Kuhn's notion of scientific progress: "Reduction" between incommensurable theories in a rigid structuralist framework

In the last two sections of Structure, Thomas Kuhn first develops his famous threefold conception of the incommensurability of scientific paradigms and, subsequently, a conception of scientific progress as growth of empirical strength. The latter conception seems to be at odds with the former in that semantic incommensurability appears to imply the existence of situations where scientific progress in Kuhns sense can no longer exist. In contrast to this seeming inconsistency of Kuhns conception, we will try to show in this study that the semantic incommensurability of scientific terms appears to be fully compatible with scientific progress. Our argumentation is based on an improved version of the formalization of Kuhns conception as developed in the 1970s by Joseph Sneed and Wolfgang Stegmüller: In order to be comparable, incommensurable theories need the specification of relations that refer to the concrete ontologies of these theories and involve certain truth claims. The original structuralist account of reduction fails to provide such relations, because (1) it is too structural and (2) it is too wide. Moreover, the original structuralist account also fails to cover important cases of incommensurable theories in being too restrictive for them. In this paper, we develop an improved notion of “reduction” that allows us to avoid these shortcomings by means of a more flexible device for the formalization of (partially reductive) relations between theories. For that purpose, we use a framework of rigid logic, i. e., logic that is based on a fixed collection of objects.