Grim, Omniscience, and Cantor’s Theorem
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Although recent evidence is somewhat ambiguous, if not confusing, Patrick Grim still seems to believe that his Cantorian argument against omniscience is sound. According to this argument, it follows by Cantor’s power set theorem that there can be no set of all truths. Hence, assuming that omniscience presupposes precisely such a set, there can be no omniscient being. Reconsidering this argument, however, guided in particular by Alvin Plantinga’s critique thereof, I find it far from convincing. Not only does it have an enormously untoward side effect, but it is self-referentially incoherent as well.
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- Boolos, George. “The Iterative Conception of Set.” The Journal of Philosophy 68 (1971): 215–231
- Borland, Tully. “Omniscience and Divine Foreknowledge.” Internet Encyclopedia of Philosophy. Entry last modified July 7, 2006. http://www.iep.utm.edu/omnisci.
- Bringsjord, Selmer. “Grim on Logic and Omniscience.” Analysis 49 (1989): 186–189.
- Cartwright, Richard L. “Speaking of Everything.” Noûs 28 (1994): 1–20.
- Everitt, Nicholas. The Non-Existence of God. London and New York: Routledge, 2004.
- Grim, Patrick. “There Is No Set of All Truths.” Analysis 44 (1984): 206–208.
- Grim, Patrick. “On Sets and Worlds: A Reply to Menzel.” Analysis 46 (1986): 186–191.
- Grim, Patrick. “Logic and Limits of Knowledge and Truth.” Noûs 22 (1988): 341–367.
- Grim, Patrick. “On Omniscience and a ‘Set of All Truths:’ A Reply to Bringsjord.” Analysis 50 (1990): 271–276.
- Grim, Patrick. The Incomplete Universe: Totality, Knowledge, and Truth. Cambridge, MA: The MIT Press, 1991.
- Grim, Patrick. “The being that knew too much.” International Journal for Philosophy of Religion 47 (2000): 141–154.
- Grim, Patrick. “Impossibility Arguments.” In The Cambridge Companion to Atheism, edited by Michael Martin, 199–214. Cambridge: Cambridge University Press, 2007.
- Grim, Patrick. “Problems with Omniscience.” PDF on Grim’s personal website: 1–20. Accessed July 9, 2013. http://www.pgrim.org/articles/omniscience9.pdf.
- Hoffman, Joshua, and Gary S. Rosenkrantz. The Divine Attributes. Oxford: Blackwell, 2002.
- Holmes, M. Randall. “Alternative Axiomatic Set Theories.” The Stanford Encyclopedia of Philosophy. Entry last modified April 3, 2012. http://plato.stanford.edu/archives/win2012/entries/settheory-alternative.
- Hughes, Gerard J. The Nature of God. London and New York: Routledge, 1995.
- Klement, Kevin C. “Russell, His Paradoxes, and Cantor’s Theorem: Part I.” Philosophy Compass 5 (2010):16–28.
- Klement, Kevin C. “Russell, His Paradoxes, and Cantor’s Theorem: Part II.” Philosophy Compass 5 (2010): 29–41.
- Luna, Laureano. “Grim’s arguments against omniscience and indefinite extensibility.” International Journal for Philosophy of Religion 72 (2012): 89–101.
- Newman, Fred. “Omniscience Is Possible.” Australasian Journal of Philosophy 42 (1964): 102–103.
- Plantinga, Alvin, and Patrick Grim. “Truth, Omniscience, and Cantorian Arguments: An Exchange.” Philosophical Studies 71 (1993): 267–306.
- Puccetti, Roland. “Is Omniscience Possible?” Australasian Journal of Philosophy 41 (1963): 92–93.
- Quine, Willard van Orman. Set Theory and Its Logic. Cambridge, MA: Belknap Press, 1963.
- Rescher, Nicholas, and Patrick Grim. “Plenum Theory.” Noûs 42 (2008): 422–439.
- Simmons, Keith. “On an Argument Against Omniscience.” Noûs 27 (1993): 22–33.
- Simmons, Keith. “Semantical and Logical Paradox.” In A Companion to Philosophical Logic, edited by Dale Jacquette, 115–130. Malden, MA: Blackwell Publishing, 2002.
- Suppes, Patrick. Axiomatic Set Theory. New York: Dover Publications, 1972.
- Wierenga, Edward. The Nature of God: An Inquiry into Divine Attributes. Ithaca and London: Cornell UP, 1989.
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