On the choice between the Linnean system of classification and Cladistic classification in Biological systematics

The difference between the Linnean system of classification (like Evolutionary taxonomy) and Cladistic classification in Biological systematics is actually fairly simple to understand. It resides in that classification as an orthogonal system, i.e., wherein each class consists of two orthogonal classes, has two logically consistent, but orthogonal lines of reasonings starting from either the bottom level (i.e., objects, therefore called Objectivity) or one level up (i.e., classes of objects, therefore called Subjectivity). Objectivity is ambiguous with respect to the classified (i.e., objects) and ends in a paradox (in this case called Russell’s paradox), whereas Subjectivity is consistently contradictory (i.e., with respect to both objects, classes and facts, and between assumption and deduction) and likewise ends in a paradox (here called the class clade). The two end points for the two lines of reasoning are actually one and the same point, namely the opposite to their orthogonal starting point, arriving to it from their respective orthogonal line of reasoning.

The problem for us to understand this difference is due to that an orthogonal system also is orthogonally 2-dimensional, that is, an orthogonal series (or orthogonal stack) of 2-dimensional planes, which is infinite. Such orthogonally nested dimensional structure can be simplified into a single 2-dimensional system in two different ways, which are consistent with each of the two orthogonal lines of reasoning respectively: orthogonally as in the Linnean system, which is consistent with Objectivity, and "flat" as in Cladistic classification, which is consistent with Subjectivity.

It means that the choice between the Linnean system of classification and Cladistic classification actually is a choice between being ambiguous with respect to objects (i.e., the Linnean system of classification) or being contradictory with respect to both objects, classes and facts, and between assumption and deduction (i.e., Cladistic classification). In this light, the choice between the Linnean system of classification and Cladistic classification appears fairly given.

Cladistic classification is different from a simple "flat" classification only in applying a consistently contradictory classification of classes. Its reference for this kind of classification to be "natural" is nothing but an appeal to the subjectivity in us all. Unfortunately, subjectivity in this version only leads to the Wonderland (i.e., where everything is up-side-down). Also unfortunately, cladists can’t understand this fact because they presume that classes are real.