Cladistics looses itself in the fogs of simplicity

When we classify reality, there are only two aspects we have to keep consistently apart: reality and the abstract (ie, object and class), to keep reality and our perception of it consistently apart. In doing so, there is one aspect we misses, the middle. There simply is no place for a middle between reality and our perception of it. It means that classification can't pinpoint reality unambiguously.

If we, like cladists, instead claim that classification indeed can pinpoint reality consistently, then we actually claim that there is no difference between reality and the abstract, and thus that there is a middle between reality and the abstract.

If there indeed is a middle between reality and the abstract, then there is no reason to partition our perception of reality into reality and our perception of reality, and thus that reality is what we think it is.

If reality is what we think it is, then the question is: what who thinks it is? We can, obviously, disagree about both what reality is and what history is, so which comprehension is correct? If the answer is the most parsimonious comprehension, then the most generalizing perception is right. The notion thus turns simplicity into a virtue. Knowledge is in this approach only a burden. The boldest painting of reality in only black and white wins. The approach thus looses itself in the fogs of simplicity.   

Fundamental facts about classification and systematics (and cladistics)

Bertrand Russell showed 1901 that classification is paradoxically contradictory, ie, internally inconsistent, see Russell's paradox. This inconsistency is immediately due to that classes contain two kinds of classes: finite classes (ie, objects and categories) and infinite classes (ie, abstract types). The reason is that each finite class must correspond to an infinite class (ie, that each real class must correspond to an abstract class), that is, that there must be a one-to-one correspondance between finite classes and infinite classes, because it means that the total number of classes must be even, which, in turn, is impossible, since the relation between finite classes and infinite classes is orthogonal (ie, diametrically opposed), and that their numbers thus differs with one, because it means that their total number always is odd. It is thus impossible to obtain a one-to-one correspondance between finite classes and infinite classes in classification. The situation is like putting a puzzle where the last piece always is redundant.

However, using an orthogonal system of classification (ie, classifying objects into finite classes of infinite classes), like the Linnean system, transfers this internal inconsistency into a an ambiguity between classification and the classified. It means that such system, on the contrary, can't be inconsistent, ie, that every possible such system is consistent. The reason is that the numbers of finite classes and infinite classes in such system differs with one, because it makes their total number odd per definition, which neutralizes the paradoxical contradiction (ie, internal orthogonality) in classification.

These two kinds of classifications are the only kinds of classification there are. It means that the cladistic idea "a single true tree of life" is inconsistent per definition, since it requires that classification is consistent. If we, like cladists, don't acknowledge the fact that classification is inconsistent, but instead erroneously claim that classification can be consistent, then we actually just transfer the inconsistency of classification into our own heads (into our logical reasoning), thereby turning us, ourselves, inconsistent, (if we weren't before) like cladists are.

This internal inconsistency of classification can we not get rid of, but can only transfer into other positions, ie, to between classification and the classified or to our own heads, because it is fundamentally due to, or is the reason for, the ever-changing nature of reality. At this fundamental level it is impossible to distinguish cause from effect. (This, in turn, may be due to that cause and effect are orthogonal, and that a beginning actually is lacking. If so, change just follows the tracks it is bound to follow, but according to certain principles. Principles rule, but they continuously conflict, and the result is a compromise. A beginning is in any case impossible to invoke without transferring the inconsistency of classification into our own heads, ie, to our logical reasoning).

Conceptualization (classification) is a tool that can only be ambiguous or paradoxically contradictory

Conceptualization (classification) is a tool that can only be ambiguous or paradoxically contradictory. It is ambiguous in relation to the classified if it rests on the axiom that objects are real (ie, objectivity), and it is internally paradoxically contradictory if it rests on the axiom that concepts (classes) are real (ie, subjectivity).

It means that we can't say something that isn't ambiguous or paradoxically contradictory, ie, unambiguous, at all. The question whether there is a single truth to be found or not does thus have the answer no, simply because it is impossible using the only tool we have.

The reason for this answer is, however, not the tool itself, but that unambiguity is an impossibility (ie, a void) in a changing world. There's nothing wrong with conceptualization (classification) itself; it just can't create the single truth we want. It is still a very useful tool if we use it consistently, that is, resting on the axiom that objects, not classes, are real. Using it resting on the axiom that concepts (classes) are real, like cladistics, is actually a misuse of it. Science is, as also cladistics indeed claim, a practice to optimize the fit between our models of reality and reality itself, but we have to remember that optimization always is second to reality itself, on the contrary to what cladistics claim. There is no reason to assume that reality itself is optimized. Instead, optimization must always be a matter of optimizing the fit between our models and the facts of reality, as traditional science does, not optimizing the models themselves, as cladistics does.

