Pascal’s Wager
“Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is.” [Blaise Pascal, Pensées, Infini-Rien]
Pascal's Wager is an attempt to justify belief in God not with an appeal to evidence for his existence but rather with an appeal to self-interest. It is in our interests to believe in the God of Christianity, the argument suggests, and it is therefore rational for us to do so. The argument is attributed to Blaise Pascal on the basis of a section of his Pensées entitled “Infini-rien”. Some defenders of Pascal insist that his argument there is both more subtle and more defensible than the argument that we now call “Pascal’s Wager”. However, Pascal’s Wager has achieved sufficient popularity to warrant discussion irrespective of whether it is what Pascal intended in Infini-rien.
Pascal’s Wager seeks to justify Christian faith by considering the various possible consequences of belief and disbelief in the God of Christianity. If we believe in the Christian God, the argument runs, then if he exists then we will receive an infinitely great reward in heaven while if he does not then we will have lost little or nothing. If we do not believe in the Christian God, the argument continues, then if he exists then we will receive an infinitely great punishment in hell while if he does not then we will have gained little or nothing. The possible outcomes of belief in the Christian God, then, are on balance better than the possible outcomes of disbelief in the Christian God. It is better to either receive an infinitely great reward in heaven or lose little or nothing than it is to either receive an infinitely great punishment in hell or gain little or nothing.
The conclusion that Pascal’s Wager draws from this is that belief in the Christian God is the rational course of action, even if there is no evidence that he exists. If the Christian God does not exist then it is of little importance whether we believe or disbelieve in him. If the Christian God does exist then it is of great importance that we do believe in him. In order to cover ourselves in all circumstances, therefore, we ought to believe that the Christian God exists. A formal statement of this argument might be constructed as follows:
(1) It is possible that the Christian God exists and it is possible that the Christian God does not exist.
(2) If one believes in the Christian God then if he exists then one receives an infinitely great reward and if he does not exist then one loses little or nothing.
(3) If one does not believe in the Christian God then if he exists then one receives an infinitely great punishment and if he does not exist then one gains little or nothing.
(4) It is better to either receive an infinitely great reward or lose little or nothing than it is to either receive an infinitely great punishment or gain little or nothing.
Therefore:
(5) It is better to believe in the Christian God than it is to disbelieve in the Christian God.
(6) If one course of action is better than another then it is rational to follow that course of action and irrational to follow the other.
Therefore:
(7) It is rational to believe in the Christian God and irrational to disbelieve in the Christian God.
Three common objections to this argument will be considered here. A more detailed discussion of each can be found by following the appropriate link.
The first of these objections targets the third premise of the argument as it is stated above. It is the objection that Pascal’s Wager illicitly assumes a Christian view of the criteria for entrance into heaven, i.e. it illicitly assumes that if there are infinite rewards and punishments to be had then they will be distributed on the basis of belief or disbelief in the Christian god. There are many possible ways in which such rewards and punishments might be distributed; they might be distributed on the basis of belief in the Christian God, or on the basis of good deeds, or on the basis of belief in the Muslim God, for instance. In fact, distribution of heavenly rewards and infernal punishments on almost any basis imaginable appears to be possible. It is only, however, if such rewards and punishments are distributed on the basis of belief in the Christian God that belief in the Christian God is in our interests. On many of the other possible distributive schemes, it is by disbelieving in the Christian God that one receives a heavenly reward. If any of those distributive schemes were the true scheme, though, then the third premise of Pascal’s Wager would be false. It would not be the case that if one does not believe in the Christian God and the Christian God does not exist then one gains little or nothing, for if such a distributive scheme were the true scheme then one might gain a great deal (i.e. an infinite reward in heaven) by disbelieving in the Christian God. In order to demonstrate that the third premise of his argument is true, then, the advocate of Pascal’s Wager must demonstrate that the only possible criterion for entrance into heaven is belief in the Christian God and the only possible criterion for entrance into hell is disbelief in the Christian God. This, the objector suggests, cannot be demonstrated, for it is false.
