There is a perennial philosophical dream of a certain natural order for the natural kinds. The name of this dream is ‘the hierarchy requirement’. According to this postulate, proper natural kinds form a taxonomy which is both unique and traditional. Here I demonstrate that complex scientific objects exist: objects which generate different systems of scientific classification, produce myriad legitimate alternatives amongst the nonetheless still natural kinds, and make the hierarchical dream impossible to realize, except at absurdly great cost. Philosophical hopes (...) for a certain order in nature cannot be fulfilled. Natural kinds crosscut one another, ubiquitously so, and this crosscutting spells the end of the hierarchical dream. (shrink)