Pascal's Wager

Pascal's Wager (or Pascal's Gambit) is a suggestion posed by the French philosopher, mathematician and physicist Blaise Pascal that, even though the existence of God cannot be determined through reason, a person should wager as though God exists, because living life accordingly has everything to gain, and nothing to lose. Pascal formulated his suggestion uniquely on the God of Jesus Christ as implied by the greater context 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. However, some argue that Pascal's Wager also applies to gods of other religions and belief systems.

Pascal states, however, that some do not have the ability to believe. In this case, he directs them to live as though they had faith, which may lead them to belief. The Wager was set out in note 233 of his Pensées.

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]

Contents 1 The gamble 2 Context 3 Explanation 3.1 Analysis with decision theory 4 Criticism 4.1 Argument from inconsistent revelations 4.2 God rewards reasoning 4.3 Anti-Pascal wager 4.4 Assumes that one can choose belief 4.5 A scandalous inversion 5 Variations 5.1 Ancient Greece 5.2 Christianity 5.3 Islam 5.4 Sārasamuccaya 6 Other cultural references 7 See also 8 Notes 9 References 10 External links 10.1 Primary text 10.2 Revisions 10.3 Objections 10.4 Support of

[edit] The gamble

The philosophy uses the following logic (excerpts from Pensées, part III, note 233):

1. "God is, or He is not"
2. A Game is being played... where heads or tails will turn up.
3. According to reason, you can defend neither of the propositions.
4. You must wager. It is not optional.
5. 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.
6. Wager, then, without hesitation that He is. (...) 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. And so our proposition is of infinite force, when there is the finite to stake in a game where there are equal risks of gain and of loss, and the infinite to gain.

[edit] Context

The wager builds on the theme of other Pensées where Pascal systematically dismantles the notion that we can trust reason. 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:

Category	Quotation(s)
Uncertainty in all	This is what I see, and what troubles me. I look on all sides, and everywhere I see nothing but obscurity. Nature offers me nothing that is not a matter of doubt and disquiet.[2]
Uncertainty in Man's purpose	For after all what is man in nature? A nothing in relation to infinity, all in relation to nothing, a central point between nothing and all and infinitely far from understanding either.[3]
Uncertainty in reason	There is nothing so conformable to reason as this disavowal of reason.[4]
Uncertainty in science	There no doubt exist natural laws, but once this fine reason of ours was corrupted, it corrupted everything.[5]
Uncertainty in religion	If I saw no signs of a divinity, I would fix myself in denial. If I saw everywhere the marks of a Creator, I would repose peacefully in faith. But seeing too much to deny Him, and too little to assure me, I am in a pitiful state, and I would wish a hundred times that if a god sustains nature it would reveal Him without ambiguity.[6] We understand nothing of the works of God unless we take it as a principle that He wishes to blind some and to enlighten others.[7]
Uncertainty in skepticism	It is not certain that everything is uncertain.[8]

Pascal then asks the reader to analyze his 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:

“

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, taking the holy water, having masses said, etc. Even this will naturally make you believe, and deaden your acuteness.—"But this is what I am afraid of."—And why? What have you to lose? 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.[9]

”

[edit] Explanation

The wager is described in 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.[9]

”

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.

[edit] 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.)

	God exists (G)	God does not exist (~G)
Belief (B)	+∞ (heaven)	+1 (moral benefits)
Disbelief (~B)	−∞ (hell)	-1 (immoral consequences)

Given these values, the option of living as if God exists (B) dominates the option of living as if God does not exist (~B), as long as one assumes a positive probability that God exists. In other words, the expected value gained by choosing B is greater than or equal to that of choosing ~B.

