Pascal's Wager

Pascal's Wager is the French philosopher Blaise Pascal's application of decision theory to the belief in God. It is also occasionally known as Pascal's Gambit. It appears in the Pensées, a posthumous collection of Pascal's notes for an unfinished treatise on Christian apologetics. Pascal argued that it is a better "bet" to believe that God exists, because the expected value of believing that God exists is always greater than the expected value resulting from non-belief. Indeed, he claimed that the expected value is infinite. Pascal believed that it was inexcusable not to investigate this question: "Before entering into the proofs of the Christian religion, I find it necessary to point out the sinfulness of those men who live in indifference to the search for truth in a matter which is so important to them, and which touches them so nearly."

Variations of this argument may be found in other religious philosophies, such as Islam, Hinduism, and even Buddhism (see below). Pascal's Wager is also similar in structure to the precautionary principle.



Explanation
The Wager is described by Pascal in the Pensées this way :

"Let us now speak according to natural lights...Let us then examine this point, and say, 'God is, or He is not.' But to which side shall we incline? Reason can decide nothing here. There is an infinite chaos which separated us. A game is being played at the extremity of this infinite distance where heads or tails will turn up… Which will you choose then? Let us see. Since you must choose, let us see which interests you least. You have two things to lose, the true and the good; and two things to stake, your reason and your will, your knowledge and your happiness; and your nature has two things to shun, error and misery. Your reason is no more shocked in choosing one rather than the other, since you must of necessity choose. This is one point settled. But your happiness? 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."

In his Wager, Pascal provides an analytical process for a person to evaluate options in regarding belief in God. As Pascal sets it out, the options are two: believe or not believe. There is no third possibility.

Therefore, we are faced with the following possibilities:
 * You believe in God.
 * If God exists, you go to heaven: your gain is infinite.
 * If God does not exist, your loss (the investment in your mistaken belief) is finite and therefore negligible.
 * You do not believe in God.
 * If God exists, you go to hell: your loss is infinite.
 * If God does not exist, your gain is finite and therefore negligible.

With these possibilities, and the principles of statistics, Pascal hoped to have demonstrated that the only prudent course of action is to believe in God. It is a simple application of game theory (to which Pascal had made important contributions).

Another way of portraying the Wager is as a decision under uncertainty with the values of the following decision matrix:

Given the values that Pascal proposes, the option of believing in God (B) dominates the option of not believing in God (~B). In other words, the expected value gained by choosing B is always greater than or equal to that of choosing ~B, regardless of the likelihood that God exists.

Reasons for its importance and seriousness
Some Christians feel that because one could die anytime, suddenly and unexpectedly, the Wager is especially important and one should take it very seriously and urgently. According to Christianity, God (Jesus Christ) will judge everybody after his Second Coming and the Second Coming could also occur at any time. Many Christians also believe that there are also signs that the Second Coming will occur soon. Some Christians believe and claim that the description of fire in hell and of hell being a lake of fire is literal indeed, making hell even more terrifying. These are all reasons that many Christians feel it is important to take Pascal's Wager more seriously.

Criticisms of Pascal's wager
Before entering the criticisms of the Wager, one fair and important thing to note is that Pascal hoped that if the wager doesn't convince unbelievers to become Christians, then it would at least show them, especially the "happy agnostics", the meaning, value, and probable necessity of considering the question of the existence of God.

In his other works, Pascal hoped to prove that the Christian faith (and not, for example, Islam or Paganism, which Pascal himself mentions in his Pensées) is correct. The criticism below works for the most part only when the wager is removed from its original context and considered separately, as many thinkers have done before the original plan of Pascal's apologia was discovered.

Pascal's argument has been severely criticized by many thinkers, including Voltaire. The incompleteness of his argument is the origin of the term Pascal's Flaw. Some criticisms are summarized below:

Assumes God rewards belief
Some writers suggest that wager does not account for the possibility that there is a God (or gods) who, rather than behaving as stated in certain parts of the Bible, instead rewards skepticism and punishes blind faith, or rewards honest reasoning and punishes feigned faith.

