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Infinite Return: Two Ways of Wagering with Pascal
Published online by Cambridge University Press: 24 October 2008
Abstract
Pascal's wager has fascinated philosophers far in excess of its reputation as effective apologetics. Very few of the wager's defenders, in fact, have retained more than an academic interest in its power to persuade. Partly this is a matter of good manners. Pascal is supposed to have pitched his wager at folks who understand only self-interested motivations, and today it is no longer fashionable for defenders of theism to disparage the character of their opponents. But partly the low-key concern with apologetics expresses a philosophical judgement. Pascal's defenders have found the question of the wager's audience to be less philosophically engaging than the logic of its argument. I believe that this assessment is mistaken. The most puzzling feature of Pascal's wager is its invocation of infinite utility. What are finite human beings, theists or otherwise, supposed to make of the idea of an infinitely desirable happiness? There are, I will argue, two sorts of response to this question, and depending on which sort Pascal had in mind, the logic of his wager comes out very differently.
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References
1 The wager spans numbers 418–426 of Krailsheimer's, A. J. translation of Pascal's Pensées (New York: Penguin Books, 1966)Google Scholar. Throughout this paper, I will be referring to Krailsheimer's translation, which follows the ordering favoured by the French editions of Louis Lafuma.
2 In the two situations I describe, Pascal's reasoning is explicitly probabilistic. Ian Hacking has identified a third version of the wager in which betting on God is simply the best decision no matter what the world is like. This other version circumvents considerations of probability altogether. Despite suggestive passages, I am not convinced that Pascal would have intended anyone to accept a simple strategy of dominance as a serious inducement to wager, but I admit the possibility and discuss it later on. Hacking's analysis of the wager can be found in The Emergence of Probability (Cambridge: Cambridge University Press, 1975), pp. 63–72Google Scholar.
3 See ‘Pascalian Wagering’ in Morris, Anselmian Explorations (Notre Dame: University of Notre Dame Press, 1987)Google Scholar. Morris wants to distinguish two versions of the wager. One version, ‘the epistemically unconcerned’ version, entertains a vast probability disparity between theism and atheism. The other version, ‘epistemically concerned’, takes its point of departure from counterbalancing evidential claims for and against theism. Morris contends that the second version of the wager is eminently more defensible than the first.
4 Morris does not believe that Pascal would have claimed otherwise. The Pensées, however, offer no easy access to Pascal's intentions on the matter. Note 420 (p. 153): ‘“Do you believe that it is impossible for God to be infinite and indivisible?” – “Yes.” – “Very well, I will show you something infinite and indivisible: it is a point moving everywhere at an infinite speed.”’ Pascal insists in 418 that the wager works for very low probabilities of winning. When 420 is read in conjunction with this insistence, it appears that Pascal would have allowed logical possibility alone to dictate a probability assignment for God's existence. My own suspicion is that Pascal never distinguished epistemically concerned and unconcerned versions of his wager because he assumed that degrees of probability would have no bearing on the rationality of decision-making if one of the choices were to promise an infinite payoff. Morris challenges this assumption.
5 No. 418 (p. 151).
6 No. 418 (p. 153).
7 Pascal's Wager: A Study of Practical Reasoning in Philosophical Theology (Notre Dame: University of Notre Dame Press, 1985). See especially pp. 117–20Google Scholar.
8 The maximin rule. For explication, see Resnik, Michel D., Choices: An Introduction to Decision Theory (Minneapolis: University of Minnesota Press, 1987), sec. 2–2Google Scholar.
9 The implication rests on Pascal's willingness to take not betting on God as equivalent (in effect) to betting against God.
10 Due Jean Floressas des Esseintes. À Rebour has been translated as Against Nature by Robert, Baldick (New York: Penguin Books, 1959)Google Scholar.
11 It is notorious that converts underestimate the degree of psychological continuity between their converted and unconverted ways of life.
12 Let the concept of a ‘token non-zero probability’ stand for probability assignments whose only rationale is that of logical possibility. Someone who had no reason to believe in the impossibility of God's existence, but whose ignorance of God left him or her no basis for thinking such existence likely, would if pushed assign God a token non-zero probability.
13 Note, for example, No. 427 (pp. 156–7): ‘This negligence in a matter where they themselves, their eternity, their all are at stake, fills me more with irritation than pity; it astounds and appalls me; it seems quite monstrous to me. I do not say this prompted by the pious zeal of spiritual devotion. I mean on the contrary that we ought to have this feeling from principles of human interest and self-esteem. For that we need only see what the least enlightened see.’
14 No. 199 (pp. 88–95), cf. No. 68 (p. 48).
15 Pascal's sense of the incongruity between self-knowledge and natural knowledge need not be couched in the quaint metaphysics of mind/body dualism. See, for an alternative, Thomas Nagel's richly suggestive articles, ‘The Absurd’ and ‘Subjective and Objective’, in his Mortal Questions (Cambridge: Cambridge University Press, 1979)Google Scholar.
16 No. 136 (p. 68).
17 Conf. 1.1.1: ‘…fecisti nos ad te et inquietum est cor nostrum, donec requiescat in te.’ [‘…you made us to be for you, and restless are our hearts until they rest in you.’]
18 For his argument see ‘The Makropulos Case: Reflections on the Tedium of Immortality’, in Problems of the Self (Cambridge: Cambridge University Press, 1973)Google Scholar. Richard, Sorabji offers a brief response to Williams in Time, Creation, and the Continuum (Ithaca: Cornell University Press, 1983), pp. 181–2Google Scholar.
19 I revised this paper in light of comments offered by Tom Morris, Dan Little, and William Wainwright. They have my thanks.
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