The second objection to Pascal’s Wager targets the fourth premise of the argument as it is stated above. It is the objection that the probability that God exists, and so the probability of either receiving an infinite reward in heaven or of receiving an infinite punishment in hell, is so small that these possible outcomes of belief or disbelief can be discounted. The choice between belief and disbelief is thus taken to be a choice between losing little or nothing and gaining little or nothing. As it is better to gain little or nothing than it is to lose little or nothing, this objection concludes that it is wagering on atheism, rather than wagering on theism, that is the rational course of action. It is better, the objection suggests, to take the certain benefits of disbelief (the joys of indulging in sin and of being free from religious commitments) by wagering that God doesn’t exist than it is gamble on the vastly improbable hope of a heavenly reward and almost certainly gain nothing at all.
The third objection targets the inference from the fifth and sixth premises to the conclusion. It is the objection that we cannot choose our beliefs. We form our beliefs on the basis of evidence, not on the basis of desire. No matter how much one may want to believe that a given proposition is true, one cannot bring oneself to do so simply through an act of will. Rather, in order for one to come to believe that a proposition is true one requires evidence for its truth. Pascal’s Wager, though, merely prescribes belief in God; it does not provide any evidence that such a belief would be true. As such, it asks us to do the impossible: to believe without reason.
Wagering on Atheism
The second objection to Pascal’s Wager. That the probability that the Christian God exists is so small that it is wagering on atheism, rather than wagering on theism, that is the rational course of action.
In calculating whether belief in the Christian God or disbelief in the Christian God is the more prudent course of action, it is necessary not only to take account of the various possible outcomes of belief and disbelief, but also to take account of the probability of each of these outcomes occurring.
The possible outcomes of belief in the Christian God - either receiving an infinitely great reward in heaven or losing little or nothing - are better than the possible outcomes of disbelief in the Christian God - either receiving an infinitely great punishment in hell or gaining little or nothing. If the probability of each of these outcomes were approximately equal, then belief would clearly be preferable to disbelief.
If, however, the probability that the Christian God exists were so slight as to be negligible, then we might be justified in setting aside the possibilities of heavenly rewards and infernal punishments in deciding what to believe. The choice between belief and disbelief would thus become a choice between losing little or nothing and gaining little or nothing; heaven and hell would not come into the equation. As it is better to gain little or nothing than it is to lose little or nothing, in this case it would be disbelief in the Christian God rather than belief in him that would be the prudent course of action.
Those who object to Pascal’s Wager on these grounds take themselves to be in exactly this situation; they judge the existence of the Christian God to be so unlikely that they need not seriously entertain it as a possibility. They therefore hold that it is rational to take the certain benefits of disbelief (the joys of indulging in sin and of being free from religious commitments), and irrational to gamble on the hope of a heavenly reward and almost certainly receive nothing at all.
There are three types of response to this objection available to the advocate of Pascal’s Wager.
The first response to this objection available to the advocate of Pascal’s Wager is the denial that it is improbable that the Christian God exists. One way of doing this would be to offer an argument for agnosticism. Indeed, Pascal’s discussion in “Infini-Rien” is based on just an argument; Pascal claims that because our minds are finite we cannot comprehend the infinite and so cannot decide whether or not God exists on the basis of evidence. A second way of doing this would be to offer some positive evidence for the existence of God, e.g. the argument from fine-tuning. Certainly the claim that God’s existence is unlikely is debatable, and the theist should criticise the objection to Pascal’s Wager on this point.
The second response to the objection available to the advocate of Pascal’s Wager is not only consistent with God’s existence being improbable, but is even consistent with God’s existence being impossible. This response involves the denial that a life without faith is better than a life with faith if God does not exist. Religious faith can, this response notes, bring rewards in this life even if not in the next. Even if there are no eternal rewards and punishments, it suggests, those with religious faith live lives with a sense of value and purpose that is seldom found elsewhere. It might thus be maintained that belief in God is in our interests irrespective of whether or not God exists, and so that belief in God is pragmatically justified no matter how improbable it is that such beliefs are true. The difficulty with this response is that in addition to those that have found that religion adds fulfilment to their lives there are those that have found religion stifling and oppressive. Belief in God does not always bring with it obvious rewards in this life; indeed, it is in many cases associated with suffering and persecution.
