Arguments for the Continuity of Matter in Kant and Du Châtelet

In the Metaphysical Foundations of Natural Science, Kant attempts to argue a priori from the indefinite divisibility of space to the indefinite metaphysical divisibility of matter. This is one type of argument from the continuity of space – purportedly established by Euclidean geometry – to the continuity of matter. I compare Kant’s argument to parallel reasoning in Du Châtelet, whose work he knew. Both philosophers appeal to idealism about matter in their reasoning, yet also face difficulties in explaining why continuity, though not some other properties from geometry, applies to matter. Both also risk inconsistency in adopting potentialist accounts of material parts, while also committing to realism about infinitesimals. An important difference between them is that Du Châtelet deploys at least three definitions of continuity; only one of these, amounting to indefinite divisibility, is shared with Kant.