Hume’s “Malezieu Argument”

At T 1.2.2.3 Hume offers an argument against the infinite divisibility of finite extension, which he ascribes to “Mons. Malezieu.” Scholars have long been aware that the ultimate source of the argument is the Élémens de Géométrie de Monseigneur le Duc de Bourgogne, first published in 1705. Although the argument has figured prominently in several recent discussions of Hume’s metaphysics, there exists as yet no adequate English translation of Malezieu’s text. Furthermore, very little is known about Hume’s immediate sources for the argument. In this article, I provide the original French text with translation. I then inquire into Hume’s knowledge of the text. Drawing on evidence internal to the Treatise passage itself, I consider two plausible sources: a contemporary review of Malezieu’s work in the Nouvelles de la République des Lettres and a critical discussion of the argument in Le Gendre’s Traité de l’opinion. Based on the available evidence, I suggest that the latter was most likely Hume’s source.