Two approaches to evidential reasoning compete in the biomedical and social sciences: the experimental and the pragmatist. Whereas experimentalism has received considerable philosophical analysis and support since the times of Bacon and Mill (and continues to enjoy attention and support in very recent work on causation and evidence), pragmatism about evidence has been neither articulated nor defended. The overall aim is to fill this gap and develop a theory that articulates the latter. The main ideas of the theory will be illustrated and supported by a case study on the smoking/lung cancer controversy in the 1950s.