The art of estimation and the mathematization of force in Leibniz

Abstract

From 1686 onward, Leibniz is engaged in a dispute with Cartesian physicists on the correct expression for the quantity of force in moving bodies. In the 1690s, he puts forth an argument for his own expression that is allegedly based on the science of quantity in general (or the art of estimation). Leibniz states that the latter requires the quantity of force to be determined by the real repetitions of a measure. It would follow that his expression for force is the correct one. Now, commentators have not been sensitive to the ingenuity of the argument presented here. In this paper, focussing on the exchange between Johann Bernoulli and Leibniz, we want to show how this argument consists essentially in pushing for a certain conception of the mathematization of force based, in turn, on a serious conception of measurement of quantities. This conception exploits the conservative properties of physical systems in order to apply general principles of determination of quantity to the special case of the quantity of force. We conclude by confronting our interpretation with others which posit a stronger connection between measurement and metaphysics in Leibniz.