The article presents two alternative proposals for the use of probability to analyze scientific reasoning: Bayesianism and error statistics. The debate between these two approaches is one of the most important issues in contemporary Philosophy of Science and is a continuation of the well-known debate between Popper and Kuhn. The article presents the explanations offered by Bayesianism for specific phenomena of scientific activity that other approaches have difficulty in explaining, like the ravens paradox. Despite its positive results as a research program, Bayesianism has been the target of strong criticism, for instance, because it allegedly does not offer an adequate solution to Duhemt’s problem. Error Statistics in particular proposes the application of statistical methods and probability calculus to explain scientific reasoning in a way radically different from Bayesianism. The debate started by Popper and Kuhn is continued in probabilistic terms and is far from ended.