Cantor, God, and Inconsistent Multiplicities

Aaron R. Thomas-Bolduc 1
  • 1 University of Calgary


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.

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  • Cantor, G. (1962). Gesammelte Abhandlungen Mathematischen und Philosophischen Inhalts. Hildesheim: Georg Olms, 2nd edition. E. Zermelo (ed.).

  • Copi, I. (1958). The Burali-Forti Paradox. Philosophy of Science, 25(4), 281–286.

  • Dauben, J. (1990). Georg Cantor: His Mathematics and Philosophy of the Infinite. Princeton: Princeton University Press, first paperback edition.

  • Hallett, M. (1984). Cantorian Set Theory and the Limitation of Size. Oxford: Oxford University Press.

  • Jané, I. (1995). The Role of the Absolute in Cantor’s Conception of Set. Erkenntniss, 42, 375–402.

  • Jané, I. (2010). Idealist and Realist Elements in Cantor’s Approach to Set Theory. Philosophia Mathematica, 18, 193–226.

  • Meschkowski, H. (1967). Probleme des Unendlichen: Werk und Leben Georg Cantors. Braunschweig: Friedr. Vieweg & Sohn GmbH.

  • Meschkowski, H. & Nilson, W., Eds. (1991). Georg Cantor: Briefe. Heidelberg: Springer.

  • Tapp, C. (2005). Kardinalität und Kardinäle: Wissenschafthistorische Aufarbeitung der Korrespondenz zwischen Georg Cantor und katholischen Theologen seiner Zeit. Stuttgart: Franz Steiner Verlag.

  • Tapp, C. (2012). Absolute Infinity: A Bridge Between Mathematics and Theology? In N. Tennant (Ed.), Foundational Adventures: Essays in Honor of Harvey M. Friedman. London: College Publications.

  • Ternullo, C. (T.A.). Gödel’s Cantorianism. In Gödelian Studies on the Max-Phil Notebooks, volume 1. Aix-en-Provence: Presses Universitaires de Provence. Crocco, G., Engelen, E.-M. (eds.), to appear.

  • van der Veen, J. & Horsten, L. (2013). Cantorian Infinity and Philosophical Concepts of God. European Journal for Philosophy of Religion, 5(3).

  • Welch, P. (2012). Global Reflection Principles. In Exploring the Frontiers of Incompleteness Harvard.

  • Welch, P. & Horsten, L. (U.M.). Reflecting on Absolute Infinity. Under review.


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