Darwinism consists of two parts: a phylogenesis of biological species (ours included) and the claim that the primary mechanism of the evolution of phenotypes is natural selection. I assume that Darwin’s account of phylogeny is essentially correct; attention is directed to the theory of natural selection. I claim that Darwin’s account of evolution by natural selection cannot be sustained. The basic problem is that, according to the consensus view, evolution consists in changes of the distribution of phenotypic traits in populations of organisms. An evolutionary theory must therefore explicate not just the notion of organisms being selected, but also the notion of organisms being selected for their phenotypic traits. I argue that that there is no way for a theory of natural selection to do so, and that Darwin’s assumption to the contrary was likely the consequence of placing too much weight on the analogy between natural selection and artificial selection. The paper ends with the suggestion that selectionist explanations, insofar as they are convincing, are best construed as post hoc historical narratives: natural history rather than biology.