The resolution of the first paradox of omniscience in Chapter 4, via the theory of moves, was thoroughly secular. It generally favored the stronger or quicker player, in a particular sense, and thus could be viewed as unfair to the other player, though he always obtained at least his security level in a game.
KeywordsNash Equilibrium Initial Outcome Strategy Choice Game Tree Sequential Prisoner
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- 1.Martin Gardner rejects the view that there are limitations: “Let me confess at once that I find something profoundly impious, almost blasphemous, about setting limits of any sort on the power of God to bring things about in any manner that He chooses.” Martin Gardner, The Ambidextrous Universe: Mirror Asymmetry and Time-Reversed Worlds, 2nd ed. rev. (New York: Scribner’s, 1979), p. 125.Google Scholar
- 2.For recent investigations into such questions in the philosophy of religion, see The Power of God: Readings on Omnipotence and Evil, ed. Linwood Urban and Douglas N. Walton (New York: Oxford University Press, 1978); Anthony Kenny, The God of the Philosophers (Oxford: Clarendon, 1979);Google Scholar
- 2c.and Edward Wierenger, Omnipotence defined, Philos, and Phenomenological Res. 43 (1982) (forthcoming). None of this literature analyzes the relationship between a superior and ordinary being as a game, which in my view puts the question of omnipotence, as well as omniscience, in a fundamentally new framework. Omnipotence, by the way, seems to have confounded philosophers more than omniscience, perhaps because “the notion of infinite power has seemed too obscure, too shrouded in mystery and ineffability for us to analyze our feelings of awe and bring them into the domain of pure concepts.” The Power of God, p. 4.Google Scholar
- 5.Leszek Kolakowski, Religion (New York: Oxford University Press, 1982), p. 140.Google Scholar
- 6.Material in this and the next two sections is based largely on Steven J. Brams and Marek P. Hessel, Staying power in sequential games, Theory and Decision (forthcoming); see also D. Marc Kilgour, Equilibria for far-sighted players, Theory and Decision (forthcoming), who extends the notion of nonmyopic equilibrium (see citation in note 7) to most games in which S-power is not effective.Google Scholar
- 7.Steven J. Brams and Donald Wittman, Nonmyopic equilibria in 2 × 2 games, Conflict Management and Peace Sci. 6, 1 (1983).Google Scholar
- 8.This is in fact true of S-power outcomes in all two-person finite games, as shown in Brams and Hessel, Staying power in sequential games.Google Scholar
- 9.Saint Aurelius Augustinus, The Confessions of Saint Augustine, translated by Edward B. Pusey (New York: Modern Library, 1949).Google Scholar
- 10.Karl Barth, Church Dogmatics, translated by G. W. Bromily (New York: Harper & Row, 1962); see also Hans Küng, Justification: The Doctrine of Karl Barth and a Catholic Reflection (Philadelphia: Westminister, 1981).Google Scholar
- 11.It would also imply a kind of “metaphysical determinism,” which Karl R. Popper rejects in The Open Universe: An Argument for Indeterminism, ed. W. W. Bartley III (Totowa, NJ: Rowman and Littlefield, 1982), pp 87–92.Google Scholar