Before cladistics, biological systematists searched the consistent solution of the contradiction between object and class, but cladistics turned this problem up-side-down by by confusing object and class (by equalizing properties of objects with the objects), thus turning the question from “what is the consistent fusion of object and class?” to “which is the True Tree of Life?”. This confusion does not, however, mean that cladistics found the consistent solution of the contradiction between object and class, but that it assumed that this problem already was solved, thus instead asking the next question, that is, how shall we find the True Tree of Life.

The fundamental problem of the orthogonality between object and class does, however, remain. Neither the Linnean system nor cladistics solve this problem. The Linnean system just finds the consistent solution of the contradiction between object and class, whereas cladistics just confuses object and class, None of them “solves the problem”.

A solution of this problem (ie, the orthogonality between object and class)requires a definition of what a “solution” is and which problems that can be solved. If the orthogonality between object and class is a problem, then this problem can’t be solved, because ”object” and “class” are orthogonal. If a fact is a problem, then this “problem” can’t be solved, because the “problem” resides in the approach rather than in reality.The problem is that we simply can’t understand reality consistently. Exactly where the problem resides is difficult to say, it appears to be what reality struggles with all the time. If there had been a solution to this problem, then reality would have stopped when finding it. In the meantime, we have to do what we can with what we have.

A single concept is an ambiguity between infinite class (ie, class or type) and finite class (ie, set). However, the fact that a single class contains several classes, like how the class chair contains several kinds of chairs, means that the concept class is contradictory between one and several, ie, is neither one nor several. (Realists have a tendency to interpret this “neither nor” as a “both and”, although nothing can clearly be both one and several at the same time. A single thing is a single thing and several things are several things). In summary, a single concept is an ambiguity between infinite class (ie, class or type) and finite class (ie, set), both of which are contradictory between one and several. A single concept is thus internally both ambiguous and contradictory.

This situation is impossible to solve both consistently and unambiguously, since both infinite class and finite class are contradictory. One of them, ie, either consistency or unambiguity, has to yield. The situation only has two possible solutions: to (1) adopt the axiom that a single object is a single object (ie, objectivity, or nominalism), or (2) adopt the axiom that an infinite class is a single infinite class, and thus that a single concept is a single concept (ie, subjectivity, or realism). The former means that a single concept is internally both ambiguous and contradictory, which agrees with facts, whereas the latter means that a single concept is both consistent and unambiguous, which thus both is contradictory and contradicts facts. The former is thus consistent, whereas the latter both is contradictory and contradicts facts.

Having come this far, we can begin discussing reality in an objective (ie, nominalistic) approach, because it does at least prevent us from contradicting ourselves. This objective (ie, nominalistic) approach was clearly explained by Aristotle about 2350 years ago, and extended hierarchically by Linné about 300 years ago. The built-in contradiction of conceptualization is thus not a mystery, but has been consistently solved by Aristotle and Linné.

Realists’ (ie, cladists’) confusion of object and class, leading to the realistic entrance to their contradictory and contrafactual “solution” of the problem does thus not solve this problem, but only denies it, instead acknowledging contradiction and contrafactuality. It obviously appears as a magic solution of the problem to realists (ie, cladists), but this is just in a generic sense. There is no specific consistent and unambiguous solution of this problem to be found, not even in a contradictory and contrafactual approach.

Now, a problem with this conclusion is that it contradicts one of its own axioms, namely that classes are real (ie, realism itself), by defining the smallest classes as consisting of at least three classes (ie, one class cladistics calls “an ancestor class” and two classes it calls descendant classes), thus excluding single classes from a real existence, and thereby falsifying itself. The conclusion thus actually falsifies itself by falsifying one of its axioms.

A closer look on the class clade reveals that it actually is the realistic face of the interface between realism and nominalism, whose nominalistic face is Russell’s paradox. It means that the class clade actually is a practical paradox and thus can’t be found per definition. This fact may come as a surprise for cladists, but it can also be tested empirically by trying to find a clade out there (ie, in reality). Clades are, no doubt, very vivid in cladists’ minds, but real can they none the less never become (per definition). This fact does also actually falsify the whole fundament for cladistics, that is, both its axioms and its conclusion. It shows that cladistics actually doesn’t have a single right, ie, is totally wrong.

Cladists  ought to have read William of Ockham more carefully when referring to his principle of parsimony (ie, Occam’s  razor). The principle is indeed a fundamental guiding principle in discussions on reality, providing that we can distinguish discussion and reality. Otherwise, it guides into the world of paradoxical reasoning (for prime examples of this case, see Willi Hennig, Malte Ebach, Steve Farris and Gareth Nelson, among many, many others).

Cladistics is thus something as weird as the opposite to objective empirical science, that is, contradictory applied typology.