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]

	God exists (G)	God does not exist (~G)
Belief (B)	+∞	f1
Disbelief (~B)	f2	f3

[edit] Criticism

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] Pascal, however, did not intend the wager as a proof.^[12]

[edit] 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]

[edit] God rewards reasoning

Richard Dawkins suggests that instead of the deity Pascal assumed, God might reward honest attempted reasoning and punish blind or feigned faith.^[20]

This harkens back to an argument given by Thomas Jefferson:

“

Question with boldness even the existence of a god; because, if there be one, he must more approve the homage of reason, than that of blindfolded fear.[21]

”

Richard Carrier expands this argument as such:

“

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.[22]

”

This would require changes to the initial 4-box set, because it did not address the possibility of a god who rewards honest unbelief or punishes dishonest belief. (Essentially Carrier is highlighting the positive aspects of doubt and reason, whereas Pascal highlighted the positive aspects of faith - - in both cases, regardless of whether God(s) exist.) A revised set, might look like this:

	God rewards reasoning	God does not exist
honesty / reasoning	+∞ (heaven)	+1 (a rational, scientific life)
dishonesty / lack of reason	-∞ (hell)	-1 (irrationality, insanity)

[edit] 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 worshiping him, sacrificing to him, fighting and dying for him, etc."^[23]

Dawkins's "Anti-Pascal Wager argument" could be visualized like this:

	God exists (G)	God does not exist (~G)
Living as if God exists (B)	+1 (heaven)	-∞ (waste of time, effort)
Living as if God does not exist (~B)	-1 (hell)	+∞ (better, fuller life)

Essentially Dawkins's argument boils down to debating the right column of Pascal's Wager theory: disputing Pascal's claim that faith in an nonexistent God yet leads to present benefits, and instead claiming that faith in an nonexistent God leads to an unfulfilled life. However, for Dawkins to present this counterclaim, also required Dawkins to change to the far left column from "belief / unbelief" to "living as". (Blaise Pascal, an adherent of Jansenism, wrote within the context of sola fide (aka justification by faith apart from works.)) Dawkins is also debating the middle column of Pascal's Wager, in that Dawkins believes a "better, fuller life" in the here and now outweighs the "small chance" of eternal bliss.

[edit] 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.^[24] 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"]."^[25]

Pascal introduces this point by an appeal to reasoned belief, which leads some critics to claim his argument here, like the rest of the wager, is based on reasoned belief. They argue that since he begins with the assumption that the wager is valid and concludes that inability to believe is therefore irrational, the argument that one cannot consciously choose to believe still stands (and the wager is invalid precisely because one cannot choose to believe). So read, the argument for the wager's validity would only work if it were assumed to be valid and Pascal's point here would be an example of begging the question. Others understand Pascal to be arguing not from reasoned belief but from external practice. He claims that by acting as if one believed externally, one can come to believe, internally. In this reading, the key word is the final verb, "abêtir", which literally means to be made a beast or animal. Pascal seems to be arguing that for those incapable of believing through reason, faith is attainable through the practice of faith, a practice which naturally deadens reason.

Pascal is asking if a particular description of a creator, a story, is true, correct, or perhaps more accurate than all other descriptions of a creator. Since he begins with the assumption that the story is correct, he is handing the reader a false dilemma as well. Either this description of a creator of a universe is an accurate depiction or it is not, but how one chooses will determine either eternal pain or eternal bliss. This rules out that an omnipotent creator is the ultimate authority or judge whether or not a person has lived as if there were a god, and leaves this up to the individual who makes the choice, simply to believe the story to be accurate or not. This rewards both those who sincerely believe it accurate and those who claim to, while acting disingenuously. This ignores who actually makes the final judgment, according to the story itself.

The imperative that "you must choose" is arbitrary and is only a component of the story, when considering the notion of original sin. The force or urgency to choose belief sounds very similar to the dialogue or message of evangelicals when they repeat the message and "spread the word" or "good news," a story that people were born guilty as sinners explicitly because of original sin and must believe to be saved—it is a choice one must make—according to the story, which one may not sincerely believe to be accurate anyway, and so is as arbitrary as the unfair notion of original sin.

