William Whewell is famous for his philosophy of scientific discovery. Too few recognize that Whewell has important things to say on the normative question of theory testing, perhaps because J. S. Mill minimized Whewell‘s contribution at every point. We aim to show how the many facets of their debate arise systematically from a single key issue—the normative function of concepts in science. The resulting theory of scientific inference could provide new insights into to the nature of inference in general
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