The fundamental problem is that conceptualization offers two alternative entrances: starting with the axiom that objects or classes are real, respectively. Now, these two entrances were shown to lead to the logical end points the ancient Greeks Heracleitos and Parmenides described, respectively, none of which is practically useful for explaining the reality we perceive. For this reason, the ancient Greeks developed a compromise conceptualization between these two entrances, leading to the approach called atomism, and which was formulated by Aristotle in terms of generics, specifics and specific differences. They thus fused the two possible, but practically useless, alternative entrances to conceptualization into a practically useful compromise conceptualization. This compromise has to rest on the axiom that objects are real to be logically consistent, because otherwise it is consistently inconsistent, that is, contradictory. BUT, it also has to accept the fact that objects can’t be real, because they are infinitely divisible. The compromise thus allows us to discuss reality consistently and unambiguously at the expense of allowing reality to be ambiguous, that is, giving up the idea that reality can be both consistent and unambiguous. Among the choices we had then and still have, this was the choice the development of conceptualization among the ancient Greeks led to.

Understanding of how cladistics confuses concepts and why this confusion is contradictory thus requires keeping track of both the two possible entrances to conceptualization and the useful compromise we use today. Our way of expressing and discussing reality today thus rests on the compromise conceptualization the ancient Greeks invented.

Now, Carl von Linné extended this compromise conceptualization to hierarchical relationships between objects (or entities). He thus discovered the consistent conceptualization of hierarchical relationships. This is why his seemingly simple system appeals to us so much. It is simply consistent (although ambiguous with regard to reality).

Linné’s system inspired both Darwin and many other biological historians into the thought that biological organisms have originated from a single primordial form, but they just couldn’t figure out either whether this idea is a conclusion or an assumption, or how to illustrate such origin consistently. Finally, Darwin was more or less forced to publish his idea together with the best illustration he could come up with, that is, as biological species originating by dichotomous splitting. This illustration is, however, incompatible with the compromise conceptualization by assuming as an axiom that classes are real (ie, the class biological species), because the compromise assumes as an axiom that objects, or entities, are real, not classes.

At this point, the reasoning begins to get complicated. If biological species are entities, then the illustration has to be consistent although it is incompatible with consistency, which is impossible. So, wherein resides the inconsistency? Well, the inconsistency resides in that biological species can’t be entities if single objects (ie, organisms) are objects, because biological species are the opposite to single objects per definition (ie, in the compromise conceptualization). It is thus inconsistent to assume that both biological  species and organisms are entities at the same time. The two assumptions is simply not up, not compatible, inconsistent.

This problem was left hanging for about 100 years, when Willi Hennig suddenly claimed that it is time to accept Darwin’s illustration (not in a scientific article, but in a book), that is, to accept its inconsistency between organism and biological species. The problem discussed in this blog post is thus to explain how this “acceptance” (today called cladistics) confuses concepts and why this conceptual confusion is consistently inconsistent.

The explanation resting on the explanations above is that Hennig’s ”acceptance” confuses concepts at a fundamental level by equalizing the generic with the specific, thus rewinding the compromise conceptualization to the logical end point of assuming as an axiom that classes are real as Parmenides described, which is consistently inconsistent by denying change, that is, also denying all facts we have derived since then using the compromise conceptualization, among others, the fact that time is relative to space. Hennig’s ”acceptance” does thus actually take us back about 2,500 years to the prescientific development of conceptualization, to the inconsistent entrance to conceptualization assuming as an axiom that classes are real.

The fundamental problem for biological systematics is that there isn’t any unambiguous generic description of evolution to be found, because the specific descriptions differ, and that the generic can’t be fused, but only consistently compromised, with the specific, which is accomplished using an orthogonal system of the Linnean kind. We simply can’t come closer with a classification of a hierarchical relationship to the hierarchical relationship than with an orthogonal system of the Linnean kind. The hierarchical relationship can’t be turned into a class (actually a set), because it leads into an infinite regression, ie, a paradox (like all belifs do). This paradox was described by Bertrand Russelll and is today called Russell’s paradox. It is just as impossible for us to find a True Tree of Life as it is for reality to find an end.

Instead, cladists denies this kind of factual relation, claiming (asserting) that the class clade makes this distinction redundant by organizing all entities (ie, all clades) into clades. They thus assume that clades are real as an axiom, thus being possible to organize into clades. But, we have to have something to start with and where can we find clades? I have, at least, not seen any clade in my life. Have you? Have Steve Farris? Have Gareth Nelson, Malte Ebach, Kåre Bremer, Jim Carpenter, Per Sundberg, Mikael Härlin, Diana Lipscomb, or any other cladist? If so, can anyone of them (or any other cladist) show me one (in reality, I mean)?

As far as I can see, cladistics is nothing but a paranoic circularity starting with clades and ending with clades in an eternal merry-go-round without any attachment to reality. Everyone of us can thus choose any entrance to this merry-go-round and come out of it with the same classification as we entered it with. The criterion cladists call parsimony is nothing but self-confirmation, ie, the most parsimonious solution given my entrance is my entrance.

Can a situation be more absurd? These people (ie, cladists) have furthermore occupied leading positions in Swedish universities THANKS TO this paranoic reasoning. Haven’t something gone terribly wrong? Are these people really good models for our kids or good decisionmakers for the public? What are their qualities (apart from having a tendency for paranoia)?

(In Swedish “kladda” means messing things up. Cladism does thus in Swedish, ie, “Kladism”, “kladdar” things up. It consistently confuses concepts by defining them by conjunction (ie, as synonyms), thus ultimately “kladdande” (messing up) all concepts. It thus gives a face to confusion).

Carl von Linné found the system that keeps this balance in classification of hierarchical relationships (also used in evolutionary taxonomy), whereas Willi Hennig fell into the side of belief (where every possible solution thus is contradictory). Linné believed in God, whereas Hennig believed in classification.

(Evolution isn’t a matter of belief, just as change isn’t, but of understanding, which Darwin understood).

It means that classification has to be divided into two levels (like in the Linnean system of classes in categories), because classification on a single level (like cladistics) is contradictory by attempting to fuse orthogonalities.

This does not mean that classification on a single level is impossible, on the contrary, such classification can be done in as many ways as the number of entities permit, but it means that every possible such classification is contradictory with respect to the properties of the entities. This, in turn, means that there isn’t any single most parsimonious such classification to be found, since it would mean that entity and class are not orthogonal, which they are. A single most parsimonious such classification (by cladists called The Tree of Life) is thus a definitional impossibility, that is, a pie in the sky.

Cladistics is thus the approach that attempts to solve the problem (problem for typologists like cladists, but actually a fact) that entity and class are orthogonal. It moreover appears to believe that it already has solved the problem (ie, fact) by simply denying it, when the truth is that it just has opened a route into a practical chase for this pie in the sky. It has also been successful, since a majority of biological systematists appear to be hooked on this bait today. A neutral observer has to conclude that biological systematists obviously have freaked out, but he will just be met with silence. There is no cladist out there today that is ready to defend cladistics in public, although there are lots of them chasing this pie in the sky, all of them getting paid for this vain chase by mecenates who do not understand better. In this sense, it is also a major fraud.

Can it get more absurd?

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.