Cantor, God, and Inconsistent Multiplicities*

Abstract

The importance of Georg Cantor's religious convictions is often neglected in discussions of his mathematics and metaphysics. Herein I argue, pace Jané (1995), that due to the importance of Christianity to Cantor, he would have never thought of absolutely infinite collections/inconsistent multiplicities, as being merely potential, or as being purely mathematical entities. I begin by considering and rejecting two arguments due to Ignacio Jané based on letters to Hilbert and the generating principles for ordinals, respectively, showing that my reading of Cantor is consistent with that evidence. I then argue that evidence from Cantor's later writings shows that he was still very religious later in his career, and thus would not have given up on the reality of the absolute, as that would imply an imperfection on the part of God.The theological acceptance of his set theory was very important to Cantor. Despite this, the influence of theology on his conception of absolutely infinite collections, or inconsistent multiplicities, is often ignored in contemporary literature. 1 I will be arguing that due in part to his religious convictions, and despite an apparent tension between his earlier and later writings, Cantor would never have considered inconsistent multiplicities (similar to what we now call proper classes) as completed in a mathematical sense, though they are completed in Intellectus Divino.Before delving into the issue of the actuality or otherwise of certain infinite collections, it will be informative to give an explanation of Cantor's terminology, as well a sketch of Cantor's relationship with religion and religious figures. Such will comprise the first part of this paper, after which I will argue that although there is tension between how Cantor discusses the absolute infinite before roughly 1896, and inconsistent multiplicities thereafter, due to his continuing and even strengthening religious convictions, Cantor would have maintained his earlier position that inconsistent multiplicities are not mathematically extant, but also not merely potential. I achieve this aim by first pointing out that the evidence taken by Jané (1995) to show