Willi Hennig’s idea, ie, cladistics, is, to say the least, peculiar

The fact that classification is orthogonal,that is, that every class include other classes, means that classification is inherently contradictory and that classes thus have to be arranged hierarchically differentiating classes from their included classes to avoid contradiction, which science traditionally does using classes (infinite) and categories (finite).

Cladists, however, don’t even see the contradiction in this fact, because they assume that classes are real and thus interprets this fact as merely a truism, ie, that classes consist of classes.

The fundamental question in this disagreement is thus whether the fact that classes include classes is a contradiction or not? The answer is that it is a contradiction, because the fact that classes can be both infinite, ie, types, and finite, ie, sets, means that the class class includes both the class infinite class and the class finite class, which are not equal (nor have a one-to-one correspondance), and that the class class thus is contradictory per definition. The fact that classes include classes is thus a contradiction.

How come, then, that cladists don’t even see this contradiction? Well, it’s because they conflate infinite class, ie, type, which we discern by classification, with finite class, ie, set, which we distinguish by categorization, because they thereby think that they see finite classes, ie, think that they don’t classify anything. Instead, they think that finite classes actually exist, ie, are real, and that they thus merely discern “natural groups” (of classes, but in their perspective of anything, that is, any class or classes or whatever).

The fact that classification is inherently contradictory does, however, mean that hierarchical relations between objects (or between entities of any kind) can’t be classified unambiguously, but only either ambiguously with respect to objects (or entities of whatever kind) using a hierarchical classification, as the Linnean system, or contradictory using a “flat” classification, as the class clade in cladistics. There isn’t any unambiguous classification of this kind of process to be found, neither in two dimensions nor in n dimensions, because it requires that classification isn’t inherently contradictory, which it, on the contrary, is. Many problems can be solved, but not the problem that requires that the matter isn’t what it is, in this case that classification isn’t inherently contradictory.

The class clade is interesting by being the orthogonal opposite to single objects, thus conflating the two aspects of single objects, that is, process and pattern, by giving the class an interesting general significance. It thereby reveals that there indeed is a class that is just as impossible as single objects are possible, thus revealing that the orthogonality of classification not only means that classification has to be either ambiguous with respects to objects or contradictory, but that it also can be paradoxically contradictory.

This kind of paradoxical contradiction was not, however, discovered by Willi Hennig in the 1950-ies, but by Bertrand Russell in 1901 following the discoveries of Georg Cantor (ie, the diagonal argument), and it is traditionally called Russell’s paradox in science. The difference between Bertrand Russell and Willi Hennig is that whereas Russell comprehended it as an abstract paradox, Hennig instead comprehended it as a real paradox (thus devising a method to look for it).

Fact in the matter is thus that classification is orthogonal and that there therfore is a paradoxical contradiction to be found in classification, which objective science calls Russell’s paradox and subjectivity calls the class clade, that actually is the interface between objective and subjective classification. The difference between objective science and subjectivity is that whereas objective science views it as an abstract paradox, subjectivity instead looks for it by analysis. Objective science thus views the same thing as subjectivity views as a reality as a mind ghost. And, as explained above, objective science is right. Russell’s paradox (ie, the class clade) is a mind-ghost.

Willi Hennig’s idea, ie, cladistics, is thus, to say the least, peculiar. Hennig may have been a child of nazistic typology, but how could he gather followers from the 1960-ies to this day? Is typology a fundamental property in humans? Can a majority of us not liberate ourselves from prejudices, although the paradoxical contradiction of this approach stares us in our own eyes? Can we not liberate ourselves from our prejudices, but instead have to do our best to make an approach of them. Cladistics has no more eligibility than nazism has. Both are just as typological. God save us from both cladists and nazists.

Another contribution to understanding of conceptualization http://menvall.wordpress.com/

Read more at Menvall’s Blog: change on different levels