Pascal's wager

Blaise Pascal

Pascal's Wager (or Pascal's Gambit) is a suggestion posed by the French philosopher Blaise Pascal that even though the existence of God cannot be determined through reason, a person should wager as though God exists, because so living has everything to gain, and nothing to lose. It was set out in note 233 of his Pensées, a posthumously published collection of notes made by Pascal in his last years as he worked on a treatise on Christian apologetics.

Historically, Pascal's Wager was groundbreaking as it had charted new territory in probability theory, was one of the first attempts to make use of the concept of infinity, marked the first formal use of decision theory, and anticipated the future philosophies of pragmatism and voluntarism.^[1]

Context

Blaise Pascal argued that if reason cannot be trusted, it is a better "bet" to believe in God than not to do so.

The wager builds on the theme of other Pensées where Pascal systematically dismantles the notion that we can trust reason, especially in the areas of religion. Although his notes were found without definite order after his death (the Pensées numbering scheme was added by publishers for reference purposes), it can be inferred that the section regarding the wager would have followed his other thoughts that supply the foundation. Much of the book attacks certainty, and is often cited as the first work on existentialism for thoughts like the following:

Pascal then asks the reader to analyze their position. If reason is truly corrupt and cannot be relied upon to decide the matter of God's existence, only a coin toss remains. In Pascal's assessment, placing a wager is unavoidable, and anyone who is incapable of trusting any evidence either for or against God's existence, must at least face the prospect that infinite happiness is at risk. The "infinite" expected value of believing is always greater than the expected value of not believing.

However, Pascal did not treat acceptance of the wager to be in itself sufficient for salvation. In the same note where the wager is found, Pascal goes on to explain that understanding his conclusion is just the impetus for faith, not faith itself:

Explication

The wager is described in Pensées this way:

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" and our "happiness". 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. That being the case, we then must decide it according to our happiness... by weighing the gain and loss in believing that God exists. 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.

Analysis with decision theory

The possibilities defined by Pascal's Wager can be thought of as a decision under uncertainty with the values of the following decision matrix. (Pascal did not mention hell, nor did he address what the outcome would be of "God exists + Living as if God does not exist," the prospect of infinite gain being sufficient to make his point. Pascal also assumed that the combination of B and ~G would simply be -N, though many people dispute that.) Note that it is necessary to assume that the probability of G is both positive and finite in this situation.

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.

In fact, according to decision theory, the only value that matters in the above matrix is the +∞. Any matrix of the following type (where f₁, f₂, and f₃ are all finite positive or negative numbers) results in (B) as being the only rational decision. ^[10]

Criticisms

Pascal's Wager has been the target of much criticism, starting in its own day. Voltaire, writing a generation after Pascal, rejected the wager as "indecent and childish... the interest I have to believe a thing is no proof that such a thing exists." ^[11] But Voltaire, like many other critics, misunderstood the Wager. Pascal did not offer the wager as a proof. ^[12] It is merely a conclusion to his arguments against certainty that relies on the notion that reason is untrustworthy and that discerning God's actual existence appears to be "a coin toss." If reason can be trusted on the question of God's existence, then the wager simply does not apply.

Argument from Inconsistent Revelations

Since there have been many religions throughout history, and therefore many potential gods, some assert that all of them need to be factored into the wager, in an argument known as the argument from inconsistent revelations. This would lead to a high probability of believing in the wrong god, which destroys the mathematical advantage Pascal claimed with his Wager. Denis Diderot, a contemporary of Voltaire, concisely expressed this opinion when asked about the wager, saying "an Imam could reason the same way".^[13] J. L. Mackie notes that "the church within which alone salvation is to be found is not necessarily the Church of Rome, but perhaps that of the Anabaptists or the Mormons or the Muslim Sunnis or the worshipers of Kali or of Odin." ^[14]

Pascal himself didn't address the question of other religions in his section on the wager, presumably because throughout the rest of Pensées (and in his other works) he examined alternatives, like stoicism, paganism, Islam, and Judaism, and concluded that if any faith is correct, it would be the Christian faith.

Nonetheless, as this criticism has surfaced, apologists of his wager counter that, of the rival options, only the ones that award infinite happiness affect the Wager's dominance. They claim that neither Odin's nor Kali's finite, semi-blissful promise could contend with the infinite bliss offered by Jesus Christ, so they drop out of consideration.^[15] Also, the infinite bliss the rival god offers has to be mutually exclusive. If Christ's promise of bliss can be attained concurrently with Jehovah's and Allah's (all three being identified as the God of Abraham), there is no conflict in the decision matrix in the case where the cost of believing in the wrong god is neutral (limbo/purgatory/spiritual death), although this would be countered with an infinite cost in the case where not believing in the correct god results in punishment (hell). ^[15]

And furthermore, ecumenical interpretations of the Wager^[16] argue that it could even be suggested that believing in an anonymous god or a god by the wrong name, is acceptable so long as that god has the same essential characteristics (like the God of Aristotle). Proponents of this line of reasoning suggest that either all of the gods of history truly boil down to just a small set of "genuine options",^[17] or that if the wager can simply bring one to believe in "generic theism" it has done its job.^[18] Critics respond by stating that the wager must account for all potential gods and goddesses, without specifying whether they belong to a historical religion or not.^[19]

God rewards belief

Pascal's Wager suffers from the logical fallacy of the false dilemma, relying on the assumption that the only possibilities are:

1. a benevolent god exists and punishes or rewards according to one's belief, or
2. a benevolent god does not exist.

