Many systematists (eg, cladists and particle physicists) search for a “natural” classification.
The problem with this search, however, is that “classification” is artificial per definition, and that the expression “natural classification” thus is a definitional contradiction. Such a thing is both “natural” and “artificial” at the same time per definition, although one excludes the other per definition. If such a thing indeed could be found, then we would not be able to distinguish it in any case, because we would not be able to distinguish it from “artificial” classifications.
This problem means that there are more than one “natural” classification per definition. Exactly how many such “natural” classifications there are depends on how many many consistent classifications of the included things there are. The reason for this fact is that a “natural” classification has to be consistent, and that there is no way to distinguish between different consistent classifications. The number of consistent classifications may be reduced by “parsimony” (ie, preferring simpler alternatives), but can’t be reduced to one, because every imaginary such solution is contradictory per definition. Instead, there must always be more than one “natural” classification.
The search for a “natural” classification (eg, cladistics and particle physics) is thus vain. Charles Darwin expressed this vanity as “an indefinite continuation to define the indefinable”.
(Recently, Peter Higgs was awarded the Nobel Prize for the formulation of the “natural” classification in particle physics, because particle physicists claimed to have found this classification, which, thus, is wrong per definition. If it indeed is right, then it falsifies itself by falsifying its foundation.)