There are two missing premises in the wager. First is an assumption that the reader has heard the particular Christian description of a universal creator, and sees mental images of a creator similar to his own when he refers to "God," without providing a definition of the term. The reader would need to understand the story portrays the creator as jealous and demanding of obedience, while also determining the quality of one's afterlife. The second missing premise is that "live as if there were a god," or following God's commands (the Divine Command Theory), is what morality is. Morality, or how one ought to live, is assumed equivalent to following the religious doctrine of God's commands. Arguably, an understanding of "what God wants" and the emphasis or priority given to a rule varies among religions, among denominations; among the individuals within them. American moral philosopher James Rachels described this in The Elements of Moral Philosophy as an "almost automatic assumption" that morality depends on particular religious rules. The assumption is made easily, including by elected public officials and may have a consequential influence on certain public policy. He further wrote that this assumption that God's commands are synonymous with moral rules is problematic in that any absolute rule (a command of God) will encounter a case where an exception to the rule could and should be made. Rachels provided an example such as euthanasia or mercy killing. In this case, conflict arises because of the particular wording of a [Christian] religious rule that the killing of any innocent is murder. If it is a dying patient's wish to die with dignity at a time of their choosing, if the patient has a dismal prognosis, is suffering interminably and medicine cannot ease their suffering, then in such cases there should be room for exception.

[edit] A scandalous inversion

The French intellectual Louis Althusser is critical of Pascal for inverting the order of things. By arguing that we should first act and then gain faith Pascal is in fact subjecting us to physical domination through use of ideological power (i.e. we are being forced to physically kneel down, pray, etc.). For this reason Althusser claims that Pascal brings 'like Christ, not peace but strife, and in addition something hardly Christian... scandal itself'.^[26]

[edit] Variations

[edit] Ancient Greece

The Sophist Protagoras had an agnostic position regarding the gods, but he nevertheless continued to worship the gods. This could be considered as an early version of the wager.^[27]

In the famous tragedy of Euripides Bacchae, Kadmos states an early version of Pascal´s wager. It is noteworthy that at the end of the tragedy Dionysos, the god to whom Kadmos referred, appears and punishes him for thinking in this way. Euripides, quite clearly, considered and dismissed the wager in this tragedy.^[28]

[edit] Christianity

The Christian apologist Arnobius of Sicca (d.330) stated an early version of the argument in his book Against the Pagans.^[29]

[edit] 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.^[30]

[edit] Sārasamuccaya

In the Sanskrit classic Sārasamuccaya, Vararuci makes a similar argument to Pascal's wager.^[31]

[edit] 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, a comedic fantasy 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...'"

• Approaching other problems with the logic set forth in Pascal's Wager has been done by some. Oleg Atbashian mocks proponents of the Global warming by attributing Pascal's Wager-like thinking to them: regardless of whether the warming is real it is good to act as if it were real. If it is real, and we act accordingly, we save ourselves. If it is not real, and we act as if it is, we achieve less significant benefits but ones not necessary to prevent actual disaster. If it is real and we act as if it were not, we suffer a grave disaster.

• Adam Fawer uses the wager as example given by the character David Caine in the book Improbable to a statistics class.

• On April 13th, 1991, on an episode of Doogie Howser, M.D., Doogie was told about Pascal's Wager by a poster of Albert Einstein. The episode was called Doogie's Wager, and it was the 23rd episode of the second season.

[edit] See also

• Appeal to consequences
• Atheist's Wager
• Decision Theory
• Determinism
• Fatalism
• Game Theory
• Predestination
• Smith's Wager

[edit] Notes

[edit] 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)

[edit] External links

[edit] 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

[edit] Revisions

• Theistic Belief and Religious Uncertainty by Jeffrey Jordan

[edit] Objections

• The End of Pascal's Wager: Only Nontheists Go to Heaven (2002) by Richard Carrier
• The Empty Wager by Sam Harris
• The Rejection of Pascal's Wager (2010) by Paul Tobin
• Pascal's Wager: The Atheist's Wager
• The Macroeconomics of Pascal's Wager: Adaptive Learning and the Prevalence of Religion (2010) by Paul Shea, University of Kentucky, July 30, 2010

[edit] Support of

• Pascal's Wager: Pragmatic Arguments and Belief in God (2006) by Jordan, Jeff, University of Delaware, 2006
• Ambiguity, Pessimism, and Rational Religious Choice (2010) by Tigran Melkonyan and Mark Pingle Theory and Decision, 2010, Volume 69, Number 3, Pages 417-438

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