Incommensurability

Along with “paradigm” and “scientific revolution,” “incommensurability” is one of the three most influential expressions associated with the “new philosophy of science” first articulated in the early 1960s by Thomas Kuhn and Paul Feyerabend (see kuhn and feyerabend). But, despite the fact that it has been widely discussed, opinions still differ widely as to the content and significance of the claim of incommensurability. What is uncontroversial is that the term “incommensurability” was borrowed from mathematics, where it can be used, for example, to apply to the relation between the side of a square and its diagonal. Since the side of a square is measured by a rational number, and its diagonal by an irrational number, and since an irrational number cannot be represented by a point on the rational number line, the two quantities are said to have no common measure; they are literally incommensurable. Kuhn and Feyerabend adapted this term and applied it to some pairs of rival scientific theories, to indicate that such theories also had no common measure, or, in some sense to be determined, could not be compared directly. Both Kuhn and Feyerabend agree that they hit upon the term independently and used it in print for the first time in 1962, in The Structure of Scientific Revolutions and “Explanation, reduction, and empiricism,” respectively. But the two writers explicate the claim and argue for it rather differently. After tackling the concept of incommensurability as it appears in the works of each of these authors in turn, some reactions and responses will be sampled.