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.