On classification and cladism

The major problem to understand classification (conceptualization) is that it is three-dimensional. Two of the dimensions are due to that there are classes of classes, and the third is that classification “hangs” between reality and abstraction. 

The first two dimensions mean that classification is inherently ambiguous (i.e., that the concept class includes two incompatible classes), which are traditionally distinguished as class and category. The difference between them is just that a single of each contains at least two of the other (i.e., that their relation can be described by the formula X/Y=Y/X).  

The third dimension is more difficult to understand. The fact that it has “one foot” in reality and “one foot” in abstraction means that it is abstract from a reality’s pont of view, real from an abstract’s point of view, and both abstract and real from an objective point of view. This relation can, however, also be regarded as an ambiguity, here between reality and abstraction, where both (i.e., objectivity) corresponds to either class or category, reality corresponds to either two classes or two categories, and abstract corresponds to either two classes or categories (if reality corresponds to two classes, then the abstract corresponds to two categories, and vice versa).

The first two dimensions are thus orthogonal (i.e., diametrical) to each other, and the third dimension is orthogonal to the first two. This nested orthogonality is actually typical for members of the concept  dimension. Dimensions are orthogonal in order.

This ordered (nested) orthogonality is the most difficult in classification to understand. In principle, it means that dimensions are compatible between every other level, but (totally) incompatible between adjacent levels. Assumption on one level is deduction on an adjacent level, and vice versa. Logic merely traverses the ordered (nested) orthogonality of classification consistently (that is, every other level to where it started from). It can be analogized with only using even or odd numbered dimension numbers.

The starting point for logic reasoning is decided by its fundamental axiom. This offers two choices: that objects exist or that classes exist. Starting from the axiom that objects exist means that it enters classification in one dimension, that is, in classification itself, wheras starting from the axiom that classes exist means that it enters classification with classes, and thus that it ends up one dimensional level out of order. It means that starting with the axiom that classes exist leads into a logical reasoning where every concept has the opposite meaning as in a correct entering into logical reasoning.  The entering into logical reasoning is thus crucial in that it has to get object and class right. Calling object class and class object merely turns the meanings of concepts up-side-down. The reasoning is the same; it is only dressed in contrary concepts.

These properties of classification means that an unambiguous classification of reality is impossible per definition. The orthogonality between the even and odd numbered dimensions cannot be traversed. This fact is acknowledged by the Linnean classification, but not by the Hennigian cladification. The difference between them is thus that the Linnean classification does not try to find a classification that cannot be found, which the Hennigian cladification does. Hennigian cladification thus tries to catch the carrot in front of the donkey’s eyes.