@article {300874, title = {Mathematical models in {N}ewton{\textquoteright}s Principia: a new view of the {\textquoteright}{N}ewtonian Style{\textquoteright}.}, journal = {International Studies in the Philosophy of Science}, volume = {19}, number = {1}, year = {2005}, pages = {1{\textendash}19}, abstract = {

In this essay I argue against I. Bernard 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 dynamic 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 differently from the hypothetical-deductive 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’.

}, issn = {0269-8595}, author = {Ducheyne, Steffen} }