The cladistic idea of a “correct” clade (ultimately A Single Tree of Life) rests on the idea that classes are real (ie, exist). This fact may not be immediately obvious for everyone, especially not for cladists, since the route into the idea is catalyzed by a confusion of “object” and “class”, and the idea thus is characterized by a blindness for the difference between “object” and “class”. There is, however, no doubt that the idea requires real classes (the cladists’ interpretation of “biological species”) that have originated by a real origination process, and thus a resulting class, namely the class “clade”. There is, thus, acually nothing else than classes in cladistics.

William of Ockham, however, was instead a pioneer of nominalism (after Heracleitos, of course), by some even being considered the father of modern epistemology, because of his strongly argued position that only individuals exist, rather than supra-individual universals, essences, classes, or forms, and that universals are the products of abstraction from individuals by the human mind and have no extra-mental existence. He denied the real existence of metaphysical universals and advocated the reduction of ontology. Ockham is sometimes considered an advocate of conceptualism rather than nominalism, for whereas nominalists held that universals were merely names, i.e. words rather than existing realities, conceptualists held that they were mental concepts, i.e. the names were names of concepts, which do exist, although only in the mind. Therefore, the universal concept has for its object not a reality existing in the world outside us, but an internal representation which is a product of the understanding itself and which “supposes” in the mind the things to which the mind attributes it; that is, it holds, for the time being, the place of the things which it represents.  It is the term of the reflective act of the mind. Hence the universal is not a mere word, as Roscelin taught, nor a sermo, as Abelard held, namely the word as used in the sentence, but the mental substitute for real things, and the term of the reflective process. For this reason Ockham has even been called a “terminist”, to distinguish him from both a nominalist and a conceptualist. (Most of the paragraph above being copied from Wikipedia). William of Ockham was thus a very, very convinced anti-cladist (of the same understanding as me). He thus denied cladistics in the first place.

Occam’s razor does thus have nothing to do with cladists’ confusion of classes into the paradoxical class “clade” (actually Russell’s paradox). William of Ockham is not the least responsible for cladists’ mental somersault. Cladists’ confusion is nothing but a total misunderstanding of conceptualization itself, believing that concepts, instead of the conceptualized, are real, and a corollary misusage of both the terms and the tools (ie, operations on terms) we have to discuss reality. Cladistics is thus totally, and by totally I mean Totally, lost. It simply looks at reality in an up-side-down fashion believing that paradoxes are real instead of a mental construct (and also actually searching for them).

Cladists have thus grasped the meaning of Occam’s razor, but not what to do with it or how. The question whether they understand what they are doing remains to be answered. Most of them probably do not, whereas the rest are simply using cladistics to make a career, abandoning it when it no longer is useful. It is a catalyst to a career, just as confusion of “object” and “class” is a catalyst to cladistics, because there are many mecenates out there confusing “object” and “class”. Feed them with what they want and they will feed you with money.

A definition is a set of words that is one, not by conjunction, like the “Iliad”; but because it deals with one object.

and continued with:

That is why it is necessary to divide the unity from the beginning according to several (axes), as we have said.

He then used the three concepts “genos” [genus], “eidos” [species] and “diafora” [specific differences] to accomplish this division. He explained that:

For everything that differs, differs either in “genos” [generics] or in “eidos” [specifics]. In “genos” if the things do not have their matter in common [ie, are without a common measure, or a common denominator] and are not generated out of each other, as are the beings that have their form different in category, and in “eidos” if they have the same “genos“.

He then added that:

The things that differ in “genos” have no path to another, but are too distant and without common measure.

and:

“Genos” means that by which two things are said to be essentially the same.

Aristotle’s main contribution in this field was thus that he distinguished the two kinds of difference there are: pure otherness and specific difference, respectively.

It is this distinction cladistics fails to understand. It instead defines concepts consistently by conjunction, like the Iliad, thus returning to prescientific times adopting the approach of Parmenides. If this is not pure ignorance, then it is a bold denial of science as a whole (maybe a mixture of them). It is difficult to decide which is worst. Contradictory is it in any case, just as contradictory as it was 2500 years ago.

The reason is that a two-level, orthogonal system keeps representations and the represented consistently apart. A one-level system confuses representations and the represented per definition. Cladistics is, moreover, a particularly serious one-level confusion by confusing representations and the represented in a generic sense, since it means that it has a particularly wide variance, actually including all possible specific applications. It means that cladistics is just as inconsistent as the Linnean system is consistent, that is, totally.

Between these, there is nothing. We can only either keep representations and the represented apart or confuse them. But, whereas there are lots of ways to confuse them, whereof cladistics is the only consistent way, there is only one way of keeping them apart – a two-level, orthogonal system. It means that we can only produce either ambiguous or contradictory classifications. The cladistic idea “a single consistent and unambiguous classification”, like The Tree of Life, is thus an impossibility. Never will this idea materialize. Never will it overcome its internal contradiction.

The fact that classification rests on a fundamental distinction of the classified and classification, ie, entity and class, this difference means that Linnean systematics keeps entity and class consistently apart, whereas cladistic classification confuses them.

About Linnean systematics there is thus not more to say, whereas the confusion of entity and class in cladistic classification means that this classification both distinguishes and confuses entity and class at the same time, which, obviously, is inconsistent (i.e., contradictory).

