Abstract:Eliminative reasoning is an important inferential tool in the sciences, but this is a minority view in philosophy. Those that do defend eliminative reasoning see this inference tool as important for theory chocies: evidence rules out all but one of a set of alternative theories. Whichever theory remains, however improbable, must be the truth. Yet statistical evidence does not fit into an eliminative framework well at all. And the prevalence of statistical evidence in the sciences, especially in evolutionary biology, suggests that elimination has an inconsequential role to play. This majority view relies on probabilistic theories of confirmation to understand almost all reasoning about evidence. Here I will review the standard picture of eliminative inference and its problems. I want to suggest that eliminative reasoning has an important and different role to play in science, a role that is compatible with probabilistic approaches to evidence. Eliminative reasoning is a crucial part of case building, a scientific activity that determines the context for evaluating statistical evidence. I will illustrate the activity of case building with examples taken from molecular evolutionary biology.