Realism (like cladistics) simply can't be correct, since it contradicts itself

Humanity is since the dawn of conceptualization split into two approaches in our discussion about reality:

1. the belief (i.e., axiom) that classes are real, therefore called realism, first formulated by the ancient Greek Parmenides, and

2. the axiom that single objects are real (and thus that classes are only inventions of our mind), called nominalism, first formulated by the ancient Greek Heracleitos (although his writings are largely lost).

These two approaches are the only possible approaches in conceptualization, since we can only assume as an axiom that either classes or single objects are real. The difference in their entrances to conceptualization means that they talk past each other although using the same terminology, since assumption in one of them is conclusion in the other, and vice versa. Their relation is thus of the kind that is called orthogonal, that is diametrically opposed.

In their logically consistent versions, each of these approaches has its particular ultimate set of conclusions, which thus are orthogonal. One of the ultimate conclusions of realism is that there must be a single true dichotomously branching consensus origin of all objects, i.e., a single true origin of classes, which realists call The True Tree of Life (the class clade), but which in nominalism corresponds to the ultimate conclusion that classification is contradictory, called Russell's paradox. Interestingly, this is a meeting point of realism and nominalism, although realism views it as a reality whereas nominalism views it as a paradox. It thus has the potential to test the two approaches against each other. If this thing (i.e., class clade or Russell's paradox) is real, then realism is correct, whereas if it is not real, then nominalism is correct.

The issue thus melts down to the question whether paradoxes are real or not. If they are real, then realism is correct, whereas if they are not real, then nominalism is correct. This question can also be tested empirically, but in this post, I content myself to conclude that if paradoxes indeed are real, which realism thus concludes, then "real things" may be contradictory, a conclusion that is difficult to evaluate, but which does at least allow us to conclude that such "real things" cannot be found unambiguously like in the realistic idea of a single True Tree of Life. The conclusion thus allows us to conclude that realism is contradictory: if there is a single True Tree of Life, then paradoxes can't be real, whereas if paradoxes can be real, then there can't be a single True Tree of Life.

The meeting point of realism and nominalism thus allows us to shed light on the contradiction of realism. Realism simply can't be correct, since it contradicts itself. Nominalism, on the contrary, does not suffer of any such internal consistency problems.