Central to Imre Lakatos’s philosophy is the methodological continuity between mathematics and the empirical sciences, especially the central role played by counterexamples (refutations) in both fields. It is unclear, however, to what extent the original framework conceived in Proofs and Refutations can be extended beyond the particular case study that motivated it in the first place. In this paper, I argue that, with suitable adjustments, the framework not only illuminates important aspects of the discovery of new logics (such as intuitionistic, paraconsistent and quantum logics), but it also can have a far more extensive role than Lakatos himself seems to have acknowledged in the empirical sciences as well.