In recent years epidemiology has come under increasing criticism in regulatory and public arenas for being "unscientific." The tobacco industry has taken advantage of this, insisting for decades that evidence linking cigarettes and lung cancer falls short of proof. Moreover, many epidemiologists remain unduly skeptical and self-conscious about the status of their own causal claims. This situation persists in part because of a widespread belief that only the laboratory can provide evidence sufficient for scientific proof. Adherents of this view erroneously believe that there is no element of uncertainty or inductive inference in the "direct observation" of the laboratory researcher and that epidemiology provides mere "circumstantial" evidence. The historical roots of this attitude can be traced to philosopher John Stuart Mill and physiologist Claude Bernard and their influence on modern experimental thinking. The author uses the debate over cigarettes and lung cancer to examine ideas of proof in medical science and public health, concluding that inductive inference from a limited sample to a larger population is an element in all empirical science.