From the two Notions of Paradigm and Reduction between Theories to a New Multilinear History of Physics

Abstract

In last century, the historians of physics improved their historical accounts till up to obtain be interpretative accounts. The two main interpretative accounts have posed fundamental problems. Koyré: whether in theoretical physics mathematics is also idealistic in nature; Kuhn: whether and how the notions of paradigm, anomaly, crisis, scientific revolution and incommensurability are essential for a deep understanding of the history of physics. For their part, the philosophers of science have suggested a program for unifying the entire science; hence, they attributed to the concept of reduction between two theories insisting on the same field of phenomena a crucial role. A great debate tried to define this notion of reduction. Since longtime a particular, but more accurate notion of reduction has been applied by physicists: the reduction through a limit of a fundamental parameter of the reducing theory. But Berry, Rohrlich and Batterman pointed out that this reduction is impossible when the limit is singular, as it occurs in the cases of physical optics and geometric optics, statistical mechanics and thermodynamics, quantum mechanics and classical mechanics, etc. Hence, to represent an entire theory as the final point of a singular limit operation applies idealistic mathematics more than what was suggested by Koyré, i.e. to represent a physical law through an idealistic mathematical notion. In addition, a new mathematics—the constructive one—characterizes a singular limit as undecidable. Hence, a singular limit between two theories actually represents a difference between two different kinds of mathematics. This particular situation suggests a mathematical definition of the notion of incommensurability. As a consequence of the resulting incommensurability among many couples of theories the foundations of physical theories are pluralist, not only in both epistemological and ontological senses, but also in a mathematical sense. Hence, the traditional vision of the historical growth of theoretical physics as a series of theories as concentric circles, each theory being compatible with the previous ones is denied; since longtime the history of physics is developing along a plurilinear path.