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


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Steffen Ducheyne
University of Ghent
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'.
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DOI 10.1080/02698590500051035
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References found in this work BETA

The Cambridge Companion to Newton.I. Bernard Cohen & George E. Smith (eds.) - 2002 - Cambridge University Press.
Newton's Argument for Universal Gravitation.William Harper - 2002 - In I. Bernard Cohen & George E. Smith (eds.), The Cambridge Companion to Newton. Cambridge University Press. pp. 174--201.
The Correspondence of Isaac Newton.Isaac Newton & H. W. Turnbull - 1961 - British Journal for the Philosophy of Science 12 (47):255-258.

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Citations of this work BETA

Two Styles of Reasoning in Scientific Practices: Experimental and Mathematical Traditions.Mieke Boon - 2011 - International Studies in the Philosophy of Science 25 (3):255 - 278.
The Argument(s) for Universal Gravitation.Steffen Ducheyne - 2006 - Foundations of Science 11 (4):419-447.

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