In Phylogenetic Systematics (1966), Willi Hennig conflates the Linnaean hierarchy with what Hennig refers to as the divisional hierarchy. In doing so, he lays the foundations of that school of biological taxonomy known as cladism on a philosophically ambiguous basis. This paper compares and contrasts the two hierarchies and demonstrates that Hennig conflates them. It shows that Hennig's followers also conflate them. Finally, it illuminates five persistent problems in cladism by suggesting that they arise from Hennig's original confusion.