William of Auvergne and the “Wilderness of the Infinite”

Abstract Chapter 3 studies William of Auvergne’s (ca. 1180–1190, 1249) engagement with the mathematical infinite and the theological context that motivated it. The chapter discusses first William’s use of paradoxes of infinity to argue that no infinite continua exist. It is then shown that the discussion in William is influenced by a text by Algazel (al-Ghazālī) that was translated in the late twelfth century, thereby showing that, contrary to John Murdoch’s claims, the Latin West does not discover the paradoxes of infinity on its own but, at least in this case, was dependent on Islamic sources. The second part of the chapter investigates William’s theory of mathematical infinity, applications of infinitary mathematics to theological issues, and some interesting ideas he put forward on the comparison of unequal infinities.