The most read of my posts is “The fundamental difference between Linnean and cladistic systematics”.
At this point (after all my posts), I think I can simplify this difference into that cladistic “systematics” actually is not a systematics at all, but rather plain classification of classes in classes. As such, it is ultimately paradoxically contradictory, which Russell’s paradox demonstrates, meaning that every possible solution (ie, every “tree of life”) is paradoxically contradictory. It is simply impossible to merge things (ie, “species”) with properties without running into a paradoxical contradiction.
Linnean systematics, on the contrary, is a systematics by classifying things into categories (ie, genera, families and so on) of classes (ie, species). It is actually an orthogonal system. The advantage with this kind of system is that it is consistent, ie, free from contradictions, meaning that every particular such system is consistent. This consistency is achieved by that categories are finite per definition, which reality also is, but classes aren’t.
The problem for biological systematists with this difference is that there is nothing between these two “systematics”, that is, no single consistent system of classification (ie, “true” system) among only inconsistent systems (ie, “false” systems), which realists among biological systematists assume there is as an axiom. The problem is thus that the difference shows that these realists simply are fundamentally wrong.
So, what do you think that these realists do when they are confronted with this fact? Rethink? No, no. They refrain to claiming (asserting) that there indeed is a single consistent system of classification (ie, “true” system) among only inconsistent systems (ie, “false” systems), ie, “a true tree of life”, although Russell’s paradox demonstrated that there isn’t any already in 1901. They are so blinded by their erroneous axiomatic assumption, thus actually a belief, that they can’t rethink even when the paradoxical contradiction is staring them in the eyes. There is simply no way to make them rethink, because their belief makes them prepared to abandon both facts and sense.
This behavior of realists in biological systematics actually displays the nature of belief. It starts as realism (ie, oversimplification) and continues via an abandoning of first facts and then sense. And, there is no other way than battle that the rest of us can stop this process, because there are no other means than facts, sense and ultimately battle.
This difference can be boiled down into the question: which is fundamental – difference or similarity? – which realists like cladists answer with “similarity”, but which can only be answered consistently with “difference”, since similarity requires difference, whereas difference doesn’t require similarity. It means that in the middle of everything there is a fundamental difference.