A paradigm instructs in how to do research successfully. Analytic philosophy of science, currently dominant, models paradigmatic rational science as a system of logical inferences. It is, however, an abundantly inadequate paradigm. This paper presents an alternative paradigm: science as an organized collection of problem solving processes. This position is backed, on the one side, by a cognitive model of problem solving process applicable to all problem solving circumstances and, on the other, by a non-formal conception of rationality that provides a wider enriched notion of rational research process than is available to the analytic paradigm. The result is a very different way of looking at science and of doing history and philosophy of science. The position is developed sufficiently to display its nature and merits.