Biological systematicians have searched a “natural” classification of life for about 2,500 years, without defining “natural”.
Evaluating how sensible this search is, leads into two diverging questions:
- How can we decide when we have found what we search if we don’t know what we search?
- Can we define a single thing?
The answer to the first must be that we can’t.
The answer to the second is that we can’t, for the simple reason that things and their properties are orthogonal (see Russell’s paradox).
The result of the evaluation is thus that the search is insensible. The first problem is that it is not possible to decide when it has found what it searches for, and the second problem is that it can’t find what it searches for. The word “natural” is obviously fundamentally inconsistent.
This result explains why biological systematicians haven’t found a “natural” classification in 2,500 years. The reason is thus not that such a classification is difficult to find, but that it is insensible to search. Instead, a consistent classification requires an orthogonal system of classification, like the Linnean system.