PSA2016: The 25th Biennial Meeting of the Philosophy of Science Association

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On the differential calculus and mathematical constraints

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 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 the dome thought experiment by John Norton. We argue that the pathological nature of Norton's dome cannot serve as a argument to sustain the claim that Newton's second law is indeterministic. This is because the constraints of the differential calculus dictate that the structure of Norton's dome cannot be defined within the confines of Newtonian theory.

Author Information:

Noah Stemeroff    

Charles Dyer    

 

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