"Suppose there is a god who is watching us and choosing which souls of the deceased to bring to heaven, and this god really does want only the morally good to populate heaven. He will probably select from only those who made a significant and responsible effort to discover the truth. For all others are untrustworthy, being cognitively or morally inferior, or both. They will also be less likely ever to discover and commit to true beliefs about right and wrong. That is, if they have a significant and trustworthy concern for doing right and avoiding wrong, it follows necessarily that they must have a significant and trustworthy concern for knowing right and wrong. Since this knowledge requires knowledge about many fundamental facts of the universe (such as whether there is a god), it follows necessarily that such people must have a significant and trustworthy concern for always seeking out, testing, and confirming that their beliefs about such things are probably correct. Therefore, only such people can be sufficiently moral and trustworthy to deserve a place in heaven — unless god wishes to fill heaven with the morally lazy, irresponsible, or untrustworthy. (Richard Carrier)"

Assumes Christianity is the only religion which makes such a claim
The wager assumes that Christianity is the only religion which claims that a person will be judged, condemned, and punished by God if that person does not believe. However, Christianity is not the only religion which makes such a claim. There are also other religions which also claim that God will judge, condemn, and punish people who do not believe in him and their religion. They include Islam and some denominations of Hinduism.

Therefore, if one claims that others should believe in Christianity (or any other religion), solely for the possibility of being punished for not believing in it, then what would one say about other religions which make such a claim? As one who believes in a religion which makes that claim, what would one think about similar claims made by other religions anyway?

Even without similar claims from other religions, we can still find indefinitely many other possibilities offering eternal bliss and threatening eternal torment. For example, some unknown non-Christian gods might exist, and punish Christian believers for their failure to believe in them. Or some powerful entity might decide to punish those who believe in a god while rewarding non-believers.

In this way, Pascal's Wager can be used to deduce that it is advisable to believe in any or all of a variety of gods. However, the beliefs and claims of many separate religions have mutual exclusivity to each other. This means that they cannot both be true, or at least not both be the "one true religion". Complicating matters further, the belief systems of monotheistic religions require exclusive belief in the god of that religion, so the Wager is invalid when applied to such religions. This is the basis of the argument from inconsistent revelations. However, this problem does not apply to Hinduism and other pantheistic religions. The vast majority of the world's religions have been polytheistic. In polytheistic religions there may or may not be a fixed pantheon of deities; many or most pagan religions are open to the addition of new deities to the pantheon (although these additions are sometimes cast as new aspects of deities that were already in the pantheon). The Jewish faith expects a Gentile only to obey the Noahide Laws in order to receive reward in afterlife. In addition, some religions, including Buddhism, do not require a focus on a deity. A "many-gods" version of Pascal's Wager is reported by the 10th century Persian chronicler Ibn Rustah to have been taken by a king in the Caucasus, who observed Muslim, Jewish, and Christian rites equally, declaring that "I have decided to hedge my bets."

Does not constitute a true belief
Another common argument against the wager is that if a person is uncertain whether a particular religion is true and the god of that religion is real, but that person still "believes" in them because of the expectation of a reward and the fear of punishment, then that belief is not a true valid belief or a true faith in that religion and its god.

William James, in The Will to Believe, summarized this argument:

"Surely Pascal's own personal belief in masses and holy water had far other springs; and this celebrated page of his is but an argument for others, a last desperate snatch at a weapon against the hardness of the unbelieving heart. We feel that a faith in masses and holy water adopted willfully after such a mechanical calculation would lack the inner soul of faith's reality; and if we were ourselves in the place of the Deity, we should probably take particular pleasure in cutting off believers of this pattern from their infinite reward."

