Realists (like cladists) discuss the built-in contradiction of conceptualization as if it is mystery, see for example Wikipedia’s discussion about what William of Ockham “really” was, ie, a “nominalist”, “conceptualist” or “terminist”. It isn’t. It is an extremely clear-cut issue. We just have to keep concepts consistently apart to understand it.
A single concept is an ambiguity between infinite class (ie, class or type) and finite class (ie, set). However, the fact that a single class contains several classes, like how the class chair contains several kinds of chairs, means that the concept class is contradictory between one and several, ie, is neither one nor several. (Realists have a tendency to interpret this “neither nor” as a “both and”, although nothing can clearly be both one and several at the same time. A single thing is a single thing and several things are several things). In summary, a single concept is an ambiguity between infinite class (ie, class or type) and finite class (ie, set), both of which are contradictory between one and several. A single concept is thus internally both ambiguous and contradictory.
This situation is impossible to solve both consistently and unambiguously, since both infinite class and finite class are contradictory. One of them, ie, either consistency or unambiguity, has to yield. The situation only has two possible solutions: to (1) adopt the axiom that a single object is a single object (ie, objectivity, or nominalism), or (2) adopt the axiom that an infinite class is a single infinite class, and thus that a single concept is a single concept (ie, subjectivity, or realism). The former means that a single concept is internally both ambiguous and contradictory, which agrees with facts, whereas the latter means that a single concept is both consistent and unambiguous, which thus both is contradictory and contradicts facts. The former is thus consistent, whereas the latter both is contradictory and contradicts facts.
Having come this far, we can begin discussing reality in an objective (ie, nominalistic) approach, because it does at least prevent us from contradicting ourselves. This objective (ie, nominalistic) approach was clearly explained by Aristotle about 2350 years ago, and extended hierarchically by Linné about 300 years ago. The built-in contradiction of conceptualization is thus not a mystery, but has been consistently solved by Aristotle and Linné.
Realists’ (ie, cladists’) confusion of object and class, leading to the realistic entrance to their contradictory and contrafactual “solution” of the problem does thus not solve this problem, but only denies it, instead acknowledging contradiction and contrafactuality. It obviously appears as a magic solution of the problem to realists (ie, cladists), but this is just in a generic sense. There is no specific consistent and unambiguous solution of this problem to be found, not even in a contradictory and contrafactual approach.
