The task for biological systematics is to arrange all biological organisms in a single system.
Approaching this task, one first has to decide whether kinds are real (ie, shall be found) or our inventions (ie, shall be partitioned).
This decision is further complicated by that the former alternative ends in paradoxical contradiction (ie, that there isn’t any solution), and that the latter ends in ambiguity (ie, that all solutions are consistent).
Now, if one decides to believe that kinds are real, because one believes in the origin of the biodiversity by evolution, then this belief is inconsistent, actually paradoxically contradictory.
It is thus not inconsistent to not believe in evolution, but inconsistent to believe in evolution. The problem is that belief in itself is inconsistent. It does thus not matter whether you believe in a God or in Evolution, both are just as inconsistent. Only not believing is consistent.
The biological discipline called “cladistics” is not hypotetico-deductive but inductive (ie, a faith rather than a science and therefore more correctly called “cladism). It means that it is inconsistent, actually paradoxically self-contradictory (see Russell’s paradox). The fundamental component that makes it inductive is assuming that kinds are real, ie, can be found.
This fact means that the discipline in practice is “a vain search to define the indefinable”, as Charles Darwin expressed it. It’s end point is actually a paradox.
Language is the limit. What language can’t reach, we can’t reach.
The problem to solve in seeking an understanding of reality is not about reasoning in itself, but about finding a solution of the fact that the classification by language that underlies reasoning is either paradoxically contradictory or ambiguous depending on whether one assumes that classes are real or not.
Understanding reality is thus not about reasoning at all, but about finding a third way out of the dichotomy between paradoxical contradiction and ambiguity. The problem to solve is to find a position for classes between real and not real.
Understanding requires at least two assumptions, and delivers at least one conclusion (ie, the understanding).
The problem with this method is that the assumptions include classification (inherent in words) and thus that the fundamental assumption is whether classes are real (ie, can be found) or just our inventions (ie, mental abstractions). This assumption is thus hidden within the assumptions of the method (ie, within “understanding).
The problem with this hidden assumption is that neither of the two alternative options (ie, that classes are real or that classes are our inventions) leads to a singularity, but that the first leads to paradoxical contradiction and the latter leads to ambiguity. This problem means that “understanding” can’t reach unambiguity, or, in other words, that it can’t reach a single truth.
This fact (ie, that understanding can’t reach a single truth) means that the method will circulate around this empty middle forever. In this circulation, the inconsistent notion of a single truth will form the hub (or the God) for the religion that is called “rational thinking”. This fact is not a problem for mathematics, but it is an insurmountable problem for understanding.
The problem for rationality is to decide whether classes are real (ie, can be found) or our inventions, to reach a consistent rational understanding of reality. This problem is, however, just a warm-up for the next problem: that the former entrance ends in paradoxical contradiction, whereas the latter ends in ambiguity.
The insurmountable problem to reach a consistent understanding of reality is thus that reality in rational understanding is either paradoxically contradictory or ambiguous, or both. It dwells in the incomprehensible black hole between paradoxical contradiction and ambiguity. The truth is thus that we can’t reach a consistent understanding of reality. (So, don’t believe in a “Higgs particle” or a “tree of life”, both of these are faiths rather than rationality).
Philosophers have put forward the idea that rationality can free itself from reality and create a rational world separated from reality. The problem with this idea is that rationality is fundamentally paradoxically contradictory. If rationality had been consistent, then it could have created such a world, but since it isn’t, it can’t. Instead, rationality can only create consistent models of how reality works, not of what reality is. Rationality will thus always be second to reality.
This fact is why rationality can’t compete with belief. Both of them are fundamentally paradoxically contradictory.