Omniscience and Partial Omniscience

  • Steven J. Brams


The picture presented in Chapter 2 is a bleak one, at least for the questing agnostic searching for more than straws in the wind to ward off doubt and uncertainty and justify his beliefs/expectations. If the Revelation Game accurately represents his preferences as well as SB’s (or a possible God’s), the strategy choices are clear: SB would not reveal himself, or establish his existence, and P, anticipating SB’s dominant strategy choice, would not believe in his existence. Hence, P would presumably remain an agnostic, which reverses the rationalistic faith argument Küng sets forth in Does God Exist?1: it is in fact rational, if one is playing the Revelation Game, not to believe in SB’s existence. Recall, though, that this strategy choice does not imply that it is rational for the agnostic to believe in SB’s nonexistence, a strategy choice not available to P in the Revelation Game as I interpreted it, because SB could exist without revealing himself.


Nash Equilibrium Dominant Strategy Choice Rule Strategy Choice Payoff Matrix 
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  1. 1.
    Hans Küng, Does God Exist? An Answer for Today, translated by Edward Quinn (New York: Doubleday, 1980).Google Scholar
  2. 2.
    An interesting side issue: Does SB’s omniscience abrogate P’s free will? Probably not, because SB’s accurate prediction only implies that the predictor has discovered causes that underlie P’s choices; it does not follow that he forces them and thereby prevents P from choosing freely.Google Scholar
  3. 3.
    Quoted in Some Strangeness in the Proportion: A Centennial Symposium to Celebrate the Achievements of Albert Einstein, ed. Harry Woolf (Reading MA: Addison-Wesley, 1980), p. 379. On his religious beliefs, Einstein is quoted as saying (p. 16): “I believe in Spinoza’s God who reveals himself in the orderly harmony of what exists, not in a God who concerns himself with the fate and actions of human beings.” Spinoza speaks for himself in Benedictus de Spinoza, Chief Works, translated by R. H. M. Elwes (New York: Dover, 1951).Google Scholar
  4. 4.
    Some Strangeness in the Proportion, p. 480.Google Scholar
  5. 5.
    Robert Nozick, Newcomb’s problem and two principles of choice, in Essays in Honor of Carl G. Hempel, ed. Nicholas Rescher (Dordrecht, Netherlands: D. Reidel, 1969), pp. 114–146.CrossRefGoogle Scholar
  6. 6.
    Martin Gardner, Mathematical games, Scientific American (July 1973), 104–108.Google Scholar
  7. 7.
    See Nozick’s reply to those who responded to Gardner’s Scientific American article (note 6) in Martin Gardner, Mathematical games, Scientific American (March 1974), 102–108. Since Nozick’s reply, the literature on Newcomb’s problem has expanded rapidly and is too large to cite here. One recent article of note, with a number of citations, that bears directly on the argument to be made in this chapter, is David Lewis, Prisoners’ Dilemma is a Newcomb problem, Philos. Public Affairs 8, 3 (Spring 1979), 235–240.Google Scholar
  8. 7.a
    See also Isaac Levi, A Note on Newcombmania, J. Philos. 79, 6 (June 1982), 337–342;CrossRefGoogle Scholar
  9. 7.b
    7.b and Ellery Eells, Rational Decision and Causality (Cambridge: Cambridge University Press, 1982).Google Scholar
  10. 8.
    Sections 3.3–3.7 are based on Steven J. Brams, Newcomb’s problem and Prisoners’ Dilemma, J. Conflict Resolution 19, 4 (December 1975), 596–612. This material was also used in Brams, Paradoxes in Politics: An Introduction to the Non-obvious in Politics (New York: Free Press, 1976), Chap. 8.Google Scholar
  11. 9.
    Nozick, Newcomb’s problem and two principles of choice, p. 117. 10. Nozick’s reply in Gardner, Mathematical games, Scientific American (March 1974), 108.Google Scholar
  12. 12.
    The so-called Stackelberg solution in duopoly theory in economics also distinguishes between a “leader” and a “follower.” See John M. Henderson and Richard E. Quandt, Microeconomic Theory: A Mathematical Approach, 2nd Ed. (New York: McGraw-Hill, 1971), pp. 229–231.zbMATHGoogle Scholar
  13. 13.
    Nigel Howard, Paradoxes of Rationality: Theory of Metagames and Political Behavior (Cambridge, MA: MIT Press, 1971). For an overview of this theory, with examples, and some of the controversy it has generated, see Brams, Paradoxes in Politics, Chaps. 4 and 5. For a refinement of Howard’s notion of metarational outcomes,Google Scholar
  14. 13a.
    see Niall M. Fraser and Keith W. Hipel, Solving complex conflicts, IEEE Trans. Systems, Man, and Cybernetics SCM-9, 12 (December 1979), 805–816.CrossRefGoogle Scholar
  15. 14.
    This framework has been extended in Steven J. Brams, Morton D. Davis, and Philip D. Straffin, Jr., The geometry of the arms race, Int. Studies Quarterly 23, 4 (December 1979), 567–588; see the comment on this article by Raymond Dacey, Detection and disarmament, pp. 589–598, and Brams, Davis, and Straffin, A reply to “Detection and disarmament,” pp. 599–600, in the same issue. Further refinements in this framework can be found in Dacey, Detection, inference and the arms race, in Reason and Decision, Bowling Green Studies in Applied Philosophy, Vol. III-1981, ed. Michael Bradie and Kenneth Sayre (Bowling Green, OH: Applied Philosophy Program, Bowling Green State University, 1982), pp. 87–100.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1983

Authors and Affiliations

  • Steven J. Brams
    • 1
  1. 1.Department of PoliticsNew York UniversityNew YorkUSA

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