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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”. [Preprint]

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    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”.


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    Item Type: Preprint
    Additional Information: This version will appear in International Studies in the Philosophy of Science.
    Keywords: Isaac Newton; Principia; (hypothetical-deductive) methodology; I. Bernard Cohen; Newtonian Style; models; models as mediators
    Subjects: Specific Sciences > Physics > Classical Physics
    General Issues > Structure of Theories
    General Issues > Models and Idealization
    General Issues > History of Philosophy of Science
    General Issues > Laws of Nature
    General Issues > Theory/Observation
    General Issues > Explanation
    General Issues > History of Science Case Studies
    Depositing User: Steffen Ducheyne
    Date Deposited: 15 Jan 2005
    Last Modified: 07 Oct 2010 11:13
    Item ID: 2155
    URI: http://philsci-archive.pitt.edu/id/eprint/2155

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