On the number of gods



A god is a cosmic designer-creator. Atheism says the number of gods is 0. But it is hard to defeat the minimal thesis that some possible universe is actualized by some possible god. Monotheists say the number of gods is 1. Yet no degree of perfection can be coherently assigned to any unique god. Lewis says the number of gods is at least the second beth number. Yet polytheists cannot defend an arbitrary plural number of gods. An alternative is that, for every ordinal, there is a god whose perfection is proportional to it. The n-th god actualizes the best universe(s) in the n-th level of an axiological hierarchy of possible universes. Despite its unorthodoxy, ordinal polytheism has many metaphysically attractive features and merits more serious study.


Gods Atheism Monotheism Polytheism Infinity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Augustine. (1993). On the free choice of the will (T. Williams, Trans.). Indianapolis, IN: Hackett.Google Scholar
  2. Bostrom N. (2003) Are you living in a computer simulation?. Philosophical Quarterly 53(211): 243–255CrossRefGoogle Scholar
  3. Copeland B. J. (1998) Super-turing machines. Complexity 4(1): 30–32CrossRefGoogle Scholar
  4. Cowan, J. (1965) The paradox of omniscience. Analysis, 25(Supplement), 102–108. (Reprinted in Martin and Monnier (2003), Chap. 28).Google Scholar
  5. Cowan, J. (1974). The paradox of omniscience revisited. Canadian Journal of Philosophy, 3(3), 435–445. (Reprinted in Martin and Monnier (2003), Chap. 29).Google Scholar
  6. Crutchfield J., Mitchell M. (1995) The evolution of emergent computation. Proceedings of the National Academy of Sciences of the USA 92(23): 10742–10746CrossRefGoogle Scholar
  7. Dauben J. W. (1977) Georg Cantor and Pope Leo XIII: Mathematics, theology, and the infinite. Journal of the History of Ideas 38(1): 85–108CrossRefGoogle Scholar
  8. Dauben J. W. (1990) Georg Cantor: His mathematics and philosophy of the infinite. Princeton University Press, Princeton, NJGoogle Scholar
  9. Dawkins R. (2008) The god delusion. Houghton-Mifflin, New York, NYGoogle Scholar
  10. Descartes, R. (1644). Principles of philosophy (J. Cottingham, R. Stoothoff & D. Murdoch, Trans.) (1985). The philosophical writings of descartes (Vol. 1). New York, NY: Cambridge University Press.Google Scholar
  11. Devlin K. (1991) The joy of sets: Fundamentals of contemporary set theory. Springer-Verlag, New York, NYGoogle Scholar
  12. Doore G. (1980) The argument from design: Some better reasons for agreeing with Hume. Religious Studies 16(2): 145–161CrossRefGoogle Scholar
  13. Drake F. (1974) Set theory: An introduction to large cardinals. American Elsevier, New York, NYGoogle Scholar
  14. Drange T. (1998) Non-belief and evil: Two arguments for the nonexistence of god. Prometheus Books, Amherst, NYGoogle Scholar
  15. Gardner J. (2003) Biocosm: The new scientific theory of evolution: Intelligent life is the architect of the universe. Inner Ocean Publishing, Makawao, HIGoogle Scholar
  16. Grim P. (1988) Logic and limits of knowledge and truth. Nous 22: 341–367CrossRefGoogle Scholar
  17. Grover S. (1988) Why only the best is good enough. Analysis 48(4): 224CrossRefGoogle Scholar
  18. Grover S. (2004) Rival creator arguments and the best of all possible worlds. Sophia 43(1): 101–115CrossRefGoogle Scholar
  19. Hallett M. (1988) Cantorian set theory and limitation of size. Oxford University Press, New York, NYGoogle Scholar
  20. Hamilton A. (1982) Numbers, sets, and axioms: The apparatus of mathematics. Cambridge University Press, New York, NYGoogle Scholar
  21. Hamkins J. (2002) Infinite time Turing machines. Minds and Machines 12(4): 521–539CrossRefGoogle Scholar
  22. Harris S. (2008) Letter to a Christian nation. Vintage Books, New York, NYGoogle Scholar
