Mathematical Models in Newton’s Principia: A New View of the “Newtonian Style”

Ducheyne, Steffen (2005) Mathematical Models in Newton’s Principia: A New View of the “Newtonian Style”.

Abstract

In this essay I argue against Bernard I. Cohen’s influential account of Newton’s methodology in the Principia: the “Newtonian Style”. The crux of Cohen’s account is the successive adaptation of “mental constructs” through comparisons with nature. In Cohen’s view there is a direct dynamics between the mental constructs and physical systems. I argue that his account is essentially hypothetical-deductive which is at odds with Newton’s rejection of the hypothetical-deductive method. An adequate account of Newton’s methodology needs to show how Newton’s method proceeds different from the hypotheticaldeductive method. In the constructive part I argue for my own account which is model-based: it focuses on how Newton constructed his models in Book I of the Principia. I will show that Newton understood Book I as an exercise in determining the mathematical consequences of certain force functions. The growing complexity of Newton’s models is a result of exploring increasingly complex force functions (intra-theoretical dynamics) rather than a successive comparison with nature (extra-theoretical dynamics). Nature did not enter the scene here. This intra-theoretical dynamics is related to the
“autonomy of the models”.