It tries to realize an idea (which to them already appears realized) that can't be realized. Cladistics is thus clearly inconsistent, although consistently inconsistent.