On the differential calculus and mathematical constraints

Abstract

In this article, we argue that the application of mathematics in the construction of physical theories constrains the form of our scientific understanding. Specifically, we discuss the constraints that the mathematical structure of the differential calculus imposes on the understanding of the structure of the world within a Newtonian worldview. In the first section of the paper, we develop the formal structure of the differential calculus. In the second section, we provide a discussion of the constraints that the differential calculus imposes on the application of Newton's second law. In the final section, we present a case study of a thought experiment by John Norton, simply called `the dome'. We argue that the pathological nature of Norton's dome cannot serve as an argument to sustain the claim that Newton's second law is indeterministic because the constraints of the differential calculus dictate that Newton's second law cannot be well-defined in the infinitesimal neighbourhood of the apex of Norton's dome