American Catholic Philosophical Quarterly

Volume 83, Issue 4, Fall 2009

Anne Newstead
Pages 533-553

Cantor on Infinity in Nature, Number, and the Divine Mind

The mathematician Georg Cantor strongly believed in the existence of actually infinite numbers and sets. Cantor’s “actualism” went against the Aristotelian tradition in metaphysics and mathematics. Under the pressures to defend his theory, his metaphysics changed from Spinozistic monism to Leibnizian voluntarist dualism. The factor motivating this change was two-fold: the desire to avoid antinomies associated with the notion of a universal collection and the desire to avoid the heresy of necessitarian pantheism. We document the changes in Cantor’s thought with reference to his main philosophical-mathematical treatise, the Grundlagen (1883) as well as with reference to his article, “Über die verschiedenen Standpunkte in bezug auf das aktuelle Unendliche” (“Concerning Various Perspectives on the Actual Infinite”) (1885).