From the two notions of paradigm and reduction between theories to a new multilinear History of physics

TL;DR

This paper introduces a new constructive mathematics framework to understand incommensurability between physical theories, emphasizing a pluralist and multilinear approach to the history and foundations of physics.

Contribution

It proposes a mathematical definition of incommensurability based on constructive mathematics, linking it to the pluralist nature of physical theories' foundations.

Findings

Singular limits are characterized as undecidable in constructive mathematics.

Incommensurability among theories leads to a pluralist view of physical foundations.

The history of physics follows a multilinear development path.

Abstract

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.