In modern times, this criticism is often leveled against evangelistic Christianity, especially those who try to incite fear by portraying such events as the Rapture in popular media. Such a belief is sometimes called "afterlife insurance," "Hell avoidance insurance," or "Heaven insurance."

Assumes one can choose belief
This criticism is similar to the last one. The wager says that if one is uncertain whether Christianity is true or not, then one should still believe in it just in case it is true. But, in order to believe that something is true, then that person must know and be certain that it is true (in contrast with the statement made by St. Augustine, "I believe, therefore I understand."). But if a person doesn't believe that it is true, then that person doesn't know and is uncertain that it is true. But, it is not as if someone doesn't know and is uncertain that something is true, then that person could decide to know and be and become certain that it is true. Basically, this argument says that even with the wager, such a reason to believe, true belief, knowledge, and certainty of something can only come to actually knowing, being certain, and seeing evidences that it is true. But if we can see evidences that it is true, then it is unnecessary to resort to the wager, a precautionary principle, as a reason to decide why we should believe in it.

However, some individuals such as Kierkegaard considered that a faith one has never doubted is of little value, and that doubt and faith are inseparable.

Another point related to this is that some Christians, such as Calvinists, believe that the human will is so affected by sin that God alone can bring about belief. However, they would still affirm that God can use rational arguments as one of his means to this end.

Pascal acknowledged that there would be some difficulty for an atheist intellectual persuaded by this argument, in putting it into effect. Belief may not come. But in such a case, he said, one could begin by acting as if it had come, hear a mass, and take holy water. Belief might then follow. Anyway, Pascal was a Roman Catholic, and some Protestants believe and claim that Catholics are not really Christians, so Pascal himself might be going to hell.

There is also the argument that one could "game" the wager in a scenario where the deathbed conversion is possible, as is the case in some streams of Christianity. The person who converts on their deathbed could have failed to have been dutiful in fulfilling their doctrinal obligations, and still gain the happiness associated with the Christian concept of "heaven." The danger here is well known to most Christians, as this is a common theme of sermons in a variety of denominations. The risk of taking this gamble only to die suddenly and unexpectedly or to experience the tribulation within one's own lifetime is often portrayed as a risk too great to take. Some others consider that one cannot fool God, and that such deathbed conversions could very well be dishonest. There are also a few Christians, such as Roman Catholics, who disagree with the doctrine of salvation by faith alone and that God also rewards good works.

Opportunity costs
The wager fails to mention any costs relating to belief. It is argued that there may be both direct costs (time, health, wealth) and opportunity costs, in the here and now. (These costs are distinct from the potentially infinite future cost of having bet on the wrong God, only to be punished after death by the true God.) Most modern religions require their followers to spend time attending religious services at houses of worship and to donate money to the maintenance of these places and their associated staffs of religious professionals, and/or to the needy, when possible. As a result, if a person believes in a God that does not exist, then that person has lost time and money that could have been used for some other purpose. This has been starkly illustrated by the destruction of expensive houses of worship in natural disasters for which the local populace failed to adequately prepare (e.g., Hurricane Katrina; the 2004 Indian Ocean earthquake and tsunami). Even in impoverished regions such as those affected by the Indian Ocean tsunami, organized religions extract enough wealth from their adherents to build comparatively lavish temples, mosques, and/or churches; while those who trusted futilely in various Gods to protect them would clearly have been better off investing their resources in protective measures with a demonstrated chance of helping, such as taller levees, tsunami warning systems, or the simple strategy of building on higher ground.