  23. Harrison E. (1995) The natural selection of universes containing intelligent life. Quarterly Journal of the Royal Astronomical Society 36: 193–203Google Scholar
  24. Harwood R. (1999) Polytheism, pantheism, and the ontological argument. Religious Studies 35: 477–491CrossRefGoogle Scholar
  25. Henle P. (1961) Uses of the ontological argument. The Philosophical Review 70(1): 102–109CrossRefGoogle Scholar
  26. Hopcroft J. (1984) Turing machines. Scientific American 250(5): 86–107CrossRefGoogle Scholar
  27. Hume D. (1779) Dialogues concerning natural religion. Penguin, New York, NYGoogle Scholar
  28. Kane R. (1984) The modal ontological argument. Mind 43: 336–350CrossRefGoogle Scholar
  29. Kant, I. (1986). Lectures on philosophical theology (A. Wood & G. Clark, Trans.). Ithaca, NY: Cornell University Press.Google Scholar
  30. Koepke, P. (2006). Computing a model of set theory. In S. B. Cooper et al. (Eds.), New computational paradigms. Lecture notes in computer science (Vol. 3988, pp. 223–232). New York, NY: Springer.Google Scholar
  31. Koepke P., Siders R. (2008) Register computations on ordinals. Archive for Mathematical Logic 47: 529–548CrossRefGoogle Scholar
  32. Kraay K. (2010) Theism, possible worlds, and the multiverse. Philosophical Studies 147(3): 355–368CrossRefGoogle Scholar
  33. Leftow B. (1988) Anselmian polytheism. International Journal for the Philosophy of Religion 23(2): 77–104CrossRefGoogle Scholar
  34. Leibniz, G. W. (1686/1989). Discourse on metaphysics. (G. Montgomery, Trans.). La Salle, IL: Open Court Press.Google Scholar
  35. Leibniz, G. W. (1697/1988). On the ultimate origination of the universe. In P. Schrecker & A. Schrecker (1988) Leibniz: Monadology and other essays. New York, NY: Macmillan Publishing.Google Scholar
  36. Leslie J. (2001) Infinite minds: A philosophical cosmology. Oxford, New York, NYGoogle Scholar
  37. Leslie J. (2007) Immortality defended. Blackwell, Malden, MACrossRefGoogle Scholar
  38. Lewis D. (1983) Philosophical papers. Oxford University Press, New York, NYGoogle Scholar
  39. Lloyd S. (2002) Computational capacity of the universe. Physical Review Letters 88(23): 237901-5CrossRefGoogle Scholar
  40. Lohn J., Reggia J. (1997) Automatic discovery of self-replicating structures in cellular automata. IEEE Transactions of Evolutionary Computation 1(3): 165–178CrossRefGoogle Scholar
  41. Maitzen S. (2005) Anselmian atheism. Philosophy and Phenomenological Research 70(1): 225–239CrossRefGoogle Scholar
  42. Martin M. (1993) The case against Christianity. Temple University Press, Philadelphia, PAGoogle Scholar
  43. Martin M., Monnier R. (2003) The impossibility of god. Prometheus Books, Amherst, NYGoogle Scholar
  44. Miller R. (2001) Moderate modal realism. Philosophia 28(1–4): 3–38CrossRefGoogle Scholar
  45. Morris T. (1987) Perfect being theology. Nous 21(1): 19–30Google Scholar
  46. Oppy G. (2006) Philosophical perspectives on infinity. Cambridge University Press, New York, NYCrossRefGoogle Scholar
  47. Rucker R. (1995) Infinity and the mind. Princeton University Press, Princeton, NJGoogle Scholar
  48. Russell R. J. (2011) God and infinity: Theological insights from Cantor’s mathematics. In: Heller M., Hugh Woodin W. (eds) Infinity: New research frontiers. Cambridge University Press, New York, NY, pp 275–289CrossRefGoogle Scholar
  49. Stenger V. (2007) God: The failed hypothesis. How science shows that god does not exist. Prometheus Books, Amherst, NYGoogle Scholar
  50. Tipler F. (1995) The physics of immortality: Modern cosmology, god and the resurrection of the dead. Anchor Books, New York, NYGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of PhilosophyWilliam Paterson UniversityWayneUSA

Personalised recommendations