“In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate on the Physical Significance of Mathematical Objects

In Between Leibniz, Newton, and Kant, Second Edition. Springer (forthcoming)
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Abstract
Du Châtelet holds that mathematical representations play an explanatory role in natural science. Moreover, things proceed in nature as they do in geometry. How should we square these assertions with Du Châtelet’s idealism about mathematical objects, on which they are ‘fictions’ dependent on acts of abstraction? The question is especially pressing because some of her important interlocutors (Wolff, Maupertuis, and Voltaire) denied that mathematics informs us about the properties of real things. After situating Du Châtelet in this debate, this chapter argues, first, that her account of the origins of mathematical objects is less subjectivist than it might seem. Mathematical objects are non-arbitrary, public entities. While mathematical objects are partly mind-dependent, so too are material things. Mathematical objects can approximate the material. Second, it is argued that this moderate metaphysical position underlies Du Châtelet’s persistent claims that mathematics is required for certain kinds of general knowledge, including in natural science. The chapter concludes with an illustrative example: an analysis of Du Châtelet’s argument that matter is continuous. A key but overlooked premise in the argument is that mathematical representations and material nature correspond.
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