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 living life accordingly 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.
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:
|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.|
|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.|
|Uncertainty in reason||Nothing is so conformable to reason as to disavow reason.|
|Uncertainty in science||There no doubt exist natural laws, but once this fine reason of ours was corrupted, it corrupted everything.|
|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.
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.
|Uncertainty in skepticism||It is not certain that everything is uncertain.|
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, 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.
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.
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.)
|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/spiritual death)
or −∞ (hell)
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. 
|God exists (G)||God does not exist (~G)|
|Living as if God exists (B)||+∞||f1|
|Living as if God does not exist (~B)||f2||f3|
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." 
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". 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." 
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. 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). 
And furthermore, ecumenical interpretations of the Wager 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", or that if the wager can simply bring one to believe in "generic theism" it has done its job. 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.
God rewards belief
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.||”|
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:
|God rewards theists||God rewards atheists||No God|
|Belief||+∞ (heaven)||Undefined||No result|
|Disbelief||Undefined||+∞ (heaven)||No result|
Apologists reply that hypotheses such as these lack the backing of tradition that genuine religions have, and thus should be disregarded. 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. 
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."  Pascal addressed this in his original account, as mentioned above.
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.  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"]."
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.
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. 
In the Sanskrit classic Sārasamuccaya, Vararuci makes a similar argument to Pascal's wager.
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...'"
- 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.
- Appeal to consequences
- Atheist's Wager
- Decision Theory
- Game Theory
- Alan Hájek, Stanford Encyclopedia of Philosophy
- Pensée #229
- Pensée #72
- Pensée #272
- Pensée #294
- Pensée #229
- Pensée #565
- Pensée #387
- Pensée #233
- Alan Hájek, Stanford Encyclopedia of Philosophy
- Voltaire Remarques sur les Pensees de PascalXI
- Diderot, Denis (1875-77) . J. Assézar. ed (in French). Pensées philosophiques, LIX, Volume 1. pp. 167.
- Mackie, J. L.. 1982. The Miracle of Theism, Oxford, pg. 203
- Alan Hájek, Stanford Encyclopedia of Philosophy
- For example: Jeff Jordan, Gambling on God: Essays on Pascal's Wager, 1994, Rowman & Littlefield.
- Paul Saka, The Internet Encyclopedia of Philosophy - Pascal's Wager
- Paul Saka, The Internet Encyclopedia of Philosophy - Pascal's Wager
- The God Delusion pp. 105.
- The God Delusion pp. 103-105.
- The End of Pascal's Wager: Only Nontheists Go to Heaven
- The God Delusion
- The God Delusion pp. 104.
- Pensée #233. Gérard Ferreyrolles, ed. Paris: Librairie Générale Française, 2000.
- al-Juwayni A Guide to Conclusive Proofs for the Principles of Belief, 6
- Nicholas Ostler, Empires of the World, HarperCollins, 2005.
- 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)
- Pascal's Pensees Part III — "The Necessity of the Wager" The wager argument itself is found in #233 (Trotter translation).
- Pascal's Wager in the Internet Encyclopedia of Philosophy
- Pascal's Wager in the Stanford Encyclopedia of Philosophy
- Theistic Belief and Religious Uncertainty by Jeffrey Jordan
- 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
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