  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 incommensurabilities
among many couples of theories the foundations of physical theories are
pluralist, not only in both epistemological and ontological senses, but also in
mathematical sense. Hence since longtime the history of physics is developing
along a plurilinear path.
