Pascal's wager

Pascal's Wager (or Pascal's Gambit) is the application by the French philosopher Blaise Pascal of decision theory to the belief in God. It was set out in the Pensées, a posthumously published collection of notes made by Pascal towards his unfinished treatise on Christian apologetics.

The Wager posits that it is a better "bet" to believe that God exists than not to believe, because the expected value of believing (which Pascal assessed as infinite) is always greater than the expected value of not believing. In Pascal's assessment, it is inexcusable not to investigate this issue:

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, and Hinduism. Pascal's Wager is also similar in structure to the precautionary principle.

Blaise Pascal argued that it is a better "bet" to believe in God than not to do so.

Explanation

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

If there is a God, He is infinitely incomprehensible, since, having neither parts nor limits, He has no affinity to us. We are then incapable of knowing either what He is or if He is....

..."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. What will you wager? According to reason, you can do neither the one thing nor the other; according to reason, you can defend neither of the propositions.

Do not, then, reprove for error those who have made a choice; for you know nothing about it. "No, but I blame them for having made, not this choice, but a choice; for again both he who chooses heads and he who chooses tails are equally at fault, they are both in the wrong. The true course is not to wager at all."

Yes; but you must wager. It is not optional. You are embarked. 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. "That is very fine. Yes, I must wager; but I may perhaps wager too much." Let us see. Since there is an equal risk of gain and of loss, if you had only to gain two lives, instead of one, you might still wager. But if there were three lives to gain, you would have to play (since you are under the necessity of playing), and you would be imprudent, when you are forced to play, not to chance your life to gain three at a game where there is an equal risk of loss and gain. But there is an eternity of life and happiness. And this being so, if there were an infinity of chances, of which one only would be for you, you would still be right in wagering one to win two, and you would act stupidly, being obliged to play, by refusing to stake one life against three at a game in which out of an infinity of chances there is one for you, if there were an infinity of an infinitely happy life to gain. But there is here an infinity of an infinitely happy life to gain, a chance of gain against a finite number of chances of loss, and what you stake is finite.

Pascal begins with the premise that the existence or non-existence of God is not provable by human reason, since the essence of God is "infinitely incomprehensible". Since reason cannot decide the question, one must "wager", either by guessing or making a leap of faith. Agnosticism on this point is not possible, in Pascal's view, for we are already "embarked", effectively living out our choice.

We only have two things to stake, our "reason" or "knowledge", and our "will" or "happiness". Since reason cannot decide the issue, and both options are equally unfounded in reason, we should decide it according to our happiness. This is accomplished by weighing the gain and loss in believing that God exists. Pascal considers that there is "equal risk of loss and gain", a coin toss, since human reason is powerless to address the question of God's existence. He contends the wise decision is to wager that God exists, since "If you gain, you gain all; if you lose, you lose nothing", meaning one can gain eternal life if God exists, but if not, one will be no worse off in death than if one had not believed.

Pascal recognizes that the wagerer is risking something, namely his life on earth, by devoting it to one cause or another, but here he uses probabilistic analysis to show that it would be a wise wager, at the even odds he assumes, even if one were to gain only three lives at the risk of losing one. Considering that everyone is forced to wager and the potential gain is actually infinite life, it would be acting "stupidly" not to wager that God exists.

The possibilities defined by Pascal's Wager can be expanded more fully, though it should be noted that Pascal did not address the last two possibilities explicitly in his account, nor did he mention hell.

• You live as though God exists.
  • If God exists, you go to heaven: your gain is infinite.
  • If God does not exist, you gain nothing and lose nothing.

• You live as though God does not exist.
  • If God exists, the text is unspecified, but it could be implied that you go to limbo, purgatory, or hell: your loss is either null or infinite.
  • If God does not exist, you gain nothing and lose nothing.

With these possibilities, and the principles of statistics, Pascal attempted to demonstrate that the only prudent course of action is to live as if God exists. 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:

	God exists (G)	God does not exist (~G)
Living as if God exists (B)	+∞ (heaven)	−N (none)
Living as if God does not exist (~B)	?? (not specified, perhaps N (limbo/purgatory) or −∞ (hell))	+N (none)

Given these values, the option of living as if God exists(B) dominates the option of living as if God does not exist (~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.

Criticisms

Pascal hoped that if the wager did not 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, Judaism or Paganism, which Pascal himself mentions in his Pensées) is correct. The criticisms below work, 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 criticized, most notably by Voltaire and Diderot. Some criticisms are summarized below:

Assumes God rewards belief

Some writers suggest that the wager does not account for the possibility that there is a god that, 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, The End of Pascal's Wager: Only Nontheists Go to Heaven

This would render the initial 4-box set inaccurate, because it does not include the possibility of gods who reward nonbelief or punish belief. A revised set, still incomplete by other arguments, would look like this:

	God rewards theists	God rewards atheists	No God
Belief	Heaven	Hell	No result
Disbelief	Hell	Heaven	No result

Atheist's Wager

A specific argument challenging the assumption that belief is rewarded is known as the Atheist'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 may judge you on your merits coupled with your commitments, and not just on whether or not you believed in him.

It is supposed that a god may exist that will reward disbelief or punish belief. The atheist's wager asserts that in the absence of clear knowledge of what, if anything, will benefit the gambler's hereafter, it is better to concentrate on improving conditions in the present.

Assumes belief has no cost

The wager assumes that theism and atheism have no costs, making the two wagers equal in a world where no gods exist. Critics of the argument object that in some cases, religious edicts (such as prohibitions over when one may work or what may be eaten) constitute inconveniences that do not apply to atheists. They conclude that, in a godless universe, the atheistic wager produces better results than some theistic ones.

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.

However, a full reading shows that Pascal didn't intend the wager to be the summation of one's belief, but rather the starting point for any reader who agreed with him that reason truly was incapable of settling the question of God's existence.

Endeavour then to convince yourself, not by increase of proofs of God, but by the abatement of your passions. You would like to attain faith, and do not know the way; you would like to cure yourself of unbelief, and ask the remedy for it. Learn of those who have been bound like you, and who now stake all their possessions. These are people who know the way which you would follow, and who are cured of an ill of which you would be cured. Follow the way by which they began; by acting as if they believed, bless yourself with holy water, have Masses said, and so on; by a simple and natural process this will make you believe, and will dull you—will quiet your proudly critical intellect... Now, what harm will befall you in taking this side? You will be faithful, honest, humble, grateful, generous, a sincere friend, truthful. Certainly you will not have those poisonous pleasures, glory and luxury; but will you not have others? I will tell you that you will thereby gain in this life, and that, at each step you take on this road, you will see so great certainty of gain, so much nothingness in what you risk, that you will at last recognize that you have wagered for something certain and infinite, for which you have given nothing.

Assumes divine rewards (punishments) are infinite

The Wager assumes that an existent god will reward believers with eternal life, or something else of infinite value. Variations that mention hell similarly assume eternal or infinite punishment.

However, some people believe that an infinite utility could only be finitely enjoyed by finite humans. Even some Christians argue that the utility of salvation cannot be infinite. (See Calvinism and Arminianism)

Assumes that the correct god is worshipped

Since there are many religions, especially throughout history, and therefore many alleged gods, it is impossible to determine which to believe in based on the wager. Hence there is a high probability of believing in the wrong god, which could lead to severe punishment if a different god exists and is jealous and vengeful.

Variations

Many-way tie

Given that the choice of wagering has an infinite return, 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:

	God exists (G)	God does not exist (~G)
Belief in God (B)	$a$	$b$
Non-belief in God (~B)	$c$	$d$

The total utility for believing in God is then $a\times P+b\times (1-P)$ while the total utility for non-belief is $c\times P+d\times (1-P)$, 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 $b\geq d$. The first inequality requires 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.

Appearances elsewhere

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."

Another appearance of this argument was in the sermon "Sinners in the Hands of an Angry God" by the pastor Jonathan Edwards in 1741 in New England.

In the Evangelical Christian apologetics book Understanding Christian Theology, contributing author J. Carl Laney, Jr. states regarding Pascal's Wager:

Blaise Pascal...proposed that we "wager" on the possibility of God's existence. If our gamble for God is right, we will win everything - happiness and eternal life. But nothing is lost if we turn out to be wrong. In other words it is better to live as if God exists and discover that He doesn't, than to live as if He doesn't exist and discover that He does!"

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 is not 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 another 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.

References in popular culture

• My Night at Maud's is a film by Eric Rohmer that discusses Pascal's wager and its application to real life at great length. In the plot, a Christian, a Marxist and a free thinker debate Pascal's wager even as they unwittingly accept or decline smaller-scale versions through their choices about life and love.

• In an episode of the television show Father Dowling Mysteries, the title character makes reference to Pascal's wager, summarizing the argument. The woman he explains this to responds that she doesn't gamble.

• In the Discworld series of novels by Terry Pratchett, there is a reference to a character who makes a statement very similar to the Wager. When he dies, he finds himself surrounded by gods carrying heavy sticks and saying, "We're going to show you what we think of Mr. Clever Dick in these parts."

• Les paris stupides (Stupid Wagers), a Jacques Prévert poem, simply reads, "Un certain Blaise Pascal, etc. etc." (One Blaise Pascal said, etc. etc.)

See also

• Wager
• Gambit
• Sinners in the Hands of an Angry God
• Probabilism
• Appeal to consequences

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.)
• Jamie Whyte, Crimes against Logic, McGraw-Hill, 2004, (Section with argument about Wager)
• 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.)
• Pascal's Wager: The Atheist's Wager

External links

Primary text:

• Pascal's Pensees Part III — "The Necessity of the Wager" The wager argument itself is found in #233 (Trotter translation).

Standard references:

• Pascal's Wager in the Internet Encyclopedia of Philosophy
• Pascal's Wager in the Stanford Encyclopedia of Philosophy

Objections:

• The Rejection of Pascal's Wager
• The End of Pascal's Wager: Only Nontheists Go to Heaven (2002)
• Arguments against Pascal's Wager
• Pascal's Wager on the OCRT site
• Bill Watterson illustrates Pascal's Wager using Santa Claus
• Atheist's Wager
• The Empty Wager by Sam Harris