Abstract
A person who does not have good intellectual reasons for believing in God can, depending on his probabilities and values for consequences of believing, have good practical reasons. Pascalian wagers founded on a variety of possible probability/value profiles are examined from a Bayesian perspective central to which is the idea that states and options are pragmatically reasonable only if they maximize subjective expected value. Attention is paid to problems posed by representations of values by Cantorian infinities. An appendix attends to Robinsonian hyperreals. Another appendix presents for comparison Newcomb's Problem and a problem in some ways like it suggested, I think, by ideas of John Calvin.
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References
Arnauld, A.: 1964, The Art of Thinking (Port Royal Logic), tr. J. Dickoff and P. James, Bobbs-Merrill, Indianapolis.
Bennett, J.: 1990, ‘Why Is Belief Involuntary?’, Analysis 50, 87–107.
Boolos, G.: 1987, ‘The Consistency of Frege's Foundations of Arithmetic’, in J. J. Thomson (ed.), On Being and Saying: Essays for Richard Cartwright, MIT, Cambridge, Massachusetts, pp. 3–20.
Clifford, W. K.: 1989, ‘The Ethics of Belief’, in J. Feinberg (ed.), Reason and Responsibility, Seventh Edition, Wadsworth, Belmont, California, pp. 76–9.
Conway, J. H.: 1976, On Numbers and Games, Academic Press, London.
Davis, M. and R. Hersh: 1972, ‘Nonstandard Analysis’, Scientific American, 78–86.
Duff, A.: 1986, ‘Pascal's Wager and Infinite Utilities’, Analysis 46, 107–9.
Falk, W. D.: 1968, ‘Morality, Self, and Others’, in J. J. Thomson and G. Dworkin (eds.), Ethics, MIT, New York, pp. 349–90.
Hacking, I.: 1972, ‘The Logic of Pascal's Wager’, American Philosophical Quarterly 9, 186–92.
Hàjek, A.: 1994, ‘Waging War on Pascal's Wager’, draft of September 9, 1994.
Henle, J. M and E. M. Kleinberg: 1979, Infinitesimal Calculus, MIT Press, Cambridge, Massachusetts.
Holton, R.: 1994, ‘Deciding to Trust, Coming to Believe’, Australasian Journal of Philosophy 72, 63–76.
Hume, D.: 1902, in L. A. Selby-Bigge (ed.), Enquiries Concerning the Human Understanding and Concerning the Principles of Morals, Second Edition, Clarendon Press, Oxford. (First published in 1748 and 1751 respectively.)
Hunter, G.: 1973, Metalogic: An Introduction to the Metatheory of Standard First Order Logic, University of California, Berkeley and Los Angeles.
Hunter, G.: 1988, ‘Is Consistency Enough for Existence in Mathematics?’, Analysis 18, 3–5.
James, W.: The Will to Believe and Other Essays in Popular Philosophy and Human Immortality, Dover Publications.
Jeffrey, R. C.: 1985, ‘Probability and the Art of Judgment’, in P. Achinstein and O. Hannaway (eds.), Observation, Experiment, and Hypothesis in Modern Physical Science, MIT, Cambridge, Massachusetts, pp. 95–126.
Jeffrey, R. C.: 1990, The Logic of Decision: Second Edition, University of Chicago Press, Chicago.
Jeffrey, R. C.: 1995, ‘Decision Theory’, in R. Audi (ed.), The Cambridge Dictionary of Philosophy, University Press, Cambridge.
Jordan, J. (ed.): 1994, Gambling on God: Essays on Pascal's Wager, Rowman and Littlefield Publishers, Lanham, Maryland.
Koons, R.: 1993, ‘Faith, Probability and Infinite Passion: Ramseyian Decision Theory and Kierkegaard's Account of Christian Faith’, Faith and Philosophy 10, 145–60.
Lycan, W. C. and G. Schlesinger: 1989, ‘You Bet Your Life: Pascal's Wager Defended’, in J. Feinberg (ed.), Reason and Responsibilities, Seventh Edition, Wadsworth, Belmont, California, pp. 82–90.
