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Pascal’s Wager
Glenn
Mason-Riseborough (13/3/2000)
Terminology: To use modern (Bayesian) terminology, Pascal formulates his Wager in terms of decision theory. Both the possible relevant states of the world and the possible actions of the agent are considered. Often this is depicted graphically as a decision matrix, in which the columns represent the former and the rows the latter. Utilities, numbers that correspond to the degree to which the agent values them, are assigned to each box in the matrix. In decisions under risk, the columns (states of the world) are additionally given subjective probability weightings; in decisions under uncertainty, no probabilities are given. When considering decisions under risk, rationality requires that one should choose the row with the greatest expected utility (EU) or expectation. That is, one should choose the row with greatest total value when the utilities are multiplied by the respective probabilities and are added across the rows. When considering decisions under uncertainty, the best action superdominates the worst action. That is, rationality requires that one chooses the row in which the worst outcome is at least as good as the best outcome of the other row.
In a single paragraph of his Pensées, Pascal gives at least three separate arguments that might be called wagers, only the third of which is usually called Pascal’s Wager. This third formulation is a decision under risk, and the probability of God’s existence is given as non-zero and non-infinitesimal. The decision matrix of Pascal’s Wager is:
|
|
God Exists |
God Does Not Exist |
|
Wager For God |
Infinite Gain |
Finite Loss |
|
Wager Against God |
Infinite Loss |
Finite Gain |
Some possible objections (consider if
they work, and how they might be replied to):
1. The Utilities may be questioned: (a) It is not possible to have an infinite utility. Either the utility of salvation must be finite or, alternatively, human conception is so limited that infinite reward could only be finitely appreciated. (b) Different utilities for different people. Either God’s “Chosen People” are predestined for reward and others are not (no matter what they believe), or salvation might appeal to some people more than it does to others. (c) It is possible to have infinite reward on earth, even as finite beings in the face of God’s non-existence (perhaps it could be further said that those who wager for God’s existence are not fully flourishing human beings and have infinite loss).
2. The matrix should have more columns (Many-Gods objection): The “God Does Not Exist” column could be subdivided into various other theistic hypotheses. In fact, one might say that there are infinitely many gods to consider.
3. The matrix should have more rows: (a) There is more than one way to wager for God, and maybe His rewards vary accordingly. E.g., He might give less reward to those who wager for the mercenary reasons that Pascal gives. (b) There is more than one way to wager against God – consider agnosticism vs. atheism.
4. Assigning a probability for God’s existence: (a) The probability of God’s existence remains undefined because it is impossible to assign. To assign a probability is to feign having evidence that one, in fact, lacks. (b) Contrary to Pascal, there are evidential considerations. E.g., the Argument from Evil tells us that the theistic concept of God is incoherent, and thus the probability of God existing is zero. (c) Given (2) above, the probability of God existing is infinitesimal if we assume equal probability to each possible god.
5. Rationality does not require maximising expected utility: (a) Some paradoxes show that maximising expectation can lead one to perform intuitively sub-optimal actions. (b) We might also distinguish between practical rationality and theoretical rationality. The first requires one to maximise expected utility, but the second requires proportioning belief to the amount of evidence available.
6. The argument is invalid: At the extreme, even if you devote all your energy to avoiding belief in God, there is still a non-zero probability of your efforts failing and, despite your best intentions, wagering for God. Even in this case there will be an infinite expected utility, and thus there is no single maximum expected utility.
7. Moral objections: Even assuming it is prudential to wager for God, it does not follow that one should wager thusly. It might not be moral to wager for God. E.g., (a) the putative divine plan might itself be morally wrong; or (b) believing something on insufficient grounds harms society by promoting credulity; or (c) wagering and appealing to self-interest are unworthy of theistic belief.
8. What does it mean to “Wager for God”? Even if one is convinced by
the Wager, it still may be difficult, or even impossible, to become a believer,
and rationality cannot require the impossible.
Pascal considers this objection and argues that through acting like a
believer one will eventually be a believer. We might question Pascal’s theory of the psychology of belief
formation and suggest that some people may fail.
One way of summarising some parts of the first three objections in the form of a decision matrix is to change the utilities as follows:
|
|
God Exists |
God Does Not Exist |
|
Wager For God |
Possible Infinite Gain |
Infinite Loss |
|
Wager Against God |
Infinite Loss |
Possible Infinite Gain |
The upper-right utility is a summary of the flourishing objection (1c); the lower-right utility is a summary of the many-Gods objection (2); the upper-left utility is a summary of the many-rows objection (3a). When these modifications are made, it is clear that both rows have the same expected utility, and rationality does not require wagering for God.