Classification (ie, conceptualization) offers only two possibilities: plain (like cladistics and particle physics) and orthogonal (like Linnean systematics).
Plain is the choice if one believes in classes, ie, think that classes are real, an approach called realism, whereas orthogonal is the choice if one does not believe that classes are real.
The difference between them is that plain classification only classifies things into classes, whereas orthogonal classification classifies things into categories of classes.
This difference means that plain classification is internally paradoxically contradictory, ie, ends in paradoxical contradiction, as demonstrated by Russell’s paradox, which cladists call “the true tree of life” and particle physicists call “Higgs particle”, whereas orthogonal classification is internally consistent but ambiguous in relation to the reality it classifies, ie, that there are infinitely many consistent classifications of this reality.
The problem with this fact is that it means there isn’t any single “true” classification. The reason is that among all infinitely many possible consistent classifications, there isn’t any that “can be real”, ie, isn’t any that is paradoxically contradictory. This statement captures the complexity of classification. It actually doesn’t matter “what” the context of classification “is” (eg, what reality “is”), classification still can’t “catch it” unambiguously. The rational door to heaven is simply closed.
This fact is the sinker for rational science as a religion, ie, as more than a practical way to handle reality. It explains that cladists’ “true tree of life” and particle physicists’ “Higgs particle” actually just are rational illusions. These “things” simply can’t be found, because they are both contradictions and contradictory. True is that they must be real for reality to be rationally comprehensible, but unfortunately they can’t be, and would moreover leave reality incomprehensible if they could. As I stated above, the rational door to heaven is simply closed.