The problem with classification is that it is ultimately paradoxically contradictory, as Russell’s paradox demonstrates. The solution to this problem is an orthogonal classification, like Linnean systematics, by making classification consistent.
The problem is fundamentally that classification cuts reality, and that it can’t cut reality consistently without cutting it both across and along, that is, acknowledge classes both in time and over time. “In time” means the classes we normally acknowledge, like bears and humans, whereas “over time” means classes that are continuities, like me today and me yesterday as one class, or, as in Linnean systematics, one species that is one genus. The “over time”-aspect of classification is often overlooked in classification by that classes “in time” are considered to also BE classes “over time”. It is just as if we in some moment turn from classifying things into finding classes of things, as if we in some moment turn from classifying into believing in classes.
This simple solution of the paradoxical contradiction of classification (ie, to also acknowledge classes “over time”) thus makes classification consistent by avoiding Russell’s paradox. This it does by avoiding the empty middle that is called Russell’s paradox by opening a route around it.
However, if we ask the question “which tree of life is the true tree of life” (like cladsts do), then we overlook this problem, Then, we don’t acknowledge the fact that classification is ultimately paradoxically contradictory but instead beg of an answer from the paradoxical contradiction. Instead of acknowledging the paradoxical contradiction, we thus ask what the paradoxical contradiction is. The answer to this question is thus simply: a paradox. The tree of life that is the true tree of life is simply a paradoxical contradiction.
The question “which tree of life is the true tree of life?” does thus lack a consistent answer, because the answer is a paradox. It means that those that are searching an answer to this question (ie, cladists) can search forever without finding an answer, because there isn’t any consistent answer to be found.