There may be opportunity costs for those who choose to believe in particular religions whose doctrines have real-world consequences: for example, scientific theories such as evolution (or heliocentrism) that appear to some to contradict scripture could theoretically enable a non-believer to discover things and accomplish things the creationist (or a geocentrist) could not. (In practice, when faced with overwhelming evidence for the value of an idea such as heliocentrism, or overwhelming social change such as the abolition of slavery, followers of a religion may be pragmatic enough to re-interpret or simply ignore scripture as necessary, perhaps after a delay of several centuries. Something similar may eventually occur among religious opponents of stem cell research if the technology gives rise to dramatic cures for serious illnesses.) It is also argued that belief incurs a cost by not allowing the believing person to participate in and enjoy actions forbidden by dogma. (Again, religions tend to relax restrictions over time for actions that become popular enough among their followers, e.g., rock music, the wearing of cosmetics by women, and divorce, potentially reducing this cost over time, although with unknown impact on the continued efficacy of the evolving belief system to spare its adherents from eternal damnation.) Many devout people make more noticeable sacrifices for their religious beliefs. For example, Jehovah's Witnesses do not accept blood transfusions; Islamic terrorists may sacrifice their lives in suicide attacks; snake handlers may be bitten and die.

Every religion requires its adherents to believe in some set of claims about the supernatural which are not supported by conclusive evidence. Thus its followers must set aside critical thinking in favor of faith when it comes to the pronouncements of religious authority, potentially increasing their risk of becoming victims of fraud (e.g., pious fraud, affinity fraud). Frauds occur in every realm of human activity, to be sure, but those with a rational world view may be more likely to expect fraudulent behavior, and thus try harder to guard against it, because they are aware of the evolutionary utility of lying. Contrast frauds in science, which were often exposed, and fairly quickly, by fellow scientists who systematically test each other's claims as a matter of course, to religious frauds which often had to be exposed by critics outside the religion.

On the surface, this claim of too much opportunity costs can be easily refuted by saying that the Bible itself claims that there are opportunity costs to the Christian faith. As the Apostle Paul states in 1 Corinthians 15:12-19 that if Christ was not raised from the dead (a central tenet of Christianity), then Christians are the most pitiable of all men: 12Now if Christ is proclaimed as raised from the dead, how can some of you say that there is no resurrection of the dead? 13But if there is no resurrection of the dead, then not even Christ has been raised. 14And if Christ has not been raised, then our preaching is in vain and your faith is in vain. 15We are even found to be misrepresenting God, because we testified about God that he raised Christ, whom he did not raise if it is true that the dead are not raised. 16For if the dead are not raised, not even Christ has been raised. 17And if Christ has not been raised, your faith is futile and you are still in your sins. 18Then those also who have fallen asleep in Christ have perished. 19 If in this life only we have hoped in Christ, we are of all people most to be pitied. (ESV, emphasis added)

To Pascal, however, such costs were insignificant. He considered secular life to be without meaning, consisting only in the vacuity of what he called "divertissement." On the other hand, he considered that only the contemplative life of a Christian feeling the love of God was truly rewarding for the human soul, God being to him the "supreme good."

Others have argued that the utility of salvation cannot be infinite, either via strict finitists or belief that an infinite utility could only be finitely enjoyed by finite humans.

Others believe that the punishment for unbelief is not always infinite either. They include Roman Catholics, who believe in the doctrine of purgatory.

Atheist's Wager
The Atheist's Wager is an atheistic response to Pascal's Wager. While Pascal suggested that it is better to take the chance of believing in a God that might not exist rather than to risk losing infinite happiness by disbelieving in a god that does, the Atheist's Wager suggests that:


 * You should live your life and try to make the world a better place for your being in it, whether or not you believe in God. If there is no God, you have lost nothing and will be remembered fondly by those you left behind. If there is a benevolent God, he will judge you on your merits and not just on whether or not you believed in him.

Many-way tie
Given that the choice of wagering has an infinite return, then under a mixed strategy the return is also infinite. Flipping a coin and taking the wager based on the result would then have an infinite return, as would the chance that after rejecting the wager you end up taking it after all. The choice would then not be between zero reward (or negative infinite) and infinite reward, but rather between different infinite rewards.

Decision-theoretic arguments
The above criticisms are addressed explicitly in a generalised decision-theoretic version of Pascal's argument, with probabilities interpreted in the Bayesian sense of expressing degrees of belief, and each option carrying certain utilities or payoffs.