The third possible line of defence for the advocate of Pascal’s Wager stresses the magnitude of the possible punishments and rewards that are at stake when we decide whether or not to believe. What is at stake when one decides whether to believe or to disbelieve in God, the argument suggests, is not the possibility of receiving either a great reward or a great punishment. Rather, what is at stake is the possibility of receiving either an infinite reward or an infinite punishment. It is sometimes argued that where infinite rewards and punishments are at stake, we ought to be prepared to take any finite risk in attempting to secure the reward and to avoid the punishment, irrespective of the probability of our succeeding in doing so. What ought we not to risk in pursuit of such a prize as heaven?
We Cannot Choose our Beliefs
The third objection to Pascal’s Wager relates to a philosophical theory called “doxastic voluntarism”. “Doxastic” means “pertaining to belief”. “Voluntarist” theories are theories that emphasise the primacy of the will. Doxastic voluntarism is thus the theory that belief is subject to the will, i.e. that we are able to choose what to believe.
There are certain cases in which doxastic voluntarism clearly does not hold. We cannot simply choose to believe that it is the year 2020 and that elephants rule the Earth; we cannot induce this belief in ourselves by a sheer act of will. Many philosophers think that doxastic voluntarism is false in all circumstances; that belief is entirely subject to reason rather than to the will. If this is true, then it presents a problem for Pascal’s Wager.
The objection to Pascal’s Wager is that we form our beliefs on the basis of evidence, not on the basis of desire, i.e. that we cannot choose our beliefs. No matter how much I may want to believe that a given proposition is true, I cannot bring myself to do so simply by willing that I do so. Rather, in order to come to believe that the proposition is true I require some evidence for its truth.
If this is correct, then in prescribing that we choose to believe in God Pascal’s Wager is prescribing the impossible. Pascal’s Wager may be sound insofar as it tells us to do all we can to bring it about that we believe in God, but if we are unable to do anything to bring it about that we believe in God then this conclusion will hardly be significant.
Some respond to this objection by mounting at least a partial defence of doxastic voluntarism. It may be that doxastic voluntarism is false with regard to certain beliefs, such as the belief that it is the year 2020 and that elephants rule the Earth. With regard to certain other beliefs, including belief in the existence of God, however, doxastic voluntarism is somewhat more plausible. We have a great deal of evidence, it might be argued, that it is not the year 2020 and that elephants do not rule the Earth, and it is this evidence that prevents us from choosing to believe both that it is and that they do. What evidence we have concerning the existence of God, however, is far less conclusive, and so an element of choice whether to believe or to disbelieve remains.
A stronger response to the objection, however, is to concentrate on the indirect control that we have over our beliefs. Doxastic voluntarism may be false, i.e. it may be false that we can induce in ourselves a belief in God simply by willing that we so believe, but Pascal’s Wager does not distinguish between beliefs formed by the will and beliefs formed in any other way. Pascal’s Wager prescribes belief in God; it does not prescribe belief in God by a sheer act of will. There are other means by which it is possible to induce in oneself a belief in God, and if the only problem with Pascal’s Wager were that doxastic voluntarism is false then it would demonstrate that we ought to use these other means in order to bring ourselves to believe.
Though we do not have direct, voluntary control over our beliefs, it does seem that we have indirect control over them. We are able, for instance, to exercise control over the kinds of evidence to which we are exposed. We can choose to associate with people who believe in God; we can choose to read books by noted apologists; we can choose to act is if we believe and see what happens. Each of these choices would increase the likelihood of our coming to believe in God. If Pascal’s Wager is correct in saying that we ought to exercise what control we can over our beliefs in an attempt to induce in ourselves a belief in God, therefore, then we ought to do each of these things.
There are also other, more cynical ways in which we can exercise control over our beliefs. Using the techniques of hypnosis it is possible to induce beliefs in a subject without any regard for evidence at all. If one were thoroughly convinced of Pascal’s Wager, therefore, then one might choose to exercise control over one’s beliefs by hiring a hypnotist.
There are, then, some things that we can do to influence our beliefs even if doxastic voluntarism is false. Even if we cannot induce in ourselves a belief in God simply by an act of will, we can exercise control over our beliefs in other ways. If Pascal’s Wager is to be resisted, therefore, then this must be done on some other ground than that we cannot choose our beliefs.
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