Biological systematics contains two different approaches: Linnean systematics and cladistics. So, what’s the difference between these two classificatory systems?
Well, the difference is that Linnean systematics assumes we that we decide the classes (traditionally called “nominalism), whereas cladistics instead assumes that we find the classes (traditionally called “realism”, but more correctly called “class-realism”).
So, why are these two approaches different? Why can’t they unite on a single system of classification (and much less on a single classification)? Well, the reason is that they do not share any feature at all, but instead are orthogonal to each other. This relation means that one (Linnean systematics) classifies the boundaries in the other (cladistics), and vice versa. The two approaches are thus different by relation – if one is right, then the other must be wrong. We can’t, obviously, both decide and find the same classes at the same time.
This conclusion intuitively appears correct, but it leads to the question what we actually do? Do we actually decide or find classes? The answer to this question is, however, ambiguous, since deciding classes leads into a fundamental ambiguity, whereas finding classes leads into a fundamental paradoxical contradiction. The answer is thus that “we” obviously both decide and find classes at the same time, although these two approaches are incompatible. We thus obviously enter the contradiction between the two approaches, although this contradiction can’t be solved.
So, what are our real options? Well, one of them (e, nominalism) is to accept a fundamental ambiguity in what we say about reality, whereas the other (ie, class-realism) is to accept paradoxical contradiction. Concerning biological systematics, these options thus mean that we have to choose between being ambiguous or paradoxically contradictory about reality. We thus can’t be both, but have to choose one of them.
The problem with the latter is that reality can’t be paradoxically contradictory, since it obeys to what we call “natural laws”. It leaves biological systematics with the Linnean systematics. This approach is furthermore internally consistent, which cladistics isn’t.
Cladistics thus appears to be a dead end, just as class realism is. Science n biological systematics has to take it on from there.