Conceptualization and the contrary, ie, cladistics

We (humans) conceptualize the reality we perceive using a tool composed of three components: objects (aka entities), infinite classes (aka imaginary types) and finite classes (aka categories). We perform conceptualization by distinguishing objects and allocating them to finite classes using infinite classes. In this process, infinite classes functions as a catalyst for allocation of objects into categories. The only requirement of conceptualization is that we keep objects, infinite classes and finite classes consistently apart, because if we don't, then we confuse conceptualization itself by conflating them.

However, there is an inconsistency internally in conceptualization in the concept of "the finite class of all finite classes" (ie, the category of all categories) residing in the definitional fact that finite classes (ie, categories) are not single objects, but several objects, whereas the notion of "the finite class of all finite classes" is a single object consisting of several finite classes and thus both (ie, paradoxically contradictory between) an object and a finite class, that is, a single object and several objects. This notion is thus empty per definition by being both an object and a class at the same time, that is, a paradox (ie, Russell's paradox).

The German Nazi entomologist Willi Hennig did, however, turn this fact up-side-down by comprehending the finite class of all finite classes as "the only natural group". The problem with this comprehension is thus that it is inconsistent (ie, paradoxically contradictory). He (and others) may thus comprehend this "group" as "the only natural group", but neither he nor others can ever pinpoint this "group" without contradiction, because it is paradoxically contradictory per definition. If it hadn't been, then it could also have had an ancestor.

Willi Hennig and his followers (ie, cladists) obviously think that finite classes are real instead of objects, which leads them to conflation of "finite class" with "infinite class", and thus to conflation of conceptualization itself. Instead of conceptualizing reality, they, obviously, search for "the true" conceptualized reality, which in practice is their own conceptualization of reality, whichever it is, but paradoxically contradictory per definition.

This spin around the internal inconsistency of conceptualization can only be halted by considering what we talk about (ie, objects, like humans, or classes, like human).