Émilie Du Châtelet’s Mathematical Fictionalism

Émilie Du ChâteletDu Châtelet was a fictionalistFictionalist about mathematics. Mathematical fictionalismMathematical fictionalism (henceforth, fictionalismFictionalism) is the view that, strictly speaking, mathematical entitiesMathematical entities such as numbersNumbers, functions, and sets, are fictions that are useful for human purposes, but are not themselves real in an ontologicalOntological sense. I first explain fictionalism. Then I illustrate Du Châtelet’s position with regard to mathematical entities and give textual evidence of her fictionalism from Institutions de Physique. I offer a sketch of the philosophical-scientific issues that motivated Du Châtelet’s fictionalism: explaining the behavior of bodies, as well as the ontological extraneity of mathematical entities, had they been taken to be real abstracta. Finally, I argue that Du Châtelet’s fictionalism was plausibly motivated by Leibniz’sLeibniz, Wolff’sWolff, and other mathematicians’ views who themselves held fictionalist positions with regard to certain mathematical issues. Although I project onto Du Châtelet a philosophical position which was not identified as such at the time of her writing, I do so with the aim of highlighting her systematicity and making sense of her priorities, as well as showing a link between historical and contemporary uses of fictions, and issues in the metaphysicsMetaphysics of scienceScience.