This leads to the following matrix, where a, b, c and d are the utilities arising from each of the four options:

The total utility for believing in God is then aP + b( 1 − P ) while the total utility for non-belief is cP + d( 1 − P ), where P is the probability of the existence of God. Belief in God is thus optimal in decision-theoretic terms for all P > 0 if the values for the utilities satisfy the inequalities a > c and b ≥ d. The first inequality is relatively uncontroversial, as it requires simply that one considers a well-founded belief in God to have a higher utility than an ill-founded disbelief in God. However, the second inequality holds only if one regards the benefits of an ill-founded belief in God to be no less than those from a well-founded disbelief in God. This is patently a matter of personal choice. Many people maintain they do indeed get tangible benefits here and now from their belief in God, and that these exceed those that would accrue from not having such a belief (e.g. no requirement for regular observance of religious practices). On the other hand, many agnostics would argue the opposite case. The analysis shows atheists are not absolved from having to assess the utilities through setting P = 0; they must also be confident that d > b.

This requirement for such an assessment of utilities suggests that Pascal's Wager should be regarded as a criterion by which the coherence of one's existing beliefs can be judged, rather than as a method of choosing what to believe.

Other Christian thinkers
The basic premise of the argument is reflected in a passage from C.S. Lewis: "Christianity, if false, is of no importance, and if true, is of infinite importance. The only thing it cannot be is moderately important."

Buddhism
The decision-theoretic approach to Pascal's Wager appears explicitly in the 6th Century BC Buddhist Kalama Sutta, in which the Buddha argues that regardless of whether the concepts of reincarnation and karma are valid, acting as if they are brings tangible rewards here and now. However it is possible to see how this isn't an exact application of Pascal's wager. Most notably the benefit does fall onto others, as the idea of Karma is that good will to other means good will to you in return. Also, it isn't an argument to become Buddhist or to follow Buddhist thought but just to see the good in it.

Homer Simpson
In a reference to Pascal's wager and its criticisms, Homer Simpson once pointed this out to his wife Marge, "But Marge, what if we picked the wrong religion? Every week, we're just making God madder and madder!". 

Cryonics
It has been argued by some supporters of cryonics (though the argument is not deployed by cryonicists themselves, as it is viewed as pernicious advertisement) that their decision to have themselves subjected to the procedure of cryopreservation is based upon the logic that:


 * If you are not cryopreserved,
 * It does not work, and you die
 * or
 * It does work, and you die


 * If you are cryopreserved,
 * It does not work, and you die
 * or
 * It does work, and you live

The argument becomes more complex if factors such as the actual probabilities of success and the various costs of the attempts are taken into account, but ultimately, only one conclusion is supported:


 * If you are not cryopreserved,
 * You definitely die


 * If you are cryopreserved,
 * You probably die

Which, according to the argument, makes cryopreservation a worthy investment, and cryonics a worthy enterprise.

Notes and References

 * Nicholas Rescher, Pascal’s Wager: A Study of Practical Reasoning in Philosophical Theology, University of Notre Dame Press, 1985. (The first book-length treatment of the Wager in English.)
 * Michael Martin, Atheism, Philadelphia: Temple University Press, 1990, (Pp. 229–238 presents the argument about a god who punishes believers.)
 * Leslie Armour, Infini Rien: Pascal's Wager and the Human Paradox (The Journal of the History of Philosophy Monograph Series), Carbondale: Southern Illinois University Press, 1993.
 * Jeff Jordan, ed. Gambling on God, Lanham MD: Rowman & Littlefield, 1994. (A collection of the most recent articles on the Wager with a full bibliography.)
 * Jeff Jordan, Pascal's Wager: Pragmatic Arguments and Belief in God, Oxford University Press, 2007 (No doubt not the "final word", but certainly the most thorough and definitive discussion thus far.