We must, however, abandon our paradoxically contradictory idea that there is a single truth, like The Tree of Life, to be found, and instead acknowledge the fact that there isn't. Understanding is superior to belief in painting reality, because it does in any case close up on the most accurate painting of reality. Painting reality is moreover not only a matter of black and white, but of Plato's three-folded division in his geometrical (or mathematical) atomism, wherein perfection is ultimately reduced to geometry (ie, to the world of ideas), which we today know is paradoxically contradictory (ie, Russell's paradox). However, this world is thus not a perfect reality of forms, as Plato claimed and cladists claim, since it is paradoxically contradictory, but instead a paradoxically contradictory mind construction which ultimately depends on the real, but changing, objects.

Conceptualization (classification) is thus a tool that can help us understand reality, but it can't produce a single truth. The belief that it can, ie, cladism, is indeed visionary, but wrong. It does thus not lead to a single truth, but only to a conceptual mess. If we want to keep thoughts clear, we have to abandon vision and accept facts, for example that conceptualization (classification) is a tool that can only be ambiguous or paradoxically contradictory. It is perhaps sad, but a fact. 

On classification and the cladistic idea of a "true tree of life"

1,a Classification of objects (ie, entities, like you, me, a cell and a mitochondrion) is ambiguous, because every object can be assigned to at least two classes of objects.

1.b Classification of classes of objects (like classes of biological organisms, eg, humans, cells and mitochondria) is contradictory, because every object of a class is contradictory between at least two classes of objects.

2,a Classification of classes of classes of objects (like Linnean genera) is ambiguous, because every class of class of objects can be assigned to at least two classes of classes of objects.

2.b Classification of classes of classes of classes of objects (like the different Linnean genera) is contradictory, because every class of class of class of objects is contradictory between at least two classes of classes of objects.

3a Classification of classes of classes of classes of classes of objects (like Linnean families) is ambiguous, because every class of class of class of objects can be assigned to at least two classes of classes of objects.

3.b Classification of classes of classes of classes of classes of objects (like the different Linnean genera) is contradictory, because every class of class of class of class of objects is contradictory between at least two classes of classes of classes of objects.

And so on ...

In this scheme, we can see that there are two principally different components of classification: objects and classes. We can also see that each of these components occurs at every second level of a classification into more inclusive classes (ie, objects in 1.a, 2.a and 3.a, and classes in 1.b, 2.b and 3.b), and that objects consistently are ambiguous between their classes, whereas classes consistently are contradictory between their classes, and that the classes of objects are the same as the classes of the classes (ie, 1.a and 1.b, 2.a and 2.b and 3.a and 3.b). This fact is just a consequence of the two facts that every object can be assigned to at least two classes, and that every class is contradictory between at least two classes, whereof "can be assigned to" ultimately equals "is contradictory between", because the relation between object and class is orthogonal. The relation between object and class is simply both ambiguous and contradictory at the same time.

The scheme thus paints the practical picture of the orthogonality of classification. This orthogonality means that classification itself neither can be "true" nor can contain the "truth", because it is fundamentally orthogonally circular. Its output totally depends on its input. There is a saying that "shit in", "shit out", but in this case it is rather "anything in", "the same thing out", but always contradictory. Every particular solution simply points at another solution. Consistency (ie, not pointing to another solution) can only be found using an orthogonal system of classification (like the Linnean systematics), consistently keeping objects and classes apart.

The question whether this means that there isn't a single true tree of life (to be found) has the answer that it depends on whether this hypothetical tree is orthogonally consistent or not. If it isn't, then there isn't, whereas if it is, then there is. If the classes that every object "can be assigned to" actually equals the classes that every object "is contradictory between", then there is indeed a true tree of life, but if thy don't, then there is not a true tree of life. The existence of a true tree of life does thus depend on the actual history of life: if the history of all included classes are congruent, then there is a true tree of life, but if they aren't, then there isn't. The probability that there isn't is, however, vastly larger than the probability that there is. A true tree of life actually requires a multiple of two entities, which have a totally symmetrical origin, and wherein all properties also are totally consistently distributed. The probability of such a tree is almost zero.

The probability that there is a single true tree of life is thus almost zero. Moreover, if there indeed should be one, then our fundamental partitioning of reality into objects and classes, and thus the foundation for this tree, should be wrong. If cladistics should be right, then all of us, including the cladists, thus should be wrong.

Cladistics is thus a huge problem for science. How do we get rid of it? How can we explain that it is impossible, ie, a vain serch to define the indefinable, as Darwin called it?

  

  

On the barrier between us and a single truth

The fundamental problem for classification is that it is paradoxically contradictory between in time (ie, class) and over time (ie, continuity), just like entity (object) displays two different aspects: pattern and process. It means that the two different aspects of entity (object) correspond to the paradoxical contradiction for classification. The two aspects and the paradoxical contradiction are thus actually two aspects of the same paradox, ie, an interface between them, which is called Russell's paradox.