So, what is the problem with the contradictory distinction and confusion of entity and class at the same time in cladistic classification? Well, it is simply that it is contradictory, because contradictory means that every specific such distinction and confusion is contradictory, and thus that no such distinction and confusion is not contradictory. The problem with the contradictory distinction and confusion of entity and class at the same time in cladistic classification is thus that it is consistently contradictory (what we traditionally call paradoxical). More generically, contradicting oneself is, of course, contradictory.

The difference between Linnean systematics and cladistic classification is thus that Linnean systematics is a consistent classification of reality, whereas cladistic classification is a contradictory, simultaneous distinction and confusion of entity and class, thus lacking a consistent state.

I know that this explanation opens a black hole for typologists, but in the choice between opening this hole and denying objective sense, I choose opening this hole. It wasn’t I that started the on-going battle between objectivity (ie, Linnean classification) and subjectivity (ie, cladistic classification) in biological systematics, but Hennig that did. I merely choose to explain that biological systematics can only be either ambiguous (as in the objective Linnean systematics) or contradictory (as in the subjective cladistic classification), and that there thus is no neutral ground between the two, meaning that the goal typologists seek is lacking (sorry to say). I judge that keeping the cladistic dream of a single consistent and unambiguous classification does more harm than acknowledging the fact that such classification is not to be found does. I thus choose to deny Santa explicitly instead of keeping the dream alive, because, in this case, the dream does more harm than good.

The difference between Linnean systematics and cladistic classification raises the question whether biological systematics can get rid of its fundamentalists, that is, typologists, or if the fundamentalists will stay in the power they seized when Steve Farris and Gareth Nelson overturned sense with cladistic fundamentalism. My bet is that cladistics will fade away in consistent splitting combined with its fundamental contradiction being overturned by an increased understanding of the matter due to object-oriented computer programs (ie, so-called “apps”). Linnean systematics is so fundamental in its principle that it can never be overturned permanently. Its principle is simply the fundamental building block of conceptualization. Long Live Linné!

The problem with this approach is that it also is the orthogonal opposite to being consistent, that is, is consistently inconsistent. It has a unique logical line of reasoning, but in this, conclusions do not agree with assumptions, but, on the contrary, consistently disagree. It does thus not converge towards a single point of view (ie, the truth), but, on the contrary, diverge towards every possible point of view. Cladistics thus actually IS what it erroneously assumes can be found, that is, the clade it erroneously assumes is finite but which actually is infinite by being paradoxical. It means that it is doomed to eternal splitting.

Over history there has been many different approaches in our continuing discussion on reality, but no one that has explicitly denied that it also conceptualizes, like cladistics does. Cladistics is thus a challenge to all of us that try to understand. Here is an approach that explicitly denies that it creates any concept, instead implicitly claiming that concepts arrives to it ready-made. The challenge is thus to lead adherents of this approach, or at least everyone else, to the insight that also they conceptualize but at the same time as they confuse their conceptualization. The challenge is to explain that they confirm their conceptualiation in a paranoic circular method of conclusion, and that this conclusion is contradictory per definition.

The challenge is like explaining to a child that Santa does not exist. Cladistics is a mental desease by definition in adulthood. It is nice in childhood, but a mental desease in adulthood. Santa does not exist. He (she) can’t be found. I’m extremely sorry for this fact, cladists. I’m not, however, responsible for this lack, but just have to stop the vain search for him. There simply is no True Tree of Life to be found, because all possible candidates are contradictory. I do not like to destroy your belief, but have to stop the contamination of it. We all would liked it to have been a possibility, but, unfortunately, it is not.

The only remaining problem for cladistics is thus whether it is possible to “reconstruct” the null-hypothesis by classification of a classification, because a definition can’t, of course, change a fact of whether something is possible or not.

So, is it possible to “reconstruct” the null-hypothesis by classification of a classification or not? Well, the only possibility would be to classify the first classification exactly AS it, which, however, is a so narrow circular reasoning that the two classifications in fact is one and the same classification. All other possibilities result in a second classification that contradicts the first classification. The second classification simply has to contradict the first classification to be different from it. Classification of a classification can thus be only either the same or contradictory, independently of the null-hypothesis. The question thus includes two generically different questions: (1) whether the null-hypothesis can be found (“reconstructed”), and (2) if it can be found, whether it can be found by classification of a classification. The answer is thus that it does not matter whether the null-hypothesis can be found or not, it can in any case not be found by classification of a classification.

Cladistics’ construction of a classification system based on its axiom thus appears as an irrational moving of things in advance. It first have to explain away the facts that both rational reasoning and available empirical evidence contradicts (actually falsify) the possibility to “reconstruct” anything non-contradictory by classification of a classification.

Typology thus obviously does not solve the “problem” of the two aspects of reality: pattern and process. It merely defines that it does not exist, and denies that it exists, thus leading us into only contradiction. How on earth shall we now get rid of this stupid idea?