Newtonianism, Monadism and the Problem of Continuous Extension in Germany


Researcher: Henny Blomme

Studies of the debates between Leibnizians and Newtonians in 18th-century Germany have focused on dynamics and the method of fluxions (Dunham 2007).

This subproject is driven by the hypothesis that the challenge posed by a deficiency in the Cartesian theory of continuous extension played an equally important role in these debates – a problem to which Newtonianism offered a solution, while monadism could not. The project examines the disputes on the nature of matter during the Newtonian-Wolffian controversy led by Maupertuis and Euler at the Berlin Academy of Sciences (1740-1759), in view of the following research questions:


  1. To what extent was an adherence to monadism and non-extended theories of matter motivated by the problem of continuous extension?
  2.  To what extent was the Newtonian theory of absolute space (Kochiras 2012) seen as a solution to the problem of continuous extension?


Challenging the Cartesian theory of matter, Leibniz held that continuous extension, since it cannot accommodate non-extended points, is a mere phenomenon and that all that exists is actually non-extended (Arthur 2018).

Boscovich denied extension altogether (A Theory of Natural Philosophy, 1758). Wolff considered extended atoms to be constituted by non-extended ‘simples’. By contrast, Euler, adhering to a Cartesian theory of infinitely divisible matter, held that monadist accounts were inconsistent with Euclidean geometry, which required a continuous space (see the Letters of Euler on different subjects, 1843).

The issue was put up for a prize by the Academy in the year 1748 and won by the anti-monadist Justi. Kant tackled the same issue in his Physical Monadology (1756). Newtonianism seems to do away with the problem: by distinguishing space from body, the former can be posited as continuous while avoiding problems of contact; bodies, for their part, need not be continuous (Evans 1955).

The project finally examines the extent to which this debate contributed to 18th-century German debates on the demarcation between the sciences (Pelletier 2019) and between natural science and philosophy.