This paradox is thus the core of classification. It is what we end up in when we search the truth in classification (like cladistics does). It is also the barrier between us and a single truth, because without a single non-contradictory classification we cannot, of course, find a single truth.

The idea of a single truth (ie, a single True Tree of Life, or single consistent system) will thus forever be hidden behind a fundamental paradoxical contradiction in classification. If this means that the idea is wrong depends on how we define "wrong". A more suitable word appears to be "impossible". A single True Tree of Life, or single consistent system, is simply impossible. It is, actually, an unreachable state between reality and our classification of it, which is consistently classified using an orthogonal system like the Linnean classification. Such system thus touches a single Truth, but, unfortunately, just as one aspect of it. The single Truth remains hidden behind the fundamental paradoxical contradiction in classification, called Russell's paradox.

Cladistics may claim that matters are the other way around, that is, that the idea of a single truth (ie, a single True Tree of Life, or single consistent system) is within reach, but it can't change the fact that it isn't. It can only lure people into a vain search for it. An unwanted understanding can be suppressed by an irrational wish, but can't be conjured away. In the long run, we must accept also unwanted facts, because striving for impossibilities is vain.   

Cladists have really stuck in an infinite loop

The fact that classification is orthogonal, ie, that every single class contains at least two classes, means that it has to be arranged orthogonally, ie, classifying entities into categories of classes, as in the Linnean system, to avoid the inherent contradiction of an orthogonality (see Russell's paradox).

However, such orthogonal system of classification is ambiguous in relation to the classified per definition, since it actually consists of two orthogonal classifications.

The approach in biological systematics called "cladistics" simply ignores this fact (ie, that classification is orthogonal) instead entering the inherent contradiction of an orthogonality (see Russell's paradox) while asserting (actually defining) that it, ie, the contradiction, indeed is real (ie, can be found). In this approach, ie, assuming that the contradiction is real, it is actually an infinite recursion, ie, an infinite loop. But, how can cladists possibly understand that they have entered an infinite loop when they don't understand that classification is orthogonal in the first place (actually not even that they classify)? No, they have indeed stuck in this infinite loop.

On the limits for classification (and the practical impossibility of cladistic classification)

The fact that classification is orthogonal, ie, that every single class contains several classes within every single set of entities (eg, the class "primates" and all different classes of primates), and that finite class thus is orthogonal to infinite class, means that classification is fundamentally contradictory between single and several, since orthogonalities are contradictory between single and several per definition. Cladistic classification accepts this contradiction, ie, accepts being contradictory, by equalizing the concepts finite class and infinite class.

The only way to avoid this orthogonal contradiction, ie, to achieve consistency, in practical classification is to use an orthogonal system of classification, classifying entities into categories of classes, like the Linnean system, in order to thereby keep finite classes and infinite classes (ie, the orthogonal concepts finite class and infinite class) consistently apart. Such orthogonal system of classification is, however, ambiguous in relation to reality per definition, simply by keeping the orthogonal concepts finite class and infinite class) consistently apart.

It means that classification can only be either internally contradictory or ambiguous in relation to reality. The fundamental reason for this impossibility to achieve unambiguity is that classes can't be (and thus aren't) real per definition, but can only be (and thus are) an artificial invention.

On the black hole for classification called "cladistics"

The class clade is an infinite recursion that you enter when you conflate infinite class with finite class, ie, type with set, that is, when you don't "see" your own typification and subsequent categorization, and thereby can't distinguish them.

Conflation of these for conceptualization so fundamental concepts makes you turn Russell's paradox, ie, the fact that set theory leads to contradiction, up-side-down into the comprehension that contradiction instead is consistent, ie, forming a consistent class, that is, the class clade.

This comprehension is ambiguous between being correct in that clade is a consistent infinite class, but wrong in that clade is a consistent finite class, thus forming an infinite recursion between consistent and inconsistent, ie, a consistently inconsistent infinite loop, which you can't see because you're in it. Instead, you're convinced that there is a consistent solution at the end of this infinite recursion, which there thus isn't per definition.

Cladistics is thus a black hole in conceptualization that you enter when you conflate infinite class with finite class, ie, when you don't "see" your own typification and subsequent categorization, and thereby can't distinguish them. You simply don't know what you're doing.

The correct understanding of Russell's paradox is that classification is ultimately contradictory. This fact also means that process can't be classified consistently, ie, that there are always more than one consistent classification of a single process, because continuity is indistinguishable from class. Consistent classifications, in turn, can we only produce using an orthogonal system of classification, like the Linnean system. Instead ignoring Russell's paradox leads into an eternal orthogonal merry-go-round between inconsistent (contradictory) classifications, because it is infinitely recursive (per definition). Russell's paradox is thus a fact we need to relate to, not something we can ignore or a solvable problem. It is fundamentally due to the unavoidable fact that classification is orthogonal.

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.