If we want to divide all things of a particular kind, like “particles”, “species” or “butterflies”, into several subkinds, then there are two different (actually orthogonal) methods to achieve this goal. One is to partition the whole group into subkinds, then partition each of these kinds into subkinds, then partition each of these kinds into subkinds, and so on. The other is to join similar things of the kind into kinds, join these kinds into superkinds, join these classes into superkinds, and so on. The former thus starts with the kind itself and ends with all possible subkinds, whereas the latter starts with all things of the kind and ends with the kind itself.

Now, the fact that the former method doesn’t end with the things of the kind themselves, but with all possible subkinds of the kind, means that the two methods can’t reach the same division, since the number of partitions in them differ by one. The two methods are simply incompatible, actually orthogonally contradictory.

This fact did Carl von Linné understand, either consciously or unconsciously, and found out that the only way to to join these orthogonal methods consistently is to first partition the kind into two nested sets of kinds, one generic and one specific, whereafter the generic sets can be consistently joined into superkinds. Linné did thus find a solution of the inherent inconsistency of classification.

What this problem and solution tells us is that no question has an unambiguous answer, because in order to find the answer we have to classify, and classification is inherently either inconsistent or ambiguous.

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