Theology and the Actual Infinite: Burley and Cantor

Abstract

Aristotle held that there is no limit to how small a line segment can be, but he insisted that a segment is not composed of points. Points are a potential infinity, since there is no limit to the ability to produce them (say, by continually bisecting a line segment), but there is no actual infinity of points. Like most thinkers of his period, Walter Burley accepted this Aristotelian conception of the continuum, but he argued that God can and does see all of the points on a given line segment. One of the main founders of the contemporary conception of the continuum, Georg Cantor, invoked similar, but more far-reaching theological themes and arguments in his spirited articulation and defense of the actual infinite, ultimately yielding the contemporary conception that a line segment is, literally, composed of points.