Mackie, J. L.: 1982, The Miracle of Theism: Arguments for and Against the Existence of God, Clarendon Press, Oxford.
Martin, W.: 1990, Atheism: A Philosophical Justification, Temple University Press, Philadelphia.
Mavrodes, G.: 1981, ‘Belief, Proportionality, and Probability’, in M. Bradie and K. Saryre (eds.), Reason and Decision (Bowling Green Studies in Applied Philosophy, Vol. III), pp. 58–68.
McClennen, E. F.: 1994, ‘Pascal's Wager and Finite Decision Theory’, in Jordan 1994.
Moore, G. E.: 1993, in Thomas Baldwin (ed.), Principia Ethica: Revised Edition, Cambridge University Press, Cambridge.
Nalebuff, B.: 1989, ‘Puzzles: The Other Person's Envelope is Always Greener’, Journal of Economic Perspectives 3, 171–91.
Nozick, R.: 1969, ‘Newcomb's Problem and Two Principles of Choice’, in N. Rescher (ed.), Essays in Honor of Carl G. Hempel, Dordrecht.
Pascal, B.: 1947, Pascal's Pensées (with an English translation, brief notes, and introduction by H. F. Stewart), Modern Library, New York.
Pascal, B.: 1962, Pascal's Pensées, tr. M. Turnell, Harper and Row, New York.
Pascal, B.: 1989, ‘The Wager’, translation by W. F. Trottier (New York: Collier and Son, 1922), in J. Feinberg (ed.), Reason and Responsibility, Seventh Edition, Wadsworth, Belmont, California, pp. 80–2. (Let me make the following correction. Insert after ‘infinity’ in line 1, second column, page 81: ‘of chances there is one for you, if there were an infinity’.)
Plantinga, A.: 1974, God, Freedom, and Evil, Harper and Row, New York.
Rowe, W.: 1993, Philosophy of Religion: An Introduction, Second Edition, Belmont, California.
Rescher, N.: 1985, Pascal's Wager: A Study of Practical Reasoning in Philosophical Theology, University of Notre Dame, Notre Dame.
Schlesinger, G.: 1994, ‘A Central Theistic Argument’, in Jordan 1994.
Sobel, J. H.: 1983, ‘Expected Utilities and Rational Actions and Choices’, Theoria 49, 159–83 (revised in Sobel 1994).
Sobel, J. H.: 1986, ‘Notes on Decision Theory: Old Wine in New Bottles’, Australasian Journal of Philosophy 64, 407–37 (revised in Sobel 1994).
Sobel, J. H.: 1988, ‘Infallible Predictors’, Philosophical Review 97, 3–24 (revised in Sobel 1994).
Sobel, J. H.: 1990, ‘Maximization, Stability of Decision, and Actions in Accordance with Reason’, Philosophy of Science 57, 60–77 (revised in Sobel 1994).
Sobel, J. H.: 1994, Taking Chances: Essays on Rational Choice, Cambridge University Press, Cambridge.
Sobel, J. H.: forthcoming, ‘Cyclical Preferences and World Bayesianism’.
Sorensen, R.: 1994, ‘Infinite Decision Theory’, in Jordan 1994.
Swinburne, R. G.: 1969, ‘The Christian Wager’, Religious Studies 4, 217–28.
Williams, B.: 1973, ‘Deciding to Believe’, in Problems of the Self, University Press, Cambridge, pp. 135–51.
Zakon, E.: 1969, ‘Remarks on the Nonstandard Real Axis’, in W. A. J. Luxemburg (ed.), Applications of Model Theory to Algebra, Analysis and Probability, Holt, Rinehart, and Winston, New York, pp. 195–227.
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Sobel, J.H. Pascalian wagers. Synthese 108, 11–61 (1996). https://doi.org/10.1007/BF00414004
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DOI: https://doi.org/10.1007/BF00414004