God could either be malevolent or not reward belief. In this view, a benevolent god, by definition, would give priority to the belief of the individual in determining rewards or punishments, rather than basing rewards on the basis of the individual's actions, such as rewarding kindness, generosity, humility or sincerity. Perhaps instead God rewards honest attempted reasoning and indeed might punish blind or feigned faith.^[20] Also see the Atheist's Wager as examples of assuming a different set of possibilities.

Richard Carrier expands this argument as such:

This would render the initial 4-box set inaccurate, because it does not include the possibility of a god who rewards honest unbelief or punishes dishonest belief. A revised set, would look like this:

Apologists reply that hypotheses such as these lack the backing of tradition that genuine religions have, and thus should be disregarded (although see Argumentum ad populum). More precisely, these other hypotheses should be assigned zero (or perhaps infinitesimal) probability, so that they do not upset Pascal's expectation calculations. The debate then turns on what exactly rationality requires of one's probability assignments. ^[15]

Anti-Pascal wager

Richard Dawkins argues for an "anti-Pascal wager" in his book, The God Delusion. "Suppose we grant that there is indeed some small chance that God exists. Nevertheless, it could be said that you will lead a better, fuller life if you bet on his not existing, than if you bet on his existing and therefore squander your precious time on worshipping him, sacrificing to him, fighting and dying for him, etc." ^[22]

Assumes that one can choose belief

The wager assumes that one can consciously decide. Critics argue that they cannot do this, and therefore Pascal's Wager could only ever be an argument for feigning belief in God. In addition, an omniscient God would presumably see through the deception. ^[23] Richard Dawkins writes "Would you bet on God's valuing dishonestly faked belief (or even honest belief) over honest skepticism?" However, Pascal explicitly addresses inability ("impuissance") to believe. If the Wager is valid, inability to believe is irrational, and therefore caused by the passions: "your inability to believe, because reason compels you to [believe] and yet you cannot, [comes] from your passions." Therefore, this inability can be overcome by diminishing the passions through the practice of belief: "Learn from those who were bound like you. . . . Follow the way by which they began: that is by doing everything as if they believed, by taking holy water, by having Masses said, etc. Naturally, even this will make you believe and will dull you ["vous abêtira"]."^[24]

Variations

Islam

An Instantiation of this argument, within the Islamic kalam tradition, was discussed by Imam al-Haramayn al-Juwayni (d. 478/1085) in his Kitab al-irshad ila-qawati al-adilla fi usul al-i'tiqad, or A Guide to the Conclusive Proofs for the Principles of Belief, nearly 600 years before its formal publication by Pascal, albeit relying solely on the Islamic beliefs. ^[25]

Sārasamuccaya

In the Sanskrit classic Sārasamuccaya, Vararuci makes a similar argument to Pascal's wager.^[26]

Other cultural references

• William James uses Pascal's Wager as an example of choosing a 'living option' in his Will to Believe Doctrine.

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

• 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 Catholic, 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.

• Repeated reference is made to the wager in Graham Greene's novel The Quiet American.

• Terry Pratchett satirized Pascal's Wager in Hogfather, his novel about the nature of belief. A philosopher claimed, "Possibly the gods exist, and possibly they do not. So why not believe in them in any case? If it's all true you'll go to a lovely place when you die, and if it isn't then you've lost nothing, right?" When the philosopher died, "he woke up in a circle of gods holding nasty-looking sticks and one of them said, 'We're going to show you what we think of Mr Clever Dick in these parts...'"

• Black Swan Theory is referred to in Taleb's popularised account of the implications of randomness especially in his assessment of the need to consider consequence of outcome as opposed to probability of outcome.

See also

• Appeal to consequences
• Atheist's Wager
• Decision Theory
• Determinism
• Fatalism
• Game Theory
• Kupczyński's Wager
• Paddy Power, an Irish bookmaker accepting bets on proof being found for God's existence
• Predestination

Notes

References

• al-Juwayni, Imam al-Haramayn; Dr. Paul E. Walker (translator) (2000). A Guide to Conclusive Proofs for the Principles of Belief. Reading, UK: Garnet Publishing. pp. 6–7. ISBN 1 85964 157 1. 
• 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.
• James Cargile, "Pascal's Wager," in Contemporary Perspectives on Religious Epistemology, eds. R. Douglas Geivett and Brendan Sweetman, Oxford University Press, 1992.
• 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.)
• William G. Lycan and George N. Schlesinger, "You Bet Your Life: Pascal's Wager Defended," in Contemporary Perspectives on Religious Epistemology, eds. R. Douglas Geivett and Brendan Sweetman, Oxford University Press, 1992.
• Michael Martin, Atheism, Philadelphia: Temple University Press, 1990, (Pp. 229–238 presents the argument about a god who punishes believers.)
• Thomas V. Morris, "Pascalian Wagering," in Contemporary Perspectives on Religious Epistemology, eds. R. Douglas Geivett and Brendan Sweetman, Oxford University Press, 1992.
• 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.)
• Jamie Whyte, Crimes against Logic, McGraw-Hill, 2004, (Section with argument about Wager)
• Elizabeth Holowecky, "Taxes and God", KPMG Press, 2008, (Phone interview)

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

Revisions

• Theistic Belief and Religious Uncertainty by Jeffrey Jordan

Objections

• The End of Pascal's Wager: Only Nontheists Go to Heaven (2002) by Richard Carrier
• Pascal's Wager with 3rd Order Probability Integration
• The Empty Wager by Sam Harris
• The Rejection of Pascal's Wager (2000) by Paul Tobin
• Pascal's Wager: The Atheist's Wager