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19. Pascal's Wager is not to be accepted.

19.1 There is an argument, known as Pascal's Wager, to the effect that although we are unsure whether there is a God or not, we still ought to believe in him on the basis of expected reward (using "expected" in the probabilistic sense of V * p, where V = "value of outcome" & p = "probability of occurrence of outcome").

19.2 The argument proceeds as follows. Since the gain obtained if our belief in the Christian God turns out to be well placed is infinite (eternal bliss) whereas the loss incurred by believing in vain is finite (loss of some pleasure during a finite life), we are being rational to believe however low the probability of our belief being correct is taken to be, because our expected gain is infinite, whereas our expected loss is finite.

19.3 This argument is fallacious for several reasons.

19.3.1 It does not work in the very case for which Pascal is arguing - ie. there is no evidence in the Bible or from Christian tradition to suggest that God would award eternal life to anyone whose faith was of this "insurance policy" type.

19.3.2 It is not possible to "turn on" belief at will. The most that can be done is to make a pretence, which would not deceive an omniscient God.

19.3.3 The argument is the ultimate abuse of the laws of probability, which are aimed at events that occur, or may be induced to occur, many times. Admittedly, we have on occasion used probabilities in this irregular sense ourselves, but we have not multiplied these numbers by infinities. As is well known, the product of two variables, one of which tends asymptotically to infinity while the other tends to zero, may be zero, infinity or any value in between depending on the relationship between the variables. Consequently, we have no assurance that the "expected reward" of our pseudo-faith is non-zero.

19.3.4 Because it is difficult to justify assigning a zero probability to any non self-contradictory statement, Pascal's wager could be applied equally validly to any belief with potentially infinite rewards. If the argument is correct, we would be as rational to become Muslims as Christians. Indeed, we would be more rational to become Muslims, since we would be more likely to reap our reward, if there is one, under the terms of Islam than under those of Christianity.

19.4 The reason I have stressed this point is because religion is for many an insurance policy, and many seem to accept the Wager on this basis. It would be easy to slide from belief to this position. To do so would be to evade all the issues.

© Theo Todman 1992 - 2000.
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