TITLE:
From the two Notions of Paradigm and Reduction between Theories to a New Multilinear History of Physics
AUTHORS:
Antonino Drago
KEYWORDS:
New Historiography of Physics, Reduction between Two Scientific Theories, The Debate on the Definition of Reduction, Limit Reduction, Incommensurability, Pluralist Foundations, Plurilinear History
JOURNAL NAME:
Advances in Historical Studies,
Vol.10 No.2,
June
30,
2021
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.