Darwin claimed that a unique inclusively hierarchical pattern of relationships between all organisms based on their similarities and differences [the Tree of Life (TOL)] was a fact of nature, for which evolution, and in particular a branching process of descent with modification, was the explanation. However, there is no independent evidence that the natural order is an inclusive hierarchy, and incorporation of prokaryotes into the TOL is especially problematic. The only data sets from which we might construct a universal hierarchy including prokaryotes, the sequences of genes, often disagree and can seldom be proven to agree. Hierarchical structure can always be imposed on or extracted from such data sets by algorithms designed to do so, but at its base the universal TOL rests on an unproven assumption about pattern that, given what we know about process, is unlikely to be broadly true. This is not to say that similarities and differences between organisms are not to be accounted for by evolutionary mechanisms, but descent with modification is only one of these mechanisms, and a single tree-like pattern is not the necessary (or expected) result of their collective operation. Pattern pluralism (the recognition that different evolutionary models and representations of relationships will be appropriate, and true, for different taxa or at different scales or for different purposes) is an attractive alternative to the quixotic pursuit of a single true TOL.