Deductively Disjoint

The term ‘incommensurable’ means ‘to have no common measure’. The idea traces back to Euclid’s Elements, where it was applied to magnitudes. For example, there is no common measure between the sides and the diagonal of a square. Today, such incommensurable relations are represented by irrational numbers. The metaphorical application of the mathematical notion specifically to the relation between successive scientific theories became controversial in 1962 after it was popularised by two influential philosophers of science: Thomas Kuhn and Paul Feyerabend. They appeared to be challenging the rationality of science and so were often considered to be among “the worst enemies of science” (Theocharis and Psimopoulos 1987, 596; cf. Preston et al. 2000). Since 1962, the incommensurability of scientific theories has been a widely discussed, controversial idea that was instrumental in the historical turn in the philosophy of science and the establishment of the sociology of science as a professional discipline.