The difference between cladists and non-cladists in biological systematics

Assuming that there is a single True Tree of Life means that there are two different ways to classify the entities of this tree (ie, species) using their properties:

1. in a (multidimensional) rectangular (Cartesian) coordinate system, or

2. in a (multidimensional) polar (like HSV) coordinate system,

because only these two orthogonal coordinate systems avoid the inherent contradiction in classification (ie, Russell’s paradox).

The fact that these two coordinate systems are orthogonal means that they can be converted into each other using n (ie, all) properties of the rectangular system, and n-1 transfomed properties plus one property specifying the overall strength of all properties of either system of the polar system (like the RGB values of the rectangular RGB-coordinate system and the alfa and beta values plus the V value of the polar HSV-coordinate system for colors).

The Linnean system for classification of such assumed “species” is a classification of the rectangular (Cartesian) kind. A polar system for classification of such assumed “species” remains to be invented.

The reason for the fact that there are two orthogonal coordinate systems to choose between is that classification is inherently contradictory, because there are always two orthogonal ways to bypass contradiction – to the left or to the right, above or under, etcetera. The flopping (ie, triangulating) property between these two systems is that they are ambiguous as to whether the total number of properties is even or odd, given that it is larger than 1 (in which case the polar system is inapplicable).

The new classification of such assumed “species” called cladistics (ie, classifying them into “clades”) is actually both a confusion of these two orthogonal systems of classification and a simple (thus inherently contradictory) classification at the same time. As such, it actually demolishes the Art of Classification by over-simplification. The problem it encounters is the inherent contradiction of classification, that is, Russell’s paradox, meaning that it can’t find a single consistent classification because there is none to be found. It is thus actually a setback for the Art of Classification using a general confusion of classification by classification, leaving us with infinite recursion. The class “clade” thus functions as a catalyst demolishing what we have accomplished in the Art of Classification.

So, assuming that there is a single True Tree of Life means that there are two orthogonal ways to classify this Tree, rectangular and polar, which cladistics confuses. The disagreement between cladists and non-cladists in biological systematics is thus not between whether there is a single True Tree of Life or not, but between whether such a True Tree of Life can be classified unambiguously or not. Cladists believe (actually claim) that it can, whereas we, non-cladists, merely can explain that it can’t.

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