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

Contents

Explanation

Criticisms

Assumes God rewards belief

Atheist's Wager

Does not constitute a true belief

Assumes divine rewards (punishments) are infinite

Variations

Many-way tie

Decision-theoretic arguments

Appearances elsewhere

Other Christian thinkers

Buddhism

References in popular culture

See also

Notes

References

External links

Explanation

The Wager is described by Pascal in the ''Pensées'' this way:^[1]
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 is. 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 possiblities 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 & lose nothing.

★ You live as though God does not exist.

★
★ If God exists, you go to hell: your loss is infinite.

★
★ If God does not exist, you gain nothing & 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)	−∞ (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 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 criticized by many thinkers, most notably Voltaire and Diderot. Some criticisms are summarized below:

Assumes God rewards belief

Some writers^[2] suggest that the 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.
However, in contrast to this, it can be seen that this is part of the wager that is the fundamental point of this argument. This would render the initial 4-box set inaccurate, however, because it does not include the possibilities involving non-theist reward. 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:
A god may exist who will reward disbelief or punish belief. In the absence of clear knowledge of what if anything will benefit the gambler's hereafter it is better to concentrate on improving conditions here. Reality may or may not be generated by us. However, we are still left to affect them any way we can. The Atheist here must then exclude ''any'' probability in a mathematical possibility of an external agent affecting their condition.

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:
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."
The fact that a person can not choose to believe something by will alone, but as a consequence of an internal process, is illustrated in humorous terms by Douglas Adams in "Dirk Gently's Holistic Detective Agency". In this novel, he describes a fictional device, an "Electric Monk" that can believe things for you; all sort of things, even "things they'd have difficulty believing in Salt Lake City".^[3]
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.
Other Christians such as Kierkegaard considered that a faith one has never doubted is of little value, and that doubt and faith are inseparable.
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.

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 & Arminianism)

Variations

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:

	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 $a\; imes\; P\; +\; b\; imes\; (1\; -\; P)$ while the total utility for non-belief is $c\; imes\; P\; +\; d\; imes\; (1\; -\; P)$, 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 ''dis''belief 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:

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 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

★ 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 Quiet American'' by Graham Greene, the protagonist Fowler refers to Pascal numerous times in relation to Vigot, the police chief investigating Pyle's death.

★ 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."^[4]

★ ''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

★ Sinners in the Hands of an Angry God

★ Probabilism

★ Appeal to consequences

Notes

1. Pascal ''Pensées'' 233 [2]
2. ''E.g.'' Richard Dawkins, ''The God Delusion'' pp. 103–105.
3. Dirk Gently's Holistic Detective Agency (extract